1,1,11,0,0.0179375,"\int \frac{x}{\left(-1+x^2\right)^{3/4}} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
2,1,12,0,0.0576845,"\int \frac{1+3 x^2}{\sqrt{-1+x+x^3}} \, dx","Int[(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",1,1,18,0.05556,1,"{1588}"
3,1,12,0,0.0091892,"\int \frac{-1+x^8}{\sqrt{-1+x^4} \left(1-2 x^4+x^8\right)} \, dx","Int[(-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",3,3,27,0.1111,1,"{28, 1404, 383}"
4,1,13,0,0.0019167,"\int \frac{x}{\sqrt[3]{-1+x^2}} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
5,1,13,0,0.0018034,"\int \frac{x}{\sqrt[4]{-1+x^2}} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
6,1,13,0,0.0019987,"\int x \sqrt[4]{-1+x^2} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
7,1,13,0,0.0017262,"\int x \sqrt[3]{-1+x^2} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
8,1,13,0,0.0019369,"\int x \left(-1+x^2\right)^{2/3} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
9,1,13,0,0.0021855,"\int x \left(-1+x^2\right)^{3/4} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
10,1,13,0,0.0019968,"\int \frac{x}{\sqrt[3]{1+x^2}} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
11,1,13,0,0.0019398,"\int \frac{x}{\sqrt[4]{1+x^2}} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
12,1,13,0,0.001843,"\int x \sqrt[4]{1+x^2} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
13,1,13,0,0.0017041,"\int x \sqrt[3]{1+x^2} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
14,1,13,0,0.0020739,"\int x \left(1+x^2\right)^{3/4} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
15,1,13,0,0.0025515,"\int \frac{x^2}{\sqrt[4]{-1+x^3}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
16,1,13,0,0.0022528,"\int x^2 \sqrt[4]{-1+x^3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
17,1,13,0,0.002911,"\int x^2 \left(-1+x^3\right)^{3/4} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
18,1,13,0,0.0023878,"\int \frac{x^2}{\sqrt{1+x^3}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
19,1,13,0,0.0025731,"\int \frac{x^2}{\sqrt[4]{1+x^3}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
20,1,13,0,0.0023635,"\int x^2 \sqrt[4]{1+x^3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
21,1,13,0,0.0025925,"\int x^2 \sqrt[3]{1+x^3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
22,1,13,0,0.0024567,"\int x^2 \sqrt{1+x^3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
23,1,13,0,0.002783,"\int x^2 \left(1+x^3\right)^{2/3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
24,1,13,0,0.0027849,"\int x^2 \left(1+x^3\right)^{3/4} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
25,1,13,0,0.0066593,"\int \left(1+3 x^2\right) \sqrt[3]{x+x^3} \, dx","Int[(1 + 3*x^2)*(x + x^3)^(1/3),x]","\frac{3}{4} \left(x^3+x\right)^{4/3}","\frac{3}{4} \left(x^3+x\right)^{4/3}",1,"(3*(x + x^3)^(4/3))/4","A",1,1,17,0.05882,1,"{1588}"
26,1,13,0,0.0039044,"\int \frac{1}{x^2 \left(-1+x^4\right)^{3/4}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
27,1,13,0,0.0024241,"\int \frac{x^3}{\sqrt[3]{-1+x^4}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
28,1,13,0,0.0029336,"\int x^3 \sqrt[3]{-1+x^4} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
29,1,13,0,0.0027668,"\int x^3 \left(-1+x^4\right)^{2/3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
30,1,13,0,0.0027809,"\int x^3 \left(-1+x^4\right)^{3/4} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
31,1,13,0,0.0056821,"\int \frac{-1+x^4}{x^2 \sqrt{1+x^4}} \, dx","Int[(-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",1,1,18,0.05556,1,"{449}"
32,1,13,0,0.0024867,"\int \frac{x^3}{\sqrt[3]{1+x^4}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
33,1,13,0,0.0026946,"\int x^3 \sqrt[4]{1+x^4} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
34,1,13,0,0.0023401,"\int x^3 \sqrt[3]{1+x^4} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
35,1,13,0,0.0031113,"\int x^3 \left(1+x^4\right)^{2/3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
36,1,13,0,0.0030788,"\int x^4 \left(-1+x^5\right)^{2/3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
37,1,13,0,0.0025412,"\int x^4 \left(1+x^5\right)^{2/3} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
38,1,13,0,0.0026274,"\int \frac{x^5}{\sqrt[3]{-1+x^6}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
39,1,13,0,0.002651,"\int x^5 \sqrt[4]{-1+x^6} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
40,1,13,0,0.0025263,"\int x^5 \sqrt[3]{-1+x^6} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
41,1,13,0,0.0023692,"\int x^5 \sqrt{-1+x^6} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
42,1,13,0,0.0028473,"\int x^5 \left(-1+x^6\right)^{3/4} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
43,1,13,0,0.005972,"\int \frac{-2+x^6}{x^3 \sqrt{1+x^6}} \, dx","Int[(-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",1,1,18,0.05556,1,"{449}"
44,1,13,0,0.0023327,"\int \frac{x^5}{\sqrt[3]{1+x^6}} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
45,1,13,0,0.0024139,"\int x^5 \sqrt[4]{1+x^6} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
46,1,13,0,0.0023068,"\int x^5 \sqrt[3]{1+x^6} \, dx","Int[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",1,1,13,0.07692,1,"{261}"
47,1,14,0,0.0063396,"\int \frac{-4+x^3}{x^2 \left(-1+x^3\right)^{3/4}} \, dx","Int[(-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",1,1,18,0.05556,1,"{449}"
48,1,14,0,0.0077972,"\int \frac{1}{x \sqrt{1+x^3}} \, dx","Int[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",3,3,13,0.2308,1,"{266, 63, 207}"
49,1,14,0,0.0060292,"\int \frac{4+x^3}{x^2 \left(1+x^3\right)^{3/4}} \, dx","Int[(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",1,1,18,0.05556,1,"{449}"
50,1,14,0,0.0844747,"\int \frac{\left(2+3 x^2\right) \sqrt[3]{x+x^3}}{1+x^2} \, dx","Int[((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",2,2,24,0.08333,1,"{2056, 449}"
51,1,16,0,0.0633702,"\int \frac{-2+x}{(-1+x) \sqrt[4]{-x^2+x^3}} \, dx","Int[(-2 + x)/((-1 + x)*(-x^2 + x^3)^(1/4)),x]","\frac{4 x}{\sqrt[4]{x^3-x^2}}","\frac{4 x}{\sqrt[4]{(x-1) x^2}}",1,"(4*x)/(-x^2 + x^3)^(1/4)","A",2,2,22,0.09091,1,"{2056, 74}"
52,1,14,0,0.0596974,"\int \frac{2+x}{(1+x) \sqrt[4]{x^2+x^3}} \, dx","Int[(2 + x)/((1 + x)*(x^2 + x^3)^(1/4)),x]","\frac{4 x}{\sqrt[4]{x^3+x^2}}","\frac{4 x}{\sqrt[4]{x^2 (x+1)}}",1,"(4*x)/(x^2 + x^3)^(1/4)","A",2,2,20,0.1000,1,"{2056, 74}"
53,1,14,0,0.0029111,"\int \frac{1}{x^2 \left(1+x^4\right)^{3/4}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
54,1,14,0,0.0052953,"\int \frac{3+x^4}{x^4 \sqrt{1+x^4}} \, dx","Int[(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",1,1,18,0.05556,1,"{449}"
55,1,14,0,0.0101886,"\int \frac{-1+4 x^3}{\sqrt{-1-2 x+2 x^4}} \, dx","Int[(-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",1,1,22,0.04545,1,"{1588}"
56,1,14,0,0.0065019,"\int \frac{-4+x^5}{x^2 \left(1+x^5\right)^{3/4}} \, dx","Int[(-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",1,1,18,0.05556,1,"{449}"
57,1,14,0,0.0058677,"\int \frac{4+x^5}{x^2 \left(-1+x^5\right)^{3/4}} \, dx","Int[(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",1,1,18,0.05556,1,"{449}"
58,0,0,0,0.5440432,"\int \frac{2+5 x^3}{\sqrt{1+x^3} \left(1+x^2+x^5\right)} \, dx","Int[(2 + 5*x^3)/(Sqrt[1 + x^3]*(1 + x^2 + x^5)),x]","\int \frac{2+5 x^3}{\sqrt{1+x^3} \left(1+x^2+x^5\right)} \, dx","2 \tan ^{-1}\left(x \sqrt{x^3+1}\right)",1,"2*Defer[Int][1/(Sqrt[1 + x^3]*(1 + x^2 + x^5)), x] + 5*Defer[Int][x^3/(Sqrt[1 + x^3]*(1 + x^2 + x^5)), x]","F",0,0,0,0,-1,"{}"
59,1,14,0,0.0065448,"\int \frac{1}{x \sqrt{-1+x^6}} \, dx","Int[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",3,3,13,0.2308,1,"{266, 63, 203}"
60,1,14,0,0.005876,"\int \frac{-2+x^6}{x^2 \left(1+x^6\right)^{3/4}} \, dx","Int[(-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",1,1,18,0.05556,1,"{449}"
61,1,14,0,0.0069019,"\int \frac{1}{x \sqrt{1+x^6}} \, dx","Int[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",3,3,13,0.2308,1,"{266, 63, 207}"
62,1,14,0,0.0067383,"\int \frac{2+x^6}{x^2 \left(-1+x^6\right)^{3/4}} \, dx","Int[(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",1,1,18,0.05556,1,"{449}"
63,0,0,0,0.5581032,"\int \frac{-1+2 x^6}{\sqrt{1+x^6} \left(1-x^2+x^6\right)} \, dx","Int[(-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,"(x*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x^2)/(1 + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x^2*(1 + x^2))/(1 + (1 + Sqrt[3])*x^2)^2]*Sqrt[1 + x^6]) - 3*Defer[Int][1/(Sqrt[1 + x^6]*(1 - x^2 + x^6)), x] + 2*Defer[Int][x^2/(Sqrt[1 + x^6]*(1 - x^2 + x^6)), x]","F",0,0,0,0,-1,"{}"
64,0,0,0,0.5188422,"\int \frac{1+2 x^6}{\sqrt{-1+x^6} \left(-1+x^2+x^6\right)} \, dx","Int[(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,"(x*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x^2)/(1 - (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[-((x^2*(1 - x^2))/(1 - (1 + Sqrt[3])*x^2)^2)]*Sqrt[-1 + x^6]) + 3*Defer[Int][1/(Sqrt[-1 + x^6]*(-1 + x^2 + x^6)), x] - 2*Defer[Int][x^2/(Sqrt[-1 + x^6]*(-1 + x^2 + x^6)), x]","F",0,0,0,0,-1,"{}"
65,1,15,0,0.0075309,"\int \frac{-1+3 x^2}{\sqrt[3]{-x+x^3}} \, dx","Int[(-1 + 3*x^2)/(-x + x^3)^(1/3),x]","\frac{3}{2} \left(x^3-x\right)^{2/3}","\frac{3}{2} \left(x^3-x\right)^{2/3}",1,"(3*(-x + x^3)^(2/3))/2","A",1,1,19,0.05263,1,"{1588}"
66,1,15,0,0.007298,"\int \left(-1+3 x^2\right) \sqrt[3]{-x+x^3} \, dx","Int[(-1 + 3*x^2)*(-x + x^3)^(1/3),x]","\frac{3}{4} \left(x^3-x\right)^{4/3}","\frac{3}{4} \left(x^3-x\right)^{4/3}",1,"(3*(-x + x^3)^(4/3))/4","A",1,1,19,0.05263,1,"{1588}"
67,0,0,0,2.0809246,"\int \frac{2+x-x^3}{\sqrt{1+x+x^3} \left(1+x-x^2+x^3\right)} \, dx","Int[(2 + x - x^3)/(Sqrt[1 + x + x^3]*(1 + x - x^2 + x^3)),x]","\int \frac{2+x-x^3}{\sqrt{1+x+x^3} \left(1+x-x^2+x^3\right)} \, dx","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^3+x+1}}\right)",1,"(((-2*I)/3)*Sqrt[(2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3) + 6^(2/3)*x)/(6*(3/(-9 + Sqrt[93]))^(1/3) - 3*(2*(-9 + Sqrt[93]))^(1/3) - I*6^(1/6)*Sqrt[12 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3)])]*Sqrt[6 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3) - 6*3^(1/3)*((6/(-9 + Sqrt[93]))^(1/3) - ((-9 + Sqrt[93])/2)^(1/3))*x + 18*x^2]*EllipticF[ArcSin[Sqrt[I*(6^(1/3)*(2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3) - I*6^(1/6)*Sqrt[12 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3)]) - 12*x)]/(2^(3/4)*(3*(12 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3)))^(1/4))], (2*6^(1/6)*Sqrt[12 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3)])/(I*(6*(3/(-9 + Sqrt[93]))^(1/3) - 3*(2*(-9 + Sqrt[93]))^(1/3)) + 6^(1/6)*Sqrt[12 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3)])])/Sqrt[1 + x + x^3] + 3*Defer[Int][1/(Sqrt[1 + x + x^3]*(1 + x - x^2 + x^3)), x] + 2*Defer[Int][x/(Sqrt[1 + x + x^3]*(1 + x - x^2 + x^3)), x] - Defer[Int][x^2/(Sqrt[1 + x + x^3]*(1 + x - x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
68,1,15,0,0.0873514,"\int \frac{1+x^4}{\left(1-x^4\right) \sqrt{-1+x^2+x^4}} \, dx","Int[(1 + x^4)/((1 - x^4)*Sqrt[-1 + x^2 + x^4]),x]","\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2-1}}\right)","\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2-1}}\right)",1,"ArcTanh[x/Sqrt[-1 + x^2 + x^4]]","A",2,2,27,0.07407,1,"{2112, 206}"
69,1,16,0,0.0097933,"\int \frac{-4+x^3}{x^4 \sqrt[4]{-1+x^3}} \, dx","Int[(-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",2,2,18,0.1111,1,"{446, 74}"
70,1,16,0,0.0025921,"\int \frac{\sqrt[3]{-1+x^3}}{x^5} \, dx","Int[(-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",1,1,13,0.07692,1,"{264}"
71,1,16,0,0.0032297,"\int \frac{\left(-1+x^3\right)^{2/3}}{x^6} \, dx","Int[(-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",1,1,13,0.07692,1,"{264}"
72,1,16,0,0.0025676,"\int \frac{\sqrt[3]{1+x^3}}{x^5} \, dx","Int[(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",1,1,13,0.07692,1,"{264}"
73,1,16,0,0.0028268,"\int \frac{\left(1+x^3\right)^{2/3}}{x^6} \, dx","Int[(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",1,1,13,0.07692,1,"{264}"
74,1,16,0,0.0066697,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{3/2}}{x^6} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
75,1,16,0,0.0097937,"\int \frac{4+x^3}{x^4 \sqrt[4]{1+x^3}} \, dx","Int[(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",2,2,18,0.1111,1,"{446, 74}"
76,1,16,0,0.0196997,"\int \frac{1}{x^2 \sqrt[3]{x+x^3}} \, dx","Int[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",1,1,13,0.07692,1,"{2014}"
77,1,33,0,0.2587092,"\int \frac{\left(1+x^2\right) \left(3+x^2\right)}{x^6 \sqrt[4]{x+x^3}} \, dx","Int[((1 + x^2)*(3 + x^2))/(x^6*(x + x^3)^(1/4)),x]","-\frac{4 \left(x^3+x\right)^{3/4}}{7 x^6}-\frac{4 \left(x^3+x\right)^{3/4}}{7 x^4}","-\frac{4 \left(x^3+x\right)^{7/4}}{7 x^7}",1,"(-4*(x + x^3)^(3/4))/(7*x^6) - (4*(x + x^3)^(3/4))/(7*x^4)","B",14,4,23,0.1739,1,"{2052, 2025, 2011, 364}"
78,1,16,0,0.0173785,"\int \frac{\sqrt[3]{x+x^3}}{x^4} \, dx","Int[(x + x^3)^(1/3)/x^4,x]","-\frac{3 \left(x^3+x\right)^{4/3}}{8 x^4}","-\frac{3 \left(x^3+x\right)^{4/3}}{8 x^4}",1,"(-3*(x + x^3)^(4/3))/(8*x^4)","A",1,1,13,0.07692,1,"{2014}"
79,1,16,0,0.0026844,"\int \frac{1}{x^4 \sqrt[4]{-1+x^4}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
80,1,16,0,0.0029732,"\int \frac{\left(-1+x^4\right)^{3/4}}{x^8} \, dx","Int[(-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",1,1,13,0.07692,1,"{264}"
81,1,78,0,0.090196,"\int \frac{-1+x^4}{x^2 \sqrt{x+x^3}} \, dx","Int[(-1 + x^4)/(x^2*Sqrt[x + x^3]),x]","\frac{2 \sqrt{x^3+x}}{3}+\frac{2 \sqrt{x^3+x}}{3 x^2}+\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \sqrt{x^3+x}}","\frac{2 \left(x^3+x\right)^{3/2}}{3 x^3}",1,"(2*Sqrt[x + x^3])/3 + (2*Sqrt[x + x^3])/(3*x^2) + (Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(3*Sqrt[x + x^3])","C",5,5,18,0.2778,0,"{2048, 2025, 2011, 329, 220}"
82,1,16,0,0.0031014,"\int \frac{1}{x^4 \sqrt[4]{1+x^4}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
83,1,16,0,0.0085618,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^5} \, dx","Int[((-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",2,2,18,0.1111,1,"{446, 74}"
84,1,16,0,0.0187915,"\int \frac{\left(-1+x^2\right) \left(1+x^2\right) \sqrt{1+x^4}}{x^4} \, dx","Int[((-1 + x^2)*(1 + x^2)*Sqrt[1 + x^4])/x^4,x]","\frac{\left(x^4+1\right)^{3/2}}{3 x^3}","\frac{\left(x^4+1\right)^{3/2}}{3 x^3}",1,"(1 + x^4)^(3/2)/(3*x^3)","A",2,2,23,0.08696,1,"{517, 449}"
85,1,16,0,0.0059774,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3}}{x^6} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
86,1,16,0,0.0028856,"\int \frac{\left(1+x^4\right)^{3/4}}{x^8} \, dx","Int[(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",1,1,13,0.07692,1,"{264}"
87,1,16,0,0.0059349,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right)}{x^6} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
88,1,16,0,0.0089824,"\int \frac{\sqrt[3]{1+x^4} \left(3+x^4\right)}{x^9} \, dx","Int[((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",2,2,18,0.1111,1,"{446, 74}"
89,1,16,0,0.0187709,"\int \frac{1}{x^2 \sqrt{x+x^4}} \, dx","Int[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",1,1,13,0.07692,1,"{2014}"
90,1,33,0,0.1114949,"\int \frac{1+x^3}{x^6 \sqrt[4]{x+x^4}} \, dx","Int[(1 + x^3)/(x^6*(x + x^4)^(1/4)),x]","-\frac{4 \left(x^4+x\right)^{3/4}}{21 x^6}-\frac{4 \left(x^4+x\right)^{3/4}}{21 x^3}","-\frac{4 \left(x^4+x\right)^{7/4}}{21 x^7}",1,"(-4*(x + x^4)^(3/4))/(21*x^6) - (4*(x + x^4)^(3/4))/(21*x^3)","B",5,3,18,0.1667,1,"{2052, 2016, 2014}"
91,1,21,0,0.0614325,"\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^4}}{\left(1+x^3\right)^2} \, dx","Int[((-2 + x^3)*(x + x^4)^(1/3))/(1 + x^3)^2,x]","-\frac{3 x \sqrt[3]{x^4+x}}{2 \left(x^3+1\right)}","-\frac{3 x^2}{2 \left(x^4+x\right)^{2/3}}",1,"(-3*x*(x + x^4)^(1/3))/(2*(1 + x^3))","A",2,2,22,0.09091,1,"{2056, 449}"
92,1,16,0,0.0323381,"\int \frac{\sqrt[4]{x^2+x^4}}{x^2 \left(1+x^2\right)} \, dx","Int[(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",5,5,22,0.2273,1,"{1311, 2000, 1146, 271, 264}"
93,1,16,0,0.0095156,"\int \frac{\left(-6+x^5\right) \left(-1+x^5\right)^{2/3}}{x^{11}} \, dx","Int[((-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",2,2,18,0.1111,1,"{446, 74}"
94,1,16,0,0.0062536,"\int \frac{\left(-4+x^5\right) \left(1+x^5\right)^{3/4}}{x^8} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
95,1,16,0,0.005883,"\int \frac{\left(-1+x^5\right)^{3/4} \left(4+x^5\right)}{x^8} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
96,1,16,0,0.0096407,"\int \frac{\left(1+x^5\right)^{2/3} \left(6+x^5\right)}{x^{11}} \, dx","Int[((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",2,2,18,0.1111,1,"{446, 74}"
97,1,33,0,0.2322643,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)}{x^6 \sqrt[4]{x+x^5}} \, dx","Int[((-3 + x^4)*(1 + x^4))/(x^6*(x + x^5)^(1/4)),x]","\frac{4 \left(x^5+x\right)^{3/4}}{7 x^6}+\frac{4 \left(x^5+x\right)^{3/4}}{7 x^2}","\frac{4 \left(x^5+x\right)^{7/4}}{7 x^7}",1,"(4*(x + x^5)^(3/4))/(7*x^6) + (4*(x + x^5)^(3/4))/(7*x^2)","B",11,4,23,0.1739,1,"{2052, 2025, 2032, 364}"
98,1,16,0,0.1413567,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^3+x^5}}{x^2 \left(1+x^2\right)} \, dx","Int[((-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",2,2,27,0.07407,1,"{2056, 449}"
99,0,0,0,0.8350945,"\int \frac{-2 b+3 a x^5}{\sqrt{b+a x^5} \left(b+x^2+a x^5\right)} \, dx","Int[(-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,"(3*x*Sqrt[1 + (a*x^5)/b]*Hypergeometric2F1[1/5, 1/2, 6/5, -((a*x^5)/b)])/Sqrt[b + a*x^5] - 5*b*Defer[Int][1/(Sqrt[b + a*x^5]*(b + x^2 + a*x^5)), x] - 3*Defer[Int][x^2/(Sqrt[b + a*x^5]*(b + x^2 + a*x^5)), x]","F",0,0,0,0,-1,"{}"
100,1,16,0,0.0026168,"\int \frac{1}{x^4 \sqrt{-1+x^6}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
101,1,16,0,0.0029006,"\int \frac{\sqrt[3]{-1+x^6}}{x^9} \, dx","Int[(-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",1,1,13,0.07692,1,"{264}"
102,1,16,0,0.002839,"\int \frac{\sqrt{-1+x^6}}{x^{10}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
103,1,16,0,0.0026143,"\int \frac{1}{x^4 \sqrt{1+x^6}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
104,1,16,0,0.0026264,"\int \frac{1}{x^5 \sqrt[3]{1+x^6}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
105,1,16,0,0.0055137,"\int \frac{-2+x^6}{x^4 \sqrt[4]{1+x^6}} \, dx","Int[(-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",1,1,18,0.05556,1,"{449}"
106,1,16,0,0.0025389,"\int \frac{\sqrt{1+x^6}}{x^{10}} \, dx","Int[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",1,1,13,0.07692,1,"{264}"
107,1,16,0,0.0064754,"\int \frac{\left(-2+x^6\right) \left(1+x^6\right)^{3/4}}{x^8} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
108,1,16,0,0.0054847,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^5} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
109,1,16,0,0.0058612,"\int \frac{2+x^6}{x^4 \sqrt[4]{-1+x^6}} \, dx","Int[(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",1,1,18,0.05556,1,"{449}"
110,1,16,0,0.0067457,"\int \frac{\left(-1+x^6\right)^{3/4} \left(2+x^6\right)}{x^8} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
111,1,16,0,0.015483,"\int \frac{-3+2 x^5}{x^3 \sqrt[4]{x+x^6}} \, dx","Int[(-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",1,1,20,0.05000,1,"{1590}"
112,1,47,0,0.1927602,"\int \frac{\sqrt[3]{x+x^4} \left(-2-x^3+x^6\right)}{x^6} \, dx","Int[((x + x^4)^(1/3)*(-2 - x^3 + x^6))/x^6,x]","\frac{3}{7} \sqrt[3]{x^4+x} x+\frac{3 \sqrt[3]{x^4+x}}{7 x^5}+\frac{6 \sqrt[3]{x^4+x}}{7 x^2}","\frac{3 \left(x^4+x\right)^{7/3}}{7 x^7}",1,"(3*(x + x^4)^(1/3))/(7*x^5) + (6*(x + x^4)^(1/3))/(7*x^2) + (3*x*(x + x^4)^(1/3))/7","B",12,6,23,0.2609,1,"{2052, 2004, 2032, 364, 2020, 2025}"
113,0,0,0,0.753624,"\int \frac{x \left(2+x^6\right)}{\sqrt{-1+x^6} \left(-1-x^4+x^6\right)} \, dx","Int[(x*(2 + x^6))/(Sqrt[-1 + x^6]*(-1 - x^4 + x^6)),x]","\int \frac{x \left(2+x^6\right)}{\sqrt{-1+x^6} \left(-1-x^4+x^6\right)} \, dx","-\tanh ^{-1}\left(\frac{x^2}{\sqrt{x^6-1}}\right)",1,"-((Sqrt[2 - Sqrt[3]]*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - Sqrt[3] - x^2)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x^2)/(1 - Sqrt[3] - x^2)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x^2)/(1 - Sqrt[3] - x^2)^2)]*Sqrt[-1 + x^6])) + (3*Defer[Subst][Defer[Int][1/(Sqrt[-1 + x^3]*(-1 - x^2 + x^3)), x], x, x^2])/2 + Defer[Subst][Defer[Int][x^2/(Sqrt[-1 + x^3]*(-1 - x^2 + x^3)), x], x, x^2]/2","F",0,0,0,0,-1,"{}"
114,1,16,0,0.0125555,"\int \frac{-1+x^8}{x^4 \sqrt{-1+x^4}} \, dx","Int[(-1 + x^8)/(x^4*Sqrt[-1 + x^4]),x]","\frac{\left(x^4-1\right)^{3/2}}{3 x^3}","\frac{\left(x^4-1\right)^{3/2}}{3 x^3}",1,"(-1 + x^4)^(3/2)/(3*x^3)","A",2,2,18,0.1111,1,"{1479, 449}"
115,1,16,0,0.0056907,"\int \frac{\left(-1+x^8\right) \sqrt{1+x^8}}{x^7} \, dx","Int[((-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",1,1,18,0.05556,1,"{449}"
116,0,0,0,0.7482577,"\int \frac{2+x+2 x^2}{(-1+2 x) \sqrt{x+x^4}} \, dx","Int[(2 + x + 2*x^2)/((-1 + 2*x)*Sqrt[x + x^4]),x]","\int \frac{2+x+2 x^2}{(-1+2 x) \sqrt{x+x^4}} \, dx","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)])/(3*Sqrt[x + x^4]) + (x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4]) - (3*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((1 - Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4] - (3*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((1 + Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4]","F",0,0,0,0,-1,"{}"
117,1,17,0,0.0371886,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]","-\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)","-\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"-ArcTan[x/Sqrt[1 + x^2 + x^4]]","A",2,2,25,0.08000,1,"{1698, 203}"
118,1,17,0,0.0815539,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1+x^2+x^4}} \, dx","Int[(-1 + x^4)/((1 + x^4)*Sqrt[1 + x^2 + x^4]),x]","-\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)","-\tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)",1,"-ArcTanh[x/Sqrt[1 + x^2 + x^4]]","A",2,2,25,0.08000,1,"{2112, 206}"
119,0,0,0,0.394405,"\int \frac{-1+2 x^2+2 x^4}{\left(1+2 x^2\right) \sqrt{-1+x^6}} \, dx","Int[(-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,"ArcTanh[x^3/Sqrt[-1 + x^6]]/3 + (x*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x^2)/(1 - (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(4*3^(1/4)*Sqrt[-((x^2*(1 - x^2))/(1 - (1 + Sqrt[3])*x^2)^2)]*Sqrt[-1 + x^6]) - ((3*I)/4)*Defer[Int][1/((I - Sqrt[2]*x)*Sqrt[-1 + x^6]), x] - ((3*I)/4)*Defer[Int][1/((I + Sqrt[2]*x)*Sqrt[-1 + x^6]), x]","F",0,0,0,0,-1,"{}"
120,1,25,0,0.0099895,"\int \frac{x^3}{\left(-1+x^2\right)^{3/4}} \, dx","Int[x^3/(-1 + x^2)^(3/4),x]","\frac{2}{5} \left(x^2-1\right)^{5/4}+2 \sqrt[4]{x^2-1}","\frac{2}{5} \sqrt[4]{x^2-1} \left(x^2+4\right)",1,"2*(-1 + x^2)^(1/4) + (2*(-1 + x^2)^(5/4))/5","A",3,2,13,0.1538,1,"{266, 43}"
121,1,20,0,0.0077099,"\int \frac{3+x}{(-1+x)^2 \sqrt[3]{-1+x^2}} \, dx","Int[(3 + x)/((-1 + x)^2*(-1 + x^2)^(1/3)),x]","-\frac{3 \left(x^2-1\right)^{2/3}}{2 (1-x)^2}","-\frac{3 \left(x^2-1\right)^{2/3}}{2 (x-1)^2}",1,"(-3*(-1 + x^2)^(2/3))/(2*(1 - x)^2)","A",1,1,18,0.05556,1,"{787}"
122,1,27,0,0.010256,"\int \frac{x^3}{\left(1+x^2\right)^{2/3}} \, dx","Int[x^3/(1 + x^2)^(2/3),x]","\frac{3}{8} \left(x^2+1\right)^{4/3}-\frac{3}{2} \sqrt[3]{x^2+1}","\frac{3}{8} \left(x^2-3\right) \sqrt[3]{x^2+1}",1,"(-3*(1 + x^2)^(1/3))/2 + (3*(1 + x^2)^(4/3))/8","A",3,2,13,0.1538,1,"{266, 43}"
123,1,18,0,0.0197036,"\int \frac{1}{x^2 \sqrt[3]{-x+x^3}} \, dx","Int[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",1,1,15,0.06667,1,"{2014}"
124,1,18,0,0.0187351,"\int \frac{\sqrt[3]{-x+x^3}}{x^4} \, dx","Int[(-x + x^3)^(1/3)/x^4,x]","\frac{3 \left(x^3-x\right)^{4/3}}{8 x^4}","\frac{3 \left(x^3-x\right)^{4/3}}{8 x^4}",1,"(3*(-x + x^3)^(4/3))/(8*x^4)","A",1,1,15,0.06667,1,"{2014}"
125,1,12,0,0.0703022,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+x^3}} \, dx","Int[(-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",2,2,22,0.09091,1,"{2056, 449}"
126,1,18,0,0.0217172,"\int \frac{1}{x \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x*(x^2 + x^3)^(1/3)),x]","-\frac{3 \left(x^3+x^2\right)^{2/3}}{2 x^2}","-\frac{3 \left(x^3+x^2\right)^{2/3}}{2 x^2}",1,"(-3*(x^2 + x^3)^(2/3))/(2*x^2)","A",1,1,15,0.06667,1,"{2014}"
127,1,18,0,0.0161523,"\int \frac{2+x}{x^2 \sqrt[4]{x^2+x^3}} \, dx","Int[(2 + x)/(x^2*(x^2 + x^3)^(1/4)),x]","-\frac{4 \left(x^3+x^2\right)^{3/4}}{3 x^3}","-\frac{4 \left(x^3+x^2\right)^{3/4}}{3 x^3}",1,"(-4*(x^2 + x^3)^(3/4))/(3*x^3)","A",1,1,18,0.05556,1,"{1590}"
128,1,18,0,0.01394,"\int \frac{\left(-2 b+a x^3\right) \sqrt{b+a x^3}}{x^4} \, dx","Int[((-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",2,2,24,0.08333,1,"{446, 74}"
129,1,68,0,0.4070773,"\int \frac{1+x+x^2}{(-1+x)^2 \sqrt{-1+x^4}} \, dx","Int[(1 + x + x^2)/((-1 + x)^2*Sqrt[-1 + x^4]),x]","\frac{x \left(x^2+1\right)}{\left(1-x^2\right) \sqrt{x^4-1}}+\frac{\sqrt{x^4-1}}{2 \left(1-x^2\right)}-\frac{\sqrt{x^4-1}}{\left(1-x^2\right)^2}","-\frac{\sqrt{x^4-1}}{2 (x-1)^2}",1,"(x*(1 + x^2))/((1 - x^2)*Sqrt[-1 + x^4]) - Sqrt[-1 + x^4]/(1 - x^2)^2 + Sqrt[-1 + x^4]/(2*(1 - x^2))","B",32,19,21,0.9048,1,"{6742, 222, 2153, 1152, 414, 527, 524, 427, 424, 253, 1248, 659, 651, 1256, 471, 21, 1725, 423, 426}"
130,1,96,0,0.0951887,"\int \frac{-1+x^4}{x^2 \sqrt{-x+x^3}} \, dx","Int[(-1 + x^4)/(x^2*Sqrt[-x + x^3]),x]","\frac{2 \sqrt{x^3-x}}{3}-\frac{\sqrt{2} \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^3-x}}-\frac{2 \sqrt{x^3-x}}{3 x^2}","\frac{2 \left(x^3-x\right)^{3/2}}{3 x^3}",1,"(2*Sqrt[-x + x^3])/3 - (2*Sqrt[-x + x^3])/(3*x^2) - (Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(3*Sqrt[-x + x^3])","C",5,5,20,0.2500,0,"{2048, 2025, 2011, 329, 222}"
131,1,18,0,0.0206925,"\int \frac{1}{x^2 \sqrt{-x+x^4}} \, dx","Int[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",1,1,15,0.06667,1,"{2014}"
132,1,18,0,0.0207299,"\int \frac{1}{x^3 \sqrt[4]{-x+x^4}} \, dx","Int[1/(x^3*(-x + x^4)^(1/4)),x]","\frac{4 \left(x^4-x\right)^{3/4}}{9 x^3}","\frac{4 \left(x^4-x\right)^{3/4}}{9 x^3}",1,"(4*(-x + x^4)^(3/4))/(9*x^3)","A",1,1,15,0.06667,1,"{2014}"
133,1,37,0,0.1221657,"\int \frac{-1+x^3}{x^6 \sqrt[4]{-x+x^4}} \, dx","Int[(-1 + x^3)/(x^6*(-x + x^4)^(1/4)),x]","\frac{4 \left(x^4-x\right)^{3/4}}{21 x^3}-\frac{4 \left(x^4-x\right)^{3/4}}{21 x^6}","\frac{4 \left(x^4-x\right)^{7/4}}{21 x^7}",1,"(-4*(-x + x^4)^(3/4))/(21*x^6) + (4*(-x + x^4)^(3/4))/(21*x^3)","B",5,3,20,0.1500,1,"{2052, 2016, 2014}"
134,1,18,0,0.0205986,"\int \frac{\sqrt[4]{-x+x^4}}{x^5} \, dx","Int[(-x + x^4)^(1/4)/x^5,x]","\frac{4 \left(x^4-x\right)^{5/4}}{15 x^5}","\frac{4 \left(x^4-x\right)^{5/4}}{15 x^5}",1,"(4*(-x + x^4)^(5/4))/(15*x^5)","A",1,1,15,0.06667,1,"{2014}"
135,1,25,0,0.0688582,"\int \frac{\left(2+x^3\right) \sqrt[3]{-x+x^4}}{\left(-1+x^3\right)^2} \, dx","Int[((2 + x^3)*(-x + x^4)^(1/3))/(-1 + x^3)^2,x]","\frac{3 x \sqrt[3]{x^4-x}}{2 \left(1-x^3\right)}","-\frac{3 x^2}{2 \left(x^4-x\right)^{2/3}}",1,"(3*x*(-x + x^4)^(1/3))/(2*(1 - x^3))","A",2,2,24,0.08333,1,"{2056, 449}"
136,1,18,0,0.0199163,"\int \frac{\sqrt{-x+x^4}}{x^6} \, dx","Int[Sqrt[-x + x^4]/x^6,x]","\frac{2 \left(x^4-x\right)^{3/2}}{9 x^6}","\frac{2 \left(x^4-x\right)^{3/2}}{9 x^6}",1,"(2*(-x + x^4)^(3/2))/(9*x^6)","A",1,1,15,0.06667,1,"{2014}"
137,1,18,0,0.0156759,"\int \frac{x}{\sqrt{x+x^4}} \, dx","Int[x/Sqrt[x + x^4],x]","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(2*ArcTanh[x^2/Sqrt[x + x^4]])/3","A",2,2,11,0.1818,1,"{2029, 206}"
138,1,12,0,0.0753681,"\int \frac{-2+x^3}{\left(1+x^3\right) \sqrt[3]{x+x^4}} \, dx","Int[(-2 + x^3)/((1 + x^3)*(x + x^4)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{x^4+x}}","-\frac{3 \left(x^4+x\right)^{2/3}}{x^3+1}",1,"(-3*x)/(x + x^4)^(1/3)","A",2,2,22,0.09091,1,"{2056, 449}"
139,1,18,0,0.0652672,"\int \frac{-1+x^2}{x \sqrt[3]{x^2+x^4}} \, dx","Int[(-1 + x^2)/(x*(x^2 + x^4)^(1/3)),x]","\frac{3 \left(x^4+x^2\right)^{2/3}}{2 x^2}","\frac{3 \left(x^4+x^2\right)^{2/3}}{2 x^2}",1,"(3*(x^2 + x^4)^(2/3))/(2*x^2)","A",2,2,20,0.1000,1,"{2034, 763}"
140,1,18,0,0.0226406,"\int \frac{1}{x^2 \sqrt[4]{x^2+x^4}} \, dx","Int[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",1,1,15,0.06667,1,"{2014}"
141,1,18,0,0.0212461,"\int \frac{\sqrt[4]{x^2+x^4}}{x^4} \, dx","Int[(x^2 + x^4)^(1/4)/x^4,x]","-\frac{2 \left(x^4+x^2\right)^{5/4}}{5 x^5}","-\frac{2 \left(x^4+x^2\right)^{5/4}}{5 x^5}",1,"(-2*(x^2 + x^4)^(5/4))/(5*x^5)","A",1,1,15,0.06667,1,"{2014}"
142,1,18,0,0.0165277,"\int \frac{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}}{x^3} \, dx","Int[((-1 + x^2)*(x^2 + x^4)^(1/3))/x^3,x]","\frac{3 \left(x^4+x^2\right)^{4/3}}{4 x^4}","\frac{3 \left(x^4+x^2\right)^{4/3}}{4 x^4}",1,"(3*(x^2 + x^4)^(4/3))/(4*x^4)","A",1,1,20,0.05000,1,"{1590}"
143,1,18,0,0.0233262,"\int \frac{1}{x \sqrt[4]{x^3+x^4}} \, dx","Int[1/(x*(x^3 + x^4)^(1/4)),x]","-\frac{4 \left(x^4+x^3\right)^{3/4}}{3 x^3}","-\frac{4 \left(x^4+x^3\right)^{3/4}}{3 x^3}",1,"(-4*(x^3 + x^4)^(3/4))/(3*x^3)","A",1,1,15,0.06667,1,"{2014}"
144,1,37,0,0.1211341,"\int \frac{(1+x) \sqrt[4]{x^3+x^4}}{x^4} \, dx","Int[((1 + x)*(x^3 + x^4)^(1/4))/x^4,x]","-\frac{4 \left(x^4+x^3\right)^{5/4}}{9 x^6}-\frac{4 \left(x^4+x^3\right)^{5/4}}{9 x^5}","-\frac{4 \left(x^4+x^3\right)^{9/4}}{9 x^9}",1,"(-4*(x^3 + x^4)^(5/4))/(9*x^6) - (4*(x^3 + x^4)^(5/4))/(9*x^5)","B",5,3,18,0.1667,1,"{2052, 2016, 2014}"
145,0,0,0,0.4593346,"\int \frac{-2-x+2 x^4}{\left(1+x+x^4\right) \sqrt{1+x+x^2+x^4}} \, dx","Int[(-2 - x + 2*x^4)/((1 + x + x^4)*Sqrt[1 + x + x^2 + x^4]),x]","\int \frac{-2-x+2 x^4}{\left(1+x+x^4\right) \sqrt{1+x+x^2+x^4}} \, dx","-2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+x+1}}\right)",1,"2*Defer[Int][1/Sqrt[1 + x + x^2 + x^4], x] - 4*Defer[Int][1/((1 + x + x^4)*Sqrt[1 + x + x^2 + x^4]), x] - 3*Defer[Int][x/((1 + x + x^4)*Sqrt[1 + x + x^2 + x^4]), x]","F",0,0,0,0,-1,"{}"
146,1,18,0,0.0171269,"\int \frac{3+x^4}{x^3 \sqrt[4]{-x+x^5}} \, dx","Int[(3 + x^4)/(x^3*(-x + x^5)^(1/4)),x]","\frac{4 \left(x^5-x\right)^{3/4}}{3 x^3}","\frac{4 \left(x^5-x\right)^{3/4}}{3 x^3}",1,"(4*(-x + x^5)^(3/4))/(3*x^3)","A",1,1,20,0.05000,1,"{1590}"
147,1,37,0,0.2591455,"\int \frac{\left(-1+x^4\right) \left(3+x^4\right)}{x^6 \sqrt[4]{-x+x^5}} \, dx","Int[((-1 + x^4)*(3 + x^4))/(x^6*(-x + x^5)^(1/4)),x]","\frac{4 \left(x^5-x\right)^{3/4}}{7 x^2}-\frac{4 \left(x^5-x\right)^{3/4}}{7 x^6}","\frac{4 \left(x^5-x\right)^{7/4}}{7 x^7}",1,"(-4*(-x + x^5)^(3/4))/(7*x^6) + (4*(-x + x^5)^(3/4))/(7*x^2)","B",14,5,25,0.2000,1,"{2052, 2025, 2032, 365, 364}"
148,1,12,0,0.06786,"\int \frac{-3+x^4}{\left(1+x^4\right) \sqrt[4]{x+x^5}} \, dx","Int[(-3 + x^4)/((1 + x^4)*(x + x^5)^(1/4)),x]","-\frac{4 x}{\sqrt[4]{x^5+x}}","-\frac{4 \left(x^5+x\right)^{3/4}}{x^4+1}",1,"(-4*x)/(x + x^5)^(1/4)","A",2,2,22,0.09091,1,"{2056, 449}"
149,1,18,0,0.0170883,"\int \frac{\left(-1+2 x^3\right) \sqrt[3]{x^2+x^5}}{x^3} \, dx","Int[((-1 + 2*x^3)*(x^2 + x^5)^(1/3))/x^3,x]","\frac{3 \left(x^5+x^2\right)^{4/3}}{4 x^4}","\frac{3 \left(x^5+x^2\right)^{4/3}}{4 x^4}",1,"(3*(x^2 + x^5)^(4/3))/(4*x^4)","A",1,1,22,0.04545,1,"{1590}"
150,1,18,0,0.0567805,"\int \frac{-1+x^2}{x \sqrt[4]{x^3+x^5}} \, dx","Int[(-1 + x^2)/(x*(x^3 + x^5)^(1/4)),x]","\frac{4 \left(x^5+x^3\right)^{3/4}}{3 x^3}","\frac{4 \left(x^5+x^3\right)^{3/4}}{3 x^3}",1,"(4*(x^3 + x^5)^(3/4))/(3*x^3)","A",1,1,20,0.05000,1,"{2036}"
151,1,53,0,0.1811706,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^3+x^5}}{x^4} \, dx","Int[((-1 + x^4)*(x^3 + x^5)^(1/4))/x^4,x]","\frac{4}{9} \sqrt[4]{x^5+x^3} x+\frac{8 \sqrt[4]{x^5+x^3}}{9 x}+\frac{4 \sqrt[4]{x^5+x^3}}{9 x^3}","\frac{4 \left(x^5+x^3\right)^{9/4}}{9 x^9}",1,"(4*(x^3 + x^5)^(1/4))/(9*x^3) + (8*(x^3 + x^5)^(1/4))/(9*x) + (4*x*(x^3 + x^5)^(1/4))/9","B",9,6,20,0.3000,1,"{2052, 2004, 2032, 364, 2020, 2025}"
152,1,18,0,0.0078982,"\int \frac{x^2}{\sqrt{-1+x^6}} \, dx","Int[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",3,3,13,0.2308,1,"{275, 217, 206}"
153,1,8,0,0.0035426,"\int \frac{x^2}{\sqrt{1+x^6}} \, dx","Int[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",2,2,13,0.1538,1,"{275, 215}"
154,1,37,0,0.2653188,"\int \frac{\left(-1+x^5\right) \left(3+2 x^5\right)}{x^6 \sqrt[4]{-x+x^6}} \, dx","Int[((-1 + x^5)*(3 + 2*x^5))/(x^6*(-x + x^6)^(1/4)),x]","\frac{4 \left(x^6-x\right)^{3/4}}{7 x}-\frac{4 \left(x^6-x\right)^{3/4}}{7 x^6}","\frac{4 \left(x^6-x\right)^{7/4}}{7 x^7}",1,"(-4*(-x + x^6)^(3/4))/(7*x^6) + (4*(-x + x^6)^(3/4))/(7*x)","B",14,5,27,0.1852,1,"{2052, 2025, 2032, 365, 364}"
155,1,18,0,0.0231585,"\int \frac{1}{x^3 \sqrt[3]{x^2+x^6}} \, dx","Int[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",1,1,15,0.06667,1,"{2014}"
156,1,18,0,0.0163295,"\int \frac{-1+x^4}{x^2 \sqrt[4]{x^2+x^6}} \, dx","Int[(-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",1,1,20,0.05000,1,"{1590}"
157,1,18,0,0.015805,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{x^4} \, dx","Int[((-1 + x^4)*(x^2 + x^6)^(1/4))/x^4,x]","\frac{2 \left(x^6+x^2\right)^{5/4}}{5 x^5}","\frac{2 \left(x^6+x^2\right)^{5/4}}{5 x^5}",1,"(2*(x^2 + x^6)^(5/4))/(5*x^5)","A",1,1,20,0.05000,1,"{1590}"
158,0,0,0,0.083724,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[1 + x^2]]/Sqrt[1 + x^2],x]","\int \frac{\sqrt{1+\sqrt{1+x^2}}}{\sqrt{1+x^2}} \, dx","\frac{2 x}{\sqrt{\sqrt{x^2+1}+1}}",1,"Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/Sqrt[1 + x^2], x]","F",0,0,0,0,-1,"{}"
159,1,719,0,1.9190091,"\int \frac{-2-2 x+x^2}{\left(1+x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(-2 - 2*x + x^2)/((1 + x + x^2)*Sqrt[-1 + x^3]),x]","\frac{2 (1-x)}{\sqrt{x^3-1}}+\frac{2 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(\sqrt{3}+i\right) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} (1-x) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\left(3+(2+i) \sqrt{3}\right) \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \sqrt[4]{3} \left(-\sqrt{3}+i\right) \sqrt{2-\sqrt{3}} \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} (1-x) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\left(3+(2-i) \sqrt{3}\right) \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \sqrt{2-\sqrt{3}} \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} (1-x) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{6 \sqrt[4]{3} \left(\sqrt{3}+(-2+i)\right) \left(\sqrt{3}+i\right) \sqrt{26+15 \sqrt{3}} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (1-x) E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\left(3+(2+i) \sqrt{3}\right)^3 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{6 \sqrt[4]{3} \left(1+i \sqrt{3}\right) \left(\sqrt{3}+(-2-i)\right) \sqrt{26+15 \sqrt{3}} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (1-x) E\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\left(3 i+(1+2 i) \sqrt{3}\right)^3 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{2 \sqrt{x^3-1}}{x^2+x+1}",1,"(2*(1 - x))/Sqrt[-1 + x^3] + (6*3^(1/4)*(1 + I*Sqrt[3])*((-2 - I) + Sqrt[3])*Sqrt[26 + 15*Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/((3*I + (1 + 2*I)*Sqrt[3])^3*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3]) - (6*3^(1/4)*((-2 + I) + Sqrt[3])*(I + Sqrt[3])*Sqrt[26 + 15*Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/((3 + (2 + I)*Sqrt[3])^3*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3]) - (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (2*3^(1/4)*(I - Sqrt[3])*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/((3 + (2 - I)*Sqrt[3])*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (2*3^(1/4)*Sqrt[2 - Sqrt[3]]*(I + Sqrt[3])*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/((3 + (2 + I)*Sqrt[3])*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","C",27,10,26,0.3846,1,"{6728, 219, 2136, 2142, 2113, 21, 414, 424, 444, 37}"
160,1,19,0,0.1013683,"\int \frac{b+a x^2}{x \sqrt{-b x+a x^3}} \, dx","Int[(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",1,1,25,0.04000,1,"{2036}"
161,0,0,0,1.8978266,"\int \frac{-1-2 x+2 x^2}{\left(1+2 x^2\right) \sqrt{x+x^4}} \, dx","Int[(-1 - 2*x + 2*x^2)/((1 + 2*x^2)*Sqrt[x + x^4]),x]","\int \frac{-1-2 x+2 x^2}{\left(1+2 x^2\right) \sqrt{x+x^4}} \, dx","\tan ^{-1}\left(\frac{2 \sqrt{x^4+x}}{2 x-1}\right)",1,"(x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4]) - ((1/2 + I/2)*(I + Sqrt[2])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/(((-1)^(1/4) - 2^(1/4)*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4] + ((1/2 + I/2)*(1 + I*Sqrt[2])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((-(-1)^(3/4) - 2^(1/4)*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4] - ((1/2 + I/2)*(I + Sqrt[2])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/(((-1)^(1/4) + 2^(1/4)*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4] + ((1/2 + I/2)*(1 + I*Sqrt[2])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((-(-1)^(3/4) + 2^(1/4)*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4]","F",0,0,0,0,-1,"{}"
162,1,19,0,0.0924471,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{-1-x^2+x^4}} \, dx","Int[(1 + x^4)/((-1 + x^4)*Sqrt[-1 - x^2 + x^4]),x]","-\tan ^{-1}\left(\frac{x}{\sqrt{x^4-x^2-1}}\right)","-\tan ^{-1}\left(\frac{x}{\sqrt{x^4-x^2-1}}\right)",1,"-ArcTan[x/Sqrt[-1 - x^2 + x^4]]","A",2,2,27,0.07407,1,"{2112, 204}"
163,1,33,0,0.023347,"\int \frac{x}{\sqrt[5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx","Int[x/(1 - 4*x + 6*x^2 - 4*x^3 + x^4)^(1/5),x]","\frac{5 (x-1)^2}{6 \sqrt[5]{(x-1)^4}}+\frac{5 (x-1)}{\sqrt[5]{(x-1)^4}}","\frac{5 (x-1) (x+5)}{6 \sqrt[5]{(x-1)^4}}",1,"(5*(-1 + x))/((-1 + x)^4)^(1/5) + (5*(-1 + x)^2)/(6*((-1 + x)^4)^(1/5))","A",4,3,24,0.1250,1,"{1680, 15, 43}"
164,1,19,0,0.0217187,"\int \frac{-2+x^6}{x^4 \sqrt[4]{1+x^4+x^6}} \, dx","Int[(-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",1,1,21,0.04762,1,"{1590}"
165,1,19,0,0.0191855,"\int \frac{1+x^8}{x^4 \sqrt[4]{-1+x^4+x^8}} \, dx","Int[(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",1,1,21,0.04762,1,"{1590}"
166,1,19,0,0.0195064,"\int \frac{-1+x^8}{x^4 \sqrt[4]{1+x^4+x^8}} \, dx","Int[(-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",1,1,21,0.04762,1,"{1590}"
167,1,14,0,0.0750089,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(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",2,2,24,0.08333,1,"{2056, 449}"
168,1,14,0,0.0343056,"\int \frac{1}{\left(1+x^2\right) \sqrt[3]{x+x^3}} \, dx","Int[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",2,2,17,0.1176,1,"{2056, 264}"
169,1,20,0,0.0232616,"\int \frac{1}{x \sqrt[3]{-x^2+x^3}} \, dx","Int[1/(x*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left(x^3-x^2\right)^{2/3}}{2 x^2}","\frac{3 \left(x^3-x^2\right)^{2/3}}{2 x^2}",1,"(3*(-x^2 + x^3)^(2/3))/(2*x^2)","A",1,1,17,0.05882,1,"{2014}"
170,1,20,0,0.0054602,"\int \frac{x^2}{\sqrt{-b+a x^3}} \, dx","Int[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",1,1,17,0.05882,1,"{261}"
171,1,20,0,0.0041539,"\int x^2 \sqrt{-b+a x^3} \, dx","Int[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",1,1,17,0.05882,1,"{261}"
172,1,20,0,0.0156008,"\int \frac{\sqrt{-b+a x^3} \left(2 b+a x^3\right)}{x^4} \, dx","Int[(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",2,2,26,0.07692,1,"{446, 74}"
173,1,20,0,0.0247017,"\int \frac{1}{x^2 \sqrt[4]{-x^2+x^4}} \, dx","Int[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",1,1,17,0.05882,1,"{2014}"
174,1,20,0,0.0231268,"\int \frac{\sqrt[4]{-x^2+x^4}}{x^4} \, dx","Int[(-x^2 + x^4)^(1/4)/x^4,x]","\frac{2 \left(x^4-x^2\right)^{5/4}}{5 x^5}","\frac{2 \left(x^4-x^2\right)^{5/4}}{5 x^5}",1,"(2*(-x^2 + x^4)^(5/4))/(5*x^5)","A",1,1,17,0.05882,1,"{2014}"
175,1,20,0,0.0175951,"\int \frac{\left(1+x^2\right) \sqrt[3]{-x^2+x^4}}{x^3} \, dx","Int[((1 + x^2)*(-x^2 + x^4)^(1/3))/x^3,x]","\frac{3 \left(x^4-x^2\right)^{4/3}}{4 x^4}","\frac{3 \left(x^4-x^2\right)^{4/3}}{4 x^4}",1,"(3*(-x^2 + x^4)^(4/3))/(4*x^4)","A",1,1,22,0.04545,1,"{1590}"
176,1,20,0,0.0228006,"\int \frac{1}{x \sqrt[4]{-x^3+x^4}} \, dx","Int[1/(x*(-x^3 + x^4)^(1/4)),x]","\frac{4 \left(x^4-x^3\right)^{3/4}}{3 x^3}","\frac{4 \left(x^4-x^3\right)^{3/4}}{3 x^3}",1,"(4*(-x^3 + x^4)^(3/4))/(3*x^3)","A",1,1,17,0.05882,1,"{2014}"
177,1,41,0,0.126236,"\int \frac{(-1+x) \sqrt[4]{-x^3+x^4}}{x^4} \, dx","Int[((-1 + x)*(-x^3 + x^4)^(1/4))/x^4,x]","\frac{4 \left(x^4-x^3\right)^{5/4}}{9 x^5}-\frac{4 \left(x^4-x^3\right)^{5/4}}{9 x^6}","\frac{4 \left(x^4-x^3\right)^{9/4}}{9 x^9}",1,"(-4*(-x^3 + x^4)^(5/4))/(9*x^6) + (4*(-x^3 + x^4)^(5/4))/(9*x^5)","B",5,3,20,0.1500,1,"{2052, 2016, 2014}"
178,1,20,0,0.0220604,"\int \frac{\sqrt[4]{-x^3+x^4}}{x^3} \, dx","Int[(-x^3 + x^4)^(1/4)/x^3,x]","\frac{4 \left(x^4-x^3\right)^{5/4}}{5 x^5}","\frac{4 \left(x^4-x^3\right)^{5/4}}{5 x^5}",1,"(4*(-x^3 + x^4)^(5/4))/(5*x^5)","A",1,1,17,0.05882,1,"{2014}"
179,1,20,0,0.0158373,"\int x \left(1+2 x^2\right) \sqrt{-1+2 x^2+2 x^4} \, dx","Int[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",2,2,25,0.08000,1,"{1247, 629}"
180,1,20,0,0.0177342,"\int \frac{\left(1+2 x^3\right) \sqrt[3]{-x^2+x^5}}{x^3} \, dx","Int[((1 + 2*x^3)*(-x^2 + x^5)^(1/3))/x^3,x]","\frac{3 \left(x^5-x^2\right)^{4/3}}{4 x^4}","\frac{3 \left(x^5-x^2\right)^{4/3}}{4 x^4}",1,"(3*(-x^2 + x^5)^(4/3))/(4*x^4)","A",1,1,24,0.04167,1,"{1590}"
181,1,41,0,0.1483934,"\int \frac{-1+x^4}{x^2 \sqrt[4]{-x^3+x^5}} \, dx","Int[(-1 + x^4)/(x^2*(-x^3 + x^5)^(1/4)),x]","\frac{4 \left(x^5-x^3\right)^{3/4}}{7 x^2}-\frac{4 \left(x^5-x^3\right)^{3/4}}{7 x^4}","\frac{4 \left(x^5-x^3\right)^{7/4}}{7 x^7}",1,"(-4*(-x^3 + x^5)^(3/4))/(7*x^4) + (4*(-x^3 + x^5)^(3/4))/(7*x^2)","B",10,6,22,0.2727,1,"{2052, 2025, 2011, 365, 364, 2024}"
182,1,59,0,0.1961293,"\int \frac{\left(-1+x^4\right) \sqrt[4]{-x^3+x^5}}{x^4} \, dx","Int[((-1 + x^4)*(-x^3 + x^5)^(1/4))/x^4,x]","\frac{4}{9} \sqrt[4]{x^5-x^3} x-\frac{8 \sqrt[4]{x^5-x^3}}{9 x}+\frac{4 \sqrt[4]{x^5-x^3}}{9 x^3}","\frac{4 \left(x^5-x^3\right)^{9/4}}{9 x^9}",1,"(4*(-x^3 + x^5)^(1/4))/(9*x^3) - (8*(-x^3 + x^5)^(1/4))/(9*x) + (4*x*(-x^3 + x^5)^(1/4))/9","B",11,7,22,0.3182,1,"{2052, 2004, 2032, 365, 364, 2020, 2025}"
183,0,0,0,0.5935524,"\int \frac{-1-2 x^2+2 x^4}{x^2 \left(1+x^2\right) \sqrt{1+x^6}} \, dx","Int[(-1 - 2*x^2 + 2*x^4)/(x^2*(1 + x^2)*Sqrt[1 + x^6]),x]","\int \frac{-1-2 x^2+2 x^4}{x^2 \left(1+x^2\right) \sqrt{1+x^6}} \, dx","\frac{\sqrt{x^6+1}}{x \left(x^2+1\right)}",1,"Sqrt[1 + x^6]/x - ((1 + Sqrt[3])*x*Sqrt[1 + x^6])/(1 + (1 + Sqrt[3])*x^2) + (3^(1/4)*x*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(1 + (1 - Sqrt[3])*x^2)/(1 + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(Sqrt[(x^2*(1 + x^2))/(1 + (1 + Sqrt[3])*x^2)^2]*Sqrt[1 + x^6]) + (x*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x^2)/(1 + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x^2*(1 + x^2))/(1 + (1 + Sqrt[3])*x^2)^2]*Sqrt[1 + x^6]) + ((1 - Sqrt[3])*x*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x^2)/(1 + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2*3^(1/4)*Sqrt[(x^2*(1 + x^2))/(1 + (1 + Sqrt[3])*x^2)^2]*Sqrt[1 + x^6]) - ((3*I)/2)*Defer[Int][1/((I - x)*Sqrt[1 + x^6]), x] - ((3*I)/2)*Defer[Int][1/((I + x)*Sqrt[1 + x^6]), x]","F",0,0,0,0,-1,"{}"
184,1,20,0,0.0247051,"\int \frac{1}{x^3 \sqrt[3]{-x^2+x^6}} \, dx","Int[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",1,1,17,0.05882,1,"{2014}"
185,1,20,0,0.0198466,"\int \frac{1+x^4}{x^2 \sqrt[4]{-x^2+x^6}} \, dx","Int[(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",1,1,22,0.04545,1,"{1590}"
186,1,20,0,0.0180395,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}}{x^4} \, dx","Int[((1 + x^4)*(-x^2 + x^6)^(1/4))/x^4,x]","\frac{2 \left(x^6-x^2\right)^{5/4}}{5 x^5}","\frac{2 \left(x^6-x^2\right)^{5/4}}{5 x^5}",1,"(2*(-x^2 + x^6)^(5/4))/(5*x^5)","A",1,1,22,0.04545,1,"{1590}"
187,1,41,0,0.1613302,"\int \frac{-1+x^8}{x^4 \sqrt[4]{-x^2+x^6}} \, dx","Int[(-1 + x^8)/(x^4*(-x^2 + x^6)^(1/4)),x]","\frac{2 \left(x^6-x^2\right)^{3/4}}{7 x}-\frac{2 \left(x^6-x^2\right)^{3/4}}{7 x^5}","\frac{2 \left(x^6-x^2\right)^{7/4}}{7 x^7}",1,"(-2*(-x^2 + x^6)^(3/4))/(7*x^5) + (2*(-x^2 + x^6)^(3/4))/(7*x)","B",12,7,22,0.3182,1,"{2052, 2025, 2011, 329, 246, 245, 2024}"
188,1,14,0,0.0043219,"\int \frac{1+x^8}{\sqrt[4]{1-x^8} \left(-1+x^8\right)} \, dx","Int[(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",2,2,24,0.08333,1,"{21, 383}"
189,1,20,0,0.0054882,"\int \frac{1}{\sqrt{-x^2+x^8}} \, dx","Int[1/Sqrt[-x^2 + x^8],x]","-\frac{1}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^8-x^2}}\right)","-\frac{1}{3} \tan ^{-1}\left(\frac{x}{\sqrt{x^8-x^2}}\right)",1,"-1/3*ArcTan[x/Sqrt[-x^2 + x^8]]","A",2,2,13,0.1538,1,"{2008, 203}"
190,0,0,0,0.2310338,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{1+x^2} \, dx","Int[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,"(I/2)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(I - x), x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(I + x), x]","F",0,0,0,0,-1,"{}"
191,1,25,0,0.0563856,"\int \frac{-1+x}{(2+x) \sqrt{-1+x^3}} \, dx","Int[(-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",2,2,18,0.1111,1,"{2138, 203}"
192,1,18,0,0.0636962,"\int \frac{-2-2 x+x^2}{\left(2+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(-2 - 2*x + x^2)/((2 + x^2)*Sqrt[-1 + x^3]),x]","2 \tanh ^{-1}\left(\frac{1-x}{\sqrt{x^3-1}}\right)","-2 \tanh ^{-1}\left(\frac{\sqrt{x^3-1}}{x^2+x+1}\right)",1,"2*ArcTanh[(1 - x)/Sqrt[-1 + x^3]]","A",2,2,25,0.08000,1,"{2146, 206}"
193,1,402,0,0.5384479,"\int \frac{-2-2 x+x^2}{\left(2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(-2 - 2*x + x^2)/((2*x + x^2)*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(\sqrt{x^3-1}\right)-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt[4]{3} \sqrt{2 \left(7-4 \sqrt{3}\right)} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt{2 \left(7-4 \sqrt{3}\right)} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3-1}}{x^2+x+1}\right)",1,"(2*ArcTan[(1 - x)^2/(3*Sqrt[-1 + x^3])])/3 - (2*ArcTan[Sqrt[-1 + x^3]])/3 + (Sqrt[2*(7 - 4*Sqrt[3])]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (3^(1/4)*Sqrt[2*(7 - 4*Sqrt[3])]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","C",13,9,27,0.3333,0,"{1593, 6742, 219, 266, 63, 203, 2136, 2139, 2138}"
194,0,0,0,1.1894654,"\int \frac{-1+2 x+2 x^2}{(-1+x) x \sqrt{-x+x^4}} \, dx","Int[(-1 + 2*x + 2*x^2)/((-1 + x)*x*Sqrt[-x + x^4]),x]","\int \frac{-1+2 x+2 x^2}{(-1+x) x \sqrt{-x+x^4}} \, dx","-\frac{2 \sqrt{x^4-x}}{(x-1) x}",1,"(-2*(1 - x^3))/Sqrt[-x + x^4] - (2*(1 + Sqrt[3])*x*(1 - x^3))/((1 - (1 + Sqrt[3])*x)*Sqrt[-x + x^4]) + (2*3^(1/4)*(1 - x)*x*Sqrt[(1 + x + x^2)/(1 - (1 + Sqrt[3])*x)^2]*EllipticE[ArcCos[(1 - (1 - Sqrt[3])*x)/(1 - (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(Sqrt[-(((1 - x)*x)/(1 - (1 + Sqrt[3])*x)^2)]*Sqrt[-x + x^4]) + (2*(1 - x)*x*Sqrt[(1 + x + x^2)/(1 - (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x)/(1 - (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[-(((1 - x)*x)/(1 - (1 + Sqrt[3])*x)^2)]*Sqrt[-x + x^4]) + ((1 - Sqrt[3])*(1 - x)*x*Sqrt[(1 + x + x^2)/(1 - (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x)/(1 - (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[-(((1 - x)*x)/(1 - (1 + Sqrt[3])*x)^2)]*Sqrt[-x + x^4]) + (3*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((-1 + x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4] - (3*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((1 + x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4]","F",0,0,0,0,-1,"{}"
195,0,0,0,1.764222,"\int \frac{-1+2 x+2 x^2}{\left(1+2 x^2\right) \sqrt{-x+x^4}} \, dx","Int[(-1 + 2*x + 2*x^2)/((1 + 2*x^2)*Sqrt[-x + x^4]),x]","\int \frac{-1+2 x+2 x^2}{\left(1+2 x^2\right) \sqrt{-x+x^4}} \, dx","\tan ^{-1}\left(\frac{2 \sqrt{x^4-x}}{2 x+1}\right)",1,"((1 - x)*x*Sqrt[(1 + x + x^2)/(1 - (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x)/(1 - (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[-(((1 - x)*x)/(1 - (1 + Sqrt[3])*x)^2)]*Sqrt[-x + x^4]) + ((1/2 + I/2)*(I - Sqrt[2])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/(((-1)^(1/4) - 2^(1/4)*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4] - ((1/2 - I/2)*(I + Sqrt[2])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((-(-1)^(3/4) - 2^(1/4)*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4] + ((1/2 + I/2)*(I - Sqrt[2])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/(((-1)^(1/4) + 2^(1/4)*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4] - ((1/2 - I/2)*(I + Sqrt[2])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((-(-1)^(3/4) + 2^(1/4)*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4]","F",0,0,0,0,-1,"{}"
196,0,0,0,0.6915844,"\int \frac{-1-2 x+2 x^2}{(-1+2 x) \sqrt{x+x^4}} \, dx","Int[(-1 - 2*x + 2*x^2)/((-1 + 2*x)*Sqrt[x + x^4]),x]","\int \frac{-1-2 x+2 x^2}{(-1+2 x) \sqrt{x+x^4}} \, dx","\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)])/(3*Sqrt[x + x^4]) - (x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4]) + (3*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((1 - Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[x + x^4]) + (3*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((1 + Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[x + x^4])","F",0,0,0,0,-1,"{}"
197,0,0,0,2.2827102,"\int \frac{-1-2 x+2 x^2}{\left(1-x+x^2\right) \sqrt{x+x^4}} \, dx","Int[(-1 - 2*x + 2*x^2)/((1 - x + x^2)*Sqrt[x + x^4]),x]","\int \frac{-1-2 x+2 x^2}{\left(1-x+x^2\right) \sqrt{x+x^4}} \, dx","-\frac{2 \sqrt{x^4+x}}{x^2-x+1}",1,"(2*x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4]) + ((2*I)*Sqrt[3]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(Sqrt[1 - I*Sqrt[3]]*Sqrt[x + x^4]) - ((2*I)*Sqrt[3]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(Sqrt[1 + I*Sqrt[3]]*Sqrt[x + x^4]) + ((2*I)*Sqrt[3]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(Sqrt[1 - I*Sqrt[3]]*Sqrt[x + x^4]) - ((2*I)*Sqrt[3]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(Sqrt[1 + I*Sqrt[3]]*Sqrt[x + x^4])","F",0,0,0,0,-1,"{}"
198,1,14,0,0.0303654,"\int \frac{1}{(1+x) \sqrt[4]{x^3+x^4}} \, dx","Int[1/((1 + x)*(x^3 + x^4)^(1/4)),x]","\frac{4 x}{\sqrt[4]{x^4+x^3}}","\frac{4 \left(x^4+x^3\right)^{3/4}}{x^2 (x+1)}",1,"(4*x)/(x^3 + x^4)^(1/4)","A",2,2,17,0.1176,1,"{2056, 37}"
199,1,21,0,0.1072544,"\int \frac{1+2 x^4}{\left(-1+2 x^4\right) \sqrt{-1-x^2+2 x^4}} \, dx","Int[(1 + 2*x^4)/((-1 + 2*x^4)*Sqrt[-1 - x^2 + 2*x^4]),x]","-\tan ^{-1}\left(\frac{x}{\sqrt{2 x^4-x^2-1}}\right)","-\tan ^{-1}\left(\frac{x}{\sqrt{2 x^4-x^2-1}}\right)",1,"-ArcTan[x/Sqrt[-1 - x^2 + 2*x^4]]","A",2,2,33,0.06061,1,"{2112, 204}"
200,1,21,0,0.1216372,"\int \frac{-1+2 x^4}{\left(1+2 x^2+2 x^4\right) \sqrt{1+3 x^2+2 x^4}} \, dx","Int[(-1 + 2*x^4)/((1 + 2*x^2 + 2*x^4)*Sqrt[1 + 3*x^2 + 2*x^4]),x]","-\tanh ^{-1}\left(\frac{x}{\sqrt{2 x^4+3 x^2+1}}\right)","-\tanh ^{-1}\left(\frac{x}{\sqrt{2 x^4+3 x^2+1}}\right)",1,"-ArcTanh[x/Sqrt[1 + 3*x^2 + 2*x^4]]","A",2,2,38,0.05263,1,"{2112, 206}"
201,1,21,0,0.0205318,"\int \frac{\sqrt[4]{-1+x^4-x^5} \left(-4+x^5\right)}{x^6} \, dx","Int[((-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",1,1,23,0.04348,1,"{1590}"
202,1,21,0,0.0198026,"\int \frac{\left(1+x^8\right) \sqrt{-1-2 x^4+x^8}}{x^7} \, dx","Int[((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",1,1,23,0.04348,1,"{1590}"
203,1,19,0,0.4407309,"\int \frac{x^2 \left(-2+x^3\right) \sqrt{1+x^3}}{4+12 x^3+13 x^6+4 x^9} \, dx","Int[(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{2 \left(x^3+1\right)^{3/2}}{x^3}\right)","-\frac{1}{3} \tan ^{-1}\left(\frac{x^3}{2 \left(x^3+1\right)^{3/2}}\right)",1,"ArcTan[(2*(1 + x^3)^(3/2))/x^3]/3","A",4,3,37,0.08108,1,"{6715, 2094, 203}"
204,1,16,0,0.0408641,"\int \frac{1}{\left(-1+x^2\right) \sqrt[3]{-x+x^3}} \, dx","Int[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",2,2,19,0.1053,1,"{2056, 264}"
205,1,16,0,0.0416603,"\int \frac{1}{\left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Int[1/((-1 + x^3)*(-x + x^4)^(1/4)),x]","-\frac{4 x}{3 \sqrt[4]{x^4-x}}","-\frac{4 \left(x^4-x\right)^{3/4}}{3 \left(x^3-1\right)}",1,"(-4*x)/(3*(-x + x^4)^(1/4))","A",2,2,19,0.1053,1,"{2056, 264}"
206,0,0,0,0.1765405,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{b^2+a x^2}} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]]/Sqrt[b^2 + a*x^2],x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\sqrt{b^2+a x^2}} \, dx","\frac{2 x}{\sqrt{\sqrt{a x^2+b^2}+b}}",1,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/Sqrt[b^2 + a*x^2], x]","F",0,0,0,0,-1,"{}"
207,1,23,0,0.0139654,"\int \frac{1}{x \sqrt[4]{1+x^2}} \, dx","Int[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",5,5,13,0.3846,1,"{266, 63, 298, 203, 206}"
208,1,36,0,0.0059856,"\int \frac{-5+2 x}{\sqrt[4]{4-4 x+x^2}} \, dx","Int[(-5 + 2*x)/(4 - 4*x + x^2)^(1/4),x]","\frac{2 (2-x)}{\sqrt[4]{x^2-4 x+4}}+\frac{4}{3} \left(x^2-4 x+4\right)^{3/4}","\frac{2 \left((x-2)^2\right)^{3/4} (2 x-7)}{3 (x-2)}",1,"(2*(2 - x))/(4 - 4*x + x^2)^(1/4) + (4*(4 - 4*x + x^2)^(3/4))/3","A",2,2,18,0.1111,1,"{640, 609}"
209,1,27,0,0.0107622,"\int x^5 \sqrt[3]{1+x^3} \, dx","Int[x^5*(1 + x^3)^(1/3),x]","\frac{1}{7} \left(x^3+1\right)^{7/3}-\frac{1}{4} \left(x^3+1\right)^{4/3}","\frac{1}{28} \sqrt[3]{x^3+1} \left(4 x^6+x^3-3\right)",1,"-1/4*(1 + x^3)^(4/3) + (1 + x^3)^(7/3)/7","A",3,2,13,0.1538,1,"{266, 43}"
210,1,18,0,0.0164208,"\int \frac{\left(1+3 x^2\right) \sqrt[3]{-x+x^3}}{x^2} \, dx","Int[((1 + 3*x^2)*(-x + x^3)^(1/3))/x^2,x]","\frac{3 \left(x^3-x\right)^{4/3}}{2 x^2}","\frac{3 \left(x^2-1\right) \sqrt[3]{x^3-x}}{2 x}",1,"(3*(-x + x^3)^(4/3))/(2*x^2)","A",1,1,22,0.04545,1,"{1590}"
211,1,16,0,0.0312168,"\int \frac{1}{(-1+x) \sqrt[3]{-x^2+x^3}} \, dx","Int[1/((-1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{x^3-x^2}}","-\frac{3 \left(x^3-x^2\right)^{2/3}}{(x-1) x}",1,"(-3*x)/(-x^2 + x^3)^(1/3)","A",2,2,19,0.1053,1,"{2056, 37}"
212,1,37,0,0.0477009,"\int \frac{1}{x^2 \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x^2*(x^2 + x^3)^(1/3)),x]","\frac{9 \left(x^3+x^2\right)^{2/3}}{10 x^2}-\frac{3 \left(x^3+x^2\right)^{2/3}}{5 x^3}","\frac{3 (3 x-2) \left(x^3+x^2\right)^{2/3}}{10 x^3}",1,"(-3*(x^2 + x^3)^(2/3))/(5*x^3) + (9*(x^2 + x^3)^(2/3))/(10*x^2)","A",2,2,15,0.1333,1,"{2016, 2014}"
213,1,23,0,0.0834284,"\int \frac{\left(3+2 x^2\right) \sqrt{x+2 x^3}}{\left(1+2 x^2\right)^2} \, dx","Int[((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",2,2,28,0.07143,1,"{2056, 449}"
214,1,33,0,0.0069637,"\int \frac{1}{x^6 \left(-1+x^4\right)^{3/4}} \, dx","Int[1/(x^6*(-1 + x^4)^(3/4)),x]","\frac{4 \sqrt[4]{x^4-1}}{5 x}+\frac{\sqrt[4]{x^4-1}}{5 x^5}","\frac{\sqrt[4]{x^4-1} \left(4 x^4+1\right)}{5 x^5}",1,"(-1 + x^4)^(1/4)/(5*x^5) + (4*(-1 + x^4)^(1/4))/(5*x)","A",2,2,13,0.1538,1,"{271, 264}"
215,1,31,0,0.0051836,"\int \frac{1}{x^4 \left(1+x^4\right)^{5/4}} \, dx","Int[1/(x^4*(1 + x^4)^(5/4)),x]","-\frac{4 x}{3 \sqrt[4]{x^4+1}}-\frac{1}{3 \sqrt[4]{x^4+1} x^3}","\frac{-4 x^4-1}{3 x^3 \sqrt[4]{x^4+1}}",1,"-1/3*1/(x^3*(1 + x^4)^(1/4)) - (4*x)/(3*(1 + x^4)^(1/4))","A",2,2,13,0.1538,1,"{271, 191}"
216,1,33,0,0.0067628,"\int \frac{1}{x^6 \left(1+x^4\right)^{3/4}} \, dx","Int[1/(x^6*(1 + x^4)^(3/4)),x]","\frac{4 \sqrt[4]{x^4+1}}{5 x}-\frac{\sqrt[4]{x^4+1}}{5 x^5}","\frac{\sqrt[4]{x^4+1} \left(4 x^4-1\right)}{5 x^5}",1,"-1/5*(1 + x^4)^(1/4)/x^5 + (4*(1 + x^4)^(1/4))/(5*x)","A",2,2,13,0.1538,1,"{271, 264}"
217,1,33,0,0.0114181,"\int \frac{-1+x^4}{x^6 \left(1+x^4\right)^{3/4}} \, dx","Int[(-1 + x^4)/(x^6*(1 + x^4)^(3/4)),x]","\frac{\sqrt[4]{x^4+1}}{5 x^5}-\frac{9 \sqrt[4]{x^4+1}}{5 x}","\frac{\left(1-9 x^4\right) \sqrt[4]{x^4+1}}{5 x^5}",1,"(1 + x^4)^(1/4)/(5*x^5) - (9*(1 + x^4)^(1/4))/(5*x)","A",2,2,18,0.1111,1,"{453, 264}"
218,1,23,0,0.0353868,"\int \frac{1+x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","Int[(1 + x^2)/((1 - x^2)*Sqrt[1 + x^4]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]","A",2,2,24,0.08333,1,"{1699, 206}"
219,0,0,0,0.7152545,"\int \frac{-1+2 x+2 x^2}{(1+2 x) \sqrt{-x+x^4}} \, dx","Int[(-1 + 2*x + 2*x^2)/((1 + 2*x)*Sqrt[-x + x^4]),x]","\int \frac{-1+2 x+2 x^2}{(1+2 x) \sqrt{-x+x^4}} \, dx","\tanh ^{-1}\left(\frac{2 \sqrt{x^4-x}}{2 x^2+1}\right)",1,"(2*Sqrt[x]*Sqrt[-1 + x^3]*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]])/(3*Sqrt[-x + x^4]) + ((1 - x)*x*Sqrt[(1 + x + x^2)/(1 - (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x)/(1 - (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*Sqrt[-(((1 - x)*x)/(1 - (1 + Sqrt[3])*x)^2)]*Sqrt[-x + x^4]) - (((3*I)/2)*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((I - Sqrt[2]*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4] - (((3*I)/2)*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((I + Sqrt[2]*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/Sqrt[-x + x^4]","F",0,0,0,0,-1,"{}"
220,1,33,0,0.0403423,"\int \frac{1}{x^5 \sqrt{x+x^4}} \, dx","Int[1/(x^5*Sqrt[x + x^4]),x]","\frac{4 \sqrt{x^4+x}}{9 x^2}-\frac{2 \sqrt{x^4+x}}{9 x^5}","\frac{2 \left(2 x^3-1\right) \sqrt{x^4+x}}{9 x^5}",1,"(-2*Sqrt[x + x^4])/(9*x^5) + (4*Sqrt[x + x^4])/(9*x^2)","A",2,2,13,0.1538,1,"{2016, 2014}"
221,1,33,0,0.0745052,"\int \frac{-1+x^3}{x^6 \sqrt[4]{x+x^4}} \, dx","Int[(-1 + x^3)/(x^6*(x + x^4)^(1/4)),x]","\frac{4 \left(x^4+x\right)^{3/4}}{21 x^6}-\frac{44 \left(x^4+x\right)^{3/4}}{63 x^3}","-\frac{4 \left(11 x^3-3\right) \left(x^4+x\right)^{3/4}}{63 x^6}",1,"(4*(x + x^4)^(3/4))/(21*x^6) - (44*(x + x^4)^(3/4))/(63*x^3)","A",2,2,18,0.1111,1,"{2038, 2014}"
222,1,33,0,0.0745907,"\int \frac{1+2 x^3}{x^6 \sqrt[4]{x+x^4}} \, dx","Int[(1 + 2*x^3)/(x^6*(x + x^4)^(1/4)),x]","-\frac{4 \left(x^4+x\right)^{3/4}}{21 x^6}-\frac{40 \left(x^4+x\right)^{3/4}}{63 x^3}","-\frac{4 \left(10 x^3+3\right) \left(x^4+x\right)^{3/4}}{63 x^6}",1,"(-4*(x + x^4)^(3/4))/(21*x^6) - (40*(x + x^4)^(3/4))/(63*x^3)","A",2,2,20,0.1000,1,"{2038, 2014}"
223,1,14,0,0.0821048,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Int[(-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",2,2,24,0.08333,1,"{2056, 449}"
224,1,14,0,0.0105277,"\int \frac{1}{\left(1+x^2\right) \sqrt[4]{x^2+x^4}} \, dx","Int[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",2,2,19,0.1053,1,"{1146, 264}"
225,1,16,0,0.0319863,"\int \frac{1}{(-1+x) \sqrt[4]{-x^3+x^4}} \, dx","Int[1/((-1 + x)*(-x^3 + x^4)^(1/4)),x]","-\frac{4 x}{\sqrt[4]{x^4-x^3}}","-\frac{4 \left(x^4-x^3\right)^{3/4}}{(x-1) x^2}",1,"(-4*x)/(-x^3 + x^4)^(1/4)","A",2,2,19,0.1053,1,"{2056, 37}"
226,1,37,0,0.0294373,"\int \frac{1}{x \sqrt{x^3+x^4}} \, dx","Int[1/(x*Sqrt[x^3 + x^4]),x]","\frac{4 \sqrt{x^4+x^3}}{3 x^2}-\frac{2 \sqrt{x^4+x^3}}{3 x^3}","\frac{2 (2 x-1) \sqrt{x^4+x^3}}{3 x^3}",1,"(-2*Sqrt[x^3 + x^4])/(3*x^3) + (4*Sqrt[x^3 + x^4])/(3*x^2)","A",2,2,15,0.1333,1,"{2016, 2000}"
227,1,37,0,0.0496208,"\int \frac{1}{x^2 \sqrt[4]{x^3+x^4}} \, dx","Int[1/(x^2*(x^3 + x^4)^(1/4)),x]","\frac{16 \left(x^4+x^3\right)^{3/4}}{21 x^3}-\frac{4 \left(x^4+x^3\right)^{3/4}}{7 x^4}","\frac{4 (4 x-3) \left(x^4+x^3\right)^{3/4}}{21 x^4}",1,"(-4*(x^3 + x^4)^(3/4))/(7*x^4) + (16*(x^3 + x^4)^(3/4))/(21*x^3)","A",2,2,15,0.1333,1,"{2016, 2014}"
228,1,11,0,0.0528614,"\int \frac{1+2 x}{\sqrt{3+x^2+2 x^3+x^4}} \, dx","Int[(1 + 2*x)/Sqrt[3 + x^2 + 2*x^3 + x^4],x]","\sinh ^{-1}\left(\frac{x (x+1)}{\sqrt{3}}\right)","\log \left(x^2+\sqrt{x^4+2 x^3+x^2+3}+x\right)",1,"ArcSinh[(x*(1 + x))/Sqrt[3]]","A",5,5,23,0.2174,1,"{1680, 12, 1107, 619, 215}"
229,1,33,0,0.0096788,"\int \frac{-1+2 x^4}{x^8 \sqrt[4]{-1+x^4}} \, dx","Int[(-1 + 2*x^4)/(x^8*(-1 + x^4)^(1/4)),x]","\frac{10 \left(x^4-1\right)^{3/4}}{21 x^3}-\frac{\left(x^4-1\right)^{3/4}}{7 x^7}","\frac{\left(x^4-1\right)^{3/4} \left(10 x^4-3\right)}{21 x^7}",1,"-1/7*(-1 + x^4)^(3/4)/x^7 + (10*(-1 + x^4)^(3/4))/(21*x^3)","A",2,2,20,0.1000,1,"{453, 264}"
230,1,31,0,0.0086258,"\int \frac{1+2 x^4}{x^4 \left(1+x^4\right)^{5/4}} \, dx","Int[(1 + 2*x^4)/(x^4*(1 + x^4)^(5/4)),x]","\frac{2 x}{3 \sqrt[4]{x^4+1}}-\frac{1}{3 x^3 \sqrt[4]{x^4+1}}","\frac{2 x^4-1}{3 x^3 \sqrt[4]{x^4+1}}",1,"-1/3*1/(x^3*(1 + x^4)^(1/4)) + (2*x)/(3*(1 + x^4)^(1/4))","A",2,2,20,0.1000,1,"{453, 191}"
231,1,42,0,0.363893,"\int \frac{\left(1+4 x^3\right) \left(1+2 x+2 x^4\right)}{\sqrt{x+x^4}} \, dx","Int[((1 + 4*x^3)*(1 + 2*x + 2*x^4))/Sqrt[x + x^4],x]","\frac{4}{3} \sqrt{x^4+x} x^4+\frac{4}{3} \sqrt{x^4+x} x+2 \sqrt{x^4+x}","\frac{2}{3} \sqrt{x^4+x} \left(2 x^4+2 x+3\right)",1,"2*Sqrt[x + x^4] + (4*x*Sqrt[x + x^4])/3 + (4*x^4*Sqrt[x + x^4])/3","A",18,7,27,0.2593,1,"{2053, 2011, 329, 225, 2029, 206, 2024}"
232,1,14,0,0.0794431,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^3+x^5}} \, dx","Int[(-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",2,2,24,0.08333,1,"{2056, 449}"
233,1,33,0,0.0068159,"\int \frac{1}{x^{10} \sqrt{-1+x^6}} \, dx","Int[1/(x^10*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1}}{9 x^9}+\frac{2 \sqrt{x^6-1}}{9 x^3}","\frac{\sqrt{x^6-1} \left(2 x^6+1\right)}{9 x^9}",1,"Sqrt[-1 + x^6]/(9*x^9) + (2*Sqrt[-1 + x^6])/(9*x^3)","A",2,2,13,0.1538,1,"{271, 264}"
234,1,33,0,0.0103079,"\int \frac{1+x^6}{x^{10} \sqrt{-1+x^6}} \, dx","Int[(1 + x^6)/(x^10*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1}}{9 x^9}+\frac{5 \sqrt{x^6-1}}{9 x^3}","\frac{\sqrt{x^6-1} \left(5 x^6+1\right)}{9 x^9}",1,"Sqrt[-1 + x^6]/(9*x^9) + (5*Sqrt[-1 + x^6])/(9*x^3)","A",2,2,18,0.1111,1,"{453, 264}"
235,1,14,0,0.0792966,"\int \frac{-1+3 x^4}{\left(1+x^4\right) \sqrt[3]{x^2+x^6}} \, dx","Int[(-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",2,2,26,0.07692,1,"{2056, 449}"
236,1,14,0,0.074098,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(-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",2,2,24,0.08333,1,"{2056, 449}"
237,1,23,0,0.0315032,"\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","Int[(x^2*(3 + 2*x^2)*(1 + x^2 + 2*x^6))/((1 + x^2)^2*Sqrt[1 + x^2 + x^6]),x]","\frac{x^3 \sqrt{x^6+x^2+1}}{x^2+1}","\frac{x^3 \sqrt{x^6+x^2+1}}{x^2+1}",1,"(x^3*Sqrt[1 + x^2 + x^6])/(1 + x^2)","A",1,1,40,0.02500,1,"{1590}"
238,1,40,0,0.0423069,"\int \frac{1}{\sqrt{3-5 x+x^2+x^3}} \, dx","Int[1/Sqrt[3 - 5*x + x^2 + x^3],x]","\frac{(1-x) \sqrt{x+3} \tanh ^{-1}\left(\frac{\sqrt{x+3}}{2}\right)}{\sqrt{x^3+x^2-5 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[3 - 5*x + x^2 + x^3]","A",4,4,15,0.2667,1,"{2067, 2064, 63, 206}"
239,1,46,0,0.400123,"\int \frac{-1+x}{(1+x) \sqrt{x+x^2+x^3}} \, dx","Int[(-1 + x)/((1 + x)*Sqrt[x + x^2 + x^3]),x]","-\frac{2 \sqrt{x} \sqrt{x^2+x+1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+x+1}}\right)}{\sqrt{x^3+x^2+x}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)",1,"(-2*Sqrt[x]*Sqrt[1 + x + x^2]*ArcTan[Sqrt[x]/Sqrt[1 + x + x^2]])/Sqrt[x + x^2 + x^3]","A",4,4,21,0.1905,1,"{2056, 6733, 1698, 203}"
240,1,320,0,1.0277439,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[x + x^2 + x^3]),x]","\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+x+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{4}\right)}{\sqrt{x^3+x^2+x}}-\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-i-\sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}","-2 \tanh ^{-1}\left(\frac{\sqrt{x^3+x^2+x}}{x^2+x+1}\right)",1,"(Sqrt[x]*(1 + x)*Sqrt[(1 + x + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/4])/Sqrt[x + x^2 + x^3] - (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-I - Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(I + Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3])","C",17,8,25,0.3200,0,"{2056, 6725, 716, 1103, 934, 169, 538, 537}"
241,1,24,0,0.0342933,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 + x^4]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"-(ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2])","A",2,2,22,0.09091,1,"{1699, 203}"
242,1,24,0,0.0350784,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","Int[(1 + x^2)/((-1 + x^2)*Sqrt[1 + x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}",1,"-(ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2])","A",2,2,22,0.09091,1,"{1699, 207}"
243,0,0,0,0.7074206,"\int \frac{2-3 x^5}{\sqrt{1+x^5} \left(1-a x^2+x^5\right)} \, dx","Int[(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,"-3*x*Hypergeometric2F1[1/5, 1/2, 6/5, -x^5] - 5*Defer[Int][1/((-1 + a*x^2 - x^5)*Sqrt[1 + x^5]), x] + 3*a*Defer[Int][x^2/((-1 + a*x^2 - x^5)*Sqrt[1 + x^5]), x]","F",0,0,0,0,-1,"{}"
244,0,0,0,0.6997225,"\int \frac{2+3 x^5}{\sqrt{-1+x^5} \left(-1-a x^2+x^5\right)} \, dx","Int[(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,"(3*x*Sqrt[1 - x^5]*Hypergeometric2F1[1/5, 1/2, 6/5, x^5])/Sqrt[-1 + x^5] - 5*Defer[Int][1/((1 + a*x^2 - x^5)*Sqrt[-1 + x^5]), x] - 3*a*Defer[Int][x^2/((1 + a*x^2 - x^5)*Sqrt[-1 + x^5]), x]","F",0,0,0,0,-1,"{}"
245,0,0,0,0.6775774,"\int \frac{2+3 x^5}{\sqrt{-1+x^5} \left(-a-x^2+a x^5\right)} \, dx","Int[(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,"(3*x*Sqrt[1 - x^5]*Hypergeometric2F1[1/5, 1/2, 6/5, x^5])/(a*Sqrt[-1 + x^5]) + 5*Defer[Int][1/(Sqrt[-1 + x^5]*(-a - x^2 + a*x^5)), x] + (3*Defer[Int][x^2/(Sqrt[-1 + x^5]*(-a - x^2 + a*x^5)), x])/a","F",0,0,0,0,-1,"{}"
246,0,0,0,0.622476,"\int \frac{-2+3 x^5}{\sqrt{1+x^5} \left(a-x^2+a x^5\right)} \, dx","Int[(-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,"(3*x*Hypergeometric2F1[1/5, 1/2, 6/5, -x^5])/a - 5*Defer[Int][1/(Sqrt[1 + x^5]*(a - x^2 + a*x^5)), x] + (3*Defer[Int][x^2/(Sqrt[1 + x^5]*(a - x^2 + a*x^5)), x])/a","F",0,0,0,0,-1,"{}"
247,0,0,0,0.9734779,"\int \frac{-1-2 x^2+2 x^4}{\left(1-x^2+x^4\right) \sqrt{1+x^6}} \, dx","Int[(-1 - 2*x^2 + 2*x^4)/((1 - x^2 + x^4)*Sqrt[1 + x^6]),x]","\int \frac{-1-2 x^2+2 x^4}{\left(1-x^2+x^4\right) \sqrt{1+x^6}} \, dx","-\frac{x \sqrt{x^6+1}}{x^4-x^2+1}",1,"(x*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x^2)/(1 + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x^2*(1 + x^2))/(1 + (1 + Sqrt[3])*x^2)^2]*Sqrt[1 + x^6]) + (I*Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[1 + x^6]), x])/Sqrt[(1 - I*Sqrt[3])/3] - (I*Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[1 + x^6]), x])/Sqrt[(1 + I*Sqrt[3])/3] + (I*Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[1 + x^6]), x])/Sqrt[(1 - I*Sqrt[3])/3] - (I*Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[1 + x^6]), x])/Sqrt[(1 + I*Sqrt[3])/3]","F",0,0,0,0,-1,"{}"
248,0,0,0,1.0741708,"\int \frac{-1+4 x^5}{\left(1-a x+x^5\right) \sqrt{x+x^6}} \, dx","Int[(-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,"(8*x*Sqrt[1 + x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, -x^5])/Sqrt[x + x^6] + (10*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][1/((-1 + a*x^2 - x^10)*Sqrt[1 + x^10]), x], x, Sqrt[x]])/Sqrt[x + x^6] - (8*a*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^2/((-1 + a*x^2 - x^10)*Sqrt[1 + x^10]), x], x, Sqrt[x]])/Sqrt[x + x^6]","F",0,0,0,0,-1,"{}"
249,0,0,0,0.9614592,"\int \frac{-1+4 x^5}{\left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","Int[(-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,"(8*x*Sqrt[1 + x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, -x^5])/(a*Sqrt[x + x^6]) - (10*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][1/(Sqrt[1 + x^10]*(a - x^2 + a*x^10)), x], x, Sqrt[x]])/Sqrt[x + x^6] + (8*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + x^10]*(a - x^2 + a*x^10)), x], x, Sqrt[x]])/(a*Sqrt[x + x^6])","F",0,0,0,0,-1,"{}"
250,1,27,0,0.0123616,"\int x^3 \left(-1+x^2\right)^{2/3} \, dx","Int[x^3*(-1 + x^2)^(2/3),x]","\frac{3}{16} \left(x^2-1\right)^{8/3}+\frac{3}{10} \left(x^2-1\right)^{5/3}","\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))/10 + (3*(-1 + x^2)^(8/3))/16","A",3,2,13,0.1538,1,"{266, 43}"
251,1,27,0,0.0127569,"\int x^3 \left(-1+x^2\right)^{3/4} \, dx","Int[x^3*(-1 + x^2)^(3/4),x]","\frac{2}{11} \left(x^2-1\right)^{11/4}+\frac{2}{7} \left(x^2-1\right)^{7/4}","\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))/7 + (2*(-1 + x^2)^(11/4))/11","A",3,2,13,0.1538,1,"{266, 43}"
252,1,25,0,0.0144221,"\int \frac{1}{x \left(1+x^2\right)^{3/4}} \, dx","Int[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",5,5,13,0.3846,1,"{266, 63, 212, 206, 203}"
253,1,27,0,0.0161486,"\int x^3 \left(1+x^2\right)^{3/4} \, dx","Int[x^3*(1 + x^2)^(3/4),x]","\frac{2}{11} \left(x^2+1\right)^{11/4}-\frac{2}{7} \left(x^2+1\right)^{7/4}","\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))/7 + (2*(1 + x^2)^(11/4))/11","A",3,2,13,0.1538,1,"{266, 43}"
254,1,27,0,0.0126109,"\int x^5 \sqrt[3]{-1+x^3} \, dx","Int[x^5*(-1 + x^3)^(1/3),x]","\frac{1}{7} \left(x^3-1\right)^{7/3}+\frac{1}{4} \left(x^3-1\right)^{4/3}","\frac{1}{28} \sqrt[3]{x^3-1} \left(4 x^6-x^3-3\right)",1,"(-1 + x^3)^(4/3)/4 + (-1 + x^3)^(7/3)/7","A",3,2,13,0.1538,1,"{266, 43}"
255,1,27,0,0.0115422,"\int x^5 \left(-1+x^3\right)^{3/4} \, dx","Int[x^5*(-1 + x^3)^(3/4),x]","\frac{4}{33} \left(x^3-1\right)^{11/4}+\frac{4}{21} \left(x^3-1\right)^{7/4}","\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))/21 + (4*(-1 + x^3)^(11/4))/33","A",3,2,13,0.1538,1,"{266, 43}"
256,1,40,0,0.0156846,"\int \frac{x^8}{\sqrt[4]{1+x^3}} \, dx","Int[x^8/(1 + x^3)^(1/4),x]","\frac{4}{33} \left(x^3+1\right)^{11/4}-\frac{8}{21} \left(x^3+1\right)^{7/4}+\frac{4}{9} \left(x^3+1\right)^{3/4}","\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))/9 - (8*(1 + x^3)^(7/4))/21 + (4*(1 + x^3)^(11/4))/33","A",3,2,13,0.1538,1,"{266, 43}"
257,1,27,0,0.0113144,"\int x^5 \left(1+x^3\right)^{2/3} \, dx","Int[x^5*(1 + x^3)^(2/3),x]","\frac{1}{8} \left(x^3+1\right)^{8/3}-\frac{1}{5} \left(x^3+1\right)^{5/3}","\frac{1}{40} \left(x^3+1\right)^{2/3} \left(5 x^6+2 x^3-3\right)",1,"-1/5*(1 + x^3)^(5/3) + (1 + x^3)^(8/3)/8","A",3,2,13,0.1538,1,"{266, 43}"
258,1,41,0,0.0533319,"\int \frac{1}{x^2 \sqrt[3]{-x^2+x^3}} \, dx","Int[1/(x^2*(-x^2 + x^3)^(1/3)),x]","\frac{9 \left(x^3-x^2\right)^{2/3}}{10 x^2}+\frac{3 \left(x^3-x^2\right)^{2/3}}{5 x^3}","\frac{3 (3 x+2) \left(x^3-x^2\right)^{2/3}}{10 x^3}",1,"(3*(-x^2 + x^3)^(2/3))/(5*x^3) + (9*(-x^2 + x^3)^(2/3))/(10*x^2)","A",2,2,17,0.1176,1,"{2016, 2014}"
259,1,27,0,0.012038,"\int x^7 \left(1+x^4\right)^{2/3} \, dx","Int[x^7*(1 + x^4)^(2/3),x]","\frac{3}{32} \left(x^4+1\right)^{8/3}-\frac{3}{20} \left(x^4+1\right)^{5/3}","\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))/20 + (3*(1 + x^4)^(8/3))/32","A",3,2,13,0.1538,1,"{266, 43}"
260,1,37,0,0.0468906,"\int \frac{1}{x^5 \sqrt{-x+x^4}} \, dx","Int[1/(x^5*Sqrt[-x + x^4]),x]","\frac{2 \sqrt{x^4-x}}{9 x^5}+\frac{4 \sqrt{x^4-x}}{9 x^2}","\frac{2 \left(2 x^3+1\right) \sqrt{x^4-x}}{9 x^5}",1,"(2*Sqrt[-x + x^4])/(9*x^5) + (4*Sqrt[-x + x^4])/(9*x^2)","A",2,2,15,0.1333,1,"{2016, 2014}"
261,1,37,0,0.0787525,"\int \frac{1+x^3}{x^6 \sqrt[4]{-x+x^4}} \, dx","Int[(1 + x^3)/(x^6*(-x + x^4)^(1/4)),x]","\frac{4 \left(x^4-x\right)^{3/4}}{21 x^6}+\frac{44 \left(x^4-x\right)^{3/4}}{63 x^3}","\frac{4 \left(11 x^3+3\right) \left(x^4-x\right)^{3/4}}{63 x^6}",1,"(4*(-x + x^4)^(3/4))/(21*x^6) + (44*(-x + x^4)^(3/4))/(63*x^3)","A",2,2,20,0.1000,1,"{2038, 2014}"
262,1,16,0,0.0847916,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{-x^2+x^4}} \, dx","Int[(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",2,2,26,0.07692,1,"{2056, 449}"
263,1,16,0,0.0122666,"\int \frac{1}{\left(-1+x^2\right) \sqrt[4]{-x^2+x^4}} \, dx","Int[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",2,2,21,0.09524,1,"{1146, 264}"
264,1,37,0,0.0480729,"\int \frac{1}{x^4 \sqrt[4]{x^2+x^4}} \, dx","Int[1/(x^4*(x^2 + x^4)^(1/4)),x]","\frac{8 \left(x^4+x^2\right)^{3/4}}{21 x^3}-\frac{2 \left(x^4+x^2\right)^{3/4}}{7 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 + x^4)^(3/4))/(7*x^5) + (8*(x^2 + x^4)^(3/4))/(21*x^3)","A",2,2,15,0.1333,1,"{2016, 2014}"
265,1,27,0,0.0544238,"\int \frac{-1+2 x}{\sqrt{-3+x^2-2 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[-3 + x^2 - 2*x^3 + x^4],x]","-\tanh ^{-1}\left(\frac{(1-x) x}{\sqrt{x^4-2 x^3+x^2-3}}\right)","\log \left(x^2+\sqrt{x^4-2 x^3+x^2-3}-x\right)",1,"-ArcTanh[((1 - x)*x)/Sqrt[-3 + x^2 - 2*x^3 + x^4]]","A",5,5,23,0.2174,1,"{1680, 12, 1107, 621, 206}"
266,1,9,0,0.0410144,"\int \frac{-1+2 x}{\sqrt{4+x^2-2 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[4 + x^2 - 2*x^3 + x^4],x]","\sinh ^{-1}\left(\frac{1}{2} (x-1) x\right)","\log \left(x^2+\sqrt{x^4-2 x^3+x^2+4}-x\right)",1,"ArcSinh[((-1 + x)*x)/2]","A",5,5,23,0.2174,1,"{1680, 12, 1107, 619, 215}"
267,1,15,0,0.0556386,"\int \frac{-1+2 x}{\sqrt{13+x^2-2 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[13 + x^2 - 2*x^3 + x^4],x]","-\sinh ^{-1}\left(\frac{(1-x) x}{\sqrt{13}}\right)","\log \left(x^2+\sqrt{x^4-2 x^3+x^2+13}-x\right)",1,"-ArcSinh[((1 - x)*x)/Sqrt[13]]","A",5,5,23,0.2174,1,"{1680, 12, 1107, 619, 215}"
268,1,41,0,0.05114,"\int \frac{1}{x^2 \sqrt[4]{-x^3+x^4}} \, dx","Int[1/(x^2*(-x^3 + x^4)^(1/4)),x]","\frac{16 \left(x^4-x^3\right)^{3/4}}{21 x^3}+\frac{4 \left(x^4-x^3\right)^{3/4}}{7 x^4}","\frac{4 (4 x+3) \left(x^4-x^3\right)^{3/4}}{21 x^4}",1,"(4*(-x^3 + x^4)^(3/4))/(7*x^4) + (16*(-x^3 + x^4)^(3/4))/(21*x^3)","A",2,2,17,0.1176,1,"{2016, 2014}"
269,1,37,0,0.011185,"\int \frac{-1+x^4}{x^8 \sqrt[4]{-1+2 x^4}} \, dx","Int[(-1 + x^4)/(x^8*(-1 + 2*x^4)^(1/4)),x]","-\frac{\left(2 x^4-1\right)^{3/4}}{7 x^7}-\frac{\left(2 x^4-1\right)^{3/4}}{21 x^3}","\frac{\left(-x^4-3\right) \left(2 x^4-1\right)^{3/4}}{21 x^7}",1,"-1/7*(-1 + 2*x^4)^(3/4)/x^7 - (-1 + 2*x^4)^(3/4)/(21*x^3)","A",2,2,20,0.1000,1,"{453, 264}"
270,1,16,0,0.0876307,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[4]{-x^3+x^5}} \, dx","Int[(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",2,2,26,0.07692,1,"{2056, 449}"
271,1,16,0,0.0851455,"\int \frac{1+3 x^4}{\left(-1+x^4\right) \sqrt[3]{-x^2+x^6}} \, dx","Int[(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",2,2,28,0.07143,1,"{2056, 449}"
272,1,16,0,0.0807845,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Int[(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",2,2,26,0.07692,1,"{2056, 449}"
273,1,37,0,0.0470969,"\int \frac{1}{x^7 \sqrt[3]{x^2+x^6}} \, dx","Int[1/(x^7*(x^2 + x^6)^(1/3)),x]","\frac{9 \left(x^6+x^2\right)^{2/3}}{40 x^4}-\frac{3 \left(x^6+x^2\right)^{2/3}}{20 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 + x^6)^(2/3))/(20*x^8) + (9*(x^2 + x^6)^(2/3))/(40*x^4)","A",2,2,15,0.1333,1,"{2016, 2014}"
274,1,33,0,0.0063502,"\int \frac{\sqrt[3]{-1+x^3}}{x^8} \, dx","Int[(-1 + x^3)^(1/3)/x^8,x]","\frac{\left(x^3-1\right)^{4/3}}{7 x^7}+\frac{3 \left(x^3-1\right)^{4/3}}{28 x^4}","\frac{\sqrt[3]{x^3-1} \left(3 x^6+x^3-4\right)}{28 x^7}",1,"(-1 + x^3)^(4/3)/(7*x^7) + (3*(-1 + x^3)^(4/3))/(28*x^4)","A",2,2,13,0.1538,1,"{271, 264}"
275,1,17,0,0.1509481,"\int \frac{b+a x^2}{\left(-b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Int[(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",2,2,33,0.06061,1,"{2056, 449}"
276,0,0,0,1.177191,"\int \frac{-2 b+a x^3}{\sqrt{b+a x^3} \left(b-c x^2+a x^3\right)} \, dx","Int[(-2*b + a*x^3)/(Sqrt[b + a*x^3]*(b - c*x^2 + a*x^3)),x]","\int \frac{-2 b+a x^3}{\sqrt{b+a x^3} \left(b-c x^2+a x^3\right)} \, dx","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a x^3+b}}\right)}{\sqrt{c}}",1,"(2*Sqrt[2 + Sqrt[3]]*(b^(1/3) + a^(1/3)*x)*Sqrt[(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*b^(1/3) + a^(1/3)*x)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a^(1/3)*Sqrt[(b^(1/3)*(b^(1/3) + a^(1/3)*x))/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*Sqrt[b + a*x^3]) - c*Defer[Int][x^2/((-b + c*x^2 - a*x^3)*Sqrt[b + a*x^3]), x] - 3*b*Defer[Int][1/(Sqrt[b + a*x^3]*(b - c*x^2 + a*x^3)), x]","F",0,0,0,0,-1,"{}"
277,0,0,0,0.9106432,"\int \frac{-2 b+a x^3}{\sqrt{b+a x^3} \left(b+c x^2+a x^3\right)} \, dx","Int[(-2*b + a*x^3)/(Sqrt[b + a*x^3]*(b + c*x^2 + a*x^3)),x]","\int \frac{-2 b+a x^3}{\sqrt{b+a x^3} \left(b+c x^2+a x^3\right)} \, dx","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a x^3+b}}\right)}{\sqrt{c}}",1,"(2*Sqrt[2 + Sqrt[3]]*(b^(1/3) + a^(1/3)*x)*Sqrt[(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*b^(1/3) + a^(1/3)*x)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a^(1/3)*Sqrt[(b^(1/3)*(b^(1/3) + a^(1/3)*x))/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*Sqrt[b + a*x^3]) - 3*b*Defer[Int][1/(Sqrt[b + a*x^3]*(b + c*x^2 + a*x^3)), x] - c*Defer[Int][x^2/(Sqrt[b + a*x^3]*(b + c*x^2 + a*x^3)), x]","F",0,0,0,0,-1,"{}"
278,1,131,0,0.6533315,"\int \frac{1+x^2}{\left(-1+x^2\right) \left(2+x^2\right) \sqrt{-3+x^4}} \, dx","Int[(1 + x^2)/((-1 + x^2)*(2 + x^2)*Sqrt[-3 + x^4]),x]","\frac{\sqrt{\sqrt{3}-x^2} \sqrt{\sqrt{3} x^2+3} \Pi \left(-\frac{\sqrt{3}}{2};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{3}}\right)\right|-1\right)}{6 \sqrt{3} \sqrt{x^4-3}}-\frac{2 \sqrt{\sqrt{3}-x^2} \sqrt{\sqrt{3} x^2+3} \Pi \left(\sqrt{3};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{3}}\right)\right|-1\right)}{3 \sqrt{3} \sqrt{x^4-3}}","\frac{\tan ^{-1}\left(\frac{x \sqrt{x^4-3}}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"(Sqrt[Sqrt[3] - x^2]*Sqrt[3 + Sqrt[3]*x^2]*EllipticPi[-1/2*Sqrt[3], ArcSin[x/3^(1/4)], -1])/(6*Sqrt[3]*Sqrt[-3 + x^4]) - (2*Sqrt[Sqrt[3] - x^2]*Sqrt[3 + Sqrt[3]*x^2]*EllipticPi[Sqrt[3], ArcSin[x/3^(1/4)], -1])/(3*Sqrt[3]*Sqrt[-3 + x^4])","C",18,8,29,0.2759,0,"{6725, 1215, 223, 1457, 540, 253, 538, 537}"
279,1,33,0,0.011541,"\int \frac{\left(-4+x^4\right) \left(1+x^4\right)^{3/4}}{x^{12}} \, dx","Int[((-4 + x^4)*(1 + x^4)^(3/4))/x^12,x]","\frac{4 \left(x^4+1\right)^{7/4}}{11 x^{11}}-\frac{27 \left(x^4+1\right)^{7/4}}{77 x^7}","\frac{\left(x^4+1\right)^{3/4} \left(-27 x^8+x^4+28\right)}{77 x^{11}}",1,"(4*(1 + x^4)^(7/4))/(11*x^11) - (27*(1 + x^4)^(7/4))/(77*x^7)","A",2,2,18,0.1111,1,"{453, 264}"
280,1,291,0,0.9806365,"\int \frac{\sqrt{-1+x^4} \left(1+x^4\right)}{x^2 \left(-1+x^2+x^4\right)} \, dx","Int[(Sqrt[-1 + x^4]*(1 + x^4))/(x^2*(-1 + x^2 + x^4)),x]","\frac{\sqrt{x^4-1}}{x}+\frac{\left(1+\sqrt{5}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{x^4-1}}+\frac{\left(1-\sqrt{5}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{x^4-1}}-\frac{\sqrt{2} \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^4-1}}+\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{2} \left(1-\sqrt{5}\right);\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{x^4-1}}+\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{x^4-1}}","\frac{\sqrt{x^4-1}}{x}+\tan ^{-1}\left(\frac{x}{\sqrt{x^4-1}}\right)",1,"Sqrt[-1 + x^4]/x - (Sqrt[2]*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/Sqrt[-1 + x^4] + ((1 - Sqrt[5])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(2*Sqrt[2]*Sqrt[-1 + x^4]) + ((1 + Sqrt[5])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(2*Sqrt[2]*Sqrt[-1 + x^4]) + (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[(1 - Sqrt[5])/2, ArcSin[x], -1])/Sqrt[-1 + x^4] + (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[x], -1])/Sqrt[-1 + x^4]","C",32,13,28,0.4643,1,"{6728, 277, 306, 222, 1185, 1209, 1188, 1215, 1457, 540, 253, 538, 537}"
281,1,44,0,0.116214,"\int \frac{\left(-1+x^4\right) \left(1+x^2+x^4\right)}{x^4 \sqrt{1+x^4}} \, dx","Int[((-1 + x^4)*(1 + x^2 + x^4))/(x^4*Sqrt[1 + x^4]),x]","\frac{1}{3} \sqrt{x^4+1} x+\frac{\sqrt{x^4+1}}{x}+\frac{\sqrt{x^4+1}}{3 x^3}","\frac{\sqrt{x^4+1} \left(x^4+3 x^2+1\right)}{3 x^3}",1,"Sqrt[1 + x^4]/(3*x^3) + Sqrt[1 + x^4]/x + (x*Sqrt[1 + x^4])/3","A",5,4,26,0.1538,1,"{1835, 1586, 1584, 383}"
282,1,47,0,0.1313092,"\int \frac{\left(-4+x^3\right) \left(-1+x^3+x^4\right)}{x^6 \left(-1+x^3\right)^{3/4}} \, dx","Int[((-4 + x^3)*(-1 + x^3 + x^4))/(x^6*(-1 + x^3)^(3/4)),x]","-\frac{4 \sqrt[4]{x^3-1}}{x}+\frac{4 \sqrt[4]{x^3-1}}{5 x^5}-\frac{4 \sqrt[4]{x^3-1}}{5 x^2}","-\frac{4 \sqrt[4]{x^3-1} \left(5 x^4+x^3-1\right)}{5 x^5}",1,"(4*(-1 + x^3)^(1/4))/(5*x^5) - (4*(-1 + x^3)^(1/4))/(5*x^2) - (4*(-1 + x^3)^(1/4))/x","A",5,3,26,0.1154,1,"{1835, 1586, 449}"
283,0,0,0,1.3637627,"\int \frac{1+3 x^4}{\left(-1-a x+x^4\right) \sqrt{-x+x^5}} \, dx","Int[(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,"((3 + 3*I)*x^2*Sqrt[-(((-1)^(3/4)*(1 + (-1)^(1/4)*x)^2)/x)]*Sqrt[(I*(1 - x^4))/x^2]*EllipticF[ArcSin[Sqrt[((-1)^(3/4)*(Sqrt[2] - 2*(-1)^(1/4)*x + I*Sqrt[2]*x^2))/x]/2], -2*(1 - Sqrt[2])])/(Sqrt[2*(2 + Sqrt[2])]*(1 + (-1)^(1/4)*x)*Sqrt[-x + x^5]) - ((3 + 3*I)*x^2*Sqrt[((-1)^(3/4)*(1 - (-1)^(1/4)*x)^2)/x]*Sqrt[(I*(1 - x^4))/x^2]*EllipticF[ArcSin[Sqrt[-(((-1)^(3/4)*(Sqrt[2] + 2*(-1)^(1/4)*x + I*Sqrt[2]*x^2))/x)]/2], -2*(1 - Sqrt[2])])/(Sqrt[2*(2 + Sqrt[2])]*(1 - (-1)^(1/4)*x)*Sqrt[-x + x^5]) - (8*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][1/((1 + a*x^2 - x^8)*Sqrt[-1 + x^8]), x], x, Sqrt[x]])/Sqrt[-x + x^5] - (6*a*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^2/((1 + a*x^2 - x^8)*Sqrt[-1 + x^8]), x], x, Sqrt[x]])/Sqrt[-x + x^5]","F",0,0,0,0,-1,"{}"
284,0,0,0,1.3415719,"\int \frac{1+3 x^4}{\left(-a-x+a x^4\right) \sqrt{-x+x^5}} \, dx","Int[(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,"((3 + 3*I)*x^2*Sqrt[-(((-1)^(3/4)*(1 + (-1)^(1/4)*x)^2)/x)]*Sqrt[(I*(1 - x^4))/x^2]*EllipticF[ArcSin[Sqrt[((-1)^(3/4)*(Sqrt[2] - 2*(-1)^(1/4)*x + I*Sqrt[2]*x^2))/x]/2], -2*(1 - Sqrt[2])])/(Sqrt[2*(2 + Sqrt[2])]*a*(1 + (-1)^(1/4)*x)*Sqrt[-x + x^5]) - ((3 + 3*I)*x^2*Sqrt[((-1)^(3/4)*(1 - (-1)^(1/4)*x)^2)/x]*Sqrt[(I*(1 - x^4))/x^2]*EllipticF[ArcSin[Sqrt[-(((-1)^(3/4)*(Sqrt[2] + 2*(-1)^(1/4)*x + I*Sqrt[2]*x^2))/x)]/2], -2*(1 - Sqrt[2])])/(Sqrt[2*(2 + Sqrt[2])]*a*(1 - (-1)^(1/4)*x)*Sqrt[-x + x^5]) + (8*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][1/(Sqrt[-1 + x^8]*(-a - x^2 + a*x^8)), x], x, Sqrt[x]])/Sqrt[-x + x^5] + (6*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^2/(Sqrt[-1 + x^8]*(-a - x^2 + a*x^8)), x], x, Sqrt[x]])/(a*Sqrt[-x + x^5])","F",0,0,0,0,-1,"{}"
285,1,44,0,0.1028649,"\int \frac{\left(4+x^5\right) \left(-1+x^4+x^5\right)}{x^6 \left(-1+x^5\right)^{3/4}} \, dx","Int[((4 + x^5)*(-1 + x^4 + x^5))/(x^6*(-1 + x^5)^(3/4)),x]","\frac{4 \sqrt[4]{x^5-1}}{x}-\frac{4 \sqrt[4]{x^5-1}}{5 x^5}+\frac{4}{5} \sqrt[4]{x^5-1}","\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 - (4*(-1 + x^5)^(1/4))/(5*x^5) + (4*(-1 + x^5)^(1/4))/x","A",5,4,26,0.1538,1,"{1835, 1585, 12, 261}"
286,1,44,0,0.0988754,"\int \frac{\left(-4+x^5\right) \left(1+x^4+x^5\right)}{x^6 \left(1+x^5\right)^{3/4}} \, dx","Int[((-4 + x^5)*(1 + x^4 + x^5))/(x^6*(1 + x^5)^(3/4)),x]","\frac{4 \sqrt[4]{x^5+1}}{x}+\frac{4 \sqrt[4]{x^5+1}}{5 x^5}+\frac{4}{5} \sqrt[4]{x^5+1}","\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 + (4*(1 + x^5)^(1/4))/(5*x^5) + (4*(1 + x^5)^(1/4))/x","A",5,4,26,0.1538,1,"{1835, 1585, 12, 261}"
287,1,33,0,0.0065673,"\int \frac{\sqrt{-1+x^6}}{x^{16}} \, dx","Int[Sqrt[-1 + x^6]/x^16,x]","\frac{\left(x^6-1\right)^{3/2}}{15 x^{15}}+\frac{2 \left(x^6-1\right)^{3/2}}{45 x^9}","\frac{\sqrt{x^6-1} \left(2 x^{12}+x^6-3\right)}{45 x^{15}}",1,"(-1 + x^6)^(3/2)/(15*x^15) + (2*(-1 + x^6)^(3/2))/(45*x^9)","A",2,2,13,0.1538,1,"{271, 264}"
288,0,0,0,0.8889424,"\int \frac{-1-2 x^2+2 x^4}{\left(1+2 x^4\right) \sqrt{1+x^6}} \, dx","Int[(-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,"(x*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x^2)/(1 + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2*3^(1/4)*Sqrt[(x^2*(1 + x^2))/(1 + (1 + Sqrt[3])*x^2)^2]*Sqrt[1 + x^6]) - (1/4 + I/4)*(I + Sqrt[2])*Defer[Int][1/(((-1)^(1/4) - 2^(1/4)*x)*Sqrt[1 + x^6]), x] + (1/4 + I/4)*(1 + I*Sqrt[2])*Defer[Int][1/((-(-1)^(3/4) - 2^(1/4)*x)*Sqrt[1 + x^6]), x] - (1/4 + I/4)*(I + Sqrt[2])*Defer[Int][1/(((-1)^(1/4) + 2^(1/4)*x)*Sqrt[1 + x^6]), x] + (1/4 + I/4)*(1 + I*Sqrt[2])*Defer[Int][1/((-(-1)^(3/4) + 2^(1/4)*x)*Sqrt[1 + x^6]), x]","F",0,0,0,0,-1,"{}"
289,0,0,0,1.1947615,"\int \frac{1+4 x^5}{\left(-1-a x+x^5\right) \sqrt{-x+x^6}} \, dx","Int[(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,"(8*x*Sqrt[1 - x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, x^5])/Sqrt[-x + x^6] - (10*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][1/((1 + a*x^2 - x^10)*Sqrt[-1 + x^10]), x], x, Sqrt[x]])/Sqrt[-x + x^6] - (8*a*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^2/((1 + a*x^2 - x^10)*Sqrt[-1 + x^10]), x], x, Sqrt[x]])/Sqrt[-x + x^6]","F",0,0,0,0,-1,"{}"
290,0,0,0,1.2075796,"\int \frac{1+4 x^5}{\left(-a-x+a x^5\right) \sqrt{-x+x^6}} \, dx","Int[(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,"(8*x*Sqrt[1 - x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, x^5])/(a*Sqrt[-x + x^6]) + (10*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][1/(Sqrt[-1 + x^10]*(-a - x^2 + a*x^10)), x], x, Sqrt[x]])/Sqrt[-x + x^6] + (8*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[-1 + x^10]*(-a - x^2 + a*x^10)), x], x, Sqrt[x]])/(a*Sqrt[-x + x^6])","F",0,0,0,0,-1,"{}"
291,1,31,0,0.103556,"\int \frac{\left(2+x^6\right) \left(-1-x^4+x^6\right)}{x^6 \left(-1+x^6\right)^{3/4}} \, dx","Int[((2 + x^6)*(-1 - x^4 + x^6))/(x^6*(-1 + x^6)^(3/4)),x]","\frac{2 \left(x^6-1\right)^{5/4}}{5 x^5}-\frac{2 \sqrt[4]{x^6-1}}{x}","\frac{2 \sqrt[4]{x^6-1} \left(x^6-5 x^4-1\right)}{5 x^5}",1,"(-2*(-1 + x^6)^(1/4))/x + (2*(-1 + x^6)^(5/4))/(5*x^5)","A",6,4,28,0.1429,1,"{1833, 1584, 449, 1478}"
292,1,31,0,0.0984221,"\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{x^6 \left(1+x^6\right)^{3/4}} \, dx","Int[((-2 + x^6)*(1 - x^4 + x^6))/(x^6*(1 + x^6)^(3/4)),x]","\frac{2 \left(x^6+1\right)^{5/4}}{5 x^5}-\frac{2 \sqrt[4]{x^6+1}}{x}","\frac{2 \sqrt[4]{x^6+1} \left(x^6-5 x^4+1\right)}{5 x^5}",1,"(-2*(1 + x^6)^(1/4))/x + (2*(1 + x^6)^(5/4))/(5*x^5)","A",6,4,28,0.1429,1,"{1833, 1584, 449, 1478}"
293,0,0,0,0.771168,"\int \frac{\sqrt{-1+x^6} \left(1+2 x^6\right)}{x^2 \left(-1+x^2+x^6\right)} \, dx","Int[(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,"Sqrt[-1 + x^6]/x + (3*(1 + Sqrt[3])*x*Sqrt[-1 + x^6])/(2*(1 - (1 + Sqrt[3])*x^2)) + (3*3^(1/4)*x*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(1 - (1 - Sqrt[3])*x^2)/(1 - (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2*Sqrt[-((x^2*(1 - x^2))/(1 - (1 + Sqrt[3])*x^2)^2)]*Sqrt[-1 + x^6]) + (3^(3/4)*(1 - Sqrt[3])*x*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x^2)/(1 - (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(4*Sqrt[-((x^2*(1 - x^2))/(1 - (1 + Sqrt[3])*x^2)^2)]*Sqrt[-1 + x^6]) + Defer[Int][Sqrt[-1 + x^6]/(-1 + x^2 + x^6), x] + 3*Defer[Int][(x^4*Sqrt[-1 + x^6])/(-1 + x^2 + x^6), x]","F",0,0,0,0,-1,"{}"
294,1,26,0,0.3231843,"\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","Int[((-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",2,2,50,0.04000,1,"{6688, 1590}"
295,0,0,0,1.7127529,"\int \frac{x^4 \left(9+4 x^5\right)}{\sqrt{x+x^6} \left(-a-a x^5+x^9\right)} \, dx","Int[(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,"(8*x*Sqrt[1 + x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, -x^5])/Sqrt[x + x^6] - (8*a*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][1/(Sqrt[1 + x^10]*(a + a*x^10 - x^18)), x], x, Sqrt[x]])/Sqrt[x + x^6] - (8*a*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^10/(Sqrt[1 + x^10]*(a + a*x^10 - x^18)), x], x, Sqrt[x]])/Sqrt[x + x^6] + (18*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^8/(Sqrt[1 + x^10]*(-a - a*x^10 + x^18)), x], x, Sqrt[x]])/Sqrt[x + x^6]","F",0,0,0,0,-1,"{}"
296,0,0,0,1.4193247,"\int \frac{x^4 \left(9+5 x^4\right)}{\sqrt{x+x^5} \left(-1-x^4+a x^9\right)} \, dx","Int[(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,"(18*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^8/(Sqrt[1 + x^8]*(-1 - x^8 + a*x^18)), x], x, Sqrt[x]])/Sqrt[x + x^5] + (10*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^16/(Sqrt[1 + x^8]*(-1 - x^8 + a*x^18)), x], x, Sqrt[x]])/Sqrt[x + x^5]","F",0,0,0,0,-1,"{}"
297,0,0,0,1.5359089,"\int \frac{x^4 \left(9+4 x^5\right)}{\sqrt{x+x^6} \left(-1-x^5+a x^9\right)} \, dx","Int[(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,"(8*x*Sqrt[1 + x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, -x^5])/(a*Sqrt[x + x^6]) + (8*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][1/(Sqrt[1 + x^10]*(-1 - x^10 + a*x^18)), x], x, Sqrt[x]])/(a*Sqrt[x + x^6]) + (18*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^8/(Sqrt[1 + x^10]*(-1 - x^10 + a*x^18)), x], x, Sqrt[x]])/Sqrt[x + x^6] + (8*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^10/(Sqrt[1 + x^10]*(-1 - x^10 + a*x^18)), x], x, Sqrt[x]])/(a*Sqrt[x + x^6])","F",0,0,0,0,-1,"{}"
298,1,31,0,0.0157696,"\int x^5 \sqrt{1-2 x^3} \, dx","Int[x^5*Sqrt[1 - 2*x^3],x]","\frac{1}{30} \left(1-2 x^3\right)^{5/2}-\frac{1}{18} \left(1-2 x^3\right)^{3/2}","\frac{1}{45} \sqrt{1-2 x^3} \left(6 x^6-x^3-1\right)",1,"-1/18*(1 - 2*x^3)^(3/2) + (1 - 2*x^3)^(5/2)/30","A",3,2,15,0.1333,1,"{266, 43}"
299,1,1340,0,3.9440312,"\int \frac{2+x}{(-1+x) \sqrt{-1+3 x+x^3}} \, dx","Int[(2 + x)/((-1 + x)*Sqrt[-1 + 3*x + x^3]),x]","\frac{2 i 2^{5/6} \sqrt{\frac{x-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+\sqrt[3]{\frac{2}{1+\sqrt{5}}}}{\frac{6}{\sqrt[3]{1+\sqrt{5}}}-3 \sqrt[3]{2 \left(1+\sqrt{5}\right)}-i \sqrt[6]{2} \sqrt{3 \left(4+2 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+\sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}\right)}}} \sqrt{x^2-\left(\sqrt[3]{\frac{2}{1+\sqrt{5}}}-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}\right) x+\left(\frac{1}{2} \left(1+\sqrt{5}\right)\right)^{2/3}+\left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+1} F\left(\sin ^{-1}\left(\sqrt{\frac{i \left(-2 x-i \sqrt{6+3 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+3 \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right)^{2/3}}-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+\sqrt[3]{\frac{2}{1+\sqrt{5}}}\right)}{\sqrt{6 \left(4+2 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+\sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}\right)}}}\right)|\frac{2 \sqrt[6]{2} \sqrt{3 \left(4+2 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+\sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}\right)}}{\frac{6 i}{\sqrt[3]{1+\sqrt{5}}}-3 i \sqrt[3]{2 \left(1+\sqrt{5}\right)}+\sqrt[6]{2} \sqrt{3 \left(4+2 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+\sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}\right)}}\right)}{\sqrt{x^3+3 x-1}}-\frac{3 \sqrt[6]{\frac{2}{1+\sqrt{5}}} \sqrt{6-3 \sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}+i \sqrt[6]{2} \sqrt[3]{1+\sqrt{5}} \sqrt{3 \left(4+2 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+\sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}\right)}} \sqrt{x-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+\sqrt[3]{\frac{2}{1+\sqrt{5}}}} \sqrt{1-\frac{2 \left(x-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+\sqrt[3]{\frac{2}{1+\sqrt{5}}}\right)}{3 \sqrt[3]{\frac{2}{1+\sqrt{5}}}-3 \sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}-i \sqrt{6+3 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+3 \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right)^{2/3}}}} \sqrt{1-\frac{2 \left(x-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+\sqrt[3]{\frac{2}{1+\sqrt{5}}}\right)}{3 \sqrt[3]{\frac{2}{1+\sqrt{5}}}-3 \sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+i \sqrt{6+3 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+3 \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right)^{2/3}}}} \Pi \left(\frac{3 \sqrt[3]{\frac{2}{1+\sqrt{5}}}-3 \sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+i \sqrt{6+3 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+3 \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right)^{2/3}}}{2 \left(1+\sqrt[3]{\frac{2}{1+\sqrt{5}}}-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}\right)};\sin ^{-1}\left(\frac{2^{5/6} \sqrt[6]{1+\sqrt{5}} \sqrt{x-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+\sqrt[3]{\frac{2}{1+\sqrt{5}}}}}{\sqrt{6-3 \sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}+i \sqrt[6]{2} \sqrt[3]{1+\sqrt{5}} \sqrt{3 \left(4+2 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+\sqrt[3]{2} \left(1+\sqrt{5}\right)^{2/3}\right)}}}\right)|\frac{3 \sqrt[3]{\frac{2}{1+\sqrt{5}}}-3 \sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}+i \sqrt{6+3 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+3 \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right)^{2/3}}}{3 \sqrt[3]{\frac{2}{1+\sqrt{5}}}-3 \sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\right)}-i \sqrt{6+3 \left(\frac{2}{1+\sqrt{5}}\right)^{2/3}+3 \left(\frac{1}{2} \left(1+\sqrt{5}\right)\right)^{2/3}}}\right)}{\left(1+\sqrt[3]{\frac{2}{1+\sqrt{5}}}-\sqrt[3]{\frac{1}{2} \left(1+\sqrt{5}\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*I)*2^(5/6)*Sqrt[((2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3) + x)/(6/(1 + Sqrt[5])^(1/3) - 3*(2*(1 + Sqrt[5]))^(1/3) - I*2^(1/6)*Sqrt[3*(4 + 2*(2/(1 + Sqrt[5]))^(2/3) + 2^(1/3)*(1 + Sqrt[5])^(2/3))])]*Sqrt[1 + (2/(1 + Sqrt[5]))^(2/3) + ((1 + Sqrt[5])/2)^(2/3) - ((2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3))*x + x^2]*EllipticF[ArcSin[Sqrt[(I*((2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3) - I*Sqrt[6 + 3*(2/(1 + Sqrt[5]))^(2/3) + 3*((1 + Sqrt[5])/2)^(2/3)] - 2*x))/Sqrt[6*(4 + 2*(2/(1 + Sqrt[5]))^(2/3) + 2^(1/3)*(1 + Sqrt[5])^(2/3))]]], (2*2^(1/6)*Sqrt[3*(4 + 2*(2/(1 + Sqrt[5]))^(2/3) + 2^(1/3)*(1 + Sqrt[5])^(2/3))])/((6*I)/(1 + Sqrt[5])^(1/3) - (3*I)*(2*(1 + Sqrt[5]))^(1/3) + 2^(1/6)*Sqrt[3*(4 + 2*(2/(1 + Sqrt[5]))^(2/3) + 2^(1/3)*(1 + Sqrt[5])^(2/3))])])/Sqrt[-1 + 3*x + x^3] - (3*(2/(1 + Sqrt[5]))^(1/6)*Sqrt[6 - 3*2^(1/3)*(1 + Sqrt[5])^(2/3) + I*2^(1/6)*(1 + Sqrt[5])^(1/3)*Sqrt[3*(4 + 2*(2/(1 + Sqrt[5]))^(2/3) + 2^(1/3)*(1 + Sqrt[5])^(2/3))]]*Sqrt[(2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3) + x]*Sqrt[1 - (2*((2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3) + x))/(3*(2/(1 + Sqrt[5]))^(1/3) - 3*((1 + Sqrt[5])/2)^(1/3) - I*Sqrt[6 + 3*(2/(1 + Sqrt[5]))^(2/3) + 3*((1 + Sqrt[5])/2)^(2/3)])]*Sqrt[1 - (2*((2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3) + x))/(3*(2/(1 + Sqrt[5]))^(1/3) - 3*((1 + Sqrt[5])/2)^(1/3) + I*Sqrt[6 + 3*(2/(1 + Sqrt[5]))^(2/3) + 3*((1 + Sqrt[5])/2)^(2/3)])]*EllipticPi[(3*(2/(1 + Sqrt[5]))^(1/3) - 3*((1 + Sqrt[5])/2)^(1/3) + I*Sqrt[6 + 3*(2/(1 + Sqrt[5]))^(2/3) + 3*((1 + Sqrt[5])/2)^(2/3)])/(2*(1 + (2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3))), ArcSin[(2^(5/6)*(1 + Sqrt[5])^(1/6)*Sqrt[(2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3) + x])/Sqrt[6 - 3*2^(1/3)*(1 + Sqrt[5])^(2/3) + I*2^(1/6)*(1 + Sqrt[5])^(1/3)*Sqrt[3*(4 + 2*(2/(1 + Sqrt[5]))^(2/3) + 2^(1/3)*(1 + Sqrt[5])^(2/3))]]], (3*(2/(1 + Sqrt[5]))^(1/3) - 3*((1 + Sqrt[5])/2)^(1/3) + I*Sqrt[6 + 3*(2/(1 + Sqrt[5]))^(2/3) + 3*((1 + Sqrt[5])/2)^(2/3)])/(3*(2/(1 + Sqrt[5]))^(1/3) - 3*((1 + Sqrt[5])/2)^(1/3) - I*Sqrt[6 + 3*(2/(1 + Sqrt[5]))^(2/3) + 3*((1 + Sqrt[5])/2)^(2/3)])])/((1 + (2/(1 + Sqrt[5]))^(1/3) - ((1 + Sqrt[5])/2)^(1/3))*Sqrt[-1 + 3*x + x^3])","C",11,9,21,0.4286,0,"{6742, 2066, 718, 419, 2080, 934, 169, 538, 537}"
300,1,537,0,1.0243651,"\int \frac{-1+2 x}{(1+x) \sqrt{-x-x^2+x^3}} \, dx","Int[(-1 + 2*x)/((1 + x)*Sqrt[-x - x^2 + x^3]),x]","\frac{3 \sqrt{2} \left(1+\sqrt{5}\right) \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\left(3+\sqrt{5}\right) \sqrt{x^3-x^2-x}}-\frac{6 \sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \left(3+\sqrt{5}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}+\frac{2 \sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}-\frac{6 \sqrt{2} \left(2+\sqrt{5}\right) \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(-1-\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\left(3+\sqrt{5}\right) \sqrt{x^3-x^2-x}}","2 \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{2 x+1}\right)",1,"(3*Sqrt[2]*(1 + Sqrt[5])*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/((3 + Sqrt[5])*Sqrt[-x - x^2 + x^3]) + (2*Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (6*Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*(3 + Sqrt[5])*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (6*Sqrt[2]*(2 + Sqrt[5])*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1 - Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/((3 + Sqrt[5])*Sqrt[-x - x^2 + x^3])","C",12,11,27,0.4074,0,"{2056, 6733, 1710, 1098, 1214, 1456, 540, 421, 419, 538, 537}"
301,1,38,0,0.0266391,"\int \frac{x^5}{\sqrt{b+a x^3}} \, dx","Int[x^5/Sqrt[b + a*x^3],x]","\frac{2 \left(a x^3+b\right)^{3/2}}{9 a^2}-\frac{2 b \sqrt{a x^3+b}}{3 a^2}","\frac{2 \left(a x^3-2 b\right) \sqrt{a x^3+b}}{9 a^2}",1,"(-2*b*Sqrt[b + a*x^3])/(3*a^2) + (2*(b + a*x^3)^(3/2))/(9*a^2)","A",3,2,15,0.1333,1,"{266, 43}"
302,1,41,0,0.0537858,"\int \frac{1}{x^4 \sqrt[4]{-x^2+x^4}} \, dx","Int[1/(x^4*(-x^2 + x^4)^(1/4)),x]","\frac{2 \left(x^4-x^2\right)^{3/4}}{7 x^5}+\frac{8 \left(x^4-x^2\right)^{3/4}}{21 x^3}","\frac{2 \left(4 x^2+3\right) \left(x^4-x^2\right)^{3/4}}{21 x^5}",1,"(2*(-x^2 + x^4)^(3/4))/(7*x^5) + (8*(-x^2 + x^4)^(3/4))/(21*x^3)","A",2,2,17,0.1176,1,"{2016, 2014}"
303,1,27,0,0.0213227,"\int \frac{1}{x \sqrt{b+a x^4}} \, dx","Int[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",3,3,15,0.2000,1,"{266, 63, 208}"
304,1,41,0,0.0555428,"\int \frac{1}{x^7 \sqrt[3]{-x^2+x^6}} \, dx","Int[1/(x^7*(-x^2 + x^6)^(1/3)),x]","\frac{3 \left(x^6-x^2\right)^{2/3}}{20 x^8}+\frac{9 \left(x^6-x^2\right)^{2/3}}{40 x^4}","\frac{3 \left(3 x^4+2\right) \left(x^6-x^2\right)^{2/3}}{40 x^8}",1,"(3*(-x^2 + x^6)^(2/3))/(20*x^8) + (9*(-x^2 + x^6)^(2/3))/(40*x^4)","A",2,2,17,0.1176,1,"{2016, 2014}"
305,1,28,0,0.010675,"\int \frac{\sqrt{-1+x^3}}{x} \, dx","Int[Sqrt[-1 + x^3]/x,x]","\frac{2 \sqrt{x^3-1}}{3}-\frac{2}{3} \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",4,4,13,0.3077,1,"{266, 50, 63, 203}"
306,1,33,0,0.0090339,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^8} \, dx","Int[((-1 + x^3)*(1 + x^3)^(1/3))/x^8,x]","\frac{\left(x^3+1\right)^{4/3}}{7 x^7}-\frac{5 \left(x^3+1\right)^{4/3}}{14 x^4}","\frac{\sqrt[3]{x^3+1} \left(-5 x^6-3 x^3+2\right)}{14 x^7}",1,"(1 + x^3)^(4/3)/(7*x^7) - (5*(1 + x^3)^(4/3))/(14*x^4)","A",2,2,18,0.1111,1,"{453, 264}"
307,1,28,0,0.0102805,"\int \frac{\sqrt{1+x^3}}{x} \, dx","Int[Sqrt[1 + x^3]/x,x]","\frac{2 \sqrt{x^3+1}}{3}-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{2 \sqrt{x^3+1}}{3}-\frac{2}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(2*Sqrt[1 + x^3])/3 - (2*ArcTanh[Sqrt[1 + x^3]])/3","A",4,4,13,0.3077,1,"{266, 50, 63, 207}"
308,1,33,0,0.0085018,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^8} \, dx","Int[((-1 + x^3)^(1/3)*(1 + x^3))/x^8,x]","\frac{\left(x^3-1\right)^{4/3}}{7 x^7}+\frac{5 \left(x^3-1\right)^{4/3}}{14 x^4}","\frac{\sqrt[3]{x^3-1} \left(5 x^6-3 x^3-2\right)}{14 x^7}",1,"(-1 + x^3)^(4/3)/(7*x^7) + (5*(-1 + x^3)^(4/3))/(14*x^4)","A",2,2,18,0.1111,1,"{453, 264}"
309,1,33,0,0.0093733,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^9} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^3))/x^9,x]","\frac{\left(x^3-1\right)^{5/3}}{4 x^8}+\frac{7 \left(x^3-1\right)^{5/3}}{20 x^5}","\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)/(4*x^8) + (7*(-1 + x^3)^(5/3))/(20*x^5)","A",2,2,18,0.1111,1,"{453, 264}"
310,1,33,0,0.0103272,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^9} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^3))/x^9,x]","-\frac{\left(x^3+1\right)^{5/3}}{4 x^8}-\frac{\left(x^3+1\right)^{5/3}}{20 x^5}","\frac{\left(x^3+1\right)^{2/3} \left(-x^6-6 x^3-5\right)}{20 x^8}",1,"-1/4*(1 + x^3)^(5/3)/x^8 - (1 + x^3)^(5/3)/(20*x^5)","A",2,2,18,0.1111,1,"{453, 264}"
311,1,49,0,0.0612858,"\int \frac{1}{x^6 \sqrt[3]{x+x^3}} \, dx","Int[1/(x^6*(x + x^3)^(1/3)),x]","-\frac{3 \left(x^3+x\right)^{2/3}}{16 x^6}+\frac{9 \left(x^3+x\right)^{2/3}}{40 x^4}-\frac{27 \left(x^3+x\right)^{2/3}}{80 x^2}","-\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))/(16*x^6) + (9*(x + x^3)^(2/3))/(40*x^4) - (27*(x + x^3)^(2/3))/(80*x^2)","A",3,2,13,0.1538,1,"{2016, 2014}"
312,1,36,0,0.1338744,"\int \frac{-2-x+2 x^2}{(-1+x) x \sqrt[4]{-x^2+x^3}} \, dx","Int[(-2 - x + 2*x^2)/((-1 + x)*x*(-x^2 + x^3)^(1/4)),x]","\frac{4}{\sqrt[4]{x^3-x^2}}-\frac{8 (1-x)}{\sqrt[4]{x^3-x^2}}","\frac{4 (2 x-1) \left(x^3-x^2\right)^{3/4}}{(x-1) x^2}",1,"4/(-x^2 + x^3)^(1/4) - (8*(1 - x))/(-x^2 + x^3)^(1/4)","A",3,3,32,0.09375,1,"{2056, 949, 74}"
313,1,533,0,0.8942097,"\int \frac{2+x}{(-1+x) \sqrt{-x-x^2+x^3}} \, dx","Int[(2 + x)/((-1 + x)*Sqrt[-x - x^2 + x^3]),x]","\frac{3 \sqrt{2} \left(1+\sqrt{5}\right) \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\left(1-\sqrt{5}\right) \sqrt{x^3-x^2-x}}-\frac{6 \sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \left(1-\sqrt{5}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}+\frac{\sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}+\frac{6 \sqrt{2} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\left(1-\sqrt{5}\right) \sqrt{x^3-x^2-x}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{(x-2) x}\right)",1,"(3*Sqrt[2]*(1 + Sqrt[5])*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/((1 - Sqrt[5])*Sqrt[-x - x^2 + x^3]) + (Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (6*Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*(1 - Sqrt[5])*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) + (6*Sqrt[2]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/((1 - Sqrt[5])*Sqrt[-x - x^2 + x^3])","C",12,11,25,0.4400,0,"{2056, 6733, 1710, 1098, 1214, 1456, 540, 421, 419, 538, 537}"
314,1,49,0,0.3619728,"\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)}{x^6 \sqrt[4]{x+x^3}} \, dx","Int[((3 + x^2)*(1 + x^2 + x^3))/(x^6*(x + x^3)^(1/4)),x]","-\frac{4 \left(x^3+x\right)^{3/4}}{3 x^3}-\frac{4 \left(x^3+x\right)^{3/4}}{7 x^6}-\frac{4 \left(x^3+x\right)^{3/4}}{7 x^4}","-\frac{4 \left(x^3+x\right)^{3/4} \left(7 x^3+3 x^2+3\right)}{21 x^6}",1,"(-4*(x + x^3)^(3/4))/(7*x^6) - (4*(x + x^3)^(3/4))/(7*x^4) - (4*(x + x^3)^(3/4))/(3*x^3)","A",21,5,26,0.1923,1,"{2052, 2025, 2011, 364, 2032}"
315,1,49,0,0.0129942,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^{11}} \, dx","Int[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^11,x]","-\frac{\left(x^3-1\right)^{4/3}}{10 x^{10}}+\frac{\left(x^3-1\right)^{4/3}}{5 x^7}+\frac{3 \left(x^3-1\right)^{4/3}}{20 x^4}","\frac{\left(x^3-1\right)^{4/3} \left(3 x^6+4 x^3-2\right)}{20 x^{10}}",1,"-1/10*(-1 + x^3)^(4/3)/x^10 + (-1 + x^3)^(4/3)/(5*x^7) + (3*(-1 + x^3)^(4/3))/(20*x^4)","A",3,3,20,0.1500,1,"{453, 271, 264}"
316,1,33,0,0.0095162,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^8} \, dx","Int[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^8,x]","\frac{11 \left(x^3-1\right)^{4/3}}{28 x^4}-\frac{\left(x^3-1\right)^{4/3}}{7 x^7}","\frac{\sqrt[3]{x^3-1} \left(11 x^6-15 x^3+4\right)}{28 x^7}",1,"-1/7*(-1 + x^3)^(4/3)/x^7 + (11*(-1 + x^3)^(4/3))/(28*x^4)","A",2,2,20,0.1000,1,"{453, 264}"
317,1,49,0,0.3640487,"\int \frac{\left(3+x^2\right) \left(-1-x^2+2 x^3\right)}{x^6 \sqrt[4]{x+x^3}} \, dx","Int[((3 + x^2)*(-1 - x^2 + 2*x^3))/(x^6*(x + x^3)^(1/4)),x]","-\frac{8 \left(x^3+x\right)^{3/4}}{3 x^3}+\frac{4 \left(x^3+x\right)^{3/4}}{7 x^6}+\frac{4 \left(x^3+x\right)^{3/4}}{7 x^4}","-\frac{4 \left(x^3+x\right)^{3/4} \left(14 x^3-3 x^2-3\right)}{21 x^6}",1,"(4*(x + x^3)^(3/4))/(7*x^6) + (4*(x + x^3)^(3/4))/(7*x^4) - (8*(x + x^3)^(3/4))/(3*x^3)","A",21,5,30,0.1667,1,"{2052, 2025, 2011, 364, 2032}"
318,0,0,0,1.0352742,"\int \frac{2 b+a x^3}{\sqrt{-b+a x^3} \left(-b+x^2+a x^3\right)} \, dx","Int[(2*b + a*x^3)/(Sqrt[-b + a*x^3]*(-b + x^2 + a*x^3)),x]","\int \frac{2 b+a x^3}{\sqrt{-b+a x^3} \left(-b+x^2+a x^3\right)} \, dx","2 \tan ^{-1}\left(\frac{x \sqrt{a x^3-b}}{b-a x^3}\right)",1,"(-2*Sqrt[2 - Sqrt[3]]*(b^(1/3) - a^(1/3)*x)*Sqrt[(b^(2/3) + a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/((1 - Sqrt[3])*b^(1/3) - a^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*b^(1/3) - a^(1/3)*x)/((1 - Sqrt[3])*b^(1/3) - a^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*a^(1/3)*Sqrt[-((b^(1/3)*(b^(1/3) - a^(1/3)*x))/((1 - Sqrt[3])*b^(1/3) - a^(1/3)*x)^2)]*Sqrt[-b + a*x^3]) - 3*b*Defer[Int][1/((b - x^2 - a*x^3)*Sqrt[-b + a*x^3]), x] - Defer[Int][x^2/(Sqrt[-b + a*x^3]*(-b + x^2 + a*x^3)), x]","F",0,0,0,0,-1,"{}"
319,1,33,0,0.0120356,"\int \frac{\left(-4+x^4\right) \left(-1+x^4\right)^{3/4}}{x^{12}} \, dx","Int[((-4 + x^4)*(-1 + x^4)^(3/4))/x^12,x]","-\frac{4 \left(x^4-1\right)^{7/4}}{11 x^{11}}-\frac{5 \left(x^4-1\right)^{7/4}}{77 x^7}","\frac{\left(x^4-1\right)^{3/4} \left(-5 x^8-23 x^4+28\right)}{77 x^{11}}",1,"(-4*(-1 + x^4)^(7/4))/(11*x^11) - (5*(-1 + x^4)^(7/4))/(77*x^7)","A",2,2,18,0.1111,1,"{453, 264}"
320,1,28,0,0.0110295,"\int \frac{\sqrt{1+x^4}}{x} \, dx","Int[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",4,4,13,0.3077,1,"{266, 50, 63, 207}"
321,1,37,0,0.0405589,"\int \frac{\sqrt[4]{-x+x^4}}{x^8} \, dx","Int[(-x + x^4)^(1/4)/x^8,x]","\frac{4 \left(x^4-x\right)^{5/4}}{27 x^8}+\frac{16 \left(x^4-x\right)^{5/4}}{135 x^5}","\frac{4 \sqrt[4]{x^4-x} \left(4 x^6+x^3-5\right)}{135 x^7}",1,"(4*(-x + x^4)^(5/4))/(27*x^8) + (16*(-x + x^4)^(5/4))/(135*x^5)","A",2,2,15,0.1333,1,"{2016, 2014}"
322,1,33,0,0.0375384,"\int \frac{\sqrt[4]{x+x^4}}{x^8} \, dx","Int[(x + x^4)^(1/4)/x^8,x]","\frac{16 \left(x^4+x\right)^{5/4}}{135 x^5}-\frac{4 \left(x^4+x\right)^{5/4}}{27 x^8}","\frac{4 \sqrt[4]{x^4+x} \left(4 x^6-x^3-5\right)}{135 x^7}",1,"(-4*(x + x^4)^(5/4))/(27*x^8) + (16*(x + x^4)^(5/4))/(135*x^5)","A",2,2,13,0.1538,1,"{2016, 2014}"
323,1,520,0,0.3235705,"\int \frac{2+x^2}{\left(-1+x^2\right) \sqrt{-1-x^2+x^4}} \, dx","Int[(2 + x^2)/((-1 + x^2)*Sqrt[-1 - x^2 + x^4]),x]","\frac{3 \left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{2} \left(1-\sqrt{5}\right) \sqrt{x^4-x^2-1}}-\frac{3 \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \left(1-\sqrt{5}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{2 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{3 \sqrt{2} \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\left(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,"(3*(1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(Sqrt[2]*(1 - Sqrt[5])*Sqrt[-1 - x^2 + x^4]) + (Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(2*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (3*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(5^(1/4)*(1 - Sqrt[5])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + (3*Sqrt[2]*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/((1 - Sqrt[5])*Sqrt[-1 - x^2 + x^4])","C",10,9,27,0.3333,0,"{1710, 1098, 1214, 1456, 540, 421, 419, 538, 537}"
324,1,47,0,0.1207557,"\int \frac{\left(4+x^3\right) \left(-1-x^3+x^4\right)}{x^6 \left(1+x^3\right)^{3/4}} \, dx","Int[((4 + x^3)*(-1 - x^3 + x^4))/(x^6*(1 + x^3)^(3/4)),x]","-\frac{4 \sqrt[4]{x^3+1}}{x}+\frac{4 \sqrt[4]{x^3+1}}{5 x^5}+\frac{4 \sqrt[4]{x^3+1}}{5 x^2}","-\frac{4 \sqrt[4]{x^3+1} \left(5 x^4-x^3-1\right)}{5 x^5}",1,"(4*(1 + x^3)^(1/4))/(5*x^5) + (4*(1 + x^3)^(1/4))/(5*x^2) - (4*(1 + x^3)^(1/4))/x","A",5,3,28,0.1071,1,"{1835, 1586, 449}"
325,1,49,0,0.1133142,"\int \frac{\left(4+x^3\right) \left(-1-x^3+x^4\right)}{x^8 \sqrt[4]{1+x^3}} \, dx","Int[((4 + x^3)*(-1 - x^3 + x^4))/(x^8*(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}}{7 x^7}+\frac{4 \left(x^3+1\right)^{3/4}}{7 x^4}","-\frac{4 \left(x^3+1\right)^{3/4} \left(7 x^4-3 x^3-3\right)}{21 x^7}",1,"(4*(1 + x^3)^(3/4))/(7*x^7) + (4*(1 + x^3)^(3/4))/(7*x^4) - (4*(1 + x^3)^(3/4))/(3*x^3)","A",6,4,28,0.1429,1,"{1835, 1586, 446, 74}"
326,1,49,0,0.1119845,"\int \frac{\left(-4+x^3\right) \left(1-x^3+x^4\right)}{x^8 \sqrt[4]{-1+x^3}} \, dx","Int[((-4 + x^3)*(1 - x^3 + x^4))/(x^8*(-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}}{7 x^7}+\frac{4 \left(x^3-1\right)^{3/4}}{7 x^4}","-\frac{4 \left(x^3-1\right)^{3/4} \left(7 x^4-3 x^3+3\right)}{21 x^7}",1,"(-4*(-1 + x^3)^(3/4))/(7*x^7) + (4*(-1 + x^3)^(3/4))/(7*x^4) - (4*(-1 + x^3)^(3/4))/(3*x^3)","A",6,4,28,0.1429,1,"{1835, 1586, 446, 74}"
327,1,18,0,0.0219661,"\int \frac{x}{\sqrt{x^3+x^4}} \, dx","Int[x/Sqrt[x^3 + x^4],x]","2 \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x^3}}\right)","\log (x)-\log \left(-2 x^2+2 \sqrt{x^4+x^3}-x\right)",1,"2*ArcTanh[x^2/Sqrt[x^3 + x^4]]","A",2,2,13,0.1538,1,"{2029, 206}"
328,1,32,0,0.0979325,"\int \frac{1}{x (1+x) \sqrt[4]{x^3+x^4}} \, dx","Int[1/(x*(1 + x)*(x^3 + x^4)^(1/4)),x]","\frac{4}{\sqrt[4]{x^4+x^3}}-\frac{16 (x+1)}{3 \sqrt[4]{x^4+x^3}}","-\frac{4 (4 x+1) \left(x^4+x^3\right)^{3/4}}{3 x^3 (x+1)}",1,"4/(x^3 + x^4)^(1/4) - (16*(1 + x))/(3*(x^3 + x^4)^(1/4))","A",3,3,20,0.1500,1,"{2056, 45, 37}"
329,1,47,0,0.1240926,"\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","Int[((4 + x^3)*(-1 - x^3 + 2*x^4))/(x^6*(1 + x^3)^(3/4)),x]","-\frac{8 \sqrt[4]{x^3+1}}{x}+\frac{4 \sqrt[4]{x^3+1}}{5 x^5}+\frac{4 \sqrt[4]{x^3+1}}{5 x^2}","-\frac{4 \sqrt[4]{x^3+1} \left(10 x^4-x^3-1\right)}{5 x^5}",1,"(4*(1 + x^3)^(1/4))/(5*x^5) + (4*(1 + x^3)^(1/4))/(5*x^2) - (8*(1 + x^3)^(1/4))/x","A",5,3,30,0.1000,1,"{1835, 1586, 449}"
330,1,49,0,0.3031251,"\int \frac{\left(-3+x^4\right) \left(1-x^3+x^4\right)}{x^6 \sqrt[4]{x+x^5}} \, dx","Int[((-3 + x^4)*(1 - x^3 + x^4))/(x^6*(x + x^5)^(1/4)),x]","\frac{4 \left(x^5+x\right)^{3/4}}{7 x^6}-\frac{4 \left(x^5+x\right)^{3/4}}{3 x^3}+\frac{4 \left(x^5+x\right)^{3/4}}{7 x^2}","\frac{4 \left(3 x^4-7 x^3+3\right) \left(x^5+x\right)^{3/4}}{21 x^6}",1,"(4*(x + x^5)^(3/4))/(7*x^6) - (4*(x + x^5)^(3/4))/(3*x^3) + (4*(x + x^5)^(3/4))/(7*x^2)","A",16,4,28,0.1429,1,"{2052, 2025, 2032, 364}"
331,1,28,0,0.0100019,"\int \frac{\sqrt{-1+x^6}}{x} \, dx","Int[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",4,4,13,0.3077,1,"{266, 50, 63, 203}"
332,1,28,0,0.0132471,"\int \frac{-1+x^6}{x \sqrt{1+x^6}} \, dx","Int[(-1 + x^6)/(x*Sqrt[1 + x^6]),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",4,4,18,0.2222,1,"{446, 80, 63, 207}"
333,1,28,0,0.0110615,"\int \frac{\sqrt{1+x^6}}{x} \, dx","Int[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",4,4,13,0.3077,1,"{266, 50, 63, 207}"
334,1,33,0,0.0098761,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^{15}} \, dx","Int[((-1 + x^6)^(1/3)*(1 + x^6))/x^15,x]","\frac{\left(x^6-1\right)^{4/3}}{14 x^{14}}+\frac{5 \left(x^6-1\right)^{4/3}}{28 x^8}","\frac{\sqrt[3]{x^6-1} \left(5 x^{12}-3 x^6-2\right)}{28 x^{14}}",1,"(-1 + x^6)^(4/3)/(14*x^14) + (5*(-1 + x^6)^(4/3))/(28*x^8)","A",2,2,18,0.1111,1,"{453, 264}"
335,1,49,0,0.3197883,"\int \frac{\left(1-x^3+x^5\right) \left(-3+2 x^5\right)}{x^6 \sqrt[4]{x+x^6}} \, dx","Int[((1 - x^3 + x^5)*(-3 + 2*x^5))/(x^6*(x + x^6)^(1/4)),x]","\frac{4 \left(x^6+x\right)^{3/4}}{7 x}+\frac{4 \left(x^6+x\right)^{3/4}}{7 x^6}-\frac{4 \left(x^6+x\right)^{3/4}}{3 x^3}","\frac{4 \left(3 x^5-7 x^3+3\right) \left(x^6+x\right)^{3/4}}{21 x^6}",1,"(4*(x + x^6)^(3/4))/(7*x^6) - (4*(x + x^6)^(3/4))/(3*x^3) + (4*(x + x^6)^(3/4))/(7*x)","A",16,4,30,0.1333,1,"{2052, 2025, 2032, 364}"
336,1,33,0,0.0798275,"\int \frac{\left(-2+x^6\right) \left(1-x^4+x^6\right)}{x^8 \sqrt[4]{1+x^6}} \, dx","Int[((-2 + x^6)*(1 - x^4 + x^6))/(x^8*(1 + x^6)^(1/4)),x]","\frac{2 \left(x^6+1\right)^{7/4}}{7 x^7}-\frac{2 \left(x^6+1\right)^{3/4}}{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*(1 + x^6)^(3/4))/(3*x^3) + (2*(1 + x^6)^(7/4))/(7*x^7)","A",6,4,28,0.1429,1,"{1833, 1584, 449, 1478}"
337,1,33,0,0.0096801,"\int \frac{\sqrt[3]{-1+x^6} \left(-1+2 x^6\right)}{x^{15}} \, dx","Int[((-1 + x^6)^(1/3)*(-1 + 2*x^6))/x^15,x]","\frac{11 \left(x^6-1\right)^{4/3}}{56 x^8}-\frac{\left(x^6-1\right)^{4/3}}{14 x^{14}}","\frac{\sqrt[3]{x^6-1} \left(11 x^{12}-15 x^6+4\right)}{56 x^{14}}",1,"-1/14*(-1 + x^6)^(4/3)/x^14 + (11*(-1 + x^6)^(4/3))/(56*x^8)","A",2,2,20,0.1000,1,"{453, 264}"
338,1,28,0,0.3840181,"\int \frac{x^2 \left(-2+x^3\right) \sqrt{1+x^3}}{1+3 x^3+x^9} \, dx","Int[(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",4,3,30,0.1000,1,"{6715, 2094, 207}"
339,0,0,0,1.6704696,"\int \frac{x^4 \left(-9+4 x^5\right)}{\sqrt{-x+x^6} \left(a-a x^5+x^9\right)} \, dx","Int[(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,"(8*x*Sqrt[1 - x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, x^5])/Sqrt[-x + x^6] + (8*a*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][1/(Sqrt[-1 + x^10]*(-a + a*x^10 - x^18)), x], x, Sqrt[x]])/Sqrt[-x + x^6] - (8*a*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^10/(Sqrt[-1 + x^10]*(-a + a*x^10 - x^18)), x], x, Sqrt[x]])/Sqrt[-x + x^6] - (18*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^8/(Sqrt[-1 + x^10]*(a - a*x^10 + x^18)), x], x, Sqrt[x]])/Sqrt[-x + x^6]","F",0,0,0,0,-1,"{}"
340,0,0,0,1.3784348,"\int \frac{x^4 \left(-9+5 x^4\right)}{\sqrt{-x+x^5} \left(1-x^4+a x^9\right)} \, dx","Int[(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,"(-18*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^8/(Sqrt[-1 + x^8]*(1 - x^8 + a*x^18)), x], x, Sqrt[x]])/Sqrt[-x + x^5] + (10*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^16/(Sqrt[-1 + x^8]*(1 - x^8 + a*x^18)), x], x, Sqrt[x]])/Sqrt[-x + x^5]","F",0,0,0,0,-1,"{}"
341,0,0,0,1.5484197,"\int \frac{x^4 \left(-9+4 x^5\right)}{\sqrt{-x+x^6} \left(1-x^5+a x^9\right)} \, dx","Int[(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,"(8*x*Sqrt[1 - x^5]*Hypergeometric2F1[1/10, 1/2, 11/10, x^5])/(a*Sqrt[-x + x^6]) - (8*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][1/(Sqrt[-1 + x^10]*(1 - x^10 + a*x^18)), x], x, Sqrt[x]])/(a*Sqrt[-x + x^6]) - (18*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^8/(Sqrt[-1 + x^10]*(1 - x^10 + a*x^18)), x], x, Sqrt[x]])/Sqrt[-x + x^6] + (8*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^10/(Sqrt[-1 + x^10]*(1 - x^10 + a*x^18)), x], x, Sqrt[x]])/(a*Sqrt[-x + x^6])","F",0,0,0,0,-1,"{}"
342,1,49,0,0.0296323,"\int \frac{1+x^{12}}{x^{16} \sqrt{-1+x^6}} \, dx","Int[(1 + x^12)/(x^16*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1}}{15 x^{15}}+\frac{4 \sqrt{x^6-1}}{45 x^9}+\frac{23 \sqrt{x^6-1}}{45 x^3}","\frac{\sqrt{x^6-1} \left(23 x^{12}+4 x^6+3\right)}{45 x^{15}}",1,"Sqrt[-1 + x^6]/(15*x^15) + (4*Sqrt[-1 + x^6])/(45*x^9) + (23*Sqrt[-1 + x^6])/(45*x^3)","A",4,4,18,0.2222,1,"{1487, 453, 271, 264}"
343,1,262,0,1.1207218,"\int \frac{-1+x}{(-3+x) (1+x) \sqrt[4]{-2-2 x+x^2}} \, dx","Int[(-1 + x)/((-3 + x)*(1 + x)*(-2 - 2*x + x^2)^(1/4)),x]","-\frac{\sqrt[4]{-x^2+2 x+2} \log \left(\sqrt{-x^2+2 x+2}+\sqrt{2} \sqrt[4]{-x^2+2 x+2}+1\right)}{2 \sqrt{2} \sqrt[4]{x^2-2 x-2}}+\frac{\sqrt[4]{-x^2+2 x+2} \log \left(3 \sqrt{-x^2+2 x+2}-3 \sqrt{2} \sqrt[4]{-x^2+2 x+2}+3\right)}{2 \sqrt{2} \sqrt[4]{x^2-2 x-2}}-\frac{\sqrt[4]{-x^2+2 x+2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3-(1-x)^2}\right)}{\sqrt{2} \sqrt[4]{x^2-2 x-2}}+\frac{\sqrt[4]{-x^2+2 x+2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{3-(1-x)^2}+1\right)}{\sqrt{2} \sqrt[4]{x^2-2 x-2}}","\tan ^{-1}\left(\sqrt[4]{x^2-2 x-2}\right)-\tanh ^{-1}\left(\sqrt[4]{x^2-2 x-2}\right)",1,"-(((2 + 2*x - x^2)^(1/4)*ArcTan[1 - Sqrt[2]*(3 - (1 - x)^2)^(1/4)])/(Sqrt[2]*(-2 - 2*x + x^2)^(1/4))) + ((2 + 2*x - x^2)^(1/4)*ArcTan[1 + Sqrt[2]*(3 - (1 - x)^2)^(1/4)])/(Sqrt[2]*(-2 - 2*x + x^2)^(1/4)) - ((2 + 2*x - x^2)^(1/4)*Log[1 + Sqrt[2]*(2 + 2*x - x^2)^(1/4) + Sqrt[2 + 2*x - x^2]])/(2*Sqrt[2]*(-2 - 2*x + x^2)^(1/4)) + ((2 + 2*x - x^2)^(1/4)*Log[3 - 3*Sqrt[2]*(2 + 2*x - x^2)^(1/4) + 3*Sqrt[2 + 2*x - x^2]])/(2*Sqrt[2]*(-2 - 2*x + x^2)^(1/4))","B",42,16,26,0.6154,1,"{6742, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 297, 1162, 617, 204, 1165, 628}"
344,1,27,0,0.0232287,"\int \frac{1}{(-1+x) \sqrt[4]{2-2 x+x^2}} \, dx","Int[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",6,6,18,0.3333,1,"{694, 266, 63, 298, 203, 206}"
345,1,27,0,0.0239088,"\int \frac{1}{(1+x) \sqrt[4]{2+2 x+x^2}} \, dx","Int[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",6,6,18,0.3333,1,"{694, 266, 63, 298, 203, 206}"
346,1,29,0,0.0147911,"\int \frac{1}{x \sqrt[4]{1+x^3}} \, dx","Int[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",5,5,13,0.3846,1,"{266, 63, 298, 203, 206}"
347,1,29,0,0.0187482,"\int \frac{1}{x \sqrt{-b+a x^3}} \, dx","Int[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",3,3,17,0.1765,1,"{266, 63, 205}"
348,1,42,0,0.0252492,"\int \frac{x^5}{\sqrt{-b+a x^3}} \, dx","Int[x^5/Sqrt[-b + a*x^3],x]","\frac{2 \left(a x^3-b\right)^{3/2}}{9 a^2}+\frac{2 b \sqrt{a x^3-b}}{3 a^2}","\frac{2 \sqrt{a x^3-b} \left(a x^3+2 b\right)}{9 a^2}",1,"(2*b*Sqrt[-b + a*x^3])/(3*a^2) + (2*(-b + a*x^3)^(3/2))/(9*a^2)","A",3,2,17,0.1176,1,"{266, 43}"
349,1,46,0,0.1110567,"\int \frac{1+x}{(-1+x) \sqrt{1-x^2+x^4}} \, dx","Int[(1 + x)/((-1 + x)*Sqrt[1 - x^2 + x^4]),x]","-\tanh ^{-1}\left(\frac{x}{\sqrt{x^4-x^2+1}}\right)-\tanh ^{-1}\left(\frac{x^2+1}{2 \sqrt{x^4-x^2+1}}\right)","-2 \tanh ^{-1}\left(\frac{x}{x^2+\sqrt{x^4-x^2+1}-2 x+1}\right)",1,"-ArcTanh[x/Sqrt[1 - x^2 + x^4]] - ArcTanh[(1 + x^2)/(2*Sqrt[1 - x^2 + x^4])]","A",7,6,23,0.2609,1,"{1741, 12, 1247, 724, 206, 1698}"
350,1,35,0,0.0498008,"\int \frac{\left(-1+x^4\right) \left(1+x^4\right)}{\left(1+x^2+x^4\right)^{5/2}} \, dx","Int[((-1 + x^4)*(1 + x^4))/(1 + x^2 + x^4)^(5/2),x]","\frac{x^3}{3 \left(x^4+x^2+1\right)^{3/2}}-\frac{x}{\sqrt{x^4+x^2+1}}","-\frac{x \left(3 x^4+2 x^2+3\right)}{3 \left(x^4+x^2+1\right)^{3/2}}",1,"x^3/(3*(1 + x^2 + x^4)^(3/2)) - x/Sqrt[1 + x^2 + x^4]","A",2,2,23,0.08696,1,"{1678, 1588}"
351,0,0,0,1.0382759,"\int \frac{x^2 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(1-x^3+x^4\right)} \, dx","Int[(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,"(x*(1 - x^3)^(3/4)*Hypergeometric2F1[1/3, 3/4, 4/3, x^3])/(-1 + x^3)^(3/4) + (x^2*(1 - x^3)^(3/4)*Hypergeometric2F1[2/3, 3/4, 5/3, x^3])/(2*(-1 + x^3)^(3/4)) - Defer[Int][1/((-1 + x^3)^(3/4)*(1 - x^3 + x^4)), x] - Defer[Int][x/((-1 + x^3)^(3/4)*(1 - x^3 + x^4)), x] - 4*Defer[Int][x^2/((-1 + x^3)^(3/4)*(1 - x^3 + x^4)), x] + Defer[Int][x^3/((-1 + x^3)^(3/4)*(1 - x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
352,1,39,0,0.0510964,"\int \frac{1+2 x}{\sqrt{-4-4 x-3 x^2+2 x^3+x^4}} \, dx","Int[(1 + 2*x)/Sqrt[-4 - 4*x - 3*x^2 + 2*x^3 + x^4],x]","-\tanh ^{-1}\left(\frac{9-4 \left(x+\frac{1}{2}\right)^2}{\sqrt{16 \left(x+\frac{1}{2}\right)^4-72 \left(x+\frac{1}{2}\right)^2-47}}\right)","\log \left(x^2+\sqrt{x^4+2 x^3-3 x^2-4 x-4}+x-2\right)",1,"-ArcTanh[(9 - 4*(1/2 + x)^2)/Sqrt[-47 - 72*(1/2 + x)^2 + 16*(1/2 + x)^4]]","A",5,5,28,0.1786,1,"{1680, 12, 1107, 621, 206}"
353,1,29,0,0.019772,"\int \frac{1}{x \sqrt{-b+a x^4}} \, dx","Int[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",3,3,17,0.1765,1,"{266, 63, 205}"
354,0,0,0,1.5544573,"\int \frac{-1+2 x^6}{\left(1+x^6\right) \sqrt{1-2 x^2+x^6}} \, dx","Int[(-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,"2*Defer[Int][1/Sqrt[1 - 2*x^2 + x^6], x] - (I/2)*Defer[Int][1/((I - x)*Sqrt[1 - 2*x^2 + x^6]), x] - (I/2)*Defer[Int][1/((I + x)*Sqrt[1 - 2*x^2 + x^6]), x] - (Sqrt[1 - I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[1 - 2*x^2 + x^6]), x])/2 - (Sqrt[1 + I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[1 - 2*x^2 + x^6]), x])/2 - (Sqrt[1 - I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[1 - 2*x^2 + x^6]), x])/2 - (Sqrt[1 + I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[1 - 2*x^2 + x^6]), x])/2","F",0,0,0,0,-1,"{}"
355,0,0,0,1.1510184,"\int \frac{1+2 x^6}{\left(-1+x^6\right) \sqrt{-1-2 x^2+x^6}} \, dx","Int[(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,"2*Defer[Int][1/Sqrt[-1 - 2*x^2 + x^6], x] + Defer[Int][1/((-1 + x)*Sqrt[-1 - 2*x^2 + x^6]), x]/2 - Defer[Int][1/((1 + x)*Sqrt[-1 - 2*x^2 + x^6]), x]/2 + ((1 + I*Sqrt[3])*Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*Sqrt[-1 - 2*x^2 + x^6]), x])/2 - ((1 - I*Sqrt[3])*Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*Sqrt[-1 - 2*x^2 + x^6]), x])/2 + ((1 - I*Sqrt[3])*Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*Sqrt[-1 - 2*x^2 + x^6]), x])/2 - ((1 + I*Sqrt[3])*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*Sqrt[-1 - 2*x^2 + x^6]), x])/2","F",0,0,0,0,-1,"{}"
356,1,40,0,0.0156119,"\int x^8 \sqrt[3]{-1+x^3} \, dx","Int[x^8*(-1 + x^3)^(1/3),x]","\frac{1}{10} \left(x^3-1\right)^{10/3}+\frac{2}{7} \left(x^3-1\right)^{7/3}+\frac{1}{4} \left(x^3-1\right)^{4/3}","\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)/4 + (2*(-1 + x^3)^(7/3))/7 + (-1 + x^3)^(10/3)/10","A",3,2,13,0.1538,1,"{266, 43}"
357,1,40,0,0.015109,"\int x^8 \sqrt[4]{1+x^3} \, dx","Int[x^8*(1 + x^3)^(1/4),x]","\frac{4}{39} \left(x^3+1\right)^{13/4}-\frac{8}{27} \left(x^3+1\right)^{9/4}+\frac{4}{15} \left(x^3+1\right)^{5/4}","\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))/15 - (8*(1 + x^3)^(9/4))/27 + (4*(1 + x^3)^(13/4))/39","A",3,2,13,0.1538,1,"{266, 43}"
358,1,55,0,0.0673155,"\int \frac{1}{x^6 \sqrt[3]{-x+x^3}} \, dx","Int[1/(x^6*(-x + x^3)^(1/3)),x]","\frac{3 \left(x^3-x\right)^{2/3}}{16 x^6}+\frac{9 \left(x^3-x\right)^{2/3}}{40 x^4}+\frac{27 \left(x^3-x\right)^{2/3}}{80 x^2}","\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))/(16*x^6) + (9*(-x + x^3)^(2/3))/(40*x^4) + (27*(-x + x^3)^(2/3))/(80*x^2)","A",3,2,15,0.1333,1,"{2016, 2014}"
359,1,61,0,0.0768525,"\int \frac{1}{x^3 \sqrt[3]{-x^2+x^3}} \, dx","Int[1/(x^3*(-x^2 + x^3)^(1/3)),x]","\frac{27 \left(x^3-x^2\right)^{2/3}}{40 x^2}+\frac{9 \left(x^3-x^2\right)^{2/3}}{20 x^3}+\frac{3 \left(x^3-x^2\right)^{2/3}}{8 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*(-x^2 + x^3)^(2/3))/(8*x^4) + (9*(-x^2 + x^3)^(2/3))/(20*x^3) + (27*(-x^2 + x^3)^(2/3))/(40*x^2)","B",3,2,17,0.1176,1,"{2016, 2014}"
360,1,55,0,0.4336728,"\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)}{x^6 \sqrt[4]{-x+x^3}} \, dx","Int[((-3 + x^2)*(1 - x^2 + x^3))/(x^6*(-x + x^3)^(1/4)),x]","-\frac{4 \left(x^3-x\right)^{3/4}}{3 x^3}-\frac{4 \left(x^3-x\right)^{3/4}}{7 x^6}+\frac{4 \left(x^3-x\right)^{3/4}}{7 x^4}","-\frac{4 \left(x^3-x\right)^{3/4} \left(7 x^3-3 x^2+3\right)}{21 x^6}",1,"(-4*(-x + x^3)^(3/4))/(7*x^6) + (4*(-x + x^3)^(3/4))/(7*x^4) - (4*(-x + x^3)^(3/4))/(3*x^3)","A",26,6,30,0.2000,1,"{2052, 2025, 2011, 365, 364, 2032}"
361,1,373,0,0.9966259,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Int[(1 + x^2)/((-1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","\frac{\sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(-1-\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}","-2 \tan ^{-1}\left(\frac{\sqrt{x^3-x^2-x}}{x^2-x-1}\right)",1,"(Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1 - Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3] - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3]","C",15,8,29,0.2759,0,"{2056, 6725, 716, 1098, 934, 168, 538, 537}"
362,1,31,0,0.1455687,"\int \frac{-1+x^3}{x^3 \left(1+x^3\right) \sqrt[4]{x+x^4}} \, dx","Int[(-1 + x^3)/(x^3*(1 + x^3)*(x + x^4)^(1/4)),x]","\frac{28 x}{9 \sqrt[4]{x^4+x}}+\frac{4}{9 \sqrt[4]{x^4+x} x^2}","\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/(9*x^2*(x + x^4)^(1/4)) + (28*x)/(9*(x + x^4)^(1/4))","A",3,3,25,0.1200,1,"{2056, 453, 264}"
363,1,41,0,0.0481101,"\int \frac{\sqrt[4]{-x^2+x^4}}{x^6} \, dx","Int[(-x^2 + x^4)^(1/4)/x^6,x]","\frac{2 \left(x^4-x^2\right)^{5/4}}{9 x^7}+\frac{8 \left(x^4-x^2\right)^{5/4}}{45 x^5}","\frac{2 \sqrt[4]{x^4-x^2} \left(4 x^4+x^2-5\right)}{45 x^5}",1,"(2*(-x^2 + x^4)^(5/4))/(9*x^7) + (8*(-x^2 + x^4)^(5/4))/(45*x^5)","A",2,2,17,0.1176,1,"{2016, 2014}"
364,1,23,0,0.0526887,"\int \frac{-1+2 x}{\sqrt{1+x-2 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[1 + x - 2*x^3 + x^4],x]","-\sinh ^{-1}\left(\frac{3-4 \left(x-\frac{1}{2}\right)^2}{2 \sqrt{3}}\right)","-\log \left(-2 x^2+2 \sqrt{x^4-2 x^3+x+1}+2 x+1\right)",1,"-ArcSinh[(3 - 4*(-1/2 + x)^2)/(2*Sqrt[3])]","A",5,5,21,0.2381,1,"{1680, 12, 1107, 619, 215}"
365,1,36,0,0.1558618,"\int \frac{1+x}{(-1+x) x \sqrt[4]{-x^3+x^4}} \, dx","Int[(1 + x)/((-1 + x)*x*(-x^3 + x^4)^(1/4)),x]","\frac{4}{3 \sqrt[4]{x^4-x^3}}-\frac{28 x}{3 \sqrt[4]{x^4-x^3}}","-\frac{4 (7 x-1) \left(x^4-x^3\right)^{3/4}}{3 (x-1) x^3}",1,"4/(3*(-x^3 + x^4)^(1/4)) - (28*x)/(3*(-x^3 + x^4)^(1/4))","A",3,3,25,0.1200,1,"{2056, 78, 37}"
366,1,55,0,0.3575758,"\int \frac{\left(3+x^4\right) \left(-1-x^3+x^4\right)}{x^6 \sqrt[4]{-x+x^5}} \, dx","Int[((3 + x^4)*(-1 - x^3 + x^4))/(x^6*(-x + x^5)^(1/4)),x]","-\frac{4 \left(x^5-x\right)^{3/4}}{7 x^6}-\frac{4 \left(x^5-x\right)^{3/4}}{3 x^3}+\frac{4 \left(x^5-x\right)^{3/4}}{7 x^2}","\frac{4 \left(3 x^4-7 x^3-3\right) \left(x^5-x\right)^{3/4}}{21 x^6}",1,"(-4*(-x + x^5)^(3/4))/(7*x^6) - (4*(-x + x^5)^(3/4))/(3*x^3) + (4*(-x + x^5)^(3/4))/(7*x^2)","A",21,5,30,0.1667,1,"{2052, 2025, 2032, 365, 364}"
367,1,55,0,0.3495014,"\int \frac{\left(3+x^4\right) \left(-1+x^3+x^4\right)}{x^6 \sqrt[4]{-x+x^5}} \, dx","Int[((3 + x^4)*(-1 + x^3 + x^4))/(x^6*(-x + x^5)^(1/4)),x]","-\frac{4 \left(x^5-x\right)^{3/4}}{7 x^6}+\frac{4 \left(x^5-x\right)^{3/4}}{3 x^3}+\frac{4 \left(x^5-x\right)^{3/4}}{7 x^2}","\frac{4 \left(3 x^4+7 x^3-3\right) \left(x^5-x\right)^{3/4}}{21 x^6}",1,"(-4*(-x + x^5)^(3/4))/(7*x^6) + (4*(-x + x^5)^(3/4))/(3*x^3) + (4*(-x + x^5)^(3/4))/(7*x^2)","A",21,5,28,0.1786,1,"{2052, 2025, 2032, 365, 364}"
368,0,0,0,1.2228565,"\int \frac{-1+3 x^4}{\left(1-a x+x^4\right) \sqrt{x+x^5}} \, dx","Int[(-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,"(3*x^2*Sqrt[(1 + x)^2/x]*Sqrt[-((1 + x^4)/x^2)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x + Sqrt[2]*x^2)/x)]/2], -2*(1 - Sqrt[2])])/(Sqrt[2 + Sqrt[2]]*(1 + x)*Sqrt[x + x^5]) - (3*Sqrt[-((1 - x)^2/x)]*x^2*Sqrt[-((1 + x^4)/x^2)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x + Sqrt[2]*x^2)/x]/2], -2*(1 - Sqrt[2])])/(Sqrt[2 + Sqrt[2]]*(1 - x)*Sqrt[x + x^5]) + (8*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][1/((-1 + a*x^2 - x^8)*Sqrt[1 + x^8]), x], x, Sqrt[x]])/Sqrt[x + x^5] - (6*a*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^2/((-1 + a*x^2 - x^8)*Sqrt[1 + x^8]), x], x, Sqrt[x]])/Sqrt[x + x^5]","F",0,0,0,0,-1,"{}"
369,0,0,0,1.1208401,"\int \frac{-1+3 x^4}{\left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","Int[(-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,"(3*x^2*Sqrt[(1 + x)^2/x]*Sqrt[-((1 + x^4)/x^2)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x + Sqrt[2]*x^2)/x)]/2], -2*(1 - Sqrt[2])])/(Sqrt[2 + Sqrt[2]]*a*(1 + x)*Sqrt[x + x^5]) - (3*Sqrt[-((1 - x)^2/x)]*x^2*Sqrt[-((1 + x^4)/x^2)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x + Sqrt[2]*x^2)/x]/2], -2*(1 - Sqrt[2])])/(Sqrt[2 + Sqrt[2]]*a*(1 - x)*Sqrt[x + x^5]) - (8*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][1/(Sqrt[1 + x^8]*(a - x^2 + a*x^8)), x], x, Sqrt[x]])/Sqrt[x + x^5] + (6*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + x^8]*(a - x^2 + a*x^8)), x], x, Sqrt[x]])/(a*Sqrt[x + x^5])","F",0,0,0,0,-1,"{}"
370,0,0,0,1.0050719,"\int \frac{\sqrt{-1+x^6} \left(2+x^6\right)}{x^3 \left(-1-x^4+x^6\right)} \, dx","Int[(Sqrt[-1 + x^6]*(2 + x^6))/(x^3*(-1 - x^4 + x^6)),x]","\int \frac{\sqrt{-1+x^6} \left(2+x^6\right)}{x^3 \left(-1-x^4+x^6\right)} \, dx","\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 + (3*Sqrt[-1 + x^6])/(1 - Sqrt[3] - x^2) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - Sqrt[3] - x^2)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x^2)/(1 - Sqrt[3] - x^2)], -7 + 4*Sqrt[3]])/(2*Sqrt[-((1 - x^2)/(1 - Sqrt[3] - x^2)^2)]*Sqrt[-1 + x^6]) + (Sqrt[2]*3^(3/4)*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - Sqrt[3] - x^2)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x^2)/(1 - Sqrt[3] - x^2)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x^2)/(1 - Sqrt[3] - x^2)^2)]*Sqrt[-1 + x^6]) - Defer[Subst][Defer[Int][Sqrt[-1 + x^3]/(-1 - x^2 + x^3), x], x, x^2] + (3*Defer[Subst][Defer[Int][(x*Sqrt[-1 + x^3])/(-1 - x^2 + x^3), x], x, x^2])/2","F",0,0,0,0,-1,"{}"
371,0,0,0,0.8383025,"\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right)}{x^2 \left(-1-x^2+x^6\right)} \, dx","Int[(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,"Sqrt[1 - x^6]/x + (3*(1 + Sqrt[3])*x*Sqrt[1 - x^6])/(2*(1 - (1 + Sqrt[3])*x^2)) - (3*3^(1/4)*x*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - (1 + Sqrt[3])*x^2)^2]*EllipticE[ArcCos[(1 - (1 - Sqrt[3])*x^2)/(1 - (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(2*Sqrt[-((x^2*(1 - x^2))/(1 - (1 + Sqrt[3])*x^2)^2)]*Sqrt[1 - x^6]) - (3^(3/4)*(1 - Sqrt[3])*x*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x^2)/(1 - (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(4*Sqrt[-((x^2*(1 - x^2))/(1 - (1 + Sqrt[3])*x^2)^2)]*Sqrt[1 - x^6]) + Defer[Int][Sqrt[1 - x^6]/(1 + x^2 - x^6), x] + 3*Defer[Int][(x^4*Sqrt[1 - x^6])/(-1 - x^2 + x^6), x]","F",0,0,0,0,-1,"{}"
372,1,31,0,0.0130302,"\int \frac{1}{x^4 \sqrt{-1+x^3}} \, dx","Int[1/(x^4*Sqrt[-1 + x^3]),x]","\frac{\sqrt{x^3-1}}{3 x^3}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^3-1}\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]/(3*x^3) + ArcTan[Sqrt[-1 + x^3]]/3","A",4,4,13,0.3077,1,"{266, 51, 63, 203}"
373,1,27,0,0.0748549,"\int \frac{-2-2 x+x^2}{\left(3-x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(-2 - 2*x + x^2)/((3 - x + x^2)*Sqrt[-1 + x^3]),x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} (1-x)}{\sqrt{x^3-1}}\right)","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3-1}}{x^2+x+1}\right)",1,"Sqrt[2]*ArcTanh[(Sqrt[2]*(1 - x))/Sqrt[-1 + x^3]]","A",2,2,28,0.07143,1,"{2145, 206}"
374,1,27,0,0.0700098,"\int \frac{-2-2 x+x^2}{\left(-1+3 x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(-2 - 2*x + x^2)/((-1 + 3*x + x^2)*Sqrt[-1 + x^3]),x]","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} (1-x)}{\sqrt{x^3-1}}\right)","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3-1}}{x^2+x+1}\right)",1,"Sqrt[2]*ArcTan[(Sqrt[2]*(1 - x))/Sqrt[-1 + x^3]]","A",2,2,28,0.07143,1,"{2145, 203}"
375,1,31,0,0.0103675,"\int \frac{\sqrt{-1+x^3}}{x^4} \, dx","Int[Sqrt[-1 + x^3]/x^4,x]","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{\sqrt{x^3-1}}{3 x^3}","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{\sqrt{x^3-1}}{3 x^3}",1,"-1/3*Sqrt[-1 + x^3]/x^3 + ArcTan[Sqrt[-1 + x^3]]/3","A",4,4,13,0.3077,1,"{266, 47, 63, 203}"
376,1,31,0,0.0118009,"\int \frac{1}{x^4 \sqrt{1+x^3}} \, dx","Int[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",4,4,13,0.3077,1,"{266, 51, 63, 207}"
377,1,23,0,0.0581684,"\int \frac{1+x}{(-2+x) \sqrt{1+x^3}} \, dx","Int[(1 + x)/((-2 + x)*Sqrt[1 + x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\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,"(-2*ArcTanh[(1 + x)^2/(3*Sqrt[1 + x^3])])/3","A",2,2,18,0.1111,1,"{2138, 206}"
378,1,31,0,0.0119014,"\int \frac{\sqrt{1+x^3}}{x^4} \, dx","Int[Sqrt[1 + x^3]/x^4,x]","-\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}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"-1/3*Sqrt[1 + x^3]/x^3 - ArcTanh[Sqrt[1 + x^3]]/3","A",4,4,13,0.3077,1,"{266, 47, 63, 207}"
379,0,0,0,0.7357294,"\int \frac{1+x}{(-1+2 x) \sqrt{x+x^4}} \, dx","Int[(1 + x)/((-1 + 2*x)*Sqrt[x + x^4]),x]","\int \frac{1+x}{(-1+2 x) \sqrt{x+x^4}} \, dx","-\frac{2}{3} \tanh ^{-1}\left(\frac{\frac{x^2}{3}+\frac{2 x}{3}+\frac{1}{3}}{\sqrt{x^4+x}}\right)",1,"(x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4]) - (3*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((1 - Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[x + x^4]) - (3*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((1 + Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[x + x^4])","F",0,0,0,0,-1,"{}"
380,1,33,0,0.0403291,"\int \frac{-1+x}{\sqrt{-5+4 x^2-4 x^3+x^4}} \, dx","Int[(-1 + x)/Sqrt[-5 + 4*x^2 - 4*x^3 + x^4],x]","-\frac{1}{2} \tanh ^{-1}\left(\frac{1-(x-1)^2}{\sqrt{(x-1)^4-2 (x-1)^2-4}}\right)","\frac{1}{2} \log \left(x^2+\sqrt{x^4-4 x^3+4 x^2-5}-2 x\right)",1,"-1/2*ArcTanh[(1 - (-1 + x)^2)/Sqrt[-4 - 2*(-1 + x)^2 + (-1 + x)^4]]","A",4,4,23,0.1739,1,"{1680, 1107, 621, 206}"
381,1,20,0,0.0481438,"\int \frac{2+x}{\sqrt{13+16 x^2+8 x^3+x^4}} \, dx","Int[(2 + x)/Sqrt[13 + 16*x^2 + 8*x^3 + x^4],x]","-\frac{1}{2} \sinh ^{-1}\left(\frac{4-(x+2)^2}{\sqrt{13}}\right)","\frac{1}{2} \log \left(x^2+\sqrt{x^4+8 x^3+16 x^2+13}+4 x\right)",1,"-1/2*ArcSinh[(4 - (2 + x)^2)/Sqrt[13]]","A",4,4,23,0.1739,1,"{1680, 1107, 619, 215}"
382,1,30,0,0.0184528,"\int \frac{x}{\sqrt{b+a x^4}} \, dx","Int[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",3,3,13,0.2308,1,"{275, 217, 206}"
383,1,31,0,0.0107672,"\int \frac{1}{x^7 \sqrt{-1+x^6}} \, dx","Int[1/(x^7*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1}}{6 x^6}+\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\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]/(6*x^6) + ArcTan[Sqrt[-1 + x^6]]/6","A",4,4,13,0.3077,1,"{266, 51, 63, 203}"
384,1,31,0,0.0109591,"\int \frac{\sqrt{-1+x^6}}{x^7} \, dx","Int[Sqrt[-1 + x^6]/x^7,x]","\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\sqrt{x^6-1}}{6 x^6}","\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\sqrt{x^6-1}}{6 x^6}",1,"-1/6*Sqrt[-1 + x^6]/x^6 + ArcTan[Sqrt[-1 + x^6]]/6","A",4,4,13,0.3077,1,"{266, 47, 63, 203}"
385,1,31,0,0.0154821,"\int \frac{-1+x^6}{x^7 \sqrt{1+x^6}} \, dx","Int[(-1 + x^6)/(x^7*Sqrt[1 + x^6]),x]","\frac{\sqrt{x^6+1}}{6 x^6}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^6+1}\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]/(6*x^6) - ArcTanh[Sqrt[1 + x^6]]/2","A",4,4,18,0.2222,1,"{446, 78, 63, 207}"
386,1,31,0,0.0124354,"\int \frac{\sqrt{1+x^6}}{x^7} \, dx","Int[Sqrt[1 + x^6]/x^7,x]","-\frac{\sqrt{x^6+1}}{6 x^6}-\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*Sqrt[1 + x^6]/x^6 - ArcTanh[Sqrt[1 + x^6]]/6","A",4,4,13,0.3077,1,"{266, 47, 63, 207}"
387,1,31,0,0.1065559,"\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","Int[((2 + x^6)*(1 - 2*x^6 + x^8 + x^12))/(x^10*(-1 + x^6)^(3/4)),x]","\frac{2 \sqrt[4]{x^6-1}}{x}+\frac{2 \left(x^6-1\right)^{9/4}}{9 x^9}","\frac{2 \sqrt[4]{x^6-1} \left(x^{12}+9 x^8-2 x^6+1\right)}{9 x^9}",1,"(2*(-1 + x^6)^(1/4))/x + (2*(-1 + x^6)^(9/4))/(9*x^9)","A",7,5,31,0.1613,1,"{1833, 1584, 449, 1586, 1478}"
388,0,0,0,2.4107789,"\int \frac{-1+2 x+2 x^2}{\left(1-x+3 x^2\right) \sqrt{-x+x^4}} \, dx","Int[(-1 + 2*x + 2*x^2)/((1 - x + 3*x^2)*Sqrt[-x + x^4]),x]","\int \frac{-1+2 x+2 x^2}{\left(1-x+3 x^2\right) \sqrt{-x+x^4}} \, dx","\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{x^4-x}}{x^2+x+1}\right)",1,"(2*(1 - x)*x*Sqrt[(1 + x + x^2)/(1 - (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x)/(1 - (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3*3^(1/4)*Sqrt[-(((1 - x)*x)/(1 - (1 + Sqrt[3])*x)^2)]*Sqrt[-x + x^4]) - (2*(4 - I*Sqrt[11])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 - I*Sqrt[11]] - Sqrt[6]*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/(3*Sqrt[1 - I*Sqrt[11]]*Sqrt[-x + x^4]) - (2*(4 + I*Sqrt[11])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 + I*Sqrt[11]] - Sqrt[6]*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/(3*Sqrt[1 + I*Sqrt[11]]*Sqrt[-x + x^4]) - (2*(4 - I*Sqrt[11])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 - I*Sqrt[11]] + Sqrt[6]*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/(3*Sqrt[1 - I*Sqrt[11]]*Sqrt[-x + x^4]) - (2*(4 + I*Sqrt[11])*Sqrt[x]*Sqrt[-1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[1 + I*Sqrt[11]] + Sqrt[6]*x)*Sqrt[-1 + x^6]), x], x, Sqrt[x]])/(3*Sqrt[1 + I*Sqrt[11]]*Sqrt[-x + x^4])","F",0,0,0,0,-1,"{}"
389,1,35,0,0.1568294,"\int \frac{1+x^3}{x^3 \left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Int[(1 + x^3)/(x^3*(-1 + x^3)*(-x + x^4)^(1/4)),x]","\frac{4}{9 x^2 \sqrt[4]{x^4-x}}-\frac{28 x}{9 \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/(9*x^2*(-x + x^4)^(1/4)) - (28*x)/(9*(-x + x^4)^(1/4))","A",3,3,27,0.1111,1,"{2056, 453, 264}"
390,0,0,0,2.0763512,"\int \frac{-1-2 x+2 x^2}{\left(-1+3 x+x^2\right) \sqrt{x+x^4}} \, dx","Int[(-1 - 2*x + 2*x^2)/((-1 + 3*x + x^2)*Sqrt[x + x^4]),x]","\int \frac{-1-2 x+2 x^2}{\left(-1+3 x+x^2\right) \sqrt{x+x^4}} \, dx","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^4+x}}{x^2-x+1}\right)",1,"(2*x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4]) + (Sqrt[-17 + 5*Sqrt[13]]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[-3 + Sqrt[13]] - Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4] - (I*Sqrt[17 + 5*Sqrt[13]]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((I*Sqrt[3 + Sqrt[13]] - Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4] + (Sqrt[-17 + 5*Sqrt[13]]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[-3 + Sqrt[13]] + Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4] - (I*Sqrt[17 + 5*Sqrt[13]]*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((I*Sqrt[3 + Sqrt[13]] + Sqrt[2]*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/Sqrt[x + x^4]","F",0,0,0,0,-1,"{}"
391,1,35,0,0.161882,"\int \frac{-1+x^2}{x^2 \left(1+x^2\right) \sqrt[4]{x^2+x^4}} \, dx","Int[(-1 + x^2)/(x^2*(1 + x^2)*(x^2 + x^4)^(1/4)),x]","\frac{14 x}{3 \sqrt[4]{x^4+x^2}}+\frac{2}{3 \sqrt[4]{x^4+x^2} x}","\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/(3*x*(x^2 + x^4)^(1/4)) + (14*x)/(3*(x^2 + x^4)^(1/4))","A",3,3,27,0.1111,1,"{2056, 453, 264}"
392,1,37,0,0.0511059,"\int \frac{-1+2 x}{\sqrt{-8 x+9 x^2-2 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[-8*x + 9*x^2 - 2*x^3 + x^4],x]","\tanh ^{-1}\left(\frac{4 \left(x-\frac{1}{2}\right)^2+15}{\sqrt{16 \left(x-\frac{1}{2}\right)^4+120 \left(x-\frac{1}{2}\right)^2-31}}\right)","-\log \left(-x^2+\sqrt{x^4-2 x^3+9 x^2-8 x}+x-4\right)",1,"ArcTanh[(15 + 4*(-1/2 + x)^2)/Sqrt[-31 + 120*(-1/2 + x)^2 + 16*(-1/2 + x)^4]]","A",5,5,27,0.1852,1,"{1680, 12, 1107, 621, 206}"
393,0,0,0,0.0261032,"\int \frac{-a+2 x}{\left(-1+b-a x+x^2\right) \sqrt[4]{b-a x+x^2}} \, dx","Int[(-a + 2*x)/((-1 + b - a*x + x^2)*(b - a*x + x^2)^(1/4)),x]","\int \frac{-a+2 x}{\left(-1+b-a x+x^2\right) \sqrt[4]{b-a x+x^2}} \, dx","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,"Defer[Int][(-a + 2*x)/((-1 + b - a*x + x^2)*(b - a*x + x^2)^(1/4)), x]","F",0,0,0,0,-1,"{}"
394,1,49,0,0.0159806,"\int \frac{\left(-4+x^3\right) \left(-1+x^3\right)^{2/3}}{x^{12}} \, dx","Int[((-4 + x^3)*(-1 + x^3)^(2/3))/x^12,x]","-\frac{4 \left(x^3-1\right)^{5/3}}{11 x^{11}}-\frac{13 \left(x^3-1\right)^{5/3}}{88 x^8}-\frac{39 \left(x^3-1\right)^{5/3}}{440 x^5}","\frac{\left(x^3-1\right)^{2/3} \left(-39 x^9-26 x^6-95 x^3+160\right)}{440 x^{11}}",1,"(-4*(-1 + x^3)^(5/3))/(11*x^11) - (13*(-1 + x^3)^(5/3))/(88*x^8) - (39*(-1 + x^3)^(5/3))/(440*x^5)","A",3,3,18,0.1667,1,"{453, 271, 264}"
395,1,26,0,0.0706729,"\int \frac{-2+2 x+x^2}{\left(-1-3 x+x^2\right) \sqrt{1+x^3}} \, dx","Int[(-2 + 2*x + x^2)/((-1 - 3*x + x^2)*Sqrt[1 + x^3]),x]","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} (x+1)}{\sqrt{x^3+1}}\right)","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+1}}{x^2-x+1}\right)",1,"-(Sqrt[2]*ArcTanh[(Sqrt[2]*(1 + x))/Sqrt[1 + x^3]])","A",2,2,28,0.07143,1,"{2145, 206}"
396,1,26,0,0.0784148,"\int \frac{-2+2 x+x^2}{\left(3-x+2 x^2\right) \sqrt{1+x^3}} \, dx","Int[(-2 + 2*x + x^2)/((3 - x + 2*x^2)*Sqrt[1 + x^3]),x]","-\sqrt{2} \tan ^{-1}\left(\frac{x+1}{\sqrt{2} \sqrt{x^3+1}}\right)","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{x^3+1}}{\sqrt{2} \left(x^2-x+1\right)}\right)",1,"-(Sqrt[2]*ArcTan[(1 + x)/(Sqrt[2]*Sqrt[1 + x^3])])","A",2,2,30,0.06667,1,"{2145, 203}"
397,1,26,0,0.0727343,"\int \frac{-2+2 x+x^2}{\left(2-4 x+3 x^2\right) \sqrt{1+x^3}} \, dx","Int[(-2 + 2*x + x^2)/((2 - 4*x + 3*x^2)*Sqrt[1 + x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{x+1}{\sqrt{3} \sqrt{x^3+1}}\right)}{\sqrt{3}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^3+1}}{\sqrt{3} \left(x^2-x+1\right)}\right)}{\sqrt{3}}",1,"(-2*ArcTanh[(1 + x)/(Sqrt[3]*Sqrt[1 + x^3])])/Sqrt[3]","A",2,2,30,0.06667,1,"{2145, 206}"
398,1,49,0,0.0138763,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^{11}} \, dx","Int[((-1 + x^3)*(1 + x^3)^(1/3))/x^11,x]","\frac{\left(x^3+1\right)^{4/3}}{10 x^{10}}-\frac{8 \left(x^3+1\right)^{4/3}}{35 x^7}+\frac{6 \left(x^3+1\right)^{4/3}}{35 x^4}","\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)/(10*x^10) - (8*(1 + x^3)^(4/3))/(35*x^7) + (6*(1 + x^3)^(4/3))/(35*x^4)","A",3,3,18,0.1667,1,"{453, 271, 264}"
399,1,49,0,0.0130518,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^{11}} \, dx","Int[((-1 + x^3)^(1/3)*(1 + x^3))/x^11,x]","\frac{\left(x^3-1\right)^{4/3}}{10 x^{10}}+\frac{8 \left(x^3-1\right)^{4/3}}{35 x^7}+\frac{6 \left(x^3-1\right)^{4/3}}{35 x^4}","\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)/(10*x^10) + (8*(-1 + x^3)^(4/3))/(35*x^7) + (6*(-1 + x^3)^(4/3))/(35*x^4)","A",3,3,18,0.1667,1,"{453, 271, 264}"
400,1,70,0,0.1935878,"\int \frac{-1-2 x+x^2+3 x^3}{\sqrt[4]{-1+3 x-3 x^2+x^3}} \, dx","Int[(-1 - 2*x + x^2 + 3*x^3)/(-1 + 3*x - 3*x^2 + x^3)^(1/4),x]","\frac{12 (1-x)^4}{13 \sqrt[4]{(x-1)^3}}+\frac{36 (1-x)^2}{5 \sqrt[4]{(x-1)^3}}-\frac{4 (1-x)}{\sqrt[4]{(x-1)^3}}+\frac{40}{9} \left((x-1)^3\right)^{3/4}","\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))/((-1 + x)^3)^(1/4) + (36*(1 - x)^2)/(5*((-1 + x)^3)^(1/4)) + (12*(1 - x)^4)/(13*((-1 + x)^3)^(1/4)) + (40*((-1 + x)^3)^(3/4))/9","B",17,6,31,0.1935,1,"{6742, 2067, 15, 30, 2081, 43}"
401,1,72,0,0.1850673,"\int \sqrt[4]{-1+3 x-3 x^2+x^3} \left(-1-2 x+x^2+3 x^3\right) \, dx","Int[(-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3),x]","\frac{12}{19} \sqrt[4]{(x-1)^3} (1-x)^4+\frac{36}{11} \sqrt[4]{(x-1)^3} (1-x)^2-\frac{4}{7} \sqrt[4]{(x-1)^3} (1-x)+\frac{8}{3} \left((x-1)^3\right)^{5/4}","\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))/7 + (36*(1 - x)^2*((-1 + x)^3)^(1/4))/11 + (12*(1 - x)^4*((-1 + x)^3)^(1/4))/19 + (8*((-1 + x)^3)^(5/4))/3","B",17,6,31,0.1935,1,"{6742, 2067, 15, 30, 2081, 43}"
402,0,0,0,1.224012,"\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","Int[((-2*b + a*x^3)*Sqrt[b + a*x^3])/(x^2*(b - x^2 + a*x^3)),x]","\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","\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 - (6*a^(1/3)*Sqrt[b + a*x^3])/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*(b^(1/3) + a^(1/3)*x)*Sqrt[(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*b^(1/3) + a^(1/3)*x)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)], -7 - 4*Sqrt[3]])/(Sqrt[(b^(1/3)*(b^(1/3) + a^(1/3)*x))/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*Sqrt[b + a*x^3]) - (2*Sqrt[2]*3^(3/4)*a^(1/3)*b^(1/3)*(b^(1/3) + a^(1/3)*x)*Sqrt[(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*b^(1/3) + a^(1/3)*x)/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)], -7 - 4*Sqrt[3]])/(Sqrt[(b^(1/3)*(b^(1/3) + a^(1/3)*x))/((1 + Sqrt[3])*b^(1/3) + a^(1/3)*x)^2]*Sqrt[b + a*x^3]) - 2*Defer[Int][Sqrt[b + a*x^3]/(b - x^2 + a*x^3), x] + 3*a*Defer[Int][(x*Sqrt[b + a*x^3])/(b - x^2 + a*x^3), x]","F",0,0,0,0,-1,"{}"
403,1,33,0,0.0054546,"\int \frac{1}{\sqrt[4]{1+x^4}} \, dx","Int[(1 + x^4)^(-1/4),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)","\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 + ArcTanh[x/(1 + x^4)^(1/4)]/2","A",4,4,9,0.4444,1,"{240, 212, 206, 203}"
404,0,0,0,2.4876012,"\int \frac{-1-2 x+2 x^2}{\left(1+2 x+4 x^2\right) \sqrt{x+x^4}} \, dx","Int[(-1 - 2*x + 2*x^2)/((1 + 2*x + 4*x^2)*Sqrt[x + x^4]),x]","\int \frac{-1-2 x+2 x^2}{\left(1+2 x+4 x^2\right) \sqrt{x+x^4}} \, dx","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x^4+x}}{x^2-x+1}\right)}{\sqrt{3}}",1,"(x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4]) + (Sqrt[3]*(I + Sqrt[3])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[3]] - 2*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[-1 - I*Sqrt[3]]*Sqrt[x + x^4]) - (Sqrt[3]*(I - Sqrt[3])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[3]] - 2*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[I*(I + Sqrt[3])]*Sqrt[x + x^4]) + (Sqrt[3]*(I + Sqrt[3])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[-1 - I*Sqrt[3]] + 2*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[-1 - I*Sqrt[3]]*Sqrt[x + x^4]) - (Sqrt[3]*(I - Sqrt[3])*Sqrt[x]*Sqrt[1 + x^3]*Defer[Subst][Defer[Int][1/((Sqrt[-1 + I*Sqrt[3]] + 2*x)*Sqrt[1 + x^6]), x], x, Sqrt[x]])/(2*Sqrt[I*(I + Sqrt[3])]*Sqrt[x + x^4])","F",0,0,0,0,-1,"{}"
405,1,33,0,0.0204888,"\int \sqrt{x+x^4} \, dx","Int[Sqrt[x + x^4],x]","\frac{1}{3} \sqrt{x^4+x} x+\frac{1}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)","\frac{1}{3} \sqrt{x^4+x} x+\frac{1}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)",1,"(x*Sqrt[x + x^4])/3 + ArcTanh[x^2/Sqrt[x + x^4]]/3","A",3,3,9,0.3333,1,"{2004, 2029, 206}"
406,1,89,0,0.023555,"\int \frac{1}{\sqrt[4]{-x^2+x^4}} \, dx","Int[(-x^2 + x^4)^(-1/4),x]","\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}+\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}","\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)])/(-x^2 + x^4)^(1/4) + (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4)","B",6,6,13,0.4615,1,"{2011, 329, 240, 212, 206, 203}"
407,1,489,0,0.6406641,"\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(-b-a x^2+x^4\right)} \, dx","Int[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(-b - a*x^2 + x^4)),x]","\frac{\sqrt[4]{b} \left(a-\sqrt{a^2+4 b}\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{2} \sqrt{b}}{\sqrt{a^2-\sqrt{a^2+4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} x \sqrt{-a \sqrt{a^2+4 b}+a^2+2 b}}-\frac{\sqrt[4]{b} \left(a-\sqrt{a^2+4 b}\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{2} \sqrt{b}}{\sqrt{a^2-\sqrt{a^2+4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} x \sqrt{-a \sqrt{a^2+4 b}+a^2+2 b}}+\frac{\sqrt[4]{b} \left(\sqrt{a^2+4 b}+a\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{2} \sqrt{b}}{\sqrt{a^2+\sqrt{a^2+4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} x \sqrt{a \sqrt{a^2+4 b}+a^2+2 b}}-\frac{\sqrt[4]{b} \left(\sqrt{a^2+4 b}+a\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{2} \sqrt{b}}{\sqrt{a^2+\sqrt{a^2+4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} x \sqrt{a \sqrt{a^2+4 b}+a^2+2 b}}","\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,"(b^(1/4)*(a - Sqrt[a^2 + 4*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[-((Sqrt[2]*Sqrt[b])/Sqrt[a^2 + 2*b - a*Sqrt[a^2 + 4*b]]), ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(Sqrt[2]*Sqrt[a^2 + 2*b - a*Sqrt[a^2 + 4*b]]*x) - (b^(1/4)*(a - Sqrt[a^2 + 4*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[(Sqrt[2]*Sqrt[b])/Sqrt[a^2 + 2*b - a*Sqrt[a^2 + 4*b]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(Sqrt[2]*Sqrt[a^2 + 2*b - a*Sqrt[a^2 + 4*b]]*x) + (b^(1/4)*(a + Sqrt[a^2 + 4*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[-((Sqrt[2]*Sqrt[b])/Sqrt[a^2 + 2*b + a*Sqrt[a^2 + 4*b]]), ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(Sqrt[2]*Sqrt[a^2 + 2*b + a*Sqrt[a^2 + 4*b]]*x) - (b^(1/4)*(a + Sqrt[a^2 + 4*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[(Sqrt[2]*Sqrt[b])/Sqrt[a^2 + 2*b + a*Sqrt[a^2 + 4*b]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(Sqrt[2]*Sqrt[a^2 + 2*b + a*Sqrt[a^2 + 4*b]]*x)","C",10,4,36,0.1111,1,"{1692, 399, 490, 1218}"
408,1,37,0,0.052971,"\int \frac{-1+2 x}{\sqrt{-2-2 x+3 x^2-2 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[-2 - 2*x + 3*x^2 - 2*x^3 + x^4],x]","\tanh ^{-1}\left(\frac{4 \left(x-\frac{1}{2}\right)^2+3}{\sqrt{16 \left(x-\frac{1}{2}\right)^4+24 \left(x-\frac{1}{2}\right)^2-39}}\right)","-\log \left(-x^2+\sqrt{x^4-2 x^3+3 x^2-2 x-2}+x-1\right)",1,"ArcTanh[(3 + 4*(-1/2 + x)^2)/Sqrt[-39 + 24*(-1/2 + x)^2 + 16*(-1/2 + x)^4]]","A",5,5,28,0.1786,1,"{1680, 12, 1107, 621, 206}"
409,1,37,0,0.052937,"\int \frac{-1+2 x}{\sqrt{-4-4 x+5 x^2-2 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[-4 - 4*x + 5*x^2 - 2*x^3 + x^4],x]","\tanh ^{-1}\left(\frac{4 \left(x-\frac{1}{2}\right)^2+7}{\sqrt{16 \left(x-\frac{1}{2}\right)^4+56 \left(x-\frac{1}{2}\right)^2-79}}\right)","-\log \left(-x^2+\sqrt{x^4-2 x^3+5 x^2-4 x-4}+x-2\right)",1,"ArcTanh[(7 + 4*(-1/2 + x)^2)/Sqrt[-79 + 56*(-1/2 + x)^2 + 16*(-1/2 + x)^4]]","A",5,5,28,0.1786,1,"{1680, 12, 1107, 621, 206}"
410,1,73,0,0.102625,"\int \frac{1}{x^4 \sqrt[4]{x^3+x^4}} \, dx","Int[1/(x^4*(x^3 + x^4)^(1/4)),x]","\frac{512 \left(x^4+x^3\right)^{3/4}}{1155 x^3}-\frac{128 \left(x^4+x^3\right)^{3/4}}{385 x^4}-\frac{4 \left(x^4+x^3\right)^{3/4}}{15 x^6}+\frac{16 \left(x^4+x^3\right)^{3/4}}{55 x^5}","\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 + x^4)^(3/4))/(15*x^6) + (16*(x^3 + x^4)^(3/4))/(55*x^5) - (128*(x^3 + x^4)^(3/4))/(385*x^4) + (512*(x^3 + x^4)^(3/4))/(1155*x^3)","B",4,2,15,0.1333,1,"{2016, 2014}"
411,1,32,0,0.0194517,"\int \frac{x}{\sqrt{-b+a x^4}} \, dx","Int[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",3,3,15,0.2000,1,"{275, 217, 206}"
412,1,49,0,0.0312258,"\int \frac{\left(1+x^3\right)^{2/3} \left(1-x^3+2 x^6\right)}{x^{12}} \, dx","Int[((1 + x^3)^(2/3)*(1 - x^3 + 2*x^6))/x^12,x]","-\frac{\left(x^3+1\right)^{5/3}}{11 x^{11}}+\frac{17 \left(x^3+1\right)^{5/3}}{88 x^8}-\frac{227 \left(x^3+1\right)^{5/3}}{440 x^5}","\frac{\left(x^3+1\right)^{2/3} \left(-227 x^9-142 x^6+45 x^3-40\right)}{440 x^{11}}",1,"-1/11*(1 + x^3)^(5/3)/x^11 + (17*(1 + x^3)^(5/3))/(88*x^8) - (227*(1 + x^3)^(5/3))/(440*x^5)","A",4,4,25,0.1600,1,"{1486, 453, 271, 264}"
413,0,0,0,2.093492,"\int \frac{\left(3+x^4\right) \sqrt{x-x^5}}{1-2 x^4-x^6+x^8} \, dx","Int[((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,"(-3*Sqrt[x - x^5]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 - x^8])/(-1 - x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 - x^4]) + (4*Sqrt[x - x^5]*Defer[Subst][Defer[Int][(x^4*Sqrt[1 - x^8])/(-1 - x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 - x^4]) - (3*Sqrt[x - x^5]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 - x^8])/(-1 + x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 - x^4]) - (4*Sqrt[x - x^5]*Defer[Subst][Defer[Int][(x^4*Sqrt[1 - x^8])/(-1 + x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 - x^4])","F",0,0,0,0,-1,"{}"
414,1,47,0,0.0665261,"\int \frac{-1+x^{16}}{x^8 \sqrt{-1+x^4}} \, dx","Int[(-1 + x^16)/(x^8*Sqrt[-1 + x^4]),x]","\frac{1}{7} x \left(x^4-1\right)^{3/2}+\frac{\left(x^4-1\right)^{3/2}}{7 x^7}+\frac{8 \left(x^4-1\right)^{3/2}}{21 x^3}","\frac{\sqrt{x^4-1} \left(3 x^{12}+5 x^8-5 x^4-3\right)}{21 x^7}",1,"(-1 + x^4)^(3/2)/(7*x^7) + (8*(-1 + x^4)^(3/2))/(21*x^3) + (x*(-1 + x^4)^(3/2))/7","A",5,5,18,0.2778,1,"{1586, 1835, 1585, 1486, 449}"
415,1,19,0,0.2891944,"\int \frac{(-1+x)^{3/2}+(1+x)^{3/2}}{(-1+x)^{3/2} (1+x)^{3/2}} \, dx","Int[((-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",2,1,30,0.03333,1,"{6688}"
416,1,56,0,0.4092448,"\int \frac{1+x}{(-1+x) \sqrt{x+x^2+x^3}} \, dx","Int[(1 + x)/((-1 + x)*Sqrt[x + x^2 + x^3]),x]","-\frac{2 \sqrt{x} \sqrt{x^2+x+1} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x}}{\sqrt{x^2+x+1}}\right)}{\sqrt{3} \sqrt{x^3+x^2+x}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)}{\sqrt{3}}",1,"(-2*Sqrt[x]*Sqrt[1 + x + x^2]*ArcTanh[(Sqrt[3]*Sqrt[x])/Sqrt[1 + x + x^2]])/(Sqrt[3]*Sqrt[x + x^2 + x^3])","A",4,4,21,0.1905,1,"{2056, 6733, 1698, 207}"
417,1,315,0,1.2114582,"\int \frac{-1+x^2}{\left(1-x+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Int[(-1 + x^2)/((1 - x + x^2)*Sqrt[x + x^2 + x^3]),x]","\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+x+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{4}\right)}{\sqrt{x^3+x^2+x}}-\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(-1;\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{\left(1+i \sqrt{3}\right) \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(-\frac{i+\sqrt{3}}{i-\sqrt{3}};\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\sqrt{x^3+x^2+x}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+x^2+x}}{x^2+x+1}\right)",1,"(Sqrt[x]*(1 + x)*Sqrt[(1 + x + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/4])/Sqrt[x + x^2 + x^3] - (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[-1, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - ((1 + I*Sqrt[3])*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[-((I + Sqrt[3])/(I - Sqrt[3])), ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/Sqrt[x + x^2 + x^3]","C",17,8,28,0.2857,0,"{2056, 6728, 716, 1103, 934, 169, 538, 537}"
418,1,52,0,0.0899629,"\int \frac{-1+x}{(1+x) \sqrt{1+x^4}} \, dx","Int[(-1 + x)/((1 + x)*Sqrt[1 + x^4]),x]","\frac{\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2+2 x+1}\right)",1,"-(ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]) + ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/Sqrt[2]","A",7,6,18,0.3333,1,"{1742, 12, 1248, 725, 206, 1699}"
419,1,53,0,0.0894378,"\int \frac{1+x}{(-1+x) \sqrt{1+x^4}} \, dx","Int[(1 + x)/((-1 + x)*Sqrt[1 + x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{\sqrt{2}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2-2 x+1}\right)",1,"-(ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2]) - ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/Sqrt[2]","A",7,6,18,0.3333,1,"{1742, 12, 1248, 725, 206, 1699}"
420,1,62,0,0.1125936,"\int \frac{1+x}{(-1+x) \sqrt{1+x^2+x^4}} \, dx","Int[(1 + x)/((-1 + x)*Sqrt[1 + x^2 + x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+x^2+1}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(x^2+1\right)}{2 \sqrt{x^4+x^2+1}}\right)}{\sqrt{3}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x^4+x^2+1}}{x^2+x+1}\right)}{\sqrt{3}}",1,"-(ArcTanh[(Sqrt[3]*x)/Sqrt[1 + x^2 + x^4]]/Sqrt[3]) - ArcTanh[(Sqrt[3]*(1 + x^2))/(2*Sqrt[1 + x^2 + x^4])]/Sqrt[3]","A",7,6,21,0.2857,1,"{1741, 12, 1247, 724, 206, 1698}"
421,0,0,0,0.4744915,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Int[(1 + x^2)/((-1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","2 \tanh ^{-1}\left(\frac{x}{x^2-\sqrt{x^4+x^3-x^2-x+1}-1}\right)",1,"Defer[Int][1/Sqrt[1 - x - x^2 + x^3 + x^4], x] + Defer[Int][1/((-1 + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x] - Defer[Int][1/((1 + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x]","F",0,0,0,0,-1,"{}"
422,0,0,0,0.058216,"\int \frac{x}{\sqrt{11-11 x-3 x^2+2 x^3+x^4}} \, dx","Int[x/Sqrt[11 - 11*x - 3*x^2 + 2*x^3 + x^4],x]","\int \frac{x}{\sqrt{11-11 x-3 x^2+2 x^3+x^4}} \, dx","\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,"Defer[Int][x/Sqrt[11 - 11*x - 3*x^2 + 2*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
423,0,0,0,0.1535965,"\int \frac{1+x}{\sqrt{2-5 x-3 x^2+2 x^3+x^4}} \, dx","Int[(1 + x)/Sqrt[2 - 5*x - 3*x^2 + 2*x^3 + x^4],x]","\int \frac{1+x}{\sqrt{2-5 x-3 x^2+2 x^3+x^4}} \, dx","\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,"Defer[Int][1/Sqrt[2 - 5*x - 3*x^2 + 2*x^3 + x^4], x] + Defer[Int][x/Sqrt[2 - 5*x - 3*x^2 + 2*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
424,0,0,0,0.067098,"\int \frac{x}{\sqrt{-3+3 x-3 x^2+2 x^3+x^4}} \, dx","Int[x/Sqrt[-3 + 3*x - 3*x^2 + 2*x^3 + x^4],x]","\int \frac{x}{\sqrt{-3+3 x-3 x^2+2 x^3+x^4}} \, dx","\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,"Defer[Int][x/Sqrt[-3 + 3*x - 3*x^2 + 2*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
425,0,0,0,1.078081,"\int \frac{\sqrt{1-x^6} \left(2+x^6\right)}{x^3 \left(-1+x^4+x^6\right)} \, dx","Int[(Sqrt[1 - x^6]*(2 + x^6))/(x^3*(-1 + x^4 + x^6)),x]","\int \frac{\sqrt{1-x^6} \left(2+x^6\right)}{x^3 \left(-1+x^4+x^6\right)} \, dx","\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 + (3*Sqrt[1 - x^6])/(1 + Sqrt[3] - x^2) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 + Sqrt[3] - x^2)^2]*EllipticE[ArcSin[(1 - Sqrt[3] - x^2)/(1 + Sqrt[3] - x^2)], -7 - 4*Sqrt[3]])/(2*Sqrt[(1 - x^2)/(1 + Sqrt[3] - x^2)^2]*Sqrt[1 - x^6]) + (Sqrt[2]*3^(3/4)*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 + Sqrt[3] - x^2)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x^2)/(1 + Sqrt[3] - x^2)], -7 - 4*Sqrt[3]])/(Sqrt[(1 - x^2)/(1 + Sqrt[3] - x^2)^2]*Sqrt[1 - x^6]) + Defer[Subst][Defer[Int][Sqrt[1 - x^3]/(-1 + x^2 + x^3), x], x, x^2] + (3*Defer[Subst][Defer[Int][(x*Sqrt[1 - x^3])/(-1 + x^2 + x^3), x], x, x^2])/2","F",0,0,0,0,-1,"{}"
426,1,35,0,0.0203599,"\int \frac{\sqrt{x}}{\left(-2+x^2\right)^{3/4}} \, dx","Int[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",5,5,15,0.3333,1,"{329, 331, 298, 203, 206}"
427,0,0,0,0.0235463,"\int \frac{a+x}{\left(-1+2 b+2 a x+x^2\right) \sqrt[4]{2 b+2 a x+x^2}} \, dx","Int[(a + x)/((-1 + 2*b + 2*a*x + x^2)*(2*b + 2*a*x + x^2)^(1/4)),x]","\int \frac{a+x}{\left(-1+2 b+2 a x+x^2\right) \sqrt[4]{2 b+2 a x+x^2}} \, dx","\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,"Defer[Int][(a + x)/((-1 + 2*b + 2*a*x + x^2)*(2*b + 2*a*x + x^2)^(1/4)), x]","F",0,0,0,0,-1,"{}"
428,1,36,0,0.0115875,"\int \frac{1}{\sqrt{c+b x+a x^2}} \, dx","Int[1/Sqrt[c + b*x + a*x^2],x]","\frac{\tanh ^{-1}\left(\frac{2 a x+b}{2 \sqrt{a} \sqrt{a x^2+b x+c}}\right)}{\sqrt{a}}","-\frac{\log \left(-2 \sqrt{a} \sqrt{a x^2+b x+c}+2 a x+b\right)}{\sqrt{a}}",1,"ArcTanh[(b + 2*a*x)/(2*Sqrt[a]*Sqrt[c + b*x + a*x^2])]/Sqrt[a]","A",2,2,14,0.1429,1,"{621, 206}"
429,1,53,0,0.019903,"\int x^{11} \sqrt[3]{-1+x^3} \, dx","Int[x^11*(-1 + x^3)^(1/3),x]","\frac{1}{13} \left(x^3-1\right)^{13/3}+\frac{3}{10} \left(x^3-1\right)^{10/3}+\frac{3}{7} \left(x^3-1\right)^{7/3}+\frac{1}{4} \left(x^3-1\right)^{4/3}","\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)/4 + (3*(-1 + x^3)^(7/3))/7 + (3*(-1 + x^3)^(10/3))/10 + (-1 + x^3)^(13/3)/13","A",3,2,13,0.1538,1,"{266, 43}"
430,1,229,0,0.9156851,"\int \frac{-1-2 x+x^2}{\left(1+2 x+3 x^2\right) \sqrt{-x+x^3}} \, dx","Int[(-1 - 2*x + x^2)/((1 + 2*x + 3*x^2)*Sqrt[-x + x^3]),x]","\frac{\sqrt{2} \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^3-x}}+\frac{2 \left(1+2 i \sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{3}{4-i \sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{3 \left(\sqrt{2}+4 i\right) \sqrt{x^3-x}}-\frac{2 \left(1-2 i \sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{3}{4+i \sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{3 \left(-\sqrt{2}+4 i\right) \sqrt{x^3-x}}","-\frac{2 \tanh ^{-1}\left(\frac{\frac{x}{\sqrt{3}}-\frac{1}{\sqrt{3}}}{\sqrt{x^3-x}}\right)}{\sqrt{3}}",1,"(Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(3*Sqrt[-x + x^3]) + (2*(1 + (2*I)*Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[3/(4 - I*Sqrt[2]), ArcSin[Sqrt[1 - x]], 1/2])/(3*(4*I + Sqrt[2])*Sqrt[-x + x^3]) - (2*(1 - (2*I)*Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[3/(4 + I*Sqrt[2]), ArcSin[Sqrt[1 - x]], 1/2])/(3*(4*I - Sqrt[2])*Sqrt[-x + x^3])","C",13,7,32,0.2188,0,"{2056, 6728, 329, 222, 933, 168, 537}"
431,0,0,0,2.6881449,"\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","Int[((-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]","\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","\frac{\sqrt{-x^4-4 x^3-5 x^2-4 x-1}}{x^2+3 x+1}",1,"(-6*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(-3 + Sqrt[5] - 2*x)^2, x])/5 + (2*(3 - Sqrt[5])*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(-3 + Sqrt[5] - 2*x)^2, x])/5 - ((1 + I*Sqrt[3])*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(1 - I*Sqrt[3] + 2*x), x])/4 - ((1 - I*Sqrt[3])*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(1 + I*Sqrt[3] + 2*x), x])/4 + ((5 - Sqrt[5])*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(3 - Sqrt[5] + 2*x), x])/20 - (6*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(3 + Sqrt[5] + 2*x)^2, x])/5 + (2*(3 + Sqrt[5])*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(3 + Sqrt[5] + 2*x)^2, x])/5 + ((5 + Sqrt[5])*Defer[Int][Sqrt[-1 - 4*x - 5*x^2 - 4*x^3 - x^4]/(3 + Sqrt[5] + 2*x), x])/20","F",0,0,0,0,-1,"{}"
432,1,25,0,0.01001,"\int \frac{-1+x^4}{x^3 \sqrt{1+x^4}} \, dx","Int[(-1 + x^4)/(x^3*Sqrt[1 + x^4]),x]","\frac{1}{2} \sinh ^{-1}\left(x^2\right)+\frac{\sqrt{x^4+1}}{2 x^2}","\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]/(2*x^2) + ArcSinh[x^2]/2","A",3,3,18,0.1667,1,"{451, 275, 215}"
433,1,47,0,0.1691896,"\int \frac{-1+x^3}{x^6 \left(1+x^3\right) \sqrt[4]{x+x^4}} \, dx","Int[(-1 + x^3)/(x^6*(1 + x^3)*(x + x^4)^(1/4)),x]","-\frac{80 x}{21 \sqrt[4]{x^4+x}}+\frac{4}{21 \sqrt[4]{x^4+x} x^5}-\frac{20}{21 \sqrt[4]{x^4+x} x^2}","-\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/(21*x^5*(x + x^4)^(1/4)) - 20/(21*x^2*(x + x^4)^(1/4)) - (80*x)/(21*(x + x^4)^(1/4))","A",4,4,25,0.1600,1,"{2056, 453, 271, 264}"
434,1,35,0,0.0351634,"\int \frac{\sqrt{x+x^4}}{x^3} \, dx","Int[Sqrt[x + x^4]/x^3,x]","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)-\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*ArcTanh[x^2/Sqrt[x + x^4]])/3","A",3,3,13,0.2308,1,"{2020, 2029, 206}"
435,1,73,0,0.0994983,"\int \frac{1}{x^8 \sqrt[4]{x^2+x^4}} \, dx","Int[1/(x^8*(x^2 + x^4)^(1/4)),x]","-\frac{2 \left(x^4+x^2\right)^{3/4}}{15 x^9}+\frac{8 \left(x^4+x^2\right)^{3/4}}{55 x^7}-\frac{64 \left(x^4+x^2\right)^{3/4}}{385 x^5}+\frac{256 \left(x^4+x^2\right)^{3/4}}{1155 x^3}","\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))/(15*x^9) + (8*(x^2 + x^4)^(3/4))/(55*x^7) - (64*(x^2 + x^4)^(3/4))/(385*x^5) + (256*(x^2 + x^4)^(3/4))/(1155*x^3)","B",4,2,15,0.1333,1,"{2016, 2014}"
436,1,37,0,0.0533894,"\int \frac{1-2 x}{\sqrt{5+5 x-4 x^2-2 x^3+x^4}} \, dx","Int[(1 - 2*x)/Sqrt[5 + 5*x - 4*x^2 - 2*x^3 + x^4],x]","\tanh ^{-1}\left(\frac{11-4 \left(x-\frac{1}{2}\right)^2}{\sqrt{16 \left(x-\frac{1}{2}\right)^4-88 \left(x-\frac{1}{2}\right)^2+101}}\right)","\log \left(-2 x^2+2 \sqrt{x^4-2 x^3-4 x^2+5 x+5}+2 x+5\right)",1,"ArcTanh[(11 - 4*(-1/2 + x)^2)/Sqrt[101 - 88*(-1/2 + x)^2 + 16*(-1/2 + x)^4]]","A",5,5,28,0.1786,1,"{1680, 12, 1107, 621, 206}"
437,1,81,0,0.1037631,"\int \frac{1}{x^4 \sqrt[4]{-x^3+x^4}} \, dx","Int[1/(x^4*(-x^3 + x^4)^(1/4)),x]","\frac{512 \left(x^4-x^3\right)^{3/4}}{1155 x^3}+\frac{128 \left(x^4-x^3\right)^{3/4}}{385 x^4}+\frac{4 \left(x^4-x^3\right)^{3/4}}{15 x^6}+\frac{16 \left(x^4-x^3\right)^{3/4}}{55 x^5}","\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 + x^4)^(3/4))/(15*x^6) + (16*(-x^3 + x^4)^(3/4))/(55*x^5) + (128*(-x^3 + x^4)^(3/4))/(385*x^4) + (512*(-x^3 + x^4)^(3/4))/(1155*x^3)","B",4,2,17,0.1176,1,"{2016, 2014}"
438,1,39,0,0.0546855,"\int \frac{1+2 x}{\sqrt{-4-3 x-2 x^2+2 x^3+x^4}} \, dx","Int[(1 + 2*x)/Sqrt[-4 - 3*x - 2*x^2 + 2*x^3 + x^4],x]","-\tanh ^{-1}\left(\frac{7-4 \left(x+\frac{1}{2}\right)^2}{\sqrt{16 \left(x+\frac{1}{2}\right)^4-56 \left(x+\frac{1}{2}\right)^2-51}}\right)","\log \left(2 x^2+2 \sqrt{x^4+2 x^3-2 x^2-3 x-4}+2 x-3\right)",1,"-ArcTanh[(7 - 4*(1/2 + x)^2)/Sqrt[-51 - 56*(1/2 + x)^2 + 16*(1/2 + x)^4]]","A",5,5,28,0.1786,1,"{1680, 12, 1107, 621, 206}"
439,0,0,0,0.7391069,"\int \frac{4 b+a x^3}{\sqrt[4]{b+a x^3} \left(-b-a x^3+x^4\right)} \, dx","Int[(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,"-4*b*Defer[Int][1/((b + a*x^3)^(1/4)*(b + a*x^3 - x^4)), x] - a*Defer[Int][x^3/((b + a*x^3)^(1/4)*(b + a*x^3 - x^4)), x]","F",0,0,0,0,-1,"{}"
440,1,35,0,0.0152895,"\int \frac{x^8}{\sqrt{-1+x^6}} \, dx","Int[x^8/Sqrt[-1 + x^6],x]","\frac{1}{6} \sqrt{x^6-1} x^3+\frac{1}{6} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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])/6 + ArcTanh[x^3/Sqrt[-1 + x^6]]/6","A",4,4,13,0.3077,1,"{275, 321, 217, 206}"
441,1,35,0,0.0140089,"\int \frac{\sqrt{-1+x^6}}{x^4} \, dx","Int[Sqrt[-1 + x^6]/x^4,x]","\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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 + ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",4,4,13,0.3077,1,"{275, 277, 217, 206}"
442,1,35,0,0.0138003,"\int x^2 \sqrt{-1+x^6} \, dx","Int[x^2*Sqrt[-1 + x^6],x]","\frac{1}{6} x^3 \sqrt{x^6-1}-\frac{1}{6} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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 - ArcTanh[x^3/Sqrt[-1 + x^6]]/6","A",4,4,13,0.3077,1,"{275, 195, 217, 206}"
443,1,25,0,0.0099621,"\int \frac{x^8}{\sqrt{1+x^6}} \, dx","Int[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",3,3,13,0.2308,1,"{275, 321, 215}"
444,1,25,0,0.0096106,"\int \frac{\sqrt{1+x^6}}{x^4} \, dx","Int[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",3,3,13,0.2308,1,"{275, 277, 215}"
445,1,47,0,0.1651564,"\int \frac{1+x^6}{x^6 \left(1+x^3\right) \sqrt[4]{x+x^4}} \, dx","Int[(1 + x^6)/(x^6*(1 + x^3)*(x + x^4)^(1/4)),x]","\frac{212 x}{63 \sqrt[4]{x^4+x}}-\frac{4}{21 \sqrt[4]{x^4+x} x^5}+\frac{32}{63 \sqrt[4]{x^4+x} x^2}","\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/(21*x^5*(x + x^4)^(1/4)) + 32/(63*x^2*(x + x^4)^(1/4)) + (212*x)/(63*(x + x^4)^(1/4))","A",5,5,25,0.2000,1,"{2056, 1487, 453, 271, 264}"
446,1,35,0,0.0370178,"\int x \sqrt{x+x^6} \, dx","Int[x*Sqrt[x + x^6],x]","\frac{1}{5} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6+x}}\right)+\frac{1}{5} \sqrt{x^6+x} x^2","\frac{1}{5} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6+x}}\right)+\frac{1}{5} \sqrt{x^6+x} x^2",1,"(x^2*Sqrt[x + x^6])/5 + ArcTanh[x^3/Sqrt[x + x^6]]/5","A",3,3,11,0.2727,1,"{2021, 2029, 206}"
447,0,0,0,1.1436483,"\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","Int[(-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,"(c*x*(1 + (a*x^6)/b)^(1/4)*Hypergeometric2F1[1/6, 1/4, 7/6, -((a*x^6)/b)])/(b + a*x^6)^(1/4) - c^5*Defer[Int][x^4/((-b + c^4*x^4 - a*x^6)*(b + a*x^6)^(1/4)), x] - 3*b*c*Defer[Int][1/((b + a*x^6)^(1/4)*(b - c^4*x^4 + a*x^6)), x]","F",0,0,0,0,-1,"{}"
448,1,35,0,0.0140084,"\int \frac{1}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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",3,2,15,0.1333,1,"{2117, 14}"
449,1,36,0,0.0163257,"\int \frac{\sqrt[4]{1+x^2}}{x} \, dx","Int[(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",6,6,13,0.4615,1,"{266, 50, 63, 212, 206, 203}"
450,1,47,0,0.0172003,"\int \frac{\sqrt{-1+x^3}}{x^7} \, dx","Int[Sqrt[-1 + x^3]/x^7,x]","\frac{\sqrt{x^3-1}}{12 x^3}+\frac{1}{12} \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{\sqrt{x^3-1}}{6 x^6}","\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,"-1/6*Sqrt[-1 + x^3]/x^6 + Sqrt[-1 + x^3]/(12*x^3) + ArcTan[Sqrt[-1 + x^3]]/12","A",5,5,13,0.3846,1,"{266, 47, 51, 63, 203}"
451,1,289,0,1.9894542,"\int \frac{-b+a x^2}{\left(b+c x+a x^2\right) \sqrt{b x+a x^3}} \, dx","Int[(-b + a*x^2)/((b + c*x + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{2 \sqrt[4]{b} \sqrt{x} \sqrt{\frac{a x^2}{b}+1} \Pi \left(\frac{2 \sqrt{-a} \sqrt{b}}{c-\sqrt{c^2-4 a b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{-a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{-a} \sqrt{a x^3+b x}}-\frac{2 \sqrt[4]{b} \sqrt{x} \sqrt{\frac{a x^2}{b}+1} \Pi \left(\frac{2 \sqrt{-a} \sqrt{b}}{c+\sqrt{c^2-4 a b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{-a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{-a} \sqrt{a x^3+b x}}+\frac{\sqrt{x} \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \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,"(Sqrt[x]*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]) - (2*b^(1/4)*Sqrt[x]*Sqrt[1 + (a*x^2)/b]*EllipticPi[(2*Sqrt[-a]*Sqrt[b])/(c - Sqrt[-4*a*b + c^2]), ArcSin[((-a)^(1/4)*Sqrt[x])/b^(1/4)], -1])/((-a)^(1/4)*Sqrt[b*x + a*x^3]) - (2*b^(1/4)*Sqrt[x]*Sqrt[1 + (a*x^2)/b]*EllipticPi[(2*Sqrt[-a]*Sqrt[b])/(c + Sqrt[-4*a*b + c^2]), ArcSin[((-a)^(1/4)*Sqrt[x])/b^(1/4)], -1])/((-a)^(1/4)*Sqrt[b*x + a*x^3])","C",13,7,35,0.2000,0,"{2056, 6728, 329, 220, 933, 168, 537}"
452,0,0,0,0.1364953,"\int \frac{-1+x}{\sqrt{-2-x+6 x^2-4 x^3+x^4}} \, dx","Int[(-1 + x)/Sqrt[-2 - x + 6*x^2 - 4*x^3 + x^4],x]","\int \frac{-1+x}{\sqrt{-2-x+6 x^2-4 x^3+x^4}} \, dx","\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,"-Defer[Int][1/Sqrt[-2 - x + 6*x^2 - 4*x^3 + x^4], x] + Defer[Int][x/Sqrt[-2 - x + 6*x^2 - 4*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
453,1,47,0,0.0166595,"\int \frac{\sqrt{-1+x^6}}{x^{13}} \, dx","Int[Sqrt[-1 + x^6]/x^13,x]","\frac{\sqrt{x^6-1}}{24 x^6}+\frac{1}{24} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\sqrt{x^6-1}}{12 x^{12}}","\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,"-1/12*Sqrt[-1 + x^6]/x^12 + Sqrt[-1 + x^6]/(24*x^6) + ArcTan[Sqrt[-1 + x^6]]/24","A",5,5,13,0.3846,1,"{266, 47, 51, 63, 203}"
454,0,0,0,0.6942352,"\int \frac{-1-2 x^2+2 x^4}{\left(2-3 x^2+x^4\right) \sqrt{1+x^6}} \, dx","Int[(-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,"(x*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x^2)/(1 + (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x^2*(1 + x^2))/(1 + (1 + Sqrt[3])*x^2)^2]*Sqrt[1 + x^6]) - (3*Defer[Int][1/((Sqrt[2] - x)*Sqrt[1 + x^6]), x])/(2*Sqrt[2]) + Defer[Int][1/((-1 + x)*Sqrt[1 + x^6]), x]/2 - Defer[Int][1/((1 + x)*Sqrt[1 + x^6]), x]/2 - (3*Defer[Int][1/((Sqrt[2] + x)*Sqrt[1 + x^6]), x])/(2*Sqrt[2])","F",0,0,0,0,-1,"{}"
455,1,154,0,0.6383819,"\int \frac{-1+k x}{(1+k x) \sqrt{(1-x) x \left(1-k^2 x\right)}} \, dx","Int[(-1 + k*x)/((1 + k*x)*Sqrt[(1 - x)*x*(1 - k^2*x)]),x]","\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{4 \sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(\frac{k}{k+1};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{(k+1) \sqrt{(1-x) x \left(1-k^2 x\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*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + (4*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[k/(1 + k), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((1 + k)*Sqrt[(1 - x)*x*(1 - k^2*x)])","C",6,6,32,0.1875,1,"{6718, 1607, 168, 538, 537, 115}"
456,1,159,0,0.5532225,"\int \frac{1+k x}{(-1+k x) \sqrt{(1-x) x \left(1-k^2 x\right)}} \, dx","Int[(1 + k*x)/((-1 + k*x)*Sqrt[(1 - x)*x*(1 - k^2*x)]),x]","\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{4 \sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(-\frac{k}{1-k};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{(1-k) \sqrt{(1-x) x \left(1-k^2 x\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*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + (4*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[-(k/(1 - k)), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((1 - k)*Sqrt[(1 - x)*x*(1 - k^2*x)])","C",6,6,32,0.1875,1,"{6718, 1607, 168, 538, 537, 115}"
457,1,37,0,0.3344863,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{x^2 \left(1+x^2\right)} \, dx","Int[((-1 + x^2)*Sqrt[1 + x^4])/(x^2*(1 + x^2)),x]","\frac{\sqrt{x^4+1}}{x}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)","\frac{\sqrt{x^4+1}}{x}+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)",1,"Sqrt[1 + x^4]/x + Sqrt[2]*ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]","A",12,9,25,0.3600,1,"{6725, 277, 305, 220, 1196, 1209, 1211, 1699, 203}"
458,1,53,0,0.1648826,"\int \frac{1+x^3}{x^6 \left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Int[(1 + x^3)/(x^6*(-1 + x^3)*(-x + x^4)^(1/4)),x]","-\frac{80 x}{21 \sqrt[4]{x^4-x}}+\frac{4}{21 \sqrt[4]{x^4-x} x^5}+\frac{20}{21 \sqrt[4]{x^4-x} x^2}","-\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/(21*x^5*(-x + x^4)^(1/4)) + 20/(21*x^2*(-x + x^4)^(1/4)) - (80*x)/(21*(-x + x^4)^(1/4))","A",4,4,27,0.1481,1,"{2056, 453, 271, 264}"
459,1,37,0,0.0225858,"\int \sqrt{-x+x^4} \, dx","Int[Sqrt[-x + x^4],x]","\frac{1}{3} x \sqrt{x^4-x}-\frac{1}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)","\frac{1}{3} x \sqrt{x^4-x}-\frac{1}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)",1,"(x*Sqrt[-x + x^4])/3 - ArcTanh[x^2/Sqrt[-x + x^4]]/3","A",3,3,11,0.2727,1,"{2004, 2029, 206}"
460,1,81,0,0.105082,"\int \frac{1}{x^8 \sqrt[4]{-x^2+x^4}} \, dx","Int[1/(x^8*(-x^2 + x^4)^(1/4)),x]","\frac{2 \left(x^4-x^2\right)^{3/4}}{15 x^9}+\frac{8 \left(x^4-x^2\right)^{3/4}}{55 x^7}+\frac{64 \left(x^4-x^2\right)^{3/4}}{385 x^5}+\frac{256 \left(x^4-x^2\right)^{3/4}}{1155 x^3}","\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))/(15*x^9) + (8*(-x^2 + x^4)^(3/4))/(55*x^7) + (64*(-x^2 + x^4)^(3/4))/(385*x^5) + (256*(-x^2 + x^4)^(3/4))/(1155*x^3)","B",4,2,17,0.1176,1,"{2016, 2014}"
461,1,33,0,0.0405803,"\int \frac{-1+x}{\sqrt{-1+4 x+2 x^2-4 x^3+x^4}} \, dx","Int[(-1 + x)/Sqrt[-1 + 4*x + 2*x^2 - 4*x^3 + x^4],x]","-\frac{1}{2} \tanh ^{-1}\left(\frac{2-(x-1)^2}{\sqrt{(x-1)^4-4 (x-1)^2+2}}\right)","-\frac{1}{2} \log \left(-x^2+\sqrt{x^4-4 x^3+2 x^2+4 x-1}+2 x+1\right)",1,"-1/2*ArcTanh[(2 - (-1 + x)^2)/Sqrt[2 - 4*(-1 + x)^2 + (-1 + x)^4]]","A",4,4,26,0.1538,1,"{1680, 1107, 621, 206}"
462,1,83,0,0.1096112,"\int \frac{\sqrt[4]{-x^3+x^4}}{(-1+x) x} \, dx","Int[(-x^3 + x^4)^(1/4)/((-1 + x)*x),x]","\frac{2 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} 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,"(2*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + (2*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","B",6,6,22,0.2727,1,"{2056, 63, 240, 212, 206, 203}"
463,1,33,0,0.0289078,"\int \frac{-2+x^3}{x \sqrt{-1+x^6}} \, dx","Int[(-2 + x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)-\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}\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]])/3 + ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",7,7,18,0.3889,1,"{1475, 844, 217, 206, 266, 63, 203}"
464,1,33,0,0.0328309,"\int \frac{1+x^3}{x \sqrt{-1+x^6}} \, dx","Int[(1 + x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\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)+\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}+x^3\right)",1,"ArcTan[Sqrt[-1 + x^6]]/3 + ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",7,7,18,0.3889,1,"{1475, 844, 217, 206, 266, 63, 203}"
465,1,33,0,0.0326317,"\int \frac{-1+2 x^3}{x \sqrt{-1+x^6}} \, dx","Int[(-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",7,7,20,0.3500,1,"{1475, 844, 217, 206, 266, 63, 203}"
466,1,33,0,0.0305369,"\int \frac{1+2 x^3}{x \sqrt{-1+x^6}} \, dx","Int[(1 + 2*x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{2}{3} \tanh ^{-1}\left(\frac{x^3}{\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,"ArcTan[Sqrt[-1 + x^6]]/3 + (2*ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",7,7,20,0.3500,1,"{1475, 844, 217, 206, 266, 63, 203}"
467,1,33,0,0.029304,"\int \frac{1+4 x^3}{x \sqrt{-1+x^6}} \, dx","Int[(1 + 4*x^3)/(x*Sqrt[-1 + x^6]),x]","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{4}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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]]/3 + (4*ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",7,7,20,0.3500,1,"{1475, 844, 217, 206, 266, 63, 203}"
468,1,53,0,0.1665214,"\int \frac{1+x^6}{x^6 \left(-1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Int[(1 + x^6)/(x^6*(-1 + x^3)*(-x + x^4)^(1/4)),x]","-\frac{212 x}{63 \sqrt[4]{x^4-x}}+\frac{4}{21 \sqrt[4]{x^4-x} x^5}+\frac{32}{63 \sqrt[4]{x^4-x} x^2}","-\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/(21*x^5*(-x + x^4)^(1/4)) + 32/(63*x^2*(-x + x^4)^(1/4)) - (212*x)/(63*(-x + x^4)^(1/4))","A",5,5,27,0.1852,1,"{2056, 1487, 453, 271, 264}"
469,0,0,0,0.9234603,"\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","Int[(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,"-8*b*Defer[Int][x/((b + a*x^3)^(1/4)*(b + a*x^3 - x^8)), x] - 5*a*Defer[Int][x^4/((b + a*x^3)^(1/4)*(b + a*x^3 - x^8)), x]","F",0,0,0,0,-1,"{}"
470,1,37,0,0.0134924,"\int \sqrt{x+\sqrt{1+x^2}} \, dx","Int[Sqrt[x + Sqrt[1 + x^2]],x]","\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\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,"-(1/Sqrt[x + Sqrt[1 + x^2]]) + (x + Sqrt[1 + x^2])^(3/2)/3","A",3,2,15,0.1333,1,"{2117, 14}"
471,1,273,0,6.4516125,"\int \frac{a b-x^2}{\sqrt{x (-a+x) (-b+x)} \left(a b-(a+b+d) x+x^2\right)} \, dx","Int[(a*b - x^2)/(Sqrt[x*(-a + x)*(-b + x)]*(a*b - (a + b + d)*x + x^2)),x]","\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \Pi \left(\frac{2 a}{a+b+d-\sqrt{a^2-2 (b-d) a+(b+d)^2}};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{\sqrt{x (a-x) (b-x)}}+\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \Pi \left(\frac{2 a}{a+b+d+\sqrt{a^2-2 (b-d) a+(b+d)^2}};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{\sqrt{x (a-x) (b-x)}}-\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} F\left(\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{\sqrt{x (a-x) (b-x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt{d}}",1,"(-2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a)/(a + b + d - Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a)/(a + b + d + Sqrt[a^2 - 2*a*(b - d) + (b + d)^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/Sqrt[(a - x)*(b - x)*x]","C",15,7,42,0.1667,1,"{6718, 6728, 117, 116, 169, 538, 537}"
472,1,308,0,8.6994274,"\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","Int[(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 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \Pi \left(\frac{2 a d}{a d+b d-\sqrt{a^2 d^2+2 a (1-b d) d+(b d+1)^2}+1};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{d \sqrt{x (a-x) (b-x)}}+\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \Pi \left(\frac{2 a d}{a d+b d+\sqrt{a^2 d^2+2 a (1-b d) d+(b d+1)^2}+1};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{d \sqrt{x (a-x) (b-x)}}-\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} F\left(\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{d \sqrt{x (a-x) (b-x)}}","\frac{2 \tanh ^{-1}\left(\frac{x}{\sqrt{d} \sqrt{x^2 (-a-b)+a b x+x^3}}\right)}{\sqrt{d}}",1,"(-2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(d*Sqrt[(a - x)*(b - x)*x]) + (2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a*d)/(1 + a*d + b*d - Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(d*Sqrt[(a - x)*(b - x)*x]) + (2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a*d)/(1 + a*d + b*d + Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(d*Sqrt[(a - x)*(b - x)*x])","C",15,7,49,0.1429,1,"{6718, 6728, 117, 116, 169, 538, 537}"
473,1,113,0,0.9744762,"\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","Int[(-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} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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])/Sqrt[(1 - x^2)*(1 - k^2*x^2)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",5,4,39,0.1026,1,"{6719, 6725, 419, 537}"
474,1,111,0,0.7789491,"\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","Int[(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} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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])/Sqrt[(1 - x^2)*(1 - k^2*x^2)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",5,4,39,0.1026,1,"{6719, 6725, 419, 537}"
475,1,26,0,0.772203,"\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","Int[(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 (1-x)}{\sqrt{(1-x) x \left(1-k^2 x\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",4,4,47,0.08511,1,"{6718, 21, 1614, 8}"
476,1,47,0,0.0174732,"\int \frac{1}{x^7 \sqrt{-1+x^3}} \, dx","Int[1/(x^7*Sqrt[-1 + x^3]),x]","\frac{\sqrt{x^3-1}}{4 x^3}+\frac{1}{4} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{\sqrt{x^3-1}}{6 x^6}","\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,"Sqrt[-1 + x^3]/(6*x^6) + Sqrt[-1 + x^3]/(4*x^3) + ArcTan[Sqrt[-1 + x^3]]/4","A",5,4,13,0.3077,1,"{266, 51, 63, 203}"
477,1,47,0,0.0175233,"\int \frac{1}{x^7 \sqrt{1+x^3}} \, dx","Int[1/(x^7*Sqrt[1 + x^3]),x]","\frac{\sqrt{x^3+1}}{4 x^3}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{6 x^6}","\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,"-1/6*Sqrt[1 + x^3]/x^6 + Sqrt[1 + x^3]/(4*x^3) - ArcTanh[Sqrt[1 + x^3]]/4","A",5,4,13,0.3077,1,"{266, 51, 63, 207}"
478,1,47,0,0.018401,"\int \frac{\sqrt{1+x^3}}{x^7} \, dx","Int[Sqrt[1 + x^3]/x^7,x]","-\frac{\sqrt{x^3+1}}{12 x^3}+\frac{1}{12} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{6 x^6}","\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,"-1/6*Sqrt[1 + x^3]/x^6 - Sqrt[1 + x^3]/(12*x^3) + ArcTanh[Sqrt[1 + x^3]]/12","A",5,5,13,0.3846,1,"{266, 47, 51, 63, 207}"
479,1,47,0,0.0197342,"\int \frac{1+x^3}{x^7 \sqrt{-1+x^3}} \, dx","Int[(1 + x^3)/(x^7*Sqrt[-1 + x^3]),x]","\frac{7 \sqrt{x^3-1}}{12 x^3}+\frac{7}{12} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{\sqrt{x^3-1}}{6 x^6}","\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]/(6*x^6) + (7*Sqrt[-1 + x^3])/(12*x^3) + (7*ArcTan[Sqrt[-1 + x^3]])/12","A",5,5,18,0.2778,1,"{446, 78, 51, 63, 203}"
480,0,0,0,0.6906066,"\int \frac{\sqrt{-1+x^3} \left(2+x^3\right)}{x^2 \left(-2-4 x^2+2 x^3\right)} \, dx","Int[(Sqrt[-1 + x^3]*(2 + x^3))/(x^2*(-2 - 4*x^2 + 2*x^3)),x]","\int \frac{\sqrt{-1+x^3} \left(2+x^3\right)}{x^2 \left(-2-4 x^2+2 x^3\right)} \, dx","\frac{\sqrt{x^3-1}}{x}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^3-1}}\right)",1,"(3*Sqrt[-1 + x^3])/(1 - Sqrt[3] - x) + Sqrt[-1 + x^3]/x - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(2*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (Sqrt[2]*3^(3/4)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - 2*Defer[Int][Sqrt[-1 + x^3]/(-1 - 2*x^2 + x^3), x] + (3*Defer[Int][(x*Sqrt[-1 + x^3])/(-1 - 2*x^2 + x^3), x])/2","F",0,0,0,0,-1,"{}"
481,1,38,0,0.0280651,"\int x^5 \sqrt{b+a x^3} \, dx","Int[x^5*Sqrt[b + a*x^3],x]","\frac{2 \left(a x^3+b\right)^{5/2}}{15 a^2}-\frac{2 b \left(a x^3+b\right)^{3/2}}{9 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*(b + a*x^3)^(3/2))/(9*a^2) + (2*(b + a*x^3)^(5/2))/(15*a^2)","A",3,2,15,0.1333,1,"{266, 43}"
482,1,33,0,0.0831461,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4} \left(1+x^3+x^4\right)}{x^8} \, dx","Int[((-3 + x^4)*(1 + x^4)^(1/3)*(1 + x^3 + x^4))/x^8,x]","\frac{3 \left(x^4+1\right)^{4/3}}{4 x^4}+\frac{3 \left(x^4+1\right)^{7/3}}{7 x^7}","\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*(1 + x^4)^(4/3))/(4*x^4) + (3*(1 + x^4)^(7/3))/(7*x^7)","A",7,6,26,0.2308,1,"{1833, 1584, 446, 74, 1478, 449}"
483,1,33,0,0.0865562,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3} \left(1+x^3+x^4\right)}{x^9} \, dx","Int[((-3 + x^4)*(1 + x^4)^(2/3)*(1 + x^3 + x^4))/x^9,x]","\frac{3 \left(x^4+1\right)^{8/3}}{8 x^8}+\frac{3 \left(x^4+1\right)^{5/3}}{5 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,"(3*(1 + x^4)^(5/3))/(5*x^5) + (3*(1 + x^4)^(8/3))/(8*x^8)","A",7,6,26,0.2308,1,"{1833, 1584, 449, 1474, 847, 74}"
484,1,33,0,0.0907718,"\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","Int[((-1 + x^4)^(2/3)*(3 + x^4)*(-2 - x^3 + 2*x^4))/x^9,x]","\frac{3 \left(x^4-1\right)^{8/3}}{4 x^8}-\frac{3 \left(x^4-1\right)^{5/3}}{5 x^5}","\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,"(-3*(-1 + x^4)^(5/3))/(5*x^5) + (3*(-1 + x^4)^(8/3))/(4*x^8)","A",7,6,30,0.2000,1,"{1833, 1584, 449, 1474, 847, 74}"
485,1,88,0,0.1920612,"\int \frac{\left(-1+x^5\right)^{3/4} \left(4+x^5\right) \left(-1-x^4+x^5\right)}{x^{12}} \, dx","Int[((-1 + x^5)^(3/4)*(4 + x^5)*(-1 - x^4 + x^5))/x^12,x]","\frac{15 \left(x^5-1\right)^{3/4}}{11 x}-\frac{5 \left(x^5-1\right)^{3/4}}{22 x^6}-\frac{15 \left(x^5-1\right)^{3/4}}{14 x^2}+\frac{1}{154} \left(x^5-1\right)^{3/4} \left(\frac{56}{x^{11}}+\frac{88}{x^7}-\frac{77}{x^6}+\frac{77}{x^2}-\frac{154}{x}\right)","\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,"((56/x^11 + 88/x^7 - 77/x^6 + 77/x^2 - 154/x)*(-1 + x^5)^(3/4))/154 - (5*(-1 + x^5)^(3/4))/(22*x^6) - (15*(-1 + x^5)^(3/4))/(14*x^2) + (15*(-1 + x^5)^(3/4))/(11*x)","B",7,5,28,0.1786,1,"{1820, 1825, 1835, 1586, 449}"
486,1,89,0,0.170199,"\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","Int[((1 + x^5)^(2/3)*(1 + x^3 + x^5)*(-3 + 2*x^5))/x^9,x]","-\frac{6 \left(x^5+1\right)^{2/3}}{5 x^5}-\frac{15 \left(x^5+1\right)^{2/3}}{56 x^8}+\frac{15 \left(x^5+1\right)^{2/3}}{4 x^3}+\frac{3 \left(x^5+1\right)^{2/3} \left(35 x^{11}+56 x^9-280 x^6+168 x^4+60 x\right)}{280 x^9}","\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,"(-15*(1 + x^5)^(2/3))/(56*x^8) - (6*(1 + x^5)^(2/3))/(5*x^5) + (15*(1 + x^5)^(2/3))/(4*x^3) + (3*(1 + x^5)^(2/3)*(60*x + 168*x^4 - 280*x^6 + 56*x^9 + 35*x^11))/(280*x^9)","B",7,5,28,0.1786,1,"{1826, 1835, 1586, 1584, 449}"
487,1,89,0,0.1714337,"\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","Int[((-1 + x^5)^(2/3)*(-1 + x^3 + x^5)*(3 + 2*x^5))/x^9,x]","\frac{6 \left(x^5-1\right)^{2/3}}{5 x^5}-\frac{15 \left(x^5-1\right)^{2/3}}{56 x^8}-\frac{15 \left(x^5-1\right)^{2/3}}{4 x^3}+\frac{3 \left(x^5-1\right)^{2/3} \left(35 x^{11}+56 x^9+280 x^6-168 x^4+60 x\right)}{280 x^9}","\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,"(-15*(-1 + x^5)^(2/3))/(56*x^8) + (6*(-1 + x^5)^(2/3))/(5*x^5) - (15*(-1 + x^5)^(2/3))/(4*x^3) + (3*(-1 + x^5)^(2/3)*(60*x - 168*x^4 + 280*x^6 + 56*x^9 + 35*x^11))/(280*x^9)","B",7,5,28,0.1786,1,"{1826, 1835, 1586, 1584, 449}"
488,1,88,0,0.1947579,"\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","Int[((-4 + x^5)*(1 + x^5)^(3/4)*(2 - x^4 + 2*x^5))/x^12,x]","\frac{30 \left(x^5+1\right)^{3/4}}{11 x}+\frac{5 \left(x^5+1\right)^{3/4}}{11 x^6}-\frac{15 \left(x^5+1\right)^{3/4}}{14 x^2}+\frac{1}{154} \left(x^5+1\right)^{3/4} \left(\frac{112}{x^{11}}-\frac{88}{x^7}+\frac{154}{x^6}+\frac{77}{x^2}-\frac{308}{x}\right)","\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,"((112/x^11 - 88/x^7 + 154/x^6 + 77/x^2 - 308/x)*(1 + x^5)^(3/4))/154 + (5*(1 + x^5)^(3/4))/(11*x^6) - (15*(1 + x^5)^(3/4))/(14*x^2) + (30*(1 + x^5)^(3/4))/(11*x)","B",7,5,30,0.1667,1,"{1820, 1825, 1835, 1586, 449}"
489,1,87,0,0.1735574,"\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","Int[((1 + x^5)^(2/3)*(-3 + 2*x^5)*(4 + 3*x^3 + 4*x^5))/x^9,x]","-\frac{18 \left(x^5+1\right)^{2/3}}{5 x^5}-\frac{15 \left(x^5+1\right)^{2/3}}{14 x^8}+\frac{15 \left(x^5+1\right)^{2/3}}{x^3}+\frac{3 \left(x^5+1\right)^{2/3} \left(35 x^{11}+42 x^9-280 x^6+126 x^4+60 x\right)}{70 x^9}","\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,"(-15*(1 + x^5)^(2/3))/(14*x^8) - (18*(1 + x^5)^(2/3))/(5*x^5) + (15*(1 + x^5)^(2/3))/x^3 + (3*(1 + x^5)^(2/3)*(60*x + 126*x^4 - 280*x^6 + 42*x^9 + 35*x^11))/(70*x^9)","B",7,5,32,0.1562,1,"{1826, 1835, 1586, 1584, 449}"
490,1,47,0,0.0167833,"\int \frac{1}{x^{13} \sqrt{-1+x^6}} \, dx","Int[1/(x^13*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1}}{8 x^6}+\frac{1}{8} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1}}{12 x^{12}}","\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]/(12*x^12) + Sqrt[-1 + x^6]/(8*x^6) + ArcTan[Sqrt[-1 + x^6]]/8","A",5,4,13,0.3077,1,"{266, 51, 63, 203}"
491,1,47,0,0.0208898,"\int \frac{-1+x^6}{x^{13} \sqrt{1+x^6}} \, dx","Int[(-1 + x^6)/(x^13*Sqrt[1 + x^6]),x]","-\frac{7 \sqrt{x^6+1}}{24 x^6}+\frac{7}{24} \tanh ^{-1}\left(\sqrt{x^6+1}\right)+\frac{\sqrt{x^6+1}}{12 x^{12}}","\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,"Sqrt[1 + x^6]/(12*x^12) - (7*Sqrt[1 + x^6])/(24*x^6) + (7*ArcTanh[Sqrt[1 + x^6]])/24","A",5,5,18,0.2778,1,"{446, 78, 51, 63, 207}"
492,1,47,0,0.0169924,"\int \frac{\sqrt{1+x^6}}{x^{13}} \, dx","Int[Sqrt[1 + x^6]/x^13,x]","-\frac{\sqrt{x^6+1}}{24 x^6}+\frac{1}{24} \tanh ^{-1}\left(\sqrt{x^6+1}\right)-\frac{\sqrt{x^6+1}}{12 x^{12}}","\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,"-1/12*Sqrt[1 + x^6]/x^12 - Sqrt[1 + x^6]/(24*x^6) + ArcTanh[Sqrt[1 + x^6]]/24","A",5,5,13,0.3846,1,"{266, 47, 51, 63, 207}"
493,1,47,0,0.0187358,"\int \frac{1+x^6}{x^{13} \sqrt{-1+x^6}} \, dx","Int[(1 + x^6)/(x^13*Sqrt[-1 + x^6]),x]","\frac{7 \sqrt{x^6-1}}{24 x^6}+\frac{7}{24} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1}}{12 x^{12}}","\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]/(12*x^12) + (7*Sqrt[-1 + x^6])/(24*x^6) + (7*ArcTan[Sqrt[-1 + x^6]])/24","A",5,5,18,0.2778,1,"{446, 78, 51, 63, 203}"
494,1,49,0,0.1269303,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right) \left(-1+x^3+x^6\right)}{x^8} \, dx","Int[((-1 + x^6)^(1/3)*(1 + x^6)*(-1 + x^3 + x^6))/x^8,x]","\frac{\left(x^6-1\right)^{4/3}}{7 x}-\frac{\left(x^6-1\right)^{4/3}}{7 x^7}+\frac{\left(x^6-1\right)^{4/3}}{4 x^4}","\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,"-1/7*(-1 + x^6)^(4/3)/x^7 + (-1 + x^6)^(4/3)/(4*x^4) + (-1 + x^6)^(4/3)/(7*x)","A",6,4,26,0.1538,1,"{1835, 1586, 1584, 449}"
495,1,33,0,0.0884122,"\int \frac{\left(-1+x^6\right)^{3/4} \left(2+x^6\right) \left(-1-x^4+x^6\right)}{x^{12}} \, dx","Int[((-1 + x^6)^(3/4)*(2 + x^6)*(-1 - x^4 + x^6))/x^12,x]","\frac{2 \left(x^6-1\right)^{11/4}}{11 x^{11}}-\frac{2 \left(x^6-1\right)^{7/4}}{7 x^7}","\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*(-1 + x^6)^(7/4))/(7*x^7) + (2*(-1 + x^6)^(11/4))/(11*x^11)","A",6,4,28,0.1429,1,"{1833, 1584, 449, 1478}"
496,1,33,0,0.0851478,"\int \frac{\left(-2+x^6\right) \left(1+x^6\right)^{3/4} \left(1-x^4+x^6\right)}{x^{12}} \, dx","Int[((-2 + x^6)*(1 + x^6)^(3/4)*(1 - x^4 + x^6))/x^12,x]","\frac{2 \left(x^6+1\right)^{11/4}}{11 x^{11}}-\frac{2 \left(x^6+1\right)^{7/4}}{7 x^7}","\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*(1 + x^6)^(7/4))/(7*x^7) + (2*(1 + x^6)^(11/4))/(11*x^11)","A",6,4,28,0.1429,1,"{1833, 1584, 449, 1478}"
497,0,0,0,0.3968055,"\int \frac{-2 x+3 x^2}{\sqrt{5-4 x^2+4 x^3+x^4-2 x^5+x^6}} \, dx","Int[(-2*x + 3*x^2)/Sqrt[5 - 4*x^2 + 4*x^3 + x^4 - 2*x^5 + x^6],x]","\int \frac{-2 x+3 x^2}{\sqrt{5-4 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^3-4 x^2+5}+2\right)",1,"-2*Defer[Int][x/Sqrt[5 - 4*x^2 + 4*x^3 + x^4 - 2*x^5 + x^6], x] + 3*Defer[Int][x^2/Sqrt[5 - 4*x^2 + 4*x^3 + x^4 - 2*x^5 + x^6], x]","F",0,0,0,0,-1,"{}"
498,1,38,0,0.0495823,"\int \frac{-2+5 x^6}{x \sqrt{-1+x^6} \left(2+x^6\right)} \, dx","Int[(-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",6,4,27,0.1481,1,"{573, 156, 63, 203}"
499,1,38,0,0.049865,"\int \frac{-1+10 x^6}{x \sqrt{-1+x^6} \left(-1+4 x^6\right)} \, dx","Int[(-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 \sqrt{x^6-1}}{\sqrt{3}}\right)}{\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,"ArcTan[Sqrt[-1 + x^6]]/3 + ArcTan[(2*Sqrt[-1 + x^6])/Sqrt[3]]/Sqrt[3]","A",6,4,29,0.1379,1,"{573, 156, 63, 203}"
500,1,39,0,0.0463735,"\int \frac{2+x+x^2}{x^2 \left(1+x^2\right)^{3/4}} \, dx","Int[(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",6,6,19,0.3158,1,"{1807, 266, 63, 212, 206, 203}"
501,0,0,0,1.1498263,"\int \frac{-3+2 x}{\sqrt[4]{-x+x^2} \left(1-x+x^3\right)} \, dx","Int[(-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,"(-12*(-1 + x)^(1/4)*x^(1/4)*Defer[Subst][Defer[Int][x^2/((-1 + x^4)^(1/4)*(1 - x^4 + x^12)), x], x, x^(1/4)])/(-x + x^2)^(1/4) + (8*(-1 + x)^(1/4)*x^(1/4)*Defer[Subst][Defer[Int][x^6/((-1 + x^4)^(1/4)*(1 - x^4 + x^12)), x], x, x^(1/4)])/(-x + x^2)^(1/4)","F",0,0,0,0,-1,"{}"
502,1,2062,0,9.4242478,"\int \frac{\left(-1+x^2\right) \sqrt{x+x^3}}{\left(1+x^2\right) \left(1+x+x^2\right)^2} \, dx","Int[((-1 + x^2)*Sqrt[x + x^3])/((1 + x^2)*(1 + x + x^2)^2),x]","-\frac{\left(i+\sqrt{3}\right) \sqrt{x^3+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+1}}\right)}{2 \left(i-\sqrt{3}\right) \sqrt{x} \sqrt{x^2+1}}-\frac{\left(i-\sqrt{3}\right) \sqrt{x^3+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+1}}\right)}{2 \left(i+\sqrt{3}\right) \sqrt{x} \sqrt{x^2+1}}-\frac{\sqrt{x^3+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+1}}\right)}{\sqrt{3} \left(i+\sqrt{3}\right) \sqrt{x} \sqrt{x^2+1}}-\frac{\left(1+i \sqrt{3}\right) \sqrt{x^3+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+1}}\right)}{6 \sqrt{x} \sqrt{x^2+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt{x^3+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+1}}\right)}{6 \sqrt{x} \sqrt{x^2+1}}+\frac{\sqrt{x^3+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+1}}\right)}{\sqrt{3} \left(i-\sqrt{3}\right) \sqrt{x} \sqrt{x^2+1}}-\frac{2 \sqrt{x^3+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+1}}\right)}{3 \sqrt{x} \sqrt{x^2+1}}-\frac{\sqrt{x^3+x} \tanh ^{-1}\left(\frac{2-\left(1-i \sqrt{3}\right) x}{\sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^2+1}}\right)}{2 \left(i+\sqrt{3}\right) \sqrt{x} \sqrt{x^2+1}}+\frac{\sqrt{x^3+x} \tanh ^{-1}\left(\frac{\left(1+i \sqrt{3}\right)^2 x+4}{2 \sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^2+1}}\right)}{2 \left(i+\sqrt{3}\right) \sqrt{x} \sqrt{x^2+1}}-\frac{\left(i+\sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} E\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \left(i-\sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}-\frac{\left(i-\sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} E\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \left(i+\sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}-\frac{2 (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} E\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \left(1+i \sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}-\frac{2 (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} E\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \left(1-i \sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}-\frac{\left(1+i \sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{4 \sqrt{x} \left(x^2+1\right)}+\frac{(x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \left(1+i \sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}-\frac{\left(1-i \sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{4 \sqrt{x} \left(x^2+1\right)}+\frac{(x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \left(1-i \sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}+\frac{(x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 \sqrt{x} \left(x^2+1\right)}+\frac{\left(i+\sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} \Pi \left(\frac{1}{4};2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{4 \left(i-\sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}+\frac{\left(i-\sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} \Pi \left(\frac{1}{4};2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{4 \left(i+\sqrt{3}\right) \sqrt{x} \left(x^2+1\right)}+\frac{\left(3+i \sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} \Pi \left(\frac{1}{4};2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{24 \sqrt{x} \left(x^2+1\right)}+\frac{\left(3-i \sqrt{3}\right) (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{x^3+x} \Pi \left(\frac{1}{4};2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{24 \sqrt{x} \left(x^2+1\right)}+\frac{\left(i+\sqrt{3}\right) \sqrt{x^3+x}}{3 \left(i-\sqrt{3}\right) \left(-2 \sqrt{x}-i \sqrt{3}+1\right) \sqrt{x}}+\frac{2 \sqrt{x^3+x}}{3 \left(1+i \sqrt{3}\right) \left(-2 \sqrt{x}-i \sqrt{3}+1\right) \sqrt{x}}+\frac{\left(i-\sqrt{3}\right) \sqrt{x^3+x}}{3 \left(i+\sqrt{3}\right) \left(-2 \sqrt{x}+i \sqrt{3}+1\right) \sqrt{x}}+\frac{2 \sqrt{x^3+x}}{3 \left(1-i \sqrt{3}\right) \left(-2 \sqrt{x}+i \sqrt{3}+1\right) \sqrt{x}}-\frac{\left(i+\sqrt{3}\right) \sqrt{x^3+x}}{3 \left(i-\sqrt{3}\right) \left(2 \sqrt{x}-i \sqrt{3}+1\right) \sqrt{x}}-\frac{2 \sqrt{x^3+x}}{3 \left(1+i \sqrt{3}\right) \left(2 \sqrt{x}-i \sqrt{3}+1\right) \sqrt{x}}-\frac{\left(i-\sqrt{3}\right) \sqrt{x^3+x}}{3 \left(i+\sqrt{3}\right) \left(2 \sqrt{x}+i \sqrt{3}+1\right) \sqrt{x}}-\frac{2 \sqrt{x^3+x}}{3 \left(1-i \sqrt{3}\right) \left(2 \sqrt{x}+i \sqrt{3}+1\right) \sqrt{x}}+\frac{\left(i+\sqrt{3}\right) \sqrt{x^3+x}}{3 \left(i-\sqrt{3}\right) (x+1)}+\frac{\left(i-\sqrt{3}\right) \sqrt{x^3+x}}{3 \left(i+\sqrt{3}\right) (x+1)}+\frac{2 \sqrt{x^3+x}}{3 \left(1+i \sqrt{3}\right) (x+1)}+\frac{2 \sqrt{x^3+x}}{3 \left(1-i \sqrt{3}\right) (x+1)}","\frac{\sqrt{x^3+x}}{x^2+x+1}-\tan ^{-1}\left(\frac{\sqrt{x^3+x}}{x^2+1}\right)",1,"(2*Sqrt[x + x^3])/(3*(1 + I*Sqrt[3])*(1 - I*Sqrt[3] - 2*Sqrt[x])*Sqrt[x]) + ((I + Sqrt[3])*Sqrt[x + x^3])/(3*(I - Sqrt[3])*(1 - I*Sqrt[3] - 2*Sqrt[x])*Sqrt[x]) + (2*Sqrt[x + x^3])/(3*(1 - I*Sqrt[3])*(1 + I*Sqrt[3] - 2*Sqrt[x])*Sqrt[x]) + ((I - Sqrt[3])*Sqrt[x + x^3])/(3*(I + Sqrt[3])*(1 + I*Sqrt[3] - 2*Sqrt[x])*Sqrt[x]) - (2*Sqrt[x + x^3])/(3*(1 + I*Sqrt[3])*(1 - I*Sqrt[3] + 2*Sqrt[x])*Sqrt[x]) - ((I + Sqrt[3])*Sqrt[x + x^3])/(3*(I - Sqrt[3])*(1 - I*Sqrt[3] + 2*Sqrt[x])*Sqrt[x]) - (2*Sqrt[x + x^3])/(3*(1 - I*Sqrt[3])*(1 + I*Sqrt[3] + 2*Sqrt[x])*Sqrt[x]) - ((I - Sqrt[3])*Sqrt[x + x^3])/(3*(I + Sqrt[3])*(1 + I*Sqrt[3] + 2*Sqrt[x])*Sqrt[x]) + (2*Sqrt[x + x^3])/(3*(1 - I*Sqrt[3])*(1 + x)) + (2*Sqrt[x + x^3])/(3*(1 + I*Sqrt[3])*(1 + x)) + ((I - Sqrt[3])*Sqrt[x + x^3])/(3*(I + Sqrt[3])*(1 + x)) + ((I + Sqrt[3])*Sqrt[x + x^3])/(3*(I - Sqrt[3])*(1 + x)) - (2*Sqrt[x + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x^2]])/(3*Sqrt[x]*Sqrt[1 + x^2]) + (Sqrt[x + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x^2]])/(Sqrt[3]*(I - Sqrt[3])*Sqrt[x]*Sqrt[1 + x^2]) - ((1 - I*Sqrt[3])*Sqrt[x + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x^2]])/(6*Sqrt[x]*Sqrt[1 + x^2]) - ((1 + I*Sqrt[3])*Sqrt[x + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x^2]])/(6*Sqrt[x]*Sqrt[1 + x^2]) - (Sqrt[x + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x^2]])/(Sqrt[3]*(I + Sqrt[3])*Sqrt[x]*Sqrt[1 + x^2]) - ((I - Sqrt[3])*Sqrt[x + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x^2]])/(2*(I + Sqrt[3])*Sqrt[x]*Sqrt[1 + x^2]) - ((I + Sqrt[3])*Sqrt[x + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x^2]])/(2*(I - Sqrt[3])*Sqrt[x]*Sqrt[1 + x^2]) - (Sqrt[x + x^3]*ArcTanh[(2 - (1 - I*Sqrt[3])*x)/(Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^2])])/(2*(I + Sqrt[3])*Sqrt[x]*Sqrt[1 + x^2]) + (Sqrt[x + x^3]*ArcTanh[(4 + (1 + I*Sqrt[3])^2*x)/(2*Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^2])])/(2*(I + Sqrt[3])*Sqrt[x]*Sqrt[1 + x^2]) - (2*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticE[2*ArcTan[Sqrt[x]], 1/2])/(3*(1 - I*Sqrt[3])*Sqrt[x]*(1 + x^2)) - (2*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticE[2*ArcTan[Sqrt[x]], 1/2])/(3*(1 + I*Sqrt[3])*Sqrt[x]*(1 + x^2)) - ((I - Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticE[2*ArcTan[Sqrt[x]], 1/2])/(3*(I + Sqrt[3])*Sqrt[x]*(1 + x^2)) - ((I + Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticE[2*ArcTan[Sqrt[x]], 1/2])/(3*(I - Sqrt[3])*Sqrt[x]*(1 + x^2)) + ((1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(3*Sqrt[x]*(1 + x^2)) + ((1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(3*(1 - I*Sqrt[3])*Sqrt[x]*(1 + x^2)) - ((1 - I*Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(4*Sqrt[x]*(1 + x^2)) + ((1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(3*(1 + I*Sqrt[3])*Sqrt[x]*(1 + x^2)) - ((1 + I*Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(4*Sqrt[x]*(1 + x^2)) + ((3 - I*Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticPi[1/4, 2*ArcTan[Sqrt[x]], 1/2])/(24*Sqrt[x]*(1 + x^2)) + ((3 + I*Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticPi[1/4, 2*ArcTan[Sqrt[x]], 1/2])/(24*Sqrt[x]*(1 + x^2)) + ((I - Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticPi[1/4, 2*ArcTan[Sqrt[x]], 1/2])/(4*(I + Sqrt[3])*Sqrt[x]*(1 + x^2)) + ((I + Sqrt[3])*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*Sqrt[x + x^3]*EllipticPi[1/4, 2*ArcTan[Sqrt[x]], 1/2])/(4*(I - Sqrt[3])*Sqrt[x]*(1 + x^2))","C",196,18,30,0.6000,1,"{2056, 6733, 6742, 1727, 1742, 12, 1248, 725, 206, 1715, 1196, 1709, 220, 1707, 1725, 1217, 2, 6728}"
503,0,0,0,74.0890056,"\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","Int[((-2 + x^3)*Sqrt[2 + x^2 + 2*x^3])/((1 + x^3)*(1 + x^2 + x^3)),x]","\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","-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,"(-2*Sqrt[2 + x^2 + 2*x^3])/3 + ((1 - I*Sqrt[3])*Sqrt[2 + x^2 + 2*x^3])/3 + ((1 + I*Sqrt[3])*Sqrt[2 + x^2 + 2*x^3])/3 - ((5*I)*Sqrt[2]*Sqrt[2 + x^2 + 2*x^3]*EllipticE[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) - (1 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((109 - 6*Sqrt[330])^(1/6)*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3))*(1 + 6*x) + (1 + 6*x)^2]) - ((13*I - Sqrt[3])*Sqrt[2 + x^2 + 2*x^3]*EllipticE[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/(Sqrt[2]*(109 - 6*Sqrt[330])^(1/6)*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((1 + (109 - 6*Sqrt[330])^(2/3))*(1 + 6*x))/(109 - 6*Sqrt[330])^(1/3) + (1 + 6*x)^2]) - ((13*I + Sqrt[3])*Sqrt[2 + x^2 + 2*x^3]*EllipticE[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/(Sqrt[2]*(109 - 6*Sqrt[330])^(1/6)*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((1 + (109 - 6*Sqrt[330])^(2/3))*(1 + 6*x))/(109 - 6*Sqrt[330])^(1/3) + (1 + 6*x)^2]) + ((46*I)*Sqrt[2]*(109 - 6*Sqrt[330])^(1/6)*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + x^2 + 2*x^3]*EllipticF[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) - (1 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3))*(1 + 6*x) + (1 + 6*x)^2]) + ((10*I)*Sqrt[2]*(1 + (109 - 6*Sqrt[330])^(2/3))*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + x^2 + 2*x^3]*EllipticF[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) - (1 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((109 - 6*Sqrt[330])^(1/6)*(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3))*(1 + 6*x) + (1 + 6*x)^2]) + (Sqrt[2]*(13*I - 24*Sqrt[3])*(1 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(1/6)*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + x^2 + 2*x^3]*EllipticF[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((1 + (109 - 6*Sqrt[330])^(2/3))*(1 + 6*x))/(109 - 6*Sqrt[330])^(1/3) + (1 + 6*x)^2]) + (Sqrt[2]*(13 - (24*I)*Sqrt[3])*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/6)*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + x^2 + 2*x^3]*EllipticF[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((1 + (109 - 6*Sqrt[330])^(2/3))*(1 + 6*x))/(109 - 6*Sqrt[330])^(1/3) + (1 + 6*x)^2]) + (Sqrt[2]*(4 + (3*I)*Sqrt[3])*(I + Sqrt[3])*(1 + (109 - 6*Sqrt[330])^(2/3))*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + x^2 + 2*x^3]*EllipticF[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((109 - 6*Sqrt[330])^(1/6)*(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((1 + (109 - 6*Sqrt[330])^(2/3))*(1 + 6*x))/(109 - 6*Sqrt[330])^(1/3) + (1 + 6*x)^2]) + (Sqrt[2]*(1 + I*Sqrt[3])*(4*I + 3*Sqrt[3])*(1 + (109 - 6*Sqrt[330])^(2/3))*Sqrt[(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + x^2 + 2*x^3]*EllipticF[ArcSin[((109 - 6*Sqrt[330])^(1/6)*Sqrt[I*(2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x)])/(3^(1/4)*Sqrt[2*(1 - (109 - 6*Sqrt[330])^(2/3))])], (-2*Sqrt[3]*(1 - (109 - 6*Sqrt[330])^(2/3)))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((109 - 6*Sqrt[330])^(1/6)*(1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x)*Sqrt[-1 + (109 - 6*Sqrt[330])^(-2/3) + (109 - 6*Sqrt[330])^(2/3) - ((1 + (109 - 6*Sqrt[330])^(2/3))*(1 + 6*x))/(109 - 6*Sqrt[330])^(1/3) + (1 + 6*x)^2]) - (27*(1 - I*Sqrt[3])^2*Sqrt[2*(109 - 6*Sqrt[330])*(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + (I*(I + Sqrt[3]))/(109 - 6*Sqrt[330])^(1/3) - (1 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x]*Sqrt[2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x]*Sqrt[2 + x^2 + 2*x^3]*Sqrt[1 - (2*(1 + (109 - 6*Sqrt[330])^(2/3) + (109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)))/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[1 - (2*(1 + (109 - 6*Sqrt[330])^(2/3) + (109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)))/(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*EllipticPi[(3*I + Sqrt[3] + (3*I - Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))/(2*(I + ((8*I - 6*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3))/2 + I*(109 - 6*Sqrt[330])^(2/3))), ArcSin[(Sqrt[2]*(109 - 6*Sqrt[330])^(1/6)*Sqrt[1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x])/Sqrt[3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3)]], (3*I + Sqrt[3] + (3*I - Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((1 + (4 + (3*I)*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + (109 - 6*Sqrt[330])^(2/3))*Sqrt[1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x]*Sqrt[-1 + I*Sqrt[3] - (1 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3) + 2*(109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)]*Sqrt[-1 - I*Sqrt[3] + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3) + 2*(109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)]*(1 - (109 - 6*Sqrt[330])^(-2/3) - (109 - 6*Sqrt[330])^(2/3) + ((109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3))*(1 + 6*x) - (1 + 6*x)^2)) - (108*Sqrt[2*(109 - 6*Sqrt[330])*(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + (I*(I + Sqrt[3]))/(109 - 6*Sqrt[330])^(1/3) - (1 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x]*Sqrt[2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x]*Sqrt[2 + x^2 + 2*x^3]*Sqrt[1 - (2*(1 + (109 - 6*Sqrt[330])^(2/3) + (109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)))/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[1 - (2*(1 + (109 - 6*Sqrt[330])^(2/3) + (109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)))/(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*EllipticPi[(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))/(2*(1 - 5*(109 - 6*Sqrt[330])^(1/3) + (109 - 6*Sqrt[330])^(2/3))), ArcSin[(Sqrt[2]*(109 - 6*Sqrt[330])^(1/6)*Sqrt[1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x])/Sqrt[3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3)]], (3*I + Sqrt[3] + (3*I - Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((1 - 5*(109 - 6*Sqrt[330])^(1/3) + (109 - 6*Sqrt[330])^(2/3))*Sqrt[1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x]*Sqrt[-1 + I*Sqrt[3] - (1 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3) + 2*(109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)]*Sqrt[-1 - I*Sqrt[3] + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3) + 2*(109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)]*(1 - (109 - 6*Sqrt[330])^(-2/3) - (109 - 6*Sqrt[330])^(2/3) + ((109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3))*(1 + 6*x) - (1 + 6*x)^2)) - (27*(1 + I*Sqrt[3])^2*Sqrt[2*(109 - 6*Sqrt[330])*(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[2 + (I*(I + Sqrt[3]))/(109 - 6*Sqrt[330])^(1/3) - (1 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x]*Sqrt[2 - (1 + I*Sqrt[3])/(109 - 6*Sqrt[330])^(1/3) + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + 12*x]*Sqrt[2 + x^2 + 2*x^3]*Sqrt[1 - (2*(1 + (109 - 6*Sqrt[330])^(2/3) + (109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)))/(3 + I*Sqrt[3] + (3 - I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*Sqrt[1 - (2*(1 + (109 - 6*Sqrt[330])^(2/3) + (109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)))/(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))]*EllipticPi[(3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))/(2*(1 + (4 - (3*I)*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + (109 - 6*Sqrt[330])^(2/3))), ArcSin[(Sqrt[2]*(109 - 6*Sqrt[330])^(1/6)*Sqrt[1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x])/Sqrt[3 - I*Sqrt[3] + (3 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3)]], (3*I + Sqrt[3] + (3*I - Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))/(3*I - Sqrt[3] + (3*I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3))])/((1 + (4 - (3*I)*Sqrt[3])*(109 - 6*Sqrt[330])^(1/3) + (109 - 6*Sqrt[330])^(2/3))*Sqrt[1 + (109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3) + 6*x]*Sqrt[-1 + I*Sqrt[3] - (1 + I*Sqrt[3])*(109 - 6*Sqrt[330])^(2/3) + 2*(109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)]*Sqrt[-1 - I*Sqrt[3] + I*(I + Sqrt[3])*(109 - 6*Sqrt[330])^(2/3) + 2*(109 - 6*Sqrt[330])^(1/3)*(1 + 6*x)]*(1 - (109 - 6*Sqrt[330])^(-2/3) - (109 - 6*Sqrt[330])^(2/3) + ((109 - 6*Sqrt[330])^(-1/3) + (109 - 6*Sqrt[330])^(1/3))*(1 + 6*x) - (1 + 6*x)^2)) - 2*Defer[Int][Sqrt[2 + x^2 + 2*x^3]/(1 + x^2 + x^3), x] - 3*Defer[Int][(x*Sqrt[2 + x^2 + 2*x^3])/(1 + x^2 + x^3), x]","F",0,0,0,0,-1,"{}"
504,1,254,0,1.9943506,"\int \frac{b+a x^2}{\left(-b+c x+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Int[(b + a*x^2)/((-b + c*x + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","-\frac{2 \sqrt[4]{b} \sqrt{x} \sqrt{1-\frac{a x^2}{b}} \Pi \left(-\frac{2 \sqrt{a} \sqrt{b}}{c-\sqrt{c^2+4 a b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a x^3-b x}}-\frac{2 \sqrt[4]{b} \sqrt{x} \sqrt{1-\frac{a x^2}{b}} \Pi \left(-\frac{2 \sqrt{a} \sqrt{b}}{c+\sqrt{c^2+4 a b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a x^3-b x}}+\frac{2 \sqrt[4]{b} \sqrt{x} \sqrt{1-\frac{a x^2}{b}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{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*b^(1/4)*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticF[ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-(b*x) + a*x^3]) - (2*b^(1/4)*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[(-2*Sqrt[a]*Sqrt[b])/(c - Sqrt[4*a*b + c^2]), ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-(b*x) + a*x^3]) - (2*b^(1/4)*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[(-2*Sqrt[a]*Sqrt[b])/(c + Sqrt[4*a*b + c^2]), ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-(b*x) + a*x^3])","C",14,8,36,0.2222,1,"{2056, 6728, 329, 224, 221, 933, 168, 537}"
505,1,35,0,0.0122914,"\int x \sqrt{-1+x^4} \, dx","Int[x*Sqrt[-1 + x^4],x]","\frac{1}{4} x^2 \sqrt{x^4-1}-\frac{1}{4} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-1}}\right)","\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,"(x^2*Sqrt[-1 + x^4])/4 - ArcTanh[x^2/Sqrt[-1 + x^4]]/4","A",4,4,11,0.3636,1,"{275, 195, 217, 206}"
506,1,39,0,0.0378047,"\int \frac{\sqrt{-x+x^4}}{x^3} \, dx","Int[Sqrt[-x + x^4]/x^3,x]","\frac{2}{3} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)-\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*ArcTanh[x^2/Sqrt[-x + x^4]])/3","A",3,3,15,0.2000,1,"{2020, 2029, 206}"
507,1,49,0,0.0622679,"\int x^3 \sqrt{x+x^4} \, dx","Int[x^3*Sqrt[x + x^4],x]","\frac{1}{6} \sqrt{x^4+x} x^4+\frac{1}{12} \sqrt{x^4+x} x-\frac{1}{12} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)","\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,"(x*Sqrt[x + x^4])/12 + (x^4*Sqrt[x + x^4])/6 - ArcTanh[x^2/Sqrt[x + x^4]]/12","A",4,4,13,0.3077,1,"{2021, 2024, 2029, 206}"
508,1,36,0,0.040859,"\int \frac{1+x}{\sqrt{16+18 x+13 x^2+4 x^3+x^4}} \, dx","Int[(1 + x)/Sqrt[16 + 18*x + 13*x^2 + 4*x^3 + x^4],x]","\frac{1}{2} \tanh ^{-1}\left(\frac{2 (x+1)^2+7}{2 \sqrt{(x+1)^4+7 (x+1)^2+8}}\right)","\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,"ArcTanh[(7 + 2*(1 + x)^2)/(2*Sqrt[8 + 7*(1 + x)^2 + (1 + x)^4])]/2","A",4,4,26,0.1538,1,"{1680, 1107, 621, 206}"
509,0,0,0,0.7922016,"\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{x^2 \left(-1-a x^2+x^5\right)} \, dx","Int[(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,"(2*Sqrt[-1 + x^5])/x - (5*x^4*Sqrt[1 - x^5]*Hypergeometric2F1[1/2, 4/5, 9/5, x^5])/(4*Sqrt[-1 + x^5]) + 2*a*Defer[Int][Sqrt[-1 + x^5]/(1 + a*x^2 - x^5), x] + 5*Defer[Int][(x^3*Sqrt[-1 + x^5])/(-1 - a*x^2 + x^5), x]","F",0,0,0,0,-1,"{}"
510,1,39,0,0.0442422,"\int x \sqrt{-x+x^6} \, dx","Int[x*Sqrt[-x + x^6],x]","\frac{1}{5} x^2 \sqrt{x^6-x}-\frac{1}{5} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-x}}\right)","\frac{1}{5} x^2 \sqrt{x^6-x}-\frac{1}{5} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-x}}\right)",1,"(x^2*Sqrt[-x + x^6])/5 - ArcTanh[x^3/Sqrt[-x + x^6]]/5","A",3,3,13,0.2308,1,"{2021, 2029, 206}"
511,0,0,0,1.2350241,"\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","Int[((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,"(2*(1 + x^5))/Sqrt[x + x^6] - (10*x^5*Sqrt[1 + x^5]*Hypergeometric2F1[1/2, 9/10, 19/10, -x^5])/(9*Sqrt[x + x^6]) + (2*a*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^10]/(-1 + a*x^2 - x^10), x], x, Sqrt[x]])/Sqrt[x + x^6] + (10*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][(x^8*Sqrt[1 + x^10])/(1 - a*x^2 + x^10), x], x, Sqrt[x]])/Sqrt[x + x^6]","F",0,0,0,0,-1,"{}"
512,1,39,0,0.0157004,"\int \frac{1}{\sqrt{x-\sqrt{-1+x^2}}} \, dx","Int[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",3,2,17,0.1176,1,"{2117, 14}"
513,1,387,0,1.2800682,"\int \frac{1+x^2}{\left(-1+2 x+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Int[(1 + x^2)/((-1 + 2*x + x^2)*Sqrt[-x - x^2 + x^3]),x]","\frac{\sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(1-\sqrt{2}\right) \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(1+\sqrt{2}\right) \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{x^3-x^2-x}}{x^2-x-1}\right)}{\sqrt{3}}",1,"(Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[((1 - Sqrt[2])*(1 + Sqrt[5]))/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3] - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[((1 + Sqrt[2])*(1 + Sqrt[5]))/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3]","C",15,8,32,0.2500,0,"{2056, 6728, 716, 1098, 934, 168, 538, 537}"
514,-1,0,0,180.0042284,"\int \frac{\left(2+x^3\right) \sqrt{-1+x^2+x^3}}{\left(-1+x^3\right)^2} \, dx","Int[((2 + x^3)*Sqrt[-1 + x^2 + x^3])/(-1 + x^3)^2,x]","\text{\$Aborted}","-\frac{\sqrt{x^3+x^2-1} x}{x^3-1}-\tanh ^{-1}\left(\frac{x}{\sqrt{x^3+x^2-1}}\right)",1,"$Aborted","F",0,0,0,0,-1,"{}"
515,1,355,0,1.0520607,"\int \frac{2+x^2}{\left(-2+x^2\right) \sqrt{-2 x+2 x^2+x^3}} \, dx","Int[(2 + x^2)/((-2 + x^2)*Sqrt[-2*x + 2*x^2 + x^3]),x]","\frac{\sqrt{x} \sqrt{\frac{2-\left(1-\sqrt{3}\right) x}{2-\left(1+\sqrt{3}\right) x}} \sqrt{\left(1+\sqrt{3}\right) x-2} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{3} \sqrt{x}}{\sqrt{\left(1+\sqrt{3}\right) x-2}}\right)|\frac{1}{6} \left(3+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{\frac{1}{2-\left(1+\sqrt{3}\right) x}} \sqrt{x^3+2 x^2-2 x}}-\frac{2 \sqrt{2-\sqrt{3}} \sqrt{x} \sqrt{x+\sqrt{3}+1} \sqrt{\frac{x}{1-\sqrt{3}}+1} \Pi \left(-\frac{1-\sqrt{3}}{\sqrt{2}};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{-1+\sqrt{3}}}\right)|-2+\sqrt{3}\right)}{\sqrt{x^3+2 x^2-2 x}}-\frac{2 \sqrt{2-\sqrt{3}} \sqrt{x} \sqrt{x+\sqrt{3}+1} \sqrt{\frac{x}{1-\sqrt{3}}+1} \Pi \left(\frac{1-\sqrt{3}}{\sqrt{2}};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{-1+\sqrt{3}}}\right)|-2+\sqrt{3}\right)}{\sqrt{x^3+2 x^2-2 x}}","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x^3+2 x^2-2 x}}{x^2+2 x-2}\right)",1,"(Sqrt[x]*Sqrt[(2 - (1 - Sqrt[3])*x)/(2 - (1 + Sqrt[3])*x)]*Sqrt[-2 + (1 + Sqrt[3])*x]*EllipticF[ArcSin[(Sqrt[2]*3^(1/4)*Sqrt[x])/Sqrt[-2 + (1 + Sqrt[3])*x]], (3 + Sqrt[3])/6])/(3^(1/4)*Sqrt[(2 - (1 + Sqrt[3])*x)^(-1)]*Sqrt[-2*x + 2*x^2 + x^3]) - (2*Sqrt[2 - Sqrt[3]]*Sqrt[x]*Sqrt[1 + Sqrt[3] + x]*Sqrt[1 + x/(1 - Sqrt[3])]*EllipticPi[-((1 - Sqrt[3])/Sqrt[2]), ArcSin[Sqrt[x]/Sqrt[-1 + Sqrt[3]]], -2 + Sqrt[3]])/Sqrt[-2*x + 2*x^2 + x^3] - (2*Sqrt[2 - Sqrt[3]]*Sqrt[x]*Sqrt[1 + Sqrt[3] + x]*Sqrt[1 + x/(1 - Sqrt[3])]*EllipticPi[(1 - Sqrt[3])/Sqrt[2], ArcSin[Sqrt[x]/Sqrt[-1 + Sqrt[3]]], -2 + Sqrt[3]])/Sqrt[-2*x + 2*x^2 + x^3]","C",15,8,29,0.2759,0,"{2056, 6725, 716, 1098, 934, 168, 538, 537}"
516,1,5379,0,137.416547,"\int \frac{2+x}{(-1+x) \sqrt{-1+3 x+a x^2+x^3}} \, dx","Int[(2 + x)/((-1 + x)*Sqrt[-1 + 3*x + a*x^2 + x^3]),x]","\frac{\sqrt[3]{2} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}} \sqrt{\frac{2 \sqrt[3]{2} a^2-2 \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} a-6 \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} x+\left(-4 a^3+54 a+6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}-18 \sqrt[3]{2}}{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}-54}} \sqrt{-\frac{\frac{2\ 2^{2/3} \left(9-a^2\right)^2}{\left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}+2 \left(9-a^2\right)+18 \left(\frac{a}{3}+x\right)^2-\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right) (a+3 x)}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}{\frac{\left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)^2}{18 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}-\frac{2}{9} \left(\frac{2\ 2^{2/3} \left(9-a^2\right)^2}{\left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}+2 \left(9-a^2\right)+\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{2 \sqrt[3]{2} a^2+4 \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} a+12 \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} x+\left(-4 a^3+54 a+6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}-18 \sqrt[3]{2}}{\sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}}}}{2^{3/4} \sqrt[4]{3}}\right)|-\frac{2 \sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}}{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{3 \sqrt{3} \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} \sqrt{x^3+a x^2+3 x-1}}-\frac{3\ 2^{2/3} \sqrt{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54} \sqrt{2 a+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+6 x} \sqrt{\frac{\sqrt[3]{2} \left(2 a^2+\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-18\right)}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}+4 (a+3 x)-\frac{\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}} \sqrt{\frac{\sqrt[3]{2} \left(2 a^2+\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-18\right)}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}+4 (a+3 x)+\frac{\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}} \sqrt{\frac{2 \left(-2 a^2+2^{2/3} \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a+3 x)-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}+18\right)}{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-54}+1} \sqrt{\frac{2 \left(-2 a^2+2^{2/3} \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a+3 x)-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}+18\right)}{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-54}+1} \Pi \left(\frac{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}{2^{2/3} \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27} \left(2 (a+3)+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}\right)};\sin ^{-1}\left(\frac{\sqrt[3]{2} \sqrt[6]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} \sqrt{2 a+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+6 x}}{\sqrt{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}}\right)|\frac{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{\sqrt[6]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} \left(2 (a+3)+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}\right) \sqrt{x^3+a x^2+3 x-1} \sqrt{\frac{2 \sqrt[3]{2} a^2+4 \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a+3 x)+\left(-4 a^3+54 a+6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}-\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-18 \sqrt[3]{2}}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}} \sqrt{\frac{2 \sqrt[3]{2} a^2+4 \sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a+3 x)+\left(-4 a^3+54 a+6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a+3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-18 \sqrt[3]{2}}{\sqrt[3]{-2 a^3+27 a+3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}}}","-\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^(1/3)*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)]*Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 - 2*a*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) + (54 + 54*a - 4*a^3 + 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 6*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*x)/(-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)])]*Sqrt[-((2*(9 - a^2) + (2*2^(2/3)*(9 - a^2)^2)/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 18*(a/3 + x)^2 - (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3))*(a + 3*x))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3))/((18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3))^2/(18*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)) - (2*(2*(9 - a^2) + (2*2^(2/3)*(9 - a^2)^2)/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/9))]*EllipticF[ArcSin[Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 + 4*a*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) + (54 + 54*a - 4*a^3 + 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)] + 12*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*x)/Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)]]/(2^(3/4)*3^(1/4))], (-2*2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])])/(3*Sqrt[3]*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*Sqrt[-1 + 3*x + a*x^2 + x^3]) - (3*2^(2/3)*Sqrt[54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)]]*Sqrt[2*a + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3) + 6*x]*Sqrt[(2^(1/3)*(-18 + 2*a^2 + 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3)))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) - (Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)])/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) + 4*(a + 3*x)]*Sqrt[(2^(1/3)*(-18 + 2*a^2 + 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3)))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) + (Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)])/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) + 4*(a + 3*x)]*Sqrt[1 + (2*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 2^(2/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a + 3*x)))/(-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])]*Sqrt[1 + (2*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 2^(2/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a + 3*x)))/(-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])]*EllipticPi[(54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])/(2^(2/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3)*(2*(3 + a) + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3))), ArcSin[(2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/6)*Sqrt[2*a + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3) + 6*x])/Sqrt[54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)]]], (54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])])/((27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/6)*(2*(3 + a) + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3))*Sqrt[-1 + 3*x + a*x^2 + x^3]*Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 + (54 + 54*a - 4*a^3 + 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)] + 4*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a + 3*x))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)]*Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 + (54 + 54*a - 4*a^3 + 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)] + 4*(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a + 3*x))/(27 + 27*a - 2*a^3 + 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)])","C",13,11,26,0.4231,0,"{6742, 2067, 2066, 718, 419, 2081, 2080, 934, 169, 538, 537}"
517,1,5437,0,131.8130724,"\int \frac{-2+x}{(1+x) \sqrt{1+3 x+a x^2+x^3}} \, dx","Int[(-2 + x)/((1 + x)*Sqrt[1 + 3*x + a*x^2 + x^3]),x]","\frac{\sqrt[3]{2} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}} \sqrt{\frac{2 \sqrt[3]{2} a^2+2 \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} a+6 \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} x+\left(4 a^3-54 a-6 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+54\right)^{2/3}-18 \sqrt[3]{2}}{6 a^2+3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}-54}} \sqrt{-\frac{\frac{2 \left(9-a^2\right)^2}{\left(a^3-\frac{27 a}{2}+\frac{3}{2} \left(9-\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}\right)\right)^{2/3}}+2 \left(9-a^2\right)+18 \left(\frac{a}{3}+x\right)^2+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right) (a+3 x)}{\sqrt[3]{2 a^3-27 a+3 \left(9-\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}\right)}}+\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}}{\frac{\left(-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right)^2}{18 \sqrt[3]{2} \left(2 a^3-27 a+3 \left(9-\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}\right)\right)^{2/3}}-\frac{2}{9} \left(\frac{2 \left(9-a^2\right)^2}{\left(a^3-\frac{27 a}{2}+\frac{3}{2} \left(9-\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}\right)\right)^{2/3}}+2 \left(9-a^2\right)+\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{-2 \sqrt[3]{2} a^2+4 \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} a+12 \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} x-\left(4 a^3-54 a-6 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}}}{2^{3/4} \sqrt[4]{3}}\right)|\frac{2 \sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{3 \sqrt{3} \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} \sqrt{x^3+a x^2+3 x+1}}-\frac{6 \sqrt[6]{2} \sqrt{3} \sqrt{6 a^2+3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}-54} \sqrt{\frac{a}{3}+\frac{2 a^2+\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-18}{3\ 2^{2/3} \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27}}+x} \sqrt{-\frac{2 a^2+\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-18}{\sqrt[3]{a^3-\frac{27 a}{2}-\frac{3}{2} \left(\sqrt{3} \sqrt{(a-3)^2 (4 a+15)}-9\right)}}+4 (a+3 x)-\frac{\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27}}} \sqrt{-\frac{2 a^2+\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-18}{\sqrt[3]{a^3-\frac{27 a}{2}-\frac{3}{2} \left(\sqrt{3} \sqrt{(a-3)^2 (4 a+15)}-9\right)}}+4 (a+3 x)+\frac{\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27}}} \sqrt{1-\frac{2 \left(-2 a^2-2^{2/3} \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} (a+3 x)-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}+18\right)}{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}} \sqrt{\frac{2 \left(-2 a^2-2^{2/3} \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} (a+3 x)-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}+18\right)}{6 a^2+3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}-54}+1} \Pi \left(\frac{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}{2 \left(-2 a^2-2^{2/3} \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} a-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+3\ 2^{2/3} \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27}+18\right)};\sin ^{-1}\left(\frac{\sqrt[3]{2} \sqrt[6]{2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} \sqrt{\frac{2 a^2+\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-18}{\sqrt[3]{a^3-\frac{27 a}{2}-\frac{3}{2} \left(\sqrt{3} \sqrt{(a-3)^2 (4 a+15)}-9\right)}}+2 (a+3 x)}}{\sqrt{6 a^2+3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}-54}}\right)|\frac{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{\sqrt[6]{2 a^3-27 a+3 \left(9-\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}\right)} \left(-2 a+\frac{-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18}{\sqrt[3]{a^3-\frac{27 a}{2}+\frac{3}{2} \left(9-\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}\right)}}+6\right) \sqrt{x^3+a x^2+3 x+1} \sqrt{\frac{-2 \sqrt[3]{2} a^2+4 \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} (a+3 x)-\left(4 a^3-54 a-6 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+54\right)^{2/3}-\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27}}} \sqrt{\frac{-2 \sqrt[3]{2} a^2+4 \sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} (a+3 x)-\left(4 a^3-54 a-6 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt[3]{2 a^3-27 a-3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27}}}}","-\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^(1/3)*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)]*Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 + (54 - 54*a + 4*a^3 - 6*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 2*a*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3) + 6*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*x)/(-54 + 6*a^2 + 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)])]*Sqrt[-((2*(9 - a^2) + 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + (2*(9 - a^2)^2)/((-27*a)/2 + a^3 + (3*(9 - Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(2/3) + 18*(a/3 + x)^2 + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))*(a + 3*x))/(-27*a + 2*a^3 + 3*(9 - Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))^(1/3))/((18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))^2/(18*2^(1/3)*(-27*a + 2*a^3 + 3*(9 - Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))^(2/3)) - (2*(2*(9 - a^2) + 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + (2*(9 - a^2)^2)/((-27*a)/2 + a^3 + (3*(9 - Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(2/3)))/9))]*EllipticF[ArcSin[Sqrt[(18*2^(1/3) - 2*2^(1/3)*a^2 - (54 - 54*a + 4*a^3 - 6*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)] + 12*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*x)/Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)]]/(2^(3/4)*3^(1/4))], (2*2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])])/(3*Sqrt[3]*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*Sqrt[1 + 3*x + a*x^2 + x^3]) - (6*2^(1/6)*Sqrt[3]*Sqrt[-54 + 6*a^2 + 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)]]*Sqrt[a/3 + (-18 + 2*a^2 + 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3))/(3*2^(2/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)) + x]*Sqrt[-((Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)])/(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)) - (-18 + 2*a^2 + 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3))/((-27*a)/2 + a^3 - (3*(-9 + Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)]))/2)^(1/3) + 4*(a + 3*x)]*Sqrt[(Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)])/(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3) - (-18 + 2*a^2 + 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3))/((-27*a)/2 + a^3 - (3*(-9 + Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)]))/2)^(1/3) + 4*(a + 3*x)]*Sqrt[1 - (2*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(2/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*(a + 3*x)))/(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)])]*Sqrt[1 + (2*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(2/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*(a + 3*x)))/(-54 + 6*a^2 + 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)])]*EllipticPi[(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])/(2*(18 - 2*a^2 + 3*2^(2/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3) - 2^(2/3)*a*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))), ArcSin[(2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/6)*Sqrt[(-18 + 2*a^2 + 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3))/((-27*a)/2 + a^3 - (3*(-9 + Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)]))/2)^(1/3) + 2*(a + 3*x)])/Sqrt[-54 + 6*a^2 + 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)]]], (54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])])/((-27*a + 2*a^3 + 3*(9 - Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))^(1/6)*(6 - 2*a + (18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))/((-27*a)/2 + a^3 + (3*(9 - Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(1/3))*Sqrt[1 + 3*x + a*x^2 + x^3]*Sqrt[(18*2^(1/3) - 2*2^(1/3)*a^2 - (54 - 54*a + 4*a^3 - 6*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)] + 4*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*(a + 3*x))/(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)]*Sqrt[(18*2^(1/3) - 2*2^(1/3)*a^2 - (54 - 54*a + 4*a^3 - 6*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)] + 4*(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*(a + 3*x))/(27 - 27*a + 2*a^3 - 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)])","C",13,11,26,0.4231,0,"{6742, 2067, 2066, 718, 419, 2081, 2080, 934, 169, 538, 537}"
518,0,0,0,16.4298124,"\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","Int[(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]","\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","-\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*Sqrt[b]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[b]], b/a])/Sqrt[(a - x)*(b - x)*x] - (2*(3*a*b - a*d - b*d)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(a*b*d - a*(1 + b/a)*d*x^2 + d*x^4 - x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*(2*a + 2*b - d)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^4/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(a*b*d - a*(1 + b/a)*d*x^2 + d*x^4 - x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*a*b*d*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][1/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(-(a*b*d) + a*(1 + b/a)*d*x^2 - d*x^4 + x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
519,0,0,0,11.9648656,"\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","Int[(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]","\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","-\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*Sqrt[b]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[b]], b/a])/(d*Sqrt[(a - x)*(b - x)*x]) + (2*(a + b - 3*a*b*d)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(a*b - a*(1 + b/a)*x^2 + x^4 - d*x^6)), x], x, Sqrt[x]])/(d*Sqrt[(a - x)*(b - x)*x]) - (2*(1 - 2*a*d - 2*b*d)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^4/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(a*b - a*(1 + b/a)*x^2 + x^4 - d*x^6)), x], x, Sqrt[x]])/(d*Sqrt[(a - x)*(b - x)*x]) + (2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][1/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(-(a*b) + a*(1 + b/a)*x^2 - x^4 + d*x^6)), x], x, Sqrt[x]])/(d*Sqrt[(a - x)*(b - x)*x])","F",0,0,0,0,-1,"{}"
520,1,74,0,0.6614575,"\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","Int[((-1 + x^2)*Sqrt[1 + 2*x^2 + x^4])/((1 + x^2)*(1 + x^4)),x]","\frac{\sqrt{x^4+2 x^2+1} \tanh ^{-1}\left((-1)^{3/4} x\right)}{\sqrt{2} \left(x^2+1\right)}+\frac{i \sqrt{x^4+2 x^2+1} \tan ^{-1}\left((-1)^{3/4} x\right)}{\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,"(I*Sqrt[1 + 2*x^2 + x^4]*ArcTan[(-1)^(3/4)*x])/(Sqrt[2]*(1 + x^2)) + (Sqrt[1 + 2*x^2 + x^4]*ArcTanh[(-1)^(3/4)*x])/(Sqrt[2]*(1 + x^2))","C",12,7,34,0.2059,1,"{6725, 1147, 8, 1148, 388, 206, 203}"
521,0,0,0,0.1789584,"\int \frac{-1+x}{\sqrt{-7+4 x+14 x^2-12 x^3+x^4}} \, dx","Int[(-1 + x)/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4],x]","\int \frac{-1+x}{\sqrt{-7+4 x+14 x^2-12 x^3+x^4}} \, dx","\log (x-1)-\log \left(-x^2+\sqrt{x^4-12 x^3+14 x^2+4 x-7}+6 x-5\right)",1,"-Defer[Int][1/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4], x] + Defer[Int][x/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
522,1,451,0,1.7120019,"\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","Int[(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{k^2 x \left(1-x^2\right)}{\left(1-k^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{k^2 \left(1-x^2\right)}{\left(1-k^2\right) x \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\left(1-2 k^2\right) \left(1-x^2\right) \left(1-k^2 x^2\right)}{\left(1-k^2\right) x \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{2 k^2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} E\left(\sin ^{-1}(x)|k^2\right)}{\left(1-k^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{k \sqrt{1-x^2} \sqrt{1-k^2 x^2} E\left(\sin ^{-1}(k x)|\frac{1}{k^2}\right)}{\left(1-k^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\left(1-2 k^2\right) \sqrt{1-x^2} \sqrt{1-k^2 x^2} E\left(\sin ^{-1}(x)|k^2\right)}{\left(1-k^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 k^4 x \left(1-x^2\right)}{\left(1-k^2\right) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}","-\frac{\sqrt{k^2 x^4+\left(-k^2-1\right) x^2+1}}{x \left(k^2 x^2-1\right)}",1,"(k^2*(1 - x^2))/((1 - k^2)*x*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) + (k^2*x*(1 - x^2))/((1 - k^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (2*k^4*x*(1 - x^2))/((1 - k^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) + ((1 - 2*k^2)*(1 - x^2)*(1 - k^2*x^2))/((1 - k^2)*x*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) + (2*k^2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticE[ArcSin[x], k^2])/((1 - k^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) + ((1 - 2*k^2)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticE[ArcSin[x], k^2])/((1 - k^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (k*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticE[ArcSin[k*x], k^(-2)])/((1 - k^2)*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)]","C",14,10,54,0.1852,1,"{6719, 21, 6742, 414, 424, 472, 583, 524, 419, 471}"
523,1,40,0,0.0489174,"\int \frac{-2+x^6}{x \sqrt{-1+x^6} \left(2+x^6\right)} \, dx","Int[(-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",6,4,25,0.1600,1,"{573, 156, 63, 203}"
524,1,54,0,0.096936,"\int \frac{\left(2+x^3\right) \left(1+x^3+x^6\right)}{x \sqrt{1+x^3}} \, dx","Int[((2 + x^3)*(1 + x^3 + x^6))/(x*Sqrt[1 + x^3]),x]","\frac{2}{15} \left(x^3+1\right)^{5/2}+\frac{2}{9} \left(x^3+1\right)^{3/2}+\frac{2 \sqrt{x^3+1}}{3}-\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])/3 + (2*(1 + x^3)^(3/2))/9 + (2*(1 + x^3)^(5/2))/15 - (4*ArcTanh[Sqrt[1 + x^3]])/3","A",5,4,26,0.1538,1,"{1821, 1612, 63, 207}"
525,0,0,0,0.4154499,"\int \frac{4 x+3 x^2}{\sqrt{-5+4 x^2+2 x^3+4 x^4+4 x^5+x^6}} \, dx","Int[(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,"4*Defer[Int][x/Sqrt[-5 + 4*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + x^6], x] + 3*Defer[Int][x^2/Sqrt[-5 + 4*x^2 + 2*x^3 + 4*x^4 + 4*x^5 + x^6], x]","F",0,0,0,0,-1,"{}"
526,1,40,0,0.6730818,"\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","Int[(x^2*Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(b*x^6 + a*(q + p*x^5)^3),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a} \left(p x^5+q\right)^{3/2}}{\sqrt{b} x^3}\right)}{3 \sqrt{a} \sqrt{b}}","-\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,"(2*ArcTan[(Sqrt[a]*(q + p*x^5)^(3/2))/(Sqrt[b]*x^3)])/(3*Sqrt[a]*Sqrt[b])","A",2,2,44,0.04545,1,"{6714, 205}"
527,1,65,0,0.0441183,"\int \frac{x^8}{\sqrt{-b+a x^3}} \, dx","Int[x^8/Sqrt[-b + a*x^3],x]","\frac{2 b^2 \sqrt{a x^3-b}}{3 a^3}+\frac{2 \left(a x^3-b\right)^{5/2}}{15 a^3}+\frac{4 b \left(a x^3-b\right)^{3/2}}{9 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*b^2*Sqrt[-b + a*x^3])/(3*a^3) + (4*b*(-b + a*x^3)^(3/2))/(9*a^3) + (2*(-b + a*x^3)^(5/2))/(15*a^3)","A",3,2,17,0.1176,1,"{266, 43}"
528,1,42,0,0.0283002,"\int x^5 \sqrt{-b+a x^3} \, dx","Int[x^5*Sqrt[-b + a*x^3],x]","\frac{2 \left(a x^3-b\right)^{5/2}}{15 a^2}+\frac{2 b \left(a x^3-b\right)^{3/2}}{9 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*(-b + a*x^3)^(3/2))/(9*a^2) + (2*(-b + a*x^3)^(5/2))/(15*a^2)","A",3,2,17,0.1176,1,"{266, 43}"
529,0,0,0,1.2283883,"\int \frac{2 b+a x^3}{\sqrt{-b+a x^3} \left(-2 b-3 x^2+2 a x^3\right)} \, dx","Int[(2*b + a*x^3)/(Sqrt[-b + a*x^3]*(-2*b - 3*x^2 + 2*a*x^3)),x]","\int \frac{2 b+a x^3}{\sqrt{-b+a x^3} \left(-2 b-3 x^2+2 a x^3\right)} \, dx","\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[2 - Sqrt[3]]*(b^(1/3) - a^(1/3)*x)*Sqrt[(b^(2/3) + a^(1/3)*b^(1/3)*x + a^(2/3)*x^2)/((1 - Sqrt[3])*b^(1/3) - a^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*b^(1/3) - a^(1/3)*x)/((1 - Sqrt[3])*b^(1/3) - a^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*a^(1/3)*Sqrt[-((b^(1/3)*(b^(1/3) - a^(1/3)*x))/((1 - Sqrt[3])*b^(1/3) - a^(1/3)*x)^2)]*Sqrt[-b + a*x^3])) - 3*b*Defer[Int][1/((2*b + 3*x^2 - 2*a*x^3)*Sqrt[-b + a*x^3]), x] + (3*Defer[Int][x^2/(Sqrt[-b + a*x^3]*(-2*b - 3*x^2 + 2*a*x^3)), x])/2","F",0,0,0,0,-1,"{}"
530,1,334,0,1.1893427,"\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","Int[((-1 + x^4)*Sqrt[1 + x^4]*(1 + x^2 + x^4))/(x^4*(1 - x^2 + x^4)),x]","\frac{1}{3} \sqrt{x^4+1} x+\frac{2 \sqrt{x^4+1}}{x}-2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)+\frac{\sqrt{x^4+1}}{3 x^3}-\frac{\left(\sqrt{3}+i\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\left(\sqrt{3}+3 i\right) \sqrt{x^4+1}}+\frac{\left(3+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}+\frac{\left(3-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}-\frac{\left(-\sqrt{3}+i\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\left(-\sqrt{3}+3 i\right) \sqrt{x^4+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\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,"Sqrt[1 + x^4]/(3*x^3) + (2*Sqrt[1 + x^4])/x + (x*Sqrt[1 + x^4])/3 - 2*ArcTanh[x/Sqrt[1 + x^4]] - (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] - ((I - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/((3*I - Sqrt[3])*Sqrt[1 + x^4]) + ((3 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) + ((3 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) - ((I + Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/((3*I + Sqrt[3])*Sqrt[1 + x^4])","C",26,10,38,0.2632,1,"{6728, 195, 220, 277, 305, 1196, 1209, 1198, 1217, 1707}"
531,0,0,0,1.2246832,"\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","Int[(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,"-4*c*Defer[Int][1/((c + b*x + a*x^2)^(1/4)*(c + b*x + a*x^2 - x^4)), x] - 3*b*Defer[Int][x/((c + b*x + a*x^2)^(1/4)*(c + b*x + a*x^2 - x^4)), x] - 2*a*Defer[Int][x^2/((c + b*x + a*x^2)^(1/4)*(c + b*x + a*x^2 - x^4)), x]","F",0,0,0,0,-1,"{}"
532,1,57,0,0.1187488,"\int \frac{\left(2+x^3\right) \left(1+x^3+x^6\right)}{x^4 \sqrt{1+x^3}} \, dx","Int[((2 + x^3)*(1 + x^3 + x^6))/(x^4*Sqrt[1 + x^3]),x]","\frac{2}{9} \left(x^3+1\right)^{3/2}-\frac{2 \sqrt{x^3+1}}{3 x^3}+\frac{4 \sqrt{x^3+1}}{3}-\frac{4}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\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,"(4*Sqrt[1 + x^3])/3 - (2*Sqrt[1 + x^3])/(3*x^3) + (2*(1 + x^3)^(3/2))/9 - (4*ArcTanh[Sqrt[1 + x^3]])/3","A",8,5,26,0.1923,1,"{1821, 1612, 51, 63, 207}"
533,1,63,0,0.0677225,"\int \frac{\sqrt{-1+x^3} \left(-2+x^3+2 x^6\right)}{x^{10}} \, dx","Int[(Sqrt[-1 + x^3]*(-2 + x^3 + 2*x^6))/x^10,x]","-\frac{2 \sqrt{x^3-1}}{3 x^3}+\frac{2}{3} \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{2 \sqrt{x^3-1}}{9 x^9}-\frac{2 \sqrt{x^3-1}}{9 x^6}","\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])/(9*x^9) - (2*Sqrt[-1 + x^3])/(9*x^6) - (2*Sqrt[-1 + x^3])/(3*x^3) + (2*ArcTan[Sqrt[-1 + x^3]])/3","A",7,7,23,0.3043,1,"{1474, 897, 1257, 1157, 12, 288, 203}"
534,1,41,0,0.0557587,"\int \frac{-4+13 x^6}{x \sqrt{-1+x^6} \left(-1+4 x^6\right)} \, dx","Int[(-4 + 13*x^6)/(x*Sqrt[-1 + x^6]*(-1 + 4*x^6)),x]","\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}}","\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,"(4*ArcTan[Sqrt[-1 + x^6]])/3 - ArcTan[(2*Sqrt[-1 + x^6])/Sqrt[3]]/(2*Sqrt[3])","A",6,4,29,0.1379,1,"{573, 156, 63, 203}"
535,0,0,0,1.7149008,"\int \frac{-b+2 a x^3}{\left(b-x+a x^3\right) \sqrt[4]{b x^3+a x^6}} \, dx","Int[(-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,"(8*x*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/12, 1/4, 13/12, -((a*x^3)/b)])/(b*x^3 + a*x^6)^(1/4) - (12*b*x^(3/4)*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][1/((b + a*x^12)^(1/4)*(b - x^4 + a*x^12)), x], x, x^(1/4)])/(b*x^3 + a*x^6)^(1/4) + (8*x^(3/4)*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^4/((b + a*x^12)^(1/4)*(b - x^4 + a*x^12)), x], x, x^(1/4)])/(b*x^3 + a*x^6)^(1/4)","F",0,0,0,0,-1,"{}"
536,1,187,0,1.4368676,"\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","Int[(x^3*(b + 2*a*x^5))/((b*x + a*x^6)^(1/4)*(-1 + b*x^5 + a*x^10)),x]","\frac{8 a x^4 \sqrt[4]{\frac{a x^5}{b}+1} F_1\left(\frac{3}{4};1,\frac{1}{4};\frac{7}{4};-\frac{2 a x^5}{b-\sqrt{b^2+4 a}},-\frac{a x^5}{b}\right)}{15 \left(b-\sqrt{4 a+b^2}\right) \sqrt[4]{a x^6+b x}}+\frac{8 a x^4 \sqrt[4]{\frac{a x^5}{b}+1} F_1\left(\frac{3}{4};1,\frac{1}{4};\frac{7}{4};-\frac{2 a x^5}{b+\sqrt{b^2+4 a}},-\frac{a x^5}{b}\right)}{15 \left(\sqrt{4 a+b^2}+b\right) \sqrt[4]{a x^6+b x}}","\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,"(8*a*x^4*(1 + (a*x^5)/b)^(1/4)*AppellF1[3/4, 1, 1/4, 7/4, (-2*a*x^5)/(b - Sqrt[4*a + b^2]), -((a*x^5)/b)])/(15*(b - Sqrt[4*a + b^2])*(b*x + a*x^6)^(1/4)) + (8*a*x^4*(1 + (a*x^5)/b)^(1/4)*AppellF1[3/4, 1, 1/4, 7/4, (-2*a*x^5)/(b + Sqrt[4*a + b^2]), -((a*x^5)/b)])/(15*(b + Sqrt[4*a + b^2])*(b*x + a*x^6)^(1/4))","C",11,6,39,0.1538,0,"{2056, 6728, 466, 465, 511, 510}"
537,1,42,0,0.0173864,"\int \frac{\sqrt[4]{1+x^3}}{x} \, dx","Int[(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",6,6,13,0.4615,1,"{266, 50, 63, 212, 206, 203}"
538,0,0,0,2.6343182,"\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","Int[(-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]","\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","\frac{2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt{p x^3+q}}{\sqrt{c} (a x+b)}\right)}{\sqrt{c} \sqrt{d}}",1,"(2*Sqrt[2 + Sqrt[3]]*a*(q^(1/3) + p^(1/3)*x)*Sqrt[(q^(2/3) - p^(1/3)*q^(1/3)*x + p^(2/3)*x^2)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*q^(1/3) + p^(1/3)*x)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*d*p^(1/3)*Sqrt[(q^(1/3)*(q^(1/3) + p^(1/3)*x))/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*Sqrt[q + p*x^3]) - (a*(b^2*c + 3*d*q)*Defer[Int][1/(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])/d - (2*a^2*b*c*Defer[Int][x/(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])/d - ((a^3*c - 3*b*d*p)*Defer[Int][x^2/(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])/d","F",0,0,0,0,-1,"{}"
539,0,0,0,0.6799761,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^7 \left(1+x^3\right)} \, dx","Int[((-1 + x^3)*Sqrt[-1 + x^6])/(x^7*(1 + x^3)),x]","\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^7 \left(1+x^3\right)} \, dx","\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,"(-2*Sqrt[-1 + x^6])/3 + Sqrt[-1 + x^6]/(6*x^6) - (2*Sqrt[-1 + x^6])/(3*x^3) + ArcTan[Sqrt[-1 + x^6]]/2 + (2*ArcTanh[x^3/Sqrt[-1 + x^6]])/3 + (2*Defer[Int][Sqrt[-1 + x^6]/(1 + x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(-1 - I*Sqrt[3] + 2*x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(-1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
540,0,0,0,0.6268063,"\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x^7 \left(-1+x^3\right)} \, dx","Int[((1 + x^3)*Sqrt[-1 + x^6])/(x^7*(-1 + x^3)),x]","\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x^7 \left(-1+x^3\right)} \, dx","\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,"(-2*Sqrt[-1 + x^6])/3 + Sqrt[-1 + x^6]/(6*x^6) + (2*Sqrt[-1 + x^6])/(3*x^3) + ArcTan[Sqrt[-1 + x^6]]/2 - (2*ArcTanh[x^3/Sqrt[-1 + x^6]])/3 + (2*Defer[Int][Sqrt[-1 + x^6]/(-1 + x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(1 - I*Sqrt[3] + 2*x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
541,1,42,0,0.0180213,"\int \frac{\sqrt[4]{1+x^6}}{x} \, dx","Int[(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",6,6,13,0.4615,1,"{266, 50, 63, 212, 206, 203}"
542,1,51,0,0.0289826,"\int \frac{1+x^{12}}{x^4 \sqrt{-1+x^6}} \, dx","Int[(1 + x^12)/(x^4*Sqrt[-1 + x^6]),x]","\frac{1}{6} \sqrt{x^6-1} x^3+\frac{\sqrt{x^6-1}}{3 x^3}+\frac{1}{6} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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]/(3*x^3) + (x^3*Sqrt[-1 + x^6])/6 + ArcTanh[x^3/Sqrt[-1 + x^6]]/6","A",5,5,18,0.2778,1,"{1487, 451, 275, 217, 206}"
543,1,63,0,0.0254915,"\int \frac{1}{x^{10} \sqrt{1+x^3}} \, dx","Int[1/(x^10*Sqrt[1 + x^3]),x]","-\frac{5 \sqrt{x^3+1}}{24 x^3}+\frac{5}{24} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{9 x^9}+\frac{5 \sqrt{x^3+1}}{36 x^6}","\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,"-1/9*Sqrt[1 + x^3]/x^9 + (5*Sqrt[1 + x^3])/(36*x^6) - (5*Sqrt[1 + x^3])/(24*x^3) + (5*ArcTanh[Sqrt[1 + x^3]])/24","A",6,4,13,0.3077,1,"{266, 51, 63, 207}"
544,1,109,0,0.3175757,"\int \frac{-1+x^3}{x^6 \sqrt[3]{x^2+x^3}} \, dx","Int[(-1 + x^3)/(x^6*(x^2 + x^3)^(1/3)),x]","-\frac{57213 \left(x^3+x^2\right)^{2/3}}{52360 x^2}+\frac{19071 \left(x^3+x^2\right)^{2/3}}{26180 x^3}+\frac{3 \left(x^3+x^2\right)^{2/3}}{17 x^7}-\frac{45 \left(x^3+x^2\right)^{2/3}}{238 x^6}+\frac{270 \left(x^3+x^2\right)^{2/3}}{1309 x^5}-\frac{6357 \left(x^3+x^2\right)^{2/3}}{10472 x^4}","-\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 + x^3)^(2/3))/(17*x^7) - (45*(x^2 + x^3)^(2/3))/(238*x^6) + (270*(x^2 + x^3)^(2/3))/(1309*x^5) - (6357*(x^2 + x^3)^(2/3))/(10472*x^4) + (19071*(x^2 + x^3)^(2/3))/(26180*x^3) - (57213*(x^2 + x^3)^(2/3))/(52360*x^2)","B",11,3,20,0.1500,1,"{2052, 2016, 2014}"
545,0,0,0,0.9603521,"\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","Int[((-2 + x^3)*Sqrt[1 + x^3]*(2 + x^2 + 2*x^3))/(x^4*(1 + x^2 + x^3)),x]","\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","\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*Sqrt[1 + x^3])/3 + (4*Sqrt[1 + x^3])/(3*x^3) - (2*Sqrt[1 + x^3])/x + (6*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[2]*3^(3/4)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - 2*Defer[Int][Sqrt[1 + x^3]/(1 + x^2 + x^3), x] - 3*Defer[Int][(x*Sqrt[1 + x^3])/(1 + x^2 + x^3), x]","F",0,0,0,0,-1,"{}"
546,1,350,0,1.4319978,"\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","Int[((-1 + x^4)*Sqrt[1 + x^2 + x^4])/((1 + x^4)*(1 - x^2 + x^4)),x]","\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)-\frac{\left(\sqrt{3}+i\right) \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\left(\sqrt{3}+3 i\right) \sqrt{x^4+x^2+1}}+\frac{\left(5+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}+\frac{\left(5-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}-\frac{\left(-\sqrt{3}+i\right) \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\left(-\sqrt{3}+3 i\right) \sqrt{x^4+x^2+1}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{2 \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,"ArcTanh[x/Sqrt[1 + x^2 + x^4]] - Sqrt[2]*ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^2 + x^4]] - (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(2*Sqrt[1 + x^2 + x^4]) - ((I - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/((3*I - Sqrt[3])*Sqrt[1 + x^2 + x^4]) + ((5 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4]) + ((5 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4]) - ((I + Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/((3*I + Sqrt[3])*Sqrt[1 + x^2 + x^4])","C",34,8,37,0.2162,1,"{6725, 1208, 1197, 1103, 1195, 1216, 1706, 6728}"
547,0,0,0,0.5915582,"\int \frac{\sqrt{1+x+x^2+x^4} \left(-2-x+2 x^4\right)}{\left(1+x+x^4\right)^2} \, dx","Int[(Sqrt[1 + x + x^2 + x^4]*(-2 - x + 2*x^4))/(1 + x + x^4)^2,x]","\int \frac{\sqrt{1+x+x^2+x^4} \left(-2-x+2 x^4\right)}{\left(1+x+x^4\right)^2} \, dx","-\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,"-4*Defer[Int][Sqrt[1 + x + x^2 + x^4]/(1 + x + x^4)^2, x] - 3*Defer[Int][(x*Sqrt[1 + x + x^2 + x^4])/(1 + x + x^4)^2, x] + 2*Defer[Int][Sqrt[1 + x + x^2 + x^4]/(1 + x + x^4), x]","F",0,0,0,0,-1,"{}"
548,0,0,0,1.4039842,"\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","Int[((-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,"(-2*(1 - x^4))/Sqrt[-x + x^5] - (8*x^4*Sqrt[1 - x^4]*Hypergeometric2F1[1/2, 7/8, 15/8, x^4])/(7*Sqrt[-x + x^5]) + (2*a*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][Sqrt[-1 + x^8]/(1 + a*x^2 - x^8), x], x, Sqrt[x]])/Sqrt[-x + x^5] + (8*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][(x^6*Sqrt[-1 + x^8])/(-1 - a*x^2 + x^8), x], x, Sqrt[x]])/Sqrt[-x + x^5]","F",0,0,0,0,-1,"{}"
549,1,63,0,0.026359,"\int \frac{1}{x^{19} \sqrt{-1+x^6}} \, dx","Int[1/(x^19*Sqrt[-1 + x^6]),x]","\frac{5 \sqrt{x^6-1}}{48 x^6}+\frac{5}{48} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1}}{18 x^{18}}+\frac{5 \sqrt{x^6-1}}{72 x^{12}}","\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]/(18*x^18) + (5*Sqrt[-1 + x^6])/(72*x^12) + (5*Sqrt[-1 + x^6])/(48*x^6) + (5*ArcTan[Sqrt[-1 + x^6]])/48","A",6,4,13,0.3077,1,"{266, 51, 63, 203}"
550,1,51,0,0.0249698,"\int \frac{x^{14}}{\sqrt{-1+x^6}} \, dx","Int[x^14/Sqrt[-1 + x^6],x]","\frac{1}{12} \sqrt{x^6-1} x^9+\frac{1}{8} \sqrt{x^6-1} x^3+\frac{1}{8} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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])/8 + (x^9*Sqrt[-1 + x^6])/12 + ArcTanh[x^3/Sqrt[-1 + x^6]]/8","A",5,4,13,0.3077,1,"{275, 321, 217, 206}"
551,1,63,0,0.0252802,"\int \frac{\sqrt{-1+x^6}}{x^{19}} \, dx","Int[Sqrt[-1 + x^6]/x^19,x]","\frac{\sqrt{x^6-1}}{48 x^6}+\frac{1}{48} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\sqrt{x^6-1}}{18 x^{18}}+\frac{\sqrt{x^6-1}}{72 x^{12}}","\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,"-1/18*Sqrt[-1 + x^6]/x^18 + Sqrt[-1 + x^6]/(72*x^12) + Sqrt[-1 + x^6]/(48*x^6) + ArcTan[Sqrt[-1 + x^6]]/48","A",6,5,13,0.3846,1,"{266, 47, 51, 63, 203}"
552,1,51,0,0.025319,"\int x^8 \sqrt{-1+x^6} \, dx","Int[x^8*Sqrt[-1 + x^6],x]","\frac{1}{12} \sqrt{x^6-1} x^9-\frac{1}{24} \sqrt{x^6-1} x^3-\frac{1}{24} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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,"-1/24*(x^3*Sqrt[-1 + x^6]) + (x^9*Sqrt[-1 + x^6])/12 - ArcTanh[x^3/Sqrt[-1 + x^6]]/24","A",5,5,13,0.3846,1,"{275, 279, 321, 217, 206}"
553,1,216,0,0.6839373,"\int \frac{-1+x^6}{\sqrt{1+x^4} \left(1+x^6\right)} \, dx","Int[(-1 + x^6)/(Sqrt[1 + x^4]*(1 + x^6)),x]","-\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)-\frac{\left(\sqrt{3}+i\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \left(\sqrt{3}+3 i\right) \sqrt{x^4+1}}-\frac{\left(-\sqrt{3}+i\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \left(-\sqrt{3}+3 i\right) \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}","-\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,"-1/3*ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] - (2*ArcTanh[x/Sqrt[1 + x^4]])/3 + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4]) - ((I - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*(3*I - Sqrt[3])*Sqrt[1 + x^4]) - ((I + Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*(3*I + Sqrt[3])*Sqrt[1 + x^4])","C",17,9,22,0.4091,1,"{6725, 220, 2073, 1211, 1699, 203, 6728, 1217, 1707}"
554,1,41,0,0.0163541,"\int \frac{x^{14}}{\sqrt{1+x^6}} \, dx","Int[x^14/Sqrt[1 + x^6],x]","\frac{1}{8} \sinh ^{-1}\left(x^3\right)+\frac{1}{12} \sqrt{x^6+1} x^9-\frac{1}{8} \sqrt{x^6+1} x^3","\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,"-1/8*(x^3*Sqrt[1 + x^6]) + (x^9*Sqrt[1 + x^6])/12 + ArcSinh[x^3]/8","A",4,3,13,0.2308,1,"{275, 321, 215}"
555,1,63,0,0.0251789,"\int \frac{-1+x^6}{x^{19} \sqrt{1+x^6}} \, dx","Int[(-1 + x^6)/(x^19*Sqrt[1 + x^6]),x]","\frac{11 \sqrt{x^6+1}}{48 x^6}-\frac{11}{48} \tanh ^{-1}\left(\sqrt{x^6+1}\right)+\frac{\sqrt{x^6+1}}{18 x^{18}}-\frac{11 \sqrt{x^6+1}}{72 x^{12}}","\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]/(18*x^18) - (11*Sqrt[1 + x^6])/(72*x^12) + (11*Sqrt[1 + x^6])/(48*x^6) - (11*ArcTanh[Sqrt[1 + x^6]])/48","A",6,5,18,0.2778,1,"{446, 78, 51, 63, 207}"
556,1,354,0,1.5477969,"\int \frac{1+x^6}{\sqrt{1+x^4} \left(1-x^6\right)} \, dx","Int[(1 + x^6)/(Sqrt[1 + x^4]*(1 - x^6)),x]","\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}}+\frac{\left(1+i \sqrt{3}\right) \tanh ^{-1}\left(\frac{2-\left(1-i \sqrt{3}\right) x^2}{\sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{6 \sqrt{2 \left(1-i \sqrt{3}\right)}}-\frac{\left(1+i \sqrt{3}\right) \tanh ^{-1}\left(\frac{4+\left(1+i \sqrt{3}\right)^2 x^2}{2 \sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{6 \sqrt{2 \left(1-i \sqrt{3}\right)}}+\frac{\left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}+\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}","\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,"(2*ArcTan[x/Sqrt[1 + x^4]])/3 + ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(3*Sqrt[2]) + ((1 + I*Sqrt[3])*ArcTanh[(2 - (1 - I*Sqrt[3])*x^2)/(Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/(6*Sqrt[2*(1 - I*Sqrt[3])]) - ((1 + I*Sqrt[3])*ArcTanh[(4 + (1 + I*Sqrt[3])^2*x^2)/(2*Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/(6*Sqrt[2*(1 - I*Sqrt[3])]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4]) + ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4]) + ((1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4])","C",41,13,24,0.5417,1,"{6725, 220, 2073, 1211, 1699, 207, 6728, 1725, 1217, 1707, 1248, 725, 206}"
557,1,354,0,1.3188091,"\int \frac{1+x^6}{\sqrt{1+x^4} \left(-1+x^6\right)} \, dx","Int[(1 + x^6)/(Sqrt[1 + x^4]*(-1 + x^6)),x]","-\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}}-\frac{\left(1+i \sqrt{3}\right) \tanh ^{-1}\left(\frac{2-\left(1-i \sqrt{3}\right) x^2}{\sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{6 \sqrt{2 \left(1-i \sqrt{3}\right)}}+\frac{\left(1+i \sqrt{3}\right) \tanh ^{-1}\left(\frac{4+\left(1+i \sqrt{3}\right)^2 x^2}{2 \sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{6 \sqrt{2 \left(1-i \sqrt{3}\right)}}-\frac{\left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}-\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}","-\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,"(-2*ArcTan[x/Sqrt[1 + x^4]])/3 - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(3*Sqrt[2]) - ((1 + I*Sqrt[3])*ArcTanh[(2 - (1 - I*Sqrt[3])*x^2)/(Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/(6*Sqrt[2*(1 - I*Sqrt[3])]) + ((1 + I*Sqrt[3])*ArcTanh[(4 + (1 + I*Sqrt[3])^2*x^2)/(2*Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/(6*Sqrt[2*(1 - I*Sqrt[3])]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4]) - ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4]) - ((1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4])","C",41,13,22,0.5909,1,"{6725, 220, 2073, 1211, 1699, 207, 6728, 1725, 1217, 1707, 1248, 725, 206}"
558,0,0,0,1.253157,"\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","Int[((-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,"(-2*(1 - x^5))/Sqrt[-x + x^6] - (10*x^5*Sqrt[1 - x^5]*Hypergeometric2F1[1/2, 9/10, 19/10, x^5])/(9*Sqrt[-x + x^6]) + (2*a*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][Sqrt[-1 + x^10]/(1 + a*x^2 - x^10), x], x, Sqrt[x]])/Sqrt[-x + x^6] + (10*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][(x^8*Sqrt[-1 + x^10])/(-1 - a*x^2 + x^10), x], x, Sqrt[x]])/Sqrt[-x + x^6]","F",0,0,0,0,-1,"{}"
559,1,60,0,0.1139251,"\int \frac{\left(2+x^3\right) \left(1+x^3+x^6\right)}{x^7 \sqrt{1+x^3}} \, dx","Int[((2 + x^3)*(1 + x^3 + x^6))/(x^7*Sqrt[1 + x^3]),x]","-\frac{\sqrt{x^3+1}}{2 x^3}+\frac{2 \sqrt{x^3+1}}{3}-\frac{3}{2} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{\sqrt{x^3+1}}{3 x^6}","\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,"(2*Sqrt[1 + x^3])/3 - Sqrt[1 + x^3]/(3*x^6) - Sqrt[1 + x^3]/(2*x^3) - (3*ArcTanh[Sqrt[1 + x^3]])/2","A",12,5,26,0.1923,1,"{1821, 1612, 51, 63, 207}"
560,0,0,0,1.7544844,"\int \frac{-x+4 x^6}{\left(1+x^5\right) \left(a-x+a x^5\right) \sqrt{x+x^6}} \, dx","Int[(-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,"(8*x^2)/(5*a*Sqrt[x + x^6]) + (16*x^2*Sqrt[1 + x^5]*Hypergeometric2F1[3/10, 1/2, 13/10, -x^5])/(15*a*Sqrt[x + x^6]) - (10*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^2/((1 + x^10)^(3/2)*(a - x^2 + a*x^10)), x], x, Sqrt[x]])/Sqrt[x + x^6] + (8*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^4/((1 + x^10)^(3/2)*(a - x^2 + a*x^10)), x], x, Sqrt[x]])/(a*Sqrt[x + x^6])","F",0,0,0,0,-1,"{}"
561,0,0,0,1.1417527,"\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","Int[(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,"-1/6*ArcTan[(1 + x^6)^(1/4)] + ArcTanh[(1 + x^6)^(1/4)]/6 + (7*Defer[Subst][Defer[Int][1/((1 + x^2)^(1/4)*(-4 + 5*x - 4*x^2 + x^3)), x], x, x^3])/6 - Defer[Subst][Defer[Int][x/((1 + x^2)^(1/4)*(-4 + 5*x - 4*x^2 + x^3)), x], x, x^3]/3 + Defer[Subst][Defer[Int][x^2/((1 + x^2)^(1/4)*(-4 + 5*x - 4*x^2 + x^3)), x], x, x^3]/6","F",0,0,0,0,-1,"{}"
562,1,102,0,0.0619,"\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","Int[(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{13 \sqrt[5]{\left(4 x^2-13 x+3\right)^5} x^2}{2 \left(4 x^2-13 x+3\right)}+\frac{3 \sqrt[5]{\left(4 x^2-13 x+3\right)^5} x}{4 x^2-13 x+3}+\frac{4 \sqrt[5]{\left(4 x^2-13 x+3\right)^5} x^3}{3 \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,"(3*x*((3 - 13*x + 4*x^2)^5)^(1/5))/(3 - 13*x + 4*x^2) - (13*x^2*((3 - 13*x + 4*x^2)^5)^(1/5))/(2*(3 - 13*x + 4*x^2)) + (4*x^3*((3 - 13*x + 4*x^2)^5)^(1/5))/(3*(3 - 13*x + 4*x^2))","B",3,2,54,0.03704,1,"{6688, 6720}"
563,1,189,0,1.484067,"\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","Int[(-(b*x^3) + 2*a*x^8)/((-(b*x) + a*x^6)^(1/4)*(-1 - b*x^5 + a*x^10)),x]","-\frac{8 a x^4 \sqrt[4]{1-\frac{a x^5}{b}} F_1\left(\frac{3}{4};1,\frac{1}{4};\frac{7}{4};\frac{2 a x^5}{b-\sqrt{b^2+4 a}},\frac{a x^5}{b}\right)}{15 \left(b-\sqrt{4 a+b^2}\right) \sqrt[4]{a x^6-b x}}-\frac{8 a x^4 \sqrt[4]{1-\frac{a x^5}{b}} F_1\left(\frac{3}{4};1,\frac{1}{4};\frac{7}{4};\frac{2 a x^5}{b+\sqrt{b^2+4 a}},\frac{a x^5}{b}\right)}{15 \left(\sqrt{4 a+b^2}+b\right) \sqrt[4]{a x^6-b x}}","\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,"(-8*a*x^4*(1 - (a*x^5)/b)^(1/4)*AppellF1[3/4, 1, 1/4, 7/4, (2*a*x^5)/(b - Sqrt[4*a + b^2]), (a*x^5)/b])/(15*(b - Sqrt[4*a + b^2])*(-(b*x) + a*x^6)^(1/4)) - (8*a*x^4*(1 - (a*x^5)/b)^(1/4)*AppellF1[3/4, 1, 1/4, 7/4, (2*a*x^5)/(b + Sqrt[4*a + b^2]), (a*x^5)/b])/(15*(b + Sqrt[4*a + b^2])*(-(b*x) + a*x^6)^(1/4))","C",12,7,43,0.1628,0,"{1593, 2056, 6728, 466, 465, 511, 510}"
564,0,0,0,2.7871873,"\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","Int[(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,"(28*b*x^(3/4)*(-b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^20/((-b + a*x^12)^(1/4)*(1 + b*x^28 - a*x^40)), x], x, x^(1/4)])/(-(b*x^3) + a*x^6)^(1/4) + (40*a*x^(3/4)*(-b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^32/((-b + a*x^12)^(1/4)*(-1 - b*x^28 + a*x^40)), x], x, x^(1/4)])/(-(b*x^3) + a*x^6)^(1/4)","F",0,0,0,0,-1,"{}"
565,0,0,0,1.7688031,"\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","Int[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]","\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","\frac{2 b \sqrt{b x \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x^2}}{a x}",1,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
566,1,377,0,6.2457427,"\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","Int[(a*b - 2*a*x + x^2)/(Sqrt[x*(-a + x)*(-b + x)]*(a*d - (b + d)*x + x^2)),x]","\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \left(\sqrt{-4 a d+b^2+2 b d+d^2}+2 a-b-d\right) \Pi \left(\frac{2 a}{b+d-\sqrt{b^2+2 d b+d^2-4 a d}};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{\left(-\sqrt{-4 a d+b^2+2 b d+d^2}+b+d\right) \sqrt{x (a-x) (b-x)}}+\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \left(-\sqrt{-4 a d+b^2+2 b d+d^2}+2 a-b-d\right) \Pi \left(\frac{2 a}{b+d+\sqrt{b^2+2 d b+d^2-4 a d}};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{\left(\sqrt{-4 a d+b^2+2 b d+d^2}+b+d\right) \sqrt{x (a-x) (b-x)}}+\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} F\left(\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{\sqrt{x (a-x) (b-x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{x^2 (-a-b)+a b x+x^3}}{\sqrt{d} (a-x)}\right)}{\sqrt{d}}",1,"(2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[a]*(2*a - b - d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2])*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a)/(b + d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/((b + d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2])*Sqrt[(a - x)*(b - x)*x]) + (2*Sqrt[a]*(2*a - b - d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2])*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a)/(b + d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/((b + d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2])*Sqrt[(a - x)*(b - x)*x])","C",15,7,43,0.1628,1,"{6718, 6728, 117, 116, 169, 538, 537}"
567,1,376,0,7.2863765,"\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","Int[(a*b - 2*a*x + x^2)/(Sqrt[x*(-a + x)*(-b + x)]*(a - (1 + b*d)*x + d*x^2)),x]","\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} F\left(\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{d \sqrt{x (a-x) (b-x)}}-\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \left(-\sqrt{(b d+1)^2-4 a d}-2 a d+b d+1\right) \Pi \left(\frac{2 a d}{b d-\sqrt{(b d+1)^2-4 a d}+1};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{d \left(-\sqrt{(b d+1)^2-4 a d}+b d+1\right) \sqrt{x (a-x) (b-x)}}-\frac{2 \sqrt{a} \sqrt{x} \sqrt{1-\frac{x}{a}} \sqrt{1-\frac{x}{b}} \left(\sqrt{(b d+1)^2-4 a d}-2 a d+b d+1\right) \Pi \left(\frac{2 a d}{b d+\sqrt{(b d+1)^2-4 a d}+1};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a}}\right)|\frac{a}{b}\right)}{d \left(\sqrt{(b d+1)^2-4 a d}+b d+1\right) \sqrt{x (a-x) (b-x)}}","\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*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(d*Sqrt[(a - x)*(b - x)*x]) - (2*Sqrt[a]*(1 - 2*a*d + b*d - Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a*d)/(1 + b*d - Sqrt[-4*a*d + (1 + b*d)^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(d*(1 + b*d - Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[(a - x)*(b - x)*x]) - (2*Sqrt[a]*(1 - 2*a*d + b*d + Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticPi[(2*a*d)/(1 + b*d + Sqrt[-4*a*d + (1 + b*d)^2]), ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(d*(1 + b*d + Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[(a - x)*(b - x)*x])","C",15,7,45,0.1556,1,"{6718, 6728, 117, 116, 169, 538, 537}"
568,-1,0,0,180.0035252,"\int \frac{\left(-2+x^3\right) \sqrt{1-x^2+x^3}}{\left(1+x^3\right)^2} \, dx","Int[((-2 + x^3)*Sqrt[1 - x^2 + x^3])/(1 + x^3)^2,x]","\text{\$Aborted}","-\frac{\sqrt{x^3-x^2+1} x}{x^3+1}-\tan ^{-1}\left(\frac{x}{\sqrt{x^3-x^2+1}}\right)",1,"$Aborted","F",0,0,0,0,-1,"{}"
569,0,0,0,7.2968561,"\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","Int[(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]","\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","-\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*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][Sqrt[-a + x^2]/(Sqrt[-b + x^2]*(a^3 - 3*a^2*(1 + (b*d)/(3*a^2))*x^2 + 3*a*(1 + d/(3*a))*x^4 - x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] - (4*(a - b)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(a^3 - 3*a^2*(1 + (b*d)/(3*a^2))*x^2 + 3*a*(1 + d/(3*a))*x^4 - x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(-a^3 + 3*a^2*(1 + (b*d)/(3*a^2))*x^2 - 3*a*(1 + d/(3*a))*x^4 + x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
570,0,0,0,7.7450582,"\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","Int[(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]","\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","-\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*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][Sqrt[-a + x^2]/(Sqrt[-b + x^2]*(a^3*d - b*(1 + (3*a^2*d)/b)*x^2 + (1 + 3*a*d)*x^4 - d*x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] - (4*(a - b)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(a^3*d - b*(1 + (3*a^2*d)/b)*x^2 + (1 + 3*a*d)*x^4 - d*x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(-(a^3*d) + b*(1 + (3*a^2*d)/b)*x^2 - (1 + 3*a*d)*x^4 + d*x^6)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
571,0,0,0,1.3791565,"\int \frac{-3 x+2 x^2}{\left(-2+2 x+x^3\right) \sqrt{-2 x+2 x^2+3 x^4}} \, dx","Int[(-3*x + 2*x^2)/((-2 + 2*x + x^3)*Sqrt[-2*x + 2*x^2 + 3*x^4]),x]","\int \frac{-3 x+2 x^2}{\left(-2+2 x+x^3\right) \sqrt{-2 x+2 x^2+3 x^4}} \, dx","\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,"(-6*Sqrt[x]*Sqrt[-2 + 2*x + 3*x^3]*Defer[Subst][Defer[Int][x^2/((-2 + 2*x^2 + x^6)*Sqrt[-2 + 2*x^2 + 3*x^6]), x], x, Sqrt[x]])/Sqrt[-2*x + 2*x^2 + 3*x^4] + (4*Sqrt[x]*Sqrt[-2 + 2*x + 3*x^3]*Defer[Subst][Defer[Int][x^4/((-2 + 2*x^2 + x^6)*Sqrt[-2 + 2*x^2 + 3*x^6]), x], x, Sqrt[x]])/Sqrt[-2*x + 2*x^2 + 3*x^4]","F",0,0,0,0,-1,"{}"
572,0,0,0,4.0754532,"\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","Int[(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]","\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","-\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,"(2*Sqrt[2 + Sqrt[3]]*p^(2/3)*(q^(1/3) + p^(1/3)*x)*Sqrt[(q^(2/3) - p^(1/3)*q^(1/3)*x + p^(2/3)*x^2)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*q^(1/3) + p^(1/3)*x)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a*c*Sqrt[(q^(1/3)*(q^(1/3) + p^(1/3)*x))/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*Sqrt[q + p*x^3]) - (p*(b^2*c + d*q)*Defer[Int][1/(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])/(a*c) + 4*a*q*Defer[Int][x/(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] - 5*b*p*Defer[Int][x^2/(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] - (d*p^2*Defer[Int][x^3/(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])/(a*c)","F",0,0,0,0,-1,"{}"
573,1,51,0,0.0303714,"\int \frac{1+x^{12}}{x^{10} \sqrt{-1+x^6}} \, dx","Int[(1 + x^12)/(x^10*Sqrt[-1 + x^6]),x]","\frac{\sqrt{x^6-1}}{9 x^9}+\frac{2 \sqrt{x^6-1}}{9 x^3}+\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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]/(9*x^9) + (2*Sqrt[-1 + x^6])/(9*x^3) + ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",7,6,18,0.3333,1,"{1489, 271, 264, 275, 217, 206}"
574,1,44,0,0.4004344,"\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","Int[(-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{x^4+1} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{\sqrt{2} \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,"-((Sqrt[1 + x^4]*ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]])/(Sqrt[2]*((1 + x^4)^5)^(1/10)))","A",4,4,42,0.09524,1,"{6688, 6720, 1699, 203}"
575,0,0,0,0.5403672,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{b^2+a x^2} \, dx","Int[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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[-a]*x), x]/(2*b) + Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[-a]*x), x]/(2*b)","F",0,0,0,0,-1,"{}"
576,1,31,0,0.0563569,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Int[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",2,2,27,0.07407,1,"{2132, 206}"
577,1,45,0,0.0184835,"\int \frac{1}{x^3 \left(1+x^2\right)^{3/4}} \, dx","Int[1/(x^3*(1 + x^2)^(3/4)),x]","-\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)","-\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,"-1/2*(1 + x^2)^(1/4)/x^2 + (3*ArcTan[(1 + x^2)^(1/4)])/4 + (3*ArcTanh[(1 + x^2)^(1/4)])/4","A",6,6,13,0.4615,1,"{266, 51, 63, 212, 206, 203}"
578,1,45,0,0.0190095,"\int \frac{1}{x^4 \sqrt[4]{1+x^3}} \, dx","Int[1/(x^4*(1 + x^3)^(1/4)),x]","-\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)","-\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,"-1/3*(1 + x^3)^(3/4)/x^3 - ArcTan[(1 + x^3)^(1/4)]/6 + ArcTanh[(1 + x^3)^(1/4)]/6","A",6,6,13,0.4615,1,"{266, 51, 63, 298, 203, 206}"
579,1,45,0,0.017555,"\int \frac{\sqrt[4]{1+x^3}}{x^4} \, dx","Int[(1 + x^3)^(1/4)/x^4,x]","-\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)","-\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,"-1/3*(1 + x^3)^(1/4)/x^3 - ArcTan[(1 + x^3)^(1/4)]/6 - ArcTanh[(1 + x^3)^(1/4)]/6","A",6,6,13,0.4615,1,"{266, 47, 63, 212, 206, 203}"
580,1,55,0,0.0658264,"\int x^3 \sqrt{-x+x^4} \, dx","Int[x^3*Sqrt[-x + x^4],x]","\frac{1}{6} \sqrt{x^4-x} x^4-\frac{1}{12} \sqrt{x^4-x} x-\frac{1}{12} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)","\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,"-1/12*(x*Sqrt[-x + x^4]) + (x^4*Sqrt[-x + x^4])/6 - ArcTanh[x^2/Sqrt[-x + x^4]]/12","A",4,4,15,0.2667,1,"{2021, 2024, 2029, 206}"
581,0,0,0,1.2443794,"\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","Int[((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,"(2*(1 + x^4))/Sqrt[x + x^5] - (8*x^4*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 7/8, 15/8, -x^4])/(7*Sqrt[x + x^5]) + (2*a*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][Sqrt[1 + x^8]/(-1 + a*x^2 - x^8), x], x, Sqrt[x]])/Sqrt[x + x^5] + (8*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][(x^6*Sqrt[1 + x^8])/(1 - a*x^2 + x^8), x], x, Sqrt[x]])/Sqrt[x + x^5]","F",0,0,0,0,-1,"{}"
582,0,0,0,1.6396046,"\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","Int[(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,"Defer[Int][Sqrt[1 + x^2 + x^5]/(1 + x), x] + Defer[Int][Sqrt[1 + x^2 + x^5]/(-1 + x - x^2 + x^3 - x^4), x] + 2*Defer[Int][(x*Sqrt[1 + x^2 + x^5])/(1 - x + x^2 - x^3 + x^4), x] - 3*Defer[Int][(x^2*Sqrt[1 + x^2 + x^5])/(1 - x + x^2 - x^3 + x^4), x] - Defer[Int][(x^3*Sqrt[1 + x^2 + x^5])/(1 - x + x^2 - x^3 + x^4), x] - 2*Defer[Int][Sqrt[1 + x^2 + x^5]/(1 - x^2 + x^5), x] + 5*Defer[Int][(x^3*Sqrt[1 + x^2 + x^5])/(1 - x^2 + x^5), x]","F",0,0,0,0,-1,"{}"
583,1,45,0,0.0185836,"\int \frac{\sqrt[4]{1+x^6}}{x^7} \, dx","Int[(1 + x^6)^(1/4)/x^7,x]","-\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)","-\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,"-1/6*(1 + x^6)^(1/4)/x^6 - ArcTan[(1 + x^6)^(1/4)]/12 - ArcTanh[(1 + x^6)^(1/4)]/12","A",6,6,13,0.4615,1,"{266, 47, 63, 212, 206, 203}"
584,0,0,0,14.3538961,"\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","Int[((-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,"(16*(1 + x)^(3/4)*Defer[Subst][Defer[Int][1/((-1 - 2*x^4 + x^8)^(1/4)*(16 + x^4 - 56*x^8 + 72*x^12 - 39*x^16 + 10*x^20 - x^24)), x], x, (1 + x)^(1/4)])/((-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)) - (16*(1 + x)^(3/4)*Defer[Subst][Defer[Int][1/((-1 - 2*x^4 + x^8)^(1/4)*(-16 - x^4 + 56*x^8 - 72*x^12 + 39*x^16 - 10*x^20 + x^24)), x], x, (1 + x)^(1/4)])/((-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)) - (16*(1 + x)^(3/4)*Defer[Subst][Defer[Int][x^4/((-1 - 2*x^4 + x^8)^(1/4)*(-16 - x^4 + 56*x^8 - 72*x^12 + 39*x^16 - 10*x^20 + x^24)), x], x, (1 + x)^(1/4)])/((-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)) - (120*(1 + x)^(3/4)*Defer[Subst][Defer[Int][x^8/((-1 - 2*x^4 + x^8)^(1/4)*(-16 - x^4 + 56*x^8 - 72*x^12 + 39*x^16 - 10*x^20 + x^24)), x], x, (1 + x)^(1/4)])/((-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)) + (228*(1 + x)^(3/4)*Defer[Subst][Defer[Int][x^12/((-1 - 2*x^4 + x^8)^(1/4)*(-16 - x^4 + 56*x^8 - 72*x^12 + 39*x^16 - 10*x^20 + x^24)), x], x, (1 + x)^(1/4)])/((-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)) - (120*(1 + x)^(3/4)*Defer[Subst][Defer[Int][x^16/((-1 - 2*x^4 + x^8)^(1/4)*(-16 - x^4 + 56*x^8 - 72*x^12 + 39*x^16 - 10*x^20 + x^24)), x], x, (1 + x)^(1/4)])/((-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)) + (20*(1 + x)^(3/4)*Defer[Subst][Defer[Int][x^20/((-1 - 2*x^4 + x^8)^(1/4)*(-16 - x^4 + 56*x^8 - 72*x^12 + 39*x^16 - 10*x^20 + x^24)), x], x, (1 + x)^(1/4)])/((-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4))","F",0,0,0,0,-1,"{}"
585,0,0,0,1.9805031,"\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","Int[(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,"(-20*b*Sqrt[x]*(b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^4/((b + a*x^2)^(1/4)*(b + a*x^2 - x^20)), x], x, Sqrt[x]])/(b*x^2 + a*x^3)^(1/4) - (18*a*Sqrt[x]*(b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^6/((b + a*x^2)^(1/4)*(b + a*x^2 - x^20)), x], x, Sqrt[x]])/(b*x^2 + a*x^3)^(1/4)","F",0,0,0,0,-1,"{}"
586,1,2243,0,7.4057313,"\int \frac{-1+x^{16}}{\sqrt{1+x^4} \left(1+x^{16}\right)} \, dx","Int[(-1 + x^16)/(Sqrt[1 + x^4]*(1 + x^16)),x]","\frac{1}{32} \sqrt[16]{-1} \left((1+i)+\sqrt{2}\right) \sqrt{-4+(2+2 i) \sqrt{2}} \tan ^{-1}\left(\frac{(-1)^{3/16} \sqrt{-1+\sqrt[4]{-1}} x}{\sqrt{x^4+1}}\right)-\frac{1}{16} (-1)^{13/16} \sqrt{-1+\sqrt[4]{-1}} \left((1+i)+i \sqrt{2}\right) \tan ^{-1}\left(\frac{(-1)^{3/16} \sqrt{-1+\sqrt[4]{-1}} x}{\sqrt{x^4+1}}\right)-\frac{(-1)^{5/8} \sqrt{(-1)^{3/8}-(-1)^{5/8}} \left(1+(-1)^{5/8}\right) \left((1-i)+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{(-1)^{3/8}-(-1)^{5/8}} x}{\sqrt{x^4+1}}\right)}{16 \left(i-\sqrt[8]{-1}\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{(-1)^{3/8}-(-1)^{5/8}} x}{\sqrt{x^4+1}}\right)}{8 \sqrt{(-1)^{3/8}-(-1)^{5/8}}}-\frac{1}{16} (-1)^{11/16} \sqrt{-1+(-1)^{3/4}} \left((-1+i)+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt[16]{-1} \sqrt{-1+(-1)^{3/4}} x}{\sqrt{x^4+1}}\right)+\frac{(-1)^{15/16} \tan ^{-1}\left(\frac{\sqrt[16]{-1} \sqrt{-1+(-1)^{3/4}} x}{\sqrt{x^4+1}}\right)}{4 \sqrt{-4-(2-2 i) \sqrt{2}}}+\frac{1}{16} (-1)^{5/8} \sqrt{\sqrt[8]{-1}-(-1)^{7/8}} \left((-1+i)+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt[8]{-1}-(-1)^{7/8}} x}{\sqrt{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[8]{-1}-(-1)^{7/8}} x}{\sqrt{x^4+1}}\right)}{8 \sqrt{\sqrt[8]{-1}-(-1)^{7/8}}}+\frac{\sqrt[4]{-1} \left(1+(-1)^{5/8}\right) \left((1+i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{\sqrt[4]{-1} \left(1-(-1)^{5/8}\right) \left((1+i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}-\frac{\left(1+(-1)^{5/8}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{2} \left((1+i)+\sqrt{2}\right) \sqrt{x^4+1}}-\frac{\left(1-(-1)^{5/8}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{2} \left((1+i)+\sqrt{2}\right) \sqrt{x^4+1}}+\frac{(-1)^{5/8} \left(i-\sqrt[8]{-1}\right) \left((1-i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}-\frac{(-1)^{5/8} \left(1+\sqrt[8]{-1}\right) \left((-1+i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{(-1)^{5/8} \left(1-\sqrt[8]{-1}\right) \left((-1+i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{\sqrt[4]{-1} \left(1+\sqrt[8]{-1}\right) \left((-1-i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{\sqrt[4]{-1} \left(1-\sqrt[8]{-1}\right) \left((-1-i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}-\frac{\left(1+\sqrt[8]{-1}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{2} \left((-1-i)+\sqrt{2}\right) \sqrt{x^4+1}}-\frac{\left(1-\sqrt[8]{-1}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{2} \left((-1-i)+\sqrt{2}\right) \sqrt{x^4+1}}-\frac{\sqrt[8]{-1} \left(i+\sqrt[8]{-1}\right) \left((1+i)+i \sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}-\frac{\sqrt[8]{-1} \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \left(1+\sqrt[8]{-1}\right) \sqrt{x^4+1}}-\frac{\sqrt[8]{-1} \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \left(i+\sqrt[8]{-1}\right) \sqrt{x^4+1}}+\frac{\sqrt[8]{-1} \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \left(1-\sqrt[8]{-1}\right) \sqrt{x^4+1}}+\frac{\sqrt[8]{-1} \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \left(i-\sqrt[8]{-1}\right) \sqrt{x^4+1}}+\frac{\left((-1+i)+(2+2 i) \sqrt[8]{-1}+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4} (-1)^{3/8} \left(i-\sqrt[8]{-1}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \left((1-i)+\sqrt{2}\right) \sqrt{x^4+1}}-\frac{\left((-1+i)+(2+2 i) (-1)^{5/8}-\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4} (-1)^{7/8} \left(1-\sqrt[8]{-1}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \left((-1+i)+\sqrt{2}\right) \sqrt{x^4+1}}-\frac{\sqrt[8]{-1} \left(1-(-1)^{3/8}\right) \left(1+(-1)^{5/8}\right) \left((-1+i)+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{1}{4} (-1)^{3/8} \left(i+\sqrt[8]{-1}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{32 \sqrt{x^4+1}}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) \left((-1+i)+\sqrt[8]{-1}-(-1)^{5/8}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{1}{4} (-1)^{7/8} \left(1+\sqrt[8]{-1}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\left(1+\sqrt[8]{-1}\right) \sqrt{x^4+1}}-\frac{\left(i-\sqrt[4]{-1}-2 (-1)^{7/8}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4} \left(2+(-1)^{3/8}-(-1)^{5/8}\right);2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \left(i+\sqrt[4]{-1}\right) \sqrt{x^4+1}}-\frac{\left(i-\sqrt[4]{-1}+2 (-1)^{7/8}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4} \left(2-(-1)^{3/8}+(-1)^{5/8}\right);2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \left(i+\sqrt[4]{-1}\right) \sqrt{x^4+1}}+\frac{\left((1+i)-(2-2 i) (-1)^{3/8}+\sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4} \left(2+\sqrt[8]{-1}-(-1)^{7/8}\right);2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \left((-1-i)+\sqrt{2}\right) \sqrt{x^4+1}}-\frac{\left(i+\sqrt[4]{-1}+2 (-1)^{3/8}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4} \left(2-\sqrt[8]{-1}+(-1)^{7/8}\right);2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \left(i-\sqrt[4]{-1}\right) \sqrt{x^4+1}}","\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,"-1/16*((-1)^(13/16)*Sqrt[-1 + (-1)^(1/4)]*((1 + I) + I*Sqrt[2])*ArcTan[((-1)^(3/16)*Sqrt[-1 + (-1)^(1/4)]*x)/Sqrt[1 + x^4]]) + ((-1)^(1/16)*((1 + I) + Sqrt[2])*Sqrt[-4 + (2 + 2*I)*Sqrt[2]]*ArcTan[((-1)^(3/16)*Sqrt[-1 + (-1)^(1/4)]*x)/Sqrt[1 + x^4]])/32 - ArcTan[(Sqrt[(-1)^(3/8) - (-1)^(5/8)]*x)/Sqrt[1 + x^4]]/(8*Sqrt[(-1)^(3/8) - (-1)^(5/8)]) - ((-1)^(5/8)*Sqrt[(-1)^(3/8) - (-1)^(5/8)]*(1 + (-1)^(5/8))*((1 - I) + Sqrt[2])*ArcTan[(Sqrt[(-1)^(3/8) - (-1)^(5/8)]*x)/Sqrt[1 + x^4]])/(16*(I - (-1)^(1/8))) + ((-1)^(15/16)*ArcTan[((-1)^(1/16)*Sqrt[-1 + (-1)^(3/4)]*x)/Sqrt[1 + x^4]])/(4*Sqrt[-4 - (2 - 2*I)*Sqrt[2]]) - ((-1)^(11/16)*Sqrt[-1 + (-1)^(3/4)]*((-1 + I) + Sqrt[2])*ArcTan[((-1)^(1/16)*Sqrt[-1 + (-1)^(3/4)]*x)/Sqrt[1 + x^4]])/16 - ArcTan[(Sqrt[(-1)^(1/8) - (-1)^(7/8)]*x)/Sqrt[1 + x^4]]/(8*Sqrt[(-1)^(1/8) - (-1)^(7/8)]) + ((-1)^(5/8)*Sqrt[(-1)^(1/8) - (-1)^(7/8)]*((-1 + I) + Sqrt[2])*ArcTan[(Sqrt[(-1)^(1/8) - (-1)^(7/8)]*x)/Sqrt[1 + x^4]])/16 + ((-1)^(1/8)*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*(I - (-1)^(1/8))*Sqrt[1 + x^4]) + ((-1)^(1/8)*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*(1 - (-1)^(1/8))*Sqrt[1 + x^4]) - ((-1)^(1/8)*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*(I + (-1)^(1/8))*Sqrt[1 + x^4]) - ((-1)^(1/8)*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*(1 + (-1)^(1/8))*Sqrt[1 + x^4]) - ((-1)^(1/8)*(I + (-1)^(1/8))*((1 + I) + I*Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) - ((1 - (-1)^(1/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[2]*((-1 - I) + Sqrt[2])*Sqrt[1 + x^4]) - ((1 + (-1)^(1/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[2]*((-1 - I) + Sqrt[2])*Sqrt[1 + x^4]) + ((-1)^(1/4)*(1 - (-1)^(1/8))*((-1 - I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) + ((-1)^(1/4)*(1 + (-1)^(1/8))*((-1 - I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) + ((-1)^(5/8)*(1 - (-1)^(1/8))*((-1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) - ((-1)^(5/8)*(1 + (-1)^(1/8))*((-1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) + ((-1)^(5/8)*(I - (-1)^(1/8))*((1 - I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) - ((1 - (-1)^(5/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[2]*((1 + I) + Sqrt[2])*Sqrt[1 + x^4]) - ((1 + (-1)^(5/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[2]*((1 + I) + Sqrt[2])*Sqrt[1 + x^4]) + ((-1)^(1/4)*(1 - (-1)^(5/8))*((1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) + ((-1)^(1/4)*(1 + (-1)^(5/8))*((1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) + (((-1 + I) + (2 + 2*I)*(-1)^(1/8) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[((-1)^(3/8)*(I - (-1)^(1/8))^2)/4, 2*ArcTan[x], 1/2])/(16*((1 - I) + Sqrt[2])*Sqrt[1 + x^4]) - (((-1 + I) + (2 + 2*I)*(-1)^(5/8) - Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[((-1)^(7/8)*(1 - (-1)^(1/8))^2)/4, 2*ArcTan[x], 1/2])/(16*((-1 + I) + Sqrt[2])*Sqrt[1 + x^4]) - ((-1)^(1/8)*(1 - (-1)^(3/8))*(1 + (-1)^(5/8))*((-1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[-1/4*((-1)^(3/8)*(I + (-1)^(1/8))^2), 2*ArcTan[x], 1/2])/(32*Sqrt[1 + x^4]) + ((1/32 + I/32)*((-1 + I) + (-1)^(1/8) - (-1)^(5/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[-1/4*((-1)^(7/8)*(1 + (-1)^(1/8))^2), 2*ArcTan[x], 1/2])/((1 + (-1)^(1/8))*Sqrt[1 + x^4]) - ((I - (-1)^(1/4) - 2*(-1)^(7/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(2 + (-1)^(3/8) - (-1)^(5/8))/4, 2*ArcTan[x], 1/2])/(16*(I + (-1)^(1/4))*Sqrt[1 + x^4]) - ((I - (-1)^(1/4) + 2*(-1)^(7/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(2 - (-1)^(3/8) + (-1)^(5/8))/4, 2*ArcTan[x], 1/2])/(16*(I + (-1)^(1/4))*Sqrt[1 + x^4]) + (((1 + I) - (2 - 2*I)*(-1)^(3/8) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(2 + (-1)^(1/8) - (-1)^(7/8))/4, 2*ArcTan[x], 1/2])/(16*((-1 - I) + Sqrt[2])*Sqrt[1 + x^4]) - ((I + (-1)^(1/4) + 2*(-1)^(3/8))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(2 - (-1)^(1/8) + (-1)^(7/8))/4, 2*ArcTan[x], 1/2])/(16*(I - (-1)^(1/4))*Sqrt[1 + x^4])","C",227,16,22,0.7273,0,"{1586, 6725, 1729, 1209, 1198, 220, 1196, 1217, 1707, 1248, 735, 844, 215, 725, 206, 204}"
587,1,2783,0,10.7486647,"\int \frac{-1+x^{16}}{\sqrt{-1+x^4} \left(1-x^8+x^{16}\right)} \, dx","Int[(-1 + x^16)/(Sqrt[-1 + x^4]*(1 - x^8 + x^16)),x]","\frac{\left(i+\sqrt{3}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{6} \sqrt{x^4-1}}-\frac{\left(i-\sqrt{3}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{6} \sqrt{x^4-1}}-\frac{\left(2+\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i+\sqrt{3}\right) \sqrt{x^4-1}}+\frac{i \left(2+\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(3+i \sqrt{3}\right) \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{24 \sqrt{x^4-1}}-\frac{i \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(2+\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i+\sqrt{3}\right) \sqrt{x^4-1}}+\frac{i \left(2+\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(3+i \sqrt{3}\right) \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{24 \sqrt{x^4-1}}-\frac{i \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(-i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \sqrt{x^4-1}}+\frac{\left(2+\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i-\sqrt{3}\right) \sqrt{x^4-1}}-\frac{i \left(2+\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(3-i \sqrt{3}\right) \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{24 \sqrt{x^4-1}}+\frac{i \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \sqrt{x^4-1}}+\frac{\left(2+\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i-\sqrt{3}\right) \sqrt{x^4-1}}-\frac{i \left(2+\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(3-i \sqrt{3}\right) \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{24 \sqrt{x^4-1}}+\frac{i \left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\sqrt{\frac{1}{2} \left(i-\sqrt{3}\right)};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(2-\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i+\sqrt{3}\right) \sqrt{x^4-1}}+\frac{i \left(2-\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(\frac{1}{24}-\frac{i}{24}\right) \left(3-\sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{x^4-1}}+\frac{i \left(3-(2-i) \sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{24 \sqrt{x^4-1}}-\frac{\left(2-\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i+\sqrt{3}\right) \sqrt{x^4-1}}+\frac{i \left(2-\sqrt{2-2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(\frac{1}{24}-\frac{i}{24}\right) \left(3-\sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{x^4-1}}+\frac{i \left(3-(2-i) \sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{24 \sqrt{x^4-1}}+\frac{\left(2-\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i-\sqrt{3}\right) \sqrt{x^4-1}}-\frac{i \left(2-\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(\frac{1}{24}+\frac{i}{24}\right) \left(3-\sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{x^4-1}}-\frac{i \left(3-(2+i) \sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{24 \sqrt{x^4-1}}+\frac{\left(2-\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{3} \left(i-\sqrt{3}\right) \sqrt{x^4-1}}-\frac{i \left(2-\sqrt{2+2 i \sqrt{3}}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{8 \sqrt{3} \sqrt{x^4-1}}-\frac{\left(\frac{1}{24}+\frac{i}{24}\right) \left(3-\sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{x^4-1}}-\frac{i \left(3-(2+i) \sqrt{3}\right) \sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt[4]{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{24 \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,"-1/2*((I - Sqrt[3])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(Sqrt[6]*Sqrt[-1 + x^4]) + ((I + Sqrt[3])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(2*Sqrt[6]*Sqrt[-1 + x^4]) - ((I/4)*(1 + 1/Sqrt[(1 - I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((3 + I*Sqrt[3])*(1 + 1/Sqrt[(1 - I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(24*Sqrt[-1 + x^4]) + ((I/8)*(2 + Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((2 + Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(4*Sqrt[3]*(I + Sqrt[3])*Sqrt[-1 + x^4]) - ((I/4)*(1 + 1/Sqrt[(1 - I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((3 + I*Sqrt[3])*(1 + 1/Sqrt[(1 - I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(24*Sqrt[-1 + x^4]) + ((I/8)*(2 + Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((2 + Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(-I - Sqrt[3])/2], ArcSin[x], -1])/(4*Sqrt[3]*(I + Sqrt[3])*Sqrt[-1 + x^4]) + ((I/4)*(1 + 1/Sqrt[(1 + I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((3 - I*Sqrt[3])*(1 + 1/Sqrt[(1 + I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(24*Sqrt[-1 + x^4]) - ((I/8)*(2 + Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) + ((2 + Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(4*Sqrt[3]*(I - Sqrt[3])*Sqrt[-1 + x^4]) + ((I/4)*(1 + 1/Sqrt[(1 + I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((3 - I*Sqrt[3])*(1 + 1/Sqrt[(1 + I*Sqrt[3])/2])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(24*Sqrt[-1 + x^4]) - ((I/8)*(2 + Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) + ((2 + Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[Sqrt[(I - Sqrt[3])/2], ArcSin[x], -1])/(4*Sqrt[3]*(I - Sqrt[3])*Sqrt[-1 + x^4]) + ((I/24)*(3 - (2 - I)*Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] - ((1/24 - I/24)*(3 - Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] + ((I/8)*(2 - Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((2 - Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(4*Sqrt[3]*(I + Sqrt[3])*Sqrt[-1 + x^4]) + ((I/24)*(3 - (2 - I)*Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] - ((1/24 - I/24)*(3 - Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] + ((I/8)*(2 - Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) - ((2 - Sqrt[2 - (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 - I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(4*Sqrt[3]*(I + Sqrt[3])*Sqrt[-1 + x^4]) - ((I/24)*(3 - (2 + I)*Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] - ((1/24 + I/24)*(3 - Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] - ((I/8)*(2 - Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) + ((2 - Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(4*Sqrt[3]*(I - Sqrt[3])*Sqrt[-1 + x^4]) - ((I/24)*(3 - (2 + I)*Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] - ((1/24 + I/24)*(3 - Sqrt[3])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/Sqrt[-1 + x^4] - ((I/8)*(2 - Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(Sqrt[3]*Sqrt[-1 + x^4]) + ((2 - Sqrt[2 + (2*I)*Sqrt[3]])*Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[((1 + I*Sqrt[3])/2)^(-1/4), ArcSin[x], -1])/(4*Sqrt[3]*(I - Sqrt[3])*Sqrt[-1 + x^4])","C",319,14,27,0.5185,0,"{1586, 6728, 1429, 406, 222, 409, 1215, 1457, 540, 253, 538, 537, 1519, 6725}"
588,1,18,0,0.18053,"\int \frac{\sqrt{x^2+x \sqrt{-1+x^2}}}{x \sqrt{-1+x^2}} \, dx","Int[Sqrt[x^2 + x*Sqrt[-1 + x^2]]/(x*Sqrt[-1 + x^2]),x]","\sqrt{2} \sinh ^{-1}\left(\sqrt{x^2-1}+x\right)","-\sqrt{2} \log \left(\sqrt{x^2-1}-\sqrt{2} \sqrt{x^2+\sqrt{x^2-1} x}+x\right)",1,"Sqrt[2]*ArcSinh[x + Sqrt[-1 + x^2]]","A",2,2,32,0.06250,1,"{2130, 215}"
589,1,65,0,0.0834429,"\int x^6 \sqrt{x+x^4} \, dx","Int[x^6*Sqrt[x + x^4],x]","\frac{1}{36} \sqrt{x^4+x} x^4-\frac{1}{24} \sqrt{x^4+x} x+\frac{1}{9} \sqrt{x^4+x} x^7+\frac{1}{24} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)","\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,"-1/24*(x*Sqrt[x + x^4]) + (x^4*Sqrt[x + x^4])/36 + (x^7*Sqrt[x + x^4])/9 + ArcTanh[x^2/Sqrt[x + x^4]]/24","A",5,4,13,0.3077,1,"{2021, 2024, 2029, 206}"
590,1,39,0,0.2041493,"\int \frac{(-1+x) (1+x)^3}{\left(1+x^2\right)^2 \sqrt{1+x^2+x^4}} \, dx","Int[((-1 + x)*(1 + x)^3)/((1 + x^2)^2*Sqrt[1 + x^2 + x^4]),x]","\frac{2 \sqrt{x^4+x^2+1}}{x^2+1}-\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)","\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*Sqrt[1 + x^2 + x^4])/(1 + x^2) - ArcTan[x/Sqrt[1 + x^2 + x^4]]","A",6,6,28,0.2143,1,"{1687, 1586, 1698, 203, 1685, 802}"
591,0,0,0,0.4812159,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2-x^3+x^4}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 - x - x^2 - x^3 + x^4]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2-x^3+x^4}} \, dx","\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,"Defer[Int][1/Sqrt[1 - x - x^2 - x^3 + x^4], x] - I*Defer[Int][1/((I - x)*Sqrt[1 - x - x^2 - x^3 + x^4]), x] - I*Defer[Int][1/((I + x)*Sqrt[1 - x - x^2 - x^3 + x^4]), x]","F",0,0,0,0,-1,"{}"
592,0,0,0,0.3100373,"\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","Int[(-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,"-Defer[Int][1/Sqrt[-3 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6], x] - 2*Defer[Int][x/Sqrt[-3 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6], x] + 3*Defer[Int][x^2/Sqrt[-3 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6], x]","F",0,0,0,0,-1,"{}"
593,1,113,0,0.6107483,"\int \frac{-x+x^2}{\sqrt{-2 x+4 x^2-2 x^3+x^4-2 x^5+x^6}} \, dx","Int[(-x + x^2)/Sqrt[-2*x + 4*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6],x]","-\frac{2 (1-x) \sqrt{x} \sqrt{x^3-2} \sqrt{x^5-2 x^4+x^3-2 x^2+4 x-2} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-2}}\right)}{3 \sqrt{-(1-x)^2 \left(2-x^3\right)} \sqrt{x^6-2 x^5+x^4-2 x^3+4 x^2-2 x}}","\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]*Sqrt[-2 + 4*x - 2*x^2 + x^3 - 2*x^4 + x^5]*ArcTanh[x^(3/2)/Sqrt[-2 + x^3]])/(3*Sqrt[-((1 - x)^2*(2 - x^3))]*Sqrt[-2*x + 4*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6])","B",8,8,37,0.2162,1,"{1593, 2056, 6688, 6719, 329, 275, 217, 206}"
594,1,47,0,0.0116625,"\int \frac{\sqrt[4]{-1+x^4}}{x^2} \, dx","Int[(-1 + x^4)^(1/4)/x^2,x]","-\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)","-\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)/x) - ArcTan[x/(-1 + x^4)^(1/4)]/2 + ArcTanh[x/(-1 + x^4)^(1/4)]/2","A",5,5,13,0.3846,1,"{277, 331, 298, 203, 206}"
595,1,53,0,0.0235901,"\int \frac{\left(-1+x^4\right) \sqrt[4]{1+x^4}}{x} \, dx","Int[((-1 + x^4)*(1 + x^4)^(1/4))/x,x]","\frac{1}{5} \left(x^4+1\right)^{5/4}-\sqrt[4]{x^4+1}+\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{x^4+1}\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{x^4+1}\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,"-(1 + x^4)^(1/4) + (1 + x^4)^(5/4)/5 + ArcTan[(1 + x^4)^(1/4)]/2 + ArcTanh[(1 + x^4)^(1/4)]/2","A",7,7,18,0.3889,1,"{446, 80, 50, 63, 212, 206, 203}"
596,0,0,0,0.0133989,"\int \frac{1}{\sqrt{3+4 x+x^4}} \, dx","Int[1/Sqrt[3 + 4*x + x^4],x]","\int \frac{1}{\sqrt{3+4 x+x^4}} \, dx","\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,"Defer[Int][1/Sqrt[3 + 4*x + x^4], x]","F",0,0,0,0,-1,"{}"
597,1,1670,0,2.6110124,"\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","Int[((1 + x^4)*Sqrt[-1 + 2*x^2 + x^4])/((-1 + x^4)*(-1 + x^2 + x^4)),x]","\frac{\sqrt{3-2 \sqrt{2}} \left(1-\sqrt{5}\right) \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} F\left(\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\left(1-2 \sqrt{2}+\sqrt{5}\right) \sqrt{x^4+2 x^2-1}}+\frac{\sqrt{3-2 \sqrt{2}} \left(1+\sqrt{5}\right) \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} F\left(\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\left(1-2 \sqrt{2}-\sqrt{5}\right) \sqrt{x^4+2 x^2-1}}+\frac{\sqrt{2 \left(3-2 \sqrt{2}\right)} \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} F\left(\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\sqrt{x^4+2 x^2-1}}+\frac{\sqrt{2} \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} F\left(\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\sqrt{x^4+2 x^2-1}}-\frac{\left(1+2 \sqrt{2}+\sqrt{5}\right) \sqrt{\frac{1-\left(1-\sqrt{2}\right) x^2}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{\left(1+\sqrt{2}\right) x^2-1} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\left(1+\sqrt{2}\right) x^2-1}}\right)|\frac{1}{4} \left(2+\sqrt{2}\right)\right)}{2\ 2^{3/4} \sqrt{\frac{1}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{x^4+2 x^2-1}}-\frac{\left(1-\sqrt{5}\right) \sqrt{\frac{1-\left(1-\sqrt{2}\right) x^2}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{\left(1+\sqrt{2}\right) x^2-1} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\left(1+\sqrt{2}\right) x^2-1}}\right)|\frac{1}{4} \left(2+\sqrt{2}\right)\right)}{2^{3/4} \left(1-2 \sqrt{2}+\sqrt{5}\right) \sqrt{\frac{1}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{x^4+2 x^2-1}}-\frac{\left(1+\sqrt{5}\right) \sqrt{\frac{1-\left(1-\sqrt{2}\right) x^2}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{\left(1+\sqrt{2}\right) x^2-1} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\left(1+\sqrt{2}\right) x^2-1}}\right)|\frac{1}{4} \left(2+\sqrt{2}\right)\right)}{2^{3/4} \left(1-2 \sqrt{2}-\sqrt{5}\right) \sqrt{\frac{1}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{x^4+2 x^2-1}}-\frac{\left(1+2 \sqrt{2}-\sqrt{5}\right) \sqrt{\frac{1-\left(1-\sqrt{2}\right) x^2}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{\left(1+\sqrt{2}\right) x^2-1} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\left(1+\sqrt{2}\right) x^2-1}}\right)|\frac{1}{4} \left(2+\sqrt{2}\right)\right)}{2\ 2^{3/4} \sqrt{\frac{1}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{x^4+2 x^2-1}}+\frac{\left(1+\sqrt{2}\right) \sqrt{\frac{1-\left(1-\sqrt{2}\right) x^2}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{\left(1+\sqrt{2}\right) x^2-1} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\left(1+\sqrt{2}\right) x^2-1}}\right)|\frac{1}{4} \left(2+\sqrt{2}\right)\right)}{\sqrt[4]{2} \sqrt{\frac{1}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{x^4+2 x^2-1}}-\frac{\sqrt[4]{2} \sqrt{\frac{1-\left(1-\sqrt{2}\right) x^2}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{\left(1+\sqrt{2}\right) x^2-1} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\left(1+\sqrt{2}\right) x^2-1}}\right)|\frac{1}{4} \left(2+\sqrt{2}\right)\right)}{\left(2-\sqrt{2}\right) \sqrt{\frac{1}{1-\left(1+\sqrt{2}\right) x^2}} \sqrt{x^4+2 x^2-1}}-\frac{2 \sqrt{3-2 \sqrt{2}} \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} \Pi \left(1-\sqrt{2};\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\sqrt{x^4+2 x^2-1}}-\frac{2 \sqrt{3-2 \sqrt{2}} \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} \Pi \left(-1+\sqrt{2};\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\sqrt{x^4+2 x^2-1}}+\frac{\sqrt{3-2 \sqrt{2}} \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} \Pi \left(\frac{2 \left(1-\sqrt{2}\right)}{1-\sqrt{5}};\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\sqrt{x^4+2 x^2-1}}+\frac{\sqrt{3-2 \sqrt{2}} \sqrt{x^2+\sqrt{2}+1} \sqrt{1-\left(1+\sqrt{2}\right) x^2} \Pi \left(\frac{2 \left(1-\sqrt{2}\right)}{1+\sqrt{5}};\sin ^{-1}\left(\sqrt{1+\sqrt{2}} x\right)|-3+2 \sqrt{2}\right)}{\sqrt{x^4+2 x^2-1}}","\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,"(Sqrt[2]*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/Sqrt[-1 + 2*x^2 + x^4] + (Sqrt[2*(3 - 2*Sqrt[2])]*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/Sqrt[-1 + 2*x^2 + x^4] + (Sqrt[3 - 2*Sqrt[2]]*(1 + Sqrt[5])*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/((1 - 2*Sqrt[2] - Sqrt[5])*Sqrt[-1 + 2*x^2 + x^4]) + (Sqrt[3 - 2*Sqrt[2]]*(1 - Sqrt[5])*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/((1 - 2*Sqrt[2] + Sqrt[5])*Sqrt[-1 + 2*x^2 + x^4]) - (2^(1/4)*Sqrt[(1 - (1 - Sqrt[2])*x^2)/(1 - (1 + Sqrt[2])*x^2)]*Sqrt[-1 + (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-1 + (1 + Sqrt[2])*x^2]], (2 + Sqrt[2])/4])/((2 - Sqrt[2])*Sqrt[(1 - (1 + Sqrt[2])*x^2)^(-1)]*Sqrt[-1 + 2*x^2 + x^4]) + ((1 + Sqrt[2])*Sqrt[(1 - (1 - Sqrt[2])*x^2)/(1 - (1 + Sqrt[2])*x^2)]*Sqrt[-1 + (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-1 + (1 + Sqrt[2])*x^2]], (2 + Sqrt[2])/4])/(2^(1/4)*Sqrt[(1 - (1 + Sqrt[2])*x^2)^(-1)]*Sqrt[-1 + 2*x^2 + x^4]) - ((1 + 2*Sqrt[2] - Sqrt[5])*Sqrt[(1 - (1 - Sqrt[2])*x^2)/(1 - (1 + Sqrt[2])*x^2)]*Sqrt[-1 + (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-1 + (1 + Sqrt[2])*x^2]], (2 + Sqrt[2])/4])/(2*2^(3/4)*Sqrt[(1 - (1 + Sqrt[2])*x^2)^(-1)]*Sqrt[-1 + 2*x^2 + x^4]) - ((1 + Sqrt[5])*Sqrt[(1 - (1 - Sqrt[2])*x^2)/(1 - (1 + Sqrt[2])*x^2)]*Sqrt[-1 + (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-1 + (1 + Sqrt[2])*x^2]], (2 + Sqrt[2])/4])/(2^(3/4)*(1 - 2*Sqrt[2] - Sqrt[5])*Sqrt[(1 - (1 + Sqrt[2])*x^2)^(-1)]*Sqrt[-1 + 2*x^2 + x^4]) - ((1 - Sqrt[5])*Sqrt[(1 - (1 - Sqrt[2])*x^2)/(1 - (1 + Sqrt[2])*x^2)]*Sqrt[-1 + (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-1 + (1 + Sqrt[2])*x^2]], (2 + Sqrt[2])/4])/(2^(3/4)*(1 - 2*Sqrt[2] + Sqrt[5])*Sqrt[(1 - (1 + Sqrt[2])*x^2)^(-1)]*Sqrt[-1 + 2*x^2 + x^4]) - ((1 + 2*Sqrt[2] + Sqrt[5])*Sqrt[(1 - (1 - Sqrt[2])*x^2)/(1 - (1 + Sqrt[2])*x^2)]*Sqrt[-1 + (1 + Sqrt[2])*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-1 + (1 + Sqrt[2])*x^2]], (2 + Sqrt[2])/4])/(2*2^(3/4)*Sqrt[(1 - (1 + Sqrt[2])*x^2)^(-1)]*Sqrt[-1 + 2*x^2 + x^4]) - (2*Sqrt[3 - 2*Sqrt[2]]*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticPi[1 - Sqrt[2], ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/Sqrt[-1 + 2*x^2 + x^4] - (2*Sqrt[3 - 2*Sqrt[2]]*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticPi[-1 + Sqrt[2], ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/Sqrt[-1 + 2*x^2 + x^4] + (Sqrt[3 - 2*Sqrt[2]]*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticPi[(2*(1 - Sqrt[2]))/(1 - Sqrt[5]), ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/Sqrt[-1 + 2*x^2 + x^4] + (Sqrt[3 - 2*Sqrt[2]]*Sqrt[1 + Sqrt[2] + x^2]*Sqrt[1 - (1 + Sqrt[2])*x^2]*EllipticPi[(2*(1 - Sqrt[2]))/(1 + Sqrt[5]), ArcSin[Sqrt[1 + Sqrt[2]]*x], -3 + 2*Sqrt[2]])/Sqrt[-1 + 2*x^2 + x^4]","C",52,13,37,0.3514,0,"{6725, 1208, 1187, 1098, 1184, 1214, 1456, 540, 421, 419, 538, 537, 6728}"
598,0,0,0,0.6033131,"\int \frac{\sqrt{-1+x-x^2+x^4} \left(2-x+2 x^4\right)}{\left(-1+x+x^4\right)^2} \, dx","Int[(Sqrt[-1 + x - x^2 + x^4]*(2 - x + 2*x^4))/(-1 + x + x^4)^2,x]","\int \frac{\sqrt{-1+x-x^2+x^4} \left(2-x+2 x^4\right)}{\left(-1+x+x^4\right)^2} \, dx","-\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,"4*Defer[Int][Sqrt[-1 + x - x^2 + x^4]/(-1 + x + x^4)^2, x] - 3*Defer[Int][(x*Sqrt[-1 + x - x^2 + x^4])/(-1 + x + x^4)^2, x] + 2*Defer[Int][Sqrt[-1 + x - x^2 + x^4]/(-1 + x + x^4), x]","F",0,0,0,0,-1,"{}"
599,0,0,0,2.2328939,"\int \frac{x+3 x^5}{\left(-1+x^4\right) \left(-a-x+a x^4\right) \sqrt{-x+x^5}} \, dx","Int[(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,"(-3*x^2)/(2*a*Sqrt[-x + x^5]) + (3*x^2*Sqrt[-(((-1)^(3/4)*(1 + (-1)^(1/4)*x)^2)/x)]*Sqrt[(I*(1 - x^4))/x^2]*EllipticF[ArcSin[Sqrt[((-1)^(3/4)*(Sqrt[2] - 2*(-1)^(1/4)*x + I*Sqrt[2]*x^2))/x]/2], -2*(1 - Sqrt[2])])/(4*Sqrt[2 + Sqrt[2]]*a*(1 + (-1)^(1/4)*x)*Sqrt[-x + x^5]) + (3*x^2*Sqrt[((-1)^(3/4)*(1 - (-1)^(1/4)*x)^2)/x]*Sqrt[(I*(1 - x^4))/x^2]*EllipticF[ArcSin[Sqrt[-(((-1)^(3/4)*(Sqrt[2] + 2*(-1)^(1/4)*x + I*Sqrt[2]*x^2))/x)]/2], -2*(1 - Sqrt[2])])/(4*Sqrt[2 + Sqrt[2]]*a*(1 - (-1)^(1/4)*x)*Sqrt[-x + x^5]) + (8*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^2/((-1 + x^8)^(3/2)*(-a - x^2 + a*x^8)), x], x, Sqrt[x]])/Sqrt[-x + x^5] + (6*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^4/((-1 + x^8)^(3/2)*(-a - x^2 + a*x^8)), x], x, Sqrt[x]])/(a*Sqrt[-x + x^5])","F",0,0,0,0,-1,"{}"
600,0,0,0,1.9266383,"\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","Int[(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,"(-1/2*I)*Defer[Int][Sqrt[1 + x^2 + x^6]/(I - x), x] - (I/2)*Defer[Int][Sqrt[1 + x^2 + x^6]/(I + x), x] + Defer[Int][Sqrt[1 + x^2 + x^6]/(Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x), x]/Sqrt[1 - I*Sqrt[3]] + Defer[Int][Sqrt[1 + x^2 + x^6]/(Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x), x]/Sqrt[1 + I*Sqrt[3]] + Defer[Int][Sqrt[1 + x^2 + x^6]/(Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x), x]/Sqrt[1 - I*Sqrt[3]] + Defer[Int][Sqrt[1 + x^2 + x^6]/(Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x), x]/Sqrt[1 + I*Sqrt[3]] + Defer[Int][Sqrt[1 + x^2 + x^6]/(-2 + x^2 - 2*x^6), x] + 6*Defer[Int][(x^4*Sqrt[1 + x^2 + x^6])/(2 - x^2 + 2*x^6), x]","F",0,0,0,0,-1,"{}"
601,0,0,0,1.9499443,"\int \frac{x+4 x^6}{\left(-1+x^5\right) \left(-a-x+a x^5\right) \sqrt{-x+x^6}} \, dx","Int[(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,"(-8*x^2)/(5*a*Sqrt[-x + x^6]) - (16*x^2*Sqrt[1 - x^5]*Hypergeometric2F1[3/10, 1/2, 13/10, x^5])/(15*a*Sqrt[-x + x^6]) + (10*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^2/((-1 + x^10)^(3/2)*(-a - x^2 + a*x^10)), x], x, Sqrt[x]])/Sqrt[-x + x^6] + (8*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^4/((-1 + x^10)^(3/2)*(-a - x^2 + a*x^10)), x], x, Sqrt[x]])/(a*Sqrt[-x + x^6])","F",0,0,0,0,-1,"{}"
602,0,0,0,1.8042682,"\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","Int[((-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,"(-4*Sqrt[x + 2*x^5]*Defer[Subst][Defer[Int][1/(Sqrt[1 + 2*x^8]*(1 - x^2 + 2*x^8)), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^4]) + (3*Sqrt[x + 2*x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + 2*x^8]*(1 - x^2 + 2*x^8)), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^4]) + (4*Sqrt[x + 2*x^5]*Defer[Subst][Defer[Int][1/(Sqrt[1 + 2*x^8]*(1 + x^2 + 2*x^8)), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^4]) + (3*Sqrt[x + 2*x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + 2*x^8]*(1 + x^2 + 2*x^8)), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^4])","F",0,0,0,0,-1,"{}"
603,1,35,0,0.0125947,"\int \sqrt{1+\sqrt{1+x}} \, dx","Int[Sqrt[1 + Sqrt[1 + x]],x]","\frac{4}{5} \left(\sqrt{x+1}+1\right)^{5/2}-\frac{4}{3} \left(\sqrt{x+1}+1\right)^{3/2}","\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))/3 + (4*(1 + Sqrt[1 + x])^(5/2))/5","A",4,3,13,0.2308,1,"{247, 190, 43}"
604,1,47,0,0.1140469,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x} \, dx","Int[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",7,6,19,0.3158,1,"{371, 1398, 783, 80, 63, 207}"
605,1,215,0,0.1986816,"\int \frac{1}{1+\sqrt[4]{9-6 x+x^2}} \, dx","Int[(1 + (9 - 6*x + x^2)^(1/4))^(-1),x]","-\frac{2 \left(x^2-6 x+9\right)^{3/4}}{3-x}+\frac{\sqrt{x^2-6 x+9} \log (2-x)}{2 (3-x)}+\frac{\sqrt{x^2-6 x+9} \log (4-x)}{2 (3-x)}-\frac{\left(x^2-6 x+9\right)^{3/4} \tan ^{-1}\left(\sqrt{x-3}\right)}{(x-3)^{3/2}}+\frac{\sqrt[4]{x^2-6 x+9} \tan ^{-1}\left(\sqrt{x-3}\right)}{\sqrt{x-3}}-\frac{\left(x^2-6 x+9\right)^{3/4} \tanh ^{-1}\left(\sqrt{x-3}\right)}{(x-3)^{3/2}}-\frac{\sqrt[4]{x^2-6 x+9} \tanh ^{-1}\left(\sqrt{x-3}\right)}{\sqrt{x-3}}+\frac{1}{2} \log (2-x)-\frac{1}{2} \log (4-x)","\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*(9 - 6*x + x^2)^(3/4))/(3 - x) + ((9 - 6*x + x^2)^(1/4)*ArcTan[Sqrt[-3 + x]])/Sqrt[-3 + x] - ((9 - 6*x + x^2)^(3/4)*ArcTan[Sqrt[-3 + x]])/(-3 + x)^(3/2) - ((9 - 6*x + x^2)^(1/4)*ArcTanh[Sqrt[-3 + x]])/Sqrt[-3 + x] - ((9 - 6*x + x^2)^(3/4)*ArcTanh[Sqrt[-3 + x]])/(-3 + x)^(3/2) + Log[2 - x]/2 + (Sqrt[9 - 6*x + x^2]*Log[2 - x])/(2*(3 - x)) - Log[4 - x]/2 + (Sqrt[9 - 6*x + x^2]*Log[4 - x])/(2*(3 - x))","B",26,7,16,0.4375,1,"{6742, 646, 50, 63, 204, 207, 43}"
606,1,48,0,0.0148972,"\int \frac{x^2}{\left(-2+x^2\right) \left(-1+x^2\right)^{3/4}} \, dx","Int[x^2/((-2 + x^2)*(-1 + x^2)^(3/4)),x]","\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}}","\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,"ArcTan[x/(Sqrt[2]*(-1 + x^2)^(1/4))]/Sqrt[2] - ArcTanh[x/(Sqrt[2]*(-1 + x^2)^(1/4))]/Sqrt[2]","A",1,1,20,0.05000,1,"{442}"
607,1,72,0,0.3628224,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{\left(1+x^2\right)^3} \, dx","Int[((-1 + x^2)*Sqrt[1 + x^4])/(1 + x^2)^3,x]","-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)+\frac{3 \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}","-\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 + (3*ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]])/(2*Sqrt[2]) - Sqrt[2]*ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]","A",20,10,22,0.4545,1,"{1721, 220, 1224, 1697, 1713, 1196, 1701, 1699, 203, 1211}"
608,0,0,0,0.7704477,"\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","Int[(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]","\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","\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,"(-5*Defer[Int][1/Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4], x])/23 - (24*(27 + 10*Sqrt[2])*Defer[Int][1/((82 - 48*Sqrt[2] - 46*x)*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4]), x])/23 - (24*(27 - 10*Sqrt[2])*Defer[Int][1/((82 + 48*Sqrt[2] - 46*x)*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4]), x])/23","F",0,0,0,0,-1,"{}"
609,1,94,0,0.1563475,"\int \frac{(-1+x) \sqrt[4]{x^3+x^4}}{x (1+x)} \, dx","Int[((-1 + x)*(x^3 + x^4)^(1/4))/(x*(1 + x)),x]","\sqrt[4]{x^4+x^3}+\frac{7 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 x^{3/4} \sqrt[4]{x+1}}-\frac{7 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 x^{3/4} \sqrt[4]{x+1}}","\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 + x^4)^(1/4) + (7*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(2*x^(3/4)*(1 + x)^(1/4)) - (7*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(2*x^(3/4)*(1 + x)^(1/4))","A",7,7,23,0.3043,1,"{2056, 80, 63, 331, 298, 203, 206}"
610,1,109,0,0.2570196,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^3+x^4}}{x^8} \, dx","Int[((-1 + x^4)*(x^3 + x^4)^(1/4))/x^8,x]","\frac{4 \left(x^4+x^3\right)^{5/4}}{25 x^{10}}-\frac{16 \left(x^4+x^3\right)^{5/4}}{105 x^9}+\frac{256 \left(x^4+x^3\right)^{5/4}}{1785 x^8}-\frac{1024 \left(x^4+x^3\right)^{5/4}}{7735 x^7}-\frac{22748 \left(x^4+x^3\right)^{5/4}}{69615 x^6}+\frac{90992 \left(x^4+x^3\right)^{5/4}}{348075 x^5}","\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 + x^4)^(5/4))/(25*x^10) - (16*(x^3 + x^4)^(5/4))/(105*x^9) + (256*(x^3 + x^4)^(5/4))/(1785*x^8) - (1024*(x^3 + x^4)^(5/4))/(7735*x^7) - (22748*(x^3 + x^4)^(5/4))/(69615*x^6) + (90992*(x^3 + x^4)^(5/4))/(348075*x^5)","B",10,3,20,0.1500,1,"{2052, 2016, 2014}"
611,0,0,0,2.5849988,"\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","Int[(-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]","\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","\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,"(Sqrt[1 - 2*x^2]*EllipticF[ArcSin[Sqrt[2]*x], -1])/(Sqrt[2]*Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) + (8*Sqrt[1 - 2*x^2]*Defer[Int][x/(Sqrt[1 - 4*x^4]*(-1 - 4*x + 12*x^2 - 8*x^3 + 4*x^4)), x])/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) - (16*Sqrt[1 - 2*x^2]*Defer[Int][x^2/(Sqrt[1 - 4*x^4]*(-1 - 4*x + 12*x^2 - 8*x^3 + 4*x^4)), x])/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) + (8*Sqrt[1 - 2*x^2]*Defer[Int][x^3/(Sqrt[1 - 4*x^4]*(-1 - 4*x + 12*x^2 - 8*x^3 + 4*x^4)), x])/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2])","F",0,0,0,0,-1,"{}"
612,1,208,0,0.5653148,"\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","Int[((-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{8 \sqrt[4]{x^4+1} x^5 \, _2F_1\left(\frac{19}{16},\frac{5}{4};\frac{35}{16};-x^4\right)}{19 \sqrt[4]{x^5+x}}-\frac{8 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{3}{16},\frac{5}{4};\frac{19}{16};-x^4\right)}{\sqrt[4]{x^5+x}}+\frac{4 \sqrt[4]{x^4+1} x^7 \, _2F_1\left(\frac{5}{4},\frac{27}{16};\frac{43}{16};-x^4\right)}{27 \sqrt[4]{x^5+x}}+\frac{4 \sqrt[4]{x^4+1} x^3 \, _2F_1\left(\frac{11}{16},\frac{5}{4};\frac{27}{16};-x^4\right)}{7 \sqrt[4]{x^5+x}}+\frac{8}{7 \sqrt[4]{x^5+x} x}+\frac{4}{7 \sqrt[4]{x^5+x} x^5}-\frac{4 \left(x^4+1\right)}{\sqrt[4]{x^5+x} x^2}","\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/(7*x^5*(x + x^5)^(1/4)) + 8/(7*x*(x + x^5)^(1/4)) - (4*(1 + x^4))/(x^2*(x + x^5)^(1/4)) - (8*x*(1 + x^4)^(1/4)*Hypergeometric2F1[3/16, 5/4, 19/16, -x^4])/(x + x^5)^(1/4) + (4*x^3*(1 + x^4)^(1/4)*Hypergeometric2F1[11/16, 5/4, 27/16, -x^4])/(7*(x + x^5)^(1/4)) + (8*x^5*(1 + x^4)^(1/4)*Hypergeometric2F1[19/16, 5/4, 35/16, -x^4])/(19*(x + x^5)^(1/4)) + (4*x^7*(1 + x^4)^(1/4)*Hypergeometric2F1[5/4, 27/16, 43/16, -x^4])/(27*(x + x^5)^(1/4))","C",18,9,45,0.2000,1,"{2056, 1833, 1585, 1478, 449, 1835, 1586, 1844, 364}"
613,1,67,0,0.0300039,"\int \frac{x^{20}}{\sqrt{-1+x^6}} \, dx","Int[x^20/Sqrt[-1 + x^6],x]","\frac{1}{18} \sqrt{x^6-1} x^{15}+\frac{5}{72} \sqrt{x^6-1} x^9+\frac{5}{48} \sqrt{x^6-1} x^3+\frac{5}{48} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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,"(5*x^3*Sqrt[-1 + x^6])/48 + (5*x^9*Sqrt[-1 + x^6])/72 + (x^15*Sqrt[-1 + x^6])/18 + (5*ArcTanh[x^3/Sqrt[-1 + x^6]])/48","A",6,4,13,0.3077,1,"{275, 321, 217, 206}"
614,1,67,0,0.0297891,"\int x^{14} \sqrt{-1+x^6} \, dx","Int[x^14*Sqrt[-1 + x^6],x]","\frac{1}{18} \sqrt{x^6-1} x^{15}-\frac{1}{72} \sqrt{x^6-1} x^9-\frac{1}{48} \sqrt{x^6-1} x^3-\frac{1}{48} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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,"-1/48*(x^3*Sqrt[-1 + x^6]) - (x^9*Sqrt[-1 + x^6])/72 + (x^15*Sqrt[-1 + x^6])/18 - ArcTanh[x^3/Sqrt[-1 + x^6]]/48","A",6,5,13,0.3846,1,"{275, 279, 321, 217, 206}"
615,1,57,0,0.023474,"\int \frac{x^{20}}{\sqrt{1+x^6}} \, dx","Int[x^20/Sqrt[1 + x^6],x]","-\frac{5}{48} \sinh ^{-1}\left(x^3\right)+\frac{1}{18} \sqrt{x^6+1} x^{15}-\frac{5}{72} \sqrt{x^6+1} x^9+\frac{5}{48} \sqrt{x^6+1} x^3","\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,"(5*x^3*Sqrt[1 + x^6])/48 - (5*x^9*Sqrt[1 + x^6])/72 + (x^15*Sqrt[1 + x^6])/18 - (5*ArcSinh[x^3])/48","A",5,3,13,0.2308,1,"{275, 321, 215}"
616,0,0,0,1.5121652,"\int \frac{x-4 x^6}{\sqrt{x+x^6} \left(1-a x^2+2 x^5+x^{10}\right)} \, dx","Int[(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,"(2*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + x^10]*(1 - a*x^4 + 2*x^10 + x^20)), x], x, Sqrt[x]])/Sqrt[x + x^6] - (8*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^12/(Sqrt[1 + x^10]*(1 - a*x^4 + 2*x^10 + x^20)), x], x, Sqrt[x]])/Sqrt[x + x^6]","F",0,0,0,0,-1,"{}"
617,0,0,0,1.5987903,"\int \frac{-x+4 x^6}{\sqrt{x+x^6} \left(a-x^2+2 a x^5+a x^{10}\right)} \, dx","Int[(-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,"(-2*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + x^10]*(a - x^4 + 2*a*x^10 + a*x^20)), x], x, Sqrt[x]])/Sqrt[x + x^6] + (8*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^12/(Sqrt[1 + x^10]*(a - x^4 + 2*a*x^10 + a*x^20)), x], x, Sqrt[x]])/Sqrt[x + x^6]","F",0,0,0,0,-1,"{}"
618,0,0,0,0.1447573,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + x^2],x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2}} \, dx","4 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + x^2], x]","F",0,0,0,0,-1,"{}"
619,0,0,0,2.1066668,"\int \frac{-3 b+2 a x}{\sqrt[4]{-b x+a x^2} \left(b-a x+x^3\right)} \, dx","Int[(-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,"(-8*a*x^(1/4)*(-b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^6/((-b + a*x^4)^(1/4)*(-b + a*x^4 - x^12)), x], x, x^(1/4)])/(-(b*x) + a*x^2)^(1/4) - (12*b*x^(1/4)*(-b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^2/((-b + a*x^4)^(1/4)*(b - a*x^4 + x^12)), x], x, x^(1/4)])/(-(b*x) + a*x^2)^(1/4)","F",0,0,0,0,-1,"{}"
620,0,0,0,51.1696076,"\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","Int[((-4 + x^3)*Sqrt[2 - x^2 + x^3])/((2 + x^3)*(2 + x^2 + x^3)),x]","\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","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,"-1/3*((-2)^(2/3)*Sqrt[2 - x^2 + x^3]) - (2^(2/3)*Sqrt[2 - x^2 + x^3])/3 + ((-1)^(1/3)*2^(2/3)*Sqrt[2 - x^2 + x^3])/3 + ((1 - 3*(-2)^(1/3))*(-2*(26 + 15*Sqrt[3]))^(1/6)*Sqrt[2 - x^2 + x^3]*EllipticE[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/(Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) + (I*((-1)^(1/3) - 3*2^(1/3))*(2*(26 + 15*Sqrt[3]))^(1/6)*Sqrt[2 - x^2 + x^3]*EllipticE[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/(Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) - (I*(1 + 3*2^(1/3))*(2*(26 + 15*Sqrt[3]))^(1/6)*Sqrt[2 - x^2 + x^3]*EllipticE[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/(Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) - (2*(1 + 6*(-2)^(1/3) - 9*(-2)^(2/3))*(-2*(26 - 15*Sqrt[3]))^(1/6)*Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[2 - x^2 + x^3]*EllipticF[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) + ((2*I)*(1 - 6*2^(1/3) - 9*2^(2/3))*(2*(26 - 15*Sqrt[3]))^(1/6)*Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[2 - x^2 + x^3]*EllipticF[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) - (2*(-1)^(5/6)*(1 - 6*(-1)^(2/3)*2^(1/3) + 9*(-1)^(1/3)*2^(2/3))*(2*(26 - 15*Sqrt[3]))^(1/6)*Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[2 - x^2 + x^3]*EllipticF[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) + (2*(1 - 3*(-2)^(1/3))*(-2*(26 + 15*Sqrt[3]))^(1/6)*(1 + (26 - 15*Sqrt[3])^(2/3))*Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[2 - x^2 + x^3]*EllipticF[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) + ((2*I)*((-1)^(1/3) - 3*2^(1/3))*(2*(26 + 15*Sqrt[3]))^(1/6)*(1 + (26 - 15*Sqrt[3])^(2/3))*Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[2 - x^2 + x^3]*EllipticF[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) - ((2*I)*(1 + 3*2^(1/3))*(2*(26 + 15*Sqrt[3]))^(1/6)*(1 + (26 - 15*Sqrt[3])^(2/3))*Sqrt[-((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3])))]*Sqrt[2 - x^2 + x^3]*EllipticF[ArcSin[((26 - 15*Sqrt[3])^(1/6)*Sqrt[(-I)*(2 + (26 - 15*Sqrt[3])^(1/3)*(1 - I*Sqrt[3]) + (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) - 6*x)])/(3^(1/4)*Sqrt[2*(1 - (26 - 15*Sqrt[3])^(2/3))])], (-2*Sqrt[3]*(1 - (26 - 15*Sqrt[3])^(2/3)))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/((1 - (26 - 15*Sqrt[3])^(-1/3) - (26 - 15*Sqrt[3])^(1/3) - 3*x)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2]) + (27*2^(5/6)*Sqrt[(26 - 15*Sqrt[3])*(3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3]))]*Sqrt[1 - (2*(1 + (26 - 15*Sqrt[3])^(2/3) - (26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)))/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3]))]*Sqrt[1 - (2*(1 + (26 - 15*Sqrt[3])^(2/3) - (26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)))/(3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3]))]*Sqrt[-2 - (26 - 15*Sqrt[3])^(1/3)*(1 + I*Sqrt[3]) + (I*(I + Sqrt[3]))/(26 - 15*Sqrt[3])^(1/3) + 6*x]*Sqrt[-2 - (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) + I*(26 - 15*Sqrt[3])^(1/3)*(I + Sqrt[3]) + 6*x]*Sqrt[2 - x^2 + x^3]*EllipticPi[(3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3]))/(2*(1 - 3*(52 - 30*Sqrt[3])^(1/3) - (26 - 15*Sqrt[3])^(1/3) + (26 - 15*Sqrt[3])^(2/3))), ArcSin[(Sqrt[2]*(26 - 15*Sqrt[3])^(1/6)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x])/Sqrt[3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3])]], (3*I + Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I - Sqrt[3]))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/((1 - 3*(52 - 30*Sqrt[3])^(1/3) - (26 - 15*Sqrt[3])^(1/3) + (26 - 15*Sqrt[3])^(2/3))*Sqrt[-1 + I*Sqrt[3] - (26 - 15*Sqrt[3])^(2/3)*(1 + I*Sqrt[3]) - 2*(26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)]*Sqrt[-1 - I*Sqrt[3] + I*(26 - 15*Sqrt[3])^(2/3)*(I + Sqrt[3]) - 2*(26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)]*(1 - (26 - 15*Sqrt[3])^(-2/3) - (26 - 15*Sqrt[3])^(2/3) - ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) - (1 - 3*x)^2)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x]) + (27*2^(5/6)*(26 - 15*Sqrt[3])^(1/6)*Sqrt[3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3])]*Sqrt[1 - (2*(1 + (26 - 15*Sqrt[3])^(2/3) - (26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)))/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3]))]*Sqrt[1 - (2*(1 + (26 - 15*Sqrt[3])^(2/3) - (26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)))/(3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3]))]*Sqrt[-2 - (26 - 15*Sqrt[3])^(1/3)*(1 + I*Sqrt[3]) + (I*(I + Sqrt[3]))/(26 - 15*Sqrt[3])^(1/3) + 6*x]*Sqrt[-2 - (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) + I*(26 - 15*Sqrt[3])^(1/3)*(I + Sqrt[3]) + 6*x]*Sqrt[2 - x^2 + x^3]*EllipticPi[-1/2*((-26 - 15*Sqrt[3])^(1/3)*(3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3])))/((-1)^(1/3) - 3*2^(1/3) - (-26 - 15*Sqrt[3])^(1/3) - (-26 + 15*Sqrt[3])^(1/3)), ArcSin[(Sqrt[2]*(26 - 15*Sqrt[3])^(1/6)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x])/Sqrt[3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3])]], (3*I + Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I - Sqrt[3]))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/(((-1)^(1/3) - 3*2^(1/3) - (-26 - 15*Sqrt[3])^(1/3) - (-26 + 15*Sqrt[3])^(1/3))*Sqrt[-1 + I*Sqrt[3] - (26 - 15*Sqrt[3])^(2/3)*(1 + I*Sqrt[3]) - 2*(26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)]*Sqrt[-1 - I*Sqrt[3] + I*(26 - 15*Sqrt[3])^(2/3)*(I + Sqrt[3]) - 2*(26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)]*(1 - (26 - 15*Sqrt[3])^(-2/3) - (26 - 15*Sqrt[3])^(2/3) - ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) - (1 - 3*x)^2)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x]) + (27*2^(5/6)*Sqrt[(26 - 15*Sqrt[3])*(3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3]))]*Sqrt[1 - (2*(1 + (26 - 15*Sqrt[3])^(2/3) - (26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)))/(3 + I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 - I*Sqrt[3]))]*Sqrt[1 - (2*(1 + (26 - 15*Sqrt[3])^(2/3) - (26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)))/(3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3]))]*Sqrt[-2 - (26 - 15*Sqrt[3])^(1/3)*(1 + I*Sqrt[3]) + (I*(I + Sqrt[3]))/(26 - 15*Sqrt[3])^(1/3) + 6*x]*Sqrt[-2 - (1 + I*Sqrt[3])/(26 - 15*Sqrt[3])^(1/3) + I*(26 - 15*Sqrt[3])^(1/3)*(I + Sqrt[3]) + 6*x]*Sqrt[2 - x^2 + x^3]*EllipticPi[((-1)^(1/6)*(3*I + Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I - Sqrt[3])))/(2*((-1)^(2/3) - 3*(52 - 30*Sqrt[3])^(1/3) - (-1)^(2/3)*(26 - 15*Sqrt[3])^(1/3) + (-26 + 15*Sqrt[3])^(2/3))), ArcSin[(Sqrt[2]*(26 - 15*Sqrt[3])^(1/6)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x])/Sqrt[3 - I*Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3 + I*Sqrt[3])]], (3*I + Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I - Sqrt[3]))/(3*I - Sqrt[3] + (26 - 15*Sqrt[3])^(2/3)*(3*I + Sqrt[3]))])/(((-1)^(2/3) - 3*(52 - 30*Sqrt[3])^(1/3) - (-1)^(2/3)*(26 - 15*Sqrt[3])^(1/3) + (-26 + 15*Sqrt[3])^(2/3))*Sqrt[-1 + I*Sqrt[3] - (26 - 15*Sqrt[3])^(2/3)*(1 + I*Sqrt[3]) - 2*(26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)]*Sqrt[-1 - I*Sqrt[3] + I*(26 - 15*Sqrt[3])^(2/3)*(I + Sqrt[3]) - 2*(26 - 15*Sqrt[3])^(1/3)*(1 - 3*x)]*(1 - (26 - 15*Sqrt[3])^(-2/3) - (26 - 15*Sqrt[3])^(2/3) - ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) - (1 - 3*x)^2)*Sqrt[-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x]) - 2*Defer[Int][Sqrt[2 - x^2 + x^3]/(2 + x^2 + x^3), x] - 3*Defer[Int][(x*Sqrt[2 - x^2 + x^3])/(2 + x^2 + x^3), x]","F",0,0,0,0,-1,"{}"
621,1,49,0,0.0133,"\int x^2 \sqrt[4]{-1+x^4} \, dx","Int[x^2*(-1 + x^4)^(1/4),x]","\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","\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))/4 + ArcTan[x/(-1 + x^4)^(1/4)]/8 - ArcTanh[x/(-1 + x^4)^(1/4)]/8","A",5,5,13,0.3846,1,"{279, 331, 298, 203, 206}"
622,1,49,0,0.0132726,"\int x^2 \sqrt[4]{1+x^4} \, dx","Int[x^2*(1 + x^4)^(1/4),x]","-\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","-\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))/4 - ArcTan[x/(1 + x^4)^(1/4)]/8 + ArcTanh[x/(1 + x^4)^(1/4)]/8","A",5,5,13,0.3846,1,"{279, 331, 298, 203, 206}"
623,1,60,0,0.0844856,"\int \frac{\left(-b+a x^3\right) \sqrt{x+x^4}}{x^3} \, dx","Int[((-b + a*x^3)*Sqrt[x + x^4])/x^3,x]","\frac{1}{3} x \sqrt{x^4+x} (a-2 b)+\frac{1}{3} (a-2 b) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)+\frac{2 b \left(x^4+x\right)^{3/2}}{3 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,"((a - 2*b)*x*Sqrt[x + x^4])/3 + (2*b*(x + x^4)^(3/2))/(3*x^3) + ((a - 2*b)*ArcTanh[x^2/Sqrt[x + x^4]])/3","A",4,4,22,0.1818,1,"{2038, 2004, 2029, 206}"
624,1,277,0,0.1814565,"\int \frac{1}{\left(-2+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Int[1/((-2 + x^4)*(x^2 + x^4)^(1/4)),x]","-\frac{\sqrt[4]{2-\sqrt{2}} \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x^2+1}}\right)}{4 \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{2+\sqrt{2}} \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x^2+1}}\right)}{4 \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{2-\sqrt{2}} \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x^2+1}}\right)}{4 \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{2+\sqrt{2}} \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x^2+1}}\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*((2 - Sqrt[2])^(1/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[Sqrt[x]/((2 - Sqrt[2])^(1/4)*(1 + x^2)^(1/4))])/(x^2 + x^4)^(1/4) - ((2 + Sqrt[2])^(1/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[Sqrt[x]/((2 + Sqrt[2])^(1/4)*(1 + x^2)^(1/4))])/(4*(x^2 + x^4)^(1/4)) - ((2 - Sqrt[2])^(1/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/((2 - Sqrt[2])^(1/4)*(1 + x^2)^(1/4))])/(4*(x^2 + x^4)^(1/4)) - ((2 + Sqrt[2])^(1/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/((2 + Sqrt[2])^(1/4)*(1 + x^2)^(1/4))])/(4*(x^2 + x^4)^(1/4))","B",11,7,19,0.3684,1,"{2056, 1270, 1429, 377, 212, 206, 203}"
625,0,0,0,0.8443609,"\int \frac{-4 b+a x^3}{\sqrt[4]{-b+a x^3} \left(b-a x^3+x^4\right)} \, dx","Int[(-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,"-(a*Defer[Int][x^3/((-b + a*x^3)^(1/4)*(-b + a*x^3 - x^4)), x]) - 4*b*Defer[Int][1/((-b + a*x^3)^(1/4)*(b - a*x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
626,0,0,0,1.9979754,"\int \frac{-x+3 x^5}{\left(1+x^4\right) \left(a-x+a x^4\right) \sqrt{x+x^5}} \, dx","Int[(-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,"(3*x^2)/(2*a*Sqrt[x + x^5]) - (3*x^2*Sqrt[(1 + x)^2/x]*Sqrt[-((1 + x^4)/x^2)]*EllipticF[ArcSin[Sqrt[-((Sqrt[2] - 2*x + Sqrt[2]*x^2)/x)]/2], -2*(1 - Sqrt[2])])/(4*Sqrt[2 + Sqrt[2]]*a*(1 + x)*Sqrt[x + x^5]) - (3*Sqrt[-((1 - x)^2/x)]*x^2*Sqrt[-((1 + x^4)/x^2)]*EllipticF[ArcSin[Sqrt[(Sqrt[2] + 2*x + Sqrt[2]*x^2)/x]/2], -2*(1 - Sqrt[2])])/(4*Sqrt[2 + Sqrt[2]]*a*(1 - x)*Sqrt[x + x^5]) - (8*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^2/((1 + x^8)^(3/2)*(a - x^2 + a*x^8)), x], x, Sqrt[x]])/Sqrt[x + x^5] + (6*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^4/((1 + x^8)^(3/2)*(a - x^2 + a*x^8)), x], x, Sqrt[x]])/(a*Sqrt[x + x^5])","F",0,0,0,0,-1,"{}"
627,1,47,0,0.0354887,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^{10}} \, dx","Int[((-1 + x^3)*Sqrt[-1 + x^6])/x^10,x]","-\frac{\sqrt{x^6-1}}{6 x^6}+\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\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,"-1/6*Sqrt[-1 + x^6]/x^6 - (-1 + x^6)^(3/2)/(9*x^9) + ArcTan[Sqrt[-1 + x^6]]/6","A",6,6,18,0.3333,1,"{1475, 807, 266, 47, 63, 203}"
628,-1,0,0,180.0034405,"\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1+x^3-x^6\right)} \, dx","Int[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 + x^3 - x^6)),x]","\text{\$Aborted}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^{12}+3 \text{$\#$1}^4-1\&,\frac{\log \left(\sqrt[4]{x^5-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"$Aborted","F",0,0,0,0,-1,"{}"
629,-1,0,0,180.0045918,"\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1+x^3-x^6\right)} \, dx","Int[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 + x^3 - x^6)),x]","\text{\$Aborted}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^{12}+3 \text{$\#$1}^4-1\&,\frac{\log \left(\sqrt[4]{x^5-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"$Aborted","F",0,0,0,0,-1,"{}"
630,0,0,0,1.8405483,"\int \frac{x (6 b+5 a x)}{\sqrt[4]{b x^2+a x^3} \left(-b-a x+x^6\right)} \, dx","Int[(x*(6*b + 5*a*x))/((b*x^2 + a*x^3)^(1/4)*(-b - a*x + x^6)),x]","\int \frac{x (6 b+5 a x)}{\sqrt[4]{b x^2+a x^3} \left(-b-a x+x^6\right)} \, dx","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,"(-12*b*Sqrt[x]*(b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^2/((b + a*x^2)^(1/4)*(b + a*x^2 - x^12)), x], x, Sqrt[x]])/(b*x^2 + a*x^3)^(1/4) - (10*a*Sqrt[x]*(b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^4/((b + a*x^2)^(1/4)*(b + a*x^2 - x^12)), x], x, Sqrt[x]])/(b*x^2 + a*x^3)^(1/4)","F",0,0,0,0,-1,"{}"
631,0,0,0,0.5398468,"\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{1-a x^4-2 x^5+x^{10}} \, dx","Int[(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,"-2*Defer[Int][Sqrt[-1 + x^5]/(-1 + a*x^4 + 2*x^5 - x^10), x] + 3*Defer[Int][(x^5*Sqrt[-1 + x^5])/(1 - a*x^4 - 2*x^5 + x^10), x]","F",0,0,0,0,-1,"{}"
632,0,0,0,0.5305202,"\int \frac{\sqrt{-1+x^5} \left(2+3 x^5\right)}{a-x^4-2 a x^5+a x^{10}} \, dx","Int[(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,"2*Defer[Int][Sqrt[-1 + x^5]/(a - x^4 - 2*a*x^5 + a*x^10), x] + 3*Defer[Int][(x^5*Sqrt[-1 + x^5])/(a - x^4 - 2*a*x^5 + a*x^10), x]","F",0,0,0,0,-1,"{}"
633,0,0,0,0.5465377,"\int \frac{\sqrt{1+x^5} \left(-2+3 x^5\right)}{a-x^4+2 a x^5+a x^{10}} \, dx","Int[(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,"-2*Defer[Int][Sqrt[1 + x^5]/(a - x^4 + 2*a*x^5 + a*x^10), x] + 3*Defer[Int][(x^5*Sqrt[1 + x^5])/(a - x^4 + 2*a*x^5 + a*x^10), x]","F",0,0,0,0,-1,"{}"
634,0,0,0,0.0187404,"\int \frac{1}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Int[1/Sqrt[1 + Sqrt[1 + x^2]],x]","\int \frac{1}{\sqrt{1+\sqrt{1+x^2}}} \, dx","\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,"Defer[Int][1/Sqrt[1 + Sqrt[1 + x^2]], x]","F",0,0,0,0,-1,"{}"
635,1,73,0,0.0938634,"\int x^6 \sqrt{-x+x^4} \, dx","Int[x^6*Sqrt[-x + x^4],x]","-\frac{1}{36} \sqrt{x^4-x} x^4-\frac{1}{24} \sqrt{x^4-x} x+\frac{1}{9} \sqrt{x^4-x} x^7-\frac{1}{24} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)","\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,"-1/24*(x*Sqrt[-x + x^4]) - (x^4*Sqrt[-x + x^4])/36 + (x^7*Sqrt[-x + x^4])/9 - ArcTanh[x^2/Sqrt[-x + x^4]]/24","A",5,4,15,0.2667,1,"{2021, 2024, 2029, 206}"
636,1,121,0,0.3121949,"\int \frac{\left(-1+x^2\right) \sqrt[4]{-x^3+x^4}}{x^8} \, dx","Int[((-1 + x^2)*(-x^3 + x^4)^(1/4))/x^8,x]","-\frac{4 \left(x^4-x^3\right)^{5/4}}{25 x^{10}}-\frac{16 \left(x^4-x^3\right)^{5/4}}{105 x^9}+\frac{164 \left(x^4-x^3\right)^{5/4}}{1785 x^8}+\frac{656 \left(x^4-x^3\right)^{5/4}}{7735 x^7}+\frac{5248 \left(x^4-x^3\right)^{5/4}}{69615 x^6}+\frac{20992 \left(x^4-x^3\right)^{5/4}}{348075 x^5}","\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*(-x^3 + x^4)^(5/4))/(25*x^10) - (16*(-x^3 + x^4)^(5/4))/(105*x^9) + (164*(-x^3 + x^4)^(5/4))/(1785*x^8) + (656*(-x^3 + x^4)^(5/4))/(7735*x^7) + (5248*(-x^3 + x^4)^(5/4))/(69615*x^6) + (20992*(-x^3 + x^4)^(5/4))/(348075*x^5)","B",12,3,22,0.1364,1,"{2052, 2016, 2014}"
637,0,0,0,0.5676821,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x \left(1+x^3\right)} \, dx","Int[((-1 + x^3)*Sqrt[-1 + x^6])/(x*(1 + x^3)),x]","\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x \left(1+x^3\right)} \, dx","\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,"-1/3*Sqrt[-1 + x^6] + ArcTan[Sqrt[-1 + x^6]]/3 + (2*Defer[Int][Sqrt[-1 + x^6]/(1 + x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(-1 - I*Sqrt[3] + 2*x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(-1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
638,0,0,0,0.5286234,"\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x \left(-1+x^3\right)} \, dx","Int[((1 + x^3)*Sqrt[-1 + x^6])/(x*(-1 + x^3)),x]","\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x \left(-1+x^3\right)} \, dx","\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,"-1/3*Sqrt[-1 + x^6] + ArcTan[Sqrt[-1 + x^6]]/3 + (2*Defer[Int][Sqrt[-1 + x^6]/(-1 + x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(1 - I*Sqrt[3] + 2*x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
639,1,397,0,0.9324215,"\int \frac{2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Int[(2*b + a*x^4)/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","-\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)}{4 \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)}{4 \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)}{4 \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)}{4 \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}","\frac{1}{8} \text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"-1/4*((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(4*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)) - ((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(4*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(4*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4))","B",10,5,36,0.1389,1,"{6728, 377, 212, 208, 205}"
640,1,397,0,0.5198974,"\int \frac{2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Int[(2*b + a*x^4)/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","-\frac{\sqrt[4]{a-\sqrt{a^2+2 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{\sqrt{a^2+2 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{a-\sqrt{a^2+2 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{\sqrt{a^2+2 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}","\frac{1}{8} \text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"-1/4*((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(4*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)) - ((a - Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(4*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ((a + Sqrt[a^2 + 2*b])^(1/4)*ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))])/(4*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4))","B",10,5,36,0.1389,1,"{6728, 377, 212, 208, 205}"
641,0,0,0,1.6272306,"\int \frac{\left(-1+x^6\right) \left(1+x^6\right)}{\sqrt[4]{x-x^4+x^7} \left(1+3 x^6+x^{12}\right)} \, dx","Int[((-1 + x^6)*(1 + x^6))/((x - x^4 + x^7)^(1/4)*(1 + 3*x^6 + x^12)),x]","\int \frac{\left(-1+x^6\right) \left(1+x^6\right)}{\sqrt[4]{x-x^4+x^7} \left(1+3 x^6+x^{12}\right)} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^8+2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^7-x^4+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(4*x*(1 - (2*x^3)/(1 - I*Sqrt[3]))^(1/4)*(1 - (2*x^3)/(1 + I*Sqrt[3]))^(1/4)*AppellF1[1/4, 1/4, 1/4, 5/4, (2*x^3)/(1 + I*Sqrt[3]), (2*x^3)/(1 - I*Sqrt[3])])/(3*(x - x^4 + x^7)^(1/4)) - (((2*I)/3)*Sqrt[3 - Sqrt[5]]*x^(1/4)*(1 - x^3 + x^6)^(1/4)*Defer[Subst][Defer[Int][1/((I*Sqrt[3 - Sqrt[5]] - Sqrt[2]*x^4)*(1 - x^4 + x^8)^(1/4)), x], x, x^(3/4)])/(x - x^4 + x^7)^(1/4) - (((2*I)/3)*Sqrt[3 + Sqrt[5]]*x^(1/4)*(1 - x^3 + x^6)^(1/4)*Defer[Subst][Defer[Int][1/((I*Sqrt[3 + Sqrt[5]] - Sqrt[2]*x^4)*(1 - x^4 + x^8)^(1/4)), x], x, x^(3/4)])/(x - x^4 + x^7)^(1/4) - (((2*I)/3)*Sqrt[3 - Sqrt[5]]*x^(1/4)*(1 - x^3 + x^6)^(1/4)*Defer[Subst][Defer[Int][1/((I*Sqrt[3 - Sqrt[5]] + Sqrt[2]*x^4)*(1 - x^4 + x^8)^(1/4)), x], x, x^(3/4)])/(x - x^4 + x^7)^(1/4) - (((2*I)/3)*Sqrt[3 + Sqrt[5]]*x^(1/4)*(1 - x^3 + x^6)^(1/4)*Defer[Subst][Defer[Int][1/((I*Sqrt[3 + Sqrt[5]] + Sqrt[2]*x^4)*(1 - x^4 + x^8)^(1/4)), x], x, x^(3/4)])/(x - x^4 + x^7)^(1/4)","F",0,0,0,0,-1,"{}"
642,1,41,0,0.0077343,"\int \sqrt{1+\sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[1 + x^2]],x]","\frac{2 x}{\sqrt{\sqrt{x^2+1}+1}}+\frac{2 x^3}{3 \left(\sqrt{x^2+1}+1\right)^{3/2}}","\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*x^3)/(3*(1 + Sqrt[1 + x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 + x^2]]","A",1,1,15,0.06667,1,"{2129}"
643,0,0,0,0.0769369,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x^2} \, dx","Int[Sqrt[1 + Sqrt[1 + x^2]]/x^2,x]","\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x^2} \, dx","\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,"Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/x^2, x]","F",0,0,0,0,-1,"{}"
644,1,51,0,0.0413683,"\int \frac{1}{x \left(b+a x^2\right)^{3/4}} \, dx","Int[1/(x*(b + a*x^2)^(3/4)),x]","-\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}}","-\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)]/b^(3/4)) - ArcTanh[(b + a*x^2)^(1/4)/b^(1/4)]/b^(3/4)","A",5,5,15,0.3333,1,"{266, 63, 212, 206, 203}"
645,0,0,0,0.321515,"\int \frac{-7+x}{(-11+5 x) \sqrt{-60+83 x-21 x^2-3 x^3+x^4}} \, dx","Int[(-7 + x)/((-11 + 5*x)*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4]),x]","\int \frac{-7+x}{(-11+5 x) \sqrt{-60+83 x-21 x^2-3 x^3+x^4}} \, dx","-\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,"Defer[Int][1/Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4], x]/5 - (24*Defer[Int][1/((-11 + 5*x)*Sqrt[-60 + 83*x - 21*x^2 - 3*x^3 + x^4]), x])/5","F",0,0,0,0,-1,"{}"
646,1,51,0,0.0524168,"\int \frac{\left(-2+x^6\right) \sqrt{-1+x^6}}{x \left(2+x^6\right)} \, dx","Int[((-2 + x^6)*Sqrt[-1 + x^6])/(x*(2 + x^6)),x]","\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}}","\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]/3 + ArcTan[Sqrt[-1 + x^6]]/3 - (2*ArcTan[Sqrt[-1 + x^6]/Sqrt[3]])/Sqrt[3]","A",7,5,25,0.2000,1,"{573, 154, 156, 63, 203}"
647,0,0,0,1.5580095,"\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","Int[(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,"Defer[Int][Sqrt[-1 - x^2 + x^6]/(-1 + x), x]/2 - Defer[Int][Sqrt[-1 - x^2 + x^6]/(1 + x), x]/2 + ((1 - I*Sqrt[3])*Defer[Int][Sqrt[-1 - x^2 + x^6]/(-1 - I*Sqrt[3] + 2*x), x])/2 - ((1 + I*Sqrt[3])*Defer[Int][Sqrt[-1 - x^2 + x^6]/(1 - I*Sqrt[3] + 2*x), x])/2 + ((1 + I*Sqrt[3])*Defer[Int][Sqrt[-1 - x^2 + x^6]/(-1 + I*Sqrt[3] + 2*x), x])/2 - ((1 - I*Sqrt[3])*Defer[Int][Sqrt[-1 - x^2 + x^6]/(1 + I*Sqrt[3] + 2*x), x])/2 + Defer[Int][Sqrt[-1 - x^2 + x^6]/(2 - x^2 - 2*x^6), x] - 6*Defer[Int][(x^4*Sqrt[-1 - x^2 + x^6])/(-2 + x^2 + 2*x^6), x]","F",0,0,0,0,-1,"{}"
648,0,0,0,0.9968683,"\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","Int[(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,"-5*a*Defer[Int][x^4/((-b + a*x^3)^(1/4)*(-b + a*x^3 - x^8)), x] - 8*b*Defer[Int][x/((-b + a*x^3)^(1/4)*(b - a*x^3 + x^8)), x]","F",0,0,0,0,-1,"{}"
649,0,0,0,9.3008444,"\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","Int[(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,"(-24*(-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)*Defer[Subst][Defer[Int][x^2/((-1 - 2*x^4 + x^8)^(3/4)*(-1 - 16*x^12 + 56*x^20 - 72*x^24 + 39*x^28 - 10*x^32 + x^36)), x], x, (1 + x)^(1/4)])/(1 + x)^(3/4) - (36*(-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)*Defer[Subst][Defer[Int][x^6/((-1 - 2*x^4 + x^8)^(3/4)*(-1 - 16*x^12 + 56*x^20 - 72*x^24 + 39*x^28 - 10*x^32 + x^36)), x], x, (1 + x)^(1/4)])/(1 + x)^(3/4) + (104*(-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)*Defer[Subst][Defer[Int][x^10/((-1 - 2*x^4 + x^8)^(3/4)*(-1 - 16*x^12 + 56*x^20 - 72*x^24 + 39*x^28 - 10*x^32 + x^36)), x], x, (1 + x)^(1/4)])/(1 + x)^(3/4) - (36*(-((1 + x)/(2 - x^2)))^(3/4)*(-2 + x^2)^(3/4)*Defer[Subst][Defer[Int][x^14/((-1 - 2*x^4 + x^8)^(3/4)*(-1 - 16*x^12 + 56*x^20 - 72*x^24 + 39*x^28 - 10*x^32 + x^36)), x], x, (1 + x)^(1/4)])/(1 + x)^(3/4)","F",0,0,0,0,-1,"{}"
650,0,0,0,2.0625128,"\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","Int[(-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,"7*Defer[Int][1/Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16], x] - (-1)^(1/8)*Defer[Int][1/(((-1)^(1/8) - x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x] - (-1)^(3/8)*Defer[Int][1/(((-1)^(3/8) - x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x] + (-1)^(5/8)*Defer[Int][1/((-(-1)^(5/8) - x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x] + (-1)^(7/8)*Defer[Int][1/((-(-1)^(7/8) - x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x] - (-1)^(1/8)*Defer[Int][1/(((-1)^(1/8) + x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x] - (-1)^(3/8)*Defer[Int][1/(((-1)^(3/8) + x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x] + (-1)^(5/8)*Defer[Int][1/((-(-1)^(5/8) + x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x] + (-1)^(7/8)*Defer[Int][1/((-(-1)^(7/8) + x)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]), x]","F",0,0,0,0,-1,"{}"
651,0,0,0,0.3253318,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x^2 \sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[1 + x^2]]/(x^2*Sqrt[1 + x^2]),x]","\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x^2 \sqrt{1+x^2}} \, dx","-\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,"Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(x^2*Sqrt[1 + x^2]), x]","F",0,0,0,0,-1,"{}"
652,1,67,0,0.3052668,"\int \frac{x}{x+\sqrt{1+\sqrt{1+x}}} \, dx","Int[x/(x + Sqrt[1 + Sqrt[1 + x]]),x]","\left(\sqrt{x+1}+1\right)^2-4 \sqrt{\sqrt{x+1}+1}-2 \sqrt{x+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,"-2*Sqrt[1 + x] - 4*Sqrt[1 + Sqrt[1 + x]] + (1 + Sqrt[1 + x])^2 + (8*ArcTanh[(1 + 2*Sqrt[1 + Sqrt[1 + x]])/Sqrt[5]])/Sqrt[5]","A",6,3,19,0.1579,1,"{1628, 618, 206}"
653,0,0,0,0.0229096,"\int \frac{a+2 x}{\sqrt[4]{b+a x+x^2} \left(-1+2 b+2 a x+2 x^2\right)} \, dx","Int[(a + 2*x)/((b + a*x + x^2)^(1/4)*(-1 + 2*b + 2*a*x + 2*x^2)),x]","\int \frac{a+2 x}{\sqrt[4]{b+a x+x^2} \left(-1+2 b+2 a x+2 x^2\right)} \, dx","\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,"Defer[Int][(a + 2*x)/((b + a*x + x^2)^(1/4)*(-1 + 2*b + 2*a*x + 2*x^2)), x]","F",0,0,0,0,-1,"{}"
654,1,61,0,0.0250625,"\int \frac{1}{x^7 \sqrt[4]{1+x^3}} \, dx","Int[1/(x^7*(1 + x^3)^(1/4)),x]","\frac{5 \left(x^3+1\right)^{3/4}}{24 x^3}+\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}}{6 x^6}","\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,"-1/6*(1 + x^3)^(3/4)/x^6 + (5*(1 + x^3)^(3/4))/(24*x^3) + (5*ArcTan[(1 + x^3)^(1/4)])/48 - (5*ArcTanh[(1 + x^3)^(1/4)])/48","A",7,6,13,0.4615,1,"{266, 51, 63, 298, 203, 206}"
655,1,61,0,0.0232226,"\int \frac{\sqrt[4]{1+x^3}}{x^7} \, dx","Int[(1 + x^3)^(1/4)/x^7,x]","-\frac{\sqrt[4]{x^3+1}}{24 x^3}+\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}}{6 x^6}","\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,"-1/6*(1 + x^3)^(1/4)/x^6 - (1 + x^3)^(1/4)/(24*x^3) + ArcTan[(1 + x^3)^(1/4)]/16 + ArcTanh[(1 + x^3)^(1/4)]/16","A",7,7,13,0.5385,1,"{266, 47, 51, 63, 212, 206, 203}"
656,1,59,0,0.0432269,"\int \frac{\sqrt{b+a x^3} \left(2 b+a x^3\right)}{x} \, dx","Int[(Sqrt[b + a*x^3]*(2*b + a*x^3))/x,x]","-\frac{4}{3} b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)+\frac{4}{3} b \sqrt{a x^3+b}+\frac{2}{9} \left(a x^3+b\right)^{3/2}","\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,"(4*b*Sqrt[b + a*x^3])/3 + (2*(b + a*x^3)^(3/2))/9 - (4*b^(3/2)*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/3","A",5,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
657,0,0,0,0.6155027,"\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x^{13} \left(-1+x^3\right)} \, dx","Int[((1 + x^3)*Sqrt[-1 + x^6])/(x^13*(-1 + x^3)),x]","\int \frac{\left(1+x^3\right) \sqrt{-1+x^6}}{x^{13} \left(-1+x^3\right)} \, dx","\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,"(-2*Sqrt[-1 + x^6])/3 + Sqrt[-1 + x^6]/(12*x^12) + (7*Sqrt[-1 + x^6])/(24*x^6) + (2*Sqrt[-1 + x^6])/(3*x^3) - (2*(-1 + x^6)^(3/2))/(9*x^9) + (7*ArcTan[Sqrt[-1 + x^6]])/24 - (2*ArcTanh[x^3/Sqrt[-1 + x^6]])/3 + (2*Defer[Int][Sqrt[-1 + x^6]/(-1 + x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(1 - I*Sqrt[3] + 2*x), x])/3 + (4*Defer[Int][Sqrt[-1 + x^6]/(1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
658,1,163,0,0.2953317,"\int \frac{\sqrt{x+x^4} \left(-b+a x^6\right)}{x^6} \, dx","Int[(Sqrt[x + x^4]*(-b + a*x^6))/x^6,x]","\frac{a \left(x^4+x\right)^{3/2}}{3 x^3}-\frac{2 a \sqrt{x^4+x}}{5 x^3}+\frac{3^{3/4} a x (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^4+x}}+\frac{2 b \left(x^4+x\right)^{3/2}}{9 x^6}","\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,"(-2*a*Sqrt[x + x^4])/(5*x^3) + (2*b*(x + x^4)^(3/2))/(9*x^6) + (a*(x + x^4)^(3/2))/(3*x^3) + (3^(3/4)*a*x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(5*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[x + x^4])","C",8,7,22,0.3182,0,"{2048, 2052, 2014, 2020, 2011, 329, 225}"
659,0,0,0,2.2557494,"\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","Int[(-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,"(-20*a*x^(1/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^14/((-b + a*x^8)^(1/4)*(-b + a*x^8 - x^28)), x], x, x^(1/4)])/(-(b*x) + a*x^3)^(1/4) - (28*b*x^(1/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^6/((-b + a*x^8)^(1/4)*(b - a*x^8 + x^28)), x], x, x^(1/4)])/(-(b*x) + a*x^3)^(1/4)","F",0,0,0,0,-1,"{}"
660,0,0,0,1.4580064,"\int \frac{x+3 x^5}{\sqrt{-x+x^5} \left(1-a x^2-2 x^4+x^8\right)} \, dx","Int[(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,"(2*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^2/(Sqrt[-1 + x^8]*(1 - a*x^4 - 2*x^8 + x^16)), x], x, Sqrt[x]])/Sqrt[-x + x^5] + (6*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^10/(Sqrt[-1 + x^8]*(1 - a*x^4 - 2*x^8 + x^16)), x], x, Sqrt[x]])/Sqrt[-x + x^5]","F",0,0,0,0,-1,"{}"
661,0,0,0,1.5056527,"\int \frac{x+3 x^5}{\sqrt{-x+x^5} \left(a-x^2-2 a x^4+a x^8\right)} \, dx","Int[(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,"(2*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^2/(Sqrt[-1 + x^8]*(a - x^4 - 2*a*x^8 + a*x^16)), x], x, Sqrt[x]])/Sqrt[-x + x^5] + (6*Sqrt[x]*Sqrt[-1 + x^4]*Defer[Subst][Defer[Int][x^10/(Sqrt[-1 + x^8]*(a - x^4 - 2*a*x^8 + a*x^16)), x], x, Sqrt[x]])/Sqrt[-x + x^5]","F",0,0,0,0,-1,"{}"
662,0,0,0,1.5165105,"\int \frac{x+4 x^6}{\sqrt{-x+x^6} \left(1-a x^2-2 x^5+x^{10}\right)} \, dx","Int[(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,"(2*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[-1 + x^10]*(1 - a*x^4 - 2*x^10 + x^20)), x], x, Sqrt[x]])/Sqrt[-x + x^6] + (8*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^12/(Sqrt[-1 + x^10]*(1 - a*x^4 - 2*x^10 + x^20)), x], x, Sqrt[x]])/Sqrt[-x + x^6]","F",0,0,0,0,-1,"{}"
663,0,0,0,1.548938,"\int \frac{x+4 x^6}{\sqrt{-x+x^6} \left(a-x^2-2 a x^5+a x^{10}\right)} \, dx","Int[(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,"(2*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^2/(Sqrt[-1 + x^10]*(a - x^4 - 2*a*x^10 + a*x^20)), x], x, Sqrt[x]])/Sqrt[-x + x^6] + (8*Sqrt[x]*Sqrt[-1 + x^5]*Defer[Subst][Defer[Int][x^12/(Sqrt[-1 + x^10]*(a - x^4 - 2*a*x^10 + a*x^20)), x], x, Sqrt[x]])/Sqrt[-x + x^6]","F",0,0,0,0,-1,"{}"
664,1,66,0,0.0192462,"\int \frac{1}{(-5+2 x)^2 \sqrt[4]{4-4 x+x^2}} \, dx","Int[1/((-5 + 2*x)^2*(4 - 4*x + x^2)^(1/4)),x]","\frac{\sqrt{x-2} \tanh ^{-1}\left(\sqrt{2} \sqrt{x-2}\right)}{\sqrt{2} \sqrt[4]{x^2-4 x+4}}-\frac{2-x}{(5-2 x) \sqrt[4]{x^2-4 x+4}}","\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)/((5 - 2*x)*(4 - 4*x + x^2)^(1/4))) + (Sqrt[-2 + x]*ArcTanh[Sqrt[2]*Sqrt[-2 + x]])/(Sqrt[2]*(4 - 4*x + x^2)^(1/4))","A",4,4,20,0.2000,1,"{646, 51, 63, 207}"
665,0,0,0,0.992936,"\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","Int[((-2 + x^3)*Sqrt[1 + x^3]*(2 - x^2 + 2*x^3))/(x^4*(1 - 3*x^2 + x^3)),x]","\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","\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*Sqrt[1 + x^3])/3 + (4*Sqrt[1 + x^3])/(3*x^3) + (10*Sqrt[1 + x^3])/x - (30*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) + (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (10*Sqrt[2]*3^(3/4)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - 30*Defer[Int][Sqrt[1 + x^3]/(1 - 3*x^2 + x^3), x] + 15*Defer[Int][(x*Sqrt[1 + x^3])/(1 - 3*x^2 + x^3), x]","F",0,0,0,0,-1,"{}"
666,1,59,0,0.0436535,"\int \frac{\left(-b+a x^3\right) \sqrt{b+a x^3}}{x} \, dx","Int[((-b + a*x^3)*Sqrt[b + a*x^3])/x,x]","\frac{2}{3} b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)-\frac{2}{3} b \sqrt{a x^3+b}+\frac{2}{9} \left(a x^3+b\right)^{3/2}","\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*b*Sqrt[b + a*x^3])/3 + (2*(b + a*x^3)^(3/2))/9 + (2*b^(3/2)*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/3","A",5,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
667,1,53,0,0.1143884,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt{1+x^4}} \, dx","Int[x^2/((-1 + x^4)*Sqrt[1 + x^4]),x]","\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}}","\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,"ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(4*Sqrt[2]) - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(4*Sqrt[2])","A",9,6,20,0.3000,1,"{490, 1211, 220, 1699, 203, 206}"
668,1,53,0,0.0137793,"\int \frac{\sqrt{1+x^4}}{-1+x^4} \, dx","Int[Sqrt[1 + x^4]/(-1 + x^4),x]","-\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}}","-\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,"-1/2*ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(2*Sqrt[2])","A",4,4,17,0.2353,1,"{404, 212, 206, 203}"
669,1,86,0,0.112252,"\int \left(b+a x^3\right) \sqrt{x+x^4} \, dx","Int[(b + a*x^3)*Sqrt[x + x^4],x]","\frac{1}{6} a \sqrt{x^4+x} x^4+\frac{1}{12} a \sqrt{x^4+x} x-\frac{1}{12} a \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)+\frac{1}{3} b \sqrt{x^4+x} x+\frac{1}{3} b \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4+x}}\right)","\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,"(a*x*Sqrt[x + x^4])/12 + (b*x*Sqrt[x + x^4])/3 + (a*x^4*Sqrt[x + x^4])/6 - (a*ArcTanh[x^2/Sqrt[x + x^4]])/12 + (b*ArcTanh[x^2/Sqrt[x + x^4]])/3","A",9,6,17,0.3529,1,"{2053, 2004, 2029, 206, 2021, 2024}"
670,1,107,0,0.0568951,"\int \sqrt[4]{x^2+x^4} \, dx","Int[(x^2 + x^4)^(1/4),x]","\frac{1}{2} \sqrt[4]{x^4+x^2} x-\frac{\left(x^2+1\right)^{3/4} x^{3/2} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{4 \left(x^4+x^2\right)^{3/4}}+\frac{\left(x^2+1\right)^{3/4} x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{4 \left(x^4+x^2\right)^{3/4}}","\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,"(x*(x^2 + x^4)^(1/4))/2 - (x^(3/2)*(1 + x^2)^(3/4)*ArcTan[Sqrt[x]/(1 + x^2)^(1/4)])/(4*(x^2 + x^4)^(3/4)) + (x^(3/2)*(1 + x^2)^(3/4)*ArcTanh[Sqrt[x]/(1 + x^2)^(1/4)])/(4*(x^2 + x^4)^(3/4))","B",7,7,11,0.6364,1,"{2004, 2032, 329, 331, 298, 203, 206}"
671,1,1165,0,2.8803355,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{\left(1+3 x^2+x^4\right)^2} \, dx","Int[((-1 + x^4)*Sqrt[1 + x^4])/(1 + 3*x^2 + x^4)^2,x]","\frac{2 \sqrt{x^4+1} x}{5 \left(3+\sqrt{5}\right) \left(x^2+1\right)}+\frac{2 \sqrt{x^4+1} x}{5 \left(3-\sqrt{5}\right) \left(x^2+1\right)}-\frac{3 \sqrt{x^4+1} x}{5 \left(x^2+1\right)}-\frac{4 \sqrt{x^4+1} x}{5 \left(3-\sqrt{5}\right) \left(2 x^2-\sqrt{5}+3\right)}+\frac{3 \sqrt{x^4+1} x}{5 \left(2 x^2-\sqrt{5}+3\right)}-\frac{4 \sqrt{x^4+1} x}{5 \left(3+\sqrt{5}\right) \left(2 x^2+\sqrt{5}+3\right)}+\frac{3 \sqrt{x^4+1} x}{5 \left(2 x^2+\sqrt{5}+3\right)}-\frac{\sqrt{3} \left(2+\sqrt{5}\right) \left(3+\sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+1}}\right)}{4 \left(25+11 \sqrt{5}\right)}+\frac{\left(2+\sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+1}}\right)}{\sqrt{3} \left(25+11 \sqrt{5}\right)}+\frac{\left(2-\sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+1}}\right)}{\sqrt{3} \left(25-11 \sqrt{5}\right)}-\frac{\sqrt{3} \left(11-5 \sqrt{5}\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{x^4+1}}\right)}{4 \left(25-11 \sqrt{5}\right)}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{5 \left(3+\sqrt{5}\right) \sqrt{x^4+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{5 \left(3-\sqrt{5}\right) \sqrt{x^4+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+1}}+\frac{\left(5+\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \left(3+\sqrt{5}\right) \sqrt{x^4+1}}-\frac{3 \left(5+\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{40 \sqrt{x^4+1}}-\frac{\left(1+\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \left(3+\sqrt{5}\right) \sqrt{x^4+1}}+\frac{3 \left(1+\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{40 \sqrt{x^4+1}}+\frac{\left(5-\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \left(3-\sqrt{5}\right) \sqrt{x^4+1}}-\frac{3 \left(5-\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{40 \sqrt{x^4+1}}-\frac{\left(1-\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{10 \left(3-\sqrt{5}\right) \sqrt{x^4+1}}+\frac{3 \left(1-\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{40 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \left(3+\sqrt{5}\right) \sqrt{x^4+1}}-\frac{\left(5-2 \sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \left(25-11 \sqrt{5}\right) \sqrt{x^4+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}","-\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,"(-3*x*Sqrt[1 + x^4])/(5*(1 + x^2)) + (2*x*Sqrt[1 + x^4])/(5*(3 - Sqrt[5])*(1 + x^2)) + (2*x*Sqrt[1 + x^4])/(5*(3 + Sqrt[5])*(1 + x^2)) + (3*x*Sqrt[1 + x^4])/(5*(3 - Sqrt[5] + 2*x^2)) - (4*x*Sqrt[1 + x^4])/(5*(3 - Sqrt[5])*(3 - Sqrt[5] + 2*x^2)) + (3*x*Sqrt[1 + x^4])/(5*(3 + Sqrt[5] + 2*x^2)) - (4*x*Sqrt[1 + x^4])/(5*(3 + Sqrt[5])*(3 + Sqrt[5] + 2*x^2)) - (Sqrt[3]*(11 - 5*Sqrt[5])*ArcTan[(Sqrt[3]*x)/Sqrt[1 + x^4]])/(4*(25 - 11*Sqrt[5])) + ((2 - Sqrt[5])*ArcTan[(Sqrt[3]*x)/Sqrt[1 + x^4]])/(Sqrt[3]*(25 - 11*Sqrt[5])) + ((2 + Sqrt[5])*ArcTan[(Sqrt[3]*x)/Sqrt[1 + x^4]])/(Sqrt[3]*(25 + 11*Sqrt[5])) - (Sqrt[3]*(2 + Sqrt[5])*(3 + Sqrt[5])*ArcTan[(Sqrt[3]*x)/Sqrt[1 + x^4]])/(4*(25 + 11*Sqrt[5])) + (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(5*(3 - Sqrt[5])*Sqrt[1 + x^4]) - (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(5*(3 + Sqrt[5])*Sqrt[1 + x^4]) + (3*(1 - Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(40*Sqrt[1 + x^4]) - ((1 - Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(10*(3 - Sqrt[5])*Sqrt[1 + x^4]) - (3*(5 - Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(40*Sqrt[1 + x^4]) + ((5 - Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(10*(3 - Sqrt[5])*Sqrt[1 + x^4]) + (3*(1 + Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(40*Sqrt[1 + x^4]) - ((1 + Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(10*(3 + Sqrt[5])*Sqrt[1 + x^4]) - (3*(5 + Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(40*Sqrt[1 + x^4]) + ((5 + Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(10*(3 + Sqrt[5])*Sqrt[1 + x^4]) + (3*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[-1/4, 2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4]) - ((5 - 2*Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[-1/4, 2*ArcTan[x], 1/2])/(2*(25 - 11*Sqrt[5])*Sqrt[1 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[-1/4, 2*ArcTan[x], 1/2])/(2*(3 + Sqrt[5])*Sqrt[1 + x^4])","C",80,9,27,0.3333,1,"{6742, 1227, 1198, 220, 1196, 1217, 1707, 1209, 6728}"
672,1,145,0,0.2155322,"\int \frac{1}{x^8 \sqrt[4]{x^3+x^4}} \, dx","Int[1/(x^8*(x^3 + x^4)^(1/4)),x]","\frac{1048576 \left(x^4+x^3\right)^{3/4}}{4023459 x^3}-\frac{262144 \left(x^4+x^3\right)^{3/4}}{1341153 x^4}-\frac{4 \left(x^4+x^3\right)^{3/4}}{31 x^{10}}+\frac{112 \left(x^4+x^3\right)^{3/4}}{837 x^9}-\frac{896 \left(x^4+x^3\right)^{3/4}}{6417 x^8}+\frac{17920 \left(x^4+x^3\right)^{3/4}}{121923 x^7}-\frac{57344 \left(x^4+x^3\right)^{3/4}}{365769 x^6}+\frac{229376 \left(x^4+x^3\right)^{3/4}}{1341153 x^5}","\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 + x^4)^(3/4))/(31*x^10) + (112*(x^3 + x^4)^(3/4))/(837*x^9) - (896*(x^3 + x^4)^(3/4))/(6417*x^8) + (17920*(x^3 + x^4)^(3/4))/(121923*x^7) - (57344*(x^3 + x^4)^(3/4))/(365769*x^6) + (229376*(x^3 + x^4)^(3/4))/(1341153*x^5) - (262144*(x^3 + x^4)^(3/4))/(1341153*x^4) + (1048576*(x^3 + x^4)^(3/4))/(4023459*x^3)","B",8,2,15,0.1333,1,"{2016, 2014}"
673,0,0,0,0.1366771,"\int \frac{1+4 x}{\sqrt{1-2 x+3 x^2+2 x^3+x^4}} \, dx","Int[(1 + 4*x)/Sqrt[1 - 2*x + 3*x^2 + 2*x^3 + x^4],x]","\int \frac{1+4 x}{\sqrt{1-2 x+3 x^2+2 x^3+x^4}} \, dx","-\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,"Defer[Int][1/Sqrt[1 - 2*x + 3*x^2 + 2*x^3 + x^4], x] + 4*Defer[Int][x/Sqrt[1 - 2*x + 3*x^2 + 2*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
674,1,53,0,0.0139008,"\int \frac{1}{\sqrt[4]{-1+x^4} \left(1+3 x^4\right)} \, dx","Int[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)}{2 \sqrt{2}}+\frac{\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)]/(2*Sqrt[2]) + ArcTanh[(Sqrt[2]*x)/(-1 + x^4)^(1/4)]/(2*Sqrt[2])","A",4,4,19,0.2105,1,"{377, 212, 206, 203}"
675,0,0,0,2.294869,"\int \frac{-3 b+a x^4}{\left(b-x^3+a x^4\right) \sqrt[4]{b x+a x^5}} \, dx","Int[(-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,"(4*x*(1 + (a*x^4)/b)^(1/4)*Hypergeometric2F1[3/16, 1/4, 19/16, -((a*x^4)/b)])/(3*(b*x + a*x^5)^(1/4)) - (16*b*x^(1/4)*(b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^2/((b + a*x^16)^(1/4)*(b - x^12 + a*x^16)), x], x, x^(1/4)])/(b*x + a*x^5)^(1/4) + (4*x^(1/4)*(b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^14/((b + a*x^16)^(1/4)*(b - x^12 + a*x^16)), x], x, x^(1/4)])/(b*x + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
676,1,83,0,0.0397108,"\int x^{20} \sqrt{-1+x^6} \, dx","Int[x^20*Sqrt[-1 + x^6],x]","\frac{1}{24} \sqrt{x^6-1} x^{21}-\frac{1}{144} \sqrt{x^6-1} x^{15}-\frac{5}{576} \sqrt{x^6-1} x^9-\frac{5}{384} \sqrt{x^6-1} x^3-\frac{5}{384} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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,"(-5*x^3*Sqrt[-1 + x^6])/384 - (5*x^9*Sqrt[-1 + x^6])/576 - (x^15*Sqrt[-1 + x^6])/144 + (x^21*Sqrt[-1 + x^6])/24 - (5*ArcTanh[x^3/Sqrt[-1 + x^6]])/384","A",7,5,13,0.3846,1,"{275, 279, 321, 217, 206}"
677,0,0,0,0.5997472,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^4 \left(1+x^3\right)} \, dx","Int[((-1 + x^3)*Sqrt[-1 + x^6])/(x^4*(1 + x^3)),x]","\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^4 \left(1+x^3\right)} \, dx","\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,"(2*Sqrt[-1 + x^6])/3 + Sqrt[-1 + x^6]/(3*x^3) - (2*ArcTan[Sqrt[-1 + x^6]])/3 - ArcTanh[x^3/Sqrt[-1 + x^6]]/3 - (2*Defer[Int][Sqrt[-1 + x^6]/(1 + x), x])/3 - (4*Defer[Int][Sqrt[-1 + x^6]/(-1 - I*Sqrt[3] + 2*x), x])/3 - (4*Defer[Int][Sqrt[-1 + x^6]/(-1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
678,1,228,0,2.1501006,"\int \frac{1+x^6}{\sqrt{1-x^2+x^4} \left(1-x^6\right)} \, dx","Int[(1 + x^6)/(Sqrt[1 - x^2 + x^4]*(1 - x^6)),x]","\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)+\frac{\left(1+(-1)^{2/3}\right) \left(x^2+1\right) \sqrt{\frac{x^4-x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{3}{4}\right)}{6 \sqrt{x^4-x^2+1}}+\frac{\left(1-\sqrt[3]{-1}\right) \left(x^2+1\right) \sqrt{\frac{x^4-x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{3}{4}\right)}{6 \sqrt{x^4-x^2+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4-x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{3}{4}\right)}{6 \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,"(Sqrt[2]*ArcTan[(Sqrt[2]*x)/Sqrt[1 - x^2 + x^4]])/3 + ArcTanh[x/Sqrt[1 - x^2 + x^4]]/3 - ((1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 3/4])/(6*Sqrt[1 - x^2 + x^4]) + ((1 - (-1)^(1/3))*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 3/4])/(6*Sqrt[1 - x^2 + x^4]) + ((1 + (-1)^(2/3))*(1 + x^2)*Sqrt[(1 - x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 3/4])/(6*Sqrt[1 - x^2 + x^4])","C",95,19,29,0.6552,1,"{1586, 6725, 1728, 1208, 1139, 1103, 1195, 1210, 1698, 206, 1247, 734, 843, 619, 215, 724, 1197, 1216, 1706}"
679,1,53,0,0.0538898,"\int \frac{\left(-2+x^6\right) \sqrt{-1+x^6}}{x^7 \left(2+x^6\right)} \, dx","Int[((-2 + x^6)*Sqrt[-1 + x^6])/(x^7*(2 + x^6)),x]","\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}}","\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,"Sqrt[-1 + x^6]/(6*x^6) - ArcTan[Sqrt[-1 + x^6]]/2 + ArcTan[Sqrt[-1 + x^6]/Sqrt[3]]/Sqrt[3]","A",7,5,25,0.2000,1,"{573, 149, 156, 63, 203}"
680,0,0,0,1.9898653,"\int \frac{x (-6 b+5 a x)}{\sqrt[4]{-b x^2+a x^3} \left(b-a x+x^6\right)} \, dx","Int[(x*(-6*b + 5*a*x))/((-(b*x^2) + a*x^3)^(1/4)*(b - a*x + x^6)),x]","\int \frac{x (-6 b+5 a x)}{\sqrt[4]{-b x^2+a x^3} \left(b-a x+x^6\right)} \, dx","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,"(-10*a*Sqrt[x]*(-b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^4/((-b + a*x^2)^(1/4)*(-b + a*x^2 - x^12)), x], x, Sqrt[x]])/(-(b*x^2) + a*x^3)^(1/4) - (12*b*Sqrt[x]*(-b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^2/((-b + a*x^2)^(1/4)*(b - a*x^2 + x^12)), x], x, Sqrt[x]])/(-(b*x^2) + a*x^3)^(1/4)","F",0,0,0,0,-1,"{}"
681,1,1215,0,3.5360099,"\int \frac{\sqrt{1+x^3} \left(2+2 x^3+x^6\right)}{x \left(-1+x^6\right)} \, dx","Int[(Sqrt[1 + x^3]*(2 + 2*x^3 + x^6))/(x*(-1 + x^6)),x]","\frac{5 i (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{(3-6 i)-(2-3 i) \sqrt{3}}{(4+6 i)-(2+4 i) \sqrt{3}}} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{3 \sqrt{2} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{10 \sqrt{\frac{(6-3 i)-(3-2 i) \sqrt{3}}{(-6-4 i)+(4+2 i) \sqrt{3}}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{(6-3 i)-(3-2 i) \sqrt{3}}{(-6-4 i)+(4+2 i) \sqrt{3}}} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{3^{3/4} \left(3 i-\sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{5 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{2} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{3 \sqrt{2} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{4}{3} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{20 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \left(1+(2+i) \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{20 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \left(1+(2-i) \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{10 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{40 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(-\frac{\left(i+(1+2 i) \sqrt{3}\right)^2}{\left(1-(2+i) \sqrt{3}\right)^2};\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \left(7+i \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{40 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(-\frac{\left(1+(2+i) \sqrt{3}\right)^2}{\left(i-(1+2 i) \sqrt{3}\right)^2};\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \left(7-i \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{20 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97+56 \sqrt{3};\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 \sqrt{x^3+1}}{3}","\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,"(2*Sqrt[1 + x^3])/3 + (((5*I)/3)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[((3 - 6*I) - (2 - 3*I)*Sqrt[3])/((4 + 6*I) - (2 + 4*I)*Sqrt[3])]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(Sqrt[2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (10*Sqrt[((6 - 3*I) - (3 - 2*I)*Sqrt[3])/((-6 - 4*I) + (4 + 2*I)*Sqrt[3])]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[((6 - 3*I) - (3 - 2*I)*Sqrt[3])/((-6 - 4*I) + (4 + 2*I)*Sqrt[3])]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(3^(3/4)*(3*I - Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (5*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTanh[Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]/(Sqrt[2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(3*Sqrt[2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (4*ArcTanh[Sqrt[1 + x^3]])/3 - (10*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[2 + Sqrt[3]]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (20*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*(1 + (2 - I)*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (20*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*(1 + (2 + I)*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (40*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[-((I + (1 + 2*I)*Sqrt[3])^2/(1 - (2 + I)*Sqrt[3])^2), ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*(7 + I*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (40*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[-((1 + (2 + I)*Sqrt[3])^2/(I - (1 + 2*I)*Sqrt[3])^2), ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*(7 - I*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (20*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[97 + 56*Sqrt[3], ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","C",33,16,30,0.5333,0,"{1586, 6725, 2136, 218, 2142, 2113, 537, 571, 93, 206, 266, 63, 207, 261, 6728, 205}"
682,1,314,0,0.6506331,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{1+x^8} \, dx","Int[((-1 + x^4)*Sqrt[1 + x^4])/(1 + x^8),x]","-\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}}+\frac{i \left(\sqrt{2}+(1+i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}+\frac{i \left(\sqrt{2}+(-1+i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}+\frac{\left((-1-i)-i \sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \left(1+(-1)^{3/4}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}","-\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,"-1/2*ArcTan[(2^(1/4)*x)/Sqrt[1 + x^4]]/2^(1/4) - ArcTanh[(2^(1/4)*x)/Sqrt[1 + x^4]]/(2*2^(1/4)) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) - ((1/8 - I/8)*(1 + (-1)^(3/4))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + (((-1 - I) - I*Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*Sqrt[1 + x^4]) + ((I/8)*((-1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + ((I/8)*((1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4]","C",20,6,22,0.2727,1,"{6725, 406, 220, 409, 1217, 1707}"
683,1,314,0,0.5389243,"\int \frac{-1+x^8}{\sqrt{1+x^4} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/(Sqrt[1 + x^4]*(1 + x^8)),x]","-\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}}+\frac{i \left(\sqrt{2}+(1+i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}+\frac{i \left(\sqrt{2}+(-1+i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}+\frac{\left((-1-i)-i \sqrt{2}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \left(1+(-1)^{3/4}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}","-\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,"-1/2*ArcTan[(2^(1/4)*x)/Sqrt[1 + x^4]]/2^(1/4) - ArcTanh[(2^(1/4)*x)/Sqrt[1 + x^4]]/(2*2^(1/4)) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) - ((1/8 - I/8)*(1 + (-1)^(3/4))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + (((-1 - I) - I*Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*Sqrt[1 + x^4]) + ((I/8)*((-1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + ((I/8)*((1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4]","C",21,7,22,0.3182,1,"{1586, 6725, 406, 220, 409, 1217, 1707}"
684,1,647,0,1.4311129,"\int \frac{\sqrt{-2+x^4} \left(2+x^4\right)}{4-6 x^4+x^8} \, dx","Int[(Sqrt[-2 + x^4]*(2 + x^4))/(4 - 6*x^4 + x^8),x]","\frac{\left(1+\sqrt{5}\right) \sqrt{\frac{x^2+\sqrt{2}}{\sqrt{2}-x^2}} \sqrt{\sqrt{2} x^2-2} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\sqrt{2} x^2-2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \sqrt{\frac{1}{2-\sqrt{2} x^2}} \sqrt{x^4-2}}+\frac{\left(1-\sqrt{5}\right) \sqrt{\frac{x^2+\sqrt{2}}{\sqrt{2}-x^2}} \sqrt{\sqrt{2} x^2-2} F\left(\sin ^{-1}\left(\frac{2^{3/4} x}{\sqrt{\sqrt{2} x^2-2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \sqrt{\frac{1}{2-\sqrt{2} x^2}} \sqrt{x^4-2}}-\frac{\left(2+\sqrt{2 \left(3+\sqrt{5}\right)}\right) \sqrt{\sqrt{2}-x^2} \sqrt{\sqrt{2} x^2+2} \Pi \left(-\sqrt{\frac{2}{3+\sqrt{5}}};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)}{4 \left(\sqrt{2}+\sqrt{3+\sqrt{5}}\right) \sqrt{x^4-2}}-\frac{\left(2-\sqrt{2 \left(3+\sqrt{5}\right)}\right) \sqrt{\sqrt{2}-x^2} \sqrt{\sqrt{2} x^2+2} \Pi \left(\sqrt{\frac{2}{3+\sqrt{5}}};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)}{4 \left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right) \sqrt{x^4-2}}-\frac{\left(\sqrt{2}+\sqrt{3+\sqrt{5}}\right) \sqrt{\sqrt{2}-x^2} \sqrt{\sqrt{2} x^2+2} \Pi \left(-\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)}{2 \left(2+\sqrt{2 \left(3+\sqrt{5}\right)}\right) \sqrt{x^4-2}}-\frac{\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right) \sqrt{\sqrt{2}-x^2} \sqrt{\sqrt{2} x^2+2} \Pi \left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)};\left.\sin ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)\right|-1\right)}{2 \left(2-\sqrt{2 \left(3+\sqrt{5}\right)}\right) \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,"((1 - Sqrt[5])*Sqrt[(Sqrt[2] + x^2)/(Sqrt[2] - x^2)]*Sqrt[-2 + Sqrt[2]*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-2 + Sqrt[2]*x^2]], 1/2])/(4*2^(1/4)*Sqrt[(2 - Sqrt[2]*x^2)^(-1)]*Sqrt[-2 + x^4]) + ((1 + Sqrt[5])*Sqrt[(Sqrt[2] + x^2)/(Sqrt[2] - x^2)]*Sqrt[-2 + Sqrt[2]*x^2]*EllipticF[ArcSin[(2^(3/4)*x)/Sqrt[-2 + Sqrt[2]*x^2]], 1/2])/(4*2^(1/4)*Sqrt[(2 - Sqrt[2]*x^2)^(-1)]*Sqrt[-2 + x^4]) - ((2 + Sqrt[2*(3 + Sqrt[5])])*Sqrt[Sqrt[2] - x^2]*Sqrt[2 + Sqrt[2]*x^2]*EllipticPi[-Sqrt[2/(3 + Sqrt[5])], ArcSin[x/2^(1/4)], -1])/(4*(Sqrt[2] + Sqrt[3 + Sqrt[5]])*Sqrt[-2 + x^4]) - ((2 - Sqrt[2*(3 + Sqrt[5])])*Sqrt[Sqrt[2] - x^2]*Sqrt[2 + Sqrt[2]*x^2]*EllipticPi[Sqrt[2/(3 + Sqrt[5])], ArcSin[x/2^(1/4)], -1])/(4*(Sqrt[2] - Sqrt[3 + Sqrt[5]])*Sqrt[-2 + x^4]) - ((Sqrt[2] + Sqrt[3 + Sqrt[5]])*Sqrt[Sqrt[2] - x^2]*Sqrt[2 + Sqrt[2]*x^2]*EllipticPi[-Sqrt[(3 + Sqrt[5])/2], ArcSin[x/2^(1/4)], -1])/(2*(2 + Sqrt[2*(3 + Sqrt[5])])*Sqrt[-2 + x^4]) - ((Sqrt[2] - Sqrt[3 + Sqrt[5]])*Sqrt[Sqrt[2] - x^2]*Sqrt[2 + Sqrt[2]*x^2]*EllipticPi[Sqrt[(3 + Sqrt[5])/2], ArcSin[x/2^(1/4)], -1])/(2*(2 - Sqrt[2*(3 + Sqrt[5])])*Sqrt[-2 + x^4])","C",40,10,27,0.3704,0,"{6728, 406, 223, 409, 1215, 1457, 540, 253, 538, 537}"
685,1,421,0,0.8880929,"\int \frac{-2 b+a x^4}{\sqrt[4]{-b+a x^4} \left(-b+a x^4+2 x^8\right)} \, dx","Int[(-2*b + a*x^4)/((-b + a*x^4)^(1/4)*(-b + a*x^4 + 2*x^8)),x]","\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)}{2 \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)}{2 \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)}{2 \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)}{2 \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}","-\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+2 b\&,\frac{\log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$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))])/(2*(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))])/(2*(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))])/(2*(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))])/(2*(a^2 + 4*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",10,5,39,0.1282,1,"{6728, 377, 212, 208, 205}"
686,1,53,0,0.0590228,"\int \frac{1}{x^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[1/(x^2*Sqrt[x + Sqrt[1 + x^2]]),x]","-\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)","-\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/(x*Sqrt[x + Sqrt[1 + x^2]])) + ArcTan[Sqrt[x + Sqrt[1 + x^2]]] + ArcTanh[Sqrt[x + Sqrt[1 + x^2]]]","A",6,6,19,0.3158,1,"{2119, 457, 329, 212, 206, 203}"
687,1,199,0,1.3923896,"\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","Int[(-1 + Sqrt[k]*x)/((1 + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{(1-k) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/((1 - 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)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",9,8,43,0.1860,1,"{6719, 6742, 419, 2113, 537, 571, 93, 205}"
688,1,199,0,1.1740312,"\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","Int[(1 + Sqrt[k]*x)/((-1 + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{(1-k) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/((1 - 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)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",9,8,43,0.1860,1,"{6719, 6742, 419, 2113, 537, 571, 93, 205}"
689,1,5514,0,137.714842,"\int \frac{2+x}{(-1+x) \sqrt{-1+3 x-a x^2+x^3}} \, dx","Int[(2 + x)/((-1 + x)*Sqrt[-1 + 3*x - a*x^2 + x^3]),x]","\frac{\sqrt[3]{2} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}} \sqrt{\frac{2 \sqrt[3]{2} a^2+2 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} a-6 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} x+\left(4 a^3-54 a+6 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+54\right)^{2/3}-18 \sqrt[3]{2}}{6 a^2+3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}-54}} \sqrt{-\frac{\frac{2 \left(9-a^2\right)^2}{\left(a^3-\frac{27 a}{2}+\frac{3}{2} \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)\right)^{2/3}}+2 \left(9-a^2\right)+18 \left(x-\frac{a}{3}\right)^2-\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right) (3 x-a)}{\sqrt[3]{2 a^3-27 a+3 \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)}}+\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}}{\frac{\left(-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right)^2}{18 \sqrt[3]{2} \left(2 a^3-27 a+3 \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)\right)^{2/3}}-\frac{2}{9} \left(\frac{2 \left(9-a^2\right)^2}{\left(a^3-\frac{27 a}{2}+\frac{3}{2} \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)\right)^{2/3}}+2 \left(9-a^2\right)+\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{2 \sqrt[3]{2} a^2-4 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} a+12 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} x+\left(4 a^3-54 a+6 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}-18 \sqrt[3]{2}}{\sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}}}{2^{3/4} \sqrt[4]{3}}\right)|-\frac{2 \sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{3 \sqrt{3} \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(a-3)^2 (4 a+15)}+27} \sqrt{x^3-a x^2+3 x-1}}-\frac{3\ 2^{2/3} \sqrt{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54} \sqrt{1-\frac{2 \left(-2 a^2-2^{2/3} \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} (a-3 x)-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right)}{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}} \sqrt{1-\frac{2 \left(-2 a^2-2^{2/3} \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} (a-3 x)-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right)}{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}} \sqrt{-\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right)+4 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} (a-3 x)-\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27}}} \sqrt{-\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18\right)+4 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} (a-3 x)+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27}}} \sqrt{-2 a+\frac{-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18}{\sqrt[3]{a^3-\frac{27 a}{2}+\frac{3}{2} \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)}}+6 x} \Pi \left(\frac{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}{2 \left(-2 a^2-2^{2/3} \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} a-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+3\ 2^{2/3} \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27}+18\right)};\sin ^{-1}\left(\frac{\sqrt[3]{2} \sqrt[6]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} \sqrt{-2 a+\frac{-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18}{\sqrt[3]{a^3-\frac{27 a}{2}+\frac{3}{2} \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)}}+6 x}}{\sqrt{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}}\right)|\frac{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}{-6 a^2-3 \sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{\sqrt[6]{2 a^3-27 a+3 \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)} \left(-2 a+\frac{-2 a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}+18}{\sqrt[3]{a^3-\frac{27 a}{2}+\frac{3}{2} \left(\sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+9\right)}}+6\right) \sqrt{-\frac{-2 \sqrt[3]{2} a^2+4 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} (a-3 x)-\left(4 a^3-54 a+6 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+54\right)^{2/3}-\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27}}} \sqrt{-\frac{-2 \sqrt[3]{2} a^2+4 \sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27} (a-3 x)-\left(4 a^3-54 a+6 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{4/3}-36 \left(2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt[3]{2 a^3-27 a+3 \sqrt{3} \sqrt{(3-a)^2 (4 a+15)}+27}}} \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^(1/3)*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)]*Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 + 2*a*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3) + (54 - 54*a + 4*a^3 + 6*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 6*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*x)/(-54 + 6*a^2 + 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)])]*Sqrt[-((2*(9 - a^2) + 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + (2*(9 - a^2)^2)/((-27*a)/2 + a^3 + (3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(2/3) + 18*(-1/3*a + x)^2 - (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))*(-a + 3*x))/(-27*a + 2*a^3 + 3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))^(1/3))/((18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))^2/(18*2^(1/3)*(-27*a + 2*a^3 + 3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))^(2/3)) - (2*(2*(9 - a^2) + 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + (2*(9 - a^2)^2)/((-27*a)/2 + a^3 + (3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(2/3)))/9))]*EllipticF[ArcSin[Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 - 4*a*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3) + (54 - 54*a + 4*a^3 + 6*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)] + 12*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*x)/Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(4/3)]]/(2^(3/4)*3^(1/4))], (-2*2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])])/(3*Sqrt[3]*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(-3 + a)^2*(15 + 4*a)])^(1/3)*Sqrt[-1 + 3*x - a*x^2 + x^3]) - (3*2^(2/3)*Sqrt[54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)]]*Sqrt[1 - (2*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(2/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3)*(a - 3*x)))/(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])]*Sqrt[1 - (2*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(2/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3)*(a - 3*x)))/(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])]*Sqrt[-((2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3)) - Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)] + 4*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3)*(a - 3*x))/(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3))]*Sqrt[-((2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3)) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)] + 4*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3)*(a - 3*x))/(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3))]*Sqrt[-2*a + (18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))/((-27*a)/2 + a^3 + (3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(1/3) + 6*x]*EllipticPi[(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])/(2*(18 - 2*a^2 + 3*2^(2/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3) - 2^(2/3)*a*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))), ArcSin[(2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/6)*Sqrt[-2*a + (18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))/((-27*a)/2 + a^3 + (3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(1/3) + 6*x])/Sqrt[54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)]]], (54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)])])/((-27*a + 2*a^3 + 3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))^(1/6)*(6 - 2*a + (18 - 2*a^2 - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3))/((-27*a)/2 + a^3 + (3*(9 + Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)]))/2)^(1/3))*Sqrt[-((18*2^(1/3) - 2*2^(1/3)*a^2 - (54 - 54*a + 4*a^3 + 6*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)] + 4*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3)*(a - 3*x))/(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3))]*Sqrt[-((18*2^(1/3) - 2*2^(1/3)*a^2 - (54 - 54*a + 4*a^3 + 6*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) + 4*a^2*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(2/3) - 2^(1/3)*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(4/3)] + 4*(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3)*(a - 3*x))/(27 - 27*a + 2*a^3 + 3*Sqrt[3]*Sqrt[(3 - a)^2*(15 + 4*a)])^(1/3))]*Sqrt[-1 + 3*x - a*x^2 + x^3])","C",13,11,27,0.4074,0,"{6742, 2067, 2066, 718, 419, 2081, 2080, 934, 169, 538, 537}"
690,1,5395,0,133.5563204,"\int \frac{-2+x}{(1+x) \sqrt{1+3 x-a x^2+x^3}} \, dx","Int[(-2 + x)/((1 + x)*Sqrt[1 + 3*x - a*x^2 + x^3]),x]","\frac{\sqrt[3]{2} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}} \sqrt{\frac{2 \sqrt[3]{2} a^2-2 \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} a+6 \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} x+\left(-4 a^3+54 a-6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}-18 \sqrt[3]{2}}{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}-54}} \sqrt{-\frac{\frac{2\ 2^{2/3} \left(9-a^2\right)^2}{\left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}+2 \left(9-a^2\right)+18 \left(x-\frac{a}{3}\right)^2+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right) (3 x-a)}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}{\frac{\left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)^2}{18 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}-\frac{2}{9} \left(\frac{2\ 2^{2/3} \left(9-a^2\right)^2}{\left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}}+2 \left(9-a^2\right)+\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{-2 \sqrt[3]{2} a^2-4 \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} a+12 \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} x-\left(-4 a^3+54 a-6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}}}}{2^{3/4} \sqrt[4]{3}}\right)|\frac{2 \sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}}{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{3 \sqrt{3} \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} \sqrt{x^3-a x^2+3 x+1}}-\frac{6 \sqrt[6]{2} \sqrt{3} \sqrt{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-54} \sqrt{1-\frac{2 \left(2 a^2-2^{2/3} \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a-3 x)+\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-18\right)}{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-54}} \sqrt{1-\frac{2 \left(2 a^2-2^{2/3} \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a-3 x)+\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-18\right)}{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-54}} \sqrt{\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}-4 (a-3 x)-\frac{\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}} \sqrt{\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}-4 (a-3 x)+\frac{\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27\right)^{2/3}-162\ 2^{2/3}}}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}} \sqrt{-\frac{a}{3}+\frac{2 a^2+\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-18}{3\ 2^{2/3} \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+x} \Pi \left(\frac{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}{2^{2/3} \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27} \left(2 a+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+6\right)};\sin ^{-1}\left(\frac{2^{5/6} \sqrt{3} \sqrt[6]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27} \sqrt{-\frac{a}{3}+\frac{2 a^2+\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-18}{3\ 2^{2/3} \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+x}}{\sqrt{6 a^2+3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}-54}}\right)|\frac{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}{-6 a^2-3 \sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+\sqrt[6]{2} \sqrt{3} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+54}\right)}{\sqrt[6]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27} \left(2 a+\frac{\sqrt[3]{2} \left(-2 a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}+18\right)}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27}}+6\right) \sqrt{\frac{-2 \sqrt[3]{2} a^2-4 \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a-3 x)-\left(-4 a^3+54 a-6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}-\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}} \sqrt{\frac{-2 \sqrt[3]{2} a^2-4 \sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27} (a-3 x)-\left(-4 a^3+54 a-6 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+54\right)^{2/3}+\sqrt{6} \sqrt{-2 2^{2/3} a^4+4 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3} a^2+36\ 2^{2/3} a^2-\sqrt[3]{2} \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{4/3}-36 \left(-2 a^3+27 a-3 \sqrt{3} \sqrt{(15-4 a) (a+3)^2}+27\right)^{2/3}-162\ 2^{2/3}}+18 \sqrt[3]{2}}{\sqrt[3]{-2 a^3+27 a-3 \sqrt{3} \sqrt{-(a+3)^2 (4 a-15)}+27}}} \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^(1/3)*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)]*Sqrt[(-18*2^(1/3) + 2*2^(1/3)*a^2 + (54 + 54*a - 4*a^3 - 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2*a*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) + 6*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*x)/(-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)])]*Sqrt[-((2*(9 - a^2) + (2*2^(2/3)*(9 - a^2)^2)/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 18*(-1/3*a + x)^2 + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3))*(-a + 3*x))/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3))/((18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3))^2/(18*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)) - (2*(2*(9 - a^2) + (2*2^(2/3)*(9 - a^2)^2)/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/9))]*EllipticF[ArcSin[Sqrt[(18*2^(1/3) - 2*2^(1/3)*a^2 - (54 + 54*a - 4*a^3 - 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 4*a*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)] + 12*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*x)/Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)]]/(2^(3/4)*3^(1/4))], (2*2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])])/(3*Sqrt[3]*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*Sqrt[1 + 3*x - a*x^2 + x^3]) - (6*2^(1/6)*Sqrt[3]*Sqrt[-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)]]*Sqrt[1 - (2*(-18 + 2*a^2 + 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(2/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a - 3*x)))/(-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])]*Sqrt[1 - (2*(-18 + 2*a^2 + 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(2/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a - 3*x)))/(-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])]*Sqrt[(2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3) - (Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)])/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) - 4*(a - 3*x)]*Sqrt[(2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3) + (Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(4/3)])/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3) - 4*(a - 3*x)]*Sqrt[-1/3*a + (-18 + 2*a^2 + 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3))/(3*2^(2/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3)) + x]*EllipticPi[(54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])/(2^(2/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3)*(6 + 2*a + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3))), ArcSin[(2^(5/6)*Sqrt[3]*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/6)*Sqrt[-1/3*a + (-18 + 2*a^2 + 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3))/(3*2^(2/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3)) + x])/Sqrt[-54 + 6*a^2 + 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)]]], (54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])/(54 - 6*a^2 - 3*2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 2^(1/6)*Sqrt[3]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)])])/((27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/6)*(6 + 2*a + (2^(1/3)*(18 - 2*a^2 - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3)))/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(1/3))*Sqrt[(18*2^(1/3) - 2*2^(1/3)*a^2 - (54 + 54*a - 4*a^3 - 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) - Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)] - 4*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a - 3*x))/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)]*Sqrt[(18*2^(1/3) - 2*2^(1/3)*a^2 - (54 + 54*a - 4*a^3 - 6*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(2/3) + Sqrt[6]*Sqrt[-162*2^(2/3) + 36*2^(2/3)*a^2 - 2*2^(2/3)*a^4 - 36*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) + 4*a^2*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(2/3) - 2^(1/3)*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[(15 - 4*a)*(3 + a)^2])^(4/3)] - 4*(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)*(a - 3*x))/(27 + 27*a - 2*a^3 - 3*Sqrt[3]*Sqrt[-((3 + a)^2*(-15 + 4*a))])^(1/3)]*Sqrt[1 + 3*x - a*x^2 + x^3])","C",13,11,27,0.4074,0,"{6742, 2067, 2066, 718, 419, 2081, 2080, 934, 169, 538, 537}"
691,1,62,0,0.0215714,"\int \frac{\left(-1+x^4\right) \sqrt[4]{1+x^4}}{x^2} \, dx","Int[((-1 + x^4)*(1 + x^4)^(1/4))/x^2,x]","\frac{\left(x^4+1\right)^{5/4}}{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)-\frac{3}{4} \sqrt[4]{x^4+1} x^3","\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,"(-3*x^3*(1 + x^4)^(1/4))/4 + (1 + x^4)^(5/4)/x + (3*ArcTan[x/(1 + x^4)^(1/4)])/8 - (3*ArcTanh[x/(1 + x^4)^(1/4)])/8","A",6,6,18,0.3333,1,"{453, 279, 331, 298, 203, 206}"
692,1,443,0,0.5977022,"\int \frac{2 b+a x^2}{\sqrt[4]{b+a x^2} \left(-2 b-2 a x^2+x^4\right)} \, dx","Int[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(-2*b - 2*a*x^2 + x^4)),x]","\frac{\sqrt[4]{b} \left(a-\sqrt{a^2+2 b}\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{b}}{\sqrt{a^2-\sqrt{a^2+2 b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{b} \left(a-\sqrt{a^2+2 b}\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{b}}{\sqrt{a^2-\sqrt{a^2+2 b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{-a \sqrt{a^2+2 b}+a^2+b}}+\frac{\sqrt[4]{b} \left(\sqrt{a^2+2 b}+a\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{b}}{\sqrt{a^2+\sqrt{a^2+2 b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{a \sqrt{a^2+2 b}+a^2+b}}-\frac{\sqrt[4]{b} \left(\sqrt{a^2+2 b}+a\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{b}}{\sqrt{a^2+\sqrt{a^2+2 b} a+b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{a \sqrt{a^2+2 b}+a^2+b}}","\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,"(b^(1/4)*(a - Sqrt[a^2 + 2*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[-(Sqrt[b]/Sqrt[a^2 + b - a*Sqrt[a^2 + 2*b]]), ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[a^2 + b - a*Sqrt[a^2 + 2*b]]*x) - (b^(1/4)*(a - Sqrt[a^2 + 2*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[Sqrt[b]/Sqrt[a^2 + b - a*Sqrt[a^2 + 2*b]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[a^2 + b - a*Sqrt[a^2 + 2*b]]*x) + (b^(1/4)*(a + Sqrt[a^2 + 2*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[-(Sqrt[b]/Sqrt[a^2 + b + a*Sqrt[a^2 + 2*b]]), ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[a^2 + b + a*Sqrt[a^2 + 2*b]]*x) - (b^(1/4)*(a + Sqrt[a^2 + 2*b])*Sqrt[-((a*x^2)/b)]*EllipticPi[Sqrt[b]/Sqrt[a^2 + b + a*Sqrt[a^2 + 2*b]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[a^2 + b + a*Sqrt[a^2 + 2*b]]*x)","C",10,4,36,0.1111,1,"{1692, 399, 490, 1218}"
693,1,100,0,0.074623,"\int \frac{\sqrt[4]{-x^3+x^4}}{x} \, dx","Int[(-x^3 + x^4)^(1/4)/x,x]","\sqrt[4]{x^4-x^3}-\frac{(x-1)^{3/4} x^{9/4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{2 \left(x^4-x^3\right)^{3/4}}-\frac{(x-1)^{3/4} x^{9/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{2 \left(x^4-x^3\right)^{3/4}}","\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,"(-x^3 + x^4)^(1/4) - ((-1 + x)^(3/4)*x^(9/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(2*(-x^3 + x^4)^(3/4)) - ((-1 + x)^(3/4)*x^(9/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(2*(-x^3 + x^4)^(3/4))","A",7,7,17,0.4118,1,"{2021, 2032, 63, 240, 212, 206, 203}"
694,1,63,0,0.0457483,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^{13}} \, dx","Int[((-1 + x^3)*Sqrt[-1 + x^6])/x^13,x]","\frac{\sqrt{x^6-1}}{24 x^6}-\frac{1}{24} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\left(x^6-1\right)^{3/2}}{12 x^{12}}+\frac{\left(x^6-1\right)^{3/2}}{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,"Sqrt[-1 + x^6]/(24*x^6) - (-1 + x^6)^(3/2)/(12*x^12) + (-1 + x^6)^(3/2)/(9*x^9) - ArcTan[Sqrt[-1 + x^6]]/24","A",7,7,18,0.3889,1,"{1475, 835, 807, 266, 47, 63, 203}"
695,0,0,0,1.4993911,"\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","Int[((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{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x-x^4}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3+1}\&\right]",1,"(6*(x - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 - x^9)^(1/3))/(1 + x^6 - 2*x^9 - x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 - x^3)^(1/3)) + (3*(x - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^12*(1 - x^9)^(1/3))/(1 + x^6 - 2*x^9 - x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 - x^3)^(1/3))","F",0,0,0,0,-1,"{}"
696,0,0,0,1.079108,"\int \frac{\left(2+x^3\right) \sqrt[3]{x-x^4}}{1+x^2-2 x^3-x^4-x^5+x^6} \, dx","Int[((2 + x^3)*(x - x^4)^(1/3))/(1 + x^2 - 2*x^3 - x^4 - x^5 + x^6),x]","\int \frac{\left(2+x^3\right) \sqrt[3]{x-x^4}}{1+x^2-2 x^3-x^4-x^5+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x-x^4}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3+1}\&\right]",1,"(6*(x - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 - x^9)^(1/3))/(1 + x^6 - 2*x^9 - x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 - x^3)^(1/3)) + (3*(x - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^12*(1 - x^9)^(1/3))/(1 + x^6 - 2*x^9 - x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 - x^3)^(1/3))","F",0,0,0,0,-1,"{}"
697,1,79,0,0.0254967,"\int \frac{1}{\sqrt[8]{1+2 x^4+x^8}} \, dx","Int[(1 + 2*x^4 + x^8)^(-1/8),x]","\frac{\sqrt[4]{x^4+1} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[8]{x^8+2 x^4+1}}+\frac{\sqrt[4]{x^4+1} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[8]{x^8+2 x^4+1}}","\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)*ArcTan[x/(1 + x^4)^(1/4)])/(2*(1 + 2*x^4 + x^8)^(1/8)) + ((1 + x^4)^(1/4)*ArcTanh[x/(1 + x^4)^(1/4)])/(2*(1 + 2*x^4 + x^8)^(1/8))","A",5,5,14,0.3571,1,"{1343, 240, 212, 206, 203}"
698,1,54,0,0.0503823,"\int \frac{1}{x \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[1/(x*Sqrt[x + Sqrt[1 + x^2]]),x]","\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)","\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*ArcTan[Sqrt[x + Sqrt[1 + x^2]]] - 2*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]]","A",6,6,19,0.3158,1,"{2119, 453, 329, 298, 203, 206}"
699,1,396,0,5.0705024,"\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","Int[(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 k^2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\left(2-k^2\right) \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{k^2-1} \left(k^2+2 \sqrt{k^2-1}\right) \sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(\frac{2-k^2}{-k^2-\sqrt{k^2-1}+1};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{\left(2-k^2\right) \left(-k^2-\sqrt{k^2-1}+1\right) \sqrt{(1-x) x \left(1-k^2 x\right)}}-\frac{2 \sqrt{k^2-1} \left(k^2-2 \sqrt{k^2-1}\right) \sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(\frac{2-k^2}{-k^2+\sqrt{k^2-1}+1};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{\left(2-k^2\right) \left(-k^2+\sqrt{k^2-1}+1\right) \sqrt{(1-x) x \left(1-k^2 x\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*k^2*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/((2 - k^2)*Sqrt[(1 - x)*x*(1 - k^2*x)]) + (2*Sqrt[-1 + k^2]*(k^2 + 2*Sqrt[-1 + k^2])*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[(2 - k^2)/(1 - k^2 - Sqrt[-1 + k^2]), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((2 - k^2)*(1 - k^2 - Sqrt[-1 + k^2])*Sqrt[(1 - x)*x*(1 - k^2*x)]) - (2*Sqrt[-1 + k^2]*(k^2 - 2*Sqrt[-1 + k^2])*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[(2 - k^2)/(1 - k^2 + Sqrt[-1 + k^2]), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((2 - k^2)*(1 - k^2 + Sqrt[-1 + k^2])*Sqrt[(1 - x)*x*(1 - k^2*x)])","C",12,6,48,0.1250,1,"{6718, 6728, 115, 168, 538, 537}"
700,1,55,0,0.0377336,"\int \frac{1}{x \left(b+a x^3\right)^{3/4}} \, dx","Int[1/(x*(b + a*x^3)^(3/4)),x]","-\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}}","-\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)])/(3*b^(3/4)) - (2*ArcTanh[(b + a*x^3)^(1/4)/b^(1/4)])/(3*b^(3/4))","A",5,5,15,0.3333,1,"{266, 63, 212, 206, 203}"
701,1,63,0,0.042179,"\int \frac{\left(-b+a x^3\right) \sqrt{b+a x^3}}{x^4} \, dx","Int[((-b + a*x^3)*Sqrt[b + a*x^3])/x^4,x]","\frac{\left(a x^3+b\right)^{3/2}}{3 x^3}+\frac{1}{3} a \sqrt{a x^3+b}-\frac{1}{3} a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\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,"(a*Sqrt[b + a*x^3])/3 + (b + a*x^3)^(3/2)/(3*x^3) - (a*Sqrt[b]*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/3","A",5,5,24,0.2083,1,"{446, 78, 50, 63, 208}"
702,1,508,0,2.755139,"\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","Int[(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{k^{3/2} \sqrt{x} (k x+1) \sqrt{\frac{k^2 x^2-\left(k^2+1\right) x+1}{(k x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{k} \sqrt{x}\right)|\frac{(k+1)^2}{4 k}\right)}{\left(2-k^2\right) \sqrt{k^2 x^3-\left(k^2+1\right) x^2+x}}-\frac{2 \sqrt{-k^4+2 k^2-1} \left(k^2+2 \sqrt{k^2-1}\right) \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \sqrt{k^2 x-k^2} \Pi \left(-\frac{k^4-3 k^2+2}{k^2 \left(-k^2-\sqrt{k^2-1}+1\right)};\sin ^{-1}\left(\frac{\sqrt{k^2 x-k^2}}{\sqrt{1-k^2}}\right)|1-\frac{1}{k^2}\right)}{\left(2-k^2\right) \left(-k^2-\sqrt{k^2-1}+1\right) k^2 \sqrt{k^2 x^3-\left(k^2+1\right) x^2+x}}+\frac{2 \sqrt{-k^4+2 k^2-1} \left(k^2-2 \sqrt{k^2-1}\right) \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \sqrt{k^2 x-k^2} \Pi \left(-\frac{k^4-3 k^2+2}{k^2 \left(-k^2+\sqrt{k^2-1}+1\right)};\sin ^{-1}\left(\frac{\sqrt{k^2 x-k^2}}{\sqrt{1-k^2}}\right)|1-\frac{1}{k^2}\right)}{\left(2-k^2\right) \left(-k^2+\sqrt{k^2-1}+1\right) k^2 \sqrt{k^2 x^3-\left(k^2+1\right) x^2+x}}","\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,"-((k^(3/2)*Sqrt[x]*(1 + k*x)*Sqrt[(1 - (1 + k^2)*x + k^2*x^2)/(1 + k*x)^2]*EllipticF[2*ArcTan[Sqrt[k]*Sqrt[x]], (1 + k)^2/(4*k)])/((2 - k^2)*Sqrt[x - (1 + k^2)*x^2 + k^2*x^3])) - (2*Sqrt[-1 + 2*k^2 - k^4]*(k^2 + 2*Sqrt[-1 + k^2])*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[x]*Sqrt[-k^2 + k^2*x]*EllipticPi[-((2 - 3*k^2 + k^4)/(k^2*(1 - k^2 - Sqrt[-1 + k^2]))), ArcSin[Sqrt[-k^2 + k^2*x]/Sqrt[1 - k^2]], 1 - k^(-2)])/(k^2*(2 - k^2)*(1 - k^2 - Sqrt[-1 + k^2])*Sqrt[x - (1 + k^2)*x^2 + k^2*x^3]) + (2*Sqrt[-1 + 2*k^2 - k^4]*(k^2 - 2*Sqrt[-1 + k^2])*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[x]*Sqrt[-k^2 + k^2*x]*EllipticPi[-((2 - 3*k^2 + k^4)/(k^2*(1 - k^2 + Sqrt[-1 + k^2]))), ArcSin[Sqrt[-k^2 + k^2*x]/Sqrt[1 - k^2]], 1 - k^(-2)])/(k^2*(2 - k^2)*(1 - k^2 + Sqrt[-1 + k^2])*Sqrt[x - (1 + k^2)*x^2 + k^2*x^3])","C",17,9,58,0.1552,0,"{6, 2056, 6728, 716, 1103, 934, 168, 538, 537}"
703,1,55,0,0.0450497,"\int \frac{2+x}{x \sqrt[4]{1+x^4}} \, dx","Int[(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",11,8,16,0.5000,1,"{1833, 240, 212, 206, 203, 266, 63, 298}"
704,1,65,0,0.0185551,"\int x^6 \sqrt[4]{1+x^4} \, dx","Int[x^6*(1 + x^4)^(1/4),x]","\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}{8} \sqrt[4]{x^4+1} x^7+\frac{1}{32} \sqrt[4]{x^4+1} x^3","\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))/32 + (x^7*(1 + x^4)^(1/4))/8 + (3*ArcTan[x/(1 + x^4)^(1/4)])/64 - (3*ArcTanh[x/(1 + x^4)^(1/4)])/64","A",6,6,13,0.4615,1,"{279, 321, 331, 298, 203, 206}"
705,1,109,0,0.0784406,"\int \frac{\sqrt[4]{-x+x^4}}{x^2} \, dx","Int[(-x + x^4)^(1/4)/x^2,x]","-\frac{4 \sqrt[4]{x^4-x}}{3 x}-\frac{2 x^{3/4} \left(x^3-1\right)^{3/4} \tan ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{3 \left(x^4-x\right)^{3/4}}+\frac{2 x^{3/4} \left(x^3-1\right)^{3/4} \tanh ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{3 \left(x^4-x\right)^{3/4}}","-\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 + x^4)^(1/4))/(3*x) - (2*x^(3/4)*(-1 + x^3)^(3/4)*ArcTan[x^(3/4)/(-1 + x^3)^(1/4)])/(3*(-x + x^4)^(3/4)) + (2*x^(3/4)*(-1 + x^3)^(3/4)*ArcTanh[x^(3/4)/(-1 + x^3)^(1/4)])/(3*(-x + x^4)^(3/4))","A",8,8,15,0.5333,1,"{2020, 2032, 329, 275, 331, 298, 203, 206}"
706,1,109,0,0.0756411,"\int x \sqrt[4]{-x+x^4} \, dx","Int[x*(-x + x^4)^(1/4),x]","\frac{1}{3} \sqrt[4]{x^4-x} x^2+\frac{\left(x^3-1\right)^{3/4} x^{3/4} \tan ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{6 \left(x^4-x\right)^{3/4}}-\frac{\left(x^3-1\right)^{3/4} x^{3/4} \tanh ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{6 \left(x^4-x\right)^{3/4}}","\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,"(x^2*(-x + x^4)^(1/4))/3 + (x^(3/4)*(-1 + x^3)^(3/4)*ArcTan[x^(3/4)/(-1 + x^3)^(1/4)])/(6*(-x + x^4)^(3/4)) - (x^(3/4)*(-1 + x^3)^(3/4)*ArcTanh[x^(3/4)/(-1 + x^3)^(1/4)])/(6*(-x + x^4)^(3/4))","A",8,8,13,0.6154,1,"{2021, 2032, 329, 275, 331, 298, 203, 206}"
707,1,66,0,0.0862298,"\int \frac{\left(-b+a x^3\right) \sqrt{-x+x^4}}{x^3} \, dx","Int[((-b + a*x^3)*Sqrt[-x + x^4])/x^3,x]","\frac{1}{3} x \sqrt{x^4-x} (a+2 b)-\frac{1}{3} (a+2 b) \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)-\frac{2 b \left(x^4-x\right)^{3/2}}{3 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,"((a + 2*b)*x*Sqrt[-x + x^4])/3 - (2*b*(-x + x^4)^(3/2))/(3*x^3) - ((a + 2*b)*ArcTanh[x^2/Sqrt[-x + x^4]])/3","A",4,4,24,0.1667,1,"{2038, 2004, 2029, 206}"
708,1,101,0,0.0681266,"\int \frac{\sqrt[4]{-x^3+x^4}}{x^2} \, dx","Int[(-x^3 + x^4)^(1/4)/x^2,x]","-\frac{4 \sqrt[4]{x^4-x^3}}{x}+\frac{2 (x-1)^{3/4} x^{9/4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\left(x^4-x^3\right)^{3/4}}+\frac{2 (x-1)^{3/4} x^{9/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\left(x^4-x^3\right)^{3/4}}","-\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*(-x^3 + x^4)^(1/4))/x + (2*(-1 + x)^(3/4)*x^(9/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(-x^3 + x^4)^(3/4) + (2*(-1 + x)^(3/4)*x^(9/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(-x^3 + x^4)^(3/4)","A",7,7,17,0.4118,1,"{2020, 2032, 63, 240, 212, 206, 203}"
709,0,0,0,0.0591588,"\int \frac{x}{\sqrt{-17+18 x-11 x^2+6 x^3+x^4}} \, dx","Int[x/Sqrt[-17 + 18*x - 11*x^2 + 6*x^3 + x^4],x]","\int \frac{x}{\sqrt{-17+18 x-11 x^2+6 x^3+x^4}} \, dx","-\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,"Defer[Int][x/Sqrt[-17 + 18*x - 11*x^2 + 6*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
710,0,0,0,1.7126954,"\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","Int[(Sqrt[-1 - x - x^2 + x^4]*(2 + x + 2*x^4))/((-1 - x + x^4)*(-1 - x + x^2 + x^4)),x]","\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","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,"Defer[Int][Sqrt[-1 - x - x^2 + x^4]/(1 - x), x] + 2*Defer[Int][Sqrt[-1 - x - x^2 + x^4]/(1 + 2*x + x^2 + x^3), x] - Defer[Int][(x*Sqrt[-1 - x - x^2 + x^4])/(1 + 2*x + x^2 + x^3), x] + 2*Defer[Int][(x^2*Sqrt[-1 - x - x^2 + x^4])/(1 + 2*x + x^2 + x^3), x] + Defer[Int][Sqrt[-1 - x - x^2 + x^4]/(-1 - x + x^4), x] + 4*Defer[Int][(x^2*Sqrt[-1 - x - x^2 + x^4])/(-1 - x + x^4), x] - Defer[Int][(x^3*Sqrt[-1 - x - x^2 + x^4])/(-1 - x + x^4), x]","F",0,0,0,0,-1,"{}"
711,1,55,0,0.0377384,"\int \frac{1}{x \left(b+a x^4\right)^{3/4}} \, dx","Int[1/(x*(b + a*x^4)^(3/4)),x]","-\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}}","-\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)]/b^(3/4) - ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)]/(2*b^(3/4))","A",5,5,15,0.3333,1,"{266, 63, 212, 206, 203}"
712,1,55,0,0.0372448,"\int \frac{1}{x \sqrt[4]{b+a x^4}} \, dx","Int[1/(x*(b + a*x^4)^(1/4)),x]","\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}}","\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)]/(2*b^(1/4)) - ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)]/(2*b^(1/4))","A",5,5,15,0.3333,1,"{266, 63, 298, 203, 206}"
713,1,55,0,0.0368743,"\int \frac{1}{x \left(b+a x^5\right)^{3/4}} \, dx","Int[1/(x*(b + a*x^5)^(3/4)),x]","-\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}}","-\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)])/(5*b^(3/4)) - (2*ArcTanh[(b + a*x^5)^(1/4)/b^(1/4)])/(5*b^(3/4))","A",5,5,15,0.3333,1,"{266, 63, 212, 206, 203}"
714,1,51,0,0.0429779,"\int \frac{\left(1+2 x^3\right) \sqrt{-1+x^6}}{x} \, dx","Int[((1 + 2*x^3)*Sqrt[-1 + x^6])/x,x]","-\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{1}{3} \sqrt{x^6-1} \left(x^3+1\right)-\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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)*Sqrt[-1 + x^6])/3 - ArcTan[Sqrt[-1 + x^6]]/3 - ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",8,8,20,0.4000,1,"{1475, 815, 844, 217, 206, 266, 63, 203}"
715,0,0,0,1.3885478,"\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","Int[((-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{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"(-6*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 + x^6 + x^9)^(1/3))/(1 + x^6 + 2*x^9 + x^12 + x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3)) + (3*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^12*(1 + x^6 + x^9)^(1/3))/(1 + x^6 + 2*x^9 + x^12 + x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
716,0,0,0,1.030227,"\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx","Int[((-2 + x^3)*(x + x^3 + x^4)^(1/3))/(1 + x^2 + 2*x^3 + x^4 + x^5 + x^6),x]","\int \frac{\left(-2+x^3\right) \sqrt[3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"(-6*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 + x^6 + x^9)^(1/3))/(1 + x^6 + 2*x^9 + x^12 + x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3)) + (3*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^12*(1 + x^6 + x^9)^(1/3))/(1 + x^6 + 2*x^9 + x^12 + x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
717,1,55,0,0.0365871,"\int \frac{1}{x \left(b+a x^6\right)^{3/4}} \, dx","Int[1/(x*(b + a*x^6)^(3/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}",1,"-1/3*ArcTan[(b + a*x^6)^(1/4)/b^(1/4)]/b^(3/4) - ArcTanh[(b + a*x^6)^(1/4)/b^(1/4)]/(3*b^(3/4))","A",5,5,15,0.3333,1,"{266, 63, 212, 206, 203}"
718,1,413,0,0.8523273,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Int[(-2*b + a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",10,5,35,0.1429,1,"{6728, 377, 212, 208, 205}"
719,1,413,0,0.4381835,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Int[(-2*b + a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{a-\sqrt{a^2+4 b}} \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\sqrt[4]{\sqrt{a^2+4 b}+a} \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ((a - Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) + ((a + Sqrt[a^2 + 4*b])^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",10,5,35,0.1429,1,"{6728, 377, 212, 208, 205}"
720,1,325,0,0.7885268,"\int \frac{x^2}{\left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","Int[x^2/((b + a*x^4)^(3/4)*(b^2 + a^2*x^8)),x]","-\frac{\left(-a^2\right)^{3/8} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\sqrt{-a^2}-a} x}{\sqrt[8]{-a^2} \sqrt[4]{a x^4+b}}\right)}{4 a^{3/4} \left(\sqrt{-a^2}-a\right)^{3/4} b^2}+\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\left(-a^2\right)^{3/8} \sqrt[4]{\sqrt{-a^2}-a} x}{a^{3/4} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{-a^2} \left(\sqrt{-a^2}-a\right)^{3/4} b^2}-\frac{\left(-a^2\right)^{3/8} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\sqrt{-a^2}+a} x}{\sqrt[8]{-a^2} \sqrt[4]{a x^4+b}}\right)}{4 a^{3/4} \left(\sqrt{-a^2}+a\right)^{3/4} b^2}+\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\left(-a^2\right)^{3/8} \sqrt[4]{\sqrt{-a^2}+a} x}{a^{3/4} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{-a^2} \left(\sqrt{-a^2}+a\right)^{3/4} b^2}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+2 a^2\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3}\&\right]}{8 b^2}",1,"-1/4*((-a^2)^(3/8)*ArcTan[(a^(1/4)*(-a + Sqrt[-a^2])^(1/4)*x)/((-a^2)^(1/8)*(b + a*x^4)^(1/4))])/(a^(3/4)*(-a + Sqrt[-a^2])^(3/4)*b^2) + (a^(1/4)*ArcTan[((-a^2)^(3/8)*(-a + Sqrt[-a^2])^(1/4)*x)/(a^(3/4)*(b + a*x^4)^(1/4))])/(4*(-a^2)^(1/8)*(-a + Sqrt[-a^2])^(3/4)*b^2) - ((-a^2)^(3/8)*ArcTan[(a^(1/4)*(a + Sqrt[-a^2])^(1/4)*x)/((-a^2)^(1/8)*(b + a*x^4)^(1/4))])/(4*a^(3/4)*(a + Sqrt[-a^2])^(3/4)*b^2) + (a^(1/4)*ArcTan[((-a^2)^(3/8)*(a + Sqrt[-a^2])^(1/4)*x)/(a^(3/4)*(b + a*x^4)^(1/4))])/(4*(-a^2)^(1/8)*(a + Sqrt[-a^2])^(3/4)*b^2)","B",10,4,28,0.1429,1,"{1529, 494, 298, 205}"
721,1,79,0,0.0707361,"\int \frac{1}{(-1+x) \sqrt{-\sqrt{x}+x}} \, dx","Int[1/((-1 + x)*Sqrt[-Sqrt[x] + x]),x]","\frac{\sqrt{2} \sqrt{\sqrt{x}-1} \sqrt[4]{x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x}}{\sqrt{\sqrt{x}-1}}\right)}{\sqrt{x-\sqrt{x}}}-\frac{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[-Sqrt[x] + x] + (Sqrt[2]*Sqrt[-1 + Sqrt[x]]*x^(1/4)*ArcTanh[(Sqrt[2]*x^(1/4))/Sqrt[-1 + Sqrt[x]]])/Sqrt[-Sqrt[x] + x]","A",6,6,19,0.3158,1,"{2056, 1549, 848, 94, 93, 206}"
722,1,42,0,0.0448007,"\int \frac{1}{(1+2 x) \sqrt[4]{1+2 x+2 x^2}} \, dx","Int[1/((1 + 2*x)*(1 + 2*x + 2*x^2)^(1/4)),x]","\frac{\tan ^{-1}\left(\sqrt[4]{(2 x+1)^2+1}\right)}{2^{3/4}}-\frac{\tanh ^{-1}\left(\sqrt[4]{(2 x+1)^2+1}\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[(1 + (1 + 2*x)^2)^(1/4)]/2^(3/4) - ArcTanh[(1 + (1 + 2*x)^2)^(1/4)]/2^(3/4)","A",6,6,22,0.2727,1,"{694, 266, 63, 298, 203, 206}"
723,1,63,0,0.0457804,"\int \frac{\sqrt{b+a x^3} \left(2 b+a x^3\right)}{x^4} \, dx","Int[(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{4}{3} a \sqrt{a x^3+b}-\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,"(4*a*Sqrt[b + a*x^3])/3 - (2*(b + a*x^3)^(3/2))/(3*x^3) - (4*a*Sqrt[b]*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/3","A",5,5,24,0.2083,1,"{446, 78, 50, 63, 208}"
724,0,0,0,1.5467911,"\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","Int[((-2*q + p*x^3)*Sqrt[q + p*x^3])/(x^2*(a*q + b*x^2 + a*p*x^3)),x]","\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","\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) - (6*p^(1/3)*Sqrt[q + p*x^3])/(a*((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*p^(1/3)*q^(1/3)*(q^(1/3) + p^(1/3)*x)*Sqrt[(q^(2/3) - p^(1/3)*q^(1/3)*x + p^(2/3)*x^2)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*q^(1/3) + p^(1/3)*x)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)], -7 - 4*Sqrt[3]])/(a*Sqrt[(q^(1/3)*(q^(1/3) + p^(1/3)*x))/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*Sqrt[q + p*x^3]) - (2*Sqrt[2]*3^(3/4)*p^(1/3)*q^(1/3)*(q^(1/3) + p^(1/3)*x)*Sqrt[(q^(2/3) - p^(1/3)*q^(1/3)*x + p^(2/3)*x^2)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*q^(1/3) + p^(1/3)*x)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)], -7 - 4*Sqrt[3]])/(a*Sqrt[(q^(1/3)*(q^(1/3) + p^(1/3)*x))/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x)^2]*Sqrt[q + p*x^3]) + (2*b*Defer[Int][Sqrt[q + p*x^3]/(a*q + b*x^2 + a*p*x^3), x])/a + 3*p*Defer[Int][(x*Sqrt[q + p*x^3])/(a*q + b*x^2 + a*p*x^3), x]","F",0,0,0,0,-1,"{}"
725,0,0,0,0.1424932,"\int \frac{-1+2 x}{\sqrt{-8+4 x-3 x^2-10 x^3+x^4}} \, dx","Int[(-1 + 2*x)/Sqrt[-8 + 4*x - 3*x^2 - 10*x^3 + x^4],x]","\int \frac{-1+2 x}{\sqrt{-8+4 x-3 x^2-10 x^3+x^4}} \, dx","-\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,"-Defer[Int][1/Sqrt[-8 + 4*x - 3*x^2 - 10*x^3 + x^4], x] + 2*Defer[Int][x/Sqrt[-8 + 4*x - 3*x^2 - 10*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
726,0,0,0,0.1309247,"\int \frac{-1+x}{\sqrt{4-16 x+12 x^2-8 x^3+x^4}} \, dx","Int[(-1 + x)/Sqrt[4 - 16*x + 12*x^2 - 8*x^3 + x^4],x]","\int \frac{-1+x}{\sqrt{4-16 x+12 x^2-8 x^3+x^4}} \, dx","-\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,"-Defer[Int][1/Sqrt[4 - 16*x + 12*x^2 - 8*x^3 + x^4], x] + Defer[Int][x/Sqrt[4 - 16*x + 12*x^2 - 8*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
727,0,0,0,1.4147772,"\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","Int[(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,"(2*Sqrt[q + p*x^5])/(a*x) - (5*p*x^4*Sqrt[1 + (p*x^5)/q]*Hypergeometric2F1[1/2, 4/5, 9/5, -((p*x^5)/q)])/(4*a*Sqrt[q + p*x^5]) + (2*b*Defer[Int][Sqrt[q + p*x^5]/(a*q + b*x^2 + a*p*x^5), x])/a + 5*p*Defer[Int][(x^3*Sqrt[q + p*x^5])/(a*q + b*x^2 + a*p*x^5), x]","F",0,0,0,0,-1,"{}"
728,0,0,0,1.9223317,"\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","Int[(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,"(8*x^3)/(5*a*(1 + x^5)*Sqrt[x + x^6]) + (16*x^8)/(15*a*(1 + x^5)*Sqrt[x + x^6]) - (10*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^4/((1 + x^10)^(5/2)*(a - x^2 + a*x^10)), x], x, Sqrt[x]])/Sqrt[x + x^6] + (8*Sqrt[x]*Sqrt[1 + x^5]*Defer[Subst][Defer[Int][x^6/((1 + x^10)^(5/2)*(a - x^2 + a*x^10)), x], x, Sqrt[x]])/(a*Sqrt[x + x^6])","F",0,0,0,0,-1,"{}"
729,1,178,0,0.3155362,"\int \frac{\sqrt{-x+x^4} \left(-b+a x^6\right)}{x^6} \, dx","Int[(Sqrt[-x + x^4]*(-b + a*x^6))/x^6,x]","\frac{a \left(x^4-x\right)^{3/2}}{3 x^3}+\frac{2 a \sqrt{x^4-x}}{5 x^3}-\frac{3^{3/4} a (1-x) x \sqrt{\frac{x^2+x+1}{\left(1-\left(1+\sqrt{3}\right) x\right)^2}} F\left(\cos ^{-1}\left(\frac{1-\left(1-\sqrt{3}\right) x}{1-\left(1+\sqrt{3}\right) x}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt{-\frac{(1-x) x}{\left(1-\left(1+\sqrt{3}\right) x\right)^2}} \sqrt{x^4-x}}-\frac{2 b \left(x^4-x\right)^{3/2}}{9 x^6}","\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,"(2*a*Sqrt[-x + x^4])/(5*x^3) - (2*b*(-x + x^4)^(3/2))/(9*x^6) + (a*(-x + x^4)^(3/2))/(3*x^3) - (3^(3/4)*a*(1 - x)*x*Sqrt[(1 + x + x^2)/(1 - (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x)/(1 - (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(5*Sqrt[-(((1 - x)*x)/(1 - (1 + Sqrt[3])*x)^2)]*Sqrt[-x + x^4])","C",8,7,24,0.2917,0,"{2048, 2052, 2014, 2020, 2011, 329, 225}"
730,0,0,0,2.2141978,"\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","Int[((-2*q + p*x^6)*Sqrt[q + p*x^6])/(x^3*(a*q + b*x^4 + a*p*x^6)),x]","\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","\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) - (3*p^(1/3)*Sqrt[q + p*x^6])/(a*((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x^2)) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*p^(1/3)*q^(1/3)*(q^(1/3) + p^(1/3)*x^2)*Sqrt[(q^(2/3) - p^(1/3)*q^(1/3)*x^2 + p^(2/3)*x^4)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x^2)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*q^(1/3) + p^(1/3)*x^2)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x^2)], -7 - 4*Sqrt[3]])/(2*a*Sqrt[(q^(1/3)*(q^(1/3) + p^(1/3)*x^2))/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x^2)^2]*Sqrt[q + p*x^6]) - (Sqrt[2]*3^(3/4)*p^(1/3)*q^(1/3)*(q^(1/3) + p^(1/3)*x^2)*Sqrt[(q^(2/3) - p^(1/3)*q^(1/3)*x^2 + p^(2/3)*x^4)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x^2)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*q^(1/3) + p^(1/3)*x^2)/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x^2)], -7 - 4*Sqrt[3]])/(a*Sqrt[(q^(1/3)*(q^(1/3) + p^(1/3)*x^2))/((1 + Sqrt[3])*q^(1/3) + p^(1/3)*x^2)^2]*Sqrt[q + p*x^6]) + (b*Defer[Subst][Defer[Int][Sqrt[q + p*x^3]/(a*q + b*x^2 + a*p*x^3), x], x, x^2])/a + (3*p*Defer[Subst][Defer[Int][(x*Sqrt[q + p*x^3])/(a*q + b*x^2 + a*p*x^3), x], x, x^2])/2","F",0,0,0,0,-1,"{}"
731,1,39,0,0.1419799,"\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","Int[(2*(-2*q + p*x^6)*Sqrt[q + p*x^6]*(a*q + b*x^4 + a*p*x^6))/x^11,x]","\frac{2 a \left(p x^6+q\right)^{5/2}}{5 x^{10}}+\frac{2 b \left(p x^6+q\right)^{3/2}}{3 x^6}","\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,"(2*b*(q + p*x^6)^(3/2))/(3*x^6) + (2*a*(q + p*x^6)^(5/2))/(5*x^10)","A",8,7,40,0.1750,1,"{12, 1833, 1584, 446, 74, 1478, 449}"
732,1,64,0,0.152066,"\int \frac{1}{x^3 \sqrt[8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx","Int[1/(x^3*(256 - 256*x^2 + 96*x^4 - 16*x^6 + x^8)^(1/8)),x]","\frac{\sqrt{x^2-4} \tan ^{-1}\left(\frac{\sqrt{x^2-4}}{2}\right)}{16 \sqrt[8]{\left(x^2-4\right)^4}}-\frac{4-x^2}{8 x^2 \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,"-1/8*(4 - x^2)/(x^2*((-4 + x^2)^4)^(1/8)) + (Sqrt[-4 + x^2]*ArcTan[Sqrt[-4 + x^2]/2])/(16*((-4 + x^2)^4)^(1/8))","A",6,6,28,0.2143,1,"{6688, 6720, 266, 51, 63, 203}"
733,0,0,0,2.2206823,"\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","Int[(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,"(20*b*x^(1/4)*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^14/((b + a*x^12)^(1/4)*(-2 + b*x^20 + a*x^32)), x], x, x^(1/4)])/(b*x + a*x^4)^(1/4) + (32*a*x^(1/4)*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^26/((b + a*x^12)^(1/4)*(-2 + b*x^20 + a*x^32)), x], x, x^(1/4)])/(b*x + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
734,1,52,0,0.0081505,"\int \sqrt{1-x^2-y^4} \, dx","Int[Sqrt[1 - x^2 - y^4],x]","\frac{1}{2} x \sqrt{-x^2-y^4+1}+\frac{1}{2} \left(1-y^4\right) \tan ^{-1}\left(\frac{x}{\sqrt{-x^2-y^4+1}}\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])/2 + ((1 - y^4)*ArcTan[x/Sqrt[1 - x^2 - y^4]])/2","A",3,3,16,0.1875,1,"{195, 217, 203}"
735,1,338,0,8.5110895,"\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","Int[(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 \sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(-\frac{2 (a+b) k^2}{-2 a k^2-2 b k^2+b+\sqrt{b^2+4 a k^2 b+4 a^2 k^2}};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{(a+b) \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(\frac{2 (a+b) k^2}{2 a k^2-b \left(1-2 k^2\right)+\sqrt{b^2+4 a k^2 b+4 a^2 k^2}};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{(a+b) \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{(a+b) \sqrt{(1-x) x \left(1-k^2 x\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*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/((a + b)*Sqrt[(1 - x)*x*(1 - k^2*x)]) + (2*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[(-2*(a + b)*k^2)/(b - 2*a*k^2 - 2*b*k^2 + Sqrt[b^2 + 4*a^2*k^2 + 4*a*b*k^2]), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((a + b)*Sqrt[(1 - x)*x*(1 - k^2*x)]) + (2*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[(2*(a + b)*k^2)/(2*a*k^2 - b*(1 - 2*k^2) + Sqrt[b^2 + 4*a^2*k^2 + 4*a*b*k^2]), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((a + b)*Sqrt[(1 - x)*x*(1 - k^2*x)])","C",12,6,60,0.1000,1,"{6718, 6728, 115, 168, 538, 537}"
736,0,0,0,4.7650014,"\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","Int[(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]","\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","-\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,"(2*Defer[Int][1/Sqrt[x*(-a + x)*(-b + x)*(-c + x)], x])/d - 3*a*b*c*Defer[Int][1/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c*d + (1 - b*c*d - a*(b + c)*d)*x + (a + b + c)*d*x^2 - d*x^3)), x] - (2*(1 - b*c*d - a*(b + c)*d)*Defer[Int][x/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c*d + (1 - b*c*d - a*(b + c)*d)*x + (a + b + c)*d*x^2 - d*x^3)), x])/d - (a + b + c)*Defer[Int][x^2/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c*d + (1 - b*c*d - a*(b + c)*d)*x + (a + b + c)*d*x^2 - d*x^3)), x]","F",0,0,0,0,-1,"{}"
737,1,65,0,0.019932,"\int x^6 \sqrt[4]{-1+x^4} \, dx","Int[x^6*(-1 + x^4)^(1/4),x]","\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}{8} \sqrt[4]{x^4-1} x^7-\frac{1}{32} \sqrt[4]{x^4-1} x^3","\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,"-1/32*(x^3*(-1 + x^4)^(1/4)) + (x^7*(-1 + x^4)^(1/4))/8 + (3*ArcTan[x/(-1 + x^4)^(1/4)])/64 - (3*ArcTanh[x/(-1 + x^4)^(1/4)])/64","A",6,6,13,0.4615,1,"{279, 321, 331, 298, 203, 206}"
738,1,113,0,0.1377155,"\int \frac{(-1+2 x) \sqrt[4]{x^3+x^4}}{x} \, dx","Int[((-1 + 2*x)*(x^3 + x^4)^(1/4))/x,x]","-\frac{7}{4} \sqrt[4]{x^4+x^3}+\frac{\left(x^4+x^3\right)^{5/4}}{x^3}+\frac{7 (x+1)^{3/4} x^{9/4} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{8 \left(x^4+x^3\right)^{3/4}}-\frac{7 (x+1)^{3/4} x^{9/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{8 \left(x^4+x^3\right)^{3/4}}","\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,"(-7*(x^3 + x^4)^(1/4))/4 + (x^3 + x^4)^(5/4)/x^3 + (7*x^(9/4)*(1 + x)^(3/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(8*(x^3 + x^4)^(3/4)) - (7*x^(9/4)*(1 + x)^(3/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(8*(x^3 + x^4)^(3/4))","A",8,8,20,0.4000,1,"{2039, 2021, 2032, 63, 331, 298, 203, 206}"
739,0,0,0,1.7450659,"\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","Int[(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]","\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","\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,"Defer[Int][Sqrt[-1 + x^2 - 2*x^3 + x^4]/(2 + x^2 + 4*x^3 - 2*x^4), x] + 3*Defer[Int][(x*Sqrt[-1 + x^2 - 2*x^3 + x^4])/(-1 - 2*x^3 + x^4), x] - 2*Defer[Int][(x^2*Sqrt[-1 + x^2 - 2*x^3 + x^4])/(-1 - 2*x^3 + x^4), x] - 6*Defer[Int][(x*Sqrt[-1 + x^2 - 2*x^3 + x^4])/(-2 - x^2 - 4*x^3 + 2*x^4), x] + 4*Defer[Int][(x^2*Sqrt[-1 + x^2 - 2*x^3 + x^4])/(-2 - x^2 - 4*x^3 + 2*x^4), x]","F",0,0,0,0,-1,"{}"
740,1,57,0,0.0213092,"\int \frac{x^2}{\left(b+a x^4\right)^{3/4}} \, dx","Int[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)}{2 a^{3/4}}-\frac{\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,"-1/2*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)]/(2*a^(3/4))","A",4,4,15,0.2667,1,"{331, 298, 203, 206}"
741,1,253,0,0.2112065,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-b+a x^8\right)} \, dx","Int[1/((b + a*x^4)^(1/4)*(-b + a*x^8)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}-\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}+\sqrt{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}-\sqrt{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}+\sqrt{b}}}","\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,"-1/4*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*b) - ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(4*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*b) - ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(4*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*b) - ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(4*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*b)","B",9,5,23,0.2174,1,"{1429, 377, 212, 206, 203}"
742,1,461,0,1.4801366,"\int \frac{-b+a x^8}{\sqrt[4]{b+a x^8} \left(b-c x^4+a x^8\right)} \, dx","Int[(-b + a*x^8)/((b + a*x^8)^(1/4)*(b - c*x^4 + a*x^8)),x]","-\frac{x \sqrt[4]{\frac{a x^8}{b}+1} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};-\frac{2 a^2 x^8}{2 a b-c \left(c-\sqrt{c^2-4 a b}\right)},-\frac{a x^8}{b}\right)}{\sqrt[4]{a x^8+b}}-\frac{x \sqrt[4]{\frac{a x^8}{b}+1} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};-\frac{2 a^2 x^8}{2 a b-c \left(c+\sqrt{c^2-4 a b}\right)},-\frac{a x^8}{b}\right)}{\sqrt[4]{a x^8+b}}+\frac{a x^5 \left(c-\sqrt{c^2-4 a b}\right) \sqrt[4]{\frac{a x^8}{b}+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};-\frac{2 a^2 x^8}{2 a b-c \left(c-\sqrt{c^2-4 a b}\right)},-\frac{a x^8}{b}\right)}{5 \left(2 a b-c \left(c-\sqrt{c^2-4 a b}\right)\right) \sqrt[4]{a x^8+b}}+\frac{a x^5 \left(\sqrt{c^2-4 a b}+c\right) \sqrt[4]{\frac{a x^8}{b}+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};-\frac{2 a^2 x^8}{2 a b-c \left(c+\sqrt{c^2-4 a b}\right)},-\frac{a x^8}{b}\right)}{5 \left(2 a b-c \left(\sqrt{c^2-4 a b}+c\right)\right) \sqrt[4]{a x^8+b}}+\frac{x \sqrt[4]{\frac{a x^8}{b}+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-\frac{a x^8}{b}\right)}{\sqrt[4]{a x^8+b}}","-\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,"-((x*(1 + (a*x^8)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (-2*a^2*x^8)/(2*a*b - c*(c - Sqrt[-4*a*b + c^2])), -((a*x^8)/b)])/(b + a*x^8)^(1/4)) - (x*(1 + (a*x^8)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (-2*a^2*x^8)/(2*a*b - c*(c + Sqrt[-4*a*b + c^2])), -((a*x^8)/b)])/(b + a*x^8)^(1/4) + (a*(c - Sqrt[-4*a*b + c^2])*x^5*(1 + (a*x^8)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (-2*a^2*x^8)/(2*a*b - c*(c - Sqrt[-4*a*b + c^2])), -((a*x^8)/b)])/(5*(2*a*b - c*(c - Sqrt[-4*a*b + c^2]))*(b + a*x^8)^(1/4)) + (a*(c + Sqrt[-4*a*b + c^2])*x^5*(1 + (a*x^8)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (-2*a^2*x^8)/(2*a*b - c*(c + Sqrt[-4*a*b + c^2])), -((a*x^8)/b)])/(5*(2*a*b - c*(c + Sqrt[-4*a*b + c^2]))*(b + a*x^8)^(1/4)) + (x*(1 + (a*x^8)/b)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -((a*x^8)/b)])/(b + a*x^8)^(1/4)","C",18,8,36,0.2222,0,"{6728, 246, 245, 1438, 430, 429, 511, 510}"
743,0,0,0,2.5356832,"\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","Int[((-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,"(4*(1 + x^5)^(1/4)*Hypergeometric2F1[-21/20, 1/4, -1/20, -x^5])/(7*x^5*(x + x^6)^(1/4)) + (4*(1 + x^5)^(1/4)*Hypergeometric2F1[-9/20, 1/4, 11/20, -x^5])/(3*x^2*(x + x^6)^(1/4)) + (4*(1 + x^5)^(1/4)*Hypergeometric2F1[-1/20, 1/4, 19/20, -x^5])/(x + x^6)^(1/4) + (16*x*(1 + x^5)^(1/4)*Hypergeometric2F1[3/20, 1/4, 23/20, -x^5])/(3*(x + x^6)^(1/4)) + (8*x^3*(1 + x^5)^(1/4)*Hypergeometric2F1[1/4, 11/20, 31/20, -x^5])/(11*(x + x^6)^(1/4)) + (8*x^5*(1 + x^5)^(1/4)*Hypergeometric2F1[1/4, 19/20, 39/20, -x^5])/(19*(x + x^6)^(1/4)) - (40*x^(1/4)*(1 + x^5)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 + x^20)^(1/4)*(1 - x^12 + x^20)), x], x, x^(1/4)])/(x + x^6)^(1/4) + (16*x^(1/4)*(1 + x^5)^(1/4)*Defer[Subst][Defer[Int][x^14/((1 + x^20)^(1/4)*(1 - x^12 + x^20)), x], x, x^(1/4)])/(x + x^6)^(1/4)","F",0,0,0,0,-1,"{}"
744,0,0,0,0.0203881,"\int \sqrt{x^2+\sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int \sqrt{x^2+\sqrt{1+x^4}} \, dx","\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,"Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
745,1,182,0,0.7154388,"\int \frac{-1-x+x^2}{\left(1+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(-1 - x + x^2)/((1 + x^2)*Sqrt[-x + x^3]),x]","\frac{\sqrt{2} \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^3-x}}+\frac{\left(\frac{3}{2}+\frac{i}{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2}-\frac{i}{2};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^3-x}}+\frac{\left(\frac{3}{2}-\frac{i}{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2}+\frac{i}{2};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^3-x}}","-\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,"(Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/Sqrt[-x + x^3] + ((3/2 + I/2)*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/2 - I/2, ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*Sqrt[-x + x^3]) + ((3/2 - I/2)*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/2 + I/2, ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*Sqrt[-x + x^3])","C",13,7,27,0.2593,0,"{2056, 6725, 329, 222, 933, 168, 537}"
746,1,182,0,0.6852314,"\int \frac{-1+x+x^2}{\left(1+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(-1 + x + x^2)/((1 + x^2)*Sqrt[-x + x^3]),x]","\frac{\sqrt{2} \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^3-x}}+\frac{\left(\frac{1}{2}+\frac{3 i}{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2}-\frac{i}{2};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^3-x}}+\frac{\left(\frac{1}{2}-\frac{3 i}{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2}+\frac{i}{2};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^3-x}}","-\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,"(Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/Sqrt[-x + x^3] + ((1/2 + (3*I)/2)*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/2 - I/2, ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*Sqrt[-x + x^3]) + ((1/2 - (3*I)/2)*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/2 + I/2, ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*Sqrt[-x + x^3])","C",13,7,25,0.2800,0,"{2056, 6725, 329, 222, 933, 168, 537}"
747,1,183,0,0.6879913,"\int \frac{-7+x+7 x^2}{\left(1+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(-7 + x + 7*x^2)/((1 + x^2)*Sqrt[-x + x^3]),x]","\frac{7 \sqrt{2} \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^3-x}}+\frac{\left(\frac{13}{2}+\frac{15 i}{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2}-\frac{i}{2};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^3-x}}+\frac{\left(\frac{13}{2}-\frac{15 i}{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2}+\frac{i}{2};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^3-x}}","-\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,"(7*Sqrt[2]*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/Sqrt[-x + x^3] + ((13/2 + (15*I)/2)*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/2 - I/2, ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*Sqrt[-x + x^3]) + ((13/2 - (15*I)/2)*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/2 + I/2, ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*Sqrt[-x + x^3])","C",13,7,27,0.2593,0,"{2056, 6725, 329, 222, 933, 168, 537}"
748,1,102,0,0.1586519,"\int \frac{1}{(-2+x) \sqrt[4]{-x^2+x^3}} \, dx","Int[1/((-2 + x)*(-x^2 + x^3)^(1/4)),x]","\frac{\sqrt[4]{x-1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x-1}}{\sqrt{x}}\right)}{\sqrt{2} \sqrt[4]{x^3-x^2}}-\frac{\sqrt[4]{x-1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x-1}}{\sqrt{x}}\right)}{\sqrt{2} \sqrt[4]{x^3-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)*Sqrt[x]*ArcTan[(Sqrt[2]*(-1 + x)^(1/4))/Sqrt[x]])/(Sqrt[2]*(-x^2 + x^3)^(1/4)) - ((-1 + x)^(1/4)*Sqrt[x]*ArcTanh[(Sqrt[2]*(-1 + x)^(1/4))/Sqrt[x]])/(Sqrt[2]*(-x^2 + x^3)^(1/4))","A",11,8,19,0.4211,1,"{2056, 106, 490, 1211, 220, 1699, 203, 206}"
749,1,96,0,0.1240906,"\int \left(b+a x^3\right) \sqrt{-x+x^4} \, dx","Int[(b + a*x^3)*Sqrt[-x + x^4],x]","\frac{1}{6} a \sqrt{x^4-x} x^4-\frac{1}{12} a \sqrt{x^4-x} x-\frac{1}{12} a \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)+\frac{1}{3} b \sqrt{x^4-x} x-\frac{1}{3} b \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x}}\right)","\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,"-1/12*(a*x*Sqrt[-x + x^4]) + (b*x*Sqrt[-x + x^4])/3 + (a*x^4*Sqrt[-x + x^4])/6 - (a*ArcTanh[x^2/Sqrt[-x + x^4]])/12 - (b*ArcTanh[x^2/Sqrt[-x + x^4]])/3","A",9,6,19,0.3158,1,"{2053, 2004, 2029, 206, 2021, 2024}"
750,1,46,0,0.104407,"\int \frac{-2-x+2 x^2}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","Int[(-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)-2 \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)","\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,"-2*ArcTan[x/Sqrt[1 + x^2 + x^4]] + ArcTanh[(1 - x^2)/(2*Sqrt[1 + x^2 + x^4])]/2","A",6,6,30,0.2000,1,"{1687, 1698, 203, 1247, 724, 206}"
751,0,0,0,2.6381506,"\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","Int[(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,"(20*b*x^(1/4)*(-b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^14/((-b + a*x^16)^(1/4)*(2 + b*x^20 - a*x^36)), x], x, x^(1/4)])/(-(b*x) + a*x^5)^(1/4) + (36*a*x^(1/4)*(-b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^30/((-b + a*x^16)^(1/4)*(-2 - b*x^20 + a*x^36)), x], x, x^(1/4)])/(-(b*x) + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
752,1,322,0,1.0052792,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Int[(1 + x^2)/((-1 + x^2)*Sqrt[x + x^2 + x^3]),x]","\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+x+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{4}\right)}{\sqrt{x^3+x^2+x}}-\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(1-i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-1+i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}","-\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,"(Sqrt[x]*(1 + x)*Sqrt[(1 + x + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/4])/Sqrt[x + x^2 + x^3] - (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(1 - I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-1 + I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3])","C",17,8,25,0.3200,0,"{2056, 6725, 716, 1103, 934, 169, 538, 537}"
753,0,0,0,4.3039705,"\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","Int[(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]","\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","-\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,"2*Defer[Int][1/Sqrt[x*(-a + x)*(-b + x)*(-c + x)], x] - 3*a*b*c*Defer[Int][1/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c - (b*c + a*(b + c) - d)*x + (a + b + c)*x^2 - x^3)), x] + 2*(b*c + a*(b + c) - d)*Defer[Int][x/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c - (b*c + a*(b + c) - d)*x + (a + b + c)*x^2 - x^3)), x] - (a + b + c)*Defer[Int][x^2/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c - (b*c + a*(b + c) - d)*x + (a + b + c)*x^2 - x^3)), x]","F",0,0,0,0,-1,"{}"
754,1,68,0,0.0517961,"\int \frac{\left(-b+a x^3\right) \sqrt{b+a x^3}}{x^7} \, dx","Int[((-b + a*x^3)*Sqrt[b + a*x^3])/x^7,x]","-\frac{5 a^2 \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)}{12 \sqrt{b}}-\frac{5 a \sqrt{a x^3+b}}{12 x^3}+\frac{\left(a x^3+b\right)^{3/2}}{6 x^6}","\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,"(-5*a*Sqrt[b + a*x^3])/(12*x^3) + (b + a*x^3)^(3/2)/(6*x^6) - (5*a^2*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/(12*Sqrt[b])","A",5,5,24,0.2083,1,"{446, 78, 47, 63, 208}"
755,1,68,0,0.0443787,"\int \frac{\sqrt{b+a x^3} \left(2 b+a x^3\right)}{x^7} \, dx","Int[(Sqrt[b + a*x^3]*(2*b + a*x^3))/x^7,x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{a x^3+b}}{\sqrt{b}}\right)}{6 \sqrt{b}}-\frac{a \sqrt{a x^3+b}}{6 x^3}-\frac{\left(a x^3+b\right)^{3/2}}{3 x^6}","\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*(a*Sqrt[b + a*x^3])/x^3 - (b + a*x^3)^(3/2)/(3*x^6) - (a^2*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/(6*Sqrt[b])","A",5,5,24,0.2083,1,"{446, 78, 47, 63, 208}"
756,0,0,0,6.4374284,"\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","Int[(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]","\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","\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,"-(((a + b + c)*Defer[Int][1/Sqrt[x*(-a + x)*(-b + x)*(-c + x)], x])/(1 - d)) + (a*b*c*(a + b + c)*Defer[Int][1/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c - (b*c + a*(b + c))*x + (a + b + c)*x^2 - (1 - d)*x^3)), x])/(1 - d) - ((a^2*(b + c) + b*c*(b + c) + a*(b^2 + c^2 + 3*b*c*d))*Defer[Int][x/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c - (b*c + a*(b + c))*x + (a + b + c)*x^2 - (1 - d)*x^3)), x])/(1 - d) + ((a^2 + b^2 + c^2 + 2*b*c*d + 2*a*(b + c)*d)*Defer[Int][x^2/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c - (b*c + a*(b + c))*x + (a + b + c)*x^2 - (1 - d)*x^3)), x])/(1 - d)","F",0,0,0,0,-1,"{}"
757,0,0,0,7.2414702,"\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","Int[(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]","\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","-\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,"-(((a + b + c)*Defer[Int][1/Sqrt[x*(-a + x)*(-b + x)*(-c + x)], x])/(1 - d)) + (a*b*c*(a + b + c)*d*Defer[Int][1/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c*d - (b*c + a*(b + c))*d*x + (a + b + c)*d*x^2 + (1 - d)*x^3)), x])/(1 - d) - ((a^2*(b + c)*d + b*c*(b + c)*d + a*(3*b*c + b^2*d + c^2*d))*Defer[Int][x/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c*d - (b*c + a*(b + c))*d*x + (a + b + c)*d*x^2 + (1 - d)*x^3)), x])/(1 - d) + ((2*b*c + 2*a*(b + c) + a^2*d + b^2*d + c^2*d)*Defer[Int][x^2/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*b*c*d - (b*c + a*(b + c))*d*x + (a + b + c)*d*x^2 + (1 - d)*x^3)), x])/(1 - d)","F",0,0,0,0,-1,"{}"
758,1,113,0,0.0641419,"\int \sqrt[4]{-x^2+x^4} \, dx","Int[(-x^2 + x^4)^(1/4),x]","\frac{1}{2} \sqrt[4]{x^4-x^2} x+\frac{\left(x^2-1\right)^{3/4} x^{3/2} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \left(x^4-x^2\right)^{3/4}}-\frac{\left(x^2-1\right)^{3/4} x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \left(x^4-x^2\right)^{3/4}}","\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,"(x*(-x^2 + x^4)^(1/4))/2 + (x^(3/2)*(-1 + x^2)^(3/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(3/4)) - (x^(3/2)*(-1 + x^2)^(3/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(3/4))","A",7,7,13,0.5385,1,"{2004, 2032, 329, 331, 298, 203, 206}"
759,1,125,0,0.1133395,"\int x^2 \sqrt[4]{x^2+x^4} \, dx","Int[x^2*(x^2 + x^4)^(1/4),x]","\frac{1}{16} \sqrt[4]{x^4+x^2} x+\frac{3 \left(x^2+1\right)^{3/4} x^{3/2} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{32 \left(x^4+x^2\right)^{3/4}}-\frac{3 \left(x^2+1\right)^{3/4} x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{32 \left(x^4+x^2\right)^{3/4}}+\frac{1}{4} \sqrt[4]{x^4+x^2} x^3","\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))/16 + (x^3*(x^2 + x^4)^(1/4))/4 + (3*x^(3/2)*(1 + x^2)^(3/4)*ArcTan[Sqrt[x]/(1 + x^2)^(1/4)])/(32*(x^2 + x^4)^(3/4)) - (3*x^(3/2)*(1 + x^2)^(3/4)*ArcTanh[Sqrt[x]/(1 + x^2)^(1/4)])/(32*(x^2 + x^4)^(3/4))","B",8,8,15,0.5333,1,"{2021, 2024, 2032, 329, 331, 298, 203, 206}"
760,1,253,0,2.4349161,"\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","Int[((-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 x^4+3 x^2+1} x}{-4 x^2-(2-2 i)}-\frac{i \sqrt{2 x^4+3 x^2+1} x}{4 x^2+(2+2 i)}-\frac{\left(x^2+1\right) \sqrt{\frac{2 x^2+1}{x^2+1}} F\left(\left.\tan ^{-1}(x)\right|-1\right)}{2 \sqrt{2 x^4+3 x^2+1}}+\frac{i \left(x^2+1\right) \Pi \left(\frac{1}{2}-\frac{i}{2};\tan ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{\frac{x^2+1}{2 x^2+1}} \sqrt{2 x^4+3 x^2+1}}-\frac{i \left(x^2+1\right) \Pi \left(\frac{1}{2}+\frac{i}{2};\tan ^{-1}\left(\sqrt{2} x\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{\frac{x^2+1}{2 x^2+1}} \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,"((-I)*x*Sqrt[1 + 3*x^2 + 2*x^4])/((-2 + 2*I) - 4*x^2) - (I*x*Sqrt[1 + 3*x^2 + 2*x^4])/((2 + 2*I) + 4*x^2) - ((1 + x^2)*Sqrt[(1 + 2*x^2)/(1 + x^2)]*EllipticF[ArcTan[x], -1])/(2*Sqrt[1 + 3*x^2 + 2*x^4]) + ((I/2)*(1 + x^2)*EllipticPi[1/2 - I/2, ArcTan[Sqrt[2]*x], 1/2])/(Sqrt[2]*Sqrt[(1 + x^2)/(1 + 2*x^2)]*Sqrt[1 + 3*x^2 + 2*x^4]) - ((I/2)*(1 + x^2)*EllipticPi[1/2 + I/2, ArcTan[Sqrt[2]*x], 1/2])/(Sqrt[2]*Sqrt[(1 + x^2)/(1 + 2*x^2)]*Sqrt[1 + 3*x^2 + 2*x^4])","C",90,10,38,0.2632,1,"{6742, 1226, 1189, 1100, 1136, 1214, 1456, 539, 1208, 6728}"
761,0,0,0,1.8564918,"\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","Int[(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]","\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","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,"2*Defer[Int][Sqrt[-2 + x^2 - 2*x^3 + 2*x^4]/(2 + x^2 + 2*x^3 - 2*x^4), x] + 3*Defer[Int][(x*Sqrt[-2 + x^2 - 2*x^3 + 2*x^4])/(-1 - x^3 + x^4), x] - 4*Defer[Int][(x^2*Sqrt[-2 + x^2 - 2*x^3 + 2*x^4])/(-1 - x^3 + x^4), x] - 6*Defer[Int][(x*Sqrt[-2 + x^2 - 2*x^3 + 2*x^4])/(-2 - x^2 - 2*x^3 + 2*x^4), x] + 8*Defer[Int][(x^2*Sqrt[-2 + x^2 - 2*x^3 + 2*x^4])/(-2 - x^2 - 2*x^3 + 2*x^4), x]","F",0,0,0,0,-1,"{}"
762,1,50,0,0.081158,"\int \frac{-b+a x^2}{\left(b+a x^2\right) \sqrt{b^2+a^2 x^4}} \, dx","Int[(-b + a*x^2)/((b + a*x^2)*Sqrt[b^2 + a^2*x^4]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^4+b^2}}\right)}{\sqrt{2} \sqrt{a} \sqrt{b}}","-\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,"-(ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[b]*x)/Sqrt[b^2 + a^2*x^4]]/(Sqrt[2]*Sqrt[a]*Sqrt[b]))","A",2,2,34,0.05882,1,"{1699, 205}"
763,0,0,0,2.5036407,"\int \frac{3 b+a x^4}{\left(-b-x^3+a x^4\right) \sqrt[4]{-b x+a x^5}} \, dx","Int[(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,"(4*x*(1 - (a*x^4)/b)^(1/4)*Hypergeometric2F1[3/16, 1/4, 19/16, (a*x^4)/b])/(3*(-(b*x) + a*x^5)^(1/4)) - (16*b*x^(1/4)*(-b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^2/((b + x^12 - a*x^16)*(-b + a*x^16)^(1/4)), x], x, x^(1/4)])/(-(b*x) + a*x^5)^(1/4) + (4*x^(1/4)*(-b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^14/((-b + a*x^16)^(1/4)*(-b - x^12 + a*x^16)), x], x, x^(1/4)])/(-(b*x) + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
764,1,53,0,0.0443782,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x} \, dx","Int[((-1 + x^3)*Sqrt[-1 + x^6])/x,x]","\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{1}{6} \sqrt{x^6-1} \left(2-x^3\right)-\frac{1}{6} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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,"-1/6*((2 - x^3)*Sqrt[-1 + x^6]) + ArcTan[Sqrt[-1 + x^6]]/3 - ArcTanh[x^3/Sqrt[-1 + x^6]]/6","A",8,8,18,0.4444,1,"{1475, 815, 844, 217, 206, 266, 63, 203}"
765,0,0,0,0.5734101,"\int \frac{x (3+4 x) \sqrt[3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx","Int[(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{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-2 x-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"3*Defer[Int][(x*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6), x] + 4*Defer[Int][(x^2*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6), x]","F",0,0,0,0,-1,"{}"
766,0,0,0,0.4569298,"\int \frac{x (3+4 x) \sqrt[3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx","Int[(x*(3 + 4*x)*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6),x]","\int \frac{x (3+4 x) \sqrt[3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx","-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-2 x-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"3*Defer[Int][(x*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6), x] + 4*Defer[Int][(x^2*(-1 - 2*x + x^3)^(1/3))/(-2 - 8*x - 8*x^2 + x^6), x]","F",0,0,0,0,-1,"{}"
767,0,0,0,0.4072345,"\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","Int[((3 + 2*x)*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6),x]","\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"3*Defer[Int][(1 + x + x^3)^(2/3)/(1 + 2*x + x^2 + x^3 + x^4 + x^6), x] + 2*Defer[Int][(x*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6), x]","F",0,0,0,0,-1,"{}"
768,0,0,0,0.3262524,"\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","Int[((3 + 2*x)*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6),x]","\int \frac{(3+2 x) \left(1+x+x^3\right)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"3*Defer[Int][(1 + x + x^3)^(2/3)/(1 + 2*x + x^2 + x^3 + x^4 + x^6), x] + 2*Defer[Int][(x*(1 + x + x^3)^(2/3))/(1 + 2*x + x^2 + x^3 + x^4 + x^6), x]","F",0,0,0,0,-1,"{}"
769,0,0,0,1.5758094,"\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","Int[((2 + x^3)*(x + x^3 - x^4)^(1/3))/(1 + x^2 - 2*x^3 + x^4 - x^5 + x^6),x]","\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{-x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"(6*(x + x^3 - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 + x^6 - x^9)^(1/3))/(1 + x^6 - 2*x^9 + x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 - x^3)^(1/3)) + (3*(x + x^3 - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^12*(1 + x^6 - x^9)^(1/3))/(1 + x^6 - 2*x^9 + x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 - x^3)^(1/3))","F",0,0,0,0,-1,"{}"
770,0,0,0,1.1681078,"\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","Int[((2 + x^3)*(x + x^3 - x^4)^(1/3))/(1 + x^2 - 2*x^3 + x^4 - x^5 + x^6),x]","\int \frac{\left(2+x^3\right) \sqrt[3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx","-\text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{-x^4+x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"(6*(x + x^3 - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 + x^6 - x^9)^(1/3))/(1 + x^6 - 2*x^9 + x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 - x^3)^(1/3)) + (3*(x + x^3 - x^4)^(1/3)*Defer[Subst][Defer[Int][(x^12*(1 + x^6 - x^9)^(1/3))/(1 + x^6 - 2*x^9 + x^12 - x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 - x^3)^(1/3))","F",0,0,0,0,-1,"{}"
771,0,0,0,0.6110928,"\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","Int[((3 + x^2)*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6),x]","\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"3*Defer[Int][(1 + x^2 + x^3)^(2/3)/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6), x] + Defer[Int][(x^2*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6), x]","F",0,0,0,0,-1,"{}"
772,0,0,0,0.4720508,"\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","Int[((3 + x^2)*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6),x]","\int \frac{\left(3+x^2\right) \left(1+x^2+x^3\right)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"3*Defer[Int][(1 + x^2 + x^3)^(2/3)/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6), x] + Defer[Int][(x^2*(1 + x^2 + x^3)^(2/3))/(-1 - 2*x^2 + x^3 - x^4 + x^5 + x^6), x]","F",0,0,0,0,-1,"{}"
773,1,460,0,1.4959992,"\int \frac{b+a x^8}{\sqrt[4]{b-a x^8} \left(-b+c x^4+a x^8\right)} \, dx","Int[(b + a*x^8)/((b - a*x^8)^(1/4)*(-b + c*x^4 + a*x^8)),x]","-\frac{x \sqrt[4]{1-\frac{a x^8}{b}} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{2 a^2 x^8}{c^2-\sqrt{c^2+4 a b} c+2 a b},\frac{a x^8}{b}\right)}{\sqrt[4]{b-a x^8}}-\frac{x \sqrt[4]{1-\frac{a x^8}{b}} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{2 a^2 x^8}{2 a b+c \left(c+\sqrt{c^2+4 a b}\right)},\frac{a x^8}{b}\right)}{\sqrt[4]{b-a x^8}}+\frac{a x^5 \left(c-\sqrt{4 a b+c^2}\right) \sqrt[4]{1-\frac{a x^8}{b}} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{2 a^2 x^8}{c^2-\sqrt{c^2+4 a b} c+2 a b},\frac{a x^8}{b}\right)}{5 \left(c \left(c-\sqrt{4 a b+c^2}\right)+2 a b\right) \sqrt[4]{b-a x^8}}+\frac{a x^5 \left(\sqrt{4 a b+c^2}+c\right) \sqrt[4]{1-\frac{a x^8}{b}} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{2 a^2 x^8}{2 a b+c \left(c+\sqrt{c^2+4 a b}\right)},\frac{a x^8}{b}\right)}{5 \left(c \left(\sqrt{4 a b+c^2}+c\right)+2 a b\right) \sqrt[4]{b-a x^8}}+\frac{x \sqrt[4]{1-\frac{a x^8}{b}} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};\frac{a x^8}{b}\right)}{\sqrt[4]{b-a x^8}}","-\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,"-((x*(1 - (a*x^8)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (2*a^2*x^8)/(2*a*b + c^2 - c*Sqrt[4*a*b + c^2]), (a*x^8)/b])/(b - a*x^8)^(1/4)) - (x*(1 - (a*x^8)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (2*a^2*x^8)/(2*a*b + c*(c + Sqrt[4*a*b + c^2])), (a*x^8)/b])/(b - a*x^8)^(1/4) + (a*(c - Sqrt[4*a*b + c^2])*x^5*(1 - (a*x^8)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (2*a^2*x^8)/(2*a*b + c^2 - c*Sqrt[4*a*b + c^2]), (a*x^8)/b])/(5*(2*a*b + c*(c - Sqrt[4*a*b + c^2]))*(b - a*x^8)^(1/4)) + (a*(c + Sqrt[4*a*b + c^2])*x^5*(1 - (a*x^8)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (2*a^2*x^8)/(2*a*b + c*(c + Sqrt[4*a*b + c^2])), (a*x^8)/b])/(5*(2*a*b + c*(c + Sqrt[4*a*b + c^2]))*(b - a*x^8)^(1/4)) + (x*(1 - (a*x^8)/b)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, (a*x^8)/b])/(b - a*x^8)^(1/4)","C",18,8,36,0.2222,0,"{6728, 246, 245, 1438, 430, 429, 511, 510}"
774,0,0,0,0.6799767,"\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","Int[(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,"-6*Defer[Int][(x*(2 - x^3 + x^8)^(1/3))/(4 + x^6 + 4*x^8 + x^16), x] + 5*Defer[Int][(x^9*(2 - x^3 + x^8)^(1/3))/(4 + x^6 + 4*x^8 + x^16), x]","F",0,0,0,0,-1,"{}"
775,1,440,0,15.4664144,"\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","Int[(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 \sqrt{b-a} \sqrt{x-a} \sqrt{-\frac{b-x}{a-b}} \sqrt{-\frac{c-x}{a-c}} \Pi \left(\frac{2 (a-b)}{2 a-b-c-d-\sqrt{b^2-2 c b+2 d b+c^2+d^2-4 a d+2 c d}};\sin ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{b-a}}\right)|\frac{a-b}{a-c}\right)}{\sqrt{-((a-x) (b-x) (c-x))}}-\frac{2 \sqrt{b-a} \sqrt{x-a} \sqrt{-\frac{b-x}{a-b}} \sqrt{-\frac{c-x}{a-c}} \Pi \left(\frac{2 (a-b)}{2 a-b-c-d+\sqrt{b^2-2 c b+2 d b+c^2+d^2-4 a d+2 c d}};\sin ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{b-a}}\right)|\frac{a-b}{a-c}\right)}{\sqrt{-((a-x) (b-x) (c-x))}}+\frac{2 \sqrt{b-a} \sqrt{x-a} \sqrt{-\frac{b-x}{a-b}} \sqrt{-\frac{c-x}{a-c}} F\left(\sin ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{b-a}}\right)|\frac{a-b}{a-c}\right)}{\sqrt{-((a-x) (b-x) (c-x))}}","\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*Sqrt[-a + b]*Sqrt[-((b - x)/(a - b))]*Sqrt[-((c - x)/(a - c))]*Sqrt[-a + x]*EllipticF[ArcSin[Sqrt[-a + x]/Sqrt[-a + b]], (a - b)/(a - c)])/Sqrt[-((a - x)*(b - x)*(c - x))] - (2*Sqrt[-a + b]*Sqrt[-((b - x)/(a - b))]*Sqrt[-((c - x)/(a - c))]*Sqrt[-a + x]*EllipticPi[(2*(a - b))/(2*a - b - c - d - Sqrt[b^2 - 2*b*c + c^2 - 4*a*d + 2*b*d + 2*c*d + d^2]), ArcSin[Sqrt[-a + x]/Sqrt[-a + b]], (a - b)/(a - c)])/Sqrt[-((a - x)*(b - x)*(c - x))] - (2*Sqrt[-a + b]*Sqrt[-((b - x)/(a - b))]*Sqrt[-((c - x)/(a - c))]*Sqrt[-a + x]*EllipticPi[(2*(a - b))/(2*a - b - c - d + Sqrt[b^2 - 2*b*c + c^2 - 4*a*d + 2*b*d + 2*c*d + d^2]), ArcSin[Sqrt[-a + x]/Sqrt[-a + b]], (a - b)/(a - c)])/Sqrt[-((a - x)*(b - x)*(c - x))]","C",16,7,58,0.1207,1,"{6718, 6728, 121, 120, 169, 538, 537}"
776,1,455,0,19.3841243,"\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","Int[(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 \sqrt{b-a} \sqrt{x-a} \sqrt{-\frac{b-x}{a-b}} \sqrt{-\frac{c-x}{a-c}} \Pi \left(-\frac{2 (a-b) d}{-2 a d+b d+c d-\sqrt{b^2 d^2-4 a d+2 b (1-c d) d+(c d+1)^2}+1};\sin ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{b-a}}\right)|\frac{a-b}{a-c}\right)}{d \sqrt{-((a-x) (b-x) (c-x))}}-\frac{2 \sqrt{b-a} \sqrt{x-a} \sqrt{-\frac{b-x}{a-b}} \sqrt{-\frac{c-x}{a-c}} \Pi \left(-\frac{2 (a-b) d}{-2 a d+b d+c d+\sqrt{b^2 d^2-4 a d+2 b (1-c d) d+(c d+1)^2}+1};\sin ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{b-a}}\right)|\frac{a-b}{a-c}\right)}{d \sqrt{-((a-x) (b-x) (c-x))}}+\frac{2 \sqrt{b-a} \sqrt{x-a} \sqrt{-\frac{b-x}{a-b}} \sqrt{-\frac{c-x}{a-c}} F\left(\sin ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{b-a}}\right)|\frac{a-b}{a-c}\right)}{d \sqrt{-((a-x) (b-x) (c-x))}}","\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*Sqrt[-a + b]*Sqrt[-((b - x)/(a - b))]*Sqrt[-((c - x)/(a - c))]*Sqrt[-a + x]*EllipticF[ArcSin[Sqrt[-a + x]/Sqrt[-a + b]], (a - b)/(a - c)])/(d*Sqrt[-((a - x)*(b - x)*(c - x))]) - (2*Sqrt[-a + b]*Sqrt[-((b - x)/(a - b))]*Sqrt[-((c - x)/(a - c))]*Sqrt[-a + x]*EllipticPi[(-2*(a - b)*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]), ArcSin[Sqrt[-a + x]/Sqrt[-a + b]], (a - b)/(a - c)])/(d*Sqrt[-((a - x)*(b - x)*(c - x))]) - (2*Sqrt[-a + b]*Sqrt[-((b - x)/(a - b))]*Sqrt[-((c - x)/(a - c))]*Sqrt[-a + x]*EllipticPi[(-2*(a - b)*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]), ArcSin[Sqrt[-a + x]/Sqrt[-a + b]], (a - b)/(a - c)])/(d*Sqrt[-((a - x)*(b - x)*(c - x))])","C",16,7,63,0.1111,1,"{6718, 6728, 121, 120, 169, 538, 537}"
777,1,262,0,2.3490295,"\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","Int[(-1 + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 + k^2*x^2)),x]","\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{1}{\sqrt{-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{1}{\sqrt{-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\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*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-(1/Sqrt[-k^2]), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[1/Sqrt[-k^2], ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",16,9,40,0.2250,0,"{6718, 6688, 6725, 714, 115, 934, 12, 168, 537}"
778,0,0,0,48.2161961,"\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","Int[(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]","\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","-\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*Sqrt[a - c]*(b - x)*Sqrt[-a + x]*EllipticF[ArcTan[Sqrt[-a + x]/Sqrt[a - c]], -((b - c)/(a - b))])/((a - b)*Sqrt[((a - c)*(b - x))/((a - b)*(c - x))]*Sqrt[-((a - x)*(b - x)*(c - x))]) - (2*(a - b)*(a - c)*d*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][1/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(a^2*(1 + (b*c - a*(b + c))/a^2)*d + 2*a*(1 - (b + c)/(2*a))*d*x^2 + d*x^4 - x^6)), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))] - (2*(a^2 + 2*a*d - (b + c)*d)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(a^2*(1 + (b*c - a*(b + c))/a^2)*d + 2*a*(1 - (b + c)/(2*a))*d*x^2 + d*x^4 - x^6)), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))] - (2*(2*a + d)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^4/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(a^2*(1 + (b*c - a*(b + c))/a^2)*d + 2*a*(1 - (b + c)/(2*a))*d*x^2 + d*x^4 - x^6)), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))] + (4*a*(a - b - c)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(-(a^2*(1 + (b*c - a*(b + c))/a^2)*d) - 2*a*(1 - (b + c)/(2*a))*d*x^2 - d*x^4 + x^6)), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))] + (4*(a - b - c)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^4/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(-(a^2*(1 + (b*c - a*(b + c))/a^2)*d) - 2*a*(1 - (b + c)/(2*a))*d*x^2 - d*x^4 + x^6)), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))] + (2*(3*b*c - a*(b + c))*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(-(a^2*d) + c*d*x^2 - d*x^4 + x^6 + a*d*(b + c - 2*x^2) + b*d*(-c + x^2))), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))]","F",0,0,0,0,-1,"{}"
779,-1,0,0,180.0012592,"\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","Int[((-2*c + a*x^3)*Sqrt[c + b*x^2 + a*x^3])/(c + a*x^3)^2,x]","\text{\$Aborted}","-\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,"$Aborted","F",0,0,0,0,-1,"{}"
780,1,290,0,2.1178249,"\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","Int[(-b + a^2*x^2)/((b + 2*a*b*x + a^2*x^2)*Sqrt[b*x + a^2*x^3]),x]","\frac{\sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{a} \sqrt[4]{b} \sqrt{a^2 x^3+b x}}-\frac{2 \sqrt[4]{-b} \sqrt{x} \sqrt{\frac{a^2 x^2}{b}+1} \Pi \left(\frac{\sqrt{-b}}{\left(\sqrt{b-1}-\sqrt{b}\right) \sqrt{b}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{-b}}\right)\right|-1\right)}{\sqrt{a} \sqrt{a^2 x^3+b x}}-\frac{2 \sqrt[4]{-b} \sqrt{x} \sqrt{\frac{a^2 x^2}{b}+1} \Pi \left(-\frac{\sqrt{-b}}{\left(\sqrt{b-1}+\sqrt{b}\right) \sqrt{b}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{-b}}\right)\right|-1\right)}{\sqrt{a} \sqrt{a^2 x^3+b x}}","-\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,"(Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(Sqrt[a]*b^(1/4)*Sqrt[b*x + a^2*x^3]) - (2*(-b)^(1/4)*Sqrt[x]*Sqrt[1 + (a^2*x^2)/b]*EllipticPi[Sqrt[-b]/((Sqrt[-1 + b] - Sqrt[b])*Sqrt[b]), ArcSin[(Sqrt[a]*Sqrt[x])/(-b)^(1/4)], -1])/(Sqrt[a]*Sqrt[b*x + a^2*x^3]) - (2*(-b)^(1/4)*Sqrt[x]*Sqrt[1 + (a^2*x^2)/b]*EllipticPi[-(Sqrt[-b]/((Sqrt[-1 + b] + Sqrt[b])*Sqrt[b])), ArcSin[(Sqrt[a]*Sqrt[x])/(-b)^(1/4)], -1])/(Sqrt[a]*Sqrt[b*x + a^2*x^3])","C",13,7,43,0.1628,0,"{2056, 6728, 329, 220, 933, 168, 537}"
781,0,0,0,53.0898124,"\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","Int[(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]","\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","-\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*Sqrt[a - c]*(b - x)*Sqrt[-a + x]*EllipticF[ArcTan[Sqrt[-a + x]/Sqrt[a - c]], -((b - c)/(a - b))])/((a - b)*d*Sqrt[((a - c)*(b - x))/((a - b)*(c - x))]*Sqrt[-((a - x)*(b - x)*(c - x))]) - (2*(a - b)*(a - c)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][1/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^2 + x^4 - d*x^6)), x], x, Sqrt[-a + x]])/(d*Sqrt[-((a - x)*(b - x)*(c - x))]) - (2*(2*a - b - c + a^2*d)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^2 + x^4 - d*x^6)), x], x, Sqrt[-a + x]])/(d*Sqrt[-((a - x)*(b - x)*(c - x))]) - (2*(1 + 2*a*d)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^4/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^2 + x^4 - d*x^6)), x], x, Sqrt[-a + x]])/(d*Sqrt[-((a - x)*(b - x)*(c - x))]) + (4*a*(a - b - c)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(-(a^2*(1 + (b*c - a*(b + c))/a^2)) - 2*a*(1 - (b + c)/(2*a))*x^2 - x^4 + d*x^6)), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))] + (4*(a - b - c)*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^4/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(-(a^2*(1 + (b*c - a*(b + c))/a^2)) - 2*a*(1 - (b + c)/(2*a))*x^2 - x^4 + d*x^6)), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))] + (2*(3*b*c - a*(b + c))*Sqrt[-a + x]*Sqrt[-b + x]*Sqrt[-c + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[a - b + x^2]*Sqrt[a - c + x^2]*(-(a^2*(1 + (b*c)/a^2)) + (b + c)*x^2 - x^4 + d*x^6 + a*(b + c - 2*x^2))), x], x, Sqrt[-a + x]])/Sqrt[-((a - x)*(b - x)*(c - x))]","F",0,0,0,0,-1,"{}"
782,1,46,0,0.0432354,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{x^5} \, dx","Int[((-1 + x^2)*Sqrt[1 + x^4])/x^5,x]","\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^4+1}\right)+\frac{1}{2} \sinh ^{-1}\left(x^2\right)+\frac{\sqrt{x^4+1} \left(1-2 x^2\right)}{4 x^4}","\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])/(4*x^4) + ArcSinh[x^2]/2 + ArcTanh[Sqrt[1 + x^4]]/4","A",7,7,18,0.3889,1,"{1252, 811, 844, 215, 266, 63, 207}"
783,1,44,0,0.038613,"\int \frac{\left(-1+x^2\right) \sqrt{1+x^4}}{x^3} \, dx","Int[((-1 + x^2)*Sqrt[1 + x^4])/x^3,x]","-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^4+1}\right)-\frac{1}{2} \sinh ^{-1}\left(x^2\right)+\frac{\sqrt{x^4+1} \left(x^2+1\right)}{2 x^2}","\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])/(2*x^2) - ArcSinh[x^2]/2 - ArcTanh[Sqrt[1 + x^4]]/2","A",7,7,18,0.3889,1,"{1252, 813, 844, 215, 266, 63, 207}"
784,1,56,0,0.04653,"\int \frac{\left(1+2 x^3\right) \sqrt{-1+x^6}}{x^7} \, dx","Int[((1 + 2*x^3)*Sqrt[-1 + x^6])/x^7,x]","\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\sqrt{x^6-1} \left(4 x^3+1\right)}{6 x^6}+\frac{2}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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 + 4*x^3)*Sqrt[-1 + x^6])/x^6 + ArcTan[Sqrt[-1 + x^6]]/6 + (2*ArcTanh[x^3/Sqrt[-1 + x^6]])/3","A",8,8,20,0.4000,1,"{1475, 811, 844, 217, 206, 266, 63, 203}"
785,1,56,0,0.0455299,"\int \frac{\left(1+2 x^3\right) \sqrt{-1+x^6}}{x^4} \, dx","Int[((1 + 2*x^3)*Sqrt[-1 + x^6])/x^4,x]","-\frac{2}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\sqrt{x^6-1} \left(1-2 x^3\right)}{3 x^3}+\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\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,"-1/3*((1 - 2*x^3)*Sqrt[-1 + x^6])/x^3 - (2*ArcTan[Sqrt[-1 + x^6]])/3 + ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",8,8,20,0.4000,1,"{1475, 813, 844, 217, 206, 266, 63, 203}"
786,1,720,0,13.0696622,"\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","Int[(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 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(-\frac{\sqrt[3]{-2} a b}{\sqrt[3]{-c-\sqrt{4 a^6 b^6+c^2}}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[3]{2} a b}{\sqrt[3]{-c-\sqrt{4 a^6 b^6+c^2}}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{(-1)^{2/3} \sqrt[3]{2} a b}{\sqrt[3]{-c-\sqrt{4 a^6 b^6+c^2}}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(-\frac{\sqrt[3]{-2} a b}{\sqrt[3]{\sqrt{4 a^6 b^6+c^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[3]{2} a b}{\sqrt[3]{\sqrt{4 a^6 b^6+c^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{(-1)^{2/3} \sqrt[3]{2} a b}{\sqrt[3]{\sqrt{4 a^6 b^6+c^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{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*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[-(((-2)^(1/3)*a*b)/(-c - Sqrt[4*a^6*b^6 + c^2])^(1/3)), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(2^(1/3)*a*b)/(-c - Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(2/3)*2^(1/3)*a*b)/(-c - Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[-(((-2)^(1/3)*a*b)/(-c + Sqrt[4*a^6*b^6 + c^2])^(1/3)), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(2^(1/3)*a*b)/(-c + Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(2/3)*2^(1/3)*a*b)/(-c + Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3])","B",92,13,50,0.2600,1,"{2056, 6715, 6728, 224, 221, 6725, 1725, 1219, 1218, 1248, 725, 204, 206}"
787,1,720,0,10.5673706,"\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","Int[(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 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(-\frac{\sqrt[3]{-2} a b}{\sqrt[3]{-c-\sqrt{4 a^6 b^6+c^2}}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[3]{2} a b}{\sqrt[3]{-c-\sqrt{4 a^6 b^6+c^2}}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{(-1)^{2/3} \sqrt[3]{2} a b}{\sqrt[3]{-c-\sqrt{4 a^6 b^6+c^2}}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(-\frac{\sqrt[3]{-2} a b}{\sqrt[3]{\sqrt{4 a^6 b^6+c^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[3]{2} a b}{\sqrt[3]{\sqrt{4 a^6 b^6+c^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{(-1)^{2/3} \sqrt[3]{2} a b}{\sqrt[3]{\sqrt{4 a^6 b^6+c^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{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*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[-(((-2)^(1/3)*a*b)/(-c - Sqrt[4*a^6*b^6 + c^2])^(1/3)), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(2^(1/3)*a*b)/(-c - Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(2/3)*2^(1/3)*a*b)/(-c - Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[-(((-2)^(1/3)*a*b)/(-c + Sqrt[4*a^6*b^6 + c^2])^(1/3)), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(2^(1/3)*a*b)/(-c + Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(2/3)*2^(1/3)*a*b)/(-c + Sqrt[4*a^6*b^6 + c^2])^(1/3), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3])","B",92,13,50,0.2600,1,"{2056, 6715, 6728, 224, 221, 6725, 1725, 1219, 1218, 1248, 725, 204, 206}"
788,0,0,0,1.4360447,"\int \frac{x-3 x^5}{\sqrt{x+x^5} \left(1-a x^2+2 x^4+x^8\right)} \, dx","Int[(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,"(2*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + x^8]*(1 - a*x^4 + 2*x^8 + x^16)), x], x, Sqrt[x]])/Sqrt[x + x^5] - (6*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^10/(Sqrt[1 + x^8]*(1 - a*x^4 + 2*x^8 + x^16)), x], x, Sqrt[x]])/Sqrt[x + x^5]","F",0,0,0,0,-1,"{}"
789,1,335,0,0.8922965,"\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","Int[(Sqrt[1 - 2*x^8]*(-1 + 2*x^8)*(1 + 2*x^8))/(x^7*(-1 + x^4 + 2*x^8)),x]","\frac{1}{15} \sqrt[4]{2} \left(3+5 \sqrt{2}\right) F\left(\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)-\frac{\left(1+\sqrt{2}\right) F\left(\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)}{2^{3/4}}+\frac{\left(1-\sqrt{2}\right) F\left(\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)}{2 \sqrt[4]{2}}+\frac{1}{15} 2^{3/4} \left(5-3 \sqrt{2}\right) F\left(\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)-\frac{2}{3} 2^{3/4} F\left(\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)+\frac{6}{5} \sqrt[4]{2} F\left(\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)+\frac{\Pi \left(-\frac{1}{\sqrt{2}};\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)}{2 \sqrt[4]{2}}+\frac{\Pi \left(\sqrt{2};\left.\sin ^{-1}\left(\sqrt[4]{2} x^2\right)\right|-1\right)}{2 \sqrt[4]{2}}-\frac{6}{5} \sqrt{1-2 x^8} x^6-\frac{\left(1-2 x^8\right)^{3/2}}{6 x^6}-\frac{2}{3} \sqrt{1-2 x^8} x^2-\frac{\left(1-2 x^8\right)^{3/2}}{2 x^2}+\frac{1}{15} \left(5-3 x^4\right) \sqrt{1-2 x^8} x^2+\frac{1}{15} \left(6 x^4+5\right) \sqrt{1-2 x^8} x^2","\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,"(-2*x^2*Sqrt[1 - 2*x^8])/3 - (6*x^6*Sqrt[1 - 2*x^8])/5 + (x^2*(5 - 3*x^4)*Sqrt[1 - 2*x^8])/15 + (x^2*(5 + 6*x^4)*Sqrt[1 - 2*x^8])/15 - (1 - 2*x^8)^(3/2)/(6*x^6) - (1 - 2*x^8)^(3/2)/(2*x^2) + (6*2^(1/4)*EllipticF[ArcSin[2^(1/4)*x^2], -1])/5 - (2*2^(3/4)*EllipticF[ArcSin[2^(1/4)*x^2], -1])/3 + (2^(3/4)*(5 - 3*Sqrt[2])*EllipticF[ArcSin[2^(1/4)*x^2], -1])/15 + ((1 - Sqrt[2])*EllipticF[ArcSin[2^(1/4)*x^2], -1])/(2*2^(1/4)) - ((1 + Sqrt[2])*EllipticF[ArcSin[2^(1/4)*x^2], -1])/2^(3/4) + (2^(1/4)*(3 + 5*Sqrt[2])*EllipticF[ArcSin[2^(1/4)*x^2], -1])/15 + EllipticPi[-(1/Sqrt[2]), ArcSin[2^(1/4)*x^2], -1]/(2*2^(1/4)) + EllipticPi[Sqrt[2], ArcSin[2^(1/4)*x^2], -1]/(2*2^(1/4))","C",47,17,41,0.4146,1,"{21, 6728, 275, 277, 195, 221, 279, 307, 1181, 424, 1491, 1209, 1177, 524, 248, 1213, 537}"
790,0,0,0,1.4501379,"\int \frac{-x+3 x^5}{\sqrt{x+x^5} \left(a-x^2+2 a x^4+a x^8\right)} \, dx","Int[(-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,"(-2*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^2/(Sqrt[1 + x^8]*(a - x^4 + 2*a*x^8 + a*x^16)), x], x, Sqrt[x]])/Sqrt[x + x^5] + (6*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^10/(Sqrt[1 + x^8]*(a - x^4 + 2*a*x^8 + a*x^16)), x], x, Sqrt[x]])/Sqrt[x + x^5]","F",0,0,0,0,-1,"{}"
791,0,0,0,2.3782828,"\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","Int[(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,"(28*b*x^(3/4)*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^20/((b + a*x^8)^(1/4)*(-2 + b*x^28 + a*x^36)), x], x, x^(1/4)])/(b*x^3 + a*x^5)^(1/4) + (36*a*x^(3/4)*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^28/((b + a*x^8)^(1/4)*(-2 + b*x^28 + a*x^36)), x], x, x^(1/4)])/(b*x^3 + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
792,1,141,0,0.9521167,"\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","Int[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) \log (1-4 x)}{187 \sqrt[5]{\left(4 x^2-13 x+3\right)^5}}+\frac{9 \left(4 x^2-13 x+3\right) \log (3-x)}{110 \sqrt[5]{\left(4 x^2-13 x+3\right)^5}}-\frac{13 \left(4 x^2-13 x+3\right) \log \left(x^2+1\right)}{340 \sqrt[5]{\left(4 x^2-13 x+3\right)^5}}+\frac{\left(4 x^2-13 x+3\right) \tan ^{-1}(x)}{170 \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)*ArcTan[x])/(170*((3 - 13*x + 4*x^2)^5)^(1/5)) - ((3 - 13*x + 4*x^2)*Log[1 - 4*x])/(187*((3 - 13*x + 4*x^2)^5)^(1/5)) + (9*(3 - 13*x + 4*x^2)*Log[3 - x])/(110*((3 - 13*x + 4*x^2)^5)^(1/5)) - (13*(3 - 13*x + 4*x^2)*Log[1 + x^2])/(340*((3 - 13*x + 4*x^2)^5)^(1/5))","B",9,8,65,0.1231,1,"{6688, 6720, 1075, 632, 31, 635, 203, 260}"
793,1,421,0,0.448877,"\int \frac{\sqrt[3]{1-2 x+x^2}}{2+x^2} \, dx","Int[(1 - 2*x + x^2)^(1/3)/(2 + x^2),x]","\frac{i \left(1-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^2-2 x+1} \log \left(\sqrt{2}+i x\right)}{4 \sqrt{2} (x-1)^{2/3}}-\frac{i \left(1+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^2-2 x+1} \log \left(x+i \sqrt{2}\right)}{4 \sqrt{2} (x-1)^{2/3}}-\frac{3 i \left(1-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^2-2 x+1} \log \left(\sqrt[3]{2 x-2}+\sqrt[3]{2 \left(1-i \sqrt{2}\right)}\right)}{4 \sqrt{2} (x-1)^{2/3}}+\frac{3 i \left(1+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^2-2 x+1} \log \left(\sqrt[3]{2 x-2}+\sqrt[3]{2 \left(1+i \sqrt{2}\right)}\right)}{4 \sqrt{2} (x-1)^{2/3}}-\frac{i \sqrt{\frac{3}{2}} \left(1-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^2-2 x+1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1-i \sqrt{2}}}}{\sqrt{3}}\right)}{2 (x-1)^{2/3}}+\frac{i \sqrt{\frac{3}{2}} \left(1+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^2-2 x+1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1+i \sqrt{2}}}}{\sqrt{3}}\right)}{2 (x-1)^{2/3}}","\frac{\sqrt[3]{(x-1)^2} \text{RootSum}\left[\text{$\#$1}^6+2 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)}{\text{$\#$1}^3+1}\&\right]}{2 (x-1)^{2/3}}",1,"((-1/2*I)*Sqrt[3/2]*(1 - I*Sqrt[2])^(2/3)*(1 - 2*x + x^2)^(1/3)*ArcTan[(1 - (2*(-1 + x)^(1/3))/(1 - I*Sqrt[2])^(1/3))/Sqrt[3]])/(-1 + x)^(2/3) + ((I/2)*Sqrt[3/2]*(1 + I*Sqrt[2])^(2/3)*(1 - 2*x + x^2)^(1/3)*ArcTan[(1 - (2*(-1 + x)^(1/3))/(1 + I*Sqrt[2])^(1/3))/Sqrt[3]])/(-1 + x)^(2/3) + ((I/4)*(1 - I*Sqrt[2])^(2/3)*(1 - 2*x + x^2)^(1/3)*Log[Sqrt[2] + I*x])/(Sqrt[2]*(-1 + x)^(2/3)) - ((I/4)*(1 + I*Sqrt[2])^(2/3)*(1 - 2*x + x^2)^(1/3)*Log[I*Sqrt[2] + x])/(Sqrt[2]*(-1 + x)^(2/3)) - (((3*I)/4)*(1 - I*Sqrt[2])^(2/3)*(1 - 2*x + x^2)^(1/3)*Log[(2*(1 - I*Sqrt[2]))^(1/3) + (-2 + 2*x)^(1/3)])/(Sqrt[2]*(-1 + x)^(2/3)) + (((3*I)/4)*(1 + I*Sqrt[2])^(2/3)*(1 - 2*x + x^2)^(1/3)*Log[(2*(1 + I*Sqrt[2]))^(1/3) + (-2 + 2*x)^(1/3)])/(Sqrt[2]*(-1 + x)^(2/3))","C",13,7,20,0.3500,1,"{970, 712, 50, 56, 617, 204, 31}"
794,1,417,0,0.4819983,"\int \frac{\sqrt[3]{1+2 x+x^2}}{3+x^2} \, dx","Int[(1 + 2*x + x^2)^(1/3)/(3 + x^2),x]","\frac{i \left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x^2+2 x+1} \log \left(\sqrt{3}+i x\right)}{4 \sqrt{3} (x+1)^{2/3}}-\frac{i \left(1-i \sqrt{3}\right)^{2/3} \sqrt[3]{x^2+2 x+1} \log \left(x+i \sqrt{3}\right)}{4 \sqrt{3} (x+1)^{2/3}}+\frac{i \sqrt{3} \left(1-i \sqrt{3}\right)^{2/3} \sqrt[3]{x^2+2 x+1} \log \left(-\sqrt[3]{2} \sqrt[3]{x+1}+\sqrt[3]{2 \left(1-i \sqrt{3}\right)}\right)}{4 (x+1)^{2/3}}-\frac{i \sqrt{3} \left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x^2+2 x+1} \log \left(-\sqrt[3]{2} \sqrt[3]{x+1}+\sqrt[3]{2 \left(1+i \sqrt{3}\right)}\right)}{4 (x+1)^{2/3}}+\frac{i \left(1-i \sqrt{3}\right)^{2/3} \sqrt[3]{x^2+2 x+1} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{x+1}}{\sqrt[3]{1-i \sqrt{3}}}}{\sqrt{3}}\right)}{2 (x+1)^{2/3}}-\frac{i \left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x^2+2 x+1} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{x+1}}{\sqrt[3]{1+i \sqrt{3}}}}{\sqrt{3}}\right)}{2 (x+1)^{2/3}}","\frac{\sqrt[3]{(x+1)^2} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+4\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-1}\&\right]}{2 (x+1)^{2/3}}",1,"((I/2)*(1 - I*Sqrt[3])^(2/3)*(1 + 2*x + x^2)^(1/3)*ArcTan[(1 + (2*(1 + x)^(1/3))/(1 - I*Sqrt[3])^(1/3))/Sqrt[3]])/(1 + x)^(2/3) - ((I/2)*(1 + I*Sqrt[3])^(2/3)*(1 + 2*x + x^2)^(1/3)*ArcTan[(1 + (2*(1 + x)^(1/3))/(1 + I*Sqrt[3])^(1/3))/Sqrt[3]])/(1 + x)^(2/3) + ((I/4)*(1 + I*Sqrt[3])^(2/3)*(1 + 2*x + x^2)^(1/3)*Log[Sqrt[3] + I*x])/(Sqrt[3]*(1 + x)^(2/3)) - ((I/4)*(1 - I*Sqrt[3])^(2/3)*(1 + 2*x + x^2)^(1/3)*Log[I*Sqrt[3] + x])/(Sqrt[3]*(1 + x)^(2/3)) + ((I/4)*Sqrt[3]*(1 - I*Sqrt[3])^(2/3)*(1 + 2*x + x^2)^(1/3)*Log[(2*(1 - I*Sqrt[3]))^(1/3) - 2^(1/3)*(1 + x)^(1/3)])/(1 + x)^(2/3) - ((I/4)*Sqrt[3]*(1 + I*Sqrt[3])^(2/3)*(1 + 2*x + x^2)^(1/3)*Log[(2*(1 + I*Sqrt[3]))^(1/3) - 2^(1/3)*(1 + x)^(1/3)])/(1 + x)^(2/3)","C",13,7,20,0.3500,1,"{970, 712, 50, 55, 617, 204, 31}"
795,1,87,0,0.1022833,"\int \frac{1}{(-1+x) \sqrt[4]{x+x^3}} \, dx","Int[1/((-1 + x)*(x + x^3)^(1/4)),x]","-\frac{4 \sqrt[4]{x^2+1} x^2 F_1\left(\frac{7}{8};1,\frac{1}{4};\frac{15}{8};x^2,-x^2\right)}{7 \sqrt[4]{x^3+x}}-\frac{4 \sqrt[4]{x^2+1} x F_1\left(\frac{3}{8};1,\frac{1}{4};\frac{11}{8};x^2,-x^2\right)}{3 \sqrt[4]{x^3+x}}","\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,"(-4*x*(1 + x^2)^(1/4)*AppellF1[3/8, 1, 1/4, 11/8, x^2, -x^2])/(3*(x + x^3)^(1/4)) - (4*x^2*(1 + x^2)^(1/4)*AppellF1[7/8, 1, 1/4, 15/8, x^2, -x^2])/(7*(x + x^3)^(1/4))","C",6,4,15,0.2667,0,"{2056, 959, 466, 510}"
796,1,386,0,1.0856556,"\int \frac{-1+x^4}{\sqrt{x+x^3} \left(1+x^4\right)} \, dx","Int[(-1 + x^4)/(Sqrt[x + x^3]*(1 + x^4)),x]","-\frac{\sqrt{x} \sqrt{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt{x^2+1}}\right)}{\sqrt[4]{2} \sqrt{x^3+x}}-\frac{\sqrt{x} \sqrt{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt{x^2+1}}\right)}{\sqrt[4]{2} \sqrt{x^3+x}}+\frac{i \left(\sqrt{2}+(1+i)\right) \sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{4 \sqrt{x^3+x}}+\frac{i \left(\sqrt{2}+(-1+i)\right) \sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{4 \sqrt{x^3+x}}+\frac{\left((-1-i)-i \sqrt{2}\right) \sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{4 \sqrt{x^3+x}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(1+(-1)^{3/4}\right) \sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^3+x}}+\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\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,"-((Sqrt[x]*Sqrt[1 + x^2]*ArcTan[(2^(1/4)*Sqrt[x])/Sqrt[1 + x^2]])/(2^(1/4)*Sqrt[x + x^3])) - (Sqrt[x]*Sqrt[1 + x^2]*ArcTanh[(2^(1/4)*Sqrt[x])/Sqrt[1 + x^2]])/(2^(1/4)*Sqrt[x + x^3]) + (Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[x + x^3] - ((1/4 - I/4)*(1 + (-1)^(3/4))*Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[x + x^3] + (((-1 - I) - I*Sqrt[2])*Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(4*Sqrt[x + x^3]) + ((I/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[x + x^3] + ((I/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[x + x^3]","C",23,9,22,0.4091,1,"{2056, 1586, 6715, 6725, 406, 220, 409, 1217, 1707}"
797,1,384,0,1.0310364,"\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt{1+x^4}} \, dx","Int[(1 + x^3)/((-1 + x^3)*Sqrt[1 + x^4]),x]","-\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}}-\frac{\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{3 \sqrt{2}}+\frac{\left(1-i \sqrt{3}\right) \tanh ^{-1}\left(\frac{2-\left(1+i \sqrt{3}\right) x^2}{\sqrt{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{3 \sqrt{2 \left(1+i \sqrt{3}\right)}}+\frac{\left(1+i \sqrt{3}\right) \tanh ^{-1}\left(\frac{4+\left(1+i \sqrt{3}\right)^2 x^2}{2 \sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{3 \sqrt{2 \left(1-i \sqrt{3}\right)}}-\frac{\left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}-\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}","-\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*ArcTan[x/Sqrt[1 + x^4]])/3 - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(3*Sqrt[2]) - ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/(3*Sqrt[2]) + ((1 - I*Sqrt[3])*ArcTanh[(2 - (1 + I*Sqrt[3])*x^2)/(Sqrt[2*(1 + I*Sqrt[3])]*Sqrt[1 + x^4])])/(3*Sqrt[2*(1 + I*Sqrt[3])]) + ((1 + I*Sqrt[3])*ArcTanh[(4 + (1 + I*Sqrt[3])^2*x^2)/(2*Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/(3*Sqrt[2*(1 - I*Sqrt[3])]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4]) - ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4]) - ((1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4])","C",29,12,22,0.5455,1,"{6725, 220, 2074, 1725, 1211, 1699, 206, 1248, 725, 6728, 1217, 1707}"
798,1,61,0,0.0430534,"\int \frac{-1+x}{x \sqrt[4]{1+x^4}} \, dx","Int[(-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",11,8,16,0.5000,1,"{1833, 240, 212, 206, 203, 266, 63, 298}"
799,1,61,0,0.0213226,"\int \frac{x^2}{\left(-b+a x^4\right)^{3/4}} \, dx","Int[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)}{2 a^{3/4}}-\frac{\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,"-1/2*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)]/(2*a^(3/4))","A",4,4,17,0.2353,1,"{331, 298, 203, 206}"
800,0,0,0,7.9519084,"\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","Int[((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,"((-I)*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(I - x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-2 + x^3 + x^4]) + (I*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(I*2^(1/8) - x), x], x, Sqrt[x]])/(2^(3/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) + (Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(2^(1/8) - x), x], x, Sqrt[x]])/(2^(3/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) - ((1 + I)*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/((-1)^(1/4)*2^(1/8) - x), x], x, Sqrt[x]])/(2^(7/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) - ((1 - I)*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(-((-1)^(3/4)*2^(1/8)) - x), x], x, Sqrt[x]])/(2^(7/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) - (I*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(I + x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-2 + x^3 + x^4]) + (I*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(I*2^(1/8) + x), x], x, Sqrt[x]])/(2^(3/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) + (Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(2^(1/8) + x), x], x, Sqrt[x]])/(2^(3/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) - ((1 + I)*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/((-1)^(1/4)*2^(1/8) + x), x], x, Sqrt[x]])/(2^(7/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) - ((1 - I)*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(-((-1)^(3/4)*2^(1/8)) + x), x], x, Sqrt[x]])/(2^(7/8)*Sqrt[x]*Sqrt[-2 + x^3 + x^4]) - (4*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][Sqrt[-2 + x^6 + x^8]/(-2 + 2*x^2 - 2*x^4 + x^6), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-2 + x^3 + x^4]) + (2*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][(x^2*Sqrt[-2 + x^6 + x^8])/(-2 + 2*x^2 - 2*x^4 + x^6), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-2 + x^3 + x^4]) + (2*Sqrt[-2*x + x^4 + x^5]*Defer[Subst][Defer[Int][(x^4*Sqrt[-2 + x^6 + x^8])/(-2 + 2*x^2 - 2*x^4 + x^6), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-2 + x^3 + x^4])","F",0,0,0,0,-1,"{}"
801,0,0,0,0.65165,"\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","Int[((-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{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"-3*Defer[Int][(1 - x^2 + x^3)^(2/3)/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6), x] + Defer[Int][(x^2*(1 - x^2 + x^3)^(2/3))/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6), x]","F",0,0,0,0,-1,"{}"
802,0,0,0,0.5113416,"\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx","Int[((-3 + x^2)*(1 - x^2 + x^3)^(2/3))/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6),x]","\int \frac{\left(-3+x^2\right) \left(1-x^2+x^3\right)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx","\text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2+1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-3}\&\right]",1,"-3*Defer[Int][(1 - x^2 + x^3)^(2/3)/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6), x] + Defer[Int][(x^2*(1 - x^2 + x^3)^(2/3))/(1 - 2*x^2 - x^3 + x^4 + x^5 + x^6), x]","F",0,0,0,0,-1,"{}"
803,1,67,0,0.1016844,"\int \frac{\sqrt{-1+x^6} \left(-1+2 x^6\right)^2}{x \left(-1+4 x^6\right)} \, dx","Int[(Sqrt[-1 + x^6]*(-1 + 2*x^6)^2)/(x*(-1 + 4*x^6)),x]","\frac{1}{9} \left(x^6-1\right)^{3/2}-\frac{\sqrt{x^6-1}}{4}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt{x^6-1}}{\sqrt{3}}\right)}{8 \sqrt{3}}","\frac{1}{36} \sqrt{x^6-1} \left(4 x^6-13\right)+\frac{1}{3} \tan ^{-1}\left(\sqrt{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt{x^6-1}}{\sqrt{3}}\right)}{8 \sqrt{3}}",1,"-1/4*Sqrt[-1 + x^6] + (-1 + x^6)^(3/2)/9 + ArcTan[Sqrt[-1 + x^6]]/3 - ArcTan[(2*Sqrt[-1 + x^6])/Sqrt[3]]/(8*Sqrt[3])","A",10,5,31,0.1613,1,"{573, 178, 88, 63, 203}"
804,0,0,0,0.9164697,"\int \frac{1}{\sqrt[3]{x+x^3} \left(b+a x^6\right)} \, dx","Int[1/((x + x^3)^(1/3)*(b + a*x^6)),x]","\int \frac{1}{\sqrt[3]{x+x^3} \left(b+a x^6\right)} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^9 b-3 \text{$\#$1}^6 b+3 \text{$\#$1}^3 b+a-b\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/6*(x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(1/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(2/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(1/3)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(4/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(5/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(2/3)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(7/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(8/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
805,0,0,0,0.7432718,"\int \frac{1}{\sqrt[3]{x+x^3} \left(b+a x^6\right)} \, dx","Int[1/((x + x^3)^(1/3)*(b + a*x^6)),x]","\int \frac{1}{\sqrt[3]{x+x^3} \left(b+a x^6\right)} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^9 b-3 \text{$\#$1}^6 b+3 \text{$\#$1}^3 b+a-b\&,\frac{\log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 b}",1,"-1/6*(x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(1/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(2/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(1/3)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(4/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(5/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(2/3)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) + (-1)^(7/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-b^(1/9) - (-1)^(8/9)*a^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*b^(8/9)*(x + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
806,1,444,0,2.1127451,"\int \frac{-b+a x^4}{\left(b-2 x^2+a x^4\right) \sqrt[4]{b x^2+a x^6}} \, dx","Int[(-b + a*x^4)/((b - 2*x^2 + a*x^4)*(b*x^2 + a*x^6)^(1/4)),x]","-\frac{2 x \sqrt[4]{\frac{a x^4}{b}+1} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{a^2 x^4}{-a b-2 \sqrt{1-a b}+2},-\frac{a x^4}{b}\right)}{\sqrt[4]{a x^6+b x^2}}-\frac{2 x \sqrt[4]{\frac{a x^4}{b}+1} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{a^2 x^4}{-a b+2 \sqrt{1-a b}+2},-\frac{a x^4}{b}\right)}{\sqrt[4]{a x^6+b x^2}}-\frac{2 a x^3 \left(1-\sqrt{1-a b}\right) \sqrt[4]{\frac{a x^4}{b}+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{a^2 x^4}{-a b-2 \sqrt{1-a b}+2},-\frac{a x^4}{b}\right)}{5 \left(-a b-2 \sqrt{1-a b}+2\right) \sqrt[4]{a x^6+b x^2}}-\frac{2 a x^3 \left(\sqrt{1-a b}+1\right) \sqrt[4]{\frac{a x^4}{b}+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{a^2 x^4}{-a b+2 \sqrt{1-a b}+2},-\frac{a x^4}{b}\right)}{5 \left(-a b+2 \sqrt{1-a b}+2\right) \sqrt[4]{a x^6+b x^2}}+\frac{2 x \sqrt[4]{\frac{a x^4}{b}+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-\frac{a x^4}{b}\right)}{\sqrt[4]{a x^6+b x^2}}","-\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,"(-2*x*(1 + (a*x^4)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (a^2*x^4)/(2 - a*b - 2*Sqrt[1 - a*b]), -((a*x^4)/b)])/(b*x^2 + a*x^6)^(1/4) - (2*x*(1 + (a*x^4)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (a^2*x^4)/(2 - a*b + 2*Sqrt[1 - a*b]), -((a*x^4)/b)])/(b*x^2 + a*x^6)^(1/4) - (2*a*(1 - Sqrt[1 - a*b])*x^3*(1 + (a*x^4)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (a^2*x^4)/(2 - a*b - 2*Sqrt[1 - a*b]), -((a*x^4)/b)])/(5*(2 - a*b - 2*Sqrt[1 - a*b])*(b*x^2 + a*x^6)^(1/4)) - (2*a*(1 + Sqrt[1 - a*b])*x^3*(1 + (a*x^4)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (a^2*x^4)/(2 - a*b + 2*Sqrt[1 - a*b]), -((a*x^4)/b)])/(5*(2 - a*b + 2*Sqrt[1 - a*b])*(b*x^2 + a*x^6)^(1/4)) + (2*x*(1 + (a*x^4)/b)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -((a*x^4)/b)])/(b*x^2 + a*x^6)^(1/4)","C",20,10,39,0.2564,0,"{2056, 6715, 6728, 246, 245, 1438, 430, 429, 511, 510}"
807,0,0,0,0.2759276,"\int \frac{\left(4+x^5\right) \sqrt{1-2 x^5+x^8+x^{10}}}{x^9} \, dx","Int[((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,"4*Defer[Int][Sqrt[1 - 2*x^5 + x^8 + x^10]/x^9, x] + Defer[Int][Sqrt[1 - 2*x^5 + x^8 + x^10]/x^4, x]","F",0,0,0,0,-1,"{}"
808,0,0,0,0.5482214,"\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right)^{2/3}}{1-x^6+x^{12}} \, dx","Int[((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{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^6+x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"-1/2*((1 + I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x^3), x])/Sqrt[1 - I*Sqrt[3]] - ((1 - I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x^3), x])/(2*Sqrt[1 + I*Sqrt[3]]) - ((1 + I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x^3), x])/(2*Sqrt[1 - I*Sqrt[3]]) - ((1 - I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x^3), x])/(2*Sqrt[1 + I*Sqrt[3]])","F",0,0,0,0,-1,"{}"
809,0,0,0,0.4093282,"\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right)^{2/3}}{1-x^6+x^{12}} \, dx","Int[((1 + x^6)*(-1 + x^3 + x^6)^(2/3))/(1 - x^6 + x^12),x]","\int \frac{\left(1+x^6\right) \left(-1+x^3+x^6\right)^{2/3}}{1-x^6+x^{12}} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^6+x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"-1/2*((1 + I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x^3), x])/Sqrt[1 - I*Sqrt[3]] - ((1 - I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x^3), x])/(2*Sqrt[1 + I*Sqrt[3]]) - ((1 + I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x^3), x])/(2*Sqrt[1 - I*Sqrt[3]]) - ((1 - I*Sqrt[3])*Defer[Int][(-1 + x^3 + x^6)^(2/3)/(Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x^3), x])/(2*Sqrt[1 + I*Sqrt[3]])","F",0,0,0,0,-1,"{}"
810,0,0,0,1.5344949,"\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","Int[((-2 + 5*x^7)*(2*x + x^3 + 2*x^8)^(1/3))/(4 + x^4 + 8*x^7 + 4*x^14),x]","\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{2 x^8+x^3+2 x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"(-6*(2*x + x^3 + 2*x^8)^(1/3)*Defer[Subst][Defer[Int][(x^3*(2 + x^6 + 2*x^21)^(1/3))/(4 + x^12 + 8*x^21 + 4*x^42), x], x, x^(1/3)])/(x^(1/3)*(2 + x^2 + 2*x^7)^(1/3)) + (15*(2*x + x^3 + 2*x^8)^(1/3)*Defer[Subst][Defer[Int][(x^24*(2 + x^6 + 2*x^21)^(1/3))/(4 + x^12 + 8*x^21 + 4*x^42), x], x, x^(1/3)])/(x^(1/3)*(2 + x^2 + 2*x^7)^(1/3))","F",0,0,0,0,-1,"{}"
811,0,0,0,1.0601033,"\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","Int[((-2 + 5*x^7)*(2*x + x^3 + 2*x^8)^(1/3))/(4 + x^4 + 8*x^7 + 4*x^14),x]","\int \frac{\left(-2+5 x^7\right) \sqrt[3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3+2\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{2 x^8+x^3+2 x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]",1,"(-6*(2*x + x^3 + 2*x^8)^(1/3)*Defer[Subst][Defer[Int][(x^3*(2 + x^6 + 2*x^21)^(1/3))/(4 + x^12 + 8*x^21 + 4*x^42), x], x, x^(1/3)])/(x^(1/3)*(2 + x^2 + 2*x^7)^(1/3)) + (15*(2*x + x^3 + 2*x^8)^(1/3)*Defer[Subst][Defer[Int][(x^24*(2 + x^6 + 2*x^21)^(1/3))/(4 + x^12 + 8*x^21 + 4*x^42), x], x, x^(1/3)])/(x^(1/3)*(2 + x^2 + 2*x^7)^(1/3))","F",0,0,0,0,-1,"{}"
812,1,61,0,0.0298798,"\int \frac{1}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[1/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\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}}","\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,"-1/3*b^2/(a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/a","A",3,2,23,0.08696,1,"{2117, 14}"
813,1,81,0,0.0249621,"\int x^{10} \sqrt[4]{-1+x^4} \, dx","Int[x^10*(-1 + x^4)^(1/4),x]","\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}{12} \sqrt[4]{x^4-1} x^{11}-\frac{1}{96} \sqrt[4]{x^4-1} x^7-\frac{7}{384} \sqrt[4]{x^4-1} x^3","\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,"(-7*x^3*(-1 + x^4)^(1/4))/384 - (x^7*(-1 + x^4)^(1/4))/96 + (x^11*(-1 + x^4)^(1/4))/12 + (7*ArcTan[x/(-1 + x^4)^(1/4)])/256 - (7*ArcTanh[x/(-1 + x^4)^(1/4)])/256","A",7,6,13,0.4615,1,"{279, 321, 331, 298, 203, 206}"
814,1,81,0,0.0243066,"\int x^{10} \sqrt[4]{1+x^4} \, dx","Int[x^10*(1 + x^4)^(1/4),x]","-\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}{12} \sqrt[4]{x^4+1} x^{11}+\frac{1}{96} \sqrt[4]{x^4+1} x^7-\frac{7}{384} \sqrt[4]{x^4+1} x^3","-\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,"(-7*x^3*(1 + x^4)^(1/4))/384 + (x^7*(1 + x^4)^(1/4))/96 + (x^11*(1 + x^4)^(1/4))/12 - (7*ArcTan[x/(1 + x^4)^(1/4)])/256 + (7*ArcTanh[x/(1 + x^4)^(1/4)])/256","A",7,6,13,0.4615,1,"{279, 321, 331, 298, 203, 206}"
815,1,477,0,0.5067642,"\int \frac{1+x^2}{\left(1-x^2+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Int[(1 + x^2)/((1 - x^2 + x^4)*(x^2 + x^4)^(1/4)),x]","-\frac{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \left(\sqrt{3}+i\right) \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[4]{x^2+1}}\right)}{\left(-\sqrt{3}+i\right) \sqrt[4]{x^4+x^2}}-\frac{\left(-\sqrt{3}+i\right) \sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^2+1}}\right)}{\left(\sqrt{3}+i\right) \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \left(\sqrt{3}+i\right) \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[4]{x^2+1}}\right)}{\left(-\sqrt{3}+i\right) \sqrt[4]{x^4+x^2}}-\frac{\left(-\sqrt{3}+i\right) \sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^2+1}}\right)}{\left(\sqrt{3}+i\right) \sqrt[4]{x^4+x^2}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-3}\&\right]",1,"-((((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(I + Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(1 + x^2)^(1/4))])/((I - Sqrt[3])*(x^2 + x^4)^(1/4))) - ((I - Sqrt[3])*((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(1 + x^2)^(1/4))])/((I + Sqrt[3])*(x^2 + x^4)^(1/4)) - (((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(I + Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(1 + x^2)^(1/4))])/((I - Sqrt[3])*(x^2 + x^4)^(1/4)) - ((I - Sqrt[3])*((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(1 + x^2)^(1/4))])/((I + Sqrt[3])*(x^2 + x^4)^(1/4))","C",21,11,29,0.3793,1,"{2056, 1269, 1428, 408, 240, 212, 206, 203, 377, 208, 205}"
816,1,413,0,0.4170231,"\int \frac{1}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"-1/2*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",11,7,28,0.2500,1,"{2056, 1270, 1429, 377, 212, 206, 203}"
817,1,413,0,0.351787,"\int \frac{1}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} b \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{4 b}",1,"-1/2*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",11,7,28,0.2500,1,"{2056, 1270, 1429, 377, 212, 206, 203}"
818,0,0,0,0.6761612,"\int \frac{1-x^2}{x \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(1 - x^2)/(x*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{1-x^2}{x \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","\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,"Defer[Int][1/(x*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - Defer[Int][x/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x]","F",0,0,0,0,-1,"{}"
819,0,0,0,1.9167738,"\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","Int[(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,"(7*x^3)/(8*a*Sqrt[x + x^5]) + x^3/(2*a*(1 + x^4)*Sqrt[x + x^5]) - (7*x^3*Sqrt[1 + x^4]*Hypergeometric2F1[1/2, 5/8, 13/8, -x^4])/(40*a*Sqrt[x + x^5]) - (8*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^4/((1 + x^8)^(5/2)*(a - x^2 + a*x^8)), x], x, Sqrt[x]])/Sqrt[x + x^5] + (6*Sqrt[x]*Sqrt[1 + x^4]*Defer[Subst][Defer[Int][x^6/((1 + x^8)^(5/2)*(a - x^2 + a*x^8)), x], x, Sqrt[x]])/(a*Sqrt[x + x^5])","F",0,0,0,0,-1,"{}"
820,0,0,0,2.7135041,"\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","Int[((-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,"(4*(1 + x^4)^(1/4)*Hypergeometric2F1[-21/16, 1/4, -5/16, -x^4])/(7*x^5*(x + x^5)^(1/4)) + (8*(1 + x^4)^(1/4)*Hypergeometric2F1[-5/16, 1/4, 11/16, -x^4])/(5*x*(x + x^5)^(1/4)) - (4*x*(1 + x^4)^(1/4)*Hypergeometric2F1[3/16, 1/4, 19/16, -x^4])/(3*(x + x^5)^(1/4)) + (4*x^3*(1 + x^4)^(1/4)*Hypergeometric2F1[1/4, 11/16, 27/16, -x^4])/(11*(x + x^5)^(1/4)) + (16*x^(1/4)*(1 + x^4)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 + x^16)^(1/4)*(1 - x^12 + x^16)), x], x, x^(1/4)])/(x + x^5)^(1/4) - (4*x^(1/4)*(1 + x^4)^(1/4)*Defer[Subst][Defer[Int][x^14/((1 + x^16)^(1/4)*(1 - x^12 + x^16)), x], x, x^(1/4)])/(x + x^5)^(1/4)","F",0,0,0,0,-1,"{}"
821,1,101,0,0.0623423,"\int \frac{1+x^2}{\sqrt{1+\sqrt{1+x}}} \, dx","Int[(1 + x^2)/Sqrt[1 + Sqrt[1 + x]],x]","\frac{4}{11} \left(\sqrt{x+1}+1\right)^{11/2}-\frac{20}{9} \left(\sqrt{x+1}+1\right)^{9/2}+\frac{32}{7} \left(\sqrt{x+1}+1\right)^{7/2}-\frac{16}{5} \left(\sqrt{x+1}+1\right)^{5/2}+\frac{4}{3} \left(\sqrt{x+1}+1\right)^{3/2}-4 \sqrt{\sqrt{x+1}+1}","\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]] + (4*(1 + Sqrt[1 + x])^(3/2))/3 - (16*(1 + Sqrt[1 + x])^(5/2))/5 + (32*(1 + Sqrt[1 + x])^(7/2))/7 - (20*(1 + Sqrt[1 + x])^(9/2))/9 + (4*(1 + Sqrt[1 + x])^(11/2))/11","A",3,2,19,0.1053,1,"{1900, 1620}"
822,0,0,0,0.5049341,"\int \frac{-1+2 x}{(1+x) \sqrt{-a^2 x^2+(1+x)^6}} \, dx","Int[(-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,"2*Defer[Int][1/Sqrt[-(a^2*x^2) + (1 + x)^6], x] - 3*Defer[Int][1/((1 + x)*Sqrt[-(a^2*x^2) + (1 + x)^6]), x]","F",0,0,0,0,-1,"{}"
823,1,62,0,0.2517211,"\int \frac{x}{\sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Int[x/(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)),x]","\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}}","\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,"(-2*b)/(5*a^2*(a*x + Sqrt[-b + a^2*x^2])^(5/4)) + (2*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(3*a^2)","A",3,2,40,0.05000,1,"{2120, 14}"
824,1,62,0,0.0265879,"\int \sqrt{a x+\sqrt{b^2+a^2 x^2}} \, dx","Int[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],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}}","\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,"-(b^2/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])) + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(3*a)","A",3,2,23,0.08696,1,"{2117, 14}"
825,1,61,0,0.0420683,"\int \frac{1}{\left(1+\sqrt{x}\right) \sqrt{-\sqrt{x}+x}} \, dx","Int[1/((1 + Sqrt[x])*Sqrt[-Sqrt[x] + x]),x]","\sqrt{2} \tanh ^{-1}\left(\frac{1-3 \sqrt{x}}{2 \sqrt{2} \sqrt{x-\sqrt{x}}}\right)+4 \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x-\sqrt{x}}}\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]*ArcTanh[(1 - 3*Sqrt[x])/(2*Sqrt[2]*Sqrt[-Sqrt[x] + x])] + 4*ArcTanh[Sqrt[x]/Sqrt[-Sqrt[x] + x]]","A",6,5,23,0.2174,1,"{1397, 843, 620, 206, 724}"
826,1,273,0,0.8100115,"\int \frac{x}{\left(-1+x^2\right) \sqrt{x+x^2+x^3}} \, dx","Int[x/((-1 + x^2)*Sqrt[x + x^2 + x^3]),x]","\frac{2 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(1-i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{2 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-1+i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}","\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,"(2*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(1 - I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (2*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-1 + I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3])","C",19,9,21,0.4286,0,"{2056, 6725, 943, 716, 1103, 934, 169, 538, 537}"
827,0,0,0,3.3150503,"\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","Int[(-(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]","\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","\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,"2*Defer[Int][1/Sqrt[x*(-a + x)*(-b + x)*(-c + x)], x] - a*(b*c + 2*d)*Defer[Int][1/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*d + (b*c - d)*x - (b + c)*x^2 + x^3)), x] - 2*(b*c - a*(b + c) - d)*Defer[Int][x/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*d + (b*c - d)*x - (b + c)*x^2 + x^3)), x] - (3*a - b - c)*Defer[Int][x^2/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a*d + (b*c - d)*x - (b + c)*x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
828,1,63,0,0.0926574,"\int \frac{3 b+a x^3}{x \left(-b+a x^3\right) \sqrt{b+a x^3}} \, dx","Int[(3*b + a*x^3)/(x*(-b + a*x^3)*Sqrt[b + a*x^3]),x]","\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}}","\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*ArcTanh[Sqrt[b + a*x^3]/Sqrt[b]])/Sqrt[b] - (4*Sqrt[2]*ArcTanh[Sqrt[b + a*x^3]/(Sqrt[2]*Sqrt[b])])/(3*Sqrt[b])","A",6,5,35,0.1429,1,"{573, 156, 63, 208, 207}"
829,0,0,0,3.012115,"\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","Int[((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]","\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","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,"2*(2 - b)*Defer[Int][Sqrt[c + b*x^2 + a*x^3]/(-c + (2 - b)*x^2 - a*x^3), x] - 2*(3 - b)*Defer[Int][Sqrt[c + b*x^2 + a*x^3]/(-c + (3 - b)*x^2 - a*x^3), x] + 3*a*Defer[Int][(x*Sqrt[c + b*x^2 + a*x^3])/(-c + (3 - b)*x^2 - a*x^3), x] + 3*a*Defer[Int][(x*Sqrt[c + b*x^2 + a*x^3])/(c - (2 - b)*x^2 + a*x^3), x]","F",0,0,0,0,-1,"{}"
830,0,0,0,4.0924885,"\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","Int[(-(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]","\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","\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,"(2*Defer[Int][1/Sqrt[x*(-a + x)*(-b + x)*(-c + x)], x])/d - (a*(2 + b*c*d)*Defer[Int][1/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a - (1 - b*c*d)*x - (b + c)*d*x^2 + d*x^3)), x])/d + (2*(1 - b*c*d + a*(b + c)*d)*Defer[Int][x/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a - (1 - b*c*d)*x - (b + c)*d*x^2 + d*x^3)), x])/d - (3*a - b - c)*Defer[Int][x^2/(Sqrt[x*(-a + x)*(-b + x)*(-c + x)]*(a - (1 - b*c*d)*x - (b + c)*d*x^2 + d*x^3)), x]","F",0,0,0,0,-1,"{}"
831,1,380,0,1.0399181,"\int \frac{-1+x^3}{\left(1+x^3\right) \sqrt{1+x^4}} \, dx","Int[(-1 + x^3)/((1 + x^3)*Sqrt[1 + x^4]),x]","-\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}}+\frac{\tanh ^{-1}\left(\frac{x^2+1}{\sqrt{2} \sqrt{x^4+1}}\right)}{3 \sqrt{2}}-\frac{\left(1+i \sqrt{3}\right) \tanh ^{-1}\left(\frac{2-\left(1-i \sqrt{3}\right) x^2}{\sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{3 \sqrt{2 \left(1-i \sqrt{3}\right)}}-\frac{\left(1-i \sqrt{3}\right) \tanh ^{-1}\left(\frac{2-\left(1+i \sqrt{3}\right) x^2}{\sqrt{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{3 \sqrt{2 \left(1+i \sqrt{3}\right)}}-\frac{\left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}-\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}","-\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*ArcTan[x/Sqrt[1 + x^4]])/3 - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(3*Sqrt[2]) + ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/(3*Sqrt[2]) - ((1 + I*Sqrt[3])*ArcTanh[(2 - (1 - I*Sqrt[3])*x^2)/(Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/(3*Sqrt[2*(1 - I*Sqrt[3])]) - ((1 - I*Sqrt[3])*ArcTanh[(2 - (1 + I*Sqrt[3])*x^2)/(Sqrt[2*(1 + I*Sqrt[3])]*Sqrt[1 + x^4])])/(3*Sqrt[2*(1 + I*Sqrt[3])]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4]) - ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4]) - ((1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4])","C",29,12,22,0.5455,1,"{6725, 220, 2074, 1725, 1211, 1699, 206, 1248, 725, 6728, 1217, 1707}"
832,1,127,0,0.1165317,"\int x^4 \sqrt[4]{-x+x^4} \, dx","Int[x^4*(-x + x^4)^(1/4),x]","\frac{1}{6} \sqrt[4]{x^4-x} x^5-\frac{1}{24} \sqrt[4]{x^4-x} x^2+\frac{\left(x^3-1\right)^{3/4} x^{3/4} \tan ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{16 \left(x^4-x\right)^{3/4}}-\frac{\left(x^3-1\right)^{3/4} x^{3/4} \tanh ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{16 \left(x^4-x\right)^{3/4}}","\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,"-1/24*(x^2*(-x + x^4)^(1/4)) + (x^5*(-x + x^4)^(1/4))/6 + (x^(3/4)*(-1 + x^3)^(3/4)*ArcTan[x^(3/4)/(-1 + x^3)^(1/4)])/(16*(-x + x^4)^(3/4)) - (x^(3/4)*(-1 + x^3)^(3/4)*ArcTanh[x^(3/4)/(-1 + x^3)^(1/4)])/(16*(-x + x^4)^(3/4))","B",9,9,15,0.6000,1,"{2021, 2024, 2032, 329, 275, 331, 298, 203, 206}"
833,1,122,0,0.0910642,"\int \sqrt[4]{-x^3+x^4} \, dx","Int[(-x^3 + x^4)^(1/4),x]","\frac{1}{2} \sqrt[4]{x^4-x^3} x-\frac{1}{8} \sqrt[4]{x^4-x^3}-\frac{3 (x-1)^{3/4} x^{9/4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{16 \left(x^4-x^3\right)^{3/4}}-\frac{3 (x-1)^{3/4} x^{9/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{16 \left(x^4-x^3\right)^{3/4}}","\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,"-1/8*(-x^3 + x^4)^(1/4) + (x*(-x^3 + x^4)^(1/4))/2 - (3*(-1 + x)^(3/4)*x^(9/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(16*(-x^3 + x^4)^(3/4)) - (3*(-1 + x)^(3/4)*x^(9/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(16*(-x^3 + x^4)^(3/4))","A",8,8,13,0.6154,1,"{2004, 2024, 2032, 63, 240, 212, 206, 203}"
834,0,0,0,1.6927809,"\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","Int[(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]","\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","-\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,"-3*Defer[Int][Sqrt[2 - x^3 - x^4]/(-2 - 3*x^2 + x^3 + x^4), x] + (3*Defer[Int][(x*Sqrt[2 - x^3 - x^4])/(-2 - 3*x^2 + x^3 + x^4), x])/2 + 2*Defer[Int][(x^2*Sqrt[2 - x^3 - x^4])/(-2 - 3*x^2 + x^3 + x^4), x] + Defer[Int][Sqrt[2 - x^3 - x^4]/(-2 - x^2 + x^3 + x^4), x] - (3*Defer[Int][(x*Sqrt[2 - x^3 - x^4])/(-2 - x^2 + x^3 + x^4), x])/2 - 2*Defer[Int][(x^2*Sqrt[2 - x^3 - x^4])/(-2 - x^2 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
835,1,573,0,1.1731594,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x \left(b+a x+x^2\right)} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/(x*(b + a*x + x^2)),x]","\frac{2 \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}","-\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,"(2*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4)) - (2*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4)) - (2*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4)) + (2*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4))","B",23,11,29,0.3793,1,"{2056, 911, 105, 63, 331, 298, 203, 206, 93, 205, 208}"
836,1,573,0,0.7067184,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x \left(b+a x+x^2\right)} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/(x*(b + a*x + x^2)),x]","\frac{2 \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{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+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt{a^2-4 b} \sqrt[4]{a x+b}}","-\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,"(2*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4)) - (2*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4)) - (2*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4)) + (2*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*x^(1/4))/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(1/4)*Sqrt[a^2 - 4*b]*x^(3/4)*(b + a*x)^(1/4))","B",23,11,29,0.3793,1,"{2056, 911, 105, 63, 331, 298, 203, 206, 93, 205, 208}"
837,1,49,0,0.05656,"\int \frac{x^2 \left(-4+x^6\right)}{\sqrt{-1+x^6} \left(2+x^6\right)} \, dx","Int[(x^2*(-4 + x^6))/(Sqrt[-1 + x^6]*(2 + x^6)),x]","\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)-\sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x^3}{\sqrt{x^6-1}}\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]]/3 - Sqrt[2/3]*ArcTanh[(Sqrt[3/2]*x^3)/Sqrt[-1 + x^6]]","A",6,5,25,0.2000,1,"{575, 523, 217, 206, 377}"
838,0,0,0,2.3241794,"\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","Int[((-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,"(4*(1 - x^5)^(1/4)*Hypergeometric2F1[-21/20, -3/4, -1/20, x^5])/(7*x^5*(-x + x^6)^(1/4)) - (8*(1 - x^5)^(1/4)*Hypergeometric2F1[-3/4, -9/20, 11/20, x^5])/(3*x^2*(-x + x^6)^(1/4)) + (8*(1 - x^5)^(1/4)*Hypergeometric2F1[-3/4, -1/20, 19/20, x^5])/(-x + x^6)^(1/4) - (24*x^(1/4)*(-1 + x^5)^(1/4)*Defer[Subst][Defer[Int][(x^2*(-1 + x^20)^(3/4))/(-1 - x^12 + x^20), x], x, x^(1/4)])/(-x + x^6)^(1/4) + (40*x^(1/4)*(-1 + x^5)^(1/4)*Defer[Subst][Defer[Int][(x^10*(-1 + x^20)^(3/4))/(-1 - x^12 + x^20), x], x, x^(1/4)])/(-x + x^6)^(1/4)","F",0,0,0,0,-1,"{}"
839,1,1234,0,3.4890921,"\int \frac{\sqrt{1+x^3} \left(2+2 x^3+x^6\right)}{x^7 \left(-1+x^6\right)} \, dx","Int[(Sqrt[1 + x^3]*(2 + 2*x^3 + x^6))/(x^7*(-1 + x^6)),x]","\frac{5 i (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{(3-6 i)-(2-3 i) \sqrt{3}}{(4+6 i)-(2+4 i) \sqrt{3}}} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{3 \sqrt{2} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{10 \sqrt{\frac{(6-3 i)-(3-2 i) \sqrt{3}}{(-6-4 i)+(4+2 i) \sqrt{3}}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{(6-3 i)-(3-2 i) \sqrt{3}}{(-6-4 i)+(4+2 i) \sqrt{3}}} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{3^{3/4} \left(3 i-\sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{5 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{2} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{3 \sqrt{2} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{5}{2} \tanh ^{-1}\left(\sqrt{x^3+1}\right)-\frac{20 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \left(1+(2+i) \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{20 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \left(1+(2-i) \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{10 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{40 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(-\frac{\left(i+(1+2 i) \sqrt{3}\right)^2}{\left(1-(2+i) \sqrt{3}\right)^2};\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \left(7+i \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{40 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(-\frac{\left(1+(2+i) \sqrt{3}\right)^2}{\left(i-(1+2 i) \sqrt{3}\right)^2};\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \left(7-i \sqrt{3}\right) \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{20 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97+56 \sqrt{3};\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{5 \sqrt{x^3+1}}{6 x^3}+\frac{\sqrt{x^3+1}}{3 x^6}","\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,"Sqrt[1 + x^3]/(3*x^6) + (5*Sqrt[1 + x^3])/(6*x^3) + (((5*I)/3)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[((3 - 6*I) - (2 - 3*I)*Sqrt[3])/((4 + 6*I) - (2 + 4*I)*Sqrt[3])]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(Sqrt[2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (10*Sqrt[((6 - 3*I) - (3 - 2*I)*Sqrt[3])/((-6 - 4*I) + (4 + 2*I)*Sqrt[3])]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[((6 - 3*I) - (3 - 2*I)*Sqrt[3])/((-6 - 4*I) + (4 + 2*I)*Sqrt[3])]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(3^(3/4)*(3*I - Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (5*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTanh[Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]/(Sqrt[2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(3*Sqrt[2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (5*ArcTanh[Sqrt[1 + x^3]])/2 - (10*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[2 + Sqrt[3]]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (20*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*(1 + (2 - I)*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (20*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*(1 + (2 + I)*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (40*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[-((I + (1 + 2*I)*Sqrt[3])^2/(1 - (2 + I)*Sqrt[3])^2), ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*(7 + I*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (40*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[-((1 + (2 + I)*Sqrt[3])^2/(I - (1 + 2*I)*Sqrt[3])^2), ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*(7 - I*Sqrt[3])*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (20*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[97 + 56*Sqrt[3], ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","C",41,16,30,0.5333,0,"{1586, 6725, 2136, 218, 2142, 2113, 537, 571, 93, 206, 266, 51, 63, 207, 6728, 205}"
840,0,0,0,0.4777758,"\int \frac{\sqrt{-1+x^2+x^5} \left(2+3 x^5\right)}{1+x^4-2 x^5+x^{10}} \, dx","Int[(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,"2*Defer[Int][Sqrt[-1 + x^2 + x^5]/(1 + x^4 - 2*x^5 + x^10), x] + 3*Defer[Int][(x^5*Sqrt[-1 + x^2 + x^5])/(1 + x^4 - 2*x^5 + x^10), x]","F",0,0,0,0,-1,"{}"
841,0,0,0,1.7084676,"\int \frac{1}{x \sqrt{x+x^2} \sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Int[1/(x*Sqrt[x + x^2]*Sqrt[x^2 + x*Sqrt[x + x^2]]),x]","\int \frac{1}{x \sqrt{x+x^2} \sqrt{x^2+x \sqrt{x+x^2}}} \, dx","\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,"(2*Sqrt[x]*Sqrt[1 + x]*Defer[Subst][Defer[Int][1/(x^2*Sqrt[1 + x^2]*Sqrt[x^4 + x^2*Sqrt[x^2 + x^4]]), x], x, Sqrt[x]])/Sqrt[x + x^2]","F",0,0,0,0,-1,"{}"
842,1,51,0,0.0171509,"\int \sqrt{b+\sqrt{b^2+a x^2}} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\frac{2 b x}{\sqrt{\sqrt{a x^2+b^2}+b}}+\frac{2 a x^3}{3 \left(\sqrt{a x^2+b^2}+b\right)^{3/2}}","\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*a*x^3)/(3*(b + Sqrt[b^2 + a*x^2])^(3/2)) + (2*b*x)/Sqrt[b + Sqrt[b^2 + a*x^2]]","A",1,1,19,0.05263,1,"{2129}"
843,0,0,0,0.4527825,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}}} \, dx","-\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,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]), x]","F",0,0,0,0,-1,"{}"
844,1,91,0,0.7524201,"\int \frac{-b+a x}{(b+a x) \sqrt{b^2 x+a^2 x^3}} \, dx","Int[(-b + a*x)/((b + a*x)*Sqrt[b^2*x + a^2*x^3]),x]","-\frac{\sqrt{2} \sqrt{x} \sqrt{a^2 x^2+b^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2+b^2}}\right)}{\sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}","-\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,"-((Sqrt[2]*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]))","A",4,4,32,0.1250,1,"{2056, 6733, 1699, 205}"
845,1,91,0,0.6771169,"\int \frac{b+a x}{(-b+a x) \sqrt{b^2 x+a^2 x^3}} \, dx","Int[(b + a*x)/((-b + a*x)*Sqrt[b^2*x + a^2*x^3]),x]","-\frac{\sqrt{2} \sqrt{x} \sqrt{a^2 x^2+b^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2+b^2}}\right)}{\sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}","-\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,"-((Sqrt[2]*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]))","A",4,4,32,0.1250,1,"{2056, 6733, 1699, 208}"
846,1,91,0,0.7096648,"\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","Int[(-(b*x^2) + a*x^3)/((b*x^2 + a*x^3)*Sqrt[b^2*x + a^2*x^3]),x]","-\frac{\sqrt{2} \sqrt{x} \sqrt{a^2 x^2+b^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2+b^2}}\right)}{\sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}","-\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,"-((Sqrt[2]*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]))","A",6,6,43,0.1395,1,"{1593, 1584, 2056, 6733, 1699, 205}"
847,0,0,0,0.1369077,"\int \frac{2+5 x}{\sqrt{-12+20 x+5 x^2+2 x^3+x^4}} \, dx","Int[(2 + 5*x)/Sqrt[-12 + 20*x + 5*x^2 + 2*x^3 + x^4],x]","\int \frac{2+5 x}{\sqrt{-12+20 x+5 x^2+2 x^3+x^4}} \, dx","-\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*Defer[Int][1/Sqrt[-12 + 20*x + 5*x^2 + 2*x^3 + x^4], x] + 5*Defer[Int][x/Sqrt[-12 + 20*x + 5*x^2 + 2*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
848,1,56,0,0.045228,"\int \frac{\left(-1+x^3\right) \sqrt{-1+x^6}}{x^7} \, dx","Int[((-1 + x^3)*Sqrt[-1 + x^6])/x^7,x]","-\frac{1}{6} \tan ^{-1}\left(\sqrt{x^6-1}\right)+\frac{\sqrt{x^6-1} \left(1-2 x^3\right)}{6 x^6}+\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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 - 2*x^3)*Sqrt[-1 + x^6])/(6*x^6) - ArcTan[Sqrt[-1 + x^6]]/6 + ArcTanh[x^3/Sqrt[-1 + x^6]]/3","A",8,8,18,0.4444,1,"{1475, 811, 844, 217, 206, 266, 63, 203}"
849,1,70,0,0.098021,"\int \frac{\sqrt{-1+x^6} \left(-1+2 x^6\right)^2}{x^7 \left(-1+4 x^6\right)} \, dx","Int[(Sqrt[-1 + x^6]*(-1 + 2*x^6)^2)/(x^7*(-1 + 4*x^6)),x]","\frac{\sqrt{x^6-1}}{6 x^6}+\frac{\sqrt{x^6-1}}{3}-\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}}","\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,"Sqrt[-1 + x^6]/3 + Sqrt[-1 + x^6]/(6*x^6) - ArcTan[Sqrt[-1 + x^6]]/6 - ArcTan[(2*Sqrt[-1 + x^6])/Sqrt[3]]/(2*Sqrt[3])","A",9,6,31,0.1935,1,"{573, 180, 47, 63, 203, 50}"
850,1,64,0,0.0474749,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-1+x^4+2 x^8\right)} \, dx","Int[(-2 + x^4)/((1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8)),x]","\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}}","\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) + ArcTan[(3^(1/4)*x)/(1 + x^4)^(1/4)]/(2*3^(1/4)) + ArcTanh[(3^(1/4)*x)/(1 + x^4)^(1/4)]/(2*3^(1/4))","A",7,7,27,0.2593,1,"{1454, 527, 12, 377, 212, 206, 203}"
851,1,47,0,0.0856026,"\int \frac{-x^2+10 x^8}{\sqrt{-1+x^6} \left(-1+4 x^6\right)} \, dx","Int[(-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",7,7,30,0.2333,1,"{1593, 575, 523, 217, 206, 377, 204}"
852,1,45,0,0.02085,"\int \frac{1+x^2}{\left(-1+x^2\right) \left(1+2 x^2\right)^{3/2}} \, dx","Int[(1 + x^2)/((-1 + x^2)*(1 + 2*x^2)^(3/2)),x]","-\frac{x}{3 \sqrt{2 x^2+1}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{2 x^2+1}}\right)}{3 \sqrt{3}}","-\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,"-1/3*x/Sqrt[1 + 2*x^2] - (2*ArcTanh[(Sqrt[3]*x)/Sqrt[1 + 2*x^2]])/(3*Sqrt[3])","A",4,4,24,0.1667,1,"{527, 12, 377, 207}"
853,1,65,0,0.0496782,"\int \frac{\left(b+a x^2\right)^{3/4}}{x} \, dx","Int[(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",6,6,15,0.4000,1,"{266, 50, 63, 298, 203, 206}"
854,1,172,0,0.7854968,"\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt{x+x^3}} \, dx","Int[(1 - x + x^2)/((-1 + x^2)*Sqrt[x + x^3]),x]","\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^3+x}}+\frac{\left(\frac{3}{2}-\frac{3 i}{2}\right) \sqrt{i x} \sqrt{x^2+1} \Pi \left(\frac{1}{2}-\frac{i}{2};\sin ^{-1}\left(\sqrt{1-i x}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^3+x}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{i x} \sqrt{x^2+1} \Pi \left(\frac{1}{2}+\frac{i}{2};\sin ^{-1}\left(\sqrt{1-i x}\right)|\frac{1}{2}\right)}{\sqrt{2} \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,"(Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[x + x^3] + ((3/2 - (3*I)/2)*Sqrt[I*x]*Sqrt[1 + x^2]*EllipticPi[1/2 - I/2, ArcSin[Sqrt[1 - I*x]], 1/2])/(Sqrt[2]*Sqrt[x + x^3]) - ((1/2 + I/2)*Sqrt[I*x]*Sqrt[1 + x^2]*EllipticPi[1/2 + I/2, ArcSin[Sqrt[1 - I*x]], 1/2])/(Sqrt[2]*Sqrt[x + x^3])","C",15,8,25,0.3200,0,"{2056, 6725, 329, 220, 932, 168, 538, 537}"
855,1,520,0,0.4099892,"\int \frac{-1+2 x^2}{\left(1+x^2\right) \sqrt{-1-x^2+x^4}} \, dx","Int[(-1 + 2*x^2)/((1 + x^2)*Sqrt[-1 - x^2 + x^4]),x]","\frac{3 \left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{2} \left(3+\sqrt{5}\right) \sqrt{x^4-x^2-1}}-\frac{3 \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \left(3+\sqrt{5}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{3 \sqrt{2} \left(2+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(-1-\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\left(3+\sqrt{5}\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,"(3*(1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(Sqrt[2]*(3 + Sqrt[5])*Sqrt[-1 - x^2 + x^4]) + (Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (3*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(5^(1/4)*(3 + Sqrt[5])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (3*Sqrt[2]*(2 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(-1 - Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/((3 + Sqrt[5])*Sqrt[-1 - x^2 + x^4])","C",10,9,29,0.3103,0,"{1710, 1098, 1214, 1456, 540, 421, 419, 538, 537}"
856,1,481,0,0.6669536,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[1/((-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \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*(Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",11,7,27,0.2593,1,"{2056, 1270, 1429, 377, 212, 206, 203}"
857,1,481,0,0.4081657,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[1/((-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \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*(Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",11,7,27,0.2593,1,"{2056, 1270, 1429, 377, 212, 206, 203}"
858,0,0,0,0.0821889,"\int \frac{-2 b+c x^2}{\left(-b+c x^2\right) \sqrt[4]{-b+c x^2+a x^4}} \, dx","Int[(-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,"Defer[Int][(-2*b + c*x^2)/((-b + c*x^2)*(-b + c*x^2 + a*x^4)^(1/4)), x]","F",0,0,0,0,-1,"{}"
859,0,0,0,1.0885566,"\int \frac{-4 b+a x^3}{\left(-b+a x^3\right) \sqrt[4]{b-a x^3+c x^4}} \, dx","Int[(-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,"Defer[Int][(b - a*x^3 + c*x^4)^(-1/4), x] + b^(1/3)*Defer[Int][1/((b^(1/3) - a^(1/3)*x)*(b - a*x^3 + c*x^4)^(1/4)), x] + b^(1/3)*Defer[Int][1/((b^(1/3) + (-1)^(1/3)*a^(1/3)*x)*(b - a*x^3 + c*x^4)^(1/4)), x] + b^(1/3)*Defer[Int][1/((b^(1/3) - (-1)^(2/3)*a^(1/3)*x)*(b - a*x^3 + c*x^4)^(1/4)), x]","F",0,0,0,0,-1,"{}"
860,0,0,0,0.7877245,"\int \frac{-b+a x^6}{\left(b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","Int[(-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{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+4 a b\&,\frac{\log \left(\sqrt[3]{a^3 x^3+a x^6-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(x*(1 + (2*Sqrt[a]*x^3)/(a^(5/2) - Sqrt[a^5 + 4*b]))^(1/3)*(1 + (2*Sqrt[a]*x^3)/(a^(5/2) + Sqrt[a^5 + 4*b]))^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, (-2*a*x^3)/(a^3 - Sqrt[a^6 + 4*a*b]), (-2*a*x^3)/(a^3 + Sqrt[a^6 + 4*a*b])])/(-b + a^3*x^3 + a*x^6)^(1/3) - Sqrt[b]*Defer[Int][1/((Sqrt[b] - Sqrt[-a]*x^3)*(-b + a^3*x^3 + a*x^6)^(1/3)), x] - Sqrt[b]*Defer[Int][1/((Sqrt[b] + Sqrt[-a]*x^3)*(-b + a^3*x^3 + a*x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
861,0,0,0,0.4649061,"\int \frac{-b+a x^6}{\left(b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","Int[(-b + a*x^6)/((b + a*x^6)*(-b + a^3*x^3 + a*x^6)^(1/3)),x]","\int \frac{-b+a x^6}{\left(b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3 a^3+a^6+4 a b\&,\frac{\log \left(\sqrt[3]{a^3 x^3+a x^6-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]",1,"(x*(1 + (2*Sqrt[a]*x^3)/(a^(5/2) - Sqrt[a^5 + 4*b]))^(1/3)*(1 + (2*Sqrt[a]*x^3)/(a^(5/2) + Sqrt[a^5 + 4*b]))^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, (-2*a*x^3)/(a^3 - Sqrt[a^6 + 4*a*b]), (-2*a*x^3)/(a^3 + Sqrt[a^6 + 4*a*b])])/(-b + a^3*x^3 + a*x^6)^(1/3) - Sqrt[b]*Defer[Int][1/((Sqrt[b] - Sqrt[-a]*x^3)*(-b + a^3*x^3 + a*x^6)^(1/3)), x] - Sqrt[b]*Defer[Int][1/((Sqrt[b] + Sqrt[-a]*x^3)*(-b + a^3*x^3 + a*x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
862,1,155,0,0.5382089,"\int \frac{\sqrt{1-x^4} \left(1+x^4\right)}{4-7 x^4+4 x^8} \, dx","Int[(Sqrt[1 - x^4]*(1 + x^4))/(4 - 7*x^4 + 4*x^8),x]","-\frac{1}{8} \left(1+i \sqrt{15}\right) F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{1}{8} \left(1-i \sqrt{15}\right) F\left(\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{8} \Pi \left(-\frac{2}{\sqrt{\frac{1}{2} \left(7-i \sqrt{15}\right)}};\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{8} \Pi \left(\frac{2}{\sqrt{\frac{1}{2} \left(7-i \sqrt{15}\right)}};\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{8} \Pi \left(-\frac{2}{\sqrt{\frac{1}{2} \left(7+i \sqrt{15}\right)}};\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{8} \Pi \left(\frac{2}{\sqrt{\frac{1}{2} \left(7+i \sqrt{15}\right)}};\left.\sin ^{-1}(x)\right|-1\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,"-1/8*((1 - I*Sqrt[15])*EllipticF[ArcSin[x], -1]) - ((1 + I*Sqrt[15])*EllipticF[ArcSin[x], -1])/8 + EllipticPi[-2/Sqrt[(7 - I*Sqrt[15])/2], ArcSin[x], -1]/8 + EllipticPi[2/Sqrt[(7 - I*Sqrt[15])/2], ArcSin[x], -1]/8 + EllipticPi[-2/Sqrt[(7 + I*Sqrt[15])/2], ArcSin[x], -1]/8 + EllipticPi[2/Sqrt[(7 + I*Sqrt[15])/2], ArcSin[x], -1]/8","C",16,6,31,0.1935,1,"{6728, 406, 221, 409, 1213, 537}"
863,1,269,0,0.2588219,"\int \frac{x^4}{\sqrt[4]{-b+a x^4} \left(-b+a x^8\right)} \, dx","Int[x^4/((-b + a*x^4)^(1/4)*(-b + a*x^8)),x]","-\frac{\tan ^{-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}}}+\frac{\tan ^{-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}}}-\frac{\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}}}+\frac{\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}}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"-1/4*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)]/(a^(5/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]) + ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)]/(4*a^(5/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]) - ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)]/(4*a^(5/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]) + ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)]/(4*a^(5/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b])","B",10,5,28,0.1786,1,"{1529, 377, 212, 206, 203}"
864,0,0,0,1.1471493,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Int[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2),x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"(I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x), x] + (I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x), x]","F",0,0,0,0,-1,"{}"
865,0,0,0,0.8186144,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Int[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2),x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"(I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x), x] + (I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x), x]","F",0,0,0,0,-1,"{}"
866,1,66,0,0.0615659,"\int \frac{\sqrt{-b+a x^3}}{x \left(2 b+a x^3\right)} \, dx","Int[Sqrt[-b + a*x^3]/(x*(2*b + a*x^3)),x]","\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}}","\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[b] + ArcTan[Sqrt[-b + a*x^3]/(Sqrt[3]*Sqrt[b])]/(Sqrt[3]*Sqrt[b])","A",6,5,28,0.1786,1,"{446, 83, 63, 205, 203}"
867,1,66,0,0.0883091,"\int \frac{-b+4 a x^3}{x \sqrt{-b+a x^3} \left(2 b+a x^3\right)} \, dx","Int[(-b + 4*a*x^3)/(x*Sqrt[-b + a*x^3]*(2*b + a*x^3)),x]","\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}}","\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]]/Sqrt[b] + (Sqrt[3]*ArcTan[Sqrt[-b + a*x^3]/(Sqrt[3]*Sqrt[b])])/Sqrt[b]","A",6,5,38,0.1316,1,"{573, 156, 63, 205, 203}"
868,0,0,0,0.5663852,"\int \frac{\sqrt{1+6 x^2+x^4}}{(-1+x) (1+x)^3} \, dx","Int[Sqrt[1 + 6*x^2 + x^4]/((-1 + x)*(1 + x)^3),x]","\int \frac{\sqrt{1+6 x^2+x^4}}{(-1+x) (1+x)^3} \, dx","\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,"(x*(3 + 2*Sqrt[2] + x^2))/(4*Sqrt[1 + 6*x^2 + x^4]) - ArcTanh[(2*Sqrt[2]*x)/Sqrt[1 + 6*x^2 + x^4]]/(2*Sqrt[2]) - (Sqrt[3 + 2*Sqrt[2]]*Sqrt[(1 + (3 - 2*Sqrt[2])*x^2)/(1 + (3 + 2*Sqrt[2])*x^2)]*(1 + (3 + 2*Sqrt[2])*x^2)*EllipticE[ArcTan[Sqrt[3 + 2*Sqrt[2]]*x], -4*(4 - 3*Sqrt[2])])/(4*Sqrt[1 + 6*x^2 + x^4]) + (3*Sqrt[(1 + (3 - 2*Sqrt[2])*x^2)/(1 + (3 + 2*Sqrt[2])*x^2)]*(1 + (3 + 2*Sqrt[2])*x^2)*EllipticF[ArcTan[Sqrt[3 + 2*Sqrt[2]]*x], -4*(4 - 3*Sqrt[2])])/(4*Sqrt[3 + 2*Sqrt[2]]*Sqrt[1 + 6*x^2 + x^4]) - Defer[Int][Sqrt[1 + 6*x^2 + x^4]/(1 + x)^3, x]/2 - Defer[Int][Sqrt[1 + 6*x^2 + x^4]/(1 + x)^2, x]/4","F",0,0,0,0,-1,"{}"
869,1,66,0,0.0479143,"\int \frac{\sqrt[4]{b+a x^4}}{x} \, dx","Int[(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",6,6,15,0.4000,1,"{266, 50, 63, 212, 206, 203}"
870,1,501,0,0.4842739,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((-2*b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \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*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",11,7,28,0.2500,1,"{2056, 1270, 1429, 377, 212, 206, 203}"
871,1,501,0,0.4019428,"\int \frac{1}{\left(-2 b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((-2*b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[8]{a} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}","\frac{\text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{8 b}",1,"-1/2*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",11,7,28,0.2500,1,"{2056, 1270, 1429, 377, 212, 206, 203}"
872,1,325,0,0.7246406,"\int \frac{x^6}{\left(b+a x^4\right)^{3/4} \left(b^2+a^2 x^8\right)} \, dx","Int[x^6/((b + a*x^4)^(3/4)*(b^2 + a^2*x^8)),x]","\frac{\left(-a^2\right)^{7/8} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\sqrt{-a^2}-a} x}{\sqrt[8]{-a^2} \sqrt[4]{a x^4+b}}\right)}{4 a^{11/4} \left(\sqrt{-a^2}-a\right)^{3/4} b}-\frac{\left(-a^2\right)^{3/8} \tan ^{-1}\left(\frac{\left(-a^2\right)^{3/8} \sqrt[4]{\sqrt{-a^2}-a} x}{a^{3/4} \sqrt[4]{a x^4+b}}\right)}{4 a^{7/4} \left(\sqrt{-a^2}-a\right)^{3/4} b}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{\sqrt{-a^2}+a} x}{\sqrt[8]{-a^2} \sqrt[4]{a x^4+b}}\right)}{4 a^{3/4} \sqrt[8]{-a^2} \left(\sqrt{-a^2}+a\right)^{3/4} b}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\left(-a^2\right)^{3/8} \sqrt[4]{\sqrt{-a^2}+a} x}{a^{3/4} \sqrt[4]{a x^4+b}}\right)}{4 \left(-a^2\right)^{5/8} \left(\sqrt{-a^2}+a\right)^{3/4} b}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+2 a^2\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{8 b}",1,"((-a^2)^(7/8)*ArcTan[(a^(1/4)*(-a + Sqrt[-a^2])^(1/4)*x)/((-a^2)^(1/8)*(b + a*x^4)^(1/4))])/(4*a^(11/4)*(-a + Sqrt[-a^2])^(3/4)*b) - ((-a^2)^(3/8)*ArcTan[((-a^2)^(3/8)*(-a + Sqrt[-a^2])^(1/4)*x)/(a^(3/4)*(b + a*x^4)^(1/4))])/(4*a^(7/4)*(-a + Sqrt[-a^2])^(3/4)*b) + ArcTan[(a^(1/4)*(a + Sqrt[-a^2])^(1/4)*x)/((-a^2)^(1/8)*(b + a*x^4)^(1/4))]/(4*a^(3/4)*(-a^2)^(1/8)*(a + Sqrt[-a^2])^(3/4)*b) - (a^(1/4)*ArcTan[((-a^2)^(3/8)*(a + Sqrt[-a^2])^(1/4)*x)/(a^(3/4)*(b + a*x^4)^(1/4))])/(4*(-a^2)^(5/8)*(a + Sqrt[-a^2])^(3/4)*b)","B",10,4,28,0.1429,1,"{1529, 494, 298, 205}"
873,0,0,0,0.0303624,"\int \sqrt{x^3+x^2 \sqrt{-1+x^2}} \, dx","Int[Sqrt[x^3 + x^2*Sqrt[-1 + x^2]],x]","\int \sqrt{x^3+x^2 \sqrt{-1+x^2}} \, dx","\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,"Defer[Int][Sqrt[x^3 + x^2*Sqrt[-1 + x^2]], x]","F",0,0,0,0,-1,"{}"
874,0,0,0,7.4041885,"\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","Int[((-a + x)*(-b + x)*(-(a*b) + x^2))/(x*Sqrt[x*(-a + x)*(-b + x)]*(a*b - (a + b + d)*x + x^2)),x]","\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","\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,"(-2*Sqrt[(a - x)*(b - x)*x])/x - (4*Sqrt[a]*Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/a]*EllipticE[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/((a - x)*Sqrt[x]*Sqrt[1 - x/b]) - (2*Sqrt[a]*(a - b)*Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/((a - x)*(b - x)*Sqrt[x]) + ((a + b + d + Sqrt[a^2 - 2*a*(b - d) + (b + d)^2])*Sqrt[(a - x)*(b - x)*x]*Defer[Int][(Sqrt[a - x]*Sqrt[b - x])/(x^(3/2)*(-a - b - d - Sqrt[a^2 - 2*a*b + b^2 + 2*a*d + 2*b*d + d^2] + 2*x)), x])/(Sqrt[a - x]*Sqrt[b - x]*Sqrt[x]) + ((a + b + d - Sqrt[a^2 - 2*a*(b - d) + (b + d)^2])*Sqrt[(a - x)*(b - x)*x]*Defer[Int][(Sqrt[a - x]*Sqrt[b - x])/(x^(3/2)*(-a - b - d + Sqrt[a^2 - 2*a*b + b^2 + 2*a*d + 2*b*d + d^2] + 2*x)), x])/(Sqrt[a - x]*Sqrt[b - x]*Sqrt[x])","F",0,0,0,0,-1,"{}"
875,1,651,0,0.369618,"\int \frac{1}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-\sqrt{-a^3} x\right)}{4 b \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{-a^3} x+\sqrt{b}\right)}{4 b \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3} \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3} \sqrt[3]{a^3 x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3} \sqrt[3]{a^3 x^3-b x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/((a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/(2*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[-a^3]*x])/(4*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[-a^3]*x])/(4*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)])/(4*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)])/(4*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",5,3,30,0.1000,1,"{2056, 912, 91}"
876,1,651,0,0.2911953,"\int \frac{1}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-\sqrt{-a^3} x\right)}{4 b \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{-a^3} x+\sqrt{b}\right)}{4 b \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3} \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3} \sqrt[3]{a^3 x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{\sqrt{-a^3} \sqrt{b}+a^3} \sqrt[3]{a^3 x^3-b x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/((a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/(2*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[-a^3]*x])/(4*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[-a^3]*x])/(4*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)])/(4*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)])/(4*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",5,3,30,0.1000,1,"{2056, 912, 91}"
877,1,45,0,0.0068121,"\int \frac{\sqrt{-1+x^4}}{1+x^4} \, dx","Int[Sqrt[-1 + x^4]/(1 + x^4),x]","-\frac{1}{2} \tan ^{-1}\left(\frac{x \left(1-x^2\right)}{\sqrt{x^4-1}}\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x \left(x^2+1\right)}{\sqrt{x^4-1}}\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,"-1/2*ArcTan[(x*(1 - x^2))/Sqrt[-1 + x^4]] - ArcTanh[(x*(1 + x^2))/Sqrt[-1 + x^4]]/2","A",1,1,17,0.05882,1,"{405}"
878,1,133,0,0.1222738,"\int x^2 \sqrt[4]{-x^2+x^4} \, dx","Int[x^2*(-x^2 + x^4)^(1/4),x]","-\frac{1}{16} \sqrt[4]{x^4-x^2} x+\frac{3 \left(x^2-1\right)^{3/4} x^{3/2} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{32 \left(x^4-x^2\right)^{3/4}}-\frac{3 \left(x^2-1\right)^{3/4} x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{32 \left(x^4-x^2\right)^{3/4}}+\frac{1}{4} \sqrt[4]{x^4-x^2} x^3","\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,"-1/16*(x*(-x^2 + x^4)^(1/4)) + (x^3*(-x^2 + x^4)^(1/4))/4 + (3*x^(3/2)*(-1 + x^2)^(3/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(32*(-x^2 + x^4)^(3/4)) - (3*x^(3/2)*(-1 + x^2)^(3/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(32*(-x^2 + x^4)^(3/4))","A",8,8,17,0.4706,1,"{2021, 2024, 2032, 329, 331, 298, 203, 206}"
879,0,0,0,0.060545,"\int \frac{x}{\sqrt{1+4 x+3 x^2-2 x^3+x^4}} \, dx","Int[x/Sqrt[1 + 4*x + 3*x^2 - 2*x^3 + x^4],x]","\int \frac{x}{\sqrt{1+4 x+3 x^2-2 x^3+x^4}} \, dx","\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,"Defer[Int][x/Sqrt[1 + 4*x + 3*x^2 - 2*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
880,0,0,0,0.0590721,"\int \frac{x}{\sqrt{1-4 x+3 x^2+2 x^3+x^4}} \, dx","Int[x/Sqrt[1 - 4*x + 3*x^2 + 2*x^3 + x^4],x]","\int \frac{x}{\sqrt{1-4 x+3 x^2+2 x^3+x^4}} \, dx","\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,"Defer[Int][x/Sqrt[1 - 4*x + 3*x^2 + 2*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
881,1,65,0,0.3914691,"\int \frac{3-3 x^2+2 x^4}{\sqrt[4]{-1+x^2} \left(2-3 x^2+x^4\right)} \, dx","Int[(3 - 3*x^2 + 2*x^4)/((-1 + x^2)^(1/4)*(2 - 3*x^2 + x^4)),x]","\frac{4 x}{\sqrt[4]{x^2-1}}-\frac{5 \tan ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^2-1}}\right)}{2 \sqrt{2}}-\frac{5 \tanh ^{-1}\left(\frac{x}{\sqrt{2} \sqrt[4]{x^2-1}}\right)}{2 \sqrt{2}}","\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,"(4*x)/(-1 + x^2)^(1/4) - (5*ArcTan[x/(Sqrt[2]*(-1 + x^2)^(1/4))])/(2*Sqrt[2]) - (5*ArcTanh[x/(Sqrt[2]*(-1 + x^2)^(1/4))])/(2*Sqrt[2])","A",20,10,34,0.2941,1,"{1688, 6725, 199, 230, 305, 220, 1196, 288, 403, 398}"
882,1,401,0,0.5310874,"\int \frac{x^2}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^2/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4))","B",12,7,30,0.2333,1,"{2056, 1270, 1529, 377, 212, 206, 203}"
883,1,401,0,0.4874694,"\int \frac{x^2}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^2/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{5/8} \sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"(Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(5/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4))","B",12,7,30,0.2333,1,"{2056, 1270, 1529, 377, 212, 206, 203}"
884,0,0,0,0.9213757,"\int \frac{4 b+x^3}{\left(b+x^3\right) \sqrt[4]{-b-x^3+a x^4}} \, dx","Int[(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,"Defer[Int][(-b - x^3 + a*x^4)^(-1/4), x] - b^(1/3)*Defer[Int][1/((-b^(1/3) - x)*(-b - x^3 + a*x^4)^(1/4)), x] - b^(1/3)*Defer[Int][1/((-b^(1/3) + (-1)^(1/3)*x)*(-b - x^3 + a*x^4)^(1/4)), x] - b^(1/3)*Defer[Int][1/((-b^(1/3) - (-1)^(2/3)*x)*(-b - x^3 + a*x^4)^(1/4)), x]","F",0,0,0,0,-1,"{}"
885,0,0,0,1.5011814,"\int \frac{4 b+a x^5}{\left(-b+a x^5\right) \sqrt[4]{-b+c x^4+a x^5}} \, dx","Int[(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,"Defer[Int][(-b + c*x^4 + a*x^5)^(-1/4), x] - b^(1/5)*Defer[Int][1/((b^(1/5) - a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x] - b^(1/5)*Defer[Int][1/((b^(1/5) + (-1)^(1/5)*a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x] - b^(1/5)*Defer[Int][1/((b^(1/5) - (-1)^(2/5)*a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x] - b^(1/5)*Defer[Int][1/((b^(1/5) + (-1)^(3/5)*a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x] - b^(1/5)*Defer[Int][1/((b^(1/5) - (-1)^(4/5)*a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x]","F",0,0,0,0,-1,"{}"
886,0,0,0,1.386169,"\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","Int[(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,"-2*Defer[Int][Sqrt[1 + x^2 - 2*x^6]/(-1 - 4*x^2 + 2*x^6), x] + 3*Defer[Int][(x^4*Sqrt[1 + x^2 - 2*x^6])/(-1 - 4*x^2 + 2*x^6), x] + Defer[Int][Sqrt[1 + x^2 - 2*x^6]/(-1 - 2*x^2 + 2*x^6), x] - 3*Defer[Int][(x^4*Sqrt[1 + x^2 - 2*x^6])/(-1 - 2*x^2 + 2*x^6), x]","F",0,0,0,0,-1,"{}"
887,1,58,0,0.0770058,"\int \frac{x^4}{\sqrt[4]{-1+x^4} \left(-1+x^8\right)} \, dx","Int[x^4/((-1 + x^4)^(1/4)*(-1 + x^8)),x]","-\frac{x^5 \sqrt[4]{1-x^4} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};\frac{2 x^4}{x^4+1}\right)}{5 \sqrt[4]{x^4-1} \left(x^4+1\right)^{5/4}}","-\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,"-1/5*(x^5*(1 - x^4)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, (2*x^4)/(1 + x^4)])/((-1 + x^4)^(1/4)*(1 + x^4)^(5/4))","C",3,3,20,0.1500,0,"{1479, 511, 510}"
888,1,67,0,0.0425762,"\int \frac{1}{\sqrt[4]{1+x^4} \left(-1+x^8\right)} \, dx","Int[1/((1 + x^4)^(1/4)*(-1 + x^8)),x]","-\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}}","-\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) - ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(4*2^(1/4)) - ArcTanh[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(4*2^(1/4))","A",6,6,17,0.3529,1,"{1404, 382, 377, 212, 206, 203}"
889,1,67,0,0.0642987,"\int \frac{-1+2 x^4}{\sqrt[4]{-1+x^4} \left(-1+x^8\right)} \, dx","Int[(-1 + 2*x^4)/((-1 + x^4)^(1/4)*(-1 + x^8)),x]","-\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}}","-\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*ArcTan[(2^(1/4)*x)/(-1 + x^4)^(1/4)])/(4*2^(1/4)) + (3*ArcTanh[(2^(1/4)*x)/(-1 + x^4)^(1/4)])/(4*2^(1/4))","A",7,7,24,0.2917,1,"{1455, 527, 12, 377, 212, 206, 203}"
890,1,67,0,0.3473848,"\int \frac{1+x^8}{\sqrt{1+x^4} \left(-1+x^8\right)} \, dx","Int[(1 + x^8)/(Sqrt[1 + x^4]*(-1 + x^8)),x]","-\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}}","-\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,"-1/2*x/Sqrt[1 + x^4] - ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(4*Sqrt[2]) - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(4*Sqrt[2])","A",16,10,22,0.4545,1,"{6725, 220, 1404, 414, 523, 409, 1211, 1699, 206, 203}"
891,1,1382,0,3.2239597,"\int \frac{-1+x^{12}}{\sqrt{1+x^4} \left(1+x^{12}\right)} \, dx","Int[(-1 + x^12)/(Sqrt[1 + x^4]*(1 + x^12)),x]","-\frac{2 x}{\sqrt{3} \left(3 i+\sqrt{3}\right) \sqrt{x^4+1}}+\frac{2 x}{\sqrt{3} \left(3 i-\sqrt{3}\right) \sqrt{x^4+1}}+\frac{2 i \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{3-i \sqrt{3}} x}{\sqrt[4]{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{\sqrt{3} \left(1-i \sqrt{3}\right)^{3/4} \left(3-i \sqrt{3}\right)^{3/2}}-\frac{2 i \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{-3+i \sqrt{3}} x}{\sqrt[4]{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{\sqrt{3} \left(1-i \sqrt{3}\right)^{3/4} \left(-3+i \sqrt{3}\right)^{3/2}}+\frac{2 i \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{-3-i \sqrt{3}} x}{\sqrt[4]{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{\sqrt{3} \left(-3-i \sqrt{3}\right)^{3/2} \left(1+i \sqrt{3}\right)^{3/4}}-\frac{2 i \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{3+i \sqrt{3}} x}{\sqrt[4]{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{\sqrt{3} \left(1+i \sqrt{3}\right)^{3/4} \left(3+i \sqrt{3}\right)^{3/2}}-\frac{\left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{3} \left(3 i+\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(1+\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{3} \left(3 i-\sqrt{3}\right) \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{3} \left(3 i+\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(\frac{1}{6}+\frac{i}{6}\right) \left(1-\sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\left(i+\sqrt{3}\right) \sqrt{x^4+1}}-\frac{\left(\frac{1}{6}-\frac{i}{6}\right) \left(1-\sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\left(i-\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{3} \left(3 i-\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{x^4+1}}+\frac{\left(3+\sqrt{3} \left(3 i+2 i \sqrt{2-2 i \sqrt{3}}\right)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{\left(\sqrt{2}-\sqrt{1-i \sqrt{3}}\right)^2}{4 \sqrt{2 \left(1-i \sqrt{3}\right)}};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \left(3-i \sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(3 i-\sqrt{3} \left(3-2 \sqrt{2-2 i \sqrt{3}}\right)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{\left(\sqrt{2}+\sqrt{1-i \sqrt{3}}\right)^2}{4 \sqrt{2 \left(1-i \sqrt{3}\right)}};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \left(3 i+\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(3 i+3 \sqrt{3}+2 \sqrt{6+6 i \sqrt{3}}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{\left(\sqrt{2}-\sqrt{1+i \sqrt{3}}\right)^2}{4 \sqrt{2 \left(1+i \sqrt{3}\right)}};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \left(3 i-\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(3 i+\sqrt{3} \left(3-2 \sqrt{2+2 i \sqrt{3}}\right)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{\left(\sqrt{2}+\sqrt{1+i \sqrt{3}}\right)^2}{4 \sqrt{2 \left(1+i \sqrt{3}\right)}};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \left(3 i-\sqrt{3}\right) \sqrt{x^4+1}}","-\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[3]*(3*I - Sqrt[3])*Sqrt[1 + x^4]) - (2*x)/(Sqrt[3]*(3*I + Sqrt[3])*Sqrt[1 + x^4]) + ((2*I)*2^(1/4)*ArcTan[(Sqrt[3 - I*Sqrt[3]]*x)/((2*(1 - I*Sqrt[3]))^(1/4)*Sqrt[1 + x^4])])/(Sqrt[3]*(1 - I*Sqrt[3])^(3/4)*(3 - I*Sqrt[3])^(3/2)) - ((2*I)*2^(1/4)*ArcTan[(Sqrt[-3 + I*Sqrt[3]]*x)/((2*(1 - I*Sqrt[3]))^(1/4)*Sqrt[1 + x^4])])/(Sqrt[3]*(1 - I*Sqrt[3])^(3/4)*(-3 + I*Sqrt[3])^(3/2)) + ((2*I)*2^(1/4)*ArcTan[(Sqrt[-3 - I*Sqrt[3]]*x)/((2*(1 + I*Sqrt[3]))^(1/4)*Sqrt[1 + x^4])])/(Sqrt[3]*(-3 - I*Sqrt[3])^(3/2)*(1 + I*Sqrt[3])^(3/4)) - ((2*I)*2^(1/4)*ArcTan[(Sqrt[3 + I*Sqrt[3]]*x)/((2*(1 + I*Sqrt[3]))^(1/4)*Sqrt[1 + x^4])])/(Sqrt[3]*(1 + I*Sqrt[3])^(3/4)*(3 + I*Sqrt[3])^(3/2)) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(2*Sqrt[1 + x^4]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(Sqrt[3]*(3*I - Sqrt[3])*Sqrt[1 + x^4]) - ((1/6 - I/6)*(1 - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/((I - Sqrt[3])*Sqrt[1 + x^4]) + ((1/6 + I/6)*(1 - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/((I + Sqrt[3])*Sqrt[1 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(Sqrt[3]*(3*I + Sqrt[3])*Sqrt[1 + x^4]) + ((1 + 1/Sqrt[(1 - I*Sqrt[3])/2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(Sqrt[3]*(3*I - Sqrt[3])*Sqrt[1 + x^4]) - ((1 + 1/Sqrt[(1 + I*Sqrt[3])/2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(Sqrt[3]*(3*I + Sqrt[3])*Sqrt[1 + x^4]) + ((3 + Sqrt[3]*(3*I + (2*I)*Sqrt[2 - (2*I)*Sqrt[3]]))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[-1/4*(Sqrt[2] - Sqrt[1 - I*Sqrt[3]])^2/Sqrt[2*(1 - I*Sqrt[3])], 2*ArcTan[x], 1/2])/(12*(3 - I*Sqrt[3])*Sqrt[1 + x^4]) + ((3*I - Sqrt[3]*(3 - 2*Sqrt[2 - (2*I)*Sqrt[3]]))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(Sqrt[2] + Sqrt[1 - I*Sqrt[3]])^2/(4*Sqrt[2*(1 - I*Sqrt[3])]), 2*ArcTan[x], 1/2])/(12*(3*I + Sqrt[3])*Sqrt[1 + x^4]) + ((3*I + 3*Sqrt[3] + 2*Sqrt[6 + (6*I)*Sqrt[3]])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[-1/4*(Sqrt[2] - Sqrt[1 + I*Sqrt[3]])^2/Sqrt[2*(1 + I*Sqrt[3])], 2*ArcTan[x], 1/2])/(12*(3*I - Sqrt[3])*Sqrt[1 + x^4]) + ((3*I + Sqrt[3]*(3 - 2*Sqrt[2 + (2*I)*Sqrt[3]]))*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(Sqrt[2] + Sqrt[1 + I*Sqrt[3]])^2/(4*Sqrt[2*(1 + I*Sqrt[3])]), 2*ArcTan[x], 1/2])/(12*(3*I - Sqrt[3])*Sqrt[1 + x^4])","C",25,8,22,0.3636,0,"{6725, 220, 2073, 414, 523, 409, 1217, 1707}"
892,1,56,0,0.8044265,"\int \frac{-1+x^2}{\sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(-1 + x^2)/(Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{1}{6} \left(\sqrt{x^2+1}+x\right)^{3/2}+\frac{3}{\sqrt{\sqrt{x^2+1}+x}}-\frac{1}{10 \left(\sqrt{x^2+1}+x\right)^{5/2}}","\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,"-1/10*1/(x + Sqrt[1 + x^2])^(5/2) + 3/Sqrt[x + Sqrt[1 + x^2]] + (x + Sqrt[1 + x^2])^(3/2)/6","A",7,5,30,0.1667,1,"{6742, 2122, 30, 2120, 270}"
893,1,56,0,0.1064376,"\int \frac{\sqrt{1+x^2}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + x^2]/Sqrt[x + Sqrt[1 + x^2]],x]","\frac{1}{6} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\frac{1}{10 \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,"-1/10*1/(x + Sqrt[1 + x^2])^(5/2) - 1/Sqrt[x + Sqrt[1 + x^2]] + (x + Sqrt[1 + x^2])^(3/2)/6","A",3,2,25,0.08000,1,"{2122, 270}"
894,1,618,0,0.7111722,"\int \frac{1}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-a^{3/2} x\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(a^{3/2} x+\sqrt{b}\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}}}-\sqrt[3]{x}\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}}}-\sqrt[3]{x}\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}-\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{a} b \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}+\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{a} b \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}","\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,"(Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*x^(1/3))])/(2*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*x^(1/3))])/(2*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - a^(3/2)*x])/(4*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + a^(3/2)*x])/(4*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3))])/(4*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3))])/(4*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",5,3,32,0.09375,1,"{2056, 912, 91}"
895,1,618,0,0.3832503,"\int \frac{1}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-a^{3/2} x\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(a^{3/2} x+\sqrt{b}\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}}}-\sqrt[3]{x}\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}}}-\sqrt[3]{x}\right)}{4 \sqrt{a} b \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}-\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{a} b \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}+\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{a} b \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}","\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,"(Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*x^(1/3))])/(2*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*x^(1/3))])/(2*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - a^(3/2)*x])/(4*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + a^(3/2)*x])/(4*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3))])/(4*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3))])/(4*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",5,3,32,0.09375,1,"{2056, 912, 91}"
896,1,633,0,0.452943,"\int \frac{1}{\left(b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/((b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{b}-\sqrt{-a} x\right)}{4 b \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{-a} x+\sqrt{b}\right)}{4 b \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[3]{a^3-\sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[3]{a^3+\sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{a^3-\sqrt{-a} b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{a^3+\sqrt{-a} b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(b*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(2*b*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[-a]*x])/(4*b*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[-a]*x])/(4*b*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 - Sqrt[-a]*b^(3/2))^(1/3)])/(4*b*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 + Sqrt[-a]*b^(3/2))^(1/3)])/(4*b*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",5,3,29,0.1034,1,"{2056, 912, 91}"
897,1,633,0,0.3363755,"\int \frac{1}{\left(b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/((b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{b}-\sqrt{-a} x\right)}{4 b \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{-a} x+\sqrt{b}\right)}{4 b \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[3]{a^3-\sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[3]{a^3+\sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{4 b \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{a^3-\sqrt{-a} b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[3]{x} \sqrt[3]{a^3+\sqrt{-a} b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 b \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(b*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(2*b*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[-a]*x])/(4*b*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[-a]*x])/(4*b*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 - Sqrt[-a]*b^(3/2))^(1/3)])/(4*b*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 + Sqrt[-a]*b^(3/2))^(1/3)])/(4*b*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",5,3,29,0.1034,1,"{2056, 912, 91}"
898,1,145,0,0.1832262,"\int x^7 \sqrt[4]{-x+x^4} \, dx","Int[x^7*(-x + x^4)^(1/4),x]","\frac{1}{9} \sqrt[4]{x^4-x} x^8-\frac{1}{72} \sqrt[4]{x^4-x} x^5-\frac{7}{288} \sqrt[4]{x^4-x} x^2+\frac{7 \left(x^3-1\right)^{3/4} x^{3/4} \tan ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{192 \left(x^4-x\right)^{3/4}}-\frac{7 \left(x^3-1\right)^{3/4} x^{3/4} \tanh ^{-1}\left(\frac{x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{192 \left(x^4-x\right)^{3/4}}","\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,"(-7*x^2*(-x + x^4)^(1/4))/288 - (x^5*(-x + x^4)^(1/4))/72 + (x^8*(-x + x^4)^(1/4))/9 + (7*x^(3/4)*(-1 + x^3)^(3/4)*ArcTan[x^(3/4)/(-1 + x^3)^(1/4)])/(192*(-x + x^4)^(3/4)) - (7*x^(3/4)*(-1 + x^3)^(3/4)*ArcTanh[x^(3/4)/(-1 + x^3)^(1/4)])/(192*(-x + x^4)^(3/4))","B",10,9,15,0.6000,1,"{2021, 2024, 2032, 329, 275, 331, 298, 203, 206}"
899,0,0,0,6.8392973,"\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","Int[((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,"(-2*(-1 - x^2 + x^4)^(1/4)*AppellF1[-1/2, -1/4, -1/4, 1/2, (2*x^2)/(1 + Sqrt[5]), (2*x^2)/(1 - Sqrt[5])])/(x*(1 - (2*x^2)/(1 - Sqrt[5]))^(1/4)*(1 - (2*x^2)/(1 + Sqrt[5]))^(1/4)) - ((1 - (2*x^2)/(1 - Sqrt[5]))^(5/4)*(-1 - x^2 + x^4)^(1/4)*Hypergeometric2F1[-3/2, -1/4, -1/2, (-2*(x^2/(1 - Sqrt[5]) - x^2/(1 + Sqrt[5])))/(1 - (2*x^2)/(1 - Sqrt[5]))])/(3*x^3*(1 - (2*x^2)/(1 + Sqrt[5]))^(1/4)) + (4*(1 - (2*x^2)/(1 - Sqrt[5]))*(-1 - x^2 + x^4)^(1/4)*((3*(1 - Sqrt[5]) + (13 - 3*Sqrt[5])*x^2 + 2*(1 - Sqrt[5])*x^4)*Gamma[-1/4]*Hypergeometric2F1[-1/4, 1, -1/2, (-2*Sqrt[5]*x^2)/(2 + (1 - Sqrt[5])*x^2)] + 4*x^2*(5 - Sqrt[5] + 2*Sqrt[5]*x^2)*Gamma[3/4]*Hypergeometric2F1[3/4, 2, 1/2, (-2*Sqrt[5]*x^2)/(2 + (1 - Sqrt[5])*x^2)]))/(15*(3 - Sqrt[5])*x^5*(1 + Sqrt[5] - 2*x^2)*Gamma[-1/4]) + Defer[Int][(-1 - x^2 + x^4)^(1/4)/(-1 - x^2), x]","F",0,0,0,0,-1,"{}"
900,1,114,0,0.1882339,"\int \frac{\sqrt[4]{x^3+x^4}}{x^2 \left(-1+x^2\right)} \, dx","Int[(x^3 + x^4)^(1/4)/(x^2*(-1 + x^2)),x]","\frac{4 \sqrt[4]{x^4+x^3}}{x}+\frac{\sqrt[4]{2} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{2} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}","\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^3 + x^4)^(1/4))/x + (2^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - (2^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4))","A",7,7,22,0.3182,1,"{2056, 848, 96, 93, 298, 203, 206}"
901,1,68,0,0.0535394,"\int \frac{b+2 a x^4}{x^2 \left(b+a x^4\right)^{3/4}} \, dx","Int[(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",5,5,23,0.2174,1,"{451, 331, 298, 203, 206}"
902,1,147,0,0.7561927,"\int \frac{\left(1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(-1+x^2\right)} \, dx","Int[((1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(-1 + x^2)),x]","-\frac{8 \sqrt[4]{x^6+x^2} x F_1\left(\frac{3}{8};1,\frac{3}{4};\frac{11}{8};x^4,-x^4\right)}{3 \sqrt[4]{x^4+1}}-\frac{8 \sqrt[4]{x^6+x^2} x^3 F_1\left(\frac{7}{8};1,\frac{3}{4};\frac{15}{8};x^4,-x^4\right)}{7 \sqrt[4]{x^4+1}}+\frac{4 \sqrt[4]{x^6+x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};-x^4\right)}{3 \sqrt[4]{x^4+1}}+\frac{2 \sqrt[4]{x^6+x^2}}{x}","\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,"(2*(x^2 + x^6)^(1/4))/x - (8*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, 1, 3/4, 11/8, x^4, -x^4])/(3*(1 + x^4)^(1/4)) - (8*x^3*(x^2 + x^6)^(1/4)*AppellF1[7/8, 1, 3/4, 15/8, x^4, -x^4])/(7*(1 + x^4)^(1/4)) + (4*x*(x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, -x^4])/(3*(1 + x^4)^(1/4))","C",20,11,27,0.4074,0,"{2056, 6725, 277, 329, 364, 1312, 1336, 325, 1337, 466, 510}"
903,1,88,0,0.5050819,"\int \frac{\sqrt{-1+x^3} \left(1-x^3+x^6\right)}{x^{10} \left(2+x^3\right)} \, dx","Int[(Sqrt[-1 + x^3]*(1 - x^3 + x^6))/(x^10*(2 + x^3)),x]","-\frac{\sqrt{x^3-1}}{3 x^3}+\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}}{18 x^9}+\frac{5 \sqrt{x^3-1}}{36 x^6}","\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,"-1/18*Sqrt[-1 + x^3]/x^9 + (5*Sqrt[-1 + x^3])/(36*x^6) - Sqrt[-1 + x^3]/(3*x^3) + (13*ArcTan[Sqrt[-1 + x^3]])/24 - (7*ArcTan[Sqrt[-1 + x^3]/Sqrt[3]])/(8*Sqrt[3])","A",25,8,30,0.2667,1,"{6725, 266, 47, 51, 63, 203, 50, 444}"
904,0,0,0,1.9152189,"\int \frac{\sqrt{x^2+x \sqrt{x+x^2}}}{x \sqrt{x+x^2}} \, dx","Int[Sqrt[x^2 + x*Sqrt[x + x^2]]/(x*Sqrt[x + x^2]),x]","\int \frac{\sqrt{x^2+x \sqrt{x+x^2}}}{x \sqrt{x+x^2}} \, dx","\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[x]*Sqrt[1 + x]*Defer[Subst][Defer[Int][Sqrt[x^4 + x^2*Sqrt[x^2 + x^4]]/(x^2*Sqrt[1 + x^2]), x], x, Sqrt[x]])/Sqrt[x + x^2]","F",0,0,0,0,-1,"{}"
905,1,624,0,0.5033679,"\int \frac{1}{\left(-b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/((-b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{b}-\sqrt{a} x\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{a} x+\sqrt{b}\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}-b^{3/2}}}-\sqrt[3]{x}\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}+b^{3/2}}}-\sqrt[3]{x}\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{x} \sqrt[3]{a^{5/2}-b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[6]{a} b \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{x} \sqrt[3]{a^{5/2}+b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[6]{a} b \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) - b^(3/2))^(1/3)*x^(1/3))])/(2*a^(1/6)*b*(a^(5/2) - b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) + b^(3/2))^(1/3)*x^(1/3))])/(2*a^(1/6)*b*(a^(5/2) + b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[a]*x])/(4*a^(1/6)*b*(a^(5/2) + b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[a]*x])/(4*a^(1/6)*b*(a^(5/2) - b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) - b^(3/2))^(1/3))])/(4*a^(1/6)*b*(a^(5/2) - b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) + b^(3/2))^(1/3))])/(4*a^(1/6)*b*(a^(5/2) + b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",5,3,31,0.09677,1,"{2056, 912, 91}"
906,1,624,0,0.3850884,"\int \frac{1}{\left(-b+a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/((-b + a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{b}-\sqrt{a} x\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\sqrt{a} x+\sqrt{b}\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}-b^{3/2}}}-\sqrt[3]{x}\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}+b^{3/2}}}-\sqrt[3]{x}\right)}{4 \sqrt[6]{a} b \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{x} \sqrt[3]{a^{5/2}-b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[6]{a} b \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{x} \sqrt[3]{a^{5/2}+b^{3/2}}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[6]{a} b \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) - b^(3/2))^(1/3)*x^(1/3))])/(2*a^(1/6)*b*(a^(5/2) - b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) + b^(3/2))^(1/3)*x^(1/3))])/(2*a^(1/6)*b*(a^(5/2) + b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[a]*x])/(4*a^(1/6)*b*(a^(5/2) + b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[a]*x])/(4*a^(1/6)*b*(a^(5/2) - b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) - b^(3/2))^(1/3))])/(4*a^(1/6)*b*(a^(5/2) - b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) + b^(3/2))^(1/3))])/(4*a^(1/6)*b*(a^(5/2) + b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",5,3,31,0.09677,1,"{2056, 912, 91}"
907,0,0,0,23.7142917,"\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","Int[((-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]","\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","\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*(a - x)*(b - x))/(x*Sqrt[(a - x)*(b - x)*x]) + (2*(a + b)*(a - x)*Sqrt[x]*Sqrt[1 - x/b]*EllipticE[ArcSin[Sqrt[x]/Sqrt[b]], b/a])/(a*Sqrt[b]*Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/a]) + (2*(a - b)*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[b]], b/a])/(Sqrt[b]*Sqrt[(a - x)*(b - x)*x]) - (2*(a^2 - b^2)*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[b]], b/a])/(a*Sqrt[b]*Sqrt[(a - x)*(b - x)*x]) + (2*(a + b - 3*a*b*d)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-a + x^2]*Sqrt[-b + x^2])/(a*b - a*(1 + b/a)*x^2 + x^4 - d*x^6), x], x, Sqrt[x]])/(a*b*Sqrt[(a - x)*(b - x)*x]) - (2*(a + b)*d*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-a + x^2]*Sqrt[-b + x^2])/(a*b - a*(1 + b/a)*x^2 + x^4 - d*x^6), x], x, Sqrt[x]])/(a*b*Sqrt[(a - x)*(b - x)*x]) + (2*(a^2 + b^2)*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(Sqrt[-a + x^2]*Sqrt[-b + x^2])/(-(a*b) + a*(1 + b/a)*x^2 - x^4 + d*x^6), x], x, Sqrt[x]])/(a*b*Sqrt[(a - x)*(b - x)*x])","F",0,0,0,0,-1,"{}"
908,1,111,0,0.1383832,"\int \frac{1}{\left(1+x^3\right) \sqrt[4]{-x+x^4}} \, dx","Int[1/((1 + x^3)*(-x + x^4)^(1/4)),x]","\frac{2^{3/4} \sqrt[4]{x} \sqrt[4]{x^3-1} \tan ^{-1}\left(\frac{\sqrt[4]{2} x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{3 \sqrt[4]{x^4-x}}+\frac{2^{3/4} \sqrt[4]{x} \sqrt[4]{x^3-1} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{3 \sqrt[4]{x^4-x}}","\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,"(2^(3/4)*x^(1/4)*(-1 + x^3)^(1/4)*ArcTan[(2^(1/4)*x^(3/4))/(-1 + x^3)^(1/4)])/(3*(-x + x^4)^(1/4)) + (2^(3/4)*x^(1/4)*(-1 + x^3)^(1/4)*ArcTanh[(2^(1/4)*x^(3/4))/(-1 + x^3)^(1/4)])/(3*(-x + x^4)^(1/4))","A",7,7,19,0.3684,1,"{2056, 466, 465, 377, 212, 206, 203}"
909,1,79,0,0.1777815,"\int \frac{x \sqrt{-x^2+x^4}}{-3+2 x^2} \, dx","Int[(x*Sqrt[-x^2 + x^4])/(-3 + 2*x^2),x]","\frac{1}{4} \sqrt{x^4-x^2}+\frac{1}{2} \tanh ^{-1}\left(\frac{x^2}{\sqrt{x^4-x^2}}\right)+\frac{1}{8} \sqrt{3} \tanh ^{-1}\left(\frac{3-4 x^2}{2 \sqrt{3} \sqrt{x^4-x^2}}\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,"Sqrt[-x^2 + x^4]/4 + ArcTanh[x^2/Sqrt[-x^2 + x^4]]/2 + (Sqrt[3]*ArcTanh[(3 - 4*x^2)/(2*Sqrt[3]*Sqrt[-x^2 + x^4])])/8","A",7,6,24,0.2500,1,"{2034, 734, 843, 620, 206, 724}"
910,1,6713,0,13.4967165,"\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","Int[((-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{4 \sqrt{x^4-x^2-1} x}{17 \left(1-\sqrt{17}\right) \left(-4 x^2-\sqrt{17}+1\right)}+\frac{\sqrt{x^4-x^2-1} x}{68 \left(-4 x^2-\sqrt{17}+1\right)}+\frac{4 \sqrt{x^4-x^2-1} x}{17 \left(1+\sqrt{17}\right) \left(-4 x^2+\sqrt{17}+1\right)}+\frac{\sqrt{x^4-x^2-1} x}{68 \left(-4 x^2+\sqrt{17}+1\right)}-\frac{\left(17+2 \sqrt{17}\right) \left(-2 x^2-\sqrt{5}+1\right) x}{544 \sqrt{x^4-x^2-1}}-\frac{\left(-2 x^2-\sqrt{5}+1\right) x}{34 \left(1+\sqrt{17}\right) \sqrt{x^4-x^2-1}}-\frac{\left(-2 x^2-\sqrt{5}+1\right) x}{34 \left(1-\sqrt{17}\right) \sqrt{x^4-x^2-1}}-\frac{\left(17-2 \sqrt{17}\right) \left(-2 x^2-\sqrt{5}+1\right) x}{544 \sqrt{x^4-x^2-1}}+\frac{\left(-2 x^2-\sqrt{5}+1\right) x}{17 \sqrt{x^4-x^2-1}}-\frac{\sqrt[4]{5} \left(17+2 \sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{544 \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\sqrt[4]{5} \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{34 \left(1+\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\sqrt[4]{5} \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{34 \left(1-\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\sqrt[4]{5} \left(17-2 \sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{544 \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\sqrt[4]{5} \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{17 \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(1+\sqrt{5}\right) \left(9-\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \left(8-\sqrt{5}+\sqrt{85}\right) \sqrt{x^4-x^2-1}}-\frac{\left(1+\sqrt{5}\right) \left(1-\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{8 \sqrt{34} \left(8-\sqrt{5}+\sqrt{85}\right) \sqrt{x^4-x^2-1}}+\frac{\left(1+\sqrt{5}\right) \left(9+\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \left(8-\sqrt{5}-\sqrt{85}\right) \sqrt{x^4-x^2-1}}+\frac{\left(1+\sqrt{5}\right) \left(1+\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{8 \sqrt{34} \left(8-\sqrt{5}-\sqrt{85}\right) \sqrt{x^4-x^2-1}}+\frac{3 \left(1+\sqrt{5}\right) \left(1+\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{2} \left(3+2 \sqrt{5}+\sqrt{17}\right) \sqrt{x^4-x^2-1}}-\frac{\left(1+\sqrt{5}\right) \left(1-\sqrt{17}\right) \left(2-\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \left(1+2 \sqrt{5}+\sqrt{17}\right) \sqrt{x^4-x^2-1}}+\frac{\left(1+\sqrt{5}\right) \left(1-\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{32 \sqrt{34} \left(1+2 \sqrt{5}+\sqrt{17}\right) \sqrt{x^4-x^2-1}}+\frac{\left(1+\sqrt{5}\right) \left(1+\sqrt{17}\right) \left(2+\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \left(1+2 \sqrt{5}-\sqrt{17}\right) \sqrt{x^4-x^2-1}}-\frac{\left(1+\sqrt{5}\right) \left(1+\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{32 \sqrt{34} \left(1+2 \sqrt{5}-\sqrt{17}\right) \sqrt{x^4-x^2-1}}+\frac{3 \left(1+\sqrt{5}\right) \left(1-\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{2} \left(3+2 \sqrt{5}-\sqrt{17}\right) \sqrt{x^4-x^2-1}}-\frac{\left(17+\sqrt{17} \left(1-2 \sqrt{5}\right)\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{1088 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(17-\sqrt{17} \left(1-2 \sqrt{5}\right)\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{1088 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(17-\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{136 \sqrt[4]{5} \left(8-\sqrt{5}+\sqrt{85}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(17-9 \sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{1088 \sqrt[4]{5} \left(8-\sqrt{5}+\sqrt{85}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(17+9 \sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{1088 \sqrt[4]{5} \left(8-\sqrt{5}-\sqrt{85}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(17+\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{136 \sqrt[4]{5} \left(8-\sqrt{5}-\sqrt{85}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(51+19 \sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{1088 \sqrt[4]{5} \left(1+2 \sqrt{5}-\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(1-2 \sqrt{5}-\sqrt{17}\right) \left(17+2 \sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{2176 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(3+2 \sqrt{5}+\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{136 \sqrt[4]{5} \left(1+\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(3+2 \sqrt{5}+\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{2176 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{3 \left(1+\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{64 \sqrt[4]{5} \left(3+2 \sqrt{5}+\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(17-\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{544 \sqrt[4]{5} \left(1+2 \sqrt{5}+\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(51-19 \sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{1088 \sqrt[4]{5} \left(1+2 \sqrt{5}+\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(3-2 \sqrt{5}+\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{128 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{\left(17-2 \sqrt{17}\right) \left(1-2 \sqrt{5}+\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{2176 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(17+\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{544 \sqrt[4]{5} \left(1+2 \sqrt{5}-\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(3+2 \sqrt{5}-\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{136 \sqrt[4]{5} \left(1-\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(3+2 \sqrt{5}-\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{2176 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{3 \left(1-\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{64 \sqrt[4]{5} \left(3+2 \sqrt{5}-\sqrt{17}\right) \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}+\frac{\left(3-2 \sqrt{5}-\sqrt{17}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x^2+2}{\left(1-\sqrt{5}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} x}{\sqrt{-\left(\left(1-\sqrt{5}\right) x^2\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{128 \sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x^2+2}} \sqrt{x^4-x^2-1}}-\frac{3 \left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(-\frac{2 \left(1+\sqrt{5}\right)}{1-\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{2} \sqrt{x^4-x^2-1}}-\frac{\left(1+\sqrt{5}\right) \left(2-\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{2 \left(1+\sqrt{5}\right)}{1-\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \sqrt{x^4-x^2-1}}+\frac{\left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{2 \left(1+\sqrt{5}\right)}{1-\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{4 \sqrt{34} \left(1-\sqrt{17}\right) \sqrt{x^4-x^2-1}}+\frac{3 \left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{2 \left(1+\sqrt{5}\right)}{1-\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \sqrt{x^4-x^2-1}}-\frac{3 \left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(-\frac{2 \left(1+\sqrt{5}\right)}{1+\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{2} \sqrt{x^4-x^2-1}}+\frac{\left(1+\sqrt{5}\right) \left(2+\sqrt{17}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{2 \left(1+\sqrt{5}\right)}{1+\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \sqrt{x^4-x^2-1}}-\frac{\left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{2 \left(1+\sqrt{5}\right)}{1+\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{4 \sqrt{34} \left(1+\sqrt{17}\right) \sqrt{x^4-x^2-1}}-\frac{3 \left(1+\sqrt{5}\right) \sqrt{2 x^2+\sqrt{5}-1} \sqrt{1-\frac{2 x^2}{1+\sqrt{5}}} \Pi \left(\frac{2 \left(1+\sqrt{5}\right)}{1+\sqrt{17}};\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{64 \sqrt{34} \sqrt{x^4-x^2-1}}","-\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,"(x*(1 - Sqrt[5] - 2*x^2))/(17*Sqrt[-1 - x^2 + x^4]) - ((17 - 2*Sqrt[17])*x*(1 - Sqrt[5] - 2*x^2))/(544*Sqrt[-1 - x^2 + x^4]) - (x*(1 - Sqrt[5] - 2*x^2))/(34*(1 - Sqrt[17])*Sqrt[-1 - x^2 + x^4]) - (x*(1 - Sqrt[5] - 2*x^2))/(34*(1 + Sqrt[17])*Sqrt[-1 - x^2 + x^4]) - ((17 + 2*Sqrt[17])*x*(1 - Sqrt[5] - 2*x^2))/(544*Sqrt[-1 - x^2 + x^4]) + (x*Sqrt[-1 - x^2 + x^4])/(68*(1 - Sqrt[17] - 4*x^2)) + (4*x*Sqrt[-1 - x^2 + x^4])/(17*(1 - Sqrt[17])*(1 - Sqrt[17] - 4*x^2)) + (x*Sqrt[-1 - x^2 + x^4])/(68*(1 + Sqrt[17] - 4*x^2)) + (4*x*Sqrt[-1 - x^2 + x^4])/(17*(1 + Sqrt[17])*(1 + Sqrt[17] - 4*x^2)) + (5^(1/4)*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticE[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(17*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (5^(1/4)*(17 - 2*Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticE[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(544*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (5^(1/4)*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticE[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(34*(1 - Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (5^(1/4)*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticE[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(34*(1 + Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (5^(1/4)*(17 + 2*Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticE[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(544*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + (3*(1 + Sqrt[5])*(1 - Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[2]*(3 + 2*Sqrt[5] - Sqrt[17])*Sqrt[-1 - x^2 + x^4]) - ((1 + Sqrt[5])*(1 + Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(32*Sqrt[34]*(1 + 2*Sqrt[5] - Sqrt[17])*Sqrt[-1 - x^2 + x^4]) + ((1 + Sqrt[5])*(1 + Sqrt[17])*(2 + Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*(1 + 2*Sqrt[5] - Sqrt[17])*Sqrt[-1 - x^2 + x^4]) + ((1 + Sqrt[5])*(1 - Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(32*Sqrt[34]*(1 + 2*Sqrt[5] + Sqrt[17])*Sqrt[-1 - x^2 + x^4]) - ((1 + Sqrt[5])*(1 - Sqrt[17])*(2 - Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*(1 + 2*Sqrt[5] + Sqrt[17])*Sqrt[-1 - x^2 + x^4]) + (3*(1 + Sqrt[5])*(1 + Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[2]*(3 + 2*Sqrt[5] + Sqrt[17])*Sqrt[-1 - x^2 + x^4]) + ((1 + Sqrt[5])*(1 + Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(8*Sqrt[34]*(8 - Sqrt[5] - Sqrt[85])*Sqrt[-1 - x^2 + x^4]) + ((1 + Sqrt[5])*(9 + Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*(8 - Sqrt[5] - Sqrt[85])*Sqrt[-1 - x^2 + x^4]) - ((1 + Sqrt[5])*(1 - Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(8*Sqrt[34]*(8 - Sqrt[5] + Sqrt[85])*Sqrt[-1 - x^2 + x^4]) - ((1 + Sqrt[5])*(9 - Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*(8 - Sqrt[5] + Sqrt[85])*Sqrt[-1 - x^2 + x^4]) + ((3 - 2*Sqrt[5] - Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(128*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (3*(1 - Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(64*5^(1/4)*(3 + 2*Sqrt[5] - Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + ((3 + 2*Sqrt[5] - Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(2176*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + ((3 + 2*Sqrt[5] - Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(136*5^(1/4)*(1 - Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + ((17 + Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(544*5^(1/4)*(1 + 2*Sqrt[5] - Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((17 - 2*Sqrt[17])*(1 - 2*Sqrt[5] + Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(2176*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + ((3 - 2*Sqrt[5] + Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(128*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((51 - 19*Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(1088*5^(1/4)*(1 + 2*Sqrt[5] + Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + ((17 - Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(544*5^(1/4)*(1 + 2*Sqrt[5] + Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (3*(1 + Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(64*5^(1/4)*(3 + 2*Sqrt[5] + Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + ((3 + 2*Sqrt[5] + Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(2176*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) + ((3 + 2*Sqrt[5] + Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(136*5^(1/4)*(1 + Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((1 - 2*Sqrt[5] - Sqrt[17])*(17 + 2*Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(2176*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((51 + 19*Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(1088*5^(1/4)*(1 + 2*Sqrt[5] - Sqrt[17])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((17 + Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(136*5^(1/4)*(8 - Sqrt[5] - Sqrt[85])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((17 + 9*Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(1088*5^(1/4)*(8 - Sqrt[5] - Sqrt[85])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((17 - 9*Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(1088*5^(1/4)*(8 - Sqrt[5] + Sqrt[85])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((17 - Sqrt[17])*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(136*5^(1/4)*(8 - Sqrt[5] + Sqrt[85])*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((17 - Sqrt[17]*(1 - 2*Sqrt[5]))*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(1088*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - ((17 + Sqrt[17]*(1 - 2*Sqrt[5]))*Sqrt[-2 - (1 - Sqrt[5])*x^2]*Sqrt[(2 + (1 + Sqrt[5])*x^2)/(2 + (1 - Sqrt[5])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[5])*x^2]], (5 - Sqrt[5])/10])/(1088*5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x^2)^(-1)]*Sqrt[-1 - x^2 + x^4]) - (3*(1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(-2*(1 + Sqrt[5]))/(1 - Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[2]*Sqrt[-1 - x^2 + x^4]) + (3*(1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(2*(1 + Sqrt[5]))/(1 - Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*Sqrt[-1 - x^2 + x^4]) + ((1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(2*(1 + Sqrt[5]))/(1 - Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(4*Sqrt[34]*(1 - Sqrt[17])*Sqrt[-1 - x^2 + x^4]) - ((1 + Sqrt[5])*(2 - Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(2*(1 + Sqrt[5]))/(1 - Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*Sqrt[-1 - x^2 + x^4]) - (3*(1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(-2*(1 + Sqrt[5]))/(1 + Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[2]*Sqrt[-1 - x^2 + x^4]) - (3*(1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(2*(1 + Sqrt[5]))/(1 + Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*Sqrt[-1 - x^2 + x^4]) - ((1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(2*(1 + Sqrt[5]))/(1 + Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(4*Sqrt[34]*(1 + Sqrt[17])*Sqrt[-1 - x^2 + x^4]) + ((1 + Sqrt[5])*(2 + Sqrt[17])*Sqrt[-1 + Sqrt[5] + 2*x^2]*Sqrt[1 - (2*x^2)/(1 + Sqrt[5])]*EllipticPi[(2*(1 + Sqrt[5]))/(1 + Sqrt[17]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*x], (-3 - Sqrt[5])/2])/(64*Sqrt[34]*Sqrt[-1 - x^2 + x^4])","C",156,14,51,0.2745,0,"{6728, 6742, 1226, 1187, 1098, 1184, 1214, 1456, 540, 421, 419, 538, 537, 1208}"
911,1,587,0,1.2940075,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}-\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}","-\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,"-(((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4))) + ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) - ((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) + ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4))","B",21,11,35,0.3143,1,"{2056, 1269, 1428, 408, 240, 212, 206, 203, 377, 208, 205}"
912,1,587,0,0.9146551,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}-\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}","-\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,"-(((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4))) + ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) - ((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) + ((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4))","B",21,11,35,0.3143,1,"{2056, 1269, 1428, 408, 240, 212, 206, 203, 377, 208, 205}"
913,1,69,0,0.9704132,"\int \frac{\left(-b+a x^2\right) \sqrt{b^2+a^2 x^4}}{x^2 \left(b+a x^2\right)} \, dx","Int[((-b + a*x^2)*Sqrt[b^2 + a^2*x^4])/(x^2*(b + a*x^2)),x]","\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)","\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[b^2 + a^2*x^4]/x + Sqrt[2]*Sqrt[a]*Sqrt[b]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[b]*x)/Sqrt[b^2 + a^2*x^4]]","A",12,9,37,0.2432,1,"{6725, 277, 305, 220, 1196, 1209, 1211, 1699, 205}"
914,0,0,0,1.5418856,"\int \frac{4 b+a x^3}{\left(b+a x^3\right) \sqrt[4]{-b-a x^3+c x^4}} \, dx","Int[(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,"Defer[Int][(-b - a*x^3 + c*x^4)^(-1/4), x] - b^(1/3)*Defer[Int][1/((-b^(1/3) - a^(1/3)*x)*(-b - a*x^3 + c*x^4)^(1/4)), x] - b^(1/3)*Defer[Int][1/((-b^(1/3) + (-1)^(1/3)*a^(1/3)*x)*(-b - a*x^3 + c*x^4)^(1/4)), x] - b^(1/3)*Defer[Int][1/((-b^(1/3) - (-1)^(2/3)*a^(1/3)*x)*(-b - a*x^3 + c*x^4)^(1/4)), x]","F",0,0,0,0,-1,"{}"
915,0,0,0,2.6196091,"\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","Int[((-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,"(4*(1 + x^4)^(1/4)*Hypergeometric2F1[-21/16, -3/4, -5/16, -x^4])/(7*x^5*(x + x^5)^(1/4)) + (8*(1 + x^4)^(1/4)*Hypergeometric2F1[-3/4, -9/16, 7/16, -x^4])/(3*x^2*(x + x^5)^(1/4)) - (4*(1 + x^4)^(1/4)*Hypergeometric2F1[-3/4, -5/16, 11/16, -x^4])/(5*x*(x + x^5)^(1/4)) - (24*x^(1/4)*(1 + x^4)^(1/4)*Defer[Subst][Defer[Int][(x^2*(1 + x^16)^(3/4))/(1 - x^12 + x^16), x], x, x^(1/4)])/(x + x^5)^(1/4) + (32*x^(1/4)*(1 + x^4)^(1/4)*Defer[Subst][Defer[Int][(x^6*(1 + x^16)^(3/4))/(1 - x^12 + x^16), x], x, x^(1/4)])/(x + x^5)^(1/4)","F",0,0,0,0,-1,"{}"
916,0,0,0,2.6499893,"\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","Int[((-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,"(4*(1 + x^4)^(1/4)*Hypergeometric2F1[-21/16, 1/4, -5/16, -x^4])/(7*x^5*(x + x^5)^(1/4)) + (4*(1 + x^4)^(1/4)*Hypergeometric2F1[-9/16, 1/4, 7/16, -x^4])/(3*x^2*(x + x^5)^(1/4)) + (8*(1 + x^4)^(1/4)*Hypergeometric2F1[-5/16, 1/4, 11/16, -x^4])/(5*x*(x + x^5)^(1/4)) + (8*x*(1 + x^4)^(1/4)*Hypergeometric2F1[3/16, 1/4, 19/16, -x^4])/(3*(x + x^5)^(1/4)) + (4*x^2*(1 + x^4)^(1/4)*Hypergeometric2F1[1/4, 7/16, 23/16, -x^4])/(7*(x + x^5)^(1/4)) + (4*x^3*(1 + x^4)^(1/4)*Hypergeometric2F1[1/4, 11/16, 27/16, -x^4])/(11*(x + x^5)^(1/4)) - (32*x^(1/4)*(1 + x^4)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 + x^16)^(1/4)*(1 - x^12 + x^16)), x], x, x^(1/4)])/(x + x^5)^(1/4) + (8*x^(1/4)*(1 + x^4)^(1/4)*Defer[Subst][Defer[Int][x^14/((1 + x^16)^(1/4)*(1 - x^12 + x^16)), x], x, x^(1/4)])/(x + x^5)^(1/4)","F",0,0,0,0,-1,"{}"
917,1,70,0,0.0789902,"\int \frac{\left(b+a x^3\right)^{3/4}}{x} \, dx","Int[(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",6,6,15,0.4000,1,"{266, 50, 63, 298, 203, 206}"
918,1,70,0,0.08082,"\int \frac{1+3 x+3 x^4}{x \sqrt[4]{1+x^4}} \, dx","Int[(1 + 3*x + 3*x^4)/(x*(1 + x^4)^(1/4)),x]","\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)","\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,"(1 + x^4)^(3/4) + (3*ArcTan[x/(1 + x^4)^(1/4)])/2 + ArcTan[(1 + x^4)^(1/4)]/2 + (3*ArcTanh[x/(1 + x^4)^(1/4)])/2 - ArcTanh[(1 + x^4)^(1/4)]/2","A",12,9,23,0.3913,1,"{1833, 240, 212, 206, 203, 446, 80, 63, 298}"
919,1,70,0,0.0589699,"\int \frac{\left(b+a x^4\right)^{3/4}}{x} \, dx","Int[(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",6,6,15,0.4000,1,"{266, 50, 63, 298, 203, 206}"
920,0,0,0,1.1881552,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","\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,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] - I*Defer[Int][1/((I - x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - I*Defer[Int][1/((I + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]","F",0,0,0,0,-1,"{}"
921,1,70,0,0.9705681,"\int \frac{\left(b+a x^2\right) \sqrt{b^2+a^2 x^4}}{x^2 \left(-b+a x^2\right)} \, dx","Int[((b + a*x^2)*Sqrt[b^2 + a^2*x^4])/(x^2*(-b + a*x^2)),x]","\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)","\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[b^2 + a^2*x^4]/x - Sqrt[2]*Sqrt[a]*Sqrt[b]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[b]*x)/Sqrt[b^2 + a^2*x^4]]","A",14,10,37,0.2703,1,"{6725, 277, 305, 220, 1196, 1209, 1198, 1211, 1699, 208}"
922,1,70,0,0.0883329,"\int \frac{\left(b+a x^5\right)^{3/4}}{x} \, dx","Int[(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",6,6,15,0.4000,1,"{266, 50, 63, 298, 203, 206}"
923,0,0,0,5.7242721,"\int \frac{\left(3+2 x^5\right) \sqrt{x-2 x^4-x^6}}{\left(-1+x^5\right)^2} \, dx","Int[((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,"(Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(-1 + x)^2, x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (3*Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(-1 + x), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(1 + x)^2, x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (3*Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(1 + x), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(1 - x + x^2 - x^3 + x^4)^2, x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (3*Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x*Sqrt[1 - 2*x^6 - x^10])/(1 - x + x^2 - x^3 + x^4)^2, x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 - 2*x^6 - x^10])/(1 - x + x^2 - x^3 + x^4)^2, x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(1 - x + x^2 - x^3 + x^4), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x*Sqrt[1 - 2*x^6 - x^10])/(1 - x + x^2 - x^3 + x^4), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 - 2*x^6 - x^10])/(1 - x + x^2 - x^3 + x^4), x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (3*Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x^3*Sqrt[1 - 2*x^6 - x^10])/(1 - x + x^2 - x^3 + x^4), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(1 + x + x^2 + x^3 + x^4)^2, x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (3*Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x*Sqrt[1 - 2*x^6 - x^10])/(1 + x + x^2 + x^3 + x^4)^2, x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) - (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 - 2*x^6 - x^10])/(1 + x + x^2 + x^3 + x^4)^2, x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][Sqrt[1 - 2*x^6 - x^10]/(1 + x + x^2 + x^3 + x^4), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x*Sqrt[1 - 2*x^6 - x^10])/(1 + x + x^2 + x^3 + x^4), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 - 2*x^6 - x^10])/(1 + x + x^2 + x^3 + x^4), x], x, Sqrt[x]])/(2*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5]) + (3*Sqrt[x - 2*x^4 - x^6]*Defer[Subst][Defer[Int][(x^3*Sqrt[1 - 2*x^6 - x^10])/(1 + x + x^2 + x^3 + x^4), x], x, Sqrt[x]])/(10*Sqrt[x]*Sqrt[1 - 2*x^3 - x^5])","F",0,0,0,0,-1,"{}"
924,0,0,0,2.4405878,"\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","Int[((-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,"Defer[Int][(1 - x^4 + x^6)^(1/4), x] + Defer[Int][(1 - x^4 + x^6)^(1/4)/(-1 - x), x] + Defer[Int][(1 - x^4 + x^6)^(1/4)/(-1 + x), x] - 2*Defer[Int][(1 - x^4 + x^6)^(1/4)/x^6, x] - 4*Defer[Int][(1 - x^4 + x^6)^(1/4)/x^2, x] + ((2*I)*Defer[Int][(1 - x^4 + x^6)^(1/4)/(I*Sqrt[-1 + Sqrt[5]] - Sqrt[2]*x), x])/Sqrt[-1 + Sqrt[5]] - (2*Defer[Int][(1 - x^4 + x^6)^(1/4)/(Sqrt[1 + Sqrt[5]] - Sqrt[2]*x), x])/Sqrt[1 + Sqrt[5]] + ((2*I)*Defer[Int][(1 - x^4 + x^6)^(1/4)/(I*Sqrt[-1 + Sqrt[5]] + Sqrt[2]*x), x])/Sqrt[-1 + Sqrt[5]] - (2*Defer[Int][(1 - x^4 + x^6)^(1/4)/(Sqrt[1 + Sqrt[5]] + Sqrt[2]*x), x])/Sqrt[1 + Sqrt[5]]","F",0,0,0,0,-1,"{}"
925,1,70,0,0.0762154,"\int \frac{\left(b+a x^6\right)^{3/4}}{x} \, dx","Int[(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",6,6,15,0.4000,1,"{266, 50, 63, 298, 203, 206}"
926,1,72,0,0.1170633,"\int \frac{\sqrt{1+x}}{\sqrt{x+\sqrt{1+x}}} \, dx","Int[Sqrt[1 + x]/Sqrt[x + Sqrt[1 + x]],x]","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}+\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,"(-3*Sqrt[x + Sqrt[1 + x]])/2 + Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + (7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",5,4,21,0.1905,1,"{742, 640, 621, 206}"
927,1,62,0,0.1286428,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/Sqrt[1 + x],x]","\frac{1}{2} \sqrt{x+\sqrt{x+1}} \left(2 \sqrt{x+1}+1\right)-\frac{5}{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{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,"(Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/2 - (5*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4","A",4,3,21,0.1429,1,"{612, 621, 206}"
928,0,0,0,0.5699742,"\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^2} \, dx","Int[((-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,"(2*x^3)/(3*(1 + Sqrt[1 + x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 + x^2]] - I*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(I - x), x] - I*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(I + x), x]","F",0,0,0,0,-1,"{}"
929,0,0,0,0.028192,"\int \frac{1}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[1/Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int \frac{1}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","\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,"Defer[Int][1/Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
930,0,0,0,0.1425892,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{x^2} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/x^2,x]","\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{x^2} \, 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{\sqrt{\sqrt{x^4+1}+x^2}}{x}",1,"Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/x^2, x]","F",0,0,0,0,-1,"{}"
931,1,82,0,0.2249722,"\int \frac{1}{\left(\sqrt{-1+x}+2 \sqrt{x}\right)^2 \sqrt{-1+x}} \, dx","Int[1/((Sqrt[-1 + x] + 2*Sqrt[x])^2*Sqrt[-1 + x]),x]","-\frac{2 \sqrt{x-1}}{3 (3 x+1)}+\frac{4 \sqrt{x}}{3 (3 x+1)}+\frac{4 \tan ^{-1}\left(\frac{1}{2} \sqrt{3} \sqrt{x-1}\right)}{3 \sqrt{3}}-\frac{4 \tan ^{-1}\left(\sqrt{3} \sqrt{x}\right)}{3 \sqrt{3}}","-\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,"(-2*Sqrt[-1 + x])/(3*(1 + 3*x)) + (4*Sqrt[x])/(3*(1 + 3*x)) + (4*ArcTan[(Sqrt[3]*Sqrt[-1 + x])/2])/(3*Sqrt[3]) - (4*ArcTan[Sqrt[3]*Sqrt[x]])/(3*Sqrt[3])","A",10,5,25,0.2000,1,"{6742, 51, 63, 203, 47}"
932,1,43,0,0.0152437,"\int \frac{1}{\sqrt{-1+x^2} \left(-4+3 x^2\right)^2} \, dx","Int[1/(Sqrt[-1 + x^2]*(-4 + 3*x^2)^2),x]","\frac{3 \sqrt{x^2-1} x}{8 \left(4-3 x^2\right)}+\frac{5}{16} \tanh ^{-1}\left(\frac{x}{2 \sqrt{x^2-1}}\right)","-\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,"(3*x*Sqrt[-1 + x^2])/(8*(4 - 3*x^2)) + (5*ArcTanh[x/(2*Sqrt[-1 + x^2])])/16","A",3,3,19,0.1579,1,"{382, 377, 207}"
933,1,51,0,0.0649298,"\int \frac{1}{x \sqrt[3]{1+x^3}} \, dx","Int[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",5,5,13,0.3846,1,"{266, 55, 618, 204, 31}"
934,0,0,0,18.1102804,"\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","Int[(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,"(4*(k^2 - 2*d*(1 + k))*(1 - x)^(3/4)*x*(1 - k*x)^(3/4)*AppellF1[1/4, 3/4, 3/4, 5/4, x, k*x])/(d^2*((1 - x)*x*(1 - k*x))^(3/4)) + (4*k*(1 - x)^(3/4)*x^2*(1 - k*x)^(3/4)*AppellF1[5/4, 3/4, 3/4, 9/4, x, k*x])/(5*d*((1 - x)*x*(1 - k*x))^(3/4)) - (4*(k^2 - 2*d*(1 + k))*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][1/((1 - x^4)^(3/4)*(1 - k*x^4)^(3/4)*(1 - (1 + k)*x^4 + k*x^8 - d*x^12)), x], x, x^(1/4)])/(d^2*((1 - x)*x*(1 - k*x))^(3/4)) + (4*(k^2*(1 + k) - d*(2 + 5*k + 2*k^2))*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][x^4/((1 - x^4)^(3/4)*(1 - k*x^4)^(3/4)*(1 - (1 + k)*x^4 + k*x^8 - d*x^12)), x], x, x^(1/4)])/(d^2*((1 - x)*x*(1 - k*x))^(3/4)) - (4*(3*d^2 + k^3 - 3*d*k*(1 + k))*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][x^8/((1 - x^4)^(3/4)*(1 - k*x^4)^(3/4)*(1 - (1 + k)*x^4 + k*x^8 - d*x^12)), x], x, x^(1/4)])/(d^2*((1 - x)*x*(1 - k*x))^(3/4))","F",0,0,0,0,-1,"{}"
935,1,607,0,1.5908938,"\int \frac{-b+a x^2}{\left(-b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((-b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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 x^4-b x^2}}-\frac{\sqrt{x} \left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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 x^4-b x^2}}","-\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,"-(((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4))) + ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - ((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4))","B",21,11,40,0.2750,1,"{2056, 1269, 1428, 408, 240, 212, 206, 203, 377, 208, 205}"
936,1,607,0,1.0368033,"\int \frac{-b+a x^2}{\left(-b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((-b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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 x^4-b x^2}}-\frac{\sqrt{x} \left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2-b} \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 x^4-b x^2}}","-\frac{1}{2} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-a}\&\right]",1,"-(((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(-(b*x^2) + a*x^4)^(1/4))) + ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^2)^(1/4))])/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(-(b*x^2) + a*x^4)^(1/4))","B",21,11,40,0.2750,1,"{2056, 1269, 1428, 408, 240, 212, 206, 203, 377, 208, 205}"
937,1,192,0,3.6615539,"\int \frac{\sqrt[3]{-x+x^3}}{b+a x^6} \, dx","Int[(-x + x^3)^(1/3)/(b + a*x^6),x]","\frac{x \sqrt[3]{x^3-x} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{\sqrt[3]{-a} x^2}{\sqrt[3]{b}}\right)}{4 b \sqrt[3]{1-x^2}}+\frac{x \sqrt[3]{x^3-x} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,-\frac{\sqrt[3]{-1} \sqrt[3]{-a} x^2}{\sqrt[3]{b}}\right)}{4 b \sqrt[3]{1-x^2}}+\frac{x \sqrt[3]{x^3-x} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{(-1)^{2/3} \sqrt[3]{-a} x^2}{\sqrt[3]{b}}\right)}{4 b \sqrt[3]{1-x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^9 (-b)+3 \text{$\#$1}^6 b-3 \text{$\#$1}^3 b+a+b\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 b}",1,"(x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, ((-a)^(1/3)*x^2)/b^(1/3)])/(4*b*(1 - x^2)^(1/3)) + (x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, -(((-1)^(1/3)*(-a)^(1/3)*x^2)/b^(1/3))])/(4*b*(1 - x^2)^(1/3)) + (x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, ((-1)^(2/3)*(-a)^(1/3)*x^2)/b^(1/3)])/(4*b*(1 - x^2)^(1/3))","B",55,7,21,0.3333,0,"{2056, 6725, 959, 466, 465, 511, 510}"
938,1,192,0,3.3606055,"\int \frac{\sqrt[3]{-x+x^3}}{b+a x^6} \, dx","Int[(-x + x^3)^(1/3)/(b + a*x^6),x]","\frac{x \sqrt[3]{x^3-x} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{\sqrt[3]{-a} x^2}{\sqrt[3]{b}}\right)}{4 b \sqrt[3]{1-x^2}}+\frac{x \sqrt[3]{x^3-x} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,-\frac{\sqrt[3]{-1} \sqrt[3]{-a} x^2}{\sqrt[3]{b}}\right)}{4 b \sqrt[3]{1-x^2}}+\frac{x \sqrt[3]{x^3-x} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{(-1)^{2/3} \sqrt[3]{-a} x^2}{\sqrt[3]{b}}\right)}{4 b \sqrt[3]{1-x^2}}","\frac{\text{RootSum}\left[\text{$\#$1}^9 (-b)+3 \text{$\#$1}^6 b-3 \text{$\#$1}^3 b+a+b\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 b}",1,"(x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, ((-a)^(1/3)*x^2)/b^(1/3)])/(4*b*(1 - x^2)^(1/3)) + (x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, -(((-1)^(1/3)*(-a)^(1/3)*x^2)/b^(1/3))])/(4*b*(1 - x^2)^(1/3)) + (x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, ((-1)^(2/3)*(-a)^(1/3)*x^2)/b^(1/3)])/(4*b*(1 - x^2)^(1/3))","B",55,7,21,0.3333,0,"{2056, 6725, 959, 466, 465, 511, 510}"
939,0,0,0,1.7498485,"\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","Int[((-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,"(-2*a*x^3)/(b + a*x^6)^(1/4) + (2*(b + a*x^6)^(3/4))/(3*x^3) + (2*Sqrt[a]*Sqrt[b]*(1 + (a*x^6)/b)^(1/4)*EllipticE[ArcTan[(Sqrt[a]*x^3)/Sqrt[b]]/2, 2])/(b + a*x^6)^(1/4) + 2*c*Defer[Int][(b + a*x^6)^(3/4)/(-b + c*x^4 - a*x^6), x] + 3*a*Defer[Int][(x^2*(b + a*x^6)^(3/4))/(b - c*x^4 + a*x^6), x]","F",0,0,0,0,-1,"{}"
940,0,0,0,0.9472108,"\int \frac{b+a x^8}{\left(-b+a x^8\right) \sqrt[4]{-b+c x^4+a x^8}} \, dx","Int[(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,"(x*(1 + (2*a*x^4)/(c - Sqrt[4*a*b + c^2]))^(1/4)*(1 + (2*a*x^4)/(c + Sqrt[4*a*b + c^2]))^(1/4)*AppellF1[1/4, 1/4, 1/4, 5/4, (-2*a*x^4)/(c - Sqrt[4*a*b + c^2]), (-2*a*x^4)/(c + Sqrt[4*a*b + c^2])])/(-b + c*x^4 + a*x^8)^(1/4) - Sqrt[b]*Defer[Int][1/((Sqrt[b] - Sqrt[a]*x^4)*(-b + c*x^4 + a*x^8)^(1/4)), x] - Sqrt[b]*Defer[Int][1/((Sqrt[b] + Sqrt[a]*x^4)*(-b + c*x^4 + a*x^8)^(1/4)), x]","F",0,0,0,0,-1,"{}"
941,0,0,0,0.6005332,"\int \frac{\sqrt{1+x^5} \left(-2+3 x^5\right)}{1+x^4+2 x^5+x^{10}} \, dx","Int[(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,"-2*Defer[Int][Sqrt[1 + x^5]/(1 + x^4 + 2*x^5 + x^10), x] + 3*Defer[Int][(x^5*Sqrt[1 + x^5])/(1 + x^4 + 2*x^5 + x^10), x]","F",0,0,0,0,-1,"{}"
942,1,82,0,0.1183339,"\int \frac{1}{\left(2 x+\sqrt{1+x^2}\right)^2} \, dx","Int[(2*x + Sqrt[1 + x^2])^(-2),x]","\frac{4 x}{3 \left(1-3 x^2\right)}-\frac{2 \sqrt{x^2+1}}{3 \left(1-3 x^2\right)}+\frac{\tanh ^{-1}\left(\frac{1}{2} \sqrt{3} \sqrt{x^2+1}\right)}{3 \sqrt{3}}-\frac{\tanh ^{-1}\left(\sqrt{3} x\right)}{3 \sqrt{3}}","-\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,"(4*x)/(3*(1 - 3*x^2)) - (2*Sqrt[1 + x^2])/(3*(1 - 3*x^2)) - ArcTanh[Sqrt[3]*x]/(3*Sqrt[3]) + ArcTanh[(Sqrt[3]*Sqrt[1 + x^2])/2]/(3*Sqrt[3])","A",9,6,15,0.4000,1,"{6742, 199, 207, 444, 47, 63}"
943,0,0,0,1.1865864,"\int \frac{\sqrt{a x^2+x \sqrt{-b+a^2 x^2}}}{x \sqrt{-b+a^2 x^2}} \, dx","Int[Sqrt[a*x^2 + x*Sqrt[-b + a^2*x^2]]/(x*Sqrt[-b + a^2*x^2]),x]","\int \frac{\sqrt{a x^2+x \sqrt{-b+a^2 x^2}}}{x \sqrt{-b+a^2 x^2}} \, dx","-\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,"Defer[Int][Sqrt[a*x^2 + x*Sqrt[-b + a^2*x^2]]/(x*Sqrt[-b + a^2*x^2]), x]","F",0,0,0,0,-1,"{}"
944,0,0,0,0.5469525,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]",1,"(I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I - x), x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I + x), x]","F",0,0,0,0,-1,"{}"
945,0,0,0,0.4179576,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1+x^2} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]",1,"(I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I - x), x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I + x), x]","F",0,0,0,0,-1,"{}"
946,0,0,0,0.1021272,"\int \frac{\sqrt[3]{1+2 x+x^2}}{4+x+x^2+x^3} \, dx","Int[(1 + 2*x + x^2)^(1/3)/(4 + x + x^2 + x^3),x]","\int \frac{\sqrt[3]{1+2 x+x^2}}{4+x+x^2+x^3} \, dx","\frac{\sqrt[3]{(x+1)^2} \text{RootSum}\left[\text{$\#$1}^9-2 \text{$\#$1}^6+2 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x+1}-\text{$\#$1}\right)}{3 \text{$\#$1}^6-4 \text{$\#$1}^3+2}\&\right]}{(x+1)^{2/3}}",1,"Defer[Int][(1 + 2*x + x^2)^(1/3)/(4 + x + x^2 + x^3), x]","F",0,0,0,0,-1,"{}"
947,1,2595,0,9.8649884,"\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","Int[((-1 + x^2)*Sqrt[1 + x^4])/((1 - x + x^2)*(1 + x + x^2)^2),x]","\frac{\left(i+\sqrt{3}\right) \sqrt{x^4+1} x}{3 \left(2 i x^2-\sqrt{3}+i\right)}-\frac{i \sqrt{x^4+1} x}{3 \left(2 i x^2-\sqrt{3}+i\right)}+\frac{\left(i-\sqrt{3}\right) \sqrt{x^4+1} x}{3 \left(2 i x^2+\sqrt{3}+i\right)}-\frac{i \sqrt{x^4+1} x}{3 \left(2 i x^2+\sqrt{3}+i\right)}-\frac{\left(3+2 i \sqrt{3}\right) \sqrt{x^4+1} x}{12 \left(x^2+1\right)}-\frac{\left(3-2 i \sqrt{3}\right) \sqrt{x^4+1} x}{12 \left(x^2+1\right)}-\frac{\left(1+i \sqrt{3}\right) \sqrt{x^4+1} x}{3 \left(x^2+1\right)}-\frac{\left(1-i \sqrt{3}\right) \sqrt{x^4+1} x}{3 \left(x^2+1\right)}+\frac{7 \sqrt{x^4+1} x}{6 \left(x^2+1\right)}+\frac{1}{48} \left(9+i \sqrt{3}\right) \sinh ^{-1}\left(x^2\right)-\frac{1}{32} \left(1+i \sqrt{3}\right)^2 \sinh ^{-1}\left(x^2\right)-\frac{3}{16} \left(1+i \sqrt{3}\right) \sinh ^{-1}\left(x^2\right)+\frac{1}{48} \left(9-i \sqrt{3}\right) \sinh ^{-1}\left(x^2\right)-\frac{1}{4} \left(1-i \sqrt{3}\right) \sinh ^{-1}\left(x^2\right)-\frac{1}{24} \left(3+2 i \sqrt{3}\right) \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{1}{24} \left(3-2 i \sqrt{3}\right) \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{1}{12} \left(3+i \sqrt{3}\right) \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{1}{12} \left(1+i \sqrt{3}\right) \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{1}{12} \left(3-i \sqrt{3}\right) \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{1}{12} \left(1-i \sqrt{3}\right) \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)+\frac{5}{12} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+1}}\right)-\frac{\left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{2 i-\left(i-\sqrt{3}\right) x^2}{\sqrt{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{6 \left(i-\sqrt{3}\right)}-\frac{1}{3} \tan ^{-1}\left(\frac{2 i-\left(i-\sqrt{3}\right) x^2}{\sqrt{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)+\frac{\left(i-\sqrt{3}\right) \tan ^{-1}\left(\frac{2 i-\left(i+\sqrt{3}\right) x^2}{\sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)}{6 \left(i+\sqrt{3}\right)}+\frac{1}{3} \tan ^{-1}\left(\frac{2 i-\left(i+\sqrt{3}\right) x^2}{\sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)+\frac{1}{8} i \tanh ^{-1}\left(\frac{2-\left(1-i \sqrt{3}\right) x^2}{\sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)-\frac{1}{24} \left(3 i-2 \sqrt{3}\right) \tanh ^{-1}\left(\frac{2-\left(1+i \sqrt{3}\right) x^2}{\sqrt{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)-\frac{1}{8} i \tanh ^{-1}\left(\frac{2-\left(1+i \sqrt{3}\right) x^2}{\sqrt{2 \left(1+i \sqrt{3}\right)} \sqrt{x^4+1}}\right)+\frac{1}{24} \left(3 i+2 \sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1+i \sqrt{3}\right)^2 x^2+4}{2 \sqrt{2 \left(1-i \sqrt{3}\right)} \sqrt{x^4+1}}\right)+\frac{\left(3+2 i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}+\frac{\left(3-2 i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}+\frac{\left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}+\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+1}}-\frac{7 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}+\frac{\left(3 i+\sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \left(3 i-\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(3 i-\sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \left(3 i+\sqrt{3}\right) \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{3} \left(3 i+\sqrt{3}\right) \sqrt{x^4+1}}-\frac{\left(9+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}-\frac{\left(3+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}-\frac{\left(1+i \sqrt{3}\right)^2 \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{3 \left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}-\frac{\left(9-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}-\frac{\left(3-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}+\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{3} \left(3 i-\sqrt{3}\right) \sqrt{x^4+1}}-\frac{\left(3+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}+\frac{\left(2+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{\left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}-\frac{\left(3-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{24 \sqrt{x^4+1}}+\frac{\left(2-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}+\frac{\left(i+\sqrt{3}\right) \sqrt{x^4+1}}{6 \left(2 i x^2-\sqrt{3}+i\right)}+\frac{\left(i-\sqrt{3}\right) \sqrt{x^4+1}}{3 \left(2 i x^2-\sqrt{3}+i\right)}+\frac{\left(i+\sqrt{3}\right) \sqrt{x^4+1}}{3 \left(2 i x^2+\sqrt{3}+i\right)}+\frac{\left(i-\sqrt{3}\right) \sqrt{x^4+1}}{6 \left(2 i x^2+\sqrt{3}+i\right)}-\frac{1}{48} \left(3+5 i \sqrt{3}\right) \sqrt{x^4+1}-\frac{1}{48} \left(3-5 i \sqrt{3}\right) \sqrt{x^4+1}+\frac{1}{16} \left(1+i \sqrt{3}\right) \sqrt{x^4+1}+\frac{1}{16} \left(1-i \sqrt{3}\right) \sqrt{x^4+1}","\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 - I*Sqrt[3])*Sqrt[1 + x^4])/16 + ((1 + I*Sqrt[3])*Sqrt[1 + x^4])/16 - ((3 - (5*I)*Sqrt[3])*Sqrt[1 + x^4])/48 - ((3 + (5*I)*Sqrt[3])*Sqrt[1 + x^4])/48 + ((I - Sqrt[3])*Sqrt[1 + x^4])/(3*(I - Sqrt[3] + (2*I)*x^2)) + ((I + Sqrt[3])*Sqrt[1 + x^4])/(6*(I - Sqrt[3] + (2*I)*x^2)) - ((I/3)*x*Sqrt[1 + x^4])/(I - Sqrt[3] + (2*I)*x^2) + ((I + Sqrt[3])*x*Sqrt[1 + x^4])/(3*(I - Sqrt[3] + (2*I)*x^2)) + ((I - Sqrt[3])*Sqrt[1 + x^4])/(6*(I + Sqrt[3] + (2*I)*x^2)) + ((I + Sqrt[3])*Sqrt[1 + x^4])/(3*(I + Sqrt[3] + (2*I)*x^2)) - ((I/3)*x*Sqrt[1 + x^4])/(I + Sqrt[3] + (2*I)*x^2) + ((I - Sqrt[3])*x*Sqrt[1 + x^4])/(3*(I + Sqrt[3] + (2*I)*x^2)) + (7*x*Sqrt[1 + x^4])/(6*(1 + x^2)) - ((1 - I*Sqrt[3])*x*Sqrt[1 + x^4])/(3*(1 + x^2)) - ((1 + I*Sqrt[3])*x*Sqrt[1 + x^4])/(3*(1 + x^2)) - ((3 - (2*I)*Sqrt[3])*x*Sqrt[1 + x^4])/(12*(1 + x^2)) - ((3 + (2*I)*Sqrt[3])*x*Sqrt[1 + x^4])/(12*(1 + x^2)) - ((1 - I*Sqrt[3])*ArcSinh[x^2])/4 + ((9 - I*Sqrt[3])*ArcSinh[x^2])/48 - (3*(1 + I*Sqrt[3])*ArcSinh[x^2])/16 - ((1 + I*Sqrt[3])^2*ArcSinh[x^2])/32 + ((9 + I*Sqrt[3])*ArcSinh[x^2])/48 + (5*ArcTan[x/Sqrt[1 + x^4]])/12 - ((1 - I*Sqrt[3])*ArcTan[x/Sqrt[1 + x^4]])/12 - ((3 - I*Sqrt[3])*ArcTan[x/Sqrt[1 + x^4]])/12 - ((1 + I*Sqrt[3])*ArcTan[x/Sqrt[1 + x^4]])/12 - ((3 + I*Sqrt[3])*ArcTan[x/Sqrt[1 + x^4]])/12 - ((3 - (2*I)*Sqrt[3])*ArcTan[x/Sqrt[1 + x^4]])/24 - ((3 + (2*I)*Sqrt[3])*ArcTan[x/Sqrt[1 + x^4]])/24 - ArcTan[(2*I - (I - Sqrt[3])*x^2)/(Sqrt[2*(1 + I*Sqrt[3])]*Sqrt[1 + x^4])]/3 - ((I + Sqrt[3])*ArcTan[(2*I - (I - Sqrt[3])*x^2)/(Sqrt[2*(1 + I*Sqrt[3])]*Sqrt[1 + x^4])])/(6*(I - Sqrt[3])) + ArcTan[(2*I - (I + Sqrt[3])*x^2)/(Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])]/3 + ((I - Sqrt[3])*ArcTan[(2*I - (I + Sqrt[3])*x^2)/(Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/(6*(I + Sqrt[3])) + (I/8)*ArcTanh[(2 - (1 - I*Sqrt[3])*x^2)/(Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])] - (I/8)*ArcTanh[(2 - (1 + I*Sqrt[3])*x^2)/(Sqrt[2*(1 + I*Sqrt[3])]*Sqrt[1 + x^4])] - ((3*I - 2*Sqrt[3])*ArcTanh[(2 - (1 + I*Sqrt[3])*x^2)/(Sqrt[2*(1 + I*Sqrt[3])]*Sqrt[1 + x^4])])/24 + ((3*I + 2*Sqrt[3])*ArcTanh[(4 + (1 + I*Sqrt[3])^2*x^2)/(2*Sqrt[2*(1 - I*Sqrt[3])]*Sqrt[1 + x^4])])/24 - (7*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4]) + ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4]) + ((1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(3*Sqrt[1 + x^4]) + ((3 - (2*I)*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(12*Sqrt[1 + x^4]) + ((3 + (2*I)*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/2])/(12*Sqrt[1 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(Sqrt[3]*(3*I - Sqrt[3])*Sqrt[1 + x^4]) + ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4]) - ((3 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(24*Sqrt[1 + x^4]) - ((9 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(24*Sqrt[1 + x^4]) + (3*(1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*Sqrt[1 + x^4]) - ((1 + I*Sqrt[3])^2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) - ((3 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(24*Sqrt[1 + x^4]) - ((9 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(24*Sqrt[1 + x^4]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(Sqrt[3]*(3*I + Sqrt[3])*Sqrt[1 + x^4]) + ((3*I - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(12*(3*I + Sqrt[3])*Sqrt[1 + x^4]) + ((3*I + Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(12*(3*I - Sqrt[3])*Sqrt[1 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[1/4, 2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4]) + ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[1/4, 2*ArcTan[x], 1/2])/(8*Sqrt[1 + x^4]) + ((2 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[1/4, 2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) - ((3 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[1/4, 2*ArcTan[x], 1/2])/(24*Sqrt[1 + x^4]) + ((1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[1/4, 2*ArcTan[x], 1/2])/(8*Sqrt[1 + x^4]) + ((2 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[1/4, 2*ArcTan[x], 1/2])/(16*Sqrt[1 + x^4]) - ((3 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[1/4, 2*ArcTan[x], 1/2])/(24*Sqrt[1 + x^4])","C",248,20,33,0.6061,0,"{6728, 1729, 1209, 1198, 220, 1196, 1217, 1707, 1248, 735, 844, 215, 725, 206, 6742, 2153, 1227, 733, 204, 1336}"
948,1,153,0,0.1953795,"\int x^4 \sqrt[4]{-x^2+x^4} \, dx","Int[x^4*(-x^2 + x^4)^(1/4),x]","-\frac{7}{192} \sqrt[4]{x^4-x^2} x+\frac{7 \left(x^2-1\right)^{3/4} x^{3/2} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{128 \left(x^4-x^2\right)^{3/4}}-\frac{7 \left(x^2-1\right)^{3/4} x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{128 \left(x^4-x^2\right)^{3/4}}+\frac{1}{6} \sqrt[4]{x^4-x^2} x^5-\frac{1}{48} \sqrt[4]{x^4-x^2} x^3","\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,"(-7*x*(-x^2 + x^4)^(1/4))/192 - (x^3*(-x^2 + x^4)^(1/4))/48 + (x^5*(-x^2 + x^4)^(1/4))/6 + (7*x^(3/2)*(-1 + x^2)^(3/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(128*(-x^2 + x^4)^(3/4)) - (7*x^(3/2)*(-1 + x^2)^(3/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(128*(-x^2 + x^4)^(3/4))","B",9,8,17,0.4706,1,"{2021, 2024, 2032, 329, 331, 298, 203, 206}"
949,1,168,0,0.1521743,"\int \frac{x^4 \sqrt[4]{x^3+x^4}}{1+x} \, dx","Int[(x^4*(x^3 + x^4)^(1/4))/(1 + x),x]","\frac{1}{5} \sqrt[4]{x^4+x^3} x^4-\frac{19}{80} \sqrt[4]{x^4+x^3} x^3-\frac{209}{512} \sqrt[4]{x^4+x^3} x+\frac{1463 \sqrt[4]{x^4+x^3}}{2048}+\frac{4389 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4096 \sqrt[4]{x+1} x^{3/4}}-\frac{4389 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4096 \sqrt[4]{x+1} x^{3/4}}+\frac{19}{64} \sqrt[4]{x^4+x^3} x^2","\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,"(1463*(x^3 + x^4)^(1/4))/2048 - (209*x*(x^3 + x^4)^(1/4))/512 + (19*x^2*(x^3 + x^4)^(1/4))/64 - (19*x^3*(x^3 + x^4)^(1/4))/80 + (x^4*(x^3 + x^4)^(1/4))/5 + (4389*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(4096*x^(3/4)*(1 + x)^(1/4)) - (4389*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(4096*x^(3/4)*(1 + x)^(1/4))","B",11,7,20,0.3500,1,"{2056, 50, 63, 331, 298, 203, 206}"
950,0,0,0,3.4462181,"\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","Int[((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,"(-4*(b + a*x^3)^(3/4))/(3*x^3) + 4*b*Defer[Int][1/((b + a*x^3)^(1/4)*(b + a*x^3 - 2*x^4)), x] + a*Defer[Int][x^3/((b + a*x^3)^(1/4)*(b + a*x^3 - 2*x^4)), x]","F",0,0,0,0,-1,"{}"
951,1,417,0,0.7197609,"\int \frac{b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{\text{$\#$1}^4-a}\&\right]",1,"-1/2*((a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + ((a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + ((a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4))","B",21,9,32,0.2812,1,"{2056, 1270, 1429, 408, 240, 212, 206, 203, 377}"
952,1,417,0,0.4891264,"\int \frac{b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{-a} \sqrt{b} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{\text{$\#$1}^4-a}\&\right]",1,"-1/2*((a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + ((a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + ((a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*Sqrt[-a]*Sqrt[b]*(b*x^2 + a*x^4)^(1/4))","B",21,9,32,0.2812,1,"{2056, 1270, 1429, 408, 240, 212, 206, 203, 377}"
953,1,67,0,0.1880086,"\int \frac{1-x}{\sqrt{3+2 x-5 x^2-4 x^3+x^4+2 x^5+x^6}} \, dx","Int[(1 - x)/Sqrt[3 + 2*x - 5*x^2 - 4*x^3 + x^4 + 2*x^5 + x^6],x]","-\frac{\left(1-x^2\right) \sqrt{x^2+2 x+3} \tanh ^{-1}\left(\frac{\sqrt{x^2+2 x+3}}{\sqrt{2}}\right)}{\sqrt{2} \sqrt{\left(1-x^2\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]*ArcTanh[Sqrt[3 + 2*x + x^2]/Sqrt[2]])/(Sqrt[2]*Sqrt[(1 - x^2)^2*(3 + 2*x + x^2)]))","A",7,7,36,0.1944,1,"{6688, 6719, 1033, 724, 206, 688, 207}"
954,0,0,0,2.1673477,"\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","Int[((-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,"Defer[Int][Sqrt[1 + x^2 + 2*x^4 + x^8]/(-1 - x - x^4), x]/4 + Defer[Int][Sqrt[1 + x^2 + 2*x^4 + x^8]/(-1 + x - x^4), x]/4 - Defer[Int][Sqrt[1 + x^2 + 2*x^4 + x^8]/(1 - x + x^4)^2, x]/2 + 2*Defer[Int][(x^3*Sqrt[1 + x^2 + 2*x^4 + x^8])/(1 - x + x^4)^2, x] - Defer[Int][(x^2*Sqrt[1 + x^2 + 2*x^4 + x^8])/(1 - x + x^4), x] + Defer[Int][(x^3*Sqrt[1 + x^2 + 2*x^4 + x^8])/(1 - x + x^4), x]/4 + Defer[Int][(x^2*Sqrt[1 + x^2 + 2*x^4 + x^8])/(1 + x + x^4), x] - Defer[Int][(x^3*Sqrt[1 + x^2 + 2*x^4 + x^8])/(1 + x + x^4), x]/4","F",0,0,0,0,-1,"{}"
955,1,75,0,0.0239238,"\int \sqrt{c+b x+a x^2} \, dx","Int[Sqrt[c + b*x + a*x^2],x]","\frac{(2 a x+b) \sqrt{a x^2+b x+c}}{4 a}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a x+b}{2 \sqrt{a} \sqrt{a x^2+b x+c}}\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 + b*x + a*x^2])/(4*a) - ((b^2 - 4*a*c)*ArcTanh[(b + 2*a*x)/(2*Sqrt[a]*Sqrt[c + b*x + a*x^2])])/(8*a^(3/2))","A",3,3,14,0.2143,1,"{612, 621, 206}"
956,1,103,0,0.5111031,"\int \frac{-1+x}{\left(-1-2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(-1 + x)/((-1 - 2*x + x^2)*Sqrt[-x + x^3]),x]","\frac{\sqrt{x} \sqrt{1-x^2} \Pi \left(-\frac{1}{\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}-\frac{\sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}","\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[x]*Sqrt[1 - x^2]*EllipticPi[-(1/Sqrt[2]), ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3]) - (Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/Sqrt[2], ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3])","C",9,5,25,0.2000,1,"{2056, 6728, 933, 168, 537}"
957,1,180,0,0.818996,"\int \frac{-2+3 x+x^2}{\left(-1-2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(-2 + 3*x + x^2)/((-1 - 2*x + x^2)*Sqrt[-x + x^3]),x]","\frac{\sqrt{2} \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^3-x}}+\frac{\left(5+2 \sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(-\frac{1}{\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}-\frac{\left(5-2 \sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}","\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[2]*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/Sqrt[-x + x^3] + ((5 + 2*Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[-(1/Sqrt[2]), ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3]) - ((5 - 2*Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/Sqrt[2], ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3])","C",13,7,30,0.2333,0,"{2056, 6728, 329, 222, 933, 168, 537}"
958,0,0,0,0.9085739,"\int \frac{x \left(-3+x^2\right)}{\left(-1+x^2\right)^{2/3} \left(1-x^2+x^3\right)} \, dx","Int[(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,"(3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + (-1 + x^2)^(1/3))*Sqrt[(1 - (-1 + x^2)^(1/3) + (-1 + x^2)^(2/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]*EllipticF[ArcSin[(1 - Sqrt[3] + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))], -7 - 4*Sqrt[3]])/(x*Sqrt[(1 + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]) - Defer[Int][1/((-1 + x^2)^(2/3)*(1 - x^2 + x^3)), x] - 3*Defer[Int][x/((-1 + x^2)^(2/3)*(1 - x^2 + x^3)), x] + Defer[Int][x^2/((-1 + x^2)^(2/3)*(1 - x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
959,1,162,0,0.1914728,"\int x^2 \sqrt[4]{-x^3+x^4} \, dx","Int[x^2*(-x^3 + x^4)^(1/4),x]","\frac{1}{4} \sqrt[4]{x^4-x^3} x^3-\frac{11}{384} \sqrt[4]{x^4-x^3} x-\frac{77 \sqrt[4]{x^4-x^3}}{1536}-\frac{77 (x-1)^{3/4} x^{9/4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{1024 \left(x^4-x^3\right)^{3/4}}-\frac{77 (x-1)^{3/4} x^{9/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{1024 \left(x^4-x^3\right)^{3/4}}-\frac{1}{48} \sqrt[4]{x^4-x^3} x^2","\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,"(-77*(-x^3 + x^4)^(1/4))/1536 - (11*x*(-x^3 + x^4)^(1/4))/384 - (x^2*(-x^3 + x^4)^(1/4))/48 + (x^3*(-x^3 + x^4)^(1/4))/4 - (77*(-1 + x)^(3/4)*x^(9/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(1024*(-x^3 + x^4)^(3/4)) - (77*(-1 + x)^(3/4)*x^(9/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(1024*(-x^3 + x^4)^(3/4))","B",10,8,17,0.4706,1,"{2021, 2024, 2032, 63, 240, 212, 206, 203}"
960,0,0,0,5.6786001,"\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","Int[((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,"((-I)*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/(I - x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) + ((-1)^(1/4)*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/((-1)^(1/4) - x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) - ((-1)^(3/4)*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/(-(-1)^(3/4) - x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) + (Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/(-1 + x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) - (I*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/(I + x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) - (Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/(1 + x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) + ((-1)^(1/4)*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/((-1)^(1/4) + x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) - ((-1)^(3/4)*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][Sqrt[1 + x^6 - x^8]/(-(-1)^(3/4) + x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) - (6*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 + x^6 - x^8])/(-1 + x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4]) - (8*Sqrt[x + x^4 - x^5]*Defer[Subst][Defer[Int][(x^4*Sqrt[1 + x^6 - x^8])/(-1 + x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x^3 - x^4])","F",0,0,0,0,-1,"{}"
961,1,2513,0,15.3006391,"\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","Int[((-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{\left(1-\frac{\sqrt{a} \sqrt{b}}{\sqrt{-a b-\sqrt{1-2 a b}+1}}\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right) \left(1-\sqrt{1-2 a b}\right)^2}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b-\sqrt{1-2 a b}+1\right) \sqrt{x} \left(a x^2+b\right)}-\frac{\left(\frac{\sqrt{a} \sqrt{b}}{\sqrt{-a b-\sqrt{1-2 a b}+1}}+1\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right) \left(1-\sqrt{1-2 a b}\right)^2}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b-\sqrt{1-2 a b}+1\right) \sqrt{x} \left(a x^2+b\right)}-\frac{\left(2 a^2 b^2-a \left(5-3 \sqrt{1-2 a b}\right) b-2 \sqrt{1-2 a b}+2\right) \sqrt{a x^3+b x} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-2 a b}} \sqrt{x}}{\sqrt[4]{-a b-\sqrt{1-2 a b}+1} \sqrt{a x^2+b}}\right) \left(1-\sqrt{1-2 a b}\right)^{3/2}}{4 \left(-2 a b-\sqrt{1-2 a b}+1\right) \left(-a b-\sqrt{1-2 a b}+1\right)^{7/4} \sqrt{x} \sqrt{a x^2+b}}+\frac{\left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right) \left(1-\sqrt{1-2 a b}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{x} \left(a x^2+b\right)}-\frac{\left(\sqrt{1-2 a b}-1\right)^{3/2} \left(2 a^2 b^2-a \left(5-3 \sqrt{1-2 a b}\right) b-2 \sqrt{1-2 a b}+2\right) \sqrt{a x^3+b x} \tan ^{-1}\left(\frac{\sqrt{\sqrt{1-2 a b}-1} \sqrt{x}}{\sqrt[4]{-a b-\sqrt{1-2 a b}+1} \sqrt{a x^2+b}}\right)}{4 \left(-2 a b-\sqrt{1-2 a b}+1\right) \left(-a b-\sqrt{1-2 a b}+1\right)^{7/4} \sqrt{x} \sqrt{a x^2+b}}-\frac{\left(-\sqrt{1-2 a b}-1\right)^{3/2} \sqrt{a x^3+b x} \tan ^{-1}\left(\frac{\sqrt{-\sqrt{1-2 a b}-1} \sqrt{x}}{\sqrt[4]{-a b+\sqrt{1-2 a b}+1} \sqrt{a x^2+b}}\right)}{4 \left(-a b+\sqrt{1-2 a b}+1\right)^{3/4} \sqrt{x} \sqrt{a x^2+b}}-\frac{\left(\sqrt{1-2 a b}+1\right)^{3/2} \sqrt{a x^3+b x} \tan ^{-1}\left(\frac{\sqrt{\sqrt{1-2 a b}+1} \sqrt{x}}{\sqrt[4]{-a b+\sqrt{1-2 a b}+1} \sqrt{a x^2+b}}\right)}{4 \left(-a b+\sqrt{1-2 a b}+1\right)^{3/4} \sqrt{x} \sqrt{a x^2+b}}+\frac{\left(\sqrt{1-2 a b}+1\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{x} \left(a x^2+b\right)}-\frac{\left(\sqrt{1-2 a b}+1\right)^2 \left(1-\frac{\sqrt{a} \sqrt{b}}{\sqrt{-a b+\sqrt{1-2 a b}+1}}\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b+\sqrt{1-2 a b}+1\right) \sqrt{x} \left(a x^2+b\right)}-\frac{\left(\sqrt{1-2 a b}+1\right)^2 \left(\frac{\sqrt{a} \sqrt{b}}{\sqrt{-a b+\sqrt{1-2 a b}+1}}+1\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b+\sqrt{1-2 a b}+1\right) \sqrt{x} \left(a x^2+b\right)}+\frac{\left(-\sqrt{1-2 a b}+2 \sqrt{a} \sqrt{b} \sqrt{-a b-\sqrt{1-2 a b}+1}+1\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} \Pi \left(-\frac{\left(\sqrt{a} \sqrt{b}-\sqrt{-a b-\sqrt{1-2 a b}+1}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-a b-\sqrt{1-2 a b}+1}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b-\sqrt{1-2 a b}+1\right) \sqrt{x} \left(a x^2+b\right)}+\frac{\left(-\sqrt{1-2 a b}-2 \sqrt{a} \sqrt{b} \sqrt{-a b-\sqrt{1-2 a b}+1}+1\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} \Pi \left(\frac{\left(\sqrt{a} \sqrt{b}+\sqrt{-a b-\sqrt{1-2 a b}+1}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-a b-\sqrt{1-2 a b}+1}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b-\sqrt{1-2 a b}+1\right) \sqrt{x} \left(a x^2+b\right)}+\frac{\left(\sqrt{1-2 a b}+2 \sqrt{a} \sqrt{b} \sqrt{-a b+\sqrt{1-2 a b}+1}+1\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} \Pi \left(-\frac{\left(\sqrt{a} \sqrt{b}-\sqrt{-a b+\sqrt{1-2 a b}+1}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-a b+\sqrt{1-2 a b}+1}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b+\sqrt{1-2 a b}+1\right) \sqrt{x} \left(a x^2+b\right)}+\frac{\left(\sqrt{1-2 a b}-2 \sqrt{a} \sqrt{b} \sqrt{-a b+\sqrt{1-2 a b}+1}+1\right) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} \sqrt{a x^3+b x} \Pi \left(\frac{\left(\sqrt{a} \sqrt{b}+\sqrt{-a b+\sqrt{1-2 a b}+1}\right)^2}{4 \sqrt{a} \sqrt{b} \sqrt{-a b+\sqrt{1-2 a b}+1}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{b} \left(-2 a b+\sqrt{1-2 a b}+1\right) \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,"-1/4*((1 - Sqrt[1 - 2*a*b])^(3/2)*(2 + 2*a^2*b^2 - 2*Sqrt[1 - 2*a*b] - a*b*(5 - 3*Sqrt[1 - 2*a*b]))*Sqrt[b*x + a*x^3]*ArcTan[(Sqrt[1 - Sqrt[1 - 2*a*b]]*Sqrt[x])/((1 - a*b - Sqrt[1 - 2*a*b])^(1/4)*Sqrt[b + a*x^2])])/((1 - 2*a*b - Sqrt[1 - 2*a*b])*(1 - a*b - Sqrt[1 - 2*a*b])^(7/4)*Sqrt[x]*Sqrt[b + a*x^2]) - ((-1 + Sqrt[1 - 2*a*b])^(3/2)*(2 + 2*a^2*b^2 - 2*Sqrt[1 - 2*a*b] - a*b*(5 - 3*Sqrt[1 - 2*a*b]))*Sqrt[b*x + a*x^3]*ArcTan[(Sqrt[-1 + Sqrt[1 - 2*a*b]]*Sqrt[x])/((1 - a*b - Sqrt[1 - 2*a*b])^(1/4)*Sqrt[b + a*x^2])])/(4*(1 - 2*a*b - Sqrt[1 - 2*a*b])*(1 - a*b - Sqrt[1 - 2*a*b])^(7/4)*Sqrt[x]*Sqrt[b + a*x^2]) - ((-1 - Sqrt[1 - 2*a*b])^(3/2)*Sqrt[b*x + a*x^3]*ArcTan[(Sqrt[-1 - Sqrt[1 - 2*a*b]]*Sqrt[x])/((1 - a*b + Sqrt[1 - 2*a*b])^(1/4)*Sqrt[b + a*x^2])])/(4*(1 - a*b + Sqrt[1 - 2*a*b])^(3/4)*Sqrt[x]*Sqrt[b + a*x^2]) - ((1 + Sqrt[1 - 2*a*b])^(3/2)*Sqrt[b*x + a*x^3]*ArcTan[(Sqrt[1 + Sqrt[1 - 2*a*b]]*Sqrt[x])/((1 - a*b + Sqrt[1 - 2*a*b])^(1/4)*Sqrt[b + a*x^2])])/(4*(1 - a*b + Sqrt[1 - 2*a*b])^(3/4)*Sqrt[x]*Sqrt[b + a*x^2]) + ((1 - Sqrt[1 - 2*a*b])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[x]*(b + a*x^2)) + ((1 + Sqrt[1 - 2*a*b])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[x]*(b + a*x^2)) - ((1 - Sqrt[1 - 2*a*b])^2*(1 - (Sqrt[a]*Sqrt[b])/Sqrt[1 - a*b - Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b - Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2)) - ((1 - Sqrt[1 - 2*a*b])^2*(1 + (Sqrt[a]*Sqrt[b])/Sqrt[1 - a*b - Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b - Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2)) - ((1 + Sqrt[1 - 2*a*b])^2*(1 - (Sqrt[a]*Sqrt[b])/Sqrt[1 - a*b + Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b + Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2)) - ((1 + Sqrt[1 - 2*a*b])^2*(1 + (Sqrt[a]*Sqrt[b])/Sqrt[1 - a*b + Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b + Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2)) + ((1 - Sqrt[1 - 2*a*b] + 2*Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b - Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticPi[-1/4*(Sqrt[a]*Sqrt[b] - Sqrt[1 - a*b - Sqrt[1 - 2*a*b]])^2/(Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b - Sqrt[1 - 2*a*b]]), 2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b - Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2)) + ((1 - Sqrt[1 - 2*a*b] - 2*Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b - Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticPi[(Sqrt[a]*Sqrt[b] + Sqrt[1 - a*b - Sqrt[1 - 2*a*b]])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b - Sqrt[1 - 2*a*b]]), 2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b - Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2)) + ((1 + Sqrt[1 - 2*a*b] + 2*Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b + Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticPi[-1/4*(Sqrt[a]*Sqrt[b] - Sqrt[1 - a*b + Sqrt[1 - 2*a*b]])^2/(Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b + Sqrt[1 - 2*a*b]]), 2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b + Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2)) + ((1 + Sqrt[1 - 2*a*b] - 2*Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b + Sqrt[1 - 2*a*b]])*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*Sqrt[b*x + a*x^3]*EllipticPi[(Sqrt[a]*Sqrt[b] + Sqrt[1 - a*b + Sqrt[1 - 2*a*b]])^2/(4*Sqrt[a]*Sqrt[b]*Sqrt[1 - a*b + Sqrt[1 - 2*a*b]]), 2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(1/4)*b^(1/4)*(1 - 2*a*b + Sqrt[1 - 2*a*b])*Sqrt[x]*(b + a*x^2))","C",23,9,48,0.1875,0,"{1594, 2056, 6715, 6728, 406, 220, 409, 1217, 1707}"
962,1,187,0,0.548935,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(2+x^3+x^6\right)} \, dx","Int[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(2 + x^3 + x^6)),x]","\frac{\left(3 \sqrt{7}+7 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1-i \sqrt{7}}\right)}{7 \left(\sqrt{7}+i\right)}+\frac{\left(-3 \sqrt{7}+7 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1+i \sqrt{7}}\right)}{7 \left(-\sqrt{7}+i\right)}+\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{\left(x^3+1\right)^{2/3}}{2 x^2}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) + ((7*I + 3*Sqrt[7])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-2*x^3)/(1 - I*Sqrt[7])])/(7*(I + Sqrt[7])) + ((7*I - 3*Sqrt[7])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-2*x^3)/(1 + I*Sqrt[7])])/(7*(I - Sqrt[7])) - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]/2","C",8,4,28,0.1429,0,"{6728, 277, 239, 429}"
963,1,187,0,0.468643,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(2+x^3+x^6\right)} \, dx","Int[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(2 + x^3 + x^6)),x]","\frac{\left(3 \sqrt{7}+7 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1-i \sqrt{7}}\right)}{7 \left(\sqrt{7}+i\right)}+\frac{\left(-3 \sqrt{7}+7 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1+i \sqrt{7}}\right)}{7 \left(-\sqrt{7}+i\right)}+\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{\left(x^3+1\right)^{2/3}}{2 x^2}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3+2\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) + ((7*I + 3*Sqrt[7])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-2*x^3)/(1 - I*Sqrt[7])])/(7*(I + Sqrt[7])) + ((7*I - 3*Sqrt[7])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-2*x^3)/(1 + I*Sqrt[7])])/(7*(I - Sqrt[7])) - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]/2","C",8,4,28,0.1429,0,"{6728, 277, 239, 429}"
964,0,0,0,5.5968438,"\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","Int[((-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,"((-I)*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][Sqrt[1 + 2*x^6 + x^10]/(I - x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5]) - (I*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][Sqrt[1 + 2*x^6 + x^10]/(I + x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5]) + (2*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][Sqrt[1 + 2*x^6 + x^10]/(1 - x^2 + x^4 - x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5]) - (4*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 + 2*x^6 + x^10])/(1 - x^2 + x^4 - x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5]) + (6*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][(x^4*Sqrt[1 + 2*x^6 + x^10])/(1 - x^2 + x^4 - x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5]) + (2*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][(x^6*Sqrt[1 + 2*x^6 + x^10])/(1 - x^2 + x^4 - x^6 + x^8), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5]) - (6*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 + 2*x^6 + x^10])/(1 + x^6 + x^10), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5]) - (10*Sqrt[x + 2*x^4 + x^6]*Defer[Subst][Defer[Int][(x^6*Sqrt[1 + 2*x^6 + x^10])/(1 + x^6 + x^10), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x^3 + x^5])","F",0,0,0,0,-1,"{}"
965,0,0,0,0.965303,"\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","Int[(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,"Defer[Int][Sqrt[-1 + x^2 + x^4 + x^6]/(1 - x^4 - 2*x^6 + x^8 + 2*x^10 + x^12), x] + Defer[Int][(x^4*Sqrt[-1 + x^2 + x^4 + x^6])/(1 - x^4 - 2*x^6 + x^8 + 2*x^10 + x^12), x] + 2*Defer[Int][(x^6*Sqrt[-1 + x^2 + x^4 + x^6])/(1 - x^4 - 2*x^6 + x^8 + 2*x^10 + x^12), x]","F",0,0,0,0,-1,"{}"
966,0,0,0,0.1739767,"\int \frac{\sqrt{x^2-x \sqrt{-x+x^2}}}{x^3} \, dx","Int[Sqrt[x^2 - x*Sqrt[-x + x^2]]/x^3,x]","\int \frac{\sqrt{x^2-x \sqrt{-x+x^2}}}{x^3} \, dx","\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,"Defer[Int][Sqrt[x^2 - x*Sqrt[-x + x^2]]/x^3, x]","F",0,0,0,0,-1,"{}"
967,1,54,0,0.0353185,"\int \frac{1}{x \left(1+x^2\right)^{2/3}} \, dx","Int[1/(x*(1 + x^2)^(2/3)),x]","\frac{3}{4} \log \left(1-\sqrt[3]{x^2+1}\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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[x]/2 + (3*Log[1 - (1 + x^2)^(1/3)])/4","A",5,5,13,0.3846,1,"{266, 57, 618, 204, 31}"
968,1,54,0,0.0382539,"\int \frac{1}{x \sqrt[3]{1+x^2}} \, dx","Int[1/(x*(1 + x^2)^(1/3)),x]","\frac{3}{4} \log \left(1-\sqrt[3]{x^2+1}\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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]])/2 - Log[x]/2 + (3*Log[1 - (1 + x^2)^(1/3)])/4","A",5,5,13,0.3846,1,"{266, 55, 618, 204, 31}"
969,1,422,0,0.4546108,"\int \frac{1}{\left(-1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[1/((-1 + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{x}{\sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+\sqrt[3]{-1}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-(-1)^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\sqrt[3]{-1} x+1\right)}{6 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(1-(-1)^{2/3} x\right)}{6 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\left(x^3-x^2\right)^{2/3}}{(1-x) x}",1,"-(x/(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + (-1)^(1/3))^(1/3) - x^(1/3)])/(2*(1 + (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - (-1)^(2/3))^(1/3) - x^(1/3)])/(2*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 + (-1)^(1/3)*x])/(6*(1 + (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 - (-1)^(2/3)*x])/(6*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3))","B",7,5,21,0.2381,1,"{2056, 6725, 21, 37, 91}"
970,1,422,0,0.3361273,"\int \frac{1}{\left(-1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[1/((-1 + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{x}{\sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+\sqrt[3]{-1}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-(-1)^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\sqrt[3]{-1} x+1\right)}{6 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(1-(-1)^{2/3} x\right)}{6 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-3 \text{$\#$1}^3+3\&,\frac{\log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\left(x^3-x^2\right)^{2/3}}{(1-x) x}",1,"-(x/(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + (-1)^(1/3))^(1/3) - x^(1/3)])/(2*(1 + (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - (-1)^(2/3))^(1/3) - x^(1/3)])/(2*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 + (-1)^(1/3)*x])/(6*(1 + (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 - (-1)^(2/3)*x])/(6*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3))","B",7,5,21,0.2381,1,"{2056, 6725, 21, 37, 91}"
971,0,0,0,1.3485981,"\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","Int[(Sqrt[-1 + x^3]*(2 + x^3)*(-1 - x^2 + x^3)^2)/(x^6*(-2 - 3*x^2 + 2*x^3)),x]","\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","\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*Sqrt[-1 + x^3] + (3*Sqrt[-1 + x^3])/(4*(1 - Sqrt[3] - x)) + Sqrt[-1 + x^3]/(5*x^5) + Sqrt[-1 + x^3]/(6*x^3) - (2*Sqrt[-1 + x^3])/(5*x^2) + Sqrt[-1 + x^3]/(4*x) + (x*Sqrt[-1 + x^3])/5 - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticE[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(8*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (3^(3/4)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(2*Sqrt[2]*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (3*Defer[Int][Sqrt[-1 + x^3]/(2 + 3*x^2 - 2*x^3), x])/4 + (3*Defer[Int][(x*Sqrt[-1 + x^3])/(-2 - 3*x^2 + 2*x^3), x])/4","F",0,0,0,0,-1,"{}"
972,0,0,0,0.1051294,"\int \frac{\sqrt[4]{-1+3 x-3 x^2+x^3}}{-1-2 x+x^2+3 x^3} \, dx","Int[(-1 + 3*x - 3*x^2 + x^3)^(1/4)/(-1 - 2*x + x^2 + 3*x^3),x]","\int \frac{\sqrt[4]{-1+3 x-3 x^2+x^3}}{-1-2 x+x^2+3 x^3} \, dx","\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,"Defer[Int][(-1 + 3*x - 3*x^2 + x^3)^(1/4)/(-1 - 2*x + x^2 + 3*x^3), x]","F",0,0,0,0,-1,"{}"
973,0,0,0,1.1141352,"\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","Int[((1 + x + x^2)*(2*x + x^2)*Sqrt[1 + 2*x + x^2 - x^4])/(1 + x)^4,x]","\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","\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,"Defer[Int][Sqrt[1 + 2*x + x^2 - x^4]/(-1 - x), x] - Defer[Int][Sqrt[1 + 2*x + x^2 - x^4]/(1 + x)^4, x] + Defer[Int][Sqrt[1 + 2*x + x^2 - x^4]/(1 + x)^3, x] - (64*Sqrt[1 + 2*x + x^2 - x^4]*Defer[Subst][Defer[Int][Sqrt[-240 - 128*x^2 + 256*x^4]/(2 - 4*x)^4, x], x, 1/2 + x^(-1)])/(Sqrt[-15 - 2*(1 + 2/x)^2 + (1 + 2/x)^4]*x^2)","F",0,0,0,0,-1,"{}"
974,1,74,0,0.057176,"\int \frac{-1-x+x^4}{x \sqrt[4]{1+x^4}} \, dx","Int[(-1 - x + x^4)/(x*(1 + x^4)^(1/4)),x]","\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)","\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,"(1 + x^4)^(3/4)/3 - 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",12,9,21,0.4286,1,"{1833, 240, 212, 206, 203, 446, 80, 63, 298}"
975,1,120,0,0.1546645,"\int \frac{\sqrt[4]{-x^3+x^4}}{x^2 \left(-1+x^2\right)} \, dx","Int[(-x^3 + x^4)^(1/4)/(x^2*(-1 + x^2)),x]","\frac{4 \sqrt[4]{x^4-x^3}}{x}+\frac{\sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{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^3 + x^4)^(1/4))/x + (2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - (2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","A",7,7,24,0.2917,1,"{2056, 848, 96, 93, 298, 203, 206}"
976,0,0,0,0.5935983,"\int \frac{-3+x^4}{\sqrt[3]{1+x^4} \left(1-x^3+x^4\right)} \, dx","Int[(-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,"x*Hypergeometric2F1[1/4, 1/3, 5/4, -x^4] - 4*Defer[Int][1/((1 + x^4)^(1/3)*(1 - x^3 + x^4)), x] + Defer[Int][x^3/((1 + x^4)^(1/3)*(1 - x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
977,1,587,0,1.2865337,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}+\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-3 a}\&\right]",1,"((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) + ((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4))","B",21,11,36,0.3056,1,"{2056, 1269, 1428, 408, 240, 212, 206, 203, 377, 208, 205}"
978,1,587,0,1.7424895,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}+\frac{\sqrt{x} \left(-a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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{a^2-4 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a \sqrt{a^2-4 b}+a^2+2 b\right)^{3/4} \sqrt[4]{a x^2+b} \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 x^4+b x^2}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$1}^4-3 a}\&\right]",1,"((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) + ((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4)) - ((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*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]*(b*x^2 + a*x^4)^(1/4))","B",21,11,36,0.3056,1,"{2056, 1269, 1428, 408, 240, 212, 206, 203, 377, 208, 205}"
979,1,74,0,0.0769206,"\int \frac{-b+2 a x^4}{x^2 \left(-b+a x^4\right)^{3/4}} \, dx","Int[(-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",5,5,27,0.1852,1,"{451, 331, 298, 203, 206}"
980,1,54,0,0.0509211,"\int \frac{1}{x \sqrt[3]{1+x^6}} \, dx","Int[1/(x*(1 + x^6)^(1/3)),x]","\frac{1}{4} \log \left(1-\sqrt[3]{x^6+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\log (x)}{2}","\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,"ArcTan[(1 + 2*(1 + x^6)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x]/2 + Log[1 - (1 + x^6)^(1/3)]/4","A",5,5,13,0.3846,1,"{266, 55, 618, 204, 31}"
981,1,129,0,3.7021755,"\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","Int[(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{4}{3 \left(x^2+1\right) \sqrt{\frac{1-2 x^2}{2 x^2+1}}}+\frac{2}{3 \sqrt{\frac{1-2 x^2}{2 x^2+1}}}+\frac{3 \sqrt{1-2 x^2} \tanh ^{-1}\left(\sqrt{1-2 x^2} \sqrt{2 x^2+1}\right)}{2 \sqrt{\frac{1-2 x^2}{2 x^2+1}} \sqrt{2 x^2+1}}","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,"2/(3*Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]) - 4/(3*(1 + x^2)*Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]) + (3*Sqrt[1 - 2*x^2]*ArcTanh[Sqrt[1 - 2*x^2]*Sqrt[1 + 2*x^2]])/(2*Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2])","A",17,12,62,0.1935,1,"{6688, 6719, 1586, 1606, 37, 96, 92, 206, 103, 21, 93, 203}"
982,1,198,0,2.881509,"\int \frac{\sqrt[4]{-1+2 x^4} \left(-2+x^8\right)}{x^6 \left(-1+x^4\right)^2} \, dx","Int[((-1 + 2*x^4)^(1/4)*(-2 + x^8))/(x^6*(-1 + x^4)^2),x]","-\frac{4 \sqrt[4]{2 x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};2 x^4,x^4\right)}{3 \sqrt[4]{1-2 x^4}}-\frac{\sqrt[4]{2 x^4-1} x^3 \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{x^4}{1-x^4}\right)}{3 \sqrt[4]{1-2 x^4} \left(1-x^4\right)^{3/4}}+\frac{4 \sqrt[4]{2 x^4-1}}{x}+2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4-1}}\right)-2 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4-1}}\right)-\frac{2 \left(2 x^4-1\right)^{5/4}}{5 x^5}","\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,"(4*(-1 + 2*x^4)^(1/4))/x - (2*(-1 + 2*x^4)^(5/4))/(5*x^5) - (4*x^3*(-1 + 2*x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, 2*x^4, x^4])/(3*(1 - 2*x^4)^(1/4)) + 2*2^(1/4)*ArcTan[(2^(1/4)*x)/(-1 + 2*x^4)^(1/4)] - 2*2^(1/4)*ArcTanh[(2^(1/4)*x)/(-1 + 2*x^4)^(1/4)] - (x^3*(-1 + 2*x^4)^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, x^4/(1 - x^4)])/(3*(1 - 2*x^4)^(1/4)*(1 - x^4)^(3/4))","C",176,33,27,1.222,0,"{6742, 2153, 1240, 412, 529, 237, 335, 275, 232, 407, 409, 1213, 537, 511, 510, 1248, 733, 844, 234, 220, 747, 400, 442, 444, 63, 212, 206, 203, 1336, 264, 277, 331, 298}"
983,1,75,0,0.0665205,"\int \frac{\left(b+a x^2\right)^{3/4}}{x^3} \, dx","Int[(b + a*x^2)^(3/4)/x^3,x]","-\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}}","-\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,"-1/2*(b + a*x^2)^(3/4)/x^2 + (3*a*ArcTan[(b + a*x^2)^(1/4)/b^(1/4)])/(4*b^(1/4)) - (3*a*ArcTanh[(b + a*x^2)^(1/4)/b^(1/4)])/(4*b^(1/4))","A",6,6,15,0.4000,1,"{266, 47, 63, 298, 203, 206}"
984,0,0,0,19.4553354,"\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","Int[(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,"(8*(1 + k)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^6/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(d - d*(1 + k)*x^4 + d*k*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (12*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(-d + d*(1 + k)*x^4 - d*k*x^8 + x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (4*k*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^10/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(-d + d*(1 + k)*x^4 - d*k*x^8 + x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4)","F",0,0,0,0,-1,"{}"
985,0,0,0,0.124164,"\int \frac{1}{\sqrt[4]{-1+3 x-3 x^2+x^3} \left(-1-2 x+x^2+3 x^3\right)} \, dx","Int[1/((-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3)),x]","\int \frac{1}{\sqrt[4]{-1+3 x-3 x^2+x^3} \left(-1-2 x+x^2+3 x^3\right)} \, dx","\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,"Defer[Int][1/((-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3)), x]","F",0,0,0,0,-1,"{}"
986,1,75,0,0.0690847,"\int \frac{\left(b+a x^3\right)^{3/4}}{x^4} \, dx","Int[(b + a*x^3)^(3/4)/x^4,x]","-\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}}","-\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,"-1/3*(b + a*x^3)^(3/4)/x^3 + (a*ArcTan[(b + a*x^3)^(1/4)/b^(1/4)])/(2*b^(1/4)) - (a*ArcTanh[(b + a*x^3)^(1/4)/b^(1/4)])/(2*b^(1/4))","A",6,6,15,0.4000,1,"{266, 47, 63, 298, 203, 206}"
987,1,129,0,0.2353435,"\int \frac{\sqrt[4]{x^2+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Int[(x^2 + x^4)^(1/4)/(x^4*(-1 + x^4)),x]","\frac{\sqrt[4]{x^4+x^2} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2^{3/4} \sqrt{x} \sqrt[4]{x^2+1}}-\frac{\sqrt[4]{x^4+x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2^{3/4} \sqrt{x} \sqrt[4]{x^2+1}}+\frac{2 \sqrt[4]{x^4+x^2} \left(x^2+1\right)}{5 x^3}","\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,"(2*(1 + x^2)*(x^2 + x^4)^(1/4))/(5*x^3) + ((x^2 + x^4)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)) - ((x^2 + x^4)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4))","A",9,8,22,0.3636,1,"{2056, 1254, 466, 494, 461, 298, 203, 206}"
988,0,0,0,0.9842358,"\int \frac{x \left(-3+x^4\right)}{\left(1+x^4\right)^{2/3} \left(1+x^3+x^4\right)} \, dx","Int[(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,"-1/2*(3^(3/4)*Sqrt[2 - Sqrt[3]]*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) - x*Hypergeometric2F1[1/4, 2/3, 5/4, -x^4] + Defer[Int][1/((1 + x^4)^(2/3)*(1 + x^3 + x^4)), x] - 4*Defer[Int][x/((1 + x^4)^(2/3)*(1 + x^3 + x^4)), x] + Defer[Int][x^3/((1 + x^4)^(2/3)*(1 + x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
989,1,475,0,1.7916796,"\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","Int[(Sqrt[2 - x^2 - 4*x^4]*(1 + 2*x^4))/((-1 + 2*x^4)*(-1 - x^2 + 2*x^4)),x]","-\frac{1}{4} \sqrt{3 \left(11 \sqrt{33}-59\right)} F\left(\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)+\frac{1}{4} \sqrt{3 \left(13+3 \sqrt{33}\right)} F\left(\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)+\frac{\left(1+4 \sqrt{2}-\sqrt{33}\right) F\left(\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)}{\sqrt{2 \left(1+\sqrt{33}\right)}}+\frac{\left(1-4 \sqrt{2}-\sqrt{33}\right) F\left(\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)}{\sqrt{2 \left(1+\sqrt{33}\right)}}+3 \sqrt{\frac{2}{1+\sqrt{33}}} \Pi \left(\frac{1}{4} \left(1-\sqrt{33}\right);\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)-\sqrt{\frac{2}{1+\sqrt{33}}} \Pi \left(-\frac{1-\sqrt{33}}{4 \sqrt{2}};\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)-\sqrt{\frac{2}{1+\sqrt{33}}} \Pi \left(\frac{1-\sqrt{33}}{4 \sqrt{2}};\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)+3 \sqrt{\frac{2}{1+\sqrt{33}}} \Pi \left(\frac{1}{8} \left(-1+\sqrt{33}\right);\sin ^{-1}\left(2 \sqrt{\frac{2}{-1+\sqrt{33}}} x\right)|\frac{1}{16} \left(-17+\sqrt{33}\right)\right)","\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 - 4*Sqrt[2] - Sqrt[33])*EllipticF[ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16])/Sqrt[2*(1 + Sqrt[33])] + ((1 + 4*Sqrt[2] - Sqrt[33])*EllipticF[ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16])/Sqrt[2*(1 + Sqrt[33])] + (Sqrt[3*(13 + 3*Sqrt[33])]*EllipticF[ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16])/4 - (Sqrt[3*(-59 + 11*Sqrt[33])]*EllipticF[ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16])/4 + 3*Sqrt[2/(1 + Sqrt[33])]*EllipticPi[(1 - Sqrt[33])/4, ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16] - Sqrt[2/(1 + Sqrt[33])]*EllipticPi[-1/4*(1 - Sqrt[33])/Sqrt[2], ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16] - Sqrt[2/(1 + Sqrt[33])]*EllipticPi[(1 - Sqrt[33])/(4*Sqrt[2]), ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16] + 3*Sqrt[2/(1 + Sqrt[33])]*EllipticPi[(-1 + Sqrt[33])/8, ArcSin[2*Sqrt[2/(-1 + Sqrt[33])]*x], (-17 + Sqrt[33])/16]","C",32,8,47,0.1702,0,"{6725, 1208, 1180, 524, 424, 419, 1212, 537}"
990,1,75,0,0.0225647,"\int \left(b+a x^4\right)^{3/4} \, dx","Int[(b + a*x^4)^(3/4),x]","\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}}","\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))/4 + (3*b*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(1/4)) + (3*b*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(1/4))","A",5,5,11,0.4545,1,"{195, 240, 212, 206, 203}"
991,1,75,0,0.0239462,"\int \frac{\left(b+a x^4\right)^{3/4}}{x^4} \, dx","Int[(b + a*x^4)^(3/4)/x^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{\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{\left(a x^4+b\right)^{3/4}}{3 x^3}",1,"-1/3*(b + a*x^4)^(3/4)/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",5,5,15,0.3333,1,"{277, 240, 212, 206, 203}"
992,1,75,0,0.0533804,"\int \frac{\left(b+a x^5\right)^{3/4}}{x^6} \, dx","Int[(b + a*x^5)^(3/4)/x^6,x]","-\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}}","-\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,"-1/5*(b + a*x^5)^(3/4)/x^5 + (3*a*ArcTan[(b + a*x^5)^(1/4)/b^(1/4)])/(10*b^(1/4)) - (3*a*ArcTanh[(b + a*x^5)^(1/4)/b^(1/4)])/(10*b^(1/4))","A",6,6,15,0.4000,1,"{266, 47, 63, 298, 203, 206}"
993,0,0,0,1.244604,"\int \frac{2-3 x^5}{\left(1-x^2+x^5\right) \sqrt[3]{x+x^6}} \, dx","Int[(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,"(-9*x*(1 + x^5)^(1/3)*Hypergeometric2F1[2/15, 1/3, 17/15, -x^5])/(2*(x + x^6)^(1/3)) + (15*x^(1/3)*(1 + x^5)^(1/3)*Defer[Subst][Defer[Int][x/((1 + x^15)^(1/3)*(1 - x^6 + x^15)), x], x, x^(1/3)])/(x + x^6)^(1/3) - (9*x^(1/3)*(1 + x^5)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 + x^15)^(1/3)*(1 - x^6 + x^15)), x], x, x^(1/3)])/(x + x^6)^(1/3)","F",0,0,0,0,-1,"{}"
994,1,75,0,0.0522683,"\int \frac{\left(b+a x^6\right)^{3/4}}{x^7} \, dx","Int[(b + a*x^6)^(3/4)/x^7,x]","-\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}}","-\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,"-1/6*(b + a*x^6)^(3/4)/x^6 + (a*ArcTan[(b + a*x^6)^(1/4)/b^(1/4)])/(4*b^(1/4)) - (a*ArcTanh[(b + a*x^6)^(1/4)/b^(1/4)])/(4*b^(1/4))","A",6,6,15,0.4000,1,"{266, 47, 63, 298, 203, 206}"
995,0,0,0,1.0906715,"\int \frac{2 b+a x^6}{\sqrt[4]{-b+a x^6} \left(-b-2 x^4+a x^6\right)} \, dx","Int[(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,"(x*(1 - (a*x^6)/b)^(1/4)*Hypergeometric2F1[1/6, 1/4, 7/6, (a*x^6)/b])/(-b + a*x^6)^(1/4) - 3*b*Defer[Int][1/((b + 2*x^4 - a*x^6)*(-b + a*x^6)^(1/4)), x] + 2*Defer[Int][x^4/((-b + a*x^6)^(1/4)*(-b - 2*x^4 + a*x^6)), x]","F",0,0,0,0,-1,"{}"
996,1,1128,0,1.9212623,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{1+3 x^4+x^8} \, dx","Int[((-1 + x^4)*Sqrt[1 + x^4])/(1 + 3*x^4 + x^8),x]","-\frac{\sqrt[4]{-1} \left(2 i-\sqrt{6-2 \sqrt{5}}\right) \left(2 i-\sqrt{2 \left(3+\sqrt{5}\right)}\right) \tan ^{-1}\left(\frac{\sqrt[4]{-1} x}{\sqrt{x^4+1}}\right)}{16 \sqrt{5}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \tan ^{-1}\left(\frac{\sqrt[4]{-1} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) \left(2 i+\sqrt{6-2 \sqrt{5}}\right) \left(2-i \sqrt{2 \left(3+\sqrt{5}\right)}\right) \tan ^{-1}\left(\frac{(-1)^{3/4} x}{\sqrt{x^4+1}}\right)}{\sqrt{10}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \tan ^{-1}\left(\frac{(-1)^{3/4} x}{\sqrt{x^4+1}}\right)}{\sqrt{2}}-\frac{\left(3-\sqrt{5}\right) \left(2+i \sqrt{2 \left(3+\sqrt{5}\right)}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \left(5-\sqrt{5}\right) \sqrt{x^4+1}}-\frac{\left(3-\sqrt{5}\right) \left(2-i \sqrt{2 \left(3+\sqrt{5}\right)}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{8 \left(5-\sqrt{5}\right) \sqrt{x^4+1}}-\frac{\left(3+\sqrt{5}\right) \left(1+i \sqrt{\frac{2}{3+\sqrt{5}}}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \left(5+\sqrt{5}\right) \sqrt{x^4+1}}-\frac{\left(3+\sqrt{5}\right) \left(1-i \sqrt{\frac{2}{3+\sqrt{5}}}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \left(5+\sqrt{5}\right) \sqrt{x^4+1}}+\frac{\left(1+\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}+\frac{\left(1-\sqrt{5}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}+\frac{\left(5-2 \sqrt{5}\right) \left(3+\sqrt{5}\right) \left(1+\sqrt{5}-2 i \sqrt{2 \left(3+\sqrt{5}\right)}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{4} i \sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \left(i-\sqrt{\frac{2}{3+\sqrt{5}}}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{160 \sqrt{x^4+1}}+\frac{\left(5-2 \sqrt{5}\right) \left(3+\sqrt{5}\right) \left(1+\sqrt{5}+2 i \sqrt{2 \left(3+\sqrt{5}\right)}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{1}{4} i \sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \left(i+\sqrt{\frac{2}{3+\sqrt{5}}}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{160 \sqrt{x^4+1}}-\frac{\left(2+i \sqrt{6-2 \sqrt{5}}\right) \left(2 i+\sqrt{2 \left(3+\sqrt{5}\right)}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(\frac{1}{16} i \sqrt{\frac{1}{2} \left(3-\sqrt{5}\right)} \left(2 i-\sqrt{2 \left(3+\sqrt{5}\right)}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{32 \sqrt{5} \sqrt{x^4+1}}+\frac{\left(2 i+\sqrt{6-2 \sqrt{5}}\right) \left(2+i \sqrt{2 \left(3+\sqrt{5}\right)}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} \Pi \left(-\frac{1}{16} i \sqrt{\frac{1}{2} \left(3-\sqrt{5}\right)} \left(2 i+\sqrt{2 \left(3+\sqrt{5}\right)}\right)^2;2 \tan ^{-1}(x)|\frac{1}{2}\right)}{32 \sqrt{5} \sqrt{x^4+1}}","-\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,"((-1/4 + I/4)*ArcTan[((-1)^(1/4)*x)/Sqrt[1 + x^4]])/Sqrt[2] - ((-1)^(1/4)*(2*I - Sqrt[6 - 2*Sqrt[5]])*(2*I - Sqrt[2*(3 + Sqrt[5])])*ArcTan[((-1)^(1/4)*x)/Sqrt[1 + x^4]])/(16*Sqrt[5]) + ((1/4 + I/4)*ArcTan[((-1)^(3/4)*x)/Sqrt[1 + x^4]])/Sqrt[2] + ((1/16 + I/16)*(2*I + Sqrt[6 - 2*Sqrt[5]])*(2 - I*Sqrt[2*(3 + Sqrt[5])])*ArcTan[((-1)^(3/4)*x)/Sqrt[1 + x^4]])/Sqrt[10] + ((1 - Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4]) + ((1 + Sqrt[5])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4]) - ((3 + Sqrt[5])*(1 - I*Sqrt[2/(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*(5 + Sqrt[5])*Sqrt[1 + x^4]) - ((3 + Sqrt[5])*(1 + I*Sqrt[2/(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*(5 + Sqrt[5])*Sqrt[1 + x^4]) - ((3 - Sqrt[5])*(2 - I*Sqrt[2*(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*(5 - Sqrt[5])*Sqrt[1 + x^4]) - ((3 - Sqrt[5])*(2 + I*Sqrt[2*(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(8*(5 - Sqrt[5])*Sqrt[1 + x^4]) + ((5 - 2*Sqrt[5])*(3 + Sqrt[5])*(1 + Sqrt[5] - (2*I)*Sqrt[2*(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(I/4)*Sqrt[(3 + Sqrt[5])/2]*(I - Sqrt[2/(3 + Sqrt[5])])^2, 2*ArcTan[x], 1/2])/(160*Sqrt[1 + x^4]) + ((5 - 2*Sqrt[5])*(3 + Sqrt[5])*(1 + Sqrt[5] + (2*I)*Sqrt[2*(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(-1/4*I)*Sqrt[(3 + Sqrt[5])/2]*(I + Sqrt[2/(3 + Sqrt[5])])^2, 2*ArcTan[x], 1/2])/(160*Sqrt[1 + x^4]) - ((2 + I*Sqrt[6 - 2*Sqrt[5]])*(2*I + Sqrt[2*(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(I/16)*Sqrt[(3 - Sqrt[5])/2]*(2*I - Sqrt[2*(3 + Sqrt[5])])^2, 2*ArcTan[x], 1/2])/(32*Sqrt[5]*Sqrt[1 + x^4]) + ((2*I + Sqrt[6 - 2*Sqrt[5]])*(2 + I*Sqrt[2*(3 + Sqrt[5])])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticPi[(-1/16*I)*Sqrt[(3 - Sqrt[5])/2]*(2*I + Sqrt[2*(3 + Sqrt[5])])^2, 2*ArcTan[x], 1/2])/(32*Sqrt[5]*Sqrt[1 + x^4])","C",20,6,27,0.2222,0,"{6728, 406, 220, 409, 1217, 1707}"
997,1,299,0,3.2244861,"\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","Int[(-1 + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(a + b*x + a*k^2*x^2)),x]","\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{2 a}{b-\sqrt{b^2-4 a^2 k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{a \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{2 a}{b+\sqrt{b^2-4 a^2 k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{a \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{a \sqrt{(1-x) x \left(1-k^2 x\right)}}","-\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,"(2*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/(a*Sqrt[(1 - x)*x*(1 - k^2*x)]) + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(-2*a)/(b - Sqrt[b^2 - 4*a^2*k^2]), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(a*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(-2*a)/(b + Sqrt[b^2 - 4*a^2*k^2]), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(a*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",16,9,44,0.2045,0,"{6718, 6688, 6728, 714, 115, 934, 12, 168, 537}"
998,1,52,0,0.034141,"\int \frac{1}{x \sqrt[3]{-1+x^4}} \, dx","Int[1/(x*(-1 + x^4)^(1/3)),x]","-\frac{3}{8} \log \left(\sqrt[3]{x^4-1}+1\right)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^4-1}}{\sqrt{3}}\right)+\frac{\log (x)}{2}","-\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,"-1/4*(Sqrt[3]*ArcTan[(1 - 2*(-1 + x^4)^(1/3))/Sqrt[3]]) + Log[x]/2 - (3*Log[1 + (-1 + x^4)^(1/3)])/8","A",5,5,13,0.3846,1,"{266, 56, 618, 204, 31}"
999,1,2421,0,26.5627722,"\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","Int[(x^2*(-2*b + a*x^2))/((-b + a*x^2)^(3/4)*(4*b - 4*a*x^2 + x^4)),x]","\frac{\sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(\frac{\left(\sqrt{2 a^2-2 \sqrt{a^2-b} a-b}+\sqrt{b}\right)^2}{4 \sqrt{2 a^2-2 \sqrt{a^2-b} a-b} \sqrt{b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right) \left(\sqrt{2 a^2-2 \sqrt{a^2-b} a-b}-\sqrt{b}\right)^2}{8 \left(a^2-\sqrt{a^2-b} a-b\right) \sqrt[4]{b} x}-\frac{\sqrt{b} \left(4 a^4-5 b a^2-\left(4 a^2-3 b\right) \sqrt{a^2-b} a+b^2\right) \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{a-\sqrt{a^2-b}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2 a^2-2 \sqrt{a^2-b} a-b} \sqrt{b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt{2} \sqrt{a} \sqrt{a-\sqrt{a^2-b}} \left(2 a^2-2 \sqrt{a^2-b} a-b\right)^{3/4} \left(a^2-\sqrt{a^2-b} a-b\right) x}-\frac{\sqrt{b} \left(4 a^4-5 b a^2-\left(4 a^2-3 b\right) \sqrt{a^2-b} a+b^2\right) \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{\sqrt{a^2-b}-a} \sqrt[4]{a x^2-b}}{\sqrt[4]{2 a^2-2 \sqrt{a^2-b} a-b} \sqrt{b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt{2} \sqrt{a} \sqrt{\sqrt{a^2-b}-a} \left(2 a^2-2 \sqrt{a^2-b} a-b\right)^{3/4} \left(a^2-\sqrt{a^2-b} a-b\right) x}-\frac{\sqrt[4]{2 a^2+2 \sqrt{a^2-b} a-b} \sqrt{b} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{-a-\sqrt{a^2-b}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2 a^2+2 \sqrt{a^2-b} a-b} \sqrt{b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt{2} \sqrt{a} \sqrt{-a-\sqrt{a^2-b}} x}-\frac{\sqrt[4]{2 a^2+2 \sqrt{a^2-b} a-b} \sqrt{b} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{a+\sqrt{a^2-b}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2 a^2+2 \sqrt{a^2-b} a-b} \sqrt{b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt{2} \sqrt{a} \sqrt{a+\sqrt{a^2-b}} x}-\frac{\left(1-\frac{\sqrt{b}}{\sqrt{2 a^2+2 \sqrt{a^2-b} a-b}}\right) \left(2 a^2+2 \sqrt{a^2-b} a-b\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \left(a^2+\sqrt{a^2-b} a-b\right) \sqrt[4]{b} x}-\frac{\left(\frac{\sqrt{b}}{\sqrt{2 a^2+2 \sqrt{a^2-b} a-b}}+1\right) \left(2 a^2+2 \sqrt{a^2-b} a-b\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \left(a^2+\sqrt{a^2-b} a-b\right) \sqrt[4]{b} x}-\frac{\left(1-\frac{\sqrt{b}}{\sqrt{2 a^2-2 \sqrt{a^2-b} a-b}}\right) \left(2 a^2-2 \sqrt{a^2-b} a-b\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \left(a^2-\sqrt{a^2-b} a-b\right) \sqrt[4]{b} x}-\frac{\left(\frac{\sqrt{b}}{\sqrt{2 a^2-2 \sqrt{a^2-b} a-b}}+1\right) \left(2 a^2-2 \sqrt{a^2-b} a-b\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \left(a^2-\sqrt{a^2-b} a-b\right) \sqrt[4]{b} x}+\frac{\sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b} x}+\frac{\left(\sqrt{2 a^2-2 \sqrt{a^2-b} a-b}+\sqrt{b}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(-\frac{\left(\sqrt{2 a^2-2 \sqrt{a^2-b} a-b}-\sqrt{b}\right)^2}{4 \sqrt{2 a^2-2 \sqrt{a^2-b} a-b} \sqrt{b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 \left(a^2-\sqrt{a^2-b} a-b\right) \sqrt[4]{b} x}+\frac{\left(\sqrt{2 a^2+2 \sqrt{a^2-b} a-b}+\sqrt{b}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(-\frac{\left(\sqrt{2 a^2+2 \sqrt{a^2-b} a-b}-\sqrt{b}\right)^2}{4 \sqrt{2 a^2+2 \sqrt{a^2-b} a-b} \sqrt{b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 \left(a^2+\sqrt{a^2-b} a-b\right) \sqrt[4]{b} x}+\frac{\left(\sqrt{2 a^2+2 \sqrt{a^2-b} a-b}-\sqrt{b}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(\frac{\left(\sqrt{2 a^2+2 \sqrt{a^2-b} a-b}+\sqrt{b}\right)^2}{4 \sqrt{2 a^2+2 \sqrt{a^2-b} a-b} \sqrt{b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 \left(a^2+\sqrt{a^2-b} a-b\right) \sqrt[4]{b} 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,"-1/2*(Sqrt[b]*(4*a^4 - a*(4*a^2 - 3*b)*Sqrt[a^2 - b] - 5*a^2*b + b^2)*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[a - Sqrt[a^2 - b]]*(-b + a*x^2)^(1/4))/((2*a^2 - 2*a*Sqrt[a^2 - b] - b)^(1/4)*Sqrt[b]*Sqrt[(a*x^2)/b])])/(Sqrt[2]*Sqrt[a]*Sqrt[a - Sqrt[a^2 - b]]*(2*a^2 - 2*a*Sqrt[a^2 - b] - b)^(3/4)*(a^2 - a*Sqrt[a^2 - b] - b)*x) - (Sqrt[b]*(4*a^4 - a*(4*a^2 - 3*b)*Sqrt[a^2 - b] - 5*a^2*b + b^2)*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[-a + Sqrt[a^2 - b]]*(-b + a*x^2)^(1/4))/((2*a^2 - 2*a*Sqrt[a^2 - b] - b)^(1/4)*Sqrt[b]*Sqrt[(a*x^2)/b])])/(2*Sqrt[2]*Sqrt[a]*Sqrt[-a + Sqrt[a^2 - b]]*(2*a^2 - 2*a*Sqrt[a^2 - b] - b)^(3/4)*(a^2 - a*Sqrt[a^2 - b] - b)*x) - ((2*a^2 + 2*a*Sqrt[a^2 - b] - b)^(1/4)*Sqrt[b]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[-a - Sqrt[a^2 - b]]*(-b + a*x^2)^(1/4))/((2*a^2 + 2*a*Sqrt[a^2 - b] - b)^(1/4)*Sqrt[b]*Sqrt[(a*x^2)/b])])/(2*Sqrt[2]*Sqrt[a]*Sqrt[-a - Sqrt[a^2 - b]]*x) - ((2*a^2 + 2*a*Sqrt[a^2 - b] - b)^(1/4)*Sqrt[b]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[a + Sqrt[a^2 - b]]*(-b + a*x^2)^(1/4))/((2*a^2 + 2*a*Sqrt[a^2 - b] - b)^(1/4)*Sqrt[b]*Sqrt[(a*x^2)/b])])/(2*Sqrt[2]*Sqrt[a]*Sqrt[a + Sqrt[a^2 - b]]*x) + (Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(b^(1/4)*x) - ((1 - Sqrt[b]/Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b])*(2*a^2 - 2*a*Sqrt[a^2 - b] - b)*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*(a^2 - a*Sqrt[a^2 - b] - b)*b^(1/4)*x) - ((1 + Sqrt[b]/Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b])*(2*a^2 - 2*a*Sqrt[a^2 - b] - b)*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*(a^2 - a*Sqrt[a^2 - b] - b)*b^(1/4)*x) - ((1 - Sqrt[b]/Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b])*(2*a^2 + 2*a*Sqrt[a^2 - b] - b)*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*(a^2 + a*Sqrt[a^2 - b] - b)*b^(1/4)*x) - ((1 + Sqrt[b]/Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b])*(2*a^2 + 2*a*Sqrt[a^2 - b] - b)*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*(a^2 + a*Sqrt[a^2 - b] - b)*b^(1/4)*x) + ((Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b] + Sqrt[b])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[-1/4*(Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b] - Sqrt[b])^2/(Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b]*Sqrt[b]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(8*(a^2 - a*Sqrt[a^2 - b] - b)*b^(1/4)*x) + ((Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b] - Sqrt[b])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[(Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b] + Sqrt[b])^2/(4*Sqrt[2*a^2 - 2*a*Sqrt[a^2 - b] - b]*Sqrt[b]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(8*(a^2 - a*Sqrt[a^2 - b] - b)*b^(1/4)*x) + ((Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b] + Sqrt[b])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[-1/4*(Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b] - Sqrt[b])^2/(Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b]*Sqrt[b]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(8*(a^2 + a*Sqrt[a^2 - b] - b)*b^(1/4)*x) + ((Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b] - Sqrt[b])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[(Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b] + Sqrt[b])^2/(4*Sqrt[2*a^2 + 2*a*Sqrt[a^2 - b] - b]*Sqrt[b]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(8*(a^2 + a*Sqrt[a^2 - b] - b)*b^(1/4)*x)","C",24,8,41,0.1951,0,"{1692, 234, 220, 401, 108, 409, 1217, 1707}"
1000,0,0,0,17.6628038,"\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","Int[(-(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]","\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","\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,"(2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(-(a^2*(b - x^2)^2) + 2*a*(-(b*x) + x^3)^2 - x^4*(b^2 - d - 2*b*x^2 + x^4))), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^6/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(a^2*(b - x^2)^2 - 2*a*(-(b*x) + x^3)^2 + x^4*(b^2 - d - 2*b*x^2 + x^4))), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1001,1,73,0,0.0971531,"\int \frac{\sqrt[4]{-1-x^4} \left(-1+x^4\right)}{x^6 \left(1+2 x^4\right)} \, dx","Int[((-1 - x^4)^(1/4)*(-1 + x^4))/(x^6*(1 + 2*x^4)),x]","-\frac{14 \sqrt[4]{-x^4-1}}{5 x}-\frac{3}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{-x^4-1}}\right)+\frac{3}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{-x^4-1}}\right)+\frac{\sqrt[4]{-x^4-1}}{5 x^5}","\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 - x^4)^(1/4)/(5*x^5) - (14*(-1 - x^4)^(1/4))/(5*x) - (3*ArcTan[x/(-1 - x^4)^(1/4)])/2 + (3*ArcTanh[x/(-1 - x^4)^(1/4)])/2","A",7,7,29,0.2414,1,"{580, 583, 12, 494, 298, 203, 206}"
1002,0,0,0,21.9909026,"\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","Int[(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]","\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","\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,"(2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^6/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(-(a^2*b^2*d) + 2*a^2*b*(1 + b/a)*d*x^2 + (1 - (a^2 + 4*a*b + b^2)*d)*x^4 + 2*a*(1 + b/a)*d*x^6 - d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(a^2*b^2*d - 2*a^2*b*(1 + b/a)*d*x^2 - (1 - (a^2 + 4*a*b + b^2)*d)*x^4 - 2*a*(1 + b/a)*d*x^6 + d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1003,0,0,0,23.9216384,"\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","Int[(-(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]","\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","\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,"(2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^2/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(-(a^2*b^2*d) + 2*a^2*b*(1 + b/a)*d*x^2 + (1 - (a^2 + 4*a*b + b^2)*d)*x^4 + 2*a*(1 + b/a)*d*x^6 - d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^6/(Sqrt[-a + x^2]*Sqrt[-b + x^2]*(a^2*b^2*d - 2*a^2*b*(1 + b/a)*d*x^2 - (1 - (a^2 + 4*a*b + b^2)*d)*x^4 - 2*a*(1 + b/a)*d*x^6 + d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1004,1,52,0,0.0371393,"\int \frac{1}{x \sqrt[3]{-1+x^6}} \, dx","Int[1/(x*(-1 + x^6)^(1/3)),x]","-\frac{1}{4} \log \left(\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\log (x)}{2}","-\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,"-1/2*ArcTan[(1 - 2*(-1 + x^6)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[x]/2 - Log[1 + (-1 + x^6)^(1/3)]/4","A",5,5,13,0.3846,1,"{266, 56, 618, 204, 31}"
1005,1,187,0,0.3970496,"\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","Int[((1 + x^3)^(2/3)*(2 + x^3 + 2*x^6))/(x^6*(1 + x^3 + x^6)),x]","\frac{2 x F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right)}-\frac{2 x F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right)}+\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2 \left(x^3+1\right)^{5/3}}{5 x^5}+\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{\left(x^3-4\right) \left(x^3+1\right)^{2/3}}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) - (2*(1 + x^3)^(5/3))/(5*x^5) + (2*x*AppellF1[1/3, -5/3, 1, 4/3, -x^3, (-2*x^3)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])) - (2*x*AppellF1[1/3, -5/3, 1, 4/3, -x^3, (-2*x^3)/(1 + I*Sqrt[3])])/(Sqrt[3]*(I - Sqrt[3])) - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]/2","C",8,6,33,0.1818,0,"{6728, 264, 277, 239, 1428, 429}"
1006,1,187,0,0.3305204,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3+2 x^6\right)}{x^6 \left(1+x^3+x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^3 + 2*x^6))/(x^6*(1 + x^3 + x^6)),x]","\frac{2 x F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right)}-\frac{2 x F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};-x^3,-\frac{2 x^3}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right)}+\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2 \left(x^3+1\right)^{5/3}}{5 x^5}+\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{\left(x^3-4\right) \left(x^3+1\right)^{2/3}}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) - (2*(1 + x^3)^(5/3))/(5*x^5) + (2*x*AppellF1[1/3, -5/3, 1, 4/3, -x^3, (-2*x^3)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])) - (2*x*AppellF1[1/3, -5/3, 1, 4/3, -x^3, (-2*x^3)/(1 + I*Sqrt[3])])/(Sqrt[3]*(I - Sqrt[3])) - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]/2","C",8,6,33,0.1818,0,"{6728, 264, 277, 239, 1428, 429}"
1007,1,1134,0,3.6737358,"\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","Int[((-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]","\tan ^{-1}\left(\frac{x}{\sqrt{4 x^4-x^2+4}}\right)-\frac{9 \sqrt{5} \left(i+\sqrt{15}\right)^2 \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{4 x^4-x^2+4}}\right)}{16 \left(15 i+7 \sqrt{15}\right)}-\frac{9 \sqrt{5} \left(7 i+\sqrt{15}\right) \tan ^{-1}\left(\frac{\sqrt{3} x}{\sqrt{4 x^4-x^2+4}}\right)}{8 \left(15+7 i \sqrt{15}\right)}+\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt{4 x^4-x^2+4}}\right)-\frac{9 \left(5 i+3 \sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \left(15 i+\sqrt{15}\right) \sqrt{4 x^4-x^2+4}}+\frac{\left(9 i-\sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \left(15 i+\sqrt{15}\right) \sqrt{4 x^4-x^2+4}}+\frac{\left(9 i+\sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \left(15 i-\sqrt{15}\right) \sqrt{4 x^4-x^2+4}}-\frac{\left(4+i \sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \sqrt{4 x^4-x^2+4}}-\frac{3 \left(2+i \sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \sqrt{4 x^4-x^2+4}}-\frac{\left(4-i \sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \sqrt{4 x^4-x^2+4}}-\frac{3 \left(2-i \sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \sqrt{4 x^4-x^2+4}}-\frac{9 \left(5 i-3 \sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{16 \left(15 i-\sqrt{15}\right) \sqrt{4 x^4-x^2+4}}+\frac{7 \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{9}{16}\right)}{4 \sqrt{4 x^4-x^2+4}}+\frac{45 \left(7 i-\sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} \Pi \left(\frac{3}{8};2 \tan ^{-1}(x)|\frac{9}{16}\right)}{32 \left(15 i+7 \sqrt{15}\right) \sqrt{4 x^4-x^2+4}}+\frac{45 \left(7 i+\sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} \Pi \left(\frac{3}{8};2 \tan ^{-1}(x)|\frac{9}{16}\right)}{32 \left(15 i-7 \sqrt{15}\right) \sqrt{4 x^4-x^2+4}}+\frac{3 \left(7 i-\sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} \Pi \left(\frac{5}{8};2 \tan ^{-1}(x)|\frac{9}{16}\right)}{32 \left(15 i+7 \sqrt{15}\right) \sqrt{4 x^4-x^2+4}}+\frac{3 \left(7 i+\sqrt{15}\right) \left(x^2+1\right) \sqrt{\frac{4 x^4-x^2+4}{\left(x^2+1\right)^2}} \Pi \left(\frac{5}{8};2 \tan ^{-1}(x)|\frac{9}{16}\right)}{32 \left(15 i-7 \sqrt{15}\right) \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,"ArcTan[x/Sqrt[4 - x^2 + 4*x^4]] - (9*Sqrt[5]*(7*I + Sqrt[15])*ArcTan[(Sqrt[3]*x)/Sqrt[4 - x^2 + 4*x^4]])/(8*(15 + (7*I)*Sqrt[15])) - (9*Sqrt[5]*(I + Sqrt[15])^2*ArcTan[(Sqrt[3]*x)/Sqrt[4 - x^2 + 4*x^4]])/(16*(15*I + 7*Sqrt[15])) + ArcTanh[x/Sqrt[4 - x^2 + 4*x^4]]/4 + (7*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(4*Sqrt[4 - x^2 + 4*x^4]) - (9*(5*I - 3*Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*(15*I - Sqrt[15])*Sqrt[4 - x^2 + 4*x^4]) - (3*(2 - I*Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*Sqrt[4 - x^2 + 4*x^4]) - ((4 - I*Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*Sqrt[4 - x^2 + 4*x^4]) - (3*(2 + I*Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*Sqrt[4 - x^2 + 4*x^4]) - ((4 + I*Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*Sqrt[4 - x^2 + 4*x^4]) + ((9*I + Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*(15*I - Sqrt[15])*Sqrt[4 - x^2 + 4*x^4]) + ((9*I - Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*(15*I + Sqrt[15])*Sqrt[4 - x^2 + 4*x^4]) - (9*(5*I + 3*Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 9/16])/(16*(15*I + Sqrt[15])*Sqrt[4 - x^2 + 4*x^4]) + (45*(7*I + Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticPi[3/8, 2*ArcTan[x], 9/16])/(32*(15*I - 7*Sqrt[15])*Sqrt[4 - x^2 + 4*x^4]) + (45*(7*I - Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticPi[3/8, 2*ArcTan[x], 9/16])/(32*(15*I + 7*Sqrt[15])*Sqrt[4 - x^2 + 4*x^4]) + (3*(7*I + Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticPi[5/8, 2*ArcTan[x], 9/16])/(32*(15*I - 7*Sqrt[15])*Sqrt[4 - x^2 + 4*x^4]) + (3*(7*I - Sqrt[15])*(1 + x^2)*Sqrt[(4 - x^2 + 4*x^4)/(1 + x^2)^2]*EllipticPi[5/8, 2*ArcTan[x], 9/16])/(32*(15*I + 7*Sqrt[15])*Sqrt[4 - x^2 + 4*x^4])","C",50,8,53,0.1509,1,"{6725, 1208, 1197, 1103, 1195, 1216, 1706, 6728}"
1008,1,139,0,0.0625156,"\int \sqrt[3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}} \, dx","Int[(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]{(1-3 x) \left(x^3+1\right)^3} (1-3 x)^4}{351 \left(x^3+1\right)}-\frac{\sqrt[3]{(1-3 x) \left(x^3+1\right)^3} (1-3 x)^3}{90 \left(x^3+1\right)}+\frac{\sqrt[3]{(1-3 x) \left(x^3+1\right)^3} (1-3 x)^2}{63 \left(x^3+1\right)}-\frac{7 \sqrt[3]{(1-3 x) \left(x^3+1\right)^3} (1-3 x)}{27 \left(x^3+1\right)}","\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,"(-7*(1 - 3*x)*((1 - 3*x)*(1 + x^3)^3)^(1/3))/(27*(1 + x^3)) + ((1 - 3*x)^2*((1 - 3*x)*(1 + x^3)^3)^(1/3))/(63*(1 + x^3)) - ((1 - 3*x)^3*((1 - 3*x)*(1 + x^3)^3)^(1/3))/(90*(1 + x^3)) + ((1 - 3*x)^4*((1 - 3*x)*(1 + x^3)^3)^(1/3))/(351*(1 + x^3))","A",4,3,37,0.08108,1,"{6688, 6719, 1850}"
1009,0,0,0,9.6802758,"\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","Int[(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]","\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","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*(b - x)*x)/Sqrt[(a - x)*(b - x)*x] - (4*Sqrt[a]*(b - x)*Sqrt[x]*Sqrt[1 - x/a]*EllipticE[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/b]) + (2*Sqrt[a]*b*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/Sqrt[(a - x)*(b - x)*x] - ((2*a - b - d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2])*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Int][(Sqrt[x]*Sqrt[-b + x])/((-a + x)^(3/2)*(-b - d - Sqrt[b^2 - 4*a*d + 2*b*d + d^2] + 2*x)), x])/Sqrt[(a - x)*(b - x)*x] - ((2*a - b - d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2])*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Int][(Sqrt[x]*Sqrt[-b + x])/((-a + x)^(3/2)*(-b - d + Sqrt[b^2 - 4*a*d + 2*b*d + d^2] + 2*x)), x])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1010,1,250,0,3.6840821,"\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","Int[(1 + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^2*x^2)),x]","\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\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*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",15,8,40,0.2000,0,"{6718, 6725, 115, 6688, 934, 12, 168, 537}"
1011,1,46,0,0.0048329,"\int \frac{1}{\sqrt[3]{1+x^3}} \, dx","Int[(1 + x^3)^(-1/3),x]","\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\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[-x + (1 + x^3)^(1/3)]/2","A",1,1,9,0.1111,1,"{239}"
1012,1,251,0,0.6906404,"\int \frac{x+x^2}{\left(-1-2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(x + x^2)/((-1 - 2*x + x^2)*Sqrt[-x + x^3]),x]","\frac{\left(2+\sqrt{2}\right) \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}-\frac{\left(2-\sqrt{2}\right) \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}+\frac{\left(3+2 \sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(-\frac{1}{\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}-\frac{\left(3-2 \sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}","\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,"-1/2*((2 - Sqrt[2])*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/Sqrt[-x + x^3] + ((2 + Sqrt[2])*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(2*Sqrt[-x + x^3]) + ((3 + 2*Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[-(1/Sqrt[2]), ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3]) - ((3 - 2*Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[1/Sqrt[2], ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3])","C",16,9,27,0.3333,0,"{1593, 2056, 6728, 944, 329, 222, 933, 168, 537}"
1013,0,0,0,13.6470864,"\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","Int[(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,"(4*(1 - 2*a*d - 2*b*d)*x*(1 - x/a)^(3/4)*(1 - x/b)^(3/4)*AppellF1[1/4, 3/4, 3/4, 5/4, x/a, x/b])/(d^2*((a - x)*(b - x)*x)^(3/4)) + (4*x^2*(1 - x/a)^(3/4)*(1 - x/b)^(3/4)*AppellF1[5/4, 3/4, 3/4, 9/4, x/a, x/b])/(5*d*((a - x)*(b - x)*x)^(3/4)) - (4*a*b*(1 - 2*a*d - 2*b*d)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][1/((-a + x^4)^(3/4)*(-b + x^4)^(3/4)*(a*b - a*(1 + b/a)*x^4 + x^8 - d*x^12)), x], x, x^(1/4)])/(d^2*((a - x)*(b - x)*x)^(3/4)) + (4*(a + b - 2*a^2*d - 5*a*b*d - 2*b^2*d)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][x^4/((-a + x^4)^(3/4)*(-b + x^4)^(3/4)*(a*b - a*(1 + b/a)*x^4 + x^8 - d*x^12)), x], x, x^(1/4)])/(d^2*((a - x)*(b - x)*x)^(3/4)) - (4*(1 - 3*b*d - 3*a*d*(1 - b*d))*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][x^8/((-a + x^4)^(3/4)*(-b + x^4)^(3/4)*(a*b - a*(1 + b/a)*x^4 + x^8 - d*x^12)), x], x, x^(1/4)])/(d^2*((a - x)*(b - x)*x)^(3/4))","F",0,0,0,0,-1,"{}"
1014,1,129,0,0.0963456,"\int \frac{1}{x \sqrt[4]{-1+x^4}} \, dx","Int[1/(x*(-1 + x^4)^(1/4)),x]","\frac{\log \left(\sqrt{x^4-1}-\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}-\frac{\log \left(\sqrt{x^4-1}+\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^4-1}\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{2 \sqrt{2}}","-\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,"-1/2*ArcTan[1 - Sqrt[2]*(-1 + x^4)^(1/4)]/Sqrt[2] + ArcTan[1 + Sqrt[2]*(-1 + x^4)^(1/4)]/(2*Sqrt[2]) + Log[1 - Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(4*Sqrt[2]) - Log[1 + Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(4*Sqrt[2])","A",11,8,13,0.6154,1,"{266, 63, 297, 1162, 617, 204, 1165, 628}"
1015,0,0,0,19.4255125,"\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","Int[((-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]","\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","-\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,"(2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(Sqrt[-a + x^2]*Sqrt[-b + x^2])/(-(a^2*(b - x^2)^2) + 2*a*(-(b*x) + x^3)^2 - x^4*(b^2 - d - 2*b*x^2 + x^4)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-a + x^2]*Sqrt[-b + x^2])/(a^2*(b - x^2)^2 - 2*a*(-(b*x) + x^3)^2 + x^4*(b^2 - d - 2*b*x^2 + x^4)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1016,1,77,0,0.0437335,"\int \frac{x^2 \left(-b+a x^4\right)}{\left(b+a x^4\right)^{3/4}} \, dx","Int[(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",5,5,24,0.2083,1,"{459, 331, 298, 203, 206}"
1017,1,123,0,0.073422,"\int \frac{1}{\sqrt[4]{b x+a x^4}} \, dx","Int[(b*x + a*x^4)^(-1/4),x]","\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4+b x}}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \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}}",1,"(2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4)) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4))","A",7,7,13,0.5385,1,"{2011, 329, 275, 240, 212, 206, 203}"
1018,0,0,0,31.5425188,"\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","Int[((-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]","\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","-\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,"(2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(Sqrt[-a + x^2]*Sqrt[-b + x^2])/(-(a^2*b^2*d) + 2*a^2*b*(1 + b/a)*d*x^2 + (1 - (a^2 + 4*a*b + b^2)*d)*x^4 + 2*a*(1 + b/a)*d*x^6 - d*x^8), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-a + x^2]*Sqrt[-b + x^2])/(a^2*b^2*d - 2*a^2*b*(1 + b/a)*d*x^2 - (1 - (a^2 + 4*a*b + b^2)*d)*x^4 - 2*a*(1 + b/a)*d*x^6 + d*x^8), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1019,1,129,0,0.1078847,"\int \frac{1}{x \sqrt[4]{-1+x^6}} \, dx","Int[1/(x*(-1 + x^6)^(1/4)),x]","\frac{\log \left(\sqrt{x^6-1}-\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{6 \sqrt{2}}-\frac{\log \left(\sqrt{x^6-1}+\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{6 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^6-1}\right)}{3 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{3 \sqrt{2}}","-\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,"-1/3*ArcTan[1 - Sqrt[2]*(-1 + x^6)^(1/4)]/Sqrt[2] + ArcTan[1 + Sqrt[2]*(-1 + x^6)^(1/4)]/(3*Sqrt[2]) + Log[1 - Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]]/(6*Sqrt[2]) - Log[1 + Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]]/(6*Sqrt[2])","A",11,8,13,0.6154,1,"{266, 63, 297, 1162, 617, 204, 1165, 628}"
1020,0,0,0,1.5195055,"\int \frac{1}{\sqrt[3]{-b x+a x^3} \left(d+c x^6\right)} \, dx","Int[1/((-(b*x) + a*x^3)^(1/3)*(d + c*x^6)),x]","\int \frac{1}{\sqrt[3]{-b x+a x^3} \left(d+c x^6\right)} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^9 (-d)+3 \text{$\#$1}^6 a d-3 \text{$\#$1}^3 a^2 d+a^3 d+b^3 c\&,\frac{\log \left(\sqrt[3]{a x^3-b x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 d}",1,"-1/6*(x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/3)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(4/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(5/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/3)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(7/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(8/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3))","F",0,0,0,0,-1,"{}"
1021,0,0,0,1.2780899,"\int \frac{1}{\sqrt[3]{-b x+a x^3} \left(d+c x^6\right)} \, dx","Int[1/((-(b*x) + a*x^3)^(1/3)*(d + c*x^6)),x]","\int \frac{1}{\sqrt[3]{-b x+a x^3} \left(d+c x^6\right)} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^9 (-d)+3 \text{$\#$1}^6 a d-3 \text{$\#$1}^3 a^2 d+a^3 d+b^3 c\&,\frac{\log \left(\sqrt[3]{a x^3-b x}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]}{6 d}",1,"-1/6*(x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/3)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(4/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(5/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/3)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(7/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3)) - (x^(1/3)*(-b + a*x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(8/9)*c^(1/9)*x)*(-b + a*x^3)^(1/3)), x], x, x^(2/3)])/(6*d^(8/9)*(-(b*x) + a*x^3)^(1/3))","F",0,0,0,0,-1,"{}"
1022,1,74,0,0.1875008,"\int \left(-1+x^2\right) \left(-1+x \sqrt{-1+3 x^2-x^4}\right) \, dx","Int[(-1 + x^2)*(-1 + x*Sqrt[-1 + 3*x^2 - x^4]),x]","-\frac{x^3}{3}-\frac{5}{32} \sin ^{-1}\left(\frac{3-2 x^2}{\sqrt{5}}\right)-\frac{1}{6} \left(-x^4+3 x^2-1\right)^{3/2}-\frac{1}{16} \left(3-2 x^2\right) \sqrt{-x^4+3 x^2-1}+x","-\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,"x - x^3/3 - ((3 - 2*x^2)*Sqrt[-1 + 3*x^2 - x^4])/16 - (-1 + 3*x^2 - x^4)^(3/2)/6 - (5*ArcSin[(3 - 2*x^2)/Sqrt[5]])/32","A",13,8,26,0.3077,1,"{6742, 1107, 612, 619, 216, 14, 1114, 640}"
1023,0,0,0,1.4636617,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]",1,"(I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)*Sqrt[x + Sqrt[1 + x^2]]), x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",0,0,0,0,-1,"{}"
1024,0,0,0,1.0553611,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]",1,"(I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)*Sqrt[x + Sqrt[1 + x^2]]), x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",0,0,0,0,-1,"{}"
1025,0,0,0,0.327498,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\sqrt{b+a^2 x^2}} \, dx","Int[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/Sqrt[b + a^2*x^2],x]","\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\sqrt{b+a^2 x^2}} \, dx","\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,"Defer[Int][Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/Sqrt[b + a^2*x^2], x]","F",0,0,0,0,-1,"{}"
1026,1,64,0,0.030846,"\int \frac{\sqrt{-1+x^2}}{(-i+x)^2} \, dx","Int[Sqrt[-1 + x^2]/(-I + x)^2,x]","\frac{\sqrt{x^2-1}}{-x+i}-\frac{i \tan ^{-1}\left(\frac{1-i x}{\sqrt{2} \sqrt{x^2-1}}\right)}{\sqrt{2}}+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)","\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) - (I*ArcTan[(1 - I*x)/(Sqrt[2]*Sqrt[-1 + x^2])])/Sqrt[2] + ArcTanh[x/Sqrt[-1 + x^2]]","A",6,6,17,0.3529,1,"{733, 844, 217, 206, 725, 204}"
1027,1,78,0,0.0617379,"\int \frac{1}{x^3 \left(b+a x^2\right)^{3/4}} \, dx","Int[1/(x^3*(b + a*x^2)^(3/4)),x]","\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}","\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,"-1/2*(b + a*x^2)^(1/4)/(b*x^2) + (3*a*ArcTan[(b + a*x^2)^(1/4)/b^(1/4)])/(4*b^(7/4)) + (3*a*ArcTanh[(b + a*x^2)^(1/4)/b^(1/4)])/(4*b^(7/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1028,1,248,0,0.9957164,"\int \frac{\left(-1-2 x+x^2+3 x^3\right)^4}{\sqrt[4]{-1+3 x-3 x^2+x^3}} \, dx","Int[(-1 - 2*x + x^2 + 3*x^3)^4/(-1 + 3*x - 3*x^2 + x^3)^(1/4),x]","-\frac{324 (1-x)^{13}}{49 \sqrt[4]{(x-1)^3}}+\frac{96 (1-x)^{12}}{\sqrt[4]{(x-1)^3}}-\frac{25488 (1-x)^{11}}{41 \sqrt[4]{(x-1)^3}}+\frac{87312 (1-x)^{10}}{37 \sqrt[4]{(x-1)^3}}-\frac{191416 (1-x)^9}{33 \sqrt[4]{(x-1)^3}}+\frac{278928 (1-x)^8}{29 \sqrt[4]{(x-1)^3}}-\frac{271528 (1-x)^7}{25 \sqrt[4]{(x-1)^3}}+\frac{57648 (1-x)^6}{7 \sqrt[4]{(x-1)^3}}-\frac{68820 (1-x)^5}{17 \sqrt[4]{(x-1)^3}}+\frac{16032 (1-x)^4}{13 \sqrt[4]{(x-1)^3}}+\frac{144 (1-x)^2}{5 \sqrt[4]{(x-1)^3}}-\frac{4 (1-x)}{\sqrt[4]{(x-1)^3}}+\frac{2104}{9} \left((x-1)^3\right)^{3/4}","\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 + x)^3)^(1/4) + (144*(1 - x)^2)/(5*((-1 + x)^3)^(1/4)) + (16032*(1 - x)^4)/(13*((-1 + x)^3)^(1/4)) - (68820*(1 - x)^5)/(17*((-1 + x)^3)^(1/4)) + (57648*(1 - x)^6)/(7*((-1 + x)^3)^(1/4)) - (271528*(1 - x)^7)/(25*((-1 + x)^3)^(1/4)) + (278928*(1 - x)^8)/(29*((-1 + x)^3)^(1/4)) - (191416*(1 - x)^9)/(33*((-1 + x)^3)^(1/4)) + (87312*(1 - x)^10)/(37*((-1 + x)^3)^(1/4)) - (25488*(1 - x)^11)/(41*((-1 + x)^3)^(1/4)) + (96*(1 - x)^12)/((-1 + x)^3)^(1/4) - (324*(1 - x)^13)/(49*((-1 + x)^3)^(1/4)) + (2104*((-1 + x)^3)^(3/4))/9","B",53,6,33,0.1818,1,"{6742, 2067, 15, 30, 2081, 43}"
1029,1,78,0,0.05707,"\int \frac{1}{x^4 \left(b+a x^3\right)^{3/4}} \, dx","Int[1/(x^4*(b + a*x^3)^(3/4)),x]","\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}","\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,"-1/3*(b + a*x^3)^(1/4)/(b*x^3) + (a*ArcTan[(b + a*x^3)^(1/4)/b^(1/4)])/(2*b^(7/4)) + (a*ArcTanh[(b + a*x^3)^(1/4)/b^(1/4)])/(2*b^(7/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1030,1,76,0,0.0344899,"\int \frac{x}{\sqrt{-71-96 x+10 x^2+x^4}} \, dx","Int[x/Sqrt[-71 - 96*x + 10*x^2 + x^4],x]","\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)","-\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,"Log[10001 + 3124*x^2 - 1408*x^3 + 54*x^4 - 128*x^5 + 20*x^6 + x^8 + Sqrt[-71 - 96*x + 10*x^2 + x^4]*(781 - 528*x + 27*x^2 - 80*x^3 + 15*x^4 + x^6)]/8","A",1,1,19,0.05263,1,"{2082}"
1031,0,0,0,1.0720329,"\int \frac{(8+3 x) \sqrt[4]{-2-x+2 x^4}}{x^2 \left(2+x+x^4\right)} \, dx","Int[((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,"4*Defer[Int][(-2 - x + 2*x^4)^(1/4)/x^2, x] - Defer[Int][(-2 - x + 2*x^4)^(1/4)/x, x]/2 + Defer[Int][(-2 - x + 2*x^4)^(1/4)/(2 + x + x^4), x]/2 - 4*Defer[Int][(x^2*(-2 - x + 2*x^4)^(1/4))/(2 + x + x^4), x] + Defer[Int][(x^3*(-2 - x + 2*x^4)^(1/4))/(2 + x + x^4), x]/2","F",0,0,0,0,-1,"{}"
1032,1,78,0,0.0614716,"\int \frac{1}{x^5 \left(b+a x^4\right)^{3/4}} \, dx","Int[1/(x^5*(b + a*x^4)^(3/4)),x]","\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}","\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,"-1/4*(b + a*x^4)^(1/4)/(b*x^4) + (3*a*ArcTan[(b + a*x^4)^(1/4)/b^(1/4)])/(8*b^(7/4)) + (3*a*ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)])/(8*b^(7/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1033,1,78,0,0.0573969,"\int \frac{1}{x^6 \left(b+a x^5\right)^{3/4}} \, dx","Int[1/(x^6*(b + a*x^5)^(3/4)),x]","\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}","\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,"-1/5*(b + a*x^5)^(1/4)/(b*x^5) + (3*a*ArcTan[(b + a*x^5)^(1/4)/b^(1/4)])/(10*b^(7/4)) + (3*a*ArcTanh[(b + a*x^5)^(1/4)/b^(1/4)])/(10*b^(7/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1034,1,223,0,0.1397001,"\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","Int[((-1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(1 - x^3 + x^6)),x]","-\frac{2 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};x^3,\frac{2 x^3}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{2 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};x^3,\frac{2 x^3}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{1}{2} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}+\frac{\left(x^3-1\right)^{2/3}}{2 x^2}","\frac{\left(x^3-1\right)^{2/3} \left(7 x^3-2\right)}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(2*x^2) + (-1 + x^3)^(5/3)/(5*x^5) - (2*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -5/3, 1, 4/3, x^3, (2*x^3)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])*(1 - x^3)^(2/3)) + (2*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -5/3, 1, 4/3, x^3, (2*x^3)/(1 + I*Sqrt[3])])/(Sqrt[3]*(I - Sqrt[3])*(1 - x^3)^(2/3)) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (-1 + x^3)^(1/3)]/2","C",10,7,35,0.2000,0,"{28, 1520, 277, 239, 1428, 430, 429}"
1035,1,223,0,0.1261512,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(1-x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(1 - x^3 + x^6)),x]","-\frac{2 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};x^3,\frac{2 x^3}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{2 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{5}{3},1;\frac{4}{3};x^3,\frac{2 x^3}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{1}{2} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}+\frac{\left(x^3-1\right)^{2/3}}{2 x^2}","\frac{\left(x^3-1\right)^{2/3} \left(7 x^3-2\right)}{10 x^5}-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(2*x^2) + (-1 + x^3)^(5/3)/(5*x^5) - (2*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -5/3, 1, 4/3, x^3, (2*x^3)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])*(1 - x^3)^(2/3)) + (2*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -5/3, 1, 4/3, x^3, (2*x^3)/(1 + I*Sqrt[3])])/(Sqrt[3]*(I - Sqrt[3])*(1 - x^3)^(2/3)) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (-1 + x^3)^(1/3)]/2","C",10,7,35,0.2000,0,"{28, 1520, 277, 239, 1428, 430, 429}"
1036,1,78,0,0.0625641,"\int \frac{1}{x^7 \left(b+a x^6\right)^{3/4}} \, dx","Int[1/(x^7*(b + a*x^6)^(3/4)),x]","\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}-\frac{\sqrt[4]{a x^6+b}}{6 b x^6}","\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{a x^6+b}}{\sqrt[4]{b}}\right)}{4 b^{7/4}}-\frac{\sqrt[4]{a x^6+b}}{6 b x^6}",1,"-1/6*(b + a*x^6)^(1/4)/(b*x^6) + (a*ArcTan[(b + a*x^6)^(1/4)/b^(1/4)])/(4*b^(7/4)) + (a*ArcTanh[(b + a*x^6)^(1/4)/b^(1/4)])/(4*b^(7/4))","A",6,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1037,1,113,0,0.4382153,"\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^8\right)}{x^6 \left(1+x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(-1 + x^8))/(x^6*(1 + x^8)),x]","\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,-i x^4\right)}{3 \sqrt[4]{1-x^4}}+\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,i x^4\right)}{3 \sqrt[4]{1-x^4}}-\frac{\left(x^4-1\right)^{5/4}}{5 x^5}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-1}\&\right]+\frac{\sqrt[4]{x^4-1} \left(1-x^4\right)}{5 x^5}",1,"-1/5*(-1 + x^4)^(5/4)/x^5 + (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (-I)*x^4])/(3*(1 - x^4)^(1/4)) + (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, I*x^4])/(3*(1 - x^4)^(1/4))","C",9,5,25,0.2000,0,"{6725, 264, 1529, 511, 510}"
1038,1,153,0,0.2908141,"\int \frac{-1+x^8}{\sqrt[4]{1+x^4} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((1 + x^4)^(1/4)*(1 + x^8)),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1-i}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1+i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1+i}}+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1-i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1-i}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1+i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1+i}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)",1,"ArcTan[x/(1 + x^4)^(1/4)]/2 - ArcTan[((1 - I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 - I)^(1/4)) - ArcTan[((1 + I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 + I)^(1/4)) + ArcTanh[x/(1 + x^4)^(1/4)]/2 - ArcTanh[((1 - I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 - I)^(1/4)) - ArcTanh[((1 + I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 + I)^(1/4))","C",21,8,22,0.3636,1,"{1586, 6725, 408, 240, 212, 206, 203, 377}"
1039,1,153,0,0.2346198,"\int \frac{-1+x^8}{\sqrt[4]{1+x^4} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((1 + x^4)^(1/4)*(1 + x^8)),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1-i}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1+i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1+i}}+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1-i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1-i}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1+i} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt[4]{1+i}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$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,"ArcTan[x/(1 + x^4)^(1/4)]/2 - ArcTan[((1 - I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 - I)^(1/4)) - ArcTan[((1 + I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 + I)^(1/4)) + ArcTanh[x/(1 + x^4)^(1/4)]/2 - ArcTanh[((1 - I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 - I)^(1/4)) - ArcTanh[((1 + I)^(1/4)*x)/(1 + x^4)^(1/4)]/(2*(1 + I)^(1/4))","C",21,8,22,0.3636,1,"{1586, 6725, 408, 240, 212, 206, 203, 377}"
1040,1,560,0,2.0501171,"\int \frac{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)}{x^6 \left(1+2 x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(1 - x^4 + x^8))/(x^6*(1 + 2*x^8)),x]","-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,-i \sqrt{2} x^4\right)}{6 \sqrt[4]{1-x^4}}-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,i \sqrt{2} x^4\right)}{6 \sqrt[4]{1-x^4}}+\frac{\sqrt[4]{x^4-1}}{x}-\frac{i \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}-2 i\right)^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}-2 i\right)^{3/4}}+\frac{i \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}+2 i\right)^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}+2 i\right)^{3/4}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}-2 i\right)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}-2 i\right)^{3/4}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}+2 i\right)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}+2 i\right)^{3/4}}+\frac{\left(x^4-1\right)^{5/4}}{5 x^5}","\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,"(-1 + x^4)^(1/4)/x + (-1 + x^4)^(5/4)/(5*x^5) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (-I)*Sqrt[2]*x^4])/(6*(1 - x^4)^(1/4)) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, I*Sqrt[2]*x^4])/(6*(1 - x^4)^(1/4)) + ArcTan[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(-2*I + Sqrt[2])^(3/4)) - ((I/2)*ArcTan[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(-2*I + Sqrt[2])^(3/4)) + ArcTan[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(2*I + Sqrt[2])^(3/4)) + ((I/2)*ArcTan[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(2*I + Sqrt[2])^(3/4)) - ArcTanh[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(-2*I + Sqrt[2])^(3/4)) + ((I/2)*ArcTanh[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(-2*I + Sqrt[2])^(3/4)) - ArcTanh[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(2*I + Sqrt[2])^(3/4)) - ((I/2)*ArcTanh[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(2*I + Sqrt[2])^(3/4))","C",43,12,32,0.3750,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
1041,1,560,0,1.8549738,"\int \frac{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)}{x^6 \left(1+2 x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(1 - x^4 + x^8))/(x^6*(1 + 2*x^8)),x]","-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,-i \sqrt{2} x^4\right)}{6 \sqrt[4]{1-x^4}}-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,i \sqrt{2} x^4\right)}{6 \sqrt[4]{1-x^4}}+\frac{\sqrt[4]{x^4-1}}{x}-\frac{i \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}-2 i\right)^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}-2 i\right)^{3/4}}+\frac{i \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}+2 i\right)^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}+2 i\right)^{3/4}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}-2 i\right)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}-2 i\right)^{3/4}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2}+2 i\right)^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} x}{\sqrt[8]{2} \sqrt[4]{x^4-1}}\right)}{2\ 2^{5/8} \left(\sqrt{2}+2 i\right)^{3/4}}+\frac{\left(x^4-1\right)^{5/4}}{5 x^5}","\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,"(-1 + x^4)^(1/4)/x + (-1 + x^4)^(5/4)/(5*x^5) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (-I)*Sqrt[2]*x^4])/(6*(1 - x^4)^(1/4)) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, I*Sqrt[2]*x^4])/(6*(1 - x^4)^(1/4)) + ArcTan[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(-2*I + Sqrt[2])^(3/4)) - ((I/2)*ArcTan[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(-2*I + Sqrt[2])^(3/4)) + ArcTan[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(2*I + Sqrt[2])^(3/4)) + ((I/2)*ArcTan[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(2*I + Sqrt[2])^(3/4)) - ArcTanh[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(-2*I + Sqrt[2])^(3/4)) + ((I/2)*ArcTanh[((-2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(-2*I + Sqrt[2])^(3/4)) - ArcTanh[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))]/(2*2^(5/8)*(2*I + Sqrt[2])^(3/4)) - ((I/2)*ArcTanh[((2*I + Sqrt[2])^(1/4)*x)/(2^(1/8)*(-1 + x^4)^(1/4))])/(2^(1/8)*(2*I + Sqrt[2])^(3/4))","C",43,12,32,0.3750,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
1042,1,56,0,0.0624955,"\int \frac{\left(1+2 x^4\right) \sqrt{1+2 x^8}}{x} \, dx","Int[((1 + 2*x^4)*Sqrt[1 + 2*x^8])/x,x]","-\frac{1}{4} \tanh ^{-1}\left(\sqrt{2 x^8+1}\right)+\frac{\sinh ^{-1}\left(\sqrt{2} x^4\right)}{4 \sqrt{2}}+\frac{1}{4} \sqrt{2 x^8+1} \left(x^4+1\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,"((1 + x^4)*Sqrt[1 + 2*x^8])/4 + ArcSinh[Sqrt[2]*x^4]/(4*Sqrt[2]) - ArcTanh[Sqrt[1 + 2*x^8]]/4","A",7,7,22,0.3182,1,"{1475, 815, 844, 215, 266, 63, 207}"
1043,1,79,0,0.0469687,"\int \sqrt{x+\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]],x]","\frac{2}{3} \left(x+\sqrt{x+1}\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x+1}+1\right) \sqrt{x+\sqrt{x+1}}+\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,"(2*(x + Sqrt[1 + x])^(3/2))/3 - (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",5,4,13,0.3077,1,"{640, 612, 621, 206}"
1044,1,79,0,0.0681456,"\int \frac{2 b+a x^2}{x \left(b^2+a^2 x^2\right)^{3/4}} \, dx","Int[(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",6,6,28,0.2143,1,"{446, 80, 63, 212, 206, 203}"
1045,0,0,0,13.1425739,"\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","Int[(-(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]","\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","\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*x)/((a - b)*d*Sqrt[(a - x)*(b - x)*x]) + (4*(a - x)*x)/((a - b)^2*d*Sqrt[(a - x)*(b - x)*x]) - (4*Sqrt[a]*(b - x)*Sqrt[x]*Sqrt[1 - x/a]*EllipticE[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/((a - b)^2*d*Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/b]) - (2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/((a - b)*d*Sqrt[(a - x)*(b - x)*x]) + ((1 + a*d + b*d + Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2])*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Int][Sqrt[x]/((-a + x)^(3/2)*(-b + x)^(3/2)*(-1 - a*d - b*d - Sqrt[1 + 2*a*d + 2*b*d + a^2*d^2 - 2*a*b*d^2 + b^2*d^2] + 2*d*x)), x])/(d*Sqrt[(a - x)*(b - x)*x]) + ((1 + a*d + b*d - Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2])*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Int][Sqrt[x]/((-a + x)^(3/2)*(-b + x)^(3/2)*(-1 - a*d - b*d + Sqrt[1 + 2*a*d + 2*b*d + a^2*d^2 - 2*a*b*d^2 + b^2*d^2] + 2*d*x)), x])/(d*Sqrt[(a - x)*(b - x)*x])","F",0,0,0,0,-1,"{}"
1046,0,0,0,12.5814129,"\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","Int[(-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,"(4*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(1 - 3*(1 + d/3)*x^4 + 3*(1 + (d*k)/3)*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (8*(1 - k)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^6/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(1 - 3*(1 + d/3)*x^4 + 3*(1 + (d*k)/3)*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (4*k*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^10/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(-1 + 3*(1 + d/3)*x^4 - 3*(1 + (d*k)/3)*x^8 + x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4)","F",0,0,0,0,-1,"{}"
1047,1,119,0,0.6841648,"\int \frac{1+x^4}{\sqrt{-x+x^3} \left(-1+x^4\right)} \, dx","Int[(1 + x^4)/(Sqrt[-x + x^3]*(-1 + x^4)),x]","-\frac{x}{\sqrt{x^3-x}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \sqrt{x^2-1} \sqrt{x} \tan ^{-1}\left(\frac{(1+i) \sqrt{x}}{\sqrt{x^2-1}}\right)}{\sqrt{x^3-x}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \sqrt{x^2-1} \sqrt{x} \tanh ^{-1}\left(\frac{(1+i) \sqrt{x}}{\sqrt{x^2-1}}\right)}{\sqrt{x^3-x}}","\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 + x^3]) - ((1/4 - I/4)*Sqrt[x]*Sqrt[-1 + x^2]*ArcTan[((1 + I)*Sqrt[x])/Sqrt[-1 + x^2]])/Sqrt[-x + x^3] - ((1/4 - I/4)*Sqrt[x]*Sqrt[-1 + x^2]*ArcTanh[((1 + I)*Sqrt[x])/Sqrt[-1 + x^2]])/Sqrt[-x + x^3]","C",18,12,24,0.5000,1,"{2056, 6715, 6725, 222, 1404, 414, 523, 409, 1211, 1699, 206, 203}"
1048,1,938,0,2.1350849,"\int \frac{\left(2+x^2\right) \sqrt{4-5 x^2+x^4}}{x^2 \left(-2+2 x+x^2\right)} \, dx","Int[((2 + x^2)*Sqrt[4 - 5*x^2 + x^4])/(x^2*(-2 + 2*x + x^2)),x]","\tanh ^{-1}\left(\frac{8-5 x^2}{4 \sqrt{x^4-5 x^2+4}}\right)+\frac{1}{8} \left(9+\sqrt{3}\right) \tanh ^{-1}\left(\frac{5-2 x^2}{2 \sqrt{x^4-5 x^2+4}}\right)+\frac{1}{8} \left(9-\sqrt{3}\right) \tanh ^{-1}\left(\frac{5-2 x^2}{2 \sqrt{x^4-5 x^2+4}}\right)-\frac{5}{4} \tanh ^{-1}\left(\frac{5-2 x^2}{2 \sqrt{x^4-5 x^2+4}}\right)+\frac{1}{2} \sqrt{3} \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)-\frac{1}{2} \sqrt{3} \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)-\frac{\left(2+\sqrt{3}\right) \sqrt{4-x^2} \sqrt{x^2-1} F\left(\cos ^{-1}\left(\frac{x}{2}\right)|\frac{4}{3}\right)}{\sqrt{x^4-5 x^2+4}}+\frac{\left(2-\sqrt{3}\right) \sqrt{4-x^2} \sqrt{x^2-1} F\left(\cos ^{-1}\left(\frac{x}{2}\right)|\frac{4}{3}\right)}{\sqrt{x^4-5 x^2+4}}+\frac{\left(1+2 \sqrt{3}\right) \left(x^2+2\right) \sqrt{\frac{x^4-5 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{9}{8}\right)}{2 \sqrt{2} \sqrt{x^4-5 x^2+4}}-\frac{\sqrt{\frac{3}{2}} \left(2+\sqrt{3}\right) \left(x^2+2\right) \sqrt{\frac{x^4-5 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{9}{8}\right)}{2 \sqrt{x^4-5 x^2+4}}+\frac{\sqrt{\frac{3}{2}} \left(2-\sqrt{3}\right) \left(x^2+2\right) \sqrt{\frac{x^4-5 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{9}{8}\right)}{2 \sqrt{x^4-5 x^2+4}}+\frac{\left(1-2 \sqrt{3}\right) \left(x^2+2\right) \sqrt{\frac{x^4-5 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{9}{8}\right)}{2 \sqrt{2} \sqrt{x^4-5 x^2+4}}+\frac{\left(x^2+2\right) \sqrt{\frac{x^4-5 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{9}{8}\right)}{2 \sqrt{2} \sqrt{x^4-5 x^2+4}}-\frac{3 \sqrt{1-x^2} \sqrt{4-x^2} \Pi \left(\frac{1}{2} \left(2-\sqrt{3}\right);\sin ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4-5 x^2+4}}-\frac{3 \sqrt{1-x^2} \sqrt{4-x^2} \Pi \left(\frac{1}{2} \left(2+\sqrt{3}\right);\sin ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4-5 x^2+4}}+\frac{\sqrt{x^4-5 x^2+4}}{x}+\frac{1}{4} \left(1+\sqrt{3}\right) \sqrt{x^4-5 x^2+4}+\frac{1}{4} \left(1-\sqrt{3}\right) \sqrt{x^4-5 x^2+4}-\frac{1}{2} \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,"-1/2*Sqrt[4 - 5*x^2 + x^4] + ((1 - Sqrt[3])*Sqrt[4 - 5*x^2 + x^4])/4 + ((1 + Sqrt[3])*Sqrt[4 - 5*x^2 + x^4])/4 + Sqrt[4 - 5*x^2 + x^4]/x + ArcTanh[(8 - 5*x^2)/(4*Sqrt[4 - 5*x^2 + x^4])] - (5*ArcTanh[(5 - 2*x^2)/(2*Sqrt[4 - 5*x^2 + x^4])])/4 + ((9 - Sqrt[3])*ArcTanh[(5 - 2*x^2)/(2*Sqrt[4 - 5*x^2 + x^4])])/8 + ((9 + Sqrt[3])*ArcTanh[(5 - 2*x^2)/(2*Sqrt[4 - 5*x^2 + x^4])])/8 + (Sqrt[3]*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])])/2 - (Sqrt[3]*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])])/2 + ((2 - Sqrt[3])*Sqrt[4 - x^2]*Sqrt[-1 + x^2]*EllipticF[ArcCos[x/2], 4/3])/Sqrt[4 - 5*x^2 + x^4] - ((2 + Sqrt[3])*Sqrt[4 - x^2]*Sqrt[-1 + x^2]*EllipticF[ArcCos[x/2], 4/3])/Sqrt[4 - 5*x^2 + x^4] + ((2 + x^2)*Sqrt[(4 - 5*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 9/8])/(2*Sqrt[2]*Sqrt[4 - 5*x^2 + x^4]) + ((1 - 2*Sqrt[3])*(2 + x^2)*Sqrt[(4 - 5*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 9/8])/(2*Sqrt[2]*Sqrt[4 - 5*x^2 + x^4]) + (Sqrt[3/2]*(2 - Sqrt[3])*(2 + x^2)*Sqrt[(4 - 5*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 9/8])/(2*Sqrt[4 - 5*x^2 + x^4]) - (Sqrt[3/2]*(2 + Sqrt[3])*(2 + x^2)*Sqrt[(4 - 5*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 9/8])/(2*Sqrt[4 - 5*x^2 + x^4]) + ((1 + 2*Sqrt[3])*(2 + x^2)*Sqrt[(4 - 5*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 9/8])/(2*Sqrt[2]*Sqrt[4 - 5*x^2 + x^4]) - (3*Sqrt[1 - x^2]*Sqrt[4 - x^2]*EllipticPi[(2 - Sqrt[3])/2, ArcSin[x], 1/4])/(2*Sqrt[4 - 5*x^2 + x^4]) - (3*Sqrt[1 - x^2]*Sqrt[4 - x^2]*EllipticPi[(2 + Sqrt[3])/2, ArcSin[x], 1/4])/(2*Sqrt[4 - 5*x^2 + x^4])","C",57,21,33,0.6364,0,"{6728, 1117, 1183, 1096, 1182, 1114, 734, 843, 621, 206, 724, 1728, 1208, 1214, 1456, 540, 421, 420, 538, 537, 1247}"
1049,1,45,0,0.1655292,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Int[x^2/((-1 + x^4)*(x^2 + x^4)^(1/4)),x]","-\frac{2 x^3 \, _2F_1\left(1,\frac{5}{4};\frac{9}{4};\frac{2 x^2}{x^2+1}\right)}{5 \left(x^2+1\right) \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,"(-2*x^3*Hypergeometric2F1[1, 5/4, 9/4, (2*x^2)/(1 + x^2)])/(5*(1 + x^2)*(x^2 + x^4)^(1/4))","C",4,4,22,0.1818,1,"{2056, 1254, 466, 510}"
1050,1,65,0,0.0933649,"\int \frac{\left(-2+x^6\right) \sqrt{-1+x^6}}{x^4 \left(2+x^6\right)} \, dx","Int[((-2 + x^6)*Sqrt[-1 + x^6])/(x^4*(2 + x^6)),x]","\frac{\sqrt{x^6-1}}{3 x^3}+\frac{1}{3} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)-\sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x^3}{\sqrt{x^6-1}}\right)","\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,"Sqrt[-1 + x^6]/(3*x^3) + ArcTanh[x^3/Sqrt[-1 + x^6]]/3 - Sqrt[2/3]*ArcTanh[(Sqrt[3/2]*x^3)/Sqrt[-1 + x^6]]","A",7,6,25,0.2400,1,"{575, 580, 523, 217, 206, 377}"
1051,0,0,0,4.393042,"\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","Int[((-4 + x^6)*(2 - x^4 + x^6)^(5/2))/(x^7*(2 + x^6)^2),x]","\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","\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,"(5*Defer[Int][(2 - x^4 + x^6)^(5/2)/((-2)^(1/6) - x), x])/24 + (5*Defer[Int][(2 - x^4 + x^6)^(5/2)/(-((-2)^(1/6)*(-1)^(1/3)) - x), x])/24 + (5*Defer[Int][(2 - x^4 + x^6)^(5/2)/((-2)^(1/6)*(-1)^(2/3) - x), x])/24 - Defer[Int][(2 - x^4 + x^6)^(5/2)/x^7, x] - (5*Defer[Int][(2 - x^4 + x^6)^(5/2)/((-2)^(1/6) + x), x])/24 - (5*Defer[Int][(2 - x^4 + x^6)^(5/2)/(-((-2)^(1/6)*(-1)^(1/3)) + x), x])/24 - (5*Defer[Int][(2 - x^4 + x^6)^(5/2)/((-2)^(1/6)*(-1)^(2/3) + x), x])/24 + (10935*Sqrt[3]*(2 - x^4 + x^6)^(5/2)*Defer[Subst][Defer[Int][(((1 + (26 - 15*Sqrt[3])^(2/3))/(3*(26 - 15*Sqrt[3])^(1/3)) + x)^(5/2)*((-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3))/9 - ((1 + (26 - 15*Sqrt[3])^(2/3))*x)/(3*(26 - 15*Sqrt[3])^(1/3)) + x^2)^(5/2))/(1/3 + x), x], x, (-1 + 3*x^2)/3])/(8*(-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x^2)^(5/2)*(-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x^2))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x^2)^2)^(5/2)) - (3*Defer[Subst][Defer[Int][(x^2*(2 - x^2 + x^3)^(5/2))/(2 + x^3)^2, x], x, x^2])/4","F",0,0,0,0,-1,"{}"
1052,1,161,0,0.4868587,"\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","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(2 + x^3 + 2*x^6)),x]","-\frac{8 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1-i \sqrt{15}}\right)}{\sqrt{15} \left(\sqrt{15}+i\right) \left(1-x^3\right)^{2/3}}+\frac{8 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1+i \sqrt{15}}\right)}{\sqrt{15} \left(-\sqrt{15}+i\right) \left(1-x^3\right)^{2/3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}","\frac{\left(x^3-1\right)^{5/3}}{5 x^5}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"(-1 + x^3)^(5/3)/(5*x^5) - (8*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 - I*Sqrt[15])])/(Sqrt[15]*(I + Sqrt[15])*(1 - x^3)^(2/3)) + (8*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 + I*Sqrt[15])])/(Sqrt[15]*(I - Sqrt[15])*(1 - x^3)^(2/3))","C",8,5,30,0.1667,0,"{6728, 264, 1428, 430, 429}"
1053,1,161,0,0.3657751,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(2+x^3+2 x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(2 + x^3 + 2*x^6)),x]","-\frac{8 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1-i \sqrt{15}}\right)}{\sqrt{15} \left(\sqrt{15}+i\right) \left(1-x^3\right)^{2/3}}+\frac{8 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1+i \sqrt{15}}\right)}{\sqrt{15} \left(-\sqrt{15}+i\right) \left(1-x^3\right)^{2/3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}","\frac{\left(x^3-1\right)^{5/3}}{5 x^5}-\frac{2}{3} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"(-1 + x^3)^(5/3)/(5*x^5) - (8*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 - I*Sqrt[15])])/(Sqrt[15]*(I + Sqrt[15])*(1 - x^3)^(2/3)) + (8*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 + I*Sqrt[15])])/(Sqrt[15]*(I - Sqrt[15])*(1 - x^3)^(2/3))","C",8,5,30,0.1667,0,"{6728, 264, 1428, 430, 429}"
1054,1,601,0,1.7408471,"\int \frac{x+x^7}{\left(-1+x^6\right)^{2/3} \left(-1+x^3+x^6\right)} \, dx","Int[(x + x^7)/((-1 + x^6)^(2/3)*(-1 + x^3 + x^6)),x]","\frac{\left(5-\sqrt{5}\right) \left(1-x^6\right)^{2/3} x^5 F_1\left(\frac{5}{6};\frac{2}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{25 \left(3-\sqrt{5}\right) \left(x^6-1\right)^{2/3}}-\frac{4 \left(1-x^6\right)^{2/3} x^5 F_1\left(\frac{5}{6};\frac{2}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{5 \sqrt{5} \left(3-\sqrt{5}\right) \left(x^6-1\right)^{2/3}}+\frac{\left(5+\sqrt{5}\right) \left(1-x^6\right)^{2/3} x^5 F_1\left(\frac{5}{6};\frac{2}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3+\sqrt{5}}\right)}{25 \left(3+\sqrt{5}\right) \left(x^6-1\right)^{2/3}}+\frac{4 \left(1-x^6\right)^{2/3} x^5 F_1\left(\frac{5}{6};\frac{2}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3+\sqrt{5}}\right)}{5 \sqrt{5} \left(3+\sqrt{5}\right) \left(x^6-1\right)^{2/3}}-\frac{\left(5-\sqrt{5}\right) \left(1-x^6\right)^{2/3} x^2 F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{5 \left(3-\sqrt{5}\right) \left(x^6-1\right)^{2/3}}+\frac{\left(1-x^6\right)^{2/3} x^2 F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{2 \sqrt{5} \left(x^6-1\right)^{2/3}}-\frac{\left(5+\sqrt{5}\right) \left(1-x^6\right)^{2/3} x^2 F_1\left(\frac{1}{3};1,\frac{2}{3};\frac{4}{3};\frac{2 x^6}{3+\sqrt{5}},x^6\right)}{5 \left(3+\sqrt{5}\right) \left(x^6-1\right)^{2/3}}-\frac{\left(1-x^6\right)^{2/3} x^2 F_1\left(\frac{1}{3};1,\frac{2}{3};\frac{4}{3};\frac{2 x^6}{3+\sqrt{5}},x^6\right)}{2 \sqrt{5} \left(x^6-1\right)^{2/3}}+\frac{\left(1-x^6\right)^{2/3} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};x^6\right)}{2 \left(x^6-1\right)^{2/3}}","\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,"(x^2*(1 - x^6)^(2/3)*AppellF1[1/3, 2/3, 1, 4/3, x^6, (2*x^6)/(3 - Sqrt[5])])/(2*Sqrt[5]*(-1 + x^6)^(2/3)) - ((5 - Sqrt[5])*x^2*(1 - x^6)^(2/3)*AppellF1[1/3, 2/3, 1, 4/3, x^6, (2*x^6)/(3 - Sqrt[5])])/(5*(3 - Sqrt[5])*(-1 + x^6)^(2/3)) - (x^2*(1 - x^6)^(2/3)*AppellF1[1/3, 1, 2/3, 4/3, (2*x^6)/(3 + Sqrt[5]), x^6])/(2*Sqrt[5]*(-1 + x^6)^(2/3)) - ((5 + Sqrt[5])*x^2*(1 - x^6)^(2/3)*AppellF1[1/3, 1, 2/3, 4/3, (2*x^6)/(3 + Sqrt[5]), x^6])/(5*(3 + Sqrt[5])*(-1 + x^6)^(2/3)) - (4*x^5*(1 - x^6)^(2/3)*AppellF1[5/6, 2/3, 1, 11/6, x^6, (2*x^6)/(3 - Sqrt[5])])/(5*Sqrt[5]*(3 - Sqrt[5])*(-1 + x^6)^(2/3)) + ((5 - Sqrt[5])*x^5*(1 - x^6)^(2/3)*AppellF1[5/6, 2/3, 1, 11/6, x^6, (2*x^6)/(3 - Sqrt[5])])/(25*(3 - Sqrt[5])*(-1 + x^6)^(2/3)) + (4*x^5*(1 - x^6)^(2/3)*AppellF1[5/6, 2/3, 1, 11/6, x^6, (2*x^6)/(3 + Sqrt[5])])/(5*Sqrt[5]*(3 + Sqrt[5])*(-1 + x^6)^(2/3)) + ((5 + Sqrt[5])*x^5*(1 - x^6)^(2/3)*AppellF1[5/6, 2/3, 1, 11/6, x^6, (2*x^6)/(3 + Sqrt[5])])/(25*(3 + Sqrt[5])*(-1 + x^6)^(2/3)) + (x^2*(1 - x^6)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, x^6])/(2*(-1 + x^6)^(2/3))","C",40,11,25,0.4400,0,"{1593, 6728, 275, 246, 245, 1562, 465, 430, 429, 511, 510}"
1055,0,0,0,0.5111987,"\int \frac{\sqrt{1-x^6} \left(1+2 x^6\right)}{1+x^4-2 x^6+x^{12}} \, dx","Int[(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,"Defer[Int][Sqrt[1 - x^6]/(1 + x^4 - 2*x^6 + x^12), x] + 2*Defer[Int][(x^6*Sqrt[1 - x^6])/(1 + x^4 - 2*x^6 + x^12), x]","F",0,0,0,0,-1,"{}"
1056,0,0,0,0.0987605,"\int \frac{\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + x^2]/Sqrt[1 + Sqrt[1 + x^2]],x]","\int \frac{\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","\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,"Defer[Int][Sqrt[1 + x^2]/Sqrt[1 + Sqrt[1 + x^2]], x]","F",0,0,0,0,-1,"{}"
1057,1,77,0,0.0441409,"\int \frac{1+x^2}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(1 + x^2)/Sqrt[x + Sqrt[1 + x^2]],x]","\frac{1}{20} \left(\sqrt{x^2+1}+x\right)^{5/2}+\frac{3}{4} \sqrt{\sqrt{x^2+1}+x}-\frac{1}{4 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\frac{1}{28 \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,"-1/28*1/(x + Sqrt[1 + x^2])^(7/2) - 1/(4*(x + Sqrt[1 + x^2])^(3/2)) + (3*Sqrt[x + Sqrt[1 + x^2]])/4 + (x + Sqrt[1 + x^2])^(5/2)/20","A",3,2,21,0.09524,1,"{2122, 270}"
1058,0,0,0,0.1002034,"\int \frac{x^2}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[x^2/Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int \frac{x^2}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","\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,"Defer[Int][x^2/Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
1059,0,0,0,0.100072,"\int \frac{\sqrt{1+x^4}}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[Sqrt[1 + x^4]/Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int \frac{\sqrt{1+x^4}}{\sqrt{x^2+\sqrt{1+x^4}}} \, dx","\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,"Defer[Int][Sqrt[1 + x^4]/Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
1060,0,0,0,0.4125233,"\int \frac{-3+x^2}{\sqrt[3]{-1+x^2} \left(-1+x^2+x^3\right)} \, dx","Int[(-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,"-3*Defer[Int][1/((-1 + x^2)^(1/3)*(-1 + x^2 + x^3)), x] + Defer[Int][x^2/((-1 + x^2)^(1/3)*(-1 + x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
1061,0,0,0,12.2159464,"\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","Int[(-(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]","\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","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,"(-4*Sqrt[(a - x)*(b - x)*x])/(b^2*d*x) + (2*Sqrt[(a - x)*(b - x)*x])/(b*d*(b - x)*x) - (4*Sqrt[a]*Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/a]*EllipticE[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(b^2*d*(a - x)*Sqrt[x]*Sqrt[1 - x/b]) + (2*Sqrt[a]*Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(b*d*(a - x)*(b - x)*Sqrt[x]) + ((1 - 2*a*d + b*d + Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[(a - x)*(b - x)*x]*Defer[Int][Sqrt[a - x]/((b - x)^(3/2)*x^(3/2)*(-1 - b*d - Sqrt[1 - 4*a*d + 2*b*d + b^2*d^2] + 2*d*x)), x])/(d*Sqrt[a - x]*Sqrt[b - x]*Sqrt[x]) + ((1 - 2*a*d + b*d - Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[(a - x)*(b - x)*x]*Defer[Int][Sqrt[a - x]/((b - x)^(3/2)*x^(3/2)*(-1 - b*d + Sqrt[1 - 4*a*d + 2*b*d + b^2*d^2] + 2*d*x)), x])/(d*Sqrt[a - x]*Sqrt[b - x]*Sqrt[x])","F",0,0,0,0,-1,"{}"
1062,1,945,0,1.362592,"\int \frac{1}{\left(b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(-a x-\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{-1} a x-\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(-(-1)^{2/3} a x-\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}","-\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^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 + b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))) - (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-b^(1/3) - a*x])/(6*a^(1/3)*(a^2 + b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-b^(1/3) + (-1)^(1/3)*a*x])/(6*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*a*x])/(6*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 + b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 + b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",6,3,30,0.1000,1,"{2056, 6725, 91}"
1063,1,945,0,0.9223706,"\int \frac{1}{\left(b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(-a x-\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{-1} a x-\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(-(-1)^{2/3} a x-\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}","-\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^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 + b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))) - (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-b^(1/3) - a*x])/(6*a^(1/3)*(a^2 + b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-b^(1/3) + (-1)^(1/3)*a*x])/(6*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*a*x])/(6*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 + b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 + b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",6,3,30,0.1000,1,"{2056, 6725, 91}"
1064,0,0,0,1.1387312,"\int \frac{x^2 \left(-4+x^3\right)}{\left(-1+x^3\right)^{3/4} \left(-1+x^3+x^4\right)} \, dx","Int[(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,"-((x*(1 - x^3)^(3/4)*Hypergeometric2F1[1/3, 3/4, 4/3, x^3])/(-1 + x^3)^(3/4)) + (x^2*(1 - x^3)^(3/4)*Hypergeometric2F1[2/3, 3/4, 5/3, x^3])/(2*(-1 + x^3)^(3/4)) - Defer[Int][1/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x] + Defer[Int][x/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x] - 4*Defer[Int][x^2/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x] + Defer[Int][x^3/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1065,1,80,0,0.0360373,"\int \frac{x^6}{\left(b+a x^4\right)^{3/4}} \, dx","Int[x^6/(b + a*x^4)^(3/4),x]","\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}","\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,"(x^3*(b + a*x^4)^(1/4))/(4*a) + (3*b*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(7/4)) - (3*b*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(7/4))","A",5,5,15,0.3333,1,"{321, 331, 298, 203, 206}"
1066,1,142,0,0.1480923,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Int[(b*x^2 + a*x^4)^(1/4)/x^2,x]","-\frac{2 \sqrt[4]{a x^4+b x^2}}{x}-\frac{\sqrt[4]{a} x^{3/2} \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\left(a x^4+b x^2\right)^{3/4}}+\frac{\sqrt[4]{a} x^{3/2} \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\left(a x^4+b x^2\right)^{3/4}}","-\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))/x - (a^(1/4)*x^(3/2)*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(3/4) + (a^(1/4)*x^(3/2)*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(3/4)","A",7,7,19,0.3684,1,"{2020, 2032, 329, 331, 298, 203, 206}"
1067,1,877,0,2.3458791,"\int \frac{\sqrt[4]{2+x^4} \left(-4+x^8\right)}{x^6 \left(-4-2 x^4+x^8\right)} \, dx","Int[((2 + x^4)^(1/4)*(-4 + x^8))/(x^6*(-4 - 2*x^4 + x^8)),x]","-\frac{F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};-\frac{x^4}{2},\frac{x^4}{1-\sqrt{5}}\right) x^3}{3\ 2^{3/4} \sqrt{5} \left(1-\sqrt{5}\right)}+\frac{F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{x^4}{1+\sqrt{5}},-\frac{x^4}{2}\right) x^3}{3\ 2^{3/4} \sqrt{5} \left(1+\sqrt{5}\right)}+\frac{\sqrt[4]{\frac{1}{2} \left(-29+13 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{4 \sqrt{5}}+\frac{\sqrt[4]{-2+\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{29+13 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{2+\sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}\right)}{2 \sqrt{10}}-\frac{\sqrt[4]{29+13 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}+1\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{2+\sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}+1\right)}{2 \sqrt{10}}-\frac{\sqrt[4]{\frac{1}{2} \left(-29+13 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{4 \sqrt{5}}-\frac{\sqrt[4]{-2+\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{29+13 \sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}-\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{2+\sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}-\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{29+13 \sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}+\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{2+\sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}+\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{x^4+2}}{2 x}-\frac{\left(x^4+2\right)^{5/4}}{10 x^5}","\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,"(2 + x^4)^(1/4)/(2*x) - (2 + x^4)^(5/4)/(10*x^5) - (x^3*AppellF1[3/4, -1/4, 1, 7/4, -1/2*x^4, x^4/(1 - Sqrt[5])])/(3*2^(3/4)*Sqrt[5]*(1 - Sqrt[5])) + (x^3*AppellF1[3/4, 1, -1/4, 7/4, x^4/(1 + Sqrt[5]), -1/2*x^4])/(3*2^(3/4)*Sqrt[5]*(1 + Sqrt[5])) + ((-2 + Sqrt[5])^(1/4)*ArcTan[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(2*Sqrt[5]) + (((-29 + 13*Sqrt[5])/2)^(1/4)*ArcTan[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[5]) - ((2 + Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(2*Sqrt[10]) + ((29 + 13*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(4*2^(3/4)*Sqrt[5]) + ((2 + Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(2*Sqrt[10]) - ((29 + 13*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(4*2^(3/4)*Sqrt[5]) - ((-2 + Sqrt[5])^(1/4)*ArcTanh[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(2*Sqrt[5]) - (((-29 + 13*Sqrt[5])/2)^(1/4)*ArcTanh[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[5]) + ((2 + Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] - (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[10]) - ((29 + 13*Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] - (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(8*2^(3/4)*Sqrt[5]) - ((2 + Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] + (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[10]) + ((29 + 13*Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] + (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(8*2^(3/4)*Sqrt[5])","B",53,17,30,0.5667,0,"{6728, 264, 277, 331, 298, 203, 206, 1528, 510, 1518, 494, 297, 1162, 617, 204, 1165, 628}"
1068,1,877,0,2.0991852,"\int \frac{\sqrt[4]{2+x^4} \left(-4+x^8\right)}{x^6 \left(-4-2 x^4+x^8\right)} \, dx","Int[((2 + x^4)^(1/4)*(-4 + x^8))/(x^6*(-4 - 2*x^4 + x^8)),x]","-\frac{F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};-\frac{x^4}{2},\frac{x^4}{1-\sqrt{5}}\right) x^3}{3\ 2^{3/4} \sqrt{5} \left(1-\sqrt{5}\right)}+\frac{F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{x^4}{1+\sqrt{5}},-\frac{x^4}{2}\right) x^3}{3\ 2^{3/4} \sqrt{5} \left(1+\sqrt{5}\right)}+\frac{\sqrt[4]{\frac{1}{2} \left(-29+13 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{4 \sqrt{5}}+\frac{\sqrt[4]{-2+\sqrt{5}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{29+13 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{2+\sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}\right)}{2 \sqrt{10}}-\frac{\sqrt[4]{29+13 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}+1\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{2+\sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{1+\sqrt{5}} \sqrt[4]{x^4+2}}+1\right)}{2 \sqrt{10}}-\frac{\sqrt[4]{\frac{1}{2} \left(-29+13 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{4 \sqrt{5}}-\frac{\sqrt[4]{-2+\sqrt{5}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{-1+\sqrt{5}}} x}{\sqrt[4]{x^4+2}}\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{29+13 \sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}-\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{2+\sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}-\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{29+13 \sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}+\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{2+\sqrt{5}} \log \left(\frac{2 x^2}{\sqrt{x^4+2}}+\frac{2 \sqrt[4]{2 \left(1+\sqrt{5}\right)} x}{\sqrt[4]{x^4+2}}+\sqrt{2 \left(1+\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{x^4+2}}{2 x}-\frac{\left(x^4+2\right)^{5/4}}{10 x^5}","\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,"(2 + x^4)^(1/4)/(2*x) - (2 + x^4)^(5/4)/(10*x^5) - (x^3*AppellF1[3/4, -1/4, 1, 7/4, -1/2*x^4, x^4/(1 - Sqrt[5])])/(3*2^(3/4)*Sqrt[5]*(1 - Sqrt[5])) + (x^3*AppellF1[3/4, 1, -1/4, 7/4, x^4/(1 + Sqrt[5]), -1/2*x^4])/(3*2^(3/4)*Sqrt[5]*(1 + Sqrt[5])) + ((-2 + Sqrt[5])^(1/4)*ArcTan[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(2*Sqrt[5]) + (((-29 + 13*Sqrt[5])/2)^(1/4)*ArcTan[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[5]) - ((2 + Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(2*Sqrt[10]) + ((29 + 13*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(4*2^(3/4)*Sqrt[5]) + ((2 + Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(2*Sqrt[10]) - ((29 + 13*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/((1 + Sqrt[5])^(1/4)*(2 + x^4)^(1/4))])/(4*2^(3/4)*Sqrt[5]) - ((-2 + Sqrt[5])^(1/4)*ArcTanh[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(2*Sqrt[5]) - (((-29 + 13*Sqrt[5])/2)^(1/4)*ArcTanh[((2/(-1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[5]) + ((2 + Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] - (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[10]) - ((29 + 13*Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] - (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(8*2^(3/4)*Sqrt[5]) - ((2 + Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] + (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(4*Sqrt[10]) + ((29 + 13*Sqrt[5])^(1/4)*Log[Sqrt[2*(1 + Sqrt[5])] + (2*x^2)/Sqrt[2 + x^4] + (2*(2*(1 + Sqrt[5]))^(1/4)*x)/(2 + x^4)^(1/4)])/(8*2^(3/4)*Sqrt[5])","B",53,17,30,0.5667,0,"{6728, 264, 277, 331, 298, 203, 206, 1528, 510, 1518, 494, 297, 1162, 617, 204, 1165, 628}"
1069,1,165,0,0.5614879,"\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","Int[((-1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8))/(x^6*(1 - x^4 + x^8)),x]","\frac{2 \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,\frac{2 x^4}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) \sqrt[4]{1-x^4}}-\frac{2 \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{2 x^4}{1+i \sqrt{3}},x^4\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) \sqrt[4]{1-x^4}}-\frac{\left(x^4-1\right)^{5/4}}{5 x^5}","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]+\frac{\sqrt[4]{x^4-1} \left(1-x^4\right)}{5 x^5}",1,"-1/5*(-1 + x^4)^(5/4)/x^5 + (2*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (2*x^4)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])*(1 - x^4)^(1/4)) - (2*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (2*x^4)/(1 + I*Sqrt[3]), x^4])/(Sqrt[3]*(I - Sqrt[3])*(1 - x^4)^(1/4))","C",9,5,35,0.1429,0,"{6728, 264, 1528, 511, 510}"
1070,1,165,0,0.4635483,"\int \frac{\sqrt[4]{-1+x^4} \left(-1+x^4+2 x^8\right)}{x^6 \left(1-x^4+x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(-1 + x^4 + 2*x^8))/(x^6*(1 - x^4 + x^8)),x]","\frac{2 \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,\frac{2 x^4}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) \sqrt[4]{1-x^4}}-\frac{2 \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{2 x^4}{1+i \sqrt{3}},x^4\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) \sqrt[4]{1-x^4}}-\frac{\left(x^4-1\right)^{5/4}}{5 x^5}","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]+\frac{\sqrt[4]{x^4-1} \left(1-x^4\right)}{5 x^5}",1,"-1/5*(-1 + x^4)^(5/4)/x^5 + (2*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (2*x^4)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])*(1 - x^4)^(1/4)) - (2*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (2*x^4)/(1 + I*Sqrt[3]), x^4])/(Sqrt[3]*(I - Sqrt[3])*(1 - x^4)^(1/4))","C",9,5,35,0.1429,0,"{6728, 264, 1528, 511, 510}"
1071,0,0,0,5.9058669,"\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","Int[(-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,"((a + b + Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Int][1/(Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*(-((a + b)*d) - Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x^2)^(1/4) + ((a + b - Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Int][1/(Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*(-((a + b)*d) + Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x^2)^(1/4)","F",0,0,0,0,-1,"{}"
1072,1,61,0,0.0463965,"\int \frac{\sqrt[3]{1+x^3}}{x} \, dx","Int[(1 + x^3)^(1/3)/x,x]","\sqrt[3]{x^3+1}+\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}","\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[x]/2 + Log[1 - (1 + x^3)^(1/3)]/2","A",6,6,13,0.4615,1,"{266, 50, 57, 618, 204, 31}"
1073,0,0,0,16.8100739,"\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","Int[(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,"(8*(a + b)*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^6/((-a + x^4)^(1/4)*(-b + x^4)^(1/4)*(a*b*d - a*(1 + b/a)*d*x^4 + d*x^8 - x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(1/4) + (12*a*b*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((-a + x^4)^(1/4)*(-b + x^4)^(1/4)*(-(a*b*d) + a*(1 + b/a)*d*x^4 - d*x^8 + x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(1/4) + (4*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^10/((-a + x^4)^(1/4)*(-b + x^4)^(1/4)*(-(a*b*d) + a*(1 + b/a)*d*x^4 - d*x^8 + x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(1/4)","F",0,0,0,0,-1,"{}"
1074,1,946,0,1.3355459,"\int \frac{1}{\left(-b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((-b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{b}-a x\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{-1} a x+\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{b}-(-1)^{2/3} a x\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}","\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^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 - b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[b^(1/3) - a*x])/(6*a^(1/3)*(a^2 - b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[b^(1/3) + (-1)^(1/3)*a*x])/(6*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*a*x])/(6*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 - b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 - b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",6,3,32,0.09375,1,"{2056, 6725, 91}"
1075,1,946,0,0.994006,"\int \frac{1}{\left(-b+a^3 x^3\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[1/((-b + a^3*x^3)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{b}-a x\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{-1} a x+\sqrt[3]{b}\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt[3]{b}-(-1)^{2/3} a x\right)}{6 \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a^3 x^3-b x^2}}","\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^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 - b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[b^(1/3) - a*x])/(6*a^(1/3)*(a^2 - b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[b^(1/3) + (-1)^(1/3)*a*x])/(6*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*a*x])/(6*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 - b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 - b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3)) + (x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3))])/(2*a^(1/3)*(a^2 - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a^3*x^3)^(1/3))","B",6,3,32,0.09375,1,"{2056, 6725, 91}"
1076,0,0,0,5.3463921,"\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","Int[(-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,"((a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Int][Sqrt[x]/((-a + x)^(3/4)*(-b + x)^(3/4)*(a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x^2)^(3/4) + ((a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Int][Sqrt[x]/((-a + x)^(3/4)*(-b + x)^(3/4)*(a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x^2)^(3/4)","F",0,0,0,0,-1,"{}"
1077,1,81,0,0.0351481,"\int \frac{\left(-1+x^4\right)^{3/4}}{1+x^4} \, dx","Int[(-1 + x^4)^(3/4)/(1 + x^4),x]","\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}}","\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,"ArcTan[x/(-1 + x^4)^(1/4)]/2 - ArcTan[(2^(1/4)*x)/(-1 + x^4)^(1/4)]/2^(1/4) + ArcTanh[x/(-1 + x^4)^(1/4)]/2 - ArcTanh[(2^(1/4)*x)/(-1 + x^4)^(1/4)]/2^(1/4)","A",9,6,17,0.3529,1,"{408, 240, 212, 206, 203, 377}"
1078,1,137,0,0.2191507,"\int \frac{\sqrt[4]{-x^2+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Int[(-x^2 + x^4)^(1/4)/(x^4*(-1 + x^4)),x]","-\frac{\sqrt[4]{x^4-x^2} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2^{3/4} \sqrt{x} \sqrt[4]{x^2-1}}+\frac{\sqrt[4]{x^4-x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2^{3/4} \sqrt{x} \sqrt[4]{x^2-1}}+\frac{2 \sqrt[4]{x^4-x^2} \left(1-x^2\right)}{5 x^3}","-\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,"(2*(1 - x^2)*(-x^2 + x^4)^(1/4))/(5*x^3) - ((-x^2 + x^4)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2^(3/4)*Sqrt[x]*(-1 + x^2)^(1/4)) + ((-x^2 + x^4)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2^(3/4)*Sqrt[x]*(-1 + x^2)^(1/4))","A",9,8,24,0.3333,1,"{2056, 1254, 466, 494, 461, 298, 203, 206}"
1079,0,0,0,0.0798933,"\int \frac{\left(1-x^2\right)^2}{\left(1+x^2\right) \left(1+6 x^2+x^4\right)^{3/4}} \, dx","Int[(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,"Defer[Int][(1 - x^2)^2/((1 + x^2)*(1 + 6*x^2 + x^4)^(3/4)), x]","F",0,0,0,0,-1,"{}"
1080,0,0,0,0.0791051,"\int \frac{1}{(1+x) \sqrt[4]{1+6 x^2+x^4}} \, dx","Int[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,"Defer[Int][1/((1 + x)*(1 + 6*x^2 + x^4)^(1/4)), x]","F",0,0,0,0,-1,"{}"
1081,0,0,0,0.175447,"\int \frac{1+x}{\sqrt{-7+4 x+14 x^2-12 x^3+x^4}} \, dx","Int[(1 + x)/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4],x]","\int \frac{1+x}{\sqrt{-7+4 x+14 x^2-12 x^3+x^4}} \, dx","-\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,"Defer[Int][1/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4], x] + Defer[Int][x/Sqrt[-7 + 4*x + 14*x^2 - 12*x^3 + x^4], x]","F",0,0,0,0,-1,"{}"
1082,0,0,0,0.6374026,"\int \frac{3+x^4}{\sqrt[3]{-1+x^4} \left(-1-8 x^3+x^4\right)} \, dx","Int[(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,"(x*(1 - x^4)^(1/3)*Hypergeometric2F1[1/4, 1/3, 5/4, x^4])/(-1 + x^4)^(1/3) + 4*Defer[Int][1/((-1 + x^4)^(1/3)*(-1 - 8*x^3 + x^4)), x] + 8*Defer[Int][x^3/((-1 + x^4)^(1/3)*(-1 - 8*x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1083,0,0,0,1.2584524,"\int \frac{(-3+2 x) \sqrt{-2 x+2 x^2+3 x^4}}{\left(-2+2 x+x^3\right)^2} \, dx","Int[((-3 + 2*x)*Sqrt[-2*x + 2*x^2 + 3*x^4])/(-2 + 2*x + x^3)^2,x]","\int \frac{(-3+2 x) \sqrt{-2 x+2 x^2+3 x^4}}{\left(-2+2 x+x^3\right)^2} \, dx","\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,"(-6*Sqrt[-2*x + 2*x^2 + 3*x^4]*Defer[Subst][Defer[Int][(x^2*Sqrt[-2 + 2*x^2 + 3*x^6])/(-2 + 2*x^2 + x^6)^2, x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-2 + 2*x + 3*x^3]) + (4*Sqrt[-2*x + 2*x^2 + 3*x^4]*Defer[Subst][Defer[Int][(x^4*Sqrt[-2 + 2*x^2 + 3*x^6])/(-2 + 2*x^2 + x^6)^2, x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-2 + 2*x + 3*x^3])","F",0,0,0,0,-1,"{}"
1084,1,81,0,0.0362543,"\int \frac{-2 b+a x^4}{x^4 \sqrt[4]{-b+a x^4}} \, dx","Int[(-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",5,5,26,0.1923,1,"{451, 240, 212, 206, 203}"
1085,1,81,0,0.0241944,"\int \left(-b+a x^4\right)^{3/4} \, dx","Int[(-b + a*x^4)^(3/4),x]","\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}}","\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))/4 - (3*b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(1/4)) - (3*b*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(1/4))","A",5,5,13,0.3846,1,"{195, 240, 212, 206, 203}"
1086,1,81,0,0.0247381,"\int \frac{\left(-b+a x^4\right)^{3/4}}{x^4} \, dx","Int[(-b + a*x^4)^(3/4)/x^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{\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{\left(a x^4-b\right)^{3/4}}{3 x^3}",1,"-1/3*(-b + a*x^4)^(3/4)/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",5,5,17,0.2941,1,"{277, 240, 212, 206, 203}"
1087,1,1221,0,1.4914575,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(b+a x^4\right)} \, dx","Int[1/((-(b*x^2) + a*x^3)^(1/3)*(b + a*x^4)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt{-\sqrt{-a}} x\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt{-\sqrt{-a}} x+\sqrt[4]{b}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt[4]{-a} x\right)}{8 \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{-a} x+\sqrt[4]{b}\right)}{8 \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a-\sqrt[4]{-a} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a+\sqrt[4]{-a} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}","-\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,"-1/4*(Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*x^(1/3))])/((a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*x^(1/3))])/(4*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a - (-a)^(1/4)*b^(3/4))^(1/3)*x^(1/3))])/(4*(a - (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a + (-a)^(1/4)*b^(3/4))^(1/3)*x^(1/3))])/(4*(a + (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - Sqrt[-Sqrt[-a]]*x])/(8*(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + Sqrt[-Sqrt[-a]]*x])/(8*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - (-a)^(1/4)*x])/(8*(a - (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + (-a)^(1/4)*x])/(8*(a + (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)])/(8*(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)])/(8*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a - (-a)^(1/4)*b^(3/4))^(1/3)])/(8*(a - (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a + (-a)^(1/4)*b^(3/4))^(1/3)])/(8*(a + (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3))","B",11,4,26,0.1538,1,"{2056, 6725, 912, 91}"
1088,1,1221,0,1.0569294,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(b+a x^4\right)} \, dx","Int[1/((-(b*x^2) + a*x^3)^(1/3)*(b + a*x^4)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt{-\sqrt{-a}} x\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt{-\sqrt{-a}} x+\sqrt[4]{b}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt[4]{-a} x\right)}{8 \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{-a} x+\sqrt[4]{b}\right)}{8 \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{-a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a-\sqrt[4]{-a} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a+\sqrt[4]{-a} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}","-\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,"-1/4*(Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*x^(1/3))])/((a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*x^(1/3))])/(4*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a - (-a)^(1/4)*b^(3/4))^(1/3)*x^(1/3))])/(4*(a - (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a + (-a)^(1/4)*b^(3/4))^(1/3)*x^(1/3))])/(4*(a + (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - Sqrt[-Sqrt[-a]]*x])/(8*(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + Sqrt[-Sqrt[-a]]*x])/(8*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - (-a)^(1/4)*x])/(8*(a - (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + (-a)^(1/4)*x])/(8*(a + (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)])/(8*(a - Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)])/(8*(a + Sqrt[-Sqrt[-a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a - (-a)^(1/4)*b^(3/4))^(1/3)])/(8*(a - (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a + (-a)^(1/4)*b^(3/4))^(1/3)])/(8*(a + (-a)^(1/4)*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3))","B",11,4,26,0.1538,1,"{2056, 6725, 912, 91}"
1089,1,135,0,0.1492571,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x^2} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/x^2,x]","-\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-\frac{2 \sqrt[4]{a} x^{9/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{\left(a x^4+b x^3\right)^{3/4}}+\frac{2 \sqrt[4]{a} x^{9/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{\left(a x^4+b x^3\right)^{3/4}}","-\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*(b*x^3 + a*x^4)^(1/4))/x - (2*a^(1/4)*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(b*x^3 + a*x^4)^(3/4) + (2*a^(1/4)*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(b*x^3 + a*x^4)^(3/4)","A",7,7,19,0.3684,1,"{2020, 2032, 63, 331, 298, 203, 206}"
1090,0,0,0,18.7636162,"\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","Int[((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,"(-4*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 - I*Sqrt[3])^(1/3) - 2*x)^2, x])/(9*((1 - I*Sqrt[3])/2)^(1/3)) + (16*2^(1/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 - I*Sqrt[3])^(1/3) - 2*x)^2, x])/(9*(1 - I*Sqrt[3])^(4/3)) - (4*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 + I*Sqrt[3])^(1/3) - 2*x)^2, x])/(9*((1 + I*Sqrt[3])/2)^(1/3)) + (16*2^(1/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 + I*Sqrt[3])^(1/3) - 2*x)^2, x])/(9*(1 + I*Sqrt[3])^(4/3)) - (4*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 + I*Sqrt[3])^(1/3) - 2*x), x])/(9*((1 + I*Sqrt[3])/2)^(2/3)) + (16*2^(2/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 + I*Sqrt[3])^(1/3) - 2*x), x])/(9*(1 + I*Sqrt[3])^(5/3)) + (((2*I)/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/((1 - I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x])/(Sqrt[3]*(1 - I*Sqrt[3])^(2/3)) - (((2*I)/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/((1 + I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x])/(Sqrt[3]*(1 + I*Sqrt[3])^(2/3)) + (8*(-2)^(1/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 - I*Sqrt[3])^(1/3) + 2*(-1)^(1/3)*x)^2, x])/(9*(1 - I*Sqrt[3])^(1/3)) - (2*(-2)^(1/3)*(1 - I*Sqrt[3])^(2/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 - I*Sqrt[3])^(1/3) + 2*(-1)^(1/3)*x)^2, x])/9 - (4*2^(1/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 + I*Sqrt[3])^(1/3) + 2*(-1)^(1/3)*x)^2, x])/(9*((-I)/(I - Sqrt[3]))^(2/3)*(1 - I*Sqrt[3])) - (16*((-2*I)/(I - Sqrt[3]))^(1/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3)*(1 + I*Sqrt[3])^(1/3) + 2*(-1)^(1/3)*x)^2, x])/(9*(1 - I*Sqrt[3])) - (16*(-1)^(1/6)*2^(1/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(-(2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + 2*(-1)^(2/3)*x)^2, x])/(9*(I - Sqrt[3])*(1 - I*Sqrt[3])^(1/3)) + (4*(-1)^(1/6)*2^(1/3)*(1 - I*Sqrt[3])^(2/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(-(2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + 2*(-1)^(2/3)*x)^2, x])/(9*(I - Sqrt[3])) - (8*(-1)^(2/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(-(2^(2/3)*(1 + I*Sqrt[3])^(1/3)) + 2*(-1)^(2/3)*x)^2, x])/(9*((1 + I*Sqrt[3])/2)^(1/3)) + (2*(-1)^(2/3)*2^(1/3)*(1 + I*Sqrt[3])^(2/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(-(2^(2/3)*(1 + I*Sqrt[3])^(1/3)) + 2*(-1)^(2/3)*x)^2, x])/9 + (((2*I)/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/((1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x), x])/(Sqrt[3]*(1 - I*Sqrt[3])^(2/3)) - (((2*I)/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/((1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x), x])/(Sqrt[3]*(1 + I*Sqrt[3])^(2/3)) + (((2*I)/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/((1 - I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x])/(Sqrt[3]*(1 - I*Sqrt[3])^(2/3)) - (((2*I)/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/((1 + I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x])/(Sqrt[3]*(1 + I*Sqrt[3])^(2/3)) + (4*(-2)^(2/3)*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3) + (1 - I*Sqrt[3])^(2/3)*x), x])/9 - (2^(2/3)*(1 + I*Sqrt[3])*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2^(2/3) + (1 - I*Sqrt[3])^(2/3)*x), x])/9 + (4*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(3*I - Sqrt[3] + 2^(1/3)*Sqrt[3]*(1 - I*Sqrt[3])^(2/3)*x), x])/(3*Sqrt[3]) - (4*(3*I + Sqrt[3])*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(3*I - Sqrt[3] + 2^(1/3)*Sqrt[3]*(1 - I*Sqrt[3])^(2/3)*x), x])/9 - (4*(1 + I*Sqrt[3])*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2 + 2^(1/3)*(1 + I*Sqrt[3])^(2/3)*x), x])/9 + ((1 + I*Sqrt[3])^2*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2 + 2^(1/3)*(1 + I*Sqrt[3])^(2/3)*x), x])/9 - (4*(-1)^(1/9)*(I - Sqrt[3])*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(I*2^(2/3)*(1 + I*Sqrt[3])^(1/3) + (I + Sqrt[3])*x), x])/9 - (2*(-1)^(1/9)*(I + Sqrt[3])*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(I*2^(2/3)*(1 + I*Sqrt[3])^(1/3) + (I + Sqrt[3])*x), x])/9 + (8*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2*(3*I - Sqrt[3]) - 2^(1/3)*(1 - I*Sqrt[3])^(2/3)*(3*I + Sqrt[3])*x), x])/(3*Sqrt[3]) - (8*(3*I + Sqrt[3])*Defer[Int][(1 - x^3 + x^4 + x^6)^(3/4)/(2*(3*I - Sqrt[3]) - 2^(1/3)*(1 - I*Sqrt[3])^(2/3)*(3*I + Sqrt[3])*x), x])/9","F",0,0,0,0,-1,"{}"
1091,1,81,0,0.0757372,"\int \frac{1+2 x^4}{\sqrt[4]{1+x^4} \left(-2-x^4+x^8\right)} \, dx","Int[(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 \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}}","\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*ArcTan[((3/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(6*2^(3/4)*3^(1/4)) - (5*ArcTanh[((3/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(6*2^(3/4)*3^(1/4))","A",7,7,29,0.2414,1,"{1454, 527, 12, 377, 212, 206, 203}"
1092,1,1017,0,2.664615,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Int[1/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} 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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a - (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a + (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a - (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a + (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",22,10,26,0.3846,1,"{2056, 6715, 6725, 1429, 377, 212, 206, 203, 208, 205}"
1093,1,1017,0,1.9628537,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Int[1/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} b \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} 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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a - (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a + (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a - (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(a + (-a)^(1/4)*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",22,10,26,0.3846,1,"{2056, 6715, 6725, 1429, 377, 212, 206, 203, 208, 205}"
1094,1,1639,0,3.5303257,"\int \frac{\left(-b^4+a^4 x^4\right) \sqrt{b^4+a^4 x^4}}{b^8+a^8 x^8} \, dx","Int[((-b^4 + a^4*x^4)*Sqrt[b^4 + a^4*x^4])/(b^8 + a^8*x^8),x]","-\frac{\left(\sqrt{-a^8}-a^4\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt[8]{-a^8} \sqrt{\sqrt{-a^8}-a^4} b x}{a^2 \sqrt{b^4+a^4 x^4}}\right) a^6}{8 \left(-a^8\right)^{13/8} b}-\frac{\left(\sqrt{-a^8}-a^4\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-a^8}-a^4} b x}{\sqrt[4]{-\sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right)}{8 \left(-\sqrt{-a^8}\right)^{3/4} b a^4}-\frac{\left(a^4+\sqrt{-a^8}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a^4+\sqrt{-a^8}} b x}{\sqrt[8]{-a^8} \sqrt{b^4+a^4 x^4}}\right)}{8 \left(-a^8\right)^{3/8} b a^4}+\frac{\left(a^4-\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 b \sqrt{b^4+a^4 x^4} a^5}+\frac{\left(a^4+\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 b \sqrt{b^4+a^4 x^4} a^5}-\frac{\left(a^2-\sqrt[4]{-a^8}\right)^3 \left(a^2+\sqrt[4]{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{\left(a^2+\sqrt[4]{-a^8}\right)^2}{4 a^2 \sqrt[4]{-a^8}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 \sqrt{-a^8} b \sqrt{b^4+a^4 x^4} a^5}-\frac{\left(a^2-\sqrt[4]{-a^8}\right) \left(a^4+\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^7}-\frac{\sqrt{-a^8} \left(a^2+\sqrt[4]{-a^8}\right) \left(a^4-\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^{11}}+\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2-\sqrt{-\sqrt{-a^8}}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^{11}}+\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2+\sqrt{-\sqrt{-a^8}}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^{11}}+\frac{\left(-\sqrt{-a^8}\right)^{5/4} \left(a^4-\sqrt{-a^8}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a^4-\sqrt{-a^8}} b x}{\sqrt[4]{-\sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right)}{8 b a^{12}}+\frac{\sqrt{-a^8} \left(a^2+\sqrt[4]{-a^8}\right)^2 \left(a^4-\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{a^6 \left(a^2-\sqrt[4]{-a^8}\right)^2}{4 \left(-a^8\right)^{5/4}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 b \sqrt{b^4+a^4 x^4} a^{13}}-\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2+\sqrt{-\sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(-\frac{\left(a^2-\sqrt{-\sqrt{-a^8}}\right)^2}{4 a^2 \sqrt{-\sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 b \sqrt{b^4+a^4 x^4} a^{13}}-\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2-\sqrt{-\sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{\left(a^2+\sqrt{-\sqrt{-a^8}}\right)^2}{4 a^2 \sqrt{-\sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 b \sqrt{b^4+a^4 x^4} a^{13}}","-\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,"((-Sqrt[-a^8])^(5/4)*(a^4 - Sqrt[-a^8])^(3/2)*ArcTan[(Sqrt[a^4 - Sqrt[-a^8]]*b*x)/((-Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(8*a^12*b) - (a^6*(-a^4 + Sqrt[-a^8])^(3/2)*ArcTan[((-a^8)^(1/8)*Sqrt[-a^4 + Sqrt[-a^8]]*b*x)/(a^2*Sqrt[b^4 + a^4*x^4])])/(8*(-a^8)^(13/8)*b) - ((-a^4 + Sqrt[-a^8])^(3/2)*ArcTan[(Sqrt[-a^4 + Sqrt[-a^8]]*b*x)/((-Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(8*a^4*(-Sqrt[-a^8])^(3/4)*b) - ((a^4 + Sqrt[-a^8])^(3/2)*ArcTan[(Sqrt[a^4 + Sqrt[-a^8]]*b*x)/((-a^8)^(1/8)*Sqrt[b^4 + a^4*x^4])])/(8*a^4*(-a^8)^(3/8)*b) + ((a^4 - Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(4*a^5*b*Sqrt[b^4 + a^4*x^4]) - (Sqrt[-a^8]*(a^2 + (-a^8)^(1/4))*(a^4 - Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^11*b*Sqrt[b^4 + a^4*x^4]) + ((a^4 + Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(4*a^5*b*Sqrt[b^4 + a^4*x^4]) - ((a^2 - (-a^8)^(1/4))*(a^4 + Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^7*b*Sqrt[b^4 + a^4*x^4]) + (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 - Sqrt[-Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^11*b*Sqrt[b^4 + a^4*x^4]) + (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 + Sqrt[-Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^11*b*Sqrt[b^4 + a^4*x^4]) + (Sqrt[-a^8]*(a^2 + (-a^8)^(1/4))^2*(a^4 - Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(a^6*(a^2 - (-a^8)^(1/4))^2)/(4*(-a^8)^(5/4)), 2*ArcTan[(a*x)/b], 1/2])/(16*a^13*b*Sqrt[b^4 + a^4*x^4]) - ((a^2 - (-a^8)^(1/4))^3*(a^2 + (-a^8)^(1/4))*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(a^2 + (-a^8)^(1/4))^2/(4*a^2*(-a^8)^(1/4)), 2*ArcTan[(a*x)/b], 1/2])/(16*a^5*Sqrt[-a^8]*b*Sqrt[b^4 + a^4*x^4]) - (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 + Sqrt[-Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[-1/4*(a^2 - Sqrt[-Sqrt[-a^8]])^2/(a^2*Sqrt[-Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(16*a^13*b*Sqrt[b^4 + a^4*x^4]) - (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 - Sqrt[-Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(a^2 + Sqrt[-Sqrt[-a^8]])^2/(4*a^2*Sqrt[-Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(16*a^13*b*Sqrt[b^4 + a^4*x^4])","C",20,6,42,0.1429,0,"{6725, 406, 220, 409, 1217, 1707}"
1095,1,1639,0,2.7366135,"\int \frac{-b^8+a^8 x^8}{\sqrt{b^4+a^4 x^4} \left(b^8+a^8 x^8\right)} \, dx","Int[(-b^8 + a^8*x^8)/(Sqrt[b^4 + a^4*x^4]*(b^8 + a^8*x^8)),x]","-\frac{\left(\sqrt{-a^8}-a^4\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt[8]{-a^8} \sqrt{\sqrt{-a^8}-a^4} b x}{a^2 \sqrt{b^4+a^4 x^4}}\right) a^6}{8 \left(-a^8\right)^{13/8} b}-\frac{\left(\sqrt{-a^8}-a^4\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-a^8}-a^4} b x}{\sqrt[4]{-\sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right)}{8 \left(-\sqrt{-a^8}\right)^{3/4} b a^4}-\frac{\left(a^4+\sqrt{-a^8}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a^4+\sqrt{-a^8}} b x}{\sqrt[8]{-a^8} \sqrt{b^4+a^4 x^4}}\right)}{8 \left(-a^8\right)^{3/8} b a^4}+\frac{\left(a^4-\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 b \sqrt{b^4+a^4 x^4} a^5}+\frac{\left(a^4+\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 b \sqrt{b^4+a^4 x^4} a^5}-\frac{\left(a^2-\sqrt[4]{-a^8}\right)^3 \left(a^2+\sqrt[4]{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{\left(a^2+\sqrt[4]{-a^8}\right)^2}{4 a^2 \sqrt[4]{-a^8}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 \sqrt{-a^8} b \sqrt{b^4+a^4 x^4} a^5}-\frac{\left(a^2-\sqrt[4]{-a^8}\right) \left(a^4+\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^7}-\frac{\sqrt{-a^8} \left(a^2+\sqrt[4]{-a^8}\right) \left(a^4-\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^{11}}+\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2-\sqrt{-\sqrt{-a^8}}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^{11}}+\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2+\sqrt{-\sqrt{-a^8}}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{8 b \sqrt{b^4+a^4 x^4} a^{11}}+\frac{\left(-\sqrt{-a^8}\right)^{5/4} \left(a^4-\sqrt{-a^8}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a^4-\sqrt{-a^8}} b x}{\sqrt[4]{-\sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right)}{8 b a^{12}}+\frac{\sqrt{-a^8} \left(a^2+\sqrt[4]{-a^8}\right)^2 \left(a^4-\sqrt{-a^8}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{a^6 \left(a^2-\sqrt[4]{-a^8}\right)^2}{4 \left(-a^8\right)^{5/4}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 b \sqrt{b^4+a^4 x^4} a^{13}}-\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2+\sqrt{-\sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(-\frac{\left(a^2-\sqrt{-\sqrt{-a^8}}\right)^2}{4 a^2 \sqrt{-\sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 b \sqrt{b^4+a^4 x^4} a^{13}}-\frac{\sqrt{-a^8} \left(a^4+\sqrt{-a^8}\right) \left(a^2-\sqrt{-\sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{\left(a^2+\sqrt{-\sqrt{-a^8}}\right)^2}{4 a^2 \sqrt{-\sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{16 b \sqrt{b^4+a^4 x^4} a^{13}}","-\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,"((-Sqrt[-a^8])^(5/4)*(a^4 - Sqrt[-a^8])^(3/2)*ArcTan[(Sqrt[a^4 - Sqrt[-a^8]]*b*x)/((-Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(8*a^12*b) - (a^6*(-a^4 + Sqrt[-a^8])^(3/2)*ArcTan[((-a^8)^(1/8)*Sqrt[-a^4 + Sqrt[-a^8]]*b*x)/(a^2*Sqrt[b^4 + a^4*x^4])])/(8*(-a^8)^(13/8)*b) - ((-a^4 + Sqrt[-a^8])^(3/2)*ArcTan[(Sqrt[-a^4 + Sqrt[-a^8]]*b*x)/((-Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(8*a^4*(-Sqrt[-a^8])^(3/4)*b) - ((a^4 + Sqrt[-a^8])^(3/2)*ArcTan[(Sqrt[a^4 + Sqrt[-a^8]]*b*x)/((-a^8)^(1/8)*Sqrt[b^4 + a^4*x^4])])/(8*a^4*(-a^8)^(3/8)*b) + ((a^4 - Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(4*a^5*b*Sqrt[b^4 + a^4*x^4]) - (Sqrt[-a^8]*(a^2 + (-a^8)^(1/4))*(a^4 - Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^11*b*Sqrt[b^4 + a^4*x^4]) + ((a^4 + Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(4*a^5*b*Sqrt[b^4 + a^4*x^4]) - ((a^2 - (-a^8)^(1/4))*(a^4 + Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^7*b*Sqrt[b^4 + a^4*x^4]) + (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 - Sqrt[-Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^11*b*Sqrt[b^4 + a^4*x^4]) + (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 + Sqrt[-Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(8*a^11*b*Sqrt[b^4 + a^4*x^4]) + (Sqrt[-a^8]*(a^2 + (-a^8)^(1/4))^2*(a^4 - Sqrt[-a^8])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(a^6*(a^2 - (-a^8)^(1/4))^2)/(4*(-a^8)^(5/4)), 2*ArcTan[(a*x)/b], 1/2])/(16*a^13*b*Sqrt[b^4 + a^4*x^4]) - ((a^2 - (-a^8)^(1/4))^3*(a^2 + (-a^8)^(1/4))*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(a^2 + (-a^8)^(1/4))^2/(4*a^2*(-a^8)^(1/4)), 2*ArcTan[(a*x)/b], 1/2])/(16*a^5*Sqrt[-a^8]*b*Sqrt[b^4 + a^4*x^4]) - (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 + Sqrt[-Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[-1/4*(a^2 - Sqrt[-Sqrt[-a^8]])^2/(a^2*Sqrt[-Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(16*a^13*b*Sqrt[b^4 + a^4*x^4]) - (Sqrt[-a^8]*(a^4 + Sqrt[-a^8])*(a^2 - Sqrt[-Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(a^2 + Sqrt[-Sqrt[-a^8]])^2/(4*a^2*Sqrt[-Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(16*a^13*b*Sqrt[b^4 + a^4*x^4])","C",21,7,42,0.1667,0,"{1586, 6725, 406, 220, 409, 1217, 1707}"
1096,0,0,0,0.2114813,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^{3/2}} \, dx","Int[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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^(3/2), x]","F",0,0,0,0,-1,"{}"
1097,1,47,0,0.1160635,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4}} \, dx","Int[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",2,2,37,0.05405,1,"{2132, 206}"
1098,1,1208,0,1.6002874,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(-b+a x^4\right)} \, dx","Int[1/((-(b*x^2) + a*x^3)^(1/3)*(-b + a*x^4)),x]","\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt{-\sqrt{a}} x\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt{-\sqrt{a}} x+\sqrt[4]{b}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt[4]{a} x\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{a} x+\sqrt[4]{b}\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}","\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,"(Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*x^(1/3))])/(4*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*x^(1/3))])/(4*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*x^(1/3))])/(4*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*x^(1/3))])/(4*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - Sqrt[-Sqrt[a]]*x])/(8*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + Sqrt[-Sqrt[a]]*x])/(8*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - a^(1/4)*x])/(8*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + a^(1/4)*x])/(8*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/12)*(a^(3/4) - b^(3/4))^(1/3))])/(8*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/12)*(a^(3/4) + b^(3/4))^(1/3))])/(8*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)])/(8*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)])/(8*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3))","B",11,4,28,0.1429,1,"{2056, 6725, 912, 91}"
1099,1,1208,0,1.3402608,"\int \frac{1}{\sqrt[3]{-b x^2+a x^3} \left(-b+a x^4\right)} \, dx","Int[1/((-(b*x^2) + a*x^3)^(1/3)*(-b + a*x^4)),x]","\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt{-\sqrt{a}} x\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt{-\sqrt{a}} x+\sqrt[4]{b}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{b}-\sqrt[4]{a} x\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[4]{a} x+\sqrt[4]{b}\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}-b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[12]{a} \sqrt[3]{a^{3/4}+b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a-\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a+\sqrt{-\sqrt{a}} b^{3/4}} b \sqrt[3]{a x^3-b x^2}}","\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,"(Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*x^(1/3))])/(4*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*x^(1/3))])/(4*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*x^(1/3))])/(4*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*x^(1/3))])/(4*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - Sqrt[-Sqrt[a]]*x])/(8*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + Sqrt[-Sqrt[a]]*x])/(8*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) - a^(1/4)*x])/(8*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/4) + a^(1/4)*x])/(8*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/12)*(a^(3/4) - b^(3/4))^(1/3))])/(8*a^(1/12)*(a^(3/4) - b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/12)*(a^(3/4) + b^(3/4))^(1/3))])/(8*a^(1/12)*(a^(3/4) + b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)])/(8*(a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (3*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)])/(8*(a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3))","B",11,4,28,0.1429,1,"{2056, 6725, 912, 91}"
1100,1,1101,0,1.6559649,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(b+a x^3\right)} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(x*(b + a*x^3)),x]","-\frac{2 (-1)^{2/3} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[3]{-1} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 (-1)^{2/3} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 (-1)^{2/3} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 (-1)^{2/3} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[3]{-1} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}","\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,"(-2*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(1/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(2/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(a^(2/3) + b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/12)*(a^(2/3) + b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(2/3)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/12)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(1/3)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/12)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(1/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(2/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(a^(2/3) + b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/12)*(a^(2/3) + b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(2/3)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/12)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(1/3)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/12)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4))","B",33,9,29,0.3103,1,"{2056, 6725, 105, 63, 331, 298, 203, 206, 93}"
1101,1,1101,0,1.2624421,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(b+a x^3\right)} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(x*(b + a*x^3)),x]","-\frac{2 (-1)^{2/3} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[3]{-1} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 (-1)^{2/3} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 (-1)^{2/3} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[12]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 (-1)^{2/3} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[3]{-1} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[12]{a} \sqrt[4]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{3 \sqrt[4]{a} b^{2/3} x^{3/4} \sqrt[4]{a x-b}}","\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,"(-2*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(1/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(2/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(a^(2/3) + b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/12)*(a^(2/3) + b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(2/3)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/12)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(1/3)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/12)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(1/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(2/3)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/12)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(a^(2/3) + b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/12)*(a^(2/3) + b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-1)^(2/3)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/12)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-1)^(1/3)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/12)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(3*a^(1/4)*b^(2/3)*x^(3/4)*(-b + a*x)^(1/4))","B",33,9,29,0.3103,1,"{2056, 6725, 105, 63, 331, 298, 203, 206, 93}"
1102,1,136,0,0.1534626,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/x,x]","-\frac{b x^{9/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{2 a^{3/4} \left(a x^4+b x^3\right)^{3/4}}+\frac{b x^{9/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{2 a^{3/4} \left(a x^4+b x^3\right)^{3/4}}+\sqrt[4]{a x^4+b x^3}","-\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,"(b*x^3 + a*x^4)^(1/4) - (b*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*(b*x^3 + a*x^4)^(3/4)) + (b*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*(b*x^3 + a*x^4)^(3/4))","A",7,7,19,0.3684,1,"{2021, 2032, 63, 331, 298, 203, 206}"
1103,1,136,0,0.3579682,"\int \frac{(-b+a x) \sqrt[4]{b x^3+a x^4}}{x (b+a x)} \, dx","Int[((-b + a*x)*(b*x^3 + a*x^4)^(1/4))/(x*(b + a*x)),x]","\frac{7 b \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{a x+b}}-\frac{7 b \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{a x+b}}+\sqrt[4]{a x^4+b x^3}","\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,"(b*x^3 + a*x^4)^(1/4) + (7*b*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - (7*b*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4))","A",7,7,33,0.2121,1,"{2056, 80, 63, 331, 298, 203, 206}"
1104,0,0,0,1.0562514,"\int \frac{-1+3 x^4}{\left(1-x+x^4\right) \sqrt[3]{x^2+x^6}} \, dx","Int[(-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,"(9*x*(1 + x^4)^(1/3)*Hypergeometric2F1[1/12, 1/3, 13/12, -x^4])/(x^2 + x^6)^(1/3) - (12*x^(2/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x^12)^(1/3)*(1 - x^3 + x^12)), x], x, x^(1/3)])/(x^2 + x^6)^(1/3) + (9*x^(2/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][x^3/((1 + x^12)^(1/3)*(1 - x^3 + x^12)), x], x, x^(1/3)])/(x^2 + x^6)^(1/3)","F",0,0,0,0,-1,"{}"
1105,1,937,0,2.4220077,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Int[1/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} 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,"-1/4*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",22,8,28,0.2857,1,"{2056, 6715, 6725, 1429, 377, 212, 206, 203}"
1106,1,937,0,1.9651041,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Int[1/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} 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,"-1/4*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",22,8,28,0.2857,1,"{2056, 6715, 6725, 1429, 377, 212, 206, 203}"
1107,1,92,0,0.0597921,"\int \frac{-b+a x^8}{x^2 \left(b+a x^4\right)^{3/4}} \, dx","Int[(-b + a*x^8)/(x^2*(b + a*x^4)^(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{\sqrt[4]{a x^4+b}}{x}+\frac{1}{4} x^3 \sqrt[4]{a x^4+b}","\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,"(b + a*x^4)^(1/4)/x + (x^3*(b + a*x^4)^(1/4))/4 + (3*b*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(3/4)) - (3*b*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(3/4))","A",6,6,24,0.2500,1,"{1487, 451, 331, 298, 203, 206}"
1108,0,0,0,2.5167589,"\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","Int[(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,"2*a*b^3*Defer[Subst][Defer[Int][x^2/(a^4*b + x^4*(b + x^4)^4), x], x, (-b + a*x^2)^(1/4)] + 14*a*b^2*Defer[Subst][Defer[Int][x^6/(a^4*b + x^4*(b + x^4)^4), x], x, (-b + a*x^2)^(1/4)] + 22*a*b*Defer[Subst][Defer[Int][x^10/(a^4*b + x^4*(b + x^4)^4), x], x, (-b + a*x^2)^(1/4)] + 10*a*Defer[Subst][Defer[Int][x^14/(a^4*b + x^4*(b + x^4)^4), x], x, (-b + a*x^2)^(1/4)]","F",0,0,0,0,-1,"{}"
1109,1,129,0,0.017157,"\int \frac{1}{\sqrt[3]{x^2+x^3}} \, dx","Int[(x^2 + x^3)^(-1/3),x]","-\frac{x^{2/3} \sqrt[3]{x+1} \log (x)}{2 \sqrt[3]{x^3+x^2}}-\frac{3 x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3+x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3+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,"-((Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[x])/(2*(x^2 + x^3)^(1/3)) - (3*x^(2/3)*(1 + x)^(1/3)*Log[-1 + (1 + x)^(1/3)/x^(1/3)])/(2*(x^2 + x^3)^(1/3))","A",2,2,11,0.1818,1,"{2011, 59}"
1110,0,0,0,6.7574006,"\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","Int[(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,"(8*a*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(1/4)*(-(a*(1 - b/a)*d) - d*x^4 + x^12)), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(1/4) + (8*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^6/((a - b + x^4)^(1/4)*(-(a*(1 - b/a)*d) - d*x^4 + x^12)), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(1/4) - (4*(a - 3*b)*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(1/4)*(a*(1 - b/a)*d + x^4*(d - x^8))), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(1/4)","F",0,0,0,0,-1,"{}"
1111,0,0,0,7.555984,"\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","Int[((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,"(8*(1 - (a - b)/(a - x))^(3/4)*(-a + x)^(3/2)*EllipticF[ArcCot[Sqrt[-a + x]/Sqrt[a - b]]/2, 2])/(Sqrt[a - b]*d*((a - x)*(b - x))^(3/4)) + (8*(a - b)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][1/((a - b + x^4)^(3/4)*(a*(1 - b/a) + x^4 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*((a - x)*(b - x))^(3/4)) + (8*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][x^4/((a - b + x^4)^(3/4)*(a*(1 - b/a) + x^4 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*((a - x)*(b - x))^(3/4)) + (8*a*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][x^8/((a - b + x^4)^(3/4)*(a*(1 - b/a) + x^4 - d*x^12)), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(3/4) + (4*(a - 3*b)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][x^8/((a - b + x^4)^(3/4)*(a*(1 - b/a) + x^4 - d*x^12)), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(3/4)","F",0,0,0,0,-1,"{}"
1112,0,0,0,15.0094764,"\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","Int[(-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,"(4*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(-(-1 + k*x^4)^3 - d*(x^4 - x^8))), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) - (8*(1 - k)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^6/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*(-(-1 + k*x^4)^3 - d*(x^4 - x^8))), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (4*k*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^10/((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4)*((-1 + k*x^4)^3 + d*(x^4 - x^8))), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4)","F",0,0,0,0,-1,"{}"
1113,1,78,0,0.1108079,"\int \frac{\sqrt{1+6 x^2+x^4}}{x \left(1+x^2\right)} \, dx","Int[Sqrt[1 + 6*x^2 + x^4]/(x*(1 + x^2)),x]","-\tan ^{-1}\left(\frac{1-x^2}{\sqrt{x^4+6 x^2+1}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x^2+3}{\sqrt{x^4+6 x^2+1}}\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{3 x^2+1}{\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[(1 - x^2)/Sqrt[1 + 6*x^2 + x^4]] + ArcTanh[(3 + x^2)/Sqrt[1 + 6*x^2 + x^4]]/2 - ArcTanh[(1 + 3*x^2)/Sqrt[1 + 6*x^2 + x^4]]/2","A",9,7,25,0.2800,1,"{1251, 895, 724, 206, 843, 621, 204}"
1114,0,0,0,0.5128145,"\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","Int[((-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,"-(((-1 + 2*x^2 + 2*x^4)^(1/4)*AppellF1[-1/2, -1/4, -1/4, 1/2, (-2*x^2)/(1 - Sqrt[3]), (-2*x^2)/(1 + Sqrt[3])])/(x*(1 + (2*x^2)/(1 - Sqrt[3]))^(1/4)*(1 + (2*x^2)/(1 + Sqrt[3]))^(1/4))) + Defer[Int][(-1 + 2*x^2 + 2*x^4)^(1/4)/(1 - 2*x^2), x]","F",0,0,0,0,-1,"{}"
1115,1,83,0,0.0482548,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(2 b+a x^4\right)} \, dx","Int[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)}{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}","\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))]/(2*2^(3/4)*a^(1/4)*b) + ArcTanh[(a^(1/4)*x)/(2^(1/4)*(b + a*x^4)^(1/4))]/(2*2^(3/4)*a^(1/4)*b)","A",4,4,23,0.1739,1,"{377, 212, 206, 203}"
1116,1,153,0,0.1675781,"\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^2} \, dx","Int[(-(b*x^2) + a*x^4)^(1/4)/x^2,x]","-\frac{2 \sqrt[4]{a x^4-b x^2}}{x}-\frac{\sqrt[4]{a} x^{3/2} \left(a x^2-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\left(a x^4-b x^2\right)^{3/4}}+\frac{\sqrt[4]{a} x^{3/2} \left(a x^2-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\left(a x^4-b x^2\right)^{3/4}}","-\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))/x - (a^(1/4)*x^(3/2)*(-b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(-(b*x^2) + a*x^4)^(3/4) + (a^(1/4)*x^(3/2)*(-b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(-(b*x^2) + a*x^4)^(3/4)","A",7,7,20,0.3500,1,"{2020, 2032, 329, 331, 298, 203, 206}"
1117,1,993,0,2.5200438,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(a+b x^8\right)} \, dx","Int[1/((-(b*x^2) + a*x^4)^(1/4)*(a + b*x^8)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt[4]{-a} a} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{b^{5/4}+\sqrt[4]{-a} a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt[4]{-a} a} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{b^{5/4}+\sqrt[4]{-a} 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,"-1/4*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/((-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(((-a)^(1/4)*a - b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(((-a)^(1/4)*a + b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(((-a)^(1/4)*a - b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(((-a)^(1/4)*a + b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",22,8,26,0.3077,1,"{2056, 6715, 6725, 1429, 377, 212, 208, 205}"
1118,1,993,0,1.8300138,"\int \frac{1}{\sqrt[4]{-b x^2+a x^4} \left(a+b x^8\right)} \, dx","Int[1/((-(b*x^2) + a*x^4)^(1/4)*(a + b*x^8)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt[4]{-a} a} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{b^{5/4}+\sqrt[4]{-a} a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{\sqrt{-\sqrt{-a}} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{\sqrt[4]{-a} a-b^{5/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{4 \left(-\sqrt{-a}\right)^{15/8} \sqrt[4]{b^{5/4}+\sqrt{-\sqrt{-a}} a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{b^{5/4}+\sqrt[4]{-a} a} \sqrt{x}}{\sqrt[16]{-a} \sqrt[4]{a x^2-b}}\right)}{4 (-a)^{15/16} \sqrt[4]{b^{5/4}+\sqrt[4]{-a} 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,"-1/4*(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/((-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(((-a)^(1/4)*a - b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(((-a)^(1/4)*a + b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(((-a)^(1/4)*a - b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a - b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-Sqrt[-a])^(15/8)*(Sqrt[-Sqrt[-a]]*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(((-a)^(1/4)*a + b^(5/4))^(1/4)*Sqrt[x])/((-a)^(1/16)*(-b + a*x^2)^(1/4))])/(4*(-a)^(15/16)*((-a)^(1/4)*a + b^(5/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",22,8,26,0.3077,1,"{2056, 6715, 6725, 1429, 377, 212, 208, 205}"
1119,1,103,0,0.2318343,"\int \frac{(-1+x) \sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Int[((-1 + x)*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 + x],x]","\frac{1}{2} \sqrt{x+1} \left(x+\sqrt{x+1}\right)^{3/2}-\frac{5}{12} \left(x+\sqrt{x+1}\right)^{3/2}-\frac{23}{32} \left(2 \sqrt{x+1}+1\right) \sqrt{x+\sqrt{x+1}}+\frac{115}{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-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,"(-5*(x + Sqrt[1 + x])^(3/2))/12 + (Sqrt[1 + x]*(x + Sqrt[1 + x])^(3/2))/2 - (23*Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/32 + (115*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/64","A",6,5,24,0.2083,1,"{1661, 640, 612, 621, 206}"
1120,1,103,0,0.2126849,"\int \frac{x \sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Int[(x*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 + x],x]","\frac{1}{2} \sqrt{x+1} \left(x+\sqrt{x+1}\right)^{3/2}-\frac{5}{12} \left(x+\sqrt{x+1}\right)^{3/2}-\frac{7}{32} \left(2 \sqrt{x+1}+1\right) \sqrt{x+\sqrt{x+1}}+\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,"(-5*(x + Sqrt[1 + x])^(3/2))/12 + (Sqrt[1 + x]*(x + Sqrt[1 + x])^(3/2))/2 - (7*Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/32 + (35*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/64","A",6,5,22,0.2273,1,"{1661, 640, 612, 621, 206}"
1121,1,103,0,0.1109775,"\int \sqrt{1+x} \sqrt{x+\sqrt{1+x}} \, dx","Int[Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]],x]","\frac{1}{2} \sqrt{x+1} \left(x+\sqrt{x+1}\right)^{3/2}-\frac{5}{12} \left(x+\sqrt{x+1}\right)^{3/2}+\frac{9}{32} \left(2 \sqrt{x+1}+1\right) \sqrt{x+\sqrt{x+1}}-\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,"(-5*(x + Sqrt[1 + x])^(3/2))/12 + (Sqrt[1 + x]*(x + Sqrt[1 + x])^(3/2))/2 + (9*Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/32 - (45*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/64","A",6,5,21,0.2381,1,"{742, 640, 612, 621, 206}"
1122,1,90,0,0.1665255,"\int \frac{1+\sqrt{1+x^2}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(1 + Sqrt[1 + x^2])/Sqrt[x + Sqrt[1 + x^2]],x]","\frac{1}{6} \left(\sqrt{x^2+1}+x\right)^{3/2}+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{\sqrt{\sqrt{x^2+1}+x}}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\frac{1}{10 \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,"-1/10*1/(x + Sqrt[1 + x^2])^(5/2) - 1/(3*(x + Sqrt[1 + x^2])^(3/2)) - 1/Sqrt[x + Sqrt[1 + x^2]] + Sqrt[x + Sqrt[1 + x^2]] + (x + Sqrt[1 + x^2])^(3/2)/6","A",8,5,27,0.1852,1,"{6742, 2117, 14, 2122, 270}"
1123,1,80,0,0.2933184,"\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","Int[(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]","\sqrt{\frac{1}{110} \left(17+7 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{7+\sqrt{5}}} (x-2)\right)-\sqrt{\frac{1}{110} \left(17-7 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{7-\sqrt{5}}} (x-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,"-(Sqrt[(17 - 7*Sqrt[5])/110]*ArcTanh[Sqrt[2/(7 - Sqrt[5])]*(-2 + x)]) + Sqrt[(17 + 7*Sqrt[5])/110]*ArcTanh[Sqrt[2/(7 + Sqrt[5])]*(-2 + x)]","A",5,4,67,0.05970,0,"{6688, 1680, 1166, 207}"
1124,0,0,0,5.253521,"\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","Int[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,"(2*Sqrt[x]*Sqrt[-b + a^2*x]*Defer[Subst][Defer[Int][x^4/(Sqrt[-b + a^2*x^2]*(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2)), x], x, Sqrt[x]])/Sqrt[-(b*x) + a^2*x^2]","F",0,0,0,0,-1,"{}"
1125,0,0,0,12.6590285,"\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","Int[(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]","\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","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))/(b*d*Sqrt[(a - x)*(b - x)*x]) - (4*(a - x)*x)/(b^2*d*Sqrt[(a - x)*(b - x)*x]) + (4*Sqrt[a]*(b - x)*Sqrt[x]*Sqrt[1 - x/a]*EllipticE[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(b^2*d*Sqrt[(a - x)*(b - x)*x]*Sqrt[1 - x/b]) - (2*Sqrt[a]*Sqrt[x]*Sqrt[1 - x/a]*Sqrt[1 - x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[a]], a/b])/(b*d*Sqrt[(a - x)*(b - x)*x]) - ((1 - 2*a*d + b*d + Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Int][Sqrt[-a + x]/(x^(3/2)*(-b + x)^(3/2)*(-1 - b*d - Sqrt[1 - 4*a*d + 2*b*d + b^2*d^2] + 2*d*x)), x])/(d*Sqrt[(a - x)*(b - x)*x]) - ((1 - 2*a*d + b*d - Sqrt[-4*a*d + (1 + b*d)^2])*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Int][Sqrt[-a + x]/(x^(3/2)*(-b + x)^(3/2)*(-1 - b*d + Sqrt[1 - 4*a*d + 2*b*d + b^2*d^2] + 2*d*x)), x])/(d*Sqrt[(a - x)*(b - x)*x])","F",0,0,0,0,-1,"{}"
1126,1,64,0,0.0472309,"\int \frac{\left(1+x^3\right)^{2/3}}{x} \, dx","Int[(1 + x^3)^(2/3)/x,x]","\frac{1}{2} \left(x^3+1\right)^{2/3}+\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}{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,"(1 + x^3)^(2/3)/2 + ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/2 + Log[1 - (1 + x^3)^(1/3)]/2","A",6,6,13,0.4615,1,"{266, 50, 55, 618, 204, 31}"
1127,1,146,0,0.2204353,"\int \frac{\left(-b+2 a x^2\right) \sqrt[4]{b x^2+a x^4}}{b+a x^2} \, dx","Int[((-b + 2*a*x^2)*(b*x^2 + a*x^4)^(1/4))/(b + a*x^2),x]","\frac{5 b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{5 b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}+x \sqrt[4]{a x^4+b x^2}","\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*(b*x^2 + a*x^4)^(1/4) + (5*b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (5*b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4))","A",7,7,35,0.2000,1,"{2056, 459, 329, 331, 298, 203, 206}"
1128,0,0,0,3.4564914,"\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","Int[((-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]","\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","\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,"((I/2)*x*Sqrt[1 + x^2 + x^4])/(I - x^2) + ((I/2)*x*Sqrt[1 + x^2 + x^4])/(I + x^2) + 4*ArcTanh[x/Sqrt[1 + x^2 + x^4]] - 3*Sqrt[2]*ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^2 + x^4]] - (9*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(2*Sqrt[1 + x^2 + x^4]) - (3*(I - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/((3*I - Sqrt[3])*Sqrt[1 + x^2 + x^4]) + (3*(5 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4]) + (3*(5 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4]) - (3*(I + Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/((3*I + Sqrt[3])*Sqrt[1 + x^2 + x^4]) + 2*Defer[Int][(x^2*Sqrt[1 + x^2 + x^4])/(1 + x^4)^3, x] - Defer[Int][(x^2*Sqrt[1 + x^2 + x^4])/(1 + x^4)^2, x]","F",0,0,0,0,-1,"{}"
1129,1,666,0,2.3404575,"\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","Int[((1 + x^6)*(-1 + x^3 + x^6)*Sqrt[1 + x^12])/(x^7*(-1 - x^3 + x^6)),x]","-\frac{1}{6} \left(1+\sqrt{5}\right) \sqrt{x^{12}+1}-\frac{1}{6} \left(1-\sqrt{5}\right) \sqrt{x^{12}+1}+\frac{\sqrt{x^{12}+1}}{2}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^{12}+1}\right)+\frac{1}{6} \left(1+\sqrt{5}\right) \sinh ^{-1}\left(x^6\right)+\frac{1}{6} \left(1-\sqrt{5}\right) \sinh ^{-1}\left(x^6\right)+\frac{1}{6} \sinh ^{-1}\left(x^6\right)-\frac{\sqrt{x^{12}+1}}{6 x^6}+\frac{\tanh ^{-1}\left(\frac{\left(3-\sqrt{5}\right) x^6+2}{\sqrt{6 \left(3-\sqrt{5}\right)} \sqrt{x^{12}+1}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\left(3+\sqrt{5}\right) x^6+2}{\sqrt{6 \left(3+\sqrt{5}\right)} \sqrt{x^{12}+1}}\right)}{\sqrt{3}}+\frac{2 \sqrt{x^{12}+1}}{3 x^3}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} x^3}{\sqrt{x^{12}+1}}\right)}{\sqrt{3}}+\frac{\left(5+\sqrt{5}\right) \left(x^6+1\right) \sqrt{\frac{x^{12}+1}{\left(x^6+1\right)^2}} F\left(2 \tan ^{-1}\left(x^3\right)|\frac{1}{2}\right)}{6 \sqrt{x^{12}+1}}-\frac{\left(3+\sqrt{5}\right) \left(x^6+1\right) \sqrt{\frac{x^{12}+1}{\left(x^6+1\right)^2}} F\left(2 \tan ^{-1}\left(x^3\right)|\frac{1}{2}\right)}{\left(5+\sqrt{5}\right) \sqrt{x^{12}+1}}+\frac{\left(5-\sqrt{5}\right) \left(x^6+1\right) \sqrt{\frac{x^{12}+1}{\left(x^6+1\right)^2}} F\left(2 \tan ^{-1}\left(x^3\right)|\frac{1}{2}\right)}{6 \sqrt{x^{12}+1}}-\frac{\left(3-\sqrt{5}\right) \left(x^6+1\right) \sqrt{\frac{x^{12}+1}{\left(x^6+1\right)^2}} F\left(2 \tan ^{-1}\left(x^3\right)|\frac{1}{2}\right)}{\left(5-\sqrt{5}\right) \sqrt{x^{12}+1}}-\frac{2 \left(x^6+1\right) \sqrt{\frac{x^{12}+1}{\left(x^6+1\right)^2}} F\left(2 \tan ^{-1}\left(x^3\right)|\frac{1}{2}\right)}{3 \sqrt{x^{12}+1}}+\frac{\left(3+\sqrt{5}\right) \left(x^6+1\right) \sqrt{\frac{x^{12}+1}{\left(x^6+1\right)^2}} \Pi \left(\frac{5}{4};2 \tan ^{-1}\left(x^3\right)|\frac{1}{2}\right)}{2 \left(5+3 \sqrt{5}\right) \sqrt{x^{12}+1}}+\frac{\left(3-\sqrt{5}\right) \left(x^6+1\right) \sqrt{\frac{x^{12}+1}{\left(x^6+1\right)^2}} \Pi \left(\frac{5}{4};2 \tan ^{-1}\left(x^3\right)|\frac{1}{2}\right)}{2 \left(5-3 \sqrt{5}\right) \sqrt{x^{12}+1}}","\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,"Sqrt[1 + x^12]/2 - ((1 - Sqrt[5])*Sqrt[1 + x^12])/6 - ((1 + Sqrt[5])*Sqrt[1 + x^12])/6 - Sqrt[1 + x^12]/(6*x^6) + (2*Sqrt[1 + x^12])/(3*x^3) + ArcSinh[x^6]/6 + ((1 - Sqrt[5])*ArcSinh[x^6])/6 + ((1 + Sqrt[5])*ArcSinh[x^6])/6 - (2*ArcTanh[(Sqrt[3]*x^3)/Sqrt[1 + x^12]])/Sqrt[3] + ArcTanh[(2 + (3 - Sqrt[5])*x^6)/(Sqrt[6*(3 - Sqrt[5])]*Sqrt[1 + x^12])]/Sqrt[3] - ArcTanh[(2 + (3 + Sqrt[5])*x^6)/(Sqrt[6*(3 + Sqrt[5])]*Sqrt[1 + x^12])]/Sqrt[3] - ArcTanh[Sqrt[1 + x^12]]/2 - (2*(1 + x^6)*Sqrt[(1 + x^12)/(1 + x^6)^2]*EllipticF[2*ArcTan[x^3], 1/2])/(3*Sqrt[1 + x^12]) - ((3 - Sqrt[5])*(1 + x^6)*Sqrt[(1 + x^12)/(1 + x^6)^2]*EllipticF[2*ArcTan[x^3], 1/2])/((5 - Sqrt[5])*Sqrt[1 + x^12]) + ((5 - Sqrt[5])*(1 + x^6)*Sqrt[(1 + x^12)/(1 + x^6)^2]*EllipticF[2*ArcTan[x^3], 1/2])/(6*Sqrt[1 + x^12]) - ((3 + Sqrt[5])*(1 + x^6)*Sqrt[(1 + x^12)/(1 + x^6)^2]*EllipticF[2*ArcTan[x^3], 1/2])/((5 + Sqrt[5])*Sqrt[1 + x^12]) + ((5 + Sqrt[5])*(1 + x^6)*Sqrt[(1 + x^12)/(1 + x^6)^2]*EllipticF[2*ArcTan[x^3], 1/2])/(6*Sqrt[1 + x^12]) + ((3 - Sqrt[5])*(1 + x^6)*Sqrt[(1 + x^12)/(1 + x^6)^2]*EllipticPi[5/4, 2*ArcTan[x^3], 1/2])/(2*(5 - 3*Sqrt[5])*Sqrt[1 + x^12]) + ((3 + Sqrt[5])*(1 + x^6)*Sqrt[(1 + x^12)/(1 + x^6)^2]*EllipticPi[5/4, 2*ArcTan[x^3], 1/2])/(2*(5 + 3*Sqrt[5])*Sqrt[1 + x^12])","C",45,22,38,0.5789,0,"{6728, 275, 277, 215, 305, 220, 1196, 266, 50, 63, 207, 6715, 1729, 1209, 1198, 1217, 1707, 1248, 735, 844, 725, 206}"
1130,1,56,0,0.0385033,"\int \sqrt{d+c \sqrt{b+a x}} \, dx","Int[Sqrt[d + c*Sqrt[b + a*x]],x]","\frac{4 \left(c \sqrt{a x+b}+d\right)^{5/2}}{5 a c^2}-\frac{4 d \left(c \sqrt{a x+b}+d\right)^{3/2}}{3 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*(d + c*Sqrt[b + a*x])^(3/2))/(3*a*c^2) + (4*(d + c*Sqrt[b + a*x])^(5/2))/(5*a*c^2)","A",4,3,17,0.1765,1,"{247, 190, 43}"
1131,1,65,0,0.0462519,"\int \frac{1+2 x^2}{x \left(1+x^2\right)^{2/3}} \, dx","Int[(1 + 2*x^2)/(x*(1 + x^2)^(2/3)),x]","3 \sqrt[3]{x^2+1}+\frac{3}{4} \log \left(1-\sqrt[3]{x^2+1}\right)-\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}","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[x]/2 + (3*Log[1 - (1 + x^2)^(1/3)])/4","A",6,6,20,0.3000,1,"{446, 80, 57, 618, 204, 31}"
1132,1,203,0,1.6877872,"\int \frac{x}{\sqrt{(1-x) x \left(1-k^2 x\right)} \left(-1+k^2 x^2\right)} \, dx","Int[x/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^2*x^2)),x]","\frac{\sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(-\frac{k}{1-k};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{(1-k) k \sqrt{(1-x) x \left(1-k^2 x\right)}}-\frac{\sqrt{1-x} \sqrt{x} \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(\frac{k}{k+1};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{k (k+1) \sqrt{(1-x) x \left(1-k^2 x\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,"(Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[-(k/(1 - k)), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((1 - k)*k*Sqrt[(1 - x)*x*(1 - k^2*x)]) - (Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[k/(1 + k), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/(k*(1 + k)*Sqrt[(1 - x)*x*(1 - k^2*x)])","C",13,7,32,0.2188,1,"{6718, 6725, 175, 115, 168, 538, 537}"
1133,1,137,0,0.5618755,"\int \frac{1+x}{\left(-1+2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(1 + x)/((-1 + 2*x + x^2)*Sqrt[-x + x^3]),x]","-\frac{\sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2+\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \left(2+\sqrt{2}\right) \sqrt{x^3-x}}-\frac{\sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2} \left(2+\sqrt{2}\right);\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{\sqrt{2} \left(2-\sqrt{2}\right) \sqrt{x^3-x}}","\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[x]*Sqrt[1 - x^2]*EllipticPi[(2 + Sqrt[2])^(-1), ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*(2 + Sqrt[2])*Sqrt[-x + x^3])) - (Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[(2 + Sqrt[2])/2, ArcSin[Sqrt[1 - x]], 1/2])/(Sqrt[2]*(2 - Sqrt[2])*Sqrt[-x + x^3])","C",9,5,25,0.2000,1,"{2056, 6728, 933, 168, 537}"
1134,1,257,0,0.7260351,"\int \frac{-x+x^2}{\left(-1+2 x+x^2\right) \sqrt{-x+x^3}} \, dx","Int[(-x + x^2)/((-1 + 2*x + x^2)*Sqrt[-x + x^3]),x]","\frac{\left(2+\sqrt{2}\right) \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}-\frac{\left(2-\sqrt{2}\right) \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}+\frac{\left(1+\sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2+\sqrt{2}};\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}-\frac{\left(1-\sqrt{2}\right) \sqrt{x} \sqrt{1-x^2} \Pi \left(\frac{1}{2} \left(2+\sqrt{2}\right);\sin ^{-1}\left(\sqrt{1-x}\right)|\frac{1}{2}\right)}{2 \sqrt{x^3-x}}","\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,"-1/2*((2 - Sqrt[2])*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/Sqrt[-x + x^3] + ((2 + Sqrt[2])*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(2*Sqrt[-x + x^3]) + ((1 + Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[(2 + Sqrt[2])^(-1), ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3]) - ((1 - Sqrt[2])*Sqrt[x]*Sqrt[1 - x^2]*EllipticPi[(2 + Sqrt[2])/2, ArcSin[Sqrt[1 - x]], 1/2])/(2*Sqrt[-x + x^3])","C",16,9,29,0.3103,0,"{1593, 2056, 6728, 944, 329, 222, 933, 168, 537}"
1135,0,0,0,0.4343538,"\int \frac{3+x^2}{\sqrt[3]{1+x^2} \left(1+x^2+x^3\right)} \, dx","Int[(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,"3*Defer[Int][1/((1 + x^2)^(1/3)*(1 + x^2 + x^3)), x] + Defer[Int][x^2/((1 + x^2)^(1/3)*(1 + x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
1136,1,86,0,0.0461135,"\int \frac{x}{\left(-1+x^3\right) \left(-1+2 x^3\right)^{2/3}} \, dx","Int[x/((-1 + x^3)*(-1 + 2*x^3)^(2/3)),x]","\frac{1}{3} \log \left(1-\frac{x}{\sqrt[3]{2 x^3-1}}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{2 x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{1}{6} \log \left(\frac{x}{\sqrt[3]{2 x^3-1}}+\frac{x^2}{\left(2 x^3-1\right)^{2/3}}+1\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{1}{6} \log \left(\sqrt[3]{2 x^3-1} x+\left(2 x^3-1\right)^{2/3}+x^2\right)",1,"ArcTan[(1 + (2*x)/(-1 + 2*x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[1 - x/(-1 + 2*x^3)^(1/3)]/3 - Log[1 + x^2/(-1 + 2*x^3)^(2/3) + x/(-1 + 2*x^3)^(1/3)]/6","A",7,7,20,0.3500,1,"{494, 292, 31, 634, 618, 204, 628}"
1137,0,0,0,15.0296336,"\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","Int[((-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,"(4*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(1 - k*x^4)^(5/4)/((1 - x^4)^(3/4)*(-x^4 + x^8 - d*(-1 + k*x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4) - (8*(1 - k)*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^4*(1 - k*x^4)^(5/4))/((1 - x^4)^(3/4)*(-x^4 + x^8 - d*(-1 + k*x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4) + (4*k*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(1 - k*x^4)^(5/4))/((1 - x^4)^(3/4)*(x^4 - x^8 + d*(-1 + k*x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4)","F",0,0,0,0,-1,"{}"
1138,1,654,0,1.655843,"\int \frac{-1+x^4}{\sqrt{-x+x^3} \left(1+x^4\right)} \, dx","Int[(-1 + x^4)/(Sqrt[-x + x^3]*(1 + x^4)),x]","\frac{2 \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\left(2 \sqrt{2}+(2+2 i)\right) \sqrt{x^3-x}}+\frac{2 \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\left(2 \sqrt{2}+(2-2 i)\right) \sqrt{x^3-x}}-\frac{\sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\left(\sqrt{2}+(1+i)\right) \sqrt{x^3-x}}-\frac{\sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\left(\sqrt{2}+(1-i)\right) \sqrt{x^3-x}}-\frac{\sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\left(\sqrt{2}+(-1-i)\right) \sqrt{x^3-x}}-\frac{2 \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\left(-2 \sqrt{2}+(2+2 i)\right) \sqrt{x^3-x}}+\frac{\sqrt{2} \sqrt{x-1} \sqrt{x} \sqrt{x+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{x-1}}\right)|\frac{1}{2}\right)}{\sqrt{x^3-x}}-\frac{\sqrt{1-x} \sqrt{x} \sqrt{x+1} \Pi \left(-\sqrt[4]{-1};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)}{\sqrt{x^3-x}}-\frac{\sqrt{1-x} \sqrt{x} \sqrt{x+1} \Pi \left(\sqrt[4]{-1};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)}{\sqrt{x^3-x}}-\frac{\sqrt{1-x} \sqrt{x} \sqrt{x+1} \Pi \left(-(-1)^{3/4};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)}{\sqrt{x^3-x}}-\frac{\sqrt{1-x} \sqrt{x} \sqrt{x+1} \Pi \left((-1)^{3/4};\left.\sin ^{-1}\left(\sqrt{x}\right)\right|-1\right)}{\sqrt{x^3-x}}","\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[2]*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/Sqrt[-x + x^3] - (2*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(((2 + 2*I) - 2*Sqrt[2])*Sqrt[-x + x^3]) - (Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(((-1 - I) + Sqrt[2])*Sqrt[-x + x^3]) - (Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(((1 - I) + Sqrt[2])*Sqrt[-x + x^3]) - (Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(((1 + I) + Sqrt[2])*Sqrt[-x + x^3]) + (2*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(((2 - 2*I) + 2*Sqrt[2])*Sqrt[-x + x^3]) + (2*Sqrt[-1 + x]*Sqrt[x]*Sqrt[1 + x]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[x])/Sqrt[-1 + x]], 1/2])/(((2 + 2*I) + 2*Sqrt[2])*Sqrt[-x + x^3]) - (Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + x]*EllipticPi[-(-1)^(1/4), ArcSin[Sqrt[x]], -1])/Sqrt[-x + x^3] - (Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + x]*EllipticPi[(-1)^(1/4), ArcSin[Sqrt[x]], -1])/Sqrt[-x + x^3] - (Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + x]*EllipticPi[-(-1)^(3/4), ArcSin[Sqrt[x]], -1])/Sqrt[-x + x^3] - (Sqrt[1 - x]*Sqrt[x]*Sqrt[1 + x]*EllipticPi[(-1)^(3/4), ArcSin[Sqrt[x]], -1])/Sqrt[-x + x^3]","C",43,13,24,0.5417,1,"{2056, 1586, 6715, 6725, 406, 222, 409, 1215, 1457, 540, 253, 538, 537}"
1139,1,297,0,1.1491291,"\int \frac{-1+x^2}{\left(1+x+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Int[(-1 + x^2)/((1 + x + x^2)*(x^2 + x^4)^(1/3)),x]","\frac{3 \sqrt[3]{x^2+1} x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};-\frac{4 x^2}{\left(i-\sqrt{3}\right)^2},-x^2\right)}{2 \left(1+i \sqrt{3}\right) \sqrt[3]{x^4+x^2}}+\frac{3 \sqrt[3]{x^2+1} x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};-\frac{4 x^2}{\left(i+\sqrt{3}\right)^2},-x^2\right)}{2 \left(1-i \sqrt{3}\right) \sqrt[3]{x^4+x^2}}-\frac{3 \sqrt[3]{x^2+1} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};-\frac{4 x^2}{\left(i-\sqrt{3}\right)^2},-x^2\right)}{\sqrt[3]{x^4+x^2}}-\frac{3 \sqrt[3]{x^2+1} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};-\frac{4 x^2}{\left(i+\sqrt{3}\right)^2},-x^2\right)}{\sqrt[3]{x^4+x^2}}+\frac{3 \sqrt[3]{x^2+1} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};-x^2\right)}{\sqrt[3]{x^4+x^2}}","-\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,"(-3*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-4*x^2)/(I - Sqrt[3])^2, -x^2])/(x^2 + x^4)^(1/3) - (3*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-4*x^2)/(I + Sqrt[3])^2, -x^2])/(x^2 + x^4)^(1/3) + (3*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, (-4*x^2)/(I - Sqrt[3])^2, -x^2])/(2*(1 + I*Sqrt[3])*(x^2 + x^4)^(1/3)) + (3*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, (-4*x^2)/(I + Sqrt[3])^2, -x^2])/(2*(1 - I*Sqrt[3])*(x^2 + x^4)^(1/3)) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3)","C",18,8,25,0.3200,0,"{2056, 6728, 364, 959, 466, 429, 465, 510}"
1140,1,94,0,0.0421595,"\int \frac{\left(-2 b+a x^4\right) \left(b+a x^4\right)^{3/4}}{x^8} \, dx","Int[((-2*b + a*x^4)*(b + a*x^4)^(3/4))/x^8,x]","\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{2 \left(a x^4+b\right)^{7/4}}{7 x^7}-\frac{a \left(a x^4+b\right)^{3/4}}{3 x^3}","\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,"-1/3*(a*(b + a*x^4)^(3/4))/x^3 + (2*(b + a*x^4)^(7/4))/(7*x^7) + (a^(7/4)*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/2 + (a^(7/4)*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/2","A",6,6,24,0.2500,1,"{451, 277, 240, 212, 206, 203}"
1141,1,96,0,0.0445281,"\int \frac{\left(-b+a x^4\right)^{3/4} \left(-b+2 a x^4\right)}{x^8} \, dx","Int[((-b + a*x^4)^(3/4)*(-b + 2*a*x^4))/x^8,x]","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(a x^4-b\right)^{7/4}}{7 x^7}-\frac{2 a \left(a x^4-b\right)^{3/4}}{3 x^3}","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,"(-2*a*(-b + a*x^4)^(3/4))/(3*x^3) - (-b + a*x^4)^(7/4)/(7*x^7) + a^(7/4)*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)] + a^(7/4)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]","A",6,6,27,0.2222,1,"{451, 277, 240, 212, 206, 203}"
1142,1,109,0,0.2411812,"\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","Int[((-q + p*x^2)*(a*q + b*x + a*p*x^2)*Sqrt[q^2 + p^2*x^4])/x^4,x]","\frac{a \left(p^2 x^4+q^2\right)^{3/2}}{3 x^3}-\frac{1}{2} b p q \tanh ^{-1}\left(\frac{\sqrt{p^2 x^4+q^2}}{q}\right)+\frac{b \left(p x^2+q\right) \sqrt{p^2 x^4+q^2}}{2 x^2}-\frac{1}{2} b p q \tanh ^{-1}\left(\frac{p x^2}{\sqrt{p^2 x^4+q^2}}\right)","\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,"(b*(q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(2*x^2) + (a*(q^2 + p^2*x^4)^(3/2))/(3*x^3) - (b*p*q*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]])/2 - (b*p*q*ArcTanh[Sqrt[q^2 + p^2*x^4]/q])/2","A",11,10,41,0.2439,1,"{1833, 1252, 813, 844, 217, 206, 266, 63, 208, 449}"
1143,0,0,0,0.9984832,"\int \frac{-1+2 x^3}{\left(1+x+x^3\right) \sqrt[3]{x^2+x^5}} \, dx","Int[(-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,"(6*x*(1 + x^3)^(1/3)*Hypergeometric2F1[1/9, 1/3, 10/9, -x^3])/(x^2 + x^5)^(1/3) - (9*x^(2/3)*(1 + x^3)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x^9)^(1/3)*(1 + x^3 + x^9)), x], x, x^(1/3)])/(x^2 + x^5)^(1/3) - (6*x^(2/3)*(1 + x^3)^(1/3)*Defer[Subst][Defer[Int][x^3/((1 + x^9)^(1/3)*(1 + x^3 + x^9)), x], x, x^(1/3)])/(x^2 + x^5)^(1/3)","F",0,0,0,0,-1,"{}"
1144,0,0,0,1.1918932,"\int \frac{2+3 x^5}{\left(-1+x^2+x^5\right) \sqrt[3]{-x+x^6}} \, dx","Int[(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,"(9*x*(1 - x^5)^(1/3)*Hypergeometric2F1[2/15, 1/3, 17/15, x^5])/(2*(-x + x^6)^(1/3)) + (15*x^(1/3)*(-1 + x^5)^(1/3)*Defer[Subst][Defer[Int][x/((-1 + x^15)^(1/3)*(-1 + x^6 + x^15)), x], x, x^(1/3)])/(-x + x^6)^(1/3) - (9*x^(1/3)*(-1 + x^5)^(1/3)*Defer[Subst][Defer[Int][x^7/((-1 + x^15)^(1/3)*(-1 + x^6 + x^15)), x], x, x^(1/3)])/(-x + x^6)^(1/3)","F",0,0,0,0,-1,"{}"
1145,1,79,0,0.2257661,"\int \frac{\sqrt{-1+x^6} \left(-1+2 x^6\right)^2}{x^4 \left(-1+4 x^6\right)} \, dx","Int[(Sqrt[-1 + x^6]*(-1 + 2*x^6)^2)/(x^4*(-1 + 4*x^6)),x]","\frac{1}{6} \sqrt{x^6-1} x^3+\frac{\sqrt{x^6-1}}{3 x^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} x^3}{\sqrt{x^6-1}}\right)}{4 \sqrt{3}}-\frac{5}{12} \tanh ^{-1}\left(\frac{x^3}{\sqrt{x^6-1}}\right)","\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,"Sqrt[-1 + x^6]/(3*x^3) + (x^3*Sqrt[-1 + x^6])/6 + ArcTan[(Sqrt[3]*x^3)/Sqrt[-1 + x^6]]/(4*Sqrt[3]) - (5*ArcTanh[x^3/Sqrt[-1 + x^6]])/12","A",14,9,31,0.2903,1,"{575, 586, 580, 523, 217, 206, 377, 204, 528}"
1146,1,369,0,0.4306154,"\int \frac{1+x^4}{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)} \, dx","Int[(1 + x^4)/((-1 + x^4)^(1/4)*(1 + x^4 + x^8)),x]","\frac{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \left(-\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[4]{x^4-1}}\right)}{6 \left(-\sqrt{3}+i\right)}+\frac{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \left(\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^4-1}}\right)}{6 \left(\sqrt{3}+i\right)}+\frac{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \left(-\sqrt{3}+3 i\right) \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[4]{x^4-1}}\right)}{6 \left(-\sqrt{3}+i\right)}+\frac{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \left(\sqrt{3}+3 i\right) \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^4-1}}\right)}{6 \left(\sqrt{3}+i\right)}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-2 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}}\&\right]",1,"(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(3*I - Sqrt[3])*ArcTan[x/(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))])/(6*(I - Sqrt[3])) + (((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(3*I + Sqrt[3])*ArcTan[x/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))])/(6*(I + Sqrt[3])) + (((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(3*I - Sqrt[3])*ArcTanh[x/(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))])/(6*(I - Sqrt[3])) + (((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(3*I + Sqrt[3])*ArcTanh[x/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(-1 + x^4)^(1/4))])/(6*(I + Sqrt[3]))","C",10,5,25,0.2000,1,"{6728, 377, 212, 208, 205}"
1147,1,199,0,0.4490829,"\int \frac{-1+2 x^4}{\sqrt[4]{-1+x^4} \left(-2-x^4+2 x^8\right)} \, dx","Int[(-1 + 2*x^4)/((-1 + x^4)^(1/4)*(-2 - x^4 + 2*x^8)),x]","-\frac{\sqrt[4]{487-79 \sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}+\frac{\sqrt[4]{487+79 \sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}-\frac{\sqrt[4]{487-79 \sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}+\frac{\sqrt[4]{487+79 \sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}","\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+\log (x)}{4 \text{$\#$1}^5-5 \text{$\#$1}}\&\right]",1,"-1/4*((487 - 79*Sqrt[17])^(1/4)*ArcTan[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)])/Sqrt[17] + ((487 + 79*Sqrt[17])^(1/4)*ArcTan[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/(4*Sqrt[17]) - ((487 - 79*Sqrt[17])^(1/4)*ArcTanh[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(4*Sqrt[17]) + ((487 + 79*Sqrt[17])^(1/4)*ArcTanh[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/(4*Sqrt[17])","B",10,5,31,0.1613,0,"{6728, 377, 212, 206, 203}"
1148,1,341,0,0.5021741,"\int \frac{-1+x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(1-x^4+x^8\right)} \, dx","Int[(-1 + x^4 + 2*x^8)/((-1 + x^4)^(1/4)*(1 - x^4 + x^8)),x]","\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{i \sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x^4-1}}\right)}{2 \left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4}}-\frac{1}{2} i \sqrt{3} \left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt[4]{x^4-1}}\right)+\tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{i \sqrt{3} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x^4-1}}\right)}{2 \left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4}}-\frac{1}{2} i \sqrt{3} \left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt[4]{x^4-1}}\right)","\frac{3}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$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,"ArcTan[x/(-1 + x^4)^(1/4)] + ((I/2)*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/2)*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)] + ArcTanh[x/(-1 + x^4)^(1/4)] + ((I/2)*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/2)*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)]","C",26,11,32,0.3438,1,"{6728, 240, 212, 206, 203, 21, 1428, 408, 377, 208, 205}"
1149,1,1065,0,3.5782379,"\int \frac{1}{\sqrt[4]{b x^2+a x^4} \left(-2 b+a x^8\right)} \, dx","Int[1/((b*x^2 + a*x^4)^(1/4)*(-2*b + a*x^8)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}","\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,"-1/4*(Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",22,8,27,0.2963,1,"{2056, 6715, 6725, 1429, 377, 212, 206, 203}"
1150,1,1065,0,2.5890611,"\int \frac{1}{\sqrt[4]{b x^2+a x^4} \left(-2 b+a x^8\right)} \, dx","Int[1/((b*x^2 + a*x^4)^(1/4)*(-2*b + a*x^8)),x]","-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}-b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[16]{a} \sqrt[4]{\sqrt[4]{2} a^{3/4}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[16]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{15/16} \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{\sqrt[4]{2} a}{\sqrt{-\sqrt{a}}}+b^{3/4}} b \sqrt[4]{a x^4+b x^2}}","\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,"-1/4*(Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*a^(1/16)*(2^(1/4)*a^(3/4) + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(2^(1/16)*(b + a*x^2)^(1/4))])/(4*2^(15/16)*(-Sqrt[a])^(1/8)*((2^(1/4)*a)/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",22,8,27,0.2963,1,"{2056, 6715, 6725, 1429, 377, 212, 206, 203}"
1151,0,0,0,1.9638745,"\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","Int[((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,"2*Defer[Int][(-2 + x^4 + 2*x^5)^(1/4), x] + Defer[Int][(-2 + x^4 + 2*x^5)^(1/4)/(-1 + x), x] - 8*Defer[Int][(-2 + x^4 + 2*x^5)^(1/4)/x^10, x] + 6*Defer[Int][(-2 + x^4 + 2*x^5)^(1/4)/x^5, x] - 4*Defer[Int][(-2 + x^4 + 2*x^5)^(1/4)/x^2, x] + Defer[Int][(-2 + x^4 + 2*x^5)^(1/4)/(1 + x + x^2 + x^3 + x^4), x] + 2*Defer[Int][(x*(-2 + x^4 + 2*x^5)^(1/4))/(1 + x + x^2 + x^3 + x^4), x] + 3*Defer[Int][(x^2*(-2 + x^4 + 2*x^5)^(1/4))/(1 + x + x^2 + x^3 + x^4), x] - Defer[Int][(x^3*(-2 + x^4 + 2*x^5)^(1/4))/(1 + x + x^2 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1152,1,420,0,3.0664217,"\int \frac{1+x^{12}}{\sqrt{1+x^4} \left(-1+x^{12}\right)} \, dx","Int[(1 + x^12)/(Sqrt[1 + x^4]*(-1 + x^12)),x]","-\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}}+\frac{\left(3+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}-\frac{\left(1+i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}+\frac{\left(3-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{12 \sqrt{x^4+1}}-\frac{\left(1-i \sqrt{3}\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \sqrt{x^4+1}}-\frac{\left(-\sqrt{3}+i\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \left(-\sqrt{3}+3 i\right) \sqrt{x^4+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{6 \left(1+\sqrt[3]{-1}\right) \sqrt{x^4+1}}","-\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,"-1/3*ArcTan[x/Sqrt[1 + x^4]] - ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(6*Sqrt[2]) - ArcTanh[x/Sqrt[1 + x^4]]/3 - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(6*Sqrt[2]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*(1 + (-1)^(1/3))*Sqrt[1 + x^4]) - ((I - Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*(3*I - Sqrt[3])*Sqrt[1 + x^4]) - ((1 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4]) + ((3 - I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(12*Sqrt[1 + x^4]) - ((1 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(6*Sqrt[1 + x^4]) + ((3 + I*Sqrt[3])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(12*Sqrt[1 + x^4])","C",171,18,22,0.8182,1,"{1586, 6725, 1729, 1209, 1198, 220, 1196, 1211, 1699, 206, 1248, 735, 844, 215, 725, 203, 1217, 1707}"
1153,0,0,0,2.6759731,"\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","Int[(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,"-((x*(1 - x^2)*Sqrt[(1 + x^2 + x^4)/(1 - (1 + Sqrt[3])*x^2)^2]*EllipticF[ArcCos[(1 - (1 - Sqrt[3])*x^2)/(1 - (1 + Sqrt[3])*x^2)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[-((x^2*(1 - x^2))/(1 - (1 + Sqrt[3])*x^2)^2)]*Sqrt[1 - x^6])) + Defer[Int][1/(Sqrt[1 - x^6]*(-1 - x^2 + x^6)), x] + (2*Defer[Int][x^2/(Sqrt[1 - x^6]*(-1 - x^2 + x^6)), x])/3 + 4*Defer[Int][1/(Sqrt[1 - x^6]*(1 - x^2 + x^4 - 2*x^6 + x^8 + x^12)), x] - (10*Defer[Int][x^2/(Sqrt[1 - x^6]*(1 - x^2 + x^4 - 2*x^6 + x^8 + x^12)), x])/3 + (8*Defer[Int][x^4/(Sqrt[1 - x^6]*(1 - x^2 + x^4 - 2*x^6 + x^8 + x^12)), x])/3 - 4*Defer[Int][x^6/(Sqrt[1 - x^6]*(1 - x^2 + x^4 - 2*x^6 + x^8 + x^12)), x] + (4*Defer[Int][x^8/(Sqrt[1 - x^6]*(1 - x^2 + x^4 - 2*x^6 + x^8 + x^12)), x])/3","F",0,0,0,0,-1,"{}"
1154,0,0,0,0.2791335,"\int \frac{x^2-\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Int[(x^2 - Sqrt[1 + x^2])/Sqrt[1 + Sqrt[1 + x^2]],x]","\int \frac{x^2-\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","\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,"Defer[Int][x^2/Sqrt[1 + Sqrt[1 + x^2]], x] - Defer[Int][Sqrt[1 + x^2]/Sqrt[1 + Sqrt[1 + x^2]], x]","F",0,0,0,0,-1,"{}"
1155,1,62,0,0.0540168,"\int \frac{1}{(-1+x) \sqrt[3]{2-2 x+x^2}} \, dx","Int[1/((-1 + x)*(2 - 2*x + x^2)^(1/3)),x]","\frac{3}{4} \log \left(1-\sqrt[3]{(x-1)^2+1}\right)-\frac{1}{2} \log (1-x)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{(x-1)^2+1}+1}{\sqrt{3}}\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]])/2 + (3*Log[1 - (1 + (-1 + x)^2)^(1/3)])/4 - Log[1 - x]/2","A",6,6,18,0.3333,1,"{694, 266, 55, 618, 204, 31}"
1156,1,60,0,0.0468766,"\int \frac{1}{(1+x) \sqrt[3]{2+2 x+x^2}} \, dx","Int[1/((1 + x)*(2 + 2*x + x^2)^(1/3)),x]","-\frac{1}{2} \log (x+1)+\frac{3}{4} \log \left(1-\sqrt[3]{(x+1)^2+1}\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{(x+1)^2+1}+1}{\sqrt{3}}\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]])/2 - Log[1 + x]/2 + (3*Log[1 - (1 + (1 + x)^2)^(1/3)])/4","A",6,6,18,0.3333,1,"{694, 266, 55, 618, 204, 31}"
1157,1,62,0,0.0408242,"\int \frac{\left(-1+x^3\right)^{2/3}}{x} \, dx","Int[(-1 + x^3)^(2/3)/x,x]","\frac{1}{2} \left(x^3-1\right)^{2/3}+\frac{1}{2} \log \left(\sqrt[3]{x^3-1}+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}","\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 + x^3)^(2/3)/2 + ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/2 + Log[1 + (-1 + x^3)^(1/3)]/2","A",6,6,13,0.4615,1,"{266, 50, 56, 618, 204, 31}"
1158,0,0,0,0.4386118,"\int \frac{3+x^2}{\sqrt[3]{1+x^2} \left(-1-x^2+x^3\right)} \, dx","Int[(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,"3*Defer[Int][1/((1 + x^2)^(1/3)*(-1 - x^2 + x^3)), x] + Defer[Int][x^2/((1 + x^2)^(1/3)*(-1 - x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
1159,0,0,0,5.4013706,"\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","Int[(-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,"(2*k^2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x^2/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4) + (2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][1/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4) - ((1 - k^2)*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4)","F",0,0,0,0,-1,"{}"
1160,0,0,0,5.1805819,"\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","Int[(-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,"-(((1 - k)*(1 + k)*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4)) + (2*k^2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x^2/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4) + (2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][1/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4)","F",0,0,0,0,-1,"{}"
1161,1,138,0,0.1075101,"\int \frac{\sqrt[4]{-1+x^4}}{x} \, dx","Int[(-1 + x^4)^(1/4)/x,x]","\sqrt[4]{x^4-1}+\frac{\log \left(\sqrt{x^4-1}-\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}-\frac{\log \left(\sqrt{x^4-1}+\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^4-1}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{2 \sqrt{2}}","\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,"(-1 + x^4)^(1/4) + ArcTan[1 - Sqrt[2]*(-1 + x^4)^(1/4)]/(2*Sqrt[2]) - ArcTan[1 + Sqrt[2]*(-1 + x^4)^(1/4)]/(2*Sqrt[2]) + Log[1 - Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(4*Sqrt[2]) - Log[1 + Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(4*Sqrt[2])","A",12,9,13,0.6923,1,"{266, 50, 63, 211, 1165, 628, 1162, 617, 204}"
1162,1,125,0,0.1456563,"\int \frac{\sqrt{-x+x^4}}{-b+a x^3} \, dx","Int[Sqrt[-x + x^4]/(-b + a*x^3),x]","\frac{2 \sqrt{x^4-x} \sqrt{a-b} \tan ^{-1}\left(\frac{x^{3/2} \sqrt{a-b}}{\sqrt{b} \sqrt{x^3-1}}\right)}{3 a \sqrt{b} \sqrt{x} \sqrt{x^3-1}}+\frac{2 \sqrt{x^4-x} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)}{3 a \sqrt{x} \sqrt{x^3-1}}","\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*Sqrt[a - b]*Sqrt[-x + x^4]*ArcTan[(Sqrt[a - b]*x^(3/2))/(Sqrt[b]*Sqrt[-1 + x^3])])/(3*a*Sqrt[b]*Sqrt[x]*Sqrt[-1 + x^3]) + (2*Sqrt[-x + x^4]*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]])/(3*a*Sqrt[x]*Sqrt[-1 + x^3])","A",8,8,23,0.3478,1,"{2056, 466, 465, 402, 217, 206, 377, 205}"
1163,1,131,0,0.1168367,"\int \frac{1}{\left(-1+x^4\right) \sqrt[4]{-x^2+x^4}} \, dx","Int[1/((-1 + x^4)*(-x^2 + x^4)^(1/4)),x]","-\frac{x}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{x^2-1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{x^2-1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \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/(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4))","A",8,8,21,0.3810,1,"{2056, 1254, 466, 382, 377, 212, 206, 203}"
1164,1,365,0,0.699668,"\int \frac{\sqrt[4]{-x^3+x^4}}{-1-2 x+x^2} \, dx","Int[(-x^3 + x^4)^(1/4)/(-1 - 2*x + x^2),x]","\frac{2 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{10+7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{10-7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{10+7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{10-7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}^3}\&\right]-2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-x^3}}\right)",1,"(2*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + ((10 + 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((2 - Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) + ((10 - 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((2 + Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) + (2*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - ((10 + 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((2 - Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) - ((10 - 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((2 + Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4))","B",17,10,24,0.4167,0,"{2056, 905, 63, 240, 212, 206, 203, 6728, 93, 298}"
1165,1,365,0,0.5634803,"\int \frac{\sqrt[4]{-x^3+x^4}}{-1-2 x+x^2} \, dx","Int[(-x^3 + x^4)^(1/4)/(-1 - 2*x + x^2),x]","\frac{2 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{10+7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{10-7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{10+7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{10-7 \sqrt{2}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{2} \sqrt[4]{x-1} x^{3/4}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$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,"(2*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + ((10 + 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((2 - Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) + ((10 - 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((2 + Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) + (2*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - ((10 + 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((2 - Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) - ((10 - 7*Sqrt[2])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((2 + Sqrt[2])^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[2]*(-1 + x)^(1/4)*x^(3/4))","B",17,10,24,0.4167,0,"{2056, 905, 63, 240, 212, 206, 203, 6728, 93, 298}"
1166,1,86,0,0.035791,"\int \frac{x^6}{\left(-b+a x^4\right)^{3/4}} \, dx","Int[x^6/(-b + a*x^4)^(3/4),x]","-\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}","-\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,"(x^3*(-b + a*x^4)^(1/4))/(4*a) - (3*b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(7/4)) + (3*b*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(7/4))","A",5,5,17,0.2941,1,"{321, 331, 298, 203, 206}"
1167,1,93,0,0.0446627,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{b+a x^4}}{x^2} \, dx","Int[((-b + a*x^4)*(b + a*x^4)^(1/4))/x^2,x]","\frac{\left(a x^4+b\right)^{5/4}}{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)-\frac{3}{4} a x^3 \sqrt[4]{a x^4+b}","\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,"(-3*a*x^3*(b + a*x^4)^(1/4))/4 + (b + a*x^4)^(5/4)/x + (3*a^(1/4)*b*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/8 - (3*a^(1/4)*b*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/8","A",6,6,24,0.2500,1,"{453, 279, 331, 298, 203, 206}"
1168,1,153,0,0.47081,"\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","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-4 - 2*x^3 + x^6)),x]","\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{1-\sqrt{5}}\right)}{4 \sqrt{5} \left(1-\sqrt{5}\right) \left(1-x^3\right)^{2/3}}-\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{1+\sqrt{5}}\right)}{4 \sqrt{5} \left(1+\sqrt{5}\right) \left(1-x^3\right)^{2/3}}-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"-1/10*(-1 + x^3)^(5/3)/x^5 + (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/(1 - Sqrt[5])])/(4*Sqrt[5]*(1 - Sqrt[5])*(1 - x^3)^(2/3)) - (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/(1 + Sqrt[5])])/(4*Sqrt[5]*(1 + Sqrt[5])*(1 - x^3)^(2/3))","A",8,5,30,0.1667,0,"{6728, 264, 1428, 430, 429}"
1169,1,153,0,0.4027284,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-4-2 x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-4 - 2*x^3 + x^6)),x]","\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{1-\sqrt{5}}\right)}{4 \sqrt{5} \left(1-\sqrt{5}\right) \left(1-x^3\right)^{2/3}}-\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{1+\sqrt{5}}\right)}{4 \sqrt{5} \left(1+\sqrt{5}\right) \left(1-x^3\right)^{2/3}}-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-5}\&\right]",1,"-1/10*(-1 + x^3)^(5/3)/x^5 + (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/(1 - Sqrt[5])])/(4*Sqrt[5]*(1 - Sqrt[5])*(1 - x^3)^(2/3)) - (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/(1 + Sqrt[5])])/(4*Sqrt[5]*(1 + Sqrt[5])*(1 - x^3)^(2/3))","A",8,5,30,0.1667,0,"{6728, 264, 1428, 430, 429}"
1170,1,159,0,0.4842644,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4-2 x^3+x^6\right)}{x^6 \left(-8+4 x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(4 - 2*x^3 + x^6))/(x^6*(-8 + 4*x^3 + x^6)),x]","\frac{\sqrt{3} x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{2 \left(1-\sqrt{3}\right)}\right)}{16 \left(1-\sqrt{3}\right) \left(1-x^3\right)^{2/3}}-\frac{\sqrt{3} x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{2 \left(1+\sqrt{3}\right)}\right)}{16 \left(1+\sqrt{3}\right) \left(1-x^3\right)^{2/3}}-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[8 \text{$\#$1}^6-12 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-3}\&\right]",1,"-1/10*(-1 + x^3)^(5/3)/x^5 + (Sqrt[3]*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -1/2*x^3/(1 - Sqrt[3])])/(16*(1 - Sqrt[3])*(1 - x^3)^(2/3)) - (Sqrt[3]*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -1/2*x^3/(1 + Sqrt[3])])/(16*(1 + Sqrt[3])*(1 - x^3)^(2/3))","A",8,5,35,0.1429,0,"{6728, 264, 1428, 430, 429}"
1171,1,159,0,0.4036581,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4-2 x^3+x^6\right)}{x^6 \left(-8+4 x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(4 - 2*x^3 + x^6))/(x^6*(-8 + 4*x^3 + x^6)),x]","\frac{\sqrt{3} x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{2 \left(1-\sqrt{3}\right)}\right)}{16 \left(1-\sqrt{3}\right) \left(1-x^3\right)^{2/3}}-\frac{\sqrt{3} x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{2 \left(1+\sqrt{3}\right)}\right)}{16 \left(1+\sqrt{3}\right) \left(1-x^3\right)^{2/3}}-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[8 \text{$\#$1}^6-12 \text{$\#$1}^3+3\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{4 \text{$\#$1}^3-3}\&\right]",1,"-1/10*(-1 + x^3)^(5/3)/x^5 + (Sqrt[3]*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -1/2*x^3/(1 - Sqrt[3])])/(16*(1 - Sqrt[3])*(1 - x^3)^(2/3)) - (Sqrt[3]*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -1/2*x^3/(1 + Sqrt[3])])/(16*(1 + Sqrt[3])*(1 - x^3)^(2/3))","A",8,5,35,0.1429,0,"{6728, 264, 1428, 430, 429}"
1172,1,141,0,0.4809017,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2-2 x^3+x^6\right)}{x^6 \left(-4+4 x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 - 2*x^3 + x^6))/(x^6*(-4 + 4*x^3 + x^6)),x]","-\frac{3 \left(2-\sqrt{2}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{1}{2} \left(1-\sqrt{2}\right) x^3\right)}{32 \left(1-x^3\right)^{2/3}}-\frac{3 \left(2+\sqrt{2}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{1}{2} \left(1+\sqrt{2}\right) x^3\right)}{32 \left(1-x^3\right)^{2/3}}-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-4 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"-1/10*(-1 + x^3)^(5/3)/x^5 - (3*(2 - Sqrt[2])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, ((1 - Sqrt[2])*x^3)/2])/(32*(1 - x^3)^(2/3)) - (3*(2 + Sqrt[2])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, ((1 + Sqrt[2])*x^3)/2])/(32*(1 - x^3)^(2/3))","A",8,5,35,0.1429,0,"{6728, 264, 1428, 430, 429}"
1173,1,141,0,0.4265628,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2-2 x^3+x^6\right)}{x^6 \left(-4+4 x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 - 2*x^3 + x^6))/(x^6*(-4 + 4*x^3 + x^6)),x]","-\frac{3 \left(2-\sqrt{2}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{1}{2} \left(1-\sqrt{2}\right) x^3\right)}{32 \left(1-x^3\right)^{2/3}}-\frac{3 \left(2+\sqrt{2}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{1}{2} \left(1+\sqrt{2}\right) x^3\right)}{32 \left(1-x^3\right)^{2/3}}-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}","\frac{\left(1-x^3\right) \left(x^3-1\right)^{2/3}}{10 x^5}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-4 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{2 \text{$\#$1}^3-1}\&\right]",1,"-1/10*(-1 + x^3)^(5/3)/x^5 - (3*(2 - Sqrt[2])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, ((1 - Sqrt[2])*x^3)/2])/(32*(1 - x^3)^(2/3)) - (3*(2 + Sqrt[2])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, ((1 + Sqrt[2])*x^3)/2])/(32*(1 - x^3)^(2/3))","A",8,5,35,0.1429,0,"{6728, 264, 1428, 430, 429}"
1174,1,171,0,0.2650388,"\int \frac{2+x^4}{\sqrt[4]{-1+x^4} \left(-2+x^8\right)} \, dx","Int[(2 + x^4)/((-1 + x^4)^(1/4)*(-2 + x^8)),x]","-\frac{\sqrt[4]{58-41 \sqrt{2}} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{2}}-\frac{1}{8} \left(2+\sqrt{2}\right)^{5/4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x^4-1}}\right)-\frac{\sqrt[4]{58-41 \sqrt{2}} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2-\sqrt{2}} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{2}}-\frac{1}{8} \left(2+\sqrt{2}\right)^{5/4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{2+\sqrt{2}} \sqrt[4]{x^4-1}}\right)","-\frac{1}{16} \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4+1\&,\frac{-2 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 \log (x)+3 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-3 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]",1,"-1/4*((58 - 41*Sqrt[2])^(1/4)*ArcTan[x/((2 - Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/Sqrt[2] - ((2 + Sqrt[2])^(5/4)*ArcTan[x/((2 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/8 - ((58 - 41*Sqrt[2])^(1/4)*ArcTanh[x/((2 - Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(4*Sqrt[2]) - ((2 + Sqrt[2])^(5/4)*ArcTanh[x/((2 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/8","A",10,5,22,0.2273,0,"{6725, 377, 212, 206, 203}"
1175,1,97,0,0.066762,"\int \frac{-b+a x^8}{x^6 \left(b+a x^4\right)^{3/4}} \, dx","Int[(-b + a*x^8)/(x^6*(b + a*x^4)^(3/4)),x]","-\frac{4 a \sqrt[4]{a x^4+b}}{5 b x}-\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}}{5 x^5}","-\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,"(b + a*x^4)^(1/4)/(5*x^5) - (4*a*(b + a*x^4)^(1/4))/(5*b*x) - (a^(1/4)*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/2 + (a^(1/4)*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/2","A",8,7,24,0.2917,1,"{1489, 271, 264, 331, 298, 203, 206}"
1176,1,123,0,0.1494785,"\int \frac{\sqrt{x}}{(-1+x) \sqrt{-\sqrt{x}+x}} \, dx","Int[Sqrt[x]/((-1 + x)*Sqrt[-Sqrt[x] + x]),x]","-\frac{2 \sqrt{x}}{\sqrt{x-\sqrt{x}}}+\frac{4 \sqrt{\sqrt{x}-1} \sqrt[4]{x} \sinh ^{-1}\left(\sqrt{\sqrt{x}-1}\right)}{\sqrt{x-\sqrt{x}}}-\frac{\sqrt{2} \sqrt{\sqrt{x}-1} \sqrt[4]{x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x}}{\sqrt{\sqrt{x}-1}}\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,"(-2*Sqrt[x])/Sqrt[-Sqrt[x] + x] + (4*Sqrt[-1 + Sqrt[x]]*x^(1/4)*ArcSinh[Sqrt[-1 + Sqrt[x]]])/Sqrt[-Sqrt[x] + x] - (Sqrt[2]*Sqrt[-1 + Sqrt[x]]*x^(1/4)*ArcTanh[(Sqrt[2]*x^(1/4))/Sqrt[-1 + Sqrt[x]]])/Sqrt[-Sqrt[x] + x]","A",9,9,24,0.3750,1,"{2056, 1549, 848, 98, 157, 54, 215, 93, 206}"
1177,1,67,0,0.0423504,"\int \frac{1}{x^3 \left(1+x^2\right)^{2/3}} \, dx","Int[1/(x^3*(1 + x^2)^(2/3)),x]","-\frac{\sqrt[3]{x^2+1}}{2 x^2}-\frac{1}{2} \log \left(1-\sqrt[3]{x^2+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log (x)}{3}","-\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,"-1/2*(1 + x^2)^(1/3)/x^2 + ArcTan[(1 + 2*(1 + x^2)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[x]/3 - Log[1 - (1 + x^2)^(1/3)]/2","A",6,6,13,0.4615,1,"{266, 51, 57, 618, 204, 31}"
1178,1,67,0,0.0384168,"\int \frac{\left(1+x^2\right)^{2/3}}{x^3} \, dx","Int[(1 + x^2)^(2/3)/x^3,x]","-\frac{\left(x^2+1\right)^{2/3}}{2 x^2}+\frac{1}{2} \log \left(1-\sqrt[3]{x^2+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{3}","-\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,"-1/2*(1 + x^2)^(2/3)/x^2 + ArcTan[(1 + 2*(1 + x^2)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/3 + Log[1 - (1 + x^2)^(1/3)]/2","A",6,6,13,0.4615,1,"{266, 47, 55, 618, 204, 31}"
1179,1,67,0,0.0353663,"\int \frac{\left(1+x^2\right)^{2/3}}{x} \, dx","Int[(1 + x^2)^(2/3)/x,x]","\frac{3}{4} \left(x^2+1\right)^{2/3}+\frac{3}{4} \log \left(1-\sqrt[3]{x^2+1}\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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,"(3*(1 + x^2)^(2/3))/4 + (Sqrt[3]*ArcTan[(1 + 2*(1 + x^2)^(1/3))/Sqrt[3]])/2 - Log[x]/2 + (3*Log[1 - (1 + x^2)^(1/3)])/4","A",6,6,13,0.4615,1,"{266, 50, 55, 618, 204, 31}"
1180,0,0,0,3.3817558,"\int \frac{(3+4 x) \sqrt{x+2 x^2-2 x^4}}{(1+2 x) \left(1+2 x+x^3\right)} \, dx","Int[((3 + 4*x)*Sqrt[x + 2*x^2 - 2*x^4])/((1 + 2*x)*(1 + 2*x + x^3)),x]","\int \frac{(3+4 x) \sqrt{x+2 x^2-2 x^4}}{(1+2 x) \left(1+2 x+x^3\right)} \, dx","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,"((4*I)*Sqrt[x + 2*x^2 - 2*x^4]*Defer[Subst][Defer[Int][Sqrt[1 + 2*x^2 - 2*x^6]/(I - Sqrt[2]*x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x - 2*x^3]) + ((4*I)*Sqrt[x + 2*x^2 - 2*x^4]*Defer[Subst][Defer[Int][Sqrt[1 + 2*x^2 - 2*x^6]/(I + Sqrt[2]*x), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x - 2*x^3]) - (8*Sqrt[x + 2*x^2 - 2*x^4]*Defer[Subst][Defer[Int][Sqrt[1 + 2*x^2 - 2*x^6]/(1 + 2*x^2 + x^6), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x - 2*x^3]) + (6*Sqrt[x + 2*x^2 - 2*x^4]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 + 2*x^2 - 2*x^6])/(1 + 2*x^2 + x^6), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x - 2*x^3]) - (4*Sqrt[x + 2*x^2 - 2*x^4]*Defer[Subst][Defer[Int][(x^4*Sqrt[1 + 2*x^2 - 2*x^6])/(1 + 2*x^2 + x^6), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + 2*x - 2*x^3])","F",0,0,0,0,-1,"{}"
1181,1,67,0,0.0376724,"\int \frac{\left(1+x^4\right)^{2/3}}{x} \, dx","Int[(1 + x^4)^(2/3)/x,x]","\frac{3}{8} \left(x^4+1\right)^{2/3}+\frac{3}{8} \log \left(1-\sqrt[3]{x^4+1}\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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,"(3*(1 + x^4)^(2/3))/8 + (Sqrt[3]*ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]])/4 - Log[x]/2 + (3*Log[1 - (1 + x^4)^(1/3)])/8","A",6,6,13,0.4615,1,"{266, 50, 55, 618, 204, 31}"
1182,0,0,0,0.751627,"\int \frac{\sqrt[3]{-1+x^4} \left(3+x^4\right)}{x^2 \left(-1-x^3+x^4\right)} \, dx","Int[((-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,"(3*(-1 + x^4)^(1/3)*Hypergeometric2F1[-1/3, -1/4, 3/4, x^4])/(x*(1 - x^4)^(1/3)) - 3*Defer[Int][(x*(-1 + x^4)^(1/3))/(-1 - x^3 + x^4), x] + 4*Defer[Int][(x^2*(-1 + x^4)^(1/3))/(-1 - x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1183,0,0,0,1.0600136,"\int \frac{x^2 \left(4+x^3\right)}{\left(1+x^3\right)^{3/4} \left(1+x^3+x^4\right)} \, dx","Int[(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,"-(x*Hypergeometric2F1[1/3, 3/4, 4/3, -x^3]) + (x^2*Hypergeometric2F1[2/3, 3/4, 5/3, -x^3])/2 + Defer[Int][1/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x] - Defer[Int][x/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x] + 4*Defer[Int][x^2/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x] + Defer[Int][x^3/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1184,1,87,0,0.0594081,"\int \frac{x^2}{\left(-b+a x^4\right)^{3/4} \left(b+a x^4\right)} \, dx","Int[x^2/((-b + a*x^4)^(3/4)*(b + a*x^4)),x]","\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}","\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,"-1/2*ArcTan[(2^(1/4)*a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2^(3/4)*a^(3/4)*b) + ArcTanh[(2^(1/4)*a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2*2^(3/4)*a^(3/4)*b)","A",4,4,26,0.1538,1,"{494, 298, 203, 206}"
1185,1,87,0,0.0381099,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(b+a x^4\right)} \, dx","Int[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)}{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}","\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)]/(2*2^(1/4)*a^(1/4)*b) + ArcTanh[(2^(1/4)*a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2*2^(1/4)*a^(1/4)*b)","A",4,4,23,0.1739,1,"{377, 212, 206, 203}"
1186,0,0,0,9.9535096,"\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","Int[(-(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]","\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","\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,"(4*a*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(a^2 - 2*a*x^2 + (1 - b^2*d)*x^4 + 2*b*d*x^6 - d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][Sqrt[-a + x^2]/(Sqrt[-b + x^2]*(-a^2 + 2*a*x^2 - (1 - b^2*d)*x^4 - 2*b*d*x^6 + d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(-a^2 + 2*a*x^2 - (1 - b^2*d)*x^4 - 2*b*d*x^6 + d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1187,1,169,0,1.4574113,"\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","Int[(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} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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])/Sqrt[(1 - x^2)*(1 - k^2*x^2)] - (Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)] - (Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",8,4,43,0.09302,1,"{6719, 6725, 419, 537}"
1188,0,0,0,26.0166041,"\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","Int[(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,"(-3*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - k*x^3)^(2/3))/((1 - x^3)^(1/3)*(1 - 4*(1 - c/4)*x^3 + 6*(1 + (-b - c*(2 + k))/6)*x^6 - 4*(1 - c/4 - ((b + c)*k)/2)*x^9 + (1 - k*(c + b*k))*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (3*(1 - 2*k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^7*(1 - k*x^3)^(2/3))/((1 - x^3)^(1/3)*(1 - 4*(1 - c/4)*x^3 + 6*(1 + (-b - c*(2 + k))/6)*x^6 - 4*(1 - c/4 - ((b + c)*k)/2)*x^9 + (1 - k*(c + b*k))*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
1189,1,67,0,0.0393697,"\int \frac{\left(1+x^5\right)^{2/3}}{x} \, dx","Int[(1 + x^5)^(2/3)/x,x]","\frac{3}{10} \left(x^5+1\right)^{2/3}+\frac{3}{10} \log \left(1-\sqrt[3]{x^5+1}\right)+\frac{1}{5} \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^5+1}+1}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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,"(3*(1 + x^5)^(2/3))/10 + (Sqrt[3]*ArcTan[(1 + 2*(1 + x^5)^(1/3))/Sqrt[3]])/5 - Log[x]/2 + (3*Log[1 - (1 + x^5)^(1/3)])/10","A",6,6,13,0.4615,1,"{266, 50, 55, 618, 204, 31}"
1190,1,67,0,0.0340956,"\int \frac{\left(1+x^6\right)^{2/3}}{x} \, dx","Int[(1 + x^6)^(2/3)/x,x]","\frac{1}{4} \left(x^6+1\right)^{2/3}+\frac{1}{4} \log \left(1-\sqrt[3]{x^6+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\log (x)}{2}","\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,"(1 + x^6)^(2/3)/4 + ArcTan[(1 + 2*(1 + x^6)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x]/2 + Log[1 - (1 + x^6)^(1/3)]/4","A",6,6,13,0.4615,1,"{266, 50, 55, 618, 204, 31}"
1191,0,0,0,2.5927407,"\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","Int[((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,"I*Defer[Int][Sqrt[1 - x^2 - x^4 - x^6]/(I - x), x] + Defer[Int][Sqrt[1 - x^2 - x^4 - x^6]/(-1 + x), x]/2 + I*Defer[Int][Sqrt[1 - x^2 - x^4 - x^6]/(I + x), x] - Defer[Int][Sqrt[1 - x^2 - x^4 - x^6]/(1 + x), x]/2 - 2*Defer[Int][(x^2*Sqrt[1 - x^2 - x^4 - x^6])/(-1 + x^4 + x^6), x] - 3*Defer[Int][(x^4*Sqrt[1 - x^2 - x^4 - x^6])/(-1 + x^4 + x^6), x]","F",0,0,0,0,-1,"{}"
1192,0,0,0,0.7946497,"\int \frac{\sqrt[3]{-1+x^8} \left(3+5 x^8\right)}{x^2 \left(-1-x^3+x^8\right)} \, dx","Int[((-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,"(3*(-1 + x^8)^(1/3)*Hypergeometric2F1[-1/3, -1/8, 7/8, x^8])/(x*(1 - x^8)^(1/3)) - 3*Defer[Int][(x*(-1 + x^8)^(1/3))/(-1 - x^3 + x^8), x] + 8*Defer[Int][(x^6*(-1 + x^8)^(1/3))/(-1 - x^3 + x^8), x]","F",0,0,0,0,-1,"{}"
1193,1,77,0,0.0782679,"\int \frac{\left(2+x^8\right) \sqrt{4-2 x^8+x^{16}}}{x^9} \, dx","Int[((2 + x^8)*Sqrt[4 - 2*x^8 + x^16])/x^9,x]","-\frac{1}{8} \sinh ^{-1}\left(\frac{1-x^8}{\sqrt{3}}\right)-\frac{\sqrt{x^{16}-2 x^8+4} \left(2-x^8\right)}{8 x^8}-\frac{1}{8} \tanh ^{-1}\left(\frac{4-x^8}{2 \sqrt{x^{16}-2 x^8+4}}\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,"-1/8*((2 - x^8)*Sqrt[4 - 2*x^8 + x^16])/x^8 - ArcSinh[(1 - x^8)/Sqrt[3]]/8 - ArcTanh[(4 - x^8)/(2*Sqrt[4 - 2*x^8 + x^16])]/8","A",7,7,23,0.3043,1,"{1474, 812, 843, 619, 215, 724, 206}"
1194,1,93,0,0.1544091,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1-\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(1 - Sqrt[1 + x]),x]","-\frac{1}{2} \sqrt{x+\sqrt{x+1}} \left(2 \sqrt{x+1}+5\right)-2 \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \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)","\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,"-1/2*(Sqrt[x + Sqrt[1 + x]]*(5 + 2*Sqrt[1 + x])) - 2*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",7,5,27,0.1852,1,"{814, 843, 621, 206, 724}"
1195,1,81,0,0.0624592,"\int \frac{\sqrt{c+\sqrt{b+a x}}}{d-\sqrt{b+a x}} \, dx","Int[Sqrt[c + Sqrt[b + a*x]]/(d - Sqrt[b + a*x]),x]","-\frac{4 d \sqrt{\sqrt{a x+b}+c}}{a}+\frac{4 d \sqrt{c+d} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a x+b}+c}}{\sqrt{c+d}}\right)}{a}-\frac{4 \left(\sqrt{a x+b}+c\right)^{3/2}}{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*d*Sqrt[c + Sqrt[b + a*x]])/a - (4*(c + Sqrt[b + a*x])^(3/2))/(3*a) + (4*d*Sqrt[c + d]*ArcTanh[Sqrt[c + Sqrt[b + a*x]]/Sqrt[c + d]])/a","A",6,6,31,0.1935,1,"{431, 376, 80, 50, 63, 206}"
1196,0,0,0,0.281512,"\int \left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}} \, dx","Int[(b^2 + a*x^2)*Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\int \left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}} \, dx","\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*a*b^2*x^3)/(3*(b + Sqrt[b^2 + a*x^2])^(3/2)) + (2*b^3*x)/Sqrt[b + Sqrt[b^2 + a*x^2]] + a*Defer[Int][x^2*Sqrt[b + Sqrt[b^2 + a*x^2]], x]","F",0,0,0,0,-1,"{}"
1197,0,0,0,1.0051523,"\int \frac{1}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(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{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}+3}\&\right]-\log \left(\sqrt{x^2+1}+x\right)",1,"Log[-1 - 2*x^3 + x^4]/4 + Defer[Int][x^2/(-1 - 2*x^3 + x^4), x]/2 + Defer[Int][(x*Sqrt[1 + x^2])/(-1 - 2*x^3 + x^4), x] + Defer[Int][(x*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1198,0,0,0,0.7489263,"\int \frac{1}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(x + Sqrt[x + Sqrt[1 + x^2]])^(-1),x]","\int \frac{1}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}+3}\&\right]-\log \left(\sqrt{x^2+1}+x\right)",1,"Log[-1 - 2*x^3 + x^4]/4 + Defer[Int][x^2/(-1 - 2*x^3 + x^4), x]/2 + Defer[Int][(x*Sqrt[1 + x^2])/(-1 - 2*x^3 + x^4), x] + Defer[Int][(x*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1199,1,60,0,0.0515551,"\int \frac{1}{(-2+x) \sqrt[3]{-4-4 x+x^2}} \, dx","Int[1/((-2 + x)*(-4 - 4*x + x^2)^(1/3)),x]","-\frac{3}{8} \log \left(\sqrt[3]{(x-2)^2-8}+2\right)+\frac{1}{4} \log (2-x)-\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1-\sqrt[3]{(x-2)^2-8}}{\sqrt{3}}\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,"-1/4*(Sqrt[3]*ArcTan[(1 - (-8 + (-2 + x)^2)^(1/3))/Sqrt[3]]) - (3*Log[2 + (-8 + (-2 + x)^2)^(1/3)])/8 + Log[2 - x]/4","A",6,6,18,0.3333,1,"{694, 266, 56, 618, 204, 31}"
1200,1,253,0,6.8304361,"\int \frac{-1+k x^2}{(a+b x) \sqrt{(1-x) x (1-k x)} (b+a k x)} \, dx","Int[(-1 + k*x^2)/((a + b*x)*Sqrt[(1 - x)*x*(1 - k*x)]*(b + a*k*x)),x]","\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k x} \Pi \left(-\frac{a}{b};\sin ^{-1}\left(\sqrt{-k} \sqrt{-x}\right)|\frac{1}{k}\right)}{a b \sqrt{-k} \sqrt{x-x^2} \sqrt{(1-x) x (1-k x)}}+\frac{2 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k x} \Pi \left(-\frac{b}{a k};\sin ^{-1}\left(\sqrt{-k} \sqrt{-x}\right)|\frac{1}{k}\right)}{a b \sqrt{-k} \sqrt{x-x^2} \sqrt{(1-x) x (1-k x)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k x} F\left(\left.\sin ^{-1}\left(\sqrt{x}\right)\right|k\right)}{a b \sqrt{(1-x) x (1-k x)}}","-\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*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k*x]*EllipticF[ArcSin[Sqrt[x]], k])/(a*b*Sqrt[(1 - x)*x*(1 - k*x)]) + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k*x]*EllipticPi[-(a/b), ArcSin[Sqrt[-k]*Sqrt[-x]], k^(-1)])/(a*b*Sqrt[-k]*Sqrt[(1 - x)*x*(1 - k*x)]*Sqrt[x - x^2]) + (2*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k*x]*EllipticPi[-(b/(a*k)), ArcSin[Sqrt[-k]*Sqrt[-x]], k^(-1)])/(a*b*Sqrt[-k]*Sqrt[(1 - x)*x*(1 - k*x)]*Sqrt[x - x^2])","C",14,9,40,0.2250,0,"{6718, 6688, 6742, 714, 115, 934, 12, 168, 537}"
1201,0,0,0,16.930934,"\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","Int[(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]","\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","\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,"(4*a*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-b + x^2])/(Sqrt[-a + x^2]*(a^2 - 2*a*x^2 + (1 - b^2*d)*x^4 + 2*b*d*x^6 - d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-b + x^2])/(Sqrt[-a + x^2]*(-a^2 + 2*a*x^2 - (1 - b^2*d)*x^4 - 2*b*d*x^6 + d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^6*Sqrt[-b + x^2])/(Sqrt[-a + x^2]*(-a^2 + 2*a*x^2 - (1 - b^2*d)*x^4 - 2*b*d*x^6 + d*x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1202,1,305,0,1.1571271,"\int \frac{1+x^4}{\left(-1-x^2+x^4\right) \sqrt[3]{-x+x^5}} \, dx","Int[(1 + x^4)/((-1 - x^2 + x^4)*(-x + x^5)^(1/3)),x]","-\frac{3 \sqrt[3]{1-x^4} x F_1\left(\frac{1}{6};\frac{1}{3},1;\frac{7}{6};x^4,\frac{2 x^4}{3-\sqrt{5}}\right)}{2 \sqrt[3]{x^5-x}}-\frac{3 \sqrt[3]{1-x^4} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};\frac{2 x^4}{3+\sqrt{5}},x^4\right)}{2 \sqrt[3]{x^5-x}}-\frac{3 \left(1-\sqrt{5}\right) \sqrt[3]{1-x^4} x^3 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^4,\frac{2 x^4}{3-\sqrt{5}}\right)}{8 \left(3-\sqrt{5}\right) \sqrt[3]{x^5-x}}-\frac{3 \left(1+\sqrt{5}\right) \sqrt[3]{1-x^4} x^3 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^4,\frac{2 x^4}{3+\sqrt{5}}\right)}{8 \left(3+\sqrt{5}\right) \sqrt[3]{x^5-x}}+\frac{3 \sqrt[3]{1-x^4} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};x^4\right)}{2 \sqrt[3]{x^5-x}}","\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,"(-3*x*(1 - x^4)^(1/3)*AppellF1[1/6, 1/3, 1, 7/6, x^4, (2*x^4)/(3 - Sqrt[5])])/(2*(-x + x^5)^(1/3)) - (3*x*(1 - x^4)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (2*x^4)/(3 + Sqrt[5]), x^4])/(2*(-x + x^5)^(1/3)) - (3*(1 - Sqrt[5])*x^3*(1 - x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, x^4, (2*x^4)/(3 - Sqrt[5])])/(8*(3 - Sqrt[5])*(-x + x^5)^(1/3)) - (3*(1 + Sqrt[5])*x^3*(1 - x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, x^4, (2*x^4)/(3 + Sqrt[5])])/(8*(3 + Sqrt[5])*(-x + x^5)^(1/3)) + (3*x*(1 - x^4)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^4])/(2*(-x + x^5)^(1/3))","C",22,11,29,0.3793,0,"{2056, 6715, 6728, 246, 245, 1438, 430, 429, 465, 511, 510}"
1203,1,87,0,0.0649923,"\int \frac{x^3}{\left(-1+x^6\right)^{2/3}} \, dx","Int[x^3/(-1 + x^6)^(2/3),x]","-\frac{1}{6} \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\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,"-1/2*ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 - x^2/(-1 + x^6)^(1/3)]/6 + Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)]/12","A",8,8,13,0.6154,1,"{275, 331, 292, 31, 634, 618, 204, 628}"
1204,1,53,0,0.0189933,"\int \frac{x}{\sqrt[3]{-1+x^6}} \, dx","Int[x/(-1 + x^6)^(1/3),x]","\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{4} \log \left(x^2-\sqrt[3]{x^6-1}\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,"ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x^2 - (-1 + x^6)^(1/3)]/4","A",2,2,11,0.1818,1,"{275, 239}"
1205,1,87,0,0.0639577,"\int \frac{x^3}{\left(1+x^6\right)^{2/3}} \, dx","Int[x^3/(1 + x^6)^(2/3),x]","-\frac{1}{6} \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\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,"-1/2*ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 - x^2/(1 + x^6)^(1/3)]/6 + Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)]/12","A",8,8,13,0.6154,1,"{275, 331, 292, 31, 634, 618, 204, 628}"
1206,1,53,0,0.019014,"\int \frac{x}{\sqrt[3]{1+x^6}} \, dx","Int[x/(1 + x^6)^(1/3),x]","\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{4} \log \left(x^2-\sqrt[3]{x^6+1}\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,"ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x^2 - (1 + x^6)^(1/3)]/4","A",2,2,11,0.1818,1,"{275, 239}"
1207,1,101,0,0.0595832,"\int \frac{-b+a x^8}{x^2 \left(-b+a x^4\right)^{3/4}} \, dx","Int[(-b + a*x^8)/(x^2*(-b + a*x^4)^(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{\sqrt[4]{a x^4-b}}{x}+\frac{1}{4} x^3 \sqrt[4]{a x^4-b}","-\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,"-((-b + a*x^4)^(1/4)/x) + (x^3*(-b + a*x^4)^(1/4))/4 - (3*b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(3/4)) + (3*b*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(3/4))","A",6,6,26,0.2308,1,"{1487, 451, 331, 298, 203, 206}"
1208,1,99,0,0.06091,"\int \frac{-3 b+2 a x^8}{x^8 \sqrt[4]{-b+a x^4}} \, dx","Int[(-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{3 \left(a x^4-b\right)^{3/4}}{7 x^7}-\frac{4 a \left(a x^4-b\right)^{3/4}}{7 b x^3}","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,"(-3*(-b + a*x^4)^(3/4))/(7*x^7) - (4*a*(-b + a*x^4)^(3/4))/(7*b*x^3) + 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",8,7,27,0.2593,1,"{1489, 240, 212, 206, 203, 271, 264}"
1209,1,226,0,0.8373442,"\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","Int[(-b^2 + a^2*x^8)/(x^2*(b + a*x^4)^(3/4)*(b^2 + a^2*x^8)),x]","\frac{a x^3 \sqrt[4]{a x^4+b} F_1\left(\frac{3}{4};1,-\frac{5}{4};\frac{7}{4};-\frac{\sqrt{-a^2} x^4}{b},-\frac{a x^4}{b}\right)}{6 b^2 \sqrt[4]{\frac{a x^4}{b}+1}}+\frac{a x^3 \sqrt[4]{a x^4+b} F_1\left(\frac{3}{4};1,-\frac{5}{4};\frac{7}{4};\frac{\sqrt{-a^2} x^4}{b},-\frac{a x^4}{b}\right)}{6 b^2 \sqrt[4]{\frac{a x^4}{b}+1}}+\frac{\sqrt[4]{a x^4+b}}{b x}+\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 b}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 b}","\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,"(b + a*x^4)^(1/4)/(b*x) + (a*x^3*(b + a*x^4)^(1/4)*AppellF1[3/4, 1, -5/4, 7/4, -((Sqrt[-a^2]*x^4)/b), -((a*x^4)/b)])/(6*b^2*(1 + (a*x^4)/b)^(1/4)) + (a*x^3*(b + a*x^4)^(1/4)*AppellF1[3/4, 1, -5/4, 7/4, (Sqrt[-a^2]*x^4)/b, -((a*x^4)/b)])/(6*b^2*(1 + (a*x^4)/b)^(1/4)) + (a^(1/4)*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(2*b) - (a^(1/4)*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(2*b)","B",14,10,41,0.2439,0,"{1586, 6725, 277, 331, 298, 203, 206, 1529, 511, 510}"
1210,1,46,0,0.6439173,"\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","Int[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} b \sinh ^{-1}\left(\frac{b \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x}{\sqrt{a}}\right)}{\sqrt{a}}","-\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]*b*ArcSinh[(a*x + b*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])/Sqrt[a]])/Sqrt[a]","A",2,2,59,0.03390,1,"{2130, 215}"
1211,1,65,0,0.042443,"\int \frac{\left(-1+x^2\right)^{2/3}}{x} \, dx","Int[(-1 + x^2)^(2/3)/x,x]","\frac{3}{4} \left(x^2-1\right)^{2/3}+\frac{3}{4} \log \left(\sqrt[3]{x^2-1}+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^2-1}}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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))/4 + (Sqrt[3]*ArcTan[(1 - 2*(-1 + x^2)^(1/3))/Sqrt[3]])/2 - Log[x]/2 + (3*Log[1 + (-1 + x^2)^(1/3)])/4","A",6,6,13,0.4615,1,"{266, 50, 56, 618, 204, 31}"
1212,0,0,0,0.0094175,"\int \frac{-3+x}{\sqrt[3]{-1+x^2} \left(2+x+x^2\right)} \, dx","Int[(-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,"Defer[Int][(-3 + x)/((-1 + x^2)^(1/3)*(2 + x + x^2)), x]","F",0,0,0,0,-1,"{}"
1213,1,433,0,0.9380224,"\int \frac{2+x^2}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(2 + x^2)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{x^3-1}}\right)}{3^{3/4}}+\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{3^{3/4}}-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt{2 \left(7-4 \sqrt{3}\right)} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \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,"(Sqrt[2]*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/3^(3/4) + (Sqrt[2]*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/3^(3/4) + (Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (Sqrt[2*(7 - 4*Sqrt[3])]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","C",13,6,25,0.2400,0,"{6728, 219, 2135, 2140, 206, 203}"
1214,1,75,0,0.0484371,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x} \, dx","Int[((-1 + x^3)*(1 + x^3)^(1/3))/x,x]","\frac{1}{4} \left(x^3+1\right)^{4/3}-\sqrt[3]{x^3+1}-\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}{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,"-(1 + x^3)^(1/3) + (1 + x^3)^(4/3)/4 + ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[x]/2 - Log[1 - (1 + x^3)^(1/3)]/2","A",7,7,18,0.3889,1,"{446, 80, 50, 57, 618, 204, 31}"
1215,0,0,0,13.1635606,"\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","Int[(-(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,"(4*a*b*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((-a + x^4)^(1/4)*(-b + x^4)^(1/4)*(a^3 - 3*a^2*(1 + (b*d)/(3*a^2))*x^4 + 3*a*(1 + d/(3*a))*x^8 - x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(1/4) - (8*(a - b)*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^6/((-a + x^4)^(1/4)*(-b + x^4)^(1/4)*(a^3 - 3*a^2*(1 + (b*d)/(3*a^2))*x^4 + 3*a*(1 + d/(3*a))*x^8 - x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(1/4) + (4*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^10/((-a + x^4)^(1/4)*(-b + x^4)^(1/4)*(-a^3 + 3*a^2*(1 + (b*d)/(3*a^2))*x^4 - 3*a*(1 + d/(3*a))*x^8 + x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(1/4)","F",0,0,0,0,-1,"{}"
1216,0,0,0,13.0542676,"\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","Int[((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,"(4*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(1 - x^4)^(5/4)/((1 - k*x^4)^(3/4)*(-x^4 + k*x^8 - d*(-1 + x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4) + (8*(1 - k)*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^4*(1 - x^4)^(5/4))/((1 - k*x^4)^(3/4)*(-x^4 + k*x^8 - d*(-1 + x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4) + (4*k*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(1 - x^4)^(5/4))/((1 - k*x^4)^(3/4)*(x^4 - k*x^8 + d*(-1 + x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4)","F",0,0,0,0,-1,"{}"
1217,1,541,0,2.3861643,"\int \frac{x^2}{\sqrt{x+x^2+x^3} \left(-1+x^4\right)} \, dx","Int[x^2/(Sqrt[x + x^2 + x^3]*(-1 + x^4)),x]","\frac{\sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-i-\sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{\sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(1-i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{\sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-1+i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}+\frac{\sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}","-\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,"(Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-I - Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(1 - I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-1 + I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) + (Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(I + Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3])","C",59,11,23,0.4783,0,"{2056, 6725, 957, 716, 1103, 934, 169, 538, 537, 1139, 1195}"
1218,1,155,0,3.1290965,"\int \frac{\sqrt{x+x^2+x^3}}{-1+x^4} \, dx","Int[Sqrt[x + x^2 + x^3]/(-1 + x^4),x]","\frac{\sqrt{x^3+x^2+x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+x+1}}\right)}{4 \sqrt{x} \sqrt{x^2+x+1}}+\frac{\sqrt{x^3+x^2+x} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x^2+x+1}}\right)}{2 \sqrt{x} \sqrt{x^2+x+1}}-\frac{\sqrt{3} \sqrt{x^3+x^2+x} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x}}{\sqrt{x^2+x+1}}\right)}{4 \sqrt{x} \sqrt{x^2+x+1}}","\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,"(Sqrt[x + x^2 + x^3]*ArcTan[Sqrt[x]/Sqrt[1 + x + x^2]])/(4*Sqrt[x]*Sqrt[1 + x + x^2]) + (Sqrt[x + x^2 + x^3]*ArcTanh[Sqrt[x]/Sqrt[1 + x + x^2]])/(2*Sqrt[x]*Sqrt[1 + x + x^2]) - (Sqrt[3]*Sqrt[x + x^2 + x^3]*ArcTanh[(Sqrt[3]*Sqrt[x])/Sqrt[1 + x + x^2]])/(4*Sqrt[x]*Sqrt[1 + x + x^2])","A",41,18,20,0.9000,1,"{2056, 6725, 918, 27, 6733, 1712, 1197, 1103, 1195, 1700, 1698, 206, 12, 1210, 203, 1714, 1708, 1706}"
1219,1,65,0,0.04046,"\int \frac{\left(-1+x^4\right)^{2/3}}{x} \, dx","Int[(-1 + x^4)^(2/3)/x,x]","\frac{3}{8} \left(x^4-1\right)^{2/3}+\frac{3}{8} \log \left(\sqrt[3]{x^4-1}+1\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^4-1}}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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))/8 + (Sqrt[3]*ArcTan[(1 - 2*(-1 + x^4)^(1/3))/Sqrt[3]])/4 - Log[x]/2 + (3*Log[1 + (-1 + x^4)^(1/3)])/8","A",6,6,13,0.4615,1,"{266, 50, 56, 618, 204, 31}"
1220,1,592,0,2.2281561,"\int \frac{1-x^2+x^4}{\sqrt{x+x^2+x^3} \left(-1+x^4\right)} \, dx","Int[(1 - x^2 + x^4)/(Sqrt[x + x^2 + x^3]*(-1 + x^4)),x]","\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+x+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{4}\right)}{\sqrt{x^3+x^2+x}}-\frac{3 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-i-\sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{\sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(1-i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{\sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-1+i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}-\frac{3 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(i+\sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{\left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}","-\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,"(Sqrt[x]*(1 + x)*Sqrt[(1 + x + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/4])/Sqrt[x + x^2 + x^3] - (3*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-I - Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(1 - I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-1 + I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) - (3*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(I + Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/((1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3])","C",31,8,30,0.2667,0,"{2056, 6725, 716, 1103, 934, 169, 538, 537}"
1221,0,0,0,0.6229824,"\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt{1-x+x^2-x^3+x^4}} \, dx","Int[(1 - x + x^2)/((-1 + x^2)*Sqrt[1 - x + x^2 - x^3 + x^4]),x]","\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt{1-x+x^2-x^3+x^4}} \, dx","\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,"Defer[Int][1/Sqrt[1 - x + x^2 - x^3 + x^4], x] - Defer[Int][1/((1 - x)*Sqrt[1 - x + x^2 - x^3 + x^4]), x]/2 - (3*Defer[Int][1/((1 + x)*Sqrt[1 - x + x^2 - x^3 + x^4]), x])/2","F",0,0,0,0,-1,"{}"
1222,0,0,0,11.5361347,"\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","Int[((-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]","\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","\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/(3*Sqrt[(1 - 2*x)/(1 + 2*x^2)]) + (4*(1 - 2*x))/(3*(1 + Sqrt[3] - 2*x)*Sqrt[(1 - 2*x)/(1 + 2*x^2)]) - (2 - x)/(3*Sqrt[(1 - 2*x)/(1 + 2*x^2)]) + ((I/3)*Sqrt[2]*(1 - 2*x)*EllipticE[ArcSin[Sqrt[1 - I*Sqrt[2]*x]/Sqrt[2]], (-2*Sqrt[2])/(I - Sqrt[2])])/(Sqrt[(1 - 2*x)/(1 + I*Sqrt[2])]*Sqrt[(1 - 2*x)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) - (2*Sqrt[2]*Sqrt[1 - 2*x]*(1 + Sqrt[3] - 2*x)*Sqrt[(1 + 2*x^2)/(1 + Sqrt[3] - 2*x)^2]*EllipticE[2*ArcTan[Sqrt[1 - 2*x]/3^(1/4)], (3 + Sqrt[3])/6])/(3^(3/4)*Sqrt[(1 - 2*x)/(1 + 2*x^2)]*(1 + 2*x^2)) - (Sqrt[2]*(1 - Sqrt[3])*Sqrt[1 - 2*x]*(1 + Sqrt[3] - 2*x)*Sqrt[(1 + 2*x^2)/(1 + Sqrt[3] - 2*x)^2]*EllipticF[2*ArcTan[Sqrt[1 - 2*x]/3^(1/4)], (3 + Sqrt[3])/6])/(3*3^(1/4)*Sqrt[(1 - 2*x)/(1 + 2*x^2)]*(1 + 2*x^2)) + (8*Sqrt[2]*Sqrt[1 - 2*x]*Defer[Subst][Defer[Int][Sqrt[3 - 2*x^2 + x^4]/(3 - 20*x^2 + x^8), x], x, Sqrt[1 - 2*x]])/(3*Sqrt[(1 - 2*x)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) - (5*Sqrt[2]*Sqrt[1 - 2*x]*Defer[Subst][Defer[Int][(x^2*Sqrt[3 - 2*x^2 + x^4])/(3 - 20*x^2 + x^8), x], x, Sqrt[1 - 2*x]])/(Sqrt[(1 - 2*x)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) - (Sqrt[2]*Sqrt[1 - 2*x]*Defer[Subst][Defer[Int][(x^6*Sqrt[3 - 2*x^2 + x^4])/(3 - 20*x^2 + x^8), x], x, Sqrt[1 - 2*x]])/(3*Sqrt[(1 - 2*x)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2])","F",0,0,0,0,-1,"{}"
1223,1,65,0,0.0458494,"\int \frac{\left(-1+x^5\right)^{2/3}}{x} \, dx","Int[(-1 + x^5)^(2/3)/x,x]","\frac{3}{10} \left(x^5-1\right)^{2/3}+\frac{3}{10} \log \left(\sqrt[3]{x^5-1}+1\right)+\frac{1}{5} \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^5-1}}{\sqrt{3}}\right)-\frac{\log (x)}{2}","\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))/10 + (Sqrt[3]*ArcTan[(1 - 2*(-1 + x^5)^(1/3))/Sqrt[3]])/5 - Log[x]/2 + (3*Log[1 + (-1 + x^5)^(1/3)])/10","A",6,6,13,0.4615,1,"{266, 50, 56, 618, 204, 31}"
1224,1,65,0,0.0350786,"\int \frac{\left(-1+x^6\right)^{2/3}}{x} \, dx","Int[(-1 + x^6)^(2/3)/x,x]","\frac{1}{4} \left(x^6-1\right)^{2/3}+\frac{1}{4} \log \left(\sqrt[3]{x^6-1}+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\log (x)}{2}","\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 + x^6)^(2/3)/4 + ArcTan[(1 - 2*(-1 + x^6)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x]/2 + Log[1 + (-1 + x^6)^(1/3)]/4","A",6,6,13,0.4615,1,"{266, 50, 56, 618, 204, 31}"
1225,0,0,0,0.037538,"\int \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Int[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,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
1226,1,66,0,0.0379095,"\int \frac{\left(-1+x^2\right)^{2/3}}{x^3} \, dx","Int[(-1 + x^2)^(2/3)/x^3,x]","-\frac{\left(x^2-1\right)^{2/3}}{2 x^2}-\frac{1}{2} \log \left(\sqrt[3]{x^2-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^2-1}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log (x)}{3}","-\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,"-1/2*(-1 + x^2)^(2/3)/x^2 - ArcTan[(1 - 2*(-1 + x^2)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[x]/3 - Log[1 + (-1 + x^2)^(1/3)]/2","A",6,6,13,0.4615,1,"{266, 47, 56, 618, 204, 31}"
1227,1,138,0,0.1254177,"\int \frac{-2+x+x^2}{x^2 \left(-1+x^2\right)^{3/4}} \, dx","Int[(-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",12,9,19,0.4737,1,"{1807, 266, 63, 211, 1165, 628, 1162, 617, 204}"
1228,1,70,0,0.0412133,"\int \frac{\sqrt[3]{1+x^3}}{x^4} \, dx","Int[(1 + x^3)^(1/3)/x^4,x]","-\frac{\sqrt[3]{x^3+1}}{3 x^3}+\frac{1}{6} \log \left(1-\sqrt[3]{x^3+1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\log (x)}{6}","-\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,"-1/3*(1 + x^3)^(1/3)/x^3 - ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[x]/6 + Log[1 - (1 + x^3)^(1/3)]/6","A",6,6,13,0.4615,1,"{266, 47, 57, 618, 204, 31}"
1229,1,70,0,0.0383016,"\int \frac{\left(1+x^3\right)^{2/3}}{x^4} \, dx","Int[(1 + x^3)^(2/3)/x^4,x]","-\frac{\left(x^3+1\right)^{2/3}}{3 x^3}+\frac{1}{3} \log \left(1-\sqrt[3]{x^3+1}\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\log (x)}{3}","-\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,"-1/3*(1 + x^3)^(2/3)/x^3 + (2*ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) - Log[x]/3 + Log[1 - (1 + x^3)^(1/3)]/3","A",6,6,13,0.4615,1,"{266, 47, 55, 618, 204, 31}"
1230,0,0,0,5.8457245,"\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","Int[(-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,"(2*k*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x^2/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4) + (2*k*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][1/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4) - ((1 - k^2)*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4)","F",0,0,0,0,-1,"{}"
1231,0,0,0,5.8149725,"\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","Int[(-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,"-(((1 - k)*(1 + k)*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4)) + (2*k*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][x^2/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4) + (2*k*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Int][1/((1 - x^2)^(1/4)*(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])/((1 - x^2)*(1 - k^2*x^2))^(1/4)","F",0,0,0,0,-1,"{}"
1232,1,59,0,0.0639306,"\int \frac{\left(1+x^2\right) \sqrt{1-2 x^4}}{x^5} \, dx","Int[((1 + x^2)*Sqrt[1 - 2*x^4])/x^5,x]","\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-2 x^4}\right)-\frac{\sin ^{-1}\left(\sqrt{2} x^2\right)}{\sqrt{2}}-\frac{\sqrt{1-2 x^4} \left(2 x^2+1\right)}{4 x^4}","\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,"-1/4*((1 + 2*x^2)*Sqrt[1 - 2*x^4])/x^4 - ArcSin[Sqrt[2]*x^2]/Sqrt[2] + ArcTanh[Sqrt[1 - 2*x^4]]/2","A",7,7,20,0.3500,1,"{1252, 811, 844, 216, 266, 63, 206}"
1233,1,70,0,0.0485856,"\int \frac{\left(1+x^4\right)^{2/3}}{x^5} \, dx","Int[(1 + x^4)^(2/3)/x^5,x]","-\frac{\left(x^4+1\right)^{2/3}}{4 x^4}+\frac{1}{4} \log \left(1-\sqrt[3]{x^4+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\log (x)}{3}","-\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,"-1/4*(1 + x^4)^(2/3)/x^4 + ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x]/3 + Log[1 - (1 + x^4)^(1/3)]/4","A",6,6,13,0.4615,1,"{266, 47, 55, 618, 204, 31}"
1234,0,0,0,1.101226,"\int \frac{\left(-3+x^4\right) \left(1+x^4\right)^{2/3}}{x^3 \left(1-x^3+x^4\right)} \, dx","Int[((-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,"(3*(1 + x^4)^(2/3))/(2*x^2) + (6*x^2)/(1 - Sqrt[3] - (1 + x^4)^(1/3)) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (2*Sqrt[2]*3^(3/4)*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) - 3*Defer[Int][(1 + x^4)^(2/3)/(1 - x^3 + x^4), x] + 4*Defer[Int][(x*(1 + x^4)^(2/3))/(1 - x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1235,0,0,0,0.7779054,"\int \frac{\sqrt[3]{-1+x^4} \left(3+x^4\right)}{x^2 \left(-1+x^3+x^4\right)} \, dx","Int[((-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,"(3*(-1 + x^4)^(1/3)*Hypergeometric2F1[-1/3, -1/4, 3/4, x^4])/(x*(1 - x^4)^(1/3)) + 3*Defer[Int][(x*(-1 + x^4)^(1/3))/(-1 + x^3 + x^4), x] + 4*Defer[Int][(x^2*(-1 + x^4)^(1/3))/(-1 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1236,0,0,0,1.0076099,"\int \frac{\left(-1+x^4\right)^{2/3} \left(3+x^4\right)}{x^3 \left(-1+x^3+x^4\right)} \, dx","Int[((-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,"(3*(-1 + x^4)^(2/3))/(2*x^2) - (6*x^2)/(1 + Sqrt[3] + (-1 + x^4)^(1/3)) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) - (2*Sqrt[2]*3^(3/4)*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) + 3*Defer[Int][(-1 + x^4)^(2/3)/(-1 + x^3 + x^4), x] + 4*Defer[Int][(x*(-1 + x^4)^(2/3))/(-1 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1237,0,0,0,0.7421833,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^2 \left(1+x^3+x^4\right)} \, dx","Int[((-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,"(3*Hypergeometric2F1[-1/3, -1/4, 3/4, -x^4])/x + 3*Defer[Int][(x*(1 + x^4)^(1/3))/(1 + x^3 + x^4), x] + 4*Defer[Int][(x^2*(1 + x^4)^(1/3))/(1 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1238,0,0,0,1.7074777,"\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","Int[((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,"-4*Defer[Int][(-1 - x + 2*x^4)^(1/4)/x^6, x] - 3*Defer[Int][(-1 - x + 2*x^4)^(1/4)/x^5, x] + 8*Defer[Int][(-1 - x + 2*x^4)^(1/4)/x^2, x] - 2*Defer[Int][(-1 - x + 2*x^4)^(1/4)/x, x] + 2*Defer[Int][(-1 - x + 2*x^4)^(1/4)/(1 + x + x^4), x] - 8*Defer[Int][(x^2*(-1 - x + 2*x^4)^(1/4))/(1 + x + x^4), x] + 2*Defer[Int][(x^3*(-1 - x + 2*x^4)^(1/4))/(1 + x + x^4), x]","F",0,0,0,0,-1,"{}"
1239,1,77,0,0.0321793,"\int \frac{\sqrt{1+3 x^4}}{-1+3 x^4} \, dx","Int[Sqrt[1 + 3*x^4]/(-1 + 3*x^4),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{3} x}{\sqrt{3 x^4+1}}\right)}{2 \sqrt{2} \sqrt[4]{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{3} x}{\sqrt{3 x^4+1}}\right)}{2 \sqrt{2} \sqrt[4]{3}}","-\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,"-1/2*ArcTan[(Sqrt[2]*3^(1/4)*x)/Sqrt[1 + 3*x^4]]/(Sqrt[2]*3^(1/4)) - ArcTanh[(Sqrt[2]*3^(1/4)*x)/Sqrt[1 + 3*x^4]]/(2*Sqrt[2]*3^(1/4))","A",4,4,21,0.1905,1,"{404, 212, 206, 203}"
1240,1,160,0,0.2355561,"\int \frac{\left(b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{-b+a x^2} \, dx","Int[((b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(-b + a*x^2),x]","-\frac{7 b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b}}+\frac{7 b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b}}+\frac{1}{2} x \sqrt[4]{a x^4-b x^2}","-\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,"(x*(-(b*x^2) + a*x^4)^(1/4))/2 - (7*b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)) + (7*b*(-(b*x^2) + a*x^4)^(1/4)*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",7,7,35,0.2000,1,"{2056, 459, 329, 331, 298, 203, 206}"
1241,1,141,0,0.2080954,"\int \frac{-b+2 a x^2}{\left(b+a x^2\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + 2*a*x^2)/((b + a*x^2)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{6 x}{\sqrt[4]{a x^4+b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}","-\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,"(-6*x)/(b*x^2 + a*x^4)^(1/4) + (2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) + (2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4))","A",7,7,35,0.2000,1,"{2056, 452, 329, 240, 212, 206, 203}"
1242,1,70,0,0.0453738,"\int \frac{\left(1+x^5\right)^{2/3}}{x^6} \, dx","Int[(1 + x^5)^(2/3)/x^6,x]","-\frac{\left(x^5+1\right)^{2/3}}{5 x^5}+\frac{1}{5} \log \left(1-\sqrt[3]{x^5+1}\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^5+1}+1}{\sqrt{3}}\right)}{5 \sqrt{3}}-\frac{\log (x)}{3}","-\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,"-1/5*(1 + x^5)^(2/3)/x^5 + (2*ArcTan[(1 + 2*(1 + x^5)^(1/3))/Sqrt[3]])/(5*Sqrt[3]) - Log[x]/3 + Log[1 - (1 + x^5)^(1/3)]/5","A",6,6,13,0.4615,1,"{266, 47, 55, 618, 204, 31}"
1243,0,0,0,0.7629088,"\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","Int[((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,"(3*Hypergeometric2F1[-2/3, -2/5, 3/5, -x^5])/(2*x^2) - 3*Defer[Int][(1 + x^5)^(2/3)/(1 - x^3 + x^5), x] + 5*Defer[Int][(x^2*(1 + x^5)^(2/3))/(1 - x^3 + x^5), x]","F",0,0,0,0,-1,"{}"
1244,0,0,0,0.7873533,"\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","Int[((-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,"(3*(-1 + x^5)^(2/3)*Hypergeometric2F1[-2/3, -2/5, 3/5, x^5])/(2*x^2*(1 - x^5)^(2/3)) - 3*Defer[Int][(-1 + x^5)^(2/3)/(-1 - x^3 + x^5), x] + 5*Defer[Int][(x^2*(-1 + x^5)^(2/3))/(-1 - x^3 + x^5), x]","F",0,0,0,0,-1,"{}"
1245,1,142,0,0.1059035,"\int \frac{\sqrt[4]{-1+x^6}}{x} \, dx","Int[(-1 + x^6)^(1/4)/x,x]","\frac{2}{3} \sqrt[4]{x^6-1}+\frac{\log \left(\sqrt{x^6-1}-\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{6 \sqrt{2}}-\frac{\log \left(\sqrt{x^6-1}+\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{6 \sqrt{2}}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^6-1}\right)}{3 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{3 \sqrt{2}}","\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,"(2*(-1 + x^6)^(1/4))/3 + ArcTan[1 - Sqrt[2]*(-1 + x^6)^(1/4)]/(3*Sqrt[2]) - ArcTan[1 + Sqrt[2]*(-1 + x^6)^(1/4)]/(3*Sqrt[2]) + Log[1 - Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]]/(6*Sqrt[2]) - Log[1 + Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]]/(6*Sqrt[2])","A",12,9,13,0.6923,1,"{266, 50, 63, 211, 1165, 628, 1162, 617, 204}"
1246,1,70,0,0.0434769,"\int \frac{1}{x^7 \sqrt[3]{1+x^6}} \, dx","Int[1/(x^7*(1 + x^6)^(1/3)),x]","-\frac{\left(x^6+1\right)^{2/3}}{6 x^6}-\frac{1}{12} \log \left(1-\sqrt[3]{x^6+1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{\log (x)}{6}","-\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,"-1/6*(1 + x^6)^(2/3)/x^6 - ArcTan[(1 + 2*(1 + x^6)^(1/3))/Sqrt[3]]/(6*Sqrt[3]) + Log[x]/6 - Log[1 - (1 + x^6)^(1/3)]/12","A",6,6,13,0.4615,1,"{266, 51, 55, 618, 204, 31}"
1247,1,70,0,0.0392198,"\int \frac{\left(1+x^6\right)^{2/3}}{x^7} \, dx","Int[(1 + x^6)^(2/3)/x^7,x]","-\frac{\left(x^6+1\right)^{2/3}}{6 x^6}+\frac{1}{6} \log \left(1-\sqrt[3]{x^6+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\log (x)}{3}","-\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,"-1/6*(1 + x^6)^(2/3)/x^6 + ArcTan[(1 + 2*(1 + x^6)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[x]/3 + Log[1 - (1 + x^6)^(1/3)]/6","A",6,6,13,0.4615,1,"{266, 47, 55, 618, 204, 31}"
1248,0,0,0,6.4803773,"\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","Int[((-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,"(-4*k^2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - k^2 + k^2*x^4)^(1/4)*(d*(1 - k^2) + d*k^2*x^4 - x^12)), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(1/4) - (4*k^2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Subst][Defer[Int][x^6/((1 - k^2 + k^2*x^4)^(1/4)*(-(d*(1 - k^2)) - d*k^2*x^4 + x^12)), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(1/4) + (2*(3 - k^2)*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - k^2 + k^2*x^4)^(1/4)*(d - x^12 + d*k^2*(-1 + x^4))), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(1/4)","F",0,0,0,0,-1,"{}"
1249,0,0,0,0.7230691,"\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","Int[((-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,"(3*(-1 + x^7)^(2/3)*Hypergeometric2F1[-2/3, -2/7, 5/7, x^7])/(2*x^2*(1 - x^7)^(2/3)) + 3*Defer[Int][(-1 + x^7)^(2/3)/(-1 + x^3 + x^7), x] + 7*Defer[Int][(x^4*(-1 + x^7)^(2/3))/(-1 + x^3 + x^7), x]","F",0,0,0,0,-1,"{}"
1250,0,0,0,4.3909726,"\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","Int[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,"(2*Sqrt[x]*Sqrt[-b + a^2*x]*Defer[Subst][Defer[Int][x^2/(Sqrt[-b + a^2*x^2]*(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2)), x], x, Sqrt[x]])/Sqrt[-(b*x) + a^2*x^2]","F",0,0,0,0,-1,"{}"
1251,1,146,0,0.8650458,"\int \frac{-\sqrt{a b}+x}{\sqrt{x (a+x) (b+x)} \left(\sqrt{a b}+x\right)} \, dx","Int[(-Sqrt[a*b] + x)/(Sqrt[x*(a + x)*(b + x)]*(Sqrt[a*b] + x)),x]","\frac{2 \sqrt{-a} \sqrt{x} \sqrt{\frac{x}{a}+1} \sqrt{\frac{x}{b}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{-a}}\right)|\frac{a}{b}\right)}{\sqrt{x (a+x) (b+x)}}-\frac{4 \sqrt{-a} \sqrt{x} \sqrt{\frac{x}{a}+1} \sqrt{\frac{x}{b}+1} \Pi \left(\frac{a}{\sqrt{a b}};\sin ^{-1}\left(\frac{\sqrt{x}}{\sqrt{-a}}\right)|\frac{a}{b}\right)}{\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*Sqrt[-a]*Sqrt[x]*Sqrt[1 + x/a]*Sqrt[1 + x/b]*EllipticF[ArcSin[Sqrt[x]/Sqrt[-a]], a/b])/Sqrt[x*(a + x)*(b + x)] - (4*Sqrt[-a]*Sqrt[x]*Sqrt[1 + x/a]*Sqrt[1 + x/b]*EllipticPi[a/Sqrt[a*b], ArcSin[Sqrt[x]/Sqrt[-a]], a/b])/Sqrt[x*(a + x)*(b + x)]","C",8,7,35,0.2000,1,"{6718, 1607, 169, 538, 537, 117, 116}"
1252,1,135,0,0.0183058,"\int \frac{1}{\sqrt[3]{-x^2+x^3}} \, dx","Int[(-x^2 + x^3)^(-1/3),x]","-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-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,"-((Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3)) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3))","A",2,2,13,0.1538,1,"{2011, 59}"
1253,0,0,0,0.0539051,"\int \frac{3-x^2}{\left(1-x^2\right) \sqrt[4]{1-6 x^2+x^4}} \, dx","Int[(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,"Defer[Int][(3 - x^2)/((1 - x^2)*(1 - 6*x^2 + x^4)^(1/4)), x]","F",0,0,0,0,-1,"{}"
1254,0,0,0,8.1964222,"\int \frac{-3+x^4}{\left(1+x^4\right) \sqrt[4]{-3 x+4 x^4-3 x^5}} \, dx","Int[(-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,"-(((-1)^(3/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(1/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4)) - ((-1)^(9/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(3/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) - ((-1)^(15/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(5/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(5/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(7/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) - ((-1)^(11/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(9/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(1/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(11/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(7/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(13/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(13/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(15/16) - x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + (4*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][x^2/(-3 + 4*x^12 - 3*x^16)^(1/4), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) - ((-1)^(3/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(1/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) - ((-1)^(9/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(3/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) - ((-1)^(15/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(5/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(5/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/(((-1)^(7/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) - ((-1)^(11/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(9/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(1/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(11/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(7/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(13/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4) + ((-1)^(13/16)*x^(1/4)*(-3 + 4*x^3 - 3*x^4)^(1/4)*Defer[Subst][Defer[Int][1/((-(-1)^(15/16) + x)*(-3 + 4*x^12 - 3*x^16)^(1/4)), x], x, x^(1/4)])/(-3*x + 4*x^4 - 3*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
1255,1,593,0,1.7027322,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^2 \left(-1+x^3+x^6\right)} \, dx","Int[((-1 + x^6)^(1/3)*(1 + x^6))/(x^2*(-1 + x^3 + x^6)),x]","-\frac{2 \left(5-\sqrt{5}\right) \sqrt[3]{x^6-1} x^5 F_1\left(\frac{5}{6};-\frac{1}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{25 \left(3-\sqrt{5}\right) \sqrt[3]{1-x^6}}-\frac{2 \sqrt[3]{x^6-1} x^5 F_1\left(\frac{5}{6};-\frac{1}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{5 \sqrt{5} \left(3-\sqrt{5}\right) \sqrt[3]{1-x^6}}-\frac{2 \left(5+\sqrt{5}\right) \sqrt[3]{x^6-1} x^5 F_1\left(\frac{5}{6};-\frac{1}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3+\sqrt{5}}\right)}{25 \left(3+\sqrt{5}\right) \sqrt[3]{1-x^6}}+\frac{2 \sqrt[3]{x^6-1} x^5 F_1\left(\frac{5}{6};-\frac{1}{3},1;\frac{11}{6};x^6,\frac{2 x^6}{3+\sqrt{5}}\right)}{5 \sqrt{5} \left(3+\sqrt{5}\right) \sqrt[3]{1-x^6}}-\frac{\left(5-\sqrt{5}\right) \sqrt[3]{x^6-1} x^2 F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{10 \left(3-\sqrt{5}\right) \sqrt[3]{1-x^6}}-\frac{\sqrt[3]{x^6-1} x^2 F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{\sqrt{5} \sqrt[3]{1-x^6}}-\frac{\left(5+\sqrt{5}\right) \sqrt[3]{x^6-1} x^2 F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{2 x^6}{3+\sqrt{5}},x^6\right)}{10 \left(3+\sqrt{5}\right) \sqrt[3]{1-x^6}}+\frac{\sqrt[3]{x^6-1} x^2 F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{2 x^6}{3+\sqrt{5}},x^6\right)}{\sqrt{5} \sqrt[3]{1-x^6}}+\frac{\sqrt[3]{x^6-1} \, _2F_1\left(-\frac{1}{3},-\frac{1}{6};\frac{5}{6};x^6\right)}{\sqrt[3]{1-x^6} x}","\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,"-((x^2*(-1 + x^6)^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, x^6, (2*x^6)/(3 - Sqrt[5])])/(Sqrt[5]*(1 - x^6)^(1/3))) - ((5 - Sqrt[5])*x^2*(-1 + x^6)^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, x^6, (2*x^6)/(3 - Sqrt[5])])/(10*(3 - Sqrt[5])*(1 - x^6)^(1/3)) + (x^2*(-1 + x^6)^(1/3)*AppellF1[1/3, 1, -1/3, 4/3, (2*x^6)/(3 + Sqrt[5]), x^6])/(Sqrt[5]*(1 - x^6)^(1/3)) - ((5 + Sqrt[5])*x^2*(-1 + x^6)^(1/3)*AppellF1[1/3, 1, -1/3, 4/3, (2*x^6)/(3 + Sqrt[5]), x^6])/(10*(3 + Sqrt[5])*(1 - x^6)^(1/3)) - (2*x^5*(-1 + x^6)^(1/3)*AppellF1[5/6, -1/3, 1, 11/6, x^6, (2*x^6)/(3 - Sqrt[5])])/(5*Sqrt[5]*(3 - Sqrt[5])*(1 - x^6)^(1/3)) - (2*(5 - Sqrt[5])*x^5*(-1 + x^6)^(1/3)*AppellF1[5/6, -1/3, 1, 11/6, x^6, (2*x^6)/(3 - Sqrt[5])])/(25*(3 - Sqrt[5])*(1 - x^6)^(1/3)) + (2*x^5*(-1 + x^6)^(1/3)*AppellF1[5/6, -1/3, 1, 11/6, x^6, (2*x^6)/(3 + Sqrt[5])])/(5*Sqrt[5]*(3 + Sqrt[5])*(1 - x^6)^(1/3)) - (2*(5 + Sqrt[5])*x^5*(-1 + x^6)^(1/3)*AppellF1[5/6, -1/3, 1, 11/6, x^6, (2*x^6)/(3 + Sqrt[5])])/(25*(3 + Sqrt[5])*(1 - x^6)^(1/3)) + ((-1 + x^6)^(1/3)*Hypergeometric2F1[-1/3, -1/6, 5/6, x^6])/(x*(1 - x^6)^(1/3))","C",38,9,28,0.3214,0,"{6728, 365, 364, 1562, 465, 430, 429, 511, 510}"
1256,0,0,0,0.4901975,"\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{1+x^2+3 x^4+x^6+x^8} \, dx","Int[((-1 + x^4)*Sqrt[1 + x^4])/(1 + x^2 + 3*x^4 + x^6 + x^8),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+x^4}}{1+x^2+3 x^4+x^6+x^8} \, dx","-\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,"Defer[Int][Sqrt[1 + x^4]/(-1 - x^2 - 3*x^4 - x^6 - x^8), x] + Defer[Int][(x^4*Sqrt[1 + x^4])/(1 + x^2 + 3*x^4 + x^6 + x^8), x]","F",0,0,0,0,-1,"{}"
1257,1,91,0,0.2031571,"\int \frac{-1+2 x^8}{\sqrt[4]{1+x^4} \left(-1+x^8\right)} \, dx","Int[(-1 + 2*x^8)/((1 + x^4)^(1/4)*(-1 + x^8)),x]","-\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}}","-\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) + ArcTan[x/(1 + x^4)^(1/4)] - ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(4*2^(1/4)) + ArcTanh[x/(1 + x^4)^(1/4)] - ArcTanh[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(4*2^(1/4))","A",12,8,24,0.3333,1,"{6725, 240, 212, 206, 203, 1404, 382, 377}"
1258,1,149,0,0.1350501,"\int \sqrt[4]{b x^5+a x^8} \, dx","Int[(b*x^5 + a*x^8)^(1/4),x]","-\frac{b x^{15/4} \left(a x^3+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{6 a^{3/4} \left(a x^8+b x^5\right)^{3/4}}+\frac{b x^{15/4} \left(a x^3+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{6 a^{3/4} \left(a x^8+b x^5\right)^{3/4}}+\frac{1}{3} x \sqrt[4]{a x^8+b x^5}","\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,"(x*(b*x^5 + a*x^8)^(1/4))/3 - (b*x^(15/4)*(b + a*x^3)^(3/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(6*a^(3/4)*(b*x^5 + a*x^8)^(3/4)) + (b*x^(15/4)*(b + a*x^3)^(3/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(6*a^(3/4)*(b*x^5 + a*x^8)^(3/4))","A",8,8,15,0.5333,1,"{2004, 2032, 329, 275, 331, 298, 203, 206}"
1259,1,83,0,0.4353586,"\int \frac{\sqrt{x-\sqrt{1+x^2}}}{1-\sqrt{1+x^2}} \, dx","Int[Sqrt[x - Sqrt[1 + x^2]]/(1 - Sqrt[1 + x^2]),x]","\frac{\sqrt{x-\sqrt{x^2+1}}}{x}+2 \sqrt{x-\sqrt{x^2+1}}-\frac{1}{x \sqrt{x-\sqrt{x^2+1}}}-2 \tan ^{-1}\left(\sqrt{x-\sqrt{x^2+1}}\right)","\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/(x*Sqrt[x - Sqrt[1 + x^2]])) + 2*Sqrt[x - Sqrt[1 + x^2]] + Sqrt[x - Sqrt[1 + x^2]]/x - 2*ArcTan[Sqrt[x - Sqrt[1 + x^2]]]","A",16,12,33,0.3636,1,"{6742, 2119, 457, 329, 298, 203, 206, 2120, 463, 12, 321, 212}"
1260,0,0,0,0.3332198,"\int \frac{(-1+x) (3+x)}{\left(-1+x^2\right)^{2/3} \left(2-x+x^2\right)} \, dx","Int[((-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,"(3^(3/4)*Sqrt[2 + Sqrt[3]]*(1 + (-1 + x^2)^(1/3))*Sqrt[(1 - (-1 + x^2)^(1/3) + (-1 + x^2)^(2/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]*EllipticF[ArcSin[(1 - Sqrt[3] + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))], -7 - 4*Sqrt[3]])/(x*Sqrt[(1 + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]) - Defer[Int][(5 - 3*x)/((-1 + x^2)^(2/3)*(2 - x + x^2)), x]","F",0,0,0,0,-1,"{}"
1261,1,68,0,0.0412415,"\int \frac{\sqrt[3]{-1+x^3}}{x^4} \, dx","Int[(-1 + x^3)^(1/3)/x^4,x]","-\frac{\sqrt[3]{x^3-1}}{3 x^3}+\frac{1}{6} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\log (x)}{6}","-\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,"-1/3*(-1 + x^3)^(1/3)/x^3 - ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[x]/6 + Log[1 + (-1 + x^3)^(1/3)]/6","A",6,6,13,0.4615,1,"{266, 47, 58, 618, 204, 31}"
1262,1,68,0,0.0414719,"\int \frac{\left(-1+x^3\right)^{2/3}}{x^4} \, dx","Int[(-1 + x^3)^(2/3)/x^4,x]","-\frac{\left(x^3-1\right)^{2/3}}{3 x^3}-\frac{1}{3} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\log (x)}{3}","-\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,"-1/3*(-1 + x^3)^(2/3)/x^3 - (2*ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + Log[x]/3 - Log[1 + (-1 + x^3)^(1/3)]/3","A",6,6,13,0.4615,1,"{266, 47, 56, 618, 204, 31}"
1263,1,93,0,0.0457243,"\int \frac{\sqrt[3]{1+x^3}}{x^2} \, dx","Int[(1 + x^3)^(1/3)/x^2,x]","-\frac{\sqrt[3]{x^3+1}}{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{\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,"-((1 + x^3)^(1/3)/x) - 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",8,8,13,0.6154,1,"{277, 331, 292, 31, 634, 618, 204, 628}"
1264,1,53,0,0.0588211,"\int \frac{-1+x}{(1+x) \sqrt[3]{2+x^3}} \, dx","Int[(-1 + x)/((1 + x)*(2 + x^3)^(1/3)),x]","-\frac{3}{2} \log \left(-\sqrt[3]{x^3+2}+x+2\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (x+2)}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)+\log (x+1)","-\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,"Sqrt[3]*ArcTan[(1 + (2*(2 + x))/(2 + x^3)^(1/3))/Sqrt[3]] + Log[1 + x] - (3*Log[2 + x - (2 + x^3)^(1/3)])/2","A",1,1,18,0.05556,1,"{2151}"
1265,1,104,0,0.0798421,"\int \frac{1}{x^7 \left(b+a x^3\right)^{3/4}} \, dx","Int[1/(x^7*(b + a*x^3)^(3/4)),x]","-\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{7 a \sqrt[4]{a x^3+b}}{24 b^2 x^3}-\frac{\sqrt[4]{a x^3+b}}{6 b x^6}","-\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,"-1/6*(b + a*x^3)^(1/4)/(b*x^6) + (7*a*(b + a*x^3)^(1/4))/(24*b^2*x^3) - (7*a^2*ArcTan[(b + a*x^3)^(1/4)/b^(1/4)])/(16*b^(11/4)) - (7*a^2*ArcTanh[(b + a*x^3)^(1/4)/b^(1/4)])/(16*b^(11/4))","A",7,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1266,0,0,0,28.7640832,"\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","Int[((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,"(Sqrt[2]*k^(3/2)*Sqrt[-1 + k^2]*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*Sqrt[(1 + k^2*(1 - 2*x^2))^2/((1 - k^2)^2*(1 - (2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)])/(1 - k^2))^2)]*(1 - (2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)])/(1 - k^2))*EllipticF[2*ArcTan[(Sqrt[2]*Sqrt[k]*((1 - x^2)*(1 - k^2*x^2))^(1/4))/Sqrt[-1 + k^2]], 1/2])/((d - k^2)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]) + ((k^2 + 5*k^4 - d*(1 - 3*k^2))*x*((1 - x^2)/(1 - k^2*x^2))^(3/4)*(1 - k^2*x^2)*Hypergeometric2F1[1/2, 3/4, 3/2, ((1 - k^2)*x^2)/(1 - k^2*x^2)])/((d - k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) - ((k^2 + 7*k^4 + 3*d^2*(1 - k^2) - d*(1 + 2*k^2 + 5*k^4))*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][1/((1 - x^2)^(3/4)*(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])/((d - k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) + ((k^2 - k^6 - 6*d^2*(1 - k^2) - d*(1 - 14*k^2 - 19*k^4))*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][x/((1 - x^2)^(3/4)*(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])/((d - k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) + ((24*d*k^4 - 3*d^2*(1 - k^2) + k^4*(3 + 5*k^2))*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][x^2/((1 - x^2)^(3/4)*(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])/((d - k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4))","F",0,0,0,0,-1,"{}"
1267,1,68,0,0.0467353,"\int \frac{1}{x^5 \sqrt[3]{-1+x^4}} \, dx","Int[1/(x^5*(-1 + x^4)^(1/3)),x]","\frac{\left(x^4-1\right)^{2/3}}{4 x^4}-\frac{1}{8} \log \left(\sqrt[3]{x^4-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^4-1}}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\log (x)}{6}","\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,"(-1 + x^4)^(2/3)/(4*x^4) - ArcTan[(1 - 2*(-1 + x^4)^(1/3))/Sqrt[3]]/(4*Sqrt[3]) + Log[x]/6 - Log[1 + (-1 + x^4)^(1/3)]/8","A",6,6,13,0.4615,1,"{266, 51, 56, 618, 204, 31}"
1268,0,0,0,19.1154637,"\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","Int[(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]","\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","-\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,"(4*a*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-b + x^2])/(Sqrt[-a + x^2]*(a^2*d - 2*a*d*x^2 - b^2*(1 - d/b^2)*x^4 + 2*b*x^6 - x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-b + x^2])/(Sqrt[-a + x^2]*(-(a^2*d) + 2*a*d*x^2 + b^2*(1 - d/b^2)*x^4 - 2*b*x^6 + x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^6*Sqrt[-b + x^2])/(Sqrt[-a + x^2]*(-(a^2*d) + 2*a*d*x^2 + b^2*(1 - d/b^2)*x^4 - 2*b*x^6 + x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1269,1,104,0,0.0798298,"\int \frac{1}{x^9 \left(b+a x^4\right)^{3/4}} \, dx","Int[1/(x^9*(b + a*x^4)^(3/4)),x]","-\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{7 a \sqrt[4]{a x^4+b}}{32 b^2 x^4}-\frac{\sqrt[4]{a x^4+b}}{8 b x^8}","-\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,"-1/8*(b + a*x^4)^(1/4)/(b*x^8) + (7*a*(b + a*x^4)^(1/4))/(32*b^2*x^4) - (21*a^2*ArcTan[(b + a*x^4)^(1/4)/b^(1/4)])/(64*b^(11/4)) - (21*a^2*ArcTanh[(b + a*x^4)^(1/4)/b^(1/4)])/(64*b^(11/4))","A",7,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1270,1,101,0,0.0432151,"\int x^4 \left(b+a x^4\right)^{3/4} \, dx","Int[x^4*(b + a*x^4)^(3/4),x]","-\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{3 b x \left(a x^4+b\right)^{3/4}}{32 a}+\frac{1}{8} x^5 \left(a x^4+b\right)^{3/4}","-\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,"(3*b*x*(b + a*x^4)^(3/4))/(32*a) + (x^5*(b + a*x^4)^(3/4))/8 - (3*b^2*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(64*a^(5/4)) - (3*b^2*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(64*a^(5/4))","A",6,6,15,0.4000,1,"{279, 321, 240, 212, 206, 203}"
1271,1,589,0,1.432246,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(d+c x+x^2\right)} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(x*(d + c*x + x^2)),x]","\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b}}{\sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b}}{\sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b}}{\sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b}}{\sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}","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,"(2*(2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c - Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c - Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4)) - (2*(2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4)) - (2*(2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c - Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c - Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4)) + (2*(2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4))","B",23,11,30,0.3667,1,"{2056, 911, 105, 63, 331, 298, 203, 206, 93, 205, 208}"
1272,1,589,0,0.8965905,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x \left(d+c x+x^2\right)} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(x*(d + c*x + x^2)),x]","\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b}}{\sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b}}{\sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(c-\sqrt{c^2-4 d}\right)+2 b}}{\sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{c-\sqrt{c^2-4 d}} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2-4 d}+c\right)+2 b}}{\sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2-4 d}+c} \sqrt{c^2-4 d} \sqrt[4]{a x-b}}","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,"(2*(2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c - Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c - Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4)) - (2*(2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4)) - (2*(2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((2*b + a*(c - Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c - Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c - Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4)) + (2*(2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((2*b + a*(c + Sqrt[c^2 - 4*d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 - 4*d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 - 4*d])^(1/4)*Sqrt[c^2 - 4*d]*x^(3/4)*(-b + a*x)^(1/4))","B",23,11,30,0.3667,1,"{2056, 911, 105, 63, 331, 298, 203, 206, 93, 205, 208}"
1273,1,68,0,0.0420794,"\int \frac{\left(-1+x^5\right)^{2/3}}{x^6} \, dx","Int[(-1 + x^5)^(2/3)/x^6,x]","-\frac{\left(x^5-1\right)^{2/3}}{5 x^5}-\frac{1}{5} \log \left(\sqrt[3]{x^5-1}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^5-1}}{\sqrt{3}}\right)}{5 \sqrt{3}}+\frac{\log (x)}{3}","-\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,"-1/5*(-1 + x^5)^(2/3)/x^5 - (2*ArcTan[(1 - 2*(-1 + x^5)^(1/3))/Sqrt[3]])/(5*Sqrt[3]) + Log[x]/3 - Log[1 + (-1 + x^5)^(1/3)]/5","A",6,6,13,0.4615,1,"{266, 47, 56, 618, 204, 31}"
1274,1,104,0,0.0756665,"\int \frac{1}{x^{11} \left(b+a x^5\right)^{3/4}} \, dx","Int[1/(x^11*(b + a*x^5)^(3/4)),x]","-\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{7 a \sqrt[4]{a x^5+b}}{40 b^2 x^5}-\frac{\sqrt[4]{a x^5+b}}{10 b x^{10}}","-\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,"-1/10*(b + a*x^5)^(1/4)/(b*x^10) + (7*a*(b + a*x^5)^(1/4))/(40*b^2*x^5) - (21*a^2*ArcTan[(b + a*x^5)^(1/4)/b^(1/4)])/(80*b^(11/4)) - (21*a^2*ArcTanh[(b + a*x^5)^(1/4)/b^(1/4)])/(80*b^(11/4))","A",7,6,15,0.4000,1,"{266, 51, 63, 212, 206, 203}"
1275,1,68,0,0.0405792,"\int \frac{1}{x^7 \sqrt[3]{-1+x^6}} \, dx","Int[1/(x^7*(-1 + x^6)^(1/3)),x]","\frac{\left(x^6-1\right)^{2/3}}{6 x^6}-\frac{1}{12} \log \left(\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{\log (x)}{6}","\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)/(6*x^6) - ArcTan[(1 - 2*(-1 + x^6)^(1/3))/Sqrt[3]]/(6*Sqrt[3]) + Log[x]/6 - Log[1 + (-1 + x^6)^(1/3)]/12","A",6,6,13,0.4615,1,"{266, 51, 56, 618, 204, 31}"
1276,1,68,0,0.0400281,"\int \frac{\left(-1+x^6\right)^{2/3}}{x^7} \, dx","Int[(-1 + x^6)^(2/3)/x^7,x]","-\frac{\left(x^6-1\right)^{2/3}}{6 x^6}-\frac{1}{6} \log \left(\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\log (x)}{3}","-\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,"-1/6*(-1 + x^6)^(2/3)/x^6 - ArcTan[(1 - 2*(-1 + x^6)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) + Log[x]/3 - Log[1 + (-1 + x^6)^(1/3)]/6","A",6,6,13,0.4615,1,"{266, 47, 56, 618, 204, 31}"
1277,0,0,0,2.3944483,"\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","Int[((-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,"(3*(x + x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][x/(1 + x^6 + x^9)^(2/3), x], x, x^(2/3)])/(x^(1/3)*(1 + x^4 + x^6)^(1/3)) - (9*(x + x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][x/((1 + x^6 + x^9)^(2/3)*(1 - x^3 + x^6 + x^9)), x], x, x^(2/3)])/(2*x^(1/3)*(1 + x^4 + x^6)^(1/3)) + (3*(x + x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][x^4/((1 + x^6 + x^9)^(2/3)*(1 - x^3 + x^6 + x^9)), x], x, x^(2/3)])/(x^(1/3)*(1 + x^4 + x^6)^(1/3)) - (3*(x + x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 + x^6 + x^9)^(2/3)*(1 - x^3 + x^6 + x^9)), x], x, x^(2/3)])/(2*x^(1/3)*(1 + x^4 + x^6)^(1/3))","F",0,0,0,0,-1,"{}"
1278,1,114,0,0.2880595,"\int \frac{\sqrt{1+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Int[Sqrt[1 + Sqrt[1 + x]]/(x - Sqrt[1 + x]),x]","4 \sqrt{\sqrt{x+1}+1}-2 \sqrt{\frac{2}{5} \left(7+3 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)-2 \sqrt{\frac{2}{5} \left(7-3 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{\sqrt{x+1}+1}\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,"4*Sqrt[1 + Sqrt[1 + x]] - 2*Sqrt[(2*(7 + 3*Sqrt[5]))/5]*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] - 2*Sqrt[(2*(7 - 3*Sqrt[5]))/5]*ArcTanh[Sqrt[(3 + Sqrt[5])/2]*Sqrt[1 + Sqrt[1 + x]]]","A",6,4,27,0.1481,0,"{824, 826, 1166, 207}"
1279,1,145,0,0.1144724,"\int \frac{1}{x^3 \left(-1+x^2\right)^{3/4}} \, dx","Int[1/(x^3*(-1 + x^2)^(3/4)),x]","\frac{\sqrt[4]{x^2-1}}{2 x^2}-\frac{3 \log \left(\sqrt{x^2-1}-\sqrt{2} \sqrt[4]{x^2-1}+1\right)}{8 \sqrt{2}}+\frac{3 \log \left(\sqrt{x^2-1}+\sqrt{2} \sqrt[4]{x^2-1}+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^2-1}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^2-1}+1\right)}{4 \sqrt{2}}","\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,"(-1 + x^2)^(1/4)/(2*x^2) - (3*ArcTan[1 - Sqrt[2]*(-1 + x^2)^(1/4)])/(4*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*(-1 + x^2)^(1/4)])/(4*Sqrt[2]) - (3*Log[1 - Sqrt[2]*(-1 + x^2)^(1/4) + Sqrt[-1 + x^2]])/(8*Sqrt[2]) + (3*Log[1 + Sqrt[2]*(-1 + x^2)^(1/4) + Sqrt[-1 + x^2]])/(8*Sqrt[2])","A",12,9,13,0.6923,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
1280,1,62,0,0.0084273,"\int \frac{\left(-1+x^3\right)^{2/3}}{x^3} \, dx","Int[(-1 + x^3)^(2/3)/x^3,x]","-\frac{1}{2} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3-1\right)^{2/3}}{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*(-1 + x^3)^(2/3)/x^2 + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (-1 + x^3)^(1/3)]/2","A",2,2,13,0.1538,1,"{277, 239}"
1281,1,386,0,0.9406654,"\int \frac{2+x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Int[(2 + x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{3^{3/4}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{3^{3/4}}-\frac{\sqrt{2 \left(7+4 \sqrt{3}\right)} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \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,"-((Sqrt[2]*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/3^(3/4)) - (Sqrt[2]*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/3^(3/4) - (Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (Sqrt[2*(7 + 4*Sqrt[3])]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","C",13,6,25,0.2400,0,"{6728, 218, 2135, 2140, 206, 203}"
1282,1,62,0,0.0082406,"\int \frac{\left(1+x^3\right)^{2/3}}{x^3} \, dx","Int[(1 + x^3)^(2/3)/x^3,x]","-\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3+1\right)^{2/3}}{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*(1 + x^3)^(2/3)/x^2 + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]/2","A",2,2,13,0.1538,1,"{277, 239}"
1283,0,0,0,10.1807719,"\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","Int[(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,"(4*a*b*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((-a + x^2)^(1/4)*(-b + x^2)^(1/4)*(a^3 - 3*a^2*x^2 + 3*a*(1 - (b*d)/(3*a))*x^4 - (1 - d)*x^6)), x], x, Sqrt[x]])/((a - x)*(b - x)*x^2)^(1/4) - (2*(3*a - b)*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^4/((-a + x^2)^(1/4)*(-b + x^2)^(1/4)*(a^3 - 3*a^2*x^2 + 3*a*(1 - (b*d)/(3*a))*x^4 - (1 - d)*x^6)), x], x, Sqrt[x]])/((a - x)*(b - x)*x^2)^(1/4)","F",0,0,0,0,-1,"{}"
1284,1,145,0,0.1161513,"\int \frac{\sqrt[4]{-1+x^4}}{x^5} \, dx","Int[(-1 + x^4)^(1/4)/x^5,x]","-\frac{\sqrt[4]{x^4-1}}{4 x^4}-\frac{\log \left(\sqrt{x^4-1}-\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{16 \sqrt{2}}+\frac{\log \left(\sqrt{x^4-1}+\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{16 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^4-1}\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{8 \sqrt{2}}","-\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,"-1/4*(-1 + x^4)^(1/4)/x^4 - ArcTan[1 - Sqrt[2]*(-1 + x^4)^(1/4)]/(8*Sqrt[2]) + ArcTan[1 + Sqrt[2]*(-1 + x^4)^(1/4)]/(8*Sqrt[2]) - Log[1 - Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(16*Sqrt[2]) + Log[1 + Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(16*Sqrt[2])","A",12,9,13,0.6923,1,"{266, 47, 63, 211, 1165, 628, 1162, 617, 204}"
1285,1,293,0,1.2532626,"\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-x^2+x^4}} \, dx","Int[(1 + x^2)/((-1 + x + x^2)*(-x^2 + x^4)^(1/3)),x]","\frac{3 \sqrt[3]{1-x^2} x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};\frac{4 x^2}{\left(1-\sqrt{5}\right)^2},x^2\right)}{2 \left(1-\sqrt{5}\right) \sqrt[3]{x^4-x^2}}+\frac{3 \sqrt[3]{1-x^2} x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};\frac{4 x^2}{\left(1+\sqrt{5}\right)^2},x^2\right)}{2 \left(1+\sqrt{5}\right) \sqrt[3]{x^4-x^2}}-\frac{3 \sqrt[3]{1-x^2} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};\frac{4 x^2}{\left(1-\sqrt{5}\right)^2},x^2\right)}{\sqrt[3]{x^4-x^2}}-\frac{3 \sqrt[3]{1-x^2} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};\frac{4 x^2}{\left(1+\sqrt{5}\right)^2},x^2\right)}{\sqrt[3]{x^4-x^2}}+\frac{3 \sqrt[3]{1-x^2} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};x^2\right)}{\sqrt[3]{x^4-x^2}}","-\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,"(-3*x*(1 - x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (4*x^2)/(1 - Sqrt[5])^2, x^2])/(-x^2 + x^4)^(1/3) - (3*x*(1 - x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (4*x^2)/(1 + Sqrt[5])^2, x^2])/(-x^2 + x^4)^(1/3) + (3*x^2*(1 - x^2)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, (4*x^2)/(1 - Sqrt[5])^2, x^2])/(2*(1 - Sqrt[5])*(-x^2 + x^4)^(1/3)) + (3*x^2*(1 - x^2)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, (4*x^2)/(1 + Sqrt[5])^2, x^2])/(2*(1 + Sqrt[5])*(-x^2 + x^4)^(1/3)) + (3*x*(1 - x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^2])/(-x^2 + x^4)^(1/3)","C",23,11,27,0.4074,0,"{2056, 6728, 365, 364, 959, 466, 430, 429, 465, 511, 510}"
1286,0,0,0,1.8274263,"\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","Int[((-1 + 2*x)*(2 - x + x^2)*Sqrt[-2 + x^2 - 2*x^3 + x^4])/(3 - 2*x + 2*x^2),x]","\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","\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,"-1/4*((1 - x)*x*Sqrt[-2 + x^2 - 2*x^3 + x^4]) + ArcTanh[((1 - x)*x)/Sqrt[-2 + x^2 - 2*x^3 + x^4]]/2 + Defer[Int][Sqrt[-2 + x^2 - 2*x^3 + x^4]/(-2 - (2*I)*Sqrt[5] + 4*x), x] + Defer[Int][Sqrt[-2 + x^2 - 2*x^3 + x^4]/(-2 + (2*I)*Sqrt[5] + 4*x), x]","F",0,0,0,0,-1,"{}"
1287,1,185,0,0.15027,"\int \frac{\sqrt[4]{-x^3+x^4}}{x (1+x)} \, dx","Int[(-x^3 + x^4)^(1/4)/(x*(1 + x)),x]","\frac{2 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}","-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,"(2*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + (2*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + (2*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - (2*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","A",11,9,22,0.4091,1,"{2042, 105, 63, 240, 212, 206, 203, 93, 298}"
1288,0,0,0,1.0103159,"\int \frac{1+2 x^3}{\left(-1+x+x^3\right) \sqrt[3]{-x^2+x^5}} \, dx","Int[(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,"(6*x*(1 - x^3)^(1/3)*Hypergeometric2F1[1/9, 1/3, 10/9, x^3])/(-x^2 + x^5)^(1/3) + (9*x^(2/3)*(-1 + x^3)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x^9)^(1/3)*(-1 + x^3 + x^9)), x], x, x^(1/3)])/(-x^2 + x^5)^(1/3) - (6*x^(2/3)*(-1 + x^3)^(1/3)*Defer[Subst][Defer[Int][x^3/((-1 + x^9)^(1/3)*(-1 + x^3 + x^9)), x], x, x^(1/3)])/(-x^2 + x^5)^(1/3)","F",0,0,0,0,-1,"{}"
1289,1,145,0,0.1103046,"\int \frac{\sqrt[4]{-1+x^6}}{x^7} \, dx","Int[(-1 + x^6)^(1/4)/x^7,x]","-\frac{\sqrt[4]{x^6-1}}{6 x^6}-\frac{\log \left(\sqrt{x^6-1}-\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{24 \sqrt{2}}+\frac{\log \left(\sqrt{x^6-1}+\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{24 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^6-1}\right)}{12 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^6-1}+1\right)}{12 \sqrt{2}}","-\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,"-1/6*(-1 + x^6)^(1/4)/x^6 - ArcTan[1 - Sqrt[2]*(-1 + x^6)^(1/4)]/(12*Sqrt[2]) + ArcTan[1 + Sqrt[2]*(-1 + x^6)^(1/4)]/(12*Sqrt[2]) - Log[1 - Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]]/(24*Sqrt[2]) + Log[1 + Sqrt[2]*(-1 + x^6)^(1/4) + Sqrt[-1 + x^6]]/(24*Sqrt[2])","A",12,9,13,0.6923,1,"{266, 47, 63, 211, 1165, 628, 1162, 617, 204}"
1290,0,0,0,0.9908927,"\int \frac{1+3 x^4}{\left(-1+x+x^4\right) \sqrt[3]{-x^2+x^6}} \, dx","Int[(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,"(9*x*(1 - x^4)^(1/3)*Hypergeometric2F1[1/12, 1/3, 13/12, x^4])/(-x^2 + x^6)^(1/3) + (12*x^(2/3)*(-1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x^12)^(1/3)*(-1 + x^3 + x^12)), x], x, x^(1/3)])/(-x^2 + x^6)^(1/3) - (9*x^(2/3)*(-1 + x^4)^(1/3)*Defer[Subst][Defer[Int][x^3/((-1 + x^12)^(1/3)*(-1 + x^3 + x^12)), x], x, x^(1/3)])/(-x^2 + x^6)^(1/3)","F",0,0,0,0,-1,"{}"
1291,0,0,0,0.6725852,"\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","Int[((2 + x^3)*Sqrt[-1 - x^2 + x^3])/(1 - x^2 - 2*x^3 - x^4 + x^5 + x^6),x]","\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","\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,"2*Defer[Int][Sqrt[-1 - x^2 + x^3]/(1 - x^2 - 2*x^3 - x^4 + x^5 + x^6), x] + Defer[Int][(x^3*Sqrt[-1 - x^2 + x^3])/(1 - x^2 - 2*x^3 - x^4 + x^5 + x^6), x]","F",0,0,0,0,-1,"{}"
1292,0,0,0,0.5896842,"\int \frac{\left(1+x^4\right) \sqrt{-1-x^2+x^4}}{1-x^2-3 x^4+x^6+x^8} \, dx","Int[((1 + x^4)*Sqrt[-1 - x^2 + x^4])/(1 - x^2 - 3*x^4 + x^6 + x^8),x]","\int \frac{\left(1+x^4\right) \sqrt{-1-x^2+x^4}}{1-x^2-3 x^4+x^6+x^8} \, dx","\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,"Defer[Int][Sqrt[-1 - x^2 + x^4]/(1 - x^2 - 3*x^4 + x^6 + x^8), x] + Defer[Int][(x^4*Sqrt[-1 - x^2 + x^4])/(1 - x^2 - 3*x^4 + x^6 + x^8), x]","F",0,0,0,0,-1,"{}"
1293,1,147,0,0.4146471,"\int \frac{x^2 \sqrt{x+\sqrt{1+x}}}{\sqrt{1+x}} \, dx","Int[(x^2*Sqrt[x + Sqrt[1 + x]])/Sqrt[1 + x],x]","\frac{1}{3} (x+1)^{3/2} \left(x+\sqrt{x+1}\right)^{3/2}-\frac{3}{10} (x+1) \left(x+\sqrt{x+1}\right)^{3/2}-\frac{39}{80} \sqrt{x+1} \left(x+\sqrt{x+1}\right)^{3/2}+\frac{33}{160} \left(x+\sqrt{x+1}\right)^{3/2}+\frac{77}{256} \left(2 \sqrt{x+1}+1\right) \sqrt{x+\sqrt{x+1}}-\frac{385}{512} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","\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,"(33*(x + Sqrt[1 + x])^(3/2))/160 - (39*Sqrt[1 + x]*(x + Sqrt[1 + x])^(3/2))/80 - (3*(1 + x)*(x + Sqrt[1 + x])^(3/2))/10 + ((1 + x)^(3/2)*(x + Sqrt[1 + x])^(3/2))/3 + (77*Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/256 - (385*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/512","A",8,5,24,0.2083,1,"{1661, 640, 612, 621, 206}"
1294,1,63,0,0.0095614,"\int \left(-1+x^3\right)^{2/3} \, dx","Int[(-1 + x^3)^(2/3),x]","\frac{1}{3} \left(x^3-1\right)^{2/3} x+\frac{1}{3} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{2 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{3 \sqrt{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,"(x*(-1 + x^3)^(2/3))/3 - (2*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/3","A",2,2,9,0.2222,1,"{195, 239}"
1295,1,63,0,0.010465,"\int \left(1+x^3\right)^{2/3} \, dx","Int[(1 + x^3)^(2/3),x]","\frac{1}{3} \left(x^3+1\right)^{2/3} x-\frac{1}{3} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{2 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{3 \sqrt{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,"(x*(1 + x^3)^(2/3))/3 + (2*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) - Log[-x + (1 + x^3)^(1/3)]/3","A",2,2,9,0.2222,1,"{195, 239}"
1296,1,63,0,0.0121938,"\int \frac{-1+x^3}{\sqrt[3]{2+x^3}} \, dx","Int[(-1 + x^3)/(2 + x^3)^(1/3),x]","\frac{1}{3} \left(x^3+2\right)^{2/3} x+\frac{5}{6} \log \left(\sqrt[3]{x^3+2}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+2}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\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,"(x*(2 + x^3)^(2/3))/3 - (5*ArcTan[(1 + (2*x)/(2 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + (5*Log[-x + (2 + x^3)^(1/3)])/6","A",2,2,15,0.1333,1,"{388, 239}"
1297,1,178,0,0.1313502,"\int \sqrt[3]{x+x^3} \, dx","Int[(x + x^3)^(1/3),x]","\frac{1}{2} \sqrt[3]{x^3+x} x-\frac{\left(x^2+1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{6 \left(x^3+x\right)^{2/3}}+\frac{\left(x^2+1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{12 \left(x^3+x\right)^{2/3}}-\frac{\left(x^2+1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} \left(x^3+x\right)^{2/3}}","\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,"(x*(x + x^3)^(1/3))/2 - (x^(2/3)*(1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*(x + x^3)^(2/3)) - (x^(2/3)*(1 + x^2)^(2/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(6*(x + x^3)^(2/3)) + (x^(2/3)*(1 + x^2)^(2/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(12*(x + x^3)^(2/3))","A",11,11,9,1.222,1,"{2004, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1298,0,0,0,35.3506789,"\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","Int[((-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,"(Sqrt[2]*k^(3/2)*Sqrt[-1 + k^2]*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*Sqrt[(1 + k^2*(1 - 2*x^2))^2/((1 - k^2)^2*(1 - (2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)])/(1 - k^2))^2)]*(1 - (2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)])/(1 - k^2))*EllipticF[2*ArcTan[(Sqrt[2]*Sqrt[k]*((1 - x^2)*(1 - k^2*x^2))^(1/4))/Sqrt[-1 + k^2]], 1/2])/((1 - d*k^2)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]) - (k*(5 + (1 + 3*d)*k^2 - d*k^4)*x*((1 - x^2)/(1 - k^2*x^2))^(3/4)*(1 - k^2*x^2)*Hypergeometric2F1[1/2, 3/4, 3/2, ((1 - k^2)*x^2)/(1 - k^2*x^2)])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) + (k*(7 + k^2 - 3*d^2*k^2*(1 - k^2) - d*(5 + 2*k^2 + k^4))*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][1/((1 - x^2)^(3/4)*(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])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) + ((1 - k^4 - 6*d^2*k^4*(1 - k^2) - d*k^2*(19 + 14*k^2 - k^4))*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][x/((1 - x^2)^(3/4)*(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])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) - (k*(5 + 3*(1 + 8*d)*k^2 + 3*d^2*k^4 - 3*d^2*k^6)*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][x^2/((1 - x^2)^(3/4)*(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])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4))","F",0,0,0,0,-1,"{}"
1299,1,105,0,0.118572,"\int \frac{\left(-1+x^4\right)^{3/4} \left(4+x^4\right)}{x^8 \left(-4+x^4\right)} \, dx","Int[((-1 + x^4)^(3/4)*(4 + x^4))/(x^8*(-4 + x^4)),x]","-\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}}{7 x^7}+\frac{\left(x^4-1\right)^{3/4}}{42 x^3}","-\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)/(7*x^7) + (-1 + x^4)^(3/4)/(42*x^3) - (3^(3/4)*ArcTan[(3^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/(8*Sqrt[2]) - (3^(3/4)*ArcTanh[(3^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/(8*Sqrt[2])","A",7,7,25,0.2800,1,"{580, 583, 12, 377, 212, 206, 203}"
1300,0,0,0,0.7176944,"\int \frac{4 b+a x^3}{\sqrt[4]{b+a x^3} \left(b+a x^3+x^4\right)} \, dx","Int[(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,"4*b*Defer[Int][1/((b + a*x^3)^(1/4)*(b + a*x^3 + x^4)), x] + a*Defer[Int][x^3/((b + a*x^3)^(1/4)*(b + a*x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1301,0,0,0,10.4934207,"\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","Int[(-(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]","\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","\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,"(4*a*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(a^2*d - 2*a*d*x^2 - b^2*(1 - d/b^2)*x^4 + 2*b*x^6 - x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*a*b*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][Sqrt[-a + x^2]/(Sqrt[-b + x^2]*(-(a^2*d) + 2*a*d*x^2 + b^2*(1 - d/b^2)*x^4 - 2*b*x^6 + x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x] + (2*Sqrt[x]*Sqrt[-a + x]*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^4*Sqrt[-a + x^2])/(Sqrt[-b + x^2]*(-(a^2*d) + 2*a*d*x^2 + b^2*(1 - d/b^2)*x^4 - 2*b*x^6 + x^8)), x], x, Sqrt[x]])/Sqrt[(a - x)*(b - x)*x]","F",0,0,0,0,-1,"{}"
1302,1,169,0,0.2944517,"\int \frac{-2 b+a x^4}{x^4 \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-2*b + a*x^4)/(x^4*(b*x^2 + a*x^4)^(1/4)),x]","\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a x^4+b x^2}}+\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a x^4+b x^2}}+\frac{4 \left(a x^4+b x^2\right)^{3/4}}{7 x^5}-\frac{16 a \left(a x^4+b x^2\right)^{3/4}}{21 b x^3}","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*(b*x^2 + a*x^4)^(3/4))/(7*x^5) - (16*a*(b*x^2 + a*x^4)^(3/4))/(21*b*x^3) + (a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(1/4) + (a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(1/4)","A",10,9,28,0.3214,1,"{2052, 2011, 329, 240, 212, 206, 203, 2016, 2014}"
1303,1,169,0,0.2852268,"\int \frac{2 b+a x^4}{x^4 \sqrt[4]{b x^2+a x^4}} \, dx","Int[(2*b + a*x^4)/(x^4*(b*x^2 + a*x^4)^(1/4)),x]","\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a x^4+b x^2}}+\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a x^4+b x^2}}-\frac{4 \left(a x^4+b x^2\right)^{3/4}}{7 x^5}+\frac{16 a \left(a x^4+b x^2\right)^{3/4}}{21 b x^3}","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*(b*x^2 + a*x^4)^(3/4))/(7*x^5) + (16*a*(b*x^2 + a*x^4)^(3/4))/(21*b*x^3) + (a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(1/4) + (a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(1/4)","A",10,9,28,0.3214,1,"{2052, 2011, 329, 240, 212, 206, 203, 2016, 2014}"
1304,0,0,0,0.5727196,"\int \frac{-1+x}{(1+x) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(-1 + x)/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{-1+x}{(1+x) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","-\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,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] - 2*Defer[Int][1/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]","F",0,0,0,0,-1,"{}"
1305,0,0,0,0.5045703,"\int \frac{1+x}{(-1+x) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(1 + x)/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{1+x}{(-1+x) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","-\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,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] + 2*Defer[Int][1/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]","F",0,0,0,0,-1,"{}"
1306,1,87,0,1.1007283,"\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","Int[x^2/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(-1 + k^2*x^4)),x]","\frac{\tan ^{-1}\left(\frac{(k+1) x}{\sqrt{k^2 x^4-\left(k^2+1\right) x^2+1}}\right)}{4 k (k+1)}-\frac{\tan ^{-1}\left(\frac{(1-k) x}{\sqrt{k^2 x^4-\left(k^2+1\right) x^2+1}}\right)}{4 (1-k) k}","\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,"-1/4*ArcTan[((1 - k)*x)/Sqrt[1 - (1 + k^2)*x^2 + k^2*x^4]]/((1 - k)*k) + ArcTan[((1 + k)*x)/Sqrt[1 - (1 + k^2)*x^2 + k^2*x^4]]/(4*k*(1 + k))","A",11,7,37,0.1892,1,"{1992, 6725, 1210, 1103, 1698, 204, 203}"
1307,1,313,0,0.9141329,"\int \frac{\left(-1+x^6\right)^{2/3} \left(1+x^6\right)}{x^3 \left(-1-x^3+x^6\right)} \, dx","Int[((-1 + x^6)^(2/3)*(1 + x^6))/(x^3*(-1 - x^3 + x^6)),x]","-\frac{\left(1-\sqrt{5}\right) \left(x^6-1\right)^{2/3} x F_1\left(\frac{1}{6};-\frac{2}{3},1;\frac{7}{6};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{\left(3-\sqrt{5}\right) \left(1-x^6\right)^{2/3}}-\frac{\left(1+\sqrt{5}\right) \left(x^6-1\right)^{2/3} x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};\frac{2 x^6}{3+\sqrt{5}},x^6\right)}{\left(3+\sqrt{5}\right) \left(1-x^6\right)^{2/3}}-\frac{\left(x^6-1\right)^{2/3} x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{2 \left(3-\sqrt{5}\right) \left(1-x^6\right)^{2/3}}-\frac{\left(x^6-1\right)^{2/3} x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};x^6,\frac{2 x^6}{3+\sqrt{5}}\right)}{2 \left(3+\sqrt{5}\right) \left(1-x^6\right)^{2/3}}+\frac{\left(x^6-1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{2}{3};x^6\right)}{2 \left(1-x^6\right)^{2/3} x^2}","\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,"-(((1 - Sqrt[5])*x*(-1 + x^6)^(2/3)*AppellF1[1/6, -2/3, 1, 7/6, x^6, (2*x^6)/(3 - Sqrt[5])])/((3 - Sqrt[5])*(1 - x^6)^(2/3))) - ((1 + Sqrt[5])*x*(-1 + x^6)^(2/3)*AppellF1[1/6, 1, -2/3, 7/6, (2*x^6)/(3 + Sqrt[5]), x^6])/((3 + Sqrt[5])*(1 - x^6)^(2/3)) - (x^4*(-1 + x^6)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, x^6, (2*x^6)/(3 - Sqrt[5])])/(2*(3 - Sqrt[5])*(1 - x^6)^(2/3)) - (x^4*(-1 + x^6)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, x^6, (2*x^6)/(3 + Sqrt[5])])/(2*(3 + Sqrt[5])*(1 - x^6)^(2/3)) + ((-1 + x^6)^(2/3)*Hypergeometric2F1[-2/3, -1/3, 2/3, x^6])/(2*x^2*(1 - x^6)^(2/3))","C",21,10,30,0.3333,0,"{6728, 275, 365, 364, 1438, 430, 429, 465, 511, 510}"
1308,1,247,0,0.7917295,"\int \frac{\left(-1+x^6\right) \left(1+x^6\right)^{2/3}}{x^3 \left(1-x^3+x^6\right)} \, dx","Int[((-1 + x^6)*(1 + x^6)^(2/3))/(x^3*(1 - x^3 + x^6)),x]","\frac{\left(-\sqrt{3}+i\right) x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};-\frac{2 x^6}{1-i \sqrt{3}},-x^6\right)}{\sqrt{3}+i}+\frac{\left(\sqrt{3}+i\right) x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};-\frac{2 x^6}{1+i \sqrt{3}},-x^6\right)}{-\sqrt{3}+i}+\frac{x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-x^6,-\frac{2 x^6}{1-i \sqrt{3}}\right)}{2 \left(1-i \sqrt{3}\right)}+\frac{x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-x^6,-\frac{2 x^6}{1+i \sqrt{3}}\right)}{2 \left(1+i \sqrt{3}\right)}+\frac{\, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{2}{3};-x^6\right)}{2 x^2}","\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,"((I - Sqrt[3])*x*AppellF1[1/6, 1, -2/3, 7/6, (-2*x^6)/(1 - I*Sqrt[3]), -x^6])/(I + Sqrt[3]) + ((I + Sqrt[3])*x*AppellF1[1/6, 1, -2/3, 7/6, (-2*x^6)/(1 + I*Sqrt[3]), -x^6])/(I - Sqrt[3]) + (x^4*AppellF1[2/3, -2/3, 1, 5/3, -x^6, (-2*x^6)/(1 - I*Sqrt[3])])/(2*(1 - I*Sqrt[3])) + (x^4*AppellF1[2/3, -2/3, 1, 5/3, -x^6, (-2*x^6)/(1 + I*Sqrt[3])])/(2*(1 + I*Sqrt[3])) + Hypergeometric2F1[-2/3, -1/3, 2/3, -x^6]/(2*x^2)","C",16,7,30,0.2333,0,"{6728, 275, 364, 1438, 429, 465, 510}"
1309,1,4085,0,30.6853016,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^4} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((-x^2 + x^4)^(1/4)*(1 + x^8)),x]","\frac{(-1)^{7/16} \left((-1+i)+\sqrt{2}\right) \sqrt{x^2-1} x^{3/2}}{8 \sqrt[4]{x^4-x^2} \left(\sqrt{x^2-1}+1\right)}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (-1)^{11/16} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt{x^2-1} x^{3/2}}{\sqrt[4]{x^4-x^2} \left(\sqrt{x^2-1}+1\right)}-\frac{i \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{i \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left((1+i)-i \sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1+\sqrt[4]{-1}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{i \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[16]{-1} \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+i \sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{-1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{-1} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{(-1)^{9/16} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{(-1)^{13/16} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{16 \sqrt[4]{x^4-x^2}}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}-\frac{i \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{i \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left((1+i)-i \sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1+\sqrt[4]{-1}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{i \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[16]{-1} \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+i \sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{-1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{-1} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{(-1)^{9/16} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{(-1)^{13/16} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{16 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{(-1)^{13/16} \left((-1+i)+\sqrt{2}\right) \left(1-x^2\right) \sqrt{x}}{24 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{24}-\frac{i}{24}\right) \sqrt[16]{-1} \left(1-\frac{1-i}{\sqrt{2}}\right) \left(1-x^2\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{(-1)^{9/16} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[8]{-1} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{32 \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[8]{-1} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{13/16} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{5/8} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{32 \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{5/8} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{7/16} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (-1)^{11/16} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{3/16} \left(2+\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(2 i+(2+2 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{11/16} \left(2-\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{8 \left(4 i+(4+4 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{11/16} \left(2-\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(2 i+(2+2 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{15/16} \left(2-\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{32 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{11/16} \left(1+\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{8 \left(2 i+(2+2 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{11/16} \left(1+\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(i+(1+i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{15/16} \left(1+\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{3/16} \left(1-\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{4 \left(4 i+(4+4 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{7/16} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) (-1)^{11/16} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{7/16} \sqrt{-1-\sqrt[4]{-1}} \left((-1+i)+\sqrt{2}\right) \left(1-\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2-\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{64 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{\left(\frac{1}{64}-\frac{i}{64}\right) (-1)^{11/16} \sqrt{\frac{1}{2} \left(-1-\sqrt[4]{-1}\right)} \left((-1+i)+\sqrt{2}\right) \left(1-\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2-\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{7/16} \sqrt{-1-\sqrt[4]{-1}} \left((-1+i)+\sqrt{2}\right) \left(1+\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2+\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{64 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{\left(\frac{1}{64}-\frac{i}{64}\right) (-1)^{11/16} \sqrt{\frac{1}{2} \left(-1-\sqrt[4]{-1}\right)} \left((-1+i)+\sqrt{2}\right) \left(1+\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2+\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}","\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,"((1/24 - I/24)*(-1)^(1/16)*(1 - (1 - I)/Sqrt[2])*Sqrt[x]*(1 - x^2))/(-x^2 + x^4)^(1/4) + ((-1)^(13/16)*((-1 + I) + Sqrt[2])*Sqrt[x]*(1 - x^2))/(24*(-x^2 + x^4)^(1/4)) - ((1/8 - I/8)*(-1)^(11/16)*(1 - (1 - I)/Sqrt[2])*x^(3/2)*Sqrt[-1 + x^2])/((-x^2 + x^4)^(1/4)*(1 + Sqrt[-1 + x^2])) + ((-1)^(7/16)*((-1 + I) + Sqrt[2])*x^(3/2)*Sqrt[-1 + x^2])/(8*(-x^2 + x^4)^(1/4)*(1 + Sqrt[-1 + x^2])) + ((1/4 + I/4)*(1 + (-1)^(1/4))*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + (((1 + I) - I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) + ((I/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((I/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + ((I/4)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 - (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((-1)^(1/16)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(15/16)*(-1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(1/4)*(1 + (-1)^(1/4))^(3/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(9/16)*(1 + (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(15/16)*(1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((1/16 - I/16)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(-x^2 + x^4)^(1/4) - ((-1)^(13/16)*(-1 - (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(16*(-x^2 + x^4)^(1/4)) + ((1/32 + I/32)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(1/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(9/16)*(1 + (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(1/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(32*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((1/32 - I/32)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(5/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(13/16)*(-1 - (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(5/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(32*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((1/4 + I/4)*(1 + (-1)^(1/4))*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + (((1 + I) - I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) + ((I/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((I/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + ((I/4)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 - (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((-1)^(1/16)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((-1)^(15/16)*(-1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(1/4)*(1 + (-1)^(1/4))^(3/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(9/16)*(1 + (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((-1)^(15/16)*(1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) + ((1/16 - I/16)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(-x^2 + x^4)^(1/4) + ((-1)^(13/16)*(-1 - (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(16*(-x^2 + x^4)^(1/4)) + ((1/8 - I/8)*(-1)^(11/16)*(1 - (1 - I)/Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticE[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(7/16)*((-1 + I) + Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticE[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(8*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((1/16 - I/16)*(-1)^(11/16)*(1 - (1 - I)/Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(7/16)*((-1 + I) + Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(3/16)*(1 - Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(4*(4*I + (4 + 4*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(15/16)*(1 + Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(11/16)*(1 + Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(I + (1 + I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(11/16)*(1 + Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(8*(2*I + (2 + 2*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(15/16)*(2 - Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(32*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(11/16)*(2 - Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(2*I + (2 + 2*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(11/16)*(2 - Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(8*(4*I + (4 + 4*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(3/16)*(2 + Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(2*I + (2 + 2*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((1/64 - I/64)*(-1)^(11/16)*Sqrt[(-1 - (-1)^(1/4))/2]*((-1 + I) + Sqrt[2])*(1 - Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 - (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/((2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(7/16)*Sqrt[-1 - (-1)^(1/4)]*((-1 + I) + Sqrt[2])*(1 - Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 - (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(64*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((1/64 - I/64)*(-1)^(11/16)*Sqrt[(-1 - (-1)^(1/4))/2]*((-1 + I) + Sqrt[2])*(1 + Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 + (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/((2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(7/16)*Sqrt[-1 - (-1)^(1/4)]*((-1 + I) + Sqrt[2])*(1 + Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 + (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(64*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4))","C",581,31,26,1.192,0,"{2056, 1586, 6715, 6725, 2153, 1240, 408, 240, 212, 206, 203, 377, 208, 205, 511, 510, 1248, 735, 844, 230, 305, 220, 1196, 746, 399, 490, 1217, 1707, 444, 63, 298}"
1310,1,4085,0,27.8615134,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^4} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((-x^2 + x^4)^(1/4)*(1 + x^8)),x]","\frac{(-1)^{7/16} \left((-1+i)+\sqrt{2}\right) \sqrt{x^2-1} x^{3/2}}{8 \sqrt[4]{x^4-x^2} \left(\sqrt{x^2-1}+1\right)}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (-1)^{11/16} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt{x^2-1} x^{3/2}}{\sqrt[4]{x^4-x^2} \left(\sqrt{x^2-1}+1\right)}-\frac{i \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{i \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left((1+i)-i \sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1+\sqrt[4]{-1}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{i \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[16]{-1} \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+i \sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{-1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{-1} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{(-1)^{9/16} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{(-1)^{13/16} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{16 \sqrt[4]{x^4-x^2}}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}-\frac{i \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{i \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left((1+i)-i \sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1+\sqrt[4]{-1}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{i \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[16]{-1} \left(-1+\sqrt[4]{-1}\right)^{3/4} \left((1+i)+i \sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{-1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{-1} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1-i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}-\frac{(-1)^{9/16} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{(-1)^{15/16} \sqrt[4]{1+\sqrt[4]{-1}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right) \sqrt{x}}{4 \sqrt[4]{x^4-x^2}}+\frac{(-1)^{13/16} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{16 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{(-1)^{13/16} \left((-1+i)+\sqrt{2}\right) \left(1-x^2\right) \sqrt{x}}{24 \sqrt[4]{x^4-x^2}}+\frac{\left(\frac{1}{24}-\frac{i}{24}\right) \sqrt[16]{-1} \left(1-\frac{1-i}{\sqrt{2}}\right) \left(1-x^2\right) \sqrt{x}}{\sqrt[4]{x^4-x^2}}+\frac{(-1)^{9/16} \left(1+\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[8]{-1} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{32 \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[8]{-1} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{13/16} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left((-1+i)+\sqrt{2}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{5/8} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{32 \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) \sqrt[16]{-1} \left(-1-\sqrt[4]{-1}\right)^{3/4} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt{x^2} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{(-1)^{5/8} \sqrt[4]{x^2-1}}{\sqrt[4]{-1-\sqrt[4]{-1}} \sqrt{x^2}}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{7/16} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (-1)^{11/16} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{3/16} \left(2+\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(2 i+(2+2 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{11/16} \left(2-\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{8 \left(4 i+(4+4 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{11/16} \left(2-\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(2 i+(2+2 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{15/16} \left(2-\sqrt{-4-(2+2 i) \sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{32 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{11/16} \left(1+\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{8 \left(2 i+(2+2 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{11/16} \left(1+\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(i+(1+i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{15/16} \left(1+\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{3/16} \left(1-\sqrt{-1-\frac{1+i}{\sqrt{2}}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{4 \left(4 i+(4+4 i) \sqrt{2}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{7/16} \left((-1+i)+\sqrt{2}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) (-1)^{11/16} \left(1-\frac{1-i}{\sqrt{2}}\right) \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{(-1)^{7/16} \sqrt{-1-\sqrt[4]{-1}} \left((-1+i)+\sqrt{2}\right) \left(1-\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2-\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{64 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{\left(\frac{1}{64}-\frac{i}{64}\right) (-1)^{11/16} \sqrt{\frac{1}{2} \left(-1-\sqrt[4]{-1}\right)} \left((-1+i)+\sqrt{2}\right) \left(1-\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2-\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}+\frac{(-1)^{7/16} \sqrt{-1-\sqrt[4]{-1}} \left((-1+i)+\sqrt{2}\right) \left(1+\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2+\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{64 \left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}-\frac{\left(\frac{1}{64}-\frac{i}{64}\right) (-1)^{11/16} \sqrt{\frac{1}{2} \left(-1-\sqrt[4]{-1}\right)} \left((-1+i)+\sqrt{2}\right) \left(1+\sqrt{-1-\sqrt[4]{-1}}\right)^2 \sqrt[4]{x^2-1} \sqrt{\frac{x^2}{\left(\sqrt{x^2-1}+1\right)^2}} \left(\sqrt{x^2-1}+1\right) \Pi \left(\frac{1}{4} \left(2+\frac{\sqrt[4]{-1}}{\sqrt{-1-\sqrt[4]{-1}}}\right);2 \tan ^{-1}\left(\sqrt[4]{x^2-1}\right)|\frac{1}{2}\right)}{\left(2+\sqrt[4]{-1}\right) \sqrt[4]{x^4-x^2} \sqrt{x}}","\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,"((1/24 - I/24)*(-1)^(1/16)*(1 - (1 - I)/Sqrt[2])*Sqrt[x]*(1 - x^2))/(-x^2 + x^4)^(1/4) + ((-1)^(13/16)*((-1 + I) + Sqrt[2])*Sqrt[x]*(1 - x^2))/(24*(-x^2 + x^4)^(1/4)) - ((1/8 - I/8)*(-1)^(11/16)*(1 - (1 - I)/Sqrt[2])*x^(3/2)*Sqrt[-1 + x^2])/((-x^2 + x^4)^(1/4)*(1 + Sqrt[-1 + x^2])) + ((-1)^(7/16)*((-1 + I) + Sqrt[2])*x^(3/2)*Sqrt[-1 + x^2])/(8*(-x^2 + x^4)^(1/4)*(1 + Sqrt[-1 + x^2])) + ((1/4 + I/4)*(1 + (-1)^(1/4))*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + (((1 + I) - I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) + ((I/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((I/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + ((I/4)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 - (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((-1)^(1/16)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(15/16)*(-1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(1/4)*(1 + (-1)^(1/4))^(3/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(9/16)*(1 + (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(15/16)*(1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((1/16 - I/16)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(-x^2 + x^4)^(1/4) - ((-1)^(13/16)*(-1 - (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(16*(-x^2 + x^4)^(1/4)) + ((1/32 + I/32)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(1/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(9/16)*(1 + (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(1/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(32*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((1/32 - I/32)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(5/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(13/16)*(-1 - (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x^2]*(-1 + x^2)^(1/4)*ArcTan[((-1)^(5/8)*(-1 + x^2)^(1/4))/((-1 - (-1)^(1/4))^(1/4)*Sqrt[x^2])])/(32*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((1/4 + I/4)*(1 + (-1)^(1/4))*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + (((1 + I) - I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) + ((I/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((I/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + ((I/4)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 - (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - ((-1)^(1/16)*(-1 + (-1)^(1/4))^(3/4)*((1 + I) + I*Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((-1)^(15/16)*(-1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(1/4)*(1 + (-1)^(1/4))^(3/4)*((-1 - I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) - ((-1)^(9/16)*(1 + (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((-1)^(15/16)*(1 + (-1)^(1/4))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(-x^2 + x^4)^(1/4)) + ((1/16 - I/16)*(-1)^(1/16)*(-1 - (-1)^(1/4))^(3/4)*(1 - (1 - I)/Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(-x^2 + x^4)^(1/4) + ((-1)^(13/16)*(-1 - (-1)^(1/4))^(3/4)*((-1 + I) + Sqrt[2])*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(-1 + x^2)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/(16*(-x^2 + x^4)^(1/4)) + ((1/8 - I/8)*(-1)^(11/16)*(1 - (1 - I)/Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticE[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(7/16)*((-1 + I) + Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticE[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(8*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((1/16 - I/16)*(-1)^(11/16)*(1 - (1 - I)/Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(7/16)*((-1 + I) + Sqrt[2])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(3/16)*(1 - Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(4*(4*I + (4 + 4*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(15/16)*(1 + Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(11/16)*(1 + Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(I + (1 + I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(11/16)*(1 + Sqrt[-1 - (1 + I)/Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(8*(2*I + (2 + 2*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(15/16)*(2 - Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(32*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(11/16)*(2 - Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(2*I + (2 + 2*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(11/16)*(2 - Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(8*(4*I + (4 + 4*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(3/16)*(2 + Sqrt[-4 - (2 + 2*I)*Sqrt[2]])*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticF[2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(16*(2*I + (2 + 2*I)*Sqrt[2])*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((1/64 - I/64)*(-1)^(11/16)*Sqrt[(-1 - (-1)^(1/4))/2]*((-1 + I) + Sqrt[2])*(1 - Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 - (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/((2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((-1)^(7/16)*Sqrt[-1 - (-1)^(1/4)]*((-1 + I) + Sqrt[2])*(1 - Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 - (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(64*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) - ((1/64 - I/64)*(-1)^(11/16)*Sqrt[(-1 - (-1)^(1/4))/2]*((-1 + I) + Sqrt[2])*(1 + Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 + (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/((2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4)) + ((-1)^(7/16)*Sqrt[-1 - (-1)^(1/4)]*((-1 + I) + Sqrt[2])*(1 + Sqrt[-1 - (-1)^(1/4)])^2*(-1 + x^2)^(1/4)*Sqrt[x^2/(1 + Sqrt[-1 + x^2])^2]*(1 + Sqrt[-1 + x^2])*EllipticPi[(2 + (-1)^(1/4)/Sqrt[-1 - (-1)^(1/4)])/4, 2*ArcTan[(-1 + x^2)^(1/4)], 1/2])/(64*(2 + (-1)^(1/4))*Sqrt[x]*(-x^2 + x^4)^(1/4))","C",581,31,26,1.192,0,"{2056, 1586, 6715, 6725, 2153, 1240, 408, 240, 212, 206, 203, 377, 208, 205, 511, 510, 1248, 735, 844, 230, 305, 220, 1196, 746, 399, 490, 1217, 1707, 444, 63, 298}"
1311,1,347,0,0.7948058,"\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","Int[(1 + 3*x^4 + x^8)/(x^2*(1 + x^4)^(3/4)*(1 + 3*x^4 + 3*x^8)),x]","-\frac{\sqrt[4]{x^4+1}}{x}-\frac{1}{6} \left(3+i \sqrt{3}\right) \sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}} \tan ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt[4]{x^4+1}}\right)-\frac{\left(3-i \sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}}}+\frac{1}{6} \left(3+i \sqrt{3}\right) \sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}} \sqrt[4]{x^4+1}}\right)+\frac{\left(3-i \sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{-\frac{-\sqrt{3}+3 i}{\sqrt{3}+3 i}}}","-\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,"-((1 + x^4)^(1/4)/x) - ((3 + I*Sqrt[3])*(-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*ArcTan[x/((-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*(1 + x^4)^(1/4))])/6 - ((3 - I*Sqrt[3])*ArcTan[((-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*x)/(1 + x^4)^(1/4)])/(6*(-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4)) + ((3 + I*Sqrt[3])*(-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*ArcTanh[x/((-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*(1 + x^4)^(1/4))])/6 + ((3 - I*Sqrt[3])*ArcTanh[((-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*x)/(1 + x^4)^(1/4)])/(6*(-((3*I - Sqrt[3])/(3*I + Sqrt[3])))^(1/4))","C",13,7,37,0.1892,0,"{6728, 264, 1528, 494, 298, 205, 208}"
1312,0,0,0,0.9380408,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{b+a^2 x^2} \, dx","Int[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(b + a^2*x^2),x]","\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{b+a^2 x^2} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c+c^2}\&\right]}{a}",1,"-1/2*Defer[Int][Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(Sqrt[-b] - a*x), x]/Sqrt[-b] - Defer[Int][Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(Sqrt[-b] + a*x), x]/(2*Sqrt[-b])","F",0,0,0,0,-1,"{}"
1313,0,0,0,0.6569644,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{b+a^2 x^2} \, dx","Int[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(b + a^2*x^2),x]","\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{b+a^2 x^2} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c+c^2}\&\right]}{a}",1,"-1/2*Defer[Int][Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(Sqrt[-b] - a*x), x]/Sqrt[-b] - Defer[Int][Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/(Sqrt[-b] + a*x), x]/(2*Sqrt[-b])","F",0,0,0,0,-1,"{}"
1314,1,86,0,0.0814364,"\int \frac{-1+x}{x^4 \sqrt[3]{1+x^3}} \, dx","Int[(-1 + x)/(x^4*(1 + x^3)^(1/3)),x]","\frac{\left(x^3+1\right)^{2/3}}{3 x^3}+\frac{1}{6} \log \left(1-\sqrt[3]{x^3+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}-\frac{\log (x)}{6}","\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 + x^3)^(2/3)/(3*x^3) - (1 + x^3)^(2/3)/(2*x^2) + ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[x]/6 + Log[1 - (1 + x^3)^(1/3)]/6","A",9,8,16,0.5000,1,"{1844, 266, 51, 55, 618, 204, 31, 264}"
1315,0,0,0,1.4738742,"\int \frac{(3+2 x) \sqrt[3]{1+x+x^3}}{x^2 (1+x)} \, dx","Int[((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,"(9*2^(2/3)*(1 + x + x^3)^(1/3)*Defer[Int][(((2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3))/6^(2/3) + x)^(1/3)*((6 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3))/18 - (((6/(-9 + Sqrt[93]))^(1/3) - ((-9 + Sqrt[93])/2)^(1/3))*x)/3^(2/3) + x^2)^(1/3))/x^2, x])/((6^(1/3)*(2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3)) + 6*x)^(1/3)*(6 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3) - 6*3^(1/3)*((6/(-9 + Sqrt[93]))^(1/3) - ((-9 + Sqrt[93])/2)^(1/3))*x + 18*x^2)^(1/3)) - (3*2^(2/3)*(1 + x + x^3)^(1/3)*Defer[Int][(((2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3))/6^(2/3) + x)^(1/3)*((6 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3))/18 - (((6/(-9 + Sqrt[93]))^(1/3) - ((-9 + Sqrt[93])/2)^(1/3))*x)/3^(2/3) + x^2)^(1/3))/x, x])/((6^(1/3)*(2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3)) + 6*x)^(1/3)*(6 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3) - 6*3^(1/3)*((6/(-9 + Sqrt[93]))^(1/3) - ((-9 + Sqrt[93])/2)^(1/3))*x + 18*x^2)^(1/3)) + (3*2^(2/3)*(1 + x + x^3)^(1/3)*Defer[Int][(((2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3))/6^(2/3) + x)^(1/3)*((6 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3))/18 - (((6/(-9 + Sqrt[93]))^(1/3) - ((-9 + Sqrt[93])/2)^(1/3))*x)/3^(2/3) + x^2)^(1/3))/(1 + x), x])/((6^(1/3)*(2*(3/(-9 + Sqrt[93]))^(1/3) - (2*(-9 + Sqrt[93]))^(1/3)) + 6*x)^(1/3)*(6 + 6*3^(1/3)*(2/(-9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(-9 + Sqrt[93]))^(2/3) - 6*3^(1/3)*((6/(-9 + Sqrt[93]))^(1/3) - ((-9 + Sqrt[93])/2)^(1/3))*x + 18*x^2)^(1/3))","F",0,0,0,0,-1,"{}"
1316,0,0,0,11.5951018,"\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","Int[((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,"(4*a*b*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(-a + x^4)^(5/4)/((-b + x^4)^(3/4)*(a^3*d - b*(1 + (3*a^2*d)/b)*x^4 + (1 + 3*a*d)*x^8 - d*x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(3/4) - (8*(a - b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^4*(-a + x^4)^(5/4))/((-b + x^4)^(3/4)*(a^3*d - b*(1 + (3*a^2*d)/b)*x^4 + (1 + 3*a*d)*x^8 - d*x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(3/4) + (4*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(-a + x^4)^(5/4))/((-b + x^4)^(3/4)*(-(a^3*d) + b*(1 + (3*a^2*d)/b)*x^4 - (1 + 3*a*d)*x^8 + d*x^12)), x], x, x^(1/4)])/((a - x)*(b - x)*x)^(3/4)","F",0,0,0,0,-1,"{}"
1317,0,0,0,0.0714076,"\int \frac{\left(1+x^2\right)^2}{\left(1-x^2\right) \left(1-6 x^2+x^4\right)^{3/4}} \, dx","Int[(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,"Defer[Int][(1 + x^2)^2/((1 - x^2)*(1 - 6*x^2 + x^4)^(3/4)), x]","F",0,0,0,0,-1,"{}"
1318,0,0,0,1.4133285,"\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","Int[((-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,"(-4*(1 - x^3)^(3/4)*Hypergeometric2F1[-1/3, 3/4, 2/3, x^3])/(x*(-1 + x^3)^(3/4)) - (2*x*(1 - x^3)^(3/4)*Hypergeometric2F1[1/3, 3/4, 4/3, x^3])/(-1 + x^3)^(3/4) + (x^2*(1 - x^3)^(3/4)*Hypergeometric2F1[2/3, 3/4, 5/3, x^3])/(2*(-1 + x^3)^(3/4)) + 2*Defer[Int][1/((-1 + x^3)^(3/4)*(1 - x^3 - x^4)), x] + 2*Defer[Int][x/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x] - 8*Defer[Int][x^2/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x] + 2*Defer[Int][x^3/((-1 + x^3)^(3/4)*(-1 + x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1319,0,0,0,2.4517372,"\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","Int[((-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,"(4*(1 - x^4)^(1/4)*Hypergeometric2F1[-21/16, -3/4, -5/16, x^4])/(7*x^5*(-x + x^5)^(1/4)) - (4*(1 - x^4)^(1/4)*Hypergeometric2F1[-3/4, -9/16, 7/16, x^4])/(3*x^2*(-x + x^5)^(1/4)) + (4*(1 - x^4)^(1/4)*Hypergeometric2F1[-3/4, -5/16, 11/16, x^4])/(5*x*(-x + x^5)^(1/4)) - (24*x^(1/4)*(-1 + x^4)^(1/4)*Defer[Subst][Defer[Int][(x^2*(-1 + x^16)^(3/4))/(-1 - 2*x^12 + x^16), x], x, x^(1/4)])/(-x + x^5)^(1/4) + (16*x^(1/4)*(-1 + x^4)^(1/4)*Defer[Subst][Defer[Int][(x^6*(-1 + x^16)^(3/4))/(-1 - 2*x^12 + x^16), x], x, x^(1/4)])/(-x + x^5)^(1/4)","F",0,0,0,0,-1,"{}"
1320,0,0,0,4.9566849,"\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","Int[((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,"(-4*b*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[-1/5, 3/4, 4/5, (a*x^5)/b])/(x*(-b + a*x^5)^(3/4)) + (2*c^3*x*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[1/5, 3/4, 6/5, (a*x^5)/b])/(a^2*(-b + a*x^5)^(3/4)) + (c^2*x^2*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, (a*x^5)/b])/(a*(-b + a*x^5)^(3/4)) + (2*c*x^3*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[3/5, 3/4, 8/5, (a*x^5)/b])/(3*(-b + a*x^5)^(3/4)) + (a*x^4*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[3/4, 4/5, 9/5, (a*x^5)/b])/(4*(-b + a*x^5)^(3/4)) - (2*b*c^3*Defer[Int][1/((b + c*x^4 - a*x^5)*(-b + a*x^5)^(3/4)), x])/a^2 - (2*c^4*Defer[Int][x^4/((b + c*x^4 - a*x^5)*(-b + a*x^5)^(3/4)), x])/a^2 + (2*b*c^2*Defer[Int][x/((-b + a*x^5)^(3/4)*(-b - c*x^4 + a*x^5)), x])/a + 10*b*c*Defer[Int][x^2/((-b + a*x^5)^(3/4)*(-b - c*x^4 + a*x^5)), x]","F",0,0,0,0,-1,"{}"
1321,0,0,0,1.0319002,"\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","Int[((-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,"(2*(1 + x^6)^(3/4))/(3*x^3) - 2*x*Hypergeometric2F1[1/6, 1/4, 7/6, -x^6] + 6*Defer[Int][1/((1 + x^6)^(1/4)*(1 + x^4 + x^6)), x] + 2*Defer[Int][x^4/((1 + x^6)^(1/4)*(1 + x^4 + x^6)), x]","F",0,0,0,0,-1,"{}"
1322,0,0,0,2.9405072,"\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","Int[(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,"(b*Defer[Int][1/((b + x^4 - a*x^6)^2*(-b + a*x^6)^(1/4)), x])/a^2 + (b*Defer[Int][x^2/((b + x^4 - a*x^6)^2*(-b + a*x^6)^(1/4)), x])/a + (a^(-2) + 3*b)*Defer[Int][x^4/((b + x^4 - a*x^6)^2*(-b + a*x^6)^(1/4)), x] + Defer[Int][1/((-b + a*x^6)^(1/4)*(-b - x^4 + a*x^6)), x]/a^2 + Defer[Int][x^2/((-b + a*x^6)^(1/4)*(-b - x^4 + a*x^6)), x]/a + Defer[Int][x^4/((-b + a*x^6)^(1/4)*(-b - x^4 + a*x^6)), x]","F",0,0,0,0,-1,"{}"
1323,0,0,0,3.7763732,"\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","Int[((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,"(2*(-b + a*x^6)^(3/4))/(3*x^3) + (x*(1 - (a*x^6)/b)^(1/4)*Hypergeometric2F1[1/6, 1/4, 7/6, (a*x^6)/b])/(-b + a*x^6)^(1/4) - 3*b*Defer[Int][1/((b + 2*x^4 - a*x^6)*(-b + a*x^6)^(1/4)), x] + 2*Defer[Int][x^4/((-b + a*x^6)^(1/4)*(-b - 2*x^4 + a*x^6)), x]","F",0,0,0,0,-1,"{}"
1324,0,0,0,4.3381052,"\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","Int[(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,"-1/2*Defer[Int][Sqrt[-1 - 2*x^2 - 2*x^3 - x^8]/(1 + x), x] + Defer[Int][Sqrt[-1 - 2*x^2 - 2*x^3 - x^8]/(1 - x + x^2 + x^3 - x^4 + x^5 - x^6 + x^7), x]/2 + 2*Defer[Int][(x*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 - x + x^2 + x^3 - x^4 + x^5 - x^6 + x^7), x] - (3*Defer[Int][(x^2*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 - x + x^2 + x^3 - x^4 + x^5 - x^6 + x^7), x])/2 + 2*Defer[Int][(x^3*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 - x + x^2 + x^3 - x^4 + x^5 - x^6 + x^7), x] - (5*Defer[Int][(x^4*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 - x + x^2 + x^3 - x^4 + x^5 - x^6 + x^7), x])/2 + 3*Defer[Int][(x^5*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 - x + x^2 + x^3 - x^4 + x^5 - x^6 + x^7), x] + Defer[Int][(x^6*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 - x + x^2 + x^3 - x^4 + x^5 - x^6 + x^7), x]/2 + Defer[Int][Sqrt[-1 - 2*x^2 - 2*x^3 - x^8]/(-1 - x^2 - 2*x^3 - x^8), x] - 3*Defer[Int][(x*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 + x^2 + 2*x^3 + x^8), x] - 4*Defer[Int][(x^6*Sqrt[-1 - 2*x^2 - 2*x^3 - x^8])/(1 + x^2 + 2*x^3 + x^8), x]","F",0,0,0,0,-1,"{}"
1325,0,0,0,0.5579669,"\int \frac{\left(1+x^6\right) \sqrt{-2-x^2+x^6}}{4-3 x^4-4 x^6+x^{12}} \, dx","Int[((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,"Defer[Int][Sqrt[-2 - x^2 + x^6]/(4 - 3*x^4 - 4*x^6 + x^12), x] + Defer[Int][(x^6*Sqrt[-2 - x^2 + x^6])/(4 - 3*x^4 - 4*x^6 + x^12), x]","F",0,0,0,0,-1,"{}"
1326,1,97,0,0.0489122,"\int x \sqrt[3]{-1+x^3} \, dx","Int[x*(-1 + x^3)^(1/3),x]","\frac{1}{9} \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)}{3 \sqrt{3}}+\frac{1}{3} \sqrt[3]{x^3-1} x^2-\frac{1}{18} \log \left(\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+1\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*(-1 + x^3)^(1/3))/3 + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) + Log[1 - x/(-1 + x^3)^(1/3)]/9 - Log[1 + x^2/(-1 + x^3)^(2/3) + x/(-1 + x^3)^(1/3)]/18","A",8,8,11,0.7273,1,"{279, 331, 292, 31, 634, 618, 204, 628}"
1327,1,97,0,0.0472751,"\int x \sqrt[3]{1+x^3} \, dx","Int[x*(1 + x^3)^(1/3),x]","-\frac{1}{9} \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)}{3 \sqrt{3}}+\frac{1}{3} \sqrt[3]{x^3+1} x^2+\frac{1}{18} \log \left(\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\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*(1 + x^3)^(1/3))/3 - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[1 - x/(1 + x^3)^(1/3)]/9 + Log[1 + x^2/(1 + x^3)^(2/3) + x/(1 + x^3)^(1/3)]/18","A",8,8,11,0.7273,1,"{279, 331, 292, 31, 634, 618, 204, 628}"
1328,1,180,0,0.1265005,"\int \frac{\sqrt[3]{x+x^3}}{x^2} \, dx","Int[(x + x^3)^(1/3)/x^2,x]","-\frac{3 \sqrt[3]{x^3+x}}{2 x}-\frac{x^{2/3} \left(x^2+1\right)^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{2 \left(x^3+x\right)^{2/3}}+\frac{x^{2/3} \left(x^2+1\right)^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{4 \left(x^3+x\right)^{2/3}}-\frac{\sqrt{3} x^{2/3} \left(x^2+1\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \left(x^3+x\right)^{2/3}}","-\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))/(2*x) - (Sqrt[3]*x^(2/3)*(1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*(x + x^3)^(2/3)) - (x^(2/3)*(1 + x^2)^(2/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(2*(x + x^3)^(2/3)) + (x^(2/3)*(1 + x^2)^(2/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(4*(x + x^3)^(2/3))","A",11,11,13,0.8462,1,"{2020, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1329,0,0,0,16.645783,"\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","Int[((-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,"(4*(1 - x)^(3/4)*(1 - k*x)^(3/4)*AppellF1[-3/4, -1/4, -1/4, 1/4, x, k*x])/((1 - x)*x*(1 - k*x))^(3/4) + (8*k*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^4*(1 - x^4)^(1/4)*(1 - k*x^4)^(1/4))/(1 - (1 + k)*x^4 + k*x^8 - d*x^12), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4) + (4*(1 + k)*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][((1 - x^4)^(1/4)*(1 - k*x^4)^(1/4))/(-1 + (1 + k)*x^4 - k*x^8 + d*x^12), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4) + (12*d*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(1 - x^4)^(1/4)*(1 - k*x^4)^(1/4))/(-1 + (1 + k)*x^4 - k*x^8 + d*x^12), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4)","F",0,0,0,0,-1,"{}"
1330,-1,0,0,180.0072478,"\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","Int[((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]","\text{\$Aborted}","\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,"$Aborted","F",0,0,0,0,-1,"{}"
1331,1,153,0,0.3294147,"\int \frac{x^2}{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[x^2/((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{a^{5/4} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{a^{5/4} \sqrt[4]{a x^4-b x^2}}-\frac{2 x}{a \sqrt[4]{a x^4-b x^2}}","\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,"(-2*x)/(a*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(5/4)*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(5/4)*(-(b*x^2) + a*x^4)^(1/4))","A",7,7,31,0.2258,1,"{2056, 288, 329, 240, 212, 206, 203}"
1332,0,0,0,5.4849624,"\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","Int[(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,"(2*a*q*Sqrt[q + p*x^5])/(3*c*x^3) + (2*(b*c - a*d)*Sqrt[q + p*x^5])/(c^2*x) + (2*a*p*x^2*Sqrt[q + p*x^5])/(3*c) - (5*(b*c - a*d)*p*x^4*Sqrt[1 + (p*x^5)/q]*Hypergeometric2F1[1/2, 4/5, 9/5, -((p*x^5)/q)])/(4*c^2*Sqrt[q + p*x^5]) + (2*d*(b*c - a*d)*Defer[Int][Sqrt[q + p*x^5]/(c*q + d*x^2 + c*p*x^5), x])/c^2 + (5*(b*c - a*d)*p*Defer[Int][(x^3*Sqrt[q + p*x^5])/(c*q + d*x^2 + c*p*x^5), x])/c","F",0,0,0,0,-1,"{}"
1333,1,115,0,0.0942172,"\int \frac{x}{\sqrt[3]{x^2+x^6}} \, dx","Int[x/(x^2 + x^6)^(1/3),x]","\frac{\sqrt{3} \sqrt[3]{x^2} \sqrt[3]{x^4+1} \tan ^{-1}\left(\frac{\frac{2 \left(x^2\right)^{2/3}}{\sqrt[3]{x^4+1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{x^6+x^2}}-\frac{3 \sqrt[3]{x^2} \sqrt[3]{x^4+1} \log \left(\left(x^2\right)^{2/3}-\sqrt[3]{x^4+1}\right)}{8 \sqrt[3]{x^6+x^2}}","-\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,"(Sqrt[3]*(x^2)^(1/3)*(1 + x^4)^(1/3)*ArcTan[(1 + (2*(x^2)^(2/3))/(1 + x^4)^(1/3))/Sqrt[3]])/(4*(x^2 + x^6)^(1/3)) - (3*(x^2)^(1/3)*(1 + x^4)^(1/3)*Log[(x^2)^(2/3) - (1 + x^4)^(1/3)])/(8*(x^2 + x^6)^(1/3))","A",5,5,13,0.3846,1,"{2013, 2011, 329, 275, 239}"
1334,1,319,0,1.0744365,"\int \frac{-1+x^4}{\left(1+x^2+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(-1 + x^4)/((1 + x^2 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};-\frac{2 x^4}{1-i \sqrt{3}},-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{2 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};-\frac{2 x^4}{1+i \sqrt{3}},-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{2 \left(-\sqrt{3}+i\right) \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,-\frac{2 x^4}{1-i \sqrt{3}}\right)}{5 \left(\sqrt{3}+i\right) \sqrt[4]{x^6+x^2}}-\frac{2 \left(\sqrt{3}+i\right) \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,-\frac{2 x^4}{1+i \sqrt{3}}\right)}{5 \left(-\sqrt{3}+i\right) \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\sqrt[4]{x^6+x^2}}","-\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,"(-2*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (-2*x^4)/(1 - I*Sqrt[3]), -x^4])/(x^2 + x^6)^(1/4) - (2*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (-2*x^4)/(1 + I*Sqrt[3]), -x^4])/(x^2 + x^6)^(1/4) - (2*(I - Sqrt[3])*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1/4, 1, 13/8, -x^4, (-2*x^4)/(1 - I*Sqrt[3])])/(5*(I + Sqrt[3])*(x^2 + x^6)^(1/4)) - (2*(I + Sqrt[3])*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1/4, 1, 13/8, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/(5*(I - Sqrt[3])*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",15,7,27,0.2593,0,"{2056, 6715, 6728, 245, 1438, 429, 510}"
1335,1,319,0,0.8799148,"\int \frac{-1+x^4}{\left(1+x^2+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(-1 + x^4)/((1 + x^2 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};-\frac{2 x^4}{1-i \sqrt{3}},-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{2 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};-\frac{2 x^4}{1+i \sqrt{3}},-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{2 \left(-\sqrt{3}+i\right) \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,-\frac{2 x^4}{1-i \sqrt{3}}\right)}{5 \left(\sqrt{3}+i\right) \sqrt[4]{x^6+x^2}}-\frac{2 \left(\sqrt{3}+i\right) \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};\frac{1}{4},1;\frac{13}{8};-x^4,-\frac{2 x^4}{1+i \sqrt{3}}\right)}{5 \left(-\sqrt{3}+i\right) \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\sqrt[4]{x^6+x^2}}","-\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,"(-2*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (-2*x^4)/(1 - I*Sqrt[3]), -x^4])/(x^2 + x^6)^(1/4) - (2*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (-2*x^4)/(1 + I*Sqrt[3]), -x^4])/(x^2 + x^6)^(1/4) - (2*(I - Sqrt[3])*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1/4, 1, 13/8, -x^4, (-2*x^4)/(1 - I*Sqrt[3])])/(5*(I + Sqrt[3])*(x^2 + x^6)^(1/4)) - (2*(I + Sqrt[3])*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1/4, 1, 13/8, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/(5*(I - Sqrt[3])*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",15,7,27,0.2593,0,"{2056, 6715, 6728, 245, 1438, 429, 510}"
1336,0,0,0,2.0850381,"\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","Int[(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,"(Sqrt[(a*x^6)/(Sqrt[b] + Sqrt[-b + a*x^6])^2]*(Sqrt[b] + Sqrt[-b + a*x^6])*EllipticF[2*ArcTan[(-b + a*x^6)^(1/4)/b^(1/4)], 1/2])/(3*a*b^(1/4)*x^3) + (2*c*x*(1 - (a*x^6)/b)^(3/4)*Hypergeometric2F1[1/6, 3/4, 7/6, (a*x^6)/b])/(a*(-b + a*x^6)^(3/4)) - (2*b*c*Defer[Int][1/((b + 2*c*x^4 - a*x^6)*(-b + a*x^6)^(3/4)), x])/a - (4*c^2*Defer[Int][x^4/((b + 2*c*x^4 - a*x^6)*(-b + a*x^6)^(3/4)), x])/a + 3*b*Defer[Int][x^2/((-b + a*x^6)^(3/4)*(-b - 2*c*x^4 + a*x^6)), x]","F",0,0,0,0,-1,"{}"
1337,1,441,0,0.7154234,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Int[1/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","\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)}{4 \sqrt{a^2+2 b} \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)}{4 \sqrt{a^2+2 b} \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)}{4 \sqrt{a^2+2 b} \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)}{4 \sqrt{a^2+2 b} \left(\sqrt{a^2+2 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}","-\frac{\text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{8 b}",1,"ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)) + ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4))","B",9,5,27,0.1852,1,"{1428, 377, 212, 208, 205}"
1338,1,441,0,0.2847501,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-2 b-2 a x^4+x^8\right)} \, dx","Int[1/((b + a*x^4)^(1/4)*(-2*b - 2*a*x^4 + x^8)),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt{a^2+2 b} \left(a-\sqrt{a^2+2 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt{a^2+2 b} \left(\sqrt{a^2+2 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{a-\sqrt{a^2+2 b}} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt{a^2+2 b} \left(a-\sqrt{a^2+2 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+2 b}+a^2+b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}{\sqrt[4]{\sqrt{a^2+2 b}+a} \sqrt[4]{a x^4+b}}\right)}{4 \sqrt{a^2+2 b} \left(\sqrt{a^2+2 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+2 b}+a^2+b}}","-\frac{\text{RootSum}\left[-2 \text{$\#$1}^8+2 \text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{8 b}",1,"ArcTan[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTan[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)) + ArcTanh[((a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a - Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a - Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b - a*Sqrt[a^2 + 2*b])^(1/4)) - ArcTanh[((a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4)*x)/((a + Sqrt[a^2 + 2*b])^(1/4)*(b + a*x^4)^(1/4))]/(4*Sqrt[a^2 + 2*b]*(a + Sqrt[a^2 + 2*b])^(3/4)*(a^2 + b + a*Sqrt[a^2 + 2*b])^(1/4))","B",9,5,27,0.1852,1,"{1428, 377, 212, 208, 205}"
1339,1,499,0,1.3283698,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-b-a x^4+2 x^8\right)} \, dx","Int[(-2*b + a*x^4)/((b + a*x^4)^(1/4)*(-b - a*x^4 + 2*x^8)),x]","-\frac{\left(a-\frac{a^2-8 b}{\sqrt{a^2+8 b}}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}-\frac{\left(\frac{a^2-8 b}{\sqrt{a^2+8 b}}+a\right) \tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}-\frac{\left(a-\frac{a^2-8 b}{\sqrt{a^2+8 b}}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^4+b}}\right)}{2 \left(a-\sqrt{a^2+8 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+8 b}+a^2+4 b}}-\frac{\left(\frac{a^2-8 b}{\sqrt{a^2+8 b}}+a\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}{\sqrt[4]{\sqrt{a^2+8 b}+a} \sqrt[4]{a x^4+b}}\right)}{2 \left(\sqrt{a^2+8 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+8 b}+a^2+4 b}}","\frac{1}{4} \text{RootSum}\left[-\text{$\#$1}^8+\text{$\#$1}^4 a+2 b\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{\text{$\#$1} a-2 \text{$\#$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",10,5,38,0.1316,1,"{6728, 377, 212, 208, 205}"
1340,1,269,0,5.2901541,"\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","Int[(1 + b*x + k^2*x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^2*x^2)),x]","\frac{\sqrt{1-x} \sqrt{x} (b+2 k) \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(-\frac{k}{1-k};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{(1-k) k \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{\sqrt{1-x} \sqrt{x} \left(2-\frac{b}{k}\right) \sqrt{\frac{k^2 (1-x)}{1-k^2}+1} \Pi \left(\frac{k}{k+1};\sin ^{-1}\left(\sqrt{1-x}\right)|-\frac{k^2}{1-k^2}\right)}{(k+1) \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\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,"(2*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + ((b + 2*k)*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[-(k/(1 - k)), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((1 - k)*k*Sqrt[(1 - x)*x*(1 - k^2*x)]) + ((2 - b/k)*Sqrt[1 + (k^2*(1 - x))/(1 - k^2)]*Sqrt[1 - x]*Sqrt[x]*EllipticPi[k/(1 + k), ArcSin[Sqrt[1 - x]], -(k^2/(1 - k^2))])/((1 + k)*Sqrt[(1 - x)*x*(1 - k^2*x)])","C",12,6,43,0.1395,1,"{6718, 6725, 115, 168, 538, 537}"
1341,1,84,0,0.0562954,"\int \frac{\sqrt[3]{-1+x^3}}{x^7} \, dx","Int[(-1 + x^3)^(1/3)/x^7,x]","\frac{\sqrt[3]{x^3-1}}{18 x^3}+\frac{1}{18} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}-\frac{\sqrt[3]{x^3-1}}{6 x^6}-\frac{\log (x)}{18}","\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,"-1/6*(-1 + x^3)^(1/3)/x^6 + (-1 + x^3)^(1/3)/(18*x^3) - ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) - Log[x]/18 + Log[1 + (-1 + x^3)^(1/3)]/18","A",7,7,13,0.5385,1,"{266, 47, 51, 58, 618, 204, 31}"
1342,1,86,0,0.0545251,"\int \frac{\sqrt[3]{1+x^3}}{x^7} \, dx","Int[(1 + x^3)^(1/3)/x^7,x]","-\frac{\sqrt[3]{x^3+1}}{18 x^3}-\frac{1}{18} \log \left(1-\sqrt[3]{x^3+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}-\frac{\sqrt[3]{x^3+1}}{6 x^6}+\frac{\log (x)}{18}","-\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,"-1/6*(1 + x^3)^(1/3)/x^6 - (1 + x^3)^(1/3)/(18*x^3) + ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) + Log[x]/18 - Log[1 - (1 + x^3)^(1/3)]/18","A",7,7,13,0.5385,1,"{266, 47, 51, 57, 618, 204, 31}"
1343,1,83,0,0.0492371,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^4} \, dx","Int[((-1 + x^3)*(1 + x^3)^(1/3))/x^4,x]","\frac{\left(x^3+1\right)^{4/3}}{3 x^3}+\frac{2}{3} \sqrt[3]{x^3+1}+\frac{1}{3} \log \left(1-\sqrt[3]{x^3+1}\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\log (x)}{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,"(2*(1 + x^3)^(1/3))/3 + (1 + x^3)^(4/3)/(3*x^3) - (2*ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) - Log[x]/3 + Log[1 - (1 + x^3)^(1/3)]/3","A",7,7,18,0.3889,1,"{446, 78, 50, 57, 618, 204, 31}"
1344,0,0,0,0.8349476,"\int \frac{1+x}{\left(-1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[(1 + x)/((-1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","\int \frac{1+x}{\left(-1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","-\text{RootSum}\left[\text{$\#$1}^9-4 \text{$\#$1}^6+5 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-2 \log (x)}{3 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"(3*(-1 + x)^(1/3)*x^(2/3)*Defer[Subst][Defer[Int][1/((-1 + x^3)^(1/3)*(-1 - x^3 + x^9)), x], x, x^(1/3)])/(-x^2 + x^3)^(1/3) + (3*(-1 + x)^(1/3)*x^(2/3)*Defer[Subst][Defer[Int][x^3/((-1 + x^3)^(1/3)*(-1 - x^3 + x^9)), x], x, x^(1/3)])/(-x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
1345,0,0,0,0.6137106,"\int \frac{1+x}{\left(-1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[(1 + x)/((-1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","\int \frac{1+x}{\left(-1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","-\text{RootSum}\left[\text{$\#$1}^9-4 \text{$\#$1}^6+5 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-2 \log (x)}{3 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"(3*(-1 + x)^(1/3)*x^(2/3)*Defer[Subst][Defer[Int][1/((-1 + x^3)^(1/3)*(-1 - x^3 + x^9)), x], x, x^(1/3)])/(-x^2 + x^3)^(1/3) + (3*(-1 + x)^(1/3)*x^(2/3)*Defer[Subst][Defer[Int][x^3/((-1 + x^3)^(1/3)*(-1 - x^3 + x^9)), x], x, x^(1/3)])/(-x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
1346,1,375,0,1.168207,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","\frac{\sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}","-\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,"(Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1/2*I)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3] - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(I/2)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3]","C",15,8,29,0.2759,0,"{2056, 6725, 716, 1098, 934, 168, 538, 537}"
1347,1,142,0,0.0649623,"\int \frac{\sqrt[3]{x^2+x^3}}{x} \, dx","Int[(x^2 + x^3)^(1/3)/x,x]","\sqrt[3]{x^3+x^2}-\frac{(x+1)^{2/3} x^{4/3} \log (x+1)}{6 \left(x^3+x^2\right)^{2/3}}-\frac{(x+1)^{2/3} x^{4/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x+1}}-1\right)}{2 \left(x^3+x^2\right)^{2/3}}-\frac{(x+1)^{2/3} x^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \left(x^3+x^2\right)^{2/3}}","\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,"(x^2 + x^3)^(1/3) - (x^(4/3)*(1 + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(Sqrt[3]*(x^2 + x^3)^(2/3)) - (x^(4/3)*(1 + x)^(2/3)*Log[1 + x])/(6*(x^2 + x^3)^(2/3)) - (x^(4/3)*(1 + x)^(2/3)*Log[-1 + x^(1/3)/(1 + x)^(1/3)])/(2*(x^2 + x^3)^(2/3))","A",3,3,15,0.2000,1,"{2021, 2032, 59}"
1348,1,107,0,0.135355,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(1+2 x^3\right)} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^3))/(x^6*(1 + 2*x^3)),x]","\log \left(\frac{x}{\sqrt[3]{x^3+1}}+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{x^3+1}}}{\sqrt{3}}\right)-\frac{2 \left(x^3+1\right)^{2/3}}{5 x^5}+\frac{11 \left(x^3+1\right)^{2/3}}{10 x^2}-\frac{1}{2} \log \left(-\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\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*(1 + x^3)^(2/3))/(5*x^5) + (11*(1 + x^3)^(2/3))/(10*x^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)]","A",10,10,27,0.3704,1,"{580, 583, 12, 377, 200, 31, 634, 618, 204, 628}"
1349,1,86,0,0.0557016,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^9} \, dx","Int[((-3 + x^4)*(1 + x^4)^(1/3))/x^9,x]","-\frac{\sqrt[3]{x^4+1}}{2 x^4}+\frac{1}{4} \log \left(1-\sqrt[3]{x^4+1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{3 \left(x^4+1\right)^{4/3}}{8 x^8}-\frac{\log (x)}{3}","\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,"-1/2*(1 + x^4)^(1/3)/x^4 + (3*(1 + x^4)^(4/3))/(8*x^8) - ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x]/3 + Log[1 - (1 + x^4)^(1/3)]/4","A",7,7,18,0.3889,1,"{446, 78, 47, 57, 618, 204, 31}"
1350,1,143,0,0.1766392,"\int \frac{-b+a x^3}{x^3 \sqrt[4]{b x+a x^4}} \, dx","Int[(-b + a*x^3)/(x^3*(b*x + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}+\frac{4 \left(a x^4+b x\right)^{3/4}}{9 x^3}","\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))/(9*x^3) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4))","A",8,8,26,0.3077,1,"{2038, 2011, 329, 275, 240, 212, 206, 203}"
1351,1,143,0,0.2287582,"\int \frac{b+a x^3}{x^3 \sqrt[4]{b x+a x^4}} \, dx","Int[(b + a*x^3)/(x^3*(b*x + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}-\frac{4 \left(a x^4+b x\right)^{3/4}}{9 x^3}","\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))/(9*x^3) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4))","A",10,9,24,0.3750,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2014}"
1352,1,86,0,0.0486554,"\int \frac{1}{x^{13} \sqrt[3]{1+x^6}} \, dx","Int[1/(x^13*(1 + x^6)^(1/3)),x]","\frac{\left(x^6+1\right)^{2/3}}{9 x^6}+\frac{1}{18} \log \left(1-\sqrt[3]{x^6+1}\right)+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^6+1}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}-\frac{\left(x^6+1\right)^{2/3}}{12 x^{12}}-\frac{\log (x)}{9}","\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,"-1/12*(1 + x^6)^(2/3)/x^12 + (1 + x^6)^(2/3)/(9*x^6) + ArcTan[(1 + 2*(1 + x^6)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) - Log[x]/9 + Log[1 - (1 + x^6)^(1/3)]/18","A",7,6,13,0.4615,1,"{266, 51, 55, 618, 204, 31}"
1353,0,0,0,1.9569088,"\int \frac{-3+5 x^8}{\left(1+x^8\right) \sqrt[3]{1-x^3+x^8}} \, dx","Int[(-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,"5*Defer[Int][(1 - x^3 + x^8)^(-1/3), x] - (-1)^(1/8)*Defer[Int][1/(((-1)^(1/8) - x)*(1 - x^3 + x^8)^(1/3)), x] - (-1)^(3/8)*Defer[Int][1/(((-1)^(3/8) - x)*(1 - x^3 + x^8)^(1/3)), x] + (-1)^(5/8)*Defer[Int][1/((-(-1)^(5/8) - x)*(1 - x^3 + x^8)^(1/3)), x] + (-1)^(7/8)*Defer[Int][1/((-(-1)^(7/8) - x)*(1 - x^3 + x^8)^(1/3)), x] - (-1)^(1/8)*Defer[Int][1/(((-1)^(1/8) + x)*(1 - x^3 + x^8)^(1/3)), x] - (-1)^(3/8)*Defer[Int][1/(((-1)^(3/8) + x)*(1 - x^3 + x^8)^(1/3)), x] + (-1)^(5/8)*Defer[Int][1/((-(-1)^(5/8) + x)*(1 - x^3 + x^8)^(1/3)), x] + (-1)^(7/8)*Defer[Int][1/((-(-1)^(7/8) + x)*(1 - x^3 + x^8)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1354,1,91,0,0.1481739,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(1 + Sqrt[1 + x]),x]","-\frac{1}{2} \sqrt{x+\sqrt{x+1}} \left(3-2 \sqrt{x+1}\right)-2 \tan ^{-1}\left(\frac{\sqrt{x+1}+3}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{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{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,"-1/2*((3 - 2*Sqrt[1 + x])*Sqrt[x + Sqrt[1 + x]]) - 2*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",7,6,25,0.2400,1,"{814, 843, 621, 206, 724, 204}"
1355,1,91,0,0.8624812,"\int \frac{x+\sqrt{1+x^2}}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(x + Sqrt[1 + x^2])/(1 + Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{1}{3} \left(\sqrt{x^2+1}+x\right)^{3/2}+\sqrt{\sqrt{x^2+1}+x}-\frac{\sqrt{x^2+1}}{2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^2+1}\right)-2 \tanh ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)-\frac{x}{2}-\frac{\log (x)}{2}","\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,"-1/2*x - Sqrt[1 + x^2]/2 + Sqrt[x + Sqrt[1 + x^2]] + (x + Sqrt[1 + x^2])^(3/2)/3 + ArcTanh[Sqrt[1 + x^2]]/2 - 2*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]] - Log[x]/2","A",41,22,31,0.7097,1,"{6742, 195, 215, 2117, 14, 2119, 448, 2122, 270, 266, 50, 63, 207, 2120, 462, 459, 329, 298, 203, 206, 466, 461}"
1356,1,96,0,0.042944,"\int \frac{x^2}{\left(-2 b+a x^2\right) \left(-b+a x^2\right)^{3/4}} \, dx","Int[x^2/((-2*b + a*x^2)*(-b + a*x^2)^(3/4)),x]","\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{a} x}{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}\right)}{\sqrt{2} a^{3/2} \sqrt[4]{b}}","\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,"ArcTan[(Sqrt[a]*x)/(Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4))]/(Sqrt[2]*a^(3/2)*b^(1/4)) - ArcTanh[(Sqrt[a]*x)/(Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4))]/(Sqrt[2]*a^(3/2)*b^(1/4))","A",1,1,28,0.03571,1,"{442}"
1357,0,0,0,49.3074783,"\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","Int[((-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,"(Sqrt[2]*k^(3/2)*Sqrt[-1 + k^2]*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*Sqrt[(1 + k^2*(1 - 2*x^2))^2/((1 - k^2)^2*(1 - (2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)])/(1 - k^2))^2)]*(1 - (2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)])/(1 - k^2))*EllipticF[2*ArcTan[(Sqrt[2]*Sqrt[k]*((1 - x^2)*(1 - k^2*x^2))^(1/4))/Sqrt[-1 + k^2]], 1/2])/((1 - d*k^2)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]) + (k*(5 + (1 + 3*d)*k^2 - d*k^4)*x*((1 - x^2)/(1 - k^2*x^2))^(3/4)*(1 - k^2*x^2)*Hypergeometric2F1[1/2, 3/4, 3/2, ((1 - k^2)*x^2)/(1 - k^2*x^2)])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) - (k*(7 + k^2 - 3*d^2*k^2*(1 - k^2) - d*(5 + 2*k^2 + k^4))*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][1/((1 - x^2)^(3/4)*(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])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) + ((1 - k^4 - 6*d^2*k^4*(1 - k^2) - d*k^2*(19 + 14*k^2 - k^4))*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][x/((1 - x^2)^(3/4)*(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])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4)) + (k*(5 + 3*(1 + 8*d)*k^2 + 3*d^2*k^4 - 3*d^2*k^6)*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Int][x^2/((1 - x^2)^(3/4)*(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])/((1 - d*k^2)^2*((1 - x^2)*(1 - k^2*x^2))^(3/4))","F",0,0,0,0,-1,"{}"
1358,0,0,0,6.8908353,"\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","Int[((-1 + x^2)*(1 + x^2)*Sqrt[1 + 3*x^2 + x^4])/(x^2*(1 + x + x^2)^2),x]","\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","\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,"-((x*(3 + Sqrt[5] + 2*x^2))/Sqrt[1 + 3*x^2 + x^4]) + ((3 - I*Sqrt[3])*x*(3 + Sqrt[5] + 2*x^2))/(6*Sqrt[1 + 3*x^2 + x^4]) + ((3 + I*Sqrt[3])*x*(3 + Sqrt[5] + 2*x^2))/(6*Sqrt[1 + 3*x^2 + x^4]) + Sqrt[1 + 3*x^2 + x^4] - ((3 - I*Sqrt[3])*Sqrt[1 + 3*x^2 + x^4])/6 - ((3 + I*Sqrt[3])*Sqrt[1 + 3*x^2 + x^4])/6 + Sqrt[1 + 3*x^2 + x^4]/x + (Sqrt[(1 + I*Sqrt[3])/3]*(I + Sqrt[3])*ArcTan[(1 - (3*I)*Sqrt[3] + 2*(2 - I*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/2 - ((I - Sqrt[3])*Sqrt[(1 - I*Sqrt[3])/3]*ArcTan[(1 + (3*I)*Sqrt[3] + 2*(2 + I*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/2 + (3*ArcTanh[(3 + 2*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])])/2 - ((9 - I*Sqrt[3])*ArcTanh[(3 + 2*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])])/12 - ((9 + I*Sqrt[3])*ArcTanh[(3 + 2*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])])/12 - ArcTanh[(2 + 3*x^2)/(2*Sqrt[1 + 3*x^2 + x^4])] + ((I - Sqrt[3])*Sqrt[(3 + Sqrt[5])/6]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticE[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(2*Sqrt[1 + 3*x^2 + x^4]) - ((I + Sqrt[3])*Sqrt[(3 + Sqrt[5])/6]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticE[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(2*Sqrt[1 + 3*x^2 + x^4]) + (Sqrt[(3 + Sqrt[5])/2]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticE[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/Sqrt[1 + 3*x^2 + x^4] - ((2*I - Sqrt[3])*Sqrt[2/(3*(3 + Sqrt[5]))]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/Sqrt[1 + 3*x^2 + x^4] + ((2*I + Sqrt[3])*Sqrt[2/(3*(3 + Sqrt[5]))]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/Sqrt[1 + 3*x^2 + x^4] + (2*(I + Sqrt[3])*Sqrt[2/(3*(3 + Sqrt[5]))]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/((2 - I*Sqrt[3] - Sqrt[5])*Sqrt[1 + 3*x^2 + x^4]) - (2*(I - Sqrt[3])*Sqrt[2/(3*(3 + Sqrt[5]))]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/((2 + I*Sqrt[3] - Sqrt[5])*Sqrt[1 + 3*x^2 + x^4]) - (3*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) - (4*(1 + I*Sqrt[3])*Sqrt[(9 - 4*Sqrt[5])/3]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I - Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/((5*I + Sqrt[3] - I*Sqrt[5] - Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) + (4*(1 - I*Sqrt[3])*Sqrt[(9 - 4*Sqrt[5])/3]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I + Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/((5*I - Sqrt[3] - I*Sqrt[5] + Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) + (4*Defer[Int][Sqrt[1 + 3*x^2 + x^4]/(-1 + I*Sqrt[3] - 2*x)^2, x])/3 - (4*(1 - I*Sqrt[3])*Defer[Int][Sqrt[1 + 3*x^2 + x^4]/(-1 + I*Sqrt[3] - 2*x)^2, x])/3 + (4*Defer[Int][Sqrt[1 + 3*x^2 + x^4]/(1 + I*Sqrt[3] + 2*x)^2, x])/3 - (4*(1 + I*Sqrt[3])*Defer[Int][Sqrt[1 + 3*x^2 + x^4]/(1 + I*Sqrt[3] + 2*x)^2, x])/3","F",0,0,0,0,-1,"{}"
1359,1,93,0,0.1394959,"\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","Int[((2 + x^2)*(-4 + x + 2*x^2)*Sqrt[8 - 7*x^2 + 2*x^4])/x^4,x]","-\frac{\left(2-x^2\right) \sqrt{2 x^4-7 x^2+8}}{2 x^2}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \left(2-x^2\right)}{\sqrt{2 x^4-7 x^2+8}}\right)}{2 \sqrt{2}}+\frac{\left(2 x^4-7 x^2+8\right)^{3/2}}{3 x^3}","\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*((2 - x^2)*Sqrt[8 - 7*x^2 + 2*x^4])/x^2 + (8 - 7*x^2 + 2*x^4)^(3/2)/(3*x^3) - ArcTanh[(Sqrt[2]*(2 - x^2))/Sqrt[8 - 7*x^2 + 2*x^4]]/(2*Sqrt[2])","A",6,6,33,0.1818,1,"{1662, 1590, 1251, 812, 838, 206}"
1360,1,109,0,0.0394254,"\int x^4 \left(-b+a x^4\right)^{3/4} \, dx","Int[x^4*(-b + a*x^4)^(3/4),x]","-\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{3 b x \left(a x^4-b\right)^{3/4}}{32 a}+\frac{1}{8} x^5 \left(a x^4-b\right)^{3/4}","-\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,"(-3*b*x*(-b + a*x^4)^(3/4))/(32*a) + (x^5*(-b + a*x^4)^(3/4))/8 - (3*b^2*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(64*a^(5/4)) - (3*b^2*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(64*a^(5/4))","A",6,6,17,0.3529,1,"{279, 321, 240, 212, 206, 203}"
1361,1,170,0,0.2235639,"\int \frac{\left(-2 b+a x^2\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Int[((-2*b + a*x^2)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","-\frac{7}{2} a x \sqrt[4]{a x^4+b x^2}+\frac{7 \sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 \left(a x^4+b x^2\right)^{3/4}}-\frac{7 \sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 \left(a x^4+b x^2\right)^{3/4}}+\frac{4 \left(a x^4+b x^2\right)^{5/4}}{x^3}","\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,"(-7*a*x*(b*x^2 + a*x^4)^(1/4))/2 + (4*(b*x^2 + a*x^4)^(5/4))/x^3 + (7*a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*(b*x^2 + a*x^4)^(3/4)) - (7*a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*(b*x^2 + a*x^4)^(3/4))","A",8,8,28,0.2857,1,"{2038, 2004, 2032, 329, 331, 298, 203, 206}"
1362,1,170,0,0.2234841,"\int \frac{\left(2 b+a x^2\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Int[((2*b + a*x^2)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","\frac{9}{2} a x \sqrt[4]{a x^4+b x^2}-\frac{9 \sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 \left(a x^4+b x^2\right)^{3/4}}+\frac{9 \sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 \left(a x^4+b x^2\right)^{3/4}}-\frac{4 \left(a x^4+b x^2\right)^{5/4}}{x^3}","\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,"(9*a*x*(b*x^2 + a*x^4)^(1/4))/2 - (4*(b*x^2 + a*x^4)^(5/4))/x^3 - (9*a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*(b*x^2 + a*x^4)^(3/4)) + (9*a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*(b*x^2 + a*x^4)^(3/4))","A",8,8,28,0.2857,1,"{2038, 2004, 2032, 329, 331, 298, 203, 206}"
1363,0,0,0,10.2369736,"\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","Int[((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,"(-4*k^2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - k^2 + k^2*x^4)^(1/4)*(-1 + d*x^4 - 3*k^2*(-1 + x^4) - 3*k^4*(-1 + x^4)^2 - k^6*(-1 + x^4)^3)), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(1/4) + (2*(1 - 3*k^2)*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - k^2 + k^2*x^4)^(1/4)*(1 - d*x^4 + 3*k^2*(-1 + x^4) + 3*k^4*(-1 + x^4)^2 + k^6*(-1 + x^4)^3)), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(1/4) - (4*k^2*(1 - x^2)^(1/4)*(1 - k^2*x^2)^(1/4)*Defer[Subst][Defer[Int][x^6/((1 - k^2 + k^2*x^4)^(1/4)*(1 - d*x^4 + 3*k^2*(-1 + x^4) + 3*k^4*(-1 + x^4)^2 + k^6*(-1 + x^4)^3)), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(1/4)","F",0,0,0,0,-1,"{}"
1364,1,499,0,1.175636,"\int \frac{-b+a x^4}{\sqrt[4]{b+a x^4} \left(b-a x^4+x^8\right)} \, dx","Int[(-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(\frac{a^2-2 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)}{2 \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{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(\frac{a^2-2 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)}{2 \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{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$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 + (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))])/(2*(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)*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 + (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))","B",10,5,34,0.1471,1,"{6728, 377, 212, 208, 205}"
1365,1,499,0,0.6572035,"\int \frac{-b+a x^4}{\sqrt[4]{b+a x^4} \left(b-a x^4+x^8\right)} \, dx","Int[(-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(\frac{a^2-2 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)}{2 \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{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(\frac{a^2-2 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)}{2 \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{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"-1/2*((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)) - ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*x)/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^4)^(1/4))])/(2*(a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4))","B",10,5,34,0.1471,1,"{6728, 377, 212, 208, 205}"
1366,0,0,0,3.9546574,"\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","Int[((4 + x^5)*(1 - x^4 - 2*x^5 + x^8 + x^9 + x^10))/(x^2*(-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)),x]","\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","\frac{4 \sqrt[4]{x^5-1}}{x}-2 \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4-1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"(-4*(1 - x^5)^(3/4)*Hypergeometric2F1[-1/5, 3/4, 4/5, x^5])/(x*(-1 + x^5)^(3/4)) + (6*x*(1 - x^5)^(3/4)*Hypergeometric2F1[1/5, 3/4, 6/5, x^5])/(-1 + x^5)^(3/4) + (2*x^2*(1 - x^5)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, x^5])/(-1 + x^5)^(3/4) + (2*x^3*(1 - x^5)^(3/4)*Hypergeometric2F1[3/5, 3/4, 8/5, x^5])/(3*(-1 + x^5)^(3/4)) + (x^4*(1 - x^5)^(3/4)*Hypergeometric2F1[3/4, 4/5, 9/5, x^5])/(4*(-1 + x^5)^(3/4)) - 6*Defer[Int][1/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] - 4*Defer[Int][x/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] - 10*Defer[Int][x^2/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] - 6*Defer[Int][x^4/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 8*Defer[Int][x^5/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 14*Defer[Int][x^6/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 10*Defer[Int][x^7/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 6*Defer[Int][x^8/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 10*Defer[Int][x^9/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x]","F",0,0,0,0,-1,"{}"
1367,0,0,0,3.6054607,"\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","Int[((4 + x^5)*(1 - x^4 - 2*x^5 + x^8 + x^9 + x^10))/(x^2*(-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)),x]","\int \frac{\left(4+x^5\right) \left(1-x^4-2 x^5+x^8+x^9+x^{10}\right)}{x^2 \left(-1+x^5\right)^{3/4} \left(1+x^4-2 x^5-x^8-x^9+x^{10}\right)} \, dx","\frac{4 \sqrt[4]{x^5-1}}{x}-2 \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4-1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^5-1}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"(-4*(1 - x^5)^(3/4)*Hypergeometric2F1[-1/5, 3/4, 4/5, x^5])/(x*(-1 + x^5)^(3/4)) + (6*x*(1 - x^5)^(3/4)*Hypergeometric2F1[1/5, 3/4, 6/5, x^5])/(-1 + x^5)^(3/4) + (2*x^2*(1 - x^5)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, x^5])/(-1 + x^5)^(3/4) + (2*x^3*(1 - x^5)^(3/4)*Hypergeometric2F1[3/5, 3/4, 8/5, x^5])/(3*(-1 + x^5)^(3/4)) + (x^4*(1 - x^5)^(3/4)*Hypergeometric2F1[3/4, 4/5, 9/5, x^5])/(4*(-1 + x^5)^(3/4)) - 6*Defer[Int][1/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] - 4*Defer[Int][x/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] - 10*Defer[Int][x^2/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] - 6*Defer[Int][x^4/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 8*Defer[Int][x^5/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 14*Defer[Int][x^6/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 10*Defer[Int][x^7/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 6*Defer[Int][x^8/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x] + 10*Defer[Int][x^9/((-1 + x^5)^(3/4)*(1 + x^4 - 2*x^5 - x^8 - x^9 + x^10)), x]","F",0,0,0,0,-1,"{}"
1368,0,0,0,0.0406472,"\int \frac{1}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Int[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,"Defer[Int][1/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
1369,1,99,0,0.0778551,"\int \frac{\left(-3 b+2 a x^2\right) \left(b^2+a^2 x^2\right)^{3/4}}{x} \, dx","Int[((-3*b + 2*a*x^2)*(b^2 + a^2*x^2)^(3/4))/x,x]","-2 b \left(a^2 x^2+b^2\right)^{3/4}+\frac{4 \left(a^2 x^2+b^2\right)^{7/4}}{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*(b^2 + a^2*x^2)^(3/4) + (4*(b^2 + a^2*x^2)^(7/4))/(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",7,7,29,0.2414,1,"{446, 80, 50, 63, 298, 203, 206}"
1370,1,97,0,0.618056,"\int \frac{-1+x}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(-1 + x)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{2 \sqrt{3 \left(3+2 \sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{x^3-1}}\right)}{2 \sqrt{3 \left(2 \sqrt{3}-3\right)}}","\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,"-1/2*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]]/Sqrt[3*(-3 + 2*Sqrt[3])] + ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]]/(2*Sqrt[3*(3 + 2*Sqrt[3])])","A",10,6,23,0.2609,1,"{6728, 2135, 219, 2140, 206, 203}"
1371,1,457,0,0.749909,"\int \frac{3-x+x^2}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(3 - x + x^2)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","\frac{1}{6} \sqrt{15+14 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{x^3-1}}\right)+\frac{1}{6} \sqrt{14 \sqrt{3}-15} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt{14-5 \sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{\sqrt{38-21 \sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \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[15 + 14*Sqrt[3]]*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/6 + (Sqrt[-15 + 14*Sqrt[3]]*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/6 + (Sqrt[38 - 21*Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(2*3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (Sqrt[14 - 5*Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(2*3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","C",13,6,28,0.2143,0,"{6728, 219, 2135, 2140, 206, 203}"
1372,1,450,0,0.9966664,"\int \frac{2 x+x^2}{\left(-2-2 x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(2*x + x^2)/((-2 - 2*x + x^2)*Sqrt[-1 + x^3]),x]","-\frac{1}{3} \sqrt{2 \sqrt{3}-3} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{x^3-1}}\right)+\frac{1}{3} \sqrt{3+2 \sqrt{3}} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)+\frac{\sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\left(2-\sqrt{3}\right)^{3/2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \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,"-1/3*(Sqrt[-3 + 2*Sqrt[3]]*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]]) + (Sqrt[3 + 2*Sqrt[3]]*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/3 - (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - ((2 - Sqrt[3])^(3/2)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","C",14,7,27,0.2593,1,"{1593, 6728, 219, 2135, 2140, 206, 203}"
1373,1,84,0,0.0611297,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^7} \, dx","Int[((-1 + x^3)^(1/3)*(1 + x^3))/x^7,x]","-\frac{4 \sqrt[3]{x^3-1}}{9 x^3}+\frac{2}{9} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{4 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\left(x^3-1\right)^{4/3}}{6 x^6}-\frac{2 \log (x)}{9}","\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,"(-4*(-1 + x^3)^(1/3))/(9*x^3) + (-1 + x^3)^(4/3)/(6*x^6) - (4*ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]) - (2*Log[x])/9 + (2*Log[1 + (-1 + x^3)^(1/3)])/9","A",7,7,18,0.3889,1,"{446, 78, 47, 58, 618, 204, 31}"
1374,1,84,0,0.0535684,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^7} \, dx","Int[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^7,x]","-\frac{5 \sqrt[3]{x^3-1}}{9 x^3}+\frac{5}{18} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{5 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}-\frac{\left(x^3-1\right)^{4/3}}{6 x^6}-\frac{5 \log (x)}{18}","\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,"(-5*(-1 + x^3)^(1/3))/(9*x^3) - (-1 + x^3)^(4/3)/(6*x^6) - (5*ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]) - (5*Log[x])/18 + (5*Log[1 + (-1 + x^3)^(1/3)])/18","A",7,7,20,0.3500,1,"{446, 78, 47, 58, 618, 204, 31}"
1375,0,0,0,13.1244351,"\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","Int[((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,"(4*a*b*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(-a + x^2)^(5/4)/((-b + x^2)^(3/4)*(-(a^3*d) + 3*a^2*d*x^2 + b*(1 - (3*a*d)/b)*x^4 - (1 - d)*x^6)), x], x, Sqrt[x]])/((a - x)*(b - x)*x^2)^(3/4) + (2*(3*a - b)*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^2*(-a + x^2)^(5/4))/((-b + x^2)^(3/4)*(a^3*d - 3*a^2*d*x^2 - b*(1 - (3*a*d)/b)*x^4 + (1 - d)*x^6)), x], x, Sqrt[x]])/((a - x)*(b - x)*x^2)^(3/4)","F",0,0,0,0,-1,"{}"
1376,0,0,0,4.1788897,"\int \frac{1+x^2}{\sqrt{\frac{-2-x+2 x^2}{-1+x+x^2}} \left(1-x^2+x^4\right)} \, dx","Int[(1 + x^2)/(Sqrt[(-2 - x + 2*x^2)/(-1 + x + x^2)]*(1 - x^2 + x^4)),x]","\int \frac{1+x^2}{\sqrt{\frac{-2-x+2 x^2}{-1+x+x^2}} \left(1-x^2+x^4\right)} \, dx","\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,"-1/2*((1 + I*Sqrt[3])*Sqrt[-2 - x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/((Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[-2 - x + 2*x^2]), x])/(Sqrt[1 - I*Sqrt[3]]*Sqrt[(2 + x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) - ((1 - I*Sqrt[3])*Sqrt[-2 - x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/((Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x)*Sqrt[-2 - x + 2*x^2]), x])/(2*Sqrt[1 + I*Sqrt[3]]*Sqrt[(2 + x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) - ((1 + I*Sqrt[3])*Sqrt[-2 - x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/((Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[-2 - x + 2*x^2]), x])/(2*Sqrt[1 - I*Sqrt[3]]*Sqrt[(2 + x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) - ((1 - I*Sqrt[3])*Sqrt[-2 - x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/((Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x)*Sqrt[-2 - x + 2*x^2]), x])/(2*Sqrt[1 + I*Sqrt[3]]*Sqrt[(2 + x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2])","F",0,0,0,0,-1,"{}"
1377,1,474,0,1.5849847,"\int \frac{-2 b+a x^4}{x^4 \left(b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(-2*b + a*x^4)/(x^4*(b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{16 a \left(b-a x^2\right)}{21 b^2 x \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4-b x^2}}+\frac{4 \left(b-a x^2\right)}{7 b x^3 \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,"(4*(b - a*x^2))/(7*b*x^3*(-(b*x^2) + a*x^4)^(1/4)) + (16*a*(b - a*x^2))/(21*b^2*x*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",19,11,38,0.2895,1,"{2056, 6725, 271, 264, 1270, 1529, 1429, 377, 212, 206, 203}"
1378,1,474,0,1.2694662,"\int \frac{-2 b+a x^4}{x^4 \left(b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(-2*b + a*x^4)/(x^4*(b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{16 a \left(b-a x^2\right)}{21 b^2 x \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4-b x^2}}+\frac{3 a \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2-b}}\right)}{2 b \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4-b x^2}}+\frac{4 \left(b-a x^2\right)}{7 b x^3 \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,"(4*(b - a*x^2))/(7*b*x^3*(-(b*x^2) + a*x^4)^(1/4)) + (16*a*(b - a*x^2))/(21*b^2*x*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)) + (3*a*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4))","B",19,11,38,0.2895,1,"{2056, 6725, 271, 264, 1270, 1529, 1429, 377, 212, 206, 203}"
1379,1,168,0,0.1967237,"\int \sqrt[4]{b x^3+a x^4} \, dx","Int[(b*x^3 + a*x^4)^(1/4),x]","\frac{3 b^2 x^{9/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{16 a^{7/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{3 b^2 x^{9/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{16 a^{7/4} \left(a x^4+b x^3\right)^{3/4}}+\frac{1}{2} x \sqrt[4]{a x^4+b x^3}+\frac{b \sqrt[4]{a x^4+b x^3}}{8 a}","\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,"(b*(b*x^3 + a*x^4)^(1/4))/(8*a) + (x*(b*x^3 + a*x^4)^(1/4))/2 + (3*b^2*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(7/4)*(b*x^3 + a*x^4)^(3/4)) - (3*b^2*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(7/4)*(b*x^3 + a*x^4)^(3/4))","A",8,8,15,0.5333,1,"{2004, 2024, 2032, 63, 331, 298, 203, 206}"
1380,1,84,0,0.0608441,"\int \frac{1}{x^{13} \sqrt[3]{-1+x^6}} \, dx","Int[1/(x^13*(-1 + x^6)^(1/3)),x]","\frac{\left(x^6-1\right)^{2/3}}{9 x^6}-\frac{1}{18} \log \left(\sqrt[3]{x^6-1}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\left(x^6-1\right)^{2/3}}{12 x^{12}}+\frac{\log (x)}{9}","-\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)/(12*x^12) + (-1 + x^6)^(2/3)/(9*x^6) - ArcTan[(1 - 2*(-1 + x^6)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) + Log[x]/9 - Log[1 + (-1 + x^6)^(1/3)]/18","A",7,6,13,0.4615,1,"{266, 51, 56, 618, 204, 31}"
1381,1,483,0,1.4759732,"\int \frac{b+2 a x^4}{\sqrt[4]{b+a x^4} \left(-2 b-a x^4+x^8\right)} \, dx","Int[(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(\frac{a^2+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+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+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}}","-\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 + (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 - (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 + (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))","B",10,5,35,0.1429,1,"{6728, 377, 212, 208, 205}"
1382,1,1161,0,3.3355141,"\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","Int[(2*b + a*x^4)/((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + 2*x^8)),x]","-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}","\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,"-1/2*((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/((-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",22,8,42,0.1905,1,"{2056, 6715, 6728, 1429, 377, 212, 208, 205}"
1383,1,1161,0,2.2575603,"\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","Int[(2*b + a*x^4)/((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + 2*x^8)),x]","-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a-\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a-\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a-\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a \sqrt{a+\sqrt{a^2+8 b}}-2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt{x}}{\sqrt[8]{a+\sqrt{a^2+8 b}} \sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{a+\sqrt{a^2+8 b}} a+2 b} \sqrt[4]{a x^4+b x^2}}","\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,"-1/2*((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/((-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(-2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a - Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a - Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a - Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(-2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + Sqrt[a^2 + 8*b])^(1/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*Sqrt[x])/((a + Sqrt[a^2 + 8*b])^(1/8)*(b + a*x^2)^(1/4))])/(2*(2*b + a*Sqrt[a + Sqrt[a^2 + 8*b]])^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",22,8,42,0.1905,1,"{2056, 6715, 6728, 1429, 377, 212, 208, 205}"
1384,0,0,0,8.1620583,"\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","Int[((-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]","\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","\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,"-((Sqrt[1 - 2*x^2]*Defer[Int][Sqrt[1 - 2*x^2]/(Sqrt[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])/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2])) - (4*Sqrt[1 - 2*x^2]*Defer[Int][(x*Sqrt[1 - 2*x^2])/(Sqrt[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])/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) + (4*Sqrt[1 - 2*x^2]*Defer[Int][(x^2*Sqrt[1 - 2*x^2])/(Sqrt[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])/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2]) - (4*Sqrt[1 - 2*x^2]*Defer[Int][(x^4*Sqrt[1 - 2*x^2])/(Sqrt[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])/(Sqrt[(1 - 2*x^2)/(1 + 2*x^2)]*Sqrt[1 + 2*x^2])","F",0,0,0,0,-1,"{}"
1385,0,0,0,2.5842217,"\int \frac{\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + x^2]/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","\log \left(\sqrt{x^2+1}+x\right)-2 \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^4+5 \text{$\#$1}-2}\&\right]",1,"Defer[Int][x^2/(-1 - 2*x^5 + x^8), x] + Defer[Int][x^4/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^3*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^6*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] - Defer[Int][Sqrt[x + Sqrt[1 + x^2]]/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^4*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x]","F",0,0,0,0,-1,"{}"
1386,0,0,0,2.1091244,"\int \frac{\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + x^2]/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","\log \left(\sqrt{x^2+1}+x\right)-2 \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^4+5 \text{$\#$1}-2}\&\right]",1,"Defer[Int][x^2/(-1 - 2*x^5 + x^8), x] + Defer[Int][x^4/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^3*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^6*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] - Defer[Int][Sqrt[x + Sqrt[1 + x^2]]/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^4*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x]","F",0,0,0,0,-1,"{}"
1387,1,697,0,4.7288264,"\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","Int[(1 + k*x^2)/((-1 + c*k*x + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(\frac{4 k}{\left(c \sqrt{k}-\sqrt{k c^2+4}\right)^2};\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(\frac{4 k}{\left(\sqrt{k} c+\sqrt{k c^2+4}\right)^2};\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \left(\sqrt{c^2 k+4}+c \sqrt{k}\right) \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2} \sqrt{-c k^{3/2} \sqrt{c^2 k+4}-c^2 k^2-2 k+2}}{\sqrt{c \sqrt{k} \sqrt{c^2 k+4}-\left(2-c^2\right) k+2} \sqrt{1-k^2 x^2}}\right)}{\sqrt{c \sqrt{k} \sqrt{c^2 k+4}-\left(2-c^2\right) k+2} \sqrt{-c k^{3/2} \sqrt{c^2 k+4}-c^2 k^2-2 k+2} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \left(c \sqrt{k}-\sqrt{c^2 k+4}\right) \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2} \sqrt{c k^{3/2} \sqrt{c^2 k+4}-c^2 k^2-2 k+2}}{\sqrt{c \left(-\sqrt{k}\right) \sqrt{c^2 k+4}-\left(2-c^2\right) k+2} \sqrt{1-k^2 x^2}}\right)}{\sqrt{c \left(-\sqrt{k}\right) \sqrt{c^2 k+4}-\left(2-c^2\right) k+2} \sqrt{c k^{3/2} \sqrt{c^2 k+4}-c^2 k^2-2 k+2} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}","\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,"-(((c*Sqrt[k] + Sqrt[4 + c^2*k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[2 - 2*k - c^2*k^2 - c*k^(3/2)*Sqrt[4 + c^2*k]]*Sqrt[1 - x^2])/(Sqrt[2 - (2 - c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]]*Sqrt[1 - k^2*x^2])])/(Sqrt[2 - (2 - c^2)*k + c*Sqrt[k]*Sqrt[4 + c^2*k]]*Sqrt[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*Sqrt[k] - Sqrt[4 + c^2*k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[2 - 2*k - c^2*k^2 + c*k^(3/2)*Sqrt[4 + c^2*k]]*Sqrt[1 - x^2])/(Sqrt[2 - (2 - c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]]*Sqrt[1 - k^2*x^2])])/(Sqrt[2 - (2 - c^2)*k - c*Sqrt[k]*Sqrt[4 + c^2*k]]*Sqrt[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)] - (Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(4*k)/(c*Sqrt[k] - Sqrt[4 + c^2*k])^2, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)] - (Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(4*k)/(c*Sqrt[k] + Sqrt[4 + c^2*k])^2, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",16,8,43,0.1860,1,"{6719, 6728, 419, 2113, 537, 571, 93, 205}"
1388,1,691,0,5.1237959,"\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","Int[(-1 + k*x^2)/((1 + c*k*x + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(\frac{4 k}{\left(c \sqrt{k}-\sqrt{c^2 k-4}\right)^2};\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(\frac{4 k}{\left(\sqrt{k} c+\sqrt{c^2 k-4}\right)^2};\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \left(\sqrt{c^2 k-4}+c \sqrt{k}\right) \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2} \sqrt{-c k^{3/2} \sqrt{c^2 k-4}-c^2 k^2+2 k+2}}{\sqrt{c \left(-\sqrt{k}\right) \sqrt{c^2 k-4}+\left(2-c^2\right) k+2} \sqrt{1-k^2 x^2}}\right)}{\sqrt{c \left(-\sqrt{k}\right) \sqrt{c^2 k-4}+\left(2-c^2\right) k+2} \sqrt{-c k^{3/2} \sqrt{c^2 k-4}-c^2 k^2+2 k+2} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \left(c \sqrt{k}-\sqrt{c^2 k-4}\right) \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2} \sqrt{c k^{3/2} \sqrt{c^2 k-4}-c^2 k^2+2 k+2}}{\sqrt{c \sqrt{k} \sqrt{c^2 k-4}+\left(2-c^2\right) k+2} \sqrt{1-k^2 x^2}}\right)}{\sqrt{c \sqrt{k} \sqrt{c^2 k-4}+\left(2-c^2\right) k+2} \sqrt{c k^{3/2} \sqrt{c^2 k-4}-c^2 k^2+2 k+2} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}","\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,"((c*Sqrt[k] + Sqrt[-4 + c^2*k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[2 + 2*k - c^2*k^2 - c*k^(3/2)*Sqrt[-4 + c^2*k]]*Sqrt[1 - x^2])/(Sqrt[2 + (2 - c^2)*k - c*Sqrt[k]*Sqrt[-4 + c^2*k]]*Sqrt[1 - k^2*x^2])])/(Sqrt[2 + (2 - c^2)*k - c*Sqrt[k]*Sqrt[-4 + c^2*k]]*Sqrt[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*Sqrt[k] - Sqrt[-4 + c^2*k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[2 + 2*k - c^2*k^2 + c*k^(3/2)*Sqrt[-4 + c^2*k]]*Sqrt[1 - x^2])/(Sqrt[2 + (2 - c^2)*k + c*Sqrt[k]*Sqrt[-4 + c^2*k]]*Sqrt[1 - k^2*x^2])])/(Sqrt[2 + (2 - c^2)*k + c*Sqrt[k]*Sqrt[-4 + c^2*k]]*Sqrt[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)] - (Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(4*k)/(c*Sqrt[k] - Sqrt[-4 + c^2*k])^2, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)] - (Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(4*k)/(c*Sqrt[k] + Sqrt[-4 + c^2*k])^2, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",16,8,43,0.1860,1,"{6719, 6728, 419, 2113, 537, 571, 93, 208}"
1389,1,194,0,0.1821115,"\int x^2 \sqrt[3]{x+x^3} \, dx","Int[x^2*(x + x^3)^(1/3),x]","\frac{1}{4} \sqrt[3]{x^3+x} x^3+\frac{1}{12} \sqrt[3]{x^3+x} x+\frac{\left(x^2+1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{18 \left(x^3+x\right)^{2/3}}-\frac{\left(x^2+1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{36 \left(x^3+x\right)^{2/3}}+\frac{\left(x^2+1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{6 \sqrt{3} \left(x^3+x\right)^{2/3}}","\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))/12 + (x^3*(x + x^3)^(1/3))/4 + (x^(2/3)*(1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(6*Sqrt[3]*(x + x^3)^(2/3)) + (x^(2/3)*(1 + x^2)^(2/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(18*(x + x^3)^(2/3)) - (x^(2/3)*(1 + x^2)^(2/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(36*(x + x^3)^(2/3))","A",12,12,13,0.9231,1,"{2021, 2024, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1390,0,0,0,0.593871,"\int \frac{6+2 x+x^2}{\sqrt[3]{2+x^2} \left(1+3 x-2 x^2+x^3\right)} \, dx","Int[(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,"6*Defer[Int][1/((2 + x^2)^(1/3)*(1 + 3*x - 2*x^2 + x^3)), x] + 2*Defer[Int][x/((2 + x^2)^(1/3)*(1 + 3*x - 2*x^2 + x^3)), x] + Defer[Int][x^2/((2 + x^2)^(1/3)*(1 + 3*x - 2*x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
1391,1,147,0,0.0628499,"\int \frac{\sqrt[3]{x^2+x^3}}{x^2} \, dx","Int[(x^2 + x^3)^(1/3)/x^2,x]","-\frac{3 \sqrt[3]{x^3+x^2}}{x}-\frac{(x+1)^{2/3} x^{4/3} \log (x+1)}{2 \left(x^3+x^2\right)^{2/3}}-\frac{3 (x+1)^{2/3} x^{4/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x+1}}-1\right)}{2 \left(x^3+x^2\right)^{2/3}}-\frac{\sqrt{3} (x+1)^{2/3} x^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{\left(x^3+x^2\right)^{2/3}}","-\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 + x^3)^(1/3))/x - (Sqrt[3]*x^(4/3)*(1 + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(x^2 + x^3)^(2/3) - (x^(4/3)*(1 + x)^(2/3)*Log[1 + x])/(2*(x^2 + x^3)^(2/3)) - (3*x^(4/3)*(1 + x)^(2/3)*Log[-1 + x^(1/3)/(1 + x)^(1/3)])/(2*(x^2 + x^3)^(2/3))","A",3,3,15,0.2000,1,"{2020, 2032, 59}"
1392,1,102,0,0.0630026,"\int \frac{\sqrt[3]{1+x^4} \left(3+x^4\right)}{x^{13}} \, dx","Int[((1 + x^4)^(1/3)*(3 + x^4))/x^13,x]","\frac{\sqrt[3]{x^4+1}}{36 x^4}+\frac{1}{36} \log \left(1-\sqrt[3]{x^4+1}\right)-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)}{18 \sqrt{3}}-\frac{\left(x^4+1\right)^{4/3}}{4 x^{12}}+\frac{\sqrt[3]{x^4+1}}{12 x^8}-\frac{\log (x)}{27}","\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)^(1/3)/(12*x^8) + (1 + x^4)^(1/3)/(36*x^4) - (1 + x^4)^(4/3)/(4*x^12) - ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]]/(18*Sqrt[3]) - Log[x]/27 + Log[1 - (1 + x^4)^(1/3)]/36","A",8,8,18,0.4444,1,"{446, 78, 47, 51, 57, 618, 204, 31}"
1393,0,0,0,1.3495722,"\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","Int[((-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,"(3*(-1 + x^4)^(2/3))/x^2 - (12*x^2)/(1 + Sqrt[3] + (-1 + x^4)^(1/3)) + (6*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) - (4*Sqrt[2]*3^(3/4)*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) - (3*(-1 + x^4)^(2/3)*Hypergeometric2F1[-5/4, -2/3, -1/4, x^4])/(5*x^5*(1 - x^4)^(2/3)) - ((-1 + x^4)^(2/3)*Hypergeometric2F1[-2/3, -1/4, 3/4, x^4])/(x*(1 - x^4)^(2/3)) - 6*Defer[Int][(-1 + x^4)^(2/3)/(-1 - x^3 + x^4), x] + 8*Defer[Int][(x*(-1 + x^4)^(2/3))/(-1 - x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1394,0,0,0,1.3301543,"\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","Int[((-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,"(3*(1 + x^4)^(2/3))/x^2 + (12*x^2)/(1 - Sqrt[3] - (1 + x^4)^(1/3)) - (6*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (4*Sqrt[2]*3^(3/4)*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (3*Hypergeometric2F1[-5/4, -2/3, -1/4, -x^4])/(5*x^5) - Hypergeometric2F1[-2/3, -1/4, 3/4, -x^4]/x - 6*Defer[Int][(1 + x^4)^(2/3)/(1 - x^3 + x^4), x] + 8*Defer[Int][(x*(1 + x^4)^(2/3))/(1 - x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1395,1,627,0,2.2339699,"\int \frac{-b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \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} \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,"((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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)*(b*x^2 + a*x^4)^(1/4)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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)*(b*x^2 + a*x^4)^(1/4)) + ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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",12,7,37,0.1892,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1396,1,627,0,1.5302268,"\int \frac{-b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((b + a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4)) + ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4)) + ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",12,7,37,0.1892,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1397,1,172,0,0.5886899,"\int \frac{\left(-1+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(-1-x^3+x^6\right)} \, dx","Int[((-1 + x^3)*(1 + x^3)^(2/3))/(x^3*(-1 - x^3 + x^6)),x]","\frac{\left(5+3 \sqrt{5}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\frac{2 x^3}{1-\sqrt{5}}\right)}{5 \left(1-\sqrt{5}\right)}+\frac{\left(5-3 \sqrt{5}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\frac{2 x^3}{1+\sqrt{5}}\right)}{5 \left(1+\sqrt{5}\right)}-\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}",1,"-1/2*(1 + x^3)^(2/3)/x^2 + ((5 + 3*Sqrt[5])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (2*x^3)/(1 - Sqrt[5])])/(5*(1 - Sqrt[5])) + ((5 - 3*Sqrt[5])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (2*x^3)/(1 + Sqrt[5])])/(5*(1 + Sqrt[5])) + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]/2","A",8,4,30,0.1333,0,"{6728, 277, 239, 429}"
1398,1,172,0,0.5099473,"\int \frac{\left(-1+x^3\right) \left(1+x^3\right)^{2/3}}{x^3 \left(-1-x^3+x^6\right)} \, dx","Int[((-1 + x^3)*(1 + x^3)^(2/3))/(x^3*(-1 - x^3 + x^6)),x]","\frac{\left(5+3 \sqrt{5}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\frac{2 x^3}{1-\sqrt{5}}\right)}{5 \left(1-\sqrt{5}\right)}+\frac{\left(5-3 \sqrt{5}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\frac{2 x^3}{1+\sqrt{5}}\right)}{5 \left(1+\sqrt{5}\right)}-\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6-\text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^4-\text{$\#$1}}\&\right]-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}",1,"-1/2*(1 + x^3)^(2/3)/x^2 + ((5 + 3*Sqrt[5])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (2*x^3)/(1 - Sqrt[5])])/(5*(1 - Sqrt[5])) + ((5 - 3*Sqrt[5])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (2*x^3)/(1 + Sqrt[5])])/(5*(1 + Sqrt[5])) + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]/2","A",8,4,30,0.1333,0,"{6728, 277, 239, 429}"
1399,0,0,0,0.8725881,"\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","Int[((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,"(3*Hypergeometric2F1[-1/3, -1/7, 6/7, -2*x^7])/x + 3*Defer[Int][(x*(1 + 2*x^7)^(1/3))/(1 + x^3 + 2*x^7), x] + 14*Defer[Int][(x^5*(1 + 2*x^7)^(1/3))/(1 + x^3 + 2*x^7), x]","F",0,0,0,0,-1,"{}"
1400,1,479,0,1.2827451,"\int \frac{-b+2 a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Int[(-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{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$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 + (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",10,5,36,0.1389,1,"{6728, 377, 212, 208, 205}"
1401,1,479,0,0.7623948,"\int \frac{-b+2 a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Int[(-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{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-3 a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+3 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$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 + (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",10,5,36,0.1389,1,"{6728, 377, 212, 208, 205}"
1402,0,0,0,1.447543,"\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","Int[((-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,"-1/4*Defer[Int][Sqrt[1 + x + 2*x^4 + x^5 + x^8]/x^2, x] + Defer[Int][Sqrt[1 + x + 2*x^4 + x^5 + x^8]/x, x]/16 + Defer[Int][Sqrt[1 + x + 2*x^4 + x^5 + x^8]/(-4 - x - 4*x^4), x]/16 + 4*Defer[Int][(x^2*Sqrt[1 + x + 2*x^4 + x^5 + x^8])/(4 + x + 4*x^4), x] - Defer[Int][(x^3*Sqrt[1 + x + 2*x^4 + x^5 + x^8])/(4 + x + 4*x^4), x]/4","F",0,0,0,0,-1,"{}"
1403,1,113,0,0.0821952,"\int \frac{-b+c x^4+a x^8}{x^2 \left(-b+a x^4\right)^{3/4}} \, dx","Int[(-b + c*x^4 + a*x^8)/(x^2*(-b + a*x^4)^(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{\sqrt[4]{a x^4-b}}{x}+\frac{1}{4} x^3 \sqrt[4]{a x^4-b}","\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,"-((-b + a*x^4)^(1/4)/x) + (x^3*(-b + a*x^4)^(1/4))/4 - ((3*b + 4*c)*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(3/4)) + ((3*b + 4*c)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(8*a^(3/4))","A",6,6,31,0.1935,1,"{1486, 451, 331, 298, 203, 206}"
1404,1,100,0,0.1527237,"\int \frac{1}{(1+x) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[1/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{2}{\sqrt{\sqrt{x^2+1}+x}}+\frac{2 \tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}-\frac{2 \tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}","\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/Sqrt[x + Sqrt[1 + x^2]] + (2*ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[1 + Sqrt[2]] - (2*ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[-1 + Sqrt[2]]","A",8,7,21,0.3333,0,"{2119, 1628, 828, 826, 1166, 207, 203}"
1405,1,100,0,0.1230896,"\int \frac{1}{x \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[1/(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\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}}","\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*ArcTan[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/Sqrt[b]])/Sqrt[b] - (2*ArcTanh[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/Sqrt[b]])/Sqrt[b]","A",6,6,27,0.2222,1,"{2119, 453, 329, 298, 203, 206}"
1406,1,199,0,0.3736314,"\int \frac{(-3+x)^6 \left(-1-x+x^2\right)^{3/2}}{-1+x} \, dx","Int[((-3 + x)^6*(-1 - x + x^2)^(3/2))/(-1 + x),x]","\frac{1}{9} \left(x^2-x-1\right)^{5/2} (1-x)^4+\frac{229}{144} \left(x^2-x-1\right)^{5/2} (1-x)^3+\frac{19927 \left(x^2-x-1\right)^{5/2} (1-x)^2}{2016}+\frac{281233 \left(x^2-x-1\right)^{5/2} (1-x)}{8064}+\frac{6158183 \left(x^2-x-1\right)^{5/2}}{80640}+\frac{(903871-1283454 x) \left(x^2-x-1\right)^{3/2}}{12288}-\frac{(5567931-6941558 x) \sqrt{x^2-x-1}}{32768}-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{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,"-1/32768*((5567931 - 6941558*x)*Sqrt[-1 - x + x^2]) + ((903871 - 1283454*x)*(-1 - x + x^2)^(3/2))/12288 + (6158183*(-1 - x + x^2)^(5/2))/80640 + (281233*(1 - x)*(-1 - x + x^2)^(5/2))/8064 + (19927*(1 - x)^2*(-1 - x + x^2)^(5/2))/2016 + (229*(1 - x)^3*(-1 - x + x^2)^(5/2))/144 + ((1 - x)^4*(-1 - x + x^2)^(5/2))/9 - 64*ArcTan[(3 - x)/(2*Sqrt[-1 - x + x^2])] + (19451047*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])])/65536","A",12,7,23,0.3043,1,"{1653, 814, 843, 621, 206, 724, 204}"
1407,1,109,0,0.0477881,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^5} \, dx","Int[((-1 + x^3)*(1 + x^3)^(1/3))/x^5,x]","-\frac{\sqrt[3]{x^3+1}}{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{\left(x^3+1\right)^{4/3}}{4 x^4}+\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{\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)^(1/3)/x) + (1 + x^3)^(4/3)/(4*x^4) - 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",9,9,18,0.5000,1,"{451, 277, 331, 292, 31, 634, 618, 204, 628}"
1408,1,110,0,0.0531623,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^3}}{x^2} \, dx","Int[((-1 + x^3)*(1 + x^3)^(1/3))/x^2,x]","\frac{\left(x^3+1\right)^{4/3}}{x}+\frac{2}{9} \log \left(1-\frac{x}{\sqrt[3]{x^3+1}}\right)+\frac{2 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{2}{3} \sqrt[3]{x^3+1} x^2-\frac{1}{9} \log \left(\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\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,"(-2*x^2*(1 + x^3)^(1/3))/3 + (1 + x^3)^(4/3)/x + (2*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + (2*Log[1 - x/(1 + x^3)^(1/3)])/9 - Log[1 + x^2/(1 + x^3)^(2/3) + x/(1 + x^3)^(1/3)]/9","A",9,9,18,0.5000,1,"{453, 279, 331, 292, 31, 634, 618, 204, 628}"
1409,1,109,0,0.0491897,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^5} \, dx","Int[((-1 + x^3)^(1/3)*(1 + x^3))/x^5,x]","-\frac{\sqrt[3]{x^3-1}}{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{\left(x^3-1\right)^{4/3}}{4 x^4}+\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{\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)/x) + (-1 + x^3)^(4/3)/(4*x^4) - 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",9,9,18,0.5000,1,"{451, 277, 331, 292, 31, 634, 618, 204, 628}"
1410,1,239,0,0.9677005,"\int \frac{x}{\left(1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Int[x/((1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","\frac{i \sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}-\frac{i \sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}","-\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,"((I/2)*Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1/2*I)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3] - ((I/2)*Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(I/2)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3]","C",17,9,25,0.3600,1,"{2056, 6725, 943, 716, 1098, 934, 168, 538, 537}"
1411,1,383,0,1.2015345,"\int \frac{-1+x+x^2}{\left(1+x^2\right) \sqrt{-x-x^2+x^3}} \, dx","Int[(-1 + x + x^2)/((1 + x^2)*Sqrt[-x - x^2 + x^3]),x]","\frac{\sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}-\frac{\left(1-\frac{i}{2}\right) \sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}-\frac{\left(1+\frac{i}{2}\right) \sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{x^3-x^2-x}}","-\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,"(Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - ((1 - I/2)*Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1/2*I)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3] - ((1 + I/2)*Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(I/2)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3]","C",15,8,30,0.2667,0,"{2056, 6725, 716, 1098, 934, 168, 538, 537}"
1412,1,143,0,0.0435747,"\int \frac{x}{\sqrt[3]{x^2+x^3}} \, dx","Int[x/(x^2 + x^3)^(1/3),x]","\frac{\left(x^3+x^2\right)^{2/3}}{x}+\frac{x^{2/3} \sqrt[3]{x+1} \log (x)}{6 \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{x^3+x^2}}","\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,"(x^2 + x^3)^(2/3)/x + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(Sqrt[3]*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[x])/(6*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-1 + (1 + x)^(1/3)/x^(1/3)])/(2*(x^2 + x^3)^(1/3))","A",3,3,13,0.2308,1,"{2024, 2011, 59}"
1413,1,844,0,1.1607412,"\int \frac{1}{x^6 \left(1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x^6*(1 + x^3)*(x^2 + x^3)^(1/3)),x]","-\frac{\left(1511+4777 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}-\frac{\left(1511-4777 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}-\frac{2187 (x+1)}{1309 x \sqrt[3]{x^3+x^2}}+\frac{\left(2249+153 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(2249-153 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{3645 (x+1)}{2618 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(41+17 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}+\frac{\left(41-17 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}-\frac{1620 (x+1)}{1309 x^3 \sqrt[3]{x^3+x^2}}+\frac{\left(15+17 (-1)^{2/3}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}+\frac{\left(15-17 \sqrt[3]{-1}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}+\frac{135 (x+1)}{119 x^4 \sqrt[3]{x^3+x^2}}-\frac{20 (x+1)}{17 x^5 \sqrt[3]{x^3+x^2}}-\frac{\left(21647+11849 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}-\frac{\left(21647-11849 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}+\frac{6561 (x+1)}{2618 \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\sqrt[3]{-1} x-1\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(-(-1)^{2/3} x-1\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1+\sqrt[3]{-1}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-(-1)^{2/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{1}{x^5 \sqrt[3]{x^3+x^2}}","\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,"1/(x^5*(x^2 + x^3)^(1/3)) + (6561*(1 + x))/(2618*(x^2 + x^3)^(1/3)) - ((21647 - (11849*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) - ((21647 + (11849*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) - (20*(1 + x))/(17*x^5*(x^2 + x^3)^(1/3)) + (135*(1 + x))/(119*x^4*(x^2 + x^3)^(1/3)) + ((15 - 17*(-1)^(1/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) + ((15 + 17*(-1)^(2/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) - (1620*(1 + x))/(1309*x^3*(x^2 + x^3)^(1/3)) + ((41 - (17*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + ((41 + (17*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + (3645*(1 + x))/(2618*x^2*(x^2 + x^3)^(1/3)) + ((2249 - (153*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) + ((2249 + (153*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) - (2187*(1 + x))/(1309*x*(x^2 + x^3)^(1/3)) - ((1511 - (4777*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) - ((1511 + (4777*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-1 + (-1)^(1/3)*x])/(6*(1 + (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-1 - (-1)^(2/3)*x])/(6*(1 - (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 + (-1)^(1/3))^(1/3)])/(2*(1 + (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 - (-1)^(2/3))^(1/3)])/(2*(1 - (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3))","C",27,9,22,0.4091,1,"{2056, 6725, 21, 45, 37, 129, 155, 12, 91}"
1414,1,844,0,0.941957,"\int \frac{1}{x^6 \left(1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x^6*(1 + x^3)*(x^2 + x^3)^(1/3)),x]","-\frac{\left(1511+4777 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}-\frac{\left(1511-4777 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}-\frac{2187 (x+1)}{1309 x \sqrt[3]{x^3+x^2}}+\frac{\left(2249+153 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(2249-153 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{3645 (x+1)}{2618 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(41+17 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}+\frac{\left(41-17 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}-\frac{1620 (x+1)}{1309 x^3 \sqrt[3]{x^3+x^2}}+\frac{\left(15+17 (-1)^{2/3}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}+\frac{\left(15-17 \sqrt[3]{-1}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}+\frac{135 (x+1)}{119 x^4 \sqrt[3]{x^3+x^2}}-\frac{20 (x+1)}{17 x^5 \sqrt[3]{x^3+x^2}}-\frac{\left(21647+11849 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}-\frac{\left(21647-11849 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}+\frac{6561 (x+1)}{2618 \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\sqrt[3]{-1} x-1\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(-(-1)^{2/3} x-1\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1+\sqrt[3]{-1}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-(-1)^{2/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{1}{x^5 \sqrt[3]{x^3+x^2}}","\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,"1/(x^5*(x^2 + x^3)^(1/3)) + (6561*(1 + x))/(2618*(x^2 + x^3)^(1/3)) - ((21647 - (11849*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) - ((21647 + (11849*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) - (20*(1 + x))/(17*x^5*(x^2 + x^3)^(1/3)) + (135*(1 + x))/(119*x^4*(x^2 + x^3)^(1/3)) + ((15 - 17*(-1)^(1/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) + ((15 + 17*(-1)^(2/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) - (1620*(1 + x))/(1309*x^3*(x^2 + x^3)^(1/3)) + ((41 - (17*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + ((41 + (17*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + (3645*(1 + x))/(2618*x^2*(x^2 + x^3)^(1/3)) + ((2249 - (153*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) + ((2249 + (153*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) - (2187*(1 + x))/(1309*x*(x^2 + x^3)^(1/3)) - ((1511 - (4777*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) - ((1511 + (4777*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-1 + (-1)^(1/3)*x])/(6*(1 + (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-1 - (-1)^(2/3)*x])/(6*(1 - (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 + (-1)^(1/3))^(1/3)])/(2*(1 + (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 - (-1)^(2/3))^(1/3)])/(2*(1 - (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3))","C",27,9,22,0.4091,1,"{2056, 6725, 21, 45, 37, 129, 155, 12, 91}"
1415,1,109,0,0.0606461,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^5} \, dx","Int[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^5,x]","-\frac{2 \sqrt[3]{x^3-1}}{x}-\frac{2}{3} \log \left(1-\frac{x}{\sqrt[3]{x^3-1}}\right)-\frac{2 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3-1\right)^{4/3}}{4 x^4}+\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+1\right)","-\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,"(-2*(-1 + x^3)^(1/3))/x - (-1 + x^3)^(4/3)/(4*x^4) - (2*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - (2*Log[1 - x/(-1 + x^3)^(1/3)])/3 + Log[1 + x^2/(-1 + x^3)^(2/3) + x/(-1 + x^3)^(1/3)]/3","A",9,9,20,0.4500,1,"{451, 277, 331, 292, 31, 634, 618, 204, 628}"
1416,1,111,0,0.1298701,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-1+3 x^3\right)}{x^6 \left(-1+2 x^3\right)} \, dx","Int[((-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]{x^3-1}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3-1\right)^{2/3}}{5 x^5}+\frac{7 \left(x^3-1\right)^{2/3}}{10 x^2}-\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{\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^3)^(2/3)/x^5 + (7*(-1 + x^3)^(2/3))/(10*x^2) - 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",10,10,29,0.3448,1,"{580, 583, 12, 377, 200, 31, 634, 618, 204, 628}"
1417,1,109,0,9.8233627,"\int \frac{x^4}{\left(-1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","Int[x^4/((-1 + x^4)^2*(x^2 + x^4)^(1/4)),x]","\frac{128 x^5 \Gamma \left(\frac{13}{4}\right) \left(17 \left(-4 x^4-9 x^2+13\right) \, _2F_1\left(1,2;\frac{17}{4};-\frac{2 x^2}{1-x^2}\right)-64 x^2 \left(x^2+1\right) \, _2F_1\left(2,3;\frac{21}{4};-\frac{2 x^2}{1-x^2}\right)\right)}{89505 \left(1-x^2\right)^3 \left(x^2+1\right) \sqrt[4]{x^4+x^2} \Gamma \left(\frac{1}{4}\right)}","\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,"(128*x^5*Gamma[13/4]*(17*(13 - 9*x^2 - 4*x^4)*Hypergeometric2F1[1, 2, 17/4, (-2*x^2)/(1 - x^2)] - 64*x^2*(1 + x^2)*Hypergeometric2F1[2, 3, 21/4, (-2*x^2)/(1 - x^2)]))/(89505*(1 - x^2)^3*(1 + x^2)*(x^2 + x^4)^(1/4)*Gamma[1/4])","C",4,4,22,0.1818,0,"{2056, 1254, 466, 510}"
1418,1,193,0,1.248173,"\int \frac{\left(1+x^2\right) \sqrt[4]{x^3+x^4}}{x^2 \left(-1+x^2\right)} \, dx","Int[((1 + x^2)*(x^3 + x^4)^(1/4))/(x^2*(-1 + x^2)),x]","\frac{4 \sqrt[4]{x^4+x^3}}{x}-\frac{2 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{2 \sqrt[4]{2} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{2 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{2 \sqrt[4]{2} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}","\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 + x^4)^(1/4))/x - (2*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + (2*2^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + (2*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - (2*2^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4))","A",44,20,27,0.7407,1,"{2056, 1586, 6733, 6725, 264, 331, 298, 203, 206, 1240, 410, 237, 335, 275, 231, 407, 409, 1213, 537, 494}"
1419,0,0,0,1.4994713,"\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","Int[((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,"(4*Hypergeometric2F1[-1/3, 3/4, 2/3, -x^3])/x - 2*x*Hypergeometric2F1[1/3, 3/4, 4/3, -x^3] + (x^2*Hypergeometric2F1[2/3, 3/4, 5/3, -x^3])/2 + 2*Defer[Int][1/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x] - 2*Defer[Int][x/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x] + 8*Defer[Int][x^2/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x] + 2*Defer[Int][x^3/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1420,1,73,0,0.2657192,"\int \frac{1+x^2+2 x^4}{\sqrt[4]{1+x^2} \left(2+3 x^2+x^4\right)} \, dx","Int[(1 + x^2 + 2*x^4)/((1 + x^2)^(1/4)*(2 + 3*x^2 + x^4)),x]","\frac{4 x}{\sqrt[4]{x^2+1}}+\frac{7}{2} \tan ^{-1}\left(\frac{\sqrt{x^2+1}+1}{x \sqrt[4]{x^2+1}}\right)+\frac{7}{2} \tanh ^{-1}\left(\frac{1-\sqrt{x^2+1}}{x \sqrt[4]{x^2+1}}\right)","\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,"(4*x)/(1 + x^2)^(1/4) + (7*ArcTan[(1 + Sqrt[1 + x^2])/(x*(1 + x^2)^(1/4))])/2 + (7*ArcTanh[(1 - Sqrt[1 + x^2])/(x*(1 + x^2)^(1/4))])/2","A",9,6,32,0.1875,1,"{1688, 6725, 196, 285, 403, 397}"
1421,1,183,0,0.4716581,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{x^2} \, dx","Int[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/x^2,x]","\frac{1}{2} a x \sqrt[4]{a x^4-b x^2}+\frac{2 b \sqrt[4]{a x^4-b x^2}}{x}+\frac{5 \sqrt[4]{a} b x^{3/2} \left(a x^2-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \left(a x^4-b x^2\right)^{3/4}}-\frac{5 \sqrt[4]{a} b x^{3/2} \left(a x^2-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \left(a x^4-b x^2\right)^{3/4}}","\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))/x + (a*x*(-(b*x^2) + a*x^4)^(1/4))/2 + (5*a^(1/4)*b*x^(3/2)*(-b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-(b*x^2) + a*x^4)^(3/4)) - (5*a^(1/4)*b*x^(3/2)*(-b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*(-(b*x^2) + a*x^4)^(3/4))","A",16,9,29,0.3103,1,"{2052, 2004, 2032, 329, 331, 298, 203, 206, 2020}"
1422,1,538,0,1.7944834,"\int \frac{b+a x^4}{x^4 \left(2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^4)/(x^4*(2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{4 a \left(a x^2+b\right)}{21 b^2 x \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a} \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a} \sqrt[4]{a x^4+b x^2}}-\frac{a x^2+b}{7 b x^3 \sqrt[4]{a x^4+b x^2}}","\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,"-1/7*(b + a*x^2)/(b*x^3*(b*x^2 + a*x^4)^(1/4)) + (4*a*(b + a*x^2))/(21*b^2*x*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",19,11,37,0.2973,1,"{2056, 6725, 271, 264, 1270, 1529, 1429, 377, 212, 206, 203}"
1423,1,538,0,1.3233473,"\int \frac{b+a x^4}{x^4 \left(2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^4)/(x^4*(2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{4 a \left(a x^2+b\right)}{21 b^2 x \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a} \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{a \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{-a} \sqrt{b}+\sqrt{2} a} \sqrt[4]{a x^4+b x^2}}-\frac{a x^2+b}{7 b x^3 \sqrt[4]{a x^4+b x^2}}","\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,"-1/7*(b + a*x^2)/(b*x^3*(b*x^2 + a*x^4)^(1/4)) + (4*a*(b + a*x^2))/(21*b^2*x*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a - Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) + (a*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*a + Sqrt[-a]*Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",19,11,37,0.2973,1,"{2056, 6725, 271, 264, 1270, 1529, 1429, 377, 212, 206, 203}"
1424,0,0,0,0.9138829,"\int \frac{1-x^4}{x^2 \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(1 - x^4)/(x^2*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{1-x^4}{x^2 \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","-\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,"Defer[Int][1/(x^2*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - Defer[Int][x^2/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x]","F",0,0,0,0,-1,"{}"
1425,1,127,0,0.6399222,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(-1 + x^2)/((1 + x^2)*(x^2 + x^6)^(1/4)),x]","-\frac{4 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}+\frac{4 \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\sqrt[4]{x^6+x^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^{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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (4*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",9,7,24,0.2917,0,"{2056, 6715, 6725, 245, 1438, 429, 510}"
1426,1,127,0,0.5062363,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(-1 + x^2)/((1 + x^2)*(x^2 + x^6)^(1/4)),x]","-\frac{4 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}+\frac{4 \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\sqrt[4]{x^6+x^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^{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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (4*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",9,7,24,0.2917,0,"{2056, 6715, 6725, 245, 1438, 429, 510}"
1427,1,242,0,0.4830035,"\int \frac{\sqrt[4]{-x^3+x^4} \left(-1+x^8\right)}{x^4} \, dx","Int[((-x^3 + x^4)^(1/4)*(-1 + x^8))/x^4,x]","-\frac{1}{120} \sqrt[4]{x^4-x^3} x^4-\frac{19 \sqrt[4]{x^4-x^3} x^3}{1920}-\frac{209 \sqrt[4]{x^4-x^3} x}{12288}-\frac{1463 \sqrt[4]{x^4-x^3}}{49152}-\frac{1463 (x-1)^{3/4} x^{9/4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{32768 \left(x^4-x^3\right)^{3/4}}-\frac{1463 (x-1)^{3/4} x^{9/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{32768 \left(x^4-x^3\right)^{3/4}}-\frac{4 \left(x^4-x^3\right)^{5/4}}{9 x^6}+\frac{1}{6} \sqrt[4]{x^4-x^3} x^5-\frac{16 \left(x^4-x^3\right)^{5/4}}{45 x^5}-\frac{19 \sqrt[4]{x^4-x^3} x^2}{1536}","\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,"(-1463*(-x^3 + x^4)^(1/4))/49152 - (209*x*(-x^3 + x^4)^(1/4))/12288 - (19*x^2*(-x^3 + x^4)^(1/4))/1536 - (19*x^3*(-x^3 + x^4)^(1/4))/1920 - (x^4*(-x^3 + x^4)^(1/4))/120 + (x^5*(-x^3 + x^4)^(1/4))/6 - (4*(-x^3 + x^4)^(5/4))/(9*x^6) - (16*(-x^3 + x^4)^(5/4))/(45*x^5) - (1463*(-1 + x)^(3/4)*x^(9/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(32768*(-x^3 + x^4)^(3/4)) - (1463*(-1 + x)^(3/4)*x^(9/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(32768*(-x^3 + x^4)^(3/4))","B",16,11,22,0.5000,1,"{2052, 2016, 2014, 2021, 2024, 2032, 63, 240, 212, 206, 203}"
1428,1,425,0,1.6378093,"\int \frac{\sqrt[4]{1+x^4} \left(2+x^4\right)}{x^2 \left(-1+2 x^4+x^8\right)} \, dx","Int[((1 + x^4)^(1/4)*(2 + x^4))/(x^2*(-1 + 2*x^4 + x^8)),x]","-\frac{5}{12} \left(2-\sqrt{2}\right) x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};-x^4,\left(1-\sqrt{2}\right) x^4\right)-\frac{5}{12} \left(2+\sqrt{2}\right) x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\left(1+\sqrt{2}\right) x^4,-x^4\right)+\frac{2 \sqrt[4]{x^4+1}}{x}+\frac{1}{4} \sqrt[4]{10+7 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \sqrt[4]{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \sqrt[4]{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{10-7 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{10+7 \sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \sqrt[4]{10-7 \sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)","\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,"(2*(1 + x^4)^(1/4))/x - (5*(2 - Sqrt[2])*x^3*AppellF1[3/4, -1/4, 1, 7/4, -x^4, (1 - Sqrt[2])*x^4])/12 - (5*(2 + Sqrt[2])*x^3*AppellF1[3/4, 1, -1/4, 7/4, (1 + Sqrt[2])*x^4, -x^4])/12 + ((2 - Sqrt[2])^(1/4)*ArcTan[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 + ((10 + 7*Sqrt[2])^(1/4)*ArcTan[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((10 - 7*Sqrt[2])^(1/4)*ArcTan[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 + ((2 + Sqrt[2])^(1/4)*ArcTan[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((2 - Sqrt[2])^(1/4)*ArcTanh[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((10 + 7*Sqrt[2])^(1/4)*ArcTanh[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 + ((10 - 7*Sqrt[2])^(1/4)*ArcTanh[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((2 + Sqrt[2])^(1/4)*ArcTanh[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4","B",40,10,30,0.3333,0,"{6728, 277, 331, 298, 203, 206, 1528, 510, 1518, 494}"
1429,1,425,0,1.4885909,"\int \frac{\sqrt[4]{1+x^4} \left(2+x^4\right)}{x^2 \left(-1+2 x^4+x^8\right)} \, dx","Int[((1 + x^4)^(1/4)*(2 + x^4))/(x^2*(-1 + 2*x^4 + x^8)),x]","-\frac{5}{12} \left(2-\sqrt{2}\right) x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};-x^4,\left(1-\sqrt{2}\right) x^4\right)-\frac{5}{12} \left(2+\sqrt{2}\right) x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\left(1+\sqrt{2}\right) x^4,-x^4\right)+\frac{2 \sqrt[4]{x^4+1}}{x}+\frac{1}{4} \sqrt[4]{10+7 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \sqrt[4]{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \sqrt[4]{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{10-7 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{10+7 \sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{2-\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2-\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \sqrt[4]{2+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{4} \sqrt[4]{10-7 \sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{2}} x}{\sqrt[4]{x^4+1}}\right)","\frac{2 \sqrt[4]{x^4+1}}{x}-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{-7 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)+7 \text{$\#$1}^4 \log (x)+4 \log \left(\sqrt[4]{x^4+1}-\text{$\#$1} x\right)-4 \log (x)}{\text{$\#$1}^7-2 \text{$\#$1}^3}\&\right]",1,"(2*(1 + x^4)^(1/4))/x - (5*(2 - Sqrt[2])*x^3*AppellF1[3/4, -1/4, 1, 7/4, -x^4, (1 - Sqrt[2])*x^4])/12 - (5*(2 + Sqrt[2])*x^3*AppellF1[3/4, 1, -1/4, 7/4, (1 + Sqrt[2])*x^4, -x^4])/12 + ((2 - Sqrt[2])^(1/4)*ArcTan[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 + ((10 + 7*Sqrt[2])^(1/4)*ArcTan[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((10 - 7*Sqrt[2])^(1/4)*ArcTan[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 + ((2 + Sqrt[2])^(1/4)*ArcTan[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((2 - Sqrt[2])^(1/4)*ArcTanh[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((10 + 7*Sqrt[2])^(1/4)*ArcTanh[((2 - Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 + ((10 - 7*Sqrt[2])^(1/4)*ArcTanh[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4 - ((2 + Sqrt[2])^(1/4)*ArcTanh[((2 + Sqrt[2])^(1/4)*x)/(1 + x^4)^(1/4)])/4","B",40,10,30,0.3333,0,"{6728, 277, 331, 298, 203, 206, 1528, 510, 1518, 494}"
1430,1,325,0,0.645985,"\int \frac{-b+2 a x^4}{\sqrt[4]{-b+a x^4} \left(-b+a x^8\right)} \, dx","Int[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-b + a*x^8)),x]","-\frac{\left(2 \sqrt{a}-\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[8]{a} \sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}}}+\frac{\left(2 \sqrt{a}+\sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[8]{a} \sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}}}-\frac{\left(2 \sqrt{a}-\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[8]{a} \sqrt{b} \sqrt[4]{\sqrt{a}-\sqrt{b}}}+\frac{\left(2 \sqrt{a}+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[8]{a} \sqrt{b} \sqrt[4]{\sqrt{a}+\sqrt{b}}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))+a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"-1/4*((2*Sqrt[a] - Sqrt[b])*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)])/(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]) + ((2*Sqrt[a] + Sqrt[b])*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)])/(4*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b]) - ((2*Sqrt[a] - Sqrt[b])*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)])/(4*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[b]) + ((2*Sqrt[a] + Sqrt[b])*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(-b + a*x^4)^(1/4)])/(4*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[b])","B",10,5,35,0.1429,1,"{6725, 377, 212, 206, 203}"
1431,0,0,0,0.5686558,"\int \frac{\sqrt{1+2 x^6} \left(-1+4 x^6\right)}{2+x^4+8 x^6+8 x^{12}} \, dx","Int[(Sqrt[1 + 2*x^6]*(-1 + 4*x^6))/(2 + x^4 + 8*x^6 + 8*x^12),x]","\int \frac{\sqrt{1+2 x^6} \left(-1+4 x^6\right)}{2+x^4+8 x^6+8 x^{12}} \, dx","-\frac{\tan ^{-1}\left(\frac{2^{3/4} x \sqrt{2 x^6+1}}{2 \sqrt{2} x^6-x^2+\sqrt{2}}\right)}{4 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{2^{3/4} x \sqrt{2 x^6+1}}{2 \sqrt{2} x^6+x^2+\sqrt{2}}\right)}{4 \sqrt[4]{2}}",1,"Defer[Int][Sqrt[1 + 2*x^6]/(-2 - x^4 - 8*x^6 - 8*x^12), x] + 4*Defer[Int][(x^6*Sqrt[1 + 2*x^6])/(2 + x^4 + 8*x^6 + 8*x^12), x]","F",0,0,0,0,-1,"{}"
1432,0,0,0,0.9252783,"\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x}}}{1+x^2} \, dx","Int[((-1 + x^2)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^2),x]","\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x}}}{1+x^2} \, dx","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+1)+\frac{4}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(-4*(1 + Sqrt[1 + x])^(3/2))/3 + (4*(1 + Sqrt[1 + x])^(5/2))/5 + 8*Defer[Subst][Defer[Int][x^2/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^4/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1433,0,0,0,0.8082135,"\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x}}}{1+x^2} \, dx","Int[((-1 + x^2)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^2),x]","\int \frac{\left(-1+x^2\right) \sqrt{1+\sqrt{1+x}}}{1+x^2} \, dx","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$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*(1 + Sqrt[1 + x])^(3/2))/3 + (4*(1 + Sqrt[1 + x])^(5/2))/5 + 8*Defer[Subst][Defer[Int][x^2/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^4/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1434,0,0,0,0.1082734,"\int x^2 \sqrt{x^2+\sqrt{1+x^4}} \, dx","Int[x^2*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int x^2 \sqrt{x^2+\sqrt{1+x^4}} \, dx","\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,"Defer[Int][x^2*Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
1435,1,161,0,0.4985073,"\int \frac{\left(-1+x^4\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Int[((-1 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/Sqrt[1 + x^4],x]","\left(\frac{3}{16}-\frac{3 i}{16}\right) \sqrt{1-i x^2} x+\left(\frac{3}{16}+\frac{3 i}{16}\right) \sqrt{1+i x^2} x-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}+\left(\frac{1}{8}+\frac{i}{8}\right) \sqrt{1-i x^2} x^3+\left(\frac{1}{8}-\frac{i}{8}\right) \sqrt{1+i x^2} x^3+\frac{3 i \sin ^{-1}\left(\sqrt[4]{-1} x\right)}{8 \sqrt{2}}-\frac{3 \sinh ^{-1}\left(\sqrt[4]{-1} x\right)}{8 \sqrt{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,"(3/16 - (3*I)/16)*x*Sqrt[1 - I*x^2] + (1/8 + I/8)*x^3*Sqrt[1 - I*x^2] + (3/16 + (3*I)/16)*x*Sqrt[1 + I*x^2] + (1/8 - I/8)*x^3*Sqrt[1 + I*x^2] + (((3*I)/8)*ArcSin[(-1)^(1/4)*x])/Sqrt[2] - (3*ArcSinh[(-1)^(1/4)*x])/(8*Sqrt[2]) - ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",11,7,32,0.2188,0,"{6742, 2132, 206, 2133, 321, 216, 215}"
1436,0,0,0,0.1092855,"\int \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","Int[Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","\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,"Defer[Int][Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
1437,1,79,0,0.0203521,"\int x^3 \left(-1+x^3\right)^{2/3} \, dx","Int[x^3*(-1 + x^3)^(2/3),x]","-\frac{1}{9} \left(x^3-1\right)^{2/3} x+\frac{1}{18} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{1}{6} \left(x^3-1\right)^{2/3} x^4","\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,"-1/9*(x*(-1 + x^3)^(2/3)) + (x^4*(-1 + x^3)^(2/3))/6 - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/18","A",3,3,13,0.2308,1,"{279, 321, 239}"
1438,1,113,0,0.0561453,"\int x^4 \sqrt[3]{1+x^3} \, dx","Int[x^4*(1 + x^3)^(1/3),x]","\frac{1}{27} \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)}{9 \sqrt{3}}+\frac{1}{6} \sqrt[3]{x^3+1} x^5+\frac{1}{18} \sqrt[3]{x^3+1} x^2-\frac{1}{54} \log \left(\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+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}{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))/18 + (x^5*(1 + x^3)^(1/3))/6 + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) + Log[1 - x/(1 + x^3)^(1/3)]/27 - Log[1 + x^2/(1 + x^3)^(2/3) + x/(1 + x^3)^(1/3)]/54","A",9,9,13,0.6923,1,"{279, 321, 331, 292, 31, 634, 618, 204, 628}"
1439,1,79,0,0.0217522,"\int x^3 \left(1+x^3\right)^{2/3} \, dx","Int[x^3*(1 + x^3)^(2/3),x]","\frac{1}{9} \left(x^3+1\right)^{2/3} x+\frac{1}{18} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{1}{6} \left(x^3+1\right)^{2/3} x^4","\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))/9 + (x^4*(1 + x^3)^(2/3))/6 - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) + Log[-x + (1 + x^3)^(1/3)]/18","A",3,3,13,0.2308,1,"{279, 321, 239}"
1440,1,111,0,0.1359705,"\int \frac{\left(-2+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(-1+x^3\right)} \, dx","Int[((-2 + x^3)^(2/3)*(4 + x^3))/(x^6*(-1 + x^3)),x]","\frac{5}{3} \log \left(\frac{x}{\sqrt[3]{x^3-2}}+1\right)-\frac{5 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{x^3-2}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{4 \left(x^3-2\right)^{2/3}}{5 x^5}+\frac{21 \left(x^3-2\right)^{2/3}}{10 x^2}-\frac{5}{6} \log \left(-\frac{x}{\sqrt[3]{x^3-2}}+\frac{x^2}{\left(x^3-2\right)^{2/3}}+1\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,"(4*(-2 + x^3)^(2/3))/(5*x^5) + (21*(-2 + x^3)^(2/3))/(10*x^2) - (5*ArcTan[(1 - (2*x)/(-2 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - (5*Log[1 + x^2/(-2 + x^3)^(2/3) - x/(-2 + x^3)^(1/3)])/6 + (5*Log[1 + x/(-2 + x^3)^(1/3)])/3","A",10,10,25,0.4000,1,"{580, 583, 12, 377, 200, 31, 634, 618, 204, 628}"
1441,0,0,0,2.0008091,"\int \frac{3 b+a x^2}{\left(b+a x^2+x^3\right) \sqrt[4]{b x+a x^3}} \, dx","Int[(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,"(12*b*x^(1/4)*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/((b + a*x^8)^(1/4)*(b + a*x^8 + x^12)), x], x, x^(1/4)])/(b*x + a*x^3)^(1/4) + (4*a*x^(1/4)*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^10/((b + a*x^8)^(1/4)*(b + a*x^8 + x^12)), x], x, x^(1/4)])/(b*x + a*x^3)^(1/4)","F",0,0,0,0,-1,"{}"
1442,1,102,0,0.0730353,"\int \frac{\left(-3+x^4\right) \sqrt[3]{1+x^4}}{x^{13}} \, dx","Int[((-3 + x^4)*(1 + x^4)^(1/3))/x^13,x]","-\frac{\sqrt[3]{x^4+1}}{9 x^4}-\frac{1}{9} \log \left(1-\sqrt[3]{x^4+1}\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\left(x^4+1\right)^{4/3}}{4 x^{12}}-\frac{\sqrt[3]{x^4+1}}{3 x^8}+\frac{4 \log (x)}{27}","-\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,"-1/3*(1 + x^4)^(1/3)/x^8 - (1 + x^4)^(1/3)/(9*x^4) + (1 + x^4)^(4/3)/(4*x^12) + (2*ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]])/(9*Sqrt[3]) + (4*Log[x])/27 - Log[1 - (1 + x^4)^(1/3)]/9","A",8,8,18,0.4444,1,"{446, 78, 47, 51, 57, 618, 204, 31}"
1443,1,2432,0,11.7560491,"\int \frac{-2 b+a x^2}{\sqrt[4]{-b+a x^2} \left(-b+a x^2+x^4\right)} \, dx","Int[(-2*b + a*x^2)/((-b + a*x^2)^(1/4)*(-b + a*x^2 + x^4)),x]","-\frac{\left(a+\sqrt{a^2+4 b}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{b}+\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right) \left(\sqrt{2} \sqrt{b}-\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt[4]{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) x}-\frac{\sqrt{b} \sqrt{-a-\sqrt{a^2+4 b}} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{-a-\sqrt{a^2+4 b}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} x}-\frac{\sqrt{b} \sqrt{a+\sqrt{a^2+4 b}} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a+\sqrt{a^2+4 b}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} x}-\frac{\sqrt{b} \sqrt{a-\sqrt{a^2+4 b}} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} x}-\frac{\sqrt{b} \sqrt{\sqrt{a^2+4 b}-a} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\sqrt{a^2+4 b}-a} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} x}-\frac{\left(a+\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}-\sqrt{2} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) x}-\frac{\left(a+\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}+\sqrt{2} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) x}-\frac{\left(a-\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}-\sqrt{-2 a^2+2 \sqrt{a^2+4 b} a-4 b}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) x}-\frac{\left(a-\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}+\sqrt{-2 a^2+2 \sqrt{a^2+4 b} a-4 b}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) x}+\frac{\left(a+\sqrt{a^2+4 b}\right) \left(\sqrt{2} \sqrt{b}+\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{b}-\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) x}+\frac{\left(a-\sqrt{a^2+4 b}\right) \left(\sqrt{2} \sqrt{b}+\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{b}-\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b} x}-\frac{\left(a-\sqrt{a^2+4 b}\right) \left(\sqrt{2} \sqrt{b}-\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{b}+\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b} x}","\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,"-1/2*(Sqrt[b]*Sqrt[-a - Sqrt[a^2 + 4*b]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[-a - Sqrt[a^2 + 4*b]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x^2)/b])])/(2^(1/4)*Sqrt[a]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x) - (Sqrt[b]*Sqrt[a + Sqrt[a^2 + 4*b]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[a + Sqrt[a^2 + 4*b]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x^2)/b])])/(2*2^(1/4)*Sqrt[a]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x) - (Sqrt[b]*Sqrt[a - Sqrt[a^2 + 4*b]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[a - Sqrt[a^2 + 4*b]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x^2)/b])])/(2*2^(1/4)*Sqrt[a]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x) - (Sqrt[b]*Sqrt[-a + Sqrt[a^2 + 4*b]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[-a + Sqrt[a^2 + 4*b]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x^2)/b])])/(2*2^(1/4)*Sqrt[a]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x) - ((a + Sqrt[a^2 + 4*b])*(2*Sqrt[b] - Sqrt[2]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*x) - ((a + Sqrt[a^2 + 4*b])*(2*Sqrt[b] + Sqrt[2]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*x) - ((a - Sqrt[a^2 + 4*b])*(2*Sqrt[b] - Sqrt[-2*a^2 - 4*b + 2*a*Sqrt[a^2 + 4*b]])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*x) - ((a - Sqrt[a^2 + 4*b])*(2*Sqrt[b] + Sqrt[-2*a^2 - 4*b + 2*a*Sqrt[a^2 + 4*b]])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*x) + ((a + Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2/(Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*x) - ((a + Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2/(4*Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*x) + ((a - Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2/(Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]*x) - ((a - Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2/(4*Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]*x)","C",18,6,37,0.1622,0,"{1692, 399, 490, 1217, 220, 1707}"
1444,0,0,0,0.8650461,"\int \frac{-4 b+a x^3}{\sqrt[4]{-b+a x^3} \left(-b+a x^3+x^4\right)} \, dx","Int[(-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,"4*b*Defer[Int][1/((-b + a*x^3)^(1/4)*(b - a*x^3 - x^4)), x] + a*Defer[Int][x^3/((-b + a*x^3)^(1/4)*(-b + a*x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1445,1,651,0,2.372743,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \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,"-(((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4))) - ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)) - ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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",12,7,37,0.1892,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1446,1,651,0,1.7366903,"\int \frac{b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \left(a-\frac{a^2+2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \left(\frac{a^2+2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \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,"-(((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4))) - ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - ((a - (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)) - ((a + (a^2 + 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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",12,7,37,0.1892,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1447,1,546,0,1.8768968,"\int \frac{b+a x^4}{x^4 \left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^4)/(x^4*(-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{4 a \left(a x^2+b\right)}{21 b^2 x \sqrt[4]{a x^4+b x^2}}+\frac{a x^2+b}{7 b x^3 \sqrt[4]{a x^4+b x^2}}","\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,"(b + a*x^2)/(7*b*x^3*(b*x^2 + a*x^4)^(1/4)) - (4*a*(b + a*x^2))/(21*b^2*x*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",19,11,37,0.2973,1,"{2056, 6725, 271, 264, 1270, 1529, 1429, 377, 212, 206, 203}"
1448,1,546,0,1.5413367,"\int \frac{b+a x^4}{x^4 \left(-2 b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^4)/(x^4*(-2*b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 a^{7/8} \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}}}{\sqrt[8]{2} \sqrt[4]{a x^2+b}}\right)}{4\ 2^{7/8} b \sqrt[4]{\sqrt{2} \sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{4 a \left(a x^2+b\right)}{21 b^2 x \sqrt[4]{a x^4+b x^2}}+\frac{a x^2+b}{7 b x^3 \sqrt[4]{a x^4+b x^2}}","\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,"(b + a*x^2)/(7*b*x^3*(b*x^2 + a*x^4)^(1/4)) - (4*a*(b + a*x^2))/(21*b^2*x*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4)) - (3*a^(7/8)*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(2^(1/8)*(b + a*x^2)^(1/4))])/(4*2^(7/8)*(Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*b*(b*x^2 + a*x^4)^(1/4))","B",19,11,37,0.2973,1,"{2056, 6725, 271, 264, 1270, 1529, 1429, 377, 212, 206, 203}"
1449,1,288,0,1.2893714,"\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","Int[((-1 + x^3)*(1 + x^3)^3*(1 + x^6)^(2/3))/(x^6*(1 - x^3 + x^6)),x]","\frac{3 \left(-\sqrt{3}+i\right) x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};-\frac{2 x^6}{1-i \sqrt{3}},-x^6\right)}{\sqrt{3}+i}+\frac{3 \left(\sqrt{3}+i\right) x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};-\frac{2 x^6}{1+i \sqrt{3}},-x^6\right)}{-\sqrt{3}+i}+\frac{3 x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-x^6,-\frac{2 x^6}{1-i \sqrt{3}}\right)}{2 \left(1-i \sqrt{3}\right)}+\frac{3 x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-x^6,-\frac{2 x^6}{1+i \sqrt{3}}\right)}{2 \left(1+i \sqrt{3}\right)}+x \, _2F_1\left(-\frac{2}{3},\frac{1}{6};\frac{7}{6};-x^6\right)+\frac{\, _2F_1\left(-\frac{5}{6},-\frac{2}{3};\frac{1}{6};-x^6\right)}{5 x^5}+\frac{3 \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{2}{3};-x^6\right)}{2 x^2}","\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,"(3*(I - Sqrt[3])*x*AppellF1[1/6, 1, -2/3, 7/6, (-2*x^6)/(1 - I*Sqrt[3]), -x^6])/(I + Sqrt[3]) + (3*(I + Sqrt[3])*x*AppellF1[1/6, 1, -2/3, 7/6, (-2*x^6)/(1 + I*Sqrt[3]), -x^6])/(I - Sqrt[3]) + (3*x^4*AppellF1[2/3, -2/3, 1, 5/3, -x^6, (-2*x^6)/(1 - I*Sqrt[3])])/(2*(1 - I*Sqrt[3])) + (3*x^4*AppellF1[2/3, -2/3, 1, 5/3, -x^6, (-2*x^6)/(1 + I*Sqrt[3])])/(2*(1 + I*Sqrt[3])) + Hypergeometric2F1[-5/6, -2/3, 1/6, -x^6]/(5*x^5) + (3*Hypergeometric2F1[-2/3, -1/3, 2/3, -x^6])/(2*x^2) + x*Hypergeometric2F1[-2/3, 1/6, 7/6, -x^6]","C",18,8,37,0.2162,0,"{6728, 245, 364, 275, 1438, 429, 465, 510}"
1450,1,389,0,1.287835,"\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","Int[((-1 + x^6)^(2/3)*(1 + x^6)*(-2 + x^3 + 2*x^6))/(x^6*(-1 - x^3 + x^6)),x]","-\frac{3 \left(1-\sqrt{5}\right) \left(x^6-1\right)^{2/3} x F_1\left(\frac{1}{6};-\frac{2}{3},1;\frac{7}{6};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{\left(3-\sqrt{5}\right) \left(1-x^6\right)^{2/3}}-\frac{3 \left(1+\sqrt{5}\right) \left(x^6-1\right)^{2/3} x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};\frac{2 x^6}{3+\sqrt{5}},x^6\right)}{\left(3+\sqrt{5}\right) \left(1-x^6\right)^{2/3}}-\frac{3 \left(x^6-1\right)^{2/3} x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{2 \left(3-\sqrt{5}\right) \left(1-x^6\right)^{2/3}}-\frac{3 \left(x^6-1\right)^{2/3} x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};x^6,\frac{2 x^6}{3+\sqrt{5}}\right)}{2 \left(3+\sqrt{5}\right) \left(1-x^6\right)^{2/3}}+\frac{2 \left(x^6-1\right)^{2/3} x \, _2F_1\left(-\frac{2}{3},\frac{1}{6};\frac{7}{6};x^6\right)}{\left(1-x^6\right)^{2/3}}-\frac{2 \left(x^6-1\right)^{2/3} \, _2F_1\left(-\frac{5}{6},-\frac{2}{3};\frac{1}{6};x^6\right)}{5 \left(1-x^6\right)^{2/3} x^5}+\frac{3 \left(x^6-1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{2}{3};x^6\right)}{2 \left(1-x^6\right)^{2/3} x^2}","\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,"(-3*(1 - Sqrt[5])*x*(-1 + x^6)^(2/3)*AppellF1[1/6, -2/3, 1, 7/6, x^6, (2*x^6)/(3 - Sqrt[5])])/((3 - Sqrt[5])*(1 - x^6)^(2/3)) - (3*(1 + Sqrt[5])*x*(-1 + x^6)^(2/3)*AppellF1[1/6, 1, -2/3, 7/6, (2*x^6)/(3 + Sqrt[5]), x^6])/((3 + Sqrt[5])*(1 - x^6)^(2/3)) - (3*x^4*(-1 + x^6)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, x^6, (2*x^6)/(3 - Sqrt[5])])/(2*(3 - Sqrt[5])*(1 - x^6)^(2/3)) - (3*x^4*(-1 + x^6)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, x^6, (2*x^6)/(3 + Sqrt[5])])/(2*(3 + Sqrt[5])*(1 - x^6)^(2/3)) - (2*(-1 + x^6)^(2/3)*Hypergeometric2F1[-5/6, -2/3, 1/6, x^6])/(5*x^5*(1 - x^6)^(2/3)) + (3*(-1 + x^6)^(2/3)*Hypergeometric2F1[-2/3, -1/3, 2/3, x^6])/(2*x^2*(1 - x^6)^(2/3)) + (2*x*(-1 + x^6)^(2/3)*Hypergeometric2F1[-2/3, 1/6, 7/6, x^6])/(1 - x^6)^(2/3)","C",25,12,40,0.3000,0,"{6728, 246, 245, 365, 364, 275, 1438, 430, 429, 465, 511, 510}"
1451,1,447,0,0.7158927,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Int[1/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\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)}{\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{\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{\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{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{\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{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{4 b}",1,"ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",9,5,26,0.1923,1,"{1428, 377, 212, 208, 205}"
1452,1,447,0,0.3077815,"\int \frac{1}{\sqrt[4]{b+a x^4} \left(-b+a x^4+x^8\right)} \, dx","Int[1/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4+b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$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))]/(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)) - 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)) + 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)) - 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",9,5,26,0.1923,1,"{1428, 377, 212, 208, 205}"
1453,1,1425,0,4.8751065,"\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","Int[(-b + a*x^4)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + 2*x^8)),x]","\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \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,"((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",22,8,43,0.1860,1,"{2056, 6715, 6728, 1429, 377, 212, 208, 205}"
1454,1,1425,0,3.5707606,"\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","Int[(-b + a*x^4)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + 2*x^8)),x]","\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{-a-\sqrt{a^2+2 b}}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{-a-\sqrt{a^2+2 b}} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{-a-\sqrt{a^2+2 b}} a+2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{\sqrt{a^2+2 b}-a}-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \sqrt{x}}{\sqrt[8]{2} \sqrt[8]{\sqrt{a^2+2 b}-a} \sqrt[4]{a x^2-b}}\right)}{2\ 2^{7/8} \sqrt[4]{\sqrt{2} \sqrt{\sqrt{a^2+2 b}-a} a+2 b} \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,"((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a - Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a - Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a - Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(-2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + ((-a + Sqrt[a^2 + 2*b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*Sqrt[x])/(2^(1/8)*(-a + Sqrt[a^2 + 2*b])^(1/8)*(-b + a*x^2)^(1/4))])/(2*2^(7/8)*(2*b + Sqrt[2]*a*Sqrt[-a + Sqrt[a^2 + 2*b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",22,8,43,0.1860,1,"{2056, 6715, 6728, 1429, 377, 212, 208, 205}"
1455,0,0,0,0.3445159,"\int \frac{\sqrt{c x^2-x \sqrt{-b x+a x^2}}}{x^3} \, dx","Int[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,"Defer[Int][Sqrt[c*x^2 - x*Sqrt[-(b*x) + a*x^2]]/x^3, x]","F",0,0,0,0,-1,"{}"
1456,0,0,0,1.5386819,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[x/(x + Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{x}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2}\&\right]-2 \sqrt{\sqrt{x^2+1}+x}+x",1,"x + Log[-1 - 2*x^3 + x^4]/4 + Defer[Int][(-1 - 2*x^3 + x^4)^(-1), x] + (3*Defer[Int][x^2/(-1 - 2*x^3 + x^4), x])/2 + Defer[Int][(x^2*Sqrt[1 + x^2])/(-1 - 2*x^3 + x^4), x] + Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(x^3*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1457,0,0,0,1.0758001,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[x/(x + Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{x}{x+\sqrt{x+\sqrt{1+x^2}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2}\&\right]-2 \sqrt{\sqrt{x^2+1}+x}+x",1,"x + Log[-1 - 2*x^3 + x^4]/4 + Defer[Int][(-1 - 2*x^3 + x^4)^(-1), x] + (3*Defer[Int][x^2/(-1 - 2*x^3 + x^4), x])/2 + Defer[Int][(x^2*Sqrt[1 + x^2])/(-1 - 2*x^3 + x^4), x] + Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(x^3*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x] - Defer[Int][(x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1458,1,93,0,0.6479101,"\int \frac{1+x}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Int[(1 + x)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{2 \sqrt{3 \left(3+2 \sqrt{3}\right)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{2 \sqrt{3 \left(2 \sqrt{3}-3\right)}}","\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,"ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]/(2*Sqrt[3*(3 + 2*Sqrt[3])]) - ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]/(2*Sqrt[3*(-3 + 2*Sqrt[3])])","A",10,6,23,0.2609,1,"{6728, 2135, 218, 2140, 206, 203}"
1459,1,406,0,0.7878329,"\int \frac{3+x+x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Int[(3 + x + x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","-\frac{1}{6} \sqrt{14 \sqrt{3}-15} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)-\frac{1}{6} \sqrt{15+14 \sqrt{3}} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)-\frac{\sqrt{38+21 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{14+5 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \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,"-1/6*(Sqrt[-15 + 14*Sqrt[3]]*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]) - (Sqrt[15 + 14*Sqrt[3]]*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/6 + (2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (Sqrt[14 + 5*Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (Sqrt[38 + 21*Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","C",13,6,26,0.2308,0,"{6728, 218, 2135, 2140, 206, 203}"
1460,1,406,0,0.8892114,"\int \frac{3-x+2 x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Int[(3 - x + 2*x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","-\frac{1}{6} \sqrt{21+26 \sqrt{3}} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)-\frac{1}{6} \sqrt{26 \sqrt{3}-21} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)-\frac{\sqrt{266+153 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{4 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{26-7 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \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,"-1/6*(Sqrt[21 + 26*Sqrt[3]]*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]) - (Sqrt[-21 + 26*Sqrt[3]]*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/6 - (Sqrt[26 - 7*Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (4*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (Sqrt[266 + 153*Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","C",13,6,30,0.2000,0,"{6728, 218, 2135, 2140, 206, 203}"
1461,1,79,0,0.0237256,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3\right)}{x^3} \, dx","Int[((-1 + x^3)^(2/3)*(1 + x^3))/x^3,x]","-\frac{1}{6} x \left(x^3-1\right)^{2/3}-\frac{1}{6} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{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,"-1/6*(x*(-1 + x^3)^(2/3)) + (-1 + x^3)^(5/3)/(2*x^2) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[-x + (-1 + x^3)^(1/3)]/6","A",3,3,18,0.1667,1,"{453, 195, 239}"
1462,1,125,0,0.0553382,"\int x^8 \left(b+a x^4\right)^{3/4} \, dx","Int[x^8*(b + a*x^4)^(3/4),x]","\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{5 b^2 x \left(a x^4+b\right)^{3/4}}{128 a^2}+\frac{1}{12} x^9 \left(a x^4+b\right)^{3/4}+\frac{b x^5 \left(a x^4+b\right)^{3/4}}{32 a}","\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,"(-5*b^2*x*(b + a*x^4)^(3/4))/(128*a^2) + (b*x^5*(b + a*x^4)^(3/4))/(32*a) + (x^9*(b + a*x^4)^(3/4))/12 + (5*b^3*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(256*a^(9/4)) + (5*b^3*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(256*a^(9/4))","A",7,6,15,0.4000,1,"{279, 321, 240, 212, 206, 203}"
1463,1,149,0,0.2095574,"\int \frac{1}{\left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Int[1/((-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","-\frac{2^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} b \sqrt[4]{a x^4+b x}}-\frac{2^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} b \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,"-1/3*(2^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(a^(1/4)*b*(b*x + a*x^4)^(1/4)) - (2^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*b*(b*x + a*x^4)^(1/4))","A",7,7,25,0.2800,1,"{2056, 466, 465, 377, 212, 206, 203}"
1464,1,431,0,1.3768595,"\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","Int[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(-2 + x^3 + 2*x^6)),x]","-\frac{\sqrt[3]{\frac{1}{2} \left(5 \sqrt{17}-19\right)} \log \left(\sqrt[3]{1+\sqrt{17}}-\frac{\sqrt[3]{\sqrt{17}-3} x}{\sqrt[3]{x^3+1}}\right)}{3 \sqrt{17}}-\frac{\sqrt[3]{\frac{1}{2} \left(19+5 \sqrt{17}\right)} \log \left(\sqrt[3]{\sqrt{17}-1}-\frac{\sqrt[3]{3+\sqrt{17}} x}{\sqrt[3]{x^3+1}}\right)}{3 \sqrt{17}}+\frac{\sqrt[3]{\frac{1}{2} \left(5 \sqrt{17}-19\right)} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5-\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{51}}+\frac{\sqrt[3]{\frac{1}{2} \left(19+5 \sqrt{17}\right)} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{51}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}+\frac{\sqrt[3]{\frac{1}{2} \left(5 \sqrt{17}-19\right)} \log \left(\frac{\sqrt[3]{2 \left(7-\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{17}-3\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(1+\sqrt{17}\right)^{2/3}\right)}{6 \sqrt{17}}+\frac{\sqrt[3]{\frac{1}{2} \left(19+5 \sqrt{17}\right)} \log \left(\frac{\sqrt[3]{2 \left(7+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+\frac{\left(3+\sqrt{17}\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{17}-1\right)^{2/3}\right)}{6 \sqrt{17}}","\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 + (((-19 + 5*Sqrt[17])/2)^(1/3)*ArcTan[(1 + ((2*(5 - Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[51] + (((19 + 5*Sqrt[17])/2)^(1/3)*ArcTan[(1 + ((2*(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[51] + (((-19 + 5*Sqrt[17])/2)^(1/3)*Log[(1 + Sqrt[17])^(2/3) + ((-3 + Sqrt[17])^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(7 - Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3)])/(6*Sqrt[17]) - (((-19 + 5*Sqrt[17])/2)^(1/3)*Log[(1 + Sqrt[17])^(1/3) - ((-3 + Sqrt[17])^(1/3)*x)/(1 + x^3)^(1/3)])/(3*Sqrt[17]) - (((19 + 5*Sqrt[17])/2)^(1/3)*Log[(-1 + Sqrt[17])^(1/3) - ((3 + Sqrt[17])^(1/3)*x)/(1 + x^3)^(1/3)])/(3*Sqrt[17]) + (((19 + 5*Sqrt[17])/2)^(1/3)*Log[(-1 + Sqrt[17])^(2/3) + ((3 + Sqrt[17])^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(7 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3)])/(6*Sqrt[17])","B",22,11,30,0.3667,0,"{6728, 277, 239, 1518, 377, 200, 31, 634, 617, 204, 628}"
1465,1,431,0,1.0208903,"\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","Int[((-2 + x^3)*(1 + x^3)^(2/3))/(x^3*(-2 + x^3 + 2*x^6)),x]","-\frac{\sqrt[3]{\frac{1}{2} \left(5 \sqrt{17}-19\right)} \log \left(\sqrt[3]{1+\sqrt{17}}-\frac{\sqrt[3]{\sqrt{17}-3} x}{\sqrt[3]{x^3+1}}\right)}{3 \sqrt{17}}-\frac{\sqrt[3]{\frac{1}{2} \left(19+5 \sqrt{17}\right)} \log \left(\sqrt[3]{\sqrt{17}-1}-\frac{\sqrt[3]{3+\sqrt{17}} x}{\sqrt[3]{x^3+1}}\right)}{3 \sqrt{17}}+\frac{\sqrt[3]{\frac{1}{2} \left(5 \sqrt{17}-19\right)} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5-\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{51}}+\frac{\sqrt[3]{\frac{1}{2} \left(19+5 \sqrt{17}\right)} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2 \left(5+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{51}}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}+\frac{\sqrt[3]{\frac{1}{2} \left(5 \sqrt{17}-19\right)} \log \left(\frac{\sqrt[3]{2 \left(7-\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+\frac{\left(\sqrt{17}-3\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(1+\sqrt{17}\right)^{2/3}\right)}{6 \sqrt{17}}+\frac{\sqrt[3]{\frac{1}{2} \left(19+5 \sqrt{17}\right)} \log \left(\frac{\sqrt[3]{2 \left(7+\sqrt{17}\right)} x}{\sqrt[3]{x^3+1}}+\frac{\left(3+\sqrt{17}\right)^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+\left(\sqrt{17}-1\right)^{2/3}\right)}{6 \sqrt{17}}","\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 + (((-19 + 5*Sqrt[17])/2)^(1/3)*ArcTan[(1 + ((2*(5 - Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[51] + (((19 + 5*Sqrt[17])/2)^(1/3)*ArcTan[(1 + ((2*(5 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[51] + (((-19 + 5*Sqrt[17])/2)^(1/3)*Log[(1 + Sqrt[17])^(2/3) + ((-3 + Sqrt[17])^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(7 - Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3)])/(6*Sqrt[17]) - (((-19 + 5*Sqrt[17])/2)^(1/3)*Log[(1 + Sqrt[17])^(1/3) - ((-3 + Sqrt[17])^(1/3)*x)/(1 + x^3)^(1/3)])/(3*Sqrt[17]) - (((19 + 5*Sqrt[17])/2)^(1/3)*Log[(-1 + Sqrt[17])^(1/3) - ((3 + Sqrt[17])^(1/3)*x)/(1 + x^3)^(1/3)])/(3*Sqrt[17]) + (((19 + 5*Sqrt[17])/2)^(1/3)*Log[(-1 + Sqrt[17])^(2/3) + ((3 + Sqrt[17])^(2/3)*x^2)/(1 + x^3)^(2/3) + ((2*(7 + Sqrt[17]))^(1/3)*x)/(1 + x^3)^(1/3)])/(6*Sqrt[17])","B",22,11,30,0.3667,0,"{6728, 277, 239, 1518, 377, 200, 31, 634, 617, 204, 628}"
1466,1,117,0,0.770192,"\int \frac{x^2 \left(-2+x^4\right)}{\sqrt[3]{-x+x^5} \left(-1+x^4+x^8\right)} \, dx","Int[(x^2*(-2 + x^4))/((-x + x^5)^(1/3)*(-1 + x^4 + x^8)),x]","\frac{3 \sqrt[3]{1-x^4} x^3 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^4,-\frac{2 x^4}{1-\sqrt{5}}\right)}{8 \sqrt[3]{x^5-x}}+\frac{3 \sqrt[3]{1-x^4} x^3 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^4,-\frac{2 x^4}{1+\sqrt{5}}\right)}{8 \sqrt[3]{x^5-x}}","\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,"(3*x^3*(1 - x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, x^4, (-2*x^4)/(1 - Sqrt[5])])/(8*(-x + x^5)^(1/3)) + (3*x^3*(1 - x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, x^4, (-2*x^4)/(1 + Sqrt[5])])/(8*(-x + x^5)^(1/3))","C",11,6,30,0.2000,0,"{2056, 6728, 466, 465, 511, 510}"
1467,1,499,0,1.2611106,"\int \frac{-b+2 a x^4}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Int[(-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",10,5,39,0.1282,1,"{6728, 377, 212, 208, 205}"
1468,1,499,0,1.358661,"\int \frac{-2 b+a x^4}{\sqrt[4]{b+a x^4} \left(-2 b+a x^4+x^8\right)} \, dx","Int[(-2*b + a*x^4)/((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{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))])/(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)) + ((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",10,5,35,0.1429,1,"{6728, 377, 212, 208, 205}"
1469,1,130,0,0.2116487,"\int \frac{1}{x^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[1/(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{2 a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{b^2-\left(\sqrt{a^2 x^2+b^2}+a x\right)^2}+\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}}","-\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,"(2*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (a*x + Sqrt[b^2 + a^2*x^2])^2) + (a*ArcTan[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/Sqrt[b]])/b^(3/2) + (a*ArcTanh[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/Sqrt[b]])/b^(3/2)","A",6,6,27,0.2222,1,"{2119, 457, 329, 212, 206, 203}"
1470,1,100,0,0.11119,"\int \frac{\sqrt[3]{-1+x^3}}{x^{10}} \, dx","Int[(-1 + x^3)^(1/3)/x^10,x]","\frac{5 \sqrt[3]{x^3-1}}{162 x^3}+\frac{5}{162} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{5 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}-\frac{\sqrt[3]{x^3-1}}{9 x^9}+\frac{\sqrt[3]{x^3-1}}{54 x^6}-\frac{5 \log (x)}{162}","\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,"-1/9*(-1 + x^3)^(1/3)/x^9 + (-1 + x^3)^(1/3)/(54*x^6) + (5*(-1 + x^3)^(1/3))/(162*x^3) - (5*ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) - (5*Log[x])/162 + (5*Log[1 + (-1 + x^3)^(1/3)])/162","A",8,7,13,0.5385,1,"{266, 47, 51, 58, 618, 204, 31}"
1471,1,113,0,0.0672598,"\int x^4 \sqrt[3]{-1+x^3} \, dx","Int[x^4*(-1 + x^3)^(1/3),x]","\frac{1}{27} \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)}{9 \sqrt{3}}+\frac{1}{6} \sqrt[3]{x^3-1} x^5-\frac{1}{18} \sqrt[3]{x^3-1} x^2-\frac{1}{54} \log \left(\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+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}{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,"-1/18*(x^2*(-1 + x^3)^(1/3)) + (x^5*(-1 + x^3)^(1/3))/6 + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) + Log[1 - x/(-1 + x^3)^(1/3)]/27 - Log[1 + x^2/(-1 + x^3)^(2/3) + x/(-1 + x^3)^(1/3)]/54","A",9,9,13,0.6923,1,"{279, 321, 331, 292, 31, 634, 618, 204, 628}"
1472,1,186,0,0.1557099,"\int \sqrt[3]{-x+x^3} \, dx","Int[(-x + x^3)^(1/3),x]","\frac{1}{2} \sqrt[3]{x^3-x} x+\frac{\left(x^2-1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{6 \left(x^3-x\right)^{2/3}}-\frac{\left(x^2-1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{12 \left(x^3-x\right)^{2/3}}+\frac{\left(x^2-1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} \left(x^3-x\right)^{2/3}}","\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,"(x*(-x + x^3)^(1/3))/2 + (x^(2/3)*(-1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*(-x + x^3)^(2/3)) + (x^(2/3)*(-1 + x^2)^(2/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(6*(-x + x^3)^(2/3)) - (x^(2/3)*(-1 + x^2)^(2/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(12*(-x + x^3)^(2/3))","A",11,11,11,1.000,1,"{2004, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1473,1,100,0,0.0774777,"\int \frac{\sqrt[3]{-1+x^3} \left(-1+2 x^3\right)}{x^{10}} \, dx","Int[((-1 + x^3)^(1/3)*(-1 + 2*x^3))/x^10,x]","\frac{13 \sqrt[3]{x^3-1}}{162 x^3}+\frac{13}{162} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{13 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}-\frac{\left(x^3-1\right)^{4/3}}{9 x^9}-\frac{13 \sqrt[3]{x^3-1}}{54 x^6}-\frac{13 \log (x)}{162}","\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,"(-13*(-1 + x^3)^(1/3))/(54*x^6) + (13*(-1 + x^3)^(1/3))/(162*x^3) - (-1 + x^3)^(4/3)/(9*x^9) - (13*ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) - (13*Log[x])/162 + (13*Log[1 + (-1 + x^3)^(1/3)])/162","A",8,8,20,0.4000,1,"{446, 78, 47, 51, 58, 618, 204, 31}"
1474,1,362,0,4.134388,"\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","Int[(1 + k^3*x^3)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^3*x^3)),x]","\frac{4 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{3 \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{4 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{\sqrt[3]{-1}}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{3 \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{4 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{(-1)^{2/3}}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{3 \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\right)}}","-\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 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + (4*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(3*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + (4*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-((-1)^(1/3)/k), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(3*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + (4*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(-1)^(2/3)/k, ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(3*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",19,8,40,0.2000,0,"{6718, 6725, 115, 6688, 934, 12, 168, 537}"
1475,0,0,0,1.4133189,"\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","Int[((-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,"(9*(1 + x^4)^(2/3))/(2*x^2) + (18*x^2)/(1 - Sqrt[3] - (1 + x^4)^(1/3)) - (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (6*Sqrt[2]*3^(3/4)*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (3*Hypergeometric2F1[-5/4, -2/3, -1/4, -x^4])/(5*x^5) - Hypergeometric2F1[-2/3, -1/4, 3/4, -x^4]/x - 9*Defer[Int][(1 + x^4)^(2/3)/(1 - x^3 + x^4), x] + 12*Defer[Int][(x*(1 + x^4)^(2/3))/(1 - x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1476,1,46,0,0.0675087,"\int \frac{\left(b+a x^4\right)^{3/4}}{x^4 \left(2 b+a x^4\right)} \, dx","Int[(b + a*x^4)^(3/4)/(x^4*(2*b + a*x^4)),x]","-\frac{\left(a x^4+b\right)^{3/4} \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\frac{a x^4}{2 \left(a x^4+b\right)}\right)}{6 b x^3}","\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)*Hypergeometric2F1[-3/4, 1, 1/4, (a*x^4)/(2*(b + a*x^4))])/(b*x^3)","C",2,2,26,0.07692,1,"{511, 510}"
1477,1,154,0,0.256896,"\int \frac{-b+a x^3}{x^3 \sqrt[4]{-b x+a x^4}} \, dx","Int[(-b + a*x^3)/(x^3*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}-\frac{4 \left(a x^4-b x\right)^{3/4}}{9 x^3}","\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))/(9*x^3) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4))","A",10,9,27,0.3333,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2014}"
1478,1,154,0,0.1931686,"\int \frac{b+a x^3}{x^3 \sqrt[4]{-b x+a x^4}} \, dx","Int[(b + a*x^3)/(x^3*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{4 \left(a x^4-b x\right)^{3/4}}{9 x^3}","\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))/(9*x^3) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4))","A",8,8,25,0.3200,1,"{2038, 2011, 329, 275, 240, 212, 206, 203}"
1479,1,154,0,0.170336,"\int \frac{\sqrt[4]{-b x+a x^4}}{x^2} \, dx","Int[(-(b*x) + a*x^4)^(1/4)/x^2,x]","-\frac{4 \sqrt[4]{a x^4-b x}}{3 x}-\frac{2 \sqrt[4]{a} x^{3/4} \left(a x^3-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \left(a x^4-b x\right)^{3/4}}+\frac{2 \sqrt[4]{a} x^{3/4} \left(a x^3-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \left(a x^4-b x\right)^{3/4}}","-\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))/(3*x) - (2*a^(1/4)*x^(3/4)*(-b + a*x^3)^(3/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(3/4)) + (2*a^(1/4)*x^(3/4)*(-b + a*x^3)^(3/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(3/4))","A",8,8,18,0.4444,1,"{2020, 2032, 329, 275, 331, 298, 203, 206}"
1480,1,609,0,0.9795912,"\int \frac{1}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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{a^2-4 b} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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{a^2-4 b} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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} \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,"(2*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - (2*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + (2*Sqrt[x]*(-b + a*x^2)^(1/4)*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)) - (2*Sqrt[x]*(-b + a*x^2)^(1/4)*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",11,7,30,0.2333,1,"{2056, 1269, 1428, 377, 212, 208, 205}"
1481,1,609,0,0.634736,"\int \frac{1}{\left(b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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{a^2-4 b} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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{a^2-4 b} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \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} \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,"(2*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - (2*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + (2*Sqrt[x]*(-b + a*x^2)^(1/4)*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)) - (2*Sqrt[x]*(-b + a*x^2)^(1/4)*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",11,7,30,0.2333,1,"{2056, 1269, 1428, 377, 212, 208, 205}"
1482,1,104,0,0.052893,"\int \frac{-b+a x^4}{x^4 \sqrt[4]{-b+2 a x^4}} \, dx","Int[(-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",5,5,27,0.1852,1,"{451, 240, 212, 206, 203}"
1483,0,0,0,2.7603388,"\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","Int[(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,"-1/5*Defer[Int][1/((b^(1/5) - a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x]/a^(4/5) - Defer[Int][1/((-((-1)^(1/5)*b^(1/5)) - a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x]/(5*a^(4/5)) - Defer[Int][1/(((-1)^(2/5)*b^(1/5) - a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x]/(5*a^(4/5)) - Defer[Int][1/((-((-1)^(3/5)*b^(1/5)) - a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x]/(5*a^(4/5)) - Defer[Int][1/(((-1)^(4/5)*b^(1/5) - a^(1/5)*x)*(-b + c*x^4 + a*x^5)^(1/4)), x]/(5*a^(4/5)) + 5*b*Defer[Int][x^4/((b - a*x^5)^2*(-b + c*x^4 + a*x^5)^(1/4)), x]","F",0,0,0,0,-1,"{}"
1484,1,100,0,0.0686377,"\int \frac{1}{x^{19} \sqrt[3]{-1+x^6}} \, dx","Int[1/(x^19*(-1 + x^6)^(1/3)),x]","\frac{7 \left(x^6-1\right)^{2/3}}{81 x^6}-\frac{7}{162} \log \left(\sqrt[3]{x^6-1}+1\right)-\frac{7 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^6-1}}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{\left(x^6-1\right)^{2/3}}{18 x^{18}}+\frac{7 \left(x^6-1\right)^{2/3}}{108 x^{12}}+\frac{7 \log (x)}{81}","-\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)/(18*x^18) + (7*(-1 + x^6)^(2/3))/(108*x^12) + (7*(-1 + x^6)^(2/3))/(81*x^6) - (7*ArcTan[(1 - 2*(-1 + x^6)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) + (7*Log[x])/81 - (7*Log[1 + (-1 + x^6)^(1/3)])/162","A",8,6,13,0.4615,1,"{266, 51, 56, 618, 204, 31}"
1485,1,69,0,0.0341486,"\int \frac{x^7}{\sqrt[3]{-1+x^6}} \, dx","Int[x^7/(-1 + x^6)^(1/3),x]","\frac{1}{6} \left(x^6-1\right)^{2/3} x^2-\frac{1}{12} \log \left(x^2-\sqrt[3]{x^6-1}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}","\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,"(x^2*(-1 + x^6)^(2/3))/6 + ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(6*Sqrt[3]) - Log[x^2 - (-1 + x^6)^(1/3)]/12","A",3,3,13,0.2308,1,"{275, 321, 239}"
1486,1,103,0,0.0810137,"\int x^3 \sqrt[3]{-1+x^6} \, dx","Int[x^3*(-1 + x^6)^(1/3),x]","\frac{1}{6} \sqrt[3]{x^6-1} x^4+\frac{1}{18} \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}-\frac{1}{36} \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\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*(-1 + x^6)^(1/3))/6 + ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(6*Sqrt[3]) + Log[1 - x^2/(-1 + x^6)^(1/3)]/18 - Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)]/36","A",9,9,13,0.6923,1,"{275, 279, 331, 292, 31, 634, 618, 204, 628}"
1487,1,69,0,0.031715,"\int x \left(-1+x^6\right)^{2/3} \, dx","Int[x*(-1 + x^6)^(2/3),x]","\frac{1}{6} \left(x^6-1\right)^{2/3} x^2+\frac{1}{6} \log \left(x^2-\sqrt[3]{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{3 \sqrt{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))/6 - ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) + Log[x^2 - (-1 + x^6)^(1/3)]/6","A",3,3,11,0.2727,1,"{275, 195, 239}"
1488,1,69,0,0.0322467,"\int \frac{x^7}{\sqrt[3]{1+x^6}} \, dx","Int[x^7/(1 + x^6)^(1/3),x]","\frac{1}{6} \left(x^6+1\right)^{2/3} x^2+\frac{1}{12} \log \left(x^2-\sqrt[3]{x^6+1}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}","\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,"(x^2*(1 + x^6)^(2/3))/6 - ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/(6*Sqrt[3]) + Log[x^2 - (1 + x^6)^(1/3)]/12","A",3,3,13,0.2308,1,"{275, 321, 239}"
1489,1,103,0,0.0718889,"\int x^3 \sqrt[3]{1+x^6} \, dx","Int[x^3*(1 + x^6)^(1/3),x]","\frac{1}{6} \sqrt[3]{x^6+1} x^4-\frac{1}{18} \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{1}{36} \log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\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*(1 + x^6)^(1/3))/6 - ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/(6*Sqrt[3]) - Log[1 - x^2/(1 + x^6)^(1/3)]/18 + Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)]/36","A",9,9,13,0.6923,1,"{275, 279, 331, 292, 31, 634, 618, 204, 628}"
1490,1,69,0,0.0296889,"\int x \left(1+x^6\right)^{2/3} \, dx","Int[x*(1 + x^6)^(2/3),x]","\frac{1}{6} \left(x^6+1\right)^{2/3} x^2-\frac{1}{6} \log \left(x^2-\sqrt[3]{x^6+1}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{3 \sqrt{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))/6 + ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[x^2 - (1 + x^6)^(1/3)]/6","A",3,3,11,0.2727,1,"{275, 195, 239}"
1491,0,0,0,2.4288948,"\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","Int[((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,"(4*(1 + x^5)^(1/4)*Hypergeometric2F1[-9/20, 1/4, 11/20, -x^5])/(3*x^2*(x + x^6)^(1/4)) - (16*x*(1 + x^5)^(1/4)*Hypergeometric2F1[3/20, 1/4, 23/20, -x^5])/(3*(x + x^6)^(1/4)) + (8*x^3*(1 + x^5)^(1/4)*Hypergeometric2F1[1/4, 11/20, 31/20, -x^5])/(11*(x + x^6)^(1/4)) + (40*x^(1/4)*(1 + x^5)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 + x^20)^(1/4)*(1 + x^12 + x^20)), x], x, x^(1/4)])/(x + x^6)^(1/4) + (16*x^(1/4)*(1 + x^5)^(1/4)*Defer[Subst][Defer[Int][x^14/((1 + x^20)^(1/4)*(1 + x^12 + x^20)), x], x, x^(1/4)])/(x + x^6)^(1/4)","F",0,0,0,0,-1,"{}"
1492,1,119,0,0.0987698,"\int \frac{x}{\sqrt[3]{-x^2+x^6}} \, dx","Int[x/(-x^2 + x^6)^(1/3),x]","\frac{\sqrt{3} \sqrt[3]{x^2} \sqrt[3]{x^4-1} \tan ^{-1}\left(\frac{\frac{2 \left(x^2\right)^{2/3}}{\sqrt[3]{x^4-1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{x^6-x^2}}-\frac{3 \sqrt[3]{x^2} \sqrt[3]{x^4-1} \log \left(\left(x^2\right)^{2/3}-\sqrt[3]{x^4-1}\right)}{8 \sqrt[3]{x^6-x^2}}","-\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,"(Sqrt[3]*(x^2)^(1/3)*(-1 + x^4)^(1/3)*ArcTan[(1 + (2*(x^2)^(2/3))/(-1 + x^4)^(1/3))/Sqrt[3]])/(4*(-x^2 + x^6)^(1/3)) - (3*(x^2)^(1/3)*(-1 + x^4)^(1/3)*Log[(x^2)^(2/3) - (-1 + x^4)^(1/3)])/(8*(-x^2 + x^6)^(1/3))","A",5,5,15,0.3333,1,"{2013, 2011, 329, 275, 239}"
1493,1,211,0,0.621892,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^3 \left(-4+x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^3*(-4 + x^3 + x^6)),x]","\frac{\left(17+5 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{2 x^3}{1-\sqrt{17}}\right)}{34 \left(1-\sqrt{17}\right) \left(1-x^3\right)^{2/3}}+\frac{\left(17-5 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{2 x^3}{1+\sqrt{17}}\right)}{34 \left(1+\sqrt{17}\right) \left(1-x^3\right)^{2/3}}+\frac{1}{4} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\left(x^3-1\right)^{2/3}}{4 x^2}","\frac{\left(x^3-1\right)^{2/3}}{4 x^2}-\frac{1}{6} \text{RootSum}\left[4 \text{$\#$1}^6-7 \text{$\#$1}^3+2\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-2 \log (x)}{8 \text{$\#$1}^4-7 \text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(4*x^2) + ((17 + 5*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-2*x^3)/(1 - Sqrt[17])])/(34*(1 - Sqrt[17])*(1 - x^3)^(2/3)) + ((17 - 5*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-2*x^3)/(1 + Sqrt[17])])/(34*(1 + Sqrt[17])*(1 - x^3)^(2/3)) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/4","B",10,5,28,0.1786,0,"{6728, 277, 239, 430, 429}"
1494,1,211,0,0.5503091,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^3 \left(-4+x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^3*(-4 + x^3 + x^6)),x]","\frac{\left(17+5 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{2 x^3}{1-\sqrt{17}}\right)}{34 \left(1-\sqrt{17}\right) \left(1-x^3\right)^{2/3}}+\frac{\left(17-5 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{2 x^3}{1+\sqrt{17}}\right)}{34 \left(1+\sqrt{17}\right) \left(1-x^3\right)^{2/3}}+\frac{1}{4} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\left(x^3-1\right)^{2/3}}{4 x^2}","\frac{\left(x^3-1\right)^{2/3}}{4 x^2}-\frac{1}{6} \text{RootSum}\left[4 \text{$\#$1}^6-7 \text{$\#$1}^3+2\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-2 \log (x)}{8 \text{$\#$1}^4-7 \text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(4*x^2) + ((17 + 5*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-2*x^3)/(1 - Sqrt[17])])/(34*(1 - Sqrt[17])*(1 - x^3)^(2/3)) + ((17 - 5*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-2*x^3)/(1 + Sqrt[17])])/(34*(1 + Sqrt[17])*(1 - x^3)^(2/3)) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/4","B",10,5,28,0.1786,0,"{6728, 277, 239, 430, 429}"
1495,0,0,0,0.5167769,"\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","Int[((-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,"-3*Defer[Int][(1 - x + x^3)^(2/3)/(1 - 2*x + x^2 + 2*x^3 - 2*x^4 + 2*x^6), x] + 2*Defer[Int][(x*(1 - x + x^3)^(2/3))/(1 - 2*x + x^2 + 2*x^3 - 2*x^4 + 2*x^6), x]","F",0,0,0,0,-1,"{}"
1496,0,0,0,1.7302608,"\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","Int[((-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,"Defer[Int][(-2 + 2*x^4 + x^6)^(1/4), x]/2 + 2*Defer[Int][(-2 + 2*x^4 + x^6)^(1/4)/x^6, x] - Defer[Int][(-2 + 2*x^4 + x^6)^(1/4)/x^2, x]/2 - Defer[Int][(x^2*(-2 + 2*x^4 + x^6)^(1/4))/(-4 - x^4 + 2*x^6), x]/2 + (3*Defer[Int][(x^4*(-2 + 2*x^4 + x^6)^(1/4))/(-4 - x^4 + 2*x^6), x])/2","F",0,0,0,0,-1,"{}"
1497,1,119,0,0.3988949,"\int \frac{\left(1+x^3\right)^{2/3} \left(-1+3 x^6\right)}{x^9 \left(1+2 x^3\right)} \, dx","Int[((1 + x^3)^(2/3)*(-1 + 3*x^6))/(x^9*(1 + 2*x^3)),x]","2 x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-2 x^3\right)+\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{5/3}}{8 x^8}-\frac{19 \left(x^3+1\right)^{5/3}}{40 x^5}+\frac{\left(x^3+1\right)^{2/3}}{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{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)/(2*x^2) + (1 + x^3)^(5/3)/(8*x^8) - (19*(1 + x^3)^(5/3))/(40*x^5) + 2*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -2*x^3] - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]/2","C",8,6,29,0.2069,0,"{6725, 271, 264, 277, 239, 429}"
1498,1,139,0,0.4693145,"\int \frac{\sqrt{1-x^4} \left(1+x^4\right)}{1-x^4+x^8} \, dx","Int[(Sqrt[1 - x^4]*(1 + x^4))/(1 - x^4 + x^8),x]","-\frac{1}{2} \left(1+i \sqrt{3}\right) F\left(\left.\sin ^{-1}(x)\right|-1\right)-\frac{1}{2} \left(1-i \sqrt{3}\right) F\left(\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{2} \Pi \left(\frac{1}{2} \left(-i-\sqrt{3}\right);\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{2} \Pi \left(\frac{1}{2} \left(i-\sqrt{3}\right);\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{2} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)+\frac{1}{2} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\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,"-1/2*((1 - I*Sqrt[3])*EllipticF[ArcSin[x], -1]) - ((1 + I*Sqrt[3])*EllipticF[ArcSin[x], -1])/2 + EllipticPi[(-I - Sqrt[3])/2, ArcSin[x], -1]/2 + EllipticPi[(I - Sqrt[3])/2, ArcSin[x], -1]/2 + EllipticPi[1/Sqrt[(1 - I*Sqrt[3])/2], ArcSin[x], -1]/2 + EllipticPi[1/Sqrt[(1 + I*Sqrt[3])/2], ArcSin[x], -1]/2","C",16,6,29,0.2069,1,"{6728, 406, 221, 409, 1213, 537}"
1499,1,122,0,4.0568293,"\int \frac{x^2}{\left(b+a x^4\right)^{3/4} \left(-b^2+a^2 x^8\right)} \, dx","Int[x^2/((b + a*x^4)^(3/4)*(-b^2 + a^2*x^8)),x]","-\frac{4 x^3 \Gamma \left(\frac{7}{4}\right) \left(11 \left(-4 a^2 x^8-3 a b x^4+7 b^2\right) \, _2F_1\left(1,1;\frac{11}{4};-\frac{2 a x^4}{b-a x^4}\right)-32 a x^4 \left(a x^4+b\right) \, _2F_1\left(2,2;\frac{15}{4};-\frac{2 a x^4}{b-a x^4}\right)\right)}{693 b^2 \Gamma \left(\frac{3}{4}\right) \left(b-a x^4\right)^2 \left(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,"(-4*x^3*Gamma[7/4]*(11*(7*b^2 - 3*a*b*x^4 - 4*a^2*x^8)*Hypergeometric2F1[1, 1, 11/4, (-2*a*x^4)/(b - a*x^4)] - 32*a*x^4*(b + a*x^4)*Hypergeometric2F1[2, 2, 15/4, (-2*a*x^4)/(b - a*x^4)]))/(693*b^2*(b - a*x^4)^2*(b + a*x^4)^(3/4)*Gamma[3/4])","C",3,3,30,0.1000,0,"{1479, 511, 510}"
1500,0,0,0,0.1657456,"\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x+\sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[1 + x^2]]/(x + Sqrt[1 + x^2]),x]","\int \frac{\sqrt{1+\sqrt{1+x^2}}}{x+\sqrt{1+x^2}} \, dx","-\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*(1 + Sqrt[1 + x^2])^(3/2))/3 - (2*(1 + Sqrt[1 + x^2])^(5/2))/5 + Defer[Int][Sqrt[1 + x^2]*Sqrt[1 + Sqrt[1 + x^2]], x]","F",0,0,0,0,-1,"{}"
1501,0,0,0,0.5185565,"\int \frac{(2+x)^2}{x \left(4-2 x+x^2\right) \sqrt[3]{1+x+x^2}} \, dx","Int[(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,"(-3*((1 - I*Sqrt[3] + 2*x)/x)^(1/3)*((1 + I*Sqrt[3] + 2*x)/x)^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, -1/2*(1 - I*Sqrt[3])/x, -1/2*(1 + I*Sqrt[3])/x])/(2*2^(2/3)*(1 + x + x^2)^(1/3)) + 6*Defer[Int][1/((4 - 2*x + x^2)*(1 + x + x^2)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1502,1,101,0,0.0292632,"\int \frac{1}{\left(-2 b+a x^2\right) \sqrt[4]{-b+a x^2}} \, dx","Int[1/((-2*b + a*x^2)*(-b + a*x^2)^(1/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt{2} \sqrt{a} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt{2} \sqrt{a} b^{3/4}}","\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,"-1/2*ArcTan[(Sqrt[a]*x)/(Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4))]/(Sqrt[2]*Sqrt[a]*b^(3/4)) - ArcTanh[(Sqrt[a]*x)/(Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4))]/(2*Sqrt[2]*Sqrt[a]*b^(3/4))","A",1,1,25,0.04000,1,"{398}"
1503,1,118,0,0.0981869,"\int \frac{-1+x}{x^7 \sqrt[3]{1+x^3}} \, dx","Int[(-1 + x)/(x^7*(1 + x^3)^(1/3)),x]","-\frac{2 \left(x^3+1\right)^{2/3}}{9 x^3}-\frac{1}{9} \log \left(1-\sqrt[3]{x^3+1}\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}+\frac{\left(x^3+1\right)^{2/3}}{6 x^6}-\frac{\left(x^3+1\right)^{2/3}}{5 x^5}+\frac{3 \left(x^3+1\right)^{2/3}}{10 x^2}+\frac{\log (x)}{9}","-\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)/(6*x^6) - (1 + x^3)^(2/3)/(5*x^5) - (2*(1 + x^3)^(2/3))/(9*x^3) + (3*(1 + x^3)^(2/3))/(10*x^2) - (2*ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]) + Log[x]/9 - Log[1 - (1 + x^3)^(1/3)]/9","A",11,9,16,0.5625,1,"{1844, 266, 51, 55, 618, 204, 31, 271, 264}"
1504,0,0,0,1.1258058,"\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","Int[(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,"3*c*Defer[Int][1/((c + b*x + a*x^2)^(1/3)*(c + b*x + a*x^2 + x^3)), x] + 2*b*Defer[Int][x/((c + b*x + a*x^2)^(1/3)*(c + b*x + a*x^2 + x^3)), x] + a*Defer[Int][x^2/((c + b*x + a*x^2)^(1/3)*(c + b*x + a*x^2 + x^3)), x]","F",0,0,0,0,-1,"{}"
1505,1,445,0,1.334035,"\int \frac{-b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"((Sqrt[-a] - Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - ((Sqrt[-a] + Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + ((Sqrt[-a] - Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - ((Sqrt[-a] + Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4))","B",12,7,34,0.2059,1,"{2056, 6715, 6725, 377, 212, 206, 203}"
1506,1,445,0,1.0125081,"\int \frac{-b+a x^2}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}+\frac{\sqrt{x} \left(\sqrt{-a}-\sqrt{b}\right) \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\sqrt{-a}+\sqrt{b}\right) \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt{b} \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]",1,"((Sqrt[-a] - Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - ((Sqrt[-a] + Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) + ((Sqrt[-a] - Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4)) - ((Sqrt[-a] + Sqrt[b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[b]*(b*x^2 + a*x^4)^(1/4))","B",12,7,34,0.2059,1,"{2056, 6715, 6725, 377, 212, 206, 203}"
1507,1,201,0,1.4822631,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Int[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)),x]","-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{2 a \sqrt[4]{a x^4+b x^2}}{5 b^2 x}-\frac{2 \sqrt[4]{a x^4+b x^2}}{5 b x^3}","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}-\frac{2 \left(a x^2+b\right) \sqrt[4]{a x^4+b x^2}}{5 b^2 x^3}",1,"(-2*(b*x^2 + a*x^4)^(1/4))/(5*b*x^3) - (2*a*(b*x^2 + a*x^4)^(1/4))/(5*b^2*x) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4)) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4))","A",14,9,28,0.3214,0,"{2056, 1270, 1521, 271, 264, 6725, 1529, 511, 510}"
1508,1,201,0,1.2436293,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Int[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)),x]","-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{2 a \sqrt[4]{a x^4+b x^2}}{5 b^2 x}-\frac{2 \sqrt[4]{a x^4+b x^2}}{5 b x^3}","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}-\frac{2 \left(a x^2+b\right) \sqrt[4]{a x^4+b x^2}}{5 b^2 x^3}",1,"(-2*(b*x^2 + a*x^4)^(1/4))/(5*b*x^3) - (2*a*(b*x^2 + a*x^4)^(1/4))/(5*b^2*x) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4)) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4))","A",14,9,28,0.3214,0,"{2056, 1270, 1521, 271, 264, 6725, 1529, 511, 510}"
1509,1,201,0,1.1802532,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Int[(b*x^2 + a*x^4)^(1/4)/(x^4*(b + a*x^4)),x]","-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{2 a \sqrt[4]{a x^4+b x^2}}{5 b^2 x}-\frac{2 \sqrt[4]{a x^4+b x^2}}{5 b x^3}","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}-\frac{2 \left(a x^2+b\right) \sqrt[4]{a x^4+b x^2}}{5 b^2 x^3}",1,"(-2*(b*x^2 + a*x^4)^(1/4))/(5*b*x^3) - (2*a*(b*x^2 + a*x^4)^(1/4))/(5*b^2*x) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4)) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4))","A",14,9,28,0.3214,0,"{2056, 1270, 1521, 271, 264, 6725, 1529, 511, 510}"
1510,0,0,0,0.5513788,"\int \frac{x \left(3+5 x^2\right)}{\sqrt[3]{1+x^2} \left(-1+x^3+x^5\right)} \, dx","Int[(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,"3*Defer[Int][x/((1 + x^2)^(1/3)*(-1 + x^3 + x^5)), x] + 5*Defer[Int][x^3/((1 + x^2)^(1/3)*(-1 + x^3 + x^5)), x]","F",0,0,0,0,-1,"{}"
1511,0,0,0,1.2263724,"\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","Int[((-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,"(6*(-1 + x^5)^(2/3))/5 - (6*(-1 + x^5)^(2/3))/(5*x^5) - (3*(-1 + x^5)^(2/3)*Hypergeometric2F1[-2/3, -2/5, 3/5, x^5])/(2*x^2*(1 - x^5)^(2/3)) - 3*Defer[Int][(-1 + x^5)^(2/3)/(-1 + x^3 + x^5), x] - 5*Defer[Int][(x^2*(-1 + x^5)^(2/3))/(-1 + x^3 + x^5), x]","F",0,0,0,0,-1,"{}"
1512,1,94,0,0.0479271,"\int \frac{\left(1+x^3\right)^{2/3} \left(-2+x^3+x^6\right)}{x^9} \, dx","Int[((1 + x^3)^(2/3)*(-2 + x^3 + x^6))/x^9,x]","-\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{5/3}}{4 x^8}-\frac{7 \left(x^3+1\right)^{5/3}}{20 x^5}-\frac{\left(x^3+1\right)^{2/3}}{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{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,"-1/2*(1 + x^3)^(2/3)/x^2 + (1 + x^3)^(5/3)/(4*x^8) - (7*(1 + x^3)^(5/3))/(20*x^5) + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]/2","A",7,5,21,0.2381,1,"{1488, 271, 264, 277, 239}"
1513,1,380,0,1.1939844,"\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","Int[((-1 + x^6)^(2/3)*(1 + x^6)*(-1 - x^3 + x^6))/(x^6*(-1 + x^3 + x^6)),x]","-\frac{2 \left(1-\sqrt{5}\right) \left(x^6-1\right)^{2/3} x F_1\left(\frac{1}{6};-\frac{2}{3},1;\frac{7}{6};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{\left(3-\sqrt{5}\right) \left(1-x^6\right)^{2/3}}-\frac{2 \left(1+\sqrt{5}\right) \left(x^6-1\right)^{2/3} x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};\frac{2 x^6}{3+\sqrt{5}},x^6\right)}{\left(3+\sqrt{5}\right) \left(1-x^6\right)^{2/3}}+\frac{\left(x^6-1\right)^{2/3} x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};x^6,\frac{2 x^6}{3-\sqrt{5}}\right)}{\left(3-\sqrt{5}\right) \left(1-x^6\right)^{2/3}}+\frac{\left(x^6-1\right)^{2/3} x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};x^6,\frac{2 x^6}{3+\sqrt{5}}\right)}{\left(3+\sqrt{5}\right) \left(1-x^6\right)^{2/3}}+\frac{\left(x^6-1\right)^{2/3} x \, _2F_1\left(-\frac{2}{3},\frac{1}{6};\frac{7}{6};x^6\right)}{\left(1-x^6\right)^{2/3}}-\frac{\left(x^6-1\right)^{2/3} \, _2F_1\left(-\frac{5}{6},-\frac{2}{3};\frac{1}{6};x^6\right)}{5 \left(1-x^6\right)^{2/3} x^5}-\frac{\left(x^6-1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{2}{3};x^6\right)}{\left(1-x^6\right)^{2/3} x^2}","-\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,"(-2*(1 - Sqrt[5])*x*(-1 + x^6)^(2/3)*AppellF1[1/6, -2/3, 1, 7/6, x^6, (2*x^6)/(3 - Sqrt[5])])/((3 - Sqrt[5])*(1 - x^6)^(2/3)) - (2*(1 + Sqrt[5])*x*(-1 + x^6)^(2/3)*AppellF1[1/6, 1, -2/3, 7/6, (2*x^6)/(3 + Sqrt[5]), x^6])/((3 + Sqrt[5])*(1 - x^6)^(2/3)) + (x^4*(-1 + x^6)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, x^6, (2*x^6)/(3 - Sqrt[5])])/((3 - Sqrt[5])*(1 - x^6)^(2/3)) + (x^4*(-1 + x^6)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, x^6, (2*x^6)/(3 + Sqrt[5])])/((3 + Sqrt[5])*(1 - x^6)^(2/3)) - ((-1 + x^6)^(2/3)*Hypergeometric2F1[-5/6, -2/3, 1/6, x^6])/(5*x^5*(1 - x^6)^(2/3)) - ((-1 + x^6)^(2/3)*Hypergeometric2F1[-2/3, -1/3, 2/3, x^6])/(x^2*(1 - x^6)^(2/3)) + (x*(-1 + x^6)^(2/3)*Hypergeometric2F1[-2/3, 1/6, 7/6, x^6])/(1 - x^6)^(2/3)","C",25,12,38,0.3158,0,"{6728, 246, 245, 365, 364, 275, 1438, 430, 429, 465, 511, 510}"
1514,1,94,0,0.0484553,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-2+2 x^3+x^6\right)}{x^9} \, dx","Int[((-1 + x^3)^(2/3)*(-2 + 2*x^3 + x^6))/x^9,x]","-\frac{1}{2} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3-1\right)^{5/3}}{4 x^8}+\frac{\left(x^3-1\right)^{5/3}}{4 x^5}-\frac{\left(x^3-1\right)^{2/3}}{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{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,"-1/2*(-1 + x^3)^(2/3)/x^2 - (-1 + x^3)^(5/3)/(4*x^8) + (-1 + x^3)^(5/3)/(4*x^5) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (-1 + x^3)^(1/3)]/2","A",7,5,23,0.2174,1,"{1488, 271, 264, 277, 239}"
1515,1,105,0,0.2010539,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-2+x^4+x^8\right)} \, dx","Int[(-2 + x^4)/((1 + x^4)^(1/4)*(-2 + x^4 + x^8)),x]","\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}}","\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,"(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)) + (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",10,5,25,0.2000,1,"{6728, 377, 212, 206, 203}"
1516,1,295,0,1.5275574,"\int \frac{\sqrt[4]{-1+x^4} \left(2+x^4\right)}{x^2 \left(2+2 x^4+x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(2 + x^4))/(x^2*(2 + 2*x^4 + x^8)),x]","-\frac{\left(\frac{1}{12}+\frac{i}{12}\right) \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,\left(-\frac{1}{2}+\frac{i}{2}\right) x^4\right)}{\sqrt[4]{1-x^4}}-\frac{\left(\frac{1}{12}-\frac{i}{12}\right) \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\left(-\frac{1}{2}-\frac{i}{2}\right) x^4,x^4\right)}{\sqrt[4]{1-x^4}}-\frac{\sqrt[4]{x^4-1}}{x}-\left(\frac{1}{4}+\frac{i}{2}\right) \left(\frac{3}{5}-\frac{i}{5}\right)^{3/4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}-\frac{i}{5}} \sqrt[4]{x^4-1}}\right)-\left(\frac{1}{4}-\frac{i}{2}\right) \left(\frac{3}{5}+\frac{i}{5}\right)^{3/4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}+\frac{i}{5}} \sqrt[4]{x^4-1}}\right)+\left(\frac{1}{4}+\frac{i}{2}\right) \left(\frac{3}{5}-\frac{i}{5}\right)^{3/4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}-\frac{i}{5}} \sqrt[4]{x^4-1}}\right)+\left(\frac{1}{4}-\frac{i}{2}\right) \left(\frac{3}{5}+\frac{i}{5}\right)^{3/4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}+\frac{i}{5}} \sqrt[4]{x^4-1}}\right)","\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^8-6 \text{$\#$1}^4+5\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)+5 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-5 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{\sqrt[4]{x^4-1}}{x}",1,"-((-1 + x^4)^(1/4)/x) - ((1/12 + I/12)*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (-1/2 + I/2)*x^4])/(1 - x^4)^(1/4) - ((1/12 - I/12)*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-1/2 - I/2)*x^4, x^4])/(1 - x^4)^(1/4) - (1/4 + I/2)*(3/5 - I/5)^(3/4)*ArcTan[x/((3/5 - I/5)^(1/4)*(-1 + x^4)^(1/4))] - (1/4 - I/2)*(3/5 + I/5)^(3/4)*ArcTan[x/((3/5 + I/5)^(1/4)*(-1 + x^4)^(1/4))] + (1/4 + I/2)*(3/5 - I/5)^(3/4)*ArcTanh[x/((3/5 - I/5)^(1/4)*(-1 + x^4)^(1/4))] + (1/4 - I/2)*(3/5 + I/5)^(3/4)*ArcTanh[x/((3/5 + I/5)^(1/4)*(-1 + x^4)^(1/4))]","C",42,11,30,0.3667,0,"{6728, 277, 331, 298, 203, 206, 1528, 511, 510, 1518, 494}"
1517,1,295,0,1.4266441,"\int \frac{\sqrt[4]{-1+x^4} \left(2+x^4\right)}{x^2 \left(2+2 x^4+x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(2 + x^4))/(x^2*(2 + 2*x^4 + x^8)),x]","-\frac{\left(\frac{1}{12}+\frac{i}{12}\right) \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,\left(-\frac{1}{2}+\frac{i}{2}\right) x^4\right)}{\sqrt[4]{1-x^4}}-\frac{\left(\frac{1}{12}-\frac{i}{12}\right) \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\left(-\frac{1}{2}-\frac{i}{2}\right) x^4,x^4\right)}{\sqrt[4]{1-x^4}}-\frac{\sqrt[4]{x^4-1}}{x}-\left(\frac{1}{4}+\frac{i}{2}\right) \left(\frac{3}{5}-\frac{i}{5}\right)^{3/4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}-\frac{i}{5}} \sqrt[4]{x^4-1}}\right)-\left(\frac{1}{4}-\frac{i}{2}\right) \left(\frac{3}{5}+\frac{i}{5}\right)^{3/4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}+\frac{i}{5}} \sqrt[4]{x^4-1}}\right)+\left(\frac{1}{4}+\frac{i}{2}\right) \left(\frac{3}{5}-\frac{i}{5}\right)^{3/4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}-\frac{i}{5}} \sqrt[4]{x^4-1}}\right)+\left(\frac{1}{4}-\frac{i}{2}\right) \left(\frac{3}{5}+\frac{i}{5}\right)^{3/4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\frac{3}{5}+\frac{i}{5}} \sqrt[4]{x^4-1}}\right)","\frac{1}{8} \text{RootSum}\left[2 \text{$\#$1}^8-6 \text{$\#$1}^4+5\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)+5 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-5 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{\sqrt[4]{x^4-1}}{x}",1,"-((-1 + x^4)^(1/4)/x) - ((1/12 + I/12)*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (-1/2 + I/2)*x^4])/(1 - x^4)^(1/4) - ((1/12 - I/12)*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-1/2 - I/2)*x^4, x^4])/(1 - x^4)^(1/4) - (1/4 + I/2)*(3/5 - I/5)^(3/4)*ArcTan[x/((3/5 - I/5)^(1/4)*(-1 + x^4)^(1/4))] - (1/4 - I/2)*(3/5 + I/5)^(3/4)*ArcTan[x/((3/5 + I/5)^(1/4)*(-1 + x^4)^(1/4))] + (1/4 + I/2)*(3/5 - I/5)^(3/4)*ArcTanh[x/((3/5 - I/5)^(1/4)*(-1 + x^4)^(1/4))] + (1/4 - I/2)*(3/5 + I/5)^(3/4)*ArcTanh[x/((3/5 + I/5)^(1/4)*(-1 + x^4)^(1/4))]","C",42,11,30,0.3667,0,"{6728, 277, 331, 298, 203, 206, 1528, 511, 510, 1518, 494}"
1518,1,108,0,0.0691083,"\int \frac{-2 b-2 a x^4+x^8}{x^4 \sqrt[4]{b+a x^4}} \, dx","Int[(-2*b - 2*a*x^4 + x^8)/(x^4*(b + a*x^4)^(1/4)),x]","-\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{x \left(a x^4+b\right)^{3/4}}{4 a}+\frac{2 \left(a x^4+b\right)^{3/4}}{3 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*(b + a*x^4)^(3/4))/(3*x^3) + (x*(b + a*x^4)^(3/4))/(4*a) - ((8*a^2 + b)*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(5/4)) - ((8*a^2 + b)*ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)])/(8*a^(5/4))","A",6,6,28,0.2143,1,"{1486, 451, 240, 212, 206, 203}"
1519,1,105,0,0.2498222,"\int \frac{1-2 x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-2-x^4+x^8\right)} \, dx","Int[(1 - 2*x^4 + 2*x^8)/((1 + x^4)^(1/4)*(-2 - x^4 + x^8)),x]","-\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}}","-\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)) + ArcTan[x/(1 + x^4)^(1/4)] - (5*ArcTan[((3/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(6*2^(3/4)*3^(1/4)) + ArcTanh[x/(1 + x^4)^(1/4)] - (5*ArcTanh[((3/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(6*2^(3/4)*3^(1/4))","A",12,8,34,0.2353,1,"{6728, 240, 212, 206, 203, 1403, 382, 377}"
1520,0,0,0,3.07141,"\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","Int[((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,"(-1)^(3/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/((-1)^(1/8) - x), x] + (-1)^(1/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/((-1)^(3/8) - x), x] - (-1)^(3/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/(-(-1)^(5/8) - x), x] - (-1)^(1/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/(-(-1)^(7/8) - x), x] - 3*Defer[Int][(1 + x^3 + x^8)^(2/3)/x^3, x] - (-1)^(3/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/((-1)^(1/8) + x), x] - (-1)^(1/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/((-1)^(3/8) + x), x] + (-1)^(3/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/(-(-1)^(5/8) + x), x] + (-1)^(1/4)*Defer[Int][(1 + x^3 + x^8)^(2/3)/(-(-1)^(7/8) + x), x]","F",0,0,0,0,-1,"{}"
1521,1,291,0,0.6205125,"\int \frac{-b+2 a x^8}{\sqrt[4]{b+a x^4} \left(-b+a x^8\right)} \, dx","Int[(-b + 2*a*x^8)/((b + a*x^4)^(1/4)*(-b + a*x^8)),x]","\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[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}}}+\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[8]{a} x \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} x \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt[8]{a} \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}}\&\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) - ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(4*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)) - ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(4*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) - ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(4*a^(1/8)*(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^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4))","B",15,7,33,0.2121,1,"{6725, 240, 212, 206, 203, 1429, 377}"
1522,0,0,0,0.6091776,"\int \frac{\sqrt{-1-x^2+x^6} \left(1+2 x^6\right)}{8-x^4-16 x^6+8 x^{12}} \, dx","Int[(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,"Defer[Int][Sqrt[-1 - x^2 + x^6]/(8 - x^4 - 16*x^6 + 8*x^12), x] + 2*Defer[Int][(x^6*Sqrt[-1 - x^2 + x^6])/(8 - x^4 - 16*x^6 + 8*x^12), x]","F",0,0,0,0,-1,"{}"
1523,1,145,0,0.1478683,"\int \frac{1}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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)}{\sqrt{2}}+\frac{\log \left(\sqrt{x^2+1}+\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)}{\sqrt{2}}-\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)","\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,"-(Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]]) + Sqrt[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]]]/Sqrt[2] + Log[1 + x + Sqrt[1 + x^2] + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[2]","A",11,8,23,0.3478,1,"{2122, 329, 211, 1165, 628, 1162, 617, 204}"
1524,0,0,0,7.3248033,"\int \frac{\sqrt{x-\sqrt{1+x^2}}}{x^2+\sqrt{1+x^2}} \, dx","Int[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,"-1/2*((1 - Sqrt[5])*(I*(3 - Sqrt[5]) + 2*Sqrt[-2 + Sqrt[5]])*ArcTan[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[Sqrt[3 - Sqrt[5]] - I*Sqrt[-1 + Sqrt[5]]]])/(2^(3/4)*Sqrt[-5*(2 - Sqrt[5])*(Sqrt[3 - Sqrt[5]] - I*Sqrt[-1 + Sqrt[5]])]) + ((1 - Sqrt[5])*(I*(3 - Sqrt[5]) - 2*Sqrt[-2 + Sqrt[5]])*ArcTan[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[Sqrt[3 - Sqrt[5]] + I*Sqrt[-1 + Sqrt[5]]]])/(2*2^(3/4)*Sqrt[-5*(2 - Sqrt[5])*(Sqrt[3 - Sqrt[5]] + I*Sqrt[-1 + Sqrt[5]])]) - ((5 + Sqrt[5])*(3 + Sqrt[5] - 2*Sqrt[2 + Sqrt[5]])*ArcTan[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[-Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]]]])/(10*2^(3/4)*Sqrt[(2 + Sqrt[5])*(-Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]])]) + ((5 + Sqrt[5])*(3 + Sqrt[5] + 2*Sqrt[2 + Sqrt[5]])*ArcTan[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]]]])/(10*2^(3/4)*Sqrt[(2 + Sqrt[5])*(Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]])]) + ((1 - Sqrt[5])*(I*(3 - Sqrt[5]) + 2*Sqrt[-2 + Sqrt[5]])*ArcTanh[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[Sqrt[3 - Sqrt[5]] - I*Sqrt[-1 + Sqrt[5]]]])/(2*2^(3/4)*Sqrt[-5*(2 - Sqrt[5])*(Sqrt[3 - Sqrt[5]] - I*Sqrt[-1 + Sqrt[5]])]) - ((1 - Sqrt[5])*(I*(3 - Sqrt[5]) - 2*Sqrt[-2 + Sqrt[5]])*ArcTanh[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[Sqrt[3 - Sqrt[5]] + I*Sqrt[-1 + Sqrt[5]]]])/(2*2^(3/4)*Sqrt[-5*(2 - Sqrt[5])*(Sqrt[3 - Sqrt[5]] + I*Sqrt[-1 + Sqrt[5]])]) + ((5 + Sqrt[5])*(3 + Sqrt[5] - 2*Sqrt[2 + Sqrt[5]])*ArcTanh[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[-Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]]]])/(10*2^(3/4)*Sqrt[(2 + Sqrt[5])*(-Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]])]) - ((5 + Sqrt[5])*(3 + Sqrt[5] + 2*Sqrt[2 + Sqrt[5]])*ArcTanh[(2^(1/4)*Sqrt[x - Sqrt[1 + x^2]])/Sqrt[Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]]]])/(10*2^(3/4)*Sqrt[(2 + Sqrt[5])*(Sqrt[1 + Sqrt[5]] + Sqrt[3 + Sqrt[5]])]) + (I*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(I*Sqrt[-1 + Sqrt[5]] - Sqrt[2]*x), x])/Sqrt[5*(-1 + Sqrt[5])] + Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(Sqrt[1 + Sqrt[5]] - Sqrt[2]*x), x]/Sqrt[5*(1 + Sqrt[5])] + (I*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(I*Sqrt[-1 + Sqrt[5]] + Sqrt[2]*x), x])/Sqrt[5*(-1 + Sqrt[5])] + Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(Sqrt[1 + Sqrt[5]] + Sqrt[2]*x), x]/Sqrt[5*(1 + Sqrt[5])]","F",0,0,0,0,-1,"{}"
1525,0,0,0,0.1997675,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{x^2} \, dx","Int[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,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/x^2, x]","F",0,0,0,0,-1,"{}"
1526,1,124,0,0.6625396,"\int \frac{-1+x}{(1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-1 + x)/((1 + x)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\frac{8}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{24}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{16}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}+\frac{8}{\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/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] + (16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 + 4*Sqrt[2]*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[2]]","A",6,3,28,0.1071,1,"{1629, 63, 206}"
1527,1,127,0,0.0547484,"\int \frac{1}{(-2+x) \sqrt[3]{1+2 x+x^2}} \, dx","Int[1/((-2 + x)*(1 + 2*x + x^2)^(1/3)),x]","-\frac{(x+1)^{2/3} \log (2-x)}{2\ 3^{2/3} \sqrt[3]{x^2+2 x+1}}+\frac{\sqrt[3]{3} (x+1)^{2/3} \log \left(\sqrt[3]{3}-\sqrt[3]{x+1}\right)}{2 \sqrt[3]{x^2+2 x+1}}-\frac{(x+1)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}+\sqrt[3]{3}}{3^{5/6}}\right)}{\sqrt[6]{3} \sqrt[3]{x^2+2 x+1}}","\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 + x)^(2/3)*ArcTan[(3^(1/3) + 2*(1 + x)^(1/3))/3^(5/6)])/(3^(1/6)*(1 + 2*x + x^2)^(1/3))) - ((1 + x)^(2/3)*Log[2 - x])/(2*3^(2/3)*(1 + 2*x + x^2)^(1/3)) + (3^(1/3)*(1 + x)^(2/3)*Log[3^(1/3) - (1 + x)^(1/3)])/(2*(1 + 2*x + x^2)^(1/3))","A",5,5,18,0.2778,1,"{646, 57, 617, 204, 31}"
1528,1,188,0,0.1482115,"\int \frac{\sqrt[3]{-x+x^3}}{x^2} \, dx","Int[(-x + x^3)^(1/3)/x^2,x]","-\frac{3 \sqrt[3]{x^3-x}}{2 x}-\frac{x^{2/3} \left(x^2-1\right)^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{2 \left(x^3-x\right)^{2/3}}+\frac{x^{2/3} \left(x^2-1\right)^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{4 \left(x^3-x\right)^{2/3}}-\frac{\sqrt{3} x^{2/3} \left(x^2-1\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \left(x^3-x\right)^{2/3}}","-\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))/(2*x) - (Sqrt[3]*x^(2/3)*(-1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*(-x + x^3)^(2/3)) - (x^(2/3)*(-1 + x^2)^(2/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(2*(-x + x^3)^(2/3)) + (x^(2/3)*(-1 + x^2)^(2/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(4*(-x + x^3)^(2/3))","A",11,11,15,0.7333,1,"{2020, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1529,1,149,0,0.0723999,"\int \frac{\sqrt[3]{-x^2+x^3}}{x} \, dx","Int[(-x^2 + x^3)^(1/3)/x,x]","\sqrt[3]{x^3-x^2}+\frac{(x-1)^{2/3} x^{4/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{2 \left(x^3-x^2\right)^{2/3}}+\frac{(x-1)^{2/3} x^{4/3} \log (x-1)}{6 \left(x^3-x^2\right)^{2/3}}+\frac{(x-1)^{2/3} x^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \left(x^3-x^2\right)^{2/3}}","\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,"(-x^2 + x^3)^(1/3) + ((-1 + x)^(2/3)*x^(4/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-x^2 + x^3)^(2/3)) + ((-1 + x)^(2/3)*x^(4/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(2*(-x^2 + x^3)^(2/3)) + ((-1 + x)^(2/3)*x^(4/3)*Log[-1 + x])/(6*(-x^2 + x^3)^(2/3))","A",3,3,17,0.1765,1,"{2021, 2032, 59}"
1530,0,0,0,2.2395934,"\int \frac{-3 b+a x^2}{\left(-b+a x^2+x^3\right) \sqrt[4]{-b x+a x^3}} \, dx","Int[(-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,"(12*b*x^(1/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/((-b + a*x^8)^(1/4)*(b - a*x^8 - x^12)), x], x, x^(1/4)])/(-(b*x) + a*x^3)^(1/4) + (4*a*x^(1/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^10/((-b + a*x^8)^(1/4)*(-b + a*x^8 + x^12)), x], x, x^(1/4)])/(-(b*x) + a*x^3)^(1/4)","F",0,0,0,0,-1,"{}"
1531,1,170,0,0.3610805,"\int \frac{1}{(-2 b+a x) \sqrt[4]{-b x^2+a x^3}} \, dx","Int[1/((-2*b + a*x)*(-(b*x^2) + a*x^3)^(1/4)),x]","\frac{\sqrt{\frac{a x}{b}} \sqrt[4]{a x-b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x-b}}{\sqrt[4]{b} \sqrt{\frac{a x}{b}}}\right)}{\sqrt{2} a \sqrt[4]{b} \sqrt[4]{a x^3-b x^2}}-\frac{\sqrt{\frac{a x}{b}} \sqrt[4]{a x-b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x-b}}{\sqrt[4]{b} \sqrt{\frac{a x}{b}}}\right)}{\sqrt{2} a \sqrt[4]{b} \sqrt[4]{a x^3-b x^2}}","\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,"(Sqrt[(a*x)/b]*(-b + a*x)^(1/4)*ArcTan[(Sqrt[2]*(-b + a*x)^(1/4))/(b^(1/4)*Sqrt[(a*x)/b])])/(Sqrt[2]*a*b^(1/4)*(-(b*x^2) + a*x^3)^(1/4)) - (Sqrt[(a*x)/b]*(-b + a*x)^(1/4)*ArcTanh[(Sqrt[2]*(-b + a*x)^(1/4))/(b^(1/4)*Sqrt[(a*x)/b])])/(Sqrt[2]*a*b^(1/4)*(-(b*x^2) + a*x^3)^(1/4))","A",12,9,26,0.3462,1,"{2056, 107, 106, 490, 1211, 220, 1699, 203, 206}"
1532,1,236,0,2.1182767,"\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","Int[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(x^4*(b + a*x^4)),x]","\frac{2 a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{2 a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{4 a \sqrt[4]{a x^4-b x^2}}{5 b x}-\frac{2 \left(b-a x^2\right) \sqrt[4]{a x^4-b x^2}}{5 b x^3}+\frac{4 \sqrt[4]{a x^4-b x^2}}{5 x^3}","\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]-\frac{2 \left(a x^2-b\right) \sqrt[4]{a x^4-b x^2}}{5 b x^3}",1,"(4*(-(b*x^2) + a*x^4)^(1/4))/(5*x^3) - (4*a*(-(b*x^2) + a*x^4)^(1/4))/(5*b*x) - (2*(b - a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(5*b*x^3) + (2*a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*b*(1 - (a*x^2)/b)^(1/4)) + (2*a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*b*(1 - (a*x^2)/b)^(1/4))","B",17,9,38,0.2368,0,"{2056, 6725, 264, 1270, 1521, 271, 1529, 511, 510}"
1533,1,236,0,1.6935695,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{x^4 \left(b+a x^4\right)} \, dx","Int[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(x^4*(b + a*x^4)),x]","\frac{2 a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{2 a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{4 a \sqrt[4]{a x^4-b x^2}}{5 b x}-\frac{2 \left(b-a x^2\right) \sqrt[4]{a x^4-b x^2}}{5 b x^3}+\frac{4 \sqrt[4]{a x^4-b x^2}}{5 x^3}","\frac{1}{2} a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]-\frac{2 \left(a x^2-b\right) \sqrt[4]{a x^4-b x^2}}{5 b x^3}",1,"(4*(-(b*x^2) + a*x^4)^(1/4))/(5*x^3) - (4*a*(-(b*x^2) + a*x^4)^(1/4))/(5*b*x) - (2*(b - a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(5*b*x^3) + (2*a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*b*(1 - (a*x^2)/b)^(1/4)) + (2*a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*b*(1 - (a*x^2)/b)^(1/4))","B",17,9,38,0.2368,0,"{2056, 6725, 264, 1270, 1521, 271, 1529, 511, 510}"
1534,1,631,0,2.0956758,"\int \frac{-b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\left(a-\sqrt{a^2-4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2-4 b}+a^2+2 b} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b}}{\sqrt[4]{\sqrt{a^2-4 b}+a} \sqrt[4]{a x^2+b}}\right)}{\left(\sqrt{a^2-4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2-4 b}+a^2+2 b} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"-(((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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)*(b*x^2 + a*x^4)^(1/4))) - ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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)*(b*x^2 + a*x^4)^(1/4)) - ((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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)) - ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*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",12,7,38,0.1842,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1535,1,631,0,1.4430665,"\int \frac{-b+a x^2}{\left(b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/((b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4)),x]","-\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2+b} \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} \sqrt[4]{a x^4+b x^2}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2+b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]",1,"-(((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4))) - ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a - Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4)) - ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*Sqrt[x])/((a + Sqrt[a^2 - 4*b])^(1/4)*(b + a*x^2)^(1/4))])/((a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 + a*Sqrt[a^2 - 4*b] + 2*b)^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",12,7,38,0.1842,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1536,1,197,0,1.4005312,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Int[(b*x^2 + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{2 a \sqrt[4]{a x^4+b x^2}}{5 b^2 x}+\frac{2 \sqrt[4]{a x^4+b x^2}}{5 b x^3}","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}+\frac{2 \sqrt[4]{a x^4+b x^2} \left(a x^2+b\right)}{5 b^2 x^3}",1,"(2*(b*x^2 + a*x^4)^(1/4))/(5*b*x^3) + (2*a*(b*x^2 + a*x^4)^(1/4))/(5*b^2*x) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4)) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4))","A",14,9,30,0.3000,0,"{2056, 1270, 1521, 271, 264, 6725, 1529, 511, 510}"
1537,1,197,0,1.2362419,"\int \frac{\sqrt[4]{b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Int[(b*x^2 + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{a x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{2 a \sqrt[4]{a x^4+b x^2}}{5 b^2 x}+\frac{2 \sqrt[4]{a x^4+b x^2}}{5 b x^3}","\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}+\frac{2 \sqrt[4]{a x^4+b x^2} \left(a x^2+b\right)}{5 b^2 x^3}",1,"(2*(b*x^2 + a*x^4)^(1/4))/(5*b*x^3) + (2*a*(b*x^2 + a*x^4)^(1/4))/(5*b^2*x) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4)) - (a*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*b^2*(1 + (a*x^2)/b)^(1/4))","A",14,9,30,0.3000,0,"{2056, 1270, 1521, 271, 264, 6725, 1529, 511, 510}"
1538,1,662,0,2.8554235,"\int \frac{b^3+a^3 x^3}{\left(-b^3+a^3 x^3\right) \sqrt{b^4+a^4 x^4}} \, dx","Int[(b^3 + a^3*x^3)/((-b^3 + a^3*x^3)*Sqrt[b^4 + a^4*x^4]),x]","-\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{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a b}-\frac{\tanh ^{-1}\left(\frac{a^2 x^2+b^2}{\sqrt{2} \sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a b}-\frac{\left(a-\sqrt{3} \sqrt{-a^2}\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{6 a^2 b \sqrt{a^4 x^4+b^4}}-\frac{\left(\sqrt{3} \sqrt{-a^2}+a\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{6 a^2 b \sqrt{a^4 x^4+b^4}}+\frac{\left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{3 a b \sqrt{a^4 x^4+b^4}}+\frac{\left(a-\sqrt{3} \sqrt{-a^2}\right) \tanh ^{-1}\left(\frac{\sqrt{a} \left(\left(a-\sqrt{3} \sqrt{-a^2}\right)^2 x^2+4 b^2\right)}{2 \sqrt{2} \sqrt{\sqrt{3} \sqrt{-a^2}+a} \sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a^{3/2} \sqrt{\sqrt{3} \sqrt{-a^2}+a} b}+\frac{\left(\sqrt{3} \sqrt{-a^2}+a\right) \tanh ^{-1}\left(\frac{\sqrt{a} \left(\left(\sqrt{3} \sqrt{-a^2}+a\right)^2 x^2+4 b^2\right)}{2 \sqrt{2} \sqrt{a-\sqrt{3} \sqrt{-a^2}} \sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a^{3/2} \sqrt{a-\sqrt{3} \sqrt{-a^2}} b}","-\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,"(-2*ArcTan[(a*b*x)/Sqrt[b^4 + a^4*x^4]])/(3*a*b) - ArcTanh[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(3*Sqrt[2]*a*b) - ArcTanh[(b^2 + a^2*x^2)/(Sqrt[2]*Sqrt[b^4 + a^4*x^4])]/(3*Sqrt[2]*a*b) + ((a - Sqrt[3]*Sqrt[-a^2])*ArcTanh[(Sqrt[a]*(4*b^2 + (a - Sqrt[3]*Sqrt[-a^2])^2*x^2))/(2*Sqrt[2]*Sqrt[a + Sqrt[3]*Sqrt[-a^2]]*Sqrt[b^4 + a^4*x^4])])/(3*Sqrt[2]*a^(3/2)*Sqrt[a + Sqrt[3]*Sqrt[-a^2]]*b) + ((a + Sqrt[3]*Sqrt[-a^2])*ArcTanh[(Sqrt[a]*(4*b^2 + (a + Sqrt[3]*Sqrt[-a^2])^2*x^2))/(2*Sqrt[2]*Sqrt[a - Sqrt[3]*Sqrt[-a^2]]*Sqrt[b^4 + a^4*x^4])])/(3*Sqrt[2]*a^(3/2)*Sqrt[a - Sqrt[3]*Sqrt[-a^2]]*b) + ((b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(3*a*b*Sqrt[b^4 + a^4*x^4]) - ((a - Sqrt[3]*Sqrt[-a^2])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(6*a^2*b*Sqrt[b^4 + a^4*x^4]) - ((a + Sqrt[3]*Sqrt[-a^2])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(6*a^2*b*Sqrt[b^4 + a^4*x^4])","C",29,13,42,0.3095,1,"{6725, 220, 2074, 1725, 1211, 1699, 208, 1248, 725, 206, 6728, 1217, 1707}"
1539,1,156,0,0.5684743,"\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","Int[((1 + x^3)^(2/3)*(1 + x^3 + 2*x^6))/(x^6*(-1 + 2*x^6)),x]","-\frac{1}{2} \left(4-\sqrt{2}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\sqrt{2} x^3\right)-\frac{1}{2} \left(4+\sqrt{2}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\sqrt{2} x^3\right)+\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{5/3}}{5 x^5}+\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{\left(x^3+1\right)^{2/3} \left(7 x^3+2\right)}{10 x^5}-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3-1\&,\frac{-5 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+5 \text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) + (1 + x^3)^(5/3)/(5*x^5) - ((4 - Sqrt[2])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(Sqrt[2]*x^3)])/2 - ((4 + Sqrt[2])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, Sqrt[2]*x^3])/2 - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]/2","A",9,5,32,0.1562,0,"{6725, 264, 277, 239, 429}"
1540,1,156,0,0.5131743,"\int \frac{\left(1+x^3\right)^{2/3} \left(1+x^3+2 x^6\right)}{x^6 \left(-1+2 x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(1 + x^3 + 2*x^6))/(x^6*(-1 + 2*x^6)),x]","-\frac{1}{2} \left(4-\sqrt{2}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\sqrt{2} x^3\right)-\frac{1}{2} \left(4+\sqrt{2}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\sqrt{2} x^3\right)+\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{5/3}}{5 x^5}+\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{\left(x^3+1\right)^{2/3} \left(7 x^3+2\right)}{10 x^5}-\frac{1}{6} \text{RootSum}\left[\text{$\#$1}^6-2 \text{$\#$1}^3-1\&,\frac{-5 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+5 \text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]",1,"(1 + x^3)^(2/3)/(2*x^2) + (1 + x^3)^(5/3)/(5*x^5) - ((4 - Sqrt[2])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(Sqrt[2]*x^3)])/2 - ((4 + Sqrt[2])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, Sqrt[2]*x^3])/2 - ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]/2","A",9,5,32,0.1562,0,"{6725, 264, 277, 239, 429}"
1541,0,0,0,2.8816471,"\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","Int[((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,"((3 + I*Sqrt[7])*Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/(Sqrt[-1 - I*Sqrt[7]] - 2*x), x])/(2*Sqrt[-1 - I*Sqrt[7]]) + ((3 - I*Sqrt[7])*Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/(Sqrt[-1 + I*Sqrt[7]] - 2*x), x])/(2*Sqrt[-1 + I*Sqrt[7]]) + Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/(-1 + x), x]/4 + Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/x^10, x] - Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/x^6, x] + Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/x^4, x] + Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/x^2, x] - Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/(1 + x), x]/4 + ((3 + I*Sqrt[7])*Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/(Sqrt[-1 - I*Sqrt[7]] + 2*x), x])/(2*Sqrt[-1 - I*Sqrt[7]]) + ((3 - I*Sqrt[7])*Defer[Int][(-1 + x^4 + 2*x^6)^(5/4)/(Sqrt[-1 + I*Sqrt[7]] + 2*x), x])/(2*Sqrt[-1 + I*Sqrt[7]])","F",0,0,0,0,-1,"{}"
1542,1,2271,0,5.0411156,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-(-1)^{2/3} a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,31,0.09677,0,"{2056, 6725, 91}"
1543,1,2271,0,4.2089949,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-(-1)^{2/3} a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,31,0.09677,0,"{2056, 6725, 91}"
1544,0,0,0,12.1879448,"\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","Int[(((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,"(-4*k^2*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Subst][Defer[Int][(1 - k^2 + k^2*x^4)^(5/4)/(x^4 - d*(1 + k^2*(-1 + x^4))^3), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(3/4) + (2*(1 - 3*k^2)*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Subst][Defer[Int][(1 - k^2 + k^2*x^4)^(5/4)/(-x^4 + d*(1 + k^2*(-1 + x^4))^3), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(3/4) - (4*k^2*(1 - x^2)^(3/4)*(1 - k^2*x^2)^(3/4)*Defer[Subst][Defer[Int][(x^4*(1 - k^2 + k^2*x^4)^(5/4))/(-x^4 + d*(1 + k^2*(-1 + x^4))^3), x], x, (1 - x^2)^(1/4)])/((1 - x^2)*(1 - k^2*x^2))^(3/4)","F",0,0,0,0,-1,"{}"
1545,1,67,0,0.6530051,"\int \frac{\sqrt[4]{-1+2 x^4} \left(-1+x^4+x^8\right)}{x^6 \left(-1+x^4\right)} \, dx","Int[((-1 + 2*x^4)^(1/4)*(-1 + x^4 + x^8))/(x^6*(-1 + x^4)),x]","\frac{\left(2 x^4-1\right)^{5/4}}{5 x^5}-\frac{x^3 \sqrt[4]{2 x^4-1} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};2 x^4,x^4\right)}{3 \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)^(5/4)/(5*x^5) - (x^3*(-1 + 2*x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, 2*x^4, x^4])/(3*(1 - 2*x^4)^(1/4))","C",23,9,30,0.3000,0,"{6725, 264, 1240, 407, 409, 1213, 537, 511, 510}"
1546,1,455,0,0.711077,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Int[1/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\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)}{\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{\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{\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{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{\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{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$1}^5}\&\right]}{4 b}",1,"ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)) + ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a - Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)) - ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x)/((a + Sqrt[a^2 + 4*b])^(1/4)*(-b + a*x^4)^(1/4))]/(Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)*(a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4))","B",9,5,29,0.1724,1,"{1428, 377, 212, 208, 205}"
1547,1,455,0,0.3518524,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Int[1/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}+\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{a x^4-b}}\right)}{\sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{-a \sqrt{a^2+4 b}+a^2-2 b}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}{\sqrt[4]{\sqrt{a^2+4 b}+a} \sqrt[4]{a x^4-b}}\right)}{\sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4} \sqrt[4]{a \sqrt{a^2+4 b}+a^2-2 b}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4 a+2 a^2-b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{3 \text{$\#$1} a-2 \text{$\#$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))]/(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)) - 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)) + 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)) - 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",9,5,29,0.1724,1,"{1428, 377, 212, 208, 205}"
1548,1,95,0,0.0257409,"\int x^6 \left(-1+x^3\right)^{2/3} \, dx","Int[x^6*(-1 + x^3)^(2/3),x]","-\frac{4}{81} \left(x^3-1\right)^{2/3} x+\frac{2}{81} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{4 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{1}{9} \left(x^3-1\right)^{2/3} x^7-\frac{1}{27} \left(x^3-1\right)^{2/3} x^4","\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,"(-4*x*(-1 + x^3)^(2/3))/81 - (x^4*(-1 + x^3)^(2/3))/27 + (x^7*(-1 + x^3)^(2/3))/9 - (4*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) + (2*Log[-x + (-1 + x^3)^(1/3)])/81","A",4,3,13,0.2308,1,"{279, 321, 239}"
1549,1,95,0,0.0304871,"\int x^6 \left(1+x^3\right)^{2/3} \, dx","Int[x^6*(1 + x^3)^(2/3),x]","-\frac{4}{81} \left(x^3+1\right)^{2/3} x-\frac{2}{81} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{4 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{1}{9} \left(x^3+1\right)^{2/3} x^7+\frac{1}{27} \left(x^3+1\right)^{2/3} x^4","-\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,"(-4*x*(1 + x^3)^(2/3))/81 + (x^4*(1 + x^3)^(2/3))/27 + (x^7*(1 + x^3)^(2/3))/9 + (4*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) - (2*Log[-x + (1 + x^3)^(1/3)])/81","A",4,3,13,0.2308,1,"{279, 321, 239}"
1550,1,210,0,0.2265591,"\int x^4 \sqrt[3]{x+x^3} \, dx","Int[x^4*(x + x^3)^(1/3),x]","\frac{1}{36} \sqrt[3]{x^3+x} x^3-\frac{5}{108} \sqrt[3]{x^3+x} x+\frac{1}{6} \sqrt[3]{x^3+x} x^5-\frac{5 \left(x^2+1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{162 \left(x^3+x\right)^{2/3}}+\frac{5 \left(x^2+1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{324 \left(x^3+x\right)^{2/3}}-\frac{5 \left(x^2+1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{54 \sqrt{3} \left(x^3+x\right)^{2/3}}","-\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,"(-5*x*(x + x^3)^(1/3))/108 + (x^3*(x + x^3)^(1/3))/36 + (x^5*(x + x^3)^(1/3))/6 - (5*x^(2/3)*(1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(54*Sqrt[3]*(x + x^3)^(2/3)) - (5*x^(2/3)*(1 + x^2)^(2/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(162*(x + x^3)^(2/3)) + (5*x^(2/3)*(1 + x^2)^(2/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(324*(x + x^3)^(2/3))","A",13,12,13,0.9231,1,"{2021, 2024, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1551,0,0,0,19.1816606,"\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","Int[(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,"(4*(a + 2*b)*((b*(a - x))/(a*(b - x)))^(3/4)*(b - x)^2*x*Hypergeometric2F1[1/4, 3/4, 5/4, -(((a - b)*x)/(a*(b - x)))])/(b*(1 - d)*(-((a - x)*(b - x)^2*x))^(3/4)) + (4*a*b^2*(a + 2*b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][1/((-a + x^4)^(3/4)*Sqrt[-b + x^4]*(-(b^2*x^4) + 2*b*x^8 + (-1 + d)*x^12 + a*(b - x^4)^2)), x], x, x^(1/4)])/((1 - d)*(-((a - x)*(b - x)^2*x))^(3/4)) - (4*b*(2*a + b)*(a + 2*b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][x^4/((-a + x^4)^(3/4)*Sqrt[-b + x^4]*(-(b^2*x^4) + 2*b*x^8 + (-1 + d)*x^12 + a*(b - x^4)^2)), x], x, x^(1/4)])/((1 - d)*(-((a - x)*(b - x)^2*x))^(3/4)) + (4*(a^2 + 4*b^2 + a*(b + 3*b*d))*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][x^8/((-a + x^4)^(3/4)*Sqrt[-b + x^4]*(-(b^2*x^4) + 2*b*x^8 + (-1 + d)*x^12 + a*(b - x^4)^2)), x], x, x^(1/4)])/((1 - d)*(-((a - x)*(b - x)^2*x))^(3/4))","F",0,0,0,0,-1,"{}"
1552,1,118,0,0.0729538,"\int \frac{\sqrt[3]{1+x^4} \left(3+x^4\right)}{x^{17}} \, dx","Int[((1 + x^4)^(1/3)*(3 + x^4))/x^17,x]","-\frac{5 \sqrt[3]{x^4+1}}{216 x^4}-\frac{5}{216} \log \left(1-\sqrt[3]{x^4+1}\right)+\frac{5 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^4+1}+1}{\sqrt{3}}\right)}{108 \sqrt{3}}-\frac{3 \left(x^4+1\right)^{4/3}}{16 x^{16}}+\frac{\sqrt[3]{x^4+1}}{12 x^{12}}+\frac{\sqrt[3]{x^4+1}}{72 x^8}+\frac{5 \log (x)}{162}","-\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,"(1 + x^4)^(1/3)/(12*x^12) + (1 + x^4)^(1/3)/(72*x^8) - (5*(1 + x^4)^(1/3))/(216*x^4) - (3*(1 + x^4)^(4/3))/(16*x^16) + (5*ArcTan[(1 + 2*(1 + x^4)^(1/3))/Sqrt[3]])/(108*Sqrt[3]) + (5*Log[x])/162 - (5*Log[1 - (1 + x^4)^(1/3)])/216","A",9,8,18,0.4444,1,"{446, 78, 47, 51, 57, 618, 204, 31}"
1553,1,253,0,0.8914632,"\int \frac{\left(-2+x^2\right) \sqrt[3]{x+x^3}}{x^2 \left(4-2 x^2+x^4\right)} \, dx","Int[((-2 + x^2)*(x + x^3)^(1/3))/(x^2*(4 - 2*x^2 + x^4)),x]","\frac{\left(\sqrt{3}+3 i\right) \sqrt[3]{1-\frac{x^2}{1-i \sqrt{3}}} \sqrt[3]{x^3+x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\frac{x^2}{1-i \sqrt{3}}+x^2}{1-\frac{x^2}{1-i \sqrt{3}}}\right)}{4 \left(\sqrt{3}+i\right) x \sqrt[3]{x^2+1}}+\frac{\left(-\sqrt{3}+3 i\right) \sqrt[3]{1-\frac{x^2}{1+i \sqrt{3}}} \sqrt[3]{x^3+x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\frac{x^2}{1+i \sqrt{3}}+x^2}{1-\frac{x^2}{1+i \sqrt{3}}}\right)}{4 \left(-\sqrt{3}+i\right) x \sqrt[3]{x^2+1}}","\frac{3 \sqrt[3]{x^3+x}}{4 x}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^5-5 \text{$\#$1}^2}\&\right]",1,"((3*I + Sqrt[3])*(1 - x^2/(1 - I*Sqrt[3]))^(1/3)*(x + x^3)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -((x^2 + x^2/(1 - I*Sqrt[3]))/(1 - x^2/(1 - I*Sqrt[3])))])/(4*(I + Sqrt[3])*x*(1 + x^2)^(1/3)) + ((3*I - Sqrt[3])*(1 - x^2/(1 + I*Sqrt[3]))^(1/3)*(x + x^3)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -((x^2 + x^2/(1 + I*Sqrt[3]))/(1 - x^2/(1 + I*Sqrt[3])))])/(4*(I - Sqrt[3])*x*(1 + x^2)^(1/3))","C",9,5,30,0.1667,0,"{2056, 6728, 466, 465, 510}"
1554,1,253,0,0.7547167,"\int \frac{\left(-2+x^2\right) \sqrt[3]{x+x^3}}{x^2 \left(4-2 x^2+x^4\right)} \, dx","Int[((-2 + x^2)*(x + x^3)^(1/3))/(x^2*(4 - 2*x^2 + x^4)),x]","\frac{\left(\sqrt{3}+3 i\right) \sqrt[3]{1-\frac{x^2}{1-i \sqrt{3}}} \sqrt[3]{x^3+x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\frac{x^2}{1-i \sqrt{3}}+x^2}{1-\frac{x^2}{1-i \sqrt{3}}}\right)}{4 \left(\sqrt{3}+i\right) x \sqrt[3]{x^2+1}}+\frac{\left(-\sqrt{3}+3 i\right) \sqrt[3]{1-\frac{x^2}{1+i \sqrt{3}}} \sqrt[3]{x^3+x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{\frac{x^2}{1+i \sqrt{3}}+x^2}{1-\frac{x^2}{1+i \sqrt{3}}}\right)}{4 \left(-\sqrt{3}+i\right) x \sqrt[3]{x^2+1}}","\frac{3 \sqrt[3]{x^3+x}}{4 x}-\frac{1}{8} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^5-5 \text{$\#$1}^2}\&\right]",1,"((3*I + Sqrt[3])*(1 - x^2/(1 - I*Sqrt[3]))^(1/3)*(x + x^3)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -((x^2 + x^2/(1 - I*Sqrt[3]))/(1 - x^2/(1 - I*Sqrt[3])))])/(4*(I + Sqrt[3])*x*(1 + x^2)^(1/3)) + ((3*I - Sqrt[3])*(1 - x^2/(1 + I*Sqrt[3]))^(1/3)*(x + x^3)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -((x^2 + x^2/(1 + I*Sqrt[3]))/(1 - x^2/(1 + I*Sqrt[3])))])/(4*(I - Sqrt[3])*x*(1 + x^2)^(1/3))","C",9,5,30,0.1667,0,"{2056, 6728, 466, 465, 510}"
1555,1,194,0,0.1592836,"\int \frac{1}{\left(-1+x^4\right)^2 \sqrt[4]{-x^2+x^4}} \, dx","Int[1/((-1 + x^4)^2*(-x^2 + x^4)^(1/4)),x]","-\frac{x}{40 \left(1-x^2\right) \sqrt[4]{x^4-x^2}}+\frac{x}{4 \left(1-x^2\right) \left(x^2+1\right) \sqrt[4]{x^4-x^2}}+\frac{67 x}{80 \sqrt[4]{x^4-x^2}}+\frac{15 \sqrt[4]{x^2-1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{32 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}+\frac{15 \sqrt[4]{x^2-1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{32 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}","\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,"(67*x)/(80*(-x^2 + x^4)^(1/4)) - x/(40*(1 - x^2)*(-x^2 + x^4)^(1/4)) + x/(4*(1 - x^2)*(1 + x^2)*(-x^2 + x^4)^(1/4)) + (15*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(32*2^(1/4)*(-x^2 + x^4)^(1/4)) + (15*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(32*2^(1/4)*(-x^2 + x^4)^(1/4))","A",11,10,21,0.4762,1,"{2056, 1254, 466, 414, 527, 12, 377, 212, 206, 203}"
1556,1,5419,0,10.7560159,"\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","Int[((-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{\left(i+\sqrt{3}\right) \left(i+3 \sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i-\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{24 \left(1-3 i \sqrt{3}+\sqrt{5}+i \sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}-\frac{\left(i-\sqrt{3}\right) \left(i+3 \sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i-\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{24 \left(1-3 i \sqrt{3}+\sqrt{5}+i \sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}-\frac{\left(i+\sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i-\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{4 \left(5 i+\sqrt{3}-i \sqrt{5}-\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}+\frac{\left(i-\sqrt{3}\right) \left(1+5 i \sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i-\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{8 \left(5 i+\sqrt{3}-i \sqrt{5}-\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt{\frac{1}{3} \left(9-4 \sqrt{5}\right)} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i-\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{2 \left(5 i+\sqrt{3}-i \sqrt{5}-\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}+\frac{\left(1+3 i \sqrt{3}\right) \left(i+\sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i+\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{24 \left(i-3 \sqrt{3}+i \sqrt{5}+\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}-\frac{\left(i-\sqrt{3}\right) \left(1+3 i \sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i+\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{24 \left(i-3 \sqrt{3}+i \sqrt{5}+\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}+\frac{\left(1-5 i \sqrt{3}\right) \left(i+\sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i+\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{8 \left(5 i-\sqrt{3}-i \sqrt{5}+\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}-\frac{\left(i-\sqrt{3}\right) \sqrt{9-4 \sqrt{5}} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i+\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{4 \left(5 i-\sqrt{3}-i \sqrt{5}+\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt{\frac{1}{3} \left(9-4 \sqrt{5}\right)} \Pi \left(1-\frac{2 \left(3-\sqrt{5}\right)}{\left(i+\sqrt{3}\right)^2};\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right) \left(2 x^2+\sqrt{5}+3\right)}{2 \left(5 i-\sqrt{3}-i \sqrt{5}+\sqrt{15}\right) \sqrt{\frac{2 x^2+\sqrt{5}+3}{2 x^2-\sqrt{5}+3}} \sqrt{x^4+3 x^2+1}}+\frac{\left(i+\sqrt{3}\right) x \left(2 x^2+\sqrt{5}+3\right)}{24 \left(i-\sqrt{3}\right) \sqrt{x^4+3 x^2+1}}+\frac{\left(i-\sqrt{3}\right) x \left(2 x^2+\sqrt{5}+3\right)}{24 \left(i+\sqrt{3}\right) \sqrt{x^4+3 x^2+1}}+\frac{x \left(2 x^2+\sqrt{5}+3\right)}{12 \left(1+i \sqrt{3}\right) \sqrt{x^4+3 x^2+1}}+\frac{x \left(2 x^2+\sqrt{5}+3\right)}{12 \left(1-i \sqrt{3}\right) \sqrt{x^4+3 x^2+1}}-\frac{\left(i-3 \sqrt{3}\right) \left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{48 \left(1+i \sqrt{3}\right)^{3/2}}+\frac{\left(1-5 i \sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{16 \sqrt{1+i \sqrt{3}}}+\frac{\left(1+3 i \sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{24 \left(1+i \sqrt{3}\right)^{3/2}}+\frac{i \tan ^{-1}\left(\frac{2 \left(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)}{4 \sqrt{3 \left(1+i \sqrt{3}\right)}}-\frac{\left(1-i \sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{16 \sqrt{1+i \sqrt{3}}}+\frac{\left(1+5 i \sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{16 \sqrt{1-i \sqrt{3}}}+\frac{\left(1-3 i \sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{24 \left(1-i \sqrt{3}\right)^{3/2}}-\frac{\left(1+i \sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{16 \sqrt{1-i \sqrt{3}}}+\frac{\left(5-i \sqrt{3}\right) \tan ^{-1}\left(\frac{2 \left(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)}{24 \left(1-i \sqrt{3}\right)^{3/2}}-\frac{i \tan ^{-1}\left(\frac{2 \left(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)}{4 \sqrt{3 \left(1-i \sqrt{3}\right)}}-\frac{\left(i+\sqrt{3}\right) \sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{24 \left(i-\sqrt{3}\right) \sqrt{x^4+3 x^2+1}}-\frac{\left(i-\sqrt{3}\right) \sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{24 \left(i+\sqrt{3}\right) \sqrt{x^4+3 x^2+1}}-\frac{\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{12 \left(1+i \sqrt{3}\right) \sqrt{x^4+3 x^2+1}}-\frac{\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{12 \left(1-i \sqrt{3}\right) \sqrt{x^4+3 x^2+1}}-\frac{\left(5 i+\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{6 \sqrt{2 \left(3+\sqrt{5}\right)} \left(5 i+\sqrt{3}-i \sqrt{5}-\sqrt{15}\right) \sqrt{x^4+3 x^2+1}}+\frac{\left(i-\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{2 \left(2+i \sqrt{3}-\sqrt{5}\right) \sqrt{6 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}-\frac{\left(i+\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{2 \left(2-i \sqrt{3}-\sqrt{5}\right) \sqrt{6 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{\left(i-\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{4 \left(2 i+\sqrt{3}-i \sqrt{5}\right) \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{\left(7 i-3 \sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{4 \left(2 i+\sqrt{3}-i \sqrt{5}\right) \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{\left(7 i+3 \sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{4 \left(2 i-\sqrt{3}-i \sqrt{5}\right) \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{\left(i+\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{4 \left(2 i-\sqrt{3}-i \sqrt{5}\right) \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}-\frac{\left(2 i-\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{3 \left(i+\sqrt{3}\right) \left(2+i \sqrt{3}-\sqrt{5}\right) \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}-\frac{\left(2 i+\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{3 \left(i-\sqrt{3}\right) \left(2-i \sqrt{3}-\sqrt{5}\right) \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}-\frac{\left(5 i-\sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{6 \left(i-\sqrt{3}\right) \left(2-i \sqrt{3}-\sqrt{5}\right) \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{24 \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{24 \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{7 \sqrt{\frac{\left(3-\sqrt{5}\right) x^2+2}{\left(3+\sqrt{5}\right) x^2+2}} \left(\left(3+\sqrt{5}\right) x^2+2\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)|\frac{1}{2} \left(-5+3 \sqrt{5}\right)\right)}{6 \sqrt{2 \left(3+\sqrt{5}\right)} \sqrt{x^4+3 x^2+1}}+\frac{\left(i+\sqrt{3}\right) \sqrt{x^4+3 x^2+1}}{6 \left(i-\sqrt{3}\right) \left(-2 x-i \sqrt{3}+1\right)}+\frac{\sqrt{x^4+3 x^2+1}}{3 \left(1+i \sqrt{3}\right) \left(-2 x-i \sqrt{3}+1\right)}+\frac{\left(i-\sqrt{3}\right) \sqrt{x^4+3 x^2+1}}{6 \left(i+\sqrt{3}\right) \left(-2 x+i \sqrt{3}+1\right)}+\frac{\sqrt{x^4+3 x^2+1}}{3 \left(1-i \sqrt{3}\right) \left(-2 x+i \sqrt{3}+1\right)}","\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,"(x*(3 + Sqrt[5] + 2*x^2))/(12*(1 - I*Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) + (x*(3 + Sqrt[5] + 2*x^2))/(12*(1 + I*Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) + ((I - Sqrt[3])*x*(3 + Sqrt[5] + 2*x^2))/(24*(I + Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) + ((I + Sqrt[3])*x*(3 + Sqrt[5] + 2*x^2))/(24*(I - Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) + Sqrt[1 + 3*x^2 + x^4]/(3*(1 + I*Sqrt[3])*(1 - I*Sqrt[3] - 2*x)) + ((I + Sqrt[3])*Sqrt[1 + 3*x^2 + x^4])/(6*(I - Sqrt[3])*(1 - I*Sqrt[3] - 2*x)) + Sqrt[1 + 3*x^2 + x^4]/(3*(1 - I*Sqrt[3])*(1 + I*Sqrt[3] - 2*x)) + ((I - Sqrt[3])*Sqrt[1 + 3*x^2 + x^4])/(6*(I + Sqrt[3])*(1 + I*Sqrt[3] - 2*x)) - ((1 - I*Sqrt[3])*ArcTan[(1 - (3*I)*Sqrt[3] + 2*(2 - I*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(16*Sqrt[1 + I*Sqrt[3]]) + ((I/4)*ArcTan[(1 - (3*I)*Sqrt[3] + 2*(2 - I*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/Sqrt[3*(1 + I*Sqrt[3])] + ((1 + (3*I)*Sqrt[3])*ArcTan[(1 - (3*I)*Sqrt[3] + 2*(2 - I*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(24*(1 + I*Sqrt[3])^(3/2)) + ((1 - (5*I)*Sqrt[3])*ArcTan[(1 - (3*I)*Sqrt[3] + 2*(2 - I*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(16*Sqrt[1 + I*Sqrt[3]]) - ((I - 3*Sqrt[3])*(I + Sqrt[3])*ArcTan[(1 - (3*I)*Sqrt[3] + 2*(2 - I*Sqrt[3])*x^2)/(4*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(48*(1 + I*Sqrt[3])^(3/2)) - ((I/4)*ArcTan[(1 + (3*I)*Sqrt[3] + 2*(2 + I*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/Sqrt[3*(1 - I*Sqrt[3])] + ((5 - I*Sqrt[3])*ArcTan[(1 + (3*I)*Sqrt[3] + 2*(2 + I*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(24*(1 - I*Sqrt[3])^(3/2)) - ((1 + I*Sqrt[3])*ArcTan[(1 + (3*I)*Sqrt[3] + 2*(2 + I*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(16*Sqrt[1 - I*Sqrt[3]]) + ((1 - (3*I)*Sqrt[3])*ArcTan[(1 + (3*I)*Sqrt[3] + 2*(2 + I*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(24*(1 - I*Sqrt[3])^(3/2)) + ((1 + (5*I)*Sqrt[3])*ArcTan[(1 + (3*I)*Sqrt[3] + 2*(2 + I*Sqrt[3])*x^2)/(4*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 + 3*x^2 + x^4])])/(16*Sqrt[1 - I*Sqrt[3]]) - (Sqrt[(3 + Sqrt[5])/2]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticE[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(12*(1 - I*Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) - (Sqrt[(3 + Sqrt[5])/2]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticE[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(12*(1 + I*Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) - ((I - Sqrt[3])*Sqrt[(3 + Sqrt[5])/2]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticE[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*(I + Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) - ((I + Sqrt[3])*Sqrt[(3 + Sqrt[5])/2]*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticE[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*(I - Sqrt[3])*Sqrt[1 + 3*x^2 + x^4]) + (7*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(6*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) + ((1 - I*Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) + ((1 + I*Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) - ((5*I - Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(6*(I - Sqrt[3])*(2 - I*Sqrt[3] - Sqrt[5])*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) - ((2*I + Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(3*(I - Sqrt[3])*(2 - I*Sqrt[3] - Sqrt[5])*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) - ((2*I - Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(3*(I + Sqrt[3])*(2 + I*Sqrt[3] - Sqrt[5])*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) + ((I + Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(4*(2*I - Sqrt[3] - I*Sqrt[5])*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) + ((7*I + 3*Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(4*(2*I - Sqrt[3] - I*Sqrt[5])*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) + ((7*I - 3*Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(4*(2*I + Sqrt[3] - I*Sqrt[5])*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) + ((I - Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(4*(2*I + Sqrt[3] - I*Sqrt[5])*Sqrt[2*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) - ((I + Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(2*(2 - I*Sqrt[3] - Sqrt[5])*Sqrt[6*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) + ((I - Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(2*(2 + I*Sqrt[3] - Sqrt[5])*Sqrt[6*(3 + Sqrt[5])]*Sqrt[1 + 3*x^2 + x^4]) - ((5*I + Sqrt[3])*Sqrt[(2 + (3 - Sqrt[5])*x^2)/(2 + (3 + Sqrt[5])*x^2)]*(2 + (3 + Sqrt[5])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(6*Sqrt[2*(3 + Sqrt[5])]*(5*I + Sqrt[3] - I*Sqrt[5] - Sqrt[15])*Sqrt[1 + 3*x^2 + x^4]) + ((1 + I*Sqrt[3])*Sqrt[(9 - 4*Sqrt[5])/3]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I - Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(2*(5*I + Sqrt[3] - I*Sqrt[5] - Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) + ((I - Sqrt[3])*(1 + (5*I)*Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I - Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(8*(5*I + Sqrt[3] - I*Sqrt[5] - Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) - ((I + Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I - Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(4*(5*I + Sqrt[3] - I*Sqrt[5] - Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) - ((I - Sqrt[3])*(I + 3*Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I - Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*(1 - (3*I)*Sqrt[3] + Sqrt[5] + I*Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) + ((I + Sqrt[3])*(I + 3*Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I - Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*(1 - (3*I)*Sqrt[3] + Sqrt[5] + I*Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) - ((1 - I*Sqrt[3])*Sqrt[(9 - 4*Sqrt[5])/3]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I + Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(2*(5*I - Sqrt[3] - I*Sqrt[5] + Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) - ((I - Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I + Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(4*(5*I - Sqrt[3] - I*Sqrt[5] + Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) + ((1 - (5*I)*Sqrt[3])*(I + Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I + Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(8*(5*I - Sqrt[3] - I*Sqrt[5] + Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) - ((I - Sqrt[3])*(1 + (3*I)*Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I + Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*(I - 3*Sqrt[3] + I*Sqrt[5] + Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4]) + ((1 + (3*I)*Sqrt[3])*(I + Sqrt[3])*Sqrt[9 - 4*Sqrt[5]]*(3 + Sqrt[5] + 2*x^2)*EllipticPi[1 - (2*(3 - Sqrt[5]))/(I + Sqrt[3])^2, ArcTan[Sqrt[(3 + Sqrt[5])/2]*x], (-5 + 3*Sqrt[5])/2])/(24*(I - 3*Sqrt[3] + I*Sqrt[5] + Sqrt[15])*Sqrt[(3 + Sqrt[5] + 2*x^2)/(3 - Sqrt[5] + 2*x^2)]*Sqrt[1 + 3*x^2 + x^4])","C",136,18,54,0.3333,0,"{6688, 6728, 1099, 6742, 1726, 1741, 12, 1247, 724, 204, 1716, 1189, 1135, 1214, 1456, 539, 1724, 2}"
1557,1,165,0,0.3498954,"\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","Int[((b + a*x^3)*(b + 2*a*x^3))/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{4 a^{7/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}+\frac{4 a^{7/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}-\frac{4 b \left(a x^4+b x\right)^{3/4}}{21 x^6}-\frac{68 a \left(a x^4+b x\right)^{3/4}}{63 x^3}","\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*b*(b*x + a*x^4)^(3/4))/(21*x^6) - (68*a*(b*x + a*x^4)^(3/4))/(63*x^3) + (4*a^(7/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4)) + (4*a^(7/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4))","A",12,10,32,0.3125,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1558,1,662,0,2.6642534,"\int \frac{-b^3+a^3 x^3}{\left(b^3+a^3 x^3\right) \sqrt{b^4+a^4 x^4}} \, dx","Int[(-b^3 + a^3*x^3)/((b^3 + a^3*x^3)*Sqrt[b^4 + a^4*x^4]),x]","-\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{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a b}+\frac{\tanh ^{-1}\left(\frac{a^2 x^2+b^2}{\sqrt{2} \sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a b}-\frac{\left(a-\sqrt{3} \sqrt{-a^2}\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{6 a^2 b \sqrt{a^4 x^4+b^4}}-\frac{\left(\sqrt{3} \sqrt{-a^2}+a\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{6 a^2 b \sqrt{a^4 x^4+b^4}}+\frac{\left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{3 a b \sqrt{a^4 x^4+b^4}}-\frac{\left(a-\sqrt{3} \sqrt{-a^2}\right) \tanh ^{-1}\left(\frac{\sqrt{a} \left(\left(a-\sqrt{3} \sqrt{-a^2}\right)^2 x^2+4 b^2\right)}{2 \sqrt{2} \sqrt{\sqrt{3} \sqrt{-a^2}+a} \sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a^{3/2} \sqrt{\sqrt{3} \sqrt{-a^2}+a} b}-\frac{\left(\sqrt{3} \sqrt{-a^2}+a\right) \tanh ^{-1}\left(\frac{\sqrt{a} \left(\left(\sqrt{3} \sqrt{-a^2}+a\right)^2 x^2+4 b^2\right)}{2 \sqrt{2} \sqrt{a-\sqrt{3} \sqrt{-a^2}} \sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a^{3/2} \sqrt{a-\sqrt{3} \sqrt{-a^2}} b}","-\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,"(-2*ArcTan[(a*b*x)/Sqrt[b^4 + a^4*x^4]])/(3*a*b) - ArcTanh[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(3*Sqrt[2]*a*b) + ArcTanh[(b^2 + a^2*x^2)/(Sqrt[2]*Sqrt[b^4 + a^4*x^4])]/(3*Sqrt[2]*a*b) - ((a - Sqrt[3]*Sqrt[-a^2])*ArcTanh[(Sqrt[a]*(4*b^2 + (a - Sqrt[3]*Sqrt[-a^2])^2*x^2))/(2*Sqrt[2]*Sqrt[a + Sqrt[3]*Sqrt[-a^2]]*Sqrt[b^4 + a^4*x^4])])/(3*Sqrt[2]*a^(3/2)*Sqrt[a + Sqrt[3]*Sqrt[-a^2]]*b) - ((a + Sqrt[3]*Sqrt[-a^2])*ArcTanh[(Sqrt[a]*(4*b^2 + (a + Sqrt[3]*Sqrt[-a^2])^2*x^2))/(2*Sqrt[2]*Sqrt[a - Sqrt[3]*Sqrt[-a^2]]*Sqrt[b^4 + a^4*x^4])])/(3*Sqrt[2]*a^(3/2)*Sqrt[a - Sqrt[3]*Sqrt[-a^2]]*b) + ((b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(3*a*b*Sqrt[b^4 + a^4*x^4]) - ((a - Sqrt[3]*Sqrt[-a^2])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(6*a^2*b*Sqrt[b^4 + a^4*x^4]) - ((a + Sqrt[3]*Sqrt[-a^2])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(6*a^2*b*Sqrt[b^4 + a^4*x^4])","C",29,13,42,0.3095,1,"{6725, 220, 2074, 1725, 1211, 1699, 208, 1248, 725, 206, 6728, 1217, 1707}"
1559,0,0,0,0.1545021,"\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","Int[(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,"Defer[Int][(x^4*(-2*b + a*x^2))/((-b + a*x^2)^2*(-b + a*x^2 + c*x^4)^(1/4)), x]","F",0,0,0,0,-1,"{}"
1560,0,0,0,2.0984525,"\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","Int[((-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,"(3*x*(1 - x^4)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^4])/(2*(-x + x^5)^(1/3)) + (3*x^(1/3)*(-1 + x^4)^(1/3)*Defer[Subst][Defer[Int][x^4/((-1 + x^12)^(1/3)*(1 - x^3 + 2*x^6 + x^9 + x^12)), x], x, x^(1/3)])/(-x + x^5)^(1/3) - (24*x^(1/3)*(-1 + x^4)^(1/3)*Defer[Subst][Defer[Int][x^7/((-1 + x^12)^(1/3)*(1 - x^3 + 2*x^6 + x^9 + x^12)), x], x, x^(1/3)])/(-x + x^5)^(1/3) - (3*x^(1/3)*(-1 + x^4)^(1/3)*Defer[Subst][Defer[Int][x^10/((-1 + x^12)^(1/3)*(1 - x^3 + 2*x^6 + x^9 + x^12)), x], x, x^(1/3)])/(-x + x^5)^(1/3)","F",0,0,0,0,-1,"{}"
1561,1,167,0,0.2827126,"\int \frac{-b-a x^3+x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Int[(-b - a*x^3 + x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(a x^4+b x\right)^{3/4}}{21 x^6}+\frac{4 a \left(a x^4+b x\right)^{3/4}}{21 b x^3}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4+b x}}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \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(a x^3+b\right)}{21 b x^6}",1,"(4*(b*x + a*x^4)^(3/4))/(21*x^6) + (4*a*(b*x + a*x^4)^(3/4))/(21*b*x^3) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4)) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4))","A",12,10,30,0.3333,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1562,1,1923,0,2.8331899,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-(-1)^{2/3} a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - a*x])/(12*a^(1/3)*b*(a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - a*x])/(12*a^(1/3)*b*(a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,33,0.09091,0,"{2056, 6725, 91}"
1563,1,1923,0,2.3279742,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-(-1)^{2/3} a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - a*x])/(12*a^(1/3)*b*(a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - a*x])/(12*a^(1/3)*b*(a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) + (-1)^(1/3)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - (-1)^(2/3)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,33,0.09091,0,"{2056, 6725, 91}"
1564,1,2108,0,4.1259872,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+2 a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + 2*a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[6]{2} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-\sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x+\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[6]{2} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-(-1)^{2/3} \sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - 2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + 2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,34,0.08824,0,"{2056, 6725, 91}"
1565,1,2108,0,3.2313966,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-b+2 a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-b + 2*a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[6]{2} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-\sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x+\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[6]{2} a x-\sqrt[6]{b}\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{b}-(-1)^{2/3} \sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+\sqrt[3]{-1} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2-(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} b \sqrt[3]{a^2+(-1)^{2/3} \sqrt[6]{2} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*b*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*b*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - 2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + 2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + 2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(1/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 - (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3))])/(4*a^(1/3)*b*(a^2 + (-1)^(2/3)*2^(1/6)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,34,0.08824,0,"{2056, 6725, 91}"
1566,1,2456,0,6.1881821,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+2 a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + 2*a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[6]{2} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-\sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x+\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[6]{2} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,32,0.09375,0,"{2056, 6725, 91}"
1567,1,2456,0,5.2916283,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(b+2 a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(b + 2*a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[6]{2} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-\sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[6]{2} a x+\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[6]{2} a x-\sqrt[6]{-b}\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} a x\right)}{12 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+\sqrt[3]{-1} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{a^2 \sqrt[6]{-b}-(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{-b} a^2+(-1)^{2/3} \sqrt[6]{2} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - 2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*a*x])/(12*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + 2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(1/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) - (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + ((-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3))])/(4*a^(1/3)*(-b)^(17/18)*(a^2*(-b)^(1/6) + (-1)^(2/3)*2^(1/6)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,32,0.09375,0,"{2056, 6725, 91}"
1568,0,0,0,1.1669545,"\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","Int[(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,"-2*Defer[Int][1/((-1 + x^3)^(1/4)*(1 - x^3 + x^4)), x] + Defer[Int][x^3/((-1 + x^3)^(1/4)*(1 - x^3 + x^4)), x]/2 - 2*Defer[Int][1/((-1 + x^3)^(1/4)*(-1 + x^3 + x^4)), x] + Defer[Int][x^3/((-1 + x^3)^(1/4)*(-1 + x^3 + x^4)), x]/2","F",0,0,0,0,-1,"{}"
1569,1,44,0,0.086844,"\int \frac{x^6}{\left(b+a x^4\right)^{3/4} \left(-b^2+a^2 x^8\right)} \, dx","Int[x^6/((b + a*x^4)^(3/4)*(-b^2 + a^2*x^8)),x]","-\frac{x^7 \, _2F_1\left(1,\frac{7}{4};\frac{11}{4};\frac{2 a x^4}{a x^4+b}\right)}{7 b \left(a x^4+b\right)^{7/4}}","\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,"-1/7*(x^7*Hypergeometric2F1[1, 7/4, 11/4, (2*a*x^4)/(b + a*x^4)])/(b*(b + a*x^4)^(7/4))","C",3,3,30,0.1000,1,"{1479, 511, 510}"
1570,0,0,0,0.939011,"\int \frac{\left(-b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}}{b^2+a x^2} \, dx","Int[((-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,"(2*a*x^3)/(3*(b + Sqrt[b^2 + a*x^2])^(3/2)) + (2*b*x)/Sqrt[b + Sqrt[b^2 + a*x^2]] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[-a]*x), x] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[-a]*x), x]","F",0,0,0,0,-1,"{}"
1571,1,164,0,0.08555,"\int \sqrt[3]{x^2+x^3} \, dx","Int[(x^2 + x^3)^(1/3),x]","\frac{1}{2} \sqrt[3]{x^3+x^2} x+\frac{1}{6} \sqrt[3]{x^3+x^2}+\frac{(x+1)^{2/3} x^{4/3} \log (x+1)}{18 \left(x^3+x^2\right)^{2/3}}+\frac{(x+1)^{2/3} x^{4/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x+1}}-1\right)}{6 \left(x^3+x^2\right)^{2/3}}+\frac{(x+1)^{2/3} x^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \left(x^3+x^2\right)^{2/3}}","\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,"(x^2 + x^3)^(1/3)/6 + (x*(x^2 + x^3)^(1/3))/2 + (x^(4/3)*(1 + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(3*Sqrt[3]*(x^2 + x^3)^(2/3)) + (x^(4/3)*(1 + x)^(2/3)*Log[1 + x])/(18*(x^2 + x^3)^(2/3)) + (x^(4/3)*(1 + x)^(2/3)*Log[-1 + x^(1/3)/(1 + x)^(1/3)])/(6*(x^2 + x^3)^(2/3))","A",4,4,11,0.3636,1,"{2004, 2024, 2032, 59}"
1572,1,364,0,2.5604549,"\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","Int[(-1 + k^3*x^3)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 + k^3*x^3)),x]","\frac{4 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{3 \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{4 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{\sqrt[3]{-1}}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{3 \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{4 (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{(-1)^{2/3}}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{3 \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\right)}}","-\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 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + (4*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(3*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + (4*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(-1)^(1/3)/k, ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(3*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + (4*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-((-1)^(2/3)/k), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(3*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",20,9,40,0.2250,0,"{6718, 6688, 6725, 714, 115, 934, 12, 168, 537}"
1573,1,647,0,2.136499,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \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,"((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + ((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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",12,7,36,0.1944,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1574,1,647,0,1.5138982,"\int \frac{b+a x^2}{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + a*x^2)/((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(a-\frac{a^2-2 b}{\sqrt{a^2-4 b}}\right) \sqrt[4]{a x^2-b} \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} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \left(\frac{a^2-2 b}{\sqrt{a^2-4 b}}+a\right) \sqrt[4]{a x^2-b} \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} \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,"((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + ((a - (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)) + ((a + (a^2 - 2*b)/Sqrt[a^2 - 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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",12,7,36,0.1944,1,"{2056, 6715, 6728, 377, 212, 208, 205}"
1575,1,192,0,1.6205343,"\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","Int[(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} (b-2 c k) \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{2 k \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} (b+2 c k) \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{2 k \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{c \sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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,"(c*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticF[ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)] + ((b - 2*c*k)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/(2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - ((b + 2*c*k)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/(2*k*Sqrt[(1 - x^2)*(1 - k^2*x^2)])","C",8,4,49,0.08163,1,"{6719, 6725, 419, 537}"
1576,0,0,0,2.6186848,"\int \frac{3 b+a x^4}{\left(-b+x^3+a x^4\right) \sqrt[4]{-b x+a x^5}} \, dx","Int[(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,"(4*x*(1 - (a*x^4)/b)^(1/4)*Hypergeometric2F1[3/16, 1/4, 19/16, (a*x^4)/b])/(3*(-(b*x) + a*x^5)^(1/4)) - (16*b*x^(1/4)*(-b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^2/((b - x^12 - a*x^16)*(-b + a*x^16)^(1/4)), x], x, x^(1/4)])/(-(b*x) + a*x^5)^(1/4) - (4*x^(1/4)*(-b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^14/((-b + a*x^16)^(1/4)*(-b + x^12 + a*x^16)), x], x, x^(1/4)])/(-(b*x) + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
1577,1,151,0,0.1870256,"\int \frac{-1+x^6}{x^6 \sqrt[3]{x+x^3}} \, dx","Int[(-1 + x^6)/(x^6*(x + x^3)^(1/3)),x]","\frac{3 \left(x^3+x\right)^{2/3}}{16 x^6}-\frac{9 \left(x^3+x\right)^{2/3}}{40 x^4}+\frac{27 \left(x^3+x\right)^{2/3}}{80 x^2}-\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-\sqrt[3]{x^2+1}\right)}{4 \sqrt[3]{x^3+x}}+\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \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,"(3*(x + x^3)^(2/3))/(16*x^6) - (9*(x + x^3)^(2/3))/(40*x^4) + (27*(x + x^3)^(2/3))/(80*x^2) + (Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*(x + x^3)^(1/3)) - (3*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(4*(x + x^3)^(1/3))","A",9,7,18,0.3889,1,"{2052, 2011, 329, 275, 239, 2016, 2014}"
1578,1,97,0,0.0333914,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^6\right)}{x^6} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^6))/x^6,x]","\frac{1}{3} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{2 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{2 \left(x^3-1\right)^{5/3}}{5 x^5}+\frac{\left(x^3-1\right)^{5/3}}{3 x^2}+\frac{\left(x^3-1\right)^{2/3}}{3 x^2}","\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,"(-1 + x^3)^(2/3)/(3*x^2) + (2*(-1 + x^3)^(5/3))/(5*x^5) + (-1 + x^3)^(5/3)/(3*x^2) - (2*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/3","A",4,4,18,0.2222,1,"{1487, 451, 277, 239}"
1579,1,95,0,0.0357051,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-2+x^3+x^6\right)}{x^6} \, dx","Int[((-1 + x^3)^(2/3)*(-2 + x^3 + x^6))/x^6,x]","-\frac{1}{6} x \left(x^3-1\right)^{2/3}-\frac{1}{6} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{2 \left(x^3-1\right)^{8/3}}{5 x^5}+\frac{\left(x^3-1\right)^{5/3}}{10 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{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,"-1/6*(x*(-1 + x^3)^(2/3)) + (-1 + x^3)^(5/3)/(10*x^2) + (2*(-1 + x^3)^(8/3))/(5*x^5) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[-x + (-1 + x^3)^(1/3)]/6","A",5,5,21,0.2381,1,"{1478, 453, 277, 195, 239}"
1580,1,97,0,0.0317683,"\int \frac{\left(1+x^3\right)^{2/3} \left(1+2 x^6\right)}{x^6} \, dx","Int[((1 + x^3)^(2/3)*(1 + 2*x^6))/x^6,x]","-\frac{2}{3} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{4 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\left(x^3+1\right)^{5/3}}{5 x^5}+\frac{2 \left(x^3+1\right)^{5/3}}{3 x^2}-\frac{2 \left(x^3+1\right)^{2/3}}{3 x^2}","-\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,"(-2*(1 + x^3)^(2/3))/(3*x^2) - (1 + x^3)^(5/3)/(5*x^5) + (2*(1 + x^3)^(5/3))/(3*x^2) + (4*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) - (2*Log[-x + (1 + x^3)^(1/3)])/3","A",4,4,20,0.2000,1,"{1487, 451, 277, 239}"
1581,0,0,0,2.6198109,"\int \frac{3 b+2 a x^5}{\left(-b+x^3+a x^5\right) \sqrt[4]{-b x+a x^6}} \, dx","Int[(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,"(8*x*(1 - (a*x^5)/b)^(1/4)*Hypergeometric2F1[3/20, 1/4, 23/20, (a*x^5)/b])/(3*(-(b*x) + a*x^6)^(1/4)) - (20*b*x^(1/4)*(-b + a*x^5)^(1/4)*Defer[Subst][Defer[Int][x^2/((b - x^12 - a*x^20)*(-b + a*x^20)^(1/4)), x], x, x^(1/4)])/(-(b*x) + a*x^6)^(1/4) - (8*x^(1/4)*(-b + a*x^5)^(1/4)*Defer[Subst][Defer[Int][x^14/((-b + a*x^20)^(1/4)*(-b + x^12 + a*x^20)), x], x, x^(1/4)])/(-(b*x) + a*x^6)^(1/4)","F",0,0,0,0,-1,"{}"
1582,1,793,0,1.8652625,"\int \frac{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)}{x^6 \left(-1+2 x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(1 + x^4 + x^8))/(x^6*(-1 + 2*x^8)),x]","-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,-\sqrt{2} x^4\right)}{2 \sqrt[4]{1-x^4}}-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,\sqrt{2} x^4\right)}{2 \sqrt[4]{1-x^4}}+\frac{\sqrt[4]{x^4-1}}{x}+\frac{\sqrt[4]{5 \sqrt{2}-7} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}+\frac{1}{4} \sqrt[4]{5 \sqrt{2}-7} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)+\frac{\sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{2}}-\frac{1}{4} \sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}\right)-\frac{\sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}+1\right)}{4 \sqrt{2}}+\frac{1}{4} \sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}+1\right)-\frac{\sqrt[4]{5 \sqrt{2}-7} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}-\frac{1}{4} \sqrt[4]{5 \sqrt{2}-7} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)-\frac{\left(x^4-1\right)^{5/4}}{5 x^5}-\frac{\sqrt[4]{7+5 \sqrt{2}} \log \left(-\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)}{8 \sqrt{2}}+\frac{1}{8} \sqrt[4]{7+5 \sqrt{2}} \log \left(-\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)+\frac{\sqrt[4]{7+5 \sqrt{2}} \log \left(\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)}{8 \sqrt{2}}-\frac{1}{8} \sqrt[4]{7+5 \sqrt{2}} \log \left(\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)","\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,"(-1 + x^4)^(1/4)/x - (-1 + x^4)^(5/4)/(5*x^5) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, -(Sqrt[2]*x^4)])/(2*(1 - x^4)^(1/4)) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, Sqrt[2]*x^4])/(2*(1 - x^4)^(1/4)) + ((-7 + 5*Sqrt[2])^(1/4)*ArcTan[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 + ((-7 + 5*Sqrt[2])^(1/4)*ArcTan[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(2*Sqrt[2]) - ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 - (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 + ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 - (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(4*Sqrt[2]) + ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 + (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 - ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 + (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(4*Sqrt[2]) - ((-7 + 5*Sqrt[2])^(1/4)*ArcTanh[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 - ((-7 + 5*Sqrt[2])^(1/4)*ArcTanh[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(2*Sqrt[2]) + ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] - (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/8 - ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] - (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2]) - ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] + (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/8 + ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] + (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2])","B",55,18,30,0.6000,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494, 297, 1162, 617, 204, 1165, 628}"
1583,1,793,0,1.7509808,"\int \frac{\sqrt[4]{-1+x^4} \left(1+x^4+x^8\right)}{x^6 \left(-1+2 x^8\right)} \, dx","Int[((-1 + x^4)^(1/4)*(1 + x^4 + x^8))/(x^6*(-1 + 2*x^8)),x]","-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,-\sqrt{2} x^4\right)}{2 \sqrt[4]{1-x^4}}-\frac{\sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,\sqrt{2} x^4\right)}{2 \sqrt[4]{1-x^4}}+\frac{\sqrt[4]{x^4-1}}{x}+\frac{\sqrt[4]{5 \sqrt{2}-7} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}+\frac{1}{4} \sqrt[4]{5 \sqrt{2}-7} \tan ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)+\frac{\sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{2}}-\frac{1}{4} \sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}\right)-\frac{\sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}+1\right)}{4 \sqrt{2}}+\frac{1}{4} \sqrt[4]{7+5 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{1+\sqrt{2}} \sqrt[4]{x^4-1}}+1\right)-\frac{\sqrt[4]{5 \sqrt{2}-7} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)}{2 \sqrt{2}}-\frac{1}{4} \sqrt[4]{5 \sqrt{2}-7} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{\sqrt{2}-1} \sqrt[4]{x^4-1}}\right)-\frac{\left(x^4-1\right)^{5/4}}{5 x^5}-\frac{\sqrt[4]{7+5 \sqrt{2}} \log \left(-\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)}{8 \sqrt{2}}+\frac{1}{8} \sqrt[4]{7+5 \sqrt{2}} \log \left(-\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)+\frac{\sqrt[4]{7+5 \sqrt{2}} \log \left(\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)}{8 \sqrt{2}}-\frac{1}{8} \sqrt[4]{7+5 \sqrt{2}} \log \left(\frac{\sqrt{2} \sqrt[4]{1+\sqrt{2}} x}{\sqrt[4]{x^4-1}}+\frac{x^2}{\sqrt{x^4-1}}+\sqrt{1+\sqrt{2}}\right)","\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,"(-1 + x^4)^(1/4)/x - (-1 + x^4)^(5/4)/(5*x^5) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, -(Sqrt[2]*x^4)])/(2*(1 - x^4)^(1/4)) - (x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, Sqrt[2]*x^4])/(2*(1 - x^4)^(1/4)) + ((-7 + 5*Sqrt[2])^(1/4)*ArcTan[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 + ((-7 + 5*Sqrt[2])^(1/4)*ArcTan[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(2*Sqrt[2]) - ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 - (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 + ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 - (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(4*Sqrt[2]) + ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 + (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 - ((7 + 5*Sqrt[2])^(1/4)*ArcTan[1 + (Sqrt[2]*x)/((1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(4*Sqrt[2]) - ((-7 + 5*Sqrt[2])^(1/4)*ArcTanh[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/4 - ((-7 + 5*Sqrt[2])^(1/4)*ArcTanh[x/((-1 + Sqrt[2])^(1/4)*(-1 + x^4)^(1/4))])/(2*Sqrt[2]) + ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] - (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/8 - ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] - (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2]) - ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] + (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/8 + ((7 + 5*Sqrt[2])^(1/4)*Log[Sqrt[1 + Sqrt[2]] + x^2/Sqrt[-1 + x^4] + (Sqrt[2]*(1 + Sqrt[2])^(1/4)*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2])","B",55,18,30,0.6000,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494, 297, 1162, 617, 204, 1165, 628}"
1584,0,0,0,3.5903676,"\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","Int[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,"(2*Sqrt[-(b*x) + a^2*x^2]*Defer[Subst][Defer[Int][(x^2*Sqrt[-b + a^2*x^2])/(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-b + a^2*x])","F",0,0,0,0,-1,"{}"
1585,1,129,0,0.0676075,"\int x^7 \sqrt[3]{-1+x^3} \, dx","Int[x^7*(-1 + x^3)^(1/3),x]","\frac{5}{243} \log \left(1-\frac{x}{\sqrt[3]{x^3-1}}\right)+\frac{5 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{1}{9} \sqrt[3]{x^3-1} x^8-\frac{1}{54} \sqrt[3]{x^3-1} x^5-\frac{5}{162} \sqrt[3]{x^3-1} x^2-\frac{5}{486} \log \left(\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+1\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,"(-5*x^2*(-1 + x^3)^(1/3))/162 - (x^5*(-1 + x^3)^(1/3))/54 + (x^8*(-1 + x^3)^(1/3))/9 + (5*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) + (5*Log[1 - x/(-1 + x^3)^(1/3)])/243 - (5*Log[1 + x^2/(-1 + x^3)^(2/3) + x/(-1 + x^3)^(1/3)])/486","A",10,9,13,0.6923,1,"{279, 321, 331, 292, 31, 634, 618, 204, 628}"
1586,1,129,0,0.0651063,"\int x^7 \sqrt[3]{1+x^3} \, dx","Int[x^7*(1 + x^3)^(1/3),x]","-\frac{5}{243} \log \left(1-\frac{x}{\sqrt[3]{x^3+1}}\right)-\frac{5 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{1}{9} \sqrt[3]{x^3+1} x^8+\frac{1}{54} \sqrt[3]{x^3+1} x^5-\frac{5}{162} \sqrt[3]{x^3+1} x^2+\frac{5}{486} \log \left(\frac{x}{\sqrt[3]{x^3+1}}+\frac{x^2}{\left(x^3+1\right)^{2/3}}+1\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,"(-5*x^2*(1 + x^3)^(1/3))/162 + (x^5*(1 + x^3)^(1/3))/54 + (x^8*(1 + x^3)^(1/3))/9 - (5*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) - (5*Log[1 - x/(1 + x^3)^(1/3)])/243 + (5*Log[1 + x^2/(1 + x^3)^(2/3) + x/(1 + x^3)^(1/3)])/486","A",10,9,13,0.6923,1,"{279, 321, 331, 292, 31, 634, 618, 204, 628}"
1587,1,116,0,0.0700549,"\int \frac{\sqrt[3]{-1+x^3} \left(1+x^3\right)}{x^{13}} \, dx","Int[((-1 + x^3)^(1/3)*(1 + x^3))/x^13,x]","\frac{25 \sqrt[3]{x^3-1}}{486 x^3}+\frac{25}{486} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{25 \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{243 \sqrt{3}}+\frac{\left(x^3-1\right)^{4/3}}{12 x^{12}}-\frac{5 \sqrt[3]{x^3-1}}{27 x^9}+\frac{5 \sqrt[3]{x^3-1}}{162 x^6}-\frac{25 \log (x)}{486}","\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,"(-5*(-1 + x^3)^(1/3))/(27*x^9) + (5*(-1 + x^3)^(1/3))/(162*x^6) + (25*(-1 + x^3)^(1/3))/(486*x^3) + (-1 + x^3)^(4/3)/(12*x^12) - (25*ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]])/(243*Sqrt[3]) - (25*Log[x])/486 + (25*Log[1 + (-1 + x^3)^(1/3)])/486","A",9,8,18,0.4444,1,"{446, 78, 47, 51, 58, 618, 204, 31}"
1588,0,0,0,10.443751,"\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","Int[((-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,"(-8*a*(b - x))/(3*(a - b)*((a - x)*(b - x))^(3/4)) - (4*(a - 3*b)*(b - x))/(3*(a - b)*((a - x)*(b - x))^(3/4)) + (8*a*(1 - (a - b)/(a - x))^(3/4)*(-a + x)^(3/2)*EllipticF[ArcCot[Sqrt[-a + x]/Sqrt[a - b]]/2, 2])/(3*(a - b)^(3/2)*((a - x)*(b - x))^(3/4)) + (4*(a - 3*b)*(1 - (a - b)/(a - x))^(3/4)*(-a + x)^(3/2)*EllipticF[ArcCot[Sqrt[-a + x]/Sqrt[a - b]]/2, 2])/(3*(a - b)^(3/2)*((a - x)*(b - x))^(3/4)) + (8*b*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(a - b + x^4)^(1/4)/(a*(1 - b/a) + x^4 - d*x^12), x], x, (-a + x)^(1/4)])/((a - b)*((a - x)*(b - x))^(3/4)) - (4*(a - 3*b)*d*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(a - b + x^4)^(1/4))/(a*(1 - b/a) + x^4 - d*x^12), x], x, (-a + x)^(1/4)])/((a - b)*((a - x)*(b - x))^(3/4)) - (4*(a - 3*b)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(a - b + x^4)^(1/4)/(-(a*(1 - b/a)) - x^4 + d*x^12), x], x, (-a + x)^(1/4)])/((a - b)*((a - x)*(b - x))^(3/4)) + (8*a*d*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(a - b + x^4)^(1/4))/(-(a*(1 - b/a)) - x^4 + d*x^12), x], x, (-a + x)^(1/4)])/((a - b)*((a - x)*(b - x))^(3/4))","F",0,0,0,0,-1,"{}"
1589,1,135,0,0.0555561,"\int x^8 \left(-b+a x^4\right)^{3/4} \, dx","Int[x^8*(-b + a*x^4)^(3/4),x]","-\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{5 b^2 x \left(a x^4-b\right)^{3/4}}{128 a^2}+\frac{1}{12} x^9 \left(a x^4-b\right)^{3/4}-\frac{b x^5 \left(a x^4-b\right)^{3/4}}{32 a}","-\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,"(-5*b^2*x*(-b + a*x^4)^(3/4))/(128*a^2) - (b*x^5*(-b + a*x^4)^(3/4))/(32*a) + (x^9*(-b + a*x^4)^(3/4))/12 - (5*b^3*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(256*a^(9/4)) - (5*b^3*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(256*a^(9/4))","A",7,6,17,0.3529,1,"{279, 321, 240, 212, 206, 203}"
1590,1,159,0,0.2070328,"\int \frac{1}{\left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Int[1/((b + a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a} b \sqrt[4]{a x^4-b x}}+\frac{2^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a} b \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,"(2^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*a^(1/4)*b*(-(b*x) + a*x^4)^(1/4)) + (2^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*a^(1/4)*b*(-(b*x) + a*x^4)^(1/4))","A",7,7,24,0.2917,1,"{2056, 466, 465, 377, 212, 206, 203}"
1591,1,201,0,1.3818232,"\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Int[(-(b*x^2) + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","-\frac{a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{2 a \sqrt[4]{a x^4-b x^2}}{5 b^2 x}+\frac{2 \sqrt[4]{a x^4-b x^2}}{5 b x^3}","\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{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}",1,"(2*(-(b*x^2) + a*x^4)^(1/4))/(5*b*x^3) - (2*a*(-(b*x^2) + a*x^4)^(1/4))/(5*b^2*x) - (a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*b^2*(1 - (a*x^2)/b)^(1/4)) - (a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*b^2*(1 - (a*x^2)/b)^(1/4))","A",14,9,31,0.2903,0,"{2056, 1270, 1521, 271, 264, 6725, 1529, 511, 510}"
1592,1,201,0,1.1214797,"\int \frac{\sqrt[4]{-b x^2+a x^4}}{x^4 \left(-b+a x^4\right)} \, dx","Int[(-(b*x^2) + a*x^4)^(1/4)/(x^4*(-b + a*x^4)),x]","-\frac{a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{a x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 b^2 \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{2 a \sqrt[4]{a x^4-b x^2}}{5 b^2 x}+\frac{2 \sqrt[4]{a x^4-b x^2}}{5 b x^3}","\frac{2 \left(b-a x^2\right) \sqrt[4]{a x^4-b x^2}}{5 b^2 x^3}-\frac{a \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]}{4 b}",1,"(2*(-(b*x^2) + a*x^4)^(1/4))/(5*b*x^3) - (2*a*(-(b*x^2) + a*x^4)^(1/4))/(5*b^2*x) - (a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*b^2*(1 - (a*x^2)/b)^(1/4)) - (a*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*b^2*(1 - (a*x^2)/b)^(1/4))","A",14,9,31,0.2903,0,"{2056, 1270, 1521, 271, 264, 6725, 1529, 511, 510}"
1593,0,0,0,52.6896977,"\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-2 (1+k) x+\left(1+c+4 k+k^2\right) x^2-\left(c+2 k+c k+2 k^2\right) x^3+\left(-b+c k+k^2\right) x^4\right)} \, dx","Int[((-2 + (1 + k)*x)*(1 - (1 + k)*x + (a + k)*x^2))/(((1 - x)*x*(1 - k*x))^(1/3)*(1 - 2*(1 + k)*x + (1 + c + 4*k + k^2)*x^2 - (c + 2*k + c*k + 2*k^2)*x^3 + (-b + c*k + k^2)*x^4)),x]","\int \frac{(-2+(1+k) x) \left(1-(1+k) x+(a+k) x^2\right)}{\sqrt[3]{(1-x) x (1-k x)} \left(1-2 (1+k) x+\left(1+c+4 k+k^2\right) x^2-\left(c+2 k+c k+2 k^2\right) x^3+\left(-b+c k+k^2\right) x^4\right)} \, dx","-\text{RootSum}\left[-\text{$\#$1}^6-\text{$\#$1}^3 c+b\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-a \log \left(\sqrt[3]{k x^3+(-k-1) x^2+x}-\text{$\#$1} x\right)+a \log (x)}{2 \text{$\#$1}^4+\text{$\#$1} c}\&\right]",1,"(9*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^4/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - 2*(1 + k)*x^3 + (1 + c + k*(4 + k))*x^6 - c*(1 + (k*(2 + c + 2*k))/c)*x^9 - b*(1 - (k*(c + k))/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (3*(1 + 2*a + 4*k + k^2)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - 2*(1 + k)*x^3 + (1 + c + k*(4 + k))*x^6 - c*(1 + (k*(2 + c + 2*k))/c)*x^9 - b*(1 - (k*(c + k))/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (3*(1 + k)*(a + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^10/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - 2*(1 + k)*x^3 + (1 + c + k*(4 + k))*x^6 - c*(1 + (k*(2 + c + 2*k))/c)*x^9 - b*(1 - (k*(c + k))/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (6*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-1 + 2*(1 + k)*x^3 - (1 + c + k*(4 + k))*x^6 + c*(1 + (k*(2 + c + 2*k))/c)*x^9 + b*(1 - (k*(c + k))/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
1594,1,119,0,0.0818173,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^3} \, dx","Int[((-1 + x^6)^(1/3)*(1 + x^6))/x^3,x]","-\frac{1}{3} \sqrt[3]{x^6-1} x^4+\frac{\left(x^6-1\right)^{4/3}}{2 x^2}-\frac{1}{9} \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{1}{18} \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\right)","\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,"-1/3*(x^4*(-1 + x^6)^(1/3)) + (-1 + x^6)^(4/3)/(2*x^2) - ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - Log[1 - x^2/(-1 + x^6)^(1/3)]/9 + Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)]/18","A",10,10,18,0.5556,1,"{453, 275, 279, 331, 292, 31, 634, 618, 204, 628}"
1595,1,157,0,0.5959056,"\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","Int[((1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(-2 + x^6)),x]","-\frac{1}{8} \left(3+2 \sqrt{2}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{x^3}{\sqrt{2}}\right)-\frac{1}{8} \left(3-2 \sqrt{2}\right) x F_1\left(\frac{1}{3};1,-\frac{2}{3};\frac{4}{3};\frac{x^3}{\sqrt{2}},-x^3\right)-\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{5/3}}{10 x^5}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{1}{24} \text{RootSum}\left[2 \text{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(1-4 x^3\right)}{10 x^5}",1,"-1/2*(1 + x^3)^(2/3)/x^2 + (1 + x^3)^(5/3)/(10*x^5) - ((3 + 2*Sqrt[2])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(x^3/Sqrt[2])])/8 - ((3 - 2*Sqrt[2])*x*AppellF1[1/3, 1, -2/3, 4/3, x^3/Sqrt[2], -x^3])/8 + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]/2","A",10,6,30,0.2000,0,"{28, 6725, 264, 277, 239, 429}"
1596,1,157,0,0.5072591,"\int \frac{\left(1+x^3\right)^{2/3} \left(1-2 x^3+x^6\right)}{x^6 \left(-2+x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(1 - 2*x^3 + x^6))/(x^6*(-2 + x^6)),x]","-\frac{1}{8} \left(3+2 \sqrt{2}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{x^3}{\sqrt{2}}\right)-\frac{1}{8} \left(3-2 \sqrt{2}\right) x F_1\left(\frac{1}{3};1,-\frac{2}{3};\frac{4}{3};\frac{x^3}{\sqrt{2}},-x^3\right)-\frac{1}{2} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3+1\right)^{5/3}}{10 x^5}-\frac{\left(x^3+1\right)^{2/3}}{2 x^2}","\frac{1}{24} \text{RootSum}\left[2 \text{$\#$1}^6-4 \text{$\#$1}^3+1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+2 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(1-4 x^3\right)}{10 x^5}",1,"-1/2*(1 + x^3)^(2/3)/x^2 + (1 + x^3)^(5/3)/(10*x^5) - ((3 + 2*Sqrt[2])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(x^3/Sqrt[2])])/8 - ((3 - 2*Sqrt[2])*x*AppellF1[1/3, 1, -2/3, 4/3, x^3/Sqrt[2], -x^3])/8 + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]/2","A",10,6,30,0.2000,0,"{28, 6725, 264, 277, 239, 429}"
1597,1,115,0,0.0780256,"\int \frac{\sqrt[3]{-1+x^6} \left(-1+2 x^6\right)}{x^9} \, dx","Int[((-1 + x^6)^(1/3)*(-1 + 2*x^6))/x^9,x]","-\frac{\left(x^6-1\right)^{4/3}}{8 x^8}-\frac{\sqrt[3]{x^6-1}}{x^2}-\frac{1}{3} \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{1}{6} \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\right)","\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)/x^2) - (-1 + x^6)^(4/3)/(8*x^8) - ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[1 - x^2/(-1 + x^6)^(1/3)]/3 + Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)]/6","A",10,10,20,0.5000,1,"{451, 275, 277, 331, 292, 31, 634, 618, 204, 628}"
1598,1,225,0,0.6200357,"\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","Int[((-1 + x^3)^(2/3)*(-1 + x^6))/(x^6*(-2 + x^3 + 2*x^6)),x]","-\frac{\left(17+\sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1-\sqrt{17}}\right)}{34 \left(1-\sqrt{17}\right) \left(1-x^3\right)^{2/3}}-\frac{\left(17-\sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1+\sqrt{17}}\right)}{34 \left(1+\sqrt{17}\right) \left(1-x^3\right)^{2/3}}-\frac{1}{8} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{10 x^5}-\frac{\left(x^3-1\right)^{2/3}}{8 x^2}","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"-1/8*(-1 + x^3)^(2/3)/x^2 + (-1 + x^3)^(5/3)/(10*x^5) - ((17 + Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 - Sqrt[17])])/(34*(1 - Sqrt[17])*(1 - x^3)^(2/3)) - ((17 - Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 + Sqrt[17])])/(34*(1 + Sqrt[17])*(1 - x^3)^(2/3)) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(4*Sqrt[3]) - Log[-x + (-1 + x^3)^(1/3)]/8","B",11,6,30,0.2000,0,"{6728, 264, 277, 239, 430, 429}"
1599,1,225,0,0.5532281,"\int \frac{\left(-1+x^3\right)^{2/3} \left(-1+x^6\right)}{x^6 \left(-2+x^3+2 x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(-1 + x^6))/(x^6*(-2 + x^3 + 2*x^6)),x]","-\frac{\left(17+\sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1-\sqrt{17}}\right)}{34 \left(1-\sqrt{17}\right) \left(1-x^3\right)^{2/3}}-\frac{\left(17-\sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{4 x^3}{1+\sqrt{17}}\right)}{34 \left(1+\sqrt{17}\right) \left(1-x^3\right)^{2/3}}-\frac{1}{8} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{10 x^5}-\frac{\left(x^3-1\right)^{2/3}}{8 x^2}","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-3 \text{$\#$1}^3-1\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)-\log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+\log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"-1/8*(-1 + x^3)^(2/3)/x^2 + (-1 + x^3)^(5/3)/(10*x^5) - ((17 + Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 - Sqrt[17])])/(34*(1 - Sqrt[17])*(1 - x^3)^(2/3)) - ((17 - Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (-4*x^3)/(1 + Sqrt[17])])/(34*(1 + Sqrt[17])*(1 - x^3)^(2/3)) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(4*Sqrt[3]) - Log[-x + (-1 + x^3)^(1/3)]/8","B",11,6,30,0.2000,0,"{6728, 264, 277, 239, 430, 429}"
1600,1,121,0,0.3832508,"\int \frac{\sqrt[4]{-1+x^4} \left(2-x^4+2 x^8\right)}{x^{10} \left(-1+2 x^4\right)} \, dx","Int[((-1 + x^4)^(1/4)*(2 - x^4 + 2*x^8))/(x^10*(-1 + 2*x^4)),x]","-\frac{16 \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,2 x^4\right)}{3 \sqrt[4]{1-x^4}}+\frac{8 \sqrt[4]{x^4-1}}{x}+4 \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-4 \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{2 \left(x^4-1\right)^{5/4}}{9 x^9}-\frac{7 \left(x^4-1\right)^{5/4}}{9 x^5}","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,"(8*(-1 + x^4)^(1/4))/x - (2*(-1 + x^4)^(5/4))/(9*x^9) - (7*(-1 + x^4)^(5/4))/(9*x^5) - (16*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, 2*x^4])/(3*(1 - x^4)^(1/4)) + 4*ArcTan[x/(-1 + x^4)^(1/4)] - 4*ArcTanh[x/(-1 + x^4)^(1/4)]","C",12,10,34,0.2941,0,"{6725, 271, 264, 277, 331, 298, 203, 206, 511, 510}"
1601,0,0,0,1.2059701,"\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","Int[((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,"(-2*(-1 + x^6)^(3/4))/(3*x^3) + (2*(1 - x^6)^(1/4)*Hypergeometric2F1[-7/6, 1/4, -1/6, x^6])/(7*x^7*(-1 + x^6)^(1/4)) - ((1 - x^6)^(1/4)*Hypergeometric2F1[-1/6, 1/4, 5/6, x^6])/(x*(-1 + x^6)^(1/4)) + (2*x*(1 - x^6)^(1/4)*Hypergeometric2F1[1/6, 1/4, 7/6, x^6])/(-1 + x^6)^(1/4) + (x^5*(1 - x^6)^(1/4)*Hypergeometric2F1[1/4, 5/6, 11/6, x^6])/(5*(-1 + x^6)^(1/4)) + 6*Defer[Int][1/((-1 + x^6)^(1/4)*(-1 + x^4 + x^6)), x] - 2*Defer[Int][x^4/((-1 + x^6)^(1/4)*(-1 + x^4 + x^6)), x]","F",0,0,0,0,-1,"{}"
1602,0,0,0,1.2336214,"\int \frac{\sqrt{x+x^2}}{x \sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Int[Sqrt[x + x^2]/(x*Sqrt[x^2 + x*Sqrt[x + x^2]]),x]","\int \frac{\sqrt{x+x^2}}{x \sqrt{x^2+x \sqrt{x+x^2}}} \, dx","\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 + x^2]*Defer[Subst][Defer[Int][Sqrt[1 + x^2]/Sqrt[x^4 + x^2*Sqrt[x^2 + x^4]], x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x])","F",0,0,0,0,-1,"{}"
1603,0,0,0,0.7735355,"\int \frac{\sqrt{x^2+x \sqrt{x+x^2}}}{\sqrt{x+x^2}} \, dx","Int[Sqrt[x^2 + x*Sqrt[x + x^2]]/Sqrt[x + x^2],x]","\int \frac{\sqrt{x^2+x \sqrt{x+x^2}}}{\sqrt{x+x^2}} \, dx","\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,"(2*Sqrt[x]*Sqrt[1 + x]*Defer[Subst][Defer[Int][Sqrt[x^4 + x^2*Sqrt[x^2 + x^4]]/Sqrt[1 + x^2], x], x, Sqrt[x]])/Sqrt[x + x^2]","F",0,0,0,0,-1,"{}"
1604,0,0,0,0.0464858,"\int \frac{1}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[1/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\int \frac{1}{\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}}",1,"Defer[Int][1/Sqrt[b + Sqrt[b^2 + a*x^2]], x]","F",0,0,0,0,-1,"{}"
1605,0,0,0,0.4847332,"\int \left(b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}} \, dx","Int[(b^2 + a*x^2)^2*Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\int \left(b^2+a x^2\right)^2 \sqrt{b+\sqrt{b^2+a x^2}} \, dx","\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*a*b^4*x^3)/(3*(b + Sqrt[b^2 + a*x^2])^(3/2)) + (2*b^5*x)/Sqrt[b + Sqrt[b^2 + a*x^2]] + 2*a*b^2*Defer[Int][x^2*Sqrt[b + Sqrt[b^2 + a*x^2]], x] + a^2*Defer[Int][x^4*Sqrt[b + Sqrt[b^2 + a*x^2]], x]","F",0,0,0,0,-1,"{}"
1606,1,220,0,0.2235058,"\int \frac{1}{(1-3 x) \sqrt[3]{-x+x^3}} \, dx","Int[1/((1 - 3*x)*(-x + x^3)^(1/3)),x]","\frac{9 \sqrt[3]{1-x^2} x^2 F_1\left(\frac{5}{6};1,\frac{1}{3};\frac{11}{6};9 x^2,x^2\right)}{5 \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x^2-1} \sqrt[3]{x} \log \left(\frac{4 x^{4/3}}{\left(x^2-1\right)^{2/3}}-\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{8 \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x^2-1} \sqrt[3]{x} \log \left(\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{4 \sqrt[3]{x^3-x}}-\frac{\sqrt{3} \sqrt[3]{x^2-1} \sqrt[3]{x} \tan ^{-1}\left(\frac{1-\frac{4 x^{2/3}}{\sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{4 \sqrt[3]{x^3-x}}","\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,"(9*x^2*(1 - x^2)^(1/3)*AppellF1[5/6, 1, 1/3, 11/6, 9*x^2, x^2])/(5*(-x + x^3)^(1/3)) - (Sqrt[3]*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (4*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(4*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 + (4*x^(4/3))/(-1 + x^2)^(2/3) - (2*x^(2/3))/(-1 + x^2)^(1/3)])/(8*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 + (2*x^(2/3))/(-1 + x^2)^(1/3)])/(4*(-x + x^3)^(1/3))","C",14,13,19,0.6842,0,"{2056, 959, 466, 465, 377, 200, 31, 634, 618, 204, 628, 511, 510}"
1607,1,220,0,0.2070826,"\int \frac{1}{(1+3 x) \sqrt[3]{-x+x^3}} \, dx","Int[1/((1 + 3*x)*(-x + x^3)^(1/3)),x]","-\frac{9 \sqrt[3]{1-x^2} x^2 F_1\left(\frac{5}{6};1,\frac{1}{3};\frac{11}{6};9 x^2,x^2\right)}{5 \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x^2-1} \sqrt[3]{x} \log \left(\frac{4 x^{4/3}}{\left(x^2-1\right)^{2/3}}-\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{8 \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x^2-1} \sqrt[3]{x} \log \left(\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{4 \sqrt[3]{x^3-x}}-\frac{\sqrt{3} \sqrt[3]{x^2-1} \sqrt[3]{x} \tan ^{-1}\left(\frac{1-\frac{4 x^{2/3}}{\sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{4 \sqrt[3]{x^3-x}}","\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,"(-9*x^2*(1 - x^2)^(1/3)*AppellF1[5/6, 1, 1/3, 11/6, 9*x^2, x^2])/(5*(-x + x^3)^(1/3)) - (Sqrt[3]*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (4*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(4*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 + (4*x^(4/3))/(-1 + x^2)^(2/3) - (2*x^(2/3))/(-1 + x^2)^(1/3)])/(8*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 + (2*x^(2/3))/(-1 + x^2)^(1/3)])/(4*(-x + x^3)^(1/3))","C",14,13,19,0.6842,0,"{2056, 959, 466, 465, 377, 200, 31, 634, 618, 204, 628, 511, 510}"
1608,1,152,0,0.0429425,"\int \frac{x}{\sqrt[3]{-x^2+x^3}} \, dx","Int[x/(-x^2 + x^3)^(1/3),x]","\frac{\left(x^3-x^2\right)^{2/3}}{x}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{6 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{x^3-x^2}}","\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,"(-x^2 + x^3)^(2/3)/x - ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(Sqrt[3]*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(6*(-x^2 + x^3)^(1/3))","A",3,3,15,0.2000,1,"{2024, 2011, 59}"
1609,1,42,0,0.0205629,"\int \frac{\left(1-x^3\right)^{2/3} \left(-1+x^3\right)}{x^6 \left(-1+2 x^3\right)} \, dx","Int[((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",2,2,29,0.06897,0,"{21, 510}"
1610,1,573,0,1.388091,"\int \frac{2 b+a x}{\left(b+a x+x^2\right) \sqrt[4]{b x^2+a x^3}} \, dx","Int[(2*b + a*x)/((b + a*x + x^2)*(b*x^2 + a*x^3)^(1/4)),x]","\frac{\sqrt{2} \sqrt[4]{b} \left(\sqrt{a^2-4 b}+a\right) \sqrt{-\frac{a x}{b}} \sqrt[4]{a x+b} \Pi \left(-\frac{\sqrt{2} \sqrt{b}}{\sqrt{-a^2-\sqrt{a^2-4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b+a x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{-a \sqrt{a^2-4 b}-a^2+2 b} \sqrt[4]{a x^3+b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \left(\sqrt{a^2-4 b}+a\right) \sqrt{-\frac{a x}{b}} \sqrt[4]{a x+b} \Pi \left(\frac{\sqrt{2} \sqrt{b}}{\sqrt{-a^2-\sqrt{a^2-4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b+a x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{-a \sqrt{a^2-4 b}-a^2+2 b} \sqrt[4]{a x^3+b x^2}}+\frac{\sqrt{2} \sqrt[4]{b} \left(a-\sqrt{a^2-4 b}\right) \sqrt{-\frac{a x}{b}} \sqrt[4]{a x+b} \Pi \left(-\frac{\sqrt{2} \sqrt{b}}{\sqrt{-a^2+\sqrt{a^2-4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b+a x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{a \sqrt{a^2-4 b}-a^2+2 b} \sqrt[4]{a x^3+b x^2}}-\frac{\sqrt{2} \sqrt[4]{b} \left(a-\sqrt{a^2-4 b}\right) \sqrt{-\frac{a x}{b}} \sqrt[4]{a x+b} \Pi \left(\frac{\sqrt{2} \sqrt{b}}{\sqrt{-a^2+\sqrt{a^2-4 b} a+2 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{b+a x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{a \sqrt{a^2-4 b}-a^2+2 b} \sqrt[4]{a x^3+b x^2}}","\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,"(Sqrt[2]*(a + Sqrt[a^2 - 4*b])*b^(1/4)*Sqrt[-((a*x)/b)]*(b + a*x)^(1/4)*EllipticPi[-((Sqrt[2]*Sqrt[b])/Sqrt[-a^2 - a*Sqrt[a^2 - 4*b] + 2*b]), ArcSin[(b + a*x)^(1/4)/b^(1/4)], -1])/(Sqrt[-a^2 - a*Sqrt[a^2 - 4*b] + 2*b]*(b*x^2 + a*x^3)^(1/4)) - (Sqrt[2]*(a + Sqrt[a^2 - 4*b])*b^(1/4)*Sqrt[-((a*x)/b)]*(b + a*x)^(1/4)*EllipticPi[(Sqrt[2]*Sqrt[b])/Sqrt[-a^2 - a*Sqrt[a^2 - 4*b] + 2*b], ArcSin[(b + a*x)^(1/4)/b^(1/4)], -1])/(Sqrt[-a^2 - a*Sqrt[a^2 - 4*b] + 2*b]*(b*x^2 + a*x^3)^(1/4)) + (Sqrt[2]*(a - Sqrt[a^2 - 4*b])*b^(1/4)*Sqrt[-((a*x)/b)]*(b + a*x)^(1/4)*EllipticPi[-((Sqrt[2]*Sqrt[b])/Sqrt[-a^2 + a*Sqrt[a^2 - 4*b] + 2*b]), ArcSin[(b + a*x)^(1/4)/b^(1/4)], -1])/(Sqrt[-a^2 + a*Sqrt[a^2 - 4*b] + 2*b]*(b*x^2 + a*x^3)^(1/4)) - (Sqrt[2]*(a - Sqrt[a^2 - 4*b])*b^(1/4)*Sqrt[-((a*x)/b)]*(b + a*x)^(1/4)*EllipticPi[(Sqrt[2]*Sqrt[b])/Sqrt[-a^2 + a*Sqrt[a^2 - 4*b] + 2*b], ArcSin[(b + a*x)^(1/4)/b^(1/4)], -1])/(Sqrt[-a^2 + a*Sqrt[a^2 - 4*b] + 2*b]*(b*x^2 + a*x^3)^(1/4))","C",13,6,33,0.1818,1,"{2056, 6728, 107, 106, 490, 1218}"
1611,1,129,0,0.2626335,"\int \frac{x^3 \sqrt{x+x^4}}{-b+a x^3} \, dx","Int[(x^3*Sqrt[x + x^4])/(-b + a*x^3),x]","\frac{\sqrt{x^4+x} (a+2 b) \sinh ^{-1}\left(x^{3/2}\right)}{3 a^2 \sqrt{x^3+1} \sqrt{x}}-\frac{2 \sqrt{b} \sqrt{x^4+x} \sqrt{a+b} \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{a+b}}{\sqrt{b} \sqrt{x^3+1}}\right)}{3 a^2 \sqrt{x^3+1} \sqrt{x}}+\frac{\sqrt{x^4+x} x}{3 a}","\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,"(x*Sqrt[x + x^4])/(3*a) + ((a + 2*b)*Sqrt[x + x^4]*ArcSinh[x^(3/2)])/(3*a^2*Sqrt[x]*Sqrt[1 + x^3]) - (2*Sqrt[b]*Sqrt[a + b]*Sqrt[x + x^4]*ArcTanh[(Sqrt[a + b]*x^(3/2))/(Sqrt[b]*Sqrt[1 + x^3])])/(3*a^2*Sqrt[x]*Sqrt[1 + x^3])","A",8,8,24,0.3333,1,"{2042, 466, 465, 478, 523, 215, 377, 208}"
1612,1,119,0,0.0904702,"\int x^9 \sqrt[3]{1+x^6} \, dx","Int[x^9*(1 + x^6)^(1/3),x]","\frac{1}{12} \sqrt[3]{x^6+1} x^{10}+\frac{1}{36} \sqrt[3]{x^6+1} x^4+\frac{1}{54} \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{18 \sqrt{3}}-\frac{1}{108} \log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\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)^(1/3))/36 + (x^10*(1 + x^6)^(1/3))/12 + ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/(18*Sqrt[3]) + Log[1 - x^2/(1 + x^6)^(1/3)]/54 - Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)]/108","A",10,10,13,0.7692,1,"{275, 279, 321, 331, 292, 31, 634, 618, 204, 628}"
1613,1,185,0,0.485362,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^6)),x]","-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{i x^3}{2}\right)}{\left(1-x^3\right)^{2/3}}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};1,-\frac{2}{3};\frac{4}{3};-\frac{i x^3}{2},x^3\right)}{\left(1-x^3\right)^{2/3}}-\frac{1}{8} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{10 x^5}-\frac{\left(x^3-1\right)^{2/3}}{8 x^2}","\frac{1}{96} \text{RootSum}\left[4 \text{$\#$1}^6-8 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-5 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"-1/8*(-1 + x^3)^(2/3)/x^2 + (-1 + x^3)^(5/3)/(10*x^5) - ((1/16 - I/16)*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (I/2)*x^3])/(1 - x^3)^(2/3) - ((1/16 + I/16)*x*(-1 + x^3)^(2/3)*AppellF1[1/3, 1, -2/3, 4/3, (-1/2*I)*x^3, x^3])/(1 - x^3)^(2/3) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(4*Sqrt[3]) - Log[-x + (-1 + x^3)^(1/3)]/8","C",11,6,25,0.2400,0,"{6725, 264, 277, 239, 430, 429}"
1614,1,185,0,0.4098966,"\int \frac{\left(-1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^6)),x]","-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{i x^3}{2}\right)}{\left(1-x^3\right)^{2/3}}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};1,-\frac{2}{3};\frac{4}{3};-\frac{i x^3}{2},x^3\right)}{\left(1-x^3\right)^{2/3}}-\frac{1}{8} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{10 x^5}-\frac{\left(x^3-1\right)^{2/3}}{8 x^2}","\frac{1}{96} \text{RootSum}\left[4 \text{$\#$1}^6-8 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-5 \log (x)}{\text{$\#$1}^4-\text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(-x^3-4\right)}{40 x^5}",1,"-1/8*(-1 + x^3)^(2/3)/x^2 + (-1 + x^3)^(5/3)/(10*x^5) - ((1/16 - I/16)*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (I/2)*x^3])/(1 - x^3)^(2/3) - ((1/16 + I/16)*x*(-1 + x^3)^(2/3)*AppellF1[1/3, 1, -2/3, 4/3, (-1/2*I)*x^3, x^3])/(1 - x^3)^(2/3) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(4*Sqrt[3]) - Log[-x + (-1 + x^3)^(1/3)]/8","C",11,6,25,0.2400,0,"{6725, 264, 277, 239, 430, 429}"
1615,1,167,0,0.27319,"\int \frac{b-a x^3+x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Int[(b - a*x^3 + x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","-\frac{4 \left(a x^4+b x\right)^{3/4}}{21 x^6}+\frac{44 a \left(a x^4+b x\right)^{3/4}}{63 b x^3}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4+b x}}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \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*(b*x + a*x^4)^(3/4))/(21*x^6) + (44*a*(b*x + a*x^4)^(3/4))/(63*b*x^3) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4)) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4))","A",12,10,28,0.3571,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1616,1,167,0,0.2525562,"\int \frac{-b+a x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Int[(-b + a*x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}+\frac{4 \left(a x^4+b x\right)^{3/4}}{21 x^6}-\frac{16 a \left(a x^4+b x\right)^{3/4}}{63 b x^3}","\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,"(4*(b*x + a*x^4)^(3/4))/(21*x^6) - (16*a*(b*x + a*x^4)^(3/4))/(63*b*x^3) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4))","A",11,10,26,0.3846,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1617,1,167,0,0.259191,"\int \frac{b+a x^6}{x^6 \sqrt[4]{b x+a x^4}} \, dx","Int[(b + a*x^6)/(x^6*(b*x + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a x^4+b x}}-\frac{4 \left(a x^4+b x\right)^{3/4}}{21 x^6}+\frac{16 a \left(a x^4+b x\right)^{3/4}}{63 b x^3}","\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,"(-4*(b*x + a*x^4)^(3/4))/(21*x^6) + (16*a*(b*x + a*x^4)^(3/4))/(63*b*x^3) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*(b*x + a*x^4)^(1/4))","A",11,10,24,0.4167,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1618,0,0,0,2.4121058,"\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","Int[(-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,"(4*x*(1 + (a*x^5)/b)^(1/4)*Hypergeometric2F1[3/20, 1/4, 23/20, -((a*x^5)/b)])/(3*(b*x + a*x^6)^(1/4)) - (20*b*x^(1/4)*(b + a*x^5)^(1/4)*Defer[Subst][Defer[Int][x^2/((b + a*x^20)^(1/4)*(2*b + x^12 + 2*a*x^20)), x], x, x^(1/4)])/(b*x + a*x^6)^(1/4) - (4*x^(1/4)*(b + a*x^5)^(1/4)*Defer[Subst][Defer[Int][x^14/((b + a*x^20)^(1/4)*(2*b + x^12 + 2*a*x^20)), x], x, x^(1/4)])/(b*x + a*x^6)^(1/4)","F",0,0,0,0,-1,"{}"
1619,1,2604,0,8.3605936,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(2 b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(2*b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{-b}-a x\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{-b}-(-1)^{2/3} a x\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*(-b)^(1/6)) - a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*(-b)^(1/6) - a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*(-b)^(1/6)) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*(-b)^(1/6) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*(-b)^(1/6)) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*(-b)^(1/6) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,33,0.09091,0,"{2056, 6725, 91}"
1620,1,2604,0,7.2665315,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(2 b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(2*b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{-b}-a x\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{2} \sqrt[6]{-b}\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{-b}-(-1)^{2/3} a x\right)}{12\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+\sqrt[3]{-1} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} a^2 \sqrt[6]{-b}-(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[18]{-b} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} (-b)^{17/18} \sqrt[3]{\sqrt[6]{2} \sqrt[6]{-b} a^2+(-1)^{2/3} b^2} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*(-b)^(1/6)) - a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*(-b)^(1/6) - a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*(-b)^(1/6)) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*(-b)^(1/6) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*(-b)^(1/6)) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*(-b)^(1/6) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(1/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) - (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(-b)^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3))])/(4*2^(17/18)*a^(1/3)*(-b)^(17/18)*(2^(1/6)*a^2*(-b)^(1/6) + (-1)^(2/3)*b^2)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,33,0.09091,0,"{2056, 6725, 91}"
1621,0,0,0,1.6188361,"\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","Int[((-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]","\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","-\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*(1 - x^2))/Sqrt[1 + x^2 + x^4] - (x*(2 + x^2))/(3*Sqrt[1 + x^2 + x^4]) - (2*x*(1 + 2*x^2))/(3*Sqrt[1 + x^2 + x^4]) + (8*x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) - (8*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4]) + (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/Sqrt[1 + x^2 + x^4] - 4*Defer[Int][1/((1 + x^2 + x^4)^(3/2)*(1 + 3*x^2 + 5*x^4 + 3*x^6 + x^8)), x] - 8*Defer[Int][x^2/((1 + x^2 + x^4)^(3/2)*(1 + 3*x^2 + 5*x^4 + 3*x^6 + x^8)), x] - 12*Defer[Int][x^4/((1 + x^2 + x^4)^(3/2)*(1 + 3*x^2 + 5*x^4 + 3*x^6 + x^8)), x] - 2*Defer[Int][x^6/((1 + x^2 + x^4)^(3/2)*(1 + 3*x^2 + 5*x^4 + 3*x^6 + x^8)), x]","F",0,0,0,0,-1,"{}"
1622,1,285,0,0.5818178,"\int \frac{-b+a x^8}{\sqrt[4]{b+a x^4} \left(b+a x^8\right)} \, dx","Int[(-b + a*x^8)/((b + a*x^4)^(1/4)*(b + a*x^8)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$1}}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}",1,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*a^(1/4)) - ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)) - ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*a^(1/4)) - ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)) - ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4))","B",15,7,30,0.2333,1,"{6725, 240, 212, 206, 203, 1429, 377}"
1623,1,285,0,0.3778898,"\int \frac{-b+a x^8}{\sqrt[4]{b+a x^4} \left(b+a x^8\right)} \, dx","Int[(-b + a*x^8)/((b + a*x^4)^(1/4)*(b + a*x^8)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}-\frac{\tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$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,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*a^(1/4)) - ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)) - ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*a^(1/4)) - ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)) - ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4))","B",15,7,30,0.2333,1,"{6725, 240, 212, 206, 203, 1429, 377}"
1624,0,0,0,2.3382285,"\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","Int[((-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,"(-6*Sqrt[x - x^2 + x^6]*Defer[Subst][Defer[Int][(x^2*Sqrt[1 - x^2 + x^10])/(1 - 2*x^2 + x^4 - x^6 + x^8 + 2*x^10 - 3*x^12 - x^16 + x^20), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 - x + x^5]) + (4*Sqrt[x - x^2 + x^6]*Defer[Subst][Defer[Int][(x^4*Sqrt[1 - x^2 + x^10])/(1 - 2*x^2 + x^4 - x^6 + x^8 + 2*x^10 - 3*x^12 - x^16 + x^20), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 - x + x^5]) + (4*Sqrt[x - x^2 + x^6]*Defer[Subst][Defer[Int][(x^12*Sqrt[1 - x^2 + x^10])/(1 - 2*x^2 + x^4 - x^6 + x^8 + 2*x^10 - 3*x^12 - x^16 + x^20), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 - x + x^5])","F",0,0,0,0,-1,"{}"
1625,1,96,0,0.3691253,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2 \sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(x^2*Sqrt[1 + x]),x]","-\frac{\left(x+\sqrt{x+1}\right)^{3/2}}{x}+\sqrt{x+\sqrt{x+1}}+\frac{3}{4} \tan ^{-1}\left(\frac{\sqrt{x+1}+3}{2 \sqrt{x+\sqrt{x+1}}}\right)+\frac{1}{4} \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\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,"Sqrt[x + Sqrt[1 + x]] - (x + Sqrt[1 + x])^(3/2)/x + (3*ArcTan[(3 + Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 + ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])]/4","A",8,6,24,0.2500,1,"{976, 1021, 1033, 724, 206, 204}"
1626,1,90,0,0.264967,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x \sqrt{1+x}} \, dx","Int[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",9,6,24,0.2500,1,"{990, 621, 206, 1033, 724, 204}"
1627,1,93,0,0.1945366,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Int[Sqrt[a*x + Sqrt[-b + a*x]]/Sqrt[-b + a*x],x]","\frac{\sqrt{\sqrt{a x-b}+a x} \left(2 \sqrt{a x-b}+1\right)}{2 a}-\frac{(1-4 b) \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,"(Sqrt[a*x + Sqrt[-b + a*x]]*(1 + 2*Sqrt[-b + a*x]))/(2*a) - ((1 - 4*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(4*a)","A",4,3,31,0.09677,1,"{612, 621, 206}"
1628,1,104,0,0.5564809,"\int \frac{1-a x+b \sqrt{a+b x}}{\sqrt{a+b x} \left(x+a b \sqrt{a+b x}\right)} \, dx","Int[(1 - a*x + b*Sqrt[a + b*x])/(Sqrt[a + b*x]*(x + a*b*Sqrt[a + b*x])),x]","-\frac{2 \left(2-a \left(a^2+1\right) b^3\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*(1 + a^2)*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",8,6,43,0.1395,1,"{1984, 1657, 634, 618, 206, 628}"
1629,0,0,0,0.1556707,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^2} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]]/x^2,x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^2} \, dx","\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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/x^2, x]","F",0,0,0,0,-1,"{}"
1630,0,0,0,2.5818202,"\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","Int[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,"(2*Sqrt[x]*Sqrt[-b + a^2*x]*Defer[Subst][Defer[Int][1/(Sqrt[-b + a^2*x^2]*(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2)), x], x, Sqrt[x]])/Sqrt[-(b*x) + a^2*x^2]","F",0,0,0,0,-1,"{}"
1631,1,84,0,0.0632841,"\int \frac{1}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(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",4,3,19,0.1579,1,"{2117, 1821, 1620}"
1632,0,0,0,0.0098394,"\int \frac{-2+x}{\left(2+x^2\right) \sqrt[3]{-1+x+2 x^2}} \, dx","Int[(-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,"Defer[Int][(-2 + x)/((2 + x^2)*(-1 + x + 2*x^2)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1633,0,0,0,6.9364089,"\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","Int[((-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,"((a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Int][((-a + x)^(1/4)*(-b + x)^(1/4))/(x^(3/2)*(a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x^2)^(3/4) + ((a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Int][((-a + x)^(1/4)*(-b + x)^(1/4))/(x^(3/2)*(a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x^2)^(3/4)","F",0,0,0,0,-1,"{}"
1634,1,412,0,0.9199673,"\int \frac{1-x+x^2}{\left(-2+2 x+x^2\right) \sqrt{1+x^3}} \, dx","Int[(1 - x + x^2)/((-2 + 2*x + x^2)*Sqrt[1 + x^3]),x]","-\frac{1}{2} \sqrt{\frac{1}{3} \left(3+2 \sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)-\frac{1}{2} \sqrt{\frac{1}{3} \left(2 \sqrt{3}-3\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)-\frac{\left(2+\sqrt{3}\right)^{3/2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \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,"-1/2*(Sqrt[(3 + 2*Sqrt[3])/3]*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]) - (Sqrt[(-3 + 2*Sqrt[3])/3]*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/2 - (Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - ((2 + Sqrt[3])^(3/2)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","C",13,6,28,0.2143,1,"{6728, 218, 2135, 2140, 206, 203}"
1635,1,155,0,0.1143313,"\int \frac{-1+x}{x \sqrt[3]{-x^2+x^3}} \, dx","Int[(-1 + x)/(x*(-x^2 + x^3)^(1/3)),x]","-\frac{3 \left(x^3-x^2\right)^{2/3}}{2 x^2}-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-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*(-x^2 + x^3)^(2/3))/(2*x^2) - (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3))","A",5,4,20,0.2000,1,"{2052, 2011, 59, 2014}"
1636,1,155,0,0.0827987,"\int \frac{1+x}{x \sqrt[3]{-x^2+x^3}} \, dx","Int[(1 + x)/(x*(-x^2 + x^3)^(1/3)),x]","\frac{3 \left(x^3-x^2\right)^{2/3}}{2 x^2}-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-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*(-x^2 + x^3)^(2/3))/(2*x^2) - (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3))","A",3,3,20,0.1500,1,"{2038, 2011, 59}"
1637,1,164,0,0.0778398,"\int \frac{x^2}{\sqrt[3]{x^2+x^3}} \, dx","Int[x^2/(x^2 + x^3)^(1/3),x]","-\frac{2 \left(x^3+x^2\right)^{2/3}}{3 x}+\frac{1}{2} \left(x^3+x^2\right)^{2/3}-\frac{x^{2/3} \sqrt[3]{x+1} \log (x)}{9 \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{x}}-1\right)}{3 \sqrt[3]{x^3+x^2}}-\frac{2 x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{x^3+x^2}}","\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,"(x^2 + x^3)^(2/3)/2 - (2*(x^2 + x^3)^(2/3))/(3*x) - (2*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(3*Sqrt[3]*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[x])/(9*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[-1 + (1 + x)^(1/3)/x^(1/3)])/(3*(x^2 + x^3)^(1/3))","A",4,3,15,0.2000,1,"{2024, 2011, 59}"
1638,0,0,0,18.0957339,"\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","Int[((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,"(-4*(a - x))/((a - x)*(b - x))^(1/4) - (8*a*(1 - (a - b)/(a - x))^(1/4)*Sqrt[-a + x]*EllipticE[ArcCot[Sqrt[-a + x]/Sqrt[a - b]]/2, 2])/(Sqrt[a - b]*((a - x)*(b - x))^(1/4)) - (4*(a - 3*b)*(1 - (a - b)/(a - x))^(1/4)*Sqrt[-a + x]*EllipticE[ArcCot[Sqrt[-a + x]/Sqrt[a - b]]/2, 2])/(Sqrt[a - b]*((a - x)*(b - x))^(1/4)) + (12*Sqrt[a - b]*(1 - (a - b)/(a - x))^(1/4)*Sqrt[-a + x]*EllipticE[ArcCot[Sqrt[-a + x]/Sqrt[a - b]]/2, 2])/((a - x)*(b - x))^(1/4) + (8*a*d*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(1/4)*(-(a*(1 - b/a)*d) - d*x^4 + x^12)), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(1/4) + (8*d*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^6/((a - b + x^4)^(1/4)*(-(a*(1 - b/a)*d) - d*x^4 + x^12)), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(1/4) - (4*(a - 3*b)*d*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(1/4)*(a*(1 - b/a)*d + x^4*(d - x^8))), x], x, (-a + x)^(1/4)])/((a - x)*(b - x))^(1/4)","F",0,0,0,0,-1,"{}"
1639,0,0,0,38.5743132,"\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","Int[(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,"(4*(3 + d^2*k^3 - 3*d*k*(1 + k))*(1 - x)^(1/4)*x*(1 - k*x)^(1/4)*AppellF1[3/4, 5/4, 5/4, 7/4, x, k*x])/(3*((1 - x)*x*(1 - k*x))^(1/4)) - (4*(2 + 2*k - d*k^2)*(1 - x)^(1/4)*x^2*(1 - k*x)^(1/4)*AppellF1[7/4, 5/4, 5/4, 11/4, x, k*x])/(7*((1 - x)*x*(1 - k*x))^(1/4)) + (4*k*(1 - x)^(1/4)*x^3*(1 - k*x)^(1/4)*AppellF1[11/4, 5/4, 5/4, 15/4, x, k*x])/(11*((1 - x)*x*(1 - k*x))^(1/4)) - (4*d*(3 + d^2*k^3 - 3*d*k*(1 + k))*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^2/((1 - x^4)^(5/4)*(1 - k*x^4)^(5/4)*(d - d*(1 + k)*x^4 + d*k*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (4*d*(5 + (5 - 3*d)*k - 7*d*k^2 - (3 - d)*d*k^3 + d^2*k^4)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^6/((1 - x^4)^(5/4)*(1 - k*x^4)^(5/4)*(d - d*(1 + k)*x^4 + d*k*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) - (4*d*(2 + 8*k + (2 - 4*d)*k^2 - 4*d*k^3 + d^2*k^4)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][x^10/((1 - x^4)^(5/4)*(1 - k*x^4)^(5/4)*(d - d*(1 + k)*x^4 + d*k*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4)","F",0,0,0,0,-1,"{}"
1640,1,123,0,0.1429567,"\int \frac{\left(2+x^3\right) \left(1+2 x^3\right)^{2/3}}{x^6 \left(1+x^3\right)} \, dx","Int[((2 + x^3)*(1 + 2*x^3)^(2/3))/(x^6*(1 + x^3)),x]","\frac{1}{3} \log \left(1-\frac{x}{\sqrt[3]{2 x^3+1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{2 x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2 \left(2 x^3+1\right)^{2/3}}{5 x^5}-\frac{3 \left(2 x^3+1\right)^{2/3}}{10 x^2}-\frac{1}{6} \log \left(\frac{x}{\sqrt[3]{2 x^3+1}}+\frac{x^2}{\left(2 x^3+1\right)^{2/3}}+1\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,"(-2*(1 + 2*x^3)^(2/3))/(5*x^5) - (3*(1 + 2*x^3)^(2/3))/(10*x^2) - ArcTan[(1 + (2*x)/(1 + 2*x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + Log[1 - x/(1 + 2*x^3)^(1/3)]/3 - Log[1 + x^2/(1 + 2*x^3)^(2/3) + x/(1 + 2*x^3)^(1/3)]/6","A",10,10,27,0.3704,1,"{580, 583, 12, 377, 200, 31, 634, 618, 204, 628}"
1641,0,0,0,17.4643411,"\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","Int[(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,"(12*a*b*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-b + x^4])/((-a + x^4)^(1/4)*(a*b^2*d - 2*a*b*(1 + b/(2*a))*d*x^4 + a*(1 + (2*b)/a)*d*x^8 + (1 - d)*x^12)), x], x, x^(1/4)])/(-((a - x)*(b - x)^2*x))^(1/4) - (4*(a + 2*b)*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^6*Sqrt[-b + x^4])/((-a + x^4)^(1/4)*(a*b^2*d - 2*a*b*(1 + b/(2*a))*d*x^4 + a*(1 + (2*b)/a)*d*x^8 + (1 - d)*x^12)), x], x, x^(1/4)])/(-((a - x)*(b - x)^2*x))^(1/4)","F",0,0,0,0,-1,"{}"
1642,1,198,0,0.28471,"\int \frac{(d+c x) \sqrt[4]{-b x^3+a x^4}}{x^2} \, dx","Int[((d + c*x)*(-(b*x^3) + a*x^4)^(1/4))/x^2,x]","\frac{x^{9/4} (a x-b)^{3/4} (b c-4 a d) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{2 a^{3/4} \left(a x^4-b x^3\right)^{3/4}}-\frac{x^{9/4} (a x-b)^{3/4} (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{2 a^{3/4} \left(a x^4-b x^3\right)^{3/4}}+\frac{\sqrt[4]{a x^4-b x^3} (b c-4 a d)}{b}+\frac{4 d \left(a x^4-b x^3\right)^{5/4}}{b x^4}","\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,"((b*c - 4*a*d)*(-(b*x^3) + a*x^4)^(1/4))/b + (4*d*(-(b*x^3) + a*x^4)^(5/4))/(b*x^4) + ((b*c - 4*a*d)*x^(9/4)*(-b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(2*a^(3/4)*(-(b*x^3) + a*x^4)^(3/4)) - ((b*c - 4*a*d)*x^(9/4)*(-b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(2*a^(3/4)*(-(b*x^3) + a*x^4)^(3/4))","A",8,8,25,0.3200,1,"{2038, 2021, 2032, 63, 331, 298, 203, 206}"
1643,0,0,0,1.1195175,"\int \frac{\left(3+x^5\right) \sqrt[3]{-2+x^3+x^5}}{x^2 \left(-2+x^5\right)} \, dx","Int[((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,"-1/2*Defer[Int][(-2 + x^3 + x^5)^(1/3)/(2^(1/5) - x), x]/2^(1/5) - (3*Defer[Int][(-2 + x^3 + x^5)^(1/3)/x^2, x])/2 - ((-1)^(2/5)*Defer[Int][(-2 + x^3 + x^5)^(1/3)/(2^(1/5) + (-1)^(1/5)*x), x])/(2*2^(1/5)) - ((-1)^(4/5)*Defer[Int][(-2 + x^3 + x^5)^(1/3)/(2^(1/5) - (-1)^(2/5)*x), x])/(2*2^(1/5)) + ((-1/2)^(1/5)*Defer[Int][(-2 + x^3 + x^5)^(1/3)/(2^(1/5) + (-1)^(3/5)*x), x])/2 + ((-1)^(3/5)*Defer[Int][(-2 + x^3 + x^5)^(1/3)/(2^(1/5) - (-1)^(4/5)*x), x])/(2*2^(1/5))","F",0,0,0,0,-1,"{}"
1644,0,0,0,1.1839725,"\int \frac{\left(-3+x^5\right) \left(2+x^3+x^5\right)^{2/3}}{x^3 \left(2+x^5\right)} \, dx","Int[((-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,"(-3*Defer[Int][(2 + x^3 + x^5)^(2/3)/x^3, x])/2 + Defer[Int][(2 + x^3 + x^5)^(2/3)/(2^(1/5) + x), x]/(2*2^(2/5)) - ((-1)^(3/5)*Defer[Int][(2 + x^3 + x^5)^(2/3)/(2^(1/5) - (-1)^(1/5)*x), x])/(2*2^(2/5)) - ((-1)^(1/5)*Defer[Int][(2 + x^3 + x^5)^(2/3)/(2^(1/5) + (-1)^(2/5)*x), x])/(2*2^(2/5)) + ((-1)^(4/5)*Defer[Int][(2 + x^3 + x^5)^(2/3)/(2^(1/5) - (-1)^(3/5)*x), x])/(2*2^(2/5)) + ((-1/2)^(2/5)*Defer[Int][(2 + x^3 + x^5)^(2/3)/(2^(1/5) + (-1)^(4/5)*x), x])/2","F",0,0,0,0,-1,"{}"
1645,1,119,0,0.0733274,"\int \frac{\sqrt[3]{-1+x^6} \left(1+x^6\right)}{x^9} \, dx","Int[((-1 + x^6)^(1/3)*(1 + x^6))/x^9,x]","\frac{\left(x^6-1\right)^{4/3}}{8 x^8}-\frac{\sqrt[3]{x^6-1}}{2 x^2}-\frac{1}{6} \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{12} \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\right)","\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,"-1/2*(-1 + x^6)^(1/3)/x^2 + (-1 + x^6)^(4/3)/(8*x^8) - ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - x^2/(-1 + x^6)^(1/3)]/6 + Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)]/12","A",10,10,18,0.5556,1,"{451, 275, 277, 331, 292, 31, 634, 618, 204, 628}"
1646,1,2286,0,4.3343466,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-2 b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-2*b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{b}-a x\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{b}-(-1)^{2/3} a x\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 - b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 + b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*b^(1/6)) - a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*b^(1/6) - a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*b^(1/6)) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*b^(1/6) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*b^(1/6)) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*b^(1/6) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 - b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 + b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,33,0.09091,0,"{2056, 6725, 91}"
1647,1,2286,0,3.314543,"\int \frac{1}{\sqrt[3]{b^2 x^2+a^3 x^3} \left(-2 b+a^6 x^6\right)} \, dx","Int[1/((b^2*x^2 + a^3*x^3)^(1/3)*(-2*b + a^6*x^6)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2\ 2^{17/18} \sqrt{3} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-a x-\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{b}-a x\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x-\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} a x+\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} a x-\sqrt[6]{2} \sqrt[6]{b}\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[6]{2} \sqrt[6]{b}-(-1)^{2/3} a x\right)}{12\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+\sqrt[3]{-1} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2-(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[18]{2} \sqrt[3]{x a^3+b^2}}{\sqrt[3]{a} \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}}}-\sqrt[3]{x}\right)}{4\ 2^{17/18} \sqrt[3]{a} b \sqrt[3]{\sqrt[6]{2} a^2+(-1)^{2/3} b^{11/6}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 - b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 + b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/18)*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*x^(1/3))])/(2*2^(17/18)*Sqrt[3]*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*b^(1/6)) - a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*b^(1/6) - a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*b^(1/6)) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*b^(1/6) + (-1)^(1/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-(2^(1/6)*b^(1/6)) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[2^(1/6)*b^(1/6) - (-1)^(2/3)*a*x])/(12*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 - b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 + b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(1/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 - (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (2^(1/18)*(b^2 + a^3*x)^(1/3))/(a^(1/3)*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3))])/(4*2^(17/18)*a^(1/3)*b*(2^(1/6)*a^2 + (-1)^(2/3)*b^(11/6))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,3,33,0.09091,0,"{2056, 6725, 91}"
1648,1,121,0,0.0570704,"\int \frac{1}{\sqrt[4]{-1-3 x^4-2 x^8+2 x^{12}+3 x^{16}+x^{20}}} \, dx","Int[(-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) \tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-\left(\left(1-x^4\right) \left(x^4+1\right)^4\right)}}+\frac{\sqrt[4]{x^4-1} \left(x^4+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{-\left(\left(1-x^4\right) \left(x^4+1\right)^4\right)}}","\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)])/(2*2^(1/4)*(-((1 - x^4)*(1 + x^4)^4))^(1/4)) + ((-1 + x^4)^(1/4)*(1 + x^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",6,6,29,0.2069,1,"{6688, 6719, 377, 212, 206, 203}"
1649,1,138,0,0.4694976,"\int \frac{1+x^2}{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[(1 + x^2)/(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","-\frac{8 \left(b-3 c^2\right) \left(\sqrt{a x+b}+c\right)^{5/2}}{5 a^3}+\frac{16 c \left(b-c^2\right) \left(\sqrt{a x+b}+c\right)^{3/2}}{3 a^3}+\frac{4 \left(\sqrt{a x+b}+c\right)^{9/2}}{9 a^3}-\frac{16 c \left(\sqrt{a x+b}+c\right)^{7/2}}{7 a^3}+\frac{4 \left(a^2+\left(b-c^2\right)^2\right) \sqrt{\sqrt{a x+b}+c}}{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*(a^2 + (b - c^2)^2)*Sqrt[c + Sqrt[b + a*x]])/a^3 + (16*c*(b - c^2)*(c + Sqrt[b + a*x])^(3/2))/(3*a^3) - (8*(b - 3*c^2)*(c + Sqrt[b + a*x])^(5/2))/(5*a^3) - (16*c*(c + Sqrt[b + a*x])^(7/2))/(7*a^3) + (4*(c + Sqrt[b + a*x])^(9/2))/(9*a^3)","A",3,1,30,0.03333,1,"{1850}"
1650,1,93,0,0.3533269,"\int \frac{x^2}{\sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Int[x^2/(Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)),x]","-\frac{b^2}{9 a^3 \left(\sqrt{a^2 x^2-b}+a x\right)^{9/4}}-\frac{2 b}{a^3 \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}+\frac{\left(\sqrt{a^2 x^2-b}+a x\right)^{7/4}}{7 a^3}","\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,"-1/9*b^2/(a^3*(a*x + Sqrt[-b + a^2*x^2])^(9/4)) - (2*b)/(a^3*(a*x + Sqrt[-b + a^2*x^2])^(1/4)) + (a*x + Sqrt[-b + a^2*x^2])^(7/4)/(7*a^3)","A",3,2,42,0.04762,1,"{2120, 270}"
1651,1,204,0,0.187467,"\int x^2 \sqrt[3]{-x+x^3} \, dx","Int[x^2*(-x + x^3)^(1/3),x]","\frac{1}{4} \sqrt[3]{x^3-x} x^3-\frac{1}{12} \sqrt[3]{x^3-x} x+\frac{\left(x^2-1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{18 \left(x^3-x\right)^{2/3}}-\frac{\left(x^2-1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{36 \left(x^3-x\right)^{2/3}}+\frac{\left(x^2-1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{6 \sqrt{3} \left(x^3-x\right)^{2/3}}","\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,"-1/12*(x*(-x + x^3)^(1/3)) + (x^3*(-x + x^3)^(1/3))/4 + (x^(2/3)*(-1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(6*Sqrt[3]*(-x + x^3)^(2/3)) + (x^(2/3)*(-1 + x^2)^(2/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(18*(-x + x^3)^(2/3)) - (x^(2/3)*(-1 + x^2)^(2/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(36*(-x + x^3)^(2/3))","A",12,12,15,0.8000,1,"{2021, 2024, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1652,1,226,0,0.2432479,"\int x^6 \sqrt[3]{x+x^3} \, dx","Int[x^6*(x + x^3)^(1/3),x]","-\frac{1}{54} \sqrt[3]{x^3+x} x^3+\frac{5}{162} \sqrt[3]{x^3+x} x+\frac{1}{8} \sqrt[3]{x^3+x} x^7+\frac{1}{72} \sqrt[3]{x^3+x} x^5+\frac{5 \left(x^2+1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{243 \left(x^3+x\right)^{2/3}}-\frac{5 \left(x^2+1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{486 \left(x^3+x\right)^{2/3}}+\frac{5 \left(x^2+1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} \left(x^3+x\right)^{2/3}}","\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,"(5*x*(x + x^3)^(1/3))/162 - (x^3*(x + x^3)^(1/3))/54 + (x^5*(x + x^3)^(1/3))/72 + (x^7*(x + x^3)^(1/3))/8 + (5*x^(2/3)*(1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(81*Sqrt[3]*(x + x^3)^(2/3)) + (5*x^(2/3)*(1 + x^2)^(2/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(243*(x + x^3)^(2/3)) - (5*x^(2/3)*(1 + x^2)^(2/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(486*(x + x^3)^(2/3))","B",14,12,13,0.9231,1,"{2021, 2024, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1653,1,153,0,0.1428647,"\int \frac{-3+2 x}{x \sqrt[4]{-1+x^4}} \, dx","Int[(-3 + 2*x)/(x*(-1 + x^4)^(1/4)),x]","-\frac{3 \log \left(\sqrt{x^4-1}-\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}+\frac{3 \log \left(\sqrt{x^4-1}+\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}+\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)+\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^4-1}\right)}{2 \sqrt{2}}-\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{2 \sqrt{2}}+\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)] + (3*ArcTan[1 - Sqrt[2]*(-1 + x^4)^(1/4)])/(2*Sqrt[2]) - (3*ArcTan[1 + Sqrt[2]*(-1 + x^4)^(1/4)])/(2*Sqrt[2]) + ArcTanh[x/(-1 + x^4)^(1/4)] - (3*Log[1 - Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]])/(4*Sqrt[2]) + (3*Log[1 + Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]])/(4*Sqrt[2])","A",17,13,18,0.7222,1,"{1833, 240, 212, 206, 203, 266, 63, 297, 1162, 617, 204, 1165, 628}"
1654,0,0,0,1.1831812,"\int \frac{\sqrt[3]{-1+x^3-x^4} \left(-3+x^4\right)}{x^2 \left(1+x^4\right)} \, dx","Int[((-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,"(-1)^(3/4)*Defer[Int][(-1 + x^3 - x^4)^(1/3)/((-1)^(1/4) - x), x] - (-1)^(1/4)*Defer[Int][(-1 + x^3 - x^4)^(1/3)/(-(-1)^(3/4) - x), x] - 3*Defer[Int][(-1 + x^3 - x^4)^(1/3)/x^2, x] + (-1)^(3/4)*Defer[Int][(-1 + x^3 - x^4)^(1/3)/((-1)^(1/4) + x), x] - (-1)^(1/4)*Defer[Int][(-1 + x^3 - x^4)^(1/3)/(-(-1)^(3/4) + x), x]","F",0,0,0,0,-1,"{}"
1655,1,149,0,0.2550988,"\int \frac{x^3 \sqrt{-x+x^4}}{-b+a x^3} \, dx","Int[(x^3*Sqrt[-x + x^4])/(-b + a*x^3),x]","\frac{2 \sqrt{b} \sqrt{x^4-x} \sqrt{a-b} \tan ^{-1}\left(\frac{x^{3/2} \sqrt{a-b}}{\sqrt{b} \sqrt{x^3-1}}\right)}{3 a^2 \sqrt{x^3-1} \sqrt{x}}-\frac{\sqrt{x^4-x} (a-2 b) \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)}{3 a^2 \sqrt{x^3-1} \sqrt{x}}+\frac{\sqrt{x^4-x} x}{3 a}","\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*Sqrt[-x + x^4])/(3*a) + (2*Sqrt[a - b]*Sqrt[b]*Sqrt[-x + x^4]*ArcTan[(Sqrt[a - b]*x^(3/2))/(Sqrt[b]*Sqrt[-1 + x^3])])/(3*a^2*Sqrt[x]*Sqrt[-1 + x^3]) - ((a - 2*b)*Sqrt[-x + x^4]*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]])/(3*a^2*Sqrt[x]*Sqrt[-1 + x^3])","A",9,9,26,0.3462,1,"{2042, 466, 465, 478, 523, 217, 206, 377, 205}"
1656,1,211,0,0.6250713,"\int \frac{1+2 x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^4}} \, dx","Int[(1 + 2*x^4)/((-1 + x^4)*(x^2 + x^4)^(1/4)),x]","-\frac{3 x}{\sqrt[4]{x^4+x^2}}+\frac{2 \sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{\sqrt[4]{x^4+x^2}}-\frac{3 \sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4+x^2}}+\frac{2 \sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{\sqrt[4]{x^4+x^2}}-\frac{3 \sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2 \sqrt[4]{2} \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,"(-3*x)/(x^2 + x^4)^(1/4) + (2*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(1 + x^2)^(1/4)])/(x^2 + x^4)^(1/4) - (3*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(1/4)*(x^2 + x^4)^(1/4)) + (2*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(1 + x^2)^(1/4)])/(x^2 + x^4)^(1/4) - (3*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(1/4)*(x^2 + x^4)^(1/4))","A",14,10,26,0.3846,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1404, 382, 377}"
1657,1,55,0,0.3667155,"\int \frac{b+a x^2}{x^2 \left(-b+a x^2\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + a*x^2)/(x^2*(-b + a*x^2)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 \left(a x^2+b\right) \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\frac{2 a x^2}{a x^2+b}\right)}{3 b x \sqrt[4]{a x^4+b x^2}}","-\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*(b + a*x^2)*Hypergeometric2F1[-3/4, 1, 1/4, (2*a*x^2)/(b + a*x^2)])/(3*b*x*(b*x^2 + a*x^4)^(1/4))","C",4,4,37,0.1081,1,"{2056, 466, 511, 510}"
1658,1,196,0,0.2761702,"\int x \sqrt[4]{b x^3+a x^4} \, dx","Int[x*(b*x^3 + a*x^4)^(1/4),x]","-\frac{7 b^3 x^{9/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{64 a^{11/4} \left(a x^4+b x^3\right)^{3/4}}+\frac{7 b^3 x^{9/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{64 a^{11/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{7 b^2 \sqrt[4]{a x^4+b x^3}}{96 a^2}+\frac{b x \sqrt[4]{a x^4+b x^3}}{24 a}+\frac{1}{3} x^2 \sqrt[4]{a x^4+b x^3}","-\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,"(-7*b^2*(b*x^3 + a*x^4)^(1/4))/(96*a^2) + (b*x*(b*x^3 + a*x^4)^(1/4))/(24*a) + (x^2*(b*x^3 + a*x^4)^(1/4))/3 - (7*b^3*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(64*a^(11/4)*(b*x^3 + a*x^4)^(3/4)) + (7*b^3*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(64*a^(11/4)*(b*x^3 + a*x^4)^(3/4))","A",9,8,17,0.4706,1,"{2021, 2024, 2032, 63, 331, 298, 203, 206}"
1659,0,0,0,1.6158906,"\int \frac{-2 b+a x^3}{\left(b+x^2+a x^3\right) \sqrt[4]{b x^2+a x^5}} \, dx","Int[(-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,"(2*x*(1 + (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/6, 1/4, 7/6, -((a*x^3)/b)])/(b*x^2 + a*x^5)^(1/4) - (6*b*Sqrt[x]*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][1/((b + a*x^6)^(1/4)*(b + x^4 + a*x^6)), x], x, Sqrt[x]])/(b*x^2 + a*x^5)^(1/4) - (2*Sqrt[x]*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^4/((b + a*x^6)^(1/4)*(b + x^4 + a*x^6)), x], x, Sqrt[x]])/(b*x^2 + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
1660,1,392,0,1.9609252,"\int \frac{-b+a x^2}{\left(b+x+a x^2\right) \sqrt[4]{b x^3+a x^5}} \, dx","Int[(-b + a*x^2)/((b + x + a*x^2)*(b*x^3 + a*x^5)^(1/4)),x]","\frac{8 a x^2 \sqrt[4]{\frac{a x^2}{b}+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{4 a^2 x^2}{\left(1-\sqrt{1-4 a b}\right)^2},-\frac{a x^2}{b}\right)}{5 \left(1-\sqrt{1-4 a b}\right) \sqrt[4]{a x^5+b x^3}}+\frac{8 a x^2 \sqrt[4]{\frac{a x^2}{b}+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{4 a^2 x^2}{\left(\sqrt{1-4 a b}+1\right)^2},-\frac{a x^2}{b}\right)}{5 \left(\sqrt{1-4 a b}+1\right) \sqrt[4]{a x^5+b x^3}}-\frac{4 x \sqrt[4]{\frac{a x^2}{b}+1} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{4 a^2 x^2}{\left(1-\sqrt{1-4 a b}\right)^2},-\frac{a x^2}{b}\right)}{\sqrt[4]{a x^5+b x^3}}-\frac{4 x \sqrt[4]{\frac{a x^2}{b}+1} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{4 a^2 x^2}{\left(\sqrt{1-4 a b}+1\right)^2},-\frac{a x^2}{b}\right)}{\sqrt[4]{a x^5+b x^3}}+\frac{4 x \sqrt[4]{\frac{a x^2}{b}+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-\frac{a x^2}{b}\right)}{\sqrt[4]{a x^5+b x^3}}","-\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,"(-4*x*(1 + (a*x^2)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (4*a^2*x^2)/(1 - Sqrt[1 - 4*a*b])^2, -((a*x^2)/b)])/(b*x^3 + a*x^5)^(1/4) - (4*x*(1 + (a*x^2)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (4*a^2*x^2)/(1 + Sqrt[1 - 4*a*b])^2, -((a*x^2)/b)])/(b*x^3 + a*x^5)^(1/4) + (8*a*x^2*(1 + (a*x^2)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (4*a^2*x^2)/(1 - Sqrt[1 - 4*a*b])^2, -((a*x^2)/b)])/(5*(1 - Sqrt[1 - 4*a*b])*(b*x^3 + a*x^5)^(1/4)) + (8*a*x^2*(1 + (a*x^2)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (4*a^2*x^2)/(1 + Sqrt[1 - 4*a*b])^2, -((a*x^2)/b)])/(5*(1 + Sqrt[1 - 4*a*b])*(b*x^3 + a*x^5)^(1/4)) + (4*x*(1 + (a*x^2)/b)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -((a*x^2)/b)])/(b*x^3 + a*x^5)^(1/4)","C",21,10,35,0.2857,0,"{2056, 6728, 365, 364, 959, 466, 430, 429, 511, 510}"
1661,1,85,0,0.0403152,"\int \frac{x^{13}}{\sqrt[3]{-1+x^6}} \, dx","Int[x^13/(-1 + x^6)^(1/3),x]","\frac{1}{12} \left(x^6-1\right)^{2/3} x^8+\frac{1}{9} \left(x^6-1\right)^{2/3} x^2-\frac{1}{18} \log \left(x^2-\sqrt[3]{x^6-1}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}","-\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,"(x^2*(-1 + x^6)^(2/3))/9 + (x^8*(-1 + x^6)^(2/3))/12 + ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) - Log[x^2 - (-1 + x^6)^(1/3)]/18","A",4,3,13,0.2308,1,"{275, 321, 239}"
1662,1,119,0,0.0864721,"\int x^9 \sqrt[3]{-1+x^6} \, dx","Int[x^9*(-1 + x^6)^(1/3),x]","\frac{1}{12} \sqrt[3]{x^6-1} x^{10}-\frac{1}{36} \sqrt[3]{x^6-1} x^4+\frac{1}{54} \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{18 \sqrt{3}}-\frac{1}{108} \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\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,"-1/36*(x^4*(-1 + x^6)^(1/3)) + (x^10*(-1 + x^6)^(1/3))/12 + ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(18*Sqrt[3]) + Log[1 - x^2/(-1 + x^6)^(1/3)]/54 - Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)]/108","A",10,10,13,0.7692,1,"{275, 279, 321, 331, 292, 31, 634, 618, 204, 628}"
1663,1,85,0,0.0388034,"\int x^7 \left(-1+x^6\right)^{2/3} \, dx","Int[x^7*(-1 + x^6)^(2/3),x]","\frac{1}{12} \left(x^6-1\right)^{2/3} x^8-\frac{1}{18} \left(x^6-1\right)^{2/3} x^2+\frac{1}{36} \log \left(x^2-\sqrt[3]{x^6-1}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{18 \sqrt{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,"-1/18*(x^2*(-1 + x^6)^(2/3)) + (x^8*(-1 + x^6)^(2/3))/12 - ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]]/(18*Sqrt[3]) + Log[x^2 - (-1 + x^6)^(1/3)]/36","A",4,4,13,0.3077,1,"{275, 279, 321, 239}"
1664,1,85,0,0.0428338,"\int \frac{x^{13}}{\sqrt[3]{1+x^6}} \, dx","Int[x^13/(1 + x^6)^(1/3),x]","\frac{1}{12} \left(x^6+1\right)^{2/3} x^8-\frac{1}{9} \left(x^6+1\right)^{2/3} x^2-\frac{1}{18} \log \left(x^2-\sqrt[3]{x^6+1}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}","-\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,"-1/9*(x^2*(1 + x^6)^(2/3)) + (x^8*(1 + x^6)^(2/3))/12 + ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) - Log[x^2 - (1 + x^6)^(1/3)]/18","A",4,3,13,0.2308,1,"{275, 321, 239}"
1665,1,85,0,0.0365698,"\int x^7 \left(1+x^6\right)^{2/3} \, dx","Int[x^7*(1 + x^6)^(2/3),x]","\frac{1}{12} \left(x^6+1\right)^{2/3} x^8+\frac{1}{18} \left(x^6+1\right)^{2/3} x^2+\frac{1}{36} \log \left(x^2-\sqrt[3]{x^6+1}\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{18 \sqrt{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))/18 + (x^8*(1 + x^6)^(2/3))/12 - ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]]/(18*Sqrt[3]) + Log[x^2 - (1 + x^6)^(1/3)]/36","A",4,4,13,0.3077,1,"{275, 279, 321, 239}"
1666,0,0,0,1.2998924,"\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","Int[((1 + x^3)^(2/3)*(4 + x^3))/(x^6*(8 - 4*x^3 + x^6)),x]","\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","\frac{1}{96} \text{RootSum}\left[8 \text{$\#$1}^6-20 \text{$\#$1}^3+13\&,\frac{-32 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+32 \text{$\#$1}^3 \log (x)+39 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-39 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-3*(1 + x^3)^(2/3))/(16*x^2) - (1 + x^3)^(5/3)/(10*x^5) + (Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/8 - (3*Log[-x + (1 + x^3)^(1/3)])/16 + (1/48 - I/16)*Defer[Int][(1 + x^3)^(2/3)/((2 - 2*I) + 2*x), x] + (1/48 + I/16)*Defer[Int][(1 + x^3)^(2/3)/((2 + 2*I) + 2*x), x] + Defer[Int][(1 + x^3)^(2/3)/(4 - 4*x + 2*x^2 - 2*x^3 + x^4), x]/3 - (5*Defer[Int][(x*(1 + x^3)^(2/3))/(4 - 4*x + 2*x^2 - 2*x^3 + x^4), x])/24 - Defer[Int][(x^3*(1 + x^3)^(2/3))/(4 - 4*x + 2*x^2 - 2*x^3 + x^4), x]/48","F",0,0,0,0,-1,"{}"
1667,0,0,0,1.066876,"\int \frac{\left(1+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(8-4 x^3+x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(4 + x^3))/(x^6*(8 - 4*x^3 + x^6)),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(8-4 x^3+x^6\right)} \, dx","\frac{1}{96} \text{RootSum}\left[8 \text{$\#$1}^6-20 \text{$\#$1}^3+13\&,\frac{-32 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+32 \text{$\#$1}^3 \log (x)+39 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-39 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-3*(1 + x^3)^(2/3))/(16*x^2) - (1 + x^3)^(5/3)/(10*x^5) + (Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/8 - (3*Log[-x + (1 + x^3)^(1/3)])/16 + (1/48 - I/16)*Defer[Int][(1 + x^3)^(2/3)/((2 - 2*I) + 2*x), x] + (1/48 + I/16)*Defer[Int][(1 + x^3)^(2/3)/((2 + 2*I) + 2*x), x] + Defer[Int][(1 + x^3)^(2/3)/(4 - 4*x + 2*x^2 - 2*x^3 + x^4), x]/3 - (5*Defer[Int][(x*(1 + x^3)^(2/3))/(4 - 4*x + 2*x^2 - 2*x^3 + x^4), x])/24 - Defer[Int][(x^3*(1 + x^3)^(2/3))/(4 - 4*x + 2*x^2 - 2*x^3 + x^4), x]/48","F",0,0,0,0,-1,"{}"
1668,1,203,0,0.8545108,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right) \left(4+3 x^3\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^3)*(4 + 3*x^3))/(x^6*(4 + 2*x^3 + x^6)),x]","-\frac{\left(\sqrt{3}+9 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{x^3}{1-i \sqrt{3}}\right)}{12 \left(\sqrt{3}+i\right)}-\frac{\left(-\sqrt{3}+9 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{x^3}{1+i \sqrt{3}}\right)}{12 \left(-\sqrt{3}+i\right)}-\frac{3}{4} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)-\frac{2 \left(x^3+1\right)^{5/3}}{5 x^5}-\frac{3 \left(x^3+1\right)^{2/3}}{4 x^2}","\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-8 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+8 \text{$\#$1}^3 \log (x)+9 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-9 \log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{20 x^5}",1,"(-3*(1 + x^3)^(2/3))/(4*x^2) - (2*(1 + x^3)^(5/3))/(5*x^5) - ((9*I + Sqrt[3])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(x^3/(1 - I*Sqrt[3]))])/(12*(I + Sqrt[3])) - ((9*I - Sqrt[3])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(x^3/(1 + I*Sqrt[3]))])/(12*(I - Sqrt[3])) + (Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/2 - (3*Log[-x + (1 + x^3)^(1/3)])/4","C",9,5,37,0.1351,0,"{6728, 264, 277, 239, 429}"
1669,1,203,0,0.7776333,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right) \left(4+3 x^3\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^3)*(4 + 3*x^3))/(x^6*(4 + 2*x^3 + x^6)),x]","-\frac{\left(\sqrt{3}+9 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{x^3}{1-i \sqrt{3}}\right)}{12 \left(\sqrt{3}+i\right)}-\frac{\left(-\sqrt{3}+9 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{x^3}{1+i \sqrt{3}}\right)}{12 \left(-\sqrt{3}+i\right)}-\frac{3}{4} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)-\frac{2 \left(x^3+1\right)^{5/3}}{5 x^5}-\frac{3 \left(x^3+1\right)^{2/3}}{4 x^2}","\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-8 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+8 \text{$\#$1}^3 \log (x)+9 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-9 \log (x)}{4 \text{$\#$1}^4-3 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{20 x^5}",1,"(-3*(1 + x^3)^(2/3))/(4*x^2) - (2*(1 + x^3)^(5/3))/(5*x^5) - ((9*I + Sqrt[3])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(x^3/(1 - I*Sqrt[3]))])/(12*(I + Sqrt[3])) - ((9*I - Sqrt[3])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -(x^3/(1 + I*Sqrt[3]))])/(12*(I - Sqrt[3])) + (Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/2 - (3*Log[-x + (1 + x^3)^(1/3)])/4","C",9,5,37,0.1351,0,"{6728, 264, 277, 239, 429}"
1670,1,239,0,0.5818436,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^6\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(4 + x^6))/(x^6*(4 + 2*x^3 + x^6)),x]","\frac{\left(\sqrt{3}+3 i\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{1-i \sqrt{3}}\right)}{12 \left(\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{\left(-\sqrt{3}+3 i\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{1+i \sqrt{3}}\right)}{12 \left(-\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{1}{4} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}+\frac{\left(x^3-1\right)^{2/3}}{4 x^2}","\frac{\left(x^3-1\right)^{2/3} \left(9 x^3-4\right)}{20 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(4*x^2) + (-1 + x^3)^(5/3)/(5*x^5) + ((3*I + Sqrt[3])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -(x^3/(1 - I*Sqrt[3]))])/(12*(I + Sqrt[3])*(1 - x^3)^(2/3)) + ((3*I - Sqrt[3])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -(x^3/(1 + I*Sqrt[3]))])/(12*(I - Sqrt[3])*(1 - x^3)^(2/3)) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/4","C",11,6,30,0.2000,0,"{6728, 264, 277, 239, 430, 429}"
1671,1,239,0,0.5159003,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^6\right)}{x^6 \left(4+2 x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(4 + x^6))/(x^6*(4 + 2*x^3 + x^6)),x]","\frac{\left(\sqrt{3}+3 i\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{1-i \sqrt{3}}\right)}{12 \left(\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{\left(-\sqrt{3}+3 i\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{1+i \sqrt{3}}\right)}{12 \left(-\sqrt{3}+i\right) \left(1-x^3\right)^{2/3}}+\frac{1}{4} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}+\frac{\left(x^3-1\right)^{2/3}}{4 x^2}","\frac{\left(x^3-1\right)^{2/3} \left(9 x^3-4\right)}{20 x^5}-\frac{1}{12} \text{RootSum}\left[4 \text{$\#$1}^6-10 \text{$\#$1}^3+7\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+7 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-7 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]",1,"(-1 + x^3)^(2/3)/(4*x^2) + (-1 + x^3)^(5/3)/(5*x^5) + ((3*I + Sqrt[3])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -(x^3/(1 - I*Sqrt[3]))])/(12*(I + Sqrt[3])*(1 - x^3)^(2/3)) + ((3*I - Sqrt[3])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -(x^3/(1 + I*Sqrt[3]))])/(12*(I - Sqrt[3])*(1 - x^3)^(2/3)) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/4","C",11,6,30,0.2000,0,"{6728, 264, 277, 239, 430, 429}"
1672,1,227,0,0.6890103,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-x^3+x^6\right)}{x^6 \left(-2-x^3+2 x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(1 - x^3 + x^6))/(x^6*(-2 - x^3 + 2*x^6)),x]","\frac{\left(51+19 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{4 x^3}{1-\sqrt{17}}\right)}{34 \left(1-\sqrt{17}\right) \left(1-x^3\right)^{2/3}}+\frac{\left(51-19 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{4 x^3}{1+\sqrt{17}}\right)}{34 \left(1+\sqrt{17}\right) \left(1-x^3\right)^{2/3}}-\frac{3}{8} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}-\frac{3 \left(x^3-1\right)^{2/3}}{8 x^2}","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+1\&,\frac{-17 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+17 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-3 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(4-19 x^3\right)}{40 x^5}",1,"(-3*(-1 + x^3)^(2/3))/(8*x^2) - (-1 + x^3)^(5/3)/(10*x^5) + ((51 + 19*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (4*x^3)/(1 - Sqrt[17])])/(34*(1 - Sqrt[17])*(1 - x^3)^(2/3)) + ((51 - 19*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (4*x^3)/(1 + Sqrt[17])])/(34*(1 + Sqrt[17])*(1 - x^3)^(2/3)) + (Sqrt[3]*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/4 - (3*Log[-x + (-1 + x^3)^(1/3)])/8","B",11,6,37,0.1622,0,"{6728, 264, 277, 239, 430, 429}"
1673,1,227,0,0.6083945,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1-x^3+x^6\right)}{x^6 \left(-2-x^3+2 x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(1 - x^3 + x^6))/(x^6*(-2 - x^3 + 2*x^6)),x]","\frac{\left(51+19 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{4 x^3}{1-\sqrt{17}}\right)}{34 \left(1-\sqrt{17}\right) \left(1-x^3\right)^{2/3}}+\frac{\left(51-19 \sqrt{17}\right) x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{4 x^3}{1+\sqrt{17}}\right)}{34 \left(1+\sqrt{17}\right) \left(1-x^3\right)^{2/3}}-\frac{3}{8} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)-\frac{\left(x^3-1\right)^{5/3}}{10 x^5}-\frac{3 \left(x^3-1\right)^{2/3}}{8 x^2}","\frac{1}{12} \text{RootSum}\left[2 \text{$\#$1}^6-5 \text{$\#$1}^3+1\&,\frac{-17 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)+17 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^3-1}-\text{$\#$1} x\right)-3 \log (x)}{4 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3-1\right)^{2/3} \left(4-19 x^3\right)}{40 x^5}",1,"(-3*(-1 + x^3)^(2/3))/(8*x^2) - (-1 + x^3)^(5/3)/(10*x^5) + ((51 + 19*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (4*x^3)/(1 - Sqrt[17])])/(34*(1 - Sqrt[17])*(1 - x^3)^(2/3)) + ((51 - 19*Sqrt[17])*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (4*x^3)/(1 + Sqrt[17])])/(34*(1 + Sqrt[17])*(1 - x^3)^(2/3)) + (Sqrt[3]*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/4 - (3*Log[-x + (-1 + x^3)^(1/3)])/8","B",11,6,37,0.1622,0,"{6728, 264, 277, 239, 430, 429}"
1674,1,203,0,0.6621192,"\int \frac{\left(1+x^3\right)^{2/3} \left(4+6 x^3+3 x^6\right)}{x^6 \left(8+6 x^3+3 x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(4 + 6*x^3 + 3*x^6))/(x^6*(8 + 6*x^3 + 3*x^6)),x]","-\frac{3 \left(-\sqrt{15}+15 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{3 x^3}{3-i \sqrt{15}}\right)}{80 \left(\sqrt{15}+3 i\right)}-\frac{3 \left(\sqrt{15}+15 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{3 x^3}{3+i \sqrt{15}}\right)}{80 \left(-\sqrt{15}+3 i\right)}-\frac{3}{16} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{1}{8} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)-\frac{\left(x^3+1\right)^{5/3}}{10 x^5}-\frac{3 \left(x^3+1\right)^{2/3}}{16 x^2}","\frac{1}{16} \text{RootSum}\left[8 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-5 \log (x)}{8 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-3*(1 + x^3)^(2/3))/(16*x^2) - (1 + x^3)^(5/3)/(10*x^5) - (3*(15*I - Sqrt[15])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-3*x^3)/(3 - I*Sqrt[15])])/(80*(3*I + Sqrt[15])) - (3*(15*I + Sqrt[15])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-3*x^3)/(3 + I*Sqrt[15])])/(80*(3*I - Sqrt[15])) + (Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/8 - (3*Log[-x + (1 + x^3)^(1/3)])/16","C",9,5,39,0.1282,0,"{6728, 264, 277, 239, 429}"
1675,1,203,0,0.555055,"\int \frac{\left(1+x^3\right)^{2/3} \left(4+6 x^3+3 x^6\right)}{x^6 \left(8+6 x^3+3 x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(4 + 6*x^3 + 3*x^6))/(x^6*(8 + 6*x^3 + 3*x^6)),x]","-\frac{3 \left(-\sqrt{15}+15 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{3 x^3}{3-i \sqrt{15}}\right)}{80 \left(\sqrt{15}+3 i\right)}-\frac{3 \left(\sqrt{15}+15 i\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{3 x^3}{3+i \sqrt{15}}\right)}{80 \left(-\sqrt{15}+3 i\right)}-\frac{3}{16} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{1}{8} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)-\frac{\left(x^3+1\right)^{5/3}}{10 x^5}-\frac{3 \left(x^3+1\right)^{2/3}}{16 x^2}","\frac{1}{16} \text{RootSum}\left[8 \text{$\#$1}^6-10 \text{$\#$1}^3+5\&,\frac{-6 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)+6 \text{$\#$1}^3 \log (x)+5 \log \left(\sqrt[3]{x^3+1}-\text{$\#$1} x\right)-5 \log (x)}{8 \text{$\#$1}^4-5 \text{$\#$1}}\&\right]+\frac{\left(x^3+1\right)^{2/3} \left(-23 x^3-8\right)}{80 x^5}",1,"(-3*(1 + x^3)^(2/3))/(16*x^2) - (1 + x^3)^(5/3)/(10*x^5) - (3*(15*I - Sqrt[15])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-3*x^3)/(3 - I*Sqrt[15])])/(80*(3*I + Sqrt[15])) - (3*(15*I + Sqrt[15])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (-3*x^3)/(3 + I*Sqrt[15])])/(80*(3*I - Sqrt[15])) + (Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/8 - (3*Log[-x + (1 + x^3)^(1/3)])/16","C",9,5,39,0.1282,0,"{6728, 264, 277, 239, 429}"
1676,0,0,0,0.9947766,"\int \frac{\sqrt[3]{-1+2 x^3+x^8} \left(3+5 x^8\right)}{x^2 \left(-1+x^3+x^8\right)} \, dx","Int[((-1 + 2*x^3 + x^8)^(1/3)*(3 + 5*x^8))/(x^2*(-1 + x^3 + x^8)),x]","\int \frac{\sqrt[3]{-1+2 x^3+x^8} \left(3+5 x^8\right)}{x^2 \left(-1+x^3+x^8\right)} \, dx","\frac{3 \sqrt[3]{x^8+2 x^3-1}}{x}+\log \left(\sqrt[3]{x^8+2 x^3-1}-x\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^8+2 x^3-1}+x}\right)-\frac{1}{2} \log \left(x^2+\sqrt[3]{x^8+2 x^3-1} x+\left(x^8+2 x^3-1\right)^{2/3}\right)",1,"-3*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/x^2, x] + 3*Defer[Int][(x*(-1 + 2*x^3 + x^8)^(1/3))/(-1 + x^3 + x^8), x] + 8*Defer[Int][(x^6*(-1 + 2*x^3 + x^8)^(1/3))/(-1 + x^3 + x^8), x]","F",0,0,0,0,-1,"{}"
1677,0,0,0,0.9047627,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","Int[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^4),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}-\text{$\#$1}\right)}{\text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{2 \sqrt{x^2+1} x}{3 \sqrt{\sqrt{x^2+1}+1}}+\frac{4 x}{3 \sqrt{\sqrt{x^2+1}+1}}",1,"(2*x^3)/(3*(1 + Sqrt[1 + x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 + x^2]] - ((-1)^(1/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/((-1)^(1/4) - x), x])/2 + ((-1)^(3/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(-(-1)^(3/4) - x), x])/2 - ((-1)^(1/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/((-1)^(1/4) + x), x])/2 + ((-1)^(3/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(-(-1)^(3/4) + x), x])/2","F",0,0,0,0,-1,"{}"
1678,0,0,0,0.7257321,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","Int[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x^2]])/(1 + x^4),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\log \left(\frac{x}{\sqrt{\sqrt{x^2+1}+1}}-\text{$\#$1}\right)}{\text{$\#$1}^5+2 \text{$\#$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,"(2*x^3)/(3*(1 + Sqrt[1 + x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 + x^2]] - ((-1)^(1/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/((-1)^(1/4) - x), x])/2 + ((-1)^(3/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(-(-1)^(3/4) - x), x])/2 - ((-1)^(1/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/((-1)^(1/4) + x), x])/2 + ((-1)^(3/4)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(-(-1)^(3/4) + x), x])/2","F",0,0,0,0,-1,"{}"
1679,1,95,0,0.1349238,"\int \frac{\sqrt{b^2+a^2 x^2}}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[Sqrt[b^2 + a^2*x^2]/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","-\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}}{6 a}-\frac{b^4}{10 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}","\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,"-1/10*b^4/(a*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2)) - b^2/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(6*a)","A",3,2,39,0.05128,1,"{2122, 270}"
1680,1,3261,0,65.5182758,"\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","Int[(-2*a + b + x)/(((-a + x)*(-b + x)^2)^(1/4)*(b^2 + a*d - (2*b + d)*x + x^2)),x]","-\frac{\sqrt[4]{a-b} \left(1-\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}\right) \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{a-b}+\sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2}{4 \sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}};2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right) \left(\sqrt{2} \sqrt{a-b}-\sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2}{2 \sqrt{2} \sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}} \left(4 a-4 b-d+\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{a-b} \sqrt{\sqrt{d}-\sqrt{-4 a+4 b+d}} \sqrt{-\frac{b-x}{a-b}} \sqrt[4]{x-a} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{\sqrt{d}-\sqrt{-4 a+4 b+d}} \sqrt[4]{x-a}}{\sqrt[4]{2} \sqrt{a-b} \sqrt[4]{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt{-\frac{b-x}{a-b}}}\right)}{\sqrt[4]{2} d^{3/4} \sqrt[4]{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{a-b} \sqrt{\sqrt{-4 a+4 b+d}-\sqrt{d}} \sqrt{-\frac{b-x}{a-b}} \sqrt[4]{x-a} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{\sqrt{-4 a+4 b+d}-\sqrt{d}} \sqrt[4]{x-a}}{\sqrt[4]{2} \sqrt{a-b} \sqrt[4]{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt{-\frac{b-x}{a-b}}}\right)}{\sqrt[4]{2} d^{3/4} \sqrt[4]{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{a-b} \sqrt{\sqrt{d}+\sqrt{-4 a+4 b+d}} \sqrt{-\frac{b-x}{a-b}} \sqrt[4]{x-a} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{\sqrt{d}+\sqrt{-4 a+4 b+d}} \sqrt[4]{x-a}}{\sqrt[4]{2} \sqrt{a-b} \sqrt[4]{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt{-\frac{b-x}{a-b}}}\right)}{\sqrt[4]{2} d^{3/4} \sqrt[4]{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{b-a} \sqrt{\sqrt{d}+\sqrt{-4 a+4 b+d}} \sqrt{-\frac{b-x}{a-b}} \sqrt[4]{x-a} \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{\sqrt{d}+\sqrt{-4 a+4 b+d}} \sqrt[4]{x-a}}{\sqrt[4]{2} \sqrt{b-a} \sqrt[4]{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt{-\frac{b-x}{a-b}}}\right)}{\sqrt[4]{2} d^{3/4} \sqrt[4]{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}-\frac{\left(1-\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}\right) \left(2 a-2 b-\sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}\right) \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a-b} \left(4 a-4 b-d+\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)}}-\frac{\left(1-\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}\right) \left(2 a-2 b+\sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}\right) \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a-b} \left(4 a-4 b-d+\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)}}-\frac{\left(\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}+1\right) \left(2 a-2 b-\sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}\right) \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a-b} \left(4 a-4 b-d-\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)}}-\frac{\left(\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}+1\right) \left(2 a-2 b+\sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}\right) \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a-b} \left(4 a-4 b-d-\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt[4]{a-b} \left(1-\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}\right) \left(\sqrt{2} \sqrt{a-b}+\sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2 \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{a-b}-\sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2}{4 \sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}}};2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{-2 a+2 b+d-\sqrt{d} \sqrt{-4 a+4 b+d}} \left(4 a-4 b-d+\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt[4]{a-b} \left(\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}+1\right) \left(\sqrt{2} \sqrt{a-b}+\sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2 \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{a-b}-\sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2}{4 \sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}};2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \left(4 a-4 b-d-\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt[4]{a-b} \left(\sqrt{d}+\sqrt{-4 a+4 b+d}\right) \left(\sqrt{2} \sqrt{a-b}-\sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2 \sqrt[4]{x-a} \sqrt{-\frac{b-x}{(a-b) \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right)^2}} \left(\frac{\sqrt{x-a}}{\sqrt{a-b}}+1\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{a-b}+\sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}\right)^2}{4 \sqrt{2} \sqrt{a-b} \sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}}};2 \tan ^{-1}\left(\frac{\sqrt[4]{x-a}}{\sqrt[4]{a-b}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{d} \left(4 a-4 b-d-\sqrt{d} \sqrt{-4 a+4 b+d}\right) \sqrt{-2 a+2 b+d+\sqrt{d} \sqrt{-4 a+4 b+d}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}","\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,"(Sqrt[a - b]*Sqrt[Sqrt[d] - Sqrt[-4*a + 4*b + d]]*Sqrt[-((b - x)/(a - b))]*(-a + x)^(1/4)*ArcTan[(d^(1/4)*Sqrt[Sqrt[d] - Sqrt[-4*a + 4*b + d]]*(-a + x)^(1/4))/(2^(1/4)*Sqrt[a - b]*(-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*Sqrt[-((b - x)/(a - b))])])/(2^(1/4)*d^(3/4)*(-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) + (Sqrt[a - b]*Sqrt[-Sqrt[d] + Sqrt[-4*a + 4*b + d]]*Sqrt[-((b - x)/(a - b))]*(-a + x)^(1/4)*ArcTan[(d^(1/4)*Sqrt[-Sqrt[d] + Sqrt[-4*a + 4*b + d]]*(-a + x)^(1/4))/(2^(1/4)*Sqrt[a - b]*(-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*Sqrt[-((b - x)/(a - b))])])/(2^(1/4)*d^(3/4)*(-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) + (Sqrt[a - b]*Sqrt[Sqrt[d] + Sqrt[-4*a + 4*b + d]]*Sqrt[-((b - x)/(a - b))]*(-a + x)^(1/4)*ArcTan[(d^(1/4)*Sqrt[Sqrt[d] + Sqrt[-4*a + 4*b + d]]*(-a + x)^(1/4))/(2^(1/4)*Sqrt[a - b]*(-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*Sqrt[-((b - x)/(a - b))])])/(2^(1/4)*d^(3/4)*(-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) - (Sqrt[-a + b]*Sqrt[Sqrt[d] + Sqrt[-4*a + 4*b + d]]*Sqrt[-((b - x)/(a - b))]*(-a + x)^(1/4)*ArcTan[(d^(1/4)*Sqrt[Sqrt[d] + Sqrt[-4*a + 4*b + d]]*(-a + x)^(1/4))/(2^(1/4)*Sqrt[-a + b]*(-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*Sqrt[-((b - x)/(a - b))])])/(2^(1/4)*d^(3/4)*(-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d])^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) - ((1 - Sqrt[-4*a + 4*b + d]/Sqrt[d])*(2*a - 2*b - Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]])*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*(a - b)^(1/4)*(4*a - 4*b - d + Sqrt[d]*Sqrt[-4*a + 4*b + d])*(-((a - x)*(b - x)^2))^(1/4)) - ((1 - Sqrt[-4*a + 4*b + d]/Sqrt[d])*(2*a - 2*b + Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]])*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*(a - b)^(1/4)*(4*a - 4*b - d + Sqrt[d]*Sqrt[-4*a + 4*b + d])*(-((a - x)*(b - x)^2))^(1/4)) - ((1 + Sqrt[-4*a + 4*b + d]/Sqrt[d])*(2*a - 2*b - Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]])*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*(a - b)^(1/4)*(4*a - 4*b - d - Sqrt[d]*Sqrt[-4*a + 4*b + d])*(-((a - x)*(b - x)^2))^(1/4)) - ((1 + Sqrt[-4*a + 4*b + d]/Sqrt[d])*(2*a - 2*b + Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]])*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*(a - b)^(1/4)*(4*a - 4*b - d - Sqrt[d]*Sqrt[-4*a + 4*b + d])*(-((a - x)*(b - x)^2))^(1/4)) + ((a - b)^(1/4)*(1 - Sqrt[-4*a + 4*b + d]/Sqrt[d])*(Sqrt[2]*Sqrt[a - b] + Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[a - b] - Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2/(Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]]), 2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*Sqrt[2]*Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]]*(4*a - 4*b - d + Sqrt[d]*Sqrt[-4*a + 4*b + d])*(-((a - x)*(b - x)^2))^(1/4)) - ((a - b)^(1/4)*(1 - Sqrt[-4*a + 4*b + d]/Sqrt[d])*(Sqrt[2]*Sqrt[a - b] - Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticPi[(Sqrt[2]*Sqrt[a - b] + Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2/(4*Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]]), 2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*Sqrt[2]*Sqrt[-2*a + 2*b + d - Sqrt[d]*Sqrt[-4*a + 4*b + d]]*(4*a - 4*b - d + Sqrt[d]*Sqrt[-4*a + 4*b + d])*(-((a - x)*(b - x)^2))^(1/4)) + ((a - b)^(1/4)*(1 + Sqrt[-4*a + 4*b + d]/Sqrt[d])*(Sqrt[2]*Sqrt[a - b] + Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[a - b] - Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2/(Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]]), 2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*Sqrt[2]*(4*a - 4*b - d - Sqrt[d]*Sqrt[-4*a + 4*b + d])*Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]]*(-((a - x)*(b - x)^2))^(1/4)) - ((a - b)^(1/4)*(Sqrt[d] + Sqrt[-4*a + 4*b + d])*(Sqrt[2]*Sqrt[a - b] - Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticPi[(Sqrt[2]*Sqrt[a - b] + Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]])^2/(4*Sqrt[2]*Sqrt[a - b]*Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]]), 2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(2*Sqrt[2]*Sqrt[d]*(4*a - 4*b - d - Sqrt[d]*Sqrt[-4*a + 4*b + d])*Sqrt[-2*a + 2*b + d + Sqrt[d]*Sqrt[-4*a + 4*b + d]]*(-((a - x)*(b - x)^2))^(1/4))","C",21,8,44,0.1818,0,"{6719, 6728, 107, 106, 490, 1217, 220, 1707}"
1681,1,182,0,0.1293884,"\int x \sqrt[3]{x^2+x^3} \, dx","Int[x*(x^2 + x^3)^(1/3),x]","\frac{1}{3} \sqrt[3]{x^3+x^2} x^2+\frac{1}{18} \sqrt[3]{x^3+x^2} x-\frac{5}{54} \sqrt[3]{x^3+x^2}-\frac{5 (x+1)^{2/3} x^{4/3} \log (x+1)}{162 \left(x^3+x^2\right)^{2/3}}-\frac{5 (x+1)^{2/3} x^{4/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x+1}}-1\right)}{54 \left(x^3+x^2\right)^{2/3}}-\frac{5 (x+1)^{2/3} x^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3} \left(x^3+x^2\right)^{2/3}}","\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,"(-5*(x^2 + x^3)^(1/3))/54 + (x*(x^2 + x^3)^(1/3))/18 + (x^2*(x^2 + x^3)^(1/3))/3 - (5*x^(4/3)*(1 + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(27*Sqrt[3]*(x^2 + x^3)^(2/3)) - (5*x^(4/3)*(1 + x)^(2/3)*Log[1 + x])/(162*(x^2 + x^3)^(2/3)) - (5*x^(4/3)*(1 + x)^(2/3)*Log[-1 + x^(1/3)/(1 + x)^(1/3)])/(54*(x^2 + x^3)^(2/3))","A",5,4,13,0.3077,1,"{2021, 2024, 2032, 59}"
1682,0,0,0,7.2489998,"\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","Int[(-((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]","\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","\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,"(4*a*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[a - b + x^4])/(-(a^2*(1 + (b*(-2*a + b))/a^2)*d) - 2*a*(1 - b/a)*d*x^4 - d*x^8 + x^12), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4) + (4*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^6*Sqrt[a - b + x^4])/(-(a^2*(1 + (b*(-2*a + b))/a^2)*d) - 2*a*(1 - b/a)*d*x^4 - d*x^8 + x^12), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4) - (4*(2*a - 3*b)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[a - b + x^4])/(a^2*(1 + b^2/a^2)*d - 2*b*d*x^4 + x^8*(d - x^4) + 2*a*d*(-b + x^4)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4)","F",0,0,0,0,-1,"{}"
1683,0,0,0,26.4535824,"\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","Int[((-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,"(-4*(1 - x)^(1/4)*(1 - k*x)^(1/4)*AppellF1[-1/4, -11/4, 5/4, 3/4, x, k*x])/((1 - x)*x*(1 - k*x))^(1/4) + (4*(5 + d - 2*k)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][(x^2*(1 - x^4)^(11/4))/((1 - k*x^4)^(5/4)*(1 - 3*(1 + d/3)*x^4 + 3*(1 + (d*k)/3)*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) - (4*(3 + k + d*k)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][(x^6*(1 - x^4)^(11/4))/((1 - k*x^4)^(5/4)*(1 - 3*(1 + d/3)*x^4 + 3*(1 + (d*k)/3)*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (4*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][(x^10*(1 - x^4)^(11/4))/((1 - k*x^4)^(5/4)*(1 - 3*(1 + d/3)*x^4 + 3*(1 + (d*k)/3)*x^8 - x^12)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4)","F",0,0,0,0,-1,"{}"
1684,1,159,0,0.2352421,"\int \frac{b+a x^2}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Int[(b + a*x^2)/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{\sqrt{x} \sqrt{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}-\frac{\sqrt{x} \sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}","-\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,"-((Sqrt[x]*Sqrt[b + a*x^2]*ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3])) - (Sqrt[x]*Sqrt[b + a*x^2]*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3])","A",6,6,32,0.1875,1,"{2056, 466, 404, 212, 206, 203}"
1685,0,0,0,9.2549666,"\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","Int[((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,"(-2*(a - b)^(1/4)*(b - x)*(-a + x)^(3/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(d*(-((a - x)*(b - x)^2))^(3/4)) - (4*(2*a - 3*b)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][x^8/(Sqrt[a - b + x^4]*(a^2*(1 + (b*(-2*a + b))/a^2) + (2*a - 2*b)*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(3/4) - (4*(a - b)^2*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][1/(Sqrt[a - b + x^4]*(a^2*(1 + (b*(-2*a + b))/a^2) + 2*a*(1 - b/a)*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*(-((a - x)*(b - x)^2))^(3/4)) - (8*(a - b)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][x^4/(Sqrt[a - b + x^4]*(a^2*(1 + (b*(-2*a + b))/a^2) + 2*a*(1 - b/a)*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*(-((a - x)*(b - x)^2))^(3/4)) - (4*(1 + a*d)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][x^8/(Sqrt[a - b + x^4]*(a^2*(1 + (b*(-2*a + b))/a^2) + 2*a*(1 - b/a)*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*(-((a - x)*(b - x)^2))^(3/4))","F",0,0,0,0,-1,"{}"
1686,1,530,0,1.015559,"\int \frac{\left(-1+x^3\right) \sqrt[4]{x^3+x^4}}{1+x^3} \, dx","Int[((-1 + x^3)*(x^3 + x^4)^(1/4))/(1 + x^3),x]","\frac{1}{2} \sqrt[4]{x^4+x^3} x+\frac{1}{8} \sqrt[4]{x^4+x^3}+\frac{3 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{16 \sqrt[4]{x+1} x^{3/4}}+\frac{4 i \left(\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}\right)^{3/4} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[4]{x+1}}\right)}{\sqrt{3} \sqrt[4]{x+1} x^{3/4}}-\frac{2 \left(\sqrt{3}+i\right) \sqrt[4]{-\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x+1}}\right)}{3^{3/4} \sqrt[4]{x+1} x^{3/4}}-\frac{3 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{16 \sqrt[4]{x+1} x^{3/4}}-\frac{4 i \left(\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}\right)^{3/4} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[4]{x+1}}\right)}{\sqrt{3} \sqrt[4]{x+1} x^{3/4}}+\frac{2 \left(\sqrt{3}+i\right) \sqrt[4]{-\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[4]{x+1}}\right)}{3^{3/4} \sqrt[4]{x+1} x^{3/4}}","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,"(x^3 + x^4)^(1/4)/8 + (x*(x^3 + x^4)^(1/4))/2 + (3*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(16*x^(3/4)*(1 + x)^(1/4)) + ((4*I)*((I - Sqrt[3])/(3*I - Sqrt[3]))^(3/4)*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(1 + x)^(1/4))])/(Sqrt[3]*x^(3/4)*(1 + x)^(1/4)) - (2*(I + Sqrt[3])*(-((I + Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(1 + x)^(1/4))])/(3^(3/4)*x^(3/4)*(1 + x)^(1/4)) - (3*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(16*x^(3/4)*(1 + x)^(1/4)) - ((4*I)*((I - Sqrt[3])/(3*I - Sqrt[3]))^(3/4)*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/4)*(1 + x)^(1/4))])/(Sqrt[3]*x^(3/4)*(1 + x)^(1/4)) + (2*(I + Sqrt[3])*(-((I + Sqrt[3])/(3*I + Sqrt[3])))^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/4)*(1 + x)^(1/4))])/(3^(3/4)*x^(3/4)*(1 + x)^(1/4))","C",39,14,24,0.5833,0,"{2056, 1586, 6728, 50, 63, 331, 298, 203, 206, 911, 105, 93, 205, 208}"
1687,1,58,0,0.3842882,"\int \frac{-b+a x^2}{x^2 \left(b+a x^2\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(-b + a*x^2)/(x^2*(b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{2 \left(b-a x^2\right) \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{2 a x^2}{b-a x^2}\right)}{3 b x \sqrt[4]{a x^4-b x^2}}","\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*(b - a*x^2)*Hypergeometric2F1[-3/4, 1, 1/4, (-2*a*x^2)/(b - a*x^2)])/(3*b*x*(-(b*x^2) + a*x^4)^(1/4))","C",4,4,38,0.1053,1,"{2056, 466, 511, 510}"
1688,0,0,0,28.0107421,"\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","Int[((-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]","\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","\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,"(20*a*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[a - b + x^4])/(a^6*(1 + b^6/a^6) - 6*b^5*(1 + d/(6*b^5))*x^4 + 15*b^4*x^8 - 20*b^3*x^12 + 15*b^2*x^16 - 6*b*x^20 + x^24 - 6*a^5*(b - x^4) + 15*a^4*(b - x^4)^2 - 20*a^3*(b - x^4)^3 + 15*a^2*(b - x^4)^4 - 6*a*(b - x^4)^5), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4) + (20*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^6*Sqrt[a - b + x^4])/(a^6*(1 + b^6/a^6) - 6*b^5*(1 + d/(6*b^5))*x^4 + 15*b^4*x^8 - 20*b^3*x^12 + 15*b^2*x^16 - 6*b*x^20 + x^24 - 6*a^5*(b - x^4) + 15*a^4*(b - x^4)^2 - 20*a^3*(b - x^4)^3 + 15*a^2*(b - x^4)^4 - 6*a*(b - x^4)^5), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4) - (4*(6*a - b)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[a - b + x^4])/(b^6*(1 + (a*d)/b^6) - (6*b^5 + d)*(a + x^4) + 15*b^4*(a + x^4)^2 - 20*b^3*(a + x^4)^3 + 15*b^2*(a + x^4)^4 - 6*b*(a + x^4)^5 + (a + x^4)^6), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4)","F",0,0,0,0,-1,"{}"
1689,0,0,0,52.4501452,"\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","Int[((-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,"(20*a*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][(a - b + x^4)^(7/2)/(a^6*(1 + (b*(-6*a^5 + 15*a^4*b - 20*a^3*b^2 + 15*a^2*b^3 - 6*a*b^4 + b^5))/a^6)*d - (1 - 6*(a - b)^5*d)*x^4 + 15*a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4)*d*x^8 + 20*a^3*(1 - (b*(3*a^2 - 3*a*b + b^2))/a^3)*d*x^12 + 15*a^2*(1 + (b*(-2*a + b))/a^2)*d*x^16 + 6*a*(1 - b/a)*d*x^20 + d*x^24), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(3/4) + (20*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][(x^4*(a - b + x^4)^(7/2))/(a^6*(1 + (b*(-6*a^5 + 15*a^4*b - 20*a^3*b^2 + 15*a^2*b^3 - 6*a*b^4 + b^5))/a^6)*d - (1 - 6*(a - b)^5*d)*x^4 + 15*a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4)*d*x^8 + 20*a^3*(1 - (b*(3*a^2 - 3*a*b + b^2))/a^3)*d*x^12 + 15*a^2*(1 + (b*(-2*a + b))/a^2)*d*x^16 + 6*a*(1 - b/a)*d*x^20 + d*x^24), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(3/4) - (4*(6*a - b)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][(a - b + x^4)^(7/2)/(a*(1 + (b^6*d)/a) - (1 + 6*b^5*d)*(a + x^4) + 15*b^4*d*(a + x^4)^2 - 20*b^3*d*(a + x^4)^3 + 15*b^2*d*(a + x^4)^4 - 6*b*d*(a + x^4)^5 + d*(a + x^4)^6), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(3/4)","F",0,0,0,0,-1,"{}"
1690,1,207,0,1.1217909,"\int \frac{x^4 \sqrt[4]{x^2+x^4}}{-1+x^8} \, dx","Int[(x^4*(x^2 + x^4)^(1/4))/(-1 + x^8),x]","\frac{x \sqrt[4]{x^4+x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-i x^2,-x^2\right)}{6 \sqrt[4]{x^2+1}}+\frac{x \sqrt[4]{x^4+x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};i x^2,-x^2\right)}{6 \sqrt[4]{x^2+1}}+\frac{\sqrt[4]{x^4+x^2} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2\ 2^{3/4} \sqrt{x} \sqrt[4]{x^2+1}}-\frac{\sqrt[4]{x^4+x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2\ 2^{3/4} \sqrt{x} \sqrt[4]{x^2+1}}","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-1}\&\right]+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+x^2}}\right)}{2\ 2^{3/4}}",1,"(x*(x^2 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-I)*x^2, -x^2])/(6*(1 + x^2)^(1/4)) + (x*(x^2 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, I*x^2, -x^2])/(6*(1 + x^2)^(1/4)) + ((x^2 + x^4)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)) - ((x^2 + x^4)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4))","C",43,20,22,0.9091,0,"{2056, 1586, 6733, 6742, 1240, 410, 237, 335, 275, 231, 407, 409, 1213, 537, 494, 298, 203, 206, 1529, 510}"
1691,1,207,0,0.9568032,"\int \frac{x^4 \sqrt[4]{x^2+x^4}}{-1+x^8} \, dx","Int[(x^4*(x^2 + x^4)^(1/4))/(-1 + x^8),x]","\frac{x \sqrt[4]{x^4+x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-i x^2,-x^2\right)}{6 \sqrt[4]{x^2+1}}+\frac{x \sqrt[4]{x^4+x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};i x^2,-x^2\right)}{6 \sqrt[4]{x^2+1}}+\frac{\sqrt[4]{x^4+x^2} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2\ 2^{3/4} \sqrt{x} \sqrt[4]{x^2+1}}-\frac{\sqrt[4]{x^4+x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2\ 2^{3/4} \sqrt{x} \sqrt[4]{x^2+1}}","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$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,"(x*(x^2 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-I)*x^2, -x^2])/(6*(1 + x^2)^(1/4)) + (x*(x^2 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, I*x^2, -x^2])/(6*(1 + x^2)^(1/4)) + ((x^2 + x^4)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)) - ((x^2 + x^4)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4))","C",43,20,22,0.9091,0,"{2056, 1586, 6733, 6742, 1240, 410, 237, 335, 275, 231, 407, 409, 1213, 537, 494, 298, 203, 206, 1529, 510}"
1692,1,1033,0,3.1914455,"\int \frac{x^4}{\sqrt[4]{x^2+x^4} \left(1+x^4+x^8\right)} \, dx","Int[x^4/((x^2 + x^4)^(1/4)*(1 + x^4 + x^8)),x]","-\frac{i \left(-2+\sqrt{-2-2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3-i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}+\frac{i \left(-2+\sqrt{-2+2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3+i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}-\frac{i \left(-2+\sqrt{-2-2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3-i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}+\frac{i \left(-2+\sqrt{-2+2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3+i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}","\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,"((-I)*(-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 - I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 - I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 - I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4)) + (I*(-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 + I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 + I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 + I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4)) - (I*(-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 - I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 - I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 - I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4)) + (I*(-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 + I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 + I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 + I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4))","C",33,12,25,0.4800,0,"{2056, 6728, 1270, 1517, 240, 212, 206, 203, 1429, 377, 208, 205}"
1693,1,1033,0,2.4896232,"\int \frac{x^4}{\sqrt[4]{x^2+x^4} \left(1+x^4+x^8\right)} \, dx","Int[x^4/((x^2 + x^4)^(1/4)*(1 + x^4 + x^8)),x]","-\frac{i \left(-2+\sqrt{-2-2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3-i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}+\frac{i \left(-2+\sqrt{-2+2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3+i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}-\frac{i \left(-2+\sqrt{-2-2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3-i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1-i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1-i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2-2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}+\frac{i \left(-2+\sqrt{-2+2 i \sqrt{3}}\right)^{3/4} \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{-2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{\sqrt{3} \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{x^4+x^2}}-\frac{\left(3+i \sqrt{3}\right) \sqrt{x} \sqrt[4]{x^2+1} \tanh ^{-1}\left(\frac{\sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt{x}}{\sqrt[8]{2 \left(-1+i \sqrt{3}\right)} \sqrt[4]{x^2+1}}\right)}{3 \left(2 \left(-1+i \sqrt{3}\right)\right)^{7/8} \sqrt[4]{2+\sqrt{-2+2 i \sqrt{3}}} \sqrt[4]{x^4+x^2}}","\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,"((-I)*(-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 - I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 - I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 - I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4)) + (I*(-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 + I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 + I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 + I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4)) - (I*(-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((-2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 - I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 - I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 - I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 - I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 - (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4)) + (I*(-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((-2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(Sqrt[3]*(2*(-1 + I*Sqrt[3]))^(7/8)*(x^2 + x^4)^(1/4)) - ((3 + I*Sqrt[3])*Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*Sqrt[x])/((2*(-1 + I*Sqrt[3]))^(1/8)*(1 + x^2)^(1/4))])/(3*(2*(-1 + I*Sqrt[3]))^(7/8)*(2 + Sqrt[-2 + (2*I)*Sqrt[3]])^(1/4)*(x^2 + x^4)^(1/4))","C",33,12,25,0.4800,0,"{2056, 6728, 1270, 1517, 240, 212, 206, 203, 1429, 377, 208, 205}"
1694,0,0,0,2.1765429,"\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","Int[(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,"(x^2*Hypergeometric2F1[2/3, 3/4, 5/3, -x^3])/2 + Defer[Int][1/((1 + x^3)^(3/4)*(-1 - x^3 + x^4)), x]/2 + Defer[Int][x/((1 + x^3)^(3/4)*(-1 - x^3 + x^4)), x]/2 + 2*Defer[Int][x^2/((1 + x^3)^(3/4)*(-1 - x^3 + x^4)), x] + Defer[Int][x^3/((1 + x^3)^(3/4)*(-1 - x^3 + x^4)), x]/2 + Defer[Int][1/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x]/2 - Defer[Int][x/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x]/2 + 2*Defer[Int][x^2/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x] + Defer[Int][x^3/((1 + x^3)^(3/4)*(1 + x^3 + x^4)), x]/2","F",0,0,0,0,-1,"{}"
1695,1,145,0,0.0790064,"\int x^{10} \sqrt[3]{-1+x^3} \, dx","Int[x^10*(-1 + x^3)^(1/3),x]","\frac{10}{729} \log \left(1-\frac{x}{\sqrt[3]{x^3-1}}\right)+\frac{10 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{243 \sqrt{3}}+\frac{1}{12} \sqrt[3]{x^3-1} x^{11}-\frac{1}{108} \sqrt[3]{x^3-1} x^8-\frac{1}{81} \sqrt[3]{x^3-1} x^5-\frac{5}{243} \sqrt[3]{x^3-1} x^2-\frac{5}{729} \log \left(\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+1\right)","\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,"(-5*x^2*(-1 + x^3)^(1/3))/243 - (x^5*(-1 + x^3)^(1/3))/81 - (x^8*(-1 + x^3)^(1/3))/108 + (x^11*(-1 + x^3)^(1/3))/12 + (10*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(243*Sqrt[3]) + (10*Log[1 - x/(-1 + x^3)^(1/3)])/729 - (5*Log[1 + x^2/(-1 + x^3)^(2/3) + x/(-1 + x^3)^(1/3)])/729","A",11,9,13,0.6923,1,"{279, 321, 331, 292, 31, 634, 618, 204, 628}"
1696,1,151,0,0.0885019,"\int \frac{x}{(-1+x) \sqrt[3]{-x^2+x^3}} \, dx","Int[x/((-1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 x}{\sqrt[3]{x^3-x^2}}-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-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)/(-x^2 + x^3)^(1/3) - (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3))","A",3,3,20,0.1500,1,"{2056, 47, 59}"
1697,1,151,0,0.0867113,"\int \frac{1+x}{(-1+x) \sqrt[3]{-x^2+x^3}} \, dx","Int[(1 + x)/((-1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{6 x}{\sqrt[3]{x^3-x^2}}-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-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,"(-6*x)/(-x^2 + x^3)^(1/3) - (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3))","A",3,3,22,0.1364,1,"{2056, 78, 59}"
1698,1,2624,0,14.5087692,"\int \frac{-2 b+a x}{\left(-b+a x+x^2\right) \sqrt[4]{-b x^2+a x^3}} \, dx","Int[(-2*b + a*x)/((-b + a*x + x^2)*(-(b*x^2) + a*x^3)^(1/4)),x]","-\frac{\left(a+\sqrt{a^2+4 b}\right) \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{b}+\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right) \left(\sqrt{2} \sqrt{b}-\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2}{2 \sqrt{2} \sqrt[4]{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) \sqrt[4]{a x^3-b x^2}}-\frac{\sqrt{b} \sqrt{-a-\sqrt{a^2+4 b}} \sqrt{\frac{a x}{b}} \sqrt[4]{a x-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{-a-\sqrt{a^2+4 b}} \sqrt[4]{a x-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x}{b}}}\right)}{\sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^3-b x^2}}-\frac{\sqrt{b} \sqrt{a+\sqrt{a^2+4 b}} \sqrt{\frac{a x}{b}} \sqrt[4]{a x-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a+\sqrt{a^2+4 b}} \sqrt[4]{a x-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x}{b}}}\right)}{\sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^3-b x^2}}-\frac{\sqrt{b} \sqrt{a-\sqrt{a^2+4 b}} \sqrt{\frac{a x}{b}} \sqrt[4]{a x-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a-\sqrt{a^2+4 b}} \sqrt[4]{a x-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x}{b}}}\right)}{\sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^3-b x^2}}-\frac{\sqrt{b} \sqrt{\sqrt{a^2+4 b}-a} \sqrt{\frac{a x}{b}} \sqrt[4]{a x-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\sqrt{a^2+4 b}-a} \sqrt[4]{a x-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{\frac{a x}{b}}}\right)}{\sqrt[4]{2} \sqrt{a} \sqrt[4]{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^3-b x^2}}-\frac{\left(a+\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}-\sqrt{2} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right) \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) \sqrt[4]{a x^3-b x^2}}-\frac{\left(a+\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}+\sqrt{2} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right) \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) \sqrt[4]{a x^3-b x^2}}-\frac{\left(a-\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}-\sqrt{-2 a^2+2 \sqrt{a^2+4 b} a-4 b}\right) \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) \sqrt[4]{a x^3-b x^2}}-\frac{\left(a-\sqrt{a^2+4 b}\right) \left(2 \sqrt{b}+\sqrt{-2 a^2+2 \sqrt{a^2+4 b} a-4 b}\right) \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) \sqrt[4]{a x^3-b x^2}}+\frac{\left(a+\sqrt{a^2+4 b}\right) \left(\sqrt{2} \sqrt{b}+\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2 \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{b}-\sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt[4]{b} \sqrt{-a^2-\sqrt{a^2+4 b} a-2 b} \left(a^2+\sqrt{a^2+4 b} a+4 b\right) \sqrt[4]{a x^3-b x^2}}+\frac{\left(a-\sqrt{a^2+4 b}\right) \left(\sqrt{2} \sqrt{b}+\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2 \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{b}-\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^3-b x^2}}-\frac{\left(a-\sqrt{a^2+4 b}\right) \left(\sqrt{2} \sqrt{b}-\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2 \sqrt[4]{a x-b} \sqrt{\frac{a x}{\left(\sqrt{b}+\sqrt{a x-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x-b}\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{b}+\sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt[4]{b} \left(a^2-\sqrt{a^2+4 b} a+4 b\right) \sqrt{-a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^3-b x^2}}","\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,"-((Sqrt[b]*Sqrt[-a - Sqrt[a^2 + 4*b]]*Sqrt[(a*x)/b]*(-b + a*x)^(1/4)*ArcTan[(Sqrt[a]*Sqrt[-a - Sqrt[a^2 + 4*b]]*(-b + a*x)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x)/b])])/(2^(1/4)*Sqrt[a]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*(-(b*x^2) + a*x^3)^(1/4))) - (Sqrt[b]*Sqrt[a + Sqrt[a^2 + 4*b]]*Sqrt[(a*x)/b]*(-b + a*x)^(1/4)*ArcTan[(Sqrt[a]*Sqrt[a + Sqrt[a^2 + 4*b]]*(-b + a*x)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x)/b])])/(2^(1/4)*Sqrt[a]*(-a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*(-(b*x^2) + a*x^3)^(1/4)) - (Sqrt[b]*Sqrt[a - Sqrt[a^2 + 4*b]]*Sqrt[(a*x)/b]*(-b + a*x)^(1/4)*ArcTan[(Sqrt[a]*Sqrt[a - Sqrt[a^2 + 4*b]]*(-b + a*x)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x)/b])])/(2^(1/4)*Sqrt[a]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*(-(b*x^2) + a*x^3)^(1/4)) - (Sqrt[b]*Sqrt[-a + Sqrt[a^2 + 4*b]]*Sqrt[(a*x)/b]*(-b + a*x)^(1/4)*ArcTan[(Sqrt[a]*Sqrt[-a + Sqrt[a^2 + 4*b]]*(-b + a*x)^(1/4))/(2^(1/4)*Sqrt[b]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*Sqrt[(a*x)/b])])/(2^(1/4)*Sqrt[a]*(-a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*(-(b*x^2) + a*x^3)^(1/4)) - ((a + Sqrt[a^2 + 4*b])*(2*Sqrt[b] - Sqrt[2]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticF[2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*b^(1/4)*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*(-(b*x^2) + a*x^3)^(1/4)) - ((a + Sqrt[a^2 + 4*b])*(2*Sqrt[b] + Sqrt[2]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticF[2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*b^(1/4)*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*(-(b*x^2) + a*x^3)^(1/4)) - ((a - Sqrt[a^2 + 4*b])*(2*Sqrt[b] - Sqrt[-2*a^2 - 4*b + 2*a*Sqrt[a^2 + 4*b]])*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticF[2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*(-(b*x^2) + a*x^3)^(1/4)) - ((a - Sqrt[a^2 + 4*b])*(2*Sqrt[b] + Sqrt[-2*a^2 - 4*b + 2*a*Sqrt[a^2 + 4*b]])*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticF[2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*(-(b*x^2) + a*x^3)^(1/4)) + ((a + Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2/(Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*Sqrt[2]*b^(1/4)*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*(-(b*x^2) + a*x^3)^(1/4)) - ((a + Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticPi[(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]])^2/(4*Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*Sqrt[2]*b^(1/4)*Sqrt[-a^2 - 2*b - a*Sqrt[a^2 + 4*b]]*(a^2 + 4*b + a*Sqrt[a^2 + 4*b])*(-(b*x^2) + a*x^3)^(1/4)) + ((a - Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2/(Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*Sqrt[2]*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]*(-(b*x^2) + a*x^3)^(1/4)) - ((a - Sqrt[a^2 + 4*b])*(Sqrt[2]*Sqrt[b] - Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2*(-b + a*x)^(1/4)*Sqrt[(a*x)/(Sqrt[b] + Sqrt[-b + a*x])^2]*(Sqrt[b] + Sqrt[-b + a*x])*EllipticPi[(Sqrt[2]*Sqrt[b] + Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]])^2/(4*Sqrt[2]*Sqrt[b]*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]), 2*ArcTan[(-b + a*x)^(1/4)/b^(1/4)], 1/2])/(2*Sqrt[2]*b^(1/4)*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*Sqrt[-a^2 - 2*b + a*Sqrt[a^2 + 4*b]]*(-(b*x^2) + a*x^3)^(1/4))","C",21,8,36,0.2222,0,"{2056, 6728, 107, 106, 490, 1217, 220, 1707}"
1699,1,153,0,0.6581263,"\int \frac{\left(1+x^2\right) \sqrt[3]{-x+2 x^3}}{x^2 \left(1+x^4\right)} \, dx","Int[((1 + x^2)*(-x + 2*x^3)^(1/3))/(x^2*(1 + x^4)),x]","-\frac{\left(\frac{3}{4}-\frac{3 i}{4}\right) \sqrt[3]{1-i x^2} \sqrt[3]{2 x^3-x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};\frac{(2-i) x^2}{1-i x^2}\right)}{x \sqrt[3]{1-2 x^2}}-\frac{\left(\frac{3}{4}+\frac{3 i}{4}\right) \sqrt[3]{1+i x^2} \sqrt[3]{2 x^3-x} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};\frac{(2+i) x^2}{i x^2+1}\right)}{x \sqrt[3]{1-2 x^2}}","\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,"((-3/4 + (3*I)/4)*(1 - I*x^2)^(1/3)*(-x + 2*x^3)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, ((2 - I)*x^2)/(1 - I*x^2)])/(x*(1 - 2*x^2)^(1/3)) - ((3/4 + (3*I)/4)*(1 + I*x^2)^(1/3)*(-x + 2*x^3)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, ((2 + I)*x^2)/(1 + I*x^2)])/(x*(1 - 2*x^2)^(1/3))","C",11,6,29,0.2069,0,"{2056, 6725, 466, 465, 511, 510}"
1700,1,797,0,1.5239978,"\int \frac{-1+x}{\left(1+x+x^2\right) \sqrt[4]{1+x^4}} \, dx","Int[(-1 + x)/((1 + x + x^2)*(1 + x^4)^(1/4)),x]","-\frac{1}{6} \left(1+i \sqrt{3}\right) F_1\left(\frac{3}{4};\frac{1}{4},1;\frac{7}{4};-x^4,-\frac{2 x^4}{1-i \sqrt{3}}\right) x^3-\frac{1}{6} \left(1-i \sqrt{3}\right) F_1\left(\frac{3}{4};\frac{1}{4},1;\frac{7}{4};-x^4,-\frac{2 x^4}{1+i \sqrt{3}}\right) x^3-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} \sqrt[4]{x^4+1}}\right)}{2 \left(-\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{3/4}}-\frac{1}{2} \left(-\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1-i \sqrt{3}}}\right)+\frac{1}{2} \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1+i \sqrt{3}}}\right)-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} \sqrt[4]{x^4+1}}\right)}{2 \left(-\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{3/4}}-\frac{1}{2} \left(-\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1-i \sqrt{3}}}\right)-\frac{1}{2} \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1+i \sqrt{3}}}\right)+\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{2} \left(-i-\sqrt{3}\right);\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}-\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{2} \left(i-\sqrt{3}\right);\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}-\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}+\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}","\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,"-1/6*((1 + I*Sqrt[3])*x^3*AppellF1[3/4, 1/4, 1, 7/4, -x^4, (-2*x^4)/(1 - I*Sqrt[3])]) - ((1 - I*Sqrt[3])*x^3*AppellF1[3/4, 1/4, 1, 7/4, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/6 - ArcTan[x/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(1 + x^4)^(1/4))]/(2*(-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)) - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*ArcTan[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x)/(1 + x^4)^(1/4)])/2 + (((1 - I*Sqrt[3])/2)^(3/4)*ArcTan[(2^(1/4)*(1 + x^4)^(1/4))/(1 - I*Sqrt[3])^(1/4)])/2 + (((1 + I*Sqrt[3])/2)^(3/4)*ArcTan[(2^(1/4)*(1 + x^4)^(1/4))/(1 + I*Sqrt[3])^(1/4)])/2 - ArcTanh[x/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(1 + x^4)^(1/4))]/(2*(-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)) - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*ArcTanh[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x)/(1 + x^4)^(1/4)])/2 - (((1 - I*Sqrt[3])/2)^(3/4)*ArcTanh[(2^(1/4)*(1 + x^4)^(1/4))/(1 - I*Sqrt[3])^(1/4)])/2 - (((1 + I*Sqrt[3])/2)^(3/4)*ArcTanh[(2^(1/4)*(1 + x^4)^(1/4))/(1 + I*Sqrt[3])^(1/4)])/2 + ((I/2)*Sqrt[-x^4]*EllipticPi[(-I - Sqrt[3])/2, ArcSin[(1 + x^4)^(1/4)], -1])/x^2 - ((I/2)*Sqrt[-x^4]*EllipticPi[(I - Sqrt[3])/2, ArcSin[(1 + x^4)^(1/4)], -1])/x^2 - ((I/2)*Sqrt[-x^4]*EllipticPi[1/Sqrt[(1 - I*Sqrt[3])/2], ArcSin[(1 + x^4)^(1/4)], -1])/x^2 + ((I/2)*Sqrt[-x^4]*EllipticPi[1/Sqrt[(1 + I*Sqrt[3])/2], ArcSin[(1 + x^4)^(1/4)], -1])/x^2","C",46,19,21,0.9048,0,"{6728, 2153, 1240, 377, 212, 208, 205, 510, 1248, 746, 399, 490, 1213, 537, 444, 63, 298, 203, 206}"
1701,1,230,0,0.2076427,"\int \frac{x^2 \sqrt[4]{x^3+x^4}}{-1+x} \, dx","Int[(x^2*(x^3 + x^4)^(1/4))/(-1 + x),x]","\frac{13}{24} \sqrt[4]{x^4+x^3} x+\frac{101}{96} \sqrt[4]{x^4+x^3}-\frac{155 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{64 \sqrt[4]{x+1} x^{3/4}}+\frac{2 \sqrt[4]{2} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt[4]{x+1} x^{3/4}}+\frac{155 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{64 \sqrt[4]{x+1} x^{3/4}}-\frac{2 \sqrt[4]{2} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt[4]{x+1} x^{3/4}}+\frac{1}{3} \sqrt[4]{x^4+x^3} x^2","-\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,"(101*(x^3 + x^4)^(1/4))/96 + (13*x*(x^3 + x^4)^(1/4))/24 + (x^2*(x^3 + x^4)^(1/4))/3 - (155*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(64*x^(3/4)*(1 + x)^(1/4)) + (2*2^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + (155*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(64*x^(3/4)*(1 + x)^(1/4)) - (2*2^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4))","B",27,11,20,0.5500,1,"{2042, 101, 157, 50, 63, 331, 298, 203, 206, 105, 93}"
1702,1,177,0,0.4013132,"\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","Int[((-b + a*x^3)*(-b + 2*a*x^3))/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","\frac{4 a^{7/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{4 a^{7/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{4 b \left(a x^4-b x\right)^{3/4}}{21 x^6}-\frac{68 a \left(a x^4-b x\right)^{3/4}}{63 x^3}","\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*(-(b*x) + a*x^4)^(3/4))/(21*x^6) - (68*a*(-(b*x) + a*x^4)^(3/4))/(63*x^3) + (4*a^(7/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4)) + (4*a^(7/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4))","A",12,10,37,0.2703,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1703,1,126,0,0.674975,"\int \frac{-b+a x^4+x^8}{x^8 \left(-b+a x^4\right) \sqrt[4]{b+a x^4}} \, dx","Int[(-b + a*x^4 + x^8)/(x^8*(-b + a*x^4)*(b + a*x^4)^(1/4)),x]","\frac{4 a \left(a x^4+b\right)^{3/4}}{21 b^2 x^3}-\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}-\frac{\left(a x^4+b\right)^{3/4}}{7 b 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,"-1/7*(b + a*x^4)^(3/4)/(b*x^7) + (4*a*(b + a*x^4)^(3/4))/(21*b^2*x^3) - ArcTan[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*2^(1/4)*a^(1/4)*b) - ArcTanh[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*2^(1/4)*a^(1/4)*b)","A",8,7,38,0.1842,1,"{6725, 271, 264, 377, 212, 206, 203}"
1704,1,141,0,0.3604394,"\int \frac{1+x^4}{x^4 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(1 + x^4)/(x^4*Sqrt[x + Sqrt[1 + x^2]]),x]","\sqrt{\sqrt{x^2+1}+x}+\frac{1}{24 x \sqrt{\sqrt{x^2+1}+x}}+\frac{1}{12 x^2 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\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{1}{3 x^3 \sqrt{\sqrt{x^2+1}+x}}","-\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,"-1/3*1/(x + Sqrt[1 + x^2])^(3/2) + 1/(12*x^2*(x + Sqrt[1 + x^2])^(3/2)) - 1/(3*x^3*Sqrt[x + Sqrt[1 + x^2]]) + 1/(24*x*Sqrt[x + Sqrt[1 + x^2]]) + Sqrt[x + Sqrt[1 + x^2]] - ArcTan[Sqrt[x + Sqrt[1 + x^2]]]/8 - ArcTanh[Sqrt[x + Sqrt[1 + x^2]]]/8","A",13,11,24,0.4583,1,"{6742, 2117, 14, 2119, 457, 288, 290, 329, 212, 206, 203}"
1705,0,0,0,0.6552412,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^2 \sqrt{b^2+a x^2}} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^2*Sqrt[b^2 + a*x^2]),x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^2 \sqrt{b^2+a x^2}} \, dx","-\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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^2*Sqrt[b^2 + a*x^2]), x]","F",0,0,0,0,-1,"{}"
1706,0,0,0,0.4745098,"\int \frac{2+x^2}{x \left(2-2 x+x^2\right) \sqrt[3]{1-x+x^2}} \, dx","Int[(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,"(-3*(-((1 - I*Sqrt[3] - 2*x)/x))^(1/3)*(-((1 + I*Sqrt[3] - 2*x)/x))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (1 - I*Sqrt[3])/(2*x), (1 + I*Sqrt[3])/(2*x)])/(2*2^(2/3)*(1 - x + x^2)^(1/3)) + 2*Defer[Int][1/((2 - 2*x + x^2)*(1 - x + x^2)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1707,1,150,0,0.09889,"\int \frac{-1+x}{x^{10} \sqrt[3]{1+x^3}} \, dx","Int[(-1 + x)/(x^10*(1 + x^3)^(1/3)),x]","\frac{14 \left(x^3+1\right)^{2/3}}{81 x^3}+\frac{7}{81} \log \left(1-\sqrt[3]{x^3+1}\right)+\frac{14 \tan ^{-1}\left(\frac{2 \sqrt[3]{x^3+1}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{\left(x^3+1\right)^{2/3}}{9 x^9}-\frac{\left(x^3+1\right)^{2/3}}{8 x^8}-\frac{7 \left(x^3+1\right)^{2/3}}{54 x^6}+\frac{3 \left(x^3+1\right)^{2/3}}{20 x^5}-\frac{9 \left(x^3+1\right)^{2/3}}{40 x^2}-\frac{7 \log (x)}{81}","\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 + x^3)^(2/3)/(9*x^9) - (1 + x^3)^(2/3)/(8*x^8) - (7*(1 + x^3)^(2/3))/(54*x^6) + (3*(1 + x^3)^(2/3))/(20*x^5) + (14*(1 + x^3)^(2/3))/(81*x^3) - (9*(1 + x^3)^(2/3))/(40*x^2) + (14*ArcTan[(1 + 2*(1 + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) - (7*Log[x])/81 + (7*Log[1 - (1 + x^3)^(1/3)])/81","A",13,9,16,0.5625,1,"{1844, 266, 51, 55, 618, 204, 31, 271, 264}"
1708,1,83,0,0.0615525,"\int \frac{1}{x \sqrt[3]{b+a x^3}} \, dx","Int[1/(x*(b + a*x^3)^(1/3)),x]","\frac{\log \left(\sqrt[3]{b}-\sqrt[3]{a x^3+b}\right)}{2 \sqrt[3]{b}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a x^3+b}+\sqrt[3]{b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{\log (x)}{2 \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,"ArcTan[(b^(1/3) + 2*(b + a*x^3)^(1/3))/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*b^(1/3)) - Log[x]/(2*b^(1/3)) + Log[b^(1/3) - (b + a*x^3)^(1/3)]/(2*b^(1/3))","A",5,5,15,0.3333,1,"{266, 55, 617, 204, 31}"
1709,0,0,0,38.0866601,"\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","Int[((-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,"(-4*(1 - x)^(1/4)*(1 - k*x)^(1/4)*AppellF1[-1/4, 5/4, -11/4, 3/4, x, k*x])/((1 - x)*x*(1 - k*x))^(1/4) - (4*(2 - d - 5*k)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][(x^2*(1 - k*x^4)^(11/4))/((1 - x^4)^(5/4)*(-(-1 + k*x^4)^3 - d*(x^4 - x^8))), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) - (4*(d + k + 3*k^2)*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][(x^6*(1 - k*x^4)^(11/4))/((1 - x^4)^(5/4)*(-(-1 + k*x^4)^3 - d*(x^4 - x^8))), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4) + (4*k^3*(1 - x)^(1/4)*x^(1/4)*(1 - k*x)^(1/4)*Defer[Subst][Defer[Int][(x^10*(1 - k*x^4)^(11/4))/((1 - x^4)^(5/4)*(-(-1 + k*x^4)^3 - d*(x^4 - x^8))), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(1/4)","F",0,0,0,0,-1,"{}"
1710,0,0,0,0.9217401,"\int \frac{\left(3+x^4\right) \left(-1-x^3+x^4\right)^{2/3}}{x^3 \left(-1+x^4\right)} \, dx","Int[((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,"Defer[Int][(-1 - x^3 + x^4)^(2/3)/(I - x), x] + Defer[Int][(-1 - x^3 + x^4)^(2/3)/(-1 + x), x] - 3*Defer[Int][(-1 - x^3 + x^4)^(2/3)/x^3, x] - Defer[Int][(-1 - x^3 + x^4)^(2/3)/(I + x), x] + Defer[Int][(-1 - x^3 + x^4)^(2/3)/(1 + x), x]","F",0,0,0,0,-1,"{}"
1711,1,363,0,0.8719859,"\int \frac{\left(1+2 x^2\right) \sqrt[3]{x+2 x^3}}{x^4 \left(1+2 x^4\right)} \, dx","Int[((1 + 2*x^2)*(x + 2*x^3)^(1/3))/(x^4*(1 + 2*x^4)),x]","-\frac{3 x \sqrt[3]{2 x^3+x} F_1\left(\frac{2}{3};-\frac{4}{3},1;\frac{5}{3};-2 x^2,-i \sqrt{2} x^2\right)}{4 \sqrt[3]{2 x^2+1}}-\frac{3 x \sqrt[3]{2 x^3+x} F_1\left(\frac{2}{3};-\frac{4}{3},1;\frac{5}{3};-2 x^2,i \sqrt{2} x^2\right)}{4 \sqrt[3]{2 x^2+1}}-\frac{3 \sqrt[3]{2 x^3+x}}{x}-\frac{3 \sqrt[3]{2 x^3+x} \left(2 x^2+1\right)}{8 x^3}-\frac{\sqrt[3]{2} \sqrt[3]{2 x^3+x} \log \left(1-\frac{\sqrt[3]{2} x^{2/3}}{\sqrt[3]{2 x^2+1}}\right)}{\sqrt[3]{x} \sqrt[3]{2 x^2+1}}+\frac{\sqrt[3]{2 x^3+x} \log \left(\frac{2^{2/3} x^{4/3}}{\left(2 x^2+1\right)^{2/3}}+\frac{\sqrt[3]{2} x^{2/3}}{\sqrt[3]{2 x^2+1}}+1\right)}{2^{2/3} \sqrt[3]{x} \sqrt[3]{2 x^2+1}}-\frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{2 x^3+x} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x^{2/3}}{\sqrt[3]{2 x^2+1}}+1}{\sqrt{3}}\right)}{\sqrt[3]{x} \sqrt[3]{2 x^2+1}}","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^6-4 \text{$\#$1}^3+6\&,\frac{-\text{$\#$1}^3 \log \left(\sqrt[3]{2 x^3+x}-\text{$\#$1} x\right)+\text{$\#$1}^3 \log (x)+6 \log \left(\sqrt[3]{2 x^3+x}-\text{$\#$1} x\right)-6 \log (x)}{\text{$\#$1}^5-2 \text{$\#$1}^2}\&\right]-\frac{3 \left(10 x^2+1\right) \sqrt[3]{2 x^3+x}}{8 x^3}",1,"(-3*(x + 2*x^3)^(1/3))/x - (3*(1 + 2*x^2)*(x + 2*x^3)^(1/3))/(8*x^3) - (3*x*(x + 2*x^3)^(1/3)*AppellF1[2/3, -4/3, 1, 5/3, -2*x^2, (-I)*Sqrt[2]*x^2])/(4*(1 + 2*x^2)^(1/3)) - (3*x*(x + 2*x^3)^(1/3)*AppellF1[2/3, -4/3, 1, 5/3, -2*x^2, I*Sqrt[2]*x^2])/(4*(1 + 2*x^2)^(1/3)) - (2^(1/3)*Sqrt[3]*(x + 2*x^3)^(1/3)*ArcTan[(1 + (2*2^(1/3)*x^(2/3))/(1 + 2*x^2)^(1/3))/Sqrt[3]])/(x^(1/3)*(1 + 2*x^2)^(1/3)) - (2^(1/3)*(x + 2*x^3)^(1/3)*Log[1 - (2^(1/3)*x^(2/3))/(1 + 2*x^2)^(1/3)])/(x^(1/3)*(1 + 2*x^2)^(1/3)) + ((x + 2*x^3)^(1/3)*Log[1 + (2^(2/3)*x^(4/3))/(1 + 2*x^2)^(2/3) + (2^(1/3)*x^(2/3))/(1 + 2*x^2)^(1/3)])/(2^(2/3)*x^(1/3)*(1 + 2*x^2)^(1/3))","C",20,17,31,0.5484,0,"{2056, 1270, 1491, 1521, 264, 6725, 277, 331, 292, 31, 634, 617, 204, 628, 21, 1529, 510}"
1712,0,0,0,0.6711388,"\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1),x]","\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$1} c+a c}\&\right]",1,"Log[b + Sqrt[b + a*x]*(c + Sqrt[c + Sqrt[b + a*x]]*(a - Sqrt[c + Sqrt[b + a*x]]))] - 3*a*Defer[Subst][Defer[Int][x^2/(b - c^2 - a*c*x + 2*c*x^2 + a*x^3 - x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] - a*c*Defer[Subst][Defer[Int][(-b + c^2 + a*c*x - 2*c*x^2 - a*x^3 + x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
1713,0,0,0,0.5051282,"\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1),x]","\int \frac{1}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$1} c+a c}\&\right]",1,"Log[b + Sqrt[b + a*x]*(c + Sqrt[c + Sqrt[b + a*x]]*(a - Sqrt[c + Sqrt[b + a*x]]))] - 3*a*Defer[Subst][Defer[Int][x^2/(b - c^2 - a*c*x + 2*c*x^2 + a*x^3 - x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] - a*c*Defer[Subst][Defer[Int][(-b + c^2 + a*c*x - 2*c*x^2 - a*x^3 + x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
1714,0,0,0,0.3687582,"\int \frac{2-x+x^2}{\sqrt[3]{-1+x^2} \left(3+4 x+x^2\right)} \, dx","Int[(2 - x + x^2)/((-1 + x^2)^(1/3)*(3 + 4*x + x^2)),x]","\int \frac{2-x+x^2}{\sqrt[3]{-1+x^2} \left(3+4 x+x^2\right)} \, dx","\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*x)/(1 + Sqrt[3] + (-1 + x^2)^(1/3)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + (-1 + x^2)^(1/3))*Sqrt[(1 - (-1 + x^2)^(1/3) + (-1 + x^2)^(2/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]*EllipticE[ArcSin[(1 - Sqrt[3] + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))], -7 - 4*Sqrt[3]])/(2*x*Sqrt[(1 + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]) + (Sqrt[2]*3^(3/4)*(1 + (-1 + x^2)^(1/3))*Sqrt[(1 - (-1 + x^2)^(1/3) + (-1 + x^2)^(2/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]*EllipticF[ArcSin[(1 - Sqrt[3] + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))], -7 - 4*Sqrt[3]])/(x*Sqrt[(1 + (-1 + x^2)^(1/3))/(1 + Sqrt[3] + (-1 + x^2)^(1/3))^2]) - Defer[Int][(1 + 5*x)/((-1 + x^2)^(1/3)*(3 + 4*x + x^2)), x]","F",0,0,0,0,-1,"{}"
1715,0,0,0,20.5661382,"\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","Int[(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,"(4*k*(1 - x)^(3/4)*x*(1 - k*x)^(3/4)*AppellF1[1/4, 7/4, -1/4, 5/4, x, k*x])/(d*((1 - x)*x*(1 - k*x))^(3/4)) + (4*(d + k + 3*d*k)*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^4*(1 - k*x^4)^(1/4))/((1 - x^4)^(7/4)*(-x^4 + k*x^8 - d*(-1 + x^4)^3)), x], x, x^(1/4)])/(d*((1 - x)*x*(1 - k*x))^(3/4)) + (4*(d*(2 - 5*k) - k^2)*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(1 - k*x^4)^(1/4))/((1 - x^4)^(7/4)*(-x^4 + k*x^8 - d*(-1 + x^4)^3)), x], x, x^(1/4)])/(d*((1 - x)*x*(1 - k*x))^(3/4)) + (4*k*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(1 - k*x^4)^(1/4)/((1 - x^4)^(7/4)*(x^4 - k*x^8 + d*(-1 + x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4)","F",0,0,0,0,-1,"{}"
1716,0,0,0,21.0762534,"\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","Int[((-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,"(4*(1 - x)^(3/4)*x*(1 - k*x)^(3/4)*AppellF1[1/4, -1/4, 7/4, 5/4, x, k*x])/(d*k^2*((1 - x)*x*(1 - k*x))^(3/4)) + (4*(1 + d*k*(3 + k))*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^4*(1 - x^4)^(1/4))/((1 - k*x^4)^(7/4)*(-x^4 + x^8 - d*(-1 + k*x^4)^3)), x], x, x^(1/4)])/(d*k^2*((1 - x)*x*(1 - k*x))^(3/4)) - (4*(5 + 1/(d*k^2) - 2*k)*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(x^8*(1 - x^4)^(1/4))/((1 - k*x^4)^(7/4)*(-x^4 + x^8 - d*(-1 + k*x^4)^3)), x], x, x^(1/4)])/((1 - x)*x*(1 - k*x))^(3/4) + (4*(1 - x)^(3/4)*x^(3/4)*(1 - k*x)^(3/4)*Defer[Subst][Defer[Int][(1 - x^4)^(1/4)/((1 - k*x^4)^(7/4)*(x^4 - x^8 + d*(-1 + k*x^4)^3)), x], x, x^(1/4)])/(k^2*((1 - x)*x*(1 - k*x))^(3/4))","F",0,0,0,0,-1,"{}"
1717,1,357,0,1.9573509,"\int \frac{\left(4+x^2\right) \sqrt[3]{-2 x+x^3}}{x^4 \left(-4-4 x^2+x^4\right)} \, dx","Int[((4 + x^2)*(-2*x + x^3)^(1/3))/(x^4*(-4 - 4*x^2 + x^4)),x]","\frac{3 \left(4-\sqrt{2}\right) \sqrt[3]{x^3-2 x} \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}{2-x^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}{2-x^2}\right)+2 \left(2-x^2\right) \left(2-3 \left(1-\sqrt{2}\right) x^2\right)\right)}{256 x^3 \left(2-x^2\right)}+\frac{3 \left(4+\sqrt{2}\right) \sqrt[3]{x^3-2 x} \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}{2-x^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}{2-x^2}\right)+2 \left(2-x^2\right) \left(2-3 \left(1+\sqrt{2}\right) x^2\right)\right)}{256 x^3 \left(2-x^2\right)}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^6-4 \text{$\#$1}^3+2\&,\frac{-11 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)+11 \text{$\#$1}^3 \log (x)+6 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)-6 \log (x)}{\text{$\#$1}^5-2 \text{$\#$1}^2}\&\right]-\frac{3 \left(7 x^2-2\right) \sqrt[3]{x^3-2 x}}{16 x^3}",1,"(3*(4 - Sqrt[2])*(-2*x + x^3)^(1/3)*(2*(2 - x^2)*(2 - 3*(1 - Sqrt[2])*x^2) + (2*(2 - Sqrt[2])*x^2 - 3*(4 - 3*Sqrt[2])*x^4)*Hypergeometric2F1[2/3, 1, 5/3, -(((2 - Sqrt[2])*x^2)/(2 - x^2))] - 3*x^2*(2*(2 - Sqrt[2]) + (4 - 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, -(((2 - Sqrt[2])*x^2)/(2 - x^2))]))/(256*x^3*(2 - x^2)) + (3*(4 + Sqrt[2])*(-2*x + x^3)^(1/3)*(2*(2 - x^2)*(2 - 3*(1 + Sqrt[2])*x^2) + (2*(2 + Sqrt[2])*x^2 - 3*(4 + 3*Sqrt[2])*x^4)*Hypergeometric2F1[2/3, 1, 5/3, -(((2 + Sqrt[2])*x^2)/(2 - x^2))] - 3*x^2*(2*(2 + Sqrt[2]) + (4 + 3*Sqrt[2])*x^2)*Hypergeometric2F1[2/3, 2, 5/3, -(((2 + Sqrt[2])*x^2)/(2 - x^2))]))/(256*x^3*(2 - x^2))","B",11,6,32,0.1875,0,"{2056, 6728, 466, 465, 511, 510}"
1718,1,357,0,1.2970034,"\int \frac{\left(4+x^2\right) \sqrt[3]{-2 x+x^3}}{x^4 \left(-4-4 x^2+x^4\right)} \, dx","Int[((4 + x^2)*(-2*x + x^3)^(1/3))/(x^4*(-4 - 4*x^2 + x^4)),x]","\frac{3 \left(4-\sqrt{2}\right) \sqrt[3]{x^3-2 x} \left(-3 \left(\left(4-3 \sqrt{2}\right) x^2+2 \left(2-\sqrt{2}\right)\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};-\frac{\left(2-\sqrt{2}\right) x^2}{2-x^2}\right)+\left(2 \left(2-\sqrt{2}\right) x^2-3 \left(4-3 \sqrt{2}\right) x^4\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{\left(2-\sqrt{2}\right) x^2}{2-x^2}\right)+2 \left(2-x^2\right) \left(2-3 \left(1-\sqrt{2}\right) x^2\right)\right)}{256 x^3 \left(2-x^2\right)}+\frac{3 \left(4+\sqrt{2}\right) \sqrt[3]{x^3-2 x} \left(-3 \left(\left(4+3 \sqrt{2}\right) x^2+2 \left(2+\sqrt{2}\right)\right) x^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};-\frac{\left(2+\sqrt{2}\right) x^2}{2-x^2}\right)+\left(2 \left(2+\sqrt{2}\right) x^2-3 \left(4+3 \sqrt{2}\right) x^4\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{\left(2+\sqrt{2}\right) x^2}{2-x^2}\right)+2 \left(2-x^2\right) \left(2-3 \left(1+\sqrt{2}\right) x^2\right)\right)}{256 x^3 \left(2-x^2\right)}","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^6-4 \text{$\#$1}^3+2\&,\frac{-11 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)+11 \text{$\#$1}^3 \log (x)+6 \log \left(\sqrt[3]{x^3-2 x}-\text{$\#$1} x\right)-6 \log (x)}{\text{$\#$1}^5-2 \text{$\#$1}^2}\&\right]-\frac{3 \left(7 x^2-2\right) \sqrt[3]{x^3-2 x}}{16 x^3}",1,"(3*(4 - Sqrt[2])*(-2*x + x^3)^(1/3)*(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))]))/(256*x^3*(2 - x^2)) + (3*(4 + Sqrt[2])*(-2*x + x^3)^(1/3)*(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))]))/(256*x^3*(2 - x^2))","B",11,6,32,0.1875,0,"{2056, 6728, 466, 465, 511, 510}"
1719,0,0,0,1.7841706,"\int \frac{2 b+a x^3}{\left(-b+x^2+a x^3\right) \sqrt[4]{-b x^2+a x^5}} \, dx","Int[(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,"(2*x*(1 - (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/6, 1/4, 7/6, (a*x^3)/b])/(-(b*x^2) + a*x^5)^(1/4) - (6*b*Sqrt[x]*(-b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][1/((b - x^4 - a*x^6)*(-b + a*x^6)^(1/4)), x], x, Sqrt[x]])/(-(b*x^2) + a*x^5)^(1/4) - (2*Sqrt[x]*(-b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^4/((-b + a*x^6)^(1/4)*(-b + x^4 + a*x^6)), x], x, Sqrt[x]])/(-(b*x^2) + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
1720,1,397,0,2.1089335,"\int \frac{b+a x^2}{\left(-b+x+a x^2\right) \sqrt[4]{-b x^3+a x^5}} \, dx","Int[(b + a*x^2)/((-b + x + a*x^2)*(-(b*x^3) + a*x^5)^(1/4)),x]","\frac{8 a x^2 \sqrt[4]{1-\frac{a x^2}{b}} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{4 a^2 x^2}{\left(1-\sqrt{4 a b+1}\right)^2},\frac{a x^2}{b}\right)}{5 \left(1-\sqrt{4 a b+1}\right) \sqrt[4]{a x^5-b x^3}}+\frac{8 a x^2 \sqrt[4]{1-\frac{a x^2}{b}} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{4 a^2 x^2}{\left(\sqrt{4 a b+1}+1\right)^2},\frac{a x^2}{b}\right)}{5 \left(\sqrt{4 a b+1}+1\right) \sqrt[4]{a x^5-b x^3}}-\frac{4 x \sqrt[4]{1-\frac{a x^2}{b}} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{4 a^2 x^2}{\left(1-\sqrt{4 a b+1}\right)^2},\frac{a x^2}{b}\right)}{\sqrt[4]{a x^5-b x^3}}-\frac{4 x \sqrt[4]{1-\frac{a x^2}{b}} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{4 a^2 x^2}{\left(\sqrt{4 a b+1}+1\right)^2},\frac{a x^2}{b}\right)}{\sqrt[4]{a x^5-b x^3}}+\frac{4 x \sqrt[4]{1-\frac{a x^2}{b}} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};\frac{a x^2}{b}\right)}{\sqrt[4]{a x^5-b x^3}}","-\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,"(-4*x*(1 - (a*x^2)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (4*a^2*x^2)/(1 - Sqrt[1 + 4*a*b])^2, (a*x^2)/b])/(-(b*x^3) + a*x^5)^(1/4) - (4*x*(1 - (a*x^2)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (4*a^2*x^2)/(1 + Sqrt[1 + 4*a*b])^2, (a*x^2)/b])/(-(b*x^3) + a*x^5)^(1/4) + (8*a*x^2*(1 - (a*x^2)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (4*a^2*x^2)/(1 - Sqrt[1 + 4*a*b])^2, (a*x^2)/b])/(5*(1 - Sqrt[1 + 4*a*b])*(-(b*x^3) + a*x^5)^(1/4)) + (8*a*x^2*(1 - (a*x^2)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (4*a^2*x^2)/(1 + Sqrt[1 + 4*a*b])^2, (a*x^2)/b])/(5*(1 + Sqrt[1 + 4*a*b])*(-(b*x^3) + a*x^5)^(1/4)) + (4*x*(1 - (a*x^2)/b)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, (a*x^2)/b])/(-(b*x^3) + a*x^5)^(1/4)","C",21,10,36,0.2778,0,"{2056, 6728, 365, 364, 959, 466, 430, 429, 511, 510}"
1721,1,447,0,2.1681878,"\int \frac{b+a x^4}{\left(-b+x^2+a x^4\right) \sqrt[4]{-b x^2+a x^6}} \, dx","Int[(b + a*x^4)/((-b + x^2 + a*x^4)*(-(b*x^2) + a*x^6)^(1/4)),x]","-\frac{2 x \sqrt[4]{1-\frac{a x^4}{b}} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{2 a^2 x^4}{2 a b-\sqrt{4 a b+1}+1},\frac{a x^4}{b}\right)}{\sqrt[4]{a x^6-b x^2}}-\frac{2 x \sqrt[4]{1-\frac{a x^4}{b}} F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};\frac{2 a^2 x^4}{2 a b+\sqrt{4 a b+1}+1},\frac{a x^4}{b}\right)}{\sqrt[4]{a x^6-b x^2}}+\frac{2 a x^3 \left(1-\sqrt{4 a b+1}\right) \sqrt[4]{1-\frac{a x^4}{b}} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{2 a^2 x^4}{2 a b-\sqrt{4 a b+1}+1},\frac{a x^4}{b}\right)}{5 \left(2 a b-\sqrt{4 a b+1}+1\right) \sqrt[4]{a x^6-b x^2}}+\frac{2 a x^3 \left(\sqrt{4 a b+1}+1\right) \sqrt[4]{1-\frac{a x^4}{b}} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};\frac{2 a^2 x^4}{2 a b+\sqrt{4 a b+1}+1},\frac{a x^4}{b}\right)}{5 \left(2 a b+\sqrt{4 a b+1}+1\right) \sqrt[4]{a x^6-b x^2}}+\frac{2 x \sqrt[4]{1-\frac{a x^4}{b}} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};\frac{a x^4}{b}\right)}{\sqrt[4]{a x^6-b x^2}}","-\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,"(-2*x*(1 - (a*x^4)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (2*a^2*x^4)/(1 + 2*a*b - Sqrt[1 + 4*a*b]), (a*x^4)/b])/(-(b*x^2) + a*x^6)^(1/4) - (2*x*(1 - (a*x^4)/b)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, (2*a^2*x^4)/(1 + 2*a*b + Sqrt[1 + 4*a*b]), (a*x^4)/b])/(-(b*x^2) + a*x^6)^(1/4) + (2*a*(1 - Sqrt[1 + 4*a*b])*x^3*(1 - (a*x^4)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (2*a^2*x^4)/(1 + 2*a*b - Sqrt[1 + 4*a*b]), (a*x^4)/b])/(5*(1 + 2*a*b - Sqrt[1 + 4*a*b])*(-(b*x^2) + a*x^6)^(1/4)) + (2*a*(1 + Sqrt[1 + 4*a*b])*x^3*(1 - (a*x^4)/b)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, (2*a^2*x^4)/(1 + 2*a*b + Sqrt[1 + 4*a*b]), (a*x^4)/b])/(5*(1 + 2*a*b + Sqrt[1 + 4*a*b])*(-(b*x^2) + a*x^6)^(1/4)) + (2*x*(1 - (a*x^4)/b)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, (a*x^4)/b])/(-(b*x^2) + a*x^6)^(1/4)","C",20,10,38,0.2632,0,"{2056, 6715, 6728, 246, 245, 1438, 430, 429, 511, 510}"
1722,0,0,0,1.7664242,"\int \frac{b+2 a x^3}{\left(-b+x+a x^3\right) \sqrt[4]{-b x^3+a x^6}} \, dx","Int[(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,"(8*x*(1 - (a*x^3)/b)^(1/4)*Hypergeometric2F1[1/12, 1/4, 13/12, (a*x^3)/b])/(-(b*x^3) + a*x^6)^(1/4) - (12*b*x^(3/4)*(-b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][1/((b - x^4 - a*x^12)*(-b + a*x^12)^(1/4)), x], x, x^(1/4)])/(-(b*x^3) + a*x^6)^(1/4) - (8*x^(3/4)*(-b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^4/((-b + a*x^12)^(1/4)*(-b + x^4 + a*x^12)), x], x, x^(1/4)])/(-(b*x^3) + a*x^6)^(1/4)","F",0,0,0,0,-1,"{}"
1723,1,447,0,1.0348418,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-x^4+a x^8\right)} \, dx","Int[1/((-b + a*x^4)^(1/4)*(-b - x^4 + a*x^8)),x]","\frac{a^{3/4} \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)}{\sqrt{4 a b+1} \left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}-\frac{a^{3/4} \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)}{\sqrt{4 a b+1} \left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}+\frac{a^{3/4} \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)}{\sqrt{4 a b+1} \left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}-\frac{a^{3/4} \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)}{\sqrt{4 a b+1} \left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a-\text{$\#$1}^4+a^2-a b+a\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{2 \text{$\#$1}^5-2 \text{$\#$1} a-\text{$\#$1}}\&\right]}{4 b}",1,"(a^(3/4)*ArcTan[(a^(1/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)*x)/((1 - Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 + 4*a*b]*(1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)) - (a^(3/4)*ArcTan[(a^(1/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)*x)/((1 + Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 + 4*a*b]*(1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)) + (a^(3/4)*ArcTanh[(a^(1/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)*x)/((1 - Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 + 4*a*b]*(1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)) - (a^(3/4)*ArcTanh[(a^(1/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)*x)/((1 + Sqrt[1 + 4*a*b])^(1/4)*(-b + a*x^4)^(1/4))])/(Sqrt[1 + 4*a*b]*(1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4))","B",9,5,30,0.1667,1,"{1428, 377, 212, 208, 205}"
1724,1,447,0,0.6526407,"\int \frac{1}{\sqrt[4]{-b+a x^4} \left(-b-x^4+a x^8\right)} \, dx","Int[1/((-b + a*x^4)^(1/4)*(-b - x^4 + a*x^8)),x]","\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{1-\sqrt{4 a b+1}} \sqrt[4]{a x^4-b}}\right)}{\sqrt{4 a b+1} \left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}-\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{\sqrt{4 a b+1}+1} \sqrt[4]{a x^4-b}}\right)}{\sqrt{4 a b+1} \left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}+\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{1-\sqrt{4 a b+1}} \sqrt[4]{a x^4-b}}\right)}{\sqrt{4 a b+1} \left(1-\sqrt{4 a b+1}\right)^{3/4} \sqrt[4]{-\sqrt{4 a b+1}-2 b+1}}-\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}{\sqrt[4]{\sqrt{4 a b+1}+1} \sqrt[4]{a x^4-b}}\right)}{\sqrt{4 a b+1} \left(\sqrt{4 a b+1}+1\right)^{3/4} \sqrt[4]{\sqrt{4 a b+1}-2 b+1}}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a-\text{$\#$1}^4+a^2-a b+a\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+a \log (x)}{2 \text{$\#$1}^5-2 \text{$\#$1} a-\text{$\#$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))])/(Sqrt[1 + 4*a*b]*(1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)) - (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))])/(Sqrt[1 + 4*a*b]*(1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4)) + (a^(3/4)*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))])/(Sqrt[1 + 4*a*b]*(1 - Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b - Sqrt[1 + 4*a*b])^(1/4)) - (a^(3/4)*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))])/(Sqrt[1 + 4*a*b]*(1 + Sqrt[1 + 4*a*b])^(3/4)*(1 - 2*b + Sqrt[1 + 4*a*b])^(1/4))","B",9,5,30,0.1667,1,"{1428, 377, 212, 208, 205}"
1725,1,539,0,1.9233404,"\int \frac{b+a x^4}{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)} \, dx","Int[(b + a*x^4)/((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8)),x]","\frac{a^{3/4} \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)}{2 \left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{c^2-4 a b}}\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)}{2 \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}+\frac{a^{3/4} \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)}{2 \left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{c^2-4 a b}}\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)}{2 \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}","\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))])/(2*(c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + (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))])/(2*(c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + (a^(3/4)*(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))])/(2*(c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + (a^(3/4)*(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))])/(2*(c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4))","B",10,5,35,0.1429,1,"{6728, 377, 212, 208, 205}"
1726,1,539,0,1.2274921,"\int \frac{b+a x^4}{\sqrt[4]{-b+a x^4} \left(b+c x^4+a x^8\right)} \, dx","Int[(b + a*x^4)/((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8)),x]","\frac{a^{3/4} \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)}{2 \left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{c^2-4 a b}}\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)}{2 \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}+\frac{a^{3/4} \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)}{2 \left(c-\sqrt{c^2-4 a b}\right)^{3/4} \sqrt[4]{-\sqrt{c^2-4 a b}+2 b+c}}+\frac{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{c^2-4 a b}}\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)}{2 \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}+2 b+c}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a-\text{$\#$1}^4 c+a^2+a b+a c\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 a \log (x)}{-2 \text{$\#$1}^5+2 \text{$\#$1} a+\text{$\#$1} c}\&\right]",1,"(a^(3/4)*(1 + (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)*x)/((c - Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + (a^(3/4)*(1 - (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTan[(a^(1/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + (a^(3/4)*(1 + (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)*x)/((c - Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(c - Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c - Sqrt[-4*a*b + c^2])^(1/4)) + (a^(3/4)*(1 - (2*b - c)/Sqrt[-4*a*b + c^2])*ArcTanh[(a^(1/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4)*x)/((c + Sqrt[-4*a*b + c^2])^(1/4)*(-b + a*x^4)^(1/4))])/(2*(c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b + c + Sqrt[-4*a*b + c^2])^(1/4))","B",10,5,35,0.1429,1,"{6728, 377, 212, 208, 205}"
1727,0,0,0,2.8406281,"\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","Int[((1 + x^5)*(1 + x^3 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10)),x]","\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","\frac{3 \sqrt[3]{x^5+x^3+1}}{2 x}-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]",1,"(-3*Defer[Int][(1 + x^3 + x^5)^(1/3)/x^2, x])/2 - 3*Defer[Int][(x*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x] + 5*Defer[Int][(x^3*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x] - (3*Defer[Int][(x^4*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x])/2 - 3*Defer[Int][(x^6*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x] + 5*Defer[Int][(x^8*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x]","F",0,0,0,0,-1,"{}"
1728,0,0,0,2.4664207,"\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","Int[((1 + x^5)*(1 + x^3 + x^5)^(1/3)*(-3 + 2*x^5))/(x^2*(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10)),x]","\int \frac{\left(1+x^5\right) \sqrt[3]{1+x^3+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10}\right)} \, dx","\frac{3 \sqrt[3]{x^5+x^3+1}}{2 x}-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+3 \log \left(\sqrt[3]{x^5+x^3+1}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]",1,"(-3*Defer[Int][(1 + x^3 + x^5)^(1/3)/x^2, x])/2 - 3*Defer[Int][(x*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x] + 5*Defer[Int][(x^3*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x] - (3*Defer[Int][(x^4*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x])/2 - 3*Defer[Int][(x^6*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x] + 5*Defer[Int][(x^8*(1 + x^3 + x^5)^(1/3))/(2 - 2*x^3 + 4*x^5 - x^6 - 2*x^8 + 2*x^10), x]","F",0,0,0,0,-1,"{}"
1729,1,222,0,0.2327561,"\int x^4 \sqrt[3]{-x+x^3} \, dx","Int[x^4*(-x + x^3)^(1/3),x]","-\frac{1}{36} \sqrt[3]{x^3-x} x^3-\frac{5}{108} \sqrt[3]{x^3-x} x+\frac{1}{6} \sqrt[3]{x^3-x} x^5+\frac{5 \left(x^2-1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{162 \left(x^3-x\right)^{2/3}}-\frac{5 \left(x^2-1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{324 \left(x^3-x\right)^{2/3}}+\frac{5 \left(x^2-1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{54 \sqrt{3} \left(x^3-x\right)^{2/3}}","\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,"(-5*x*(-x + x^3)^(1/3))/108 - (x^3*(-x + x^3)^(1/3))/36 + (x^5*(-x + x^3)^(1/3))/6 + (5*x^(2/3)*(-1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(54*Sqrt[3]*(-x + x^3)^(2/3)) + (5*x^(2/3)*(-1 + x^2)^(2/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(162*(-x + x^3)^(2/3)) - (5*x^(2/3)*(-1 + x^2)^(2/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(324*(-x + x^3)^(2/3))","A",13,12,15,0.8000,1,"{2021, 2024, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1730,1,163,0,0.4628161,"\int \frac{x}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Int[x/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","\frac{\sqrt{x} \sqrt{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} \sqrt{a x^3+b x}}-\frac{\sqrt{x} \sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} \sqrt{a x^3+b x}}","\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[x]*Sqrt[b + a*x^2]*ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*Sqrt[b*x + a*x^3]) - (Sqrt[x]*Sqrt[b + a*x^2]*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*Sqrt[b*x + a*x^3])","A",11,8,26,0.3077,1,"{2042, 466, 490, 1211, 220, 1699, 205, 208}"
1731,1,163,0,0.3809542,"\int \frac{\sqrt{b x+a x^3}}{-b^2+a^2 x^4} \, dx","Int[Sqrt[b*x + a*x^3]/(-b^2 + a^2*x^4),x]","\frac{\sqrt{a x^3+b x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} \sqrt{x} \sqrt{a x^2+b}}-\frac{\sqrt{a x^3+b x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4} \sqrt{x} \sqrt{a x^2+b}}","\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[b*x + a*x^3]*ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*Sqrt[x]*Sqrt[b + a*x^2]) - (Sqrt[b*x + a*x^3]*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(2*Sqrt[2]*a^(3/4)*b^(3/4)*Sqrt[x]*Sqrt[b + a*x^2])","A",12,9,29,0.3103,1,"{2056, 1254, 466, 490, 1211, 220, 1699, 205, 208}"
1732,1,101,0,0.0501283,"\int \frac{x^{19}}{\sqrt[3]{-1+x^6}} \, dx","Int[x^19/(-1 + x^6)^(1/3),x]","\frac{1}{18} \left(x^6-1\right)^{2/3} x^{14}+\frac{7}{108} \left(x^6-1\right)^{2/3} x^8+\frac{7}{81} \left(x^6-1\right)^{2/3} x^2-\frac{7}{162} \log \left(x^2-\sqrt[3]{x^6-1}\right)+\frac{7 \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}","-\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,"(7*x^2*(-1 + x^6)^(2/3))/81 + (7*x^8*(-1 + x^6)^(2/3))/108 + (x^14*(-1 + x^6)^(2/3))/18 + (7*ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) - (7*Log[x^2 - (-1 + x^6)^(1/3)])/162","A",5,3,13,0.2308,1,"{275, 321, 239}"
1733,1,135,0,0.089456,"\int x^{15} \sqrt[3]{-1+x^6} \, dx","Int[x^15*(-1 + x^6)^(1/3),x]","\frac{1}{18} \sqrt[3]{x^6-1} x^{16}-\frac{1}{108} \sqrt[3]{x^6-1} x^{10}-\frac{5}{324} \sqrt[3]{x^6-1} x^4+\frac{5}{486} \log \left(1-\frac{x^2}{\sqrt[3]{x^6-1}}\right)+\frac{5 \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6-1}}+1}{\sqrt{3}}\right)}{162 \sqrt{3}}-\frac{5}{972} \log \left(\frac{x^4}{\left(x^6-1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6-1}}+1\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,"(-5*x^4*(-1 + x^6)^(1/3))/324 - (x^10*(-1 + x^6)^(1/3))/108 + (x^16*(-1 + x^6)^(1/3))/18 + (5*ArcTan[(1 + (2*x^2)/(-1 + x^6)^(1/3))/Sqrt[3]])/(162*Sqrt[3]) + (5*Log[1 - x^2/(-1 + x^6)^(1/3)])/486 - (5*Log[1 + x^4/(-1 + x^6)^(2/3) + x^2/(-1 + x^6)^(1/3)])/972","A",11,10,13,0.7692,1,"{275, 279, 321, 331, 292, 31, 634, 618, 204, 628}"
1734,1,101,0,0.0488511,"\int \frac{x^{19}}{\sqrt[3]{1+x^6}} \, dx","Int[x^19/(1 + x^6)^(1/3),x]","\frac{1}{18} \left(x^6+1\right)^{2/3} x^{14}-\frac{7}{108} \left(x^6+1\right)^{2/3} x^8+\frac{7}{81} \left(x^6+1\right)^{2/3} x^2+\frac{7}{162} \log \left(x^2-\sqrt[3]{x^6+1}\right)-\frac{7 \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}","\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,"(7*x^2*(1 + x^6)^(2/3))/81 - (7*x^8*(1 + x^6)^(2/3))/108 + (x^14*(1 + x^6)^(2/3))/18 - (7*ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) + (7*Log[x^2 - (1 + x^6)^(1/3)])/162","A",5,3,13,0.2308,1,"{275, 321, 239}"
1735,1,135,0,0.0961004,"\int x^{15} \sqrt[3]{1+x^6} \, dx","Int[x^15*(1 + x^6)^(1/3),x]","\frac{1}{18} \sqrt[3]{x^6+1} x^{16}+\frac{1}{108} \sqrt[3]{x^6+1} x^{10}-\frac{5}{324} \sqrt[3]{x^6+1} x^4-\frac{5}{486} \log \left(1-\frac{x^2}{\sqrt[3]{x^6+1}}\right)-\frac{5 \tan ^{-1}\left(\frac{\frac{2 x^2}{\sqrt[3]{x^6+1}}+1}{\sqrt{3}}\right)}{162 \sqrt{3}}+\frac{5}{972} \log \left(\frac{x^4}{\left(x^6+1\right)^{2/3}}+\frac{x^2}{\sqrt[3]{x^6+1}}+1\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,"(-5*x^4*(1 + x^6)^(1/3))/324 + (x^10*(1 + x^6)^(1/3))/108 + (x^16*(1 + x^6)^(1/3))/18 - (5*ArcTan[(1 + (2*x^2)/(1 + x^6)^(1/3))/Sqrt[3]])/(162*Sqrt[3]) - (5*Log[1 - x^2/(1 + x^6)^(1/3)])/486 + (5*Log[1 + x^4/(1 + x^6)^(2/3) + x^2/(1 + x^6)^(1/3)])/972","A",11,10,13,0.7692,1,"{275, 279, 321, 331, 292, 31, 634, 618, 204, 628}"
1736,1,179,0,0.3077325,"\int \frac{-b-a x^3+x^6}{x^6 \sqrt[4]{-b x+a x^4}} \, dx","Int[(-b - a*x^3 + x^6)/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","-\frac{4 \left(a x^4-b x\right)^{3/4}}{21 x^6}-\frac{44 a \left(a x^4-b x\right)^{3/4}}{63 b x^3}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4-b x}}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a} \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*(-(b*x) + a*x^4)^(3/4))/(21*x^6) - (44*a*(-(b*x) + a*x^4)^(3/4))/(63*b*x^3) + (2*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*a^(1/4)*(-(b*x) + a*x^4)^(1/4)) + (2*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*a^(1/4)*(-(b*x) + a*x^4)^(1/4))","A",12,10,31,0.3226,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1737,0,0,0,0.8926914,"\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","Int[(-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,"3*Defer[Int][(1 - x^3 - x^4 + x^6)^(-1/3), x] - 6*Defer[Int][1/((1 - x^4 + x^6)*(1 - x^3 - x^4 + x^6)^(1/3)), x] + 2*Defer[Int][x^4/((1 - x^4 + x^6)*(1 - x^3 - x^4 + x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1738,1,179,0,0.2802421,"\int \frac{-b+a x^6}{x^6 \sqrt[4]{-b x+a x^4}} \, dx","Int[(-b + a*x^6)/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}-\frac{4 \left(a x^4-b x\right)^{3/4}}{21 x^6}-\frac{16 a \left(a x^4-b x\right)^{3/4}}{63 b x^3}","\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,"(-4*(-(b*x) + a*x^4)^(3/4))/(21*x^6) - (16*a*(-(b*x) + a*x^4)^(3/4))/(63*b*x^3) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4))","A",11,10,27,0.3704,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1739,1,179,0,0.273902,"\int \frac{b+a x^6}{x^6 \sqrt[4]{-b x+a x^4}} \, dx","Int[(b + a*x^6)/(x^6*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{2 a^{3/4} \sqrt[4]{x} \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a x^4-b x}}+\frac{4 \left(a x^4-b x\right)^{3/4}}{21 x^6}+\frac{16 a \left(a x^4-b x\right)^{3/4}}{63 b x^3}","\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,"(4*(-(b*x) + a*x^4)^(3/4))/(21*x^6) + (16*a*(-(b*x) + a*x^4)^(3/4))/(63*b*x^3) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4)) + (2*a^(3/4)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*(-(b*x) + a*x^4)^(1/4))","A",11,10,25,0.4000,1,"{2052, 2011, 329, 275, 240, 212, 206, 203, 2016, 2014}"
1740,1,248,0,0.5819485,"\int \frac{\sqrt[4]{x^2+x^4} \left(-1-x^4+x^8\right)}{-1+x^4} \, dx","Int[((x^2 + x^4)^(1/4)*(-1 - x^4 + x^8))/(-1 + x^4),x]","-\frac{7}{192} \sqrt[4]{x^4+x^2} x-\frac{7 \sqrt[4]{x^4+x^2} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{128 \sqrt[4]{x^2+1} \sqrt{x}}-\frac{\sqrt[4]{x^4+x^2} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2^{3/4} \sqrt[4]{x^2+1} \sqrt{x}}+\frac{7 \sqrt[4]{x^4+x^2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{128 \sqrt[4]{x^2+1} \sqrt{x}}+\frac{\sqrt[4]{x^4+x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2^{3/4} \sqrt[4]{x^2+1} \sqrt{x}}+\frac{1}{6} \sqrt[4]{x^4+x^2} x^5+\frac{1}{48} \sqrt[4]{x^4+x^2} x^3","-\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,"(-7*x*(x^2 + x^4)^(1/4))/192 + (x^3*(x^2 + x^4)^(1/4))/48 + (x^5*(x^2 + x^4)^(1/4))/6 - (7*(x^2 + x^4)^(1/4)*ArcTan[Sqrt[x]/(1 + x^2)^(1/4)])/(128*Sqrt[x]*(1 + x^2)^(1/4)) - ((x^2 + x^4)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4)) + (7*(x^2 + x^4)^(1/4)*ArcTanh[Sqrt[x]/(1 + x^2)^(1/4)])/(128*Sqrt[x]*(1 + x^2)^(1/4)) + ((x^2 + x^4)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2^(3/4)*Sqrt[x]*(1 + x^2)^(1/4))","B",24,11,29,0.3793,1,"{2056, 1586, 6725, 321, 329, 331, 298, 203, 206, 466, 494}"
1741,1,507,0,1.1691134,"\int \frac{-b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Int[(-b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\frac{\left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4}}-\frac{\left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4}}+\frac{\left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4}}-\frac{\left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4}}+\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{$\#$1}^8+\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$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,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + ((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)) - ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + ((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)) - ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4))","B",25,10,42,0.2381,1,"{6728, 240, 212, 206, 203, 1428, 408, 377, 208, 205}"
1742,1,507,0,0.6977221,"\int \frac{-b-a x^4+2 x^8}{\sqrt[4]{b+a x^4} \left(-b-a x^4+x^8\right)} \, dx","Int[(-b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\frac{\left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4}}-\frac{\left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4}}+\frac{\left(-a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(a-\sqrt{a^2+4 b}\right)^{3/4}}-\frac{\left(a \sqrt{a^2+4 b}+a^2+2 b\right)^{3/4} \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 \sqrt{a^2+4 b} \left(\sqrt{a^2+4 b}+a\right)^{3/4}}+\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{$\#$1}^8+\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[4]{a x^4+b}-\text{$\#$1} x\right)-\text{$\#$1}^3 \log (x)}{2 \text{$\#$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,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + ((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)) - ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + ((a^2 + 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a - Sqrt[a^2 + 4*b])^(3/4)) - ((a^2 + 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*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))])/(2*Sqrt[a^2 + 4*b]*(a + Sqrt[a^2 + 4*b])^(3/4))","B",25,10,42,0.2381,1,"{6728, 240, 212, 206, 203, 1428, 408, 377, 208, 205}"
1743,0,0,0,3.9241163,"\int \frac{\sqrt{c x^2-x \sqrt{-b x+a x^2}}}{x^3 \sqrt{-b x+a x^2}} \, dx","Int[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,"(2*Sqrt[x]*Sqrt[-b + a*x]*Defer[Subst][Defer[Int][Sqrt[c*x^4 - x^2*Sqrt[-(b*x^2) + a*x^4]]/(x^6*Sqrt[-b + a*x^2]), x], x, Sqrt[x]])/Sqrt[-(b*x) + a*x^2]","F",0,0,0,0,-1,"{}"
1744,1,73,0,0.0185351,"\int \frac{b+x^3}{\sqrt[3]{a+x^3}} \, dx","Int[(b + x^3)/(a + x^3)^(1/3),x]","\frac{1}{6} (a-3 b) \log \left(\sqrt[3]{a+x^3}-x\right)-\frac{(a-3 b) \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{a+x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{1}{3} x \left(a+x^3\right)^{2/3}","\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))/3 - ((a - 3*b)*ArcTan[(1 + (2*x)/(a + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + ((a - 3*b)*Log[-x + (a + x^3)^(1/3)])/6","A",2,2,15,0.1333,1,"{388, 239}"
1745,1,223,0,0.1597794,"\int \frac{b+a x^2}{\sqrt[3]{x+x^3}} \, dx","Int[(b + a*x^2)/(x + x^3)^(1/3),x]","\frac{1}{2} a \left(x^3+x\right)^{2/3}+\frac{a \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-\sqrt[3]{x^2+1}\right)}{4 \sqrt[3]{x^3+x}}-\frac{a \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{x^3+x}}-\frac{3 b \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-\sqrt[3]{x^2+1}\right)}{4 \sqrt[3]{x^3+x}}+\frac{\sqrt{3} b \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\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,"(a*(x + x^3)^(2/3))/2 - (a*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*(x + x^3)^(1/3)) + (Sqrt[3]*b*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*(x + x^3)^(1/3)) + (a*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(4*(x + x^3)^(1/3)) - (3*b*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(4*(x + x^3)^(1/3))","A",11,6,17,0.3529,1,"{2053, 2011, 329, 275, 239, 2024}"
1746,1,174,0,0.0868113,"\int \sqrt[3]{-x^2+x^3} \, dx","Int[(-x^2 + x^3)^(1/3),x]","\frac{1}{2} \sqrt[3]{x^3-x^2} x-\frac{1}{6} \sqrt[3]{x^3-x^2}+\frac{(x-1)^{2/3} x^{4/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{6 \left(x^3-x^2\right)^{2/3}}+\frac{(x-1)^{2/3} x^{4/3} \log (x-1)}{18 \left(x^3-x^2\right)^{2/3}}+\frac{(x-1)^{2/3} x^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \left(x^3-x^2\right)^{2/3}}","\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,"-1/6*(-x^2 + x^3)^(1/3) + (x*(-x^2 + x^3)^(1/3))/2 + ((-1 + x)^(2/3)*x^(4/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(3*Sqrt[3]*(-x^2 + x^3)^(2/3)) + ((-1 + x)^(2/3)*x^(4/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(6*(-x^2 + x^3)^(2/3)) + ((-1 + x)^(2/3)*x^(4/3)*Log[-1 + x])/(18*(-x^2 + x^3)^(2/3))","A",4,4,13,0.3077,1,"{2004, 2024, 2032, 59}"
1747,1,200,0,0.189727,"\int x^2 \sqrt[3]{x^2+x^3} \, dx","Int[x^2*(x^2 + x^3)^(1/3),x]","\frac{1}{4} \sqrt[3]{x^3+x^2} x^3+\frac{1}{36} \sqrt[3]{x^3+x^2} x^2-\frac{1}{27} \sqrt[3]{x^3+x^2} x+\frac{5}{81} \sqrt[3]{x^3+x^2}+\frac{5 (x+1)^{2/3} x^{4/3} \log (x+1)}{243 \left(x^3+x^2\right)^{2/3}}+\frac{5 (x+1)^{2/3} x^{4/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x+1}}-1\right)}{81 \left(x^3+x^2\right)^{2/3}}+\frac{10 (x+1)^{2/3} x^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{81 \sqrt{3} \left(x^3+x^2\right)^{2/3}}","\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,"(5*(x^2 + x^3)^(1/3))/81 - (x*(x^2 + x^3)^(1/3))/27 + (x^2*(x^2 + x^3)^(1/3))/36 + (x^3*(x^2 + x^3)^(1/3))/4 + (10*x^(4/3)*(1 + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(81*Sqrt[3]*(x^2 + x^3)^(2/3)) + (5*x^(4/3)*(1 + x)^(2/3)*Log[1 + x])/(243*(x^2 + x^3)^(2/3)) + (5*x^(4/3)*(1 + x)^(2/3)*Log[-1 + x^(1/3)/(1 + x)^(1/3)])/(81*(x^2 + x^3)^(2/3))","A",6,4,15,0.2667,1,"{2021, 2024, 2032, 59}"
1748,0,0,0,0.1407772,"\int \frac{x^4}{\left(1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","Int[x^4/((1 + x^4)^2*(x^2 + x^4)^(1/4)),x]","\int \frac{x^4}{\left(1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]+\frac{\left(x^4+x^2\right)^{3/4} \left(x^2-1\right)}{8 x \left(x^4+1\right)}",1,"(2*Sqrt[x]*(1 + x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((1 + x^4)^(1/4)*(1 + x^8)^2), x], x, Sqrt[x]])/(x^2 + x^4)^(1/4)","F",0,0,0,0,-1,"{}"
1749,0,0,0,0.1392137,"\int \frac{x^4}{\left(1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","Int[x^4/((1 + x^4)^2*(x^2 + x^4)^(1/4)),x]","\int \frac{x^4}{\left(1+x^4\right)^2 \sqrt[4]{x^2+x^4}} \, dx","\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4+2\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4+x^2}-\text{$\#$1} x\right)-2 \log (x)}{\text{$\#$1}^5-\text{$\#$1}}\&\right]+\frac{\left(x^4+x^2\right)^{3/4} \left(x^2-1\right)}{8 x \left(x^4+1\right)}",1,"(2*Sqrt[x]*(1 + x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((1 + x^4)^(1/4)*(1 + x^8)^2), x], x, Sqrt[x]])/(x^2 + x^4)^(1/4)","F",0,0,0,0,-1,"{}"
1750,0,0,0,1.6307259,"\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","Int[((-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,"(-I)*Defer[Int][(1 + x^3 + x^4)^(2/3)/((-1)^(1/4) - x), x] + I*Defer[Int][(1 + x^3 + x^4)^(2/3)/(-(-1)^(3/4) - x), x] - 3*Defer[Int][(1 + x^3 + x^4)^(2/3)/x^6, x] + 3*Defer[Int][(1 + x^3 + x^4)^(2/3)/x^3, x] + Defer[Int][(1 + x^3 + x^4)^(2/3)/x^2, x] + I*Defer[Int][(1 + x^3 + x^4)^(2/3)/((-1)^(1/4) + x), x] - I*Defer[Int][(1 + x^3 + x^4)^(2/3)/(-(-1)^(3/4) + x), x]","F",0,0,0,0,-1,"{}"
1751,1,491,0,1.4324227,"\int \frac{-b+2 a x^4}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + 2*a*x^4)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}","\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,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) + (2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",17,9,35,0.2571,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1752,1,491,0,1.1739269,"\int \frac{-b+2 a x^4}{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + 2*a*x^4)/((b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{a-\sqrt{-a} \sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{x} \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[4]{\sqrt{-a} \sqrt{b}+a} \sqrt[4]{a x^4+b x^2}}","\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,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) + (2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a - Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*(a + Sqrt[-a]*Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",17,9,35,0.2571,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1753,1,123,0,0.5951051,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{x+x^5}} \, dx","Int[(1 + x^2)/((-1 + x^2)*(x + x^5)^(1/3)),x]","-\frac{3 \sqrt[3]{x^4+1} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};x^4,-x^4\right)}{\sqrt[3]{x^5+x}}-\frac{3 \sqrt[3]{x^4+1} x^3 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};x^4,-x^4\right)}{4 \sqrt[3]{x^5+x}}+\frac{3 \sqrt[3]{x^4+1} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};-x^4\right)}{2 \sqrt[3]{x^5+x}}","\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,"(-3*x*(1 + x^4)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, x^4, -x^4])/(x + x^5)^(1/3) - (3*x^3*(1 + x^4)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, x^4, -x^4])/(4*(x + x^5)^(1/3)) + (3*x*(1 + x^4)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^4])/(2*(x + x^5)^(1/3))","C",10,8,22,0.3636,0,"{2056, 6715, 6725, 245, 1438, 429, 465, 510}"
1754,1,147,0,0.5861415,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(1+x^2\right)} \, dx","Int[((-1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(1 + x^2)),x]","\frac{8 \sqrt[4]{x^6+x^2} x F_1\left(\frac{3}{8};1,\frac{3}{4};\frac{11}{8};x^4,-x^4\right)}{3 \sqrt[4]{x^4+1}}-\frac{8 \sqrt[4]{x^6+x^2} x^3 F_1\left(\frac{7}{8};1,\frac{3}{4};\frac{15}{8};x^4,-x^4\right)}{7 \sqrt[4]{x^4+1}}-\frac{4 \sqrt[4]{x^6+x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};-x^4\right)}{3 \sqrt[4]{x^4+1}}+\frac{2 \sqrt[4]{x^6+x^2}}{x}","\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,"(2*(x^2 + x^6)^(1/4))/x + (8*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, 1, 3/4, 11/8, x^4, -x^4])/(3*(1 + x^4)^(1/4)) - (8*x^3*(x^2 + x^6)^(1/4)*AppellF1[7/8, 1, 3/4, 15/8, x^4, -x^4])/(7*(1 + x^4)^(1/4)) - (4*x*(x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, -x^4])/(3*(1 + x^4)^(1/4))","C",20,11,27,0.4074,0,"{2056, 6725, 277, 329, 364, 1312, 1336, 325, 1337, 466, 510}"
1755,1,147,0,0.5495636,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^2+x^6}}{x^2 \left(1+x^2\right)} \, dx","Int[((-1 + x^2)*(x^2 + x^6)^(1/4))/(x^2*(1 + x^2)),x]","\frac{8 \sqrt[4]{x^6+x^2} x F_1\left(\frac{3}{8};1,\frac{3}{4};\frac{11}{8};x^4,-x^4\right)}{3 \sqrt[4]{x^4+1}}-\frac{8 \sqrt[4]{x^6+x^2} x^3 F_1\left(\frac{7}{8};1,\frac{3}{4};\frac{15}{8};x^4,-x^4\right)}{7 \sqrt[4]{x^4+1}}-\frac{4 \sqrt[4]{x^6+x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};-x^4\right)}{3 \sqrt[4]{x^4+1}}+\frac{2 \sqrt[4]{x^6+x^2}}{x}","\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,"(2*(x^2 + x^6)^(1/4))/x + (8*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, 1, 3/4, 11/8, x^4, -x^4])/(3*(1 + x^4)^(1/4)) - (8*x^3*(x^2 + x^6)^(1/4)*AppellF1[7/8, 1, 3/4, 15/8, x^4, -x^4])/(7*(1 + x^4)^(1/4)) - (4*x*(x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, -x^4])/(3*(1 + x^4)^(1/4))","C",20,11,27,0.4074,0,"{2056, 6725, 277, 329, 364, 1312, 1336, 325, 1337, 466, 510}"
1756,1,224,0,0.4808634,"\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","Int[((-1 + x^3)^(2/3)*(1 - 5*x^3 + 4*x^6))/(x^6*(-1 + 2*x^3)^2),x]","-\frac{2 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,2 x^3\right)}{\left(1-x^3\right)^{2/3}}-\frac{2 x \left(x^3-1\right)^{2/3}}{3 \left(1-2 x^3\right)}+\frac{4}{9} \log \left(\frac{x}{\sqrt[3]{x^3-1}}+1\right)+\frac{1}{2} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{4 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}+\frac{\left(x^3-1\right)^{2/3}}{2 x^2}-\frac{2}{9} \log \left(-\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+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)/(2*x^2) - (2*x*(-1 + x^3)^(2/3))/(3*(1 - 2*x^3)) + (-1 + x^3)^(5/3)/(5*x^5) - (2*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, 2*x^3])/(1 - x^3)^(2/3) - (4*ArcTan[(1 - (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - (2*Log[1 + x^2/(-1 + x^3)^(2/3) - x/(-1 + x^3)^(1/3)])/9 + (4*Log[1 + x/(-1 + x^3)^(1/3)])/9 + Log[-x + (-1 + x^3)^(1/3)]/2","C",15,14,34,0.4118,0,"{6742, 264, 277, 239, 378, 377, 200, 31, 634, 618, 204, 628, 430, 429}"
1757,1,131,0,0.4867481,"\int \frac{\sqrt{1+x} \sqrt{1+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Int[(Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])/(x - Sqrt[1 + x]),x]","\frac{4}{3} \left(\sqrt{x+1}+1\right)^{3/2}+4 \sqrt{\sqrt{x+1}+1}-4 \sqrt{\frac{1}{5} \left(9+4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} \sqrt{\sqrt{x+1}+1}\right)+4 \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} \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*(1 + Sqrt[1 + x])^(3/2))/3 - 4*Sqrt[(9 + 4*Sqrt[5])/5]*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*Sqrt[1 + Sqrt[1 + x]]] + 4*Sqrt[(9 - 4*Sqrt[5])/5]*ArcTanh[Sqrt[(3 + Sqrt[5])/2]*Sqrt[1 + Sqrt[1 + x]]]","A",7,4,34,0.1176,0,"{897, 1287, 1166, 207}"
1758,1,148,0,0.2480187,"\int \frac{\sqrt{b+a x}}{\sqrt{a b x+\sqrt{b+a x}}} \, dx","Int[Sqrt[b + a*x]/Sqrt[a*b*x + Sqrt[b + a*x]],x]","\frac{\sqrt{a x+b} \sqrt{b (a x+b)+\sqrt{a x+b}-b^2}}{a b}-\frac{3 \sqrt{b (a x+b)+\sqrt{a x+b}-b^2}}{2 a b^2}+\frac{\left(4 b^3+3\right) \tanh ^{-1}\left(\frac{2 b \sqrt{a x+b}+1}{2 \sqrt{b} \sqrt{b (a x+b)+\sqrt{a x+b}-b^2}}\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,"(-3*Sqrt[-b^2 + Sqrt[b + a*x] + b*(b + a*x)])/(2*a*b^2) + (Sqrt[b + a*x]*Sqrt[-b^2 + Sqrt[b + a*x] + b*(b + a*x)])/(a*b) + ((3 + 4*b^3)*ArcTanh[(1 + 2*b*Sqrt[b + a*x])/(2*Sqrt[b]*Sqrt[-b^2 + Sqrt[b + a*x] + b*(b + a*x)])])/(4*a*b^(5/2))","A",5,4,28,0.1429,1,"{742, 640, 621, 206}"
1759,0,0,0,0.2183716,"\int \frac{\sqrt{b+a^2 x^4}}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Int[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,"Defer[Int][Sqrt[b + a^2*x^4]/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
1760,0,0,0,3.0667695,"\int \frac{1}{(f+e x) \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Int[1/((f + e*x)*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","\int \frac{1}{(f+e x) \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","\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,"-8*d*(c - d^2)*Defer[Subst][Defer[Int][(b*e*(1 - (c^2*e - 2*c*d^2*e + d^4*e + a*f)/(b*e)) - 4*c*d*(1 - d^2/c)*e*x^2 + 2*c*(1 - (3*d^2)/c)*e*x^4 + 4*d*e*x^6 - e*x^8)^(-1), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]] + 8*(c - 3*d^2)*Defer[Subst][Defer[Int][x^2/(b*e*(1 - (c^2*e - 2*c*d^2*e + d^4*e + a*f)/(b*e)) - 4*c*d*(1 - d^2/c)*e*x^2 + 2*c*(1 - (3*d^2)/c)*e*x^4 + 4*d*e*x^6 - e*x^8), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]] + 24*d*Defer[Subst][Defer[Int][x^4/(b*e*(1 - (c^2*e - 2*c*d^2*e + d^4*e + a*f)/(b*e)) - 4*c*d*(1 - d^2/c)*e*x^2 + 2*c*(1 - (3*d^2)/c)*e*x^4 + 4*d*e*x^6 - e*x^8), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]] + 8*Defer[Subst][Defer[Int][x^6/(-(b*e*(1 - (c^2*e - 2*c*d^2*e + d^4*e + a*f)/(b*e))) + 4*c*d*(1 - d^2/c)*e*x^2 - 2*c*(1 - (3*d^2)/c)*e*x^4 - 4*d*e*x^6 + e*x^8), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]]","F",0,0,0,0,-1,"{}"
1761,0,0,0,3.9130373,"\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","Int[(-(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,"-(((a - 2*b + Sqrt[-4*a*b + 4*b^2 + a^2*d]/Sqrt[d])*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Int][1/(x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*(2*b - a*d - Sqrt[d]*Sqrt[-4*a*b + 4*b^2 + a^2*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)^2*x))^(1/4)) - ((a - 2*b - Sqrt[-4*a*b + 4*b^2 + a^2*d]/Sqrt[d])*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Int][1/(x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*(2*b - a*d + Sqrt[d]*Sqrt[-4*a*b + 4*b^2 + a^2*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)^2*x))^(1/4)","F",0,0,0,0,-1,"{}"
1762,1,161,0,0.1015432,"\int x^{13} \sqrt[3]{-1+x^3} \, dx","Int[x^13*(-1 + x^3)^(1/3),x]","\frac{22 \log \left(1-\frac{x}{\sqrt[3]{x^3-1}}\right)}{2187}+\frac{22 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{729 \sqrt{3}}+\frac{1}{15} \sqrt[3]{x^3-1} x^{14}-\frac{1}{180} \sqrt[3]{x^3-1} x^{11}-\frac{11 \sqrt[3]{x^3-1} x^8}{1620}-\frac{11 \sqrt[3]{x^3-1} x^5}{1215}-\frac{11}{729} \sqrt[3]{x^3-1} x^2-\frac{11 \log \left(\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+1\right)}{2187}","\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,"(-11*x^2*(-1 + x^3)^(1/3))/729 - (11*x^5*(-1 + x^3)^(1/3))/1215 - (11*x^8*(-1 + x^3)^(1/3))/1620 - (x^11*(-1 + x^3)^(1/3))/180 + (x^14*(-1 + x^3)^(1/3))/15 + (22*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(729*Sqrt[3]) + (22*Log[1 - x/(-1 + x^3)^(1/3)])/2187 - (11*Log[1 + x^2/(-1 + x^3)^(2/3) + x/(-1 + x^3)^(1/3)])/2187","A",12,9,13,0.6923,1,"{279, 321, 331, 292, 31, 634, 618, 204, 628}"
1763,0,0,0,9.5590461,"\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","Int[(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,"(4*(3*a - 2*b)*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^6*Sqrt[-b + x^4])/((-a + x^4)^(1/4)*(a^3 - 3*a^2*(1 - (b^2*d)/(3*a^2))*x^4 + 3*a*(1 - (2*b*d)/(3*a))*x^8 - (1 - d)*x^12)), x], x, x^(1/4)])/(-((a - x)*(b - x)^2*x))^(1/4) + (4*a*b*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[-b + x^4])/((-a + x^4)^(1/4)*(-a^3 + 3*a^2*(1 - (b^2*d)/(3*a^2))*x^4 - 3*a*(1 - (2*b*d)/(3*a))*x^8 + (1 - d)*x^12)), x], x, x^(1/4)])/(-((a - x)*(b - x)^2*x))^(1/4)","F",0,0,0,0,-1,"{}"
1764,1,504,0,1.8713774,"\int \frac{\sqrt[3]{x+2 x^3} \left(-1+x^4\right)}{x^4 \left(2-x^2+x^4\right)} \, dx","Int[((x + 2*x^3)^(1/3)*(-1 + x^4))/(x^4*(2 - x^2 + x^4)),x]","\frac{3 \left(-5 \sqrt{7}+7 i\right) \sqrt[3]{2 x^3+x} \left(-\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)\right)+3 \left(2 \left(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 \left(1+i \sqrt{7}\right) x^2-i \sqrt{7}+3\right)\right)}{224 \left(-\sqrt{7}+5 i\right) x^3 \left(2 x^2+1\right)}+\frac{3 \left(5 \sqrt{7}+7 i\right) \sqrt[3]{2 x^3+x} \left(-\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)\right)+3 \left(2 \left(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 \left(1-i \sqrt{7}\right) x^2+i \sqrt{7}+3\right)\right)}{224 \left(\sqrt{7}+5 i\right) x^3 \left(2 x^2+1\right)}-\frac{3 \sqrt[3]{2 x^3+x} \left(2 x^2+1\right)}{8 x^3}","\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*(1 + 2*x^2)*(x + 2*x^3)^(1/3))/(8*x^3) + (3*(7*I - 5*Sqrt[7])*(x + 2*x^3)^(1/3)*(2*(1 + 2*x^2)*(3 - I*Sqrt[7] - 3*(1 + 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] + 2*(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))]))/(224*(5*I - Sqrt[7])*x^3*(1 + 2*x^2)) + (3*(7*I + 5*Sqrt[7])*(x + 2*x^3)^(1/3)*(2*(1 + 2*x^2)*(3 + I*Sqrt[7] - 3*(1 - 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] + 2*(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))]))/(224*(5*I + Sqrt[7])*x^3*(1 + 2*x^2))","C",12,6,32,0.1875,0,"{2056, 6728, 264, 466, 465, 510}"
1765,1,503,0,1.3744777,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + 2*a*x^4)/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}","\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,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) + (2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",17,9,35,0.2571,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1766,1,503,0,1.1719811,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(b + 2*a*x^4)/((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2+b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^2}}","\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,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) + (2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (3*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(b*x^2 + a*x^4)^(1/4))","B",17,9,35,0.2571,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1767,0,0,0,1.5360918,"\int \frac{\left(1+x^6\right) \left(-1-x^3+x^6\right)^{2/3}}{x^3 \left(-1+x^6\right)} \, dx","Int[((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,"((-1 - x^3 + x^6)^(2/3)*AppellF1[-2/3, -2/3, -2/3, 1/3, (2*x^3)/(1 + Sqrt[5]), (2*x^3)/(1 - Sqrt[5])])/(2*x^2*(1 - (2*x^3)/(1 - Sqrt[5]))^(2/3)*(1 - (2*x^3)/(1 + Sqrt[5]))^(2/3)) + Defer[Int][(-1 - x^3 + x^6)^(2/3)/(-1 + x), x]/3 + Defer[Int][(-1 - x^3 + x^6)^(2/3)/(1 + x), x]/3 - ((1 + I*Sqrt[3])*Defer[Int][(-1 - x^3 + x^6)^(2/3)/(-1 - I*Sqrt[3] + 2*x), x])/3 - ((1 - I*Sqrt[3])*Defer[Int][(-1 - x^3 + x^6)^(2/3)/(1 - I*Sqrt[3] + 2*x), x])/3 - ((1 - I*Sqrt[3])*Defer[Int][(-1 - x^3 + x^6)^(2/3)/(-1 + I*Sqrt[3] + 2*x), x])/3 - ((1 + I*Sqrt[3])*Defer[Int][(-1 - x^3 + x^6)^(2/3)/(1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
1768,0,0,0,1.7474407,"\int \frac{\left(4+x^6\right) \sqrt[4]{-2-x^4+x^6}}{x^2 \left(-2+x^6\right)} \, dx","Int[((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,"-1/2*Defer[Int][(-2 - x^4 + x^6)^(1/4)/(2^(1/6) - x), x]/2^(1/6) - 2*Defer[Int][(-2 - x^4 + x^6)^(1/4)/x^2, x] - Defer[Int][(-2 - x^4 + x^6)^(1/4)/(2^(1/6) + x), x]/(2*2^(1/6)) - ((-1)^(2/3)*Defer[Int][(-2 - x^4 + x^6)^(1/4)/(2^(1/6) - (-1)^(1/3)*x), x])/(2*2^(1/6)) - ((-1)^(2/3)*Defer[Int][(-2 - x^4 + x^6)^(1/4)/(2^(1/6) + (-1)^(1/3)*x), x])/(2*2^(1/6)) + ((-1)^(1/3)*Defer[Int][(-2 - x^4 + x^6)^(1/4)/(2^(1/6) - (-1)^(2/3)*x), x])/(2*2^(1/6)) + ((-1)^(1/3)*Defer[Int][(-2 - x^4 + x^6)^(1/4)/(2^(1/6) + (-1)^(2/3)*x), x])/(2*2^(1/6))","F",0,0,0,0,-1,"{}"
1769,1,196,0,0.2531439,"\int \sqrt[4]{b x^7+a x^8} \, dx","Int[(b*x^7 + a*x^8)^(1/4),x]","-\frac{7 b^3 x^{21/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{64 a^{11/4} \left(a x^8+b x^7\right)^{3/4}}+\frac{7 b^3 x^{21/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{64 a^{11/4} \left(a x^8+b x^7\right)^{3/4}}-\frac{7 b^2 \sqrt[4]{a x^8+b x^7}}{96 a^2 x}+\frac{1}{3} x \sqrt[4]{a x^8+b x^7}+\frac{b \sqrt[4]{a x^8+b x^7}}{24 a}","\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,"(b*(b*x^7 + a*x^8)^(1/4))/(24*a) - (7*b^2*(b*x^7 + a*x^8)^(1/4))/(96*a^2*x) + (x*(b*x^7 + a*x^8)^(1/4))/3 - (7*b^3*x^(21/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(64*a^(11/4)*(b*x^7 + a*x^8)^(3/4)) + (7*b^3*x^(21/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(64*a^(11/4)*(b*x^7 + a*x^8)^(3/4))","A",9,8,15,0.5333,1,"{2004, 2024, 2032, 63, 331, 298, 203, 206}"
1770,0,0,0,1.2077376,"\int \frac{-1+x^{10}}{\sqrt{1+x^4} \left(1+x^{10}\right)} \, dx","Int[(-1 + x^10)/(Sqrt[1 + x^4]*(1 + x^10)),x]","\int \frac{-1+x^{10}}{\sqrt{1+x^4} \left(1+x^{10}\right)} \, dx","-\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,"-1/5*ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] + (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (8*Defer[Int][1/(Sqrt[1 + x^4]*(1 - x^2 + x^4 - x^6 + x^8)), x])/5 + (6*Defer[Int][x^2/(Sqrt[1 + x^4]*(1 - x^2 + x^4 - x^6 + x^8)), x])/5 - (4*Defer[Int][x^4/(Sqrt[1 + x^4]*(1 - x^2 + x^4 - x^6 + x^8)), x])/5 + (2*Defer[Int][x^6/(Sqrt[1 + x^4]*(1 - x^2 + x^4 - x^6 + x^8)), x])/5","F",0,0,0,0,-1,"{}"
1771,0,0,0,1.8800357,"\int \frac{1+x^{10}}{\sqrt{1+x^4} \left(-1+x^{10}\right)} \, dx","Int[(1 + x^10)/(Sqrt[1 + x^4]*(-1 + x^10)),x]","\int \frac{1+x^{10}}{\sqrt{1+x^4} \left(-1+x^{10}\right)} \, dx","-\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,"-1/5*ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] + (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (4*Defer[Int][1/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 + (3*Defer[Int][x/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 - (2*Defer[Int][x^2/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 + Defer[Int][x^3/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x]/5 - (4*Defer[Int][1/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (3*Defer[Int][x/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (2*Defer[Int][x^2/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - Defer[Int][x^3/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x]/5","F",0,0,0,0,-1,"{}"
1772,1,404,0,1.0469634,"\int \frac{1+x^{16}}{\sqrt{1+x^4} \left(-1+x^{16}\right)} \, dx","Int[(1 + x^16)/(Sqrt[1 + x^4]*(-1 + x^16)),x]","-\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}}-\frac{x \left(1-x^2\right)}{8 \sqrt{x^4+1}}-\frac{x \left(x^2+1\right)}{8 \sqrt{x^4+1}}+\frac{i \left(\sqrt{2}+(1+i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}-\frac{i \left(\sqrt{2}+(1-i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{i \left(\sqrt{2}+(-1+i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}-\frac{i \left(\sqrt{2}+(-1-i)\right) \left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{16 \sqrt{x^4+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}","-\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*(x*(1 - x^2))/Sqrt[1 + x^4] - (x*(1 + x^2))/(8*Sqrt[1 + x^4]) - ArcTan[(2^(1/4)*x)/Sqrt[1 + x^4]]/(4*2^(1/4)) - ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(8*Sqrt[2]) - ArcTanh[(2^(1/4)*x)/Sqrt[1 + x^4]]/(4*2^(1/4)) - ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(8*Sqrt[2]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4]) - ((I/16)*((-1 - I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + ((I/16)*((-1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] - ((I/16)*((1 - I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4] + ((I/16)*((1 + I) + Sqrt[2])*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/Sqrt[1 + x^4]","C",37,16,22,0.7273,1,"{6725, 220, 2073, 1222, 1179, 1196, 1211, 1699, 207, 1198, 203, 21, 1429, 409, 1217, 1707}"
1773,1,106,0,0.1186106,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{1-\sqrt{b+a x}} \, dx","Int[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(1 - Sqrt[b + a*x]),x]","-\frac{4 \left(\sqrt{a x+b}+c\right)^{5/2}}{5 a}-\frac{4 (1-c) \left(\sqrt{a x+b}+c\right)^{3/2}}{3 a}-\frac{4 \sqrt{\sqrt{a x+b}+c}}{a}+\frac{4 \sqrt{c+1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a x+b}+c}}{\sqrt{c+1}}\right)}{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]])/a - (4*(1 - c)*(c + Sqrt[b + a*x])^(3/2))/(3*a) - (4*(c + Sqrt[b + a*x])^(5/2))/(5*a) + (4*Sqrt[1 + c]*ArcTanh[Sqrt[c + Sqrt[b + a*x]]/Sqrt[1 + c]])/a","A",7,6,40,0.1500,1,"{513, 446, 88, 50, 63, 206}"
1774,0,0,0,0.3325955,"\int x \sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}} \, dx","Int[x*Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]],x]","\int x \sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}} \, dx","\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,"Defer[Int][x*Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]], x]","F",0,0,0,0,-1,"{}"
1775,1,163,0,0.490747,"\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","Int[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4]*(b*x^3 + a*(q + p*x^2)^3))/x^6,x]","\frac{a p^2 \left(p^2 x^4+q^2\right)^{3/2}}{5 x}+\frac{a q^2 \left(p^2 x^4+q^2\right)^{3/2}}{5 x^5}+\frac{2 a p q \left(p^2 x^4+q^2\right)^{3/2}}{3 x^3}-\frac{1}{2} b p q \tanh ^{-1}\left(\frac{\sqrt{p^2 x^4+q^2}}{q}\right)+\frac{b \left(p x^2+q\right) \sqrt{p^2 x^4+q^2}}{2 x^2}-\frac{1}{2} b p q \tanh ^{-1}\left(\frac{p x^2}{\sqrt{p^2 x^4+q^2}}\right)","\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,"(b*(q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(2*x^2) + (a*q^2*(q^2 + p^2*x^4)^(3/2))/(5*x^5) + (2*a*p*q*(q^2 + p^2*x^4)^(3/2))/(3*x^3) + (a*p^2*(q^2 + p^2*x^4)^(3/2))/(5*x) - (b*p*q*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]])/2 - (b*p*q*ArcTanh[Sqrt[q^2 + p^2*x^4]/q])/2","A",16,13,45,0.2889,1,"{1833, 1584, 1252, 813, 844, 217, 206, 266, 63, 208, 1835, 1586, 449}"
1776,1,113,0,0.4769676,"\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\sqrt{1+x^4}} \, dx","Int[((-1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/Sqrt[1 + x^4],x]","\left(\frac{1}{4}+\frac{i}{4}\right) \sqrt{1-i x^2} x+\left(\frac{1}{4}-\frac{i}{4}\right) \sqrt{1+i x^2} x-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}-\frac{\sin ^{-1}\left(\sqrt[4]{-1} x\right)}{2 \sqrt{2}}+\frac{i \sinh ^{-1}\left(\sqrt[4]{-1} x\right)}{2 \sqrt{2}}","\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,"(1/4 + I/4)*x*Sqrt[1 - I*x^2] + (1/4 - I/4)*x*Sqrt[1 + I*x^2] - ArcSin[(-1)^(1/4)*x]/(2*Sqrt[2]) + ((I/2)*ArcSinh[(-1)^(1/4)*x])/Sqrt[2] - ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",9,7,32,0.2188,0,"{6742, 2132, 206, 2133, 321, 216, 215}"
1777,1,127,0,0.6853592,"\int \frac{x \sqrt{1+x}}{x+\sqrt{1+\sqrt{1+x}}} \, dx","Int[(x*Sqrt[1 + x])/(x + Sqrt[1 + Sqrt[1 + x]]),x]","\frac{2}{3} \left(\sqrt{x+1}+1\right)^3-2 \left(\sqrt{x+1}+1\right)^2-\frac{4}{3} \left(\sqrt{x+1}+1\right)^{3/2}+2 \sqrt{x+1}+\frac{2}{5} \left(5-\sqrt{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)","\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,"2*Sqrt[1 + x] - (4*(1 + Sqrt[1 + x])^(3/2))/3 - 2*(1 + Sqrt[1 + x])^2 + (2*(1 + Sqrt[1 + x])^3)/3 + (2*(5 - Sqrt[5])*Log[1 - Sqrt[5] + 2*Sqrt[1 + Sqrt[1 + x]]])/5 + (2*(5 + Sqrt[5])*Log[1 + Sqrt[5] + 2*Sqrt[1 + Sqrt[1 + x]]])/5","A",7,3,26,0.1154,1,"{1628, 632, 31}"
1778,1,427,0,1.8964056,"\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","Int[((-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) \sqrt[3]{x^3-x} \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(1-x^2\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(1-x^2\right)}\right)+2 \left(1-x^2\right) \left(2 \left(\sqrt{3}+i\right)-3 \left(-\sqrt{3}+i\right) x^2\right)\right)}{64 x^3 \left(1-x^2\right)}+\frac{\left(-\sqrt{3}+6 i\right) \sqrt[3]{x^3-x} \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(1-x^2\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(1-x^2\right)}\right)+2 \left(1-x^2\right) \left(2 \left(-\sqrt{3}+i\right)-3 \left(\sqrt{3}+i\right) x^2\right)\right)}{64 x^3 \left(1-x^2\right)}-\frac{3 \sqrt[3]{x^3-x} \left(1-x^2\right)}{8 x^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,"(-3*(1 - x^2)*(-x + x^3)^(1/3))/(8*x^3) + ((6*I + Sqrt[3])*(-x + x^3)^(1/3)*(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^3*(1 - x^2)) + ((6*I - Sqrt[3])*(-x + x^3)^(1/3)*(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^3*(1 - x^2))","C",14,7,37,0.1892,0,"{2056, 6728, 264, 466, 465, 511, 510}"
1779,1,427,0,1.5956669,"\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","Int[((-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) \sqrt[3]{x^3-x} \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(1-x^2\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(1-x^2\right)}\right)+2 \left(1-x^2\right) \left(2 \left(\sqrt{3}+i\right)-3 \left(-\sqrt{3}+i\right) x^2\right)\right)}{64 x^3 \left(1-x^2\right)}+\frac{\left(-\sqrt{3}+6 i\right) \sqrt[3]{x^3-x} \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(1-x^2\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(1-x^2\right)}\right)+2 \left(1-x^2\right) \left(2 \left(-\sqrt{3}+i\right)-3 \left(\sqrt{3}+i\right) x^2\right)\right)}{64 x^3 \left(1-x^2\right)}-\frac{3 \sqrt[3]{x^3-x} \left(1-x^2\right)}{8 x^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{$\#$1}^6-6 \text{$\#$1}^3+3\&,\frac{-4 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)+4 \text{$\#$1}^3 \log (x)+9 \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-9 \log (x)}{4 \text{$\#$1}^5-3 \text{$\#$1}^2}\&\right]",1,"(-3*(1 - x^2)*(-x + x^3)^(1/3))/(8*x^3) + ((6*I + Sqrt[3])*(-x + x^3)^(1/3)*(2*(1 - x^2)*(2*(I + Sqrt[3]) - 3*(I - Sqrt[3])*x^2) + x^2*(3*I + Sqrt[3] + 3*Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 1, 5/3, (Sqrt[3]*x^2)/((I - Sqrt[3])*(1 - x^2))] - 3*x^2*(3*I + Sqrt[3] - Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 2, 5/3, (Sqrt[3]*x^2)/((I - Sqrt[3])*(1 - x^2))]))/(64*x^3*(1 - x^2)) + ((6*I - Sqrt[3])*(-x + x^3)^(1/3)*(2*(1 - x^2)*(2*(I - Sqrt[3]) - 3*(I + Sqrt[3])*x^2) + x^2*(3*I - Sqrt[3] - 3*Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 1, 5/3, -((Sqrt[3]*x^2)/((I + Sqrt[3])*(1 - x^2)))] - 3*x^2*(3*I - Sqrt[3] + Sqrt[3]*x^2)*Hypergeometric2F1[2/3, 2, 5/3, -((Sqrt[3]*x^2)/((I + Sqrt[3])*(1 - x^2)))]))/(64*x^3*(1 - x^2))","C",14,7,37,0.1892,0,"{2056, 6728, 264, 466, 465, 511, 510}"
1780,0,0,0,0.5005704,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+14 \text{$\#$1}^2-16 \text{$\#$1}+5\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+7 \text{$\#$1}-4}\&\right]",1,"Defer[Int][1/Sqrt[1 - x - x^2 + x^3 + x^4], x] - I*Defer[Int][1/((I - x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x] - I*Defer[Int][1/((I + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x]","F",0,0,0,0,-1,"{}"
1781,0,0,0,0.4059521,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+14 \text{$\#$1}^2-16 \text{$\#$1}+5\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+7 \text{$\#$1}-4}\&\right]",1,"Defer[Int][1/Sqrt[1 - x - x^2 + x^3 + x^4], x] - I*Defer[Int][1/((I - x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x] - I*Defer[Int][1/((I + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x]","F",0,0,0,0,-1,"{}"
1782,0,0,0,0.9662387,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Int[(-1 + x^4)/((1 + x^4)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+6 \text{$\#$1}^2-8 \text{$\#$1}+3\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+3 \text{$\#$1}-2}\&\right]",1,"Defer[Int][1/Sqrt[1 - x - x^2 + x^3 + x^4], x] - ((-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) - x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2 + ((-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) - x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2 - ((-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2 + ((-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2","F",0,0,0,0,-1,"{}"
1783,0,0,0,0.7874266,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Int[(-1 + x^4)/((1 + x^4)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4+6 \text{$\#$1}^2-8 \text{$\#$1}+3\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+3 \text{$\#$1}-2}\&\right]",1,"Defer[Int][1/Sqrt[1 - x - x^2 + x^3 + x^4], x] - ((-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) - x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2 + ((-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) - x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2 - ((-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2 + ((-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x])/2","F",0,0,0,0,-1,"{}"
1784,1,132,0,0.7405135,"\int \frac{b+a x^8}{x^6 \left(-b+a x^4\right) \left(b+a x^4\right)^{3/4}} \, dx","Int[(b + a*x^8)/(x^6*(-b + a*x^4)*(b + a*x^4)^(3/4)),x]","\frac{a \sqrt[4]{a x^4+b}}{5 b^2 x}+\frac{\sqrt[4]{a} (a+b) \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{\sqrt[4]{a} (a+b) \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{\sqrt[4]{a x^4+b}}{5 b x^5}","\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,"(b + a*x^4)^(1/4)/(5*b*x^5) + (a*(b + a*x^4)^(1/4))/(5*b^2*x) + (a^(1/4)*(a + b)*ArcTan[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(2*2^(3/4)*b^2) - (a^(1/4)*(a + b)*ArcTanh[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(2*2^(3/4)*b^2)","A",9,7,33,0.2121,1,"{6725, 271, 264, 494, 298, 203, 206}"
1785,1,529,0,1.7146965,"\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","Int[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-2*b - c*x^4 + 2*a*x^8)),x]","\frac{a^{3/4} \left(\frac{2 b-c}{\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{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{16 a b+c^2}}\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{a^{3/4} \left(\frac{2 b-c}{\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}}-\frac{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{16 a b+c^2}}\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{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)*(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)) - (a^(3/4)*(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)) + (a^(3/4)*(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)) - (a^(3/4)*(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",10,5,42,0.1190,1,"{6728, 377, 212, 208, 205}"
1786,1,529,0,0.9939938,"\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","Int[(-b + 2*a*x^4)/((-b + a*x^4)^(1/4)*(-2*b - c*x^4 + 2*a*x^8)),x]","\frac{a^{3/4} \left(\frac{2 b-c}{\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{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{16 a b+c^2}}\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{a^{3/4} \left(\frac{2 b-c}{\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}}-\frac{a^{3/4} \left(1-\frac{2 b-c}{\sqrt{16 a b+c^2}}\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{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)*(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)) - (a^(3/4)*(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)) + (a^(3/4)*(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)) - (a^(3/4)*(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",10,5,42,0.1190,1,"{6728, 377, 212, 208, 205}"
1787,0,0,0,63.2005659,"\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","Int[(-(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,"(-8*a*(a - b - c)*(-a + x)^(1/4)*(-b + x)^(1/4)*(-c + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(1/4)*(a - c + x^4)^(1/4)*(a^2*(1 + (b*c - a*(b + c))/a^2)*d + 2*a*(1 - (b + c)/(2*a))*d*x^4 + d*x^8 - x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)*(c - x)))^(1/4) - (8*(a - b - c)*(-a + x)^(1/4)*(-b + x)^(1/4)*(-c + x)^(1/4)*Defer[Subst][Defer[Int][x^6/((a - b + x^4)^(1/4)*(a - c + x^4)^(1/4)*(a^2*(1 + (b*c - a*(b + c))/a^2)*d + 2*a*(1 - (b + c)/(2*a))*d*x^4 + d*x^8 - x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)*(c - x)))^(1/4) + (4*a^2*(-a + x)^(1/4)*(-b + x)^(1/4)*(-c + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(1/4)*(a - c + x^4)^(1/4)*(-(a^2*(1 + (b*c - a*(b + c))/a^2)*d) - 2*a*(1 - (b + c)/(2*a))*d*x^4 - d*x^8 + x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)*(c - x)))^(1/4) + (8*a*(-a + x)^(1/4)*(-b + x)^(1/4)*(-c + x)^(1/4)*Defer[Subst][Defer[Int][x^6/((a - b + x^4)^(1/4)*(a - c + x^4)^(1/4)*(-(a^2*(1 + (b*c - a*(b + c))/a^2)*d) - 2*a*(1 - (b + c)/(2*a))*d*x^4 - d*x^8 + x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)*(c - x)))^(1/4) + (4*(-a + x)^(1/4)*(-b + x)^(1/4)*(-c + x)^(1/4)*Defer[Subst][Defer[Int][x^10/((a - b + x^4)^(1/4)*(a - c + x^4)^(1/4)*(-(a^2*(1 + (b*c - a*(b + c))/a^2)*d) - 2*a*(1 - (b + c)/(2*a))*d*x^4 - d*x^8 + x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)*(c - x)))^(1/4) - (4*(3*b*c - a*(b + c))*(-a + x)^(1/4)*(-b + x)^(1/4)*(-c + x)^(1/4)*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(1/4)*(a - c + x^4)^(1/4)*(a^3*(1 + (b*c*d)/a^3) - (3*a^2 + (b + c)*d)*(a + x^4) + (3*a + d)*(a + x^4)^2 - (a + x^4)^3)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)*(c - x)))^(1/4)","F",0,0,0,0,-1,"{}"
1788,1,150,0,0.294778,"\int \frac{1}{(-b+a x) \sqrt[4]{b^2 x+a^2 x^3}} \, dx","Int[1/((-b + a*x)*(b^2*x + a^2*x^3)^(1/4)),x]","-\frac{4 a x^2 \sqrt[4]{\frac{a^2 x^2}{b^2}+1} F_1\left(\frac{7}{8};1,\frac{1}{4};\frac{15}{8};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{b^2}\right)}{7 b^2 \sqrt[4]{a^2 x^3+b^2 x}}-\frac{4 x \sqrt[4]{\frac{a^2 x^2}{b^2}+1} F_1\left(\frac{3}{8};1,\frac{1}{4};\frac{11}{8};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{b^2}\right)}{3 b \sqrt[4]{a^2 x^3+b^2 x}}","\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,"(-4*x*(1 + (a^2*x^2)/b^2)^(1/4)*AppellF1[3/8, 1, 1/4, 11/8, (a^2*x^2)/b^2, -((a^2*x^2)/b^2)])/(3*b*(b^2*x + a^2*x^3)^(1/4)) - (4*a*x^2*(1 + (a^2*x^2)/b^2)^(1/4)*AppellF1[7/8, 1, 1/4, 15/8, (a^2*x^2)/b^2, -((a^2*x^2)/b^2)])/(7*b^2*(b^2*x + a^2*x^3)^(1/4))","C",8,5,27,0.1852,0,"{2056, 959, 466, 511, 510}"
1789,1,917,0,3.6515692,"\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","Int[((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{5}{64} \left(7+\sqrt{33}\right) \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{7}}\right)+\frac{5}{64} \left(7-\sqrt{33}\right) \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{7}}\right)-\frac{15}{32} \sinh ^{-1}\left(\frac{3-2 x^2}{\sqrt{7}}\right)+2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^4-3 x^2+4}}\right)-\frac{5}{4} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{5} x}{2 \sqrt{x^4-3 x^2+4}}\right)+\frac{5}{8} \tanh ^{-1}\left(\frac{8-3 x^2}{4 \sqrt{x^4-3 x^2+4}}\right)-\frac{5}{8} \sqrt{5} \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)+\frac{5}{8} \sqrt{5} \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)-\frac{25 \left(17+\sqrt{33}\right) \left(x^2+2\right) \sqrt{\frac{x^4-3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{7}{8}\right)}{16 \sqrt{2} \left(33+\sqrt{33}\right) \sqrt{x^4-3 x^2+4}}+\frac{5 \left(9+\sqrt{33}\right) \left(x^2+2\right) \sqrt{\frac{x^4-3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{7}{8}\right)}{32 \sqrt{2} \sqrt{x^4-3 x^2+4}}-\frac{25 \left(17-\sqrt{33}\right) \left(x^2+2\right) \sqrt{\frac{x^4-3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{7}{8}\right)}{16 \sqrt{2} \left(33-\sqrt{33}\right) \sqrt{x^4-3 x^2+4}}+\frac{5 \left(9-\sqrt{33}\right) \left(x^2+2\right) \sqrt{\frac{x^4-3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{7}{8}\right)}{32 \sqrt{2} \sqrt{x^4-3 x^2+4}}-\frac{5 \left(x^2+2\right) \sqrt{\frac{x^4-3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{7}{8}\right)}{4 \sqrt{2} \sqrt{x^4-3 x^2+4}}+\frac{25 \left(17+\sqrt{33}\right) \left(x^2+2\right) \sqrt{\frac{x^4-3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(\frac{33}{32};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{7}{8}\right)}{32 \sqrt{2} \left(33+17 \sqrt{33}\right) \sqrt{x^4-3 x^2+4}}+\frac{25 \left(17-\sqrt{33}\right) \left(x^2+2\right) \sqrt{\frac{x^4-3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(\frac{33}{32};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{7}{8}\right)}{32 \sqrt{2} \left(33-17 \sqrt{33}\right) \sqrt{x^4-3 x^2+4}}+\frac{\sqrt{x^4-3 x^2+4}}{2 x}+\frac{5}{32} \left(1+\sqrt{33}\right) \sqrt{x^4-3 x^2+4}+\frac{5}{32} \left(1-\sqrt{33}\right) \sqrt{x^4-3 x^2+4}-\frac{5}{16} \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,"(-5*Sqrt[4 - 3*x^2 + x^4])/16 + (5*(1 - Sqrt[33])*Sqrt[4 - 3*x^2 + x^4])/32 + (5*(1 + Sqrt[33])*Sqrt[4 - 3*x^2 + x^4])/32 + Sqrt[4 - 3*x^2 + x^4]/(2*x) - (15*ArcSinh[(3 - 2*x^2)/Sqrt[7]])/32 + (5*(7 - Sqrt[33])*ArcSinh[(3 - 2*x^2)/Sqrt[7]])/64 + (5*(7 + Sqrt[33])*ArcSinh[(3 - 2*x^2)/Sqrt[7]])/64 + 2*ArcTanh[x/Sqrt[4 - 3*x^2 + x^4]] - (5*Sqrt[5]*ArcTanh[(Sqrt[5]*x)/(2*Sqrt[4 - 3*x^2 + x^4])])/4 + (5*ArcTanh[(8 - 3*x^2)/(4*Sqrt[4 - 3*x^2 + x^4])])/8 - (5*Sqrt[5]*ArcTanh[(13 + 3*Sqrt[33] + 2*(5 - Sqrt[33])*x^2)/(2*Sqrt[10*(17 - Sqrt[33])]*Sqrt[4 - 3*x^2 + x^4])])/8 + (5*Sqrt[5]*ArcTanh[(13 - 3*Sqrt[33] + 2*(5 + Sqrt[33])*x^2)/(2*Sqrt[10*(17 + Sqrt[33])]*Sqrt[4 - 3*x^2 + x^4])])/8 - (5*(2 + x^2)*Sqrt[(4 - 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 7/8])/(4*Sqrt[2]*Sqrt[4 - 3*x^2 + x^4]) + (5*(9 - Sqrt[33])*(2 + x^2)*Sqrt[(4 - 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 7/8])/(32*Sqrt[2]*Sqrt[4 - 3*x^2 + x^4]) - (25*(17 - Sqrt[33])*(2 + x^2)*Sqrt[(4 - 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 7/8])/(16*Sqrt[2]*(33 - Sqrt[33])*Sqrt[4 - 3*x^2 + x^4]) + (5*(9 + Sqrt[33])*(2 + x^2)*Sqrt[(4 - 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 7/8])/(32*Sqrt[2]*Sqrt[4 - 3*x^2 + x^4]) - (25*(17 + Sqrt[33])*(2 + x^2)*Sqrt[(4 - 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 7/8])/(16*Sqrt[2]*(33 + Sqrt[33])*Sqrt[4 - 3*x^2 + x^4]) + (25*(17 - Sqrt[33])*(2 + x^2)*Sqrt[(4 - 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[33/32, 2*ArcTan[x/Sqrt[2]], 7/8])/(32*Sqrt[2]*(33 - 17*Sqrt[33])*Sqrt[4 - 3*x^2 + x^4]) + (25*(17 + Sqrt[33])*(2 + x^2)*Sqrt[(4 - 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[33/32, 2*ArcTan[x/Sqrt[2]], 7/8])/(32*Sqrt[2]*(33 + 17*Sqrt[33])*Sqrt[4 - 3*x^2 + x^4])","C",53,21,48,0.4375,0,"{6725, 1117, 1197, 1103, 1195, 1114, 734, 843, 619, 215, 724, 206, 1208, 1210, 1698, 207, 6728, 1728, 1216, 1706, 1247}"
1790,1,127,0,0.6492921,"\int \frac{1+x}{(-1+x) \sqrt[3]{x^2+x^4}} \, dx","Int[(1 + x)/((-1 + x)*(x^2 + x^4)^(1/3)),x]","-\frac{3 \sqrt[3]{x^2+1} x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};x^2,-x^2\right)}{2 \sqrt[3]{x^4+x^2}}-\frac{6 \sqrt[3]{x^2+1} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};x^2,-x^2\right)}{\sqrt[3]{x^4+x^2}}+\frac{3 \sqrt[3]{x^2+1} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};-x^2\right)}{\sqrt[3]{x^4+x^2}}","\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,"(-6*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, x^2, -x^2])/(x^2 + x^4)^(1/3) - (3*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, x^2, -x^2])/(2*(x^2 + x^4)^(1/3)) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3)","C",10,8,20,0.4000,0,"{2056, 6733, 6725, 245, 1438, 429, 465, 510}"
1791,1,1906,0,6.2321704,"\int \frac{-b^2+a^4 x^4}{\sqrt{b x+a^2 x^3} \left(b^2+a^4 x^4\right)} \, dx","Int[(-b^2 + a^4*x^4)/(Sqrt[b*x + a^2*x^3]*(b^2 + a^4*x^4)),x]","-\frac{\left(\sqrt{-a^4}-a^2\right)^{3/2} \sqrt{x} \sqrt{a^2 x^2+b} \tan ^{-1}\left(\frac{\sqrt[8]{-a^4} \sqrt{\sqrt{-a^4}-a^2} \sqrt[4]{b} \sqrt{x}}{a \sqrt{a^2 x^2+b}}\right) a^3}{4 \left(-a^4\right)^{13/8} \sqrt[4]{b} \sqrt{a^2 x^3+b x}}-\frac{\left(\sqrt{-a^4}-a^2\right)^{3/2} \sqrt{x} \sqrt{a^2 x^2+b} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-a^4}-a^2} \sqrt[4]{-b} \sqrt{x}}{\sqrt[8]{-a^4} \sqrt{a^2 x^2+b}}\right) a^2}{4 \left(-a^4\right)^{11/8} \sqrt[4]{-b} \sqrt{a^2 x^3+b x}}+\frac{\left(a^2-\sqrt{-a^4}\right)^{3/2} \sqrt{x} \sqrt{a^2 x^2+b} \tan ^{-1}\left(\frac{\sqrt{a^2-\sqrt{-a^4}} \sqrt[4]{-b} \sqrt{x}}{\sqrt[8]{-a^4} \sqrt{a^2 x^2+b}}\right)}{4 \left(-a^4\right)^{3/8} \sqrt[4]{-b} \sqrt{a^2 x^3+b x} a^2}-\frac{\left(a^2+\sqrt{-a^4}\right)^{3/2} \sqrt{x} \sqrt{a^2 x^2+b} \tan ^{-1}\left(\frac{\sqrt{a^2+\sqrt{-a^4}} \sqrt[4]{b} \sqrt{x}}{\sqrt[8]{-a^4} \sqrt{a^2 x^2+b}}\right)}{4 \left(-a^4\right)^{3/8} \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^2}+\frac{\left(a^2-\sqrt{-a^4}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^{5/2}}+\frac{\left(a^2+\sqrt{-a^4}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^{5/2}}-\frac{\left(a-\sqrt[4]{-a^4}\right) \left(a^2+\sqrt{-a^4}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^{7/2}}-\frac{\left(a+\sqrt[4]{-a^4}\right) \left(a^2+\sqrt{-a^4}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^{7/2}}-\frac{\left(a^2-\sqrt{-a^4}\right) \left(a+\frac{\sqrt[4]{-a^4} \sqrt{b}}{\sqrt{-b}}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^{7/2}}-\frac{\left(a^2-\sqrt{-a^4}\right) \left(\sqrt{b} a+\sqrt[4]{-a^4} \sqrt{-b}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 b^{3/4} \sqrt{a^2 x^3+b x} a^{7/2}}+\frac{\left(a+\sqrt[4]{-a^4}\right)^2 \left(a^2+\sqrt{-a^4}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} \Pi \left(\frac{a^3 \left(a-\sqrt[4]{-a^4}\right)^2}{4 \left(-a^4\right)^{5/4}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^{9/2}}+\frac{\left(a-\sqrt[4]{-a^4}\right)^2 \left(a^2+\sqrt{-a^4}\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} \Pi \left(\frac{\left(a+\sqrt[4]{-a^4}\right)^2}{4 a \sqrt[4]{-a^4}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{b} \sqrt{a^2 x^3+b x} a^{9/2}}+\frac{\left(a^2-\sqrt{-a^4}\right) \left(b a^2-2 \sqrt[4]{-a^4} \sqrt{-b^2} a-\sqrt{-a^4} b\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} \Pi \left(\frac{a^3 \left(a \sqrt{-b}-\sqrt[4]{-a^4} \sqrt{b}\right)^2}{4 \left(-a^4\right)^{5/4} \sqrt{-b^2}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 b^{5/4} \sqrt{a^2 x^3+b x} a^{9/2}}+\frac{\left(a^2-\sqrt{-a^4}\right) \left(b a^2+2 \sqrt[4]{-a^4} \sqrt{-b^2} a-\sqrt{-a^4} b\right) \sqrt{x} \left(a x+\sqrt{b}\right) \sqrt{\frac{a^2 x^2+b}{\left(a x+\sqrt{b}\right)^2}} \Pi \left(\frac{\left(\sqrt{-b} a+\sqrt[4]{-a^4} \sqrt{b}\right)^2}{4 a \sqrt[4]{-a^4} \sqrt{-b^2}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{8 b^{5/4} \sqrt{a^2 x^3+b x} a^{9/2}}","-\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,"((a^2 - Sqrt[-a^4])^(3/2)*Sqrt[x]*Sqrt[b + a^2*x^2]*ArcTan[(Sqrt[a^2 - Sqrt[-a^4]]*(-b)^(1/4)*Sqrt[x])/((-a^4)^(1/8)*Sqrt[b + a^2*x^2])])/(4*a^2*(-a^4)^(3/8)*(-b)^(1/4)*Sqrt[b*x + a^2*x^3]) - (a^2*(-a^2 + Sqrt[-a^4])^(3/2)*Sqrt[x]*Sqrt[b + a^2*x^2]*ArcTan[(Sqrt[-a^2 + Sqrt[-a^4]]*(-b)^(1/4)*Sqrt[x])/((-a^4)^(1/8)*Sqrt[b + a^2*x^2])])/(4*(-a^4)^(11/8)*(-b)^(1/4)*Sqrt[b*x + a^2*x^3]) - (a^3*(-a^2 + Sqrt[-a^4])^(3/2)*Sqrt[x]*Sqrt[b + a^2*x^2]*ArcTan[((-a^4)^(1/8)*Sqrt[-a^2 + Sqrt[-a^4]]*b^(1/4)*Sqrt[x])/(a*Sqrt[b + a^2*x^2])])/(4*(-a^4)^(13/8)*b^(1/4)*Sqrt[b*x + a^2*x^3]) - ((a^2 + Sqrt[-a^4])^(3/2)*Sqrt[x]*Sqrt[b + a^2*x^2]*ArcTan[(Sqrt[a^2 + Sqrt[-a^4]]*b^(1/4)*Sqrt[x])/((-a^4)^(1/8)*Sqrt[b + a^2*x^2])])/(4*a^2*(-a^4)^(3/8)*b^(1/4)*Sqrt[b*x + a^2*x^3]) - ((a^2 - Sqrt[-a^4])*((-a^4)^(1/4)*Sqrt[-b] + a*Sqrt[b])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(7/2)*b^(3/4)*Sqrt[b*x + a^2*x^3]) + ((a^2 - Sqrt[-a^4])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(2*a^(5/2)*b^(1/4)*Sqrt[b*x + a^2*x^3]) + ((a^2 + Sqrt[-a^4])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(2*a^(5/2)*b^(1/4)*Sqrt[b*x + a^2*x^3]) - ((a - (-a^4)^(1/4))*(a^2 + Sqrt[-a^4])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(7/2)*b^(1/4)*Sqrt[b*x + a^2*x^3]) - ((a + (-a^4)^(1/4))*(a^2 + Sqrt[-a^4])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(7/2)*b^(1/4)*Sqrt[b*x + a^2*x^3]) - ((a^2 - Sqrt[-a^4])*(a + ((-a^4)^(1/4)*Sqrt[b])/Sqrt[-b])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(7/2)*b^(1/4)*Sqrt[b*x + a^2*x^3]) + ((a + (-a^4)^(1/4))^2*(a^2 + Sqrt[-a^4])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticPi[(a^3*(a - (-a^4)^(1/4))^2)/(4*(-a^4)^(5/4)), 2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(8*a^(9/2)*b^(1/4)*Sqrt[b*x + a^2*x^3]) + ((a - (-a^4)^(1/4))^2*(a^2 + Sqrt[-a^4])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticPi[(a + (-a^4)^(1/4))^2/(4*a*(-a^4)^(1/4)), 2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(8*a^(9/2)*b^(1/4)*Sqrt[b*x + a^2*x^3]) + ((a^2 - Sqrt[-a^4])*(a^2*b - Sqrt[-a^4]*b - 2*a*(-a^4)^(1/4)*Sqrt[-b^2])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticPi[(a^3*(a*Sqrt[-b] - (-a^4)^(1/4)*Sqrt[b])^2)/(4*(-a^4)^(5/4)*Sqrt[-b^2]), 2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(8*a^(9/2)*b^(5/4)*Sqrt[b*x + a^2*x^3]) + ((a^2 - Sqrt[-a^4])*(a^2*b - Sqrt[-a^4]*b + 2*a*(-a^4)^(1/4)*Sqrt[-b^2])*Sqrt[x]*(Sqrt[b] + a*x)*Sqrt[(b + a^2*x^2)/(Sqrt[b] + a*x)^2]*EllipticPi[(a*Sqrt[-b] + (-a^4)^(1/4)*Sqrt[b])^2/(4*a*(-a^4)^(1/4)*Sqrt[-b^2]), 2*ArcTan[(Sqrt[a]*Sqrt[x])/b^(1/4)], 1/2])/(8*a^(9/2)*b^(5/4)*Sqrt[b*x + a^2*x^3])","C",23,9,42,0.2143,0,"{2056, 1586, 6715, 6725, 406, 220, 409, 1217, 1707}"
1792,1,123,0,0.6229959,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[3]{x+x^5}} \, dx","Int[(-1 + x^2)/((1 + x^2)*(x + x^5)^(1/3)),x]","-\frac{3 \sqrt[3]{x^4+1} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};x^4,-x^4\right)}{\sqrt[3]{x^5+x}}+\frac{3 \sqrt[3]{x^4+1} x^3 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};x^4,-x^4\right)}{4 \sqrt[3]{x^5+x}}+\frac{3 \sqrt[3]{x^4+1} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};-x^4\right)}{2 \sqrt[3]{x^5+x}}","-\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,"(-3*x*(1 + x^4)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, x^4, -x^4])/(x + x^5)^(1/3) + (3*x^3*(1 + x^4)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, x^4, -x^4])/(4*(x + x^5)^(1/3)) + (3*x*(1 + x^4)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^4])/(2*(x + x^5)^(1/3))","C",10,8,22,0.3636,0,"{2056, 6715, 6725, 245, 1438, 429, 465, 510}"
1793,1,333,0,1.1469632,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Int[((1 + x^4)*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\frac{\left(\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{9 \left(\sqrt{3}+i\right) \sqrt[4]{1-x^2}}+\frac{\left(\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{9 \left(\sqrt{3}+i\right) \sqrt[4]{1-x^2}}+\frac{\left(-\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{9 \left(-\sqrt{3}+i\right) \sqrt[4]{1-x^2}}+\frac{\left(-\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{9 \left(-\sqrt{3}+i\right) \sqrt[4]{1-x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]",1,"((3*I + Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 - I*Sqrt[3])*x^2)])/(9*(I + Sqrt[3])*(1 - x^2)^(1/4)) + ((3*I + Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 - I*Sqrt[3])*x^2)/2])/(9*(I + Sqrt[3])*(1 - x^2)^(1/4)) + ((3*I - Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 + I*Sqrt[3])*x^2)])/(9*(I - Sqrt[3])*(1 - x^2)^(1/4)) + ((3*I - Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 + I*Sqrt[3])*x^2)/2])/(9*(I - Sqrt[3])*(1 - x^2)^(1/4))","C",17,6,29,0.2069,0,"{2056, 6728, 1270, 1529, 511, 510}"
1794,1,333,0,1.0380328,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Int[((1 + x^4)*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\frac{\left(\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{9 \left(\sqrt{3}+i\right) \sqrt[4]{1-x^2}}+\frac{\left(\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{9 \left(\sqrt{3}+i\right) \sqrt[4]{1-x^2}}+\frac{\left(-\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{9 \left(-\sqrt{3}+i\right) \sqrt[4]{1-x^2}}+\frac{\left(-\sqrt{3}+3 i\right) x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{9 \left(-\sqrt{3}+i\right) \sqrt[4]{1-x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{2 \text{$\#$1}^4-1}\&\right]",1,"((3*I + Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 - I*Sqrt[3])*x^2)])/(9*(I + Sqrt[3])*(1 - x^2)^(1/4)) + ((3*I + Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 - I*Sqrt[3])*x^2)/2])/(9*(I + Sqrt[3])*(1 - x^2)^(1/4)) + ((3*I - Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 + I*Sqrt[3])*x^2)])/(9*(I - Sqrt[3])*(1 - x^2)^(1/4)) + ((3*I - Sqrt[3])*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 + I*Sqrt[3])*x^2)/2])/(9*(I - Sqrt[3])*(1 - x^2)^(1/4))","C",17,6,29,0.2069,0,"{2056, 6728, 1270, 1529, 511, 510}"
1795,1,231,0,0.5996745,"\int \frac{1-2 x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(-2-x^4+2 x^8\right)} \, dx","Int[(1 - 2*x^4 + 2*x^8)/((-1 + x^4)^(1/4)*(-2 - x^4 + 2*x^8)),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{\sqrt[4]{2047-439 \sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}-\frac{\sqrt[4]{2047+439 \sqrt{17}} \tan ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{\sqrt[4]{2047-439 \sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}-\frac{\sqrt[4]{2047+439 \sqrt{17}} \tanh ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} x}{\sqrt{2} \sqrt[4]{x^4-1}}\right)}{4 \sqrt{17}}","-\frac{1}{4} \text{RootSum}\left[2 \text{$\#$1}^8-5 \text{$\#$1}^4+1\&,\frac{-3 \text{$\#$1}^4 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)+3 \text{$\#$1}^4 \log (x)+2 \log \left(\sqrt[4]{x^4-1}-\text{$\#$1} x\right)-2 \log (x)}{4 \text{$\#$1}^5-5 \text{$\#$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,"ArcTan[x/(-1 + x^4)^(1/4)]/2 - ((2047 - 439*Sqrt[17])^(1/4)*ArcTan[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(4*Sqrt[17]) - ((2047 + 439*Sqrt[17])^(1/4)*ArcTan[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/(4*Sqrt[17]) + ArcTanh[x/(-1 + x^4)^(1/4)]/2 - ((2047 - 439*Sqrt[17])^(1/4)*ArcTanh[((2/(5 + Sqrt[17]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(4*Sqrt[17]) - ((2047 + 439*Sqrt[17])^(1/4)*ArcTanh[((5 + Sqrt[17])^(1/4)*x)/(Sqrt[2]*(-1 + x^4)^(1/4))])/(4*Sqrt[17])","A",16,6,36,0.1667,0,"{6728, 240, 212, 206, 203, 377}"
1796,0,0,0,2.0090071,"\int \frac{\sqrt{-x+x^2} \sqrt{x^2-x \sqrt{-x+x^2}}}{x^3} \, dx","Int[(Sqrt[-x + x^2]*Sqrt[x^2 - x*Sqrt[-x + x^2]])/x^3,x]","\int \frac{\sqrt{-x+x^2} \sqrt{x^2-x \sqrt{-x+x^2}}}{x^3} \, dx","\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[-x + x^2]*Defer[Subst][Defer[Int][(Sqrt[-1 + x^2]*Sqrt[x^4 - x^2*Sqrt[-x^2 + x^4]])/x^4, x], x, Sqrt[x]])/(Sqrt[-1 + x]*Sqrt[x])","F",0,0,0,0,-1,"{}"
1797,0,0,0,0.0321584,"\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","Int[(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,"Defer[Int][(b + 2*a*x)/((c + b*x + a*x^2)^(1/4)*(5*c + 4*b*x + 4*a*x^2)), x]","F",0,0,0,0,-1,"{}"
1798,1,240,0,0.2628542,"\int x^6 \sqrt[3]{-x+x^3} \, dx","Int[x^6*(-x + x^3)^(1/3),x]","-\frac{1}{54} \sqrt[3]{x^3-x} x^3-\frac{5}{162} \sqrt[3]{x^3-x} x+\frac{1}{8} \sqrt[3]{x^3-x} x^7-\frac{1}{72} \sqrt[3]{x^3-x} x^5+\frac{5 \left(x^2-1\right)^{2/3} x^{2/3} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{243 \left(x^3-x\right)^{2/3}}-\frac{5 \left(x^2-1\right)^{2/3} x^{2/3} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{486 \left(x^3-x\right)^{2/3}}+\frac{5 \left(x^2-1\right)^{2/3} x^{2/3} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{81 \sqrt{3} \left(x^3-x\right)^{2/3}}","\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,"(-5*x*(-x + x^3)^(1/3))/162 - (x^3*(-x + x^3)^(1/3))/54 - (x^5*(-x + x^3)^(1/3))/72 + (x^7*(-x + x^3)^(1/3))/8 + (5*x^(2/3)*(-1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(81*Sqrt[3]*(-x + x^3)^(2/3)) + (5*x^(2/3)*(-1 + x^2)^(2/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(243*(-x + x^3)^(2/3)) - (5*x^(2/3)*(-1 + x^2)^(2/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(486*(-x + x^3)^(2/3))","A",14,12,15,0.8000,1,"{2021, 2024, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1799,1,167,0,0.1382182,"\int \frac{1}{\sqrt[3]{-1-x+x^2+x^3}} \, dx","Int[(-1 - x + x^2 + x^3)^(-1/3),x]","-\frac{3 (-x-1)^{2/3} \sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{-x-1}}+1\right)}{2 \sqrt[3]{x^3+x^2-x-1}}-\frac{(-x-1)^{2/3} \sqrt[3]{x-1} \log \left(-\frac{8}{3} (x+1)\right)}{2 \sqrt[3]{x^3+x^2-x-1}}-\frac{\sqrt{3} (-x-1)^{2/3} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{-x-1}}\right)}{\sqrt[3]{x^3+x^2-x-1}}","-\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,"-((Sqrt[3]*(-1 - x)^(2/3)*(-1 + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*(-1 + x)^(1/3))/(Sqrt[3]*(-1 - x)^(1/3))])/(-1 - x + x^2 + x^3)^(1/3)) - (3*(-1 - x)^(2/3)*(-1 + x)^(1/3)*Log[1 + (-1 + x)^(1/3)/(-1 - x)^(1/3)])/(2*(-1 - x + x^2 + x^3)^(1/3)) - ((-1 - x)^(2/3)*(-1 + x)^(1/3)*Log[(-8*(1 + x))/3])/(2*(-1 - x + x^2 + x^3)^(1/3))","A",3,3,15,0.2000,1,"{2067, 2064, 60}"
1800,1,221,0,0.6055783,"\int \frac{1+2 x^4}{\left(-1+x^4\right) \sqrt[4]{-x^2+x^4}} \, dx","Int[(1 + 2*x^4)/((-1 + x^4)*(-x^2 + x^4)^(1/4)),x]","-\frac{3 x}{\sqrt[4]{x^4-x^2}}+\frac{2 \sqrt[4]{x^2-1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{3 \sqrt[4]{x^2-1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}+\frac{2 \sqrt[4]{x^2-1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{3 \sqrt[4]{x^2-1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \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,"(-3*x)/(-x^2 + x^4)^(1/4) + (2*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (3*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4)) + (2*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (3*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4))","A",14,10,28,0.3571,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1404, 382, 377}"
1801,1,321,0,0.4948316,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Int[((-b + a*x^4)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","\frac{3 b^2 x^{3/2} \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{32 a^{3/4} \left(a x^4+b x^2\right)^{3/4}}-\frac{3 b^2 x^{3/2} \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{32 a^{3/4} \left(a x^4+b x^2\right)^{3/4}}+\frac{1}{16} b x \sqrt[4]{a x^4+b x^2}+\frac{2 b \sqrt[4]{a x^4+b x^2}}{x}+\frac{\sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\left(a x^4+b x^2\right)^{3/4}}-\frac{\sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\left(a x^4+b x^2\right)^{3/4}}+\frac{1}{4} a x^3 \sqrt[4]{a x^4+b x^2}","\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,"(2*b*(b*x^2 + a*x^4)^(1/4))/x + (b*x*(b*x^2 + a*x^4)^(1/4))/16 + (a*x^3*(b*x^2 + a*x^4)^(1/4))/4 + (a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(3/4) + (3*b^2*x^(3/2)*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(32*a^(3/4)*(b*x^2 + a*x^4)^(3/4)) - (a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(3/4) - (3*b^2*x^(3/2)*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(32*a^(3/4)*(b*x^2 + a*x^4)^(3/4))","B",17,10,28,0.3571,1,"{2052, 2020, 2032, 329, 331, 298, 203, 206, 2021, 2024}"
1802,1,321,0,0.5070352,"\int \frac{\left(b+a x^4\right) \sqrt[4]{b x^2+a x^4}}{x^2} \, dx","Int[((b + a*x^4)*(b*x^2 + a*x^4)^(1/4))/x^2,x]","\frac{3 b^2 x^{3/2} \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{32 a^{3/4} \left(a x^4+b x^2\right)^{3/4}}-\frac{3 b^2 x^{3/2} \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{32 a^{3/4} \left(a x^4+b x^2\right)^{3/4}}+\frac{1}{16} b x \sqrt[4]{a x^4+b x^2}-\frac{2 b \sqrt[4]{a x^4+b x^2}}{x}-\frac{\sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\left(a x^4+b x^2\right)^{3/4}}+\frac{\sqrt[4]{a} b x^{3/2} \left(a x^2+b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\left(a x^4+b x^2\right)^{3/4}}+\frac{1}{4} a x^3 \sqrt[4]{a x^4+b x^2}","\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,"(-2*b*(b*x^2 + a*x^4)^(1/4))/x + (b*x*(b*x^2 + a*x^4)^(1/4))/16 + (a*x^3*(b*x^2 + a*x^4)^(1/4))/4 - (a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(3/4) + (3*b^2*x^(3/2)*(b + a*x^2)^(3/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(32*a^(3/4)*(b*x^2 + a*x^4)^(3/4)) + (a^(1/4)*b*x^(3/2)*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(b*x^2 + a*x^4)^(3/4) - (3*b^2*x^(3/2)*(b + a*x^2)^(3/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(32*a^(3/4)*(b*x^2 + a*x^4)^(3/4))","B",17,10,26,0.3846,1,"{2052, 2020, 2032, 329, 331, 298, 203, 206, 2021, 2024}"
1803,1,533,0,1.490723,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + 2*a*x^4)/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}","\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,"(2*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (2*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",17,9,36,0.2500,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1804,1,533,0,1.2319828,"\int \frac{b+2 a x^4}{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + 2*a*x^4)/((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4-b x^2}}-\frac{3 \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4-b x^2}}","\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,"(2*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (2*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (3*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",17,9,36,0.2500,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1805,1,130,0,0.0779367,"\int \frac{-b-2 a x^4+2 x^8}{\sqrt[4]{-b+a x^4}} \, dx","Int[(-b - 2*a*x^4 + 2*x^8)/(-b + a*x^4)^(1/4),x]","-\frac{1}{16} x \left(8-\frac{5 b}{a^2}\right) \left(a x^4-b\right)^{3/4}-\frac{b \left(24 a^2-5 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{32 a^{9/4}}-\frac{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{x^5 \left(a x^4-b\right)^{3/4}}{4 a}","\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,"-1/16*((8 - (5*b)/a^2)*x*(-b + a*x^4)^(3/4)) + (x^5*(-b + a*x^4)^(3/4))/(4*a) - ((24*a^2 - 5*b)*b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(32*a^(9/4)) - ((24*a^2 - 5*b)*b*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(32*a^(9/4))","A",6,6,29,0.2069,1,"{1411, 388, 240, 212, 206, 203}"
1806,0,0,0,0.0136631,"\int \frac{-1+x}{\left(-4-2 x+x^2\right) \sqrt[3]{-2-2 x+x^2}} \, dx","Int[(-1 + x)/((-4 - 2*x + x^2)*(-2 - 2*x + x^2)^(1/3)),x]","\int \frac{-1+x}{\left(-4-2 x+x^2\right) \sqrt[3]{-2-2 x+x^2}} \, dx","\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,"Defer[Int][(-1 + x)/((-4 - 2*x + x^2)*(-2 - 2*x + x^2)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1807,1,83,0,0.0710953,"\int \frac{1}{(1+x) \sqrt[3]{3+2 x+x^2}} \, dx","Int[1/((1 + x)*(3 + 2*x + x^2)^(1/3)),x]","-\frac{\log (x+1)}{2 \sqrt[3]{2}}+\frac{3 \log \left(\sqrt[3]{2}-\sqrt[3]{(x+1)^2+2}\right)}{4 \sqrt[3]{2}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{(x+1)^2+2}+1}{\sqrt{3}}\right)}{2 \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,"(Sqrt[3]*ArcTan[(1 + 2^(2/3)*(2 + (1 + x)^2)^(1/3))/Sqrt[3]])/(2*2^(1/3)) - Log[1 + x]/(2*2^(1/3)) + (3*Log[2^(1/3) - (2 + (1 + x)^2)^(1/3)])/(4*2^(1/3))","A",6,6,18,0.3333,1,"{694, 266, 55, 617, 204, 31}"
1808,1,196,0,0.2045295,"\int \frac{1}{x \left(-b+a x^2\right)^{3/4}} \, dx","Int[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)}{2 \sqrt{2} b^{3/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{2 \sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{\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,"-(ArcTan[1 - (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)]/(Sqrt[2]*b^(3/4))) + ArcTan[1 + (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)]/(Sqrt[2]*b^(3/4)) - 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)) + 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",11,8,17,0.4706,1,"{266, 63, 211, 1165, 628, 1162, 617, 204}"
1809,1,86,0,0.0681107,"\int \frac{1}{x \sqrt[3]{-b+a x^3}} \, dx","Int[1/(x*(-b + a*x^3)^(1/3)),x]","-\frac{\log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{2 \sqrt[3]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{\log (x)}{2 \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{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}",1,"-(ArcTan[(b^(1/3) - 2*(-b + a*x^3)^(1/3))/(Sqrt[3]*b^(1/3))]/(Sqrt[3]*b^(1/3))) + Log[x]/(2*b^(1/3)) - Log[b^(1/3) + (-b + a*x^3)^(1/3)]/(2*b^(1/3))","A",5,5,17,0.2941,1,"{266, 56, 617, 204, 31}"
1810,1,728,0,3.4783794,"\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","Int[(-b^3 + a^3*x^3)/(Sqrt[b^2*x + a^2*x^3]*(b^3 + a^3*x^3)),x]","-\frac{4 \sqrt{x} \sqrt{a^2 x^2+b^2} \tan ^{-1}\left(\frac{\sqrt{-a} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2+b^2}}\right)}{3 \sqrt{-a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\sqrt{2} \sqrt{x} \sqrt{a^2 x^2+b^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2+b^2}}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{2 \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{2 \left(a-\sqrt{3} \sqrt{-a^2}\right) \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a} \left(3 a-\sqrt{3} \sqrt{-a^2}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{2 \left(\sqrt{3} \sqrt{-a^2}+a\right) \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a} \left(\sqrt{3} \sqrt{-a^2}+3 a\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\sqrt{a} \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} \Pi \left(\frac{3}{4};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{3} \sqrt{-a^2} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\sqrt{-a^2} \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} \Pi \left(\frac{3}{4};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{3} a^{3/2} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}","-\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,"(-4*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[-a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[-a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (Sqrt[2]*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (2*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (2*(a - Sqrt[3]*Sqrt[-a^2])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[a]*(3*a - Sqrt[3]*Sqrt[-a^2])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (2*(a + Sqrt[3]*Sqrt[-a^2])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[a]*(3*a + Sqrt[3]*Sqrt[-a^2])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (Sqrt[a]*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[3/4, 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[3]*Sqrt[-a^2]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (Sqrt[-a^2]*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[3/4, 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[3]*a^(3/2)*Sqrt[b]*Sqrt[b^2*x + a^2*x^3])","C",19,11,44,0.2500,1,"{2056, 6715, 6725, 220, 2073, 1211, 1699, 205, 6728, 1217, 1707}"
1811,1,747,0,3.3908853,"\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","Int[(b^3 + a^3*x^3)/(Sqrt[b^2*x + a^2*x^3]*(-b^3 + a^3*x^3)),x]","-\frac{4 \sqrt{x} \sqrt{a^2 x^2+b^2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2+b^2}}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\sqrt{2} \sqrt{x} \sqrt{a^2 x^2+b^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2+b^2}}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{2 \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{4 \sqrt{a} \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{\sqrt{3} \left(3 \sqrt{-a^2}+\sqrt{3} a\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{4 \sqrt{-a^2} \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{\sqrt{3} \sqrt{a} \left(\sqrt{3} \sqrt{-a^2}+3 a\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{\left(\sqrt{3} \sqrt{-a^2}+a\right) \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{\sqrt{a} \left(3 a-\sqrt{3} \sqrt{-a^2}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{\left(a-\sqrt{3} \sqrt{-a^2}\right) \sqrt{x} (a x+b) \sqrt{\frac{a^2 x^2+b^2}{(a x+b)^2}} \Pi \left(\frac{1}{4};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{\sqrt{a} \left(\sqrt{3} \sqrt{-a^2}+3 a\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}","-\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,"(-4*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (Sqrt[2]*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (2*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (4*Sqrt[a]*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*(Sqrt[3]*a + 3*Sqrt[-a^2])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (4*Sqrt[-a^2]*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*Sqrt[a]*(3*a + Sqrt[3]*Sqrt[-a^2])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + ((a + Sqrt[3]*Sqrt[-a^2])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[1/4, 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[a]*(3*a - Sqrt[3]*Sqrt[-a^2])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + ((a - Sqrt[3]*Sqrt[-a^2])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[1/4, 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[a]*(3*a + Sqrt[3]*Sqrt[-a^2])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3])","C",19,11,44,0.2500,1,"{2056, 6715, 6725, 220, 2073, 1211, 1699, 208, 6728, 1217, 1707}"
1812,1,378,0,0.764398,"\int \frac{\sqrt[4]{x^3+x^4}}{-2+x+2 x^2} \, dx","Int[(x^3 + x^4)^(1/4)/(-2 + x + 2*x^2),x]","-\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{\frac{1}{2} \left(23-\sqrt{17}\right)} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt{17} x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{\frac{1}{2} \left(23+\sqrt{17}\right)} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} \sqrt[4]{x}}{\sqrt{2} \sqrt[4]{x+1}}\right)}{\sqrt{17} x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{\frac{1}{2} \left(23-\sqrt{17}\right)} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{5+\sqrt{17}}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt{17} x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{\frac{1}{2} \left(23+\sqrt{17}\right)} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{5+\sqrt{17}} \sqrt[4]{x}}{\sqrt{2} \sqrt[4]{x+1}}\right)}{\sqrt{17} x^{3/4} \sqrt[4]{x+1}}","-\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 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4))) + (((23 - Sqrt[17])/2)^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((2/(5 + Sqrt[17]))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(Sqrt[17]*x^(3/4)*(1 + x)^(1/4)) + (((23 + Sqrt[17])/2)^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((5 + Sqrt[17])^(1/4)*x^(1/4))/(Sqrt[2]*(1 + x)^(1/4))])/(Sqrt[17]*x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - (((23 - Sqrt[17])/2)^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((2/(5 + Sqrt[17]))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(Sqrt[17]*x^(3/4)*(1 + x)^(1/4)) - (((23 + Sqrt[17])/2)^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((5 + Sqrt[17])^(1/4)*x^(1/4))/(Sqrt[2]*(1 + x)^(1/4))])/(Sqrt[17]*x^(3/4)*(1 + x)^(1/4))","B",17,9,22,0.4091,0,"{2056, 905, 63, 331, 298, 203, 206, 6728, 93}"
1813,0,0,0,3.3219334,"\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","Int[((-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,"(4*(-b + a*x^3)^(3/4))/(3*x^3) + 8*b*Defer[Int][1/((-b + a*x^3)^(1/4)*(b - a*x^3 - x^4)), x] + 2*a*Defer[Int][x^3/((-b + a*x^3)^(1/4)*(-b + a*x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1814,0,0,0,1.0370509,"\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","Int[((-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,"(4*(-1 + x^2 + x^4)^(1/4)*AppellF1[-1/2, -1/4, -1/4, 1/2, (-2*x^2)/(1 - Sqrt[5]), (-2*x^2)/(1 + Sqrt[5])])/(x*(1 + (2*x^2)/(1 - Sqrt[5]))^(1/4)*(1 + (2*x^2)/(1 + Sqrt[5]))^(1/4)) - ((1 + (2*x^2)/(1 + Sqrt[5]))^(5/4)*(-1 + x^2 + x^4)^(1/4)*Hypergeometric2F1[-3/2, -1/4, -1/2, (-2*(x^2/(1 - Sqrt[5]) - x^2/(1 + Sqrt[5])))/(1 + (2*x^2)/(1 + Sqrt[5]))])/(3*x^3*(1 + (2*x^2)/(1 - Sqrt[5]))^(1/4)) - (4*(1 + (2*x^2)/(1 + Sqrt[5]))*(-1 + x^2 + x^4)^(1/4)*((3*(1 + Sqrt[5]) - (13 + 3*Sqrt[5])*x^2 + 2*(1 + Sqrt[5])*x^4)*Gamma[-1/4]*Hypergeometric2F1[-1/4, 1, -1/2, (-2*Sqrt[5]*x^2)/(2 - (1 + Sqrt[5])*x^2)] - 4*x^2*(5 + Sqrt[5] + 2*Sqrt[5]*x^2)*Gamma[3/4]*Hypergeometric2F1[3/4, 2, 1/2, (-2*Sqrt[5]*x^2)/(2 - (1 + Sqrt[5])*x^2)]))/(15*(3 + Sqrt[5])*x^5*(1 - Sqrt[5] + 2*x^2)*Gamma[-1/4]) + 2*Defer[Int][(-1 + x^2 + x^4)^(1/4)/(1 + x^2), x] + 4*Defer[Int][(-1 + x^2 + x^4)^(1/4)/(-1 + 2*x^2), x]","F",0,0,0,0,-1,"{}"
1815,1,224,0,0.354918,"\int x^2 \sqrt[4]{b x^3+a x^4} \, dx","Int[x^2*(b*x^3 + a*x^4)^(1/4),x]","\frac{77 b^4 x^{9/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{1024 a^{15/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{77 b^4 x^{9/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{1024 a^{15/4} \left(a x^4+b x^3\right)^{3/4}}+\frac{77 b^3 \sqrt[4]{a x^4+b x^3}}{1536 a^3}-\frac{11 b^2 x \sqrt[4]{a x^4+b x^3}}{384 a^2}+\frac{1}{4} x^3 \sqrt[4]{a x^4+b x^3}+\frac{b x^2 \sqrt[4]{a x^4+b x^3}}{48 a}","\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,"(77*b^3*(b*x^3 + a*x^4)^(1/4))/(1536*a^3) - (11*b^2*x*(b*x^3 + a*x^4)^(1/4))/(384*a^2) + (b*x^2*(b*x^3 + a*x^4)^(1/4))/(48*a) + (x^3*(b*x^3 + a*x^4)^(1/4))/4 + (77*b^4*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(1024*a^(15/4)*(b*x^3 + a*x^4)^(3/4)) - (77*b^4*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(1024*a^(15/4)*(b*x^3 + a*x^4)^(3/4))","A",10,8,19,0.4211,1,"{2021, 2024, 2032, 63, 331, 298, 203, 206}"
1816,1,785,0,2.5068283,"\int \frac{1+x^6}{\sqrt{x+x^2+x^3} \left(1-x^6\right)} \, dx","Int[(1 + x^6)/(Sqrt[x + x^2 + x^3]*(1 - x^6)),x]","\frac{2 x \left(-i \sqrt{3} x-(-1)^{2/3}+1\right)}{9 \sqrt{x^3+x^2+x}}+\frac{2 x \left(i \sqrt{3} x+\sqrt[3]{-1}+1\right)}{9 \sqrt{x^3+x^2+x}}+\frac{\left(1+i \sqrt{3}\right) \sqrt{x} (x+1) \sqrt{\frac{x^2+x+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{4}\right)}{6 \sqrt{x^3+x^2+x}}+\frac{\left(1-i \sqrt{3}\right) \sqrt{x} (x+1) \sqrt{\frac{x^2+x+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{4}\right)}{6 \sqrt{x^3+x^2+x}}-\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+x+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{4}\right)}{\sqrt{x^3+x^2+x}}+\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(-1;\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{3 \left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}+\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(1-i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{3 \left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}+\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(-1+i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{3 \left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}+\frac{4 \sqrt{x} \sqrt{1+\frac{2 x}{1-i \sqrt{3}}} \sqrt{1+\frac{2 x}{1+i \sqrt{3}}} \Pi \left(\frac{1}{2} \left(1+i \sqrt{3}\right);\sin ^{-1}\left(\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt{x}\right)|\frac{i+\sqrt{3}}{i-\sqrt{3}}\right)}{3 \left(1-i \sqrt{3}\right) \sqrt{x^3+x^2+x}}","\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 - (-1)^(2/3) - I*Sqrt[3]*x))/(9*Sqrt[x + x^2 + x^3]) + (2*x*(1 + (-1)^(1/3) + I*Sqrt[3]*x))/(9*Sqrt[x + x^2 + x^3]) - (Sqrt[x]*(1 + x)*Sqrt[(1 + x + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/4])/Sqrt[x + x^2 + x^3] + ((1 - I*Sqrt[3])*Sqrt[x]*(1 + x)*Sqrt[(1 + x + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/4])/(6*Sqrt[x + x^2 + x^3]) + ((1 + I*Sqrt[3])*Sqrt[x]*(1 + x)*Sqrt[(1 + x + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/4])/(6*Sqrt[x + x^2 + x^3]) + (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[-1, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/(3*(1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) + (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(1 - I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/(3*(1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) + (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(-1 + I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/(3*(1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3]) + (4*Sqrt[x]*Sqrt[1 + (2*x)/(1 - I*Sqrt[3])]*Sqrt[1 + (2*x)/(1 + I*Sqrt[3])]*EllipticPi[(1 + I*Sqrt[3])/2, ArcSin[((1 - I*Sqrt[3])*Sqrt[x])/2], (I + Sqrt[3])/(I - Sqrt[3])])/(3*(1 - I*Sqrt[3])*Sqrt[x + x^2 + x^3])","C",43,13,27,0.4815,0,"{2056, 6725, 716, 1103, 934, 169, 538, 537, 849, 822, 839, 1197, 1195}"
1817,1,338,0,0.8198661,"\int \frac{1-3 x^3+3 x^6}{x^6 \left(-1+2 x^3\right) \sqrt[4]{-x+x^4}} \, dx","Int[(1 - 3*x^3 + 3*x^6)/(x^6*(-1 + 2*x^3)*(-x + x^4)^(1/4)),x]","\frac{\sqrt[4]{x} \sqrt[4]{x^3-1} \log \left(\frac{x^{3/2}}{\sqrt{x^3-1}}-\frac{\sqrt{2} x^{3/4}}{\sqrt[4]{x^3-1}}+1\right)}{3 \sqrt{2} \sqrt[4]{x^4-x}}-\frac{\sqrt[4]{x} \sqrt[4]{x^3-1} \log \left(\frac{x^{3/2}}{\sqrt{x^3-1}}+\frac{\sqrt{2} x^{3/4}}{\sqrt[4]{x^3-1}}+1\right)}{3 \sqrt{2} \sqrt[4]{x^4-x}}+\frac{\sqrt{2} \sqrt[4]{x} \sqrt[4]{x^3-1} \tan ^{-1}\left(1-\frac{\sqrt{2} x^{3/4}}{\sqrt[4]{x^3-1}}\right)}{3 \sqrt[4]{x^4-x}}-\frac{\sqrt{2} \sqrt[4]{x} \sqrt[4]{x^3-1} \tan ^{-1}\left(\frac{\sqrt{2} x^{3/4}}{\sqrt[4]{x^3-1}}+1\right)}{3 \sqrt[4]{x^4-x}}+\frac{\left(1-x^3\right)^2}{21 x^5 \sqrt[4]{x^4-x}}+\frac{1-x^3}{7 x^5 \sqrt[4]{x^4-x}}-\frac{1-x^3}{7 x^2 \sqrt[4]{x^4-x}}","-\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,"(1 - x^3)/(7*x^5*(-x + x^4)^(1/4)) - (1 - x^3)/(7*x^2*(-x + x^4)^(1/4)) + (1 - x^3)^2/(21*x^5*(-x + x^4)^(1/4)) + (Sqrt[2]*x^(1/4)*(-1 + x^3)^(1/4)*ArcTan[1 - (Sqrt[2]*x^(3/4))/(-1 + x^3)^(1/4)])/(3*(-x + x^4)^(1/4)) - (Sqrt[2]*x^(1/4)*(-1 + x^3)^(1/4)*ArcTan[1 + (Sqrt[2]*x^(3/4))/(-1 + x^3)^(1/4)])/(3*(-x + x^4)^(1/4)) + (x^(1/4)*(-1 + x^3)^(1/4)*Log[1 + x^(3/2)/Sqrt[-1 + x^3] - (Sqrt[2]*x^(3/4))/(-1 + x^3)^(1/4)])/(3*Sqrt[2]*(-x + x^4)^(1/4)) - (x^(1/4)*(-1 + x^3)^(1/4)*Log[1 + x^(3/2)/Sqrt[-1 + x^3] + (Sqrt[2]*x^(3/4))/(-1 + x^3)^(1/4)])/(3*Sqrt[2]*(-x + x^4)^(1/4))","B",20,14,36,0.3889,1,"{2056, 6725, 271, 264, 466, 465, 494, 461, 211, 1165, 628, 1162, 617, 204}"
1818,1,183,0,0.3675406,"\int \frac{b+a x^6}{x^3 \left(b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Int[(b + a*x^6)/(x^3*(b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","-\frac{16 a x}{9 b \sqrt[4]{a x^4+b x}}-\frac{4 x}{3 \sqrt[4]{a x^4+b x}}-\frac{4}{9 x^2 \sqrt[4]{a x^4+b x}}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4+b x}}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4+b x}}","-\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/(9*x^2*(b*x + a*x^4)^(1/4)) - (4*x)/(3*(b*x + a*x^4)^(1/4)) - (16*a*x)/(9*b*(b*x + a*x^4)^(1/4)) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4)) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4))","A",12,11,33,0.3333,1,"{2056, 1489, 271, 264, 288, 329, 275, 240, 212, 206, 203}"
1819,0,0,0,3.0407243,"\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","Int[((-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]","\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","\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,"Defer[Int][1/Sqrt[-1 - x + x^4], x]/2 - 4*Defer[Int][1/(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] - 7*Defer[Int][x/(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] - (9*Defer[Int][x^2/(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])/2 - Defer[Int][x^3/(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]/2 + (7*Defer[Int][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])/2 + 3*Defer[Int][x^5/(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] - (5*Defer[Int][x^6/(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])/2","F",0,0,0,0,-1,"{}"
1820,0,0,0,2.9743989,"\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","Int[((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,"-(x/Sqrt[1 - x^2 + x^6]) + 2*Defer[Int][x^2/(1 - x^2 + x^6)^(3/2), x] - 3*Defer[Int][x^2/((1 - x^2 + x^6)^(3/2)*(1 - x^2 - x^4 + 2*x^6 - x^8 + x^12)), x] + Defer[Int][x^4/((1 - x^2 + x^6)^(3/2)*(1 - x^2 - x^4 + 2*x^6 - x^8 + x^12)), x] + 2*Defer[Int][x^6/((1 - x^2 + x^6)^(3/2)*(1 - x^2 - x^4 + 2*x^6 - x^8 + x^12)), x] - 3*Defer[Int][x^8/((1 - x^2 + x^6)^(3/2)*(1 - x^2 - x^4 + 2*x^6 - x^8 + x^12)), x] + 4*Defer[Int][x^10/((1 - x^2 + x^6)^(3/2)*(1 - x^2 - x^4 + 2*x^6 - x^8 + x^12)), x]","F",0,0,0,0,-1,"{}"
1821,1,74,0,0.0623551,"\int \frac{1}{\left(2 \sqrt{x}+\sqrt{1+x}\right)^2} \, dx","Int[(2*Sqrt[x] + Sqrt[1 + x])^(-2),x]","-\frac{4 \sqrt{x} \sqrt{x+1}}{3 (1-3 x)}+\frac{8}{9 (1-3 x)}+\frac{5}{9} \log (1-3 x)-\frac{8}{9} \sinh ^{-1}\left(\sqrt{x}\right)+\frac{10}{9} \tanh ^{-1}\left(\frac{2 \sqrt{x}}{\sqrt{x+1}}\right)","\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,"8/(9*(1 - 3*x)) - (4*Sqrt[x]*Sqrt[1 + x])/(3*(1 - 3*x)) - (8*ArcSinh[Sqrt[x]])/9 + (10*ArcTanh[(2*Sqrt[x])/Sqrt[1 + x]])/9 + (5*Log[1 - 3*x])/9","A",8,7,17,0.4118,1,"{6742, 97, 157, 54, 215, 93, 207}"
1822,0,0,0,0.4059172,"\int \frac{1}{x^3 \sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","Int[1/(x^3*Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]),x]","\int \frac{1}{x^3 \sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}} \, dx","\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,"Defer[Int][1/(x^3*Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]), x]","F",0,0,0,0,-1,"{}"
1823,1,196,0,0.2093419,"\int \frac{1}{x \sqrt[4]{-b+a x^2}} \, dx","Int[1/(x*(-b + a*x^2)^(1/4)),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{2 \sqrt{2} \sqrt[4]{b}}-\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{2 \sqrt{2} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)}{\sqrt{2} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} \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[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]*b^(1/4))","A",11,8,17,0.4706,1,"{266, 63, 297, 1162, 617, 204, 1165, 628}"
1824,1,610,0,3.2211455,"\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","Int[(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{1-x^2} \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{3 (1-k) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{2 (-1)^{2/3} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{k+\sqrt[3]{-1}} \sqrt{1-x^2}}{\sqrt{\sqrt[3]{-1} k+1} \sqrt{1-k^2 x^2}}\right)}{3 \sqrt{k+\sqrt[3]{-1}} \sqrt{\sqrt[3]{-1} k+1} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt[3]{-1} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{k-(-1)^{2/3}} \sqrt{1-x^2}}{\sqrt{1-(-1)^{2/3} k} \sqrt{1-k^2 x^2}}\right)}{3 \sqrt{k-(-1)^{2/3}} \sqrt{1-(-1)^{2/3} k} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-\sqrt[3]{-1} k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left((-1)^{2/3} k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/(3*(1 - k)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) + (2*(-1)^(2/3)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[(-1)^(1/3) + k]*Sqrt[1 - x^2])/(Sqrt[1 + (-1)^(1/3)*k]*Sqrt[1 - k^2*x^2])])/(3*Sqrt[(-1)^(1/3) + k]*Sqrt[1 + (-1)^(1/3)*k]*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (2*(-1)^(1/3)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[-(-1)^(2/3) + k]*Sqrt[1 - x^2])/(Sqrt[1 - (-1)^(2/3)*k]*Sqrt[1 - k^2*x^2])])/(3*Sqrt[-(-1)^(2/3) + k]*Sqrt[1 - (-1)^(2/3)*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)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/(3*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-((-1)^(1/3)*k), ArcSin[x], k^2])/(3*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-1)^(2/3)*k, ArcSin[x], k^2])/(3*Sqrt[(1 - x^2)*(1 - k^2*x^2)])","C",21,9,47,0.1915,1,"{6719, 6725, 419, 2113, 537, 571, 93, 205, 208}"
1825,1,193,0,0.2856637,"\int \frac{(-d+2 c x) \sqrt[4]{b x^3+a x^4}}{x} \, dx","Int[((-d + 2*c*x)*(b*x^3 + a*x^4)^(1/4))/x,x]","\frac{b x^{9/4} (a x+b)^{3/4} (4 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{8 a^{7/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{b x^{9/4} (a x+b)^{3/4} (4 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{8 a^{7/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{\sqrt[4]{a x^4+b x^3} (4 a d+3 b c)}{4 a}+\frac{c \left(a x^4+b x^3\right)^{5/4}}{a x^3}","\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,"-1/4*((3*b*c + 4*a*d)*(b*x^3 + a*x^4)^(1/4))/a + (c*(b*x^3 + a*x^4)^(5/4))/(a*x^3) + (b*(3*b*c + 4*a*d)*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(8*a^(7/4)*(b*x^3 + a*x^4)^(3/4)) - (b*(3*b*c + 4*a*d)*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(8*a^(7/4)*(b*x^3 + a*x^4)^(3/4))","A",8,8,27,0.2963,1,"{2039, 2021, 2032, 63, 331, 298, 203, 206}"
1826,0,0,0,2.0556133,"\int \frac{-1+x^6}{\left(1+x^6\right) \sqrt[3]{1+a^3 x^3+x^6}} \, dx","Int[(-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,"(x*(1 + (2*x^3)/(a^3 - Sqrt[-4 + a^6]))^(1/3)*(1 + (2*x^3)/(a^3 + Sqrt[-4 + a^6]))^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, (-2*x^3)/(a^3 - Sqrt[-4 + a^6]), (-2*x^3)/(a^3 + Sqrt[-4 + a^6])])/(1 + a^3*x^3 + x^6)^(1/3) - (I/3)*Defer[Int][1/((I - x)*(1 + a^3*x^3 + x^6)^(1/3)), x] - (I/3)*Defer[Int][1/((I + x)*(1 + a^3*x^3 + x^6)^(1/3)), x] - (Sqrt[1 - I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x)*(1 + a^3*x^3 + x^6)^(1/3)), x])/3 - (Sqrt[1 + I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x)*(1 + a^3*x^3 + x^6)^(1/3)), x])/3 - (Sqrt[1 - I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x)*(1 + a^3*x^3 + x^6)^(1/3)), x])/3 - (Sqrt[1 + I*Sqrt[3]]*Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x)*(1 + a^3*x^3 + x^6)^(1/3)), x])/3","F",0,0,0,0,-1,"{}"
1827,0,0,0,4.655423,"\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","Int[((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,"-(((x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3))) - (12*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][x^3/(1 + 2*x^6 - x^9 - x^18)^(2/3), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3)) + ((1 - I*Sqrt[3])*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3)) + ((1 + I*Sqrt[3])*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3)) - (3*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x^3 + 2*x^6 + x^9 + x^12 + x^15)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3)) + (12*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][x^3/((1 + x^3 + 2*x^6 + x^9 + x^12 + x^15)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3)) + (6*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][x^6/((1 + x^3 + 2*x^6 + x^9 + x^12 + x^15)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3)) + (15*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][x^9/((1 + x^3 + 2*x^6 + x^9 + x^12 + x^15)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3)) + (3*(x + 2*x^3 - x^4 - x^7)^(1/3)*Defer[Subst][Defer[Int][x^12/((1 + x^3 + 2*x^6 + x^9 + x^12 + x^15)*(1 + 2*x^6 - x^9 - x^18)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 - x^3 - x^6)^(1/3))","F",0,0,0,0,-1,"{}"
1828,0,0,0,0.2028747,"\int \frac{x^2}{\sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Int[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,"Defer[Int][x^2/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
1829,0,0,0,0.1700477,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2), x]","F",0,0,0,0,-1,"{}"
1830,0,0,0,0.1277195,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2), x]","F",0,0,0,0,-1,"{}"
1831,0,0,0,0.1195883,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{3/2}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2), x]","F",0,0,0,0,-1,"{}"
1832,1,84,0,0.0638265,"\int \frac{1}{(-1+x) \sqrt[3]{-3-2 x+x^2}} \, dx","Int[1/((-1 + x)*(-3 - 2*x + x^2)^(1/3)),x]","-\frac{3 \log \left(\sqrt[3]{(x-1)^2-4}+2^{2/3}\right)}{4\ 2^{2/3}}+\frac{\log (1-x)}{2\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\sqrt[3]{2} \sqrt[3]{(x-1)^2-4}}{\sqrt{3}}\right)}{2\ 2^{2/3}}","-\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,"-1/2*(Sqrt[3]*ArcTan[(1 - 2^(1/3)*(-4 + (-1 + x)^2)^(1/3))/Sqrt[3]])/2^(2/3) - (3*Log[2^(2/3) + (-4 + (-1 + x)^2)^(1/3)])/(4*2^(2/3)) + Log[1 - x]/(2*2^(2/3))","A",6,6,18,0.3333,1,"{694, 266, 56, 617, 204, 31}"
1833,1,84,0,0.0669763,"\int \frac{1}{(-1+x) \sqrt[3]{-1-2 x+x^2}} \, dx","Int[1/((-1 + x)*(-1 - 2*x + x^2)^(1/3)),x]","-\frac{3 \log \left(\sqrt[3]{(x-1)^2-2}+\sqrt[3]{2}\right)}{4 \sqrt[3]{2}}+\frac{\log (1-x)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-2^{2/3} \sqrt[3]{(x-1)^2-2}}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}","-\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,"-1/2*(Sqrt[3]*ArcTan[(1 - 2^(2/3)*(-2 + (-1 + x)^2)^(1/3))/Sqrt[3]])/2^(1/3) - (3*Log[2^(1/3) + (-2 + (-1 + x)^2)^(1/3)])/(4*2^(1/3)) + Log[1 - x]/(2*2^(1/3))","A",6,6,18,0.3333,1,"{694, 266, 56, 617, 204, 31}"
1834,1,82,0,0.0613877,"\int \frac{1}{(1+x) \sqrt[3]{-1+2 x+x^2}} \, dx","Int[1/((1 + x)*(-1 + 2*x + x^2)^(1/3)),x]","\frac{\log (x+1)}{2 \sqrt[3]{2}}-\frac{3 \log \left(\sqrt[3]{(x+1)^2-2}+\sqrt[3]{2}\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-2^{2/3} \sqrt[3]{(x+1)^2-2}}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}","-\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,"-1/2*(Sqrt[3]*ArcTan[(1 - 2^(2/3)*(-2 + (1 + x)^2)^(1/3))/Sqrt[3]])/2^(1/3) + Log[1 + x]/(2*2^(1/3)) - (3*Log[2^(1/3) + (-2 + (1 + x)^2)^(1/3)])/(4*2^(1/3))","A",6,6,18,0.3333,1,"{694, 266, 56, 617, 204, 31}"
1835,0,0,0,19.7857768,"\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","Int[(-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,"((a + b - Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Int][x^(3/2)/((-a + x)^(5/4)*(-b + x)^(5/4)*((a + b)*d - Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(1 - d)*x)), x])/((a - x)*(b - x)*x^2)^(1/4) + ((a + b + Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Int][x^(3/2)/((-a + x)^(5/4)*(-b + x)^(5/4)*((a + b)*d + Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(1 - d)*x)), x])/((a - x)*(b - x)*x^2)^(1/4)","F",0,0,0,0,-1,"{}"
1836,0,0,0,8.4397344,"\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","Int[((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,"(4*a*b*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][(-a + x^4)^(5/4)/(Sqrt[-b + x^4]*(-(a^3*d) - b^2*(1 - (3*a^2*d)/b^2)*x^4 + 2*b*(1 - (3*a*d)/(2*b))*x^8 - (1 - d)*x^12)), x], x, x^(1/4)])/(-((a - x)*(b - x)^2*x))^(3/4) + (4*(3*a - 2*b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][(x^4*(-a + x^4)^(5/4))/(Sqrt[-b + x^4]*(a^3*d + b^2*(1 - (3*a^2*d)/b^2)*x^4 - 2*b*(1 - (3*a*d)/(2*b))*x^8 + (1 - d)*x^12)), x], x, x^(1/4)])/(-((a - x)*(b - x)^2*x))^(3/4)","F",0,0,0,0,-1,"{}"
1837,1,610,0,2.9403881,"\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","Int[(-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{1-x^2} \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{3 (1-k) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 (-1)^{2/3} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{k+\sqrt[3]{-1}} \sqrt{1-x^2}}{\sqrt{\sqrt[3]{-1} k+1} \sqrt{1-k^2 x^2}}\right)}{3 \sqrt{k+\sqrt[3]{-1}} \sqrt{\sqrt[3]{-1} k+1} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{2 \sqrt[3]{-1} \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{k-(-1)^{2/3}} \sqrt{1-x^2}}{\sqrt{1-(-1)^{2/3} k} \sqrt{1-k^2 x^2}}\right)}{3 \sqrt{k-(-1)^{2/3}} \sqrt{1-(-1)^{2/3} k} \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-\sqrt[3]{-1} k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left((-1)^{2/3} k;\sin ^{-1}(x)|k^2\right)}{3 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/(3*(1 - k)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (2*(-1)^(2/3)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[(-1)^(1/3) + k]*Sqrt[1 - x^2])/(Sqrt[1 + (-1)^(1/3)*k]*Sqrt[1 - k^2*x^2])])/(3*Sqrt[(-1)^(1/3) + k]*Sqrt[1 + (-1)^(1/3)*k]*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) + (2*(-1)^(1/3)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[-(-1)^(2/3) + k]*Sqrt[1 - x^2])/(Sqrt[1 - (-1)^(2/3)*k]*Sqrt[1 - k^2*x^2])])/(3*Sqrt[-(-1)^(2/3) + k]*Sqrt[1 - (-1)^(2/3)*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)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/(3*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-((-1)^(1/3)*k), ArcSin[x], k^2])/(3*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[(-1)^(2/3)*k, ArcSin[x], k^2])/(3*Sqrt[(1 - x^2)*(1 - k^2*x^2)])","C",21,9,47,0.1915,1,"{6719, 6725, 419, 2113, 537, 571, 93, 205, 208}"
1838,1,1650,0,5.0818383,"\int \frac{\sqrt{-x-x^2+x^3}}{-1+x^4} \, dx","Int[Sqrt[-x - x^2 + x^3]/(-1 + x^4),x]","-\frac{\sqrt{1-2 i} \sqrt{x^3-x^2-x} \tan ^{-1}\left(\frac{\sqrt{1-2 i} \sqrt{x}}{\sqrt{x^2-x-1}}\right)}{4 \sqrt{x} \sqrt{x^2-x-1}}-\frac{\sqrt{1+2 i} \sqrt{x^3-x^2-x} \tan ^{-1}\left(\frac{\sqrt{1+2 i} \sqrt{x}}{\sqrt{x^2-x-1}}\right)}{4 \sqrt{x} \sqrt{x^2-x-1}}+\frac{\left(1+\sqrt{5}\right) \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{2} \left(3+\sqrt{5}\right) \sqrt{x} \left(-x^2+x+1\right)}+\frac{\left(1+\sqrt{5}\right) \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{2} \left(1-\sqrt{5}\right) \sqrt{x} \left(-x^2+x+1\right)}-\frac{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{2 \sqrt[4]{5} \left(3+\sqrt{5}\right) \sqrt{x} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \left(-x^2+x+1\right)}+\frac{\left(\frac{1}{8}+\frac{i}{24}\right) \left((1+2 i)+\sqrt{5}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{x} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \left(-x^2+x+1\right)}+\frac{\left(\frac{1}{8}-\frac{i}{24}\right) \left((1-2 i)+\sqrt{5}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{x} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \left(-x^2+x+1\right)}+\frac{\left(1-\sqrt{5}\right) \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{4 \sqrt[4]{5} \sqrt{x} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \left(-x^2+x+1\right)}-\frac{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{2 \sqrt[4]{5} \left(1-\sqrt{5}\right) \sqrt{x} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \left(-x^2+x+1\right)}-\frac{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{12 \sqrt[4]{5} \sqrt{x} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \left(-x^2+x+1\right)}-\frac{\left(2+\sqrt{5}\right) \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \sqrt{x^3-x^2-x} \Pi \left(\frac{1}{2} \left(-1-\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{2} \left(3+\sqrt{5}\right) \sqrt{x} \left(-x^2+x+1\right)}+\frac{\sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \sqrt{x^3-x^2-x} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{\sqrt{2} \left(1-\sqrt{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{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,"-1/4*(Sqrt[1 - 2*I]*Sqrt[-x - x^2 + x^3]*ArcTan[(Sqrt[1 - 2*I]*Sqrt[x])/Sqrt[-1 - x + x^2]])/(Sqrt[x]*Sqrt[-1 - x + x^2]) - (Sqrt[1 + 2*I]*Sqrt[-x - x^2 + x^3]*ArcTan[(Sqrt[1 + 2*I]*Sqrt[x])/Sqrt[-1 - x + x^2]])/(4*Sqrt[x]*Sqrt[-1 - x + x^2]) + ((1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[2]*(1 - Sqrt[5])*Sqrt[x]*(1 + x - x^2)) + ((1 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[2]*(3 + Sqrt[5])*Sqrt[x]*(1 + x - x^2)) - (Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(12*5^(1/4)*Sqrt[x]*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*(1 + x - x^2)) - (Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(2*5^(1/4)*(1 - Sqrt[5])*Sqrt[x]*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*(1 + x - x^2)) + ((1 - Sqrt[5])*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(4*5^(1/4)*Sqrt[x]*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*(1 + x - x^2)) + ((1/8 - I/24)*((1 - 2*I) + Sqrt[5])*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[x]*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*(1 + x - x^2)) + ((1/8 + I/24)*((1 + 2*I) + Sqrt[5])*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[x]*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*(1 + x - x^2)) - (Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*Sqrt[-x - x^2 + x^3]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(2*5^(1/4)*(3 + Sqrt[5])*Sqrt[x]*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*(1 + x - x^2)) - ((2 + Sqrt[5])*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*Sqrt[-x - x^2 + x^3]*EllipticPi[(-1 - Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(Sqrt[2]*(3 + Sqrt[5])*Sqrt[x]*(1 + x - x^2)) + (Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*Sqrt[-x - x^2 + x^3]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(Sqrt[2]*(1 - Sqrt[5])*Sqrt[x]*(1 + x - x^2))","C",55,19,24,0.7917,0,"{2056, 6725, 918, 6733, 1716, 1187, 1098, 1184, 1214, 1456, 540, 421, 419, 538, 537, 1712, 1700, 1698, 205}"
1839,1,144,0,0.3528243,"\int \frac{\left(b+a x^3\right) \sqrt{x+x^4}}{-d+c x^3} \, dx","Int[((b + a*x^3)*Sqrt[x + x^4])/(-d + c*x^3),x]","\frac{\sqrt{x^4+x} \sinh ^{-1}\left(x^{3/2}\right) (a (c+2 d)+2 b c)}{3 c^2 \sqrt{x^3+1} \sqrt{x}}-\frac{2 \sqrt{x^4+x} \sqrt{c+d} (a d+b c) \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{c+d}}{\sqrt{d} \sqrt{x^3+1}}\right)}{3 c^2 \sqrt{d} \sqrt{x^3+1} \sqrt{x}}+\frac{a \sqrt{x^4+x} x}{3 c}","\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,"(a*x*Sqrt[x + x^4])/(3*c) + ((2*b*c + a*(c + 2*d))*Sqrt[x + x^4]*ArcSinh[x^(3/2)])/(3*c^2*Sqrt[x]*Sqrt[1 + x^3]) - (2*Sqrt[c + d]*(b*c + a*d)*Sqrt[x + x^4]*ArcTanh[(Sqrt[c + d]*x^(3/2))/(Sqrt[d]*Sqrt[1 + x^3])])/(3*c^2*Sqrt[d]*Sqrt[x]*Sqrt[1 + x^3])","A",11,10,28,0.3571,1,"{2056, 581, 584, 329, 275, 215, 466, 465, 377, 208}"
1840,1,170,0,0.1403529,"\int \frac{1-2 x+2 x^4}{x \sqrt[4]{-1+x^4}} \, dx","Int[(1 - 2*x + 2*x^4)/(x*(-1 + x^4)^(1/4)),x]","\frac{2}{3} \left(x^4-1\right)^{3/4}+\frac{\log \left(\sqrt{x^4-1}-\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}-\frac{\log \left(\sqrt{x^4-1}+\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{4 \sqrt{2}}-\tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{x^4-1}\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{x^4-1}+1\right)}{2 \sqrt{2}}-\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)] - ArcTan[1 - Sqrt[2]*(-1 + x^4)^(1/4)]/(2*Sqrt[2]) + ArcTan[1 + Sqrt[2]*(-1 + x^4)^(1/4)]/(2*Sqrt[2]) - ArcTanh[x/(-1 + x^4)^(1/4)] + Log[1 - Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(4*Sqrt[2]) - Log[1 + Sqrt[2]*(-1 + x^4)^(1/4) + Sqrt[-1 + x^4]]/(4*Sqrt[2])","A",18,14,23,0.6087,1,"{1833, 240, 212, 206, 203, 446, 80, 63, 297, 1162, 617, 204, 1165, 628}"
1841,0,0,0,2.0006168,"\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","Int[(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,"(c^2*x*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[1/5, 3/4, 6/5, -((a*x^5)/b)])/(a^2*(b + a*x^5)^(3/4)) - (c*x^2*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, -((a*x^5)/b)])/(2*a*(b + a*x^5)^(3/4)) + (x^3*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[3/5, 3/4, 8/5, -((a*x^5)/b)])/(3*(b + a*x^5)^(3/4)) - (b*c^2*Defer[Int][1/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/a^2 + (b*c*Defer[Int][x/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/a - 5*b*Defer[Int][x^2/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x] - (c^3*Defer[Int][x^4/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/a^2","F",0,0,0,0,-1,"{}"
1842,1,159,0,0.04453,"\int \frac{1}{\sqrt[6]{1+2 x-x^2-4 x^3-x^4+2 x^5+x^6}} \, dx","Int[(1 + 2*x - x^2 - 4*x^3 - x^4 + 2*x^5 + x^6)^(-1/6),x]","-\frac{\sqrt[3]{x-1} (x+1)^{2/3} \log (x+1)}{2 \sqrt[6]{(1-x)^2 (x+1)^4}}-\frac{3 \sqrt[3]{x-1} (x+1)^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x+1}}-1\right)}{2 \sqrt[6]{(1-x)^2 (x+1)^4}}-\frac{\sqrt{3} \sqrt[3]{x-1} (x+1)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[6]{(1-x)^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,"-((Sqrt[3]*(-1 + x)^(1/3)*(1 + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/((1 - x)^2*(1 + x)^4)^(1/6)) - ((-1 + x)^(1/3)*(1 + x)^(2/3)*Log[1 + x])/(2*((1 - x)^2*(1 + x)^4)^(1/6)) - (3*(-1 + x)^(1/3)*(1 + x)^(2/3)*Log[-1 + (-1 + x)^(1/3)/(1 + x)^(1/3)])/(2*((1 - x)^2*(1 + x)^4)^(1/6))","A",3,3,32,0.09375,1,"{6688, 6719, 59}"
1843,0,0,0,1.6271923,"\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","Int[(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,"(2*Sqrt[b]*(1 + (a*x^6)/b)^(3/4)*EllipticF[ArcTan[(Sqrt[a]*x^3)/Sqrt[b]]/2, 2])/(3*Sqrt[a]*(b + a*x^6)^(3/4)) - (c*x*(1 + (a*x^6)/b)^(3/4)*Hypergeometric2F1[1/6, 3/4, 7/6, -((a*x^6)/b)])/(a*(b + a*x^6)^(3/4)) + (b*c*Defer[Int][1/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x])/a - 3*b*Defer[Int][x^2/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x] + (c^2*Defer[Int][x^4/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x])/a","F",0,0,0,0,-1,"{}"
1844,0,0,0,1.5915368,"\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","Int[((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,"(4*(1 + x^3)^(3/4))/(3*x^3) + 4*Defer[Int][1/((1 + x^3)^(1/4)*(-1 - x^3 + x^4)), x] + Defer[Int][x^3/((1 + x^3)^(1/4)*(-1 - x^3 + x^4)), x] + 4*Defer[Int][1/((1 + x^3)^(1/4)*(1 + x^3 + x^4)), x] + Defer[Int][x^3/((1 + x^3)^(1/4)*(1 + x^3 + x^4)), x]","F",0,0,0,0,-1,"{}"
1845,1,125,0,0.3496832,"\int \frac{2-x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-2+x^4+x^8\right)} \, dx","Int[(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",16,6,32,0.1875,1,"{6728, 240, 212, 206, 203, 377}"
1846,0,0,0,1.1733125,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^2} \, dx","Int[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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[-a]*x), x]/(4*b^3) + Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[-a]*x), x]/(4*b^3) - (a*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b - a*x)^2, x])/(4*b^2) - (a*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b + a*x)^2, x])/(4*b^2)","F",0,0,0,0,-1,"{}"
1847,1,164,0,0.3719543,"\int \frac{\left(b+a x^3\right) \sqrt{-x+x^4}}{-d+c x^3} \, dx","Int[((b + a*x^3)*Sqrt[-x + x^4])/(-d + c*x^3),x]","\frac{2 \sqrt{x^4-x} \sqrt{c-d} (a d+b c) \tan ^{-1}\left(\frac{x^{3/2} \sqrt{c-d}}{\sqrt{d} \sqrt{x^3-1}}\right)}{3 c^2 \sqrt{d} \sqrt{x^3-1} \sqrt{x}}-\frac{\sqrt{x^4-x} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right) (a c-2 a d-2 b c)}{3 c^2 \sqrt{x^3-1} \sqrt{x}}+\frac{a \sqrt{x^4-x} x}{3 c}","\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,"(a*x*Sqrt[-x + x^4])/(3*c) + (2*Sqrt[c - d]*(b*c + a*d)*Sqrt[-x + x^4]*ArcTan[(Sqrt[c - d]*x^(3/2))/(Sqrt[d]*Sqrt[-1 + x^3])])/(3*c^2*Sqrt[d]*Sqrt[x]*Sqrt[-1 + x^3]) - ((a*c - 2*b*c - 2*a*d)*Sqrt[-x + x^4]*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]])/(3*c^2*Sqrt[x]*Sqrt[-1 + x^3])","A",12,11,30,0.3667,1,"{2056, 581, 584, 329, 275, 217, 206, 466, 465, 377, 205}"
1848,1,53,0,0.3792877,"\int \frac{b+a x^3}{x^3 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Int[(b + a*x^3)/(x^3*(-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","\frac{4 \left(a x^3+b\right) \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};\frac{2 a x^3}{a x^3+b}\right)}{9 b x^2 \sqrt[4]{a x^4+b x}}","-\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*(b + a*x^3)*Hypergeometric2F1[-3/4, 1, 1/4, (2*a*x^3)/(b + a*x^3)])/(9*b*x^2*(b*x + a*x^4)^(1/4))","C",5,5,35,0.1429,1,"{2056, 466, 465, 511, 510}"
1849,0,0,0,8.9138484,"\int \frac{\left(1+2 x^6\right) \sqrt[3]{x+x^3-x^7}}{\left(-1+x^6\right)^2} \, dx","Int[((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,"(2*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(-1 + I*Sqrt[3] - 2*x)^2, x], x, x^(2/3)])/(9*x^(1/3)*(1 + x^2 - x^6)^(1/3)) - (((2*I)/9)*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(-1 + I*Sqrt[3] - 2*x), x], x, x^(2/3)])/(Sqrt[3]*x^(1/3)*(1 + x^2 - x^6)^(1/3)) + ((x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(-1 + x)^2, x], x, x^(2/3)])/(18*x^(1/3)*(1 + x^2 - x^6)^(1/3)) - ((x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(-1 + x), x], x, x^(2/3)])/(18*x^(1/3)*(1 + x^2 - x^6)^(1/3)) + ((3 - I*Sqrt[3])*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(1 - I*Sqrt[3] + 2*x), x], x, x^(2/3)])/(54*x^(1/3)*(1 + x^2 - x^6)^(1/3)) + (2*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(1 + I*Sqrt[3] + 2*x)^2, x], x, x^(2/3)])/(9*x^(1/3)*(1 + x^2 - x^6)^(1/3)) - (((2*I)/9)*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(1 + I*Sqrt[3] + 2*x), x], x, x^(2/3)])/(Sqrt[3]*x^(1/3)*(1 + x^2 - x^6)^(1/3)) + ((3 + I*Sqrt[3])*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^3 - x^9)^(1/3)/(1 + I*Sqrt[3] + 2*x), x], x, x^(2/3)])/(54*x^(1/3)*(1 + x^2 - x^6)^(1/3)) - (2*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(x*(1 + x^3 - x^9)^(1/3))/(-1 + I*Sqrt[3] - 2*x^3)^2, x], x, x^(2/3)])/(x^(1/3)*(1 + x^2 - x^6)^(1/3)) + ((1 - I*Sqrt[3])*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(x*(1 + x^3 - x^9)^(1/3))/(-1 + I*Sqrt[3] - 2*x^3)^2, x], x, x^(2/3)])/(x^(1/3)*(1 + x^2 - x^6)^(1/3)) - (2*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(x*(1 + x^3 - x^9)^(1/3))/(1 + I*Sqrt[3] + 2*x^3)^2, x], x, x^(2/3)])/(x^(1/3)*(1 + x^2 - x^6)^(1/3)) + ((1 + I*Sqrt[3])*(x + x^3 - x^7)^(1/3)*Defer[Subst][Defer[Int][(x*(1 + x^3 - x^9)^(1/3))/(1 + I*Sqrt[3] + 2*x^3)^2, x], x, x^(2/3)])/(x^(1/3)*(1 + x^2 - x^6)^(1/3))","F",0,0,0,0,-1,"{}"
1850,1,283,0,2.7296633,"\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","Int[(-((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{4 \left(1-\sqrt{-4 a d+4 b d+1}\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a-x}{a-b},-\frac{2 d (a-x)}{-2 a d+2 b d-\sqrt{-4 a d+4 b d+1}+1}\right)}{\left(-\sqrt{-4 a d+4 b d+1}-2 a d+2 b d+1\right) \sqrt{-\frac{b-x}{a-b}}}-\frac{4 \left(\sqrt{-4 a d+4 b d+1}+1\right) \sqrt[4]{-\left((a-x) (b-x)^2\right)} F_1\left(\frac{1}{4};-\frac{1}{2},1;\frac{5}{4};\frac{a-x}{a-b},-\frac{2 d (a-x)}{-2 a d+2 b d+\sqrt{-4 a d+4 b d+1}+1}\right)}{\left(\sqrt{-4 a d+4 b d+1}-2 a d+2 b d+1\right) \sqrt{-\frac{b-x}{a-b}}}","\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,"(-4*(1 - Sqrt[1 - 4*a*d + 4*b*d])*(-((a - x)*(b - x)^2))^(1/4)*AppellF1[1/4, -1/2, 1, 5/4, (a - x)/(a - b), (-2*d*(a - x))/(1 - 2*a*d + 2*b*d - Sqrt[1 - 4*a*d + 4*b*d])])/((1 - 2*a*d + 2*b*d - Sqrt[1 - 4*a*d + 4*b*d])*Sqrt[-((b - x)/(a - b))]) - (4*(1 + Sqrt[1 - 4*a*d + 4*b*d])*(-((a - x)*(b - x)^2))^(1/4)*AppellF1[1/4, -1/2, 1, 5/4, (a - x)/(a - b), (-2*d*(a - x))/(1 - 2*a*d + 2*b*d + Sqrt[1 - 4*a*d + 4*b*d])])/((1 - 2*a*d + 2*b*d + Sqrt[1 - 4*a*d + 4*b*d])*Sqrt[-((b - x)/(a - b))])","C",8,5,77,0.06494,0,"{6688, 6719, 6728, 137, 136}"
1851,1,441,0,0.9095353,"\int \frac{2+x^4}{\sqrt[4]{x^2+x^4} \left(-1-x^4+2 x^8\right)} \, dx","Int[(2 + x^4)/((x^2 + x^4)^(1/4)*(-1 - x^4 + 2*x^8)),x]","-\frac{x}{\sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}-2 i} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}+2 i} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}-2 i} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}+2 i} \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/(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((-2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(-2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((-2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(-2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4))","C",19,10,31,0.3226,1,"{2056, 6715, 6728, 1404, 382, 377, 212, 206, 203, 1429}"
1852,1,441,0,0.6980237,"\int \frac{2+x^4}{\sqrt[4]{x^2+x^4} \left(-1-x^4+2 x^8\right)} \, dx","Int[(2 + x^4)/((x^2 + x^4)^(1/4)*(-1 - x^4 + 2*x^8)),x]","-\frac{x}{\sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}-2 i} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}+2 i} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2+1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}-2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}-2 i} \sqrt[4]{x^4+x^2}}-\frac{\sqrt[4]{x^2+1} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+2 i} \sqrt{x}}{\sqrt[8]{2} \sqrt[4]{x^2+1}}\right)}{2^{7/8} \sqrt[4]{\sqrt{2}+2 i} \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/(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((-2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(-2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTan[((2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(1 + x^2)^(1/4)])/(2*2^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((-2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(-2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4)) - (Sqrt[x]*(1 + x^2)^(1/4)*ArcTanh[((2*I + Sqrt[2])^(1/4)*Sqrt[x])/(2^(1/8)*(1 + x^2)^(1/4))])/(2^(7/8)*(2*I + Sqrt[2])^(1/4)*(x^2 + x^4)^(1/4))","C",19,10,31,0.3226,1,"{2056, 6715, 6728, 1404, 382, 377, 212, 206, 203, 1429}"
1853,1,83,0,0.1362004,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2} \, dx","Int[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{1-3 \sqrt{x+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",7,5,17,0.2941,1,"{1014, 1033, 724, 206, 204}"
1854,1,136,0,0.3221485,"\int \frac{(-1+x) \sqrt{x+\sqrt{1+x^2}}}{1+x} \, dx","Int[((-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{1+\sqrt{2}} \tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)+4 \sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\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]]*ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]] + 4*Sqrt[-1 + Sqrt[2]]*ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]","A",12,9,24,0.3750,1,"{6742, 2117, 14, 2119, 1628, 826, 1166, 207, 203}"
1855,1,136,0,0.2707127,"\int \frac{(1+x) \sqrt{x+\sqrt{1+x^2}}}{-1+x} \, dx","Int[((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} \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)-4 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\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*Sqrt[-1 + Sqrt[2]]*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]] - 4*Sqrt[1 + Sqrt[2]]*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]","A",12,9,24,0.3750,1,"{6742, 2117, 14, 2119, 1628, 826, 1166, 207, 203}"
1856,0,0,0,0.4464303,"\int \frac{6+2 x+x^2}{(1+x) \sqrt[3]{2+x+x^2} \left(2-x+2 x^2\right)} \, dx","Int[(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,"(-3*((1 - I*Sqrt[7] + 2*x)/(1 + x))^(1/3)*((1 + I*Sqrt[7] + 2*x)/(1 + x))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (1 - I*Sqrt[7])/(2*(1 + x)), (1 + I*Sqrt[7])/(2*(1 + x))])/(2*2^(2/3)*(2 + x + x^2)^(1/3)) + Defer[Int][(4 - x)/((2 + x + x^2)^(1/3)*(2 - x + 2*x^2)), x]","F",0,0,0,0,-1,"{}"
1857,1,201,0,0.2112026,"\int \frac{1}{x \left(-b+a x^3\right)^{3/4}} \, dx","Int[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)}{3 \sqrt{2} b^{3/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{3 \sqrt{2} b^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{3 b^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{3 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,"-1/3*(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/b^(3/4) + (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(3*b^(3/4)) - 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)) + 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",11,8,17,0.4706,1,"{266, 63, 211, 1165, 628, 1162, 617, 204}"
1858,1,201,0,0.1931315,"\int \frac{1}{x \sqrt[4]{-b+a x^3}} \, dx","Int[1/(x*(-b + a*x^3)^(1/4)),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{3 \sqrt{2} \sqrt[4]{b}}-\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{3 \sqrt{2} \sqrt[4]{b}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{3 \sqrt[4]{b}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\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,"-1/3*(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/b^(1/4) + (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(3*b^(1/4)) + Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]]/(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]]/(3*Sqrt[2]*b^(1/4))","A",11,8,17,0.4706,1,"{266, 63, 297, 1162, 617, 204, 1165, 628}"
1859,0,0,0,5.9664133,"\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","Int[((-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,"(-4*b*(1 - (a*x^2)/b)^(1/4)*Hypergeometric2F1[-9/8, 1/4, -1/8, (a*x^2)/b])/(3*x^2*(-(b*x) + a*x^3)^(1/4)) + (4*a*(1 - (a*x^2)/b)^(1/4)*Hypergeometric2F1[-1/8, 1/4, 7/8, (a*x^2)/b])/(-(b*x) + a*x^3)^(1/4) + (24*b*x^(1/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^2/((-b + a*x^8)^(1/4)*(b - a*x^8 - x^12)), x], x, x^(1/4)])/(-(b*x) + a*x^3)^(1/4) + (8*a*x^(1/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^10/((-b + a*x^8)^(1/4)*(-b + a*x^8 + x^12)), x], x, x^(1/4)])/(-(b*x) + a*x^3)^(1/4)","F",0,0,0,0,-1,"{}"
1860,1,201,0,0.1908567,"\int \frac{1}{x \left(-b+a x^4\right)^{3/4}} \, dx","Int[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)}{4 \sqrt{2} b^{3/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{4 \sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}\right)}{2 \sqrt{2} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}+1\right)}{2 \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,"-1/2*ArcTan[1 - (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)]/(Sqrt[2]*b^(3/4)) + ArcTan[1 + (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)]/(2*Sqrt[2]*b^(3/4)) - 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)) + 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",11,8,17,0.4706,1,"{266, 63, 211, 1165, 628, 1162, 617, 204}"
1861,1,201,0,0.1793302,"\int \frac{1}{x \sqrt[4]{-b+a x^4}} \, dx","Int[1/(x*(-b + a*x^4)^(1/4)),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}\right)}{2 \sqrt{2} \sqrt[4]{b}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}+1\right)}{2 \sqrt{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,"-1/2*ArcTan[1 - (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)]/(Sqrt[2]*b^(1/4)) + ArcTan[1 + (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)]/(2*Sqrt[2]*b^(1/4)) + Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]]/(4*Sqrt[2]*b^(1/4)) - Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]]/(4*Sqrt[2]*b^(1/4))","A",11,8,17,0.4706,1,"{266, 63, 297, 1162, 617, 204, 1165, 628}"
1862,0,0,0,1.9517077,"\int \frac{1-x^5}{\sqrt{a+b x} \left(1+x^5\right)} \, dx","Int[(1 - x^5)/(Sqrt[a + b*x]*(1 + x^5)),x]","\int \frac{1-x^5}{\sqrt{a+b x} \left(1+x^5\right)} \, dx","\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*Sqrt[a + b*x])/b - (4*ArcTanh[Sqrt[a + b*x]/Sqrt[a - b]])/(5*Sqrt[a - b]) + (4*Defer[Subst][Defer[Int][x^6/(-(a^4*(1 + (b*(a^3 + a^2*b + a*b^2 + b^3))/a^4)) + 4*a^3*(1 + (b*(3*a^2 + 2*a*b + b^2))/(4*a^3))*x^2 - 6*a^2*(1 + (b*(3*a + b))/(6*a^2))*x^4 + 4*a*(1 + b/(4*a))*x^6 - x^8), x], x, Sqrt[a + b*x]])/5 + (4*(a^3 + 2*a^2*b + 3*a*b^2 + 4*b^3)*Defer[Subst][Defer[Int][(a^4*(1 + (b*(a^3 + a^2*b + a*b^2 + b^3))/a^4) - 4*a^3*(1 + (b*(3*a^2 + 2*a*b + b^2))/(4*a^3))*x^2 + 6*a^2*(1 + (b*(3*a + b))/(6*a^2))*x^4 - 4*a*(1 + b/(4*a))*x^6 + x^8)^(-1), x], x, Sqrt[a + b*x]])/5 - (4*(3*a^2 + 4*a*b + 3*b^2)*Defer[Subst][Defer[Int][x^2/(a^4*(1 + (b*(a^3 + a^2*b + a*b^2 + b^3))/a^4) - 4*a^3*(1 + (b*(3*a^2 + 2*a*b + b^2))/(4*a^3))*x^2 + 6*a^2*(1 + (b*(3*a + b))/(6*a^2))*x^4 - 4*a*(1 + b/(4*a))*x^6 + x^8), x], x, Sqrt[a + b*x]])/5 + (4*(3*a + 2*b)*Defer[Subst][Defer[Int][x^4/(a^4*(1 + (b*(a^3 + a^2*b + a*b^2 + b^3))/a^4) - 4*a^3*(1 + (b*(3*a^2 + 2*a*b + b^2))/(4*a^3))*x^2 + 6*a^2*(1 + (b*(3*a + b))/(6*a^2))*x^4 - 4*a*(1 + b/(4*a))*x^6 + x^8), x], x, Sqrt[a + b*x]])/5","F",0,0,0,0,-1,"{}"
1863,1,201,0,0.1909606,"\int \frac{1}{x \left(-b+a x^5\right)^{3/4}} \, dx","Int[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)}{5 \sqrt{2} b^{3/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{5 \sqrt{2} b^{3/4}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}\right)}{5 b^{3/4}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}+1\right)}{5 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,"-1/5*(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/b^(3/4) + (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/(5*b^(3/4)) - 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)) + 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",11,8,17,0.4706,1,"{266, 63, 211, 1165, 628, 1162, 617, 204}"
1864,1,201,0,0.1951273,"\int \frac{1}{x \left(-b+a x^6\right)^{3/4}} \, dx","Int[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)}{6 \sqrt{2} b^{3/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)}{6 \sqrt{2} b^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}\right)}{3 \sqrt{2} b^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}+1\right)}{3 \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,"-1/3*ArcTan[1 - (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)]/(Sqrt[2]*b^(3/4)) + ArcTan[1 + (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)]/(3*Sqrt[2]*b^(3/4)) - 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)) + 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",11,8,17,0.4706,1,"{266, 63, 211, 1165, 628, 1162, 617, 204}"
1865,0,0,0,2.3143429,"\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","Int[((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,"(4*x*(1 + Sqrt[5] + 2*x^2))/(3*Sqrt[-1 + x^2 + x^4]) - (x*(1 + 3*x^2)*Sqrt[-1 + x^2 + x^4])/15 + (x*(11 + 3*x^2)*Sqrt[-1 + x^2 + x^4])/15 - (4*5^(1/4)*Sqrt[(2 - (1 - Sqrt[5])*x^2)/(2 - (1 + Sqrt[5])*x^2)]*Sqrt[-2 + (1 + Sqrt[5])*x^2]*EllipticE[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[5])*x^2]], (5 + Sqrt[5])/10])/(3*Sqrt[(2 - (1 + Sqrt[5])*x^2)^(-1)]*Sqrt[-1 + x^2 + x^4]) - ((1 - Sqrt[5])*Sqrt[1 + Sqrt[5] + 2*x^2]*Sqrt[1 + (2*x^2)/(1 - Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2])/(Sqrt[2]*(3 - Sqrt[5])*Sqrt[-1 + x^2 + x^4]) - ((1 - Sqrt[5])*Sqrt[1 + Sqrt[5] + 2*x^2]*Sqrt[1 + (2*x^2)/(1 - Sqrt[5])]*EllipticF[ArcSin[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2])/(Sqrt[2]*(1 + Sqrt[5])*Sqrt[-1 + x^2 + x^4]) + ((1 - 4*Sqrt[5])*Sqrt[(2 - (1 - Sqrt[5])*x^2)/(2 - (1 + Sqrt[5])*x^2)]*Sqrt[-2 + (1 + Sqrt[5])*x^2]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[5])*x^2]], (5 + Sqrt[5])/10])/(6*5^(3/4)*Sqrt[(2 - (1 + Sqrt[5])*x^2)^(-1)]*Sqrt[-1 + x^2 + x^4]) - ((1 - Sqrt[5])*Sqrt[(2 - (1 - Sqrt[5])*x^2)/(2 - (1 + Sqrt[5])*x^2)]*Sqrt[-2 + (1 + Sqrt[5])*x^2]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[5])*x^2]], (5 + Sqrt[5])/10])/(4*5^(1/4)*Sqrt[(2 - (1 + Sqrt[5])*x^2)^(-1)]*Sqrt[-1 + x^2 + x^4]) - (Sqrt[(2 - (1 - Sqrt[5])*x^2)/(2 - (1 + Sqrt[5])*x^2)]*Sqrt[-2 + (1 + Sqrt[5])*x^2]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[5])*x^2]], (5 + Sqrt[5])/10])/(5^(1/4)*(3 - Sqrt[5])*Sqrt[(2 - (1 + Sqrt[5])*x^2)^(-1)]*Sqrt[-1 + x^2 + x^4]) + ((4 - Sqrt[5])*Sqrt[(2 - (1 - Sqrt[5])*x^2)/(2 - (1 + Sqrt[5])*x^2)]*Sqrt[-2 + (1 + Sqrt[5])*x^2]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[5])*x^2]], (5 + Sqrt[5])/10])/(6*5^(3/4)*Sqrt[(2 - (1 + Sqrt[5])*x^2)^(-1)]*Sqrt[-1 + x^2 + x^4]) - (Sqrt[(2 - (1 - Sqrt[5])*x^2)/(2 - (1 + Sqrt[5])*x^2)]*Sqrt[-2 + (1 + Sqrt[5])*x^2]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[5])*x^2]], (5 + Sqrt[5])/10])/(5^(1/4)*(1 + Sqrt[5])*Sqrt[(2 - (1 + Sqrt[5])*x^2)^(-1)]*Sqrt[-1 + x^2 + x^4]) + ((3 + Sqrt[5])*Sqrt[(2 - (1 - Sqrt[5])*x^2)/(2 - (1 + Sqrt[5])*x^2)]*Sqrt[-2 + (1 + Sqrt[5])*x^2]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[5])*x^2]], (5 + Sqrt[5])/10])/(4*5^(1/4)*Sqrt[(2 - (1 + Sqrt[5])*x^2)^(-1)]*Sqrt[-1 + x^2 + x^4]) - (Sqrt[2]*Sqrt[1 + Sqrt[5] + 2*x^2]*Sqrt[1 + (2*x^2)/(1 - Sqrt[5])]*EllipticPi[(1 - Sqrt[5])/2, ArcSin[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2])/((1 + Sqrt[5])*Sqrt[-1 + x^2 + x^4]) + (Sqrt[2]*(2 - Sqrt[5])*Sqrt[1 + Sqrt[5] + 2*x^2]*Sqrt[1 + (2*x^2)/(1 - Sqrt[5])]*EllipticPi[(-1 + Sqrt[5])/2, ArcSin[Sqrt[2/(-1 + Sqrt[5])]*x], (-3 + Sqrt[5])/2])/((3 - Sqrt[5])*Sqrt[-1 + x^2 + x^4]) + Defer[Int][(-1 + x^2 + x^4)^(3/2)/(1 + x^2 - x^4 - x^6 + x^8), x] + 2*Defer[Int][(x^2*(-1 + x^2 + x^4)^(3/2))/(1 + x^2 - x^4 - x^6 + x^8), x] - 2*Defer[Int][(x^4*(-1 + x^2 + x^4)^(3/2))/(1 + x^2 - x^4 - x^6 + x^8), x]","F",0,0,0,0,-1,"{}"
1866,0,0,0,0.4326951,"\int \frac{\left(-1+x^6\right) \left(1+x^3+x^6\right)^{2/3}}{1+x^6+x^{12}} \, dx","Int[((-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,"(x*(1 + (2*x^3)/(1 - I*Sqrt[3]))^(1/3)*(1 + (2*x^3)/(1 + I*Sqrt[3]))^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, (-2*x^3)/(1 - I*Sqrt[3]), (-2*x^3)/(1 + I*Sqrt[3])])/(1 + x^3 + x^6)^(1/3) + (1 + I*Sqrt[3])*Defer[Int][1/((-1 - I*Sqrt[3] + 2*x^3)*(1 + x^3 + x^6)^(1/3)), x] + (1 - I*Sqrt[3])*Defer[Int][1/((-1 + I*Sqrt[3] + 2*x^3)*(1 + x^3 + x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1867,0,0,0,2.322363,"\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","Int[((-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,"Sqrt[2 + 3*x^6 + 2*x^12]/6 + Sqrt[2 + 3*x^6 + 2*x^12]/(6*x^6) - (2*Sqrt[2 + 3*x^6 + 2*x^12])/(3*x^3) + (4*x^3*Sqrt[2 + 3*x^6 + 2*x^12])/(3*(1 + x^6)) - ArcSinh[(3 + 4*x^6)/Sqrt[7]]/(12*Sqrt[2]) - ArcTanh[(4 + 3*x^6)/(2*Sqrt[2]*Sqrt[2 + 3*x^6 + 2*x^12])]/(12*Sqrt[2]) - (4*Sqrt[2]*(1 + x^6)*Sqrt[(2 + 3*x^6 + 2*x^12)/(1 + x^6)^2]*EllipticE[2*ArcTan[x^3], 1/8])/(3*Sqrt[2 + 3*x^6 + 2*x^12]) + (7*(1 + x^6)*Sqrt[(2 + 3*x^6 + 2*x^12)/(1 + x^6)^2]*EllipticF[2*ArcTan[x^3], 1/8])/(3*Sqrt[2]*Sqrt[2 + 3*x^6 + 2*x^12]) + ((2*I)/3)*Defer[Int][Sqrt[2 + 3*x^6 + 2*x^12]/(I - x), x] + ((2*I)/3)*Defer[Int][Sqrt[2 + 3*x^6 + 2*x^12]/(I + x), x] + (2*(1 + I*Sqrt[3])*Defer[Int][Sqrt[2 + 3*x^6 + 2*x^12]/(Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x), x])/(3*Sqrt[1 - I*Sqrt[3]]) + (2*(1 - I*Sqrt[3])*Defer[Int][Sqrt[2 + 3*x^6 + 2*x^12]/(Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x), x])/(3*Sqrt[1 + I*Sqrt[3]]) + (2*(1 + I*Sqrt[3])*Defer[Int][Sqrt[2 + 3*x^6 + 2*x^12]/(Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x), x])/(3*Sqrt[1 - I*Sqrt[3]]) + (2*(1 - I*Sqrt[3])*Defer[Int][Sqrt[2 + 3*x^6 + 2*x^12]/(Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x), x])/(3*Sqrt[1 + I*Sqrt[3]])","F",0,0,0,0,-1,"{}"
1868,0,0,0,49.6768592,"\int \frac{\sqrt{a x-\sqrt{b+a^2 x^2}}}{a^2 x^2+\sqrt{b+a^2 x^2}} \, dx","Int[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,"-(((1 - 1/Sqrt[1 + 4*b])*(1 + 2*b - Sqrt[1 + 4*b] - Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]])*ArcTan[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] - Sqrt[1 + 2*b - Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] - Sqrt[1 + 2*b - Sqrt[1 + 4*b]]])) + ((1 - 1/Sqrt[1 + 4*b])*(1 + 2*b - Sqrt[1 + 4*b] + Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]])*ArcTan[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] + Sqrt[1 + 2*b - Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] + Sqrt[1 + 2*b - Sqrt[1 + 4*b]]]) - (Sqrt[1 + Sqrt[1 + 4*b]]*(1 + 2*b + Sqrt[1 + 4*b] - Sqrt[1 + Sqrt[1 + 4*b]]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]])*ArcTan[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] - Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 + 4*b]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] - Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]) + (Sqrt[1 + Sqrt[1 + 4*b]]*(1 + 2*b + Sqrt[1 + 4*b] + Sqrt[1 + Sqrt[1 + 4*b]]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]])*ArcTan[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] + Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 + 4*b]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] + Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]) + ((1 - 1/Sqrt[1 + 4*b])*(1 + 2*b - Sqrt[1 + 4*b] - Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]])*ArcTanh[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] - Sqrt[1 + 2*b - Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] - Sqrt[1 + 2*b - Sqrt[1 + 4*b]]]) - ((1 - 1/Sqrt[1 + 4*b])*(1 + 2*b - Sqrt[1 + 4*b] + Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]])*ArcTanh[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] + Sqrt[1 + 2*b - Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 - Sqrt[1 + 4*b]]*Sqrt[1 + 2*b - Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 - Sqrt[1 + 4*b]] + Sqrt[1 + 2*b - Sqrt[1 + 4*b]]]) + (Sqrt[1 + Sqrt[1 + 4*b]]*(1 + 2*b + Sqrt[1 + 4*b] - Sqrt[1 + Sqrt[1 + 4*b]]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]])*ArcTanh[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] - Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 + 4*b]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] - Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]) - (Sqrt[1 + Sqrt[1 + 4*b]]*(1 + 2*b + Sqrt[1 + 4*b] + Sqrt[1 + Sqrt[1 + 4*b]]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]])*ArcTanh[(2^(1/4)*Sqrt[a*x - Sqrt[b + a^2*x^2]])/Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] + Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]])/(2^(3/4)*a*Sqrt[1 + 4*b]*Sqrt[1 + 2*b + Sqrt[1 + 4*b]]*Sqrt[Sqrt[1 + Sqrt[1 + 4*b]] + Sqrt[1 + 2*b + Sqrt[1 + 4*b]]]) - Defer[Int][(Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(Sqrt[1 - Sqrt[1 + 4*b]] - Sqrt[2]*a*x), x]/(Sqrt[1 + 4*b]*Sqrt[1 - Sqrt[1 + 4*b]]) + Defer[Int][(Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(Sqrt[1 + Sqrt[1 + 4*b]] - Sqrt[2]*a*x), x]/(Sqrt[1 + 4*b]*Sqrt[1 + Sqrt[1 + 4*b]]) - Defer[Int][(Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(Sqrt[1 - Sqrt[1 + 4*b]] + Sqrt[2]*a*x), x]/(Sqrt[1 + 4*b]*Sqrt[1 - Sqrt[1 + 4*b]]) + Defer[Int][(Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(Sqrt[1 + Sqrt[1 + 4*b]] + Sqrt[2]*a*x), x]/(Sqrt[1 + 4*b]*Sqrt[1 + Sqrt[1 + 4*b]])","F",0,0,0,0,-1,"{}"
1869,1,128,0,0.114367,"\int \frac{d+c x}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\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}}","\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,"(b^4*c)/(10*a^2*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2)) - (b^2*d)/(3*a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + (d*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/a + (c*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2))/(6*a^2)","A",3,2,29,0.06897,1,"{2119, 1628}"
1870,1,70,0,0.0710356,"\int \frac{1}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[1/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]],x]","\frac{8}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}-\frac{24}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}+\frac{16}{3} \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,"(16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7","A",5,3,19,0.1579,1,"{371, 1398, 772}"
1871,1,215,0,0.2066699,"\int \frac{\left(-b+a x^2\right) \sqrt[3]{x+x^3}}{x^2} \, dx","Int[((-b + a*x^2)*(x + x^3)^(1/3))/x^2,x]","\frac{1}{2} x \sqrt[3]{x^3+x} (a-3 b)-\frac{x^{2/3} \left(x^2+1\right)^{2/3} (a-3 b) \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{6 \left(x^3+x\right)^{2/3}}+\frac{x^{2/3} \left(x^2+1\right)^{2/3} (a-3 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)}{12 \left(x^3+x\right)^{2/3}}-\frac{x^{2/3} \left(x^2+1\right)^{2/3} (a-3 b) \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} \left(x^3+x\right)^{2/3}}+\frac{3 b \left(x^3+x\right)^{4/3}}{2 x^2}","\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,"((a - 3*b)*x*(x + x^3)^(1/3))/2 + (3*b*(x + x^3)^(4/3))/(2*x^2) - ((a - 3*b)*x^(2/3)*(1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*(x + x^3)^(2/3)) - ((a - 3*b)*x^(2/3)*(1 + x^2)^(2/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(6*(x + x^3)^(2/3)) + ((a - 3*b)*x^(2/3)*(1 + x^2)^(2/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(12*(x + x^3)^(2/3))","A",12,12,22,0.5455,1,"{2038, 2004, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1872,1,1402,0,2.5099072,"\int \frac{1}{x^3 \sqrt[3]{-b x^2+a x^3} \left(d+c x^3\right)} \, dx","Int[1/(x^3*(-(b*x^2) + a*x^3)^(1/3)*(d + c*x^3)),x]","\frac{\left(4 b \sqrt[3]{c}-3 a \sqrt[3]{d}\right) (b-a x)}{20 b^2 d^{4/3} x \sqrt[3]{a x^3-b x^2}}+\frac{\left(4 (-1)^{2/3} b \sqrt[3]{c}-3 a \sqrt[3]{d}\right) (b-a x)}{20 b^2 d^{4/3} x \sqrt[3]{a x^3-b x^2}}-\frac{\left(3 \sqrt[3]{d} a+4 \sqrt[3]{-1} b \sqrt[3]{c}\right) (b-a x)}{20 b^2 d^{4/3} x \sqrt[3]{a x^3-b x^2}}+\frac{\left(-9 d^{2/3} a^2+12 (-1)^{2/3} b \sqrt[3]{c} \sqrt[3]{d} a+20 \sqrt[3]{-1} b^2 c^{2/3}\right) (b-a x)}{40 b^3 d^{5/3} \sqrt[3]{a x^3-b x^2}}-\frac{\left(9 d^{2/3} a^2-12 b \sqrt[3]{c} \sqrt[3]{d} a+20 b^2 c^{2/3}\right) (b-a x)}{40 b^3 d^{5/3} \sqrt[3]{a x^3-b x^2}}-\frac{\left(9 d^{2/3} a^2+12 \sqrt[3]{-1} b \sqrt[3]{c} \sqrt[3]{d} a+20 (-1)^{2/3} b^2 c^{2/3}\right) (b-a x)}{40 b^3 d^{5/3} \sqrt[3]{a x^3-b x^2}}-\frac{3 (b-a x)}{8 b d x^2 \sqrt[3]{a x^3-b x^2}}+\frac{c x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[9]{d} \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{\sqrt[3]{d} a+b \sqrt[3]{c}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{\sqrt[3]{d} a+b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}+\frac{c x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[9]{d} \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a \sqrt[3]{d}-\sqrt[3]{-1} b \sqrt[3]{c}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a \sqrt[3]{d}-\sqrt[3]{-1} b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}+\frac{c x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[9]{d} \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{\sqrt[3]{d} a+(-1)^{2/3} b \sqrt[3]{c}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{\sqrt[3]{d} a+(-1)^{2/3} b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}-\frac{c x^{2/3} \sqrt[3]{a x-b} \log \left(-\sqrt[3]{c} x-\sqrt[3]{d}\right)}{6 \sqrt[3]{\sqrt[3]{d} a+b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}-\frac{c x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[3]{-1} \sqrt[3]{c} x-\sqrt[3]{d}\right)}{6 \sqrt[3]{a \sqrt[3]{d}-\sqrt[3]{-1} b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}-\frac{c x^{2/3} \sqrt[3]{a x-b} \log \left(-(-1)^{2/3} \sqrt[3]{c} x-\sqrt[3]{d}\right)}{6 \sqrt[3]{\sqrt[3]{d} a+(-1)^{2/3} b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}+\frac{c x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[9]{d} \sqrt[3]{a x-b}}{\sqrt[3]{\sqrt[3]{d} a+b \sqrt[3]{c}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{\sqrt[3]{d} a+b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}+\frac{c x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[9]{d} \sqrt[3]{a x-b}}{\sqrt[3]{a \sqrt[3]{d}-\sqrt[3]{-1} b \sqrt[3]{c}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a \sqrt[3]{d}-\sqrt[3]{-1} b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}+\frac{c x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[9]{d} \sqrt[3]{a x-b}}{\sqrt[3]{\sqrt[3]{d} a+(-1)^{2/3} b \sqrt[3]{c}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{\sqrt[3]{d} a+(-1)^{2/3} b \sqrt[3]{c}} d^{17/9} \sqrt[3]{a x^3-b x^2}}","\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,"((20*(-1)^(1/3)*b^2*c^(2/3) + 12*(-1)^(2/3)*a*b*c^(1/3)*d^(1/3) - 9*a^2*d^(2/3))*(b - a*x))/(40*b^3*d^(5/3)*(-(b*x^2) + a*x^3)^(1/3)) - ((20*b^2*c^(2/3) - 12*a*b*c^(1/3)*d^(1/3) + 9*a^2*d^(2/3))*(b - a*x))/(40*b^3*d^(5/3)*(-(b*x^2) + a*x^3)^(1/3)) - ((20*(-1)^(2/3)*b^2*c^(2/3) + 12*(-1)^(1/3)*a*b*c^(1/3)*d^(1/3) + 9*a^2*d^(2/3))*(b - a*x))/(40*b^3*d^(5/3)*(-(b*x^2) + a*x^3)^(1/3)) - (3*(b - a*x))/(8*b*d*x^2*(-(b*x^2) + a*x^3)^(1/3)) + ((4*b*c^(1/3) - 3*a*d^(1/3))*(b - a*x))/(20*b^2*d^(4/3)*x*(-(b*x^2) + a*x^3)^(1/3)) + ((4*(-1)^(2/3)*b*c^(1/3) - 3*a*d^(1/3))*(b - a*x))/(20*b^2*d^(4/3)*x*(-(b*x^2) + a*x^3)^(1/3)) - ((4*(-1)^(1/3)*b*c^(1/3) + 3*a*d^(1/3))*(b - a*x))/(20*b^2*d^(4/3)*x*(-(b*x^2) + a*x^3)^(1/3)) + (c*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*d^(1/9)*(-b + a*x)^(1/3))/(Sqrt[3]*(b*c^(1/3) + a*d^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(b*c^(1/3) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) + (c*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*d^(1/9)*(-b + a*x)^(1/3))/(Sqrt[3]*(-((-1)^(1/3)*b*c^(1/3)) + a*d^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(-((-1)^(1/3)*b*c^(1/3)) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) + (c*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*d^(1/9)*(-b + a*x)^(1/3))/(Sqrt[3]*((-1)^(2/3)*b*c^(1/3) + a*d^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*((-1)^(2/3)*b*c^(1/3) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) - (c*x^(2/3)*(-b + a*x)^(1/3)*Log[-d^(1/3) - c^(1/3)*x])/(6*(b*c^(1/3) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) - (c*x^(2/3)*(-b + a*x)^(1/3)*Log[-d^(1/3) + (-1)^(1/3)*c^(1/3)*x])/(6*(-((-1)^(1/3)*b*c^(1/3)) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) - (c*x^(2/3)*(-b + a*x)^(1/3)*Log[-d^(1/3) - (-1)^(2/3)*c^(1/3)*x])/(6*((-1)^(2/3)*b*c^(1/3) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) + (c*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (d^(1/9)*(-b + a*x)^(1/3))/(b*c^(1/3) + a*d^(1/3))^(1/3)])/(2*(b*c^(1/3) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) + (c*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (d^(1/9)*(-b + a*x)^(1/3))/(-((-1)^(1/3)*b*c^(1/3)) + a*d^(1/3))^(1/3)])/(2*(-((-1)^(1/3)*b*c^(1/3)) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3)) + (c*x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (d^(1/9)*(-b + a*x)^(1/3))/((-1)^(2/3)*b*c^(1/3) + a*d^(1/3))^(1/3)])/(2*((-1)^(2/3)*b*c^(1/3) + a*d^(1/3))^(1/3)*d^(17/9)*(-(b*x^2) + a*x^3)^(1/3))","B",18,6,29,0.2069,1,"{2056, 6725, 129, 155, 12, 91}"
1873,1,625,0,1.984297,"\int \frac{-1+x^4}{\sqrt{-x-x^2+x^3} \left(1+x^4\right)} \, dx","Int[(-1 + x^4)/(Sqrt[-x - x^2 + x^3]*(1 + x^4)),x]","\frac{\sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(-\frac{1}{2} \sqrt[4]{-1} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \sqrt[4]{-1} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(-\frac{1}{2} (-1)^{3/4} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} (-1)^{3/4} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}","-\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,"(Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[-1/2*((-1)^(1/4)*(1 + Sqrt[5])), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[((-1)^(1/4)*(1 + Sqrt[5]))/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[-1/2*((-1)^(3/4)*(1 + Sqrt[5])), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[((-1)^(3/4)*(1 + Sqrt[5]))/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3])","C",27,8,29,0.2759,0,"{2056, 6725, 716, 1098, 934, 168, 538, 537}"
1874,1,209,0,0.0763824,"\int \sqrt{-1-11 x-36 x^2-27 x^3+16 x^4+9 x^5+x^6} \, dx","Int[Sqrt[-1 - 11*x - 36*x^2 - 27*x^3 + 16*x^4 + 9*x^5 + x^6],x]","-\frac{65 \sqrt{-\left(\left(-x^2+x+1\right) \left(x^2+5 x+1\right)^2\right)} (1-2 x)}{64 \left(x^2+5 x+1\right)}-\frac{x \left(-x^2+x+1\right) \sqrt{-\left(\left(-x^2+x+1\right) \left(x^2+5 x+1\right)^2\right)}}{4 \left(x^2+5 x+1\right)}-\frac{15 \left(-x^2+x+1\right) \sqrt{-\left(\left(-x^2+x+1\right) \left(x^2+5 x+1\right)^2\right)}}{8 \left(x^2+5 x+1\right)}+\frac{325 \sqrt{-\left(\left(-x^2+x+1\right) \left(x^2+5 x+1\right)^2\right)} \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)}{128 \sqrt{x^2-x-1} \left(x^2+5 x+1\right)}","-\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,"(-65*(1 - 2*x)*Sqrt[-((1 + x - x^2)*(1 + 5*x + x^2)^2)])/(64*(1 + 5*x + x^2)) - (15*(1 + x - x^2)*Sqrt[-((1 + x - x^2)*(1 + 5*x + x^2)^2)])/(8*(1 + 5*x + x^2)) - (x*(1 + x - x^2)*Sqrt[-((1 + x - x^2)*(1 + 5*x + x^2)^2)])/(4*(1 + 5*x + x^2)) + (325*Sqrt[-((1 + x - x^2)*(1 + 5*x + x^2)^2)]*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])])/(128*Sqrt[-1 - x + x^2]*(1 + 5*x + x^2))","A",7,7,32,0.2188,1,"{6688, 6719, 1661, 640, 612, 621, 206}"
1875,0,0,0,1.334676,"\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","Int[((-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,"2*b*p*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] - a*q^2*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^4, x] - b*q*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^3, x] + a*p*q*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x, x] + 2*a*p^2*Defer[Int][x^2*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
1876,1,129,0,0.3476587,"\int \frac{-2-x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(-2-x^4+x^8\right)} \, dx","Int[(-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",16,6,34,0.1765,1,"{6728, 240, 212, 206, 203, 377}"
1877,0,0,0,0.8489517,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Int[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+1)+\frac{4}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"(-4*(1 + Sqrt[1 + x])^(3/2))/3 + (4*(1 + Sqrt[1 + x])^(5/2))/5 + 8*Defer[Subst][Defer[Int][x^2/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^4/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1878,0,0,0,0.6509894,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Int[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$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*(1 + Sqrt[1 + x])^(3/2))/3 + (4*(1 + Sqrt[1 + x])^(5/2))/5 + 8*Defer[Subst][Defer[Int][x^2/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^4/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1879,1,176,0,0.6032975,"\int \frac{\left(b+a x^2\right) \sqrt{b x+a x^3}}{x^2 \left(-b+a x^2\right)} \, dx","Int[((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}}{x}+\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{\sqrt{x} \sqrt{a x^2+b}}-\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{\sqrt{x} \sqrt{a x^2+b}}","\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,"(2*Sqrt[b*x + a*x^3])/x + (Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]*ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(Sqrt[x]*Sqrt[b + a*x^2]) - (Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(Sqrt[x]*Sqrt[b + a*x^2])","A",13,10,35,0.2857,1,"{2056, 466, 474, 12, 490, 1211, 220, 1699, 205, 208}"
1880,0,0,0,28.9797919,"\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","Int[((-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,"(4*(a - x)*(1 - x/b)^(1/4)*AppellF1[-1/2, -11/4, 5/4, 1/2, x/a, x/b])/(((a - x)*(b - x)*x^2)^(1/4)*(1 - x/a)^(3/4)) + (2*(3*a - 7*b)*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][(-a + x^2)^(11/4)/((-b + x^2)^(5/4)*(a^3 - 3*a^2*x^2 + 3*a*(1 - (b*d)/(3*a))*x^4 - (1 - d)*x^6)), x], x, Sqrt[x]])/((a - x)*(b - x)*x^2)^(1/4) + (4*b*(3*a - b*d)*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][(x^2*(-a + x^2)^(11/4))/((-b + x^2)^(5/4)*(a^3 - 3*a^2*x^2 + 3*a*(1 - (b*d)/(3*a))*x^4 - (1 - d)*x^6)), x], x, Sqrt[x]])/(a^2*((a - x)*(b - x)*x^2)^(1/4)) - (4*b*(1 - d)*Sqrt[x]*(-a + x)^(1/4)*(-b + x)^(1/4)*Defer[Subst][Defer[Int][(x^4*(-a + x^2)^(11/4))/((-b + x^2)^(5/4)*(a^3 - 3*a^2*x^2 + 3*a*(1 - (b*d)/(3*a))*x^4 - (1 - d)*x^6)), x], x, Sqrt[x]])/(a^2*((a - x)*(b - x)*x^2)^(1/4))","F",0,0,0,0,-1,"{}"
1881,1,571,0,0.8409551,"\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","Int[(2*b + a*x^2)/((b + a*x^2)^(1/4)*(b*n + a*n*x^2 + 2*x^4)),x]","\frac{\sqrt[4]{b} \left(\frac{\sqrt{a^2 n-8 b}}{\sqrt{n}}+a\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(-\frac{2 \sqrt{b}}{\sqrt{-n a^2-\sqrt{n} \sqrt{a^2 n-8 b} a+4 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{-a \sqrt{n} \sqrt{a^2 n-8 b}+a^2 (-n)+4 b}}-\frac{\sqrt[4]{b} \left(\frac{\sqrt{a^2 n-8 b}}{\sqrt{n}}+a\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(\frac{2 \sqrt{b}}{\sqrt{-n a^2-\sqrt{n} \sqrt{a^2 n-8 b} a+4 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{-a \sqrt{n} \sqrt{a^2 n-8 b}+a^2 (-n)+4 b}}+\frac{\sqrt[4]{b} \left(a-\frac{\sqrt{a^2 n-8 b}}{\sqrt{n}}\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(-\frac{2 \sqrt{b}}{\sqrt{-n a^2+\sqrt{n} \sqrt{a^2 n-8 b} a+4 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{a \sqrt{n} \sqrt{a^2 n-8 b}+a^2 (-n)+4 b}}-\frac{\sqrt[4]{b} \left(a-\frac{\sqrt{a^2 n-8 b}}{\sqrt{n}}\right) \sqrt{-\frac{a x^2}{b}} \Pi \left(\frac{2 \sqrt{b}}{\sqrt{-n a^2+\sqrt{n} \sqrt{a^2 n-8 b} a+4 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a x^2+b}}{\sqrt[4]{b}}\right)\right|-1\right)}{2 x \sqrt{a \sqrt{n} \sqrt{a^2 n-8 b}+a^2 (-n)+4 b}}","\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,"(b^(1/4)*(a + Sqrt[-8*b + a^2*n]/Sqrt[n])*Sqrt[-((a*x^2)/b)]*EllipticPi[(-2*Sqrt[b])/Sqrt[4*b - a^2*n - a*Sqrt[n]*Sqrt[-8*b + a^2*n]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[4*b - a^2*n - a*Sqrt[n]*Sqrt[-8*b + a^2*n]]*x) - (b^(1/4)*(a + Sqrt[-8*b + a^2*n]/Sqrt[n])*Sqrt[-((a*x^2)/b)]*EllipticPi[(2*Sqrt[b])/Sqrt[4*b - a^2*n - a*Sqrt[n]*Sqrt[-8*b + a^2*n]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[4*b - a^2*n - a*Sqrt[n]*Sqrt[-8*b + a^2*n]]*x) + (b^(1/4)*(a - Sqrt[-8*b + a^2*n]/Sqrt[n])*Sqrt[-((a*x^2)/b)]*EllipticPi[(-2*Sqrt[b])/Sqrt[4*b - a^2*n + a*Sqrt[n]*Sqrt[-8*b + a^2*n]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[4*b - a^2*n + a*Sqrt[n]*Sqrt[-8*b + a^2*n]]*x) - (b^(1/4)*(a - Sqrt[-8*b + a^2*n]/Sqrt[n])*Sqrt[-((a*x^2)/b)]*EllipticPi[(2*Sqrt[b])/Sqrt[4*b - a^2*n + a*Sqrt[n]*Sqrt[-8*b + a^2*n]], ArcSin[(b + a*x^2)^(1/4)/b^(1/4)], -1])/(2*Sqrt[4*b - a^2*n + a*Sqrt[n]*Sqrt[-8*b + a^2*n]]*x)","C",10,4,38,0.1053,1,"{1692, 399, 490, 1218}"
1882,0,0,0,0.9795273,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}}} \, dx","Int[(Sqrt[1 + x]*(-1 + x^2))/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+11)-\frac{16}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"4*Sqrt[1 + Sqrt[1 + x]] - (8*(1 + Sqrt[1 + x])^(3/2))/3 + (4*(1 + Sqrt[1 + x])^(5/2))/5 - 8*Defer[Subst][Defer[Int][(1 + 4*x^4 - 4*x^6 + x^8)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]] + 16*Defer[Subst][Defer[Int][x^2/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^4/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1883,0,0,0,0.7704159,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}}} \, dx","Int[(Sqrt[1 + x]*(-1 + x^2))/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{4}{15} \sqrt{\sqrt{x+1}+1} (3 x+11)-\frac{16}{15} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}",1,"4*Sqrt[1 + Sqrt[1 + x]] - (8*(1 + Sqrt[1 + x])^(3/2))/3 + (4*(1 + Sqrt[1 + x])^(5/2))/5 - 8*Defer[Subst][Defer[Int][(1 + 4*x^4 - 4*x^6 + x^8)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]] + 16*Defer[Subst][Defer[Int][x^2/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^4/(1 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1884,0,0,0,0.9796169,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^4\right)} \, dx","Int[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(Sqrt[1 + x]*(1 + x^4)),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^4\right)} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-7 \text{$\#$1}^{11}+18 \text{$\#$1}^9-20 \text{$\#$1}^7+8 \text{$\#$1}^5}\&\right]+\frac{4}{3} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}+\frac{4}{3} \sqrt{\sqrt{x+1}+1}",1,"(4*(1 + Sqrt[1 + x])^(3/2))/3 - 8*Defer[Subst][Defer[Int][x^2/(1 + x^8*(-2 + x^2)^4), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1885,0,0,0,0.7576734,"\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^4\right)} \, dx","Int[((-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(Sqrt[1 + x]*(1 + x^4)),x]","\int \frac{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^4\right)} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-7 \text{$\#$1}^{11}+18 \text{$\#$1}^9-20 \text{$\#$1}^7+8 \text{$\#$1}^5}\&\right]+\frac{4}{3} \sqrt{x+1} \sqrt{\sqrt{x+1}+1}+\frac{4}{3} \sqrt{\sqrt{x+1}+1}",1,"(4*(1 + Sqrt[1 + x])^(3/2))/3 - 8*Defer[Subst][Defer[Int][x^2/(1 + x^8*(-2 + x^2)^4), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
1886,1,263,0,0.8367192,"\int \frac{1+a x^2}{\left(-1+a x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(1 + a*x^2)/((-1 + a*x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{\sqrt{x^2+1}+x}}{\sqrt{1-\sqrt{a+1}}}\right)}{\sqrt[4]{a} \sqrt{1-\sqrt{a+1}}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{a+1}+1}}\right)}{\sqrt[4]{a} \sqrt{\sqrt{a+1}+1}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{\sqrt{x^2+1}+x}}{\sqrt{1-\sqrt{a+1}}}\right)}{\sqrt[4]{a} \sqrt{1-\sqrt{a+1}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt{a+1}+1}}\right)}{\sqrt[4]{a} \sqrt{\sqrt{a+1}+1}}+\sqrt{\sqrt{x^2+1}+x}-\frac{1}{3 \left(\sqrt{x^2+1}+x\right)^{3/2}}","\text{RootSum}\left[\text{$\#$1}^8 a-2 \text{$\#$1}^4 a-4 \text{$\#$1}^4+a\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{\text{$\#$1}^7 a-\text{$\#$1}^3 a-2 \text{$\#$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]] - (2*ArcTan[(a^(1/4)*Sqrt[x + Sqrt[1 + x^2]])/Sqrt[1 - Sqrt[1 + a]]])/(a^(1/4)*Sqrt[1 - Sqrt[1 + a]]) - (2*ArcTan[(a^(1/4)*Sqrt[x + Sqrt[1 + x^2]])/Sqrt[1 + Sqrt[1 + a]]])/(a^(1/4)*Sqrt[1 + Sqrt[1 + a]]) - (2*ArcTanh[(a^(1/4)*Sqrt[x + Sqrt[1 + x^2]])/Sqrt[1 - Sqrt[1 + a]]])/(a^(1/4)*Sqrt[1 - Sqrt[1 + a]]) - (2*ArcTanh[(a^(1/4)*Sqrt[x + Sqrt[1 + x^2]])/Sqrt[1 + Sqrt[1 + a]]])/(a^(1/4)*Sqrt[1 + Sqrt[1 + a]])","B",23,10,32,0.3125,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 208, 205}"
1887,0,0,0,1.6267836,"\int \frac{x \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Int[(x*Sqrt[x + x^2])/Sqrt[x^2 + x*Sqrt[x + x^2]],x]","\int \frac{x \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","\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,"(2*Sqrt[x + x^2]*Defer[Subst][Defer[Int][(x^4*Sqrt[1 + x^2])/Sqrt[x^4 + x^2*Sqrt[x^2 + x^4]], x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x])","F",0,0,0,0,-1,"{}"
1888,1,182,0,0.3406507,"\int \frac{\sqrt{1+x}}{1+\sqrt{x+\sqrt{1+x}}} \, dx","Int[Sqrt[1 + x]/(1 + Sqrt[x + Sqrt[1 + x]]),x]","\frac{1}{2} \sqrt{x+\sqrt{x+1}} \left(2 \sqrt{x+1}+1\right)-2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}-\frac{2}{3} \log \left(1-\sqrt{x+1}\right)+\frac{8}{3} \log \left(\sqrt{x+1}+2\right)+\frac{2}{3} \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)+\frac{15}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{8}{3} \tanh ^{-1}\left(\frac{3 \sqrt{x+1}+4}{2 \sqrt{x+\sqrt{x+1}}}\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,"-2*Sqrt[1 + x] - 2*Sqrt[x + Sqrt[1 + x]] + (Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/2 + (2*ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/3 + (15*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 - (8*ArcTanh[(4 + 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/3 - (2*Log[1 - Sqrt[1 + x]])/3 + (8*Log[2 + Sqrt[1 + x]])/3","A",18,7,25,0.2800,1,"{6742, 612, 621, 206, 734, 843, 724}"
1889,1,265,0,0.6144652,"\int \frac{1+x}{(-1+x) (1+2 x) \sqrt[3]{-1+3 x^2}} \, dx","Int[(1 + x)/((-1 + x)*(1 + 2*x)*(-1 + 3*x^2)^(1/3)),x]","-\frac{2 x \sqrt[3]{1-3 x^2} F_1\left(\frac{1}{2};\frac{1}{3},1;\frac{3}{2};3 x^2,x^2\right)}{3 \sqrt[3]{3 x^2-1}}-\frac{x \sqrt[3]{1-3 x^2} F_1\left(\frac{1}{2};1,\frac{1}{3};\frac{3}{2};4 x^2,3 x^2\right)}{3 \sqrt[3]{3 x^2-1}}-\frac{\log \left(1-4 x^2\right)}{12 \sqrt[3]{2}}-\frac{\log \left(1-x^2\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{3 x^2-1}\right)}{2 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{3 x^2-1}+1\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-2\ 2^{2/3} \sqrt[3]{3 x^2-1}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{3 x^2-1}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","\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,"(-2*x*(1 - 3*x^2)^(1/3)*AppellF1[1/2, 1/3, 1, 3/2, 3*x^2, x^2])/(3*(-1 + 3*x^2)^(1/3)) - (x*(1 - 3*x^2)^(1/3)*AppellF1[1/2, 1, 1/3, 3/2, 4*x^2, 3*x^2])/(3*(-1 + 3*x^2)^(1/3)) + ArcTan[(1 - 2*2^(2/3)*(-1 + 3*x^2)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) + ArcTan[(1 + 2^(2/3)*(-1 + 3*x^2)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[1 - 4*x^2]/(12*2^(1/3)) - Log[1 - x^2]/(6*2^(1/3)) + Log[2^(1/3) - (-1 + 3*x^2)^(1/3)]/(2*2^(1/3)) + Log[1 + 2^(2/3)*(-1 + 3*x^2)^(1/3)]/(4*2^(1/3))","C",20,10,27,0.3704,0,"{6742, 757, 430, 429, 444, 55, 617, 204, 31, 56}"
1890,1,128,0,0.118714,"\int \frac{-b+a x^2}{x^2 \sqrt[3]{-x+x^3}} \, dx","Int[(-b + a*x^2)/(x^2*(-x + x^3)^(1/3)),x]","-\frac{3 a \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(x^{2/3}-\sqrt[3]{x^2-1}\right)}{4 \sqrt[3]{x^3-x}}+\frac{\sqrt{3} a \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{x^3-x}}-\frac{3 b \left(x^3-x\right)^{2/3}}{4 x^2}","\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*(-x + x^3)^(2/3))/(4*x^2) + (Sqrt[3]*a*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*(-x + x^3)^(1/3)) - (3*a*x^(1/3)*(-1 + x^2)^(1/3)*Log[x^(2/3) - (-1 + x^2)^(1/3)])/(4*(-x + x^3)^(1/3))","A",5,5,24,0.2083,1,"{2038, 2011, 329, 275, 239}"
1891,1,611,0,1.9097869,"\int \frac{1+x^4}{\sqrt{-x-x^2+x^3} \left(-1+x^4\right)} \, dx","Int[(1 + x^4)/(Sqrt[-x - x^2 + x^3]*(-1 + x^4)),x]","\frac{\sqrt{x} \sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2} \sqrt{\frac{\left(1+\sqrt{5}\right) x+2}{\left(1-\sqrt{5}\right) x+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{5} \sqrt{x}}{\sqrt{-\left(\left(1-\sqrt{5}\right) x\right)-2}}\right)|\frac{1}{10} \left(5-\sqrt{5}\right)\right)}{\sqrt[4]{5} \sqrt{\frac{1}{\left(1-\sqrt{5}\right) x+2}} \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(-1-\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{2 \sqrt{x^3-x^2-x}}","-\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,"(Sqrt[x]*Sqrt[-2 - (1 - Sqrt[5])*x]*Sqrt[(2 + (1 + Sqrt[5])*x)/(2 + (1 - Sqrt[5])*x)]*EllipticF[ArcSin[(Sqrt[2]*5^(1/4)*Sqrt[x])/Sqrt[-2 - (1 - Sqrt[5])*x]], (5 - Sqrt[5])/10])/(5^(1/4)*Sqrt[(2 + (1 - Sqrt[5])*x)^(-1)]*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1 - Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1/2*I)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(I/2)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(2*Sqrt[-x - x^2 + x^3])","C",27,8,29,0.2759,0,"{2056, 6725, 716, 1098, 934, 168, 538, 537}"
1892,0,0,0,0.5910875,"\int \frac{\left(-1+x^3\right) \sqrt[3]{1+x^6}}{x^2 \left(1+x^3\right)} \, dx","Int[((-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,"Hypergeometric2F1[-1/3, -1/6, 5/6, -x^6]/x - (2*Defer[Int][(1 + x^6)^(1/3)/(1 + x), x])/3 + (2*(1 - I*Sqrt[3])*Defer[Int][(1 + x^6)^(1/3)/(-1 - I*Sqrt[3] + 2*x), x])/3 + (2*(1 + I*Sqrt[3])*Defer[Int][(1 + x^6)^(1/3)/(-1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
1893,1,195,0,1.1833733,"\int \frac{\left(-2+x^6\right) \sqrt[3]{2+x^6}}{x^2 \left(2+2 x^3+x^6\right)} \, dx","Int[((-2 + x^6)*(2 + x^6)^(1/3))/(x^2*(2 + 2*x^3 + x^6)),x]","\frac{i x^5 F_1\left(\frac{5}{6};1,-\frac{1}{3};\frac{11}{6};-\frac{i x^6}{2},-\frac{x^6}{2}\right)}{5\ 2^{2/3}}-\frac{i x^5 F_1\left(\frac{5}{6};1,-\frac{1}{3};\frac{11}{6};\frac{i x^6}{2},-\frac{x^6}{2}\right)}{5\ 2^{2/3}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) x^2 F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};-\frac{i x^6}{2},-\frac{x^6}{2}\right)}{2^{2/3}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) x^2 F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{i x^6}{2},-\frac{x^6}{2}\right)}{2^{2/3}}+\frac{\sqrt[3]{2} \, _2F_1\left(-\frac{1}{3},-\frac{1}{6};\frac{5}{6};-\frac{x^6}{2}\right)}{x}","\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,"((1/2 - I/2)*x^2*AppellF1[1/3, 1, -1/3, 4/3, (-1/2*I)*x^6, -1/2*x^6])/2^(2/3) + ((1/2 + I/2)*x^2*AppellF1[1/3, 1, -1/3, 4/3, (I/2)*x^6, -1/2*x^6])/2^(2/3) + ((I/5)*x^5*AppellF1[5/6, 1, -1/3, 11/6, (-1/2*I)*x^6, -1/2*x^6])/2^(2/3) - ((I/5)*x^5*AppellF1[5/6, 1, -1/3, 11/6, (I/2)*x^6, -1/2*x^6])/2^(2/3) + (2^(1/3)*Hypergeometric2F1[-1/3, -1/6, 5/6, -1/2*x^6])/x","C",29,6,30,0.2000,0,"{6728, 364, 1562, 465, 429, 510}"
1894,1,134,0,0.5268396,"\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","Int[((1 + x^3)^(2/3)*(-1 - 2*x^3 + 2*x^6))/(x^6*(-1 + x^3 + 2*x^6)),x]","-\frac{2 \log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)}{\sqrt[3]{3}}+2 \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}}{5 x^5}-\frac{17 \left(x^3+1\right)^{2/3}}{10 x^2}+\frac{\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)}{\sqrt[3]{3}}","-\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,"-1/5*(1 + x^3)^(2/3)/x^5 - (17*(1 + x^3)^(2/3))/(10*x^2) + 2*3^(1/6)*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(1 + x^3)^(1/3))] - (2*Log[1 - (3^(1/3)*x)/(1 + x^3)^(1/3)])/3^(1/3) + Log[1 + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + (3^(1/3)*x)/(1 + x^3)^(1/3)]/3^(1/3)","A",13,11,37,0.2973,1,"{1586, 6725, 271, 264, 377, 200, 31, 634, 617, 204, 628}"
1895,1,323,0,0.8600008,"\int \frac{\left(1+x^3\right) \sqrt{x-x^4}}{2+4 x^3+3 x^6} \, dx","Int[((1 + x^3)*Sqrt[x - x^4])/(2 + 4*x^3 + 3*x^6),x]","-\frac{\left(2+i \sqrt{2}\right) \sqrt{x-x^4} \sin ^{-1}\left(x^{3/2}\right)}{18 \sqrt{x} \sqrt{1-x^3}}-\frac{\left(2-i \sqrt{2}\right) \sqrt{x-x^4} \sin ^{-1}\left(x^{3/2}\right)}{18 \sqrt{x} \sqrt{1-x^3}}+\frac{\left(\sqrt{2}+i\right) \sqrt{x-x^4} \tan ^{-1}\left(\frac{x^{3/2}}{\sqrt{\frac{-\sqrt{2}+2 i}{-\sqrt{2}+5 i}} \sqrt{1-x^3}}\right)}{9 \sqrt{2} \sqrt{\frac{-\sqrt{2}+2 i}{-\sqrt{2}+5 i}} \sqrt{x} \sqrt{1-x^3}}+\frac{\left(7+4 i \sqrt{2}\right) \sqrt{x-x^4} \tan ^{-1}\left(\frac{x^{3/2}}{\sqrt{\frac{\sqrt{2}+2 i}{\sqrt{2}+5 i}} \sqrt{1-x^3}}\right)}{9 \sqrt{2} \sqrt{-8+7 i \sqrt{2}} \sqrt{x} \sqrt{1-x^3}}","-\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,"-1/18*((2 - I*Sqrt[2])*Sqrt[x - x^4]*ArcSin[x^(3/2)])/(Sqrt[x]*Sqrt[1 - x^3]) - ((2 + I*Sqrt[2])*Sqrt[x - x^4]*ArcSin[x^(3/2)])/(18*Sqrt[x]*Sqrt[1 - x^3]) + ((I + Sqrt[2])*Sqrt[x - x^4]*ArcTan[x^(3/2)/(Sqrt[(2*I - Sqrt[2])/(5*I - Sqrt[2])]*Sqrt[1 - x^3])])/(9*Sqrt[2]*Sqrt[(2*I - Sqrt[2])/(5*I - Sqrt[2])]*Sqrt[x]*Sqrt[1 - x^3]) + ((7 + (4*I)*Sqrt[2])*Sqrt[x - x^4]*ArcTan[x^(3/2)/(Sqrt[(2*I + Sqrt[2])/(5*I + Sqrt[2])]*Sqrt[1 - x^3])])/(9*Sqrt[2]*Sqrt[-8 + (7*I)*Sqrt[2]]*Sqrt[x]*Sqrt[1 - x^3])","B",12,7,31,0.2258,0,"{2056, 6715, 1692, 402, 216, 377, 205}"
1896,1,491,0,1.3653099,"\int \frac{-2+a x^4}{\sqrt[4]{b+a x^4} \left(-b+a x^4+2 x^8\right)} \, dx","Int[(-2 + a*x^4)/((b + a*x^4)^(1/4)*(-b + a*x^4 + 2*x^8)),x]","\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)}{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}{\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}{\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}{\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{\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))])/(2*(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))])/(2*(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))])/(2*(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))])/(2*(a + Sqrt[a^2 + 8*b])^(3/4)*(a^2 - 4*b + a*Sqrt[a^2 + 8*b])^(1/4))","B",10,5,35,0.1429,1,"{6728, 377, 212, 208, 205}"
1897,1,134,0,0.3666612,"\int \frac{-1+x}{(1+x) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(-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}}-\frac{4 \tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}+\frac{4 \tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}","\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*ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[1 + Sqrt[2]] + (4*ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[-1 + Sqrt[2]]","A",13,10,24,0.4167,0,"{6742, 2117, 14, 2119, 1628, 828, 826, 1166, 207, 203}"
1898,1,134,0,0.3140027,"\int \frac{1+x}{(-1+x) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(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}}+\frac{4 \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}-\frac{4 \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}","\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*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[-1 + Sqrt[2]] - (4*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[1 + Sqrt[2]]","A",13,10,24,0.4167,0,"{6742, 2117, 14, 2119, 1628, 828, 826, 1166, 207, 203}"
1899,0,0,0,1.887537,"\int \frac{\sqrt{-x+x^2}}{\sqrt{x^2-x \sqrt{-x+x^2}}} \, dx","Int[Sqrt[-x + x^2]/Sqrt[x^2 - x*Sqrt[-x + x^2]],x]","\int \frac{\sqrt{-x+x^2}}{\sqrt{x^2-x \sqrt{-x+x^2}}} \, dx","\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,"(2*Sqrt[-x + x^2]*Defer[Subst][Defer[Int][(x^2*Sqrt[-1 + x^2])/Sqrt[x^4 - x^2*Sqrt[-x^2 + x^4]], x], x, Sqrt[x]])/(Sqrt[-1 + x]*Sqrt[x])","F",0,0,0,0,-1,"{}"
1900,0,0,0,0.3808083,"\int \frac{6+2 x+x^2}{(2+x) \left(2+x^2\right) \sqrt[3]{2+x+x^2}} \, dx","Int[(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,"(-3*((1 - I*Sqrt[7] + 2*x)/(2 + x))^(1/3)*((1 + I*Sqrt[7] + 2*x)/(2 + x))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (3 - I*Sqrt[7])/(2*(2 + x)), (3 + I*Sqrt[7])/(2*(2 + x))])/(2*2^(2/3)*(2 + x + x^2)^(1/3)) + 2*Defer[Int][1/((2 + x^2)*(2 + x + x^2)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1901,0,0,0,0.5210972,"\int \frac{-1+x}{x \sqrt[3]{1+2 x+2 x^2+x^3}} \, dx","Int[(-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,"(3*(1 + x)*(1 - (2*(1 + x))/(1 - I*Sqrt[3]))^(1/3)*(1 - (2*(1 + x))/(1 + I*Sqrt[3]))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, (2*(1 + x))/(1 - I*Sqrt[3]), (2*(1 + x))/(1 + I*Sqrt[3])])/(2*(1 + 2*x + 2*x^2 + x^3)^(1/3)) - ((1 + x)^(1/3)*(1 + x + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-2/3 + x)*(1/3 + x)^(1/3)*(7/9 - x/3 + x^2)^(1/3)), x], x, 2/3 + x])/(1 + 2*x + 2*x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
1902,0,0,0,1.3664754,"\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","Int[((-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,"-2*a*q^2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^7, x] - 2*b*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^5, x] - a*p*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^4, x] + b*p*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^2, x] + a*p^2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x, x]","F",0,0,0,0,-1,"{}"
1903,1,241,0,1.2422582,"\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","Int[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{\sqrt{\frac{1}{85} \left(\sqrt{170}-1\right)} \sqrt{4 x^2-13 x+3} \tan ^{-1}\left(\frac{13-\left(1-\sqrt{170}\right) x}{\sqrt{2 \left(\sqrt{170}-1\right)} \sqrt{4 x^2-13 x+3}}\right)}{2 \sqrt[10]{\left(4 x^2-13 x+3\right)^5}}-\frac{\sqrt{4 x^2-13 x+3} \tanh ^{-1}\left(\frac{13-8 x}{4 \sqrt{4 x^2-13 x+3}}\right)}{2 \sqrt[10]{\left(4 x^2-13 x+3\right)^5}}+\frac{\sqrt{\frac{1}{85} \left(1+\sqrt{170}\right)} \sqrt{4 x^2-13 x+3} \tanh ^{-1}\left(\frac{13-\left(1+\sqrt{170}\right) x}{\sqrt{2 \left(1+\sqrt{170}\right)} \sqrt{4 x^2-13 x+3}}\right)}{2 \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,"-1/2*(Sqrt[(-1 + Sqrt[170])/85]*Sqrt[3 - 13*x + 4*x^2]*ArcTan[(13 - (1 - Sqrt[170])*x)/(Sqrt[2*(-1 + Sqrt[170])]*Sqrt[3 - 13*x + 4*x^2])])/((3 - 13*x + 4*x^2)^5)^(1/10) - (Sqrt[3 - 13*x + 4*x^2]*ArcTanh[(13 - 8*x)/(4*Sqrt[3 - 13*x + 4*x^2])])/(2*((3 - 13*x + 4*x^2)^5)^(1/10)) + (Sqrt[(1 + Sqrt[170])/85]*Sqrt[3 - 13*x + 4*x^2]*ArcTanh[(13 - (1 + Sqrt[170])*x)/(Sqrt[2*(1 + Sqrt[170])]*Sqrt[3 - 13*x + 4*x^2])])/(2*((3 - 13*x + 4*x^2)^5)^(1/10))","A",10,8,65,0.1231,1,"{6688, 6720, 1079, 621, 206, 987, 1030, 204}"
1904,0,0,0,4.7797247,"\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","Int[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,"(2*Sqrt[x]*Sqrt[-b + a^2*x]*Defer[Subst][Defer[Int][1/(x^2*Sqrt[-b + a^2*x^2]*(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2)), x], x, Sqrt[x]])/Sqrt[-(b*x) + a^2*x^2]","F",0,0,0,0,-1,"{}"
1905,1,161,0,0.720709,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/((-1 + x^2)*Sqrt[1 + x^4]),x]","-\frac{1}{4} \sqrt{1-i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)+\frac{1}{4} \sqrt{1-i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)+\frac{1}{4} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)-\frac{1}{4} \sqrt{1+i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1+i} \sqrt{1+i x^2}}\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{2 \left(1+\sqrt{2}\right)} x \sqrt{\sqrt{x^4+1}+x^2}}{\sqrt{x^4+1}+x^2+1}\right)",1,"-1/4*(Sqrt[1 - I]*ArcTanh[(1 - I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])]) + (Sqrt[1 - I]*ArcTanh[(1 + I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])])/4 + (Sqrt[1 + I]*ArcTanh[(1 - I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/4 - (Sqrt[1 + I]*ArcTanh[(1 + I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/4","C",12,4,34,0.1176,0,"{6725, 2133, 725, 206}"
1906,1,88,0,0.086136,"\int \frac{1}{(1+2 x) \sqrt[3]{-1+4 x+4 x^2}} \, dx","Int[1/((1 + 2*x)*(-1 + 4*x + 4*x^2)^(1/3)),x]","\frac{\log (2 x+1)}{4 \sqrt[3]{2}}-\frac{3 \log \left(\sqrt[3]{(2 x+1)^2-2}+\sqrt[3]{2}\right)}{8 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-2^{2/3} \sqrt[3]{(2 x+1)^2-2}}{\sqrt{3}}\right)}{4 \sqrt[3]{2}}","-\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,"-1/4*(Sqrt[3]*ArcTan[(1 - 2^(2/3)*(-2 + (1 + 2*x)^2)^(1/3))/Sqrt[3]])/2^(1/3) + Log[1 + 2*x]/(4*2^(1/3)) - (3*Log[2^(1/3) + (-2 + (1 + 2*x)^2)^(1/3)])/(8*2^(1/3))","A",6,6,22,0.2727,1,"{694, 266, 56, 617, 204, 31}"
1907,1,1430,0,2.2184873,"\int \frac{1}{x^3 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^3*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{a^{2/3} \left(9 a^{16/3}-12 b^{5/3} a^{8/3}+20 b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{2/3} \left(9 a^{16/3}-12 (-1)^{2/3} b^{5/3} a^{8/3}-20 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{2/3} \left(9 a^{16/3}+12 \sqrt[3]{-1} b^{5/3} a^{8/3}+20 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{a} \left(3 a^{8/3}-4 b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{a} \left(3 a^{8/3}+4 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{a} \left(3 a^{8/3}-4 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 \left(x a^3+b^2\right)}{8 b^3 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x+\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{a} x\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"(a^(2/3)*(9*a^(16/3) - 12*a^(8/3)*b^(5/3) + 20*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(9*a^(16/3) - 12*(-1)^(2/3)*a^(8/3)*b^(5/3) - 20*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(9*a^(16/3) + 12*(-1)^(1/3)*a^(8/3)*b^(5/3) + 20*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*(b^2 + a^3*x))/(8*b^3*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(3*a^(8/3) - 4*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(3*a^(8/3) + 4*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(3*a^(8/3) - 4*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - a^(1/3)*x])/(6*b^2*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",18,6,34,0.1765,1,"{2056, 6725, 129, 155, 12, 91}"
1908,1,1430,0,1.884624,"\int \frac{1}{x^3 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^3*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{a^{2/3} \left(9 a^{16/3}-12 b^{5/3} a^{8/3}+20 b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{2/3} \left(9 a^{16/3}-12 (-1)^{2/3} b^{5/3} a^{8/3}-20 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{2/3} \left(9 a^{16/3}+12 \sqrt[3]{-1} b^{5/3} a^{8/3}+20 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{a} \left(3 a^{8/3}-4 b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{a} \left(3 a^{8/3}+4 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{a} \left(3 a^{8/3}-4 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 \left(x a^3+b^2\right)}{8 b^3 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x+\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{a} x\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"(a^(2/3)*(9*a^(16/3) - 12*a^(8/3)*b^(5/3) + 20*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(9*a^(16/3) - 12*(-1)^(2/3)*a^(8/3)*b^(5/3) - 20*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(9*a^(16/3) + 12*(-1)^(1/3)*a^(8/3)*b^(5/3) + 20*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*(b^2 + a^3*x))/(8*b^3*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(3*a^(8/3) - 4*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(3*a^(8/3) + 4*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(3*a^(8/3) - 4*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - a^(1/3)*x])/(6*b^2*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",18,6,34,0.1765,1,"{2056, 6725, 129, 155, 12, 91}"
1909,0,0,0,26.5312256,"\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","Int[(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,"(-4*(3*a - b)*(b - x)*x^2)/(3*a*(1 - d)*((a - x)*(b - x)*x^2)^(3/4)) - (2*(3*a - b)*((b*(a - x))/(a*(b - x)))^(3/4)*(b - x)*x^2*Hypergeometric2F1[1/2, 3/4, 3/2, -(((a - b)*x)/(a*(b - x)))])/(3*a*(1 - d)*((a - x)*(b - x)*x^2)^(3/4)) + (2*a^3*(3*a - b)*d*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(-b + x^2)^(1/4)/((-a + x^2)^(7/4)*(a^3*d - 3*a^2*d*x^2 - b*(1 - (3*a*d)/b)*x^4 + (1 - d)*x^6)), x], x, Sqrt[x]])/((1 - d)*((a - x)*(b - x)*x^2)^(3/4)) - (6*a^2*(3*a - b)*d*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^2*(-b + x^2)^(1/4))/((-a + x^2)^(7/4)*(a^3*d - 3*a^2*d*x^2 - b*(1 - (3*a*d)/b)*x^4 + (1 - d)*x^6)), x], x, Sqrt[x]])/((1 - d)*((a - x)*(b - x)*x^2)^(3/4)) + (2*(b^2 + 9*a^2*d - a*(b + 5*b*d))*x^(3/2)*(-a + x)^(3/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^4*(-b + x^2)^(1/4))/((-a + x^2)^(7/4)*(a^3*d - 3*a^2*d*x^2 - b*(1 - (3*a*d)/b)*x^4 + (1 - d)*x^6)), x], x, Sqrt[x]])/((1 - d)*((a - x)*(b - x)*x^2)^(3/4))","F",0,0,0,0,-1,"{}"
1910,1,467,0,3.0827864,"\int \frac{x^2}{\sqrt{-x-x^2+x^3} \left(-1+x^4\right)} \, dx","Int[x^2/(Sqrt[-x - x^2 + x^3]*(-1 + x^4)),x]","-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(-1-\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{4 \sqrt{x^3-x^2-x}}+\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(-\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{4 \sqrt{x^3-x^2-x}}+\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} i \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{4 \sqrt{x^3-x^2-x}}-\frac{\sqrt{3+\sqrt{5}} \sqrt{x} \sqrt{2 x+\sqrt{5}-1} \sqrt{1-\frac{2 x}{1+\sqrt{5}}} \Pi \left(\frac{1}{2} \left(1+\sqrt{5}\right);\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\right)|\frac{1}{2} \left(-3-\sqrt{5}\right)\right)}{4 \sqrt{x^3-x^2-x}}","-\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,"-1/4*(Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1 - Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/Sqrt[-x - x^2 + x^3] + (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(-1/2*I)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(4*Sqrt[-x - x^2 + x^3]) + (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(I/2)*(1 + Sqrt[5]), ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(4*Sqrt[-x - x^2 + x^3]) - (Sqrt[3 + Sqrt[5]]*Sqrt[x]*Sqrt[-1 + Sqrt[5] + 2*x]*Sqrt[1 - (2*x)/(1 + Sqrt[5])]*EllipticPi[(1 + Sqrt[5])/2, ArcSin[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]], (-3 - Sqrt[5])/2])/(4*Sqrt[-x - x^2 + x^3])","C",55,11,27,0.4074,1,"{2056, 6725, 957, 716, 1098, 934, 168, 538, 537, 1134, 1184}"
1911,0,0,0,1.0041949,"\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","Int[((-1 + x^2)*Sqrt[1 + x^2 + x^4])/((1 + x^2)*(1 + x + x^2 + x^3 + x^4)),x]","\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","-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,"(-2*x*Sqrt[1 + x^2 + x^4])/(1 + x^2) - ArcTan[x/Sqrt[1 + x^2 + x^4]] + (2*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/Sqrt[1 + x^2 + x^4] - (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(2*Sqrt[1 + x^2 + x^4]) + Defer[Int][Sqrt[1 + x^2 + x^4]/(1 + x + x^2 + x^3 + x^4), x] + 2*Defer[Int][(x*Sqrt[1 + x^2 + x^4])/(1 + x + x^2 + x^3 + x^4), x] + 2*Defer[Int][(x^2*Sqrt[1 + x^2 + x^4])/(1 + x + x^2 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1912,1,133,0,0.1127819,"\int \frac{x^6}{\left(-b+a x^4\right) \left(b+a x^4\right)^{3/4}} \, dx","Int[x^6/((-b + a*x^4)*(b + a*x^4)^(3/4)),x]","-\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}}","-\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,"-1/2*ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(7/4) + ArcTan[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*2^(3/4)*a^(7/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*a^(7/4)) - ArcTanh[(2^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*2^(3/4)*a^(7/4))","A",8,5,26,0.1923,1,"{494, 481, 298, 203, 206}"
1913,1,56,0,0.414011,"\int \frac{-b+a x^3}{x^3 \left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Int[(-b + a*x^3)/(x^3*(b + a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","\frac{4 \left(b-a x^3\right) \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{2 a x^3}{b-a x^3}\right)}{9 b x^2 \sqrt[4]{a x^4-b x}}","\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*(b - a*x^3)*Hypergeometric2F1[-3/4, 1, 1/4, (-2*a*x^3)/(b - a*x^3)])/(9*b*x^2*(-(b*x) + a*x^4)^(1/4))","C",5,5,36,0.1389,1,"{2056, 466, 465, 511, 510}"
1914,1,133,0,0.0710411,"\int \frac{-b+a x^4}{\sqrt[4]{b+a x^4} \left(-b+3 a x^4\right)} \, dx","Int[(-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)}{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}}","\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)]/(6*a^(1/4)) + ArcTan[(Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(3*Sqrt[2]*a^(1/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/(6*a^(1/4)) + ArcTanh[(Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(3*Sqrt[2]*a^(1/4))","A",9,6,33,0.1818,1,"{530, 240, 212, 206, 203, 377}"
1915,1,2670,0,15.7843245,"\int \frac{-2 b+a x^2}{\sqrt[4]{-b+a x^2} \left(-b+a x^2+c x^4\right)} \, dx","Int[(-2*b + a*x^2)/((-b + a*x^2)^(1/4)*(-b + a*x^2 + c*x^4)),x]","-\frac{\left(a+\sqrt{a^2+4 b c}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{b} \sqrt{c}+\sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{c} \sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right) \left(\sqrt{2} \sqrt{b} \sqrt{c}-\sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}\right)^2}{4 \sqrt{2} \sqrt[4]{b} \sqrt{c} \sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c} \left(a^2+\sqrt{a^2+4 b c} a+4 b c\right) x}-\frac{\sqrt{b} \sqrt{-a-\sqrt{a^2+4 b c}} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{-a-\sqrt{a^2+4 b c}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{-a^2-\sqrt{a^2+4 b c} a-2 b c} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{c} \sqrt[4]{-a^2-\sqrt{a^2+4 b c} a-2 b c} x}-\frac{\sqrt{b} \sqrt{a+\sqrt{a^2+4 b c}} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a+\sqrt{a^2+4 b c}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{-a^2-\sqrt{a^2+4 b c} a-2 b c} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{c} \sqrt[4]{-a^2-\sqrt{a^2+4 b c} a-2 b c} x}-\frac{\sqrt{b} \sqrt{a-\sqrt{a^2+4 b c}} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a-\sqrt{a^2+4 b c}} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{-a^2+\sqrt{a^2+4 b c} a-2 b c} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{c} \sqrt[4]{-a^2+\sqrt{a^2+4 b c} a-2 b c} x}-\frac{\sqrt{b} \sqrt{\sqrt{a^2+4 b c}-a} \sqrt{\frac{a x^2}{b}} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\sqrt{a^2+4 b c}-a} \sqrt[4]{a x^2-b}}{\sqrt[4]{2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{-a^2+\sqrt{a^2+4 b c} a-2 b c} \sqrt{\frac{a x^2}{b}}}\right)}{2 \sqrt[4]{2} \sqrt{a} \sqrt[4]{c} \sqrt[4]{-a^2+\sqrt{a^2+4 b c} a-2 b c} x}-\frac{\left(a+\sqrt{a^2+4 b c}\right) \left(2 \sqrt{b}-\frac{\sqrt{2} \sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}}{\sqrt{c}}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \left(a^2+\sqrt{a^2+4 b c} a+4 b c\right) x}-\frac{\left(a+\sqrt{a^2+4 b c}\right) \left(2 \sqrt{b}+\frac{\sqrt{2} \sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}}{\sqrt{c}}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \left(a^2+\sqrt{a^2+4 b c} a+4 b c\right) x}-\frac{\left(a-\sqrt{a^2+4 b c}\right) \left(2 \sqrt{b} \sqrt{c}-\sqrt{-2 a^2+2 \sqrt{a^2+4 b c} a-4 b c}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \sqrt{c} \left(a^2-\sqrt{a^2+4 b c} a+4 b c\right) x}-\frac{\left(a-\sqrt{a^2+4 b c}\right) \left(2 \sqrt{b} \sqrt{c}+\sqrt{-2 a^2+2 \sqrt{a^2+4 b c} a-4 b c}\right) \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{b} \sqrt{c} \left(a^2-\sqrt{a^2+4 b c} a+4 b c\right) x}+\frac{\left(a+\sqrt{a^2+4 b c}\right) \left(\sqrt{2} \sqrt{b} \sqrt{c}+\sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{b} \sqrt{c}-\sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{c} \sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{b} \sqrt{c} \sqrt{-a^2-\sqrt{a^2+4 b c} a-2 b c} \left(a^2+\sqrt{a^2+4 b c} a+4 b c\right) x}+\frac{\left(a-\sqrt{a^2+4 b c}\right) \left(\sqrt{2} \sqrt{b} \sqrt{c}+\sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(-\frac{\left(\sqrt{2} \sqrt{b} \sqrt{c}-\sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{c} \sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{b} \sqrt{c} \left(a^2-\sqrt{a^2+4 b c} a+4 b c\right) \sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c} x}-\frac{\left(a-\sqrt{a^2+4 b c}\right) \left(\sqrt{2} \sqrt{b} \sqrt{c}-\sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c}\right)^2 \sqrt{\frac{a x^2}{\left(\sqrt{b}+\sqrt{a x^2-b}\right)^2}} \left(\sqrt{b}+\sqrt{a x^2-b}\right) \Pi \left(\frac{\left(\sqrt{2} \sqrt{b} \sqrt{c}+\sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c}\right)^2}{4 \sqrt{2} \sqrt{b} \sqrt{c} \sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c}};2 \tan ^{-1}\left(\frac{\sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{b} \sqrt{c} \left(a^2-\sqrt{a^2+4 b c} a+4 b c\right) \sqrt{-a^2+\sqrt{a^2+4 b c} a-2 b c} x}","\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,"-1/2*(Sqrt[b]*Sqrt[-a - Sqrt[a^2 + 4*b*c]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[-a - Sqrt[a^2 + 4*b*c]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*c^(1/4)*(-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c])^(1/4)*Sqrt[(a*x^2)/b])])/(2^(1/4)*Sqrt[a]*c^(1/4)*(-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c])^(1/4)*x) - (Sqrt[b]*Sqrt[a + Sqrt[a^2 + 4*b*c]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[a + Sqrt[a^2 + 4*b*c]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*c^(1/4)*(-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c])^(1/4)*Sqrt[(a*x^2)/b])])/(2*2^(1/4)*Sqrt[a]*c^(1/4)*(-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c])^(1/4)*x) - (Sqrt[b]*Sqrt[a - Sqrt[a^2 + 4*b*c]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[a - Sqrt[a^2 + 4*b*c]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*c^(1/4)*(-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c])^(1/4)*Sqrt[(a*x^2)/b])])/(2*2^(1/4)*Sqrt[a]*c^(1/4)*(-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c])^(1/4)*x) - (Sqrt[b]*Sqrt[-a + Sqrt[a^2 + 4*b*c]]*Sqrt[(a*x^2)/b]*ArcTan[(Sqrt[a]*Sqrt[-a + Sqrt[a^2 + 4*b*c]]*(-b + a*x^2)^(1/4))/(2^(1/4)*Sqrt[b]*c^(1/4)*(-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c])^(1/4)*Sqrt[(a*x^2)/b])])/(2*2^(1/4)*Sqrt[a]*c^(1/4)*(-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c])^(1/4)*x) - ((a + Sqrt[a^2 + 4*b*c])*(2*Sqrt[b] - (Sqrt[2]*Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]])/Sqrt[c])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*(a^2 + 4*b*c + a*Sqrt[a^2 + 4*b*c])*x) - ((a + Sqrt[a^2 + 4*b*c])*(2*Sqrt[b] + (Sqrt[2]*Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]])/Sqrt[c])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*(a^2 + 4*b*c + a*Sqrt[a^2 + 4*b*c])*x) - ((a - Sqrt[a^2 + 4*b*c])*(2*Sqrt[b]*Sqrt[c] - Sqrt[-2*a^2 - 4*b*c + 2*a*Sqrt[a^2 + 4*b*c]])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*Sqrt[c]*(a^2 + 4*b*c - a*Sqrt[a^2 + 4*b*c])*x) - ((a - Sqrt[a^2 + 4*b*c])*(2*Sqrt[b]*Sqrt[c] + Sqrt[-2*a^2 - 4*b*c + 2*a*Sqrt[a^2 + 4*b*c]])*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticF[2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*b^(1/4)*Sqrt[c]*(a^2 + 4*b*c - a*Sqrt[a^2 + 4*b*c])*x) + ((a + Sqrt[a^2 + 4*b*c])*(Sqrt[2]*Sqrt[b]*Sqrt[c] + Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[b]*Sqrt[c] - Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]])^2/(Sqrt[2]*Sqrt[b]*Sqrt[c]*Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*Sqrt[c]*Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]]*(a^2 + 4*b*c + a*Sqrt[a^2 + 4*b*c])*x) - ((a + Sqrt[a^2 + 4*b*c])*(Sqrt[2]*Sqrt[b]*Sqrt[c] - Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[(Sqrt[2]*Sqrt[b]*Sqrt[c] + Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]])^2/(4*Sqrt[2]*Sqrt[b]*Sqrt[c]*Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*Sqrt[c]*Sqrt[-a^2 - 2*b*c - a*Sqrt[a^2 + 4*b*c]]*(a^2 + 4*b*c + a*Sqrt[a^2 + 4*b*c])*x) + ((a - Sqrt[a^2 + 4*b*c])*(Sqrt[2]*Sqrt[b]*Sqrt[c] + Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[-1/4*(Sqrt[2]*Sqrt[b]*Sqrt[c] - Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]])^2/(Sqrt[2]*Sqrt[b]*Sqrt[c]*Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*Sqrt[c]*(a^2 + 4*b*c - a*Sqrt[a^2 + 4*b*c])*Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]]*x) - ((a - Sqrt[a^2 + 4*b*c])*(Sqrt[2]*Sqrt[b]*Sqrt[c] - Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]])^2*Sqrt[(a*x^2)/(Sqrt[b] + Sqrt[-b + a*x^2])^2]*(Sqrt[b] + Sqrt[-b + a*x^2])*EllipticPi[(Sqrt[2]*Sqrt[b]*Sqrt[c] + Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]])^2/(4*Sqrt[2]*Sqrt[b]*Sqrt[c]*Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]]), 2*ArcTan[(-b + a*x^2)^(1/4)/b^(1/4)], 1/2])/(4*Sqrt[2]*b^(1/4)*Sqrt[c]*(a^2 + 4*b*c - a*Sqrt[a^2 + 4*b*c])*Sqrt[-a^2 - 2*b*c + a*Sqrt[a^2 + 4*b*c]]*x)","C",18,6,39,0.1538,0,"{1692, 399, 490, 1217, 220, 1707}"
1916,1,1209,0,7.1053689,"\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","Int[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(x^2*(a*q + b*x + a*p*x^2)),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{p^2 x^4+q^2}}{q}\right) b}{2 a^2}+\frac{\left(b-\sqrt{b^2-4 a^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right) b}{4 a^3 \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2}}+\frac{\left(b+\sqrt{b^2-4 a^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right) b}{4 a^3 \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2}}+\frac{\sqrt{p^2 x^4+q^2} b}{2 a^2 q}+\frac{\sqrt{2 a^2 p q-b^2} \tan ^{-1}\left(\frac{\sqrt{2 a^2 p q-b^2} x}{a \sqrt{p^2 x^4+q^2}}\right)}{a^2}-\frac{\left(b-\sqrt{b^2-4 a^2 p q}\right) \tanh ^{-1}\left(\frac{p x^2}{\sqrt{p^2 x^4+q^2}}\right)}{4 a^2}-\frac{\left(b+\sqrt{b^2-4 a^2 p q}\right) \tanh ^{-1}\left(\frac{p x^2}{\sqrt{p^2 x^4+q^2}}\right)}{4 a^2}+\frac{\sqrt{b^2-2 a^2 p q} \left(b+\sqrt{b^2-4 a^2 p q}\right) \sqrt{-2 p q a^2+b^2-b \sqrt{b^2-4 a^2 p q}} \tanh ^{-1}\left(\frac{p \left(4 a^2 q^2+\left(b-\sqrt{b^2-4 a^2 p q}\right)^2 x^2\right)}{2 \sqrt{2} \sqrt{b^2-2 a^2 p q} \sqrt{-2 p q a^2+b^2-b \sqrt{b^2-4 a^2 p q}} \sqrt{p^2 x^4+q^2}}\right)}{4 \sqrt{2} a^4 p q}+\frac{\sqrt{b^2-2 a^2 p q} \left(b-\sqrt{b^2-4 a^2 p q}\right) \sqrt{-2 p q a^2+b^2+b \sqrt{b^2-4 a^2 p q}} \tanh ^{-1}\left(\frac{p \left(4 a^2 q^2+\left(b+\sqrt{b^2-4 a^2 p q}\right)^2 x^2\right)}{2 \sqrt{2} \sqrt{b^2-2 a^2 p q} \sqrt{-2 p q a^2+b^2+b \sqrt{b^2-4 a^2 p q}} \sqrt{p^2 x^4+q^2}}\right)}{4 \sqrt{2} a^4 p q}-\frac{\sqrt{p} \sqrt{q} \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right)}{a \sqrt{p^2 x^4+q^2}}-\frac{\left(b-\sqrt{b^2-4 a^2 p q}\right) \sqrt{p^2 x^4+q^2}}{4 a^2 q}-\frac{\left(b+\sqrt{b^2-4 a^2 p q}\right) \sqrt{p^2 x^4+q^2}}{4 a^2 q}+\frac{\sqrt{p^2 x^4+q^2}}{a x}-\frac{\left(b^2-2 a^2 p q\right) \left(b-\sqrt{b^2-4 a^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right)}{4 a^3 \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2} b}-\frac{\left(b^2-2 a^2 p q\right) \left(b+\sqrt{b^2-4 a^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right)}{4 a^3 \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2} b}","\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,"(b*Sqrt[q^2 + p^2*x^4])/(2*a^2*q) - ((b - Sqrt[b^2 - 4*a^2*p*q])*Sqrt[q^2 + p^2*x^4])/(4*a^2*q) - ((b + Sqrt[b^2 - 4*a^2*p*q])*Sqrt[q^2 + p^2*x^4])/(4*a^2*q) + Sqrt[q^2 + p^2*x^4]/(a*x) + (Sqrt[-b^2 + 2*a^2*p*q]*ArcTan[(Sqrt[-b^2 + 2*a^2*p*q]*x)/(a*Sqrt[q^2 + p^2*x^4])])/a^2 - ((b - Sqrt[b^2 - 4*a^2*p*q])*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]])/(4*a^2) - ((b + Sqrt[b^2 - 4*a^2*p*q])*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]])/(4*a^2) + (Sqrt[b^2 - 2*a^2*p*q]*(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]]*ArcTanh[(p*(4*a^2*q^2 + (b - Sqrt[b^2 - 4*a^2*p*q])^2*x^2))/(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])])/(4*Sqrt[2]*a^4*p*q) + (Sqrt[b^2 - 2*a^2*p*q]*(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]]*ArcTanh[(p*(4*a^2*q^2 + (b + Sqrt[b^2 - 4*a^2*p*q])^2*x^2))/(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])])/(4*Sqrt[2]*a^4*p*q) - (b*ArcTanh[Sqrt[q^2 + p^2*x^4]/q])/(2*a^2) - (Sqrt[p]*Sqrt[q]*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(a*Sqrt[q^2 + p^2*x^4]) + (b*(b - Sqrt[b^2 - 4*a^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*a^3*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4]) - ((b^2 - 2*a^2*p*q)*(b - Sqrt[b^2 - 4*a^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*a^3*b*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4]) + (b*(b + Sqrt[b^2 - 4*a^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*a^3*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4]) - ((b^2 - 2*a^2*p*q)*(b + Sqrt[b^2 - 4*a^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*a^3*b*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4])","C",42,20,43,0.4651,1,"{6728, 277, 305, 220, 1196, 266, 50, 63, 208, 1729, 1209, 1198, 1217, 1707, 1248, 735, 844, 217, 206, 725}"
1917,0,0,0,0.8547273,"\int \frac{\sqrt[3]{1+x^5} \left(-3+2 x^5\right)}{x^2 \left(2-x^3+2 x^5\right)} \, dx","Int[((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,"(3*Hypergeometric2F1[-1/3, -1/5, 4/5, -x^5])/(2*x) - (3*Defer[Int][(x*(1 + x^5)^(1/3))/(2 - x^3 + 2*x^5), x])/2 + 5*Defer[Int][(x^3*(1 + x^5)^(1/3))/(2 - x^3 + 2*x^5), x]","F",0,0,0,0,-1,"{}"
1918,0,0,0,2.1489583,"\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","Int[(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,"(c^2*x*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[1/5, 3/4, 6/5, (a*x^5)/b])/(a^2*(-b + a*x^5)^(3/4)) - (c*x^2*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, (a*x^5)/b])/(2*a*(-b + a*x^5)^(3/4)) + (x^3*(1 - (a*x^5)/b)^(3/4)*Hypergeometric2F1[3/5, 3/4, 8/5, (a*x^5)/b])/(3*(-b + a*x^5)^(3/4)) - (b*c^2*Defer[Int][1/((b - c*x^4 - a*x^5)*(-b + a*x^5)^(3/4)), x])/a^2 - (b*c*Defer[Int][x/((-b + a*x^5)^(3/4)*(-b + c*x^4 + a*x^5)), x])/a + 5*b*Defer[Int][x^2/((-b + a*x^5)^(3/4)*(-b + c*x^4 + a*x^5)), x] - (c^3*Defer[Int][x^4/((-b + a*x^5)^(3/4)*(-b + c*x^4 + a*x^5)), x])/a^2","F",0,0,0,0,-1,"{}"
1919,1,241,0,0.8874305,"\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","Int[((-1 + x^6)*(1 + x^6)^(2/3))/(x^3*(2 - x^3 + 2*x^6)),x]","\frac{\left(-\sqrt{15}+i\right) x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};-\frac{8 x^6}{7-i \sqrt{15}},-x^6\right)}{\sqrt{15}+7 i}+\frac{\left(\sqrt{15}+i\right) x F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};-\frac{8 x^6}{7+i \sqrt{15}},-x^6\right)}{-\sqrt{15}+7 i}+\frac{x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-x^6,-\frac{8 x^6}{7-i \sqrt{15}}\right)}{7-i \sqrt{15}}+\frac{x^4 F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-x^6,-\frac{8 x^6}{7+i \sqrt{15}}\right)}{7+i \sqrt{15}}+\frac{\, _2F_1\left(-\frac{2}{3},-\frac{1}{3};\frac{2}{3};-x^6\right)}{4 x^2}","\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,"((I - Sqrt[15])*x*AppellF1[1/6, 1, -2/3, 7/6, (-8*x^6)/(7 - I*Sqrt[15]), -x^6])/(7*I + Sqrt[15]) + ((I + Sqrt[15])*x*AppellF1[1/6, 1, -2/3, 7/6, (-8*x^6)/(7 + I*Sqrt[15]), -x^6])/(7*I - Sqrt[15]) + (x^4*AppellF1[2/3, -2/3, 1, 5/3, -x^6, (-8*x^6)/(7 - I*Sqrt[15])])/(7 - I*Sqrt[15]) + (x^4*AppellF1[2/3, -2/3, 1, 5/3, -x^6, (-8*x^6)/(7 + I*Sqrt[15])])/(7 + I*Sqrt[15]) + Hypergeometric2F1[-2/3, -1/3, 2/3, -x^6]/(4*x^2)","C",16,7,32,0.2188,0,"{6728, 275, 364, 1438, 429, 465, 510}"
1920,0,0,0,2.0194994,"\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","Int[(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,"(Sqrt[(a*x^6)/(Sqrt[b] + Sqrt[-b + a*x^6])^2]*(Sqrt[b] + Sqrt[-b + a*x^6])*EllipticF[2*ArcTan[(-b + a*x^6)^(1/4)/b^(1/4)], 1/2])/(3*a*b^(1/4)*x^3) - (c*x*(1 - (a*x^6)/b)^(3/4)*Hypergeometric2F1[1/6, 3/4, 7/6, (a*x^6)/b])/(a*(-b + a*x^6)^(3/4)) + (b*c*Defer[Int][1/((b - c*x^4 - a*x^6)*(-b + a*x^6)^(3/4)), x])/a + 3*b*Defer[Int][x^2/((-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)), x] + (c^2*Defer[Int][x^4/((-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)), x])/a","F",0,0,0,0,-1,"{}"
1921,0,0,0,0.3446388,"\int x^2 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","Int[x^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int x^2 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","\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,"Defer[Int][x^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
1922,1,70,0,0.0696524,"\int \sqrt{1+\sqrt{1+\sqrt{1+x}}} \, dx","Int[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]],x]","\frac{8}{9} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{9/2}-\frac{24}{7} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{7/2}+\frac{16}{5} \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,"(16*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(9/2))/9","A",5,3,19,0.1579,1,"{371, 1398, 772}"
1923,0,0,0,1.3572655,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2","F",0,0,0,0,-1,"{}"
1924,0,0,0,0.9867837,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2","F",0,0,0,0,-1,"{}"
1925,1,137,0,0.163481,"\int \frac{\left(-2+x^3\right) \left(1+x^3\right)^{2/3}}{x^6 \left(-1+2 x^3\right)} \, dx","Int[((-2 + x^3)*(1 + x^3)^(2/3))/(x^6*(-1 + 2*x^3)),x]","-3^{2/3} \log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)+3 \sqrt[6]{3} \tan ^{-1}\left(\frac{2 x}{\sqrt[6]{3} \sqrt[3]{x^3+1}}+\frac{1}{\sqrt{3}}\right)-\frac{2 \left(x^3+1\right)^{2/3}}{5 x^5}-\frac{19 \left(x^3+1\right)^{2/3}}{10 x^2}+\frac{1}{2} 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)","-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,"(-2*(1 + x^3)^(2/3))/(5*x^5) - (19*(1 + x^3)^(2/3))/(10*x^2) + 3*3^(1/6)*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(1 + x^3)^(1/3))] - 3^(2/3)*Log[1 - (3^(1/3)*x)/(1 + x^3)^(1/3)] + (3^(2/3)*Log[1 + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + (3^(1/3)*x)/(1 + x^3)^(1/3)])/2","A",10,10,27,0.3704,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
1926,1,1446,0,2.2588008,"\int \frac{1}{x^3 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^3*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{a^{2/3} \left(9 a^{16/3}+12 b^{5/3} a^{8/3}+20 b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{2/3} \left(9 a^{16/3}+12 (-1)^{2/3} b^{5/3} a^{8/3}-20 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{2/3} \left(9 a^{16/3}-12 \sqrt[3]{-1} b^{5/3} a^{8/3}+20 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{a} \left(3 a^{8/3}+4 b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{a} \left(3 a^{8/3}-4 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{a} \left(3 a^{8/3}+4 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 \left(x a^3+b^2\right)}{8 b^3 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(-\sqrt[3]{a} x-\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x-\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(-(-1)^{2/3} \sqrt[3]{a} x-\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/40*(a^(2/3)*(9*a^(16/3) + 12*a^(8/3)*b^(5/3) + 20*b^(10/3))*(b^2 + a^3*x))/(b^7*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(9*a^(16/3) + 12*(-1)^(2/3)*a^(8/3)*b^(5/3) - 20*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(9*a^(16/3) - 12*(-1)^(1/3)*a^(8/3)*b^(5/3) + 20*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*(b^2 + a^3*x))/(8*b^3*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(3*a^(8/3) + 4*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(3*a^(8/3) - 4*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(3*a^(8/3) + 4*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - a^(1/3)*x])/(6*b^2*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",18,6,32,0.1875,1,"{2056, 6725, 129, 155, 12, 91}"
1927,1,1446,0,1.9352747,"\int \frac{1}{x^3 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^3*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{a^{2/3} \left(9 a^{16/3}+12 b^{5/3} a^{8/3}+20 b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{2/3} \left(9 a^{16/3}+12 (-1)^{2/3} b^{5/3} a^{8/3}-20 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{2/3} \left(9 a^{16/3}-12 \sqrt[3]{-1} b^{5/3} a^{8/3}+20 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right)}{40 b^7 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{a} \left(3 a^{8/3}+4 b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{a} \left(3 a^{8/3}-4 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{a} \left(3 a^{8/3}+4 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right)}{20 b^5 x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 \left(x a^3+b^2\right)}{8 b^3 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x a^3+b^2}}{\sqrt{3} b^2 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(-\sqrt[3]{a} x-\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x-\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{a^{8/9} x^{2/3} \log \left(-(-1)^{2/3} \sqrt[3]{a} x-\sqrt[3]{b}\right) \sqrt[3]{x a^3+b^2}}{6 b^2 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{a^{8/9} x^{2/3} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x a^3+b^2}}{2 b^2 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/40*(a^(2/3)*(9*a^(16/3) + 12*a^(8/3)*b^(5/3) + 20*b^(10/3))*(b^2 + a^3*x))/(b^7*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(9*a^(16/3) + 12*(-1)^(2/3)*a^(8/3)*b^(5/3) - 20*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(9*a^(16/3) - 12*(-1)^(1/3)*a^(8/3)*b^(5/3) + 20*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(40*b^7*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*(b^2 + a^3*x))/(8*b^3*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(3*a^(8/3) + 4*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(3*a^(8/3) - 4*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(3*a^(8/3) + 4*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(20*b^5*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^2*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - a^(1/3)*x])/(6*b^2*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^2*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(8/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^2*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",18,6,32,0.1875,1,"{2056, 6725, 129, 155, 12, 91}"
1928,1,223,0,0.7782485,"\int \frac{\left(-1+x+x^4\right) \sqrt[4]{-x^3+x^4}}{1+x} \, dx","Int[((-1 + x + x^4)*(-x^3 + x^4)^(1/4))/(1 + x),x]","\frac{4 \sqrt[4]{x^4-x^3} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x,-x\right)}{3 \sqrt[4]{1-x}}+\frac{1}{5} \sqrt[4]{x^4-x^3} x^4-\frac{21}{80} \sqrt[4]{x^4-x^3} x^3-\frac{53 \sqrt[4]{x^4-x^3} x}{1536}-\frac{6515 \sqrt[4]{x^4-x^3}}{6144}-\frac{1677 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{4096 \sqrt[4]{x-1} x^{3/4}}+\frac{1677 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{4096 \sqrt[4]{x-1} x^{3/4}}+\frac{65}{192} \sqrt[4]{x^4-x^3} x^2","-\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,"(-6515*(-x^3 + x^4)^(1/4))/6144 - (53*x*(-x^3 + x^4)^(1/4))/1536 + (65*x^2*(-x^3 + x^4)^(1/4))/192 - (21*x^3*(-x^3 + x^4)^(1/4))/80 + (x^4*(-x^3 + x^4)^(1/4))/5 + (4*(-x^3 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x, -x])/(3*(1 - x)^(1/4)) - (1677*(-x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(-1 + x)^(1/4)])/(4096*(-1 + x)^(1/4)*x^(3/4)) + (1677*(-x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(-1 + x)^(1/4)])/(4096*(-1 + x)^(1/4)*x^(3/4))","C",35,11,25,0.4400,0,"{2056, 6733, 6725, 279, 331, 298, 203, 206, 321, 511, 510}"
1929,0,0,0,1.0642117,"\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","Int[((-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,"(3*(1 + x^4)^(2/3))/(4*x^2) + (3*x^2)/(1 - Sqrt[3] - (1 + x^4)^(1/3)) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(2*x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (Sqrt[2]*3^(3/4)*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (3*Defer[Int][(1 + x^4)^(2/3)/(2 + x^3 + 2*x^4), x])/2 + 4*Defer[Int][(x*(1 + x^4)^(2/3))/(2 + x^3 + 2*x^4), x]","F",0,0,0,0,-1,"{}"
1930,1,143,0,0.1924487,"\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","Int[((-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} \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(a x^4+b\right)^{3/4}}{7 x^7}-\frac{a \left(a x^4+b\right)^{3/4}}{42 b x^3}","\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,"(b + a*x^4)^(3/4)/(7*x^7) - (a*(b + a*x^4)^(3/4))/(42*b*x^3) + (3^(3/4)*a^(7/4)*ArcTan[(3^(1/4)*a^(1/4)*x)/(Sqrt[2]*(b + a*x^4)^(1/4))])/(8*Sqrt[2]*b) + (3^(3/4)*a^(7/4)*ArcTanh[(3^(1/4)*a^(1/4)*x)/(Sqrt[2]*(b + a*x^4)^(1/4))])/(8*Sqrt[2]*b)","A",7,7,35,0.2000,1,"{580, 583, 12, 377, 212, 206, 203}"
1931,1,143,0,0.1746603,"\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","Int[((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} \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(a x^4+b\right)^{3/4}}{14 x^7}-\frac{19 a \left(a x^4+b\right)^{3/4}}{168 b x^3}","\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*(b + a*x^4)^(3/4)/x^7 - (19*a*(b + a*x^4)^(3/4))/(168*b*x^3) + (3^(3/4)*a^(7/4)*ArcTan[(3^(1/4)*a^(1/4)*x)/(Sqrt[2]*(b + a*x^4)^(1/4))])/(32*Sqrt[2]*b) + (3^(3/4)*a^(7/4)*ArcTanh[(3^(1/4)*a^(1/4)*x)/(Sqrt[2]*(b + a*x^4)^(1/4))])/(32*Sqrt[2]*b)","A",7,7,35,0.2000,1,"{580, 583, 12, 377, 212, 206, 203}"
1932,1,255,0,0.3163227,"\int \frac{x^4 \sqrt[4]{b x^3+a x^4}}{b+a x} \, dx","Int[(x^4*(b*x^3 + a*x^4)^(1/4))/(b + a*x),x]","\frac{4389 b^5 \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{4096 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}-\frac{4389 b^5 \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{4096 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{1463 b^4 \sqrt[4]{a x^4+b x^3}}{2048 a^5}-\frac{209 b^3 x \sqrt[4]{a x^4+b x^3}}{512 a^4}+\frac{19 b^2 x^2 \sqrt[4]{a x^4+b x^3}}{64 a^3}-\frac{19 b x^3 \sqrt[4]{a x^4+b x^3}}{80 a^2}+\frac{x^4 \sqrt[4]{a x^4+b x^3}}{5 a}","\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,"(1463*b^4*(b*x^3 + a*x^4)^(1/4))/(2048*a^5) - (209*b^3*x*(b*x^3 + a*x^4)^(1/4))/(512*a^4) + (19*b^2*x^2*(b*x^3 + a*x^4)^(1/4))/(64*a^3) - (19*b*x^3*(b*x^3 + a*x^4)^(1/4))/(80*a^2) + (x^4*(b*x^3 + a*x^4)^(1/4))/(5*a) + (4389*b^5*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(4096*a^(23/4)*x^(3/4)*(b + a*x)^(1/4)) - (4389*b^5*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(4096*a^(23/4)*x^(3/4)*(b + a*x)^(1/4))","A",11,7,26,0.2692,1,"{2056, 50, 63, 331, 298, 203, 206}"
1933,1,50,0,0.0965315,"\int \frac{b+a x^2}{\left(-b+a x^2\right) \sqrt{b^2+a^2 x^4}} \, dx","Int[(b + a*x^2)/((-b + a*x^2)*Sqrt[b^2 + a^2*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} x}{\sqrt{a^2 x^4+b^2}}\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}}-\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,"-(ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[b]*x)/Sqrt[b^2 + a^2*x^4]]/(Sqrt[2]*Sqrt[a]*Sqrt[b]))","A",2,2,34,0.05882,1,"{1699, 208}"
1934,0,0,0,0.457673,"\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{1+x^2}}}{-1+x^2} \, dx","Int[((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,"(2*x^3)/(3*(1 + Sqrt[1 + x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 + x^2]] - Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(1 - x), x] - Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(1 + x), x]","F",0,0,0,0,-1,"{}"
1935,1,74,0,0.0100306,"\int \frac{1}{\sqrt[3]{-b+a x^3}} \, dx","Int[(-b + a*x^3)^(-1/3),x]","\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a}}-\frac{\log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{2 \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,"ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*a^(1/3)) - Log[-(a^(1/3)*x) + (-b + a*x^3)^(1/3)]/(2*a^(1/3))","A",1,1,13,0.07692,1,"{239}"
1936,0,0,0,67.8412479,"\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","Int[((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,"(-8*(a - b - c)*(a - x)*(-((b - x)/(a - b)))^(3/4)*(-((c - x)/(a - c)))^(3/4)*AppellF1[1/4, 3/4, 3/4, 5/4, (a - x)/(a - b), (a - x)/(a - c)])/(d*(-((a - x)*(b - x)*(c - x)))^(3/4)) - (4*(1 + 2*a*d)*(a - x)*(-((b - x)/(a - b)))^(3/4)*(-((c - x)/(a - c)))^(3/4)*AppellF1[1/4, 3/4, 3/4, 5/4, (a - x)/(a - b), (a - x)/(a - c)])/(d^2*(-((a - x)*(b - x)*(c - x)))^(3/4)) + (4*(a - x)^2*(-((b - x)/(a - b)))^(3/4)*(-((c - x)/(a - c)))^(3/4)*AppellF1[5/4, 3/4, 3/4, 9/4, (a - x)/(a - b), (a - x)/(a - c)])/(5*d*(-((a - x)*(b - x)*(c - x)))^(3/4)) - (8*(a - b)*(a - c)*(a - b - c)*(-a + x)^(3/4)*(-b + x)^(3/4)*(-c + x)^(3/4)*Defer[Subst][Defer[Int][1/((a - b + x^4)^(3/4)*(a - c + x^4)^(3/4)*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*(-((a - x)*(b - x)*(c - x)))^(3/4)) - (4*(a - b)*(a - c)*(1 + 2*a*d)*(-a + x)^(3/4)*(-b + x)^(3/4)*(-c + x)^(3/4)*Defer[Subst][Defer[Int][1/((a - b + x^4)^(3/4)*(a - c + x^4)^(3/4)*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d^2*(-((a - x)*(b - x)*(c - x)))^(3/4)) - (8*(a - b - c)*(2*a - b - c)*(-a + x)^(3/4)*(-b + x)^(3/4)*(-c + x)^(3/4)*Defer[Subst][Defer[Int][x^4/((a - b + x^4)^(3/4)*(a - c + x^4)^(3/4)*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*(-((a - x)*(b - x)*(c - x)))^(3/4)) + (4*(b + c - 5*a^2*d - b*c*d - a*(2 - 3*b*d - 3*c*d))*(-a + x)^(3/4)*(-b + x)^(3/4)*(-c + x)^(3/4)*Defer[Subst][Defer[Int][x^4/((a - b + x^4)^(3/4)*(a - c + x^4)^(3/4)*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d^2*(-((a - x)*(b - x)*(c - x)))^(3/4)) - (8*(a - b - c)*(1 + a*d)*(-a + x)^(3/4)*(-b + x)^(3/4)*(-c + x)^(3/4)*Defer[Subst][Defer[Int][x^8/((a - b + x^4)^(3/4)*(a - c + x^4)^(3/4)*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d*(-((a - x)*(b - x)*(c - x)))^(3/4)) - (4*(1 + 4*a*d - b*d - c*d + a^2*d^2)*(-a + x)^(3/4)*(-b + x)^(3/4)*(-c + x)^(3/4)*Defer[Subst][Defer[Int][x^8/((a - b + x^4)^(3/4)*(a - c + x^4)^(3/4)*(a^2*(1 + (b*c - a*(b + c))/a^2) + 2*a*(1 - (b + c)/(2*a))*x^4 + x^8 - d*x^12)), x], x, (-a + x)^(1/4)])/(d^2*(-((a - x)*(b - x)*(c - x)))^(3/4)) + (4*(3*b*c - a*(b + c))*(-a + x)^(3/4)*(-b + x)^(3/4)*(-c + x)^(3/4)*Defer[Subst][Defer[Int][x^8/((a - b + x^4)^(3/4)*(a - c + x^4)^(3/4)*(-a^2 + a*(b + c - 2*x^4) + b*(-c + x^4) + x^4*(c - x^4 + d*x^8))), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)*(c - x)))^(3/4)","F",0,0,0,0,-1,"{}"
1937,0,0,0,1.3610332,"\int \frac{\left(-4+x^5\right) \sqrt[4]{1-2 x^4+x^5}}{x^2 \left(1+x^5\right)} \, dx","Int[((-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,"Defer[Int][(1 - 2*x^4 + x^5)^(1/4)/(-1 - x), x] - 4*Defer[Int][(1 - 2*x^4 + x^5)^(1/4)/x^2, x] + Defer[Int][(1 - 2*x^4 + x^5)^(1/4)/(1 - x + x^2 - x^3 + x^4), x] - 2*Defer[Int][(x*(1 - 2*x^4 + x^5)^(1/4))/(1 - x + x^2 - x^3 + x^4), x] + 3*Defer[Int][(x^2*(1 - 2*x^4 + x^5)^(1/4))/(1 - x + x^2 - x^3 + x^4), x] + Defer[Int][(x^3*(1 - 2*x^4 + x^5)^(1/4))/(1 - x + x^2 - x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
1938,1,156,0,0.1806532,"\int \frac{b+a x^6}{x^6 \sqrt[3]{x+x^3}} \, dx","Int[(b + a*x^6)/(x^6*(x + x^3)^(1/3)),x]","-\frac{3 a \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-\sqrt[3]{x^2+1}\right)}{4 \sqrt[3]{x^3+x}}+\frac{\sqrt{3} a \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{x^3+x}}-\frac{3 b \left(x^3+x\right)^{2/3}}{16 x^6}+\frac{9 b \left(x^3+x\right)^{2/3}}{40 x^4}-\frac{27 b \left(x^3+x\right)^{2/3}}{80 x^2}","\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*b*(x + x^3)^(2/3))/(16*x^6) + (9*b*(x + x^3)^(2/3))/(40*x^4) - (27*b*(x + x^3)^(2/3))/(80*x^2) + (Sqrt[3]*a*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*(x + x^3)^(1/3)) - (3*a*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(4*(x + x^3)^(1/3))","A",9,7,20,0.3500,1,"{2052, 2011, 329, 275, 239, 2016, 2014}"
1939,1,130,0,0.0882783,"\int \frac{b^2+a^2 x^2}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(b^2 + a^2*x^2)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{3 b^2 \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{4 a}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}{20 a}-\frac{b^6}{28 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}-\frac{b^4}{4 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}","\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,"-1/28*b^6/(a*(a*x + Sqrt[b^2 + a^2*x^2])^(7/2)) - b^4/(4*a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + (3*b^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(4*a) + (a*x + Sqrt[b^2 + a^2*x^2])^(5/2)/(20*a)","A",3,2,35,0.05714,1,"{2122, 270}"
1940,1,115,0,0.037769,"\int \frac{x^2}{\left(b+a x^2\right)^{3/4} \left(2 b+a x^2\right)} \, dx","Int[x^2/((b + a*x^2)^(3/4)*(2*b + a*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{b^{3/4} \left(1-\frac{\sqrt{a x^2+b}}{\sqrt{b}}\right)}{\sqrt{a} x \sqrt[4]{a x^2+b}}\right)}{a^{3/2} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(\frac{b^{3/4} \left(\frac{\sqrt{a x^2+b}}{\sqrt{b}}+1\right)}{\sqrt{a} x \sqrt[4]{a x^2+b}}\right)}{a^{3/2} \sqrt[4]{b}}","-\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,"-(ArcTan[(b^(3/4)*(1 + Sqrt[b + a*x^2]/Sqrt[b]))/(Sqrt[a]*x*(b + a*x^2)^(1/4))]/(a^(3/2)*b^(1/4))) + ArcTanh[(b^(3/4)*(1 - Sqrt[b + a*x^2]/Sqrt[b]))/(Sqrt[a]*x*(b + a*x^2)^(1/4))]/(a^(3/2)*b^(1/4))","A",1,1,26,0.03846,1,"{441}"
1941,1,130,0,0.0726687,"\int \frac{x}{\left(-b+a x^3\right)^{2/3}} \, dx","Int[x/(-b + a*x^3)^(2/3),x]","-\frac{\log \left(1-\frac{\sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}\right)}{3 a^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)}{\sqrt{3} a^{2/3}}+\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)}{6 a^{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,"-(ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*a^(2/3))) - Log[1 - (a^(1/3)*x)/(-b + a*x^3)^(1/3)]/(3*a^(2/3)) + 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^(2/3))","A",7,7,15,0.4667,1,"{331, 292, 31, 634, 617, 204, 628}"
1942,1,109,0,0.2054284,"\int \frac{x \sqrt[3]{x^2+x^4}}{1+2 x^2} \, dx","Int[(x*(x^2 + x^4)^(1/3))/(1 + 2*x^2),x]","\frac{3 \sqrt[3]{\left(2 x^2+1\right)^2-1}}{8\ 2^{2/3}}+\frac{\log \left(2 x^2+1\right)}{8\ 2^{2/3}}-\frac{3 \log \left(\sqrt[3]{\left(2 x^2+1\right)^2-1}+1\right)}{16\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\left(2 x^2+1\right)^2-1}}{\sqrt{3}}\right)}{8\ 2^{2/3}}","\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*(-1 + (1 + 2*x^2)^2)^(1/3))/(8*2^(2/3)) + (Sqrt[3]*ArcTan[(1 - 2*(-1 + (1 + 2*x^2)^2)^(1/3))/Sqrt[3]])/(8*2^(2/3)) + Log[1 + 2*x^2]/(8*2^(2/3)) - (3*Log[1 + (-1 + (1 + 2*x^2)^2)^(1/3)])/(16*2^(2/3))","A",8,8,22,0.3636,1,"{2034, 694, 266, 50, 58, 617, 204, 31}"
1943,1,132,0,4.7528357,"\int \frac{b+a x^3}{x^6 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Int[(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(a x^3+b\right)^2 \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^5 \Gamma \left(\frac{1}{4}\right) \left(b-a x^3\right)^2 \sqrt[4]{a x^4+b x}}","-\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*((b + a*x^3)^2*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^5*(b - a*x^3)^2*(b*x + a*x^4)^(1/4)*Gamma[1/4])","C",5,5,35,0.1429,0,"{2056, 466, 465, 511, 510}"
1944,1,163,0,0.4659001,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^4+x^8} \, dx","Int[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^4 + x^8),x]","\frac{2 \left(-\sqrt{3}+i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,-\frac{2 x^4}{1-i \sqrt{3}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt[4]{x^4+1}}+\frac{2 \left(\sqrt{3}+i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,-\frac{2 x^4}{1+i \sqrt{3}}\right)}{3 \left(-\sqrt{3}+i\right) \sqrt[4]{x^4+1}}","\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,"(2*(I - Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (-2*x^4)/(1 - I*Sqrt[3])])/(3*(I + Sqrt[3])*(1 + x^4)^(1/4)) + (2*(I + Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/(3*(I - Sqrt[3])*(1 + x^4)^(1/4))","C",7,4,27,0.1481,0,"{2056, 6728, 466, 510}"
1945,1,163,0,0.4310549,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^4+x^8} \, dx","Int[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^4 + x^8),x]","\frac{2 \left(-\sqrt{3}+i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,-\frac{2 x^4}{1-i \sqrt{3}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt[4]{x^4+1}}+\frac{2 \left(\sqrt{3}+i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,-\frac{2 x^4}{1+i \sqrt{3}}\right)}{3 \left(-\sqrt{3}+i\right) \sqrt[4]{x^4+1}}","\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,"(2*(I - Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (-2*x^4)/(1 - I*Sqrt[3])])/(3*(I + Sqrt[3])*(1 + x^4)^(1/4)) + (2*(I + Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/(3*(I - Sqrt[3])*(1 + x^4)^(1/4))","C",7,4,27,0.1481,0,"{2056, 6728, 466, 510}"
1946,1,166,0,0.5426273,"\int \frac{x \sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Int[(x*Sqrt[a*x + Sqrt[-b + a*x]])/Sqrt[-b + a*x],x]","\frac{\sqrt{a x-b} \left(\sqrt{a x-b}+a x\right)^{3/2}}{2 a^2}-\frac{5 \left(\sqrt{a x-b}+a x\right)^{3/2}}{12 a^2}+\frac{(12 b+5) \left(2 \sqrt{a x-b}+1\right) \sqrt{\sqrt{a x-b}+a x}}{32 a^2}-\frac{(1-4 b) (12 b+5) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{64 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,"(-5*(a*x + Sqrt[-b + a*x])^(3/2))/(12*a^2) + (Sqrt[-b + a*x]*(a*x + Sqrt[-b + a*x])^(3/2))/(2*a^2) + ((5 + 12*b)*Sqrt[a*x + Sqrt[-b + a*x]]*(1 + 2*Sqrt[-b + a*x]))/(32*a^2) - ((1 - 4*b)*(5 + 12*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(64*a^2)","A",6,5,32,0.1562,1,"{1661, 640, 612, 621, 206}"
1947,1,166,0,0.4553029,"\int \frac{(-1+a x) \sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Int[((-1 + a*x)*Sqrt[a*x + Sqrt[-b + a*x]])/Sqrt[-b + a*x],x]","\frac{\sqrt{a x-b} \left(\sqrt{a x-b}+a x\right)^{3/2}}{2 a}-\frac{5 \left(\sqrt{a x-b}+a x\right)^{3/2}}{12 a}-\frac{(11-12 b) \left(2 \sqrt{a x-b}+1\right) \sqrt{\sqrt{a x-b}+a x}}{32 a}+\frac{(11-12 b) (1-4 b) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{64 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,"(-5*(a*x + Sqrt[-b + a*x])^(3/2))/(12*a) + (Sqrt[-b + a*x]*(a*x + Sqrt[-b + a*x])^(3/2))/(2*a) - ((11 - 12*b)*Sqrt[a*x + Sqrt[-b + a*x]]*(1 + 2*Sqrt[-b + a*x]))/(32*a) + ((11 - 12*b)*(1 - 4*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(64*a)","A",6,5,36,0.1389,1,"{1661, 640, 612, 621, 206}"
1948,1,511,0,1.5392579,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(-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{(-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}-\frac{(-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}+\frac{\sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}-\frac{\sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}+\frac{(-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}-\frac{(-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}+\frac{\sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}-\frac{\sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}","-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]] + ((-1)^(3/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]] - ((-1)^(3/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[(-1)^(3/4) + Sqrt[1 - I]] + ((-1)^(1/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]] - ((-1)^(1/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[(-1)^(1/4) + Sqrt[1 + I]] + ((-1)^(3/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]] - ((-1)^(3/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[(-1)^(3/4) + Sqrt[1 - I]] + ((-1)^(1/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]] - ((-1)^(1/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]","C",43,12,28,0.4286,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 204, 206, 207, 203}"
1949,1,511,0,1.2657649,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(-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{(-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}-\frac{(-1)^{3/4} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}+\frac{\sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}-\frac{\sqrt[4]{-1} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}+\frac{(-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}-\frac{(-1)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}+\frac{\sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}-\frac{\sqrt[4]{-1} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}","-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]] + ((-1)^(3/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]] - ((-1)^(3/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[(-1)^(3/4) + Sqrt[1 - I]] + ((-1)^(1/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]] - ((-1)^(1/4)*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[(-1)^(1/4) + Sqrt[1 + I]] + ((-1)^(3/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]] - ((-1)^(3/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]])/Sqrt[(-1)^(3/4) + Sqrt[1 - I]] + ((-1)^(1/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]] - ((-1)^(1/4)*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]])/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]","C",43,12,28,0.4286,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 204, 206, 207, 203}"
1950,1,471,0,0.5621607,"\int \frac{1}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Int[1/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","-\frac{x (x+1) \left(\frac{1-x}{x+1}\right)^{5/4} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{3}{2};\frac{2 x}{x+1}\right)}{4 (1-x) \sqrt[4]{x^4-x^2}}-\frac{x \sqrt[4]{\frac{1-x}{x+1}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{2 x}{x+1}\right)}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}","\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,"-1/4*(Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/((1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*2^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*2^(1/4)*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (2*x)/(1 + x)])/(4*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(5/4)*(1 + x)*Hypergeometric2F1[1/2, 5/4, 3/2, (2*x)/(1 + x)])/(4*(1 - x)*(-x^2 + x^4)^(1/4))","C",21,10,21,0.4762,1,"{2056, 6715, 2073, 1152, 380, 377, 212, 206, 203, 1429}"
1951,1,471,0,0.5112335,"\int \frac{1}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Int[1/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","-\frac{x (x+1) \left(\frac{1-x}{x+1}\right)^{5/4} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{3}{2};\frac{2 x}{x+1}\right)}{4 (1-x) \sqrt[4]{x^4-x^2}}-\frac{x \sqrt[4]{\frac{1-x}{x+1}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{2 x}{x+1}\right)}{4 \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}","\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,"-1/4*(Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/((1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*2^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(4*2^(1/4)*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (2*x)/(1 + x)])/(4*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(5/4)*(1 + x)*Hypergeometric2F1[1/2, 5/4, 3/2, (2*x)/(1 + x)])/(4*(1 - x)*(-x^2 + x^4)^(1/4))","C",21,10,21,0.4762,1,"{2056, 6715, 2073, 1152, 380, 377, 212, 206, 203, 1429}"
1952,1,193,0,0.2681067,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-1-x^4+2 x^8\right)} \, dx","Int[(-2 + x^4)/((1 + x^4)^(1/4)*(-1 - x^4 + 2*x^8)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{2}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt{2}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}+1\right)}{6 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{x^4+1}}\right)}{6 \sqrt[4]{2}}-\frac{5 \log \left(-\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}+\frac{x^2}{\sqrt{x^4+1}}+1\right)}{12 \sqrt{2}}+\frac{5 \log \left(\frac{\sqrt{2} x}{\sqrt[4]{x^4+1}}+\frac{x^2}{\sqrt{x^4+1}}+1\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,"ArcTan[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(6*2^(1/4)) - (5*ArcTan[1 - (Sqrt[2]*x)/(1 + x^4)^(1/4)])/(6*Sqrt[2]) + (5*ArcTan[1 + (Sqrt[2]*x)/(1 + x^4)^(1/4)])/(6*Sqrt[2]) + ArcTanh[(2^(1/4)*x)/(1 + x^4)^(1/4)]/(6*2^(1/4)) - (5*Log[1 + x^2/Sqrt[1 + x^4] - (Sqrt[2]*x)/(1 + x^4)^(1/4)])/(12*Sqrt[2]) + (5*Log[1 + x^2/Sqrt[1 + x^4] + (Sqrt[2]*x)/(1 + x^4)^(1/4)])/(12*Sqrt[2])","A",16,11,29,0.3793,1,"{6728, 377, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
1953,0,0,0,0.1972627,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^{5/2}} \, dx","Int[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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b^2 + a*x^2)^(5/2), x]","F",0,0,0,0,-1,"{}"
1954,1,211,0,0.2110798,"\int \frac{\sqrt[4]{-b+a x^2}}{x} \, dx","Int[(-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",12,9,17,0.5294,1,"{266, 50, 63, 211, 1165, 628, 1162, 617, 204}"
1955,1,225,0,0.2161252,"\int \frac{\left(b+a x^2\right) \sqrt[3]{-x+x^3}}{x^2} \, dx","Int[((b + a*x^2)*(-x + x^3)^(1/3))/x^2,x]","\frac{1}{2} x \sqrt[3]{x^3-x} (a-3 b)+\frac{x^{2/3} \left(x^2-1\right)^{2/3} (a-3 b) \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{6 \left(x^3-x\right)^{2/3}}-\frac{x^{2/3} \left(x^2-1\right)^{2/3} (a-3 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)}{12 \left(x^3-x\right)^{2/3}}+\frac{x^{2/3} \left(x^2-1\right)^{2/3} (a-3 b) \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} \left(x^3-x\right)^{2/3}}+\frac{3 b \left(x^3-x\right)^{4/3}}{2 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,"((a - 3*b)*x*(-x + x^3)^(1/3))/2 + (3*b*(-x + x^3)^(4/3))/(2*x^2) + ((a - 3*b)*x^(2/3)*(-1 + x^2)^(2/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*(-x + x^3)^(2/3)) + ((a - 3*b)*x^(2/3)*(-1 + x^2)^(2/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(6*(-x + x^3)^(2/3)) - ((a - 3*b)*x^(2/3)*(-1 + x^2)^(2/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(12*(-x + x^3)^(2/3))","A",12,12,22,0.5455,1,"{2038, 2004, 2032, 329, 275, 331, 292, 31, 634, 618, 204, 628}"
1956,1,126,0,0.148217,"\int \frac{-b+a x}{x \sqrt[3]{b^3+a^3 x^3}} \, dx","Int[(-b + a*x)/(x*(b^3 + a^3*x^3)^(1/3)),x]","-\frac{1}{2} \log \left(b-\sqrt[3]{a^3 x^3+b^3}\right)-\frac{1}{2} \log \left(\sqrt[3]{a^3 x^3+b^3}-a x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 a x}{\sqrt[3]{a^3 x^3+b^3}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x^3+b^3}+b}{\sqrt{3} b}\right)}{\sqrt{3}}+\frac{\log (x)}{2}","-\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,"ArcTan[(1 + (2*a*x)/(b^3 + a^3*x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - ArcTan[(b + 2*(b^3 + a^3*x^3)^(1/3))/(Sqrt[3]*b)]/Sqrt[3] + Log[x]/2 - Log[b - (b^3 + a^3*x^3)^(1/3)]/2 - Log[-(a*x) + (b^3 + a^3*x^3)^(1/3)]/2","A",8,7,26,0.2692,1,"{1844, 239, 266, 55, 617, 204, 31}"
1957,1,258,0,0.2253709,"\int \frac{x^2 \sqrt[4]{-x^3+x^4}}{2+x} \, dx","Int[(x^2*(-x^3 + x^4)^(1/4))/(2 + x),x]","-\frac{25}{24} \sqrt[4]{x^4-x^3} x+\frac{401}{96} \sqrt[4]{x^4-x^3}-\frac{1135 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{64 \sqrt[4]{x-1} x^{3/4}}-\frac{8\ 2^{3/4} \sqrt[4]{3} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{1135 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{64 \sqrt[4]{x-1} x^{3/4}}+\frac{8\ 2^{3/4} \sqrt[4]{3} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{2}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{1}{3} \sqrt[4]{x^4-x^3} x^2","\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,"(401*(-x^3 + x^4)^(1/4))/96 - (25*x*(-x^3 + x^4)^(1/4))/24 + (x^2*(-x^3 + x^4)^(1/4))/3 - (1135*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(64*(-1 + x)^(1/4)*x^(3/4)) - (8*2^(3/4)*3^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((3/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - (1135*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(64*(-1 + x)^(1/4)*x^(3/4)) + (8*2^(3/4)*3^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((3/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","A",27,12,22,0.5455,1,"{2042, 101, 157, 50, 63, 240, 212, 206, 203, 105, 93, 298}"
1958,0,0,0,10.095766,"\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","Int[((-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,"(6*x*(1 - 2*x^2)^(2/3)*AppellF1[1/2, 2/3, 1/3, 3/2, 2*x^2, -2*x^2])/(((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3)) + (Sqrt[3]*(1 - 2*x^2)^(2/3)*ArcTan[1/Sqrt[3] + (2*(1 + 2*x^2)^(1/3))/(Sqrt[3]*(1 - 2*x^2)^(1/3))])/(2*((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3)) - ((1 - 2*x^2)^(2/3)*Log[x])/(2*((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3)) + (3*(1 - 2*x^2)^(2/3)*Log[(1 - 2*x^2)^(1/3) - (1 + 2*x^2)^(1/3)])/(4*((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3)) - (22*(1 - 2*x^2)^(2/3)*Defer[Int][1/((1 - 2*x^2)^(2/3)*(1 + 2*x^2)^(1/3)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3)) + (51*(1 - 2*x^2)^(2/3)*Defer[Int][x/((1 - 2*x^2)^(2/3)*(1 + 2*x^2)^(1/3)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3)) - (44*(1 - 2*x^2)^(2/3)*Defer[Int][x^2/((1 - 2*x^2)^(2/3)*(1 + 2*x^2)^(1/3)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3)) + (22*(1 - 2*x^2)^(2/3)*Defer[Int][x^3/((1 - 2*x^2)^(2/3)*(1 + 2*x^2)^(1/3)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(2/3)*(1 + 2*x^2)^(2/3))","F",0,0,0,0,-1,"{}"
1959,1,417,0,1.2654279,"\int \frac{b-a x^5}{\sqrt{a+b x} \left(a b+x^5\right)} \, dx","Int[(b - a*x^5)/(Sqrt[a + b*x]*(a*b + x^5)),x]","-\frac{2 \left(a^2+1\right) \sqrt[5]{b} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}-b^{6/5}}}\right)}{5 a^{9/10} \sqrt{a^{4/5}-b^{6/5}}}+\frac{2 \sqrt[5]{-1} \left(a^2+1\right) \sqrt[5]{b} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}+\sqrt[5]{-1} b^{6/5}}}\right)}{5 a^{9/10} \sqrt{a^{4/5}+\sqrt[5]{-1} b^{6/5}}}-\frac{2 (-1)^{2/5} \left(a^2+1\right) \sqrt[5]{b} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}-(-1)^{2/5} b^{6/5}}}\right)}{5 a^{9/10} \sqrt{a^{4/5}-(-1)^{2/5} b^{6/5}}}+\frac{2 (-1)^{3/5} \left(a^2+1\right) \sqrt[5]{b} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}+(-1)^{3/5} b^{6/5}}}\right)}{5 a^{9/10} \sqrt{a^{4/5}+(-1)^{3/5} b^{6/5}}}-\frac{2 (-1)^{4/5} \left(a^2+1\right) \sqrt[5]{b} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt[10]{a} \sqrt{a^{4/5}-(-1)^{4/5} b^{6/5}}}\right)}{5 a^{9/10} \sqrt{a^{4/5}-(-1)^{4/5} b^{6/5}}}-\frac{2 a \sqrt{a+b x}}{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*a*Sqrt[a + b*x])/b - (2*(1 + a^2)*b^(1/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) - b^(6/5)])])/(5*a^(9/10)*Sqrt[a^(4/5) - b^(6/5)]) + (2*(-1)^(1/5)*(1 + a^2)*b^(1/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) + (-1)^(1/5)*b^(6/5)])])/(5*a^(9/10)*Sqrt[a^(4/5) + (-1)^(1/5)*b^(6/5)]) - (2*(-1)^(2/5)*(1 + a^2)*b^(1/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) - (-1)^(2/5)*b^(6/5)])])/(5*a^(9/10)*Sqrt[a^(4/5) - (-1)^(2/5)*b^(6/5)]) + (2*(-1)^(3/5)*(1 + a^2)*b^(1/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) + (-1)^(3/5)*b^(6/5)])])/(5*a^(9/10)*Sqrt[a^(4/5) + (-1)^(3/5)*b^(6/5)]) - (2*(-1)^(4/5)*(1 + a^2)*b^(1/5)*ArcTanh[Sqrt[a + b*x]/(a^(1/10)*Sqrt[a^(4/5) - (-1)^(4/5)*b^(6/5)])])/(5*a^(9/10)*Sqrt[a^(4/5) - (-1)^(4/5)*b^(6/5)])","B",14,5,27,0.1852,0,"{6740, 6739, 12, 208, 206}"
1960,1,402,0,0.7770134,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3+x^6\right)}{x^6 \left(-1+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(1 + x^3 + x^6))/(x^6*(-1 + x^6)),x]","-\frac{\log \left(2^{2/3} \sqrt[3]{x^3-1}-x+1\right)}{4 \sqrt[3]{2}}-\frac{\log \left(2\ 2^{2/3} \sqrt[3]{x^3-1}-2 x-i \sqrt{3}-1\right)}{4 \sqrt[3]{2}}-\frac{\log \left(2\ 2^{2/3} \sqrt[3]{x^3-1}-2 x+i \sqrt{3}-1\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2+\frac{\sqrt[3]{2} \left(2 x-i \sqrt{3}+1\right)}{\sqrt[3]{x^3-1}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2+\frac{\sqrt[3]{2} \left(2 x+i \sqrt{3}+1\right)}{\sqrt[3]{x^3-1}}}{2 \sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\left(x^3-1\right)^{2/3}}{5 x^5}+\frac{3 \left(x^3-1\right)^{2/3}}{10 x^2}+\frac{\log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}+\frac{\log \left(-\left(-2 x-i \sqrt{3}+1\right)^2 \left(2 x-i \sqrt{3}+1\right)\right)}{12 \sqrt[3]{2}}+\frac{\log \left(-\left(-2 x+i \sqrt{3}+1\right)^2 \left(2 x+i \sqrt{3}+1\right)\right)}{12 \sqrt[3]{2}}","-\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,"(-1 + x^3)^(2/3)/(5*x^5) + (3*(-1 + x^3)^(2/3))/(10*x^2) + ArcTan[(1 - (2^(1/3)*(1 - x))/(-1 + x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) + ArcTan[(2 + (2^(1/3)*(1 - I*Sqrt[3] + 2*x))/(-1 + x^3)^(1/3))/(2*Sqrt[3])]/(2*2^(1/3)*Sqrt[3]) + ArcTan[(2 + (2^(1/3)*(1 + I*Sqrt[3] + 2*x))/(-1 + x^3)^(1/3))/(2*Sqrt[3])]/(2*2^(1/3)*Sqrt[3]) + Log[(1 - x)*(1 + x)^2]/(12*2^(1/3)) + Log[-((1 - I*Sqrt[3] - 2*x)^2*(1 - I*Sqrt[3] + 2*x))]/(12*2^(1/3)) + Log[-((1 + I*Sqrt[3] - 2*x)^2*(1 + I*Sqrt[3] + 2*x))]/(12*2^(1/3)) - Log[1 - x + 2^(2/3)*(-1 + x^3)^(1/3)]/(4*2^(1/3)) - Log[-1 - I*Sqrt[3] - 2*x + 2*2^(2/3)*(-1 + x^3)^(1/3)]/(4*2^(1/3)) - Log[-1 + I*Sqrt[3] - 2*x + 2*2^(2/3)*(-1 + x^3)^(1/3)]/(4*2^(1/3))","C",10,6,28,0.2143,1,"{1586, 6725, 271, 264, 2148, 6728}"
1961,0,0,0,2.6891091,"\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","Int[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\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","8 \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{15}-7 \text{$\#$1}^{13}+18 \text{$\#$1}^{11}-20 \text{$\#$1}^9+7 \text{$\#$1}^7+3 \text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]",1,"8*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - 16*Defer[Subst][Defer[Int][(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16)^(-1), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
1962,0,0,0,2.0795168,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","8 \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{15}-7 \text{$\#$1}^{13}+18 \text{$\#$1}^{11}-20 \text{$\#$1}^9+7 \text{$\#$1}^7+3 \text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]",1,"8*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - 16*Defer[Subst][Defer[Int][(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16)^(-1), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
1963,1,194,0,0.3644133,"\int \frac{x}{\left(x^2 (-a+x)\right)^{2/3} (-a d+(-1+d) x)} \, dx","Int[x/((x^2*(-a + x))^(2/3)*(-(a*d) + (-1 + d)*x)),x]","-\frac{x^{4/3} (x-a)^{2/3} \log (-a d-(1-d) x)}{2 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{d}}-\sqrt[3]{x-a}\right)}{2 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\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,"(Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*d^(1/3)*(-a + x)^(1/3))])/(a*d^(1/3)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[-(a*d) - (1 - d)*x])/(2*a*d^(1/3)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[x^(1/3)/d^(1/3) - (-a + x)^(1/3)])/(2*a*d^(1/3)*(-((a - x)*x^2))^(2/3))","A",2,2,27,0.07407,1,"{6719, 91}"
1964,1,213,0,0.2371801,"\int \frac{\left(-b+a x^2\right)^{3/4}}{x} \, dx","Int[(-b + a*x^2)^(3/4)/x,x]","-\frac{b^{3/4} \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{b^{3/4} \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{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)}{\sqrt{2}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{\sqrt{2}}+\frac{2}{3} \left(a x^2-b\right)^{3/4}","\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[1 - (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/Sqrt[2] - (b^(3/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/Sqrt[2] - (b^(3/4)*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)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(2*Sqrt[2])","A",12,9,17,0.5294,1,"{266, 50, 63, 297, 1162, 617, 204, 1165, 628}"
1965,1,851,0,1.8509171,"\int \frac{-2 x+x^2}{\left(1-x+x^2\right) \sqrt[4]{1+x^4}} \, dx","Int[(-2*x + x^2)/((1 - x + x^2)*(1 + x^4)^(1/4)),x]","-\frac{1}{6} \left(1+i \sqrt{3}\right) F_1\left(\frac{3}{4};\frac{1}{4},1;\frac{7}{4};-x^4,-\frac{2 x^4}{1-i \sqrt{3}}\right) x^3-\frac{1}{6} \left(1-i \sqrt{3}\right) F_1\left(\frac{3}{4};\frac{1}{4},1;\frac{7}{4};-x^4,-\frac{2 x^4}{1+i \sqrt{3}}\right) x^3+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \left(1+i \sqrt{3}\right) \sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} \tan ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} \sqrt[4]{x^4+1}}\right)-\frac{1}{2} \left(-\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{2} \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1-i \sqrt{3}}}\right)-\frac{1}{2} \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1+i \sqrt{3}}}\right)+\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4+1}}\right)-\frac{1}{4} \left(1+i \sqrt{3}\right) \sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} \sqrt[4]{x^4+1}}\right)-\frac{1}{2} \left(-\frac{i-\sqrt{3}}{i+\sqrt{3}}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{i-\sqrt{3}}{i+\sqrt{3}}} x}{\sqrt[4]{x^4+1}}\right)+\frac{1}{2} \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1-i \sqrt{3}}}\right)+\frac{1}{2} \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x^4+1}}{\sqrt[4]{1+i \sqrt{3}}}\right)-\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{2} \left(-i-\sqrt{3}\right);\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}+\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{2} \left(i-\sqrt{3}\right);\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}+\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}-\frac{i \sqrt{-x^4} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}\left(\sqrt[4]{x^4+1}\right)\right|-1\right)}{2 x^2}","\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,"-1/6*((1 + I*Sqrt[3])*x^3*AppellF1[3/4, 1/4, 1, 7/4, -x^4, (-2*x^4)/(1 - I*Sqrt[3])]) - ((1 - I*Sqrt[3])*x^3*AppellF1[3/4, 1/4, 1, 7/4, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/6 + ArcTan[x/(1 + x^4)^(1/4)]/2 - ((1 + I*Sqrt[3])*(-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*ArcTan[x/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(1 + x^4)^(1/4))])/4 - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*ArcTan[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x)/(1 + x^4)^(1/4)])/2 - (((1 - I*Sqrt[3])/2)^(3/4)*ArcTan[(2^(1/4)*(1 + x^4)^(1/4))/(1 - I*Sqrt[3])^(1/4)])/2 - (((1 + I*Sqrt[3])/2)^(3/4)*ArcTan[(2^(1/4)*(1 + x^4)^(1/4))/(1 + I*Sqrt[3])^(1/4)])/2 + ArcTanh[x/(1 + x^4)^(1/4)]/2 - ((1 + I*Sqrt[3])*(-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*ArcTanh[x/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(1 + x^4)^(1/4))])/4 - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*ArcTanh[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x)/(1 + x^4)^(1/4)])/2 + (((1 - I*Sqrt[3])/2)^(3/4)*ArcTanh[(2^(1/4)*(1 + x^4)^(1/4))/(1 - I*Sqrt[3])^(1/4)])/2 + (((1 + I*Sqrt[3])/2)^(3/4)*ArcTanh[(2^(1/4)*(1 + x^4)^(1/4))/(1 + I*Sqrt[3])^(1/4)])/2 - ((I/2)*Sqrt[-x^4]*EllipticPi[(-I - Sqrt[3])/2, ArcSin[(1 + x^4)^(1/4)], -1])/x^2 + ((I/2)*Sqrt[-x^4]*EllipticPi[(I - Sqrt[3])/2, ArcSin[(1 + x^4)^(1/4)], -1])/x^2 + ((I/2)*Sqrt[-x^4]*EllipticPi[1/Sqrt[(1 - I*Sqrt[3])/2], ArcSin[(1 + x^4)^(1/4)], -1])/x^2 - ((I/2)*Sqrt[-x^4]*EllipticPi[1/Sqrt[(1 + I*Sqrt[3])/2], ArcSin[(1 + x^4)^(1/4)], -1])/x^2","C",53,21,27,0.7778,0,"{1593, 6728, 240, 212, 206, 203, 2153, 1240, 377, 208, 205, 510, 1248, 746, 399, 490, 1213, 537, 444, 63, 298}"
1966,1,450,0,4.7339163,"\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","Int[(1 + k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^4*x^4)),x]","\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{1}{\sqrt{-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{1}{\sqrt{-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\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,"(2*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-(1/Sqrt[-k^2]), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[1/Sqrt[-k^2], ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",27,8,40,0.2000,0,"{6718, 6725, 115, 6688, 934, 12, 168, 537}"
1967,1,1123,0,2.7682665,"\int \frac{-b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Int[(-b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}","\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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",28,11,35,0.3143,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377, 208, 205}"
1968,1,1123,0,2.0761497,"\int \frac{-b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(b+a x^8\right)} \, dx","Int[(-b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(b + a*x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a-\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{a+\sqrt[4]{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a-\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-\sqrt{-a}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt{x}}{\sqrt[8]{-\sqrt{-a}} \sqrt[4]{a x^2-b}}\right)}{2 \sqrt[4]{\sqrt{-\sqrt{-a}} a+\sqrt{-a} b^{3/4}} \sqrt[4]{a x^4-b x^2}}","\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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a - (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a - (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((a + (-a)^(1/4)*b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(a + (-a)^(1/4)*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a - Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-Sqrt[-a])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*Sqrt[x])/((-Sqrt[-a])^(1/8)*(-b + a*x^2)^(1/4))])/(2*(Sqrt[-Sqrt[-a]]*a + Sqrt[-a]*b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",28,11,35,0.3143,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377, 208, 205}"
1969,0,0,0,1.3275439,"\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","Int[((-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,"(x*(1 - (2*x^4)/(1 - Sqrt[5]))^(1/4)*(1 - (2*x^4)/(1 + Sqrt[5]))^(1/4)*AppellF1[1/4, 1/4, 1/4, 5/4, (2*x^4)/(1 + Sqrt[5]), (2*x^4)/(1 - Sqrt[5])])/(-1 - x^4 + x^8)^(1/4) - (x*(Sqrt[3 + Sqrt[5]] - Sqrt[2]*x^4)^(1/4)*(1 + Sqrt[(3 + Sqrt[5])/2]*x^4)^(1/4)*AppellF1[1/4, 5/4, 1/4, 5/4, Sqrt[2/(3 + Sqrt[5])]*x^4, -(Sqrt[(3 + Sqrt[5])/2]*x^4)])/(2*(3 + Sqrt[5])^(1/8)*(-1 - x^4 + x^8)^(1/4)) - (x*(Sqrt[3 - Sqrt[5]] + Sqrt[2]*x^4)^(1/4)*(1 - Sqrt[(3 - Sqrt[5])/2]*x^4)^(1/4)*AppellF1[1/4, 5/4, 1/4, 5/4, -(Sqrt[(3 + Sqrt[5])/2]*x^4), Sqrt[(3 - Sqrt[5])/2]*x^4])/(2*(3 - Sqrt[5])^(1/8)*(-1 - x^4 + x^8)^(1/4)) - (Sqrt[3 - Sqrt[5]]*Defer[Int][1/((Sqrt[3 - Sqrt[5]] - Sqrt[2]*x^4)*(-1 - x^4 + x^8)^(1/4)), x])/2 - (Sqrt[3 + Sqrt[5]]*Defer[Int][1/((Sqrt[3 + Sqrt[5]] + Sqrt[2]*x^4)*(-1 - x^4 + x^8)^(1/4)), x])/2","F",0,0,0,0,-1,"{}"
1970,1,248,0,0.3805755,"\int \frac{1}{\sqrt[3]{x^2 (-a+x)} (-a d+(-1+d) x)} \, dx","Int[1/((x^2*(-a + x))^(1/3)*(-(a*d) + (-1 + d)*x)),x]","-\frac{\left(-a^2 x\right)^{2/3} \sqrt[3]{a^2 (x-a)} \log ((d-1) x-a d)}{2 a^3 d^{2/3} \sqrt[3]{x^2 (x-a)}}+\frac{3 \left(-a^2 x\right)^{2/3} \sqrt[3]{a^2 (x-a)} \log \left(-\sqrt[3]{\frac{2}{3}} \sqrt[3]{d} \sqrt[3]{a^2 (x-a)}-\sqrt[3]{\frac{2}{3}} \sqrt[3]{-a^2 x}\right)}{2 a^3 d^{2/3} \sqrt[3]{x^2 (x-a)}}+\frac{\sqrt{3} \left(-a^2 x\right)^{2/3} \sqrt[3]{a^2 (x-a)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{d} \sqrt[3]{a^2 (x-a)}}{\sqrt{3} \sqrt[3]{-a^2 x}}\right)}{a^3 d^{2/3} \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,"(Sqrt[3]*(-(a^2*x))^(2/3)*(a^2*(-a + x))^(1/3)*ArcTan[1/Sqrt[3] - (2*d^(1/3)*(a^2*(-a + x))^(1/3))/(Sqrt[3]*(-(a^2*x))^(1/3))])/(a^3*d^(2/3)*(x^2*(-a + x))^(1/3)) - ((-(a^2*x))^(2/3)*(a^2*(-a + x))^(1/3)*Log[-(a*d) + (-1 + d)*x])/(2*a^3*d^(2/3)*(x^2*(-a + x))^(1/3)) + (3*(-(a^2*x))^(2/3)*(a^2*(-a + x))^(1/3)*Log[-((2/3)^(1/3)*(-(a^2*x))^(1/3)) - (2/3)^(1/3)*d^(1/3)*(a^2*(-a + x))^(1/3)])/(2*a^3*d^(2/3)*(x^2*(-a + x))^(1/3))","A",3,3,26,0.1154,1,"{2081, 2077, 91}"
1971,1,103,0,0.0910606,"\int \frac{\sqrt[3]{6+2 x+x^2}}{1+x} \, dx","Int[(6 + 2*x + x^2)^(1/3)/(1 + x),x]","\frac{3}{2} \sqrt[3]{(x+1)^2+5}-\frac{1}{2} \sqrt[3]{5} \log (x+1)+\frac{3}{4} \sqrt[3]{5} \log \left(\sqrt[3]{5}-\sqrt[3]{(x+1)^2+5}\right)-\frac{1}{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)","\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,"(3*(5 + (1 + 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[1 + x])/2 + (3*5^(1/3)*Log[5^(1/3) - (5 + (1 + x)^2)^(1/3)])/4","A",7,7,18,0.3889,1,"{694, 266, 50, 57, 617, 204, 31}"
1972,1,94,0,0.0694383,"\int \frac{-1+x}{x \sqrt[3]{-1+x^3}} \, dx","Int[(-1 + x)/(x*(-1 + x^3)^(1/3)),x]","\frac{1}{2} \log \left(\sqrt[3]{x^3-1}+1\right)-\frac{1}{2} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 \sqrt[3]{x^3-1}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log (x)}{2}","-\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,"ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + ArcTan[(1 - 2*(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[x]/2 + Log[1 + (-1 + x^3)^(1/3)]/2 - Log[-x + (-1 + x^3)^(1/3)]/2","A",8,7,16,0.4375,1,"{1844, 239, 266, 56, 618, 204, 31}"
1973,1,145,0,0.1424645,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3\right)}{x^6 \left(-2+x^3\right)} \, dx","Int[((-1 + x^3)^(2/3)*(1 + x^3))/(x^6*(-2 + x^3)),x]","\frac{\log \left(\sqrt[3]{2}-\frac{x}{\sqrt[3]{x^3-1}}\right)}{4\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4\ 2^{2/3}}+\frac{\left(x^3-1\right)^{2/3}}{10 x^5}+\frac{11 \left(x^3-1\right)^{2/3}}{40 x^2}-\frac{\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)}{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 + x^3)^(2/3)/(10*x^5) + (11*(-1 + x^3)^(2/3))/(40*x^2) - (Sqrt[3]*ArcTan[(1 + (2^(2/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(4*2^(2/3)) + Log[2^(1/3) - x/(-1 + x^3)^(1/3)]/(4*2^(2/3)) - Log[2^(2/3) + x^2/(-1 + x^3)^(2/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)]/(8*2^(2/3))","A",10,10,25,0.4000,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
1974,1,228,0,0.3849836,"\int \frac{\left(-4+x^2\right) \sqrt[3]{x+x^3}}{x^4 \left(2+x^2\right)} \, dx","Int[((-4 + x^2)*(x + x^3)^(1/3))/(x^4*(2 + x^2)),x]","-\frac{3 \sqrt[3]{x^3+x}}{2 x}+\frac{3 \sqrt[3]{x^3+x}}{4 x^3}-\frac{3 \sqrt[3]{x^3+x} \log \left(\sqrt[3]{2}-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x} \sqrt[3]{x^2+1}}+\frac{3 \sqrt[3]{x^3+x} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{\sqrt[3]{2} x^{2/3}}{\sqrt[3]{x^2+1}}+2^{2/3}\right)}{8 \sqrt[3]{2} \sqrt[3]{x} \sqrt[3]{x^2+1}}-\frac{3 \sqrt{3} \sqrt[3]{x^3+x} \tan ^{-1}\left(\frac{\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x} \sqrt[3]{x^2+1}}","-\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*x^3) - (3*(x + x^3)^(1/3))/(2*x) - (3*Sqrt[3]*(x + x^3)^(1/3)*ArcTan[(1 + (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(4*2^(1/3)*x^(1/3)*(1 + x^2)^(1/3)) - (3*(x + x^3)^(1/3)*Log[2^(1/3) - x^(2/3)/(1 + x^2)^(1/3)])/(4*2^(1/3)*x^(1/3)*(1 + x^2)^(1/3)) + (3*(x + x^3)^(1/3)*Log[2^(2/3) + x^(4/3)/(1 + x^2)^(2/3) + (2^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(8*2^(1/3)*x^(1/3)*(1 + x^2)^(1/3))","A",13,13,25,0.5200,1,"{2056, 580, 583, 12, 466, 465, 494, 292, 31, 634, 617, 204, 628}"
1975,1,489,0,0.5115996,"\int \frac{2+x^2}{\left(1+x^2\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[(2 + x^2)/((1 + x^2)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(-\sqrt[3]{x}+\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-i}}\right)}{4 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(-\sqrt[3]{x}+\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+i}}\right)}{4 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log (-x+i)}{4 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log (x+i)}{4 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1-i} \sqrt{3} \sqrt[3]{x}}\right)}{2 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1+i} \sqrt{3} \sqrt[3]{x}}\right)}{2 \sqrt[3]{1+i} \sqrt[3]{x^3-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,"-((Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3)) - (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/((1 - I)^(1/3)*Sqrt[3]*x^(1/3))])/(2*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3)) - (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/((1 + I)^(1/3)*Sqrt[3]*x^(1/3))])/(2*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - I)^(1/3) - x^(1/3)])/(4*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3)) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + I)^(1/3) - x^(1/3)])/(4*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[I - x])/(4*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[I + x])/(4*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3))","C",8,5,26,0.1923,1,"{2056, 6725, 59, 912, 91}"
1976,1,181,0,0.5615677,"\int \frac{x}{\left(b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Int[x/((b + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","\frac{\sqrt{x} \sqrt{a x^2-b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2-b}}\right)}{2 \sqrt{2} (-a)^{3/4} b^{3/4} \sqrt{a x^3-b x}}-\frac{\sqrt{x} \sqrt{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2-b}}\right)}{2 \sqrt{2} (-a)^{3/4} b^{3/4} \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,"(Sqrt[x]*Sqrt[-b + a*x^2]*ArcTan[(Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[-b + a*x^2]])/(2*Sqrt[2]*(-a)^(3/4)*b^(3/4)*Sqrt[-(b*x) + a*x^3]) - (Sqrt[x]*Sqrt[-b + a*x^2]*ArcTanh[(Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[-b + a*x^2]])/(2*Sqrt[2]*(-a)^(3/4)*b^(3/4)*Sqrt[-(b*x) + a*x^3])","A",13,9,25,0.3600,1,"{2042, 466, 490, 1211, 224, 221, 1699, 208, 205}"
1977,1,176,0,0.2217974,"\int \frac{-b+a x^2}{\left(b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Int[(-b + a*x^2)/((b + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","-\frac{\sqrt{x} \sqrt{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{b}-\sqrt{a} x\right)}{\sqrt[4]{b} \sqrt{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}-\frac{\sqrt{x} \sqrt{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a} x+\sqrt{b}\right)}{\sqrt[4]{b} \sqrt{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{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)}{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,"-((Sqrt[x]*Sqrt[-b + a*x^2]*ArcTan[(a^(1/4)*Sqrt[x]*(Sqrt[b] - Sqrt[a]*x))/(b^(1/4)*Sqrt[-b + a*x^2])])/(a^(1/4)*b^(1/4)*Sqrt[-(b*x) + a*x^3])) - (Sqrt[x]*Sqrt[-b + a*x^2]*ArcTanh[(a^(1/4)*Sqrt[x]*(Sqrt[b] + Sqrt[a]*x))/(b^(1/4)*Sqrt[-b + a*x^2])])/(a^(1/4)*b^(1/4)*Sqrt[-(b*x) + a*x^3])","A",3,3,33,0.09091,1,"{2056, 466, 405}"
1978,1,181,0,0.4399682,"\int \frac{\sqrt{-b x+a x^3}}{-b^2+a^2 x^4} \, dx","Int[Sqrt[-(b*x) + a*x^3]/(-b^2 + a^2*x^4),x]","\frac{\sqrt{a x^3-b x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2-b}}\right)}{2 \sqrt{2} (-a)^{3/4} b^{3/4} \sqrt{x} \sqrt{a x^2-b}}-\frac{\sqrt{a x^3-b x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2-b}}\right)}{2 \sqrt{2} (-a)^{3/4} b^{3/4} \sqrt{x} \sqrt{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)}{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[-(b*x) + a*x^3]*ArcTan[(Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[-b + a*x^2]])/(2*Sqrt[2]*(-a)^(3/4)*b^(3/4)*Sqrt[x]*Sqrt[-b + a*x^2]) - (Sqrt[-(b*x) + a*x^3]*ArcTanh[(Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[-b + a*x^2]])/(2*Sqrt[2]*(-a)^(3/4)*b^(3/4)*Sqrt[x]*Sqrt[-b + a*x^2])","A",14,10,30,0.3333,1,"{2056, 1254, 466, 490, 1211, 224, 221, 1699, 208, 205}"
1979,0,0,0,1.2946093,"\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","Int[((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,"(3*(1 + x^5)^(2/3))/5 + (3*(1 + x^5)^(2/3))/(5*x^5) + (3*Hypergeometric2F1[-2/3, -2/5, 3/5, -x^5])/(2*x^2) - 3*Defer[Int][(1 + x^5)^(2/3)/(2 - x^3 + 2*x^5), x] + 10*Defer[Int][(x^2*(1 + x^5)^(2/3))/(2 - x^3 + 2*x^5), x]","F",0,0,0,0,-1,"{}"
1980,0,0,0,0.7900833,"\int \frac{b+a x^6}{\left(-b+a x^6\right) \sqrt[3]{-b+a^3 x^3+a x^6}} \, dx","Int[(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,"(x*(1 + (2*Sqrt[a]*x^3)/(a^(5/2) - Sqrt[a^5 + 4*b]))^(1/3)*(1 + (2*Sqrt[a]*x^3)/(a^(5/2) + Sqrt[a^5 + 4*b]))^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, (-2*a*x^3)/(a^3 - Sqrt[a^6 + 4*a*b]), (-2*a*x^3)/(a^3 + Sqrt[a^6 + 4*a*b])])/(-b + a^3*x^3 + a*x^6)^(1/3) - Sqrt[b]*Defer[Int][1/((Sqrt[b] - Sqrt[a]*x^3)*(-b + a^3*x^3 + a*x^6)^(1/3)), x] - Sqrt[b]*Defer[Int][1/((Sqrt[b] + Sqrt[a]*x^3)*(-b + a^3*x^3 + a*x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
1981,0,0,0,1.1388015,"\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","Int[((1 + x^2)*(1 + x^8)*Sqrt[1 + x^2 + x^4 + x^6 + x^8])/(x^7*(-1 + x^2)),x]","\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","\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,"-Defer[Int][Sqrt[1 + x^2 + x^4 + x^6 + x^8]/x^7, x] - 2*Defer[Int][Sqrt[1 + x^2 + x^4 + x^6 + x^8]/x^5, x] - 2*Defer[Int][Sqrt[1 + x^2 + x^4 + x^6 + x^8]/x^3, x] + Defer[Subst][Defer[Int][Sqrt[1 + x + x^2 + x^3 + x^4], x], x, x^2]/2 + 2*Defer[Subst][Defer[Int][Sqrt[1 + x + x^2 + x^3 + x^4]/(-1 + x), x], x, x^2] - Defer[Subst][Defer[Int][Sqrt[1 + x + x^2 + x^3 + x^4]/x, x], x, x^2]","F",0,0,0,0,-1,"{}"
1982,1,1043,0,2.6101535,"\int \frac{b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Int[(b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}","\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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",28,9,35,0.2571,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1983,1,1043,0,2.1828314,"\int \frac{b+a x^8}{\sqrt[4]{-b x^2+a x^4} \left(-b+a x^8\right)} \, dx","Int[(b + a*x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + a*x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}-b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 \sqrt[8]{-\sqrt{a}} \sqrt[4]{\frac{a}{\sqrt{-\sqrt{a}}}+b^{3/4}} \sqrt[4]{a x^4-b x^2}}","\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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] - b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*(-Sqrt[a])^(1/8)*(a/Sqrt[-Sqrt[a]] + b^(3/4))^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",28,9,35,0.2571,1,"{2056, 6715, 6725, 240, 212, 206, 203, 1429, 377}"
1984,1,513,0,1.3223204,"\int \frac{\left(-1+x^4\right) \sqrt{x+\sqrt{1+x^2}}}{1+x^4} \, dx","Int[((-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}}-(-1)^{3/4} \sqrt{-(-1)^{3/4}+\sqrt{1-i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)+(-1)^{3/4} \sqrt{(-1)^{3/4}+\sqrt{1-i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)-\sqrt[4]{-1} \sqrt{-\sqrt[4]{-1}+\sqrt{1+i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)+\sqrt[4]{-1} \sqrt{\sqrt[4]{-1}+\sqrt{1+i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)+(-1)^{3/4} \sqrt{-(-1)^{3/4}+\sqrt{1-i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)-(-1)^{3/4} \sqrt{(-1)^{3/4}+\sqrt{1-i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)+\sqrt[4]{-1} \sqrt{-\sqrt[4]{-1}+\sqrt{1+i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)-\sqrt[4]{-1} \sqrt{\sqrt[4]{-1}+\sqrt{1+i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)","-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 - (-1)^(3/4)*Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]] + (-1)^(3/4)*Sqrt[(-1)^(3/4) + Sqrt[1 - I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]] - (-1)^(1/4)*Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]] + (-1)^(1/4)*Sqrt[(-1)^(1/4) + Sqrt[1 + I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]] + (-1)^(3/4)*Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]] - (-1)^(3/4)*Sqrt[(-1)^(3/4) + Sqrt[1 - I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]] + (-1)^(1/4)*Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]] - (-1)^(1/4)*Sqrt[(-1)^(1/4) + Sqrt[1 + I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]]","C",39,11,28,0.3929,1,"{6725, 2117, 14, 2119, 1628, 826, 1166, 204, 206, 207, 203}"
1985,1,513,0,1.1288374,"\int \frac{\left(-1+x^4\right) \sqrt{x+\sqrt{1+x^2}}}{1+x^4} \, dx","Int[((-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}}-(-1)^{3/4} \sqrt{-(-1)^{3/4}+\sqrt{1-i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)+(-1)^{3/4} \sqrt{(-1)^{3/4}+\sqrt{1-i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)-\sqrt[4]{-1} \sqrt{-\sqrt[4]{-1}+\sqrt{1+i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)+\sqrt[4]{-1} \sqrt{\sqrt[4]{-1}+\sqrt{1+i}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)+(-1)^{3/4} \sqrt{-(-1)^{3/4}+\sqrt{1-i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-(-1)^{3/4}+\sqrt{1-i}}}\right)-(-1)^{3/4} \sqrt{(-1)^{3/4}+\sqrt{1-i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{(-1)^{3/4}+\sqrt{1-i}}}\right)+\sqrt[4]{-1} \sqrt{-\sqrt[4]{-1}+\sqrt{1+i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{-\sqrt[4]{-1}+\sqrt{1+i}}}\right)-\sqrt[4]{-1} \sqrt{\sqrt[4]{-1}+\sqrt{1+i}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{x^2+1}+x}}{\sqrt{\sqrt[4]{-1}+\sqrt{1+i}}}\right)","-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 - (-1)^(3/4)*Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]] + (-1)^(3/4)*Sqrt[(-1)^(3/4) + Sqrt[1 - I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]] - (-1)^(1/4)*Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]] + (-1)^(1/4)*Sqrt[(-1)^(1/4) + Sqrt[1 + I]]*ArcTan[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]] + (-1)^(3/4)*Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(3/4) + Sqrt[1 - I]]] - (-1)^(3/4)*Sqrt[(-1)^(3/4) + Sqrt[1 - I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(3/4) + Sqrt[1 - I]]] + (-1)^(1/4)*Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[-(-1)^(1/4) + Sqrt[1 + I]]] - (-1)^(1/4)*Sqrt[(-1)^(1/4) + Sqrt[1 + I]]*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]/Sqrt[(-1)^(1/4) + Sqrt[1 + I]]]","C",39,11,28,0.3929,1,"{6725, 2117, 14, 2119, 1628, 826, 1166, 204, 206, 207, 203}"
1986,0,0,0,1.7257218,"\int \frac{x^2 \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Int[(x^2*Sqrt[x + x^2])/Sqrt[x^2 + x*Sqrt[x + x^2]],x]","\int \frac{x^2 \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","\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,"(2*Sqrt[x + x^2]*Defer[Subst][Defer[Int][(x^6*Sqrt[1 + x^2])/Sqrt[x^4 + x^2*Sqrt[x^2 + x^4]], x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x])","F",0,0,0,0,-1,"{}"
1987,1,1309,0,4.1562091,"\int \frac{1}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[1/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}-\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}+\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}-\sqrt{2} (-c)^{3/4} \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a x+\sqrt{b^2+a^2 x^2}} (-c)^{3/4}+\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}+\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}","\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,"(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] - Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] + Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] - Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] + Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(1/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(1/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) + (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(3/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(3/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d])","B",30,10,33,0.3030,1,"{6725, 2119, 1628, 828, 826, 1169, 634, 618, 204, 628}"
1988,1,1309,0,3.2660185,"\int \frac{1}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[1/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}-\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}+\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}-\sqrt{2} (-c)^{3/4} \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a x+\sqrt{b^2+a^2 x^2}} (-c)^{3/4}+\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{3/4} \sqrt{d}}+\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{2 \sqrt{2} \sqrt{-b^2} (-c)^{5/4} \sqrt{d}}","\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,"(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] - Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] + Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] - Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] + Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(1/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(1/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)*Sqrt[d]) + (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(3/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d]) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Log[Sqrt[-b^2]*(-c)^(3/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)*Sqrt[d])","B",30,10,33,0.3030,1,"{6725, 2119, 1628, 828, 826, 1169, 634, 618, 204, 628}"
1989,0,0,0,1.195378,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[1 + x^2]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{1+x^2}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]/2","F",0,0,0,0,-1,"{}"
1990,0,0,0,0.8322116,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)*Sqrt[1 + x^2]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right) \sqrt{1+x^2}} \, dx","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]/2","F",0,0,0,0,-1,"{}"
1991,0,0,0,9.5584482,"\int \frac{\sqrt{b+a^2 x^2}}{x^2-\sqrt[3]{a x-\sqrt{b+a^2 x^2}}} \, dx","Int[Sqrt[b + a^2*x^2]/(x^2 - (a*x - Sqrt[b + a^2*x^2])^(1/3)),x]","\int \frac{\sqrt{b+a^2 x^2}}{x^2-\sqrt[3]{a x-\sqrt{b+a^2 x^2}}} \, dx","3 a \text{RootSum}\left[\text{$\#$1}^{12}-4 \text{$\#$1}^7 a^2-2 \text{$\#$1}^6 b+b^2\&,\frac{\text{$\#$1} a^2 \log \left(\sqrt[3]{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)+b \log \left(\sqrt[3]{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)}{-3 \text{$\#$1}^6+7 \text{$\#$1} a^2+3 b}\&\right]-a \log \left(\sqrt{a^2 x^2+b}-a x\right)",1,"b*Defer[Int][x^4/(b + 2*a*x^7 - x^12), x] + a^2*Defer[Int][x^6/(b + 2*a*x^7 - x^12), x] + a*Defer[Int][(x^5*Sqrt[b + a^2*x^2])/(b + 2*a*x^7 - x^12), x] + Defer[Int][(x^10*Sqrt[b + a^2*x^2])/(-b - 2*a*x^7 + x^12), x] + b*Defer[Int][(x^2*(a*x - Sqrt[b + a^2*x^2])^(1/3))/(b + 2*a*x^7 - x^12), x] + a^2*Defer[Int][(x^4*(a*x - Sqrt[b + a^2*x^2])^(1/3))/(b + 2*a*x^7 - x^12), x] + a*Defer[Int][(x^3*Sqrt[b + a^2*x^2]*(a*x - Sqrt[b + a^2*x^2])^(1/3))/(b + 2*a*x^7 - x^12), x] - Defer[Int][(x^8*Sqrt[b + a^2*x^2]*(a*x - Sqrt[b + a^2*x^2])^(1/3))/(b + 2*a*x^7 - x^12), x] + b*Defer[Int][(a*x - Sqrt[b + a^2*x^2])^(2/3)/(b + 2*a*x^7 - x^12), x] + a^2*Defer[Int][(x^2*(a*x - Sqrt[b + a^2*x^2])^(2/3))/(b + 2*a*x^7 - x^12), x] + a*Defer[Int][(x*Sqrt[b + a^2*x^2]*(a*x - Sqrt[b + a^2*x^2])^(2/3))/(b + 2*a*x^7 - x^12), x] - Defer[Int][(x^6*Sqrt[b + a^2*x^2]*(a*x - Sqrt[b + a^2*x^2])^(2/3))/(b + 2*a*x^7 - x^12), x]","F",0,0,0,0,-1,"{}"
1992,0,0,0,4.8431008,"\int \frac{\sqrt{b+a^2 x^2}}{x^2-\sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","Int[Sqrt[b + a^2*x^2]/(x^2 - Sqrt[a*x - Sqrt[b + a^2*x^2]]),x]","\int \frac{\sqrt{b+a^2 x^2}}{x^2-\sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","2 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^5 a^2-2 \text{$\#$1}^4 b+b^2\&,\frac{\text{$\#$1} a^2 \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)+b \log \left(\sqrt{a x-\sqrt{a^2 x^2+b}}-\text{$\#$1}\right)}{-2 \text{$\#$1}^4+5 \text{$\#$1} a^2+2 b}\&\right]-a \log \left(\sqrt{a^2 x^2+b}-a x\right)",1,"b*Defer[Int][x^2/(b + 2*a*x^5 - x^8), x] + a^2*Defer[Int][x^4/(b + 2*a*x^5 - x^8), x] + a*Defer[Int][(x^3*Sqrt[b + a^2*x^2])/(b + 2*a*x^5 - x^8), x] + Defer[Int][(x^6*Sqrt[b + a^2*x^2])/(-b - 2*a*x^5 + x^8), x] + b*Defer[Int][Sqrt[a*x - Sqrt[b + a^2*x^2]]/(b + 2*a*x^5 - x^8), x] + a^2*Defer[Int][(x^2*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(b + 2*a*x^5 - x^8), x] + a*Defer[Int][(x*Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(b + 2*a*x^5 - x^8), x] - Defer[Int][(x^4*Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(b + 2*a*x^5 - x^8), x]","F",0,0,0,0,-1,"{}"
1993,1,103,0,0.0890219,"\int \frac{\sqrt[3]{-6-2 x+x^2}}{-1+x} \, dx","Int[(-6 - 2*x + x^2)^(1/3)/(-1 + x),x]","\frac{3}{2} \sqrt[3]{(x-1)^2-7}-\frac{3}{4} \sqrt[3]{7} \log \left(\sqrt[3]{(x-1)^2-7}+\sqrt[3]{7}\right)+\frac{1}{2} \sqrt[3]{7} \log (1-x)+\frac{1}{2} \sqrt{3} \sqrt[3]{7} \tan ^{-1}\left(\frac{\sqrt[3]{7}-2 \sqrt[3]{(x-1)^2-7}}{\sqrt{3} \sqrt[3]{7}}\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,"(3*(-7 + (-1 + x)^2)^(1/3))/2 + (Sqrt[3]*7^(1/3)*ArcTan[(7^(1/3) - 2*(-7 + (-1 + x)^2)^(1/3))/(Sqrt[3]*7^(1/3))])/2 - (3*7^(1/3)*Log[7^(1/3) + (-7 + (-1 + x)^2)^(1/3)])/4 + (7^(1/3)*Log[1 - x])/2","A",7,7,18,0.3889,1,"{694, 266, 50, 58, 617, 204, 31}"
1994,1,214,0,0.2017274,"\int \frac{-1+x}{\sqrt[3]{1-x-x^2+x^3}} \, dx","Int[(-1 + x)/(1 - x - x^2 + x^3)^(1/3),x]","-\frac{(1-x) (x+1)}{\sqrt[3]{x^3-x^2-x+1}}+\frac{(3-3 x)^{2/3} \sqrt[3]{x+1} \log \left(-\frac{8}{3} (x-1)\right)}{3\ 3^{2/3} \sqrt[3]{x^3-x^2-x+1}}+\frac{(3-3 x)^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{3} \sqrt[3]{x+1}}{\sqrt[3]{3-3 x}}+1\right)}{3^{2/3} \sqrt[3]{x^3-x^2-x+1}}+\frac{2 (3-3 x)^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x+1}}{\sqrt[6]{3} \sqrt[3]{3-3 x}}\right)}{3 \sqrt[6]{3} \sqrt[3]{x^3-x^2-x+1}}","\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,"-(((1 - x)*(1 + x))/(1 - x - x^2 + x^3)^(1/3)) + (2*(3 - 3*x)^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*(1 + x)^(1/3))/(3^(1/6)*(3 - 3*x)^(1/3))])/(3*3^(1/6)*(1 - x - x^2 + x^3)^(1/3)) + ((3 - 3*x)^(2/3)*(1 + x)^(1/3)*Log[(-8*(-1 + x))/3])/(3*3^(2/3)*(1 - x - x^2 + x^3)^(1/3)) + ((3 - 3*x)^(2/3)*(1 + x)^(1/3)*Log[1 + (3^(1/3)*(1 + x)^(1/3))/(3 - 3*x)^(1/3)])/(3^(2/3)*(1 - x - x^2 + x^3)^(1/3))","A",5,5,21,0.2381,1,"{2081, 2077, 21, 50, 60}"
1995,1,191,0,0.1957271,"\int \frac{x}{\sqrt[3]{-1-x+x^2+x^3}} \, dx","Int[x/(-1 - x + x^2 + x^3)^(1/3),x]","-\frac{(1-x) (x+1)}{\sqrt[3]{x^3+x^2-x-1}}+\frac{(-x-1)^{2/3} \sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{-x-1}}+1\right)}{2 \sqrt[3]{x^3+x^2-x-1}}+\frac{(-x-1)^{2/3} \sqrt[3]{x-1} \log \left(-\frac{8}{3} (x+1)\right)}{6 \sqrt[3]{x^3+x^2-x-1}}+\frac{(-x-1)^{2/3} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{-x-1}}\right)}{\sqrt{3} \sqrt[3]{x^3+x^2-x-1}}","\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)*(1 + x))/(-1 - x + x^2 + x^3)^(1/3)) + ((-1 - x)^(2/3)*(-1 + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*(-1 + x)^(1/3))/(Sqrt[3]*(-1 - x)^(1/3))])/(Sqrt[3]*(-1 - x + x^2 + x^3)^(1/3)) + ((-1 - x)^(2/3)*(-1 + x)^(1/3)*Log[1 + (-1 + x)^(1/3)/(-1 - x)^(1/3)])/(2*(-1 - x + x^2 + x^3)^(1/3)) + ((-1 - x)^(2/3)*(-1 + x)^(1/3)*Log[(-8*(1 + x))/3])/(6*(-1 - x + x^2 + x^3)^(1/3))","A",4,4,17,0.2353,1,"{2081, 2077, 80, 60}"
1996,0,0,0,1.7610953,"\int \frac{(3+2 x) \left(1+x+3 x^3\right)^{2/3}}{x^3 \left(1+x+x^3\right)} \, dx","Int[((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,"(3*(1 + x + 3*x^3)^(2/3)*Defer[Int][(((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3) + 3*x)^(2/3)*(1 + (2/(-9 + Sqrt[85]))^(2/3) + ((-9 + Sqrt[85])/2)^(2/3) - 3*((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3))*x + 9*x^2)^(2/3))/x^3, x])/(((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3) + 3*x)^(2/3)*(1 + (2/(-9 + Sqrt[85]))^(2/3) + ((-9 + Sqrt[85])/2)^(2/3) - 3*((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3))*x + 9*x^2)^(2/3)) - ((1 + x + 3*x^3)^(2/3)*Defer[Int][(((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3) + 3*x)^(2/3)*(1 + (2/(-9 + Sqrt[85]))^(2/3) + ((-9 + Sqrt[85])/2)^(2/3) - 3*((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3))*x + 9*x^2)^(2/3))/x^2, x])/(((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3) + 3*x)^(2/3)*(1 + (2/(-9 + Sqrt[85]))^(2/3) + ((-9 + Sqrt[85])/2)^(2/3) - 3*((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3))*x + 9*x^2)^(2/3)) + ((1 + x + 3*x^3)^(2/3)*Defer[Int][(((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3) + 3*x)^(2/3)*(1 + (2/(-9 + Sqrt[85]))^(2/3) + ((-9 + Sqrt[85])/2)^(2/3) - 3*((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3))*x + 9*x^2)^(2/3))/x, x])/(((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3) + 3*x)^(2/3)*(1 + (2/(-9 + Sqrt[85]))^(2/3) + ((-9 + Sqrt[85])/2)^(2/3) - 3*((2/(-9 + Sqrt[85]))^(1/3) - ((-9 + Sqrt[85])/2)^(1/3))*x + 9*x^2)^(2/3)) - 4*Defer[Int][(1 + x + 3*x^3)^(2/3)/(1 + x + x^3), x] + Defer[Int][(x*(1 + x + 3*x^3)^(2/3))/(1 + x + x^3), x] - Defer[Int][(x^2*(1 + x + 3*x^3)^(2/3))/(1 + x + x^3), x]","F",0,0,0,0,-1,"{}"
1997,0,0,0,29.4339321,"\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","Int[(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,"(4*(b - x)^2*x*(1 - x/a)^(3/4)*(1 - x/b)^(1/4)*AppellF1[1/4, 3/4, 1/4, 5/4, x/a, x/b])/((a - x)*(b - x)^3*x)^(3/4) - (4*a*b^3*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(9/4)*Defer[Subst][Defer[Int][1/((-a + x^4)^(3/4)*(-b + x^4)^(1/4)*(a*b^3 - 3*a*b^2*(1 + b/(3*a))*x^4 + 3*a*b*(1 + b/a)*x^8 - a*(1 + (3*b + d)/a)*x^12 + x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(3/4) + (4*b^2*(3*a + b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(9/4)*Defer[Subst][Defer[Int][x^4/((-a + x^4)^(3/4)*(-b + x^4)^(1/4)*(a*b^3 - 3*a*b^2*(1 + b/(3*a))*x^4 + 3*a*b*(1 + b/a)*x^8 - a*(1 + (3*b + d)/a)*x^12 + x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(3/4) - (12*b*(2*a + b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(9/4)*Defer[Subst][Defer[Int][x^8/((-a + x^4)^(3/4)*(-b + x^4)^(1/4)*(a*b^3 - 3*a*b^2*(1 + b/(3*a))*x^4 + 3*a*b*(1 + b/a)*x^8 - a*(1 + (3*b + d)/a)*x^12 + x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(3/4) + (4*(a + 5*b + d)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(9/4)*Defer[Subst][Defer[Int][x^12/((-a + x^4)^(3/4)*(-b + x^4)^(1/4)*(a*b^3 - 3*a*b^2*(1 + b/(3*a))*x^4 + 3*a*b*(1 + b/a)*x^8 - a*(1 + (3*b + d)/a)*x^12 + x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(3/4)","F",0,0,0,0,-1,"{}"
1998,1,141,0,0.1266274,"\int \frac{x^6}{\left(-b+a x^4\right)^{3/4} \left(b+a x^4\right)} \, dx","Int[x^6/((-b + a*x^4)^(3/4)*(b + a*x^4)),x]","-\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}}","-\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,"-1/2*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(7/4) + ArcTan[(2^(1/4)*a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2*2^(3/4)*a^(7/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2*a^(7/4)) - ArcTanh[(2^(1/4)*a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2*2^(3/4)*a^(7/4))","A",8,5,26,0.1923,1,"{494, 481, 298, 203, 206}"
1999,1,265,0,0.3457319,"\int \frac{-b+2 a x^2}{\left(-b+a x^2\right) \sqrt[4]{b x^2+a x^4}} \, dx","Int[(-b + 2*a*x^2)/((-b + a*x^2)*(b*x^2 + a*x^4)^(1/4)),x]","\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{2} \sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}+\frac{2 \sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}-\frac{\sqrt{x} \sqrt[4]{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{2} \sqrt[4]{a} \sqrt[4]{a x^4+b x^2}}","\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,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2^(1/4)*a^(1/4)*(b*x^2 + a*x^4)^(1/4)) + (2*Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(1/4)*(b*x^2 + a*x^4)^(1/4)) - (Sqrt[x]*(b + a*x^2)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2^(1/4)*a^(1/4)*(b*x^2 + a*x^4)^(1/4))","A",13,9,37,0.2432,1,"{2056, 584, 329, 240, 212, 206, 203, 466, 377}"
2000,1,141,0,0.1110129,"\int \frac{-3 b+2 a x^4}{\left(-2 b+a x^4\right) \sqrt[4]{b+a x^4}} \, dx","Int[(-3*b + 2*a*x^4)/((-2*b + a*x^4)*(b + a*x^4)^(1/4)),x]","\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}}","\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,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) - ArcTan[((3/2)^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*2^(3/4)*3^(1/4)*a^(1/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) - ArcTanh[((3/2)^(1/4)*a^(1/4)*x)/(b + a*x^4)^(1/4)]/(2*2^(3/4)*3^(1/4)*a^(1/4))","A",9,6,33,0.1818,1,"{530, 240, 212, 206, 203, 377}"
2001,1,141,0,0.0761266,"\int \frac{b+a x^4}{\sqrt[4]{-b+a x^4} \left(b+3 a x^4\right)} \, dx","Int[(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)}{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}}","\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)]/(6*a^(1/4)) + ArcTan[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(3*Sqrt[2]*a^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(6*a^(1/4)) + ArcTanh[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(3*Sqrt[2]*a^(1/4))","A",9,6,31,0.1935,1,"{530, 240, 212, 206, 203, 377}"
2002,0,0,0,2.7354426,"\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","Int[((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,"Defer[Int][(1 - x^4 - x^6)^(-1/4), x] - Defer[Int][1/((-1 + I*Sqrt[3] - 2*x)^2*(1 - x^4 - x^6)^(1/4)), x]/3 + ((I/3)*Defer[Int][1/((-1 + I*Sqrt[3] - 2*x)*(1 - x^4 - x^6)^(1/4)), x])/Sqrt[3] - Defer[Int][1/((1 + I*Sqrt[3] - 2*x)^2*(1 - x^4 - x^6)^(1/4)), x]/3 + ((I/3)*Defer[Int][1/((1 + I*Sqrt[3] - 2*x)*(1 - x^4 - x^6)^(1/4)), x])/Sqrt[3] - Defer[Int][1/((-1 + x)^2*(1 - x^4 - x^6)^(1/4)), x]/12 + (5*Defer[Int][1/((-1 + x)*(1 - x^4 - x^6)^(1/4)), x])/12 - Defer[Int][1/((1 + x)^2*(1 - x^4 - x^6)^(1/4)), x]/12 - (5*Defer[Int][1/((1 + x)*(1 - x^4 - x^6)^(1/4)), x])/12 + (5*(3 + (5*I)*Sqrt[3])*Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*(1 - x^4 - x^6)^(1/4)), x])/36 - (5*(3 - (5*I)*Sqrt[3])*Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(1 - x^4 - x^6)^(1/4)), x])/36 - Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)^2*(1 - x^4 - x^6)^(1/4)), x]/3 + ((I/3)*Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*(1 - x^4 - x^6)^(1/4)), x])/Sqrt[3] + (5*(3 - (5*I)*Sqrt[3])*Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*(1 - x^4 - x^6)^(1/4)), x])/36 - Defer[Int][1/((1 + I*Sqrt[3] + 2*x)^2*(1 - x^4 - x^6)^(1/4)), x]/3 + ((I/3)*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 - x^4 - x^6)^(1/4)), x])/Sqrt[3] - (5*(3 + (5*I)*Sqrt[3])*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 - x^4 - x^6)^(1/4)), x])/36","F",0,0,0,0,-1,"{}"
2003,0,0,0,3.2393925,"\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","Int[((-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,"(-4*Sqrt[b]*c*(1 + (a*x^6)/b)^(3/4)*EllipticF[ArcTan[(Sqrt[a]*x^3)/Sqrt[b]]/2, 2])/(3*Sqrt[a]*(b + a*x^6)^(3/4)) + (2*b*(1 + (a*x^6)/b)^(3/4)*Hypergeometric2F1[-1/6, 3/4, 5/6, -((a*x^6)/b)])/(x*(b + a*x^6)^(3/4)) + (2*c^2*x*(1 + (a*x^6)/b)^(3/4)*Hypergeometric2F1[1/6, 3/4, 7/6, -((a*x^6)/b)])/(a*(b + a*x^6)^(3/4)) + (a*x^5*(1 + (a*x^6)/b)^(3/4)*Hypergeometric2F1[3/4, 5/6, 11/6, -((a*x^6)/b)])/(5*(b + a*x^6)^(3/4)) - (2*b*c^2*Defer[Int][1/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x])/a + 6*b*c*Defer[Int][x^2/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x] - (2*c^3*Defer[Int][x^4/((b + a*x^6)^(3/4)*(b + c*x^4 + a*x^6)), x])/a","F",0,0,0,0,-1,"{}"
2004,1,123,0,0.3700519,"\int \frac{\sqrt[4]{1+2 x^4} \left(-1-x^4+2 x^8\right)}{x^6 \left(2+x^4\right)} \, dx","Int[((1 + 2*x^4)^(1/4)*(-1 - x^4 + 2*x^8))/(x^6*(2 + x^4)),x]","\frac{3}{8} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{x^4}{2},-2 x^4\right)+\frac{\sqrt[4]{2 x^4+1}}{4 x}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4+1}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} x}{\sqrt[4]{2 x^4+1}}\right)}{4\ 2^{3/4}}+\frac{\left(2 x^4+1\right)^{5/4}}{10 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)/(4*x) + (1 + 2*x^4)^(5/4)/(10*x^5) + (3*x^3*AppellF1[3/4, 1, -1/4, 7/4, -1/2*x^4, -2*x^4])/8 + ArcTan[(2^(1/4)*x)/(1 + 2*x^4)^(1/4)]/(4*2^(3/4)) - ArcTanh[(2^(1/4)*x)/(1 + 2*x^4)^(1/4)]/(4*2^(3/4))","C",9,8,34,0.2353,0,"{6725, 264, 277, 331, 298, 203, 206, 510}"
2005,1,657,0,2.002113,"\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","Int[(-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]","\frac{a^3 \left(\frac{a^4 b^8-c}{\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{a^3 \left(1-\frac{a^4 b^8-c}{\sqrt{4 a^8 b^8+c^2}}\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{a^3 \left(\frac{a^4 b^8-c}{\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}}-\frac{a^3 \left(1-\frac{a^4 b^8-c}{\sqrt{4 a^8 b^8+c^2}}\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}}","\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*(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^3*(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^3*(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)) - (a^3*(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",10,5,53,0.09434,1,"{6728, 377, 212, 208, 205}"
2006,1,180,0,0.4058794,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(-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",16,11,28,0.3929,1,"{6725, 2117, 14, 2122, 329, 211, 1165, 628, 1162, 617, 204}"
2007,1,242,0,0.4203637,"\int \frac{\left(1+x^2\right) \sqrt[3]{x+2 x^3}}{x^4 \left(-1+x^2\right)} \, dx","Int[((1 + x^2)*(x + 2*x^3)^(1/3))/(x^4*(-1 + x^2)),x]","\frac{15 \sqrt[3]{2 x^3+x}}{4 x}+\frac{3 \sqrt[3]{2 x^3+x}}{8 x^3}+\frac{\sqrt[3]{3} \sqrt[3]{2 x^3+x} \log \left(1-\frac{\sqrt[3]{3} x^{2/3}}{\sqrt[3]{2 x^2+1}}\right)}{\sqrt[3]{x} \sqrt[3]{2 x^2+1}}-\frac{\sqrt[3]{3} \sqrt[3]{2 x^3+x} \log \left(\frac{3^{2/3} x^{4/3}}{\left(2 x^2+1\right)^{2/3}}+\frac{\sqrt[3]{3} x^{2/3}}{\sqrt[3]{2 x^2+1}}+1\right)}{2 \sqrt[3]{x} \sqrt[3]{2 x^2+1}}+\frac{3^{5/6} \sqrt[3]{2 x^3+x} \tan ^{-1}\left(\frac{2 x^{2/3}}{\sqrt[6]{3} \sqrt[3]{2 x^2+1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x} \sqrt[3]{2 x^2+1}}","\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*(x + 2*x^3)^(1/3))/(8*x^3) + (15*(x + 2*x^3)^(1/3))/(4*x) + (3^(5/6)*(x + 2*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(2/3))/(3^(1/6)*(1 + 2*x^2)^(1/3))])/(x^(1/3)*(1 + 2*x^2)^(1/3)) + (3^(1/3)*(x + 2*x^3)^(1/3)*Log[1 - (3^(1/3)*x^(2/3))/(1 + 2*x^2)^(1/3)])/(x^(1/3)*(1 + 2*x^2)^(1/3)) - (3^(1/3)*(x + 2*x^3)^(1/3)*Log[1 + (3^(2/3)*x^(4/3))/(1 + 2*x^2)^(2/3) + (3^(1/3)*x^(2/3))/(1 + 2*x^2)^(1/3)])/(2*x^(1/3)*(1 + 2*x^2)^(1/3))","A",13,13,27,0.4815,1,"{2056, 580, 583, 12, 466, 465, 494, 292, 31, 634, 617, 204, 628}"
2008,1,151,0,0.0979942,"\int \frac{\left(-b+a^3 x^3\right) \sqrt[3]{b+a^3 x^3}}{x^5} \, dx","Int[((-b + a^3*x^3)*(b + a^3*x^3)^(1/3))/x^5,x]","-\frac{a^3 \sqrt[3]{a^3 x^3+b}}{x}+\frac{\left(a^3 x^3+b\right)^{4/3}}{4 x^4}-\frac{1}{3} a^4 \log \left(1-\frac{a x}{\sqrt[3]{a^3 x^3+b}}\right)-\frac{a^4 \tan ^{-1}\left(\frac{\frac{2 a x}{\sqrt[3]{a^3 x^3+b}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{1}{6} a^4 \log \left(\frac{a x}{\sqrt[3]{a^3 x^3+b}}+\frac{a^2 x^2}{\left(a^3 x^3+b\right)^{2/3}}+1\right)","\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,"-((a^3*(b + a^3*x^3)^(1/3))/x) + (b + a^3*x^3)^(4/3)/(4*x^4) - (a^4*ArcTan[(1 + (2*a*x)/(b + a^3*x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - (a^4*Log[1 - (a*x)/(b + a^3*x^3)^(1/3)])/3 + (a^4*Log[1 + (a^2*x^2)/(b + a^3*x^3)^(2/3) + (a*x)/(b + a^3*x^3)^(1/3)])/6","A",9,9,28,0.3214,1,"{451, 277, 331, 292, 31, 634, 617, 204, 628}"
2009,1,539,0,0.8443267,"\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","Int[(-3*b + a*x^2)/((3*b - 2*a*x^2)^(1/4)*(3*b - 2*a*x^2 + 3*x^4)),x]","\frac{\sqrt[4]{b} \left(\sqrt{a^2-9 b}+a\right) \sqrt{\frac{a x^2}{b}} \Pi \left(-\frac{3 \sqrt{b}}{\sqrt{-2 a^2-2 \sqrt{a^2-9 b} a+9 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{3 b-2 a x^2}}{\sqrt[4]{3} \sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} 3^{3/4} x \sqrt{-2 a \sqrt{a^2-9 b}-2 a^2+9 b}}-\frac{\sqrt[4]{b} \left(\sqrt{a^2-9 b}+a\right) \sqrt{\frac{a x^2}{b}} \Pi \left(\frac{3 \sqrt{b}}{\sqrt{-2 a^2-2 \sqrt{a^2-9 b} a+9 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{3 b-2 a x^2}}{\sqrt[4]{3} \sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} 3^{3/4} x \sqrt{-2 a \sqrt{a^2-9 b}-2 a^2+9 b}}+\frac{\sqrt[4]{b} \left(a-\sqrt{a^2-9 b}\right) \sqrt{\frac{a x^2}{b}} \Pi \left(-\frac{3 \sqrt{b}}{\sqrt{-2 a^2+2 \sqrt{a^2-9 b} a+9 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{3 b-2 a x^2}}{\sqrt[4]{3} \sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} 3^{3/4} x \sqrt{2 a \sqrt{a^2-9 b}-2 a^2+9 b}}-\frac{\sqrt[4]{b} \left(a-\sqrt{a^2-9 b}\right) \sqrt{\frac{a x^2}{b}} \Pi \left(\frac{3 \sqrt{b}}{\sqrt{-2 a^2+2 \sqrt{a^2-9 b} a+9 b}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{3 b-2 a x^2}}{\sqrt[4]{3} \sqrt[4]{b}}\right)\right|-1\right)}{\sqrt{2} 3^{3/4} x \sqrt{2 a \sqrt{a^2-9 b}-2 a^2+9 b}}","-\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,"((a + Sqrt[a^2 - 9*b])*b^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[(-3*Sqrt[b])/Sqrt[-2*a^2 - 2*a*Sqrt[a^2 - 9*b] + 9*b], ArcSin[(3*b - 2*a*x^2)^(1/4)/(3^(1/4)*b^(1/4))], -1])/(Sqrt[2]*3^(3/4)*Sqrt[-2*a^2 - 2*a*Sqrt[a^2 - 9*b] + 9*b]*x) - ((a + Sqrt[a^2 - 9*b])*b^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[(3*Sqrt[b])/Sqrt[-2*a^2 - 2*a*Sqrt[a^2 - 9*b] + 9*b], ArcSin[(3*b - 2*a*x^2)^(1/4)/(3^(1/4)*b^(1/4))], -1])/(Sqrt[2]*3^(3/4)*Sqrt[-2*a^2 - 2*a*Sqrt[a^2 - 9*b] + 9*b]*x) + ((a - Sqrt[a^2 - 9*b])*b^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[(-3*Sqrt[b])/Sqrt[-2*a^2 + 2*a*Sqrt[a^2 - 9*b] + 9*b], ArcSin[(3*b - 2*a*x^2)^(1/4)/(3^(1/4)*b^(1/4))], -1])/(Sqrt[2]*3^(3/4)*Sqrt[-2*a^2 + 2*a*Sqrt[a^2 - 9*b] + 9*b]*x) - ((a - Sqrt[a^2 - 9*b])*b^(1/4)*Sqrt[(a*x^2)/b]*EllipticPi[(3*Sqrt[b])/Sqrt[-2*a^2 + 2*a*Sqrt[a^2 - 9*b] + 9*b], ArcSin[(3*b - 2*a*x^2)^(1/4)/(3^(1/4)*b^(1/4))], -1])/(Sqrt[2]*3^(3/4)*Sqrt[-2*a^2 + 2*a*Sqrt[a^2 - 9*b] + 9*b]*x)","C",10,4,41,0.09756,1,"{1692, 399, 490, 1218}"
2010,0,0,0,3.4564975,"\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","Int[((-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,"(4*b*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[-1/5, 3/4, 4/5, -((a*x^5)/b)])/(x*(b + a*x^5)^(3/4)) - (2*c^3*x*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[1/5, 3/4, 6/5, -((a*x^5)/b)])/(a^2*(b + a*x^5)^(3/4)) + (c^2*x^2*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, -((a*x^5)/b)])/(a*(b + a*x^5)^(3/4)) - (2*c*x^3*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[3/5, 3/4, 8/5, -((a*x^5)/b)])/(3*(b + a*x^5)^(3/4)) + (a*x^4*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[3/4, 4/5, 9/5, -((a*x^5)/b)])/(4*(b + a*x^5)^(3/4)) + (2*b*c^3*Defer[Int][1/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/a^2 - (2*b*c^2*Defer[Int][x/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/a + 10*b*c*Defer[Int][x^2/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x] + (2*c^4*Defer[Int][x^4/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/a^2","F",0,0,0,0,-1,"{}"
2011,0,0,0,0.9341018,"\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","Int[((-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,"Hypergeometric2F1[-5/6, -2/3, 1/6, -x^6]/(5*x^5) - (3*Hypergeometric2F1[-2/3, -1/3, 2/3, -x^6])/(2*x^2) + x*Hypergeometric2F1[-2/3, 1/6, 7/6, -x^6] - 2*Defer[Int][(1 + x^6)^(2/3)/(1 + x), x] + 2*(1 + I*Sqrt[3])*Defer[Int][(1 + x^6)^(2/3)/(-1 - I*Sqrt[3] + 2*x), x] + 2*(1 - I*Sqrt[3])*Defer[Int][(1 + x^6)^(2/3)/(-1 + I*Sqrt[3] + 2*x), x]","F",0,0,0,0,-1,"{}"
2012,0,0,0,2.2829975,"\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","Int[((-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,"(2*a*x^3)/(3*(b + Sqrt[b^2 + a*x^2])^(3/2)) + (2*b*x)/Sqrt[b + Sqrt[b^2 + a*x^2]] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[-a]*x), x] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[-a]*x), x] - a*b^2*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b - a*x)^2, x] - a*b^2*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b + a*x)^2, x]","F",0,0,0,0,-1,"{}"
2013,1,148,0,0.1708616,"\int \frac{\left(2+x^3\right) \left(1+2 x^3\right)^{2/3}}{x^6 \left(-1+x^3\right)} \, dx","Int[((2 + x^3)*(1 + 2*x^3)^(2/3))/(x^6*(-1 + x^3)),x]","3^{2/3} \log \left(1-\frac{\sqrt[3]{3} x}{\sqrt[3]{2 x^3+1}}\right)-3 \sqrt[6]{3} \tan ^{-1}\left(\frac{2 x}{\sqrt[6]{3} \sqrt[3]{2 x^3+1}}+\frac{1}{\sqrt{3}}\right)+\frac{2 \left(2 x^3+1\right)^{2/3}}{5 x^5}+\frac{23 \left(2 x^3+1\right)^{2/3}}{10 x^2}-\frac{1}{2} 3^{2/3} \log \left(\frac{\sqrt[3]{3} x}{\sqrt[3]{2 x^3+1}}+\frac{3^{2/3} x^2}{\left(2 x^3+1\right)^{2/3}}+1\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,"(2*(1 + 2*x^3)^(2/3))/(5*x^5) + (23*(1 + 2*x^3)^(2/3))/(10*x^2) - 3*3^(1/6)*ArcTan[1/Sqrt[3] + (2*x)/(3^(1/6)*(1 + 2*x^3)^(1/3))] + 3^(2/3)*Log[1 - (3^(1/3)*x)/(1 + 2*x^3)^(1/3)] - (3^(2/3)*Log[1 + (3^(2/3)*x^2)/(1 + 2*x^3)^(2/3) + (3^(1/3)*x)/(1 + 2*x^3)^(1/3)])/2","A",10,10,27,0.3704,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2014,0,0,0,0.4277686,"\int \frac{\left(-4+x^2\right) \sqrt[4]{2-x^2-2 x^4}}{x^2 \left(-2+x^2\right)} \, dx","Int[((-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,"(-2*(2 - x^2 - 2*x^4)^(1/4)*AppellF1[-1/2, -1/4, -1/4, 1/2, (-4*x^2)/(1 + Sqrt[17]), (-4*x^2)/(1 - Sqrt[17])])/(x*(1 + (4*x^2)/(1 - Sqrt[17]))^(1/4)*(1 + (4*x^2)/(1 + Sqrt[17]))^(1/4)) + Defer[Int][(2 - x^2 - 2*x^4)^(1/4)/(2 - x^2), x]","F",0,0,0,0,-1,"{}"
2015,0,0,0,0.1167026,"\int \frac{1}{(1+x) \left(-2+2 x+x^2-x^4\right)^{3/2}} \, dx","Int[1/((1 + x)*(-2 + 2*x + x^2 - x^4)^(3/2)),x]","\int \frac{1}{(1+x) \left(-2+2 x+x^2-x^4\right)^{3/2}} \, dx","-\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,"Defer[Int][1/((1 + x)*(-2 + 2*x + x^2 - x^4)^(3/2)), x]","F",0,0,0,0,-1,"{}"
2016,0,0,0,1.1683906,"\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","Int[((-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,"(3*(1 + 2*x^4)^(2/3))/(4*x^2) + (6*x^2)/(1 - Sqrt[3] - (1 + 2*x^4)^(1/3)) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 + 2*x^4)^(1/3))*Sqrt[(1 + (1 + 2*x^4)^(1/3) + (1 + 2*x^4)^(2/3))/(1 - Sqrt[3] - (1 + 2*x^4)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + 2*x^4)^(1/3))/(1 - Sqrt[3] - (1 + 2*x^4)^(1/3))], -7 + 4*Sqrt[3]])/(2*x^2*Sqrt[-((1 - (1 + 2*x^4)^(1/3))/(1 - Sqrt[3] - (1 + 2*x^4)^(1/3))^2)]) + (Sqrt[2]*3^(3/4)*(1 - (1 + 2*x^4)^(1/3))*Sqrt[(1 + (1 + 2*x^4)^(1/3) + (1 + 2*x^4)^(2/3))/(1 - Sqrt[3] - (1 + 2*x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + 2*x^4)^(1/3))/(1 - Sqrt[3] - (1 + 2*x^4)^(1/3))], -7 + 4*Sqrt[3]])/(x^2*Sqrt[-((1 - (1 + 2*x^4)^(1/3))/(1 - Sqrt[3] - (1 + 2*x^4)^(1/3))^2)]) - (3*Defer[Int][(1 + 2*x^4)^(2/3)/(2 - x^3 + 4*x^4), x])/2 + 8*Defer[Int][(x*(1 + 2*x^4)^(2/3))/(2 - x^3 + 4*x^4), x]","F",0,0,0,0,-1,"{}"
2017,1,132,0,0.5713877,"\int \frac{-b+a x^3}{x^6 \left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Int[(-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(b-a x^3\right)^2 \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}{a x^3+b}\right)-32 a x^3 \left(b-a x^3\right) \, _2F_1\left(2,2;\frac{5}{4};\frac{2 a x^3}{a x^3+b}\right)\right)}{21 b^2 x^5 \Gamma \left(\frac{1}{4}\right) \left(a x^3+b\right)^2 \sqrt[4]{a x^4-b x}}","-\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,"-1/21*((b - a*x^3)^2*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^5*(b + a*x^3)^2*(-(b*x) + a*x^4)^(1/4)*Gamma[1/4])","C",5,5,36,0.1389,0,"{2056, 466, 465, 511, 510}"
2018,1,277,0,0.4176206,"\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","Int[((-1 + x^3)^(2/3)*(4 + 4*x^3 + x^6))/(x^9*(1 + x^3)),x]","-\frac{2}{3} 2^{2/3} \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)+\frac{\log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{x^3-1}}\right)}{12 \sqrt[3]{2}}+\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}-\frac{\left(x^3-1\right)^{2/3}}{2 x^8}+\frac{11 \left(x^3-1\right)^{2/3}}{20 x^5}-\frac{79 \left(x^3-1\right)^{2/3}}{80 x^2}+\frac{1}{3} 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)-\frac{\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)}{24 \sqrt[3]{2}}","-\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,"-1/2*(-1 + x^3)^(2/3)/x^8 + (11*(-1 + x^3)^(2/3))/(20*x^5) - (79*(-1 + x^3)^(2/3))/(80*x^2) - ArcTan[(1 + (2*2^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(4*2^(1/3)*Sqrt[3]) + (2*2^(2/3)*ArcTan[(1 + (2*2^(1/3)*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] + Log[1 - (2^(1/3)*x)/(-1 + x^3)^(1/3)]/(12*2^(1/3)) - (2*2^(2/3)*Log[1 - (2^(1/3)*x)/(-1 + x^3)^(1/3)])/3 - Log[1 + (2^(2/3)*x^2)/(-1 + x^3)^(2/3) + (2^(1/3)*x)/(-1 + x^3)^(1/3)]/(24*2^(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)])/3","A",23,12,30,0.4000,0,"{28, 586, 580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2019,0,0,0,0.7098362,"\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","Int[((1 + x^3)^(2/3)*(-1 - 2*x^3 + 2*x^6))/(x^9*(-1 + x^3)),x]","\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","-\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,"-1/2*(1 + x^3)^(2/3)/x^2 - (1 + x^3)^(5/3)/(8*x^8) - (21*(1 + x^3)^(5/3))/(40*x^5) + ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]/2 - Defer[Int][(1 + x^3)^(2/3)/(-1 + x), x]/3 + ((1 - I*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(1 - I*Sqrt[3] + 2*x), x])/3 + ((1 + I*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
2020,1,601,0,1.0606365,"\int \frac{1}{\sqrt[4]{-b^4+a^4 x^4} \left(-b^8-c x^4+a^8 x^8\right)} \, dx","Int[1/((-b^4 + a^4*x^4)^(1/4)*(-b^8 - c*x^4 + a^8*x^8)),x]","-\frac{a^7 \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)}{\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^4-c}}-\frac{a^7 \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)}{\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^4+c}}-\frac{a^7 \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)}{\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^4-c}}-\frac{a^7 \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)}{\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^4+c}}","-\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))])/(Sqrt[4*a^8*b^8 + c^2]*(-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))) - (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))])/(Sqrt[4*a^8*b^8 + c^2]*(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)) - (a^7*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))])/(Sqrt[4*a^8*b^8 + c^2]*(-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)) - (a^7*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))])/(Sqrt[4*a^8*b^8 + c^2]*(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))","B",9,5,39,0.1282,1,"{1428, 377, 212, 208, 205}"
2021,1,601,0,0.4641213,"\int \frac{1}{\sqrt[4]{-b^4+a^4 x^4} \left(-b^8-c x^4+a^8 x^8\right)} \, dx","Int[1/((-b^4 + a^4*x^4)^(1/4)*(-b^8 - c*x^4 + a^8*x^8)),x]","-\frac{a^7 \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)}{\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^4-c}}-\frac{a^7 \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)}{\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^4+c}}-\frac{a^7 \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)}{\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^4-c}}-\frac{a^7 \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)}{\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^4+c}}","-\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))])/(Sqrt[4*a^8*b^8 + c^2]*(-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))) - (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))])/(Sqrt[4*a^8*b^8 + c^2]*(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)) - (a^7*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))])/(Sqrt[4*a^8*b^8 + c^2]*(-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)) - (a^7*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))])/(Sqrt[4*a^8*b^8 + c^2]*(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))","B",9,5,39,0.1282,1,"{1428, 377, 212, 208, 205}"
2022,0,0,0,0.2075338,"\int \frac{x-\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","Int[(x - Sqrt[1 + x^2])/Sqrt[1 + Sqrt[1 + x^2]],x]","\int \frac{x-\sqrt{1+x^2}}{\sqrt{1+\sqrt{1+x^2}}} \, dx","\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,"-2*Sqrt[1 + Sqrt[1 + x^2]] + (2*(1 + Sqrt[1 + x^2])^(3/2))/3 - Defer[Int][Sqrt[1 + x^2]/Sqrt[1 + Sqrt[1 + x^2]], x]","F",0,0,0,0,-1,"{}"
2023,1,141,0,0.6107372,"\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","Int[((-4 + x^3)*(-2 + x^3)*(-1 + x^3)^(2/3))/(x^9*(-2 + 3*x^3)),x]","-\frac{15 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{3 x^3}{2}\right)}{2 \left(1-x^3\right)^{2/3}}+\frac{5}{2} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3-1\right)^{5/3}}{2 x^8}-\frac{9 \left(x^3-1\right)^{5/3}}{10 x^5}+\frac{5 \left(x^3-1\right)^{2/3}}{2 x^2}","\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,"(5*(-1 + x^3)^(2/3))/(2*x^2) - (-1 + x^3)^(5/3)/(2*x^8) - (9*(-1 + x^3)^(5/3))/(10*x^5) - (15*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, (3*x^3)/2])/(2*(1 - x^3)^(2/3)) - (5*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] + (5*Log[-x + (-1 + x^3)^(1/3)])/2","C",9,7,32,0.2188,0,"{6725, 271, 264, 277, 239, 430, 429}"
2024,1,303,0,0.2315539,"\int \frac{1}{(-1+x) \left(-2 x^2-3 x^3+x^4\right)^{3/2}} \, dx","Int[1/((-1 + x)*(-2*x^2 - 3*x^3 + x^4)^(3/2)),x]","\frac{x (13-3 x)}{17 \sqrt{x^4-3 x^3-2 x^2}}+\frac{13-3 x}{17 x \sqrt{x^4-3 x^3-2 x^2}}+\frac{13-3 x}{17 \sqrt{x^4-3 x^3-2 x^2}}-\frac{(10-x) x}{34 \sqrt{x^4-3 x^3-2 x^2}}-\frac{69 \left(-x^2+3 x+2\right)}{136 x \sqrt{x^4-3 x^3-2 x^2}}+\frac{373 \left(-x^2+3 x+2\right)}{544 \sqrt{x^4-3 x^3-2 x^2}}+\frac{x \sqrt{x^2-3 x-2} \tan ^{-1}\left(\frac{x+7}{4 \sqrt{x^2-3 x-2}}\right)}{8 \sqrt{x^4-3 x^3-2 x^2}}-\frac{119 x \sqrt{x^2-3 x-2} \tan ^{-1}\left(\frac{3 x+4}{2 \sqrt{2} \sqrt{x^2-3 x-2}}\right)}{64 \sqrt{2} \sqrt{x^4-3 x^3-2 x^2}}","\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,"(13 - 3*x)/(17*Sqrt[-2*x^2 - 3*x^3 + x^4]) + (13 - 3*x)/(17*x*Sqrt[-2*x^2 - 3*x^3 + x^4]) + ((13 - 3*x)*x)/(17*Sqrt[-2*x^2 - 3*x^3 + x^4]) - ((10 - x)*x)/(34*Sqrt[-2*x^2 - 3*x^3 + x^4]) + (373*(2 + 3*x - x^2))/(544*Sqrt[-2*x^2 - 3*x^3 + x^4]) - (69*(2 + 3*x - x^2))/(136*x*Sqrt[-2*x^2 - 3*x^3 + x^4]) + (x*Sqrt[-2 - 3*x + x^2]*ArcTan[(7 + x)/(4*Sqrt[-2 - 3*x + x^2])])/(8*Sqrt[-2*x^2 - 3*x^3 + x^4]) - (119*x*Sqrt[-2 - 3*x + x^2]*ArcTan[(4 + 3*x)/(2*Sqrt[2]*Sqrt[-2 - 3*x + x^2])])/(64*Sqrt[2]*Sqrt[-2*x^2 - 3*x^3 + x^4])","B",20,8,24,0.3333,1,"{2056, 960, 740, 12, 724, 204, 834, 806}"
2025,1,351,0,0.4012312,"\int \frac{1}{\left(b+2 a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Int[1/((b + 2*a*x^3)*(b*x + a*x^4)^(1/4)),x]","-\frac{\sqrt[4]{x} \sqrt[4]{a x^3+b} \log \left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b}}-\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}+1\right)}{3 \sqrt{2} \sqrt[4]{a} b \sqrt[4]{a x^4+b x}}+\frac{\sqrt[4]{x} \sqrt[4]{a x^3+b} \log \left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b}}+\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}+1\right)}{3 \sqrt{2} \sqrt[4]{a} b \sqrt[4]{a x^4+b x}}-\frac{\sqrt{2} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} b \sqrt[4]{a x^4+b x}}+\frac{\sqrt{2} \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}+1\right)}{3 \sqrt[4]{a} b \sqrt[4]{a x^4+b x}}","\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,"-1/3*(Sqrt[2]*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[1 - (Sqrt[2]*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(a^(1/4)*b*(b*x + a*x^4)^(1/4)) + (Sqrt[2]*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[1 + (Sqrt[2]*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*b*(b*x + a*x^4)^(1/4)) - (x^(1/4)*(b + a*x^3)^(1/4)*Log[1 + (Sqrt[a]*x^(3/2))/Sqrt[b + a*x^3] - (Sqrt[2]*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*Sqrt[2]*a^(1/4)*b*(b*x + a*x^4)^(1/4)) + (x^(1/4)*(b + a*x^3)^(1/4)*Log[1 + (Sqrt[a]*x^(3/2))/Sqrt[b + a*x^3] + (Sqrt[2]*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*Sqrt[2]*a^(1/4)*b*(b*x + a*x^4)^(1/4))","B",13,10,24,0.4167,1,"{2056, 466, 465, 377, 211, 1165, 628, 1162, 617, 204}"
2026,0,0,0,1.5962138,"\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","Int[((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,"(3*Hypergeometric2F1[-1/7, 2/3, 6/7, x^7])/(2*x) - (x^2*Hypergeometric2F1[2/7, 2/3, 9/7, x^7])/4 - (x^6*Hypergeometric2F1[2/3, 6/7, 13/7, x^7])/3 - (7*Defer[Int][x/((1 - x^7)^(2/3)*(-4 + x^3 + 4*x^7)), x])/2 + Defer[Int][x^4/((1 - x^7)^(2/3)*(-4 + x^3 + 4*x^7)), x]/2","F",0,0,0,0,-1,"{}"
2027,0,0,0,3.5586491,"\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","Int[((-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]","\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","\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,"((-2*I)*Sqrt[2]*Sqrt[1 + 2*x^2 + x^4]*ArcTan[(-1)^(3/4)*x])/(1 + x^2) - (2*Sqrt[2]*Sqrt[1 + 2*x^2 + x^4]*ArcTanh[(-1)^(3/4)*x])/(1 + x^2) - (5*Sqrt[1 + 2*x^2 + x^4]*Defer[Int][(1 - x^2 + x^4 - x^6 + x^8)^(-1), x])/(1 + x^2) + (5*Sqrt[1 + 2*x^2 + x^4]*Defer[Int][x^2/(1 - x^2 + x^4 - x^6 + x^8), x])/(1 + x^2) - (5*Sqrt[1 + 2*x^2 + x^4]*Defer[Int][x^4/(1 - x^2 + x^4 - x^6 + x^8), x])/(1 + x^2) + (5*Sqrt[1 + 2*x^2 + x^4]*Defer[Int][x^6/(1 - x^2 + x^4 - x^6 + x^8), x])/(1 + x^2)","F",0,0,0,0,-1,"{}"
2028,0,0,0,0.1628471,"\int \frac{1}{x^2 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[1/(x^2*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\int \frac{1}{x^2 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","-\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,"Defer[Int][1/(x^2*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",0,0,0,0,-1,"{}"
2029,1,218,0,0.2321859,"\int \frac{\sqrt[4]{-b+a x^3}}{x} \, dx","Int[(-b + a*x^3)^(1/4)/x,x]","\frac{4}{3} \sqrt[4]{a x^3-b}+\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{3 \sqrt{2}}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{3 \sqrt{2}}+\frac{1}{3} \sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)-\frac{1}{3} \sqrt{2} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\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,"(4*(-b + a*x^3)^(1/4))/3 + (Sqrt[2]*b^(1/4)*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/3 - (Sqrt[2]*b^(1/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/3 + (b^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(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]])/(3*Sqrt[2])","A",12,9,17,0.5294,1,"{266, 50, 63, 211, 1165, 628, 1162, 617, 204}"
2030,1,218,0,0.2011869,"\int \frac{\left(-b+a x^3\right)^{3/4}}{x} \, dx","Int[(-b + a*x^3)^(3/4)/x,x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{3 \sqrt{2}}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{3 \sqrt{2}}+\frac{1}{3} \sqrt{2} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \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]{a x^3-b}}{\sqrt[4]{b}}+1\right)+\frac{4}{9} \left(a x^3-b\right)^{3/4}","\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 + (Sqrt[2]*b^(3/4)*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/3 - (Sqrt[2]*b^(3/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/3 - (b^(3/4)*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)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(3*Sqrt[2])","A",12,9,17,0.5294,1,"{266, 50, 63, 297, 1162, 617, 204, 1165, 628}"
2031,0,0,0,1.4101382,"\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","Int[((-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,"(-3*(-1 + x^4)^(2/3))/(8*x^2) + (3*x^2)/(2*(1 + Sqrt[3] + (-1 + x^4)^(1/3))) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(4*x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) + (3^(3/4)*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(Sqrt[2]*x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) - (3*(-1 + x^4)^(2/3)*Hypergeometric2F1[-5/4, -2/3, -1/4, x^4])/(10*x^5*(1 - x^4)^(2/3)) - ((-1 + x^4)^(2/3)*Hypergeometric2F1[-2/3, -1/4, 3/4, x^4])/(2*x*(1 - x^4)^(2/3)) + (3*Defer[Int][(-1 + x^4)^(2/3)/(-2 - x^3 + 2*x^4), x])/4 - 2*Defer[Int][(x*(-1 + x^4)^(2/3))/(-2 - x^3 + 2*x^4), x]","F",0,0,0,0,-1,"{}"
2032,1,218,0,0.2105013,"\int \frac{\left(-b+a x^4\right)^{3/4}}{x} \, dx","Int[(-b + a*x^4)^(3/4)/x,x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{4 \sqrt{2}}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{4 \sqrt{2}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}\right)}{2 \sqrt{2}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2}}+\frac{1}{3} \left(a x^4-b\right)^{3/4}","\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[1 - (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)])/(2*Sqrt[2]) - (b^(3/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)])/(2*Sqrt[2]) - (b^(3/4)*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)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]])/(4*Sqrt[2])","A",12,9,17,0.5294,1,"{266, 50, 63, 297, 1162, 617, 204, 1165, 628}"
2033,0,0,0,37.2291263,"\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","Int[(-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,"(12*a*b*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^2*(-b + x^4)^(5/4))/((-a + x^4)^(1/4)*(-(a*b^3*d) + 3*a*b^2*(1 + b/(3*a))*d*x^4 - 3*a*b*(1 + b/a)*d*x^8 + (1 + (a + 3*b)*d)*x^12 - d*x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(1/4) + (8*b*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^6*(-b + x^4)^(5/4))/((-a + x^4)^(1/4)*(a*b^3*d - 3*a*b^2*(1 + b/(3*a))*d*x^4 + 3*a*b*(1 + b/a)*d*x^8 - (1 + (a + 3*b)*d)*x^12 + d*x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(1/4) + (4*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^10*(-b + x^4)^(5/4))/((-a + x^4)^(1/4)*(a*b^3*d - 3*a*b^2*(1 + b/(3*a))*d*x^4 + 3*a*b*(1 + b/a)*d*x^8 - (1 + (a + 3*b)*d)*x^12 + d*x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(1/4)","F",0,0,0,0,-1,"{}"
2034,1,218,0,0.2090227,"\int \frac{\left(-b+a x^5\right)^{3/4}}{x} \, dx","Int[(-b + a*x^5)^(3/4)/x,x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{5 \sqrt{2}}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{5 \sqrt{2}}+\frac{1}{5} \sqrt{2} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \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]{a x^5-b}}{\sqrt[4]{b}}+1\right)+\frac{4}{15} \left(a x^5-b\right)^{3/4}","\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 + (Sqrt[2]*b^(3/4)*ArcTan[1 - (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/5 - (Sqrt[2]*b^(3/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/5 - (b^(3/4)*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)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(5*Sqrt[2])","A",12,9,17,0.5294,1,"{266, 50, 63, 297, 1162, 617, 204, 1165, 628}"
2035,1,143,0,0.3464171,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^3+x^6\right)}{x^9 \left(-2+x^3\right)} \, dx","Int[((-1 + x^3)^(2/3)*(4 + x^3 + x^6))/(x^9*(-2 + x^3)),x]","-\frac{5 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{2}\right)}{8 \left(1-x^3\right)^{2/3}}+\frac{5}{8} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{5 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{\left(x^3-1\right)^{5/3}}{4 x^8}-\frac{9 \left(x^3-1\right)^{5/3}}{20 x^5}+\frac{5 \left(x^3-1\right)^{2/3}}{8 x^2}","\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,"(5*(-1 + x^3)^(2/3))/(8*x^2) - (-1 + x^3)^(5/3)/(4*x^8) - (9*(-1 + x^3)^(5/3))/(20*x^5) - (5*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/2])/(8*(1 - x^3)^(2/3)) - (5*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/(4*Sqrt[3]) + (5*Log[-x + (-1 + x^3)^(1/3)])/8","C",9,7,28,0.2500,0,"{6725, 271, 264, 277, 239, 430, 429}"
2036,0,0,0,1.9411999,"\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","Int[(-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,"3*Defer[Int][(1 + 2*x + 2*x^3 + x^6)^(-1/3), x] - Defer[Int][1/((1 + x)*(1 + 2*x + 2*x^3 + x^6)^(1/3)), x] - 5*Defer[Int][1/((1 + x - x^2 + x^3 - x^4 + x^5)*(1 + 2*x + 2*x^3 + x^6)^(1/3)), x] - 4*Defer[Int][x/((1 + x - x^2 + x^3 - x^4 + x^5)*(1 + 2*x + 2*x^3 + x^6)^(1/3)), x] + 3*Defer[Int][x^2/((1 + x - x^2 + x^3 - x^4 + x^5)*(1 + 2*x + 2*x^3 + x^6)^(1/3)), x] - 2*Defer[Int][x^3/((1 + x - x^2 + x^3 - x^4 + x^5)*(1 + 2*x + 2*x^3 + x^6)^(1/3)), x] + Defer[Int][x^4/((1 + x - x^2 + x^3 - x^4 + x^5)*(1 + 2*x + 2*x^3 + x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
2037,1,218,0,0.2053384,"\int \frac{\left(-b+a x^6\right)^{3/4}}{x} \, dx","Int[(-b + a*x^6)^(3/4)/x,x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)}{6 \sqrt{2}}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)}{6 \sqrt{2}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}\right)}{3 \sqrt{2}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}+1\right)}{3 \sqrt{2}}+\frac{2}{9} \left(a x^6-b\right)^{3/4}","\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[1 - (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)])/(3*Sqrt[2]) - (b^(3/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)])/(3*Sqrt[2]) - (b^(3/4)*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)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^6)^(1/4) + Sqrt[-b + a*x^6]])/(6*Sqrt[2])","A",12,9,17,0.5294,1,"{266, 50, 63, 297, 1162, 617, 204, 1165, 628}"
2038,1,271,0,0.2284558,"\int \frac{b+a x^6}{\sqrt[3]{-x+x^3}} \, dx","Int[(b + a*x^6)/(-x + x^3)^(1/3),x]","\frac{7}{27} a \left(x^3-x\right)^{2/3}+\frac{1}{6} a \left(x^3-x\right)^{2/3} x^4+\frac{7}{36} a \left(x^3-x\right)^{2/3} x^2-\frac{7 a \sqrt[3]{x^2-1} \sqrt[3]{x} \log \left(x^{2/3}-\sqrt[3]{x^2-1}\right)}{54 \sqrt[3]{x^3-x}}+\frac{7 a \sqrt[3]{x^2-1} \sqrt[3]{x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{27 \sqrt{3} \sqrt[3]{x^3-x}}-\frac{3 b \sqrt[3]{x^2-1} \sqrt[3]{x} \log \left(x^{2/3}-\sqrt[3]{x^2-1}\right)}{4 \sqrt[3]{x^3-x}}+\frac{\sqrt{3} b \sqrt[3]{x^2-1} \sqrt[3]{x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{x^3-x}}","\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,"(7*a*(-x + x^3)^(2/3))/27 + (7*a*x^2*(-x + x^3)^(2/3))/36 + (a*x^4*(-x + x^3)^(2/3))/6 + (7*a*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(27*Sqrt[3]*(-x + x^3)^(1/3)) + (Sqrt[3]*b*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*(-x + x^3)^(1/3)) - (7*a*x^(1/3)*(-1 + x^2)^(1/3)*Log[x^(2/3) - (-1 + x^2)^(1/3)])/(54*(-x + x^3)^(1/3)) - (3*b*x^(1/3)*(-1 + x^2)^(1/3)*Log[x^(2/3) - (-1 + x^2)^(1/3)])/(4*(-x + x^3)^(1/3))","A",13,6,19,0.3158,1,"{2053, 2011, 329, 275, 239, 2024}"
2039,0,0,0,0.4999484,"\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","Int[(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]","\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","\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,"Defer[Int][(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]","F",0,0,0,0,-1,"{}"
2040,1,246,0,0.341075,"\int \frac{1}{\sqrt[3]{x^2 (-a+x)} (a+(-1+d) x)} \, dx","Int[1/((x^2*(-a + x))^(1/3)*(a + (-1 + d)*x)),x]","\frac{\left(-a^2 x\right)^{2/3} \sqrt[3]{a^2 (x-a)} \log (a+(d-1) x)}{2 a^3 \sqrt[3]{d} \sqrt[3]{x^2 (x-a)}}-\frac{3 \left(-a^2 x\right)^{2/3} \sqrt[3]{a^2 (x-a)} \log \left(-\frac{\sqrt[3]{\frac{2}{3}} \sqrt[3]{a^2 (x-a)}}{\sqrt[3]{d}}-\sqrt[3]{\frac{2}{3}} \sqrt[3]{-a^2 x}\right)}{2 a^3 \sqrt[3]{d} \sqrt[3]{x^2 (x-a)}}-\frac{\sqrt{3} \left(-a^2 x\right)^{2/3} \sqrt[3]{a^2 (x-a)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{a^2 (x-a)}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{-a^2 x}}\right)}{a^3 \sqrt[3]{d} \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,"-((Sqrt[3]*(-(a^2*x))^(2/3)*(a^2*(-a + x))^(1/3)*ArcTan[1/Sqrt[3] - (2*(a^2*(-a + x))^(1/3))/(Sqrt[3]*d^(1/3)*(-(a^2*x))^(1/3))])/(a^3*d^(1/3)*(x^2*(-a + x))^(1/3))) + ((-(a^2*x))^(2/3)*(a^2*(-a + x))^(1/3)*Log[a + (-1 + d)*x])/(2*a^3*d^(1/3)*(x^2*(-a + x))^(1/3)) - (3*(-(a^2*x))^(2/3)*(a^2*(-a + x))^(1/3)*Log[-((2/3)^(1/3)*(-(a^2*x))^(1/3)) - ((2/3)^(1/3)*(a^2*(-a + x))^(1/3))/d^(1/3)])/(2*a^3*d^(1/3)*(x^2*(-a + x))^(1/3))","A",3,3,23,0.1304,1,"{2081, 2077, 91}"
2041,0,0,0,2.6822465,"\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","Int[((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,"Defer[Int][(2 + x - x^3 - x^4)^(2/3)/(1 - x), x] + 6*Defer[Int][(2 + x - x^3 - x^4)^(2/3)/x^6, x] + 2*Defer[Int][(2 + x - x^3 - x^4)^(2/3)/x^5, x] + 3*Defer[Int][(2 + x - x^3 - x^4)^(2/3)/x^3, x] + Defer[Int][(2 + x - x^3 - x^4)^(2/3)/x^2, x]/2 + Defer[Int][(2 + x - x^3 - x^4)^(2/3)/x, x]/4 - Defer[Int][(2 + x - x^3 - x^4)^(2/3)/(2 + x), x]/4 + (1 - I*Sqrt[3])*Defer[Int][(2 + x - x^3 - x^4)^(2/3)/(1 - I*Sqrt[3] + 2*x), x] + (1 + I*Sqrt[3])*Defer[Int][(2 + x - x^3 - x^4)^(2/3)/(1 + I*Sqrt[3] + 2*x), x]","F",0,0,0,0,-1,"{}"
2042,0,0,0,1.440039,"\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","Int[((-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,"(9*(1 + x^4)^(2/3))/(16*x^2) + (9*x^2)/(4*(1 - Sqrt[3] - (1 + x^4)^(1/3))) - (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(8*x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (3*3^(3/4)*(1 - (1 + x^4)^(1/3))*Sqrt[(1 + (1 + x^4)^(1/3) + (1 + x^4)^(2/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))], -7 + 4*Sqrt[3]])/(2*Sqrt[2]*x^2*Sqrt[-((1 - (1 + x^4)^(1/3))/(1 - Sqrt[3] - (1 + x^4)^(1/3))^2)]) + (3*Hypergeometric2F1[-5/4, -2/3, -1/4, -x^4])/(10*x^5) - Hypergeometric2F1[-2/3, -1/4, 3/4, -x^4]/(2*x) - (9*Defer[Int][(1 + x^4)^(2/3)/(4 - x^3 + 4*x^4), x])/8 + 6*Defer[Int][(x*(1 + x^4)^(2/3))/(4 - x^3 + 4*x^4), x]","F",0,0,0,0,-1,"{}"
2043,0,0,0,2.2254521,"\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","Int[((-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,"(-9*(x - x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x*(1 - x^6 + x^9)^(1/3))/(1 + x^3 - x^6 + x^9)^2, x], x, x^(2/3)])/(2*x^(1/3)*(1 - x^4 + x^6)^(1/3)) - (3*(x - x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - x^6 + x^9)^(1/3))/(1 + x^3 - x^6 + x^9)^2, x], x, x^(2/3)])/(x^(1/3)*(1 - x^4 + x^6)^(1/3)) + (3*(x - x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^7*(1 - x^6 + x^9)^(1/3))/(1 + x^3 - x^6 + x^9)^2, x], x, x^(2/3)])/(2*x^(1/3)*(1 - x^4 + x^6)^(1/3)) + (3*(x - x^5 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x*(1 - x^6 + x^9)^(1/3))/(1 + x^3 - x^6 + x^9), x], x, x^(2/3)])/(x^(1/3)*(1 - x^4 + x^6)^(1/3))","F",0,0,0,0,-1,"{}"
2044,0,0,0,2.376384,"\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","Int[(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,"2*b*Defer[Int][1/((-b + a*x^3)^(1/4)*(b - a*x^3 - x^4)), x] - (a*Defer[Int][x^3/((-b + a*x^3)^(1/4)*(-b + a*x^3 - x^4)), x])/2 - 2*b*Defer[Int][1/((-b + a*x^3)^(1/4)*(b - a*x^3 + x^4)), x] + (a*Defer[Int][x^3/((-b + a*x^3)^(1/4)*(-b + a*x^3 + x^4)), x])/2","F",0,0,0,0,-1,"{}"
2045,0,0,0,1.0762926,"\int \frac{\sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}}}{1+x^2} \, dx","Int[(Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]])/(1 + x^2),x]","\int \frac{\sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}}}{1+x^2} \, dx","\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,"(I/2)*Defer[Int][(Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]])/(I - x), x] + (I/2)*Defer[Int][(Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]])/(I + x), x]","F",0,0,0,0,-1,"{}"
2046,1,192,0,0.3641274,"\int \frac{x}{\left(x^2 (-a+x)\right)^{2/3} (a+(-1+d) x)} \, dx","Int[x/((x^2*(-a + x))^(2/3)*(a + (-1 + d)*x)),x]","\frac{x^{4/3} (x-a)^{2/3} \log (a-(1-d) x)}{2 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}-\frac{3 x^{4/3} (x-a)^{2/3} \log \left(\sqrt[3]{d} \sqrt[3]{x}-\sqrt[3]{x-a}\right)}{2 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}-\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{a d^{2/3} \left(-\left(x^2 (a-x)\right)\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,"-((Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*d^(1/3)*x^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(a*d^(2/3)*(-((a - x)*x^2))^(2/3))) + (x^(4/3)*(-a + x)^(2/3)*Log[a - (1 - d)*x])/(2*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) - (3*x^(4/3)*(-a + x)^(2/3)*Log[d^(1/3)*x^(1/3) - (-a + x)^(1/3)])/(2*a*d^(2/3)*(-((a - x)*x^2))^(2/3))","A",2,2,24,0.08333,1,"{6719, 91}"
2047,1,627,0,0.8633495,"\int \frac{2+x+x^2}{\left(3+2 x+x^2\right) \sqrt[3]{x^2+x^3}} \, dx","Int[(2 + x + x^2)/((3 + 2*x + x^2)*(x^2 + x^3)^(1/3)),x]","-\frac{i x^{2/3} \sqrt[3]{x+1} \log \left(-2 x-2 \left(1-i \sqrt{2}\right)\right)}{2\ 2^{5/6} \left(2+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log (x)}{2 \sqrt[3]{x^3+x^2}}+\frac{i x^{2/3} \sqrt[3]{x+1} \log \left(2 x+2 \left(1+i \sqrt{2}\right)\right)}{2\ 2^{5/6} \left(2-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}-\frac{3 i x^{2/3} \sqrt[3]{x+1} \log \left(-\sqrt[3]{x}+\sqrt[3]{\frac{1}{2} \left(2-i \sqrt{2}\right)} \sqrt[3]{x+1}\right)}{2\ 2^{5/6} \left(2-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}+\frac{3 i x^{2/3} \sqrt[3]{x+1} \log \left(-\sqrt[3]{x}+\sqrt[3]{\frac{1}{2} \left(2+i \sqrt{2}\right)} \sqrt[3]{x+1}\right)}{2\ 2^{5/6} \left(2+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}-\frac{3 x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3+x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3+x^2}}-\frac{i \sqrt{3} x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} \sqrt[3]{2-i \sqrt{2}} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}\right)}{2^{5/6} \left(2-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}+\frac{i \sqrt{3} x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} \sqrt[3]{2+i \sqrt{2}} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}\right)}{2^{5/6} \left(2+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}","\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,"-((Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(x^2 + x^3)^(1/3)) - (I*Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(2 - I*Sqrt[2])^(1/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(5/6)*(2 - I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) + (I*Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(2 + I*Sqrt[2])^(1/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(5/6)*(2 + I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - ((I/2)*x^(2/3)*(1 + x)^(1/3)*Log[-2*(1 - I*Sqrt[2]) - 2*x])/(2^(5/6)*(2 + I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[x])/(2*(x^2 + x^3)^(1/3)) + ((I/2)*x^(2/3)*(1 + x)^(1/3)*Log[2*(1 + I*Sqrt[2]) + 2*x])/(2^(5/6)*(2 - I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - (((3*I)/2)*x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + ((2 - I*Sqrt[2])/2)^(1/3)*(1 + x)^(1/3)])/(2^(5/6)*(2 - I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) + (((3*I)/2)*x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + ((2 + I*Sqrt[2])/2)^(1/3)*(1 + x)^(1/3)])/(2^(5/6)*(2 + I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - (3*x^(2/3)*(1 + x)^(1/3)*Log[-1 + (1 + x)^(1/3)/x^(1/3)])/(2*(x^2 + x^3)^(1/3))","C",12,6,28,0.2143,1,"{2056, 6728, 59, 911, 105, 91}"
2048,1,627,0,0.6986885,"\int \frac{2+x+x^2}{\left(3+2 x+x^2\right) \sqrt[3]{x^2+x^3}} \, dx","Int[(2 + x + x^2)/((3 + 2*x + x^2)*(x^2 + x^3)^(1/3)),x]","-\frac{i x^{2/3} \sqrt[3]{x+1} \log \left(-2 x-2 \left(1-i \sqrt{2}\right)\right)}{2\ 2^{5/6} \left(2+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log (x)}{2 \sqrt[3]{x^3+x^2}}+\frac{i x^{2/3} \sqrt[3]{x+1} \log \left(2 x+2 \left(1+i \sqrt{2}\right)\right)}{2\ 2^{5/6} \left(2-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}-\frac{3 i x^{2/3} \sqrt[3]{x+1} \log \left(-\sqrt[3]{x}+\sqrt[3]{\frac{1}{2} \left(2-i \sqrt{2}\right)} \sqrt[3]{x+1}\right)}{2\ 2^{5/6} \left(2-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}+\frac{3 i x^{2/3} \sqrt[3]{x+1} \log \left(-\sqrt[3]{x}+\sqrt[3]{\frac{1}{2} \left(2+i \sqrt{2}\right)} \sqrt[3]{x+1}\right)}{2\ 2^{5/6} \left(2+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}-\frac{3 x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3+x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3+x^2}}-\frac{i \sqrt{3} x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} \sqrt[3]{2-i \sqrt{2}} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}\right)}{2^{5/6} \left(2-i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}+\frac{i \sqrt{3} x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2^{2/3} \sqrt[3]{2+i \sqrt{2}} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}\right)}{2^{5/6} \left(2+i \sqrt{2}\right)^{2/3} \sqrt[3]{x^3+x^2}}","\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,"-((Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(x^2 + x^3)^(1/3)) - (I*Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(2 - I*Sqrt[2])^(1/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(5/6)*(2 - I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) + (I*Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(2 + I*Sqrt[2])^(1/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(5/6)*(2 + I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - ((I/2)*x^(2/3)*(1 + x)^(1/3)*Log[-2*(1 - I*Sqrt[2]) - 2*x])/(2^(5/6)*(2 + I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[x])/(2*(x^2 + x^3)^(1/3)) + ((I/2)*x^(2/3)*(1 + x)^(1/3)*Log[2*(1 + I*Sqrt[2]) + 2*x])/(2^(5/6)*(2 - I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - (((3*I)/2)*x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + ((2 - I*Sqrt[2])/2)^(1/3)*(1 + x)^(1/3)])/(2^(5/6)*(2 - I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) + (((3*I)/2)*x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + ((2 + I*Sqrt[2])/2)^(1/3)*(1 + x)^(1/3)])/(2^(5/6)*(2 + I*Sqrt[2])^(2/3)*(x^2 + x^3)^(1/3)) - (3*x^(2/3)*(1 + x)^(1/3)*Log[-1 + (1 + x)^(1/3)/x^(1/3)])/(2*(x^2 + x^3)^(1/3))","C",12,6,28,0.2143,1,"{2056, 6728, 59, 911, 105, 91}"
2049,1,284,0,1.7118941,"\int \frac{b-c x+a x^2}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Int[(b - c*x + a*x^2)/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{\sqrt{x} \left(\frac{c}{\sqrt{a}}+2 \sqrt{b}\right) \sqrt{\frac{a x^2}{b}+1} \Pi \left(\frac{\sqrt{-a}}{\sqrt{a}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{-a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{a x^3+b x}}-\frac{\sqrt{x} \left(2 \sqrt{b}-\frac{c}{\sqrt{a}}\right) \sqrt{\frac{a x^2}{b}+1} \Pi \left(\frac{\sqrt{a}}{\sqrt{-a}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{-a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{a x^3+b x}}+\frac{\sqrt{x} \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}","-\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,"(Sqrt[x]*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]) - ((2*Sqrt[b] + c/Sqrt[a])*Sqrt[x]*Sqrt[1 + (a*x^2)/b]*EllipticPi[Sqrt[-a]/Sqrt[a], ArcSin[((-a)^(1/4)*Sqrt[x])/b^(1/4)], -1])/((-a)^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]) - ((2*Sqrt[b] - c/Sqrt[a])*Sqrt[x]*Sqrt[1 + (a*x^2)/b]*EllipticPi[Sqrt[a]/Sqrt[-a], ArcSin[((-a)^(1/4)*Sqrt[x])/b^(1/4)], -1])/((-a)^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3])","C",13,7,36,0.1944,0,"{2056, 6725, 329, 220, 933, 168, 537}"
2050,1,284,0,1.5049661,"\int \frac{b+c x+a x^2}{\left(-b+a x^2\right) \sqrt{b x+a x^3}} \, dx","Int[(b + c*x + a*x^2)/((-b + a*x^2)*Sqrt[b*x + a*x^3]),x]","-\frac{\sqrt{x} \left(2 \sqrt{b}-\frac{c}{\sqrt{a}}\right) \sqrt{\frac{a x^2}{b}+1} \Pi \left(\frac{\sqrt{-a}}{\sqrt{a}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{-a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{a x^3+b x}}-\frac{\sqrt{x} \left(\frac{c}{\sqrt{a}}+2 \sqrt{b}\right) \sqrt{\frac{a x^2}{b}+1} \Pi \left(\frac{\sqrt{a}}{\sqrt{-a}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{-a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{a x^3+b x}}+\frac{\sqrt{x} \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}","-\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,"(Sqrt[x]*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]) - ((2*Sqrt[b] - c/Sqrt[a])*Sqrt[x]*Sqrt[1 + (a*x^2)/b]*EllipticPi[Sqrt[-a]/Sqrt[a], ArcSin[((-a)^(1/4)*Sqrt[x])/b^(1/4)], -1])/((-a)^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]) - ((2*Sqrt[b] + c/Sqrt[a])*Sqrt[x]*Sqrt[1 + (a*x^2)/b]*EllipticPi[Sqrt[a]/Sqrt[-a], ArcSin[((-a)^(1/4)*Sqrt[x])/b^(1/4)], -1])/((-a)^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3])","C",13,7,35,0.2000,0,"{2056, 6725, 329, 220, 933, 168, 537}"
2051,1,695,0,0.9027858,"\int \frac{(1+x) \sqrt[4]{-x^3+x^4}}{1-x+x^2} \, dx","Int[((1 + x)*(-x^3 + x^4)^(1/4))/(1 - x + x^2),x]","\frac{1}{2} \left(1+i \sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{\left(7+i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\left(7-i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{\left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{\left(7+i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\left(7-i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{\left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}","-\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,"((1 - I*Sqrt[3])*(-x^3 + x^4)^(1/4))/2 + ((1 + I*Sqrt[3])*(-x^3 + x^4)^(1/4))/2 + ((7 - I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((7 + I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(-1 + x)^(1/4))])/((-1 + x)^(1/4)*x^(3/4)) + ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + ((7 - I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((7 + I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(-1 + x)^(1/4))])/((-1 + x)^(1/4)*x^(3/4)) - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","C",25,13,27,0.4815,0,"{2056, 6728, 101, 157, 63, 240, 212, 206, 203, 93, 298, 205, 208}"
2052,1,695,0,0.7343893,"\int \frac{(1+x) \sqrt[4]{-x^3+x^4}}{1-x+x^2} \, dx","Int[((1 + x)*(-x^3 + x^4)^(1/4))/(1 - x + x^2),x]","\frac{1}{2} \left(1+i \sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{1}{2} \left(1-i \sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{\left(7+i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\left(7-i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{\left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{\left(7+i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\left(7-i \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{\left(-\frac{-\sqrt{3}+i}{\sqrt{3}+i}\right)^{3/4} \left(\sqrt{3}+i\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}","-\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,"((1 - I*Sqrt[3])*(-x^3 + x^4)^(1/4))/2 + ((1 + I*Sqrt[3])*(-x^3 + x^4)^(1/4))/2 + ((7 - I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((7 + I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(-1 + x)^(1/4))])/((-1 + x)^(1/4)*x^(3/4)) + ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + ((7 - I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((7 + I*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*(-1 + x)^(1/4))])/((-1 + x)^(1/4)*x^(3/4)) - ((-((I - Sqrt[3])/(I + Sqrt[3])))^(3/4)*(I + Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[((-((I - Sqrt[3])/(I + Sqrt[3])))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","C",25,13,27,0.4815,0,"{2056, 6728, 101, 157, 63, 240, 212, 206, 203, 93, 298, 205, 208}"
2053,1,1003,0,3.8374083,"\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","Int[((b - a*x^6)^(1/3)*(b + a*x^6))/(x^2*(-b + c*x^3 + a*x^6)),x]","-\frac{2 a^2 c \sqrt[3]{b-a x^6} F_1\left(\frac{5}{6};1,-\frac{1}{3};\frac{11}{6};\frac{2 a^2 x^6}{c^2-\sqrt{c^2+4 a b} c+2 a b},\frac{a x^6}{b}\right) x^5}{5 \sqrt{c^2+4 a b} \left(c^2-\sqrt{c^2+4 a b} c+2 a b\right) \sqrt[3]{1-\frac{a x^6}{b}}}-\frac{2 a^2 \left(1-\frac{c}{\sqrt{c^2+4 a b}}\right) \sqrt[3]{b-a x^6} F_1\left(\frac{5}{6};1,-\frac{1}{3};\frac{11}{6};\frac{2 a^2 x^6}{c^2-\sqrt{c^2+4 a b} c+2 a b},\frac{a x^6}{b}\right) x^5}{5 \left(2 a b+c \left(c-\sqrt{c^2+4 a b}\right)\right) \sqrt[3]{1-\frac{a x^6}{b}}}-\frac{2 a^2 \left(\frac{c}{\sqrt{c^2+4 a b}}+1\right) \sqrt[3]{b-a x^6} F_1\left(\frac{5}{6};1,-\frac{1}{3};\frac{11}{6};\frac{2 a^2 x^6}{2 a b+c \left(c+\sqrt{c^2+4 a b}\right)},\frac{a x^6}{b}\right) x^5}{5 \left(2 a b+c \left(c+\sqrt{c^2+4 a b}\right)\right) \sqrt[3]{1-\frac{a x^6}{b}}}+\frac{2 a^2 c \sqrt[3]{b-a x^6} F_1\left(\frac{5}{6};1,-\frac{1}{3};\frac{11}{6};\frac{2 a^2 x^6}{2 a b+c \left(c+\sqrt{c^2+4 a b}\right)},\frac{a x^6}{b}\right) x^5}{5 \sqrt{c^2+4 a b} \left(2 a b+c \left(c+\sqrt{c^2+4 a b}\right)\right) \sqrt[3]{1-\frac{a x^6}{b}}}-\frac{a \sqrt[3]{b-a x^6} F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{2 a^2 x^6}{c^2-\sqrt{c^2+4 a b} c+2 a b},\frac{a x^6}{b}\right) x^2}{\sqrt{c^2+4 a b} \sqrt[3]{1-\frac{a x^6}{b}}}-\frac{a c \left(1-\frac{c}{\sqrt{c^2+4 a b}}\right) \sqrt[3]{b-a x^6} F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{2 a^2 x^6}{c^2-\sqrt{c^2+4 a b} c+2 a b},\frac{a x^6}{b}\right) x^2}{2 \left(2 a b+c \left(c-\sqrt{c^2+4 a b}\right)\right) \sqrt[3]{1-\frac{a x^6}{b}}}+\frac{a \sqrt[3]{b-a x^6} F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{2 a^2 x^6}{2 a b+c \left(c+\sqrt{c^2+4 a b}\right)},\frac{a x^6}{b}\right) x^2}{\sqrt{c^2+4 a b} \sqrt[3]{1-\frac{a x^6}{b}}}-\frac{a c \left(\frac{c}{\sqrt{c^2+4 a b}}+1\right) \sqrt[3]{b-a x^6} F_1\left(\frac{1}{3};1,-\frac{1}{3};\frac{4}{3};\frac{2 a^2 x^6}{2 a b+c \left(c+\sqrt{c^2+4 a b}\right)},\frac{a x^6}{b}\right) x^2}{2 \left(2 a b+c \left(c+\sqrt{c^2+4 a b}\right)\right) \sqrt[3]{1-\frac{a x^6}{b}}}+\frac{\sqrt[3]{b-a x^6} \, _2F_1\left(-\frac{1}{3},-\frac{1}{6};\frac{5}{6};\frac{a x^6}{b}\right)}{\sqrt[3]{1-\frac{a x^6}{b}} x}","-\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,"-((a*x^2*(b - a*x^6)^(1/3)*AppellF1[1/3, 1, -1/3, 4/3, (2*a^2*x^6)/(2*a*b + c^2 - c*Sqrt[4*a*b + c^2]), (a*x^6)/b])/(Sqrt[4*a*b + c^2]*(1 - (a*x^6)/b)^(1/3))) - (a*c*(1 - c/Sqrt[4*a*b + c^2])*x^2*(b - a*x^6)^(1/3)*AppellF1[1/3, 1, -1/3, 4/3, (2*a^2*x^6)/(2*a*b + c^2 - c*Sqrt[4*a*b + c^2]), (a*x^6)/b])/(2*(2*a*b + c*(c - Sqrt[4*a*b + c^2]))*(1 - (a*x^6)/b)^(1/3)) + (a*x^2*(b - a*x^6)^(1/3)*AppellF1[1/3, 1, -1/3, 4/3, (2*a^2*x^6)/(2*a*b + c*(c + Sqrt[4*a*b + c^2])), (a*x^6)/b])/(Sqrt[4*a*b + c^2]*(1 - (a*x^6)/b)^(1/3)) - (a*c*(1 + c/Sqrt[4*a*b + c^2])*x^2*(b - a*x^6)^(1/3)*AppellF1[1/3, 1, -1/3, 4/3, (2*a^2*x^6)/(2*a*b + c*(c + Sqrt[4*a*b + c^2])), (a*x^6)/b])/(2*(2*a*b + c*(c + Sqrt[4*a*b + c^2]))*(1 - (a*x^6)/b)^(1/3)) - (2*a^2*c*x^5*(b - a*x^6)^(1/3)*AppellF1[5/6, 1, -1/3, 11/6, (2*a^2*x^6)/(2*a*b + c^2 - c*Sqrt[4*a*b + c^2]), (a*x^6)/b])/(5*Sqrt[4*a*b + c^2]*(2*a*b + c^2 - c*Sqrt[4*a*b + c^2])*(1 - (a*x^6)/b)^(1/3)) - (2*a^2*(1 - c/Sqrt[4*a*b + c^2])*x^5*(b - a*x^6)^(1/3)*AppellF1[5/6, 1, -1/3, 11/6, (2*a^2*x^6)/(2*a*b + c^2 - c*Sqrt[4*a*b + c^2]), (a*x^6)/b])/(5*(2*a*b + c*(c - Sqrt[4*a*b + c^2]))*(1 - (a*x^6)/b)^(1/3)) + (2*a^2*c*x^5*(b - a*x^6)^(1/3)*AppellF1[5/6, 1, -1/3, 11/6, (2*a^2*x^6)/(2*a*b + c*(c + Sqrt[4*a*b + c^2])), (a*x^6)/b])/(5*Sqrt[4*a*b + c^2]*(2*a*b + c*(c + Sqrt[4*a*b + c^2]))*(1 - (a*x^6)/b)^(1/3)) - (2*a^2*(1 + c/Sqrt[4*a*b + c^2])*x^5*(b - a*x^6)^(1/3)*AppellF1[5/6, 1, -1/3, 11/6, (2*a^2*x^6)/(2*a*b + c*(c + Sqrt[4*a*b + c^2])), (a*x^6)/b])/(5*(2*a*b + c*(c + Sqrt[4*a*b + c^2]))*(1 - (a*x^6)/b)^(1/3)) + ((b - a*x^6)^(1/3)*Hypergeometric2F1[-1/3, -1/6, 5/6, (a*x^6)/b])/(x*(1 - (a*x^6)/b)^(1/3))","C",38,9,39,0.2308,0,"{6728, 365, 364, 1562, 465, 430, 429, 511, 510}"
2054,0,0,0,1.2354869,"\int \frac{x^2 \left(4+7 x^3\right)}{\sqrt[3]{x+x^4} \left(-1+x^4+x^7\right)} \, dx","Int[(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,"(12*x^(1/3)*(1 + x^3)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 + x^9)^(1/3)*(-1 + x^12 + x^21)), x], x, x^(1/3)])/(x + x^4)^(1/3) + (21*x^(1/3)*(1 + x^3)^(1/3)*Defer[Subst][Defer[Int][x^16/((1 + x^9)^(1/3)*(-1 + x^12 + x^21)), x], x, x^(1/3)])/(x + x^4)^(1/3)","F",0,0,0,0,-1,"{}"
2055,1,459,0,1.1463156,"\int \frac{2 d+c x^4}{\sqrt[4]{-b+a x^4} \left(-2 f+e x^8\right)} \, dx","Int[(2*d + c*x^4)/((-b + a*x^4)^(1/4)*(-2*f + e*x^8)),x]","-\frac{\left(c \sqrt{f}+\sqrt{2} d \sqrt{e}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{2} a \sqrt{f}-b \sqrt{e}}}{\sqrt[8]{2} \sqrt[8]{f} \sqrt[4]{a x^4-b}}\right)}{4\ 2^{3/8} \sqrt{e} f^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{f}-b \sqrt{e}}}-\frac{\left(\sqrt{2} d \sqrt{e}-c \sqrt{f}\right) \tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{2} a \sqrt{f}+b \sqrt{e}}}{\sqrt[8]{2} \sqrt[8]{f} \sqrt[4]{a x^4-b}}\right)}{4\ 2^{3/8} \sqrt{e} f^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{f}+b \sqrt{e}}}-\frac{\left(c \sqrt{f}+\sqrt{2} d \sqrt{e}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{2} a \sqrt{f}-b \sqrt{e}}}{\sqrt[8]{2} \sqrt[8]{f} \sqrt[4]{a x^4-b}}\right)}{4\ 2^{3/8} \sqrt{e} f^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{f}-b \sqrt{e}}}-\frac{\left(\sqrt{2} d \sqrt{e}-c \sqrt{f}\right) \tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{2} a \sqrt{f}+b \sqrt{e}}}{\sqrt[8]{2} \sqrt[8]{f} \sqrt[4]{a x^4-b}}\right)}{4\ 2^{3/8} \sqrt{e} f^{7/8} \sqrt[4]{\sqrt{2} a \sqrt{f}+b \sqrt{e}}}","\frac{\text{RootSum}\left[-2 \text{$\#$1}^8 f+4 \text{$\#$1}^4 a f-2 a^2 f+b^2 e\&,\frac{-2 \text{$\#$1}^4 d \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 \text{$\#$1}^4 d \log (x)+b c \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)+2 a d \log \left(\sqrt[4]{a x^4-b}-\text{$\#$1} x\right)-2 a d \log (x)-b c \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{16 f}",1,"-1/4*((Sqrt[2]*d*Sqrt[e] + c*Sqrt[f])*ArcTan[((-(b*Sqrt[e]) + Sqrt[2]*a*Sqrt[f])^(1/4)*x)/(2^(1/8)*f^(1/8)*(-b + a*x^4)^(1/4))])/(2^(3/8)*Sqrt[e]*(-(b*Sqrt[e]) + Sqrt[2]*a*Sqrt[f])^(1/4)*f^(7/8)) - ((Sqrt[2]*d*Sqrt[e] - c*Sqrt[f])*ArcTan[((b*Sqrt[e] + Sqrt[2]*a*Sqrt[f])^(1/4)*x)/(2^(1/8)*f^(1/8)*(-b + a*x^4)^(1/4))])/(4*2^(3/8)*Sqrt[e]*(b*Sqrt[e] + Sqrt[2]*a*Sqrt[f])^(1/4)*f^(7/8)) - ((Sqrt[2]*d*Sqrt[e] + c*Sqrt[f])*ArcTanh[((-(b*Sqrt[e]) + Sqrt[2]*a*Sqrt[f])^(1/4)*x)/(2^(1/8)*f^(1/8)*(-b + a*x^4)^(1/4))])/(4*2^(3/8)*Sqrt[e]*(-(b*Sqrt[e]) + Sqrt[2]*a*Sqrt[f])^(1/4)*f^(7/8)) - ((Sqrt[2]*d*Sqrt[e] - c*Sqrt[f])*ArcTanh[((b*Sqrt[e] + Sqrt[2]*a*Sqrt[f])^(1/4)*x)/(2^(1/8)*f^(1/8)*(-b + a*x^4)^(1/4))])/(4*2^(3/8)*Sqrt[e]*(b*Sqrt[e] + Sqrt[2]*a*Sqrt[f])^(1/4)*f^(7/8))","B",10,5,34,0.1471,1,"{6725, 377, 212, 208, 205}"
2056,1,217,0,0.8264503,"\int \frac{\sqrt{1+x} \left(1+x^2\right)}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(Sqrt[1 + x]*(1 + x^2))/((-1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}+\sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\left(4-\sqrt{2}\right) \sqrt{x+1}+2 \left(1+\sqrt{2}\right)}{2 \sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{x+\sqrt{x+1}}}\right)+\frac{7}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{\left(4+\sqrt{2}\right) \sqrt{x+1}+2 \left(1-\sqrt{2}\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+\sqrt{x+1}}}\right)","-16 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3-18 \text{$\#$1}^2+20 \text{$\#$1}+25\&,\frac{\text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2-9 \text{$\#$1}+5}\&\right]+\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}-\frac{7}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"(-3*Sqrt[x + Sqrt[1 + x]])/2 + Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]] + Sqrt[2*(1 + Sqrt[2])]*ArcTan[(2*(1 + Sqrt[2]) + (4 - Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[2*(-1 + Sqrt[2])]*Sqrt[x + Sqrt[1 + x]])] + (7*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 - Sqrt[2*(-1 + Sqrt[2])]*ArcTanh[(2*(1 - Sqrt[2]) + (4 + Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[2*(1 + Sqrt[2])]*Sqrt[x + Sqrt[1 + x]])]","A",13,9,33,0.2727,1,"{1586, 6725, 742, 640, 621, 206, 984, 724, 204}"
2057,1,217,0,0.5666004,"\int \frac{\sqrt{1+x} \left(1+x^2\right)}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(Sqrt[1 + x]*(1 + x^2))/((-1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","\sqrt{x+1} \sqrt{x+\sqrt{x+1}}-\frac{3}{2} \sqrt{x+\sqrt{x+1}}+\sqrt{2 \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\left(4-\sqrt{2}\right) \sqrt{x+1}+2 \left(1+\sqrt{2}\right)}{2 \sqrt{2 \left(\sqrt{2}-1\right)} \sqrt{x+\sqrt{x+1}}}\right)+\frac{7}{4} \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\sqrt{2 \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\frac{\left(4+\sqrt{2}\right) \sqrt{x+1}+2 \left(1-\sqrt{2}\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+\sqrt{x+1}}}\right)","-16 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3-18 \text{$\#$1}^2+20 \text{$\#$1}+25\&,\frac{\text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2-9 \text{$\#$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*(1 + Sqrt[2]) + (4 - Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[2*(-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*(1 - Sqrt[2]) + (4 + Sqrt[2])*Sqrt[1 + x])/(2*Sqrt[2*(1 + Sqrt[2])]*Sqrt[x + Sqrt[1 + x]])]","A",13,9,33,0.2727,1,"{1586, 6725, 742, 640, 621, 206, 984, 724, 204}"
2058,1,200,0,0.1433377,"\int \frac{\sqrt{x-\sqrt{-1+x^2}}}{x^2} \, dx","Int[Sqrt[x - Sqrt[-1 + x^2]]/x^2,x]","-\frac{2 \left(x-\sqrt{x^2-1}\right)^{3/2}}{\left(x-\sqrt{x^2-1}\right)^2+1}+\frac{\log \left(-\sqrt{x^2-1}-\sqrt{2} \sqrt{x-\sqrt{x^2-1}}+x+1\right)}{2 \sqrt{2}}-\frac{\log \left(-\sqrt{x^2-1}+\sqrt{2} \sqrt{x-\sqrt{x^2-1}}+x+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{x-\sqrt{x^2-1}}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{x-\sqrt{x^2-1}}+1\right)}{\sqrt{2}}","\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,"(-2*(x - Sqrt[-1 + x^2])^(3/2))/(1 + (x - Sqrt[-1 + x^2])^2) - ArcTan[1 - Sqrt[2]*Sqrt[x - Sqrt[-1 + x^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]]]/(2*Sqrt[2]) - Log[1 + x - Sqrt[-1 + x^2] + Sqrt[2]*Sqrt[x - Sqrt[-1 + x^2]]]/(2*Sqrt[2])","A",12,9,21,0.4286,1,"{2119, 457, 329, 297, 1162, 617, 204, 1165, 628}"
2059,1,147,0,0.2343084,"\int \frac{\left(a x+\sqrt{-b x+a^2 x^2}\right)^{3/4}}{\sqrt{-b x+a^2 x^2}} \, dx","Int[(a*x + Sqrt[-(b*x) + a^2*x^2])^(3/4)/Sqrt[-(b*x) + a^2*x^2],x]","\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}}","\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,"(4*(a*x + Sqrt[-(b*x) + a^2*x^2])^(3/4))/(3*a) + (2^(1/4)*b^(3/4)*ArcTan[(2^(1/4)*a^(1/4)*(a*x + Sqrt[-(b*x) + a^2*x^2])^(1/4))/b^(1/4)])/a^(7/4) - (2^(1/4)*b^(3/4)*ArcTanh[(2^(1/4)*a^(1/4)*(a*x + Sqrt[-(b*x) + a^2*x^2])^(1/4))/b^(1/4)])/a^(7/4)","A",6,6,41,0.1463,1,"{2121, 50, 63, 298, 205, 208}"
2060,1,708,0,0.8481579,"\int \frac{(1+x) \sqrt[4]{x^3+x^4}}{x \left(-1+x^3\right)} \, dx","Int[((1 + x)*(x^3 + x^4)^(1/4))/(x*(-1 + x^3)),x]","\frac{1}{3} (-1)^{2/3} \sqrt[4]{x^4+x^3}-\frac{1}{3} \sqrt[3]{-1} \sqrt[4]{x^4+x^3}+\frac{1}{3} \sqrt[4]{x^4+x^3}-\frac{(-1)^{2/3} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[3]{-1} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}+\frac{4 \sqrt[4]{2} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}-\frac{2^{3/4} \sqrt[4]{1-i \sqrt{3}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}+\frac{2 (-1)^{2/3} \left(1+(-1)^{2/3}\right)^{5/4} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}+\frac{(-1)^{2/3} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[3]{-1} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{6 x^{3/4} \sqrt[4]{x+1}}-\frac{4 \sqrt[4]{2} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}+\frac{2^{3/4} \sqrt[4]{1-i \sqrt{3}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}-\frac{2 (-1)^{2/3} \left(1+(-1)^{2/3}\right)^{5/4} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{3 x^{3/4} \sqrt[4]{x+1}}","\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,"(x^3 + x^4)^(1/4)/3 - ((-1)^(1/3)*(x^3 + x^4)^(1/4))/3 + ((-1)^(2/3)*(x^3 + x^4)^(1/4))/3 - ((x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(6*x^(3/4)*(1 + x)^(1/4)) + ((-1)^(1/3)*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(6*x^(3/4)*(1 + x)^(1/4)) - ((-1)^(2/3)*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(6*x^(3/4)*(1 + x)^(1/4)) + (4*2^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(3*x^(3/4)*(1 + x)^(1/4)) - (2^(3/4)*(1 - I*Sqrt[3])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(3*x^(3/4)*(1 + x)^(1/4)) + (2*(-1)^(2/3)*(1 + (-1)^(2/3))^(5/4)*(x^3 + x^4)^(1/4)*ArcTan[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(3*x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(6*x^(3/4)*(1 + x)^(1/4)) - ((-1)^(1/3)*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(6*x^(3/4)*(1 + x)^(1/4)) + ((-1)^(2/3)*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(6*x^(3/4)*(1 + x)^(1/4)) - (4*2^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(3*x^(3/4)*(1 + x)^(1/4)) + (2^(3/4)*(1 - I*Sqrt[3])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(3*x^(3/4)*(1 + x)^(1/4)) - (2*(-1)^(2/3)*(1 + (-1)^(2/3))^(5/4)*(x^3 + x^4)^(1/4)*ArcTanh[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(3*x^(3/4)*(1 + x)^(1/4))","C",54,10,25,0.4000,1,"{2056, 6725, 105, 50, 63, 331, 298, 203, 206, 93}"
2061,1,239,0,0.4394493,"\int \frac{\sqrt[4]{-b x^3+a x^4} \left(-d+c x^4\right)}{x^4} \, dx","Int[((-(b*x^3) + a*x^4)^(1/4)*(-d + c*x^4))/x^4,x]","\frac{3 b^2 c x^{9/4} (a x-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{16 a^{7/4} \left(a x^4-b x^3\right)^{3/4}}-\frac{3 b^2 c x^{9/4} (a x-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{16 a^{7/4} \left(a x^4-b x^3\right)^{3/4}}-\frac{16 a d \left(a x^4-b x^3\right)^{5/4}}{45 b^2 x^5}+\frac{1}{2} c x \sqrt[4]{a x^4-b x^3}-\frac{b c \sqrt[4]{a x^4-b x^3}}{8 a}-\frac{4 d \left(a x^4-b x^3\right)^{5/4}}{9 b x^6}","\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,"-1/8*(b*c*(-(b*x^3) + a*x^4)^(1/4))/a + (c*x*(-(b*x^3) + a*x^4)^(1/4))/2 - (4*d*(-(b*x^3) + a*x^4)^(5/4))/(9*b*x^6) - (16*a*d*(-(b*x^3) + a*x^4)^(5/4))/(45*b^2*x^5) + (3*b^2*c*x^(9/4)*(-b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(16*a^(7/4)*(-(b*x^3) + a*x^4)^(3/4)) - (3*b^2*c*x^(9/4)*(-b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(16*a^(7/4)*(-(b*x^3) + a*x^4)^(3/4))","A",12,11,29,0.3793,1,"{2052, 2004, 2024, 2032, 63, 331, 298, 203, 206, 2016, 2014}"
2062,1,162,0,0.2035158,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(4+x^3\right)} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^3))/(x^6*(4 + x^3)),x]","-\frac{\log \left(2^{2/3}-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)}{16 \sqrt[3]{6}}+\frac{\sqrt[6]{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{16 \sqrt[3]{2}}-\frac{\left(x^3+1\right)^{2/3}}{10 x^5}-\frac{13 \left(x^3+1\right)^{2/3}}{80 x^2}+\frac{\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)}{32 \sqrt[3]{6}}","-\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^3)^(2/3)/x^5 - (13*(1 + x^3)^(2/3))/(80*x^2) + (3^(1/6)*ArcTan[(1 + (6^(1/3)*x)/(1 + x^3)^(1/3))/Sqrt[3]])/(16*2^(1/3)) - Log[2^(2/3) - (3^(1/3)*x)/(1 + x^3)^(1/3)]/(16*6^(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)]/(32*6^(1/3))","A",10,10,25,0.4000,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2063,1,158,0,0.1786395,"\int \frac{\left(-1+x^3\right) \left(1+3 x^3\right)^{2/3}}{x^6 \left(1+x^3\right)} \, dx","Int[((-1 + x^3)*(1 + 3*x^3)^(2/3))/(x^6*(1 + x^3)),x]","-\frac{2}{3} 2^{2/3} \log \left(1-\frac{\sqrt[3]{2} x}{\sqrt[3]{3 x^3+1}}\right)+\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} x}{\sqrt[3]{3 x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\left(3 x^3+1\right)^{2/3}}{5 x^5}-\frac{2 \left(3 x^3+1\right)^{2/3}}{5 x^2}+\frac{1}{3} 2^{2/3} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{3 x^3+1}}+\frac{2^{2/3} x^2}{\left(3 x^3+1\right)^{2/3}}+1\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 + 3*x^3)^(2/3)/(5*x^5) - (2*(1 + 3*x^3)^(2/3))/(5*x^2) + (2*2^(2/3)*ArcTan[(1 + (2*2^(1/3)*x)/(1 + 3*x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - (2*2^(2/3)*Log[1 - (2^(1/3)*x)/(1 + 3*x^3)^(1/3)])/3 + (2^(2/3)*Log[1 + (2^(2/3)*x^2)/(1 + 3*x^3)^(2/3) + (2^(1/3)*x)/(1 + 3*x^3)^(1/3)])/3","A",10,10,27,0.3704,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2064,0,0,0,7.5651861,"\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","Int[(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,"(Sqrt[3]*(1 - 2*x^2)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 - 2*x^2)^(1/3))/(Sqrt[3]*(1 + 2*x^2)^(1/3))])/(2*((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)^(1/3)) - ((1 - 2*x^2)^(1/3)*Log[x])/(2*((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)^(1/3)) + (3*(1 - 2*x^2)^(1/3)*Log[(1 - 2*x^2)^(1/3) - (1 + 2*x^2)^(1/3)])/(4*((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)^(1/3)) + ((1 - 2*x^2)^(1/3)*Defer[Int][1/((1 - 2*x^2)^(1/3)*(1 + 2*x^2)^(2/3)*(-3 + 7*x - 7*x^2 + 6*x^3 - 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)^(1/3)) + ((1 - 2*x^2)^(1/3)*Defer[Int][x/((1 - 2*x^2)^(1/3)*(1 + 2*x^2)^(2/3)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)^(1/3)) + (6*(1 - 2*x^2)^(1/3)*Defer[Int][x^2/((1 - 2*x^2)^(1/3)*(1 + 2*x^2)^(2/3)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)^(1/3)) - (14*(1 - 2*x^2)^(1/3)*Defer[Int][x^3/((1 - 2*x^2)^(1/3)*(1 + 2*x^2)^(2/3)*(3 - 7*x + 7*x^2 - 6*x^3 + 2*x^4)), x])/(((1 - 2*x^2)/(1 + 2*x^2))^(1/3)*(1 + 2*x^2)^(1/3))","F",0,0,0,0,-1,"{}"
2065,1,187,0,0.344826,"\int \frac{x^2}{\sqrt{b x+a x^3} \left(-b^2+a^2 x^4\right)} \, dx","Int[x^2/(Sqrt[b*x + a*x^3]*(-b^2 + a^2*x^4)),x]","-\frac{\sqrt{x} \sqrt{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{4 \sqrt{2} a^{5/4} b^{5/4} \sqrt{a x^3+b x}}-\frac{\sqrt{x} \sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{4 \sqrt{2} a^{5/4} b^{5/4} \sqrt{a x^3+b x}}+\frac{x}{2 a b \sqrt{a x^3+b x}}","-\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,"x/(2*a*b*Sqrt[b*x + a*x^3]) - (Sqrt[x]*Sqrt[b + a*x^2]*ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(4*Sqrt[2]*a^(5/4)*b^(5/4)*Sqrt[b*x + a*x^3]) - (Sqrt[x]*Sqrt[b + a*x^2]*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(4*Sqrt[2]*a^(5/4)*b^(5/4)*Sqrt[b*x + a*x^3])","A",9,9,32,0.2812,1,"{2056, 1254, 466, 471, 21, 404, 212, 206, 203}"
2066,1,253,0,1.1575812,"\int \frac{b+a x^6}{x^6 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Int[(b + a*x^6)/(x^6*(-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","-\frac{2^{3/4} a^{3/4} \sqrt[4]{x} (a+b) \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 b^2 \sqrt[4]{a x^4+b x}}-\frac{2^{3/4} a^{3/4} \sqrt[4]{x} (a+b) \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 b^2 \sqrt[4]{a x^4+b x}}+\frac{4 (a+b) \left(a x^3+b\right)^2}{21 a b^2 x^5 \sqrt[4]{a x^4+b x}}-\frac{4 \left(a x^3+b\right)}{21 a x^5 \sqrt[4]{a x^4+b x}}-\frac{4 \left(a x^3+b\right)}{21 b x^2 \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(a x^3+b\right)}{21 b^2 x^6}",1,"(-4*(b + a*x^3))/(21*a*x^5*(b*x + a*x^4)^(1/4)) - (4*(b + a*x^3))/(21*b*x^2*(b*x + a*x^4)^(1/4)) + (4*(a + b)*(b + a*x^3)^2)/(21*a*b^2*x^5*(b*x + a*x^4)^(1/4)) - (2^(3/4)*a^(3/4)*(a + b)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*b^2*(b*x + a*x^4)^(1/4)) - (2^(3/4)*a^(3/4)*(a + b)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*b^2*(b*x + a*x^4)^(1/4))","A",14,11,35,0.3143,1,"{2056, 6725, 271, 264, 466, 465, 494, 461, 212, 206, 203}"
2067,0,0,0,1.5901298,"\int \frac{\sqrt[3]{-1+2 x^3+x^8} \left(3+5 x^8\right)}{x^2 \left(-1+x^8\right)} \, dx","Int[((-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,"Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/(-1 - x), x] + I*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/(I - x), x] + (-1)^(3/4)*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/((-1)^(1/4) - x), x] - (-1)^(1/4)*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/(-(-1)^(3/4) - x), x] + Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/(-1 + x), x] - 3*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/x^2, x] + I*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/(I + x), x] + (-1)^(3/4)*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/((-1)^(1/4) + x), x] - (-1)^(1/4)*Defer[Int][(-1 + 2*x^3 + x^8)^(1/3)/(-(-1)^(3/4) + x), x]","F",0,0,0,0,-1,"{}"
2068,0,0,0,0.2060898,"\int \frac{\sqrt{b^2+a x^2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[Sqrt[b^2 + a*x^2]/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\int \frac{\sqrt{b^2+a x^2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","-\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,"Defer[Int][Sqrt[b^2 + a*x^2]/Sqrt[b + Sqrt[b^2 + a*x^2]], x]","F",0,0,0,0,-1,"{}"
2069,0,0,0,1.5781889,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^3} \, dx","Int[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,"(3*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[-a]*x), x])/(16*b^5) + (3*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[-a]*x), x])/(16*b^5) + ((-a)^(3/2)*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b - a*x)^3, x])/(8*b^3) - (3*a*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b - a*x)^2, x])/(16*b^4) + ((-a)^(3/2)*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b + a*x)^3, x])/(8*b^3) - (3*a*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b + a*x)^2, x])/(16*b^4)","F",0,0,0,0,-1,"{}"
2070,1,225,0,0.2293878,"\int \frac{\left(-b+a x^2\right)^{3/4}}{x^3} \, dx","Int[(-b + a*x^2)^(3/4)/x^3,x]","-\frac{\left(a x^2-b\right)^{3/4}}{2 x^2}+\frac{3 a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{8 \sqrt{2} \sqrt[4]{b}}-\frac{3 a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{8 \sqrt{2} \sqrt[4]{b}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} \sqrt[4]{b}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}","-\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,"-1/2*(-b + a*x^2)^(3/4)/x^2 - (3*a*ArcTan[1 - (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(1/4)) + (3*a*ArcTan[1 + (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(1/4)) + (3*a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(8*Sqrt[2]*b^(1/4)) - (3*a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(8*Sqrt[2]*b^(1/4))","A",12,9,17,0.5294,1,"{266, 47, 63, 297, 1162, 617, 204, 1165, 628}"
2071,1,159,0,0.1819572,"\int \frac{\left(1+x^3\right) \left(-1+2 x^3\right)^{2/3}}{x^6 \left(1+2 x^3\right)} \, dx","Int[((1 + x^3)*(-1 + 2*x^3)^(2/3))/(x^6*(1 + 2*x^3)),x]","\frac{2}{3} \sqrt[3]{2} \log \left(1-\frac{2^{2/3} x}{\sqrt[3]{2 x^3-1}}\right)-\frac{2 \sqrt[3]{2} \tan ^{-1}\left(\frac{\frac{2\ 2^{2/3} x}{\sqrt[3]{2 x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(2 x^3-1\right)^{2/3}}{5 x^5}+\frac{9 \left(2 x^3-1\right)^{2/3}}{10 x^2}-\frac{1}{3} \sqrt[3]{2} \log \left(\frac{2^{2/3} x}{\sqrt[3]{2 x^3-1}}+\frac{2 \sqrt[3]{2} x^2}{\left(2 x^3-1\right)^{2/3}}+1\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 + 2*x^3)^(2/3)/x^5 + (9*(-1 + 2*x^3)^(2/3))/(10*x^2) - (2*2^(1/3)*ArcTan[(1 + (2*2^(2/3)*x)/(-1 + 2*x^3)^(1/3))/Sqrt[3]])/Sqrt[3] + (2*2^(1/3)*Log[1 - (2^(2/3)*x)/(-1 + 2*x^3)^(1/3)])/3 - (2^(1/3)*Log[1 + (2*2^(1/3)*x^2)/(-1 + 2*x^3)^(2/3) + (2^(2/3)*x)/(-1 + 2*x^3)^(1/3)])/3","A",10,10,29,0.3448,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2072,1,157,0,0.1582494,"\int \frac{\left(1-x^3\right)^{2/3} \left(-1+4 x^3\right)}{x^6 \left(-2+3 x^3\right)} \, dx","Int[((1 - x^3)^(2/3)*(-1 + 4*x^3))/(x^6*(-2 + 3*x^3)),x]","\frac{5 \log \left(\sqrt[3]{2}-\frac{x}{\sqrt[3]{1-x^3}}\right)}{12\ 2^{2/3}}-\frac{5 \tan ^{-1}\left(\frac{\frac{2^{2/3} x}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{4\ 2^{2/3} \sqrt{3}}-\frac{\left(1-x^3\right)^{2/3}}{10 x^5}+\frac{29 \left(1-x^3\right)^{2/3}}{40 x^2}-\frac{5 \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+\frac{x^2}{\left(1-x^3\right)^{2/3}}+2^{2/3}\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^3)^(2/3)/x^5 + (29*(1 - x^3)^(2/3))/(40*x^2) - (5*ArcTan[(1 + (2^(2/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]])/(4*2^(2/3)*Sqrt[3]) + (5*Log[2^(1/3) - x/(1 - x^3)^(1/3)])/(12*2^(2/3)) - (5*Log[2^(2/3) + x^2/(1 - x^3)^(2/3) + (2^(1/3)*x)/(1 - x^3)^(1/3)])/(24*2^(2/3))","A",10,10,31,0.3226,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2073,1,225,0,0.2216878,"\int \frac{\sqrt[4]{-b+a x^3}}{x^4} \, dx","Int[(-b + a*x^3)^(1/4)/x^4,x]","-\frac{a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{12 \sqrt{2} b^{3/4}}+\frac{a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{12 \sqrt{2} b^{3/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{6 \sqrt{2} b^{3/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{6 \sqrt{2} b^{3/4}}-\frac{\sqrt[4]{a x^3-b}}{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)}{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,"-1/3*(-b + a*x^3)^(1/4)/x^3 - (a*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(6*Sqrt[2]*b^(3/4)) + (a*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(6*Sqrt[2]*b^(3/4)) - (a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(12*Sqrt[2]*b^(3/4)) + (a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(12*Sqrt[2]*b^(3/4))","A",12,9,17,0.5294,1,"{266, 47, 63, 211, 1165, 628, 1162, 617, 204}"
2074,1,225,0,0.2115591,"\int \frac{\left(-b+a x^3\right)^{3/4}}{x^4} \, dx","Int[(-b + a*x^3)^(3/4)/x^4,x]","-\frac{\left(a x^3-b\right)^{3/4}}{3 x^3}+\frac{a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{4 \sqrt{2} \sqrt[4]{b}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{2 \sqrt{2} \sqrt[4]{b}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} \sqrt[4]{b}}","-\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,"-1/3*(-b + a*x^3)^(3/4)/x^3 - (a*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(2*Sqrt[2]*b^(1/4)) + (a*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(2*Sqrt[2]*b^(1/4)) + (a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(4*Sqrt[2]*b^(1/4)) - (a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(4*Sqrt[2]*b^(1/4))","A",12,9,17,0.5294,1,"{266, 47, 63, 297, 1162, 617, 204, 1165, 628}"
2075,0,0,0,36.9277406,"\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","Int[((-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,"(4*(a - x)*(b - x)^2*AppellF1[-3/4, -1/4, -3/2, 1/4, x/a, x/b])/((-((a - x)*(b - x)^2*x))^(3/4)*(1 - x/a)^(1/4)*Sqrt[1 - x/b]) - (4*(5*a + b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][((-a + x^4)^(1/4)*(-b + x^4)^(3/2))/(-(b^2*x^4) + 2*b*x^8 + (-1 + d)*x^12 + a*(b - x^4)^2), x], x, x^(1/4)])/(-((a - x)*(b - x)^2*x))^(3/4) + (12*(a + 2*b)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][(x^4*(-a + x^4)^(1/4)*(-b + x^4)^(3/2))/(-(b^2*x^4) + 2*b*x^8 + (-1 + d)*x^12 + a*(b - x^4)^2), x], x, x^(1/4)])/(b*(-((a - x)*(b - x)^2*x))^(3/4)) - (12*(1 - d)*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Subst][Defer[Int][(x^8*(-a + x^4)^(1/4)*(-b + x^4)^(3/2))/(-(b^2*x^4) + 2*b*x^8 + (-1 + d)*x^12 + a*(b - x^4)^2), x], x, x^(1/4)])/(b*(-((a - x)*(b - x)^2*x))^(3/4))","F",0,0,0,0,-1,"{}"
2076,1,225,0,0.2080898,"\int \frac{\left(-b+a x^5\right)^{3/4}}{x^6} \, dx","Int[(-b + a*x^5)^(3/4)/x^6,x]","-\frac{\left(a x^5-b\right)^{3/4}}{5 x^5}+\frac{3 a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{20 \sqrt{2} \sqrt[4]{b}}-\frac{3 a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{20 \sqrt{2} \sqrt[4]{b}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}\right)}{10 \sqrt{2} \sqrt[4]{b}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}+1\right)}{10 \sqrt{2} \sqrt[4]{b}}","-\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,"-1/5*(-b + a*x^5)^(3/4)/x^5 - (3*a*ArcTan[1 - (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/(10*Sqrt[2]*b^(1/4)) + (3*a*ArcTan[1 + (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/(10*Sqrt[2]*b^(1/4)) + (3*a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(20*Sqrt[2]*b^(1/4)) - (3*a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(20*Sqrt[2]*b^(1/4))","A",12,9,17,0.5294,1,"{266, 47, 63, 297, 1162, 617, 204, 1165, 628}"
2077,1,225,0,0.1980486,"\int \frac{\left(-b+a x^6\right)^{3/4}}{x^7} \, dx","Int[(-b + a*x^6)^(3/4)/x^7,x]","-\frac{\left(a x^6-b\right)^{3/4}}{6 x^6}+\frac{a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)}{8 \sqrt{2} \sqrt[4]{b}}-\frac{a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)}{8 \sqrt{2} \sqrt[4]{b}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} \sqrt[4]{b}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} \sqrt[4]{b}}","-\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,"-1/6*(-b + a*x^6)^(3/4)/x^6 - (a*ArcTan[1 - (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(1/4)) + (a*ArcTan[1 + (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(1/4)) + (a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^6)^(1/4) + Sqrt[-b + a*x^6]])/(8*Sqrt[2]*b^(1/4)) - (a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^6)^(1/4) + Sqrt[-b + a*x^6]])/(8*Sqrt[2]*b^(1/4))","A",12,9,17,0.5294,1,"{266, 47, 63, 297, 1162, 617, 204, 1165, 628}"
2078,0,0,0,14.5680847,"\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","Int[((-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,"(-3*(-2)^(1/7)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][(-2 + 2*x^6 - x^21)^(-2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + (3*2^(1/7)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][(-2 + 2*x^6 - x^21)^(-2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + (3*(-1)^(2/7)*2^(1/7)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][(-2 + 2*x^6 - x^21)^(-2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) - (3*(-1)^(3/7)*2^(1/7)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][(-2 + 2*x^6 - x^21)^(-2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + (3*(-1)^(4/7)*2^(1/7)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][(-2 + 2*x^6 - x^21)^(-2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) - (3*(-1)^(5/7)*2^(1/7)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][(-2 + 2*x^6 - x^21)^(-2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + (3*(-1)^(6/7)*2^(1/7)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][(-2 + 2*x^6 - x^21)^(-2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-2)^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-2)^(1/21) - x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + (2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-2^(1/21) - x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(8/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(2/21)*2^(1/21)) - x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(4/7)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-1)^(1/7)*2^(1/21) - x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(16/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(4/21)*2^(1/21)) - x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(20/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-1)^(5/21)*2^(1/21) - x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) - ((-1)^(1/7)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(2/7)*2^(1/21)) - x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) - (15*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][x^3/(-2 + 2*x^6 - x^21)^(2/3), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-2)^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-2)^(1/21) + (-1)^(1/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + (2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-2^(1/21) + (-1)^(1/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(8/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(2/21)*2^(1/21)) + (-1)^(1/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(4/7)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-1)^(1/7)*2^(1/21) + (-1)^(1/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(16/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(4/21)*2^(1/21)) + (-1)^(1/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(20/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-1)^(5/21)*2^(1/21) + (-1)^(1/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) - ((-1)^(1/7)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(2/7)*2^(1/21)) + (-1)^(1/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-2)^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-2)^(1/21) - (-1)^(2/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + (2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-2^(1/21) - (-1)^(2/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(8/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(2/21)*2^(1/21)) - (-1)^(2/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(4/7)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-1)^(1/7)*2^(1/21) - (-1)^(2/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(16/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(4/21)*2^(1/21)) - (-1)^(2/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) + ((-1)^(20/21)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/(((-1)^(5/21)*2^(1/21) - (-1)^(2/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3)) - ((-1)^(1/7)*2^(4/21)*(-2*x + 2*x^3 - x^8)^(1/3)*Defer[Subst][Defer[Int][1/((-((-1)^(2/7)*2^(1/21)) - (-1)^(2/3)*x)*(-2 + 2*x^6 - x^21)^(2/3)), x], x, x^(1/3)])/(x^(1/3)*(-2 + 2*x^2 - x^7)^(1/3))","F",0,0,0,0,-1,"{}"
2079,1,503,0,1.1077139,"\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","Int[(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 \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)}{\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 \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{5 b \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)}{\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 \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{\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) + (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))])/(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))])/(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)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (5*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)) - (5*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",15,9,40,0.2250,1,"{6728, 240, 212, 206, 203, 1428, 377, 208, 205}"
2080,1,501,0,1.1637795,"\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","Int[(-b + 2*a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{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{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 \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{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{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 \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{\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) + (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)) - (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)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (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*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",15,9,41,0.2195,1,"{6728, 240, 212, 206, 203, 1428, 377, 208, 205}"
2081,1,501,0,0.7527576,"\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","Int[(-b + 2*a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b + a*x^4 + x^8)),x]","\frac{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{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 \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{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{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 \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{\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) + (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)) - (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)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (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*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",15,9,41,0.2195,1,"{6728, 240, 212, 206, 203, 1428, 377, 208, 205}"
2082,1,400,0,0.7323416,"\int \frac{\sqrt{-b^4+a^4 x^4} \left(b^4+a^4 x^4\right)}{b^8+a^8 x^8} \, dx","Int[(Sqrt[-b^4 + a^4*x^4]*(b^4 + a^4*x^4))/(b^8 + a^8*x^8),x]","-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{a^6}{\left(-a^8\right)^{3/4}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}+\frac{\left(a^4-\sqrt{-a^8}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a^5 \sqrt{a^4 x^4-b^4}}+\frac{\left(\sqrt{-a^8}+a^4\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a^5 \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt[4]{-a^8}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \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,"((a^4 - Sqrt[-a^8])*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a^5*Sqrt[-b^4 + a^4*x^4]) + ((a^4 + Sqrt[-a^8])*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a^5*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[a^6/(-a^8)^(3/4), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-a^8)^(1/4)/a^2, ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(Sqrt[-Sqrt[-a^8]]/a^2), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[Sqrt[-Sqrt[-a^8]]/a^2, ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4])","C",18,7,42,0.1667,1,"{6725, 406, 224, 221, 409, 1219, 1218}"
2083,1,400,0,0.6475976,"\int \frac{-b^8+a^8 x^8}{\sqrt{-b^4+a^4 x^4} \left(b^8+a^8 x^8\right)} \, dx","Int[(-b^8 + a^8*x^8)/(Sqrt[-b^4 + a^4*x^4]*(b^8 + a^8*x^8)),x]","-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{a^6}{\left(-a^8\right)^{3/4}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}+\frac{\left(a^4-\sqrt{-a^8}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a^5 \sqrt{a^4 x^4-b^4}}+\frac{\left(\sqrt{-a^8}+a^4\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a^5 \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt[4]{-a^8}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \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,"((a^4 - Sqrt[-a^8])*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a^5*Sqrt[-b^4 + a^4*x^4]) + ((a^4 + Sqrt[-a^8])*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a^5*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[a^6/(-a^8)^(3/4), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-a^8)^(1/4)/a^2, ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(Sqrt[-Sqrt[-a^8]]/a^2), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[Sqrt[-Sqrt[-a^8]]/a^2, ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4])","C",19,8,44,0.1818,1,"{1586, 6725, 406, 224, 221, 409, 1219, 1218}"
2084,0,0,0,1.7608686,"\int \frac{x^3 \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","Int[(x^3*Sqrt[x + x^2])/Sqrt[x^2 + x*Sqrt[x + x^2]],x]","\int \frac{x^3 \sqrt{x+x^2}}{\sqrt{x^2+x \sqrt{x+x^2}}} \, dx","\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,"(2*Sqrt[x + x^2]*Defer[Subst][Defer[Int][(x^8*Sqrt[1 + x^2])/Sqrt[x^4 + x^2*Sqrt[x^2 + x^4]], x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[1 + x])","F",0,0,0,0,-1,"{}"
2085,1,230,0,0.2434472,"\int \frac{\left(-b+a x^2\right)^{3/4} \left(3 b+2 a x^2\right)}{x} \, dx","Int[((-b + a*x^2)^(3/4)*(3*b + 2*a*x^2))/x,x]","-\frac{3 b^{7/4} \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{3 b^{7/4} \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{3 b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)}{\sqrt{2}}-\frac{3 b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{\sqrt{2}}+2 b \left(a x^2-b\right)^{3/4}+\frac{4}{7} \left(a x^2-b\right)^{7/4}","\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*(-b + a*x^2)^(3/4) + (4*(-b + a*x^2)^(7/4))/7 + (3*b^(7/4)*ArcTan[1 - (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/Sqrt[2] - (3*b^(7/4)*ArcTan[1 + (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/Sqrt[2] - (3*b^(7/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(2*Sqrt[2]) + (3*b^(7/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(2*Sqrt[2])","A",13,10,27,0.3704,1,"{446, 80, 50, 63, 297, 1162, 617, 204, 1165, 628}"
2086,0,0,0,2.8787235,"\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","Int[((-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,"((9*I)*(2 - x^2 + x^3)^(2/3)*Defer[Subst][Defer[Int][(((1 + (26 - 15*Sqrt[3])^(2/3))/(3*(26 - 15*Sqrt[3])^(1/3)) + x)^(2/3)*((-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3))/9 - ((1 + (26 - 15*Sqrt[3])^(2/3))*x)/(3*(26 - 15*Sqrt[3])^(1/3)) + x^2)^(2/3))/((-8/3 + 2*I) - 2*x), x], x, -1/3 + x])/((-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x)^(2/3)*(-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2)^(2/3)) + (9*(2 - x^2 + x^3)^(2/3)*Defer[Subst][Defer[Int][(((1 + (26 - 15*Sqrt[3])^(2/3))/(3*(26 - 15*Sqrt[3])^(1/3)) + x)^(2/3)*((-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3))/9 - ((1 + (26 - 15*Sqrt[3])^(2/3))*x)/(3*(26 - 15*Sqrt[3])^(1/3)) + x^2)^(2/3))/(2/3 - x), x], x, -1/3 + x])/((-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x)^(2/3)*(-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2)^(2/3)) + (27*(2 - x^2 + x^3)^(2/3)*Defer[Subst][Defer[Int][(((1 + (26 - 15*Sqrt[3])^(2/3))/(3*(26 - 15*Sqrt[3])^(1/3)) + x)^(2/3)*((-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3))/9 - ((1 + (26 - 15*Sqrt[3])^(2/3))*x)/(3*(26 - 15*Sqrt[3])^(1/3)) + x^2)^(2/3))/(1/3 + x)^3, x], x, -1/3 + x])/((-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x)^(2/3)*(-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2)^(2/3)) + (9*(2 - x^2 + x^3)^(2/3)*Defer[Subst][Defer[Int][(((1 + (26 - 15*Sqrt[3])^(2/3))/(3*(26 - 15*Sqrt[3])^(1/3)) + x)^(2/3)*((-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3))/9 - ((1 + (26 - 15*Sqrt[3])^(2/3))*x)/(3*(26 - 15*Sqrt[3])^(1/3)) + x^2)^(2/3))/(1/3 + x), x], x, -1/3 + x])/((-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x)^(2/3)*(-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2)^(2/3)) + ((9*I)*(2 - x^2 + x^3)^(2/3)*Defer[Subst][Defer[Int][(((1 + (26 - 15*Sqrt[3])^(2/3))/(3*(26 - 15*Sqrt[3])^(1/3)) + x)^(2/3)*((-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3))/9 - ((1 + (26 - 15*Sqrt[3])^(2/3))*x)/(3*(26 - 15*Sqrt[3])^(1/3)) + x^2)^(2/3))/((8/3 + 2*I) + 2*x), x], x, -1/3 + x])/((-1 + (26 - 15*Sqrt[3])^(-1/3) + (26 - 15*Sqrt[3])^(1/3) + 3*x)^(2/3)*(-1 + (26 - 15*Sqrt[3])^(-2/3) + (26 - 15*Sqrt[3])^(2/3) + ((1 + (26 - 15*Sqrt[3])^(2/3))*(1 - 3*x))/(26 - 15*Sqrt[3])^(1/3) + (-1 + 3*x)^2)^(2/3))","F",0,0,0,0,-1,"{}"
2087,0,0,0,2.3326203,"\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","Int[(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,"(-12*a*x^(4/3)*(-a + x)^(2/3)*Defer[Subst][Defer[Int][x^7/((-a + x^3)^(2/3)*(a*d - d*x^3 + x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(2/3) + (9*x^(4/3)*(-a + x)^(2/3)*Defer[Subst][Defer[Int][x^10/((-a + x^3)^(2/3)*(a*d - d*x^3 + x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(2/3)","F",0,0,0,0,-1,"{}"
2088,1,487,0,3.8436803,"\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","Int[(-1 + k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 + k^4*x^4)),x]","\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{k^2}{\left(-k^4\right)^{3/4}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{\sqrt[4]{-k^4}}{k^2};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{\sqrt{-\sqrt{-k^4}}}{k^2};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{\sqrt{-\sqrt{-k^4}}}{k^2};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}","-\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,"(2*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[k^2/(-k^4)^(3/4), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(-k^4)^(1/4)/k^2, ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-(Sqrt[-Sqrt[-k^4]]/k^2), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[Sqrt[-Sqrt[-k^4]]/k^2, ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",28,9,40,0.2250,0,"{6718, 6688, 6725, 714, 115, 934, 12, 168, 537}"
2089,1,97,0,0.6630187,"\int \frac{1-x^4}{\left(1+x^4\right) \sqrt[4]{x^3+x^5}} \, dx","Int[(1 - x^4)/((1 + x^4)*(x^3 + x^5)^(1/4)),x]","\frac{(2-2 i) x \sqrt[4]{x^2+1} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};-i x^2,-x^2\right)}{\sqrt[4]{x^5+x^3}}+\frac{(2+2 i) x \sqrt[4]{x^2+1} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};i x^2,-x^2\right)}{\sqrt[4]{x^5+x^3}}","\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,"((2 - 2*I)*x*(1 + x^2)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, (-I)*x^2, -x^2])/(x^3 + x^5)^(1/4) + ((2 + 2*I)*x*(1 + x^2)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, I*x^2, -x^2])/(x^3 + x^5)^(1/4)","C",7,5,26,0.1923,0,"{2056, 1586, 6715, 6725, 429}"
2090,0,0,0,1.8575543,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^6\right)}{x^6 \left(-1+x^3\right)^2} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^6))/(x^6*(-1 + x^3)^2),x]","\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^6\right)}{x^6 \left(-1+x^3\right)^2} \, dx","-\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,"(-2*(1 + x^3)^(2/3))/x^2 - (2*(1 + x^3)^(5/3))/(5*x^5) + (4*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - 2*Log[-x + (1 + x^3)^(1/3)] - (4*Defer[Int][(1 + x^3)^(2/3)/(-1 + I*Sqrt[3] - 2*x)^2, x])/3 + (2*(1 - I*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(-1 + I*Sqrt[3] - 2*x)^2, x])/3 + (((2*I)/3)*Defer[Int][(1 + x^3)^(2/3)/(-1 + I*Sqrt[3] - 2*x), x])/Sqrt[3] + Defer[Int][(1 + x^3)^(2/3)/(-1 + x)^2, x]/3 - 2*Defer[Int][(1 + x^3)^(2/3)/(-1 + x), x] + (2*(9 - (8*I)*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(1 - I*Sqrt[3] + 2*x), x])/9 - (4*Defer[Int][(1 + x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x)^2, x])/3 + (2*(1 + I*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x)^2, x])/3 + (((2*I)/3)*Defer[Int][(1 + x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x), x])/Sqrt[3] + (2*(9 + (8*I)*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x), x])/9","F",0,0,0,0,-1,"{}"
2091,0,0,0,1.8787,"\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","Int[((-1 + x^3)^(2/3)*(-2 + 2*x^3 + x^6))/(x^6*(1 + x^3)^2),x]","\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","-\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,"(-3*(-1 + x^3)^(2/3))/x^2 - (2*(-1 + x^3)^(5/3))/(5*x^5) + 2*Sqrt[3]*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]] - 3*Log[-x + (-1 + x^3)^(1/3)] + (4*Defer[Int][(-1 + x^3)^(2/3)/(1 + I*Sqrt[3] - 2*x)^2, x])/3 - (2*(1 + I*Sqrt[3])*Defer[Int][(-1 + x^3)^(2/3)/(1 + I*Sqrt[3] - 2*x)^2, x])/3 - (((2*I)/3)*Defer[Int][(-1 + x^3)^(2/3)/(1 + I*Sqrt[3] - 2*x), x])/Sqrt[3] - Defer[Int][(-1 + x^3)^(2/3)/(1 + x)^2, x]/3 - (8*Defer[Int][(-1 + x^3)^(2/3)/(1 + x), x])/3 + (2*(12 + (11*I)*Sqrt[3])*Defer[Int][(-1 + x^3)^(2/3)/(-1 - I*Sqrt[3] + 2*x), x])/9 + (4*Defer[Int][(-1 + x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x)^2, x])/3 - (2*(1 - I*Sqrt[3])*Defer[Int][(-1 + x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x)^2, x])/3 - (((2*I)/3)*Defer[Int][(-1 + x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x), x])/Sqrt[3] + (2*(12 - (11*I)*Sqrt[3])*Defer[Int][(-1 + x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x), x])/9","F",0,0,0,0,-1,"{}"
2092,0,0,0,4.3725553,"\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","Int[((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,"(-2*c*Sqrt[(a*x^6)/(Sqrt[b] + Sqrt[-b + a*x^6])^2]*(Sqrt[b] + Sqrt[-b + a*x^6])*EllipticF[2*ArcTan[(-b + a*x^6)^(1/4)/b^(1/4)], 1/2])/(3*a*b^(1/4)*x^3) - (2*b*(1 - (a*x^6)/b)^(3/4)*Hypergeometric2F1[-1/6, 3/4, 5/6, (a*x^6)/b])/(x*(-b + a*x^6)^(3/4)) + (2*c^2*x*(1 - (a*x^6)/b)^(3/4)*Hypergeometric2F1[1/6, 3/4, 7/6, (a*x^6)/b])/(a*(-b + a*x^6)^(3/4)) + (a*x^5*(1 - (a*x^6)/b)^(3/4)*Hypergeometric2F1[3/4, 5/6, 11/6, (a*x^6)/b])/(5*(-b + a*x^6)^(3/4)) - (2*b*c^2*Defer[Int][1/((b - c*x^4 - a*x^6)*(-b + a*x^6)^(3/4)), x])/a - 6*b*c*Defer[Int][x^2/((-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)), x] - (2*c^3*Defer[Int][x^4/((-b + a*x^6)^(3/4)*(-b + c*x^4 + a*x^6)), x])/a","F",0,0,0,0,-1,"{}"
2093,1,122,0,0.3913194,"\int \frac{\sqrt{c+d \sqrt{b+a x^2}}}{x} \, dx","Int[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",8,6,23,0.2609,1,"{371, 1398, 825, 827, 1166, 207}"
2094,0,0,0,1.2446778,"\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","Int[((-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,"-((b*ArcTanh[(Sqrt[2]*Sqrt[a]*x)/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]])/(Sqrt[2]*Sqrt[a])) + a^2*Defer[Int][(x^4*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/Sqrt[b + a^2*x^4], x]","F",0,0,0,0,-1,"{}"
2095,0,0,0,0.1795812,"\int \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Int[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,"Defer[Int][Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
2096,1,172,0,0.3748233,"\int \frac{1}{(2 b+a x) \sqrt[4]{b x^2+a x^3}} \, dx","Int[1/((2*b + a*x)*(b*x^2 + a*x^3)^(1/4)),x]","\frac{\sqrt{-\frac{a x}{b}} \sqrt[4]{a x+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+b}}{\sqrt[4]{-b} \sqrt{-\frac{a x}{b}}}\right)}{\sqrt{2} a \sqrt[4]{-b} \sqrt[4]{a x^3+b x^2}}-\frac{\sqrt{-\frac{a x}{b}} \sqrt[4]{a x+b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+b}}{\sqrt[4]{-b} \sqrt{-\frac{a x}{b}}}\right)}{\sqrt{2} a \sqrt[4]{-b} \sqrt[4]{a x^3+b x^2}}","\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,"(Sqrt[-((a*x)/b)]*(b + a*x)^(1/4)*ArcTan[(Sqrt[2]*(b + a*x)^(1/4))/((-b)^(1/4)*Sqrt[-((a*x)/b)])])/(Sqrt[2]*a*(-b)^(1/4)*(b*x^2 + a*x^3)^(1/4)) - (Sqrt[-((a*x)/b)]*(b + a*x)^(1/4)*ArcTanh[(Sqrt[2]*(b + a*x)^(1/4))/((-b)^(1/4)*Sqrt[-((a*x)/b)])])/(Sqrt[2]*a*(-b)^(1/4)*(b*x^2 + a*x^3)^(1/4))","A",12,9,25,0.3600,1,"{2056, 107, 106, 490, 1211, 221, 1699, 203, 206}"
2097,0,0,0,1.8962714,"\int \frac{x (-4 a+3 x)}{\sqrt[3]{x^2 (-a+x)} \left(a d-d x+x^4\right)} \, dx","Int[(x*(-4*a + 3*x))/((x^2*(-a + x))^(1/3)*(a*d - d*x + x^4)),x]","\int \frac{x (-4 a+3 x)}{\sqrt[3]{x^2 (-a+x)} \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 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,"(-12*a*x^(2/3)*(-a + x)^(1/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(1/3)*(a*d - d*x^3 + x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(1/3) + (9*x^(2/3)*(-a + x)^(1/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(1/3)*(a*d - d*x^3 + x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2098,0,0,0,1.2290081,"\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","Int[((-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,"(4*(-b + a*x^5)^(3/4)*Hypergeometric2F1[-3/4, -3/5, 2/5, (a*x^5)/b])/(3*x^3*(1 - (a*x^5)/b)^(3/4)) + 4*c*Defer[Int][(-b + a*x^5)^(3/4)/(-b + c*x^4 + a*x^5), x] + 5*a*Defer[Int][(x*(-b + a*x^5)^(3/4))/(-b + c*x^4 + a*x^5), x]","F",0,0,0,0,-1,"{}"
2099,1,22,0,0.0086004,"\int \frac{\left(1+x^8\right)^{3/4}}{-1+x^8} \, dx","Int[(1 + x^8)^(3/4)/(-1 + x^8),x]","-x F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};x^8,-x^8\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,"-(x*AppellF1[1/8, 1, -3/4, 9/8, x^8, -x^8])","C",1,1,17,0.05882,0,"{429}"
2100,1,282,0,0.2648577,"\int \frac{x^4}{\sqrt[4]{-1+x^4} \left(-1+2 x^4+x^8\right)} \, dx","Int[x^4/((-1 + x^4)^(1/4)*(-1 + 2*x^4 + x^8)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4\ 2^{5/8}}-\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(1-\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}\right)}{4\ 2^{5/8} \left(2-\sqrt{2}\right)}+\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}+1\right)}{4\ 2^{5/8} \left(2-\sqrt{2}\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4\ 2^{5/8}}-\frac{\left(1-\sqrt{2}\right) \log \left(-\frac{2 x}{\sqrt[4]{x^4-1}}+\frac{2^{5/8} x^2}{\sqrt{x^4-1}}+2^{3/8}\right)}{8\ 2^{5/8} \left(2-\sqrt{2}\right)}+\frac{\left(1-\sqrt{2}\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)}{8\ 2^{5/8} \left(2-\sqrt{2}\right)}","\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,"ArcTan[(2^(1/8)*x)/(-1 + x^4)^(1/4)]/(4*2^(5/8)) - ((1 - Sqrt[2])*ArcTan[1 - (2^(5/8)*x)/(-1 + x^4)^(1/4)])/(4*2^(5/8)*(2 - Sqrt[2])) + ((1 - Sqrt[2])*ArcTan[1 + (2^(5/8)*x)/(-1 + x^4)^(1/4)])/(4*2^(5/8)*(2 - Sqrt[2])) + ArcTanh[(2^(1/8)*x)/(-1 + x^4)^(1/4)]/(4*2^(5/8)) - ((1 - Sqrt[2])*Log[2^(3/8) + (2^(5/8)*x^2)/Sqrt[-1 + x^4] - (2*x)/(-1 + x^4)^(1/4)])/(8*2^(5/8)*(2 - Sqrt[2])) + ((1 - Sqrt[2])*Log[1 + (2^(1/4)*x^2)/Sqrt[-1 + x^4] + (2^(5/8)*x)/(-1 + x^4)^(1/4)])/(8*2^(5/8)*(2 - Sqrt[2]))","A",16,11,25,0.4400,1,"{1528, 377, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
2101,1,282,0,0.2190835,"\int \frac{\left(-1+x^4\right)^{3/4}}{-1+2 x^4+x^8} \, dx","Int[(-1 + x^4)^(3/4)/(-1 + 2*x^4 + x^8),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[8]{2}}+\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(1-\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[8]{2} \left(2-\sqrt{2}\right)}-\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(\frac{2^{5/8} x}{\sqrt[4]{x^4-1}}+1\right)}{4 \sqrt[8]{2} \left(2-\sqrt{2}\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt[8]{2}}+\frac{\left(1-\sqrt{2}\right) \log \left(-\frac{2 x}{\sqrt[4]{x^4-1}}+\frac{2^{5/8} x^2}{\sqrt{x^4-1}}+2^{3/8}\right)}{8 \sqrt[8]{2} \left(2-\sqrt{2}\right)}-\frac{\left(1-\sqrt{2}\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)}{8 \sqrt[8]{2} \left(2-\sqrt{2}\right)}","\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,"ArcTan[(2^(1/8)*x)/(-1 + x^4)^(1/4)]/(4*2^(1/8)) + ((1 - Sqrt[2])*ArcTan[1 - (2^(5/8)*x)/(-1 + x^4)^(1/4)])/(4*2^(1/8)*(2 - Sqrt[2])) - ((1 - Sqrt[2])*ArcTan[1 + (2^(5/8)*x)/(-1 + x^4)^(1/4)])/(4*2^(1/8)*(2 - Sqrt[2])) + ArcTanh[(2^(1/8)*x)/(-1 + x^4)^(1/4)]/(4*2^(1/8)) + ((1 - Sqrt[2])*Log[2^(3/8) + (2^(5/8)*x^2)/Sqrt[-1 + x^4] - (2*x)/(-1 + x^4)^(1/4)])/(8*2^(1/8)*(2 - Sqrt[2])) - ((1 - Sqrt[2])*Log[1 + (2^(1/4)*x^2)/Sqrt[-1 + x^4] + (2^(5/8)*x)/(-1 + x^4)^(1/4)])/(8*2^(1/8)*(2 - Sqrt[2]))","A",25,13,22,0.5909,1,"{1428, 408, 240, 212, 206, 203, 377, 211, 1165, 628, 1162, 617, 204}"
2102,0,0,0,0.8764034,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{1+\sqrt{1+x^2}}} \, dx","Int[(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,"Defer[Int][1/Sqrt[1 + Sqrt[1 + x^2]], x] - (I/2)*Defer[Int][1/((I - x)*Sqrt[1 + Sqrt[1 + x^2]]), x] - Defer[Int][1/((1 - x)*Sqrt[1 + Sqrt[1 + x^2]]), x]/2 - (I/2)*Defer[Int][1/((I + x)*Sqrt[1 + Sqrt[1 + x^2]]), x] - Defer[Int][1/((1 + x)*Sqrt[1 + Sqrt[1 + x^2]]), x]/2","F",0,0,0,0,-1,"{}"
2103,1,228,0,0.2210437,"\int \frac{1}{x^3 \left(-b+a x^2\right)^{3/4}} \, dx","Int[1/(x^3*(-b + a*x^2)^(3/4)),x]","-\frac{3 a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{8 \sqrt{2} b^{7/4}}+\frac{3 a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^2-b}+\sqrt{a x^2-b}+\sqrt{b}\right)}{8 \sqrt{2} b^{7/4}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^2-b}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^2-b}}{2 b 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} 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,"(-b + a*x^2)^(1/4)/(2*b*x^2) - (3*a*ArcTan[1 - (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(7/4)) + (3*a*ArcTan[1 + (Sqrt[2]*(-b + a*x^2)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(7/4)) - (3*a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(8*Sqrt[2]*b^(7/4)) + (3*a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^2)^(1/4) + Sqrt[-b + a*x^2]])/(8*Sqrt[2]*b^(7/4))","A",12,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2104,0,0,0,7.4852464,"\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","Int[(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,"(4*x*(1 - x/a)^(1/4)*(1 - x/b)^(3/4)*AppellF1[3/4, 1/4, 3/4, 7/4, x/a, x/b])/(3*d*((a - x)*(b - x)^3*x)^(1/4)) + ((1 + a*d - 2*b*d + Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2])*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(3/4)*Defer[Int][1/(x^(1/4)*(-a + x)^(1/4)*(-b + x)^(3/4)*(-1 - a*d - Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2] + 2*d*x)), x])/(d*((a - x)*(b - x)^3*x)^(1/4)) + ((1 + a*d - 2*b*d - Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2])*x^(1/4)*(-a + x)^(1/4)*(-b + x)^(3/4)*Defer[Int][1/(x^(1/4)*(-a + x)^(1/4)*(-b + x)^(3/4)*(-1 - a*d + Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2] + 2*d*x)), x])/(d*((a - x)*(b - x)^3*x)^(1/4))","F",0,0,0,0,-1,"{}"
2105,1,228,0,0.2309537,"\int \frac{1}{x^4 \left(-b+a x^3\right)^{3/4}} \, dx","Int[1/(x^4*(-b + a*x^3)^(3/4)),x]","-\frac{a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{4 \sqrt{2} b^{7/4}}+\frac{a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{4 \sqrt{2} b^{7/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{2 \sqrt{2} b^{7/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^3-b}}{3 b 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} 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,"(-b + a*x^3)^(1/4)/(3*b*x^3) - (a*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(2*Sqrt[2]*b^(7/4)) + (a*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(2*Sqrt[2]*b^(7/4)) - (a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(4*Sqrt[2]*b^(7/4)) + (a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(4*Sqrt[2]*b^(7/4))","A",12,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2106,1,228,0,0.2079154,"\int \frac{1}{x^4 \sqrt[4]{-b+a x^3}} \, dx","Int[1/(x^4*(-b + a*x^3)^(1/4)),x]","\frac{a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{12 \sqrt{2} b^{5/4}}-\frac{a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{12 \sqrt{2} b^{5/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{6 \sqrt{2} b^{5/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{6 \sqrt{2} b^{5/4}}+\frac{\left(a x^3-b\right)^{3/4}}{3 b 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)}{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,"(-b + a*x^3)^(3/4)/(3*b*x^3) - (a*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(6*Sqrt[2]*b^(5/4)) + (a*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(6*Sqrt[2]*b^(5/4)) + (a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(12*Sqrt[2]*b^(5/4)) - (a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(12*Sqrt[2]*b^(5/4))","A",12,9,17,0.5294,1,"{266, 51, 63, 297, 1162, 617, 204, 1165, 628}"
2107,0,0,0,5.3165098,"\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","Int[((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]","\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","-\frac{1}{4} \text{RootSum}\left[17 \text{$\#$1}^8+14 \text{$\#$1}^4+5\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}-\text{$\#$1}\right)+5 \log \left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}-\text{$\#$1}\right)}{17 \text{$\#$1}^7+7 \text{$\#$1}^3}\&\right]+\tan ^{-1}\left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}\right)+\tanh ^{-1}\left(\sqrt[4]{\frac{-2 x^2+x+1}{4 x^2+x+1}}\right)",1,"-((((1 + x - 2*x^2)/(1 + x + 4*x^2))^(1/4)*(1 + x + 4*x^2)^(1/4)*Defer[Int][(1 + x - 2*x^2)^(1/4)/(x*(1 + x + 4*x^2)^(1/4)), x])/(1 + x - 2*x^2)^(1/4)) + (((1 + x - 2*x^2)/(1 + x + 4*x^2))^(1/4)*(1 + x + 4*x^2)^(1/4)*Defer[Int][(1 + x - 2*x^2)^(1/4)/((1 + x + 4*x^2)^(1/4)*(1 + 2*x + x^2 + x^4)), x])/(2*(1 + x - 2*x^2)^(1/4)) + (3*((1 + x - 2*x^2)/(1 + x + 4*x^2))^(1/4)*(1 + x + 4*x^2)^(1/4)*Defer[Int][(x*(1 + x - 2*x^2)^(1/4))/((1 + x + 4*x^2)^(1/4)*(1 + 2*x + x^2 + x^4)), x])/(2*(1 + x - 2*x^2)^(1/4)) + (((1 + x - 2*x^2)/(1 + x + 4*x^2))^(1/4)*(1 + x + 4*x^2)^(1/4)*Defer[Int][(x^2*(1 + x - 2*x^2)^(1/4))/((1 + x + 4*x^2)^(1/4)*(1 + 2*x + x^2 + x^4)), x])/(2*(1 + x - 2*x^2)^(1/4)) + (((1 + x - 2*x^2)/(1 + x + 4*x^2))^(1/4)*(1 + x + 4*x^2)^(1/4)*Defer[Int][(x^3*(1 + x - 2*x^2)^(1/4))/((1 + x + 4*x^2)^(1/4)*(1 + 2*x + x^2 + x^4)), x])/(1 + x - 2*x^2)^(1/4)","F",0,0,0,0,-1,"{}"
2108,0,0,0,0.7762599,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","Int[(1 + x^4)/((-1 + x^4)*Sqrt[1 - x - x^2 + x^3 + x^4]),x]","\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{1-x-x^2+x^3+x^4}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^4+14 \text{$\#$1}^2-16 \text{$\#$1}+5\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\text{$\#$1}^2 (-\log (x))-\log \left(-\text{$\#$1} x-x^2+\sqrt{x^4+x^3-x^2-x+1}+1\right)+\log (x)}{\text{$\#$1}^3+7 \text{$\#$1}-4}\&\right]+\tanh ^{-1}\left(\frac{x}{x^2-\sqrt{x^4+x^3-x^2-x+1}-1}\right)",1,"Defer[Int][1/Sqrt[1 - x - x^2 + x^3 + x^4], x] - (I/2)*Defer[Int][1/((I - x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x] + Defer[Int][1/((-1 + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x]/2 - (I/2)*Defer[Int][1/((I + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x] - Defer[Int][1/((1 + x)*Sqrt[1 - x - x^2 + x^3 + x^4]), x]/2","F",0,0,0,0,-1,"{}"
2109,1,228,0,0.2226192,"\int \frac{1}{x^5 \left(-b+a x^4\right)^{3/4}} \, dx","Int[1/(x^5*(-b + a*x^4)^(3/4)),x]","-\frac{3 a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{16 \sqrt{2} b^{7/4}}+\frac{3 a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{16 \sqrt{2} b^{7/4}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}\right)}{8 \sqrt{2} b^{7/4}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}+1\right)}{8 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^4-b}}{4 b x^4}","-\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,"(-b + a*x^4)^(1/4)/(4*b*x^4) - (3*a*ArcTan[1 - (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)])/(8*Sqrt[2]*b^(7/4)) + (3*a*ArcTan[1 + (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)])/(8*Sqrt[2]*b^(7/4)) - (3*a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]])/(16*Sqrt[2]*b^(7/4)) + (3*a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]])/(16*Sqrt[2]*b^(7/4))","A",12,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2110,0,0,0,19.2156225,"\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","Int[(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,"(4*a*b*(a - x)^(1/4)*(b - x)^(3/4)*x^(1/4)*Defer[Subst][Defer[Int][(x^2*(b - x^4)^(5/4))/((a - x^4)^(1/4)*(a^3 - 3*a^2*(1 + (b^3*d)/(3*a^2))*x^4 + 3*a*(1 + (b^2*d)/a)*x^8 - (1 + 3*b*d)*x^12 + d*x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(1/4) - (8*(2*a - b)*(a - x)^(1/4)*(b - x)^(3/4)*x^(1/4)*Defer[Subst][Defer[Int][(x^6*(b - x^4)^(5/4))/((a - x^4)^(1/4)*(a^3 - 3*a^2*(1 + (b^3*d)/(3*a^2))*x^4 + 3*a*(1 + (b^2*d)/a)*x^8 - (1 + 3*b*d)*x^12 + d*x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(1/4) + (4*(a - x)^(1/4)*(b - x)^(3/4)*x^(1/4)*Defer[Subst][Defer[Int][(x^10*(b - x^4)^(5/4))/((a - x^4)^(1/4)*(a^3 - 3*a^2*(1 + (b^3*d)/(3*a^2))*x^4 + 3*a*(1 + (b^2*d)/a)*x^8 - (1 + 3*b*d)*x^12 + d*x^16)), x], x, x^(1/4)])/((a - x)*(b - x)^3*x)^(1/4)","F",0,0,0,0,-1,"{}"
2111,1,228,0,0.2208445,"\int \frac{1}{x^6 \left(-b+a x^5\right)^{3/4}} \, dx","Int[1/(x^6*(-b + a*x^5)^(3/4)),x]","-\frac{3 a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{20 \sqrt{2} b^{7/4}}+\frac{3 a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{20 \sqrt{2} b^{7/4}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}\right)}{10 \sqrt{2} b^{7/4}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}+1\right)}{10 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^5-b}}{5 b 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} 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,"(-b + a*x^5)^(1/4)/(5*b*x^5) - (3*a*ArcTan[1 - (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/(10*Sqrt[2]*b^(7/4)) + (3*a*ArcTan[1 + (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/(10*Sqrt[2]*b^(7/4)) - (3*a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(20*Sqrt[2]*b^(7/4)) + (3*a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(20*Sqrt[2]*b^(7/4))","A",12,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2112,1,228,0,0.2120109,"\int \frac{1}{x^7 \left(-b+a x^6\right)^{3/4}} \, dx","Int[1/(x^7*(-b + a*x^6)^(3/4)),x]","-\frac{a \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)}{8 \sqrt{2} b^{7/4}}+\frac{a \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^6-b}+\sqrt{a x^6-b}+\sqrt{b}\right)}{8 \sqrt{2} b^{7/4}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{7/4}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^6-b}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{7/4}}+\frac{\sqrt[4]{a x^6-b}}{6 b 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} 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,"(-b + a*x^6)^(1/4)/(6*b*x^6) - (a*ArcTan[1 - (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(7/4)) + (a*ArcTan[1 + (Sqrt[2]*(-b + a*x^6)^(1/4))/b^(1/4)])/(4*Sqrt[2]*b^(7/4)) - (a*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^6)^(1/4) + Sqrt[-b + a*x^6]])/(8*Sqrt[2]*b^(7/4)) + (a*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^6)^(1/4) + Sqrt[-b + a*x^6]])/(8*Sqrt[2]*b^(7/4))","A",12,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2113,1,340,0,3.9312008,"\int \frac{b^6+a^6 x^6}{\sqrt{b^4+a^4 x^4} \left(-b^6+a^6 x^6\right)} \, dx","Int[(b^6 + a^6*x^6)/(Sqrt[b^4 + a^4*x^4]*(-b^6 + a^6*x^6)),x]","-\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{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a b}-\frac{\left(a-\sqrt{3} \sqrt{-a^2}\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{6 a^2 b \sqrt{a^4 x^4+b^4}}-\frac{\left(\sqrt{3} \sqrt{-a^2}+a\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{6 a^2 b \sqrt{a^4 x^4+b^4}}+\frac{\left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{3 a b \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,"(-2*ArcTan[(a*b*x)/Sqrt[b^4 + a^4*x^4]])/(3*a*b) - ArcTanh[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(3*Sqrt[2]*a*b) + ((b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(3*a*b*Sqrt[b^4 + a^4*x^4]) - ((a - Sqrt[3]*Sqrt[-a^2])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(6*a^2*b*Sqrt[b^4 + a^4*x^4]) - ((a + Sqrt[3]*Sqrt[-a^2])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(6*a^2*b*Sqrt[b^4 + a^4*x^4])","C",41,13,42,0.3095,1,"{6725, 220, 2073, 1211, 1699, 208, 6728, 1725, 1217, 1707, 1248, 725, 206}"
2114,0,0,0,0.3736552,"\int \frac{\sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}}}{1+x} \, dx","Int[(Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]])/(1 + x),x]","\int \frac{\sqrt{-1+x^2} \sqrt{x^2+x \sqrt{-1+x^2}}}{1+x} \, dx","\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,"Defer[Int][(Sqrt[-1 + x^2]*Sqrt[x^2 + x*Sqrt[-1 + x^2]])/(1 + x), x]","F",0,0,0,0,-1,"{}"
2115,0,0,0,0.7870364,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{1+x^2}}}{-1+x^4} \, dx","Int[((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,"(2*x^3)/(3*(1 + Sqrt[1 + x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 + x^2]] - (I/2)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(I - x), x] - Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(1 - x), x]/2 - (I/2)*Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(I + x), x] - Defer[Int][Sqrt[1 + Sqrt[1 + x^2]]/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
2116,0,0,0,1.0278548,"\int \frac{-b^2+a x^2}{\left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[(-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,"Defer[Int][1/Sqrt[b + Sqrt[b^2 + a*x^2]], x] - b*Defer[Int][1/((b - Sqrt[-a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] - b*Defer[Int][1/((b + Sqrt[-a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",0,0,0,0,-1,"{}"
2117,1,109,0,0.2178308,"\int \frac{x}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[x/(1 + Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{x^2}{4}-\frac{1}{4} \sqrt{x^2+1} x+\frac{1}{6} \left(\sqrt{x^2+1}+x\right)^{3/2}+\frac{1}{2} \sqrt{\sqrt{x^2+1}+x}-\frac{1}{2 \sqrt{\sqrt{x^2+1}+x}}-\frac{1}{6 \left(\sqrt{x^2+1}+x\right)^{3/2}}-\frac{x}{2}-\frac{1}{4} \sinh ^{-1}(x)","\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,"-1/2*x + x^2/4 - (x*Sqrt[1 + x^2])/4 - 1/(6*(x + Sqrt[1 + x^2])^(3/2)) - 1/(2*Sqrt[x + Sqrt[1 + x^2]]) + Sqrt[x + Sqrt[1 + x^2]]/2 + (x + Sqrt[1 + x^2])^(3/2)/6 - ArcSinh[x]/4","A",13,9,21,0.4286,1,"{6742, 195, 215, 2117, 14, 2119, 448, 2122, 270}"
2118,0,0,0,4.7991308,"\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","Int[(-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,"((1 + Sqrt[4 + b*(1 - k)^2]/Sqrt[b] + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][x^(1/3)/((1 - x)^(2/3)*(1 - k*x)^(2/3)*(-(b*(1 + k)) - Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3) + ((1 - Sqrt[4 + b*(1 - k)^2]/Sqrt[b] + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][x^(1/3)/((1 - x)^(2/3)*(1 - k*x)^(2/3)*(-(b*(1 + k)) + Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2119,1,195,0,0.7461067,"\int \frac{\left(-b+a x^2\right) \sqrt{-b x+a x^3}}{x^2 \left(b+a x^2\right)} \, dx","Int[((-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}}{x}+\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{a x^3-b x} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2-b}}\right)}{\sqrt{x} \sqrt{a x^2-b}}-\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{a x^3-b x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2-b}}\right)}{\sqrt{x} \sqrt{a x^2-b}}","-\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])/x + (Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[-(b*x) + a*x^3]*ArcTan[(Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[-b + a*x^2]])/(Sqrt[x]*Sqrt[-b + a*x^2]) - (Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[-(b*x) + a*x^3]*ArcTanh[(Sqrt[2]*(-a)^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[-b + a*x^2]])/(Sqrt[x]*Sqrt[-b + a*x^2])","A",15,11,36,0.3056,1,"{2056, 466, 474, 12, 490, 1211, 224, 221, 1699, 208, 205}"
2120,1,663,0,0.6541279,"\int \frac{\sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Int[(-x^3 + x^4)^(1/4)/(x*(1 + x^3)),x]","\frac{2 (-1)^{2/3} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \left(1-\sqrt[3]{-1}\right)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 (-1)^{2/3} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \left(1-\sqrt[3]{-1}\right)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[3]{-1} \sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$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,"(2*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(1 - (-1)^(1/3))^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(-1)^(1/3)*(1 + (-1)^(2/3))^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(1 - (-1)^(1/3))^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-1)^(1/3)*(1 + (-1)^(2/3))^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4))","B",33,10,24,0.4167,1,"{2056, 6725, 105, 63, 240, 212, 206, 203, 93, 298}"
2121,1,663,0,0.4916455,"\int \frac{\sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Int[(-x^3 + x^4)^(1/4)/(x*(1 + x^3)),x]","\frac{2 (-1)^{2/3} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \left(1-\sqrt[3]{-1}\right)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 (-1)^{2/3} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \left(1-\sqrt[3]{-1}\right)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[3]{-1} \sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}","-\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)-\log \left(\sqrt[4]{x^4-x^3}-\text{$\#$1} x\right)+\log (x)}{2 \text{$\#$1}^7-\text{$\#$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,"(2*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(1 - (-1)^(1/3))^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(-1)^(1/3)*(1 + (-1)^(2/3))^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*(-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(1 - (-1)^(1/3))^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2*(-1)^(1/3)*(1 + (-1)^(2/3))^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4))","B",33,10,24,0.4167,1,"{2056, 6725, 105, 63, 240, 212, 206, 203, 93, 298}"
2122,0,0,0,0.8195657,"\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","Int[((-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,"-3*Defer[Int][(1 - x^3 + x^4)^(2/3)/x^3, x] + 3*Defer[Int][(1 - x^3 + x^4)^(2/3)/(1 + x^3 + x^4), x] + 4*Defer[Int][(x*(1 - x^3 + x^4)^(2/3))/(1 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
2123,0,0,0,1.1882471,"\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","Int[((-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,"(2*(b + a*x^5)^(3/4)*Hypergeometric2F1[-3/4, -3/5, 2/5, -((a*x^5)/b)])/(3*x^3*(1 + (a*x^5)/b)^(3/4)) + 2*c*Defer[Int][(b + a*x^5)^(3/4)/(2*b + c*x^4 + 2*a*x^5), x] + 5*a*Defer[Int][(x*(b + a*x^5)^(3/4))/(2*b + c*x^4 + 2*a*x^5), x]","F",0,0,0,0,-1,"{}"
2124,0,0,0,2.2145006,"\int \frac{-1+x^6}{\sqrt[3]{x^2+x^4} \left(1+x^6\right)} \, dx","Int[(-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,"(-2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1/3, 1, 7/6, -x^2, (2*x^2)/(1 - I*Sqrt[3])])/(x^2 + x^4)^(1/3) - (2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1/3, 1, 7/6, -x^2, (2*x^2)/(1 + I*Sqrt[3])])/(x^2 + x^4)^(1/3) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3) - ((I/3)*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((I - x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(x^2 + x^4)^(1/3) - ((I/3)*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((I + x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(x^2 + x^4)^(1/3) - (Sqrt[1 - I*Sqrt[3]]*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] - Sqrt[2]*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(x^2 + x^4)^(1/3)) - (Sqrt[1 + I*Sqrt[3]]*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] - Sqrt[2]*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(x^2 + x^4)^(1/3)) - (Sqrt[1 - I*Sqrt[3]]*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((Sqrt[1 - I*Sqrt[3]] + Sqrt[2]*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(x^2 + x^4)^(1/3)) - (Sqrt[1 + I*Sqrt[3]]*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((Sqrt[1 + I*Sqrt[3]] + Sqrt[2]*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(x^2 + x^4)^(1/3))","F",0,0,0,0,-1,"{}"
2125,1,157,0,0.970814,"\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","Int[((2 + 3*x^4)^(1/4)*(4 + 6*x^4 + x^8))/(x^6*(1 + x^4)*(1 + 2*x^4)),x]","\frac{10}{3} \sqrt[4]{2} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-2 x^4,-\frac{3 x^4}{2}\right)+\frac{1}{3} \sqrt[4]{2} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-x^4,-\frac{3 x^4}{2}\right)+\frac{6 \sqrt[4]{3 x^4+2}}{x}+3 \sqrt[4]{3} \tan ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{3 x^4+2}}\right)-3 \sqrt[4]{3} \tanh ^{-1}\left(\frac{\sqrt[4]{3} x}{\sqrt[4]{3 x^4+2}}\right)-\frac{2 \left(3 x^4+2\right)^{5/4}}{5 x^5}","\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,"(6*(2 + 3*x^4)^(1/4))/x - (2*(2 + 3*x^4)^(5/4))/(5*x^5) + (10*2^(1/4)*x^3*AppellF1[3/4, 1, -1/4, 7/4, -2*x^4, (-3*x^4)/2])/3 + (2^(1/4)*x^3*AppellF1[3/4, 1, -1/4, 7/4, -x^4, (-3*x^4)/2])/3 + 3*3^(1/4)*ArcTan[(3^(1/4)*x)/(2 + 3*x^4)^(1/4)] - 3*3^(1/4)*ArcTanh[(3^(1/4)*x)/(2 + 3*x^4)^(1/4)]","C",10,8,41,0.1951,0,"{6725, 264, 277, 331, 298, 203, 206, 510}"
2126,1,212,0,0.8449929,"\int \frac{\sqrt[8]{256-256 x^2+96 x^4-16 x^6+x^8}}{-1+x^3} \, dx","Int[(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} \tan ^{-1}\left(\frac{4-x}{\sqrt{3} \sqrt{x^2-4}}\right)}{\sqrt{3} \sqrt{x^2-4}}-\frac{\sqrt{2 \sqrt{21}-3} \sqrt[8]{\left(x^2-4\right)^4} \tan ^{-1}\left(\frac{\left(21-4 \sqrt{21}\right) x+\sqrt{21}+21}{\sqrt{21 \left(2 \sqrt{21}-3\right)} \sqrt{x^2-4}}\right)}{3 \sqrt{x^2-4}}+\frac{\sqrt{3+2 \sqrt{21}} \sqrt[8]{\left(x^2-4\right)^4} \tanh ^{-1}\left(\frac{\left(21+4 \sqrt{21}\right) x-\sqrt{21}+21}{\sqrt{21 \left(3+2 \sqrt{21}\right)} \sqrt{x^2-4}}\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)*ArcTan[(4 - x)/(Sqrt[3]*Sqrt[-4 + x^2])])/(Sqrt[3]*Sqrt[-4 + x^2]) - (Sqrt[-3 + 2*Sqrt[21]]*((-4 + x^2)^4)^(1/8)*ArcTan[(21 + Sqrt[21] + (21 - 4*Sqrt[21])*x)/(Sqrt[21*(-3 + 2*Sqrt[21])]*Sqrt[-4 + x^2])])/(3*Sqrt[-4 + x^2]) + (Sqrt[3 + 2*Sqrt[21]]*((-4 + x^2)^4)^(1/8)*ArcTanh[(21 - Sqrt[21] + (21 + 4*Sqrt[21])*x)/(Sqrt[21*(3 + 2*Sqrt[21])]*Sqrt[-4 + x^2])])/(3*Sqrt[-4 + x^2])","A",19,14,32,0.4375,1,"{2074, 6720, 735, 844, 217, 206, 725, 204, 1020, 1080, 1037, 1031, 207, 203}"
2127,0,0,0,10.5968791,"\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","Int[(-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,"((6 + x^3)^(1/6)*ArcTan[(6 + x^3)^(1/6)/(-6 + x^3)^(1/6)])/(9*(-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) - ((6 + x^3)^(1/6)*ArcTan[Sqrt[3] - (2*(6 + x^3)^(1/6))/(-6 + x^3)^(1/6)])/(18*(-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) + ((6 + x^3)^(1/6)*ArcTan[Sqrt[3] + (2*(6 + x^3)^(1/6))/(-6 + x^3)^(1/6)])/(18*(-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) + ((6 + x^3)^(1/6)*Log[1 - (Sqrt[3]*(6 + x^3)^(1/6))/(-6 + x^3)^(1/6) + (6 + x^3)^(1/3)/(-6 + x^3)^(1/3)])/(12*Sqrt[3]*(-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) - ((6 + x^3)^(1/6)*Log[1 + (Sqrt[3]*(6 + x^3)^(1/6))/(-6 + x^3)^(1/6) + (6 + x^3)^(1/3)/(-6 + x^3)^(1/3)])/(12*Sqrt[3]*(-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) - (90*(6 + x^3)^(1/6)*Defer[Int][1/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) + (116*(6 + x^3)^(1/6)*Defer[Int][x/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) - (90*(6 + x^3)^(1/6)*Defer[Int][x^2/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) + (51*(6 + x^3)^(1/6)*Defer[Int][x^3/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) - (26*(6 + x^3)^(1/6)*Defer[Int][x^4/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) + (16*(6 + x^3)^(1/6)*Defer[Int][x^5/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) - (6*(6 + x^3)^(1/6)*Defer[Int][x^6/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6)) + ((6 + x^3)^(1/6)*Defer[Int][x^7/((-6 + x^3)^(5/6)*(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])/((-6 + x^3)^(1/6)*(-((6 + x^3)/(6 - x^3)))^(1/6))","F",0,0,0,0,-1,"{}"
2128,1,549,0,1.735864,"\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","Int[(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",16,8,41,0.1951,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2129,1,549,0,1.1842117,"\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","Int[(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",16,8,41,0.1951,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2130,0,0,0,0.725276,"\int \frac{-b+a x^8}{\left(b+a x^8\right) \sqrt[4]{b-c x^4+a x^8}} \, dx","Int[(-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,"(x*(1 - (2*a*x^4)/(c - Sqrt[-4*a*b + c^2]))^(1/4)*(1 - (2*a*x^4)/(c + Sqrt[-4*a*b + c^2]))^(1/4)*AppellF1[1/4, 1/4, 1/4, 5/4, (2*a*x^4)/(c + Sqrt[-4*a*b + c^2]), (2*a*x^4)/(c - Sqrt[-4*a*b + c^2])])/(b - c*x^4 + a*x^8)^(1/4) - Sqrt[b]*Defer[Int][1/((Sqrt[b] - Sqrt[-a]*x^4)*(b - c*x^4 + a*x^8)^(1/4)), x] - Sqrt[b]*Defer[Int][1/((Sqrt[b] + Sqrt[-a]*x^4)*(b - c*x^4 + a*x^8)^(1/4)), x]","F",0,0,0,0,-1,"{}"
2131,0,0,0,4.7675007,"\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","Int[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,"(2*Sqrt[x]*Sqrt[-b + a^2*x]*Defer[Subst][Defer[Int][1/(x^4*Sqrt[-b + a^2*x^2]*(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2)), x], x, Sqrt[x]])/Sqrt[-(b*x) + a^2*x^2]","F",0,0,0,0,-1,"{}"
2132,1,208,0,0.72267,"\int \frac{1+\sqrt{1+x^2}}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(1 + Sqrt[1 + x^2])/(1 + Sqrt[x + Sqrt[1 + x^2]]),x]","-\frac{x^2}{4}+\frac{1}{4} \sqrt{x^2+1} x+\frac{1}{6} \left(\sqrt{x^2+1}+x\right)^{3/2}-\frac{\sqrt{x^2+1}}{2}+\frac{3}{2} \sqrt{\sqrt{x^2+1}+x}+\frac{3}{2 \sqrt{\sqrt{x^2+1}+x}}-\frac{1}{2 \left(\sqrt{x^2+1}+x\right)}+\frac{1}{6 \left(\sqrt{x^2+1}+x\right)^{3/2}}+\frac{1}{2} \log \left(\sqrt{x^2+1}+x\right)-2 \log \left(\sqrt{\sqrt{x^2+1}+x}+1\right)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{x^2+1}\right)-2 \tanh ^{-1}\left(\sqrt{\sqrt{x^2+1}+x}\right)-\frac{\log (x)}{2}+\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,"-1/4*x^2 - Sqrt[1 + x^2]/2 + (x*Sqrt[1 + x^2])/4 + 1/(6*(x + Sqrt[1 + x^2])^(3/2)) - 1/(2*(x + Sqrt[1 + x^2])) + 3/(2*Sqrt[x + Sqrt[1 + x^2]]) + (3*Sqrt[x + Sqrt[1 + x^2]])/2 + (x + Sqrt[1 + x^2])^(3/2)/6 + ArcSinh[x]/4 + ArcTanh[Sqrt[1 + x^2]]/2 - 2*ArcTanh[Sqrt[x + Sqrt[1 + x^2]]] - Log[x]/2 + Log[x + Sqrt[1 + x^2]]/2 - 2*Log[1 + Sqrt[x + Sqrt[1 + x^2]]]","A",32,22,31,0.7097,1,"{6742, 2117, 1821, 1620, 195, 215, 266, 50, 63, 207, 14, 2122, 270, 2120, 462, 459, 329, 298, 203, 206, 466, 461}"
2133,0,0,0,4.4300482,"\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","Int[(-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,"((1 + Sqrt[4 + b*(1 - k)^2]/Sqrt[b] + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-(b*(1 + k)) - Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3) + ((1 - Sqrt[4 + b*(1 - k)^2]/Sqrt[b] + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-(b*(1 + k)) + Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2134,1,232,0,0.7025602,"\int \frac{\sqrt[4]{-b+a x^4} \left(-8 b+a x^8\right)}{x^{10} \left(b+a x^4\right)} \, dx","Int[((-b + a*x^4)^(1/4)*(-8*b + a*x^8))/(x^10*(b + a*x^4)),x]","\frac{a^{5/4} (8 a-b) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 b^2}-\frac{a^{5/4} (8 a-b) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 b^2}+\frac{a^2 x^3 (8 a-b) \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{a x^4}{b},\frac{a x^4}{b}\right)}{3 b^3 \sqrt[4]{1-\frac{a x^4}{b}}}+\frac{a (8 a-b) \sqrt[4]{a x^4-b}}{b^2 x}+\frac{8 a \left(a x^4-b\right)^{5/4}}{9 b^2 x^5}-\frac{8 \left(a x^4-b\right)^{5/4}}{9 b x^9}","\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,"(a*(8*a - b)*(-b + a*x^4)^(1/4))/(b^2*x) - (8*(-b + a*x^4)^(5/4))/(9*b*x^9) + (8*a*(-b + a*x^4)^(5/4))/(9*b^2*x^5) + (a^2*(8*a - b)*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((a*x^4)/b), (a*x^4)/b])/(3*b^3*(1 - (a*x^4)/b)^(1/4)) + (a^(5/4)*(8*a - b)*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(2*b^2) - (a^(5/4)*(8*a - b)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(2*b^2)","C",12,10,35,0.2857,0,"{6725, 271, 264, 277, 331, 298, 203, 206, 511, 510}"
2135,0,0,0,1.1843697,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Int[x/(x + Sqrt[x + Sqrt[1 + x]]),x]","\int \frac{x}{x+\sqrt{x+\sqrt{1+x}}} \, dx","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$1}+3}\&\right]+x-2 \sqrt{x+\sqrt{x+1}}-\log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"x + Log[2 - Sqrt[1 + x] - 3*(1 + x) + (1 + x)^2]/2 + Defer[Subst][Defer[Int][(2 - x - 3*x^2 + x^4)^(-1), x], x, Sqrt[1 + x]]/2 + Defer[Subst][Defer[Int][x/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 2*Defer[Subst][Defer[Int][x^2/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 2*Defer[Subst][Defer[Int][(x*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 2*Defer[Subst][Defer[Int][(x^3*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2136,0,0,0,0.9383269,"\int \frac{x}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Int[x/(x + Sqrt[x + Sqrt[1 + x]]),x]","\int \frac{x}{x+\sqrt{x+\sqrt{1+x}}} \, dx","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$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 + Log[2 - Sqrt[1 + x] - 3*(1 + x) + (1 + x)^2]/2 + Defer[Subst][Defer[Int][(2 - x - 3*x^2 + x^4)^(-1), x], x, Sqrt[1 + x]]/2 + Defer[Subst][Defer[Int][x/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 2*Defer[Subst][Defer[Int][x^2/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 2*Defer[Subst][Defer[Int][(x*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 2*Defer[Subst][Defer[Int][(x^3*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2137,0,0,0,9.8047349,"\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","Int[((-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,"((48/5 + (24*I)/5)*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/((-5/3 + 2*I) - 2*x)^2, x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) - (((24*I)/5)*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/((-5/3 + 2*I) - 2*x), x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) + (6*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/(-7/6 + x)^2, x], x, 1/6 + x])/(5*(1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) - (51*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/(-7/6 + x), x], x, 1/6 + x])/(5*(1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) + (18*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/(-1/6 + x)^5, x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) - (3*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/(-1/6 + x)^3, x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) + (27*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/(-1/6 + x)^2, x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) + ((51/5 + (39*I)/5)*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/((5/3 - 2*I) + 2*x), x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) + ((48/5 - (24*I)/5)*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/((5/3 + 2*I) + 2*x)^2, x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3)) + ((51/5 - (63*I)/5)*(-2 + x^2 + 2*x^3)^(1/3)*Defer[Subst][Defer[Int][((-1/3*(1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 2*x)^(1/3)*((-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3))/9 + (2*(1 + (107 + 6*Sqrt[318])^(2/3))*x)/(3*(107 + 6*Sqrt[318])^(1/3)) + 4*x^2)^(1/3))/((5/3 + 2*I) + 2*x), x], x, 1/6 + x])/((1 - (1 + (107 + 6*Sqrt[318])^(2/3))/(107 + 6*Sqrt[318])^(1/3) + 6*x)^(1/3)*(-1 + (107 + 6*Sqrt[318])^(-2/3) + (107 + 6*Sqrt[318])^(2/3) + ((1 + (107 + 6*Sqrt[318])^(2/3))*(1 + 6*x))/(107 + 6*Sqrt[318])^(1/3) + (1 + 6*x)^2)^(1/3))","F",0,0,0,0,-1,"{}"
2138,1,746,0,0.8719558,"\int \frac{(-1+x) \sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Int[((-1 + x)*(-x^3 + x^4)^(1/4))/(x*(1 + x^3)),x]","\frac{1}{3} (-1)^{2/3} \sqrt[4]{x^4-x^3}-\frac{1}{3} \sqrt[3]{-1} \sqrt[4]{x^4-x^3}+\frac{1}{3} \sqrt[4]{x^4-x^3}-\frac{(-1)^{2/3} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}-\frac{4 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{1-i \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{1+i \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{(-1)^{2/3} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}+\frac{4 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{1-i \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{1+i \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{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,"(-x^3 + x^4)^(1/4)/3 - ((-1)^(1/3)*(-x^3 + x^4)^(1/4))/3 + ((-1)^(2/3)*(-x^3 + x^4)^(1/4))/3 - ((-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) + ((-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) - ((-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) - (4*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2^(3/4)*(1 - I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2^(3/4)*(1 + I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - ((-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) + ((-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) - ((-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) + (4*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2^(3/4)*(1 - I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2^(3/4)*(1 + I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4))","C",54,11,27,0.4074,1,"{2056, 6725, 105, 50, 63, 240, 212, 206, 203, 93, 298}"
2139,1,746,0,0.6918733,"\int \frac{(-1+x) \sqrt[4]{-x^3+x^4}}{x \left(1+x^3\right)} \, dx","Int[((-1 + x)*(-x^3 + x^4)^(1/4))/(x*(1 + x^3)),x]","\frac{1}{3} (-1)^{2/3} \sqrt[4]{x^4-x^3}-\frac{1}{3} \sqrt[3]{-1} \sqrt[4]{x^4-x^3}+\frac{1}{3} \sqrt[4]{x^4-x^3}-\frac{(-1)^{2/3} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}-\frac{4 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{1-i \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{1+i \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{(-1)^{2/3} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[3]{-1} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{6 \sqrt[4]{x-1} x^{3/4}}+\frac{4 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{1-i \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-\sqrt[3]{-1}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{1+i \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+(-1)^{2/3}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{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,"(-x^3 + x^4)^(1/4)/3 - ((-1)^(1/3)*(-x^3 + x^4)^(1/4))/3 + ((-1)^(2/3)*(-x^3 + x^4)^(1/4))/3 - ((-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) + ((-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) - ((-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) - (4*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2^(3/4)*(1 - I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (2^(3/4)*(1 + I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - ((-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) + ((-1)^(1/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) - ((-1)^(2/3)*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(6*(-1 + x)^(1/4)*x^(3/4)) + (4*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2^(3/4)*(1 - I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 - (-1)^(1/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) - (2^(3/4)*(1 + I*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 + (-1)^(2/3))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4))","C",54,11,27,0.4074,1,"{2056, 6725, 105, 50, 63, 240, 212, 206, 203, 93, 298}"
2140,1,320,0,0.7448629,"\int \frac{(1+x) \sqrt[4]{x^3+x^5}}{x \left(-1+x^3\right)} \, dx","Int[((1 + x)*(x^3 + x^5)^(1/4))/(x*(-1 + x^3)),x]","-\frac{4 \left(1-\sqrt[3]{-1}\right) \sqrt[4]{x^5+x^3} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^2,-\sqrt[3]{-1} x^2\right)}{9 \sqrt[4]{x^2+1}}-\frac{4 \left(1+(-1)^{2/3}\right) \sqrt[4]{x^5+x^3} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^2,(-1)^{2/3} x^2\right)}{9 \sqrt[4]{x^2+1}}-\frac{8 \sqrt[4]{x^5+x^3} F_1\left(\frac{3}{8};1,-\frac{1}{4};\frac{11}{8};x^2,-x^2\right)}{9 \sqrt[4]{x^2+1}}-\frac{4 \left(1+(-1)^{2/3}\right) x \sqrt[4]{x^5+x^3} F_1\left(\frac{7}{8};-\frac{1}{4},1;\frac{15}{8};-x^2,-\sqrt[3]{-1} x^2\right)}{21 \sqrt[4]{x^2+1}}-\frac{4 \left(1-\sqrt[3]{-1}\right) x \sqrt[4]{x^5+x^3} F_1\left(\frac{7}{8};-\frac{1}{4},1;\frac{15}{8};-x^2,(-1)^{2/3} x^2\right)}{21 \sqrt[4]{x^2+1}}-\frac{8 x \sqrt[4]{x^5+x^3} F_1\left(\frac{7}{8};1,-\frac{1}{4};\frac{15}{8};x^2,-x^2\right)}{21 \sqrt[4]{x^2+1}}","\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,"(-4*(1 - (-1)^(1/3))*(x^3 + x^5)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^2, -((-1)^(1/3)*x^2)])/(9*(1 + x^2)^(1/4)) - (4*(1 + (-1)^(2/3))*(x^3 + x^5)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^2, (-1)^(2/3)*x^2])/(9*(1 + x^2)^(1/4)) - (8*(x^3 + x^5)^(1/4)*AppellF1[3/8, 1, -1/4, 11/8, x^2, -x^2])/(9*(1 + x^2)^(1/4)) - (4*(1 + (-1)^(2/3))*x*(x^3 + x^5)^(1/4)*AppellF1[7/8, -1/4, 1, 15/8, -x^2, -((-1)^(1/3)*x^2)])/(21*(1 + x^2)^(1/4)) - (4*(1 - (-1)^(1/3))*x*(x^3 + x^5)^(1/4)*AppellF1[7/8, -1/4, 1, 15/8, -x^2, (-1)^(2/3)*x^2])/(21*(1 + x^2)^(1/4)) - (8*x*(x^3 + x^5)^(1/4)*AppellF1[7/8, 1, -1/4, 15/8, x^2, -x^2])/(21*(1 + x^2)^(1/4))","C",18,5,25,0.2000,0,"{2056, 6725, 959, 466, 510}"
2141,1,2641,0,6.0230671,"\int \frac{x^3}{\sqrt[3]{-b x^2+a x^3} \left(-b^2+a^2 x^6\right)} \, dx","Int[x^3/((-(b*x^2) + a*x^3)^(1/3)*(-b^2 + a^2*x^6)),x]","-\frac{(-1)^{2/3} x (b-a x)}{3 a^{5/3} b^{4/3} \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt[3]{-1} x (b-a x)}{3 a^{5/3} b^{4/3} \sqrt[3]{a x^3-b x^2}}-\frac{x (b-a x)}{3 a^{5/3} b^{4/3} \sqrt[3]{a x^3-b x^2}}-\frac{(-1)^{2/3} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt[3]{-1} x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{2/3}-b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{10/9} \sqrt[3]{a^{2/3}-b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{2/3}+b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{10/9} \sqrt[3]{a^{2/3}+b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{10/9} \sqrt[3]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{2/3}+\sqrt[3]{-1} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{10/9} \sqrt[3]{a^{2/3}+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{2/3}-(-1)^{2/3} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{10/9} \sqrt[3]{a^{2/3}-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x-b}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{2/3}+(-1)^{2/3} b^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{10/9} \sqrt[3]{a^{2/3}+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{(-1)^{2/3} x^{2/3} \sqrt[3]{a x-b} \log (x)}{18 a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt[3]{-1} x^{2/3} \sqrt[3]{a x-b} \log (x)}{18 a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log (x)}{18 a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(-\sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{10/9} \sqrt[3]{a^{2/3}+b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right)}{12 a^{10/9} \sqrt[3]{a^{2/3}-b^{2/3}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{10/9} \sqrt[3]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{12 a^{10/9} \sqrt[3]{a^{2/3}+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(-(-1)^{2/3} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{10/9} \sqrt[3]{a^{2/3}+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{a} x\right)}{12 a^{10/9} \sqrt[3]{a^{2/3}-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[9]{a} \sqrt[3]{a^{2/3}-b^{2/3}}}-\sqrt[3]{x}\right)}{4 a^{10/9} \sqrt[3]{a^{2/3}-b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[9]{a} \sqrt[3]{a^{2/3}+b^{2/3}}}-\sqrt[3]{x}\right)}{4 a^{10/9} \sqrt[3]{a^{2/3}+b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[9]{a} \sqrt[3]{a^{2/3}-\sqrt[3]{-1} b^{2/3}}}-\sqrt[3]{x}\right)}{4 a^{10/9} \sqrt[3]{a^{2/3}-\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[9]{a} \sqrt[3]{a^{2/3}+\sqrt[3]{-1} b^{2/3}}}-\sqrt[3]{x}\right)}{4 a^{10/9} \sqrt[3]{a^{2/3}+\sqrt[3]{-1} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}+\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[9]{a} \sqrt[3]{a^{2/3}-(-1)^{2/3} b^{2/3}}}-\sqrt[3]{x}\right)}{4 a^{10/9} \sqrt[3]{a^{2/3}-(-1)^{2/3} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[9]{a} \sqrt[3]{a^{2/3}+(-1)^{2/3} b^{2/3}}}-\sqrt[3]{x}\right)}{4 a^{10/9} \sqrt[3]{a^{2/3}+(-1)^{2/3} b^{2/3}} b \sqrt[3]{a x^3-b x^2}}-\frac{(-1)^{2/3} x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a} \sqrt[3]{x}}-1\right)}{6 a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}+\frac{\sqrt[3]{-1} x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a} \sqrt[3]{x}}-1\right)}{6 a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a x-b} \log \left(\frac{\sqrt[3]{a x-b}}{\sqrt[3]{a} \sqrt[3]{x}}-1\right)}{6 a^2 \sqrt[3]{b} \sqrt[3]{a x^3-b x^2}}","\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,"-1/3*(x*(b - a*x))/(a^(5/3)*b^(4/3)*(-(b*x^2) + a*x^3)^(1/3)) + ((-1)^(1/3)*x*(b - a*x))/(3*a^(5/3)*b^(4/3)*(-(b*x^2) + a*x^3)^(1/3)) - ((-1)^(2/3)*x*(b - a*x))/(3*a^(5/3)*b^(4/3)*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/3)*x^(1/3))])/(3*Sqrt[3]*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) + ((-1)^(1/3)*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/3)*x^(1/3))])/(3*Sqrt[3]*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) - ((-1)^(2/3)*x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/3)*x^(1/3))])/(3*Sqrt[3]*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(2/3) - b^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(10/9)*(a^(2/3) - b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(2/3) + b^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(10/9)*(a^(2/3) + b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(10/9)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(2/3) + (-1)^(1/3)*b^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(10/9)*(a^(2/3) + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(2/3) - (-1)^(2/3)*b^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(10/9)*(a^(2/3) - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(10/9)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[x])/(18*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) + ((-1)^(1/3)*x^(2/3)*(-b + a*x)^(1/3)*Log[x])/(18*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) - ((-1)^(2/3)*x^(2/3)*(-b + a*x)^(1/3)*Log[x])/(18*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[-b^(1/3) - a^(1/3)*x])/(12*a^(10/9)*(a^(2/3) + b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/3) - a^(1/3)*x])/(12*a^(10/9)*(a^(2/3) - b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[-b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(12*a^(10/9)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(12*a^(10/9)*(a^(2/3) + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(12*a^(10/9)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(12*a^(10/9)*(a^(2/3) - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/9)*(a^(2/3) - b^(2/3))^(1/3))])/(4*a^(10/9)*(a^(2/3) - b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/9)*(a^(2/3) + b^(2/3))^(1/3))])/(4*a^(10/9)*(a^(2/3) + b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/9)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/3))])/(4*a^(10/9)*(a^(2/3) - (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/9)*(a^(2/3) + (-1)^(1/3)*b^(2/3))^(1/3))])/(4*a^(10/9)*(a^(2/3) + (-1)^(1/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) + (x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/9)*(a^(2/3) - (-1)^(2/3)*b^(2/3))^(1/3))])/(4*a^(10/9)*(a^(2/3) - (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[-x^(1/3) + (-b + a*x)^(1/3)/(a^(1/9)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/3))])/(4*a^(10/9)*(a^(2/3) + (-1)^(2/3)*b^(2/3))^(1/3)*b*(-(b*x^2) + a*x^3)^(1/3)) - (x^(2/3)*(-b + a*x)^(1/3)*Log[-1 + (-b + a*x)^(1/3)/(a^(1/3)*x^(1/3))])/(6*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) + ((-1)^(1/3)*x^(2/3)*(-b + a*x)^(1/3)*Log[-1 + (-b + a*x)^(1/3)/(a^(1/3)*x^(1/3))])/(6*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3)) - ((-1)^(2/3)*x^(2/3)*(-b + a*x)^(1/3)*Log[-1 + (-b + a*x)^(1/3)/(a^(1/3)*x^(1/3))])/(6*a^2*b^(1/3)*(-(b*x^2) + a*x^3)^(1/3))","B",67,6,35,0.1714,0,"{2056, 6725, 105, 50, 59, 91}"
2142,0,0,0,1.2982453,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(1 + x^2)/((-1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\frac{-4 (-30 x-151)+\sqrt{x+1} \left(8-24 \sqrt{\sqrt{x+1}+1}\right)+64 \sqrt{\sqrt{x+1}+1}}{105 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{2}}\right)",1,"4/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] + (16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 + 2*Sqrt[2]*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[2]] + 16*Defer[Subst][Defer[Int][x^2/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 24*Defer[Subst][Defer[Int][x^4/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + 8*Defer[Subst][Defer[Int][x^6/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2143,0,0,0,0.9563543,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(1 + x^2)/((-1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\frac{-4 (-30 x-151)+\sqrt{x+1} \left(8-24 \sqrt{\sqrt{x+1}+1}\right)+64 \sqrt{\sqrt{x+1}+1}}{105 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{2}}\right)",1,"4/Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] + (16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 + 2*Sqrt[2]*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[2]] + 16*Defer[Subst][Defer[Int][x^2/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 24*Defer[Subst][Defer[Int][x^4/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + 8*Defer[Subst][Defer[Int][x^6/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2144,0,0,0,0.5791494,"\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[(-1 + x + x^3)/((1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^9-2 \text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{3 \text{$\#$1}^3-1}\&\right]-\log \left(\sqrt[3]{x^3-x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3-x^2} x+\left(x^3-x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x^2}+x}\right)",1,"(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[(1 + (2*x^(1/3))/(-1 + x)^(1/3))/Sqrt[3]])/(-x^2 + x^3)^(1/3) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3) - x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) + (6*(-1 + x)^(1/3)*x^(2/3)*Defer[Subst][Defer[Int][(-1 + x^3)^(2/3)/(1 - x^3 + x^9), x], x, x^(1/3)])/(-x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
2145,0,0,0,0.4315944,"\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[(-1 + x + x^3)/((1 - x + x^3)*(-x^2 + x^3)^(1/3)),x]","\int \frac{-1+x+x^3}{\left(1-x+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^9-2 \text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt[3]{x^3-x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)}{3 \text{$\#$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,"(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[(1 + (2*x^(1/3))/(-1 + x)^(1/3))/Sqrt[3]])/(-x^2 + x^3)^(1/3) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3) - x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) + (6*(-1 + x)^(1/3)*x^(2/3)*Defer[Subst][Defer[Int][(-1 + x^3)^(2/3)/(1 - x^3 + x^9), x], x, x^(1/3)])/(-x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
2146,1,176,0,0.2070106,"\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","Int[((1 + 2*x^3)^(4/3)*(1 + 3*x^3))/(x^8*(1 + 4*x^3)),x]","-\frac{29 \sqrt[3]{2 x^3+1}}{14 x}+\frac{2}{3} \sqrt[3]{2} \log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{2 x^3+1}}+1\right)+\frac{2 \sqrt[3]{2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{2 x^3+1}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(2 x^3+1\right)^{4/3}}{7 x^7}-\frac{\sqrt[3]{2 x^3+1}}{28 x^4}-\frac{1}{3} \sqrt[3]{2} \log \left(-\frac{\sqrt[3]{2} x}{\sqrt[3]{2 x^3+1}}+\frac{2^{2/3} x^2}{\left(2 x^3+1\right)^{2/3}}+1\right)","\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)/x^4 - (29*(1 + 2*x^3)^(1/3))/(14*x) - (1 + 2*x^3)^(4/3)/(7*x^7) + (2*2^(1/3)*ArcTan[(1 - (2*2^(1/3)*x)/(1 + 2*x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - (2^(1/3)*Log[1 + (2^(2/3)*x^2)/(1 + 2*x^3)^(2/3) - (2^(1/3)*x)/(1 + 2*x^3)^(1/3)])/3 + (2*2^(1/3)*Log[1 + (2^(1/3)*x)/(1 + 2*x^3)^(1/3)])/3","A",11,10,31,0.3226,1,"{580, 583, 12, 494, 292, 31, 634, 617, 204, 628}"
2147,1,46,0,0.114894,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt[3]{-x^2+x^4}} \, dx","Int[(-1 + x^2)/((1 + x^2)*(-x^2 + x^4)^(1/3)),x]","-\frac{3 x \sqrt[3]{1-x^2} F_1\left(\frac{1}{6};-\frac{2}{3},1;\frac{7}{6};x^2,-x^2\right)}{\sqrt[3]{x^4-x^2}}","-\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*(1 - x^2)^(1/3)*AppellF1[1/6, -2/3, 1, 7/6, x^2, -x^2])/(-x^2 + x^4)^(1/3)","C",4,4,26,0.1538,0,"{2056, 466, 430, 429}"
2148,1,296,0,1.1145633,"\int \frac{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4\right)}{b+a x^4} \, dx","Int[((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4))/(b + a*x^4),x]","\frac{b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{\sqrt[4]{1-\frac{a x^2}{b}}}-\frac{x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{\sqrt[4]{1-\frac{a x^2}{b}}}+x \sqrt[4]{a x^4-b x^2}","-\frac{3}{4} b \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]+\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{2 a^{3/4}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{2 a^{3/4}}+x \sqrt[4]{a x^4-b x^2}",1,"x*(-(b*x^2) + a*x^4)^(1/4) - (x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), (a*x^2)/b])/(1 - (a*x^2)/b)^(1/4) - (x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], (a*x^2)/b])/(1 - (a*x^2)/b)^(1/4) + (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)) - (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4))","A",16,12,36,0.3333,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 1270, 1529, 511, 510}"
2149,1,296,0,0.9943937,"\int \frac{\sqrt[4]{-b x^2+a x^4} \left(-b+2 a x^4\right)}{b+a x^4} \, dx","Int[((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4))/(b + a*x^4),x]","\frac{b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{\sqrt[4]{1-\frac{a x^2}{b}}}-\frac{x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{\sqrt[4]{1-\frac{a x^2}{b}}}+x \sqrt[4]{a x^4-b x^2}","-\frac{3}{4} b \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$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,"x*(-(b*x^2) + a*x^4)^(1/4) - (x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), (a*x^2)/b])/(1 - (a*x^2)/b)^(1/4) - (x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], (a*x^2)/b])/(1 - (a*x^2)/b)^(1/4) + (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)) - (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4))","A",16,12,36,0.3333,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 1270, 1529, 511, 510}"
2150,0,0,0,2.2180314,"\int \frac{x^3 (-4 a+3 x)}{\left(x^2 (-a+x)\right)^{2/3} \left(a-x+d x^4\right)} \, dx","Int[(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,"(-12*a*x^(4/3)*(-a + x)^(2/3)*Defer[Subst][Defer[Int][x^7/((-a + x^3)^(2/3)*(a - x^3 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(2/3) + (9*x^(4/3)*(-a + x)^(2/3)*Defer[Subst][Defer[Int][x^10/((-a + x^3)^(2/3)*(a - x^3 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(2/3)","F",0,0,0,0,-1,"{}"
2151,1,269,0,1.1920591,"\int \frac{b+a x^6}{x^6 \left(b+a x^3\right) \sqrt[4]{-b x+a x^4}} \, dx","Int[(b + a*x^6)/(x^6*(b + a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","\frac{2^{3/4} a^{3/4} \sqrt[4]{x} (a+b) \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 b^2 \sqrt[4]{a x^4-b x}}+\frac{2^{3/4} a^{3/4} \sqrt[4]{x} (a+b) \sqrt[4]{a x^3-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 b^2 \sqrt[4]{a x^4-b x}}-\frac{4 (a+b) \left(b-a x^3\right)^2}{21 a b^2 x^5 \sqrt[4]{a x^4-b x}}+\frac{4 \left(b-a x^3\right)}{21 a x^5 \sqrt[4]{a x^4-b x}}-\frac{4 \left(b-a x^3\right)}{21 b x^2 \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))/(21*a*x^5*(-(b*x) + a*x^4)^(1/4)) - (4*(b - a*x^3))/(21*b*x^2*(-(b*x) + a*x^4)^(1/4)) - (4*(a + b)*(b - a*x^3)^2)/(21*a*b^2*x^5*(-(b*x) + a*x^4)^(1/4)) + (2^(3/4)*a^(3/4)*(a + b)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*b^2*(-(b*x) + a*x^4)^(1/4)) + (2^(3/4)*a^(3/4)*(a + b)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*b^2*(-(b*x) + a*x^4)^(1/4))","A",14,11,34,0.3235,1,"{2056, 6725, 271, 264, 466, 465, 494, 461, 212, 206, 203}"
2152,1,383,0,1.5308606,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","-\frac{i \tan ^{-1}\left(\frac{-2 \left((-2+2 i)+\sqrt{1-i}\right) \sqrt{x+1}+4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)+(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}-\frac{i \tan ^{-1}\left(\frac{2 \left((2-2 i)+\sqrt{1-i}\right) \sqrt{x+1}-4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)-(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)-(1-i)^{3/2}}}-\frac{i \tan ^{-1}\left(\frac{2 \left((-2-2 i)+\sqrt{1+i}\right) \sqrt{x+1}-(2-2 i) \left(i+(1+i)^{3/2}\right)}{4 \sqrt{(1-i)+(1+i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}-\frac{i \tan ^{-1}\left(\frac{-2 \left((2+2 i)+\sqrt{1+i}\right) \sqrt{x+1}+4 \sqrt{1+i}-(2+2 i)}{4 \sqrt{(1-i)-(1+i)^{3/2}} \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)","128 \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+12 \text{$\#$1}^6+24 \text{$\#$1}^5+470 \text{$\#$1}^4+120 \text{$\#$1}^3+300 \text{$\#$1}^2+1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+9 \text{$\#$1}^5+15 \text{$\#$1}^4+235 \text{$\#$1}^3+45 \text{$\#$1}^2+75 \text{$\#$1}+125}\&\right]-2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"((-I)*ArcTan[((2 - 2*I) + 4*Sqrt[1 - I] - 2*((-2 + 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) + (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] - (I*ArcTan[((2 - 2*I) - 4*Sqrt[1 - I] + 2*((2 - 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) - (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) - (1 - I)^(3/2)] - (I*ArcTan[((-2 + 2*I)*(I + (1 + I)^(3/2)) + 2*((-2 - 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) + (1 + I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] - (I*ArcTan[((-2 - 2*I) + 4*Sqrt[1 + I] - 2*((2 + 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) - (1 + I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) - (1 + I)^(3/2)] + 2*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])]","C",19,8,33,0.2424,1,"{1586, 6741, 6728, 621, 206, 984, 724, 204}"
2153,1,383,0,1.2985359,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","-\frac{i \tan ^{-1}\left(\frac{-2 \left((-2+2 i)+\sqrt{1-i}\right) \sqrt{x+1}+4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)+(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}-\frac{i \tan ^{-1}\left(\frac{2 \left((2-2 i)+\sqrt{1-i}\right) \sqrt{x+1}-4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)-(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)-(1-i)^{3/2}}}-\frac{i \tan ^{-1}\left(\frac{2 \left((-2-2 i)+\sqrt{1+i}\right) \sqrt{x+1}-(2-2 i) \left(i+(1+i)^{3/2}\right)}{4 \sqrt{(1-i)+(1+i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}-\frac{i \tan ^{-1}\left(\frac{-2 \left((2+2 i)+\sqrt{1+i}\right) \sqrt{x+1}+4 \sqrt{1+i}-(2+2 i)}{4 \sqrt{(1-i)-(1+i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)-(1+i)^{3/2}}}+2 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","128 \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+12 \text{$\#$1}^6+24 \text{$\#$1}^5+470 \text{$\#$1}^4+120 \text{$\#$1}^3+300 \text{$\#$1}^2+1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+9 \text{$\#$1}^5+15 \text{$\#$1}^4+235 \text{$\#$1}^3+45 \text{$\#$1}^2+75 \text{$\#$1}+125}\&\right]-2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"((-I)*ArcTan[((2 - 2*I) + 4*Sqrt[1 - I] - 2*((-2 + 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) + (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] - (I*ArcTan[((2 - 2*I) - 4*Sqrt[1 - I] + 2*((2 - 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) - (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) - (1 - I)^(3/2)] - (I*ArcTan[((-2 + 2*I)*(I + (1 + I)^(3/2)) + 2*((-2 - 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) + (1 + I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] - (I*ArcTan[((-2 - 2*I) + 4*Sqrt[1 + I] - 2*((2 + 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) - (1 + I)^(3/2)]*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]])]","C",19,8,33,0.2424,1,"{1586, 6741, 6728, 621, 206, 984, 724, 204}"
2154,0,0,0,0.1879397,"\int x^2 \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Int[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,"Defer[Int][x^2*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
2155,0,0,0,1.2555123,"\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","Int[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]","\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","-\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2156,0,0,0,28.4152673,"\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","Int[((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]","\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","-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,"(2*(a - x))/(-((a - x)*(b - x)^2))^(1/4) - (2*(2*a - 3*b)*(a - x))/((a - b)*(-((a - x)*(b - x)^2))^(1/4)) - (2*(a + d)*(a - x))/((a - b)*(-((a - x)*(b - x)^2))^(1/4)) + (2*(2*a - 3*b)*(b - x)*Sqrt[-a + x])/((a - b)^(3/2)*(-((a - x)*(b - x)^2))^(1/4)*(1 + Sqrt[-a + x]/Sqrt[a - b])) - (6*(b - x)*Sqrt[-a + x])/(Sqrt[a - b]*(-((a - x)*(b - x)^2))^(1/4)*(1 + Sqrt[-a + x]/Sqrt[a - b])) + (2*(a + d)*(b - x)*Sqrt[-a + x])/((a - b)^(3/2)*(-((a - x)*(b - x)^2))^(1/4)*(1 + Sqrt[-a + x]/Sqrt[a - b])) + (2*(2*a - 3*b)*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticE[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/((a - b)^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) - (6*(a - b)^(3/4)*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticE[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(-((a - x)*(b - x)^2))^(1/4) + (2*(a + d)*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticE[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/((a - b)^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) - ((2*a - 3*b)*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/((a - b)^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) + (3*(a - b)^(3/4)*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/(-((a - x)*(b - x)^2))^(1/4) - ((a + d)*(-a + x)^(1/4)*Sqrt[-((b - x)/((a - b)*(1 + Sqrt[-a + x]/Sqrt[a - b])^2))]*(1 + Sqrt[-a + x]/Sqrt[a - b])*EllipticF[2*ArcTan[(-a + x)^(1/4)/(a - b)^(1/4)], 1/2])/((a - b)^(1/4)*(-((a - x)*(b - x)^2))^(1/4)) - (4*(a - b)^2*d*(a + d)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^2/((a - b + x^4)^(3/2)*(a^2*(1 + (b*(-2*a + b))/a^2)*d + 2*a*(1 - b/a)*d*x^4 + d*x^8 - x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4) - (4*(a - b)*d*(3*a - b + 2*d)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^6/((a - b + x^4)^(3/2)*(a^2*(1 + (b*(-2*a + b))/a^2)*d + 2*a*(1 - b/a)*d*x^4 + d*x^8 - x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4) - (4*d*(3*a - 2*b + d)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^10/((a - b + x^4)^(3/2)*(a^2*(1 + (b*(-2*a + b))/a^2)*d + 2*a*(1 - b/a)*d*x^4 + d*x^8 - x^12)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4) - (4*(2*a - 3*b)*d*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][(x^2*Sqrt[a - b + x^4])/(a^2*(1 + b^2/a^2)*d - 2*b*d*x^4 + x^8*(d - x^4) + 2*a*d*(-b + x^4)), x], x, (-a + x)^(1/4)])/(-((a - x)*(b - x)^2))^(1/4)","F",0,0,0,0,-1,"{}"
2157,1,678,0,1.1931978,"\int \frac{\left(2-x+2 x^2\right) \sqrt[4]{-x^3+x^4}}{-2-2 x+x^2} \, dx","Int[((2 - x + 2*x^2)*(-x^3 + x^4)^(1/4))/(-2 - 2*x + x^2),x]","-\sqrt[4]{x^4-x^3} (1-x)+\frac{3}{2} \left(1+\sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{3}{2} \left(1-\sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{3}{4} \sqrt[4]{x^4-x^3}+\frac{3 \left(15+7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{3 \left(15-7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{3 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{8 \sqrt[4]{x-1} x^{3/4}}+\frac{3\ 2^{3/4} \sqrt[4]{123+71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{3+\sqrt{3}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{3\ 2^{3/4} \sqrt[4]{123-71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{3}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{3 \left(15+7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{3 \left(15-7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{3 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{8 \sqrt[4]{x-1} x^{3/4}}-\frac{3\ 2^{3/4} \sqrt[4]{123+71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{3+\sqrt{3}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{3\ 2^{3/4} \sqrt[4]{123-71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{3}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}","-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,"(3*(-x^3 + x^4)^(1/4))/4 + (3*(1 - Sqrt[3])*(-x^3 + x^4)^(1/4))/2 + (3*(1 + Sqrt[3])*(-x^3 + x^4)^(1/4))/2 - (1 - x)*(-x^3 + x^4)^(1/4) - (3*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(8*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 - 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 + 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + (3*2^(3/4)*(123 + 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((3/(3 + Sqrt[3]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + (3*2^(3/4)*(123 - 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(((3 + Sqrt[3])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - (3*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(8*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 - 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 + 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) - (3*2^(3/4)*(123 + 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((3/(3 + Sqrt[3]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - (3*2^(3/4)*(123 - 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(((3 + Sqrt[3])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","B",34,12,34,0.3529,0,"{2056, 6728, 50, 63, 240, 212, 206, 203, 101, 157, 93, 298}"
2158,1,678,0,1.0232618,"\int \frac{\left(2-x+2 x^2\right) \sqrt[4]{-x^3+x^4}}{-2-2 x+x^2} \, dx","Int[((2 - x + 2*x^2)*(-x^3 + x^4)^(1/4))/(-2 - 2*x + x^2),x]","-\sqrt[4]{x^4-x^3} (1-x)+\frac{3}{2} \left(1+\sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{3}{2} \left(1-\sqrt{3}\right) \sqrt[4]{x^4-x^3}+\frac{3}{4} \sqrt[4]{x^4-x^3}+\frac{3 \left(15+7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{3 \left(15-7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{3 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{8 \sqrt[4]{x-1} x^{3/4}}+\frac{3\ 2^{3/4} \sqrt[4]{123+71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{3}{3+\sqrt{3}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{3\ 2^{3/4} \sqrt[4]{123-71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{3}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{3 \left(15+7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{3 \left(15-7 \sqrt{3}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{3 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{8 \sqrt[4]{x-1} x^{3/4}}-\frac{3\ 2^{3/4} \sqrt[4]{123+71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{3}{3+\sqrt{3}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{3\ 2^{3/4} \sqrt[4]{123-71 \sqrt{3}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{3}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}","-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,"(3*(-x^3 + x^4)^(1/4))/4 + (3*(1 - Sqrt[3])*(-x^3 + x^4)^(1/4))/2 + (3*(1 + Sqrt[3])*(-x^3 + x^4)^(1/4))/2 - (1 - x)*(-x^3 + x^4)^(1/4) - (3*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(8*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 - 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 + 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + (3*2^(3/4)*(123 + 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((3/(3 + Sqrt[3]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + (3*2^(3/4)*(123 - 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(((3 + Sqrt[3])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - (3*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(8*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 - 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + (3*(15 + 7*Sqrt[3])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) - (3*2^(3/4)*(123 + 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((3/(3 + Sqrt[3]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) - (3*2^(3/4)*(123 - 71*Sqrt[3])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(((3 + Sqrt[3])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","B",34,12,34,0.3529,0,"{2056, 6728, 50, 63, 240, 212, 206, 203, 101, 157, 93, 298}"
2159,1,467,0,1.4715462,"\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","Int[(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]","-\sqrt{\frac{1}{2} \left(9 \sqrt{17}-37\right)} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\right)\right)+\frac{1}{2} \sqrt{3 \sqrt{17}-5} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\right)\right)+\frac{\left(1+2 \sqrt{3}-\sqrt{17}\right) F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\right)\right)}{\sqrt{2 \left(3+\sqrt{17}\right)}}+\frac{\left(1-2 \sqrt{3}-\sqrt{17}\right) F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\right)\right)}{\sqrt{2 \left(3+\sqrt{17}\right)}}+2 \sqrt{\frac{2}{3+\sqrt{17}}} \Pi \left(\frac{1}{4} \left(3-\sqrt{17}\right);\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\right)\right)-\sqrt{\frac{2}{3+\sqrt{17}}} \Pi \left(\frac{3-\sqrt{17}}{2 \left(1-\sqrt{3}\right)};\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\right)\right)-\sqrt{\frac{2}{3+\sqrt{17}}} \Pi \left(\frac{3-\sqrt{17}}{2 \left(1+\sqrt{3}\right)};\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\right)\right)+2 \sqrt{\frac{2}{3+\sqrt{17}}} \Pi \left(\frac{1}{2} \left(-3+\sqrt{17}\right);\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{17}}}\right)|\frac{1}{4} \left(-13+3 \sqrt{17}\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,"((1 - 2*Sqrt[3] - Sqrt[17])*EllipticF[ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4])/Sqrt[2*(3 + Sqrt[17])] + ((1 + 2*Sqrt[3] - Sqrt[17])*EllipticF[ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4])/Sqrt[2*(3 + Sqrt[17])] + (Sqrt[-5 + 3*Sqrt[17]]*EllipticF[ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4])/2 - Sqrt[(-37 + 9*Sqrt[17])/2]*EllipticF[ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4] + 2*Sqrt[2/(3 + Sqrt[17])]*EllipticPi[(3 - Sqrt[17])/4, ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4] - Sqrt[2/(3 + Sqrt[17])]*EllipticPi[(3 - Sqrt[17])/(2*(1 - Sqrt[3])), ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4] - Sqrt[2/(3 + Sqrt[17])]*EllipticPi[(3 - Sqrt[17])/(2*(1 + Sqrt[3])), ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4] + 2*Sqrt[2/(3 + Sqrt[17])]*EllipticPi[(-3 + Sqrt[17])/2, ArcSin[(2*x)/Sqrt[-3 + Sqrt[17]]], (-13 + 3*Sqrt[17])/4]","C",32,8,50,0.1600,0,"{6728, 1208, 1180, 524, 424, 419, 1212, 537}"
2160,1,293,0,1.1248257,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b+2 a x^4\right)}{-2 b+a x^4} \, dx","Int[((b*x^2 + a*x^4)^(1/4)*(-b + 2*a*x^4))/(-2*b + a*x^4),x]","-\frac{b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{2} \sqrt{b}},-\frac{a x^2}{b}\right)}{2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{2} \sqrt{b}},-\frac{a x^2}{b}\right)}{2 \sqrt[4]{\frac{a x^2}{b}+1}}+x \sqrt[4]{a x^4+b x^2}","\frac{3}{8} b \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^4-a}\&\right]-\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{2 a^{3/4}}+x \sqrt[4]{a x^4+b x^2}",1,"x*(b*x^2 + a*x^4)^(1/4) - (x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/(Sqrt[2]*Sqrt[b])), -((a*x^2)/b)])/(2*(1 + (a*x^2)/b)^(1/4)) - (x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/(Sqrt[2]*Sqrt[b]), -((a*x^2)/b)])/(2*(1 + (a*x^2)/b)^(1/4)) - (b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4))","A",16,12,37,0.3243,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 1270, 1529, 511, 510}"
2161,1,293,0,0.9948983,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b+2 a x^4\right)}{-2 b+a x^4} \, dx","Int[((b*x^2 + a*x^4)^(1/4)*(-b + 2*a*x^4))/(-2*b + a*x^4),x]","-\frac{b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{2} \sqrt{b}},-\frac{a x^2}{b}\right)}{2 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{2} \sqrt{b}},-\frac{a x^2}{b}\right)}{2 \sqrt[4]{\frac{a x^2}{b}+1}}+x \sqrt[4]{a x^4+b x^2}","\frac{3}{8} b \text{RootSum}\left[2 \text{$\#$1}^8-4 \text{$\#$1}^4 a+2 a^2-a b\&,\frac{\text{$\#$1} \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$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*(b*x^2 + a*x^4)^(1/4) - (x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/(Sqrt[2]*Sqrt[b])), -((a*x^2)/b)])/(2*(1 + (a*x^2)/b)^(1/4)) - (x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/(Sqrt[2]*Sqrt[b]), -((a*x^2)/b)])/(2*(1 + (a*x^2)/b)^(1/4)) - (b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4))","A",16,12,37,0.3243,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 1270, 1529, 511, 510}"
2162,0,0,0,1.7851805,"\int \frac{x (-4 a+3 x)}{\sqrt[3]{x^2 (-a+x)} \left(a-x+d x^4\right)} \, dx","Int[(x*(-4*a + 3*x))/((x^2*(-a + x))^(1/3)*(a - x + d*x^4)),x]","\int \frac{x (-4 a+3 x)}{\sqrt[3]{x^2 (-a+x)} \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 \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,"(-12*a*x^(2/3)*(-a + x)^(1/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(1/3)*(a - x^3 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(1/3) + (9*x^(2/3)*(-a + x)^(1/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(1/3)*(a - x^3 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2163,1,513,0,1.1774616,"\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","Int[(-b - 2*a*x^4 + 2*x^8)/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\frac{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{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 \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{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{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 \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{\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) + (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)) - (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)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) + (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*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",15,9,44,0.2045,1,"{6728, 240, 212, 206, 203, 1428, 377, 208, 205}"
2164,1,513,0,0.7524008,"\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","Int[(-b - 2*a*x^4 + 2*x^8)/((-b + a*x^4)^(1/4)*(-b - a*x^4 + x^8)),x]","\frac{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{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 \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{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{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 \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{\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) + (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)) - (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)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(1/4) + (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*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",15,9,44,0.2045,1,"{6728, 240, 212, 206, 203, 1428, 377, 208, 205}"
2165,1,182,0,0.0793436,"\int \frac{1}{\left(-1+x^2\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[1/((-1 + x^2)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 x}{2 \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x+1)}{4 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^3-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*x)/(2*(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2*2^(1/3)*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(4*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 + x])/(4*2^(1/3)*(-x^2 + x^3)^(1/3))","A",4,4,21,0.1905,1,"{2056, 848, 96, 91}"
2166,1,880,0,3.221361,"\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","Int[(-b^2 + a^2*x^4)/(Sqrt[-(b*x) + a*x^3]*(b^2 + c*x^2 + a^2*x^4)),x]","\frac{\sqrt[4]{b} \left(1-\frac{2 a b-c}{\sqrt{c^2-4 a^2 b^2}}\right) \sqrt{x} \sqrt{1-\frac{a x^2}{b}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a x^3-b x}}+\frac{\sqrt[4]{b} \left(\frac{2 a b-c}{\sqrt{c^2-4 a^2 b^2}}+1\right) \sqrt{x} \sqrt{1-\frac{a x^2}{b}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{a x^3-b x}}+\frac{\sqrt[4]{b} \left(4 a^2 b^2-c \left(c+\sqrt{c^2-4 a^2 b^2}\right)\right) \sqrt{x} \sqrt{1-\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{b}}{\sqrt{-c-\sqrt{c^2-4 a^2 b^2}}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{c^2-4 a^2 b^2} \left(c+\sqrt{c^2-4 a^2 b^2}\right) \sqrt{a x^3-b x}}+\frac{\sqrt[4]{b} \left(4 a^2 b^2-c \left(c+\sqrt{c^2-4 a^2 b^2}\right)\right) \sqrt{x} \sqrt{1-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{2} \sqrt{a} \sqrt{b}}{\sqrt{-c-\sqrt{c^2-4 a^2 b^2}}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{c^2-4 a^2 b^2} \left(c+\sqrt{c^2-4 a^2 b^2}\right) \sqrt{a x^3-b x}}-\frac{\sqrt[4]{b} \left(4 a^2 b^2-c \left(c-\sqrt{c^2-4 a^2 b^2}\right)\right) \sqrt{x} \sqrt{1-\frac{a x^2}{b}} \Pi \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{b}}{\sqrt{\sqrt{c^2-4 a^2 b^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{c^2-4 a^2 b^2} \left(c-\sqrt{c^2-4 a^2 b^2}\right) \sqrt{a x^3-b x}}-\frac{\sqrt[4]{b} \left(4 a^2 b^2-c \left(c-\sqrt{c^2-4 a^2 b^2}\right)\right) \sqrt{x} \sqrt{1-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{2} \sqrt{a} \sqrt{b}}{\sqrt{\sqrt{c^2-4 a^2 b^2}-c}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt{c^2-4 a^2 b^2} \left(c-\sqrt{c^2-4 a^2 b^2}\right) \sqrt{a x^3-b x}}","\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,"(b^(1/4)*(1 - (2*a*b - c)/Sqrt[-4*a^2*b^2 + c^2])*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticF[ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-(b*x) + a*x^3]) + (b^(1/4)*(1 + (2*a*b - c)/Sqrt[-4*a^2*b^2 + c^2])*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticF[ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-(b*x) + a*x^3]) + (b^(1/4)*(4*a^2*b^2 - c*(c + Sqrt[-4*a^2*b^2 + c^2]))*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[-((Sqrt[2]*Sqrt[a]*Sqrt[b])/Sqrt[-c - Sqrt[-4*a^2*b^2 + c^2]]), ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-4*a^2*b^2 + c^2]*(c + Sqrt[-4*a^2*b^2 + c^2])*Sqrt[-(b*x) + a*x^3]) + (b^(1/4)*(4*a^2*b^2 - c*(c + Sqrt[-4*a^2*b^2 + c^2]))*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[(Sqrt[2]*Sqrt[a]*Sqrt[b])/Sqrt[-c - Sqrt[-4*a^2*b^2 + c^2]], ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-4*a^2*b^2 + c^2]*(c + Sqrt[-4*a^2*b^2 + c^2])*Sqrt[-(b*x) + a*x^3]) - (b^(1/4)*(4*a^2*b^2 - c*(c - Sqrt[-4*a^2*b^2 + c^2]))*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[-((Sqrt[2]*Sqrt[a]*Sqrt[b])/Sqrt[-c + Sqrt[-4*a^2*b^2 + c^2]]), ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-4*a^2*b^2 + c^2]*(c - Sqrt[-4*a^2*b^2 + c^2])*Sqrt[-(b*x) + a*x^3]) - (b^(1/4)*(4*a^2*b^2 - c*(c - Sqrt[-4*a^2*b^2 + c^2]))*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[(Sqrt[2]*Sqrt[a]*Sqrt[b])/Sqrt[-c + Sqrt[-4*a^2*b^2 + c^2]], ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-4*a^2*b^2 + c^2]*(c - Sqrt[-4*a^2*b^2 + c^2])*Sqrt[-(b*x) + a*x^3])","C",21,10,46,0.2174,1,"{2056, 1586, 6715, 6728, 406, 224, 221, 409, 1219, 1218}"
2167,0,0,0,5.4988095,"\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","Int[((-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,"-(Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x, x]/(a*q)) + (b*Defer[Int][(x*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(a*q^2 + b*x^2 + 2*a*p*q*x^3 + a*p^2*x^6), x])/(a*q) + 4*p*Defer[Int][(x^2*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(a*q^2 + b*x^2 + 2*a*p*q*x^3 + a*p^2*x^6), x] + (p^2*Defer[Int][(x^5*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(a*q^2 + b*x^2 + 2*a*p*q*x^3 + a*p^2*x^6), x])/q","F",0,0,0,0,-1,"{}"
2168,0,0,0,6.0598378,"\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","Int[((-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,"(-2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x, x])/(a*q) + 5*p*Defer[Int][(x^2*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] + (2*b*Defer[Int][(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])/(a*q) + (2*p^2*Defer[Int][(x^5*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])/q","F",0,0,0,0,-1,"{}"
2169,0,0,0,4.0004333,"\int \frac{x^2-\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(x^2 - Sqrt[1 + x^2])/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{x^2-\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+2 \text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+5 \text{$\#$1}^2-2 \text{$\#$1}}\&\right]-\log \left(\sqrt{x^2+1}+x\right)+x",1,"x + Defer[Int][(-1 - 2*x^5 + x^8)^(-1), x] - Defer[Int][x^2/(-1 - 2*x^5 + x^8), x] - Defer[Int][x^4/(-1 - 2*x^5 + x^8), x] + Defer[Int][x^5/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^3*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^4*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^6*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] + Defer[Int][Sqrt[x + Sqrt[1 + x^2]]/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^3*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^6*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^2*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^4*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x]","F",0,0,0,0,-1,"{}"
2170,0,0,0,3.3418542,"\int \frac{x^2-\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(x^2 - Sqrt[1 + x^2])/(x^2 + Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{x^2-\sqrt{1+x^2}}{x^2+\sqrt{x+\sqrt{1+x^2}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^5-2 \text{$\#$1}^4+1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+2 \text{$\#$1} \log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x^2+1}+x}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+5 \text{$\#$1}^2-2 \text{$\#$1}}\&\right]-\log \left(\sqrt{x^2+1}+x\right)+x",1,"x + Defer[Int][(-1 - 2*x^5 + x^8)^(-1), x] - Defer[Int][x^2/(-1 - 2*x^5 + x^8), x] - Defer[Int][x^4/(-1 - 2*x^5 + x^8), x] + Defer[Int][x^5/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^3*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^4*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^6*Sqrt[1 + x^2])/(-1 - 2*x^5 + x^8), x] + Defer[Int][Sqrt[x + Sqrt[1 + x^2]]/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^2*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^3*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^6*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] - Defer[Int][(x^2*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x] + Defer[Int][(x^4*Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]])/(-1 - 2*x^5 + x^8), x]","F",0,0,0,0,-1,"{}"
2171,1,148,0,1.0298136,"\int \frac{\sqrt{1+\sqrt{1-\sqrt{1+\frac{1}{x^2}}}}}{x} \, dx","Int[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",12,5,27,0.1852,1,"{6742, 2073, 207, 1166, 203}"
2172,0,0,0,3.878657,"\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","Int[(-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,"((1 + Sqrt[4*b + (-1 + k)^2] + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][x^(1/3)/((1 - x)^(2/3)*(1 - k*x)^(2/3)*(-1 - k - Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3) + ((1 - Sqrt[4*b + (-1 + k)^2] + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][x^(1/3)/((1 - x)^(2/3)*(1 - k*x)^(2/3)*(-1 - k + Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2173,0,0,0,0.6324394,"\int \frac{2-(1+k) x}{\sqrt[3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx","Int[(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,"(3*(1 - x)^(1/3)*x*(1 - k*x)^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, x, k*x])/(2*((1 - x)*x*(1 - k*x))^(1/3)) + ((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 + (-1 - k)*x)*(1 - k*x)^(1/3)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2174,0,0,0,3.4946802,"\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","Int[(-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,"((1 + Sqrt[4*b + (-1 + k)^2] + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-1 - k - Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3) + ((1 - Sqrt[4*b + (-1 + k)^2] + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-1 - k + Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2175,0,0,0,2.5929266,"\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","Int[((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,"3*Defer[Int][(1 + 2*x^2 + 2*x^3)^(2/3)/(-1 - 2*x^2 + x^3), x] + 8*Defer[Int][(x*(1 + 2*x^2 + 2*x^3)^(2/3))/(-1 - 2*x^2 + x^3), x] - 4*Defer[Int][(x^2*(1 + 2*x^2 + 2*x^3)^(2/3))/(-1 - 2*x^2 + x^3), x] - (27*2^(2/3)*(1 + 2*x^2 + 2*x^3)^(2/3)*Defer[Subst][Defer[Int][((((31 + 3*Sqrt[105])^(1/3)*(2*2^(1/3) + (31 - 3*Sqrt[105])^(2/3)))/6 + 2*x)^(2/3)*((-4 + (62 - 6*Sqrt[105])^(2/3) + (8*2^(1/3))/(31 - 3*Sqrt[105])^(2/3))/9 - (2*((62 - 6*Sqrt[105])^(1/3) + (2*2^(2/3))/(31 - 3*Sqrt[105])^(1/3))*x)/3 + 4*x^2)^(2/3))/(-1/3 + x)^3, x], x, 1/3 + x])/((4 + (31 + 3*Sqrt[105])^(1/3)*(2*2^(1/3) + (31 - 3*Sqrt[105])^(2/3)) + 12*x)^(2/3)*(-4 + (62 - 6*Sqrt[105])^(2/3) + (8*2^(1/3))/(31 - 3*Sqrt[105])^(2/3) - 2*((62 - 6*Sqrt[105])^(1/3) + (2*2^(2/3))/(31 - 3*Sqrt[105])^(1/3))*(1 + 3*x) + 4*(1 + 3*x)^2)^(2/3)) + (36*2^(2/3)*(1 + 2*x^2 + 2*x^3)^(2/3)*Defer[Subst][Defer[Int][((((31 + 3*Sqrt[105])^(1/3)*(2*2^(1/3) + (31 - 3*Sqrt[105])^(2/3)))/6 + 2*x)^(2/3)*((-4 + (62 - 6*Sqrt[105])^(2/3) + (8*2^(1/3))/(31 - 3*Sqrt[105])^(2/3))/9 - (2*((62 - 6*Sqrt[105])^(1/3) + (2*2^(2/3))/(31 - 3*Sqrt[105])^(1/3))*x)/3 + 4*x^2)^(2/3))/(-1/3 + x), x], x, 1/3 + x])/((4 + (31 + 3*Sqrt[105])^(1/3)*(2*2^(1/3) + (31 - 3*Sqrt[105])^(2/3)) + 12*x)^(2/3)*(-4 + (62 - 6*Sqrt[105])^(2/3) + (8*2^(1/3))/(31 - 3*Sqrt[105])^(2/3) - 2*((62 - 6*Sqrt[105])^(1/3) + (2*2^(2/3))/(31 - 3*Sqrt[105])^(1/3))*(1 + 3*x) + 4*(1 + 3*x)^2)^(2/3))","F",0,0,0,0,-1,"{}"
2176,1,257,0,1.6955909,"\int \frac{-b+c x+a x^2}{\left(b+a x^2\right) \sqrt{-b x+a x^3}} \, dx","Int[(-b + c*x + a*x^2)/((b + a*x^2)*Sqrt[-(b*x) + a*x^3]),x]","-\frac{\sqrt{x} \left(2 a \sqrt{b}+\sqrt{-a} c\right) \sqrt{1-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{-a}}{\sqrt{a}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{a^{5/4} \sqrt[4]{b} \sqrt{a x^3-b x}}-\frac{\sqrt{x} \left(\frac{c}{\sqrt{-a}}+2 \sqrt{b}\right) \sqrt{1-\frac{a x^2}{b}} \Pi \left(\frac{\sqrt{a}}{\sqrt{-a}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3-b x}}+\frac{2 \sqrt[4]{b} \sqrt{x} \sqrt{1-\frac{a x^2}{b}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)\right|-1\right)}{\sqrt[4]{a} \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*b^(1/4)*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticF[ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*Sqrt[-(b*x) + a*x^3]) - ((2*a*Sqrt[b] + Sqrt[-a]*c)*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[Sqrt[-a]/Sqrt[a], ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(5/4)*b^(1/4)*Sqrt[-(b*x) + a*x^3]) - ((2*Sqrt[b] + c/Sqrt[-a])*Sqrt[x]*Sqrt[1 - (a*x^2)/b]*EllipticPi[Sqrt[a]/Sqrt[-a], ArcSin[(a^(1/4)*Sqrt[x])/b^(1/4)], -1])/(a^(1/4)*b^(1/4)*Sqrt[-(b*x) + a*x^3])","C",14,8,36,0.2222,1,"{2056, 6725, 329, 224, 221, 933, 168, 537}"
2177,0,0,0,6.1259592,"\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","Int[(-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,"-1/4*((2 + x^2)^(1/4)*ArcTan[1 - (Sqrt[2]*(2 + x^2)^(1/4))/(-2 + x^2)^(1/4)])/(Sqrt[2]*(-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) + ((2 + x^2)^(1/4)*ArcTan[1 + (Sqrt[2]*(2 + x^2)^(1/4))/(-2 + x^2)^(1/4)])/(4*Sqrt[2]*(-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) + ((2 + x^2)^(1/4)*Log[1 - (Sqrt[2]*(2 + x^2)^(1/4))/(-2 + x^2)^(1/4) + Sqrt[2 + x^2]/Sqrt[-2 + x^2]])/(8*Sqrt[2]*(-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) - ((2 + x^2)^(1/4)*Log[1 + (Sqrt[2]*(2 + x^2)^(1/4))/(-2 + x^2)^(1/4) + Sqrt[2 + x^2]/Sqrt[-2 + x^2]])/(8*Sqrt[2]*(-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) - (7*(2 + x^2)^(1/4)*Defer[Int][1/((-2 + x^2)^(3/4)*(2 + x^2)^(1/4)*(8 - 10*x + 4*x^2 + 4*x^3 - 4*x^4 + x^5)), x])/((-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) + (4*(2 + x^2)^(1/4)*Defer[Int][x/((-2 + x^2)^(3/4)*(2 + x^2)^(1/4)*(8 - 10*x + 4*x^2 + 4*x^3 - 4*x^4 + x^5)), x])/((-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) + (2*(2 + x^2)^(1/4)*Defer[Int][x^2/((-2 + x^2)^(3/4)*(2 + x^2)^(1/4)*(8 - 10*x + 4*x^2 + 4*x^3 - 4*x^4 + x^5)), x])/((-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) - ((2 + x^2)^(1/4)*Defer[Int][x^3/((-2 + x^2)^(3/4)*(2 + x^2)^(1/4)*(8 - 10*x + 4*x^2 + 4*x^3 - 4*x^4 + x^5)), x])/((-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4)) + ((2 + x^2)^(1/4)*Defer[Int][x^4/((-2 + x^2)^(3/4)*(2 + x^2)^(1/4)*(8 - 10*x + 4*x^2 + 4*x^3 - 4*x^4 + x^5)), x])/(2*(-2 + x^2)^(1/4)*(-((2 + x^2)/(2 - x^2)))^(1/4))","F",0,0,0,0,-1,"{}"
2178,0,0,0,1.2749985,"\int \frac{\sqrt{1+x} \left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Int[(Sqrt[1 + x]*(-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\int \frac{\sqrt{1+x} \left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$1}^5}\&\right]+\frac{4}{105} \sqrt{\sqrt{x+1}+1} (3 x+11)+\frac{4}{105} \sqrt{x+1} (15 x+11) \sqrt{\sqrt{x+1}+1}",1,"(4*(1 + Sqrt[1 + x])^(3/2))/3 - (8*(1 + Sqrt[1 + x])^(5/2))/5 + (4*(1 + Sqrt[1 + x])^(7/2))/7 - 8*Defer[Subst][Defer[Int][x^2/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]] + 16*Defer[Subst][Defer[Int][x^4/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^6/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
2179,0,0,0,1.0302307,"\int \frac{\sqrt{1+x} \left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","Int[(Sqrt[1 + x]*(-1 + x^4)*Sqrt[1 + Sqrt[1 + x]])/(1 + x^4),x]","\int \frac{\sqrt{1+x} \left(-1+x^4\right) \sqrt{1+\sqrt{1+x}}}{1+x^4} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+16 \text{$\#$1}^8+1\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-6 \text{$\#$1}^9+12 \text{$\#$1}^7-8 \text{$\#$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*(1 + Sqrt[1 + x])^(3/2))/3 - (8*(1 + Sqrt[1 + x])^(5/2))/5 + (4*(1 + Sqrt[1 + x])^(7/2))/7 - 8*Defer[Subst][Defer[Int][x^2/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]] + 16*Defer[Subst][Defer[Int][x^4/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]] - 8*Defer[Subst][Defer[Int][x^6/(1 + 16*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + x]]]","F",0,0,0,0,-1,"{}"
2180,1,142,0,0.1801303,"\int \frac{-d+c x}{x^4 \sqrt[3]{-b+a x^3}} \, dx","Int[(-d + c*x)/(x^4*(-b + a*x^3)^(1/3)),x]","\frac{a d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{6 b^{4/3}}+\frac{a d \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{3 \sqrt{3} b^{4/3}}-\frac{a d \log (x)}{6 b^{4/3}}+\frac{c \left(a x^3-b\right)^{2/3}}{2 b x^2}-\frac{d \left(a x^3-b\right)^{2/3}}{3 b x^3}","\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,"-1/3*(d*(-b + a*x^3)^(2/3))/(b*x^3) + (c*(-b + a*x^3)^(2/3))/(2*b*x^2) + (a*d*ArcTan[(b^(1/3) - 2*(-b + a*x^3)^(1/3))/(Sqrt[3]*b^(1/3))])/(3*Sqrt[3]*b^(4/3)) - (a*d*Log[x])/(6*b^(4/3)) + (a*d*Log[b^(1/3) + (-b + a*x^3)^(1/3)])/(6*b^(4/3))","A",9,8,24,0.3333,1,"{1844, 266, 51, 56, 617, 204, 31, 264}"
2181,1,392,0,0.6984663,"\int \frac{\sqrt[4]{-b x^3+a x^4} \left(-d+c x^4\right)}{x^2} \, dx","Int[((-(b*x^3) + a*x^4)^(1/4)*(-d + c*x^4))/x^2,x]","\frac{77 b^4 c x^{9/4} (a x-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{1024 a^{15/4} \left(a x^4-b x^3\right)^{3/4}}-\frac{77 b^4 c x^{9/4} (a x-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{1024 a^{15/4} \left(a x^4-b x^3\right)^{3/4}}-\frac{77 b^3 c \sqrt[4]{a x^4-b x^3}}{1536 a^3}-\frac{11 b^2 c x \sqrt[4]{a x^4-b x^3}}{384 a^2}+\frac{1}{4} c x^3 \sqrt[4]{a x^4-b x^3}-\frac{b c x^2 \sqrt[4]{a x^4-b x^3}}{48 a}+\frac{4 d \sqrt[4]{a x^4-b x^3}}{x}+\frac{2 \sqrt[4]{a} d x^{9/4} (a x-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{\left(a x^4-b x^3\right)^{3/4}}-\frac{2 \sqrt[4]{a} d x^{9/4} (a x-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{\left(a x^4-b x^3\right)^{3/4}}","\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,"(-77*b^3*c*(-(b*x^3) + a*x^4)^(1/4))/(1536*a^3) + (4*d*(-(b*x^3) + a*x^4)^(1/4))/x - (11*b^2*c*x*(-(b*x^3) + a*x^4)^(1/4))/(384*a^2) - (b*c*x^2*(-(b*x^3) + a*x^4)^(1/4))/(48*a) + (c*x^3*(-(b*x^3) + a*x^4)^(1/4))/4 + (77*b^4*c*x^(9/4)*(-b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(1024*a^(15/4)*(-(b*x^3) + a*x^4)^(3/4)) + (2*a^(1/4)*d*x^(9/4)*(-b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(-(b*x^3) + a*x^4)^(3/4) - (77*b^4*c*x^(9/4)*(-b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(1024*a^(15/4)*(-(b*x^3) + a*x^4)^(3/4)) - (2*a^(1/4)*d*x^(9/4)*(-b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(-(b*x^3) + a*x^4)^(3/4)","B",19,10,29,0.3448,1,"{2052, 2020, 2032, 63, 331, 298, 203, 206, 2021, 2024}"
2182,0,0,0,23.7831943,"\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","Int[(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,"(9*k*x*((1 - x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, ((1 - k)*x)/(1 - k*x)])/((1 - x)*x*(1 - k*x))^(2/3) + (9*b*k*(1 + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^3/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(b - b*(1 + k)*x^3 + b*k*x^6 - x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (12*(1 + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^12/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(b - b*(1 + k)*x^3 + b*k*x^6 - x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (9*b*k*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][1/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (9*b*k^2*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^6/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (15*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^9/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2183,0,0,0,1.5314196,"\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","Int[((-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,"-4*Defer[Int][(2 - 3*x^4 + x^5)^(1/4)/x^6, x] - 3*Defer[Int][(2 - 3*x^4 + x^5)^(1/4)/x^2, x] + Defer[Int][(2 - 3*x^4 + x^5)^(1/4)/x, x]/2 - 9*Defer[Int][(x^2*(2 - 3*x^4 + x^5)^(1/4))/(4 - 3*x^4 + 2*x^5), x] + (15*Defer[Int][(x^3*(2 - 3*x^4 + x^5)^(1/4))/(4 - 3*x^4 + 2*x^5), x])/2","F",0,0,0,0,-1,"{}"
2184,1,46,0,0.1380959,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[x^2/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 x^3 \sqrt[4]{x^4+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \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}}",1,"(-2*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4))","C",3,3,22,0.1364,0,"{2042, 466, 510}"
2185,1,46,0,0.1322834,"\int \frac{x^2}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[x^2/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{2 x^3 \sqrt[4]{x^4+1} F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \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}}",1,"(-2*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4))","C",3,3,22,0.1364,0,"{2042, 466, 510}"
2186,1,42,0,0.09358,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(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};1,-\frac{3}{4};\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, 1, -3/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4)","C",3,3,24,0.1250,0,"{2056, 466, 429}"
2187,1,42,0,0.0986558,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(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};1,-\frac{3}{4};\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, 1, -3/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4)","C",3,3,24,0.1250,0,"{2056, 466, 429}"
2188,1,127,0,0.7723503,"\int \frac{1-x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(1 - x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{4 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-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)}{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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (2*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",15,7,29,0.2414,0,"{2056, 6715, 6725, 245, 1438, 429, 510}"
2189,1,127,0,0.623331,"\int \frac{1-x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(1 - x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{4 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-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)}{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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (2*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",15,7,29,0.2414,0,"{2056, 6715, 6725, 245, 1438, 429, 510}"
2190,1,127,0,0.6416754,"\int \frac{1+x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(1 + x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{4 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{2 \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) - (2*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",15,7,27,0.2593,0,"{2056, 6715, 6725, 245, 1438, 429, 510}"
2191,1,127,0,0.5752982,"\int \frac{1+x^2+x^4}{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}} \, dx","Int[(1 + x^2 + x^4)/((-1 + x^4)*(x^2 + x^6)^(1/4)),x]","-\frac{4 \sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{2 \sqrt[4]{x^4+1} x^3 F_1\left(\frac{5}{8};1,\frac{1}{4};\frac{13}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^6+x^2}}+\frac{2 \sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) - (2*x^3*(1 + x^4)^(1/4)*AppellF1[5/8, 1, 1/4, 13/8, x^4, -x^4])/(5*(x^2 + x^6)^(1/4)) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",15,7,27,0.2593,0,"{2056, 6715, 6725, 245, 1438, 429, 510}"
2192,1,157,0,0.595543,"\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","Int[((-4 + x^3)*(-2 + x^3)*(-1 + x^3)^(2/3))/(x^6*(-2 + x^3 + x^6)),x]","-\sqrt[3]{\frac{2}{3}} \log \left(\sqrt[3]{2}-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3-1}}\right)+\sqrt[3]{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{2^{2/3} x}{\sqrt[6]{3} \sqrt[3]{x^3-1}}+\frac{1}{\sqrt{3}}\right)+\frac{4 \left(x^3-1\right)^{2/3}}{5 x^5}-\frac{13 \left(x^3-1\right)^{2/3}}{10 x^2}+\frac{\log \left(\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3-1}}+\frac{3^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+2^{2/3}\right)}{2^{2/3} \sqrt[3]{3}}","-\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,"(4*(-1 + x^3)^(2/3))/(5*x^5) - (13*(-1 + x^3)^(2/3))/(10*x^2) + 2^(1/3)*3^(1/6)*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/(3^(1/6)*(-1 + x^3)^(1/3))] - (2/3)^(1/3)*Log[2^(1/3) - (3^(1/3)*x)/(-1 + x^3)^(1/3)] + Log[2^(2/3) + (3^(2/3)*x^2)/(-1 + x^3)^(2/3) + (6^(1/3)*x)/(-1 + x^3)^(1/3)]/(2^(2/3)*3^(1/3))","A",13,11,33,0.3333,1,"{1586, 6725, 271, 264, 377, 200, 31, 634, 617, 204, 628}"
2193,1,105,0,0.3848701,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^8} \, dx","Int[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^8),x]","-\frac{\left(\frac{1}{3}-\frac{i}{3}\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};1,-\frac{1}{4};\frac{11}{8};-i x^4,-x^4\right)}{\sqrt[4]{x^4+1}}-\frac{\left(\frac{1}{3}+\frac{i}{3}\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};1,-\frac{1}{4};\frac{11}{8};i x^4,-x^4\right)}{\sqrt[4]{x^4+1}}","\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,"((-1/3 + I/3)*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, 1, -1/4, 11/8, (-I)*x^4, -x^4])/(1 + x^4)^(1/4) - ((1/3 + I/3)*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, 1, -1/4, 11/8, I*x^4, -x^4])/(1 + x^4)^(1/4)","C",7,4,24,0.1667,0,"{2056, 6725, 466, 510}"
2194,1,105,0,0.3057092,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1+x^8} \, dx","Int[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 + x^8),x]","-\frac{\left(\frac{1}{3}-\frac{i}{3}\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};1,-\frac{1}{4};\frac{11}{8};-i x^4,-x^4\right)}{\sqrt[4]{x^4+1}}-\frac{\left(\frac{1}{3}+\frac{i}{3}\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};1,-\frac{1}{4};\frac{11}{8};i x^4,-x^4\right)}{\sqrt[4]{x^4+1}}","\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,"((-1/3 + I/3)*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, 1, -1/4, 11/8, (-I)*x^4, -x^4])/(1 + x^4)^(1/4) - ((1/3 + I/3)*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, 1, -1/4, 11/8, I*x^4, -x^4])/(1 + x^4)^(1/4)","C",7,4,24,0.1667,0,"{2056, 6725, 466, 510}"
2195,1,97,0,0.529053,"\int \frac{-1+x^8}{\sqrt[4]{x^2+x^6} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((x^2 + x^6)^(1/4)*(1 + x^8)),x]","-\frac{(1-i) x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};-i x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{(1+i) x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};i x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}","-\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,"((-1 + I)*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, (-I)*x^4, -x^4])/(x^2 + x^6)^(1/4) - ((1 + I)*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, I*x^4, -x^4])/(x^2 + x^6)^(1/4)","C",7,5,24,0.2083,0,"{2056, 1586, 6715, 6725, 429}"
2196,1,97,0,0.44429,"\int \frac{-1+x^8}{\sqrt[4]{x^2+x^6} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((x^2 + x^6)^(1/4)*(1 + x^8)),x]","-\frac{(1-i) x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};-i x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{(1+i) x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};i x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}","-\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,"((-1 + I)*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, (-I)*x^4, -x^4])/(x^2 + x^6)^(1/4) - ((1 + I)*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, I*x^4, -x^4])/(x^2 + x^6)^(1/4)","C",7,5,24,0.2083,0,"{2056, 1586, 6715, 6725, 429}"
2197,0,0,0,27.473046,"\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","Int[(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,"(21*(1 + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^18/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(b - b*(1 + k)*x^3 + b*k*x^6 - x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (24*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^15/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (18*k*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^21/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2198,1,561,0,1.5057788,"\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","Int[(-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",16,8,44,0.1818,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2199,0,0,0,0.1431268,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^4} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]]/x^4,x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^4} \, dx","\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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/x^4, x]","F",0,0,0,0,-1,"{}"
2200,0,0,0,0.6404143,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^4 \sqrt{b^2+a x^2}} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^4*Sqrt[b^2 + a*x^2]),x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^4 \sqrt{b^2+a x^2}} \, dx","\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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^4*Sqrt[b^2 + a*x^2]), x]","F",0,0,0,0,-1,"{}"
2201,1,1281,0,1.7732358,"\int \frac{1}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Int[1/((x + x^3)^(1/3)*(-1 + x^6)),x]","-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}-i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}+i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(x^{2/3}+1\right)}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\left(3 i-\sqrt{3}\right) \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3}}{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}} \sqrt[3]{x^3+x}}+\frac{\left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} x^{2/3}}{\sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(1-x^{2/3}\right)^2 \left(x^{2/3}+1\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}-i \sqrt{3}+1\right) \left(2 x^{2/3}-i \sqrt{3}+1\right)^2\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}+i \sqrt{3}+1\right) \left(2 x^{2/3}+i \sqrt{3}+1\right)^2\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1-i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1+i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1+i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1-i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1-i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1+i \sqrt{3}}\right)}{6 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1+i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1-i \sqrt{3}}\right)}{6 \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-2^{2/3} \sqrt[3]{x^2+1}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}-i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}+i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \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,"-1/4*(x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(2^(1/3)*Sqrt[3]*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*Sqrt[3]*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2^(1/3)*(1 + x^(2/3)))/(1 + x^2)^(1/3))/Sqrt[3]])/(4*2^(1/3)*Sqrt[3]*(x + x^3)^(1/3)) - ((3*I - Sqrt[3])*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*x^(2/3))/(((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(1 + x^2)^(1/3)))/Sqrt[3]])/(6*2^(2/3)*(1 - I*Sqrt[3])^(1/3)*(x + x^3)^(1/3)) + ((1 + I*Sqrt[3])^(2/3)*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)*Sqrt[3]*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - x^(2/3))^2*(1 + x^(2/3))])/(24*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3] - 2*x^(2/3))*(1 - I*Sqrt[3] + 2*x^(2/3))^2])/(24*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3] - 2*x^(2/3))*(1 + I*Sqrt[3] + 2*x^(2/3))^2])/(24*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(2/3) + ((1 - I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(12*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) + (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(2/3) + ((1 + I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(12*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(1/3) + ((1 - I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(6*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) - (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(1/3) + ((1 + I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(6*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[1 + x^(2/3) - 2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[1 - I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[1 + I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3))","C",25,12,17,0.7059,0,"{2056, 6715, 2074, 2148, 6728, 377, 200, 31, 634, 617, 204, 628}"
2202,1,1281,0,1.6197779,"\int \frac{1}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Int[1/((x + x^3)^(1/3)*(-1 + x^6)),x]","-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}-i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}+i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(x^{2/3}+1\right)}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\left(3 i-\sqrt{3}\right) \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3}}{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}} \sqrt[3]{x^3+x}}+\frac{\left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} x^{2/3}}{\sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(1-x^{2/3}\right)^2 \left(x^{2/3}+1\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}-i \sqrt{3}+1\right) \left(2 x^{2/3}-i \sqrt{3}+1\right)^2\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}+i \sqrt{3}+1\right) \left(2 x^{2/3}+i \sqrt{3}+1\right)^2\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1-i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1+i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1+i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1-i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1-i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1+i \sqrt{3}}\right)}{6 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1+i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1-i \sqrt{3}}\right)}{6 \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-2^{2/3} \sqrt[3]{x^2+1}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}-i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}+i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \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,"-1/4*(x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(2^(1/3)*Sqrt[3]*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*Sqrt[3]*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2^(1/3)*(1 + x^(2/3)))/(1 + x^2)^(1/3))/Sqrt[3]])/(4*2^(1/3)*Sqrt[3]*(x + x^3)^(1/3)) - ((3*I - Sqrt[3])*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*x^(2/3))/(((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(1 + x^2)^(1/3)))/Sqrt[3]])/(6*2^(2/3)*(1 - I*Sqrt[3])^(1/3)*(x + x^3)^(1/3)) + ((1 + I*Sqrt[3])^(2/3)*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)*Sqrt[3]*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - x^(2/3))^2*(1 + x^(2/3))])/(24*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3] - 2*x^(2/3))*(1 - I*Sqrt[3] + 2*x^(2/3))^2])/(24*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3] - 2*x^(2/3))*(1 + I*Sqrt[3] + 2*x^(2/3))^2])/(24*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(2/3) + ((1 - I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(12*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) + (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(2/3) + ((1 + I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(12*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(1/3) + ((1 - I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(6*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) - (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(1/3) + ((1 + I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(6*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[1 + x^(2/3) - 2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[1 - I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[1 + I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3))","C",25,12,17,0.7059,0,"{2056, 6715, 2074, 2148, 6728, 377, 200, 31, 634, 617, 204, 628}"
2203,1,224,0,0.9624214,"\int \frac{\left(1+x^3\right) \sqrt{-2-x^3+x^6}}{x^4 \left(-1-2 x^3+x^6\right)} \, dx","Int[((1 + x^3)*Sqrt[-2 - x^3 + x^6])/(x^4*(-1 - 2*x^3 + x^6)),x]","\frac{\sqrt{x^6-x^3-2}}{3 x^3}+\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\frac{x^3+4}{2 \sqrt{2} \sqrt{x^6-x^3-2}}\right)-\frac{\tan ^{-1}\left(\frac{x^3+4}{2 \sqrt{2} \sqrt{x^6-x^3-2}}\right)}{6 \sqrt{2}}-\frac{\left(1+\sqrt{2}\right) \tan ^{-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)}{3\ 2^{3/4}}-\frac{\left(1-\sqrt{2}\right) \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)}{3\ 2^{3/4}}","\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,"Sqrt[-2 - x^3 + x^6]/(3*x^3) - ArcTan[(4 + x^3)/(2*Sqrt[2]*Sqrt[-2 - x^3 + x^6])]/(6*Sqrt[2]) + (Sqrt[2]*ArcTan[(4 + x^3)/(2*Sqrt[2]*Sqrt[-2 - x^3 + x^6])])/3 - ((1 + Sqrt[2])*ArcTan[(5 - Sqrt[2] - (1 - 2*Sqrt[2])*x^3)/(2*2^(1/4)*Sqrt[-2 - x^3 + x^6])])/(3*2^(3/4)) - ((1 - Sqrt[2])*ArcTanh[(5 + Sqrt[2] - (1 + 2*Sqrt[2])*x^3)/(2*2^(1/4)*Sqrt[-2 - x^3 + x^6])])/(3*2^(3/4))","A",26,13,35,0.3714,1,"{6728, 1357, 732, 843, 621, 206, 724, 204, 734, 6715, 1019, 1076, 1032}"
2204,0,0,0,1.3341352,"\int \frac{x^2 \left(-4+7 x^3\right)}{\sqrt[3]{-x+x^4} \left(-1-x^4+x^7\right)} \, dx","Int[(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,"(-12*x^(1/3)*(-1 + x^3)^(1/3)*Defer[Subst][Defer[Int][x^7/((-1 + x^9)^(1/3)*(-1 - x^12 + x^21)), x], x, x^(1/3)])/(-x + x^4)^(1/3) + (21*x^(1/3)*(-1 + x^3)^(1/3)*Defer[Subst][Defer[Int][x^16/((-1 + x^9)^(1/3)*(-1 - x^12 + x^21)), x], x, x^(1/3)])/(-x + x^4)^(1/3)","F",0,0,0,0,-1,"{}"
2205,1,1315,0,2.9813993,"\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","Int[(a*x^4 + x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt[4]{a x^4-b x^2}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-2 \text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3+4 \text{$\#$1}^4 a^2 b+a^4-2 a^3 b-b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",34,13,41,0.3171,1,"{1593, 2056, 6728, 1270, 1517, 240, 212, 206, 203, 1429, 377, 208, 205}"
2206,1,1315,0,2.1651639,"\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","Int[(a*x^4 + x^8)/((-(b*x^2) + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)),x]","\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt[4]{a x^4-b x^2}}+\frac{\sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{-a-\sqrt{a^2+b}}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt{x}}{\sqrt[8]{-a-\sqrt{a^2+b}} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{-a-\sqrt{a^2+b}} a+b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{a \sqrt{\sqrt{a^2+b}-a}-b} \sqrt[4]{a x^4-b x^2}}-\frac{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt{x}}{\sqrt[8]{\sqrt{a^2+b}-a} \sqrt[4]{a x^2-b}}\right)}{4 \sqrt[4]{\sqrt{\sqrt{a^2+b}-a} a+b} \sqrt[4]{a x^4-b x^2}}","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12} a+6 \text{$\#$1}^8 a^2-2 \text{$\#$1}^8 a b-4 \text{$\#$1}^4 a^3+4 \text{$\#$1}^4 a^2 b+a^4-2 a^3 b-b^3\&,\frac{\log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\log (x)}{\text{$\#$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,"(Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[((b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) + (Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(a^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a - Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a - Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a - Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(-b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4)) - ((-a + Sqrt[a^2 + b])^(1/8)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[((b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*Sqrt[x])/((-a + Sqrt[a^2 + b])^(1/8)*(-b + a*x^2)^(1/4))])/(4*(b + a*Sqrt[-a + Sqrt[a^2 + b]])^(1/4)*(-(b*x^2) + a*x^4)^(1/4))","B",34,13,41,0.3171,1,"{1593, 2056, 6728, 1270, 1517, 240, 212, 206, 203, 1429, 377, 208, 205}"
2207,0,0,0,3.4447537,"\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","Int[(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]","\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","-\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,"(2*EllipticE[ArcSin[Sqrt[-1 + Sqrt[2]]*x], -3 - 2*Sqrt[2]])/Sqrt[1 + Sqrt[2]] - ((1 + 2*Sqrt[2] - Sqrt[5])*EllipticF[ArcSin[Sqrt[-1 + Sqrt[2]]*x], -3 - 2*Sqrt[2]])/(2*Sqrt[-1 + Sqrt[2]]) - ((1 + 2*Sqrt[2] + Sqrt[5])*EllipticF[ArcSin[Sqrt[-1 + Sqrt[2]]*x], -3 - 2*Sqrt[2]])/(2*Sqrt[-1 + Sqrt[2]]) + EllipticPi[(2*(1 + Sqrt[2]))/(1 - Sqrt[5]), ArcSin[Sqrt[-1 + Sqrt[2]]*x], -3 - 2*Sqrt[2]]/Sqrt[-1 + Sqrt[2]] + EllipticPi[(2*(1 + Sqrt[2]))/(1 + Sqrt[5]), ArcSin[Sqrt[-1 + Sqrt[2]]*x], -3 - 2*Sqrt[2]]/Sqrt[-1 + Sqrt[2]] + 2*Defer[Int][Sqrt[1 + 2*x^2 - x^4]/(1 + 3*x^2 - x^4 - 3*x^6 + x^8), x] - Defer[Int][(x^2*Sqrt[1 + 2*x^2 - x^4])/(1 + 3*x^2 - x^4 - 3*x^6 + x^8), x] - 4*Defer[Int][(x^4*Sqrt[1 + 2*x^2 - x^4])/(1 + 3*x^2 - x^4 - 3*x^6 + x^8), x] + 2*Defer[Int][(x^6*Sqrt[1 + 2*x^2 - x^4])/(1 + 3*x^2 - x^4 - 3*x^6 + x^8), x]","F",0,0,0,0,-1,"{}"
2208,1,163,0,0.3374726,"\int \frac{1}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[1/((-1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]),x]","-\frac{\tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}+\frac{\tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}-\frac{\tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}+\frac{\tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}","\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,"-(ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + Sqrt[2]]) + ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[-1 + Sqrt[2]] - ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + Sqrt[2]] + ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[-1 + Sqrt[2]]","A",18,10,23,0.4348,1,"{6725, 2119, 1628, 828, 826, 1166, 204, 206, 207, 203}"
2209,0,0,0,0.5366751,"\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","Int[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]","\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","\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2210,0,0,0,0.4277189,"\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","Int[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]","\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","\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2211,0,0,0,4.0357211,"\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","Int[((-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,"(-27*(2 - x + 2*x^3)^(2/3)*Defer[Int][(((6^(2/3) + 6^(1/3)*(18 - Sqrt[318])^(2/3))/(3*(18 - Sqrt[318])^(1/3)) + 2*x)^(2/3)*((-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3))/9 - (2*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x)/3 + 4*x^2)^(2/3))/x^6, x])/(((108 - 6*Sqrt[318])^(1/3) + 6^(2/3)/(18 - Sqrt[318])^(1/3) + 6*x)^(2/3)*(-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3) - 6*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x + 36*x^2)^(2/3)) + (9*(2 - x + 2*x^3)^(2/3)*Defer[Int][(((6^(2/3) + 6^(1/3)*(18 - Sqrt[318])^(2/3))/(3*(18 - Sqrt[318])^(1/3)) + 2*x)^(2/3)*((-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3))/9 - (2*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x)/3 + 4*x^2)^(2/3))/x^5, x])/(((108 - 6*Sqrt[318])^(1/3) + 6^(2/3)/(18 - Sqrt[318])^(1/3) + 6*x)^(2/3)*(-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3) - 6*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x + 36*x^2)^(2/3)) - (27*(2 - x + 2*x^3)^(2/3)*Defer[Int][(((6^(2/3) + 6^(1/3)*(18 - Sqrt[318])^(2/3))/(3*(18 - Sqrt[318])^(1/3)) + 2*x)^(2/3)*((-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3))/9 - (2*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x)/3 + 4*x^2)^(2/3))/x^3, x])/(((108 - 6*Sqrt[318])^(1/3) + 6^(2/3)/(18 - Sqrt[318])^(1/3) + 6*x)^(2/3)*(-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3) - 6*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x + 36*x^2)^(2/3)) - (9*(2 - x + 2*x^3)^(2/3)*Defer[Int][(((6^(2/3) + 6^(1/3)*(18 - Sqrt[318])^(2/3))/(3*(18 - Sqrt[318])^(1/3)) + 2*x)^(2/3)*((-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3))/9 - (2*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x)/3 + 4*x^2)^(2/3))/x^2, x])/(2*((108 - 6*Sqrt[318])^(1/3) + 6^(2/3)/(18 - Sqrt[318])^(1/3) + 6*x)^(2/3)*(-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3) - 6*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x + 36*x^2)^(2/3)) - (9*(2 - x + 2*x^3)^(2/3)*Defer[Int][(((6^(2/3) + 6^(1/3)*(18 - Sqrt[318])^(2/3))/(3*(18 - Sqrt[318])^(1/3)) + 2*x)^(2/3)*((-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3))/9 - (2*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x)/3 + 4*x^2)^(2/3))/x, x])/(4*((108 - 6*Sqrt[318])^(1/3) + 6^(2/3)/(18 - Sqrt[318])^(1/3) + 6*x)^(2/3)*(-6 + (108 - 6*Sqrt[318])^(2/3) + (6*6^(1/3))/(18 - Sqrt[318])^(2/3) - 6*(18 + Sqrt[318])^(1/3)*(6^(1/3) + (18 - Sqrt[318])^(2/3))*x + 36*x^2)^(2/3)) + (25*Defer[Int][(2 - x + 2*x^3)^(2/3)/(-2 + x + 2*x^3), x])/4 + Defer[Int][(x*(2 - x + 2*x^3)^(2/3))/(-2 + x + 2*x^3), x] + Defer[Int][(x^2*(2 - x + 2*x^3)^(2/3))/(-2 + x + 2*x^3), x]/2","F",0,0,0,0,-1,"{}"
2212,1,166,0,0.2412465,"\int \frac{\left(1+x^3\right)^{2/3} \left(2+x^3\right)}{x^6 \left(-2-x^3+x^6\right)} \, dx","Int[((1 + x^3)^(2/3)*(2 + x^3))/(x^6*(-2 - x^3 + x^6)),x]","\frac{\log \left(\sqrt[3]{2}-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)}{3\ 2^{2/3} \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} x}{\sqrt[6]{3} \sqrt[3]{x^3+1}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} 3^{5/6}}+\frac{\left(x^3+1\right)^{2/3}}{5 x^5}+\frac{\left(x^3+1\right)^{2/3}}{5 x^2}-\frac{\log \left(\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+2^{2/3}\right)}{6\ 2^{2/3} \sqrt[3]{3}}","\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,"(1 + x^3)^(2/3)/(5*x^5) + (1 + x^3)^(2/3)/(5*x^2) - ArcTan[1/Sqrt[3] + (2^(2/3)*x)/(3^(1/6)*(1 + x^3)^(1/3))]/(2^(2/3)*3^(5/6)) + Log[2^(1/3) - (3^(1/3)*x)/(1 + x^3)^(1/3)]/(3*2^(2/3)*3^(1/3)) - Log[2^(2/3) + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + (6^(1/3)*x)/(1 + x^3)^(1/3)]/(6*2^(2/3)*3^(1/3))","A",11,10,30,0.3333,1,"{1586, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2213,0,0,0,1.5559982,"\int \frac{b+a x^6}{\sqrt[3]{x+x^3} \left(d+c x^6\right)} \, dx","Int[(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,"(Sqrt[3]*a*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*c*(x + x^3)^(1/3)) - (3*a*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(4*c*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/3)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(4/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(5/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/3)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(7/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(8/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2214,0,0,0,1.1810514,"\int \frac{b+a x^6}{\sqrt[3]{x+x^3} \left(d+c x^6\right)} \, dx","Int[(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,"(Sqrt[3]*a*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*c*(x + x^3)^(1/3)) - (3*a*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(4*c*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(1/3)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(4/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(5/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(2/3)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) + (-1)^(7/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-d^(1/9) - (-1)^(8/9)*c^(1/9)*x)*(1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(x + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2215,1,84,0,0.0149176,"\int \frac{1}{(2+x) \sqrt[3]{1+x+x^2}} \, dx","Int[1/((2 + x)*(1 + x + x^2)^(1/3)),x]","\frac{\log \left(-3^{2/3} \sqrt[3]{x^2+x+1}-x+1\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{2 (1-x)}{3 \sqrt[6]{3} \sqrt[3]{x^2+x+1}}+\frac{1}{\sqrt{3}}\right)}{3^{5/6}}-\frac{\log (x+2)}{2 \sqrt[3]{3}}","\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,"-(ArcTan[1/Sqrt[3] + (2*(1 - x))/(3*3^(1/6)*(1 + x + x^2)^(1/3))]/3^(5/6)) - Log[2 + x]/(2*3^(1/3)) + Log[1 - x - 3^(2/3)*(1 + x + x^2)^(1/3)]/(2*3^(1/3))","A",1,1,16,0.06250,1,"{750}"
2216,0,0,0,1.5756391,"\int \frac{(-3+2 x) \sqrt[3]{-1+x+x^3}}{x^2 \left(2-2 x+x^3\right)} \, dx","Int[((-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,"(-9*(-1 + x + x^3)^(1/3)*Defer[Int][(((2*(3/(9 + Sqrt[93]))^(1/3) - (2*(9 + Sqrt[93]))^(1/3))/6^(2/3) + x)^(1/3)*((6 + 6*3^(1/3)*(2/(9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[93]))^(2/3))/18 - (((6/(9 + Sqrt[93]))^(1/3) - ((9 + Sqrt[93])/2)^(1/3))*x)/3^(2/3) + x^2)^(1/3))/x^2, x])/(2^(1/3)*(6^(1/3)*(2*(3/(9 + Sqrt[93]))^(1/3) - (2*(9 + Sqrt[93]))^(1/3)) + 6*x)^(1/3)*(6 + 6*3^(1/3)*(2/(9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[93]))^(2/3) - 6*3^(1/3)*((6/(9 + Sqrt[93]))^(1/3) - ((9 + Sqrt[93])/2)^(1/3))*x + 18*x^2)^(1/3)) - (3*(-1 + x + x^3)^(1/3)*Defer[Int][(((2*(3/(9 + Sqrt[93]))^(1/3) - (2*(9 + Sqrt[93]))^(1/3))/6^(2/3) + x)^(1/3)*((6 + 6*3^(1/3)*(2/(9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[93]))^(2/3))/18 - (((6/(9 + Sqrt[93]))^(1/3) - ((9 + Sqrt[93])/2)^(1/3))*x)/3^(2/3) + x^2)^(1/3))/x, x])/(2^(1/3)*(6^(1/3)*(2*(3/(9 + Sqrt[93]))^(1/3) - (2*(9 + Sqrt[93]))^(1/3)) + 6*x)^(1/3)*(6 + 6*3^(1/3)*(2/(9 + Sqrt[93]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[93]))^(2/3) - 6*3^(1/3)*((6/(9 + Sqrt[93]))^(1/3) - ((9 + Sqrt[93])/2)^(1/3))*x + 18*x^2)^(1/3)) - Defer[Int][(-1 + x + x^3)^(1/3)/(2 - 2*x + x^3), x] + (3*Defer[Int][(x*(-1 + x + x^3)^(1/3))/(2 - 2*x + x^3), x])/2 + Defer[Int][(x^2*(-1 + x + x^3)^(1/3))/(2 - 2*x + x^3), x]/2","F",0,0,0,0,-1,"{}"
2217,1,325,0,3.338269,"\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","Int[(-((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 (a-b) (b-x) \left(\sqrt{-4 a+4 b+d}+\sqrt{d}\right) F_1\left(-\frac{1}{4};-\frac{3}{2},1;\frac{3}{4};\frac{a-x}{a-b},\frac{2 (a-x)}{2 a-2 b-d-\sqrt{d} \sqrt{-4 a+4 b+d}}\right)}{\sqrt{d} \left(-\sqrt{d} \sqrt{-4 a+4 b+d}+2 a-2 b-d\right) \sqrt{-\frac{b-x}{a-b}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}+\frac{4 (a-b) (b-x) \left(1-\frac{\sqrt{-4 a+4 b+d}}{\sqrt{d}}\right) F_1\left(-\frac{1}{4};-\frac{3}{2},1;\frac{3}{4};\frac{a-x}{a-b},\frac{2 (a-x)}{2 a-2 b-d+\sqrt{d} \sqrt{-4 a+4 b+d}}\right)}{\left(\sqrt{d} \sqrt{-4 a+4 b+d}+2 a-2 b-d\right) \sqrt{-\frac{b-x}{a-b}} \sqrt[4]{-\left((a-x) (b-x)^2\right)}}","-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*(a - b)*(Sqrt[d] + Sqrt[-4*a + 4*b + d])*(b - x)*AppellF1[-1/4, -3/2, 1, 3/4, (a - x)/(a - b), (2*(a - x))/(2*a - 2*b - d - Sqrt[d]*Sqrt[-4*a + 4*b + d])])/(Sqrt[d]*(2*a - 2*b - d - Sqrt[d]*Sqrt[-4*a + 4*b + d])*Sqrt[-((b - x)/(a - b))]*(-((a - x)*(b - x)^2))^(1/4)) + (4*(a - b)*(1 - Sqrt[-4*a + 4*b + d]/Sqrt[d])*(b - x)*AppellF1[-1/4, -3/2, 1, 3/4, (a - x)/(a - b), (2*(a - x))/(2*a - 2*b - d + Sqrt[d]*Sqrt[-4*a + 4*b + d])])/((2*a - 2*b - d + Sqrt[d]*Sqrt[-4*a + 4*b + d])*Sqrt[-((b - x)/(a - b))]*(-((a - x)*(b - x)^2))^(1/4))","C",8,5,81,0.06173,0,"{6688, 6719, 6728, 137, 136}"
2218,0,0,0,0.2284842,"\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^4/((b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a+b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(a x^2-b\right)}{4 a b x (a+b) \left(a x^4+b\right)}",1,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((b + a*x^4)^(1/4)*(b + a*x^8)^2), x], x, Sqrt[x]])/(b*x^2 + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2219,0,0,0,0.249334,"\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^4/((b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a+b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(a x^2-b\right)}{4 a b x (a+b) \left(a x^4+b\right)}",1,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((b + a*x^4)^(1/4)*(b + a*x^8)^2), x], x, Sqrt[x]])/(b*x^2 + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2220,0,0,0,0.2425157,"\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^4/((b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^4}{\left(b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$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,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((b + a*x^4)^(1/4)*(b + a*x^8)^2), x], x, Sqrt[x]])/(b*x^2 + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2221,1,255,0,0.2927068,"\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","Int[((-b + a*x^4)*(b + a*x^4)^(3/4))/(x^8*(b + 2*a*x^4)),x]","\frac{3 a^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}\right)}{2 \sqrt{2} b}-\frac{3 a^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4+b}}+1\right)}{2 \sqrt{2} b}+\frac{3 a^{7/4} \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)}{4 \sqrt{2} b}-\frac{3 a^{7/4} \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)}{4 \sqrt{2} b}+\frac{\left(a x^4+b\right)^{3/4}}{7 x^7}-\frac{6 a \left(a x^4+b\right)^{3/4}}{7 b x^3}","-\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,"(b + a*x^4)^(3/4)/(7*x^7) - (6*a*(b + a*x^4)^(3/4))/(7*b*x^3) + (3*a^(7/4)*ArcTan[1 - (Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(2*Sqrt[2]*b) - (3*a^(7/4)*ArcTan[1 + (Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(2*Sqrt[2]*b) + (3*a^(7/4)*Log[1 + (Sqrt[a]*x^2)/Sqrt[b + a*x^4] - (Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*Sqrt[2]*b) - (3*a^(7/4)*Log[1 + (Sqrt[a]*x^2)/Sqrt[b + a*x^4] + (Sqrt[2]*a^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*Sqrt[2]*b)","A",13,10,34,0.2941,1,"{580, 583, 12, 377, 211, 1165, 628, 1162, 617, 204}"
2222,0,0,0,2.1468376,"\int \frac{x \sqrt{b+a x}}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Int[(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{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{\text{$\#$1}^3 a \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$1} c+a}\&\right]-\frac{4}{3} c \sqrt{\sqrt{a x+b}+c}+\sqrt{a x+b} \left(\frac{2 (a x+b)}{3 a}-\frac{4}{3} \sqrt{\sqrt{a x+b}+c}\right)",1,"(2*c^2*Sqrt[b + a*x])/a - (4*(c + Sqrt[b + a*x])^(3/2))/3 - (2*c*(c + Sqrt[b + a*x])^2)/a + (2*(c + Sqrt[b + a*x])^3)/(3*a) + a*Log[b - c^2 - a*Sqrt[c + Sqrt[b + a*x]] + 2*c*(c + Sqrt[b + a*x]) - (c + Sqrt[b + a*x])^2] - a^2*Defer[Subst][Defer[Int][(-b + c^2 + a*x - 2*c*x^2 + x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*c*Defer[Subst][Defer[Int][x/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*b*Defer[Subst][Defer[Int][x^2/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2223,0,0,0,1.6554312,"\int \frac{x \sqrt{b+a x}}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Int[(x*Sqrt[b + a*x])/(x + Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x \sqrt{b+a x}}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","4 \text{RootSum}\left[-\text{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{\text{$\#$1}^3 a \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$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,"(2*c^2*Sqrt[b + a*x])/a - (4*(c + Sqrt[b + a*x])^(3/2))/3 - (2*c*(c + Sqrt[b + a*x])^2)/a + (2*(c + Sqrt[b + a*x])^3)/(3*a) + a*Log[b - c^2 - a*Sqrt[c + Sqrt[b + a*x]] + 2*c*(c + Sqrt[b + a*x]) - (c + Sqrt[b + a*x])^2] - a^2*Defer[Subst][Defer[Int][(-b + c^2 + a*x - 2*c*x^2 + x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*c*Defer[Subst][Defer[Int][x/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*b*Defer[Subst][Defer[Int][x^2/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2224,1,166,0,0.9828473,"\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{x} \, dx","Int[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/x,x]","-8 \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}}}}}{\sqrt{\sqrt{2}-1}}\right)+4 \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)+2 \sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{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^(-1)]]] + 2*Sqrt[-1 + Sqrt[2]]*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[-1 + Sqrt[2]]] + 4*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]] + 2*Sqrt[1 + Sqrt[2]]*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[1 + Sqrt[2]]]","A",11,5,31,0.1613,1,"{6742, 2073, 207, 1166, 203}"
2225,0,0,0,6.0779676,"\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","Int[(-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,"((a + b + Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][x^(1/3)/((-a + x)^(2/3)*(-b + x)^(2/3)*(-((a + b)*d) - Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(2/3) + ((a + b - Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][x^(1/3)/((-a + x)^(2/3)*(-b + x)^(2/3)*(-((a + b)*d) + Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(2/3)","F",0,0,0,0,-1,"{}"
2226,1,257,0,0.2546594,"\int \frac{\sqrt[4]{-b+a x^3}}{x^7} \, dx","Int[(-b + a*x^3)^(1/4)/x^7,x]","-\frac{a^2 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{32 \sqrt{2} b^{7/4}}+\frac{a^2 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{32 \sqrt{2} b^{7/4}}-\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{16 \sqrt{2} b^{7/4}}+\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{16 \sqrt{2} b^{7/4}}+\frac{a \sqrt[4]{a x^3-b}}{24 b x^3}-\frac{\sqrt[4]{a x^3-b}}{6 x^6}","-\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,"-1/6*(-b + a*x^3)^(1/4)/x^6 + (a*(-b + a*x^3)^(1/4))/(24*b*x^3) - (a^2*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(16*Sqrt[2]*b^(7/4)) + (a^2*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(16*Sqrt[2]*b^(7/4)) - (a^2*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(32*Sqrt[2]*b^(7/4)) + (a^2*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(32*Sqrt[2]*b^(7/4))","A",13,10,17,0.5882,1,"{266, 47, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2227,1,290,0,0.4158548,"\int \frac{\left(b+2 a x^2\right) \sqrt[4]{b x^2+a x^4}}{-b+a x^2} \, dx","Int[((b + 2*a*x^2)*(b*x^2 + a*x^4)^(1/4))/(-b + a*x^2),x]","-\frac{7 b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{3 \sqrt[4]{2} b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{7 b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{2 a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{3 \sqrt[4]{2} b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{a^{3/4} \sqrt{x} \sqrt[4]{a x^2+b}}+x \sqrt[4]{a x^4+b x^2}","-\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*(b*x^2 + a*x^4)^(1/4) - (7*b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (3*2^(1/4)*b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (7*b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(2*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (3*2^(1/4)*b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4))","A",14,10,35,0.2857,1,"{2056, 581, 584, 329, 331, 298, 203, 206, 466, 494}"
2228,1,518,0,1.7054413,"\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","Int[(-b^4 + a^4*x^4)/(Sqrt[-(b^2*x) + a^2*x^3]*(b^4 + a^4*x^4)),x]","-\frac{\sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[4]{-a^4}}{a};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{\sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(-\frac{\sqrt{-\sqrt{-a^4}}}{a};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{\sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt{-\sqrt{-a^4}}}{a};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{a} \sqrt{a^2 x^3-b^2 x}}+\frac{\left(a^2-\sqrt{-a^4}\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{a^{5/2} \sqrt{a^2 x^3-b^2 x}}+\frac{\left(\sqrt{-a^4}+a^2\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{a^{5/2} \sqrt{a^2 x^3-b^2 x}}-\frac{\sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{a^3}{\left(-a^4\right)^{3/4}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{\sqrt{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,"((a^2 - Sqrt[-a^4])*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(a^(5/2)*Sqrt[-(b^2*x) + a^2*x^3]) + ((a^2 + Sqrt[-a^4])*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(a^(5/2)*Sqrt[-(b^2*x) + a^2*x^3]) - (Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[a^3/(-a^4)^(3/4), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(-a^4)^(1/4)/a, ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[-(Sqrt[-Sqrt[-a^4]]/a), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[Sqrt[-Sqrt[-a^4]]/a, ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3])","C",21,10,45,0.2222,1,"{2056, 1586, 6715, 6725, 406, 224, 221, 409, 1219, 1218}"
2229,0,0,0,1.1169351,"\int \frac{-1+x^5}{\sqrt{1+x^4} \left(1+x^5\right)} \, dx","Int[(-1 + x^5)/(Sqrt[1 + x^4]*(1 + x^5)),x]","\int \frac{-1+x^5}{\sqrt{1+x^4} \left(1+x^5\right)} \, dx","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3-4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))-\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2-2}\&\right]-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2+2 x+1}\right)",1,"-1/5*ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] + ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/(5*Sqrt[2]) + (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (8*Defer[Int][1/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 + (6*Defer[Int][x/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 - (4*Defer[Int][x^2/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 + (2*Defer[Int][x^3/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5","F",0,0,0,0,-1,"{}"
2230,0,0,0,0.8986547,"\int \frac{-1+x^5}{\sqrt{1+x^4} \left(1+x^5\right)} \, dx","Int[(-1 + x^5)/(Sqrt[1 + x^4]*(1 + x^5)),x]","\int \frac{-1+x^5}{\sqrt{1+x^4} \left(1+x^5\right)} \, dx","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3-4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))-\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2-2}\&\right]-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2+2 x+1}\right)",1,"-1/5*ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] + ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/(5*Sqrt[2]) + (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (8*Defer[Int][1/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 + (6*Defer[Int][x/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 - (4*Defer[Int][x^2/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5 + (2*Defer[Int][x^3/(Sqrt[1 + x^4]*(1 - x + x^2 - x^3 + x^4)), x])/5","F",0,0,0,0,-1,"{}"
2231,0,0,0,0.9806722,"\int \frac{1+x^5}{\sqrt{1+x^4} \left(-1+x^5\right)} \, dx","Int[(1 + x^5)/(Sqrt[1 + x^4]*(-1 + x^5)),x]","\int \frac{1+x^5}{\sqrt{1+x^4} \left(-1+x^5\right)} \, dx","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))+\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)-\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2+2}\&\right]-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}+x^2-2 x+1}\right)",1,"-1/5*ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] - ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/(5*Sqrt[2]) + (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (8*Defer[Int][1/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (6*Defer[Int][x/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (4*Defer[Int][x^2/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (2*Defer[Int][x^3/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5","F",0,0,0,0,-1,"{}"
2232,0,0,0,0.8677565,"\int \frac{1+x^5}{\sqrt{1+x^4} \left(-1+x^5\right)} \, dx","Int[(1 + x^5)/(Sqrt[1 + x^4]*(-1 + x^5)),x]","\int \frac{1+x^5}{\sqrt{1+x^4} \left(-1+x^5\right)} \, dx","\frac{4}{5} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3+4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+\text{$\#$1}^2 (-\log (x))+\text{$\#$1} \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)+2 \log \left(-\text{$\#$1} x+\sqrt{x^4+1}+x^2+1\right)-\text{$\#$1} \log (x)-2 \log (x)}{2 \text{$\#$1}^3+3 \text{$\#$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,"-1/5*ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/Sqrt[2] - ArcTanh[(1 + x^2)/(Sqrt[2]*Sqrt[1 + x^4])]/(5*Sqrt[2]) + (2*(1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(5*Sqrt[1 + x^4]) - (8*Defer[Int][1/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (6*Defer[Int][x/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (4*Defer[Int][x^2/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5 - (2*Defer[Int][x^3/(Sqrt[1 + x^4]*(1 + x + x^2 + x^3 + x^4)), x])/5","F",0,0,0,0,-1,"{}"
2233,1,405,0,2.2036645,"\int \frac{-b^6+a^6 x^6}{\sqrt{b^4+a^4 x^4} \left(b^6+a^6 x^6\right)} \, dx","Int[(-b^6 + a^6*x^6)/(Sqrt[b^4 + a^4*x^4]*(b^6 + a^6*x^6)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{2} a b}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-a^2} b x}{\sqrt{a^4 x^4+b^4}}\right)}{3 \sqrt{-a^2} b}+\frac{\left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{3 a b \sqrt{a^4 x^4+b^4}}-\frac{\left(a^2-\sqrt{3} \sqrt{-a^4}\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{3 a \left(3 a^2-\sqrt{3} \sqrt{-a^4}\right) b \sqrt{a^4 x^4+b^4}}-\frac{\left(\sqrt{3} \sqrt{-a^4}+a^2\right) \left(a^2 x^2+b^2\right) \sqrt{\frac{a^4 x^4+b^4}{\left(a^2 x^2+b^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{3 a \left(\sqrt{3} \sqrt{-a^4}+3 a^2\right) b \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,"-1/3*ArcTan[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(Sqrt[2]*a*b) - (2*ArcTan[(Sqrt[-a^2]*b*x)/Sqrt[b^4 + a^4*x^4]])/(3*Sqrt[-a^2]*b) + ((b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(3*a*b*Sqrt[b^4 + a^4*x^4]) - ((a^2 - Sqrt[3]*Sqrt[-a^4])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(3*a*(3*a^2 - Sqrt[3]*Sqrt[-a^4])*b*Sqrt[b^4 + a^4*x^4]) - ((a^2 + Sqrt[3]*Sqrt[-a^4])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(3*a*(3*a^2 + Sqrt[3]*Sqrt[-a^4])*b*Sqrt[b^4 + a^4*x^4])","C",17,9,42,0.2143,1,"{6725, 220, 2073, 1211, 1699, 205, 6728, 1217, 1707}"
2234,0,0,0,5.303525,"\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","Int[(-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,"((a + b + Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(-((a + b)*d) - Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3) + ((a + b - Sqrt[2*a*b*(2 - d) + a^2*d + b^2*d]/Sqrt[d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(-((a + b)*d) + Sqrt[d]*Sqrt[4*a*b + a^2*d - 2*a*b*d + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2235,1,260,0,0.2624735,"\int \frac{1}{x^7 \left(-b+a x^3\right)^{3/4}} \, dx","Int[1/(x^7*(-b + a*x^3)^(3/4)),x]","-\frac{7 a^2 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{32 \sqrt{2} b^{11/4}}+\frac{7 a^2 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{32 \sqrt{2} b^{11/4}}-\frac{7 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{16 \sqrt{2} b^{11/4}}+\frac{7 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{16 \sqrt{2} b^{11/4}}+\frac{7 a \sqrt[4]{a x^3-b}}{24 b^2 x^3}+\frac{\sqrt[4]{a x^3-b}}{6 b x^6}","-\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,"(-b + a*x^3)^(1/4)/(6*b*x^6) + (7*a*(-b + a*x^3)^(1/4))/(24*b^2*x^3) - (7*a^2*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(16*Sqrt[2]*b^(11/4)) + (7*a^2*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(16*Sqrt[2]*b^(11/4)) - (7*a^2*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(32*Sqrt[2]*b^(11/4)) + (7*a^2*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(32*Sqrt[2]*b^(11/4))","A",13,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2236,1,260,0,0.2726701,"\int \frac{1}{x^7 \sqrt[4]{-b+a x^3}} \, dx","Int[1/(x^7*(-b + a*x^3)^(1/4)),x]","\frac{5 a^2 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{96 \sqrt{2} b^{9/4}}-\frac{5 a^2 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^3-b}+\sqrt{a x^3-b}+\sqrt{b}\right)}{96 \sqrt{2} b^{9/4}}-\frac{5 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}\right)}{48 \sqrt{2} b^{9/4}}+\frac{5 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^3-b}}{\sqrt[4]{b}}+1\right)}{48 \sqrt{2} b^{9/4}}+\frac{5 a \left(a x^3-b\right)^{3/4}}{24 b^2 x^3}+\frac{\left(a x^3-b\right)^{3/4}}{6 b x^6}","-\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,"(-b + a*x^3)^(3/4)/(6*b*x^6) + (5*a*(-b + a*x^3)^(3/4))/(24*b^2*x^3) - (5*a^2*ArcTan[1 - (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(48*Sqrt[2]*b^(9/4)) + (5*a^2*ArcTan[1 + (Sqrt[2]*(-b + a*x^3)^(1/4))/b^(1/4)])/(48*Sqrt[2]*b^(9/4)) + (5*a^2*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(96*Sqrt[2]*b^(9/4)) - (5*a^2*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^3)^(1/4) + Sqrt[-b + a*x^3]])/(96*Sqrt[2]*b^(9/4))","A",13,9,17,0.5294,1,"{266, 51, 63, 297, 1162, 617, 204, 1165, 628}"
2237,1,42,0,0.0987377,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Int[(1 + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)),x]","-\frac{3 x \sqrt[3]{x^2+1} F_1\left(\frac{1}{6};1,-\frac{2}{3};\frac{7}{6};x^2,-x^2\right)}{\sqrt[3]{x^4+x^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{\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,"(-3*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, -2/3, 7/6, x^2, -x^2])/(x^2 + x^4)^(1/3)","C",3,3,24,0.1250,0,"{2056, 466, 429}"
2238,0,0,0,1.4949988,"\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","Int[((-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,"(-3*(-1 + x^4)^(2/3))/x^2 + (12*x^2)/(1 + Sqrt[3] + (-1 + x^4)^(1/3)) - (6*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticE[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) + (4*Sqrt[2]*3^(3/4)*(1 + (-1 + x^4)^(1/3))*Sqrt[(1 - (-1 + x^4)^(1/3) + (-1 + x^4)^(2/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]*EllipticF[ArcSin[(1 - Sqrt[3] + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))], -7 - 4*Sqrt[3]])/(x^2*Sqrt[(1 + (-1 + x^4)^(1/3))/(1 + Sqrt[3] + (-1 + x^4)^(1/3))^2]) - (3*(-1 + x^4)^(2/3)*Hypergeometric2F1[-5/4, -2/3, -1/4, x^4])/(5*x^5*(1 - x^4)^(2/3)) - ((-1 + x^4)^(2/3)*Hypergeometric2F1[-2/3, -1/4, 3/4, x^4])/(x*(1 - x^4)^(2/3)) - 18*Defer[Int][(-1 + x^4)^(2/3)/(-2 + 3*x^3 + 2*x^4), x] - 16*Defer[Int][(x*(-1 + x^4)^(2/3))/(-2 + 3*x^3 + 2*x^4), x]","F",0,0,0,0,-1,"{}"
2239,1,260,0,0.2492603,"\int \frac{1}{x^9 \left(-b+a x^4\right)^{3/4}} \, dx","Int[1/(x^9*(-b + a*x^4)^(3/4)),x]","-\frac{21 a^2 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{128 \sqrt{2} b^{11/4}}+\frac{21 a^2 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^4-b}+\sqrt{a x^4-b}+\sqrt{b}\right)}{128 \sqrt{2} b^{11/4}}-\frac{21 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}\right)}{64 \sqrt{2} b^{11/4}}+\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^4-b}}{\sqrt[4]{b}}+1\right)}{64 \sqrt{2} b^{11/4}}+\frac{7 a \sqrt[4]{a x^4-b}}{32 b^2 x^4}+\frac{\sqrt[4]{a x^4-b}}{8 b x^8}","-\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,"(-b + a*x^4)^(1/4)/(8*b*x^8) + (7*a*(-b + a*x^4)^(1/4))/(32*b^2*x^4) - (21*a^2*ArcTan[1 - (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)])/(64*Sqrt[2]*b^(11/4)) + (21*a^2*ArcTan[1 + (Sqrt[2]*(-b + a*x^4)^(1/4))/b^(1/4)])/(64*Sqrt[2]*b^(11/4)) - (21*a^2*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]])/(128*Sqrt[2]*b^(11/4)) + (21*a^2*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^4)^(1/4) + Sqrt[-b + a*x^4]])/(128*Sqrt[2]*b^(11/4))","A",13,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2240,1,503,0,1.7445154,"\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","Int[(b^2 + c*x^2 + a^2*x^4)/(Sqrt[b*x + a*x^3]*(-b^2 + a^2*x^4)),x]","-\frac{\sqrt{x} (2 a b+c) \sqrt{a x^2+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{4 \sqrt{2} a^{5/4} b^{5/4} \sqrt{a x^3+b x}}-\frac{\sqrt{x} (2 a b+c) \sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}}{\sqrt{a x^2+b}}\right)}{4 \sqrt{2} a^{5/4} b^{5/4} \sqrt{a x^3+b x}}-\frac{\sqrt{x} (2 a b-c) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{5/4} b^{5/4} \sqrt{a x^3+b x}}-\frac{\sqrt{x} (2 a b+c) \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4 a^{5/4} b^{5/4} \sqrt{a x^3+b x}}-\frac{x (2 a b-c)}{2 a b \sqrt{a x^3+b x}}+\frac{\sqrt{x} \left(\sqrt{a} x+\sqrt{b}\right) \sqrt{\frac{a x^2+b}{\left(\sqrt{a} x+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{a x^3+b x}}","-\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*((2*a*b - c)*x)/(a*b*Sqrt[b*x + a*x^3]) - ((2*a*b + c)*Sqrt[x]*Sqrt[b + a*x^2]*ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(4*Sqrt[2]*a^(5/4)*b^(5/4)*Sqrt[b*x + a*x^3]) - ((2*a*b + c)*Sqrt[x]*Sqrt[b + a*x^2]*ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x])/Sqrt[b + a*x^2]])/(4*Sqrt[2]*a^(5/4)*b^(5/4)*Sqrt[b*x + a*x^3]) + (Sqrt[x]*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(a^(1/4)*b^(1/4)*Sqrt[b*x + a*x^3]) - ((2*a*b - c)*Sqrt[x]*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(5/4)*b^(5/4)*Sqrt[b*x + a*x^3]) - ((2*a*b + c)*Sqrt[x]*(Sqrt[b] + Sqrt[a]*x)*Sqrt[(b + a*x^2)/(Sqrt[b] + Sqrt[a]*x)^2]*EllipticF[2*ArcTan[(a^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4*a^(5/4)*b^(5/4)*Sqrt[b*x + a*x^3])","C",18,12,45,0.2667,1,"{2056, 6715, 6725, 220, 1455, 527, 523, 409, 1211, 1699, 206, 203}"
2241,1,260,0,0.24867,"\int \frac{1}{x^{11} \left(-b+a x^5\right)^{3/4}} \, dx","Int[1/(x^11*(-b + a*x^5)^(3/4)),x]","-\frac{21 a^2 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{160 \sqrt{2} b^{11/4}}+\frac{21 a^2 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{a x^5-b}+\sqrt{a x^5-b}+\sqrt{b}\right)}{160 \sqrt{2} b^{11/4}}-\frac{21 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}\right)}{80 \sqrt{2} b^{11/4}}+\frac{21 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x^5-b}}{\sqrt[4]{b}}+1\right)}{80 \sqrt{2} b^{11/4}}+\frac{7 a \sqrt[4]{a x^5-b}}{40 b^2 x^5}+\frac{\sqrt[4]{a x^5-b}}{10 b x^{10}}","-\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,"(-b + a*x^5)^(1/4)/(10*b*x^10) + (7*a*(-b + a*x^5)^(1/4))/(40*b^2*x^5) - (21*a^2*ArcTan[1 - (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/(80*Sqrt[2]*b^(11/4)) + (21*a^2*ArcTan[1 + (Sqrt[2]*(-b + a*x^5)^(1/4))/b^(1/4)])/(80*Sqrt[2]*b^(11/4)) - (21*a^2*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(160*Sqrt[2]*b^(11/4)) + (21*a^2*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*(-b + a*x^5)^(1/4) + Sqrt[-b + a*x^5]])/(160*Sqrt[2]*b^(11/4))","A",13,9,17,0.5294,1,"{266, 51, 63, 211, 1165, 628, 1162, 617, 204}"
2242,0,0,0,2.6390617,"\int \frac{1+x^6}{\sqrt[3]{-x^2+x^4} \left(-1+x^6\right)} \, dx","Int[(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,"(-2*x*(1 - x^2)^(1/3)*AppellF1[1/6, 1/3, 1, 7/6, x^2, (-2*x^2)/(1 - I*Sqrt[3])])/(-x^2 + x^4)^(1/3) - (2*x*(1 - x^2)^(1/3)*AppellF1[1/6, 1/3, 1, 7/6, x^2, (-2*x^2)/(1 + I*Sqrt[3])])/(-x^2 + x^4)^(1/3) + (3*x*(1 - x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^2])/(-x^2 + x^4)^(1/3) + (x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x)*(-1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(-x^2 + x^4)^(1/3)) - (x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x)*(-1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(-x^2 + x^4)^(1/3)) + ((1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*(-1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(-x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(-1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(-x^2 + x^4)^(1/3)) + ((1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*(-1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(-x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(-1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(-x^2 + x^4)^(1/3))","F",0,0,0,0,-1,"{}"
2243,1,2697,0,20.797972,"\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","Int[(-b^6 + a^6*x^6)/(Sqrt[b^2*x + a^2*x^3]*(b^6 + a^6*x^6)),x]","-\frac{4 \sqrt[4]{2} \sqrt{x} \sqrt{b^2+a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{3 a^2-\sqrt{3} \sqrt{-a^4}} \sqrt{b} \sqrt{x}}{\sqrt[4]{2} \sqrt[4]{a^2-\sqrt{3} \sqrt{-a^4}} \sqrt{b^2+a^2 x^2}}\right) a^6}{\sqrt{3} \sqrt{-a^4} \left(a^2-\sqrt{3} \sqrt{-a^4}\right)^{3/4} \left(3 a^2-\sqrt{3} \sqrt{-a^4}\right)^{3/2} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{4 \sqrt[4]{2} \sqrt{x} \sqrt{b^2+a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{\sqrt{3} \sqrt{-a^4}-3 a^2} \sqrt{b} \sqrt{x}}{\sqrt[4]{2} \sqrt[4]{a^2-\sqrt{3} \sqrt{-a^4}} \sqrt{b^2+a^2 x^2}}\right) a^6}{\sqrt{3} \sqrt{-a^4} \left(a^2-\sqrt{3} \sqrt{-a^4}\right)^{3/4} \left(\sqrt{3} \sqrt{-a^4}-3 a^2\right)^{3/2} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{4 \sqrt[4]{2} \sqrt{x} \sqrt{b^2+a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{-3 a^2-\sqrt{3} \sqrt{-a^4}} \sqrt{b} \sqrt{x}}{\sqrt[4]{2} \sqrt[4]{a^2+\sqrt{3} \sqrt{-a^4}} \sqrt{b^2+a^2 x^2}}\right) a^6}{\sqrt{3} \sqrt{-a^4} \left(-3 a^2-\sqrt{3} \sqrt{-a^4}\right)^{3/2} \left(a^2+\sqrt{3} \sqrt{-a^4}\right)^{3/4} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{4 \sqrt[4]{2} \sqrt{x} \sqrt{b^2+a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{3 a^2+\sqrt{3} \sqrt{-a^4}} \sqrt{b} \sqrt{x}}{\sqrt[4]{2} \sqrt[4]{a^2+\sqrt{3} \sqrt{-a^4}} \sqrt{b^2+a^2 x^2}}\right) a^6}{\sqrt{3} \sqrt{-a^4} \left(a^2+\sqrt{3} \sqrt{-a^4}\right)^{3/4} \left(3 a^2+\sqrt{3} \sqrt{-a^4}\right)^{3/2} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{2 \left(1-\frac{\sqrt{2} a}{\sqrt{a^2-\sqrt{3} \sqrt{-a^4}}}\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right) a^{7/2}}{\sqrt{3} \sqrt{-a^4} \left(3 a^2+\sqrt{3} \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{2 \left(\frac{\sqrt{2} a}{\sqrt{a^2-\sqrt{3} \sqrt{-a^4}}}+1\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right) a^{7/2}}{\sqrt{3} \sqrt{-a^4} \left(3 a^2+\sqrt{3} \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{2 \left(1-\frac{\sqrt{2} a}{\sqrt{a^2+\sqrt{3} \sqrt{-a^4}}}\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right) a^{7/2}}{\sqrt{3} \sqrt{-a^4} \left(3 a^2-\sqrt{3} \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{2 \left(\frac{\sqrt{2} a}{\sqrt{a^2+\sqrt{3} \sqrt{-a^4}}}+1\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right) a^{7/2}}{\sqrt{3} \sqrt{-a^4} \left(3 a^2-\sqrt{3} \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{4 x a^2}{\sqrt{3} \left(\sqrt{3} a^2-3 \sqrt{-a^4}\right) \sqrt{a^2 x^3+b^2 x}}-\frac{4 x a^2}{\sqrt{3} \left(\sqrt{3} a^2+3 \sqrt{-a^4}\right) \sqrt{a^2 x^3+b^2 x}}-\frac{2 \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right) a^{3/2}}{\sqrt{3} \left(\sqrt{3} a^2-3 \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{2 \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right) a^{3/2}}{\sqrt{3} \left(\sqrt{3} a^2+3 \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{\sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{a^2 x^3+b^2 x} \sqrt{a}}-\frac{\left(\sqrt{2} a+\sqrt{a^2-\sqrt{3} \sqrt{-a^4}}\right)^2 \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} \Pi \left(-\frac{\left(\sqrt{2} a-\sqrt{a^2-\sqrt{3} \sqrt{-a^4}}\right)^2}{4 \sqrt{2} a \sqrt{a^2-\sqrt{3} \sqrt{-a^4}}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{2 \sqrt{3} \left(\sqrt{3} a^2+3 \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x} \sqrt{a}}-\frac{\left(\sqrt{2} a-\sqrt{a^2-\sqrt{3} \sqrt{-a^4}}\right)^2 \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} \Pi \left(\frac{\left(\sqrt{2} a+\sqrt{a^2-\sqrt{3} \sqrt{-a^4}}\right)^2}{4 \sqrt{2} a \sqrt{a^2-\sqrt{3} \sqrt{-a^4}}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{2 \sqrt{3} \left(\sqrt{3} a^2+3 \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x} \sqrt{a}}-\frac{\left(\sqrt{2} a+\sqrt{a^2+\sqrt{3} \sqrt{-a^4}}\right)^2 \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} \Pi \left(-\frac{\left(\sqrt{2} a-\sqrt{a^2+\sqrt{3} \sqrt{-a^4}}\right)^2}{4 \sqrt{2} a \sqrt{a^2+\sqrt{3} \sqrt{-a^4}}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{2 \sqrt{3} \left(\sqrt{3} a^2-3 \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x} \sqrt{a}}-\frac{\left(\sqrt{2} a-\sqrt{a^2+\sqrt{3} \sqrt{-a^4}}\right)^2 \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} \Pi \left(\frac{\left(\sqrt{2} a+\sqrt{a^2+\sqrt{3} \sqrt{-a^4}}\right)^2}{4 \sqrt{2} a \sqrt{a^2+\sqrt{3} \sqrt{-a^4}}};2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{2 \sqrt{3} \left(\sqrt{3} a^2-3 \sqrt{-a^4}\right) \sqrt{b} \sqrt{a^2 x^3+b^2 x} \sqrt{a}}","-\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,"(-4*a^2*x)/(Sqrt[3]*(Sqrt[3]*a^2 - 3*Sqrt[-a^4])*Sqrt[b^2*x + a^2*x^3]) - (4*a^2*x)/(Sqrt[3]*(Sqrt[3]*a^2 + 3*Sqrt[-a^4])*Sqrt[b^2*x + a^2*x^3]) - (4*2^(1/4)*a^6*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[3*a^2 - Sqrt[3]*Sqrt[-a^4]]*Sqrt[b]*Sqrt[x])/(2^(1/4)*(a^2 - Sqrt[3]*Sqrt[-a^4])^(1/4)*Sqrt[b^2 + a^2*x^2])])/(Sqrt[3]*Sqrt[-a^4]*(a^2 - Sqrt[3]*Sqrt[-a^4])^(3/4)*(3*a^2 - Sqrt[3]*Sqrt[-a^4])^(3/2)*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (4*2^(1/4)*a^6*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[-3*a^2 + Sqrt[3]*Sqrt[-a^4]]*Sqrt[b]*Sqrt[x])/(2^(1/4)*(a^2 - Sqrt[3]*Sqrt[-a^4])^(1/4)*Sqrt[b^2 + a^2*x^2])])/(Sqrt[3]*Sqrt[-a^4]*(a^2 - Sqrt[3]*Sqrt[-a^4])^(3/4)*(-3*a^2 + Sqrt[3]*Sqrt[-a^4])^(3/2)*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (4*2^(1/4)*a^6*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[-3*a^2 - Sqrt[3]*Sqrt[-a^4]]*Sqrt[b]*Sqrt[x])/(2^(1/4)*(a^2 + Sqrt[3]*Sqrt[-a^4])^(1/4)*Sqrt[b^2 + a^2*x^2])])/(Sqrt[3]*Sqrt[-a^4]*(-3*a^2 - Sqrt[3]*Sqrt[-a^4])^(3/2)*(a^2 + Sqrt[3]*Sqrt[-a^4])^(3/4)*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (4*2^(1/4)*a^6*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[3*a^2 + Sqrt[3]*Sqrt[-a^4]]*Sqrt[b]*Sqrt[x])/(2^(1/4)*(a^2 + Sqrt[3]*Sqrt[-a^4])^(1/4)*Sqrt[b^2 + a^2*x^2])])/(Sqrt[3]*Sqrt[-a^4]*(a^2 + Sqrt[3]*Sqrt[-a^4])^(3/4)*(3*a^2 + Sqrt[3]*Sqrt[-a^4])^(3/2)*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (2*a^(3/2)*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*(Sqrt[3]*a^2 - 3*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (2*a^(3/2)*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*(Sqrt[3]*a^2 + 3*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (2*a^(7/2)*(1 - (Sqrt[2]*a)/Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*Sqrt[-a^4]*(3*a^2 + Sqrt[3]*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (2*a^(7/2)*(1 + (Sqrt[2]*a)/Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*Sqrt[-a^4]*(3*a^2 + Sqrt[3]*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (2*a^(7/2)*(1 - (Sqrt[2]*a)/Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*Sqrt[-a^4]*(3*a^2 - Sqrt[3]*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (2*a^(7/2)*(1 + (Sqrt[2]*a)/Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(Sqrt[3]*Sqrt[-a^4]*(3*a^2 - Sqrt[3]*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - ((Sqrt[2]*a + Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]])^2*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[-1/4*(Sqrt[2]*a - Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]])^2/(Sqrt[2]*a*Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]]), 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(2*Sqrt[3]*Sqrt[a]*(Sqrt[3]*a^2 + 3*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - ((Sqrt[2]*a - Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]])^2*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[(Sqrt[2]*a + Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]])^2/(4*Sqrt[2]*a*Sqrt[a^2 - Sqrt[3]*Sqrt[-a^4]]), 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(2*Sqrt[3]*Sqrt[a]*(Sqrt[3]*a^2 + 3*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - ((Sqrt[2]*a + Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]])^2*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[-1/4*(Sqrt[2]*a - Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]])^2/(Sqrt[2]*a*Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]]), 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(2*Sqrt[3]*Sqrt[a]*(Sqrt[3]*a^2 - 3*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - ((Sqrt[2]*a - Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]])^2*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticPi[(Sqrt[2]*a + Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]])^2/(4*Sqrt[2]*a*Sqrt[a^2 + Sqrt[3]*Sqrt[-a^4]]), 2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(2*Sqrt[3]*Sqrt[a]*(Sqrt[3]*a^2 - 3*Sqrt[-a^4])*Sqrt[b]*Sqrt[b^2*x + a^2*x^3])","C",27,10,44,0.2273,0,"{2056, 6715, 6725, 220, 2073, 414, 523, 409, 1217, 1707}"
2244,1,319,0,1.2627173,"\int \frac{1+a x^2}{\left(-1+a x^2\right) \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Int[(1 + a*x^2)/((-1 + a*x^2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]),x]","-\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}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b}+a x}}{\sqrt{\sqrt{a}-\sqrt{a+b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a}-\sqrt{a+b}}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b}+a x}}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{\sqrt{a} \sqrt{\sqrt{a+b}+\sqrt{a}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b}+a x}}{\sqrt{\sqrt{a}-\sqrt{a+b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a}-\sqrt{a+b}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2 x^2+b}+a x}}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{\sqrt{a} \sqrt{\sqrt{a+b}+\sqrt{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*(a*x + Sqrt[b + a^2*x^2])^(3/2)) + Sqrt[a*x + Sqrt[b + a^2*x^2]]/a - (2*ArcTan[Sqrt[a*x + Sqrt[b + a^2*x^2]]/Sqrt[Sqrt[a] - Sqrt[a + b]]])/(Sqrt[a]*Sqrt[Sqrt[a] - Sqrt[a + b]]) - (2*ArcTan[Sqrt[a*x + Sqrt[b + a^2*x^2]]/Sqrt[Sqrt[a] + Sqrt[a + b]]])/(Sqrt[a]*Sqrt[Sqrt[a] + Sqrt[a + b]]) - (2*ArcTanh[Sqrt[a*x + Sqrt[b + a^2*x^2]]/Sqrt[Sqrt[a] - Sqrt[a + b]]])/(Sqrt[a]*Sqrt[Sqrt[a] - Sqrt[a + b]]) - (2*ArcTanh[Sqrt[a*x + Sqrt[b + a^2*x^2]]/Sqrt[Sqrt[a] + Sqrt[a + b]]])/(Sqrt[a]*Sqrt[Sqrt[a] + Sqrt[a + b]])","A",23,10,38,0.2632,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 208, 205}"
2245,0,0,0,1.7767197,"\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","Int[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]","\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","\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2246,1,242,0,0.4557925,"\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","Int[((-2*q + p*x^3)*Sqrt[q + p*x^3])/(b*x^4 + a*(q + p*x^3)^2),x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a} \sqrt{p x^3+q}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a} \sqrt{p x^3+q}}+1\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(-\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{p x^3+q}}+\sqrt{a}+\frac{\sqrt{b} x^2}{p x^3+q}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{p x^3+q}}+\sqrt{a}+\frac{\sqrt{b} x^2}{p x^3+q}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}","-\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,"ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a^(1/4)*Sqrt[q + p*x^3])]/(Sqrt[2]*a^(3/4)*b^(1/4)) - ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a^(1/4)*Sqrt[q + p*x^3])]/(Sqrt[2]*a^(3/4)*b^(1/4)) + Log[Sqrt[a] + (Sqrt[b]*x^2)/(q + p*x^3) - (Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[q + p*x^3]]/(2*Sqrt[2]*a^(3/4)*b^(1/4)) - Log[Sqrt[a] + (Sqrt[b]*x^2)/(q + p*x^3) + (Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[q + p*x^3]]/(2*Sqrt[2]*a^(3/4)*b^(1/4))","A",10,7,40,0.1750,1,"{6712, 211, 1165, 628, 1162, 617, 204}"
2247,0,0,0,0.3521139,"\int x^4 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","Int[x^4*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]],x]","\int x^4 \sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}} \, dx","\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,"Defer[Int][x^4*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]], x]","F",0,0,0,0,-1,"{}"
2248,1,242,0,0.4727357,"\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","Int[(Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(b*x^4 + a*(q + p*x^5)^2),x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a} \sqrt{p x^5+q}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a} \sqrt{p x^5+q}}+1\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(-\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{p x^5+q}}+\sqrt{a}+\frac{\sqrt{b} x^2}{p x^5+q}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{p x^5+q}}+\sqrt{a}+\frac{\sqrt{b} x^2}{p x^5+q}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}","-\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,"ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a^(1/4)*Sqrt[q + p*x^5])]/(Sqrt[2]*a^(3/4)*b^(1/4)) - ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a^(1/4)*Sqrt[q + p*x^5])]/(Sqrt[2]*a^(3/4)*b^(1/4)) + Log[Sqrt[a] + (Sqrt[b]*x^2)/(q + p*x^5) - (Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[q + p*x^5]]/(2*Sqrt[2]*a^(3/4)*b^(1/4)) - Log[Sqrt[a] + (Sqrt[b]*x^2)/(q + p*x^5) + (Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[q + p*x^5]]/(2*Sqrt[2]*a^(3/4)*b^(1/4))","A",10,7,41,0.1707,1,"{6712, 211, 1165, 628, 1162, 617, 204}"
2249,1,95,0,0.0178488,"\int \frac{-3+x}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[(-3 + x)/((1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{\log \left(x^2+3\right)}{2\ 2^{2/3}}-\frac{3 \log \left((x+1)^{2/3}+\sqrt[3]{2} \sqrt[3]{1-x}\right)}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} (x+1)^{2/3}}{\sqrt{3} \sqrt[3]{1-x}}\right)}{2^{2/3}}","-\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,"(Sqrt[3]*ArcTan[1/Sqrt[3] - (2^(2/3)*(1 + x)^(2/3))/(Sqrt[3]*(1 - x)^(1/3))])/2^(2/3) + Log[3 + x^2]/(2*2^(2/3)) - (3*Log[2^(1/3)*(1 - x)^(1/3) + (1 + x)^(2/3)])/(2*2^(2/3))","A",1,1,22,0.04545,1,"{1008}"
2250,0,0,0,73.7751928,"\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","Int[(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,"(-4*(a + 2*b)*x^2*(1 - x/a)^(1/4)*Hypergeometric2F1[5/4, 7/4, 11/4, -(((a - b)*x)/(a*(b - x)))])/(7*a*b*(1 - d)*(-((a - x)*(b - x)^2*x))^(1/4)*(1 - x/b)^(5/4)) + (16*(a^2*d + 4*b^2*d + a*b*(3 + d))*x*Gamma[7/4]*(11*b*(7*b - 4*x)*(a - x)*Hypergeometric2F1[1, 5/4, 11/4, ((a - b)*x)/(b*(a - x))] + 20*(a - b)*(b - x)*x*Hypergeometric2F1[2, 9/4, 15/4, ((a - b)*x)/(b*(a - x))]))/(693*b^3*(1 - d)^2*(a - x)^2*(-((a - x)*(b - x)^2*x))^(1/4)*Gamma[3/4]) - (4*a*b^2*d*(a^2*d + 4*b^2*d + a*b*(3 + d))*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^2/((-a + x^4)^(5/4)*(-b + x^4)^(3/2)*(a*b^2*d - 2*a*b*(1 + b/(2*a))*d*x^4 + a*(1 + (2*b)/a)*d*x^8 + (1 - d)*x^12)), x], x, x^(1/4)])/((1 - d)^2*(-((a - x)*(b - x)^2*x))^(1/4)) + (4*b*d*(2*a^3*d + 4*b^3*d + a^2*b*(7 + 2*d) + a*b^2*(5 + 7*d))*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^6/((-a + x^4)^(5/4)*(-b + x^4)^(3/2)*(a*b^2*d - 2*a*b*(1 + b/(2*a))*d*x^4 + a*(1 + (2*b)/a)*d*x^8 + (1 - d)*x^12)), x], x, x^(1/4)])/((1 - d)^2*(-((a - x)*(b - x)^2*x))^(1/4)) - (4*(a + 2*b)*d*(a*b*(5 - d) + a^2*d + b^2*(1 + 3*d))*x^(1/4)*(-a + x)^(1/4)*Sqrt[-b + x]*Defer[Subst][Defer[Int][x^10/((-a + x^4)^(5/4)*(-b + x^4)^(3/2)*(a*b^2*d - 2*a*b*(1 + b/(2*a))*d*x^4 + a*(1 + (2*b)/a)*d*x^8 + (1 - d)*x^12)), x], x, x^(1/4)])/((1 - d)^2*(-((a - x)*(b - x)^2*x))^(1/4))","F",0,0,0,0,-1,"{}"
2251,0,0,0,13.173028,"\int \frac{a x+\sqrt{b^2+a^2 x^2}}{b+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(a*x + Sqrt[b^2 + a^2*x^2])/(b + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\int \frac{a x+\sqrt{b^2+a^2 x^2}}{b+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\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,"x/(4*b) - (b*x)/4 - ((1 + b^2)*x)/(4*b) + Sqrt[b^2 + a^2*x^2]/(4*a*b) + ((1 - b^2)*Sqrt[b^2 + a^2*x^2])/(4*a*b) - ((1 + b^2)*Sqrt[b^2 + a^2*x^2])/(4*a*b) - (x*Sqrt[b^2 + a^2*x^2])/(4*b) - ((1 - a*x)*Sqrt[b^2 + a^2*x^2])/(4*a*b) + 1/(4*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) - b^2/(4*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) - (1 + b^2)/(4*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + ((1 + b^2)^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(4*a*b^2) - ((1 - b^4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(4*a*b^2) + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(12*a) + ((1 + b^(-2))*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2))/(12*a) - (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(12*a*b^2) - ((1 + b^2)^2*ArcTan[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]])/(4*a*b^2) + ((1 - b^4)*ArcTan[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]])/(4*a*b^2) - ArcTanh[(a*x)/Sqrt[b^2 + a^2*x^2]]/(8*a*b) - (b*ArcTanh[(a*x)/Sqrt[b^2 + a^2*x^2]])/(4*a) - ((1 - b^2)^2*ArcTanh[(a*x)/Sqrt[b^2 + a^2*x^2]])/(8*a*b) + ((1 + 2*b^2)*ArcTanh[(a*x)/Sqrt[b^2 + a^2*x^2]])/(8*a*b) + ((1 - b^4)*ArcTanh[(a*x)/Sqrt[b^2 + a^2*x^2]])/(8*a*b) + ((1 + b^2)^2*ArcTanh[(2*b^2 - a*(1 - b^2)*x)/((1 + b^2)*Sqrt[b^2 + a^2*x^2])])/(8*a*b) - ((1 - b^4)*ArcTanh[(2*b^2 - a*(1 - b^2)*x)/((1 + b^2)*Sqrt[b^2 + a^2*x^2])])/(8*a*b) - ((1 + b^2)^2*ArcTanh[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/b])/(4*a*b) + ((1 - b^4)*ArcTanh[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/b])/(4*a*b) - ((1 + b^2)^2*Log[1 - b^2 + 2*a*x])/(8*a*b) + ((1 - b^4)*Log[1 - b^2 + 2*a*x])/(8*a*b) - Defer[Int][(Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(-1 + b^2 - 2*a*x), x]/b^2 + (1 - b^(-2))*Defer[Int][(Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(1 - b^2 + 2*a*x), x]","F",0,0,0,0,-1,"{}"
2252,1,81,0,0.0143327,"\int \frac{1}{\left(3+x^2\right) \sqrt[3]{1+3 x^2}} \, dx","Int[1/((3 + x^2)*(1 + 3*x^2)^(1/3)),x]","\frac{\tan ^{-1}\left(\frac{\left(1-\sqrt[3]{3 x^2+1}\right)^2}{3 \sqrt{3} x}\right)}{4 \sqrt{3}}-\frac{1}{4} \tanh ^{-1}\left(\frac{1-\sqrt[3]{3 x^2+1}}{x}\right)+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{4 \sqrt{3}}","\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,"ArcTan[x/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[(1 - (1 + 3*x^2)^(1/3))^2/(3*Sqrt[3]*x)]/(4*Sqrt[3]) - ArcTanh[(1 - (1 + 3*x^2)^(1/3))/x]/4","A",1,1,19,0.05263,1,"{394}"
2253,1,44,0,0.1815036,"\int \frac{\left(1+x^2\right) \sqrt[4]{x^3+x^5}}{x^2 \left(-1+x^2\right)} \, dx","Int[((1 + x^2)*(x^3 + x^5)^(1/4))/(x^2*(-1 + x^2)),x]","\frac{4 \sqrt[4]{x^5+x^3} F_1\left(-\frac{1}{8};1,-\frac{5}{4};\frac{7}{8};x^2,-x^2\right)}{x \sqrt[4]{x^2+1}}","\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,"(4*(x^3 + x^5)^(1/4)*AppellF1[-1/8, 1, -5/4, 7/8, x^2, -x^2])/(x*(1 + x^2)^(1/4))","C",3,3,27,0.1111,0,"{2056, 466, 510}"
2254,0,0,0,1.1245027,"\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","Int[((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,"-2*Defer[Int][(-2 - x^2 - 2*x^4 + 2*x^5)^(1/4)/x^2, x] + Defer[Int][(-2 - x^2 - 2*x^4 + 2*x^5)^(1/4)/(2 + x^2 - 2*x^5), x] + 5*Defer[Int][(x^3*(-2 - x^2 - 2*x^4 + 2*x^5)^(1/4))/(-2 - x^2 + 2*x^5), x]","F",0,0,0,0,-1,"{}"
2255,0,0,0,3.1500247,"\int \frac{\left(-1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^4\right)^2} \, dx","Int[((-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,"Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]], x] + (I/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/((-1)^(1/4) - x)^2, x] - ((-1)^(1/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/((-1)^(1/4) - x), x])/4 - (I/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(-(-1)^(3/4) - x)^2, x] + ((-1)^(3/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(-(-1)^(3/4) - x), x])/4 + (I/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/((-1)^(1/4) + x)^2, x] - ((-1)^(1/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/((-1)^(1/4) + x), x])/4 - (I/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(-(-1)^(3/4) + x)^2, x] + ((-1)^(3/4)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(-(-1)^(3/4) + x), x])/4","F",0,0,0,0,-1,"{}"
2256,0,0,0,2.3355938,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-6 \text{$\#$1}^{11}+12 \text{$\#$1}^9-8 \text{$\#$1}^7-\text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{8}{3} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{16}{3} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"-8*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 + 16*Defer[Subst][Defer[Int][(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16)^(-1), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 16*Defer[Subst][Defer[Int][x^2/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2257,0,0,0,1.8628491,"\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-1 + x^2)/(Sqrt[1 + x]*(1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\sqrt{1+x} \left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{13}-6 \text{$\#$1}^{11}+12 \text{$\#$1}^9-8 \text{$\#$1}^7-\text{$\#$1}^5+2 \text{$\#$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*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 + 16*Defer[Subst][Defer[Int][(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16)^(-1), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 16*Defer[Subst][Defer[Int][x^2/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2258,1,102,0,0.0583068,"\int \left(\frac{1}{\sqrt{1-\sqrt{x}}}-\sqrt{1-\sqrt{x}-x}\right) \, dx","Int[1/Sqrt[1 - Sqrt[x]] - Sqrt[1 - Sqrt[x] - x],x]","\frac{4}{3} \left(1-\sqrt{x}\right)^{3/2}-4 \sqrt{1-\sqrt{x}}+\frac{2}{3} \left(-x-\sqrt{x}+1\right)^{3/2}+\frac{1}{4} \left(2 \sqrt{x}+1\right) \sqrt{-x-\sqrt{x}+1}+\frac{5}{8} \sin ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{5}}\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,"-4*Sqrt[1 - Sqrt[x]] + (4*(1 - Sqrt[x])^(3/2))/3 + ((1 + 2*Sqrt[x])*Sqrt[1 - Sqrt[x] - x])/4 + (2*(1 - Sqrt[x] - x)^(3/2))/3 + (5*ArcSin[(1 + 2*Sqrt[x])/Sqrt[5]])/8","A",9,7,32,0.2188,1,"{190, 43, 1341, 640, 612, 619, 216}"
2259,0,0,0,0.0140687,"\int \frac{-5+x}{\sqrt[3]{-2-x+x^2} \left(-3+4 x+x^2\right)} \, dx","Int[(-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,"Defer[Int][(-5 + x)/((-2 - x + x^2)^(1/3)*(-3 + 4*x + x^2)), x]","F",0,0,0,0,-1,"{}"
2260,1,325,0,2.0505065,"\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","Int[((-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{4 (a-x)^2 (b-x) \left(1-\sqrt{-4 a d+4 b d+1}\right) \sqrt{-\frac{b-x}{a-b}} F_1\left(\frac{5}{4};\frac{3}{2},1;\frac{9}{4};\frac{a-x}{a-b},-\frac{2 d (a-x)}{-2 a d+2 b d-\sqrt{-4 a d+4 b d+1}+1}\right)}{5 (a-b) \left(-\sqrt{-4 a d+4 b d+1}-2 a d+2 b d+1\right) \left(-\left((a-x) (b-x)^2\right)\right)^{3/4}}+\frac{4 (a-x)^2 (b-x) \left(\sqrt{-4 a d+4 b d+1}+1\right) \sqrt{-\frac{b-x}{a-b}} F_1\left(\frac{5}{4};\frac{3}{2},1;\frac{9}{4};\frac{a-x}{a-b},-\frac{2 d (a-x)}{-2 a d+2 b d+\sqrt{-4 a d+4 b d+1}+1}\right)}{5 (a-b) \left(\sqrt{-4 a d+4 b d+1}-2 a d+2 b d+1\right) \left(-\left((a-x) (b-x)^2\right)\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,"(4*(1 - Sqrt[1 - 4*a*d + 4*b*d])*(a - x)^2*(b - x)*Sqrt[-((b - x)/(a - b))]*AppellF1[5/4, 3/2, 1, 9/4, (a - x)/(a - b), (-2*d*(a - x))/(1 - 2*a*d + 2*b*d - Sqrt[1 - 4*a*d + 4*b*d])])/(5*(a - b)*(1 - 2*a*d + 2*b*d - Sqrt[1 - 4*a*d + 4*b*d])*(-((a - x)*(b - x)^2))^(3/4)) + (4*(1 + Sqrt[1 - 4*a*d + 4*b*d])*(a - x)^2*(b - x)*Sqrt[-((b - x)/(a - b))]*AppellF1[5/4, 3/2, 1, 9/4, (a - x)/(a - b), (-2*d*(a - x))/(1 - 2*a*d + 2*b*d + Sqrt[1 - 4*a*d + 4*b*d])])/(5*(a - b)*(1 - 2*a*d + 2*b*d + Sqrt[1 - 4*a*d + 4*b*d])*(-((a - x)*(b - x)^2))^(3/4))","C",7,4,52,0.07692,0,"{6719, 6728, 137, 136}"
2261,0,0,0,0.2828515,"\int \frac{1+x}{\left(1+4 x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Int[(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,"((3 - Sqrt[3])*Defer[Int][1/((4 - 2*Sqrt[3] + 2*x)*(1 - x^3)^(1/3)), x])/3 + ((3 + Sqrt[3])*Defer[Int][1/((4 + 2*Sqrt[3] + 2*x)*(1 - x^3)^(1/3)), x])/3","F",0,0,0,0,-1,"{}"
2262,0,0,0,0.2479852,"\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^4/((-b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a-b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(b-a x^2\right)}{4 a b x (a-b) \left(a x^4-b\right)}",1,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((b + a*x^4)^(1/4)*(-b + a*x^8)^2), x], x, Sqrt[x]])/(b*x^2 + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2263,0,0,0,0.2315768,"\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^4/((-b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 a (a-b)}+\frac{\left(a x^4+b x^2\right)^{3/4} \left(b-a x^2\right)}{4 a b x (a-b) \left(a x^4-b\right)}",1,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((b + a*x^4)^(1/4)*(-b + a*x^8)^2), x], x, Sqrt[x]])/(b*x^2 + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2264,0,0,0,0.2578057,"\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","Int[x^4/((-b + a*x^4)^2*(b*x^2 + a*x^4)^(1/4)),x]","\int \frac{x^4}{\left(-b+a x^4\right)^2 \sqrt[4]{b x^2+a x^4}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{\text{$\#$1}^4 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 (-\log (x))-2 a \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+2 a \log (x)}{\text{$\#$1} a-\text{$\#$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,"(2*Sqrt[x]*(b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^8/((b + a*x^4)^(1/4)*(-b + a*x^8)^2), x], x, Sqrt[x]])/(b*x^2 + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2265,1,833,0,1.230689,"\int \frac{x^8}{\sqrt{-1+x^4} \left(-1+x^{16}\right)} \, dx","Int[x^8/(Sqrt[-1 + x^4]*(-1 + x^16)),x]","-\frac{x \left(1-x^2\right)}{16 \sqrt{x^4-1}}+\frac{\sqrt{x^2+1} \Pi \left(-\sqrt[4]{-1};\left.\sin ^{-1}(x)\right|-1\right) \sqrt{1-x^2}}{8 \sqrt{x^4-1}}+\frac{\sqrt{x^2+1} \Pi \left(\sqrt[4]{-1};\left.\sin ^{-1}(x)\right|-1\right) \sqrt{1-x^2}}{8 \sqrt{x^4-1}}+\frac{\sqrt{x^2+1} \Pi \left(-(-1)^{3/4};\left.\sin ^{-1}(x)\right|-1\right) \sqrt{1-x^2}}{8 \sqrt{x^4-1}}+\frac{\sqrt{x^2+1} \Pi \left((-1)^{3/4};\left.\sin ^{-1}(x)\right|-1\right) \sqrt{1-x^2}}{8 \sqrt{x^4-1}}-\left(\frac{1}{32}-\frac{i}{32}\right) \tan ^{-1}\left(\frac{(1+i) x}{\sqrt{x^4-1}}\right)-\left(\frac{1}{32}-\frac{i}{32}\right) \tanh ^{-1}\left(\frac{(1+i) x}{\sqrt{x^4-1}}\right)+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{4 \left((2-2 i)+2 \sqrt{2}\right) \sqrt{x^4-1}}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \left((1+i)+\sqrt{2}\right) \sqrt{x^4-1}}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \left((1-i)+\sqrt{2}\right) \sqrt{x^4-1}}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \left((-1+i)+\sqrt{2}\right) \sqrt{x^4-1}}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \left((-1-i)+\sqrt{2}\right) \sqrt{x^4-1}}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \left(1+(-1)^{3/4}\right) \sqrt{x^4-1}}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \left(1+\sqrt[4]{-1}\right) \sqrt{x^4-1}}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \left(1-\sqrt[4]{-1}\right) \sqrt{x^4-1}}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt{x^4-1}}-\frac{x \left(x^2+1\right)}{16 \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,"-1/16*(x*(1 - x^2))/Sqrt[-1 + x^4] - (x*(1 + x^2))/(16*Sqrt[-1 + x^4]) - (1/32 - I/32)*ArcTan[((1 + I)*x)/Sqrt[-1 + x^4]] - (1/32 - I/32)*ArcTanh[((1 + I)*x)/Sqrt[-1 + x^4]] - (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(4*Sqrt[2]*Sqrt[-1 + x^4]) + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*Sqrt[2]*(1 - (-1)^(1/4))*Sqrt[-1 + x^4]) + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*Sqrt[2]*(1 + (-1)^(1/4))*Sqrt[-1 + x^4]) + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*Sqrt[2]*(1 + (-1)^(3/4))*Sqrt[-1 + x^4]) - (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*((-1 - I) + Sqrt[2])*Sqrt[-1 + x^4]) - (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*((-1 + I) + Sqrt[2])*Sqrt[-1 + x^4]) - (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*((1 - I) + Sqrt[2])*Sqrt[-1 + x^4]) - (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*((1 + I) + Sqrt[2])*Sqrt[-1 + x^4]) + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(4*((2 - 2*I) + 2*Sqrt[2])*Sqrt[-1 + x^4]) + (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-(-1)^(1/4), ArcSin[x], -1])/(8*Sqrt[-1 + x^4]) + (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[(-1)^(1/4), ArcSin[x], -1])/(8*Sqrt[-1 + x^4]) + (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-(-1)^(3/4), ArcSin[x], -1])/(8*Sqrt[-1 + x^4]) + (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[(-1)^(3/4), ArcSin[x], -1])/(8*Sqrt[-1 + x^4])","C",57,19,20,0.9500,1,"{6725, 1152, 414, 423, 427, 424, 253, 222, 409, 1211, 1699, 206, 203, 1429, 1215, 1457, 540, 538, 537}"
2266,0,0,0,1.9744757,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{\left(b^2+a x^2\right)^4} \, dx","Int[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,"(5*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[-a]*x), x])/(32*b^7) + (5*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[-a]*x), x])/(32*b^7) + (a^2*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b - a*x)^4, x])/(16*b^4) + ((-a)^(3/2)*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b - a*x)^3, x])/(8*b^5) - (5*a*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b - a*x)^2, x])/(32*b^6) + (a^2*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b + a*x)^4, x])/(16*b^4) + ((-a)^(3/2)*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b + a*x)^3, x])/(8*b^5) - (5*a*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[-a]*b + a*x)^2, x])/(32*b^6)","F",0,0,0,0,-1,"{}"
2267,0,0,0,0.3084212,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","Int[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,"(I/2)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(I - x), x] + (I/2)*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(I + x), x]","F",0,0,0,0,-1,"{}"
2268,1,164,0,1.1817637,"\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x^2}}}}}{x} \, dx","Int[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",12,5,31,0.1613,1,"{6742, 2073, 207, 1166, 203}"
2269,1,97,0,0.0467587,"\int \frac{1}{(1+x) \sqrt[3]{1-x^3}} \, dx","Int[1/((1 + x)*(1 - x^3)^(1/3)),x]","\frac{3 \log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2}}-\frac{\log \left((1-x) (x+1)^2\right)}{4 \sqrt[3]{2}}","\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,"-1/2*(Sqrt[3]*ArcTan[(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/Sqrt[3]])/2^(1/3) - Log[(1 - x)*(1 + x)^2]/(4*2^(1/3)) + (3*Log[-1 + x + 2^(2/3)*(1 - x^3)^(1/3)])/(4*2^(1/3))","A",1,1,17,0.05882,1,"{2148}"
2270,0,0,0,6.8252217,"\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","Int[((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,"(4*(b - x)^2*x*(1 - x/a)^(3/4)*(1 - x/b)^(1/4)*AppellF1[1/4, 3/4, 1/4, 5/4, x/a, x/b])/((a - x)*(b - x)^3*x)^(3/4) + ((a - 2*b + d + Sqrt[a^2 + 2*a*d - 4*b*d + d^2])*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(9/4)*Defer[Int][1/(x^(3/4)*(-a + x)^(3/4)*(-b + x)^(1/4)*(-a - d - Sqrt[a^2 + 2*a*d - 4*b*d + d^2] + 2*x)), x])/((a - x)*(b - x)^3*x)^(3/4) + ((a - 2*b + d - Sqrt[a^2 + 2*a*d - 4*b*d + d^2])*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(9/4)*Defer[Int][1/(x^(3/4)*(-a + x)^(3/4)*(-b + x)^(1/4)*(-a - d + Sqrt[a^2 + 2*a*d - 4*b*d + d^2] + 2*x)), x])/((a - x)*(b - x)^3*x)^(3/4)","F",0,0,0,0,-1,"{}"
2271,0,0,0,4.0028553,"\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","Int[(-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,"((a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3) + ((a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2272,1,168,0,0.1904665,"\int \frac{\left(-1+x^3\right)^{2/3} \left(1+x^3\right)}{x^6 \left(2+x^3\right)} \, dx","Int[((-1 + x^3)^(2/3)*(1 + x^3))/(x^6*(2 + x^3)),x]","-\frac{\log \left(\sqrt[3]{2}-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3-1}}\right)}{4\ 2^{2/3} \sqrt[3]{3}}+\frac{\sqrt[6]{3} \tan ^{-1}\left(\frac{2^{2/3} x}{\sqrt[6]{3} \sqrt[3]{x^3-1}}+\frac{1}{\sqrt{3}}\right)}{4\ 2^{2/3}}-\frac{\left(x^3-1\right)^{2/3}}{10 x^5}-\frac{\left(x^3-1\right)^{2/3}}{40 x^2}+\frac{\log \left(\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3-1}}+\frac{3^{2/3} x^2}{\left(x^3-1\right)^{2/3}}+2^{2/3}\right)}{8\ 2^{2/3} \sqrt[3]{3}}","-\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,"-1/10*(-1 + x^3)^(2/3)/x^5 - (-1 + x^3)^(2/3)/(40*x^2) + (3^(1/6)*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/(3^(1/6)*(-1 + x^3)^(1/3))])/(4*2^(2/3)) - Log[2^(1/3) - (3^(1/3)*x)/(-1 + x^3)^(1/3)]/(4*2^(2/3)*3^(1/3)) + Log[2^(2/3) + (3^(2/3)*x^2)/(-1 + x^3)^(2/3) + (6^(1/3)*x)/(-1 + x^3)^(1/3)]/(8*2^(2/3)*3^(1/3))","A",10,10,25,0.4000,1,"{580, 583, 12, 377, 200, 31, 634, 617, 204, 628}"
2273,0,0,0,0.1445488,"\int \frac{1}{(1+x) \left(-2+3 x-2 x^2+3 x^3-2 x^4\right)^{3/2}} \, dx","Int[1/((1 + x)*(-2 + 3*x - 2*x^2 + 3*x^3 - 2*x^4)^(3/2)),x]","\int \frac{1}{(1+x) \left(-2+3 x-2 x^2+3 x^3-2 x^4\right)^{3/2}} \, dx","\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,"Defer[Int][1/((1 + x)*(-2 + 3*x - 2*x^2 + 3*x^3 - 2*x^4)^(3/2)), x]","F",0,0,0,0,-1,"{}"
2274,1,616,0,1.9929929,"\int \frac{x^2 \sqrt[4]{x^3+x^4}}{-1+x^4} \, dx","Int[(x^2*(x^3 + x^4)^(1/4))/(-1 + x^4),x]","-\frac{2 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{(1-i)^{5/4} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1-i)^{3/4} x^{3/4} \sqrt[4]{x+1}}+\frac{(1+i)^{5/4} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1+i)^{3/4} x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2^{3/4} x^{3/4} \sqrt[4]{x+1}}+\frac{2 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{(1-i)^{5/4} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1-i)^{3/4} x^{3/4} \sqrt[4]{x+1}}-\frac{(1+i)^{5/4} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1+i)^{3/4} x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2^{3/4} x^{3/4} \sqrt[4]{x+1}}","-\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,"(-2*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 - I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) + ((1 - I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 + I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) + ((1 + I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2^(3/4)*x^(3/4)*(1 + x)^(1/4)) + (2*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - ((x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 - I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) - ((1 - I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) - ((x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 + I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) - ((1 + I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) - ((x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2^(3/4)*x^(3/4)*(1 + x)^(1/4))","C",67,21,22,0.9545,1,"{2056, 1586, 6733, 6742, 331, 298, 203, 206, 1240, 410, 237, 335, 275, 231, 407, 409, 1213, 537, 494, 6725, 1529}"
2275,1,616,0,1.7939682,"\int \frac{x^2 \sqrt[4]{x^3+x^4}}{-1+x^4} \, dx","Int[(x^2*(x^3 + x^4)^(1/4))/(-1 + x^4),x]","-\frac{2 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{(1-i)^{5/4} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1-i)^{3/4} x^{3/4} \sqrt[4]{x+1}}+\frac{(1+i)^{5/4} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1+i)^{3/4} x^{3/4} \sqrt[4]{x+1}}+\frac{\sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2^{3/4} x^{3/4} \sqrt[4]{x+1}}+\frac{2 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{(1-i)^{5/4} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1-i)^{3/4} x^{3/4} \sqrt[4]{x+1}}-\frac{(1+i)^{5/4} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{4 x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 (1+i)^{3/4} x^{3/4} \sqrt[4]{x+1}}-\frac{\sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2^{3/4} x^{3/4} \sqrt[4]{x+1}}","-\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,"(-2*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 - I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) + ((1 - I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 + I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) + ((1 + I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) + ((x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2^(3/4)*x^(3/4)*(1 + x)^(1/4)) + (2*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - ((x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 - I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) - ((1 - I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) - ((x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2*(1 + I)^(3/4)*x^(3/4)*(1 + x)^(1/4)) - ((1 + I)^(5/4)*(x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(4*x^(3/4)*(1 + x)^(1/4)) - ((x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(2^(3/4)*x^(3/4)*(1 + x)^(1/4))","C",67,21,22,0.9545,1,"{2056, 1586, 6733, 6742, 331, 298, 203, 206, 1240, 410, 237, 335, 275, 231, 407, 409, 1213, 537, 494, 6725, 1529}"
2276,1,1319,0,1.9529353,"\int \frac{1}{\sqrt[3]{-x+x^3} \left(1+x^6\right)} \, dx","Int[1/((-x + x^3)^(1/3)*(1 + x^6)),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} \left(1-x^{2/3}\right)}{\sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(2 x^{2/3}-i \sqrt{3}+1\right)}{\sqrt[3]{x^2-1}}+2}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(2 x^{2/3}+i \sqrt{3}+1\right)}{\sqrt[3]{x^2-1}}+2}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\left(3 i-\sqrt{3}\right) \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3}}{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}} \sqrt[3]{x^3-x}}-\frac{\left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} x^{2/3}}{\sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(-\left(-2 i x^{2/3}-\sqrt{3}+i\right)^2 \left(2 i x^{2/3}-\sqrt{3}+i\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\left(-2 i x^{2/3}+\sqrt{3}+i\right)^2 \left(2 i x^{2/3}+\sqrt{3}+i\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(-\left(\left(1-x^{2/3}\right) \left(x^{2/3}+1\right)^2\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\left(1-i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2-1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2-1}}+\left(1+i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\left(1+i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2-1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2-1}}+\left(1-i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\sqrt[3]{1-i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2-1}}+\sqrt[3]{1+i \sqrt{3}}\right)}{6 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\sqrt[3]{1+i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2-1}}+\sqrt[3]{1-i \sqrt{3}}\right)}{6 \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(2 x^{2/3}-2\ 2^{2/3} \sqrt[3]{x^2-1}-i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(2 x^{2/3}-2\ 2^{2/3} \sqrt[3]{x^2-1}+i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(-x^{2/3}+2^{2/3} \sqrt[3]{x^2-1}+1\right)}{8 \sqrt[3]{2} \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,"(x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (2^(1/3)*(1 - x^(2/3)))/(-1 + x^2)^(1/3))/Sqrt[3]])/(4*2^(1/3)*Sqrt[3]*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(2 + (2^(1/3)*(1 - I*Sqrt[3] + 2*x^(2/3)))/(-1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*Sqrt[3]*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(2 + (2^(1/3)*(1 + I*Sqrt[3] + 2*x^(2/3)))/(-1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*Sqrt[3]*(-x + x^3)^(1/3)) + ((3*I - Sqrt[3])*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (2*x^(2/3))/(((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(-1 + x^2)^(1/3)))/Sqrt[3]])/(6*2^(2/3)*(1 - I*Sqrt[3])^(1/3)*(-x + x^3)^(1/3)) - ((1 + I*Sqrt[3])^(2/3)*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)*Sqrt[3]*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[-((I - Sqrt[3] - (2*I)*x^(2/3))^2*(I - Sqrt[3] + (2*I)*x^(2/3)))])/(24*2^(1/3)*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[(I + Sqrt[3] - (2*I)*x^(2/3))^2*(I + Sqrt[3] + (2*I)*x^(2/3))])/(24*2^(1/3)*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[-((1 - x^(2/3))*(1 + x^(2/3))^2)])/(24*2^(1/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(2/3) + ((1 - I*Sqrt[3])^(2/3)*x^(4/3))/(-1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(12*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(-x + x^3)^(1/3)) - (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(2/3) + ((1 + I*Sqrt[3])^(2/3)*x^(4/3))/(-1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(12*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(1/3) + ((1 - I*Sqrt[3])^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(6*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(-x + x^3)^(1/3)) + (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(1/3) + ((1 + I*Sqrt[3])^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(6*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 - I*Sqrt[3] + 2*x^(2/3) - 2*2^(2/3)*(-1 + x^2)^(1/3)])/(8*2^(1/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 + I*Sqrt[3] + 2*x^(2/3) - 2*2^(2/3)*(-1 + x^2)^(1/3)])/(8*2^(1/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 - x^(2/3) + 2^(2/3)*(-1 + x^2)^(1/3)])/(8*2^(1/3)*(-x + x^3)^(1/3))","C",25,12,19,0.6316,0,"{2056, 6715, 2074, 2148, 6728, 377, 200, 31, 634, 617, 204, 628}"
2277,1,1319,0,1.7072064,"\int \frac{1}{\sqrt[3]{-x+x^3} \left(1+x^6\right)} \, dx","Int[1/((-x + x^3)^(1/3)*(1 + x^6)),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} \left(1-x^{2/3}\right)}{\sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(2 x^{2/3}-i \sqrt{3}+1\right)}{\sqrt[3]{x^2-1}}+2}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(2 x^{2/3}+i \sqrt{3}+1\right)}{\sqrt[3]{x^2-1}}+2}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\left(3 i-\sqrt{3}\right) \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3}}{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}} \sqrt[3]{x^3-x}}-\frac{\left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} x^{2/3}}{\sqrt[3]{x^2-1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(-\left(-2 i x^{2/3}-\sqrt{3}+i\right)^2 \left(2 i x^{2/3}-\sqrt{3}+i\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\left(-2 i x^{2/3}+\sqrt{3}+i\right)^2 \left(2 i x^{2/3}+\sqrt{3}+i\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(-\left(\left(1-x^{2/3}\right) \left(x^{2/3}+1\right)^2\right)\right)}{24 \sqrt[3]{2} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\left(1-i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2-1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2-1}}+\left(1+i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\left(1+i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2-1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2-1}}+\left(1-i \sqrt{3}\right)^{2/3}\right)}{12 \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\sqrt[3]{1-i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2-1}}+\sqrt[3]{1+i \sqrt{3}}\right)}{6 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{\sqrt[3]{1+i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2-1}}+\sqrt[3]{1-i \sqrt{3}}\right)}{6 \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(2 x^{2/3}-2\ 2^{2/3} \sqrt[3]{x^2-1}-i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(2 x^{2/3}-2\ 2^{2/3} \sqrt[3]{x^2-1}+i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(-x^{2/3}+2^{2/3} \sqrt[3]{x^2-1}+1\right)}{8 \sqrt[3]{2} \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,"(x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (2^(1/3)*(1 - x^(2/3)))/(-1 + x^2)^(1/3))/Sqrt[3]])/(4*2^(1/3)*Sqrt[3]*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(2 + (2^(1/3)*(1 - I*Sqrt[3] + 2*x^(2/3)))/(-1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*Sqrt[3]*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(2 + (2^(1/3)*(1 + I*Sqrt[3] + 2*x^(2/3)))/(-1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*Sqrt[3]*(-x + x^3)^(1/3)) + ((3*I - Sqrt[3])*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (2*x^(2/3))/(((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(-1 + x^2)^(1/3)))/Sqrt[3]])/(6*2^(2/3)*(1 - I*Sqrt[3])^(1/3)*(-x + x^3)^(1/3)) - ((1 + I*Sqrt[3])^(2/3)*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 - (2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)*Sqrt[3]*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[-((I - Sqrt[3] - (2*I)*x^(2/3))^2*(I - Sqrt[3] + (2*I)*x^(2/3)))])/(24*2^(1/3)*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[(I + Sqrt[3] - (2*I)*x^(2/3))^2*(I + Sqrt[3] + (2*I)*x^(2/3))])/(24*2^(1/3)*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[-((1 - x^(2/3))*(1 + x^(2/3))^2)])/(24*2^(1/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(2/3) + ((1 - I*Sqrt[3])^(2/3)*x^(4/3))/(-1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(12*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(-x + x^3)^(1/3)) - (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(2/3) + ((1 + I*Sqrt[3])^(2/3)*x^(4/3))/(-1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(12*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(1/3) + ((1 - I*Sqrt[3])^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(6*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(-x + x^3)^(1/3)) + (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(1/3) + ((1 + I*Sqrt[3])^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(6*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 - I*Sqrt[3] + 2*x^(2/3) - 2*2^(2/3)*(-1 + x^2)^(1/3)])/(8*2^(1/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 + I*Sqrt[3] + 2*x^(2/3) - 2*2^(2/3)*(-1 + x^2)^(1/3)])/(8*2^(1/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 - x^(2/3) + 2^(2/3)*(-1 + x^2)^(1/3)])/(8*2^(1/3)*(-x + x^3)^(1/3))","C",25,12,19,0.6316,0,"{2056, 6715, 2074, 2148, 6728, 377, 200, 31, 634, 617, 204, 628}"
2278,1,185,0,0.2834981,"\int \frac{\sqrt{-x+x^4}}{-b+a x^6} \, dx","Int[Sqrt[-x + x^4]/(-b + a*x^6),x]","\frac{\sqrt{x^4-x} \sqrt{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{b} \sqrt{x^3-1}}\right)}{3 \sqrt{a} b^{3/4} \sqrt{x} \sqrt{x^3-1}}+\frac{\sqrt{x^4-x} \sqrt{\sqrt{a}+\sqrt{b}} \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{b} \sqrt{x^3-1}}\right)}{3 \sqrt{a} b^{3/4} \sqrt{x} \sqrt{x^3-1}}","\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[Sqrt[a] - Sqrt[b]]*Sqrt[-x + x^4]*ArcTan[(Sqrt[Sqrt[a] - Sqrt[b]]*x^(3/2))/(b^(1/4)*Sqrt[-1 + x^3])])/(3*Sqrt[a]*b^(3/4)*Sqrt[x]*Sqrt[-1 + x^3]) + (Sqrt[Sqrt[a] + Sqrt[b]]*Sqrt[-x + x^4]*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*x^(3/2))/(b^(1/4)*Sqrt[-1 + x^3])])/(3*Sqrt[a]*b^(3/4)*Sqrt[x]*Sqrt[-1 + x^3])","A",14,10,23,0.4348,1,"{2056, 1493, 1491, 1175, 402, 217, 206, 377, 205, 208}"
2279,0,0,0,3.2226277,"\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","Int[((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,"((-1 - 2*x^4 + 2*x^8)^(1/4)*AppellF1[-9/4, -1/4, -1/4, -5/4, (2*x^4)/(1 + Sqrt[3]), (2*x^4)/(1 - Sqrt[3])])/(9*x^9*(1 - (2*x^4)/(1 - Sqrt[3]))^(1/4)*(1 - (2*x^4)/(1 + Sqrt[3]))^(1/4)) + ((-1 - 2*x^4 + 2*x^8)^(1/4)*AppellF1[-1/4, -1/4, -1/4, 3/4, (2*x^4)/(1 + Sqrt[3]), (2*x^4)/(1 - Sqrt[3])])/(x*(1 - (2*x^4)/(1 - Sqrt[3]))^(1/4)*(1 - (2*x^4)/(1 + Sqrt[3]))^(1/4)) + (4*x^7*(-1 - 2*x^4 + 2*x^8)^(1/4)*AppellF1[7/4, -1/4, -1/4, 11/4, (2*x^4)/(1 + Sqrt[3]), (2*x^4)/(1 - Sqrt[3])])/(7*(1 - (2*x^4)/(1 - Sqrt[3]))^(1/4)*(1 - (2*x^4)/(1 + Sqrt[3]))^(1/4)) + ((I/2)*Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/(I - 2^(1/8)*x), x])/2^(3/4) - Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/(1 - 2^(1/8)*x), x]/(2*2^(3/4)) - ((1/4 - I/4)*Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/((-1)^(1/4) - 2^(1/8)*x), x])/2^(1/4) - ((-1)^(1/4)*Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/(-(-1)^(3/4) - 2^(1/8)*x), x])/(2*2^(3/4)) + ((I/2)*Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/(I + 2^(1/8)*x), x])/2^(3/4) - Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/(1 + 2^(1/8)*x), x]/(2*2^(3/4)) - ((1/4 - I/4)*Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/((-1)^(1/4) + 2^(1/8)*x), x])/2^(1/4) - ((-1)^(1/4)*Defer[Int][(-1 - 2*x^4 + 2*x^8)^(1/4)/(-(-1)^(3/4) + 2^(1/8)*x), x])/(2*2^(3/4))","F",0,0,0,0,-1,"{}"
2280,0,0,0,0.2391125,"\int \frac{\left(b^2+a x^2\right)^{3/2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[(b^2 + a*x^2)^(3/2)/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\int \frac{\left(b^2+a x^2\right)^{3/2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\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,"Defer[Int][(b^2 + a*x^2)^(3/2)/Sqrt[b + Sqrt[b^2 + a*x^2]], x]","F",0,0,0,0,-1,"{}"
2281,1,255,0,0.5928625,"\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","Int[(x*(-2*q + p*x^6)*Sqrt[q + p*x^6])/(b*x^8 + a*(q + p*x^6)^2),x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a} \sqrt{p x^6+q}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^2}{\sqrt[4]{a} \sqrt{p x^6+q}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(-\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2}{\sqrt{p x^6+q}}+\sqrt{a}+\frac{\sqrt{b} x^4}{p x^6+q}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x^2}{\sqrt{p x^6+q}}+\sqrt{a}+\frac{\sqrt{b} x^4}{p x^6+q}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}","-\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,"ArcTan[1 - (Sqrt[2]*b^(1/4)*x^2)/(a^(1/4)*Sqrt[q + p*x^6])]/(2*Sqrt[2]*a^(3/4)*b^(1/4)) - ArcTan[1 + (Sqrt[2]*b^(1/4)*x^2)/(a^(1/4)*Sqrt[q + p*x^6])]/(2*Sqrt[2]*a^(3/4)*b^(1/4)) + Log[Sqrt[a] + (Sqrt[b]*x^4)/(q + p*x^6) - (Sqrt[2]*a^(1/4)*b^(1/4)*x^2)/Sqrt[q + p*x^6]]/(4*Sqrt[2]*a^(3/4)*b^(1/4)) - Log[Sqrt[a] + (Sqrt[b]*x^4)/(q + p*x^6) + (Sqrt[2]*a^(1/4)*b^(1/4)*x^2)/Sqrt[q + p*x^6]]/(4*Sqrt[2]*a^(3/4)*b^(1/4))","A",10,7,41,0.1707,1,"{6714, 211, 1165, 628, 1162, 617, 204}"
2282,1,119,0,0.1601275,"\int \frac{\sqrt[3]{-1-2 x+6 x^2}}{-1+6 x} \, dx","Int[(-1 - 2*x + 6*x^2)^(1/3)/(-1 + 6*x),x]","\frac{\sqrt[3]{(6 x-1)^2-7}}{4 \sqrt[3]{6}}+\frac{1}{12} \sqrt[3]{\frac{7}{6}} \log (1-6 x)-\frac{1}{8} \sqrt[3]{\frac{7}{6}} \log \left(\sqrt[3]{(6 x-1)^2-7}+\sqrt[3]{7}\right)+\frac{\sqrt[3]{\frac{7}{2}} \tan ^{-1}\left(\frac{7-2\ 7^{2/3} \sqrt[3]{(6 x-1)^2-7}}{7 \sqrt{3}}\right)}{4\ 3^{5/6}}","\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,"(-7 + (-1 + 6*x)^2)^(1/3)/(4*6^(1/3)) + ((7/2)^(1/3)*ArcTan[(7 - 2*7^(2/3)*(-7 + (-1 + 6*x)^2)^(1/3))/(7*Sqrt[3])])/(4*3^(5/6)) + ((7/6)^(1/3)*Log[1 - 6*x])/12 - ((7/6)^(1/3)*Log[7^(1/3) + (-7 + (-1 + 6*x)^2)^(1/3)])/8","A",7,7,22,0.3182,1,"{694, 266, 50, 58, 617, 204, 31}"
2283,0,0,0,4.6321369,"\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","Int[(-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,"((a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][x^(1/3)/((-a + x)^(2/3)*(-b + x)^(2/3)*(a + b - Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(2/3) + ((a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][x^(1/3)/((-a + x)^(2/3)*(-b + x)^(2/3)*(a + b + Sqrt[a^2 - 2*a*b + b^2 + 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(2/3)","F",0,0,0,0,-1,"{}"
2284,0,0,0,9.8358842,"\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","Int[(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,"(3*x^2*(1 - x/a)^(2/3)*(1 - x/b)^(2/3)*AppellF1[2/3, 2/3, 2/3, 5/3, x/a, x/b])/(2*d*((a - x)*(b - x)*x^2)^(2/3)) + ((1 + a*d + b*d + Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2])*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*(-1 - a*d - b*d - Sqrt[1 + 2*a*d + 2*b*d + a^2*d^2 - 2*a*b*d^2 + b^2*d^2] + 2*d*x)), x])/(d*((a - x)*(b - x)*x^2)^(2/3)) + ((1 + a*d + b*d - Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2])*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*(-1 - a*d - b*d + Sqrt[1 + 2*a*d + 2*b*d + a^2*d^2 - 2*a*b*d^2 + b^2*d^2] + 2*d*x)), x])/(d*((a - x)*(b - x)*x^2)^(2/3))","F",0,0,0,0,-1,"{}"
2285,1,143,0,0.102982,"\int \frac{\left(-2+x^3\right) \left(-1+x^3\right)^{2/3}}{x^3 \left(-1+2 x^3\right)} \, dx","Int[((-2 + x^3)*(-1 + x^3)^(2/3))/(x^3*(-1 + 2*x^3)),x]","-\frac{1}{2} \log \left(\frac{x}{\sqrt[3]{x^3-1}}+1\right)-\frac{1}{4} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\left(x^3-1\right)^{2/3}}{x^2}+\frac{1}{4} \log \left(-\frac{x}{\sqrt[3]{x^3-1}}+\frac{x^2}{\left(x^3-1\right)^{2/3}}+1\right)","-\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 + x^3)^(2/3)/x^2) + (Sqrt[3]*ArcTan[(1 - (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]])/2 + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) + Log[1 + x^2/(-1 + x^3)^(2/3) - x/(-1 + x^3)^(1/3)]/4 - Log[1 + x/(-1 + x^3)^(1/3)]/2 - Log[-x + (-1 + x^3)^(1/3)]/4","A",10,10,27,0.3704,1,"{580, 530, 239, 377, 200, 31, 634, 618, 204, 628}"
2286,1,64,0,0.257253,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b+a x^2} \, dx","Int[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b + a*x^2),x]","-\frac{2 x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{5}{4};\frac{7}{4};-\frac{a x^2}{b},\frac{a x^2}{b}\right)}{3 \sqrt[4]{1-\frac{a x^2}{b}}}","\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,"(-2*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -5/4, 7/4, -((a*x^2)/b), (a*x^2)/b])/(3*(1 - (a*x^2)/b)^(1/4))","C",4,4,35,0.1143,0,"{2056, 466, 511, 510}"
2287,0,0,0,1.5358645,"\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(1 + x^3)/((-1 + x^3)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","\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,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] + (2*Defer[Int][1/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/3 - (2*(1 - I*Sqrt[3])*Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/3 - (2*(1 + I*Sqrt[3])*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/3","F",0,0,0,0,-1,"{}"
2288,0,0,0,1.5454062,"\int \frac{-b+a x^6}{\sqrt[3]{-x+x^3} \left(-d+c x^6\right)} \, dx","Int[(-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,"(Sqrt[3]*a*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*c*(-x + x^3)^(1/3)) - (3*a*x^(1/3)*(-1 + x^2)^(1/3)*Log[x^(2/3) - (-1 + x^2)^(1/3)])/(4*c*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(1/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(2/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(1/3)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(4/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(5/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(2/3)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(7/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(8/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2289,0,0,0,1.2915886,"\int \frac{-b+a x^6}{\sqrt[3]{-x+x^3} \left(-d+c x^6\right)} \, dx","Int[(-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,"(Sqrt[3]*a*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*c*(-x + x^3)^(1/3)) - (3*a*x^(1/3)*(-1 + x^2)^(1/3)*Log[x^(2/3) - (-1 + x^2)^(1/3)])/(4*c*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(1/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(2/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(1/3)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(4/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(5/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(2/3)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) + (-1)^(7/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((d^(1/9) - (-1)^(8/9)*c^(1/9)*x)*(-1 + x^3)^(1/3)), x], x, x^(2/3)])/(6*c*d^(8/9)*(-x + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2290,1,127,0,0.1632448,"\int \frac{1}{\sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Int[1/Sqrt[d + Sqrt[c + Sqrt[b + a*x]]],x]","-\frac{8 \left(c-3 d^2\right) \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{3/2}}{3 a}+\frac{8 d \left(c-d^2\right) \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{a}+\frac{8 \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{7/2}}{7 a}-\frac{24 d \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{5/2}}{5 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*d*(c - d^2)*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]])/a - (8*(c - 3*d^2)*(d + Sqrt[c + Sqrt[b + a*x]])^(3/2))/(3*a) - (24*d*(d + Sqrt[c + Sqrt[b + a*x]])^(5/2))/(5*a) + (8*(d + Sqrt[c + Sqrt[b + a*x]])^(7/2))/(7*a)","A",5,3,21,0.1429,1,"{371, 1398, 772}"
2291,1,83,0,0.0182547,"\int \frac{1}{x \sqrt[3]{3+3 x+x^2}} \, dx","Int[1/(x*(3 + 3*x + x^2)^(1/3)),x]","\frac{\log \left(3^{2/3} \sqrt[3]{x^2+3 x+3}-x-3\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{2 (x+3)}{3 \sqrt[6]{3} \sqrt[3]{x^2+3 x+3}}+\frac{1}{\sqrt{3}}\right)}{3^{5/6}}-\frac{\log (x)}{2 \sqrt[3]{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,"-(ArcTan[1/Sqrt[3] + (2*(3 + x))/(3*3^(1/6)*(3 + 3*x + x^2)^(1/3))]/3^(5/6)) - Log[x]/(2*3^(1/3)) + Log[-3 - x + 3^(2/3)*(3 + 3*x + x^2)^(1/3)]/(2*3^(1/3))","A",1,1,16,0.06250,1,"{752}"
2292,0,0,0,9.1453182,"\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","Int[(-(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,"(3*x*(1 - x/a)^(1/3)*(1 - x/b)^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, x/a, x/b])/(d*((a - x)*(b - x)*x^2)^(1/3)) + ((1 + a*d + b*d + Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2])*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(-1 - a*d - b*d - Sqrt[1 + 2*a*d + 2*b*d + a^2*d^2 - 2*a*b*d^2 + b^2*d^2] + 2*d*x)), x])/(d*((a - x)*(b - x)*x^2)^(1/3)) + ((1 + a*d + b*d - Sqrt[a^2*d^2 + 2*a*d*(1 - b*d) + (1 + b*d)^2])*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(-1 - a*d - b*d + Sqrt[1 + 2*a*d + 2*b*d + a^2*d^2 - 2*a*b*d^2 + b^2*d^2] + 2*d*x)), x])/(d*((a - x)*(b - x)*x^2)^(1/3))","F",0,0,0,0,-1,"{}"
2293,0,0,0,2.1436523,"\int \frac{(-3+2 x) \left(1-x+x^3\right)^{2/3}}{x^3 \left(-2+2 x+x^3\right)} \, dx","Int[((-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,"(27*2^(1/3)*(1 - x + x^3)^(2/3)*Defer[Int][((((18 - 2*Sqrt[69])^(1/3) + (2*(9 + Sqrt[69]))^(1/3))/6^(2/3) + x)^(2/3)*((-6 + 2^(1/3)*(27 - 3*Sqrt[69])^(2/3) + 6*3^(1/3)*(2/(9 - Sqrt[69]))^(2/3))/18 - (((9 - Sqrt[69])^(1/3) + (9 + Sqrt[69])^(1/3))*x)/(2^(1/3)*3^(2/3)) + x^2)^(2/3))/x^3, x])/((6^(1/3)*((18 - 2*Sqrt[69])^(1/3) + (2*(9 + Sqrt[69]))^(1/3)) + 6*x)^(2/3)*(-6 + 2^(1/3)*(27 - 3*Sqrt[69])^(2/3) + 6*3^(1/3)*(2/(9 - Sqrt[69]))^(2/3) - 3*2^(2/3)*3^(1/3)*((9 - Sqrt[69])^(1/3) + (9 + Sqrt[69])^(1/3))*x + 18*x^2)^(2/3)) + (9*2^(1/3)*(1 - x + x^3)^(2/3)*Defer[Int][((((18 - 2*Sqrt[69])^(1/3) + (2*(9 + Sqrt[69]))^(1/3))/6^(2/3) + x)^(2/3)*((-6 + 2^(1/3)*(27 - 3*Sqrt[69])^(2/3) + 6*3^(1/3)*(2/(9 - Sqrt[69]))^(2/3))/18 - (((9 - Sqrt[69])^(1/3) + (9 + Sqrt[69])^(1/3))*x)/(2^(1/3)*3^(2/3)) + x^2)^(2/3))/x^2, x])/((6^(1/3)*((18 - 2*Sqrt[69])^(1/3) + (2*(9 + Sqrt[69]))^(1/3)) + 6*x)^(2/3)*(-6 + 2^(1/3)*(27 - 3*Sqrt[69])^(2/3) + 6*3^(1/3)*(2/(9 - Sqrt[69]))^(2/3) - 3*2^(2/3)*3^(1/3)*((9 - Sqrt[69])^(1/3) + (9 + Sqrt[69])^(1/3))*x + 18*x^2)^(2/3)) + (9*2^(1/3)*(1 - x + x^3)^(2/3)*Defer[Int][((((18 - 2*Sqrt[69])^(1/3) + (2*(9 + Sqrt[69]))^(1/3))/6^(2/3) + x)^(2/3)*((-6 + 2^(1/3)*(27 - 3*Sqrt[69])^(2/3) + 6*3^(1/3)*(2/(9 - Sqrt[69]))^(2/3))/18 - (((9 - Sqrt[69])^(1/3) + (9 + Sqrt[69])^(1/3))*x)/(2^(1/3)*3^(2/3)) + x^2)^(2/3))/x, x])/((6^(1/3)*((18 - 2*Sqrt[69])^(1/3) + (2*(9 + Sqrt[69]))^(1/3)) + 6*x)^(2/3)*(-6 + 2^(1/3)*(27 - 3*Sqrt[69])^(2/3) + 6*3^(1/3)*(2/(9 - Sqrt[69]))^(2/3) - 3*2^(2/3)*3^(1/3)*((9 - Sqrt[69])^(1/3) + (9 + Sqrt[69])^(1/3))*x + 18*x^2)^(2/3)) - (5*Defer[Int][(1 - x + x^3)^(2/3)/(-2 + 2*x + x^3), x])/2 - Defer[Int][(x*(1 - x + x^3)^(2/3))/(-2 + 2*x + x^3), x]/2 - Defer[Int][(x^2*(1 - x + x^3)^(2/3))/(-2 + 2*x + x^3), x]/2","F",0,0,0,0,-1,"{}"
2294,0,0,0,2.0733546,"\int \frac{(-3+4 x) \left(-1+2 x+x^3\right)^{2/3}}{x^3 \left(2-4 x+x^3\right)} \, dx","Int[((-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,"(-27*2^(1/3)*(-1 + 2*x + x^3)^(2/3)*Defer[Int][(((4*(3/(9 + Sqrt[177]))^(1/3) - (2*(9 + Sqrt[177]))^(1/3))/6^(2/3) + x)^(2/3)*((12 + 24*3^(1/3)*(2/(9 + Sqrt[177]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[177]))^(2/3))/18 - ((2*(6/(9 + Sqrt[177]))^(1/3) - ((9 + Sqrt[177])/2)^(1/3))*x)/3^(2/3) + x^2)^(2/3))/x^3, x])/((6^(1/3)*(4*(3/(9 + Sqrt[177]))^(1/3) - (2*(9 + Sqrt[177]))^(1/3)) + 6*x)^(2/3)*(12 + 24*3^(1/3)*(2/(9 + Sqrt[177]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[177]))^(2/3) - 6*3^(1/3)*(2*(6/(9 + Sqrt[177]))^(1/3) - ((9 + Sqrt[177])/2)^(1/3))*x + 18*x^2)^(2/3)) - (18*2^(1/3)*(-1 + 2*x + x^3)^(2/3)*Defer[Int][(((4*(3/(9 + Sqrt[177]))^(1/3) - (2*(9 + Sqrt[177]))^(1/3))/6^(2/3) + x)^(2/3)*((12 + 24*3^(1/3)*(2/(9 + Sqrt[177]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[177]))^(2/3))/18 - ((2*(6/(9 + Sqrt[177]))^(1/3) - ((9 + Sqrt[177])/2)^(1/3))*x)/3^(2/3) + x^2)^(2/3))/x^2, x])/((6^(1/3)*(4*(3/(9 + Sqrt[177]))^(1/3) - (2*(9 + Sqrt[177]))^(1/3)) + 6*x)^(2/3)*(12 + 24*3^(1/3)*(2/(9 + Sqrt[177]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[177]))^(2/3) - 6*3^(1/3)*(2*(6/(9 + Sqrt[177]))^(1/3) - ((9 + Sqrt[177])/2)^(1/3))*x + 18*x^2)^(2/3)) - (36*2^(1/3)*(-1 + 2*x + x^3)^(2/3)*Defer[Int][(((4*(3/(9 + Sqrt[177]))^(1/3) - (2*(9 + Sqrt[177]))^(1/3))/6^(2/3) + x)^(2/3)*((12 + 24*3^(1/3)*(2/(9 + Sqrt[177]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[177]))^(2/3))/18 - ((2*(6/(9 + Sqrt[177]))^(1/3) - ((9 + Sqrt[177])/2)^(1/3))*x)/3^(2/3) + x^2)^(2/3))/x, x])/((6^(1/3)*(4*(3/(9 + Sqrt[177]))^(1/3) - (2*(9 + Sqrt[177]))^(1/3)) + 6*x)^(2/3)*(12 + 24*3^(1/3)*(2/(9 + Sqrt[177]))^(2/3) + 2^(1/3)*(3*(9 + Sqrt[177]))^(2/3) - 6*3^(1/3)*(2*(6/(9 + Sqrt[177]))^(1/3) - ((9 + Sqrt[177])/2)^(1/3))*x + 18*x^2)^(2/3)) - (13*Defer[Int][(-1 + 2*x + x^3)^(2/3)/(2 - 4*x + x^3), x])/2 + Defer[Int][(x*(-1 + 2*x + x^3)^(2/3))/(2 - 4*x + x^3), x] + 2*Defer[Int][(x^2*(-1 + 2*x + x^3)^(2/3))/(2 - 4*x + x^3), x]","F",0,0,0,0,-1,"{}"
2295,1,208,0,0.3271803,"\int \frac{\sqrt{-81+27 x+135 x^2-150 x^3+65 x^4-13 x^5+x^6}}{-1+x} \, dx","Int[Sqrt[-81 + 27*x + 135*x^2 - 150*x^3 + 65*x^4 - 13*x^5 + x^6]/(-1 + x),x]","\frac{\sqrt{-(3-x)^4 \left(-x^2+x+1\right)} (41-18 x)}{8 (3-x)^2}-\frac{\left(-x^2+x+1\right) \sqrt{-(3-x)^4 \left(-x^2+x+1\right)}}{3 (3-x)^2}+\frac{4 \sqrt{-(3-x)^4 \left(-x^2+x+1\right)} \tan ^{-1}\left(\frac{3-x}{2 \sqrt{x^2-x-1}}\right)}{(3-x)^2 \sqrt{x^2-x-1}}-\frac{77 \sqrt{-(3-x)^4 \left(-x^2+x+1\right)} \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)}{16 (3-x)^2 \sqrt{x^2-x-1}}","\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,"((41 - 18*x)*Sqrt[-((3 - x)^4*(1 + x - x^2))])/(8*(3 - x)^2) - ((1 + x - x^2)*Sqrt[-((3 - x)^4*(1 + x - x^2))])/(3*(3 - x)^2) + (4*Sqrt[-((3 - x)^4*(1 + x - x^2))]*ArcTan[(3 - x)/(2*Sqrt[-1 - x + x^2])])/((3 - x)^2*Sqrt[-1 - x + x^2]) - (77*Sqrt[-((3 - x)^4*(1 + x - x^2))]*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])])/(16*(3 - x)^2*Sqrt[-1 - x + x^2])","A",9,9,38,0.2368,1,"{6688, 6719, 1653, 814, 843, 621, 206, 724, 204}"
2296,0,0,0,2.9118545,"\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","Int[((-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,"-(Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^2, x]/a) + (b*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x, x])/(a^2*q) - (b^2*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/(a*q + b*x + a*p*x^3), x])/(a^2*q) + 3*p*Defer[Int][(x*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(a*q + b*x + a*p*x^3), x] - (b*p*Defer[Int][(x^2*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(a*q + b*x + a*p*x^3), x])/(a*q)","F",0,0,0,0,-1,"{}"
2297,1,946,0,0.9346805,"\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","Int[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{5 (x-1)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x-1}}{\sqrt{3}}\right) \left(-x^2-x+1\right)}{\sqrt{3} \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}-\frac{\sqrt{\frac{3}{5}} \sqrt[3]{\frac{1}{2} \left(123-55 \sqrt{5}\right)} (x-1)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\frac{2}{3+\sqrt{5}}} \sqrt[3]{x-1}}{\sqrt{3}}\right) \left(-x^2-x+1\right)}{\sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}+\frac{\sqrt{\frac{3}{5}} \left(3+\sqrt{5}\right)^{5/3} (x-1)^{2/3} \tan ^{-1}\left(\frac{1-2^{2/3} \sqrt[3]{3+\sqrt{5}} \sqrt[3]{x-1}}{\sqrt{3}}\right) \left(-x^2-x+1\right)}{2\ 2^{2/3} \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}+\frac{5 (x-1)^{2/3} \log \left(\sqrt[3]{x-1}+1\right) \left(-x^2-x+1\right)}{3 \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}-\frac{\left(3+\sqrt{5}\right)^{5/3} (x-1)^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{x-1}+\sqrt[3]{3-\sqrt{5}}\right) \left(-x^2-x+1\right)}{2\ 2^{2/3} \sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}+\frac{\sqrt[3]{\frac{1}{2} \left(123-55 \sqrt{5}\right)} (x-1)^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{x-1}+\sqrt[3]{3+\sqrt{5}}\right) \left(-x^2-x+1\right)}{\sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}-\frac{5 (x-1)^{2/3} \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right) \left(-x^2-x+1\right)}{6 \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}+\frac{\left(3+\sqrt{5}\right)^{5/3} (x-1)^{2/3} \log \left(2^{2/3} (x-1)^{2/3}-\sqrt[3]{2 \left(3-\sqrt{5}\right)} \sqrt[3]{x-1}+\left(3-\sqrt{5}\right)^{2/3}\right) \left(-x^2-x+1\right)}{4\ 2^{2/3} \sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}-\frac{\sqrt[3]{\frac{1}{2} \left(123-55 \sqrt{5}\right)} (x-1)^{2/3} \log \left(2^{2/3} (x-1)^{2/3}-\sqrt[3]{2 \left(3+\sqrt{5}\right)} \sqrt[3]{x-1}+\left(3+\sqrt{5}\right)^{2/3}\right) \left(-x^2-x+1\right)}{2 \sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}-\frac{(x-1)^{2/3} \left(-x^2-x+1\right)}{3 \left(\sqrt[3]{x-1}+1\right) \sqrt[3]{-(1-x)^2 \left(-x^2-x+1\right)^3}}+\frac{\left(\sqrt[3]{x-1}+1\right) (x-1)^{2/3} \left(-x^2-x+1\right)}{3 \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right) \sqrt[3]{-(1-x)^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,"-1/3*((-1 + x)^(2/3)*(1 - x - x^2))/((1 + (-1 + x)^(1/3))*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) + ((1 + (-1 + x)^(1/3))*(-1 + x)^(2/3)*(1 - x - x^2))/(3*(1 - (-1 + x)^(1/3) + (-1 + x)^(2/3))*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) - (5*(-1 + x)^(2/3)*(1 - x - x^2)*ArcTan[(1 - 2*(-1 + x)^(1/3))/Sqrt[3]])/(Sqrt[3]*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) - (Sqrt[3/5]*((123 - 55*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 - x - x^2)*ArcTan[(1 - 2*(2/(3 + Sqrt[5]))^(1/3)*(-1 + x)^(1/3))/Sqrt[3]])/(-((1 - x)^2*(1 - x - x^2)^3))^(1/3) + (Sqrt[3/5]*(3 + Sqrt[5])^(5/3)*(-1 + x)^(2/3)*(1 - x - x^2)*ArcTan[(1 - 2^(2/3)*(3 + Sqrt[5])^(1/3)*(-1 + x)^(1/3))/Sqrt[3]])/(2*2^(2/3)*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) + (5*(-1 + x)^(2/3)*(1 - x - x^2)*Log[1 + (-1 + x)^(1/3)])/(3*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) - ((3 + Sqrt[5])^(5/3)*(-1 + x)^(2/3)*(1 - x - x^2)*Log[(3 - Sqrt[5])^(1/3) + 2^(1/3)*(-1 + x)^(1/3)])/(2*2^(2/3)*Sqrt[5]*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) + (((123 - 55*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 - x - x^2)*Log[(3 + Sqrt[5])^(1/3) + 2^(1/3)*(-1 + x)^(1/3)])/(Sqrt[5]*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) - (5*(-1 + x)^(2/3)*(1 - x - x^2)*Log[1 - (-1 + x)^(1/3) + (-1 + x)^(2/3)])/(6*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) + ((3 + Sqrt[5])^(5/3)*(-1 + x)^(2/3)*(1 - x - x^2)*Log[(3 - Sqrt[5])^(2/3) - (2*(3 - Sqrt[5]))^(1/3)*(-1 + x)^(1/3) + 2^(2/3)*(-1 + x)^(2/3)])/(4*2^(2/3)*Sqrt[5]*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3)) - (((123 - 55*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 - x - x^2)*Log[(3 + Sqrt[5])^(2/3) - (2*(3 + Sqrt[5]))^(1/3)*(-1 + x)^(1/3) + 2^(2/3)*(-1 + x)^(2/3)])/(2*Sqrt[5]*(-((1 - x)^2*(1 - x - x^2)^3))^(1/3))","B",25,13,44,0.2955,0,"{6688, 6719, 897, 1424, 638, 618, 204, 634, 628, 1422, 200, 31, 617}"
2298,1,192,0,1.0834942,"\int \frac{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^2\right) \sqrt{1+x^4}} \, dx","Int[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/((-1 + x^2)*Sqrt[1 + x^4]),x]","-\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)+\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)+\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)-\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}","\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,"-1/2*(Sqrt[1 - I]*ArcTanh[(1 - I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])]) + (Sqrt[1 - I]*ArcTanh[(1 + I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])])/2 + (Sqrt[1 + I]*ArcTanh[(1 - I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/2 - (Sqrt[1 + I]*ArcTanh[(1 + I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/2 + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",16,5,39,0.1282,0,"{6725, 2132, 206, 2133, 725}"
2299,1,378,0,0.6803387,"\int \frac{2+x}{(-3+x) \sqrt[4]{1-x^2} \left(1+x^2\right)} \, dx","Int[(2 + x)/((-3 + x)*(1 - x^2)^(1/4)*(1 + x^2)),x]","\frac{\log \left(\sqrt{1-x^2}-2 \sqrt[4]{2} \sqrt[4]{1-x^2}+2 \sqrt{2}\right)}{8 \sqrt[4]{2}}-\frac{\log \left(\sqrt{1-x^2}+2 \sqrt[4]{2} \sqrt[4]{1-x^2}+2 \sqrt{2}\right)}{8 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-x^2}}{\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt[4]{1-x^2}}{\sqrt[4]{2}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{1-x^2}}{\sqrt[4]{2}}+1\right)}{4 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{1-x^2}}{\sqrt[4]{2}}\right)}{2 \sqrt[4]{2}}-\frac{\sqrt{x^2} \Pi \left(-\frac{1}{\sqrt{2}};\left.\sin ^{-1}\left(\sqrt[4]{1-x^2}\right)\right|-1\right)}{2 \sqrt{2} x}+\frac{3 i \sqrt{x^2} \Pi \left(-\frac{i}{2 \sqrt{2}};\left.\sin ^{-1}\left(\sqrt[4]{1-x^2}\right)\right|-1\right)}{4 \sqrt{2} x}-\frac{3 i \sqrt{x^2} \Pi \left(\frac{i}{2 \sqrt{2}};\left.\sin ^{-1}\left(\sqrt[4]{1-x^2}\right)\right|-1\right)}{4 \sqrt{2} x}+\frac{\sqrt{x^2} \Pi \left(\frac{1}{\sqrt{2}};\left.\sin ^{-1}\left(\sqrt[4]{1-x^2}\right)\right|-1\right)}{2 \sqrt{2} x}","-\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,"-1/2*ArcTan[(1 - x^2)^(1/4)/2^(1/4)]/2^(1/4) - ArcTan[1 - (1 - x^2)^(1/4)/2^(1/4)]/(4*2^(1/4)) + ArcTan[1 + (1 - x^2)^(1/4)/2^(1/4)]/(4*2^(1/4)) + ArcTanh[(1 - x^2)^(1/4)/2^(1/4)]/(2*2^(1/4)) - (Sqrt[x^2]*EllipticPi[-(1/Sqrt[2]), ArcSin[(1 - x^2)^(1/4)], -1])/(2*Sqrt[2]*x) + (((3*I)/4)*Sqrt[x^2]*EllipticPi[(-1/2*I)/Sqrt[2], ArcSin[(1 - x^2)^(1/4)], -1])/(Sqrt[2]*x) - (((3*I)/4)*Sqrt[x^2]*EllipticPi[(I/2)/Sqrt[2], ArcSin[(1 - x^2)^(1/4)], -1])/(Sqrt[2]*x) + (Sqrt[x^2]*EllipticPi[1/Sqrt[2], ArcSin[(1 - x^2)^(1/4)], -1])/(2*Sqrt[2]*x) + Log[2*Sqrt[2] - 2*2^(1/4)*(1 - x^2)^(1/4) + Sqrt[1 - x^2]]/(8*2^(1/4)) - Log[2*Sqrt[2] + 2*2^(1/4)*(1 - x^2)^(1/4) + Sqrt[1 - x^2]]/(8*2^(1/4))","C",32,18,27,0.6667,1,"{6725, 746, 399, 490, 1213, 537, 444, 63, 297, 1162, 617, 204, 1165, 628, 1010, 298, 203, 206}"
2300,1,223,0,0.7773605,"\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","Int[(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{(3 a b-c) \sqrt{a^2 x^3+b^2}}{3 a b}+\frac{(3 a b+c) \sqrt{a^2 x^3+b^2}}{3 a b}-\frac{\sqrt{a-b} (3 a b-c) \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a-b}}\right)}{3 a \sqrt{b}}-\frac{\sqrt{a+b} (3 a b+c) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a+b}}\right)}{3 a \sqrt{b}}-\frac{4}{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)","\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,"(-4*Sqrt[b^2 + a^2*x^3])/3 + ((3*a*b - c)*Sqrt[b^2 + a^2*x^3])/(3*a*b) + ((3*a*b + c)*Sqrt[b^2 + a^2*x^3])/(3*a*b) - (Sqrt[a - b]*(3*a*b - c)*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[a - b]*Sqrt[b])])/(3*a*Sqrt[b]) + (4*b*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/3 - (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",14,7,52,0.1346,1,"{6725, 266, 50, 63, 208, 444, 205}"
2301,1,306,0,0.4866124,"\int \frac{1-x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-1-2 x^4+x^8\right)} \, dx","Int[(1 - x^4 + 2*x^8)/((1 + x^4)^(1/4)*(-1 - 2*x^4 + x^8)),x]","\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}}-\frac{3 \left(1-\sqrt{2}\right) \tan ^{-1}\left(1-\frac{2^{5/8} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt[8]{2} \left(2-\sqrt{2}\right)}+\frac{3 \left(1-\sqrt{2}\right) \tan ^{-1}\left(\frac{2^{5/8} x}{\sqrt[4]{x^4+1}}+1\right)}{4 \sqrt[8]{2} \left(2-\sqrt{2}\right)}+\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 \left(1-\sqrt{2}\right) \log \left(-\frac{2 x}{\sqrt[4]{x^4+1}}+\frac{2^{5/8} x^2}{\sqrt{x^4+1}}+2^{3/8}\right)}{8 \sqrt[8]{2} \left(2-\sqrt{2}\right)}+\frac{3 \left(1-\sqrt{2}\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)}{8 \sqrt[8]{2} \left(2-\sqrt{2}\right)}","\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,"ArcTan[x/(1 + x^4)^(1/4)] - (3*ArcTan[(2^(1/8)*x)/(1 + x^4)^(1/4)])/(4*2^(1/8)) - (3*(1 - Sqrt[2])*ArcTan[1 - (2^(5/8)*x)/(1 + x^4)^(1/4)])/(4*2^(1/8)*(2 - Sqrt[2])) + (3*(1 - Sqrt[2])*ArcTan[1 + (2^(5/8)*x)/(1 + x^4)^(1/4)])/(4*2^(1/8)*(2 - Sqrt[2])) + ArcTanh[x/(1 + x^4)^(1/4)] - (3*ArcTanh[(2^(1/8)*x)/(1 + x^4)^(1/4)])/(4*2^(1/8)) - (3*(1 - Sqrt[2])*Log[2^(3/8) + (2^(5/8)*x^2)/Sqrt[1 + x^4] - (2*x)/(1 + x^4)^(1/4)])/(8*2^(1/8)*(2 - Sqrt[2])) + (3*(1 - Sqrt[2])*Log[1 + (2^(1/4)*x^2)/Sqrt[1 + x^4] + (2^(5/8)*x)/(1 + x^4)^(1/4)])/(8*2^(1/8)*(2 - Sqrt[2]))","A",31,14,34,0.4118,1,"{6728, 240, 212, 206, 203, 1428, 408, 377, 211, 1165, 628, 1162, 617, 204}"
2302,1,180,0,1.0068651,"\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Int[((-1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/((1 + x^2)*Sqrt[1 + x^4]),x]","\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1+i} \sqrt{1-i x^2}}\right)-\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1+i} \sqrt{1-i x^2}}\right)+\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1-i} \sqrt{1+i x^2}}\right)-\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1-i} \sqrt{1+i x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\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,"(Sqrt[1 + I]*ArcTanh[(1 - x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/2 - (Sqrt[1 + I]*ArcTanh[(1 + x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/2 + (Sqrt[1 - I]*ArcTanh[(1 - x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/2 - (Sqrt[1 - I]*ArcTanh[(1 + x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/2 + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",16,5,39,0.1282,0,"{6725, 2132, 206, 2133, 725}"
2303,0,0,0,1.2220578,"\int \frac{x}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Int[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{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{-\text{$\#$1}^2 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$1} c+a}\&\right]}{a}-4 \sqrt{\sqrt{a x+b}+c}+x",1,"(-2*c*Sqrt[b + a*x])/a - 4*Sqrt[c + Sqrt[b + a*x]] + (c + Sqrt[b + a*x])^2/a - 4*(b - c^2)*Defer[Subst][Defer[Int][(-b + c^2 + a*x - 2*c*x^2 + x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*Defer[Subst][Defer[Int][x/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*c*Defer[Subst][Defer[Int][x^2/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2304,0,0,0,0.920001,"\int \frac{x}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","Int[x/(x + Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x+\sqrt{c+\sqrt{b+a x}}} \, dx","\frac{4 \text{RootSum}\left[-\text{$\#$1}^4+2 \text{$\#$1}^2 c-\text{$\#$1} a+b-c^2\&,\frac{-\text{$\#$1}^2 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-4 \text{$\#$1} c+a}\&\right]}{a}-4 \sqrt{\sqrt{a x+b}+c}+x",1,"(-2*c*Sqrt[b + a*x])/a - 4*Sqrt[c + Sqrt[b + a*x]] + (c + Sqrt[b + a*x])^2/a - 4*(b - c^2)*Defer[Subst][Defer[Int][(-b + c^2 + a*x - 2*c*x^2 + x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*Defer[Subst][Defer[Int][x/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*c*Defer[Subst][Defer[Int][x^2/(-b + c^2 + a*x - 2*c*x^2 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2305,1,88,0,0.020405,"\int \frac{1}{(1+x) \sqrt[3]{1-x+x^2}} \, dx","Int[1/((1 + x)*(1 - x + x^2)^(1/3)),x]","\frac{\log \left(-3^{2/3} \sqrt[3]{x^2-x+1}-x+2\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{2 (2-x)}{3 \sqrt[6]{3} \sqrt[3]{x^2-x+1}}+\frac{1}{\sqrt{3}}\right)}{3^{5/6}}-\frac{\log (x+1)}{2 \sqrt[3]{3}}","\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,"-(ArcTan[1/Sqrt[3] + (2*(2 - x))/(3*3^(1/6)*(1 - x + x^2)^(1/3))]/3^(5/6)) - Log[1 + x]/(2*3^(1/3)) + Log[2 - x - 3^(2/3)*(1 - x + x^2)^(1/3)]/(2*3^(1/3))","A",1,1,18,0.05556,1,"{750}"
2306,1,608,0,1.5319108,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^3+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Int[((1 + x^4)*(-x^3 + x^4)^(1/4))/(x^4*(-1 + x^4)),x]","-\frac{16 \sqrt[4]{x^4-x^3}}{45 x}+\frac{4 \sqrt[4]{x^4-x^3}}{9 x^3}-\frac{(1-i)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1-i)^{3/4} \sqrt[4]{x-1} x^{3/4}}-\frac{(1+i)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1+i)^{3/4} \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{(1-i)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1-i)^{3/4} \sqrt[4]{x-1} x^{3/4}}+\frac{(1+i)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1+i)^{3/4} \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{4 \sqrt[4]{x^4-x^3}}{45 x^2}","\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,"(4*(-x^3 + x^4)^(1/4))/(9*x^3) - (4*(-x^3 + x^4)^(1/4))/(45*x^2) - (16*(-x^3 + x^4)^(1/4))/(45*x) - ((-x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 - I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) - ((1 - I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) - ((-x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 + I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) - ((1 + I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) + (2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + ((-x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 - I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) + ((1 - I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) + ((-x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 + I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) + ((1 + I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) - (2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","C",36,12,29,0.4138,1,"{2056, 1586, 6733, 6742, 271, 264, 494, 298, 203, 206, 6725, 1529}"
2307,1,608,0,1.3313217,"\int \frac{\left(1+x^4\right) \sqrt[4]{-x^3+x^4}}{x^4 \left(-1+x^4\right)} \, dx","Int[((1 + x^4)*(-x^3 + x^4)^(1/4))/(x^4*(-1 + x^4)),x]","-\frac{16 \sqrt[4]{x^4-x^3}}{45 x}+\frac{4 \sqrt[4]{x^4-x^3}}{9 x^3}-\frac{(1-i)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1-i)^{3/4} \sqrt[4]{x-1} x^{3/4}}-\frac{(1+i)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1+i)^{3/4} \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}+\frac{(1-i)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1-i)^{3/4} \sqrt[4]{x-1} x^{3/4}}+\frac{(1+i)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{2 \sqrt[4]{x-1} x^{3/4}}+\frac{\sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{(1+i)^{3/4} \sqrt[4]{x-1} x^{3/4}}-\frac{\sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{x-1} x^{3/4}}-\frac{4 \sqrt[4]{x^4-x^3}}{45 x^2}","\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,"(4*(-x^3 + x^4)^(1/4))/(9*x^3) - (4*(-x^3 + x^4)^(1/4))/(45*x^2) - (16*(-x^3 + x^4)^(1/4))/(45*x) - ((-x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 - I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) - ((1 - I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) - ((-x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 + I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) - ((1 + I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) + (2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4)) + ((-x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 - I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) + ((1 - I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 - I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) + ((-x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((1 + I)^(3/4)*(-1 + x)^(1/4)*x^(3/4)) + ((1 + I)^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((1 + I)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2*(-1 + x)^(1/4)*x^(3/4)) - (2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/((-1 + x)^(1/4)*x^(3/4))","C",36,12,29,0.4138,1,"{2056, 1586, 6733, 6742, 271, 264, 494, 298, 203, 206, 6725, 1529}"
2308,1,267,0,0.4149748,"\int \frac{\sqrt[3]{b x+a x^3} \left(b+a x^4\right)}{x^4} \, dx","Int[((b*x + a*x^3)^(1/3)*(b + a*x^4))/x^4,x]","\frac{\sqrt[3]{a} b x^{2/3} \left(a x^2+b\right)^{2/3} \log \left(\frac{a^{2/3} x^{4/3}}{\left(a x^2+b\right)^{2/3}}+\frac{\sqrt[3]{a} x^{2/3}}{\sqrt[3]{a x^2+b}}+1\right)}{12 \left(a x^3+b x\right)^{2/3}}+\frac{1}{2} a x \sqrt[3]{a x^3+b x}-\frac{3 \left(a x^3+b x\right)^{4/3}}{8 x^4}-\frac{\sqrt[3]{a} b x^{2/3} \left(a x^2+b\right)^{2/3} \log \left(1-\frac{\sqrt[3]{a} x^{2/3}}{\sqrt[3]{a x^2+b}}\right)}{6 \left(a x^3+b x\right)^{2/3}}-\frac{\sqrt[3]{a} b x^{2/3} \left(a x^2+b\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x^{2/3}}{\sqrt[3]{a x^2+b}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} \left(a x^3+b x\right)^{2/3}}","\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,"(a*x*(b*x + a*x^3)^(1/3))/2 - (3*(b*x + a*x^3)^(4/3))/(8*x^4) - (a^(1/3)*b*x^(2/3)*(b + a*x^2)^(2/3)*ArcTan[(1 + (2*a^(1/3)*x^(2/3))/(b + a*x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*(b*x + a*x^3)^(2/3)) - (a^(1/3)*b*x^(2/3)*(b + a*x^2)^(2/3)*Log[1 - (a^(1/3)*x^(2/3))/(b + a*x^2)^(1/3)])/(6*(b*x + a*x^3)^(2/3)) + (a^(1/3)*b*x^(2/3)*(b + a*x^2)^(2/3)*Log[1 + (a^(2/3)*x^(4/3))/(b + a*x^2)^(2/3) + (a^(1/3)*x^(2/3))/(b + a*x^2)^(1/3)])/(12*(b*x + a*x^3)^(2/3))","A",14,13,24,0.5417,1,"{2052, 2004, 2032, 329, 275, 331, 292, 31, 634, 617, 204, 628, 2014}"
2309,1,234,0,1.6265254,"\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","Int[(b^4 + a^4*x^4)/(Sqrt[-(b^2*x) + a^2*x^3]*(-b^4 + a^4*x^4)),x]","-\frac{x}{\sqrt{a^2 x^3-b^2 x}}-\frac{\sqrt{x} \sqrt{a^2 x^2-b^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^2} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2-b^2}}\right)}{2 \sqrt{2} \sqrt[4]{-a^2} \sqrt{b} \sqrt{a^2 x^3-b^2 x}}-\frac{\sqrt{x} \sqrt{a^2 x^2-b^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^2} \sqrt{b} \sqrt{x}}{\sqrt{a^2 x^2-b^2}}\right)}{2 \sqrt{2} \sqrt[4]{-a^2} \sqrt{b} \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/Sqrt[-(b^2*x) + a^2*x^3]) - (Sqrt[x]*Sqrt[-b^2 + a^2*x^2]*ArcTan[(Sqrt[2]*(-a^2)^(1/4)*Sqrt[b]*Sqrt[x])/Sqrt[-b^2 + a^2*x^2]])/(2*Sqrt[2]*(-a^2)^(1/4)*Sqrt[b]*Sqrt[-(b^2*x) + a^2*x^3]) - (Sqrt[x]*Sqrt[-b^2 + a^2*x^2]*ArcTanh[(Sqrt[2]*(-a^2)^(1/4)*Sqrt[b]*Sqrt[x])/Sqrt[-b^2 + a^2*x^2]])/(2*Sqrt[2]*(-a^2)^(1/4)*Sqrt[b]*Sqrt[-(b^2*x) + a^2*x^3])","A",22,13,45,0.2889,1,"{2056, 6715, 6725, 224, 221, 1404, 414, 523, 409, 1211, 1699, 203, 206}"
2310,1,218,0,0.724199,"\int \frac{1+x}{\left(-1+x^3\right) \sqrt[8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx","Int[(1 + x)/((-1 + x^3)*(256 - 256*x^2 + 96*x^4 - 16*x^6 + x^8)^(1/8)),x]","-\frac{2 \sqrt{x^2-4} \tan ^{-1}\left(\frac{4-x}{\sqrt{3} \sqrt{x^2-4}}\right)}{3 \sqrt{3} \sqrt[8]{\left(x^2-4\right)^4}}+\frac{\left(1-\sqrt[3]{-1}\right) \sqrt{x^2-4} \tanh ^{-1}\left(\frac{(-1)^{2/3} \left(\sqrt[3]{-1} x+4\right)}{\sqrt{1+4 \sqrt[3]{-1}} \sqrt{x^2-4}}\right)}{3 \sqrt{1+4 \sqrt[3]{-1}} \sqrt[8]{\left(x^2-4\right)^4}}-\frac{\left(1+(-1)^{2/3}\right) \sqrt{x^2-4} \tanh ^{-1}\left(\frac{\sqrt[3]{-1} \left(4-(-1)^{2/3} x\right)}{\sqrt{1-4 (-1)^{2/3}} \sqrt{x^2-4}}\right)}{3 \sqrt{1-4 (-1)^{2/3}} \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,"(-2*Sqrt[-4 + x^2]*ArcTan[(4 - x)/(Sqrt[3]*Sqrt[-4 + x^2])])/(3*Sqrt[3]*((-4 + x^2)^4)^(1/8)) + ((1 - (-1)^(1/3))*Sqrt[-4 + x^2]*ArcTanh[((-1)^(2/3)*(4 + (-1)^(1/3)*x))/(Sqrt[1 + 4*(-1)^(1/3)]*Sqrt[-4 + x^2])])/(3*Sqrt[1 + 4*(-1)^(1/3)]*((-4 + x^2)^4)^(1/8)) - ((1 + (-1)^(2/3))*Sqrt[-4 + x^2]*ArcTanh[((-1)^(1/3)*(4 - (-1)^(2/3)*x))/(Sqrt[1 - 4*(-1)^(2/3)]*Sqrt[-4 + x^2])])/(3*Sqrt[1 - 4*(-1)^(2/3)]*((-4 + x^2)^4)^(1/8))","A",10,6,35,0.1714,1,"{6688, 6720, 6725, 725, 204, 206}"
2311,1,892,0,0.9571932,"\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","Int[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]","\frac{(x-1)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x-1}}{\sqrt{3}}\right) \left(-x^2+x+1\right)}{\sqrt{3} \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}+\frac{\sqrt{\frac{3}{5}} \sqrt[3]{\frac{1}{2} \left(7-3 \sqrt{5}\right)} (x-1)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{2}{-1+\sqrt{5}}} \sqrt[3]{x-1}+1}{\sqrt{3}}\right) \left(-x^2+x+1\right)}{\sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}-\frac{\sqrt{\frac{3}{5}} \sqrt[3]{\frac{1}{2} \left(7+3 \sqrt{5}\right)} (x-1)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\frac{2}{1+\sqrt{5}}} \sqrt[3]{x-1}}{\sqrt{3}}\right) \left(-x^2+x+1\right)}{\sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}-\frac{(x-1)^{2/3} \log \left(\sqrt[3]{x-1}+1\right) \left(-x^2+x+1\right)}{3 \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}-\frac{\sqrt[3]{\frac{1}{2} \left(7-3 \sqrt{5}\right)} (x-1)^{2/3} \log \left(\sqrt[3]{-1+\sqrt{5}}-\sqrt[3]{2} \sqrt[3]{x-1}\right) \left(-x^2+x+1\right)}{\sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}+\frac{\sqrt[3]{\frac{1}{2} \left(7+3 \sqrt{5}\right)} (x-1)^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{x-1}+\sqrt[3]{1+\sqrt{5}}\right) \left(-x^2+x+1\right)}{\sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}+\frac{(x-1)^{2/3} \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right) \left(-x^2+x+1\right)}{6 \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}+\frac{\sqrt[3]{\frac{1}{2} \left(7-3 \sqrt{5}\right)} (x-1)^{2/3} \log \left(2^{2/3} (x-1)^{2/3}+\sqrt[3]{2 \left(-1+\sqrt{5}\right)} \sqrt[3]{x-1}+\left(-1+\sqrt{5}\right)^{2/3}\right) \left(-x^2+x+1\right)}{2 \sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}-\frac{\sqrt[3]{\frac{1}{2} \left(7+3 \sqrt{5}\right)} (x-1)^{2/3} \log \left(2^{2/3} (x-1)^{2/3}-\sqrt[3]{2 \left(1+\sqrt{5}\right)} \sqrt[3]{x-1}+\left(1+\sqrt{5}\right)^{2/3}\right) \left(-x^2+x+1\right)}{2 \sqrt{5} \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}-\frac{(x-1)^{2/3} \left(-x^2+x+1\right)}{3 \left(\sqrt[3]{x-1}+1\right) \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}+\frac{\left(\sqrt[3]{x-1}+1\right) (x-1)^{2/3} \left(-x^2+x+1\right)}{3 \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right) \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}","\frac{(x-1)^{2/3} \left(x^2-x-1\right) \left(-\text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^3-1\&,\frac{\text{$\#$1}^3 \log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)-\log \left(\sqrt[3]{x-1}-\text{$\#$1}\right)}{2 \text{$\#$1}^5+\text{$\#$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,"-1/3*((-1 + x)^(2/3)*(1 + x - x^2))/((1 + (-1 + x)^(1/3))*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) + ((1 + (-1 + x)^(1/3))*(-1 + x)^(2/3)*(1 + x - x^2))/(3*(1 - (-1 + x)^(1/3) + (-1 + x)^(2/3))*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) + ((-1 + x)^(2/3)*(1 + x - x^2)*ArcTan[(1 - 2*(-1 + x)^(1/3))/Sqrt[3]])/(Sqrt[3]*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) + (Sqrt[3/5]*((7 - 3*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 + x - x^2)*ArcTan[(1 + 2*(2/(-1 + Sqrt[5]))^(1/3)*(-1 + x)^(1/3))/Sqrt[3]])/(-((1 - x)^2*(1 + x - x^2)^3))^(1/3) - (Sqrt[3/5]*((7 + 3*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 + x - x^2)*ArcTan[(1 - 2*(2/(1 + Sqrt[5]))^(1/3)*(-1 + x)^(1/3))/Sqrt[3]])/(-((1 - x)^2*(1 + x - x^2)^3))^(1/3) - ((-1 + x)^(2/3)*(1 + x - x^2)*Log[1 + (-1 + x)^(1/3)])/(3*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) - (((7 - 3*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 + x - x^2)*Log[(-1 + Sqrt[5])^(1/3) - 2^(1/3)*(-1 + x)^(1/3)])/(Sqrt[5]*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) + (((7 + 3*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 + x - x^2)*Log[(1 + Sqrt[5])^(1/3) + 2^(1/3)*(-1 + x)^(1/3)])/(Sqrt[5]*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) + ((-1 + x)^(2/3)*(1 + x - x^2)*Log[1 - (-1 + x)^(1/3) + (-1 + x)^(2/3)])/(6*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) + (((7 - 3*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 + x - x^2)*Log[(-1 + Sqrt[5])^(2/3) + (2*(-1 + Sqrt[5]))^(1/3)*(-1 + x)^(1/3) + 2^(2/3)*(-1 + x)^(2/3)])/(2*Sqrt[5]*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3)) - (((7 + 3*Sqrt[5])/2)^(1/3)*(-1 + x)^(2/3)*(1 + x - x^2)*Log[(1 + Sqrt[5])^(2/3) - (2*(1 + Sqrt[5]))^(1/3)*(-1 + x)^(1/3) + 2^(2/3)*(-1 + x)^(2/3)])/(2*Sqrt[5]*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3))","B",25,13,46,0.2826,0,"{6688, 6719, 897, 1424, 638, 618, 204, 634, 628, 1422, 200, 31, 617}"
2312,0,0,0,4.258285,"\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","Int[(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]","\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","\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*x^2*(1 + (a*x^5)/b)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, -((a*x^5)/b)])/(2*a*(b + a*x^5)^(3/4)) - (c^3*Defer[Int][x^4/((-b + c*x^4 - a*x^5)*(b + a*x^5)^(3/4)), x])/(2*a^2) - (b*c^2*Defer[Int][1/((b + a*x^5)^(3/4)*(b - c*x^4 + a*x^5)), x])/(2*a^2) - (b*c*Defer[Int][x/((b + a*x^5)^(3/4)*(b - c*x^4 + a*x^5)), x])/(2*a) - (5*b*Defer[Int][x^2/((b + a*x^5)^(3/4)*(b - c*x^4 + a*x^5)), x])/2 + (b*c^2*Defer[Int][1/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/(2*a^2) - (b*c*Defer[Int][x/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/(2*a) + (5*b*Defer[Int][x^2/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/2 + (c^3*Defer[Int][x^4/((b + a*x^5)^(3/4)*(b + c*x^4 + a*x^5)), x])/(2*a^2)","F",0,0,0,0,-1,"{}"
2313,1,255,0,0.8954622,"\int \frac{x^2 \sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x}} \, dx","Int[(x^2*Sqrt[a*x + Sqrt[-b + a*x]])/Sqrt[-b + a*x],x]","\frac{\left(80 b^2+24 b+21\right) \left(2 \sqrt{a x-b}+1\right) \sqrt{\sqrt{a x-b}+a x}}{256 a^3}-\frac{(1-4 b) \left(80 b^2+24 b+21\right) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{512 a^3}+\frac{(a x-b)^{3/2} \left(\sqrt{a x-b}+a x\right)^{3/2}}{3 a^3}-\frac{(68 b+35) \left(\sqrt{a x-b}+a x\right)^{3/2}}{160 a^3}+\frac{3 (b-a x) \left(\sqrt{a x-b}+a x\right)^{3/2}}{10 a^3}+\frac{3 (20 b+7) \sqrt{a x-b} \left(\sqrt{a x-b}+a x\right)^{3/2}}{80 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,"-1/160*((35 + 68*b)*(a*x + Sqrt[-b + a*x])^(3/2))/a^3 + (3*(b - a*x)*(a*x + Sqrt[-b + a*x])^(3/2))/(10*a^3) + (3*(7 + 20*b)*Sqrt[-b + a*x]*(a*x + Sqrt[-b + a*x])^(3/2))/(80*a^3) + ((-b + a*x)^(3/2)*(a*x + Sqrt[-b + a*x])^(3/2))/(3*a^3) + ((21 + 24*b + 80*b^2)*Sqrt[a*x + Sqrt[-b + a*x]]*(1 + 2*Sqrt[-b + a*x]))/(256*a^3) - ((1 - 4*b)*(21 + 24*b + 80*b^2)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(512*a^3)","A",8,5,34,0.1471,1,"{1661, 640, 612, 621, 206}"
2314,1,495,0,7.9637682,"\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","Int[(a + b*x^2 + a*k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(-1 + k^4*x^4)),x]","-\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \left(2 a k^2+b\right) \Pi \left(-\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{2 \left(-k^2\right)^{3/2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}-\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \left(2 a k^2+b\right) \Pi \left(\frac{1}{k};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{2 \left(-k^2\right)^{3/2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \left(b-2 a k^2\right) \Pi \left(-\frac{1}{\sqrt{-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{2 \left(-k^2\right)^{3/2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \left(b-2 a k^2\right) \Pi \left(\frac{1}{\sqrt{-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{2 \left(-k^2\right)^{3/2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 a \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\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,"(2*a*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] - ((b + 2*a*k^2)*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(2*(-k^2)^(3/2)*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) - ((b + 2*a*k^2)*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[k^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(2*(-k^2)^(3/2)*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((b - 2*a*k^2)*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-(1/Sqrt[-k^2]), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(2*(-k^2)^(3/2)*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((b - 2*a*k^2)*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[1/Sqrt[-k^2], ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(2*(-k^2)^(3/2)*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",28,8,46,0.1739,0,"{6718, 6725, 115, 6688, 934, 12, 168, 537}"
2315,0,0,0,1.614367,"\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","Int[((-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,"a*p^3*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6], x] - 2*a*q^3*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^9, x] - 3*a*p*q^2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^6, x] - 2*b*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^5, x] + b*p*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^2, x]","F",0,0,0,0,-1,"{}"
2316,0,0,0,1.523158,"\int \frac{-1+x^3}{\left(1+x^3\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(-1 + x^3)/((1 + x^3)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{-1+x^3}{\left(1+x^3\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","\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,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] - (2*Defer[Int][1/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/3 + (2*(1 + I*Sqrt[3])*Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/3 + (2*(1 - I*Sqrt[3])*Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/3","F",0,0,0,0,-1,"{}"
2317,0,0,0,13.5840477,"\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","Int[(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,"(12*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - (1 + k)*x^3 + k*x^6 - b*x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (15*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^4/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-1 + (1 + k)*x^3 - k*x^6 + b*x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (9*k*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^10/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-1 + (1 + k)*x^3 - k*x^6 + b*x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2318,0,0,0,14.9683406,"\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","Int[(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,"(21*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^10/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - (1 + k)*x^3 + k*x^6 - b*x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (24*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-1 + (1 + k)*x^3 - k*x^6 + b*x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (18*k*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^13/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-1 + (1 + k)*x^3 - k*x^6 + b*x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2319,0,0,0,6.8560347,"\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","Int[(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,"(3*x^2*(1 - x/a)^(2/3)*(1 - x/b)^(2/3)*AppellF1[2/3, 2/3, 2/3, 5/3, x/a, x/b])/(2*((a - x)*(b - x)*x^2)^(2/3)) + ((a + b + d + Sqrt[a^2 - 2*a*(b - d) + (b + d)^2])*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*(-a - b - d - Sqrt[a^2 - 2*a*b + b^2 + 2*a*d + 2*b*d + d^2] + 2*x)), x])/((a - x)*(b - x)*x^2)^(2/3) + ((a + b + d - Sqrt[a^2 - 2*a*(b - d) + (b + d)^2])*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*(-a - b - d + Sqrt[a^2 - 2*a*b + b^2 + 2*a*d + 2*b*d + d^2] + 2*x)), x])/((a - x)*(b - x)*x^2)^(2/3)","F",0,0,0,0,-1,"{}"
2320,1,124,0,0.0913692,"\int \frac{\left(b+x^3\right) \left(c+x^3\right)}{\sqrt[3]{a+x^3}} \, dx","Int[((b + x^3)*(c + x^3))/(a + x^3)^(1/3),x]","-\frac{1}{18} \left(2 a^2-3 a (b+c)+9 b c\right) \log \left(\sqrt[3]{a+x^3}-x\right)+\frac{\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)}{9 \sqrt{3}}-\frac{1}{18} x \left(a+x^3\right)^{2/3} (4 a-3 b-6 c)+\frac{1}{6} x \left(a+x^3\right)^{2/3} \left(b+x^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,"-1/18*((4*a - 3*b - 6*c)*x*(a + x^3)^(2/3)) + (x*(a + x^3)^(2/3)*(b + x^3))/6 + ((2*a^2 + 9*b*c - 3*a*(b + c))*ArcTan[(1 + (2*x)/(a + x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]) - ((2*a^2 + 9*b*c - 3*a*(b + c))*Log[-x + (a + x^3)^(1/3)])/18","A",3,3,20,0.1500,1,"{528, 388, 239}"
2321,1,571,0,0.4486106,"\int \frac{1}{\left(1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[1/((1 + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log (-x-1)}{6 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\sqrt[3]{-1} x-1\right)}{6 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(-(-1)^{2/3} x-1\right)}{6 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-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)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*Sqrt[3]*(-x^2 + x^3)^(1/3))) - ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(2*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3) - x^(1/3)])/(2*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3) - x^(1/3)])/(2*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - x])/(6*2^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1)^(1/3)*x])/(6*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - (-1)^(2/3)*x])/(6*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3))","B",6,3,21,0.1429,1,"{2056, 6725, 91}"
2322,1,571,0,0.3410275,"\int \frac{1}{\left(1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[1/((1 + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log (-x-1)}{6 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\sqrt[3]{-1} x-1\right)}{6 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(-(-1)^{2/3} x-1\right)}{6 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-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)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*Sqrt[3]*(-x^2 + x^3)^(1/3))) - ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(2*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3) - x^(1/3)])/(2*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3) - x^(1/3)])/(2*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - x])/(6*2^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1)^(1/3)*x])/(6*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - (-1)^(2/3)*x])/(6*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3))","B",6,3,21,0.1429,1,"{2056, 6725, 91}"
2323,0,0,0,2.9156611,"\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","Int[((-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,"(-2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^3, x])/a + (2*b*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x, x])/(a^2*q) + 3*p*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/(a*q + b*x^2 + a*p*x^3), x] - (2*b^2*Defer[Int][(x*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(a*q + b*x^2 + a*p*x^3), x])/(a^2*q) - (2*b*p*Defer[Int][(x^2*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(a*q + b*x^2 + a*p*x^3), x])/(a*q)","F",0,0,0,0,-1,"{}"
2324,1,121,0,0.5193698,"\int \frac{\sqrt[4]{x^2+x^6} \left(1+x^8\right)}{x^4 \left(-1+x^4\right)} \, dx","Int[((x^2 + x^6)^(1/4)*(1 + x^8))/(x^4*(-1 + x^4)),x]","\frac{4 \sqrt[4]{x^6+x^2} F_1\left(-\frac{5}{8};1,-\frac{1}{4};\frac{3}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^4+1} x^3}+\frac{8 \sqrt[4]{x^6+x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};-x^4\right)}{15 \sqrt[4]{x^4+1}}+\frac{2}{5} \sqrt[4]{x^6+x^2} x-\frac{2 \sqrt[4]{x^6+x^2}}{5 x^3}","\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))/(5*x^3) + (2*x*(x^2 + x^6)^(1/4))/5 + (4*(x^2 + x^6)^(1/4)*AppellF1[-5/8, 1, -1/4, 3/8, x^4, -x^4])/(5*x^3*(1 + x^4)^(1/4)) + (8*x*(x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, -x^4])/(15*(1 + x^4)^(1/4))","C",11,8,27,0.2963,0,"{2056, 6725, 277, 329, 364, 279, 466, 510}"
2325,1,121,0,0.3940329,"\int \frac{\sqrt[4]{x^2+x^6} \left(1+x^8\right)}{x^4 \left(-1+x^4\right)} \, dx","Int[((x^2 + x^6)^(1/4)*(1 + x^8))/(x^4*(-1 + x^4)),x]","\frac{4 \sqrt[4]{x^6+x^2} F_1\left(-\frac{5}{8};1,-\frac{1}{4};\frac{3}{8};x^4,-x^4\right)}{5 \sqrt[4]{x^4+1} x^3}+\frac{8 \sqrt[4]{x^6+x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};-x^4\right)}{15 \sqrt[4]{x^4+1}}+\frac{2}{5} \sqrt[4]{x^6+x^2} x-\frac{2 \sqrt[4]{x^6+x^2}}{5 x^3}","\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))/(5*x^3) + (2*x*(x^2 + x^6)^(1/4))/5 + (4*(x^2 + x^6)^(1/4)*AppellF1[-5/8, 1, -1/4, 3/8, x^4, -x^4])/(5*x^3*(1 + x^4)^(1/4)) + (8*x*(x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, -x^4])/(15*(1 + x^4)^(1/4))","C",11,8,27,0.2963,0,"{2056, 6725, 277, 329, 364, 279, 466, 510}"
2326,1,176,0,0.0271542,"\int \frac{1}{x \sqrt[3]{2-3 x+x^2}} \, dx","Int[1/(x*(2 - 3*x + x^2)^(1/3)),x]","\frac{3 \sqrt[3]{x-2} \sqrt[3]{x-1} \log \left(-\frac{(x-2)^{2/3}}{\sqrt[3]{2}}-\sqrt[3]{2} \sqrt[3]{x-1}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^2-3 x+2}}-\frac{\sqrt[3]{x-2} \sqrt[3]{x-1} \log (x)}{2 \sqrt[3]{2} \sqrt[3]{x^2-3 x+2}}-\frac{\sqrt{3} \sqrt[3]{x-2} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{\sqrt[3]{2} (x-2)^{2/3}}{\sqrt{3} \sqrt[3]{x-1}}\right)}{2 \sqrt[3]{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,"-1/2*(Sqrt[3]*(-2 + x)^(1/3)*(-1 + x)^(1/3)*ArcTan[1/Sqrt[3] - (2^(1/3)*(-2 + x)^(2/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(2^(1/3)*(2 - 3*x + x^2)^(1/3)) + (3*(-2 + x)^(1/3)*(-1 + x)^(1/3)*Log[-((-2 + x)^(2/3)/2^(1/3)) - 2^(1/3)*(-1 + x)^(1/3)])/(4*2^(1/3)*(2 - 3*x + x^2)^(1/3)) - ((-2 + x)^(1/3)*(-1 + x)^(1/3)*Log[x])/(2*2^(1/3)*(2 - 3*x + x^2)^(1/3))","A",2,2,16,0.1250,1,"{755, 123}"
2327,0,0,0,6.3342448,"\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","Int[(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,"(-3*x*(1 - x/a)^(1/3)*(1 - x/b)^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, x/a, x/b])/((a - x)*(b - x)*x^2)^(1/3) - ((a + b + d + Sqrt[a^2 - 2*a*(b - d) + (b + d)^2])*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(-a - b - d - Sqrt[a^2 - 2*a*b + b^2 + 2*a*d + 2*b*d + d^2] + 2*x)), x])/((a - x)*(b - x)*x^2)^(1/3) - ((a + b + d - Sqrt[a^2 - 2*a*(b - d) + (b + d)^2])*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(-a - b - d + Sqrt[a^2 - 2*a*b + b^2 + 2*a*d + 2*b*d + d^2] + 2*x)), x])/((a - x)*(b - x)*x^2)^(1/3)","F",0,0,0,0,-1,"{}"
2328,0,0,0,1.2606353,"\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","Int[((-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,"2*b*p*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] - a*q^3*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^5, x] - b*q*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^3, x] + 3*a*p^2*q*Defer[Int][x*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 2*a*p^3*Defer[Int][x^4*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2329,0,0,0,1.5783204,"\int \frac{1+x}{(-1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(1 + x)/((-1 + x)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{1+x}{(-1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 + 32*Defer[Subst][Defer[Int][x^2/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 48*Defer[Subst][Defer[Int][x^4/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + 16*Defer[Subst][Defer[Int][x^6/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2330,0,0,0,1.210089,"\int \frac{1+x}{(-1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(1 + x)/((-1 + x)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{1+x}{(-1+x) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}}\&\right]+\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 + 32*Defer[Subst][Defer[Int][x^2/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 48*Defer[Subst][Defer[Int][x^4/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + 16*Defer[Subst][Defer[Int][x^6/(-2 + 4*x^4 - 4*x^6 + x^8), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2331,0,0,0,6.1540313,"\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1),x]","\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\frac{2 \text{RootSum}\left[\text{$\#$1}^4 (-c)-2 \text{$\#$1}^3 a-2 \text{$\#$1}^2 a d+b^2 c\&,\frac{\text{$\#$1}^2 c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+a d \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1} a \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{2 \text{$\#$1}^2 c+3 \text{$\#$1} a+2 a d}\&\right]}{c}-\frac{\log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{c}",1,"Log[b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4]/(4*c) - (a*d^2*Defer[Int][(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4)^(-1), x])/(2*c) - a*d*Defer[Int][x/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] - (a*c*Defer[Int][x^2/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x])/2 + d*Defer[Int][Sqrt[b^2 + a^2*x^2]/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + c*Defer[Int][(x*Sqrt[b^2 + a^2*x^2])/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + d^2*Defer[Int][Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] - (a - 2*c*d)*Defer[Int][(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + c^2*Defer[Int][(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + Defer[Int][(Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x]","F",0,0,0,0,-1,"{}"
2332,0,0,0,5.1753117,"\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1),x]","\int \frac{1}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\frac{2 \text{RootSum}\left[\text{$\#$1}^4 (-c)-2 \text{$\#$1}^3 a-2 \text{$\#$1}^2 a d+b^2 c\&,\frac{\text{$\#$1}^2 c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+a d \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1} a \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{2 \text{$\#$1}^2 c+3 \text{$\#$1} a+2 a d}\&\right]}{c}-\frac{\log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{c}",1,"Log[b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4]/(4*c) - (a*d^2*Defer[Int][(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4)^(-1), x])/(2*c) - a*d*Defer[Int][x/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] - (a*c*Defer[Int][x^2/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x])/2 + d*Defer[Int][Sqrt[b^2 + a^2*x^2]/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + c*Defer[Int][(x*Sqrt[b^2 + a^2*x^2])/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + d^2*Defer[Int][Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] - (a - 2*c*d)*Defer[Int][(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + c^2*Defer[Int][(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + Defer[Int][(Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x]","F",0,0,0,0,-1,"{}"
2333,1,198,0,0.2474193,"\int \frac{-d+c x}{x^7 \sqrt[3]{-b+a x^3}} \, dx","Int[(-d + c*x)/(x^7*(-b + a*x^3)^(1/3)),x]","\frac{a^2 d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{9 b^{7/3}}+\frac{2 a^2 d \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{9 \sqrt{3} b^{7/3}}-\frac{a^2 d \log (x)}{9 b^{7/3}}+\frac{3 a c \left(a x^3-b\right)^{2/3}}{10 b^2 x^2}-\frac{2 a d \left(a x^3-b\right)^{2/3}}{9 b^2 x^3}+\frac{c \left(a x^3-b\right)^{2/3}}{5 b x^5}-\frac{d \left(a x^3-b\right)^{2/3}}{6 b x^6}","\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,"-1/6*(d*(-b + a*x^3)^(2/3))/(b*x^6) + (c*(-b + a*x^3)^(2/3))/(5*b*x^5) - (2*a*d*(-b + a*x^3)^(2/3))/(9*b^2*x^3) + (3*a*c*(-b + a*x^3)^(2/3))/(10*b^2*x^2) + (2*a^2*d*ArcTan[(b^(1/3) - 2*(-b + a*x^3)^(1/3))/(Sqrt[3]*b^(1/3))])/(9*Sqrt[3]*b^(7/3)) - (a^2*d*Log[x])/(9*b^(7/3)) + (a^2*d*Log[b^(1/3) + (-b + a*x^3)^(1/3)])/(9*b^(7/3))","A",11,9,24,0.3750,1,"{1844, 266, 51, 56, 617, 204, 31, 271, 264}"
2334,1,94,0,0.6526662,"\int \frac{1+x^2+x^4}{\left(1-x^4\right) \sqrt[4]{x^3+x^5}} \, dx","Int[(1 + x^2 + x^4)/((1 - x^4)*(x^3 + x^5)^(1/4)),x]","\frac{6 \sqrt[4]{x^2+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^2,-x^2\right)}{\sqrt[4]{x^5+x^3}}-\frac{3 \sqrt[4]{x^2+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^2\right)}{\sqrt[4]{x^5+x^3}}+\frac{x}{\sqrt[4]{x^5+x^3}}","\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,"x/(x^3 + x^5)^(1/4) + (6*x*(1 + x^2)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^2, -x^2])/(x^3 + x^5)^(1/4) - (3*x*(1 + x^2)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^2])/(x^3 + x^5)^(1/4)","C",10,8,29,0.2759,0,"{2056, 6715, 6725, 245, 1455, 527, 530, 429}"
2335,1,226,0,0.9061628,"\int \frac{\sqrt{-1+2 x^4} \left(-1+2 x^8\right)}{x^7 \left(-1+2 x^4+x^8\right)} \, dx","Int[(Sqrt[-1 + 2*x^4]*(-1 + 2*x^8))/(x^7*(-1 + 2*x^4 + x^8)),x]","\frac{\left(2 x^4-1\right)^{3/2}}{6 x^6}-\frac{\sqrt{2 x^4-1}}{x^2}-\frac{1}{4} \sqrt{\frac{1}{2} \left(5 \sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\sqrt{\sqrt{2}-1} x^2}{\sqrt{2 x^4-1}}\right)-\frac{1}{4} \left(1+2 \sqrt{2}\right) \tanh ^{-1}\left(\frac{\sqrt{2} x^2}{\sqrt{2 x^4-1}}\right)+\frac{1}{4} \left(1-2 \sqrt{2}\right) \tanh ^{-1}\left(\frac{\sqrt{2} x^2}{\sqrt{2 x^4-1}}\right)+\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} x^2}{\sqrt{2 x^4-1}}\right)+\frac{1}{4} \sqrt{\frac{1}{2} \left(1+5 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{2}} x^2}{\sqrt{2 x^4-1}}\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,"-(Sqrt[-1 + 2*x^4]/x^2) + (-1 + 2*x^4)^(3/2)/(6*x^6) - (Sqrt[(-1 + 5*Sqrt[2])/2]*ArcTan[(Sqrt[-1 + Sqrt[2]]*x^2)/Sqrt[-1 + 2*x^4]])/4 + Sqrt[2]*ArcTanh[(Sqrt[2]*x^2)/Sqrt[-1 + 2*x^4]] + ((1 - 2*Sqrt[2])*ArcTanh[(Sqrt[2]*x^2)/Sqrt[-1 + 2*x^4]])/4 - ((1 + 2*Sqrt[2])*ArcTanh[(Sqrt[2]*x^2)/Sqrt[-1 + 2*x^4]])/4 + (Sqrt[(1 + 5*Sqrt[2])/2]*ArcTanh[(Sqrt[1 + Sqrt[2]]*x^2)/Sqrt[-1 + 2*x^4]])/4","A",20,11,34,0.3235,0,"{6728, 264, 275, 277, 217, 206, 6715, 1692, 402, 377, 204}"
2336,1,162,0,1.7539515,"\int \frac{\sqrt{1+x} \sqrt{1+\sqrt{1+x}}}{x \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])/(x*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\frac{8}{5} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{5/2}-\frac{16}{3} \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}+8 \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)","\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,"8*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]] - (16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 - 2*Sqrt[2*(1 + Sqrt[2])]*ArcTan[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[-1 + Sqrt[2]]] - 2*Sqrt[2*(-1 + Sqrt[2])]*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[1 + Sqrt[2]]]","A",10,6,43,0.1395,1,"{1586, 898, 1287, 1093, 207, 203}"
2337,1,238,0,0.5719148,"\int \frac{1+x}{(3+x) (1+2 x) \sqrt[3]{1+x^2}} \, dx","Int[(1 + x)/((3 + x)*(1 + 2*x)*(1 + x^2)^(1/3)),x]","\frac{2}{15} x F_1\left(\frac{1}{2};1,\frac{1}{3};\frac{3}{2};\frac{x^2}{9},-x^2\right)+\frac{1}{5} x F_1\left(\frac{1}{2};1,\frac{1}{3};\frac{3}{2};4 x^2,-x^2\right)-\frac{\log \left(1-4 x^2\right)}{20 \sqrt[3]{10}}-\frac{\log \left(9-x^2\right)}{10 \sqrt[3]{10}}+\frac{3 \log \left(\sqrt[3]{10}-2 \sqrt[3]{x^2+1}\right)}{20 \sqrt[3]{10}}+\frac{3 \log \left(\sqrt[3]{10}-\sqrt[3]{x^2+1}\right)}{10 \sqrt[3]{10}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2+1}+\sqrt[3]{5}}{\sqrt{3} \sqrt[3]{5}}\right)}{5 \sqrt[3]{10}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2\ 2^{2/3} \sqrt[3]{x^2+1}+\sqrt[3]{5}}{\sqrt{3} \sqrt[3]{5}}\right)}{10 \sqrt[3]{10}}","\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,"(2*x*AppellF1[1/2, 1, 1/3, 3/2, x^2/9, -x^2])/15 + (x*AppellF1[1/2, 1, 1/3, 3/2, 4*x^2, -x^2])/5 + (Sqrt[3]*ArcTan[(5^(1/3) + 2^(2/3)*(1 + x^2)^(1/3))/(Sqrt[3]*5^(1/3))])/(5*10^(1/3)) + (Sqrt[3]*ArcTan[(5^(1/3) + 2*2^(2/3)*(1 + x^2)^(1/3))/(Sqrt[3]*5^(1/3))])/(10*10^(1/3)) - Log[1 - 4*x^2]/(20*10^(1/3)) - Log[9 - x^2]/(10*10^(1/3)) + (3*Log[10^(1/3) - 2*(1 + x^2)^(1/3)])/(20*10^(1/3)) + (3*Log[10^(1/3) - (1 + x^2)^(1/3)])/(10*10^(1/3))","C",18,8,25,0.3200,0,"{6742, 757, 429, 444, 55, 617, 204, 31}"
2338,1,701,0,0.7190217,"\int \frac{\sqrt[3]{-x^2+x^3}}{1+x+x^2} \, dx","Int[(-x^2 + x^3)^(1/3)/(1 + x + x^2),x]","-\frac{3 i \sqrt[3]{x^3-x^2} \log \left(-\sqrt[3]{x-1}+\frac{\sqrt[3]{x}}{\sqrt[3]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}}}\right)}{\sqrt[3]{\sqrt{3}-i} \left(\sqrt{3}-3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{3 i \sqrt[3]{x^3-x^2} \log \left(-\sqrt[3]{x-1}+\frac{\sqrt[3]{x}}{\sqrt[3]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}}}\right)}{\sqrt[3]{\sqrt{3}+i} \left(\sqrt{3}+3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{3 \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{2 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{x^3-x^2} \log (x-1)}{2 \sqrt[3]{x-1} x^{2/3}}-\frac{i \sqrt[3]{x^3-x^2} \log \left(2 x-i \sqrt{3}+1\right)}{\sqrt[3]{\sqrt{3}+i} \left(\sqrt{3}+3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{i \sqrt[3]{x^3-x^2} \log \left(2 x+i \sqrt{3}+1\right)}{\sqrt[3]{\sqrt{3}-i} \left(\sqrt{3}-3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{2 i \sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[3]{x-1}}\right)}{\sqrt[3]{\sqrt{3}-i} \left(\sqrt{3}-3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{2 i \sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[3]{x-1}}\right)}{\sqrt[3]{\sqrt{3}+i} \left(\sqrt{3}+3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}","-\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,"-((Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3))) - ((2*I)*Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/3)*(-1 + x)^(1/3))])/((-I + Sqrt[3])^(1/3)*(-3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((2*I)*Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/3)*(-1 + x)^(1/3))])/((I + Sqrt[3])^(1/3)*(3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - ((3*I)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + x^(1/3)/((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/3)])/((-I + Sqrt[3])^(1/3)*(-3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((3*I)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + x^(1/3)/((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/3)])/((I + Sqrt[3])^(1/3)*(3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - (3*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(2*(-1 + x)^(1/3)*x^(2/3)) - ((-x^2 + x^3)^(1/3)*Log[-1 + x])/(2*(-1 + x)^(1/3)*x^(2/3)) - (I*(-x^2 + x^3)^(1/3)*Log[1 - I*Sqrt[3] + 2*x])/((I + Sqrt[3])^(1/3)*(3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + (I*(-x^2 + x^3)^(1/3)*Log[1 + I*Sqrt[3] + 2*x])/((-I + Sqrt[3])^(1/3)*(-3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3))","C",7,5,22,0.2273,1,"{2056, 905, 59, 6728, 91}"
2339,1,701,0,0.5510187,"\int \frac{\sqrt[3]{-x^2+x^3}}{1+x+x^2} \, dx","Int[(-x^2 + x^3)^(1/3)/(1 + x + x^2),x]","-\frac{3 i \sqrt[3]{x^3-x^2} \log \left(-\sqrt[3]{x-1}+\frac{\sqrt[3]{x}}{\sqrt[3]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}}}\right)}{\sqrt[3]{\sqrt{3}-i} \left(\sqrt{3}-3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{3 i \sqrt[3]{x^3-x^2} \log \left(-\sqrt[3]{x-1}+\frac{\sqrt[3]{x}}{\sqrt[3]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}}}\right)}{\sqrt[3]{\sqrt{3}+i} \left(\sqrt{3}+3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{3 \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{2 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{x^3-x^2} \log (x-1)}{2 \sqrt[3]{x-1} x^{2/3}}-\frac{i \sqrt[3]{x^3-x^2} \log \left(2 x-i \sqrt{3}+1\right)}{\sqrt[3]{\sqrt{3}+i} \left(\sqrt{3}+3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{i \sqrt[3]{x^3-x^2} \log \left(2 x+i \sqrt{3}+1\right)}{\sqrt[3]{\sqrt{3}-i} \left(\sqrt{3}-3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{2 i \sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} \sqrt[3]{x-1}}\right)}{\sqrt[3]{\sqrt{3}-i} \left(\sqrt{3}-3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{2 i \sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt[3]{x-1}}\right)}{\sqrt[3]{\sqrt{3}+i} \left(\sqrt{3}+3 i\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}","-\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,"-((Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3))) - ((2*I)*Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/3)*(-1 + x)^(1/3))])/((-I + Sqrt[3])^(1/3)*(-3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((2*I)*Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/3)*(-1 + x)^(1/3))])/((I + Sqrt[3])^(1/3)*(3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - ((3*I)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + x^(1/3)/((I - Sqrt[3])/(3*I - Sqrt[3]))^(1/3)])/((-I + Sqrt[3])^(1/3)*(-3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((3*I)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + x^(1/3)/((I + Sqrt[3])/(3*I + Sqrt[3]))^(1/3)])/((I + Sqrt[3])^(1/3)*(3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - (3*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(2*(-1 + x)^(1/3)*x^(2/3)) - ((-x^2 + x^3)^(1/3)*Log[-1 + x])/(2*(-1 + x)^(1/3)*x^(2/3)) - (I*(-x^2 + x^3)^(1/3)*Log[1 - I*Sqrt[3] + 2*x])/((I + Sqrt[3])^(1/3)*(3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + (I*(-x^2 + x^3)^(1/3)*Log[1 + I*Sqrt[3] + 2*x])/((-I + Sqrt[3])^(1/3)*(-3*I + Sqrt[3])^(2/3)*(-1 + x)^(1/3)*x^(2/3))","C",7,5,22,0.2273,1,"{2056, 905, 59, 6728, 91}"
2340,0,0,0,15.977731,"\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","Int[(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,"(12*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(b - b*(1 + k)*x^3 + b*k*x^6 - x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (15*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^4/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (9*k*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^10/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2341,1,81,0,0.5804777,"\int \frac{1+x^4}{\left(1-x^4\right) \sqrt[4]{x^3+x^5}} \, dx","Int[(1 + x^4)/((1 - x^4)*(x^3 + x^5)^(1/4)),x]","\frac{8 x \sqrt[4]{x^2+1} F_1\left(\frac{1}{8};1,\frac{5}{4};\frac{9}{8};x^2,-x^2\right)}{\sqrt[4]{x^5+x^3}}-\frac{4 x \sqrt[4]{x^2+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^2\right)}{\sqrt[4]{x^5+x^3}}","\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,"(8*x*(1 + x^2)^(1/4)*AppellF1[1/8, 1, 5/4, 9/8, x^2, -x^2])/(x^3 + x^5)^(1/4) - (4*x*(1 + x^2)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^2])/(x^3 + x^5)^(1/4)","C",7,6,26,0.2308,0,"{2056, 6715, 6725, 245, 1404, 429}"
2342,1,264,0,0.5001902,"\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","Int[((1 + x^3)^(2/3)*(2 + x^3 + x^6))/(x^6*(-2 + x^3)^2),x]","\frac{3}{8} x F_1\left(\frac{1}{3};1,-\frac{2}{3};\frac{4}{3};\frac{x^3}{2},-x^3\right)+\frac{x \left(x^3+1\right)^{2/3}}{3 \left(2-x^3\right)}-\frac{1}{9} \sqrt[3]{\frac{2}{3}} \log \left(\sqrt[3]{2}-\frac{\sqrt[3]{3} x}{\sqrt[3]{x^3+1}}\right)-\frac{3}{8} \log \left(\sqrt[3]{x^3+1}-x\right)+\frac{1}{4} \sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{2^{2/3} x}{\sqrt[6]{3} \sqrt[3]{x^3+1}}+\frac{1}{\sqrt{3}}\right)}{3\ 3^{5/6}}-\frac{\left(x^3+1\right)^{5/3}}{10 x^5}-\frac{3 \left(x^3+1\right)^{2/3}}{8 x^2}+\frac{\log \left(\frac{\sqrt[3]{6} x}{\sqrt[3]{x^3+1}}+\frac{3^{2/3} x^2}{\left(x^3+1\right)^{2/3}}+2^{2/3}\right)}{9\ 2^{2/3} \sqrt[3]{3}}","-\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,"(-3*(1 + x^3)^(2/3))/(8*x^2) + (x*(1 + x^3)^(2/3))/(3*(2 - x^3)) - (1 + x^3)^(5/3)/(10*x^5) + (3*x*AppellF1[1/3, 1, -2/3, 4/3, x^3/2, -x^3])/8 + (Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/4 + (2^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*x)/(3^(1/6)*(1 + x^3)^(1/3))])/(3*3^(5/6)) - ((2/3)^(1/3)*Log[2^(1/3) - (3^(1/3)*x)/(1 + x^3)^(1/3)])/9 + Log[2^(2/3) + (3^(2/3)*x^2)/(1 + x^3)^(2/3) + (6^(1/3)*x)/(1 + x^3)^(1/3)]/(9*2^(2/3)*3^(1/3)) - (3*Log[-x + (1 + x^3)^(1/3)])/8","C",14,13,28,0.4643,0,"{6742, 264, 277, 239, 378, 377, 200, 31, 634, 617, 204, 628, 429}"
2343,1,81,0,0.5382599,"\int \frac{1+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Int[(1 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","\frac{2 x \sqrt[4]{x^4+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{4 x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};1,\frac{5}{4};\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)}{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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 5/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",7,6,24,0.2500,0,"{2056, 6715, 6725, 245, 1404, 429}"
2344,1,81,0,0.4085534,"\int \frac{1+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Int[(1 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","\frac{2 x \sqrt[4]{x^4+1} \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{\sqrt[4]{x^6+x^2}}-\frac{4 x \sqrt[4]{x^4+1} F_1\left(\frac{1}{8};1,\frac{5}{4};\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)}{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,"(-4*x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 5/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (2*x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(x^2 + x^6)^(1/4)","C",7,6,24,0.2500,0,"{2056, 6715, 6725, 245, 1404, 429}"
2345,0,0,0,20.4562701,"\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","Int[(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,"(21*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^10/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(b - b*(1 + k)*x^3 + b*k*x^6 - x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (24*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (18*k*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^13/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-b + b*(1 + k)*x^3 - b*k*x^6 + x^24)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2346,1,225,0,0.1637318,"\int \frac{1}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[1/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{\sqrt{\sqrt{x^2+1}+x}}{2 \left(\left(\sqrt{x^2+1}+x\right)^2+1\right)}-\frac{2 \sqrt{\sqrt{x^2+1}+x}}{\left(\left(\sqrt{x^2+1}+x\right)^2+1\right)^2}-\frac{3 \log \left(\sqrt{x^2+1}-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)}{8 \sqrt{2}}+\frac{3 \log \left(\sqrt{x^2+1}+\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+x+1\right)}{8 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sqrt{x^2+1}+x}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\sqrt{x^2+1}+x}+1\right)}{4 \sqrt{2}}","\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,"(-2*Sqrt[x + Sqrt[1 + x^2]])/(1 + (x + Sqrt[1 + x^2])^2)^2 + Sqrt[x + Sqrt[1 + x^2]]/(2*(1 + (x + Sqrt[1 + x^2])^2)) - (3*ArcTan[1 - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]])/(4*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]])/(4*Sqrt[2]) - (3*Log[1 + x + Sqrt[1 + x^2] - Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]])/(8*Sqrt[2]) + (3*Log[1 + x + Sqrt[1 + x^2] + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]])/(8*Sqrt[2])","A",13,10,23,0.4348,1,"{2122, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
2347,0,0,0,4.781117,"\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","Int[(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,"((a - 2*b - Sqrt[a^2 - 4*a*b*d + 4*b^2*d])*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Int][(x^(1/4)*(-a + x)^(1/4))/((-b + x)^(3/2)*(a - 2*b*d - Sqrt[a^2 - 4*a*b*d + 4*b^2*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)^2*x))^(3/4) + ((a - 2*b + Sqrt[a^2 - 4*a*b*d + 4*b^2*d])*x^(3/4)*(-a + x)^(3/4)*(-b + x)^(3/2)*Defer[Int][(x^(1/4)*(-a + x)^(1/4))/((-b + x)^(3/2)*(a - 2*b*d + Sqrt[a^2 - 4*a*b*d + 4*b^2*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)^2*x))^(3/4)","F",0,0,0,0,-1,"{}"
2348,0,0,0,6.1401089,"\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","Int[((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]","\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","\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,"(Sqrt[-2 + x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/Sqrt[-2 + x + 2*x^2], x])/(Sqrt[(2 - x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) + (Sqrt[-2 + x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/(x^2*Sqrt[-2 + x + 2*x^2]), x])/(Sqrt[(2 - x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) + (Sqrt[-2 + x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/(x*Sqrt[-2 + x + 2*x^2]), x])/(Sqrt[(2 - x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) + (Sqrt[-2 + x + 2*x^2]*Defer[Int][Sqrt[-1 + x + x^2]/(Sqrt[-2 + x + 2*x^2]*(1 - x - 3*x^2 + x^3 + x^4)), x])/(Sqrt[(2 - x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) + (3*Sqrt[-2 + x + 2*x^2]*Defer[Int][(x*Sqrt[-1 + x + x^2])/(Sqrt[-2 + x + 2*x^2]*(1 - x - 3*x^2 + x^3 + x^4)), x])/(Sqrt[(2 - x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) - (Sqrt[-2 + x + 2*x^2]*Defer[Int][(x^2*Sqrt[-1 + x + x^2])/(Sqrt[-2 + x + 2*x^2]*(1 - x - 3*x^2 + x^3 + x^4)), x])/(Sqrt[(2 - x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2]) - (2*Sqrt[-2 + x + 2*x^2]*Defer[Int][(x^3*Sqrt[-1 + x + x^2])/(Sqrt[-2 + x + 2*x^2]*(1 - x - 3*x^2 + x^3 + x^4)), x])/(Sqrt[(2 - x - 2*x^2)/(1 - x - x^2)]*Sqrt[-1 + x + x^2])","F",0,0,0,0,-1,"{}"
2349,0,0,0,18.2683435,"\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","Int[(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,"(9*k*x*((1 - x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, ((1 - k)*x)/(1 - k*x)])/(b*((1 - x)*x*(1 - k*x))^(2/3)) + (9*k*(1 + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^3/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - (1 + k)*x^3 + k*x^6 - b*x^15)), x], x, x^(1/3)])/(b*((1 - x)*x*(1 - k*x))^(2/3)) + (12*(1 + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^12/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - (1 + k)*x^3 + k*x^6 - b*x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (9*k*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][1/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-1 + (1 + k)*x^3 - k*x^6 + b*x^15)), x], x, x^(1/3)])/(b*((1 - x)*x*(1 - k*x))^(2/3)) + (9*k^2*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^6/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-1 + (1 + k)*x^3 - k*x^6 + b*x^15)), x], x, x^(1/3)])/(b*((1 - x)*x*(1 - k*x))^(2/3)) + (15*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^9/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-1 + (1 + k)*x^3 - k*x^6 + b*x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2350,1,1539,0,3.1151194,"\int \frac{\left(-2+x^4\right) \sqrt{2+x^4}}{4+3 x^4+x^8} \, dx","Int[((-2 + x^4)*Sqrt[2 + x^4])/(4 + 3*x^4 + x^8),x]","-\frac{\sqrt{1-i \sqrt{7}} \left(5 i+\sqrt{7}\right) \tan ^{-1}\left(\frac{\sqrt{1-i \sqrt{7}} x}{\sqrt[4]{2 \left(-3-i \sqrt{7}\right)} \sqrt{x^4+2}}\right)}{2 \left(3 i-\sqrt{7}\right) \left(2 \left(-3-i \sqrt{7}\right)\right)^{3/4}}-\frac{\left(1-3 i \sqrt{7}\right) \tan ^{-1}\left(\frac{\sqrt{-1-i \sqrt{7}} x}{\sqrt[4]{2 \left(-3+i \sqrt{7}\right)} \sqrt{x^4+2}}\right)}{2^{3/4} \sqrt{-1-i \sqrt{7}} \left(-3+i \sqrt{7}\right)^{7/4}}-\frac{\left(1+3 i \sqrt{7}\right) \tan ^{-1}\left(\frac{\sqrt{-1+i \sqrt{7}} x}{\sqrt[4]{2 \left(-3-i \sqrt{7}\right)} \sqrt{x^4+2}}\right)}{2^{3/4} \left(-3-i \sqrt{7}\right)^{7/4} \sqrt{-1+i \sqrt{7}}}-\frac{\left(5 i-\sqrt{7}\right) \sqrt{1+i \sqrt{7}} \tan ^{-1}\left(\frac{\sqrt{1+i \sqrt{7}} x}{\sqrt[4]{2 \left(-3+i \sqrt{7}\right)} \sqrt{x^4+2}}\right)}{2 \left(2 \left(-3+i \sqrt{7}\right)\right)^{3/4} \left(3 i+\sqrt{7}\right)}+\frac{\left(1+i \sqrt{7}\right)^2 \left(1+\frac{2}{\sqrt{-3+i \sqrt{7}}}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{2} \left(7-i \sqrt{7}\right) \sqrt{x^4+2}}+\frac{\left(1+i \sqrt{7}\right)^2 \left(1-\frac{2}{\sqrt{-3+i \sqrt{7}}}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{2} \left(7-i \sqrt{7}\right) \sqrt{x^4+2}}+\frac{\left(1-i \sqrt{7}\right)^2 \left(1+\frac{2}{\sqrt{-3-i \sqrt{7}}}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{2} \left(7+i \sqrt{7}\right) \sqrt{x^4+2}}+\frac{\left(1-i \sqrt{7}\right)^2 \left(1-\frac{2}{\sqrt{-3-i \sqrt{7}}}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{2} \left(7+i \sqrt{7}\right) \sqrt{x^4+2}}+\frac{\left(1+i \sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \sqrt{x^4+2}}+\frac{\left(1-i \sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \sqrt{x^4+2}}-\frac{\left(3 i-\sqrt{7}\right) \left(2+\sqrt{-3-i \sqrt{7}}\right)^2 \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} \Pi \left(-\frac{\left(2-\sqrt{-3-i \sqrt{7}}\right)^2}{8 \sqrt{-3-i \sqrt{7}}};2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} \left(7 i-5 \sqrt{7}\right) \sqrt{x^4+2}}-\frac{\left(3 i-\sqrt{7}\right) \left(2-\sqrt{-3-i \sqrt{7}}\right)^2 \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} \Pi \left(\frac{\left(2+\sqrt{-3-i \sqrt{7}}\right)^2}{8 \sqrt{-3-i \sqrt{7}}};2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} \left(7 i-5 \sqrt{7}\right) \sqrt{x^4+2}}-\frac{\left(3 i+\sqrt{7}\right) \left(2+\sqrt{-3+i \sqrt{7}}\right)^2 \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} \Pi \left(-\frac{\left(2-\sqrt{-3+i \sqrt{7}}\right)^2}{8 \sqrt{-3+i \sqrt{7}}};2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} \left(7 i+5 \sqrt{7}\right) \sqrt{x^4+2}}-\frac{\left(3 i+\sqrt{7}\right) \left(2-\sqrt{-3+i \sqrt{7}}\right)^2 \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} \Pi \left(\frac{\left(2+\sqrt{-3+i \sqrt{7}}\right)^2}{8 \sqrt{-3+i \sqrt{7}}};2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{16 \sqrt[4]{2} \left(7 i+5 \sqrt{7}\right) \sqrt{x^4+2}}","-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*(Sqrt[1 - I*Sqrt[7]]*(5*I + Sqrt[7])*ArcTan[(Sqrt[1 - I*Sqrt[7]]*x)/((2*(-3 - I*Sqrt[7]))^(1/4)*Sqrt[2 + x^4])])/((3*I - Sqrt[7])*(2*(-3 - I*Sqrt[7]))^(3/4)) - ((1 - (3*I)*Sqrt[7])*ArcTan[(Sqrt[-1 - I*Sqrt[7]]*x)/((2*(-3 + I*Sqrt[7]))^(1/4)*Sqrt[2 + x^4])])/(2^(3/4)*Sqrt[-1 - I*Sqrt[7]]*(-3 + I*Sqrt[7])^(7/4)) - ((1 + (3*I)*Sqrt[7])*ArcTan[(Sqrt[-1 + I*Sqrt[7]]*x)/((2*(-3 - I*Sqrt[7]))^(1/4)*Sqrt[2 + x^4])])/(2^(3/4)*(-3 - I*Sqrt[7])^(7/4)*Sqrt[-1 + I*Sqrt[7]]) - ((5*I - Sqrt[7])*Sqrt[1 + I*Sqrt[7]]*ArcTan[(Sqrt[1 + I*Sqrt[7]]*x)/((2*(-3 + I*Sqrt[7]))^(1/4)*Sqrt[2 + x^4])])/(2*(2*(-3 + I*Sqrt[7]))^(3/4)*(3*I + Sqrt[7])) + ((1 - I*Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*Sqrt[2 + x^4]) + ((1 + I*Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*Sqrt[2 + x^4]) + ((1 - I*Sqrt[7])^2*(1 - 2/Sqrt[-3 - I*Sqrt[7]])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(8*2^(1/4)*(7 + I*Sqrt[7])*Sqrt[2 + x^4]) + ((1 - I*Sqrt[7])^2*(1 + 2/Sqrt[-3 - I*Sqrt[7]])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(8*2^(1/4)*(7 + I*Sqrt[7])*Sqrt[2 + x^4]) + ((1 + I*Sqrt[7])^2*(1 - 2/Sqrt[-3 + I*Sqrt[7]])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(8*2^(1/4)*(7 - I*Sqrt[7])*Sqrt[2 + x^4]) + ((1 + I*Sqrt[7])^2*(1 + 2/Sqrt[-3 + I*Sqrt[7]])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(8*2^(1/4)*(7 - I*Sqrt[7])*Sqrt[2 + x^4]) - ((3*I - Sqrt[7])*(2 + Sqrt[-3 - I*Sqrt[7]])^2*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticPi[-1/8*(2 - Sqrt[-3 - I*Sqrt[7]])^2/Sqrt[-3 - I*Sqrt[7]], 2*ArcTan[x/2^(1/4)], 1/2])/(16*2^(1/4)*(7*I - 5*Sqrt[7])*Sqrt[2 + x^4]) - ((3*I - Sqrt[7])*(2 - Sqrt[-3 - I*Sqrt[7]])^2*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticPi[(2 + Sqrt[-3 - I*Sqrt[7]])^2/(8*Sqrt[-3 - I*Sqrt[7]]), 2*ArcTan[x/2^(1/4)], 1/2])/(16*2^(1/4)*(7*I - 5*Sqrt[7])*Sqrt[2 + x^4]) - ((3*I + Sqrt[7])*(2 + Sqrt[-3 + I*Sqrt[7]])^2*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticPi[-1/8*(2 - Sqrt[-3 + I*Sqrt[7]])^2/Sqrt[-3 + I*Sqrt[7]], 2*ArcTan[x/2^(1/4)], 1/2])/(16*2^(1/4)*(7*I + 5*Sqrt[7])*Sqrt[2 + x^4]) - ((3*I + Sqrt[7])*(2 - Sqrt[-3 + I*Sqrt[7]])^2*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticPi[(2 + Sqrt[-3 + I*Sqrt[7]])^2/(8*Sqrt[-3 + I*Sqrt[7]]), 2*ArcTan[x/2^(1/4)], 1/2])/(16*2^(1/4)*(7*I + 5*Sqrt[7])*Sqrt[2 + x^4])","C",20,6,27,0.2222,0,"{6728, 406, 220, 409, 1217, 1707}"
2351,1,299,0,0.3647172,"\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","Int[(-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{3 \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3} (1-x)}{5 \left(-x^2+x+1\right)}-\frac{\sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}{x \left(-x^2+x+1\right)}+\frac{3 \sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3}}{2 \left(-x^2+x+1\right)}+\frac{\sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3} \log \left(\sqrt[3]{x-1}+1\right)}{3 (x-1)^{2/3} \left(-x^2+x+1\right)}-\frac{\sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3} \log \left((x-1)^{2/3}-\sqrt[3]{x-1}+1\right)}{6 (x-1)^{2/3} \left(-x^2+x+1\right)}+\frac{\sqrt[3]{-(1-x)^2 \left(-x^2+x+1\right)^3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{x-1}}{\sqrt{3}}\right)}{\sqrt{3} (x-1)^{2/3} \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,"(3*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3))/(2*(1 + x - x^2)) + (3*(1 - x)*(-((1 - x)^2*(1 + x - x^2)^3))^(1/3))/(5*(1 + x - x^2)) - (-((1 - x)^2*(1 + x - x^2)^3))^(1/3)/(x*(1 + x - x^2)) + ((-((1 - x)^2*(1 + x - x^2)^3))^(1/3)*ArcTan[(1 - 2*(-1 + x)^(1/3))/Sqrt[3]])/(Sqrt[3]*(-1 + x)^(2/3)*(1 + x - x^2)) + ((-((1 - x)^2*(1 + x - x^2)^3))^(1/3)*Log[1 + (-1 + x)^(1/3)])/(3*(-1 + x)^(2/3)*(1 + x - x^2)) - ((-((1 - x)^2*(1 + x - x^2)^3))^(1/3)*Log[1 - (-1 + x)^(1/3) + (-1 + x)^(2/3)])/(6*(-1 + x)^(2/3)*(1 + x - x^2))","A",12,11,46,0.2391,1,"{6688, 6719, 897, 1482, 1489, 292, 31, 634, 618, 204, 628}"
2352,0,0,0,1.1763338,"\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","Int[((-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,"-((b*ArcTanh[(Sqrt[2]*Sqrt[a]*x)/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]])/(Sqrt[2]*Sqrt[a])) + a^2*Defer[Int][(x^2*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/Sqrt[b + a^2*x^4], x]","F",0,0,0,0,-1,"{}"
2353,0,0,0,0.5779948,"\int \frac{\sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Int[Sqrt[1 + x]/(x + Sqrt[x + Sqrt[1 + x]]),x]","\int \frac{\sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3-2 \text{$\#$1}^2+25\&,\frac{3 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2-\text{$\#$1}}\&\right]+2 \sqrt{x+1}+2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[1 + x] - 4*Defer[Subst][Defer[Int][(2 - x - 3*x^2 + x^4)^(-1), x], x, Sqrt[1 + x]] + 2*Defer[Subst][Defer[Int][x/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 4*Defer[Subst][Defer[Int][x^2/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 2*Defer[Subst][Defer[Int][(x^2*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2354,0,0,0,0.4724337,"\int \frac{\sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Int[Sqrt[1 + x]/(x + Sqrt[x + Sqrt[1 + x]]),x]","\int \frac{\sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3-2 \text{$\#$1}^2+25\&,\frac{3 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2-\text{$\#$1}}\&\right]+2 \sqrt{x+1}+2 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[1 + x] - 4*Defer[Subst][Defer[Int][(2 - x - 3*x^2 + x^4)^(-1), x], x, Sqrt[1 + x]] + 2*Defer[Subst][Defer[Int][x/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 4*Defer[Subst][Defer[Int][x^2/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 2*Defer[Subst][Defer[Int][(x^2*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2355,1,201,0,1.4511457,"\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","Int[(-I + Sqrt[k]*x)/((I + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{2 i \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{(k+1) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/((1 + 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)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",9,8,47,0.1702,1,"{6719, 6742, 419, 2113, 537, 571, 93, 208}"
2356,1,201,0,1.2184633,"\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","Int[(I + Sqrt[k]*x)/((-I + Sqrt[k]*x)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","-\frac{2 i \sqrt{1-x^2} \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{(k+1) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{2 \sqrt{1-x^2} \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/((1 + 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)] - (2*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/Sqrt[(1 - x^2)*(1 - k^2*x^2)]","C",9,8,47,0.1702,1,"{6719, 6742, 419, 2113, 537, 571, 93, 208}"
2357,0,0,0,0.101062,"\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","Int[1/((-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3)^4),x]","\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","\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{$\#$1}^{12}+10 \text{$\#$1}^8+9 \text{$\#$1}^4+1\&,\frac{566085546 \text{$\#$1}^8 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)-234521814 \text{$\#$1}^4 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)-41317673 \log \left(\sqrt[4]{x-1}-\text{$\#$1}\right)}{9 \text{$\#$1}^{11}+20 \text{$\#$1}^7+9 \text{$\#$1}^3}\&\right]}{3813248}\right)}{(x-1)^{9/4}}",1,"Defer[Int][1/((-1 + 3*x - 3*x^2 + x^3)^(1/4)*(-1 - 2*x + x^2 + 3*x^3)^4), x]","F",0,0,0,0,-1,"{}"
2358,1,406,0,1.4564049,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}+\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}-\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}-\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}+\frac{4 \sqrt[4]{a x^4+b x^3}}{d x}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4+b x^3}}{d x}",1,"(4*(b*x^3 + a*x^4)^(1/4))/(d*x) + ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4)) + ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4)) - ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4)) - ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4))","B",13,8,30,0.2667,1,"{2056, 908, 37, 6725, 93, 298, 205, 208}"
2359,1,406,0,1.129501,"\int \frac{\sqrt[4]{b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}+\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}-\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}-\frac{\sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x+b}}+\frac{4 \sqrt[4]{a x^4+b x^3}}{d x}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4+b x^3}}{d x}",1,"(4*(b*x^3 + a*x^4)^(1/4))/(d*x) + ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4)) + ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4)) - ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4)) - ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(b + a*x)^(1/4))","B",13,8,30,0.2667,1,"{2056, 908, 37, 6725, 93, 298, 205, 208}"
2360,1,46,0,0.1506272,"\int \frac{x^4}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Int[x^4/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{2 x^5 \sqrt[4]{x^4+1} F_1\left(\frac{9}{8};1,\frac{5}{4};\frac{17}{8};x^4,-x^4\right)}{9 \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,"(-2*x^5*(1 + x^4)^(1/4)*AppellF1[9/8, 1, 5/4, 17/8, x^4, -x^4])/(9*(x^2 + x^6)^(1/4))","C",4,4,22,0.1818,0,"{2056, 1479, 466, 510}"
2361,1,46,0,0.150319,"\int \frac{x^4}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Int[x^4/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{2 x^5 \sqrt[4]{x^4+1} F_1\left(\frac{9}{8};1,\frac{5}{4};\frac{17}{8};x^4,-x^4\right)}{9 \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,"(-2*x^5*(1 + x^4)^(1/4)*AppellF1[9/8, 1, 5/4, 17/8, x^4, -x^4])/(9*(x^2 + x^6)^(1/4))","C",4,4,22,0.1818,0,"{2056, 1479, 466, 510}"
2362,1,163,0,0.5094305,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1-x^4+x^8} \, dx","Int[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 - x^4 + x^8),x]","-\frac{2 \left(\sqrt{3}+3 i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,\frac{2 x^4}{1-i \sqrt{3}}\right)}{9 \left(\sqrt{3}+i\right) \sqrt[4]{x^4+1}}-\frac{2 \left(-\sqrt{3}+3 i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,\frac{2 x^4}{1+i \sqrt{3}}\right)}{9 \left(-\sqrt{3}+i\right) \sqrt[4]{x^4+1}}","\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,"(-2*(3*I + Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (2*x^4)/(1 - I*Sqrt[3])])/(9*(I + Sqrt[3])*(1 + x^4)^(1/4)) - (2*(3*I - Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (2*x^4)/(1 + I*Sqrt[3])])/(9*(I - Sqrt[3])*(1 + x^4)^(1/4))","C",7,4,29,0.1379,0,"{2056, 6728, 466, 510}"
2363,1,163,0,0.4412712,"\int \frac{\left(-1+x^4\right) \sqrt[4]{x^2+x^6}}{1-x^4+x^8} \, dx","Int[((-1 + x^4)*(x^2 + x^6)^(1/4))/(1 - x^4 + x^8),x]","-\frac{2 \left(\sqrt{3}+3 i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,\frac{2 x^4}{1-i \sqrt{3}}\right)}{9 \left(\sqrt{3}+i\right) \sqrt[4]{x^4+1}}-\frac{2 \left(-\sqrt{3}+3 i\right) x \sqrt[4]{x^6+x^2} F_1\left(\frac{3}{8};-\frac{1}{4},1;\frac{11}{8};-x^4,\frac{2 x^4}{1+i \sqrt{3}}\right)}{9 \left(-\sqrt{3}+i\right) \sqrt[4]{x^4+1}}","\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,"(-2*(3*I + Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (2*x^4)/(1 - I*Sqrt[3])])/(9*(I + Sqrt[3])*(1 + x^4)^(1/4)) - (2*(3*I - Sqrt[3])*x*(x^2 + x^6)^(1/4)*AppellF1[3/8, -1/4, 1, 11/8, -x^4, (2*x^4)/(1 + I*Sqrt[3])])/(9*(I - Sqrt[3])*(1 + x^4)^(1/4))","C",7,4,29,0.1379,0,"{2056, 6728, 466, 510}"
2364,1,99,0,0.5558711,"\int \frac{1-x^4+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Int[(1 - x^4 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{\sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}+\frac{\sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{2 \sqrt[4]{x^6+x^2}}-\frac{3 x}{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,"(-3*x)/(2*(x^2 + x^6)^(1/4)) - (x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(2*(x^2 + x^6)^(1/4))","C",10,8,29,0.2759,0,"{2056, 6715, 6725, 245, 1455, 527, 530, 429}"
2365,1,99,0,0.4500573,"\int \frac{1-x^4+x^8}{\sqrt[4]{x^2+x^6} \left(-1+x^8\right)} \, dx","Int[(1 - x^4 + x^8)/((x^2 + x^6)^(1/4)*(-1 + x^8)),x]","-\frac{\sqrt[4]{x^4+1} x F_1\left(\frac{1}{8};1,\frac{1}{4};\frac{9}{8};x^4,-x^4\right)}{\sqrt[4]{x^6+x^2}}+\frac{\sqrt[4]{x^4+1} x \, _2F_1\left(\frac{1}{8},\frac{1}{4};\frac{9}{8};-x^4\right)}{2 \sqrt[4]{x^6+x^2}}-\frac{3 x}{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,"(-3*x)/(2*(x^2 + x^6)^(1/4)) - (x*(1 + x^4)^(1/4)*AppellF1[1/8, 1, 1/4, 9/8, x^4, -x^4])/(x^2 + x^6)^(1/4) + (x*(1 + x^4)^(1/4)*Hypergeometric2F1[1/8, 1/4, 9/8, -x^4])/(2*(x^2 + x^6)^(1/4))","C",10,8,29,0.2759,0,"{2056, 6715, 6725, 245, 1455, 527, 530, 429}"
2366,1,139,0,0.1138693,"\int \frac{1}{(-b+a x) \sqrt[4]{-x^3+x^4}} \, dx","Int[1/((-b + a*x)*(-x^3 + x^4)^(1/4)),x]","-\frac{2 \sqrt[4]{x-1} x^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a}}{\sqrt[4]{b} \sqrt[4]{x-1}}\right)}{b^{3/4} \sqrt[4]{x^4-x^3} \sqrt[4]{b-a}}-\frac{2 \sqrt[4]{x-1} x^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a}}{\sqrt[4]{b} \sqrt[4]{x-1}}\right)}{b^{3/4} \sqrt[4]{x^4-x^3} \sqrt[4]{b-a}}","\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,"(-2*(-1 + x)^(1/4)*x^(3/4)*ArcTan[((-a + b)^(1/4)*x^(1/4))/(b^(1/4)*(-1 + x)^(1/4))])/(b^(3/4)*(-a + b)^(1/4)*(-x^3 + x^4)^(1/4)) - (2*(-1 + x)^(1/4)*x^(3/4)*ArcTanh[((-a + b)^(1/4)*x^(1/4))/(b^(1/4)*(-1 + x)^(1/4))])/(b^(3/4)*(-a + b)^(1/4)*(-x^3 + x^4)^(1/4))","A",5,5,23,0.2174,1,"{2056, 93, 212, 208, 205}"
2367,1,455,0,2.3871632,"\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","Int[(-x + x^2)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(1 - 2*x + k^2*x^2)),x]","\frac{\left(-k^2-\sqrt{1-k^2}+1\right) (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{1}{1-\sqrt{1-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\left(-k^2\right)^{3/2} \sqrt{1-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}-\frac{\left(-k^2+\sqrt{1-k^2}+1\right) (1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{1}{\sqrt{1-k^2}+1};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\left(-k^2\right)^{3/2} \sqrt{1-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}-\frac{\left(-k^2-\sqrt{1-k^2}+2\right) \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{k^2 \sqrt{1-k^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{\left(-k^2+\sqrt{1-k^2}+2\right) \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{k^2 \sqrt{1-k^2} \sqrt{(1-x) x \left(1-k^2 x\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,"-(((2 - k^2 - Sqrt[1 - k^2])*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/(k^2*Sqrt[1 - k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)])) + ((2 - k^2 + Sqrt[1 - k^2])*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/(k^2*Sqrt[1 - k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]) + ((1 - k^2 - Sqrt[1 - k^2])*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(1 - Sqrt[1 - k^2])^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/((-k^2)^(3/2)*Sqrt[1 - k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) - ((1 - k^2 + Sqrt[1 - k^2])*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(1 + Sqrt[1 - k^2])^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/((-k^2)^(3/2)*Sqrt[1 - k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",26,14,41,0.3415,0,"{1593, 6718, 21, 6688, 6728, 922, 934, 12, 168, 537, 843, 714, 110, 115}"
2368,1,821,0,1.1180371,"\int \frac{-b+a^3 x^2}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[(-b + a^3*x^2)/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log (x)}{2 a \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-\sqrt{-a^3} x\right)}{2 \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{-a^3} x+\sqrt{b}\right)}{2 \sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3-b x^2}}","\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,"-((Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(-(b*x^2) + a^3*x^3)^(1/3))) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/((a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/((a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[x])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[-a^3]*x])/(2*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[-a^3]*x])/(2*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)])/(2*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)])/(2*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-1 + (-b + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3))","B",8,5,41,0.1220,1,"{2056, 6725, 59, 912, 91}"
2369,1,821,0,0.8957099,"\int \frac{-b+a^3 x^2}{\left(b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[(-b + a^3*x^2)/((b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log (x)}{2 a \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-\sqrt{-a^3} x\right)}{2 \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{-a^3} x+\sqrt{b}\right)}{2 \sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a^3-\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a^3+\sqrt{-a^3} \sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3-b x^2}}","\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,"-((Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(-(b*x^2) + a^3*x^3)^(1/3))) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/((a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*x^(1/3))])/((a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[x])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[-a^3]*x])/(2*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[-a^3]*x])/(2*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)])/(2*(a^3 - Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)])/(2*(a^3 + Sqrt[-a^3]*Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-1 + (-b + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3))","B",8,5,41,0.1220,1,"{2056, 6725, 59, 912, 91}"
2370,0,0,0,0.769847,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(1 + x^2)/((-1 + x^2)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","-\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,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] + Defer[Int][1/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - Defer[Int][1/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]","F",0,0,0,0,-1,"{}"
2371,1,273,0,1.149074,"\int \frac{x^4 \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Int[(x^4*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}+\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}-\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}-\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+3 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 - I*Sqrt[3])*x^2)])/(Sqrt[3]*(1 - x^2)^(1/4)) + ((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 - I*Sqrt[3])*x^2)/2])/(Sqrt[3]*(1 - x^2)^(1/4)) - ((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 + I*Sqrt[3])*x^2)])/(Sqrt[3]*(1 - x^2)^(1/4)) - ((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 + I*Sqrt[3])*x^2)/2])/(Sqrt[3]*(1 - x^2)^(1/4))","C",29,12,27,0.4444,0,"{2056, 6728, 1270, 1517, 279, 331, 298, 203, 206, 1529, 511, 510}"
2372,1,273,0,1.1388642,"\int \frac{x^4 \sqrt[4]{-x^2+x^4}}{1+x^4+x^8} \, dx","Int[(x^4*(-x^2 + x^4)^(1/4))/(1 + x^4 + x^8),x]","\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}+\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1-i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}-\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,-\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}-\frac{i x \sqrt[4]{x^4-x^2} F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^2,\frac{1}{2} \left(1+i \sqrt{3}\right) x^2\right)}{3 \sqrt{3} \sqrt[4]{1-x^2}}","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-3 \text{$\#$1}^4+3\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+3 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-3 \log (x)}{2 \text{$\#$1}^7-3 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4+1\&,\frac{-\text{$\#$1}^4 \log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \log (x)+\log \left(\sqrt[4]{x^4-x^2}-\text{$\#$1} x\right)-\log (x)}{2 \text{$\#$1}^7-\text{$\#$1}^3}\&\right]",1,"((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 - I*Sqrt[3])*x^2)])/(Sqrt[3]*(1 - x^2)^(1/4)) + ((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 - I*Sqrt[3])*x^2)/2])/(Sqrt[3]*(1 - x^2)^(1/4)) - ((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, -1/2*((1 + I*Sqrt[3])*x^2)])/(Sqrt[3]*(1 - x^2)^(1/4)) - ((I/3)*x*(-x^2 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^2, ((1 + I*Sqrt[3])*x^2)/2])/(Sqrt[3]*(1 - x^2)^(1/4))","C",29,12,27,0.4444,0,"{2056, 6728, 1270, 1517, 279, 331, 298, 203, 206, 1529, 511, 510}"
2373,0,0,0,1.3427115,"\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","Int[((-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]","\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","-\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,"-2*q*Defer[Int][Sqrt[q + p*x^3]/(a*q^2 + b*q*x^2 + 2*a*p*q*x^3 + c*x^4 + b*p*x^5 + a*p^2*x^6), x] + p*Defer[Int][(x^3*Sqrt[q + p*x^3])/(a*q^2 + b*q*x^2 + 2*a*p*q*x^3 + c*x^4 + b*p*x^5 + a*p^2*x^6), x]","F",0,0,0,0,-1,"{}"
2374,0,0,0,2.7547198,"\int \frac{\left(-1+x^4\right)^2}{\left(1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[(-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,"-4*ArcTanh[x/Sqrt[x^2 + Sqrt[1 + x^4]]] + Defer[Int][1/Sqrt[x^2 + Sqrt[1 + x^4]], x] + (I/4)*Defer[Int][1/(((-1)^(1/4) - x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + (3*(-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) - x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x])/4 - (I/4)*Defer[Int][1/((-(-1)^(3/4) - x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - (3*(-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) - x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x])/4 + (I/4)*Defer[Int][1/(((-1)^(1/4) + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + (3*(-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) + x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x])/4 - (I/4)*Defer[Int][1/((-(-1)^(3/4) + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - (3*(-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) + x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x])/4","F",0,0,0,0,-1,"{}"
2375,1,405,0,1.4611641,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(1+x^2\right)^2 \sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x^2)^2*Sqrt[1 + x^4]),x]","\frac{i \sqrt{1-i x^2}}{8 (-x+i)}-\frac{i \sqrt{1-i x^2}}{8 (x+i)}-\frac{i \sqrt{1+i x^2}}{8 (-x+i)}+\frac{i \sqrt{1+i x^2}}{8 (x+i)}-\frac{1}{8} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1+i} \sqrt{1-i x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{1-x}{\sqrt{1+i} \sqrt{1-i x^2}}\right)}{4 (1+i)^{5/2}}+\frac{1}{8} \sqrt{1+i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1+i} \sqrt{1-i x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{x+1}{\sqrt{1+i} \sqrt{1-i x^2}}\right)}{4 (1+i)^{5/2}}-\frac{1}{8} \sqrt{1-i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1-i} \sqrt{1+i x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{1-x}{\sqrt{1-i} \sqrt{1+i x^2}}\right)}{4 (1-i)^{5/2}}+\frac{1}{8} \sqrt{1-i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1-i} \sqrt{1+i x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{x+1}{\sqrt{1-i} \sqrt{1+i x^2}}\right)}{4 (1-i)^{5/2}}","\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,"((I/8)*Sqrt[1 - I*x^2])/(I - x) - ((I/8)*Sqrt[1 - I*x^2])/(I + x) - ((I/8)*Sqrt[1 + I*x^2])/(I - x) + ((I/8)*Sqrt[1 + I*x^2])/(I + x) + ArcTanh[(1 - x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])]/(4*(1 + I)^(5/2)) - (Sqrt[1 + I]*ArcTanh[(1 - x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/8 - ArcTanh[(1 + x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])]/(4*(1 + I)^(5/2)) + (Sqrt[1 + I]*ArcTanh[(1 + x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/8 + ArcTanh[(1 - x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])]/(4*(1 - I)^(5/2)) - (Sqrt[1 - I]*ArcTanh[(1 - x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/8 - ArcTanh[(1 + x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])]/(4*(1 - I)^(5/2)) + (Sqrt[1 - I]*ArcTanh[(1 + x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/8","C",28,6,34,0.1765,0,"{6742, 2133, 731, 725, 206, 6725}"
2376,0,0,0,1.3724881,"\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","Int[(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,"-2*q*Defer[Int][Sqrt[q + p*x^5]/(a*q^2 + b*q*x^2 + c*x^4 + 2*a*p*q*x^5 + b*p*x^7 + a*p^2*x^10), x] + 3*p*Defer[Int][(x^5*Sqrt[q + p*x^5])/(a*q^2 + b*q*x^2 + c*x^4 + 2*a*p*q*x^5 + b*p*x^7 + a*p^2*x^10), x]","F",0,0,0,0,-1,"{}"
2377,0,0,0,1.4701779,"\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","Int[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,"Defer[Int][1/(x*Sqrt[a*x + Sqrt[-b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]]), x]","F",0,0,0,0,-1,"{}"
2378,1,70,0,0.0098208,"\int \frac{1}{\sqrt[3]{1+x^2} \left(9+x^2\right)} \, dx","Int[1/((1 + x^2)^(1/3)*(9 + x^2)),x]","\frac{1}{12} \tan ^{-1}\left(\frac{\left(1-\sqrt[3]{x^2+1}\right)^2}{3 x}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{x^2+1}\right)}{x}\right)}{4 \sqrt{3}}+\frac{1}{12} \tan ^{-1}\left(\frac{x}{3}\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,"ArcTan[x/3]/12 + ArcTan[(1 - (1 + x^2)^(1/3))^2/(3*x)]/12 - ArcTanh[(Sqrt[3]*(1 - (1 + x^2)^(1/3)))/x]/(4*Sqrt[3])","A",1,1,17,0.05882,1,"{394}"
2379,1,788,0,1.2000621,"\int \frac{b+a^3 x^2}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[(b + a^3*x^2)/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \log (x) \sqrt[3]{a^3 x-b}}{2 a \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-a^{3/2} x\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(a^{3/2} x+\sqrt{b}\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}-\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}+\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}","\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,"-((Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(-(b*x^2) + a^3*x^3)^(1/3))) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*x^(1/3))])/(Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*x^(1/3))])/(Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[x])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - a^(3/2)*x])/(2*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + a^(3/2)*x])/(2*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3))])/(2*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3))])/(2*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-1 + (-b + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3))","B",8,5,41,0.1220,1,"{2056, 6725, 59, 912, 91}"
2380,1,788,0,1.0174215,"\int \frac{b+a^3 x^2}{\left(-b+a^3 x^2\right) \sqrt[3]{-b x^2+a^3 x^3}} \, dx","Int[(b + a^3*x^2)/((-b + a^3*x^2)*(-(b*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \log (x) \sqrt[3]{a^3 x-b}}{2 a \sqrt[3]{a^3 x^3-b x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3-b x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\sqrt{b}-a^{3/2} x\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b} \log \left(a^{3/2} x+\sqrt{b}\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b} \log \left(\frac{\sqrt[3]{a^3 x-b}}{\sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}}}-\sqrt[3]{x}\right)}{2 \sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}-\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{a} \sqrt[3]{a^{3/2}-\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b}}{\sqrt{3} \sqrt{a} \sqrt[3]{x} \sqrt[3]{a^{3/2}+\sqrt{b}}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{a} \sqrt[3]{a^{3/2}+\sqrt{b}} \sqrt[3]{a^3 x^3-b x^2}}","\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,"-((Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(-(b*x^2) + a^3*x^3)^(1/3))) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*x^(1/3))])/(Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (Sqrt[3]*x^(2/3)*(-b + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b + a^3*x)^(1/3))/(Sqrt[3]*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*x^(1/3))])/(Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[x])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] - a^(3/2)*x])/(2*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b + a^3*x)^(1/3)*Log[Sqrt[b] + a^(3/2)*x])/(2*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3))])/(2*Sqrt[a]*(a^(3/2) - Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-x^(1/3) + (-b + a^3*x)^(1/3)/(Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3))])/(2*Sqrt[a]*(a^(3/2) + Sqrt[b])^(1/3)*(-(b*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b + a^3*x)^(1/3)*Log[-1 + (-b + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(-(b*x^2) + a^3*x^3)^(1/3))","B",8,5,41,0.1220,1,"{2056, 6725, 59, 912, 91}"
2381,0,0,0,8.0901703,"\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","Int[(-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,"((5*d + k^(-2))*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*d*k^(2/3)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) - ((1 - d + 5*d*k^2 - 8*d^2*k^2)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (2 + d)*x + (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d^2*k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((2 + d + 11*d*k^2 + 2*d^2*k^2*(1 - k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (2 + d)*x + (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d^2*k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((1 + 8*d*k^2 + 2*d^2*(k^2 + 3*k^4))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (2 + d)*x + (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d^2*k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))","F",0,0,0,0,-1,"{}"
2382,1,211,0,0.6081062,"\int \frac{\sqrt[4]{x^3+x^5} \left(1+x^4+x^8\right)}{x^4 \left(-1+x^4\right)} \, dx","Int[((x^3 + x^5)^(1/4)*(1 + x^4 + x^8))/(x^4*(-1 + x^4)),x]","\frac{4 \sqrt[4]{x^5+x^3} F_1\left(-\frac{9}{8};1,\frac{3}{4};-\frac{1}{8};x^2,-x^2\right)}{3 \sqrt[4]{x^2+1} x^3}+\frac{4 \sqrt[4]{x^5+x^3} x^3 \, _2F_1\left(\frac{3}{4},\frac{15}{8};\frac{23}{8};-x^2\right)}{15 \sqrt[4]{x^2+1}}+\frac{4 \sqrt[4]{x^5+x^3} x \, _2F_1\left(\frac{3}{4},\frac{7}{8};\frac{15}{8};-x^2\right)}{7 \sqrt[4]{x^2+1}}-\frac{8 \sqrt[4]{x^5+x^3} \, _2F_1\left(-\frac{1}{8},\frac{3}{4};\frac{7}{8};-x^2\right)}{\sqrt[4]{x^2+1} x}-\frac{8 \sqrt[4]{x^5+x^3} \, _2F_1\left(-\frac{9}{8},\frac{3}{4};-\frac{1}{8};-x^2\right)}{9 \sqrt[4]{x^2+1} x^3}","\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,"(4*(x^3 + x^5)^(1/4)*AppellF1[-9/8, 1, 3/4, -1/8, x^2, -x^2])/(3*x^3*(1 + x^2)^(1/4)) - (8*(x^3 + x^5)^(1/4)*Hypergeometric2F1[-9/8, 3/4, -1/8, -x^2])/(9*x^3*(1 + x^2)^(1/4)) - (8*(x^3 + x^5)^(1/4)*Hypergeometric2F1[-1/8, 3/4, 7/8, -x^2])/(x*(1 + x^2)^(1/4)) + (4*x*(x^3 + x^5)^(1/4)*Hypergeometric2F1[3/4, 7/8, 15/8, -x^2])/(7*(1 + x^2)^(1/4)) + (4*x^3*(x^3 + x^5)^(1/4)*Hypergeometric2F1[3/4, 15/8, 23/8, -x^2])/(15*(1 + x^2)^(1/4))","C",10,6,30,0.2000,0,"{2056, 1586, 6725, 364, 466, 510}"
2383,1,264,0,0.3318802,"\int \frac{1}{\left(b+a x^2\right) \sqrt[3]{x+x^3}} \, dx","Int[1/((b + a*x^2)*(x + x^3)^(1/3)),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2+1}}+\sqrt[3]{b}\right)}{2 b^{2/3} \sqrt[3]{x^3+x} \sqrt[3]{a-b}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{x^{4/3} (a-b)^{2/3}}{\left(x^2+1\right)^{2/3}}-\frac{\sqrt[3]{b} x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2+1}}+b^{2/3}\right)}{4 b^{2/3} \sqrt[3]{x^3+x} \sqrt[3]{a-b}}-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[3]{b}-\frac{2 x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2+1}}}{\sqrt{3} \sqrt[3]{b}}\right)}{2 b^{2/3} \sqrt[3]{x^3+x} \sqrt[3]{a-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,"-1/2*(Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(b^(1/3) - (2*(a - b)^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/(Sqrt[3]*b^(1/3))])/((a - b)^(1/3)*b^(2/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[b^(1/3) + ((a - b)^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*(a - b)^(1/3)*b^(2/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[b^(2/3) + ((a - b)^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - ((a - b)^(1/3)*b^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(4*(a - b)^(1/3)*b^(2/3)*(x + x^3)^(1/3))","A",10,10,19,0.5263,1,"{2056, 466, 465, 377, 200, 31, 634, 617, 204, 628}"
2384,1,427,0,1.4568806,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}+\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}+\frac{4 \sqrt[4]{a x^4-b x^3}}{d x}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4-b x^3}}{d x}",1,"(4*(-(b*x^3) + a*x^4)^(1/4))/(d*x) + ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4)) + ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4)) - ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4)) - ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4))","B",13,8,31,0.2581,1,"{2056, 908, 37, 6725, 93, 298, 205, 208}"
2385,1,427,0,1.1103408,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x^2 \left(-d+c x^2\right)} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(x^2*(-d + c*x^2)),x]","\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}+\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{d^{9/8} x^{3/4} \sqrt[4]{a x-b}}+\frac{4 \sqrt[4]{a x^4-b x^3}}{d x}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4-b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{2 d^2}+\frac{4 \sqrt[4]{a x^4-b x^3}}{d x}",1,"(4*(-(b*x^3) + a*x^4)^(1/4))/(d*x) + ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4)) + ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4)) - ((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4)) - ((b*Sqrt[c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(d^(9/8)*x^(3/4)*(-b + a*x)^(1/4))","B",13,8,31,0.2581,1,"{2056, 908, 37, 6725, 93, 298, 205, 208}"
2386,1,412,0,3.062969,"\int \frac{\sqrt[3]{x+x^3} \left(b+a x^6\right)}{d+c x^6} \, dx","Int[((x + x^3)^(1/3)*(b + a*x^6))/(d + c*x^6),x]","\frac{\sqrt[3]{x^3+x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-x^2,\frac{\sqrt[3]{-c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{x^2+1}}+\frac{\sqrt[3]{x^3+x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-x^2,-\frac{\sqrt[3]{-1} \sqrt[3]{-c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{x^2+1}}+\frac{\sqrt[3]{x^3+x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-x^2,\frac{(-1)^{2/3} \sqrt[3]{-c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{x^2+1}}+\frac{a \sqrt[3]{x^3+x} x}{2 c}-\frac{a \sqrt[3]{x^3+x} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{6 c \sqrt[3]{x^2+1} \sqrt[3]{x}}+\frac{a \sqrt[3]{x^3+x} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{12 c \sqrt[3]{x^2+1} \sqrt[3]{x}}-\frac{a \sqrt[3]{x^3+x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} c \sqrt[3]{x^2+1} \sqrt[3]{x}}","\frac{(a d-b c) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3+x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$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,"(a*x*(x + x^3)^(1/3))/(2*c) + ((b*c - a*d)*x*(x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -x^2, ((-c)^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 + x^2)^(1/3)) + ((b*c - a*d)*x*(x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -x^2, -(((-1)^(1/3)*(-c)^(1/3)*x^2)/d^(1/3))])/(4*c*d*(1 + x^2)^(1/3)) + ((b*c - a*d)*x*(x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -x^2, ((-1)^(2/3)*(-c)^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 + x^2)^(1/3)) - (a*(x + x^3)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*c*x^(1/3)*(1 + x^2)^(1/3)) - (a*(x + x^3)^(1/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(6*c*x^(1/3)*(1 + x^2)^(1/3)) + (a*(x + x^3)^(1/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(12*c*x^(1/3)*(1 + x^2)^(1/3))","B",55,16,26,0.6154,0,"{2056, 6725, 279, 329, 275, 331, 292, 31, 634, 618, 204, 628, 959, 466, 465, 510}"
2387,1,412,0,2.7475676,"\int \frac{\sqrt[3]{x+x^3} \left(b+a x^6\right)}{d+c x^6} \, dx","Int[((x + x^3)^(1/3)*(b + a*x^6))/(d + c*x^6),x]","\frac{\sqrt[3]{x^3+x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-x^2,\frac{\sqrt[3]{-c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{x^2+1}}+\frac{\sqrt[3]{x^3+x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-x^2,-\frac{\sqrt[3]{-1} \sqrt[3]{-c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{x^2+1}}+\frac{\sqrt[3]{x^3+x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-x^2,\frac{(-1)^{2/3} \sqrt[3]{-c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{x^2+1}}+\frac{a \sqrt[3]{x^3+x} x}{2 c}-\frac{a \sqrt[3]{x^3+x} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{6 c \sqrt[3]{x^2+1} \sqrt[3]{x}}+\frac{a \sqrt[3]{x^3+x} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{12 c \sqrt[3]{x^2+1} \sqrt[3]{x}}-\frac{a \sqrt[3]{x^3+x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} c \sqrt[3]{x^2+1} \sqrt[3]{x}}","\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,"(a*x*(x + x^3)^(1/3))/(2*c) + ((b*c - a*d)*x*(x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -x^2, ((-c)^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 + x^2)^(1/3)) + ((b*c - a*d)*x*(x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -x^2, -(((-1)^(1/3)*(-c)^(1/3)*x^2)/d^(1/3))])/(4*c*d*(1 + x^2)^(1/3)) + ((b*c - a*d)*x*(x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -x^2, ((-1)^(2/3)*(-c)^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 + x^2)^(1/3)) - (a*(x + x^3)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*c*x^(1/3)*(1 + x^2)^(1/3)) - (a*(x + x^3)^(1/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(6*c*x^(1/3)*(1 + x^2)^(1/3)) + (a*(x + x^3)^(1/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(12*c*x^(1/3)*(1 + x^2)^(1/3))","B",55,16,26,0.6154,0,"{2056, 6725, 279, 329, 275, 331, 292, 31, 634, 618, 204, 628, 959, 466, 465, 510}"
2388,0,0,0,6.5408697,"\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","Int[((-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,"((x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/(-1 + x), x], x, x^(2/3)])/(2*x^(1/3)*(1 + x^6)^(1/3)) - ((1 + I*Sqrt[3])*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/(1 - I*Sqrt[3] + 2*x), x], x, x^(2/3)])/(2*x^(1/3)*(1 + x^6)^(1/3)) - ((1 - I*Sqrt[3])*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/(1 + I*Sqrt[3] + 2*x), x], x, x^(2/3)])/(2*x^(1/3)*(1 + x^6)^(1/3)) - ((-1 - Sqrt[5])^(2/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((1 + Sqrt[5])^(1/3) - (-2)^(1/3)*x), x], x, x^(2/3)])/(2^(1/3)*Sqrt[5]*x^(1/3)*(1 + x^6)^(1/3)) + ((-1)^(2/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((1 + Sqrt[5])^(1/3) - (-2)^(1/3)*x), x], x, x^(2/3)])/(Sqrt[5]*(2*(1 + Sqrt[5]))^(1/3)*x^(1/3)*(1 + x^6)^(1/3)) - ((1 - Sqrt[5])^(2/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((-1 + Sqrt[5])^(1/3) + (-2)^(1/3)*x), x], x, x^(2/3)])/(2^(1/3)*Sqrt[5]*x^(1/3)*(1 + x^6)^(1/3)) - ((-1)^(2/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((-1 + Sqrt[5])^(1/3) + (-2)^(1/3)*x), x], x, x^(2/3)])/(Sqrt[5]*(2*(-1 + Sqrt[5]))^(1/3)*x^(1/3)*(1 + x^6)^(1/3)) - ((-1 + Sqrt[5])^(2/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((-1 + Sqrt[5])^(1/3) - 2^(1/3)*x), x], x, x^(2/3)])/(2^(1/3)*Sqrt[5]*x^(1/3)*(1 + x^6)^(1/3)) - ((x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((-1 + Sqrt[5])^(1/3) - 2^(1/3)*x), x], x, x^(2/3)])/(Sqrt[5]*(2*(-1 + Sqrt[5]))^(1/3)*x^(1/3)*(1 + x^6)^(1/3)) - ((1 + Sqrt[5])^(2/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((1 + Sqrt[5])^(1/3) + 2^(1/3)*x), x], x, x^(2/3)])/(2^(1/3)*Sqrt[5]*x^(1/3)*(1 + x^6)^(1/3)) + ((x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((1 + Sqrt[5])^(1/3) + 2^(1/3)*x), x], x, x^(2/3)])/(Sqrt[5]*(2*(1 + Sqrt[5]))^(1/3)*x^(1/3)*(1 + x^6)^(1/3)) + ((-1 - Sqrt[5])^(1/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((-1 + Sqrt[5])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(2/3)])/(2*Sqrt[5]*x^(1/3)*(1 + x^6)^(1/3)) + ((-1 - Sqrt[5])^(1/3)*(5 - Sqrt[5])*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((-1 + Sqrt[5])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(2/3)])/(10*x^(1/3)*(1 + x^6)^(1/3)) - ((1 - Sqrt[5])^(1/3)*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((1 + Sqrt[5])^(1/3) + (-1)^(2/3)*2^(1/3)*x), x], x, x^(2/3)])/(2*Sqrt[5]*x^(1/3)*(1 + x^6)^(1/3)) + ((1 - Sqrt[5])^(1/3)*(5 + Sqrt[5])*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(1 + x^9)^(1/3)/((1 + Sqrt[5])^(1/3) + (-1)^(2/3)*2^(1/3)*x), x], x, x^(2/3)])/(10*x^(1/3)*(1 + x^6)^(1/3)) + (3*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(x*(1 + x^9)^(1/3))/(1 - x^3 + x^9), x], x, x^(2/3)])/(2*x^(1/3)*(1 + x^6)^(1/3)) - (9*(x + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^7*(1 + x^9)^(1/3))/(1 - x^3 + x^9), x], x, x^(2/3)])/(2*x^(1/3)*(1 + x^6)^(1/3))","F",0,0,0,0,-1,"{}"
2389,0,0,0,1.3174298,"\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","Int[((-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,"p*(2*b + 3*a*p*q^2)*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] - a*q^4*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^6, x] - q*(b + a*p*q^2)*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^3, x] + 5*a*p^3*q*Defer[Int][x^3*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 2*a*p^4*Defer[Int][x^6*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2390,0,0,0,2.697423,"\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","Int[(-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,"-(((1 + Sqrt[4 + b - 4*k]/Sqrt[b] - 2*k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - k*x)^(1/3)*(-2 - b - Sqrt[b]*Sqrt[4 + b - 4*k] + 2*(1 + b*k)*x)*(x - x^2)^(1/3)), x])/((1 - x)*x*(1 - k*x))^(1/3)) - ((1 - Sqrt[4 + b - 4*k]/Sqrt[b] - 2*k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - k*x)^(1/3)*(-2 - b + Sqrt[b]*Sqrt[4 + b - 4*k] + 2*(1 + b*k)*x)*(x - x^2)^(1/3)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2391,0,0,0,7.8311112,"\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","Int[(-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,"-(((1 + 5*d*k^2)*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/(d^2*k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*d*k^(2/3)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) - ((1 - d + 5*d*k^2 - 8*d^2*k^2)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(-1 + d + (2 + d)*x - (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d^2*k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((2 + d + 11*d*k^2 + 2*d^2*k^2*(1 - k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)), x])/(d^2*k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) + ((1 + 8*d*k^2 + 2*d^2*(k^2 + 3*k^4))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)), x])/(d^2*k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))","F",0,0,0,0,-1,"{}"
2392,1,617,0,1.6355622,"\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","Int[(b - 3*a*x^3 + 3*x^6)/(x^6*(-b + 2*a*x^3)*(-(b*x) + a*x^4)^(1/4)),x]","-\frac{\sqrt[4]{x} \left(2 a^2-3 b\right) \sqrt[4]{a x^3-b} \log \left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3-b}}-\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}+1\right)}{3 \sqrt{2} \sqrt[4]{a} b^2 \sqrt[4]{a x^4-b x}}+\frac{\sqrt[4]{x} \left(2 a^2-3 b\right) \sqrt[4]{a x^3-b} \log \left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3-b}}+\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}+1\right)}{3 \sqrt{2} \sqrt[4]{a} b^2 \sqrt[4]{a x^4-b x}}-\frac{\sqrt{2} \sqrt[4]{x} \left(2 a^2-3 b\right) \sqrt[4]{a x^3-b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}\right)}{3 \sqrt[4]{a} b^2 \sqrt[4]{a x^4-b x}}+\frac{\sqrt{2} \sqrt[4]{x} \left(2 a^2-3 b\right) \sqrt[4]{a x^3-b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3-b}}+1\right)}{3 \sqrt[4]{a} b^2 \sqrt[4]{a x^4-b x}}-\frac{\left(2 a^2-3 b\right) \left(b-a x^3\right)^2}{21 a^2 b^2 x^5 \sqrt[4]{a x^4-b x}}+\frac{4 a \left(2-\frac{b}{a^2}\right) \left(b-a x^3\right)}{21 b^2 x^2 \sqrt[4]{a x^4-b x}}-\frac{\left(2 a^2-3 b\right) \left(b-a x^3\right)}{3 a b^2 x^2 \sqrt[4]{a x^4-b x}}+\frac{\left(2-\frac{b}{a^2}\right) \left(b-a x^3\right)}{7 b x^5 \sqrt[4]{a x^4-b x}}-\frac{2 \left(b-a x^3\right)}{3 a b x^2 \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,"((2 - b/a^2)*(b - a*x^3))/(7*b*x^5*(-(b*x) + a*x^4)^(1/4)) - ((2*a^2 - 3*b)*(b - a*x^3))/(3*a*b^2*x^2*(-(b*x) + a*x^4)^(1/4)) - (2*(b - a*x^3))/(3*a*b*x^2*(-(b*x) + a*x^4)^(1/4)) + (4*a*(2 - b/a^2)*(b - a*x^3))/(21*b^2*x^2*(-(b*x) + a*x^4)^(1/4)) - ((2*a^2 - 3*b)*(b - a*x^3)^2)/(21*a^2*b^2*x^5*(-(b*x) + a*x^4)^(1/4)) - (Sqrt[2]*(2*a^2 - 3*b)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[1 - (Sqrt[2]*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*a^(1/4)*b^2*(-(b*x) + a*x^4)^(1/4)) + (Sqrt[2]*(2*a^2 - 3*b)*x^(1/4)*(-b + a*x^3)^(1/4)*ArcTan[1 + (Sqrt[2]*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*a^(1/4)*b^2*(-(b*x) + a*x^4)^(1/4)) - ((2*a^2 - 3*b)*x^(1/4)*(-b + a*x^3)^(1/4)*Log[1 + (Sqrt[a]*x^(3/2))/Sqrt[-b + a*x^3] - (Sqrt[2]*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*Sqrt[2]*a^(1/4)*b^2*(-(b*x) + a*x^4)^(1/4)) + ((2*a^2 - 3*b)*x^(1/4)*(-b + a*x^3)^(1/4)*Log[1 + (Sqrt[a]*x^(3/2))/Sqrt[-b + a*x^3] + (Sqrt[2]*a^(1/4)*x^(3/4))/(-b + a*x^3)^(1/4)])/(3*Sqrt[2]*a^(1/4)*b^2*(-(b*x) + a*x^4)^(1/4))","B",20,14,43,0.3256,1,"{2056, 6725, 271, 264, 466, 465, 494, 461, 211, 1165, 628, 1162, 617, 204}"
2393,0,0,0,1.3315348,"\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","Int[((-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,"-2*a*q^4*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^11, x] - 5*a*p*q^3*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^8, x] - q*(2*b + 3*a*p^2*q)*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^5, x] + p*(b + a*p^2*q)*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^2, x] + a*p^4*Defer[Int][x*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2394,0,0,0,1.7265878,"\int \frac{x \sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Int[(x*Sqrt[1 + x])/(x + Sqrt[x + Sqrt[1 + x]]),x]","\int \frac{x \sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-3 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$1}+3}\&\right]+\sqrt{x+1} \left(\frac{2 (x+4)}{3}-\sqrt{x+\sqrt{x+1}}\right)-\frac{1}{2} \sqrt{x+\sqrt{x+1}}+\frac{3}{4} \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[1 + x] + (2*(1 + x)^(3/2))/3 - (Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/2 + (5*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 + Log[2 - Sqrt[1 + x] - 3*(1 + x) + (1 + x)^2]/2 - (7*Defer[Subst][Defer[Int][(2 - x - 3*x^2 + x^4)^(-1), x], x, Sqrt[1 + x]])/2 + 5*Defer[Subst][Defer[Int][x/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 4*Defer[Subst][Defer[Int][x^2/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 4*Defer[Subst][Defer[Int][Sqrt[-1 + x + x^2]/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 2*Defer[Subst][Defer[Int][(x*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 4*Defer[Subst][Defer[Int][(x^2*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2395,0,0,0,1.3435772,"\int \frac{x \sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","Int[(x*Sqrt[1 + x])/(x + Sqrt[x + Sqrt[1 + x]]),x]","\int \frac{x \sqrt{1+x}}{x+\sqrt{x+\sqrt{1+x}}} \, dx","4 \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-5 \text{$\#$1}^2+3 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-3 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^3+6 \text{$\#$1}^2-10 \text{$\#$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,"2*Sqrt[1 + x] + (2*(1 + x)^(3/2))/3 - (Sqrt[x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/2 + (5*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])])/4 + Log[2 - Sqrt[1 + x] - 3*(1 + x) + (1 + x)^2]/2 - (7*Defer[Subst][Defer[Int][(2 - x - 3*x^2 + x^4)^(-1), x], x, Sqrt[1 + x]])/2 + 5*Defer[Subst][Defer[Int][x/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 4*Defer[Subst][Defer[Int][x^2/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] + 4*Defer[Subst][Defer[Int][Sqrt[-1 + x + x^2]/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 2*Defer[Subst][Defer[Int][(x*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]] - 4*Defer[Subst][Defer[Int][(x^2*Sqrt[-1 + x + x^2])/(2 - x - 3*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2396,1,266,0,0.2769266,"\int \frac{x^2}{\sqrt{\frac{b+a x}{d+c x}}} \, dx","Int[x^2/Sqrt[(b + a*x)/(d + c*x)],x]","-\frac{(3 a d+5 b c) (b c-a d)^2 \sqrt{\frac{a x+b}{c x+d}}}{12 a^2 c^2 \left(a-\frac{c (a x+b)}{c x+d}\right)^2}-\frac{\left(a^2 d^2+2 a b c d+5 b^2 c^2\right) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a x+b}{c x+d}}}{\sqrt{a}}\right)}{8 a^{7/2} c^{5/2}}+\frac{(c x+d) \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \sqrt{\frac{a x+b}{c x+d}}}{8 a^3 c^2}-\frac{(b c-a d)^2 \sqrt{\frac{a x+b}{c x+d}} \left(b-\frac{d (a x+b)}{c x+d}\right)}{3 a c \left(a-\frac{c (a x+b)}{c x+d}\right)^3}","\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,"((5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*Sqrt[(b + a*x)/(d + c*x)]*(d + c*x))/(8*a^3*c^2) - ((b*c - a*d)^2*(5*b*c + 3*a*d)*Sqrt[(b + a*x)/(d + c*x)])/(12*a^2*c^2*(a - (c*(b + a*x))/(d + c*x))^2) - ((b*c - a*d)^2*Sqrt[(b + a*x)/(d + c*x)]*(b - (d*(b + a*x))/(d + c*x)))/(3*a*c*(a - (c*(b + a*x))/(d + c*x))^3) - ((b*c - a*d)*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)])/Sqrt[a]])/(8*a^(7/2)*c^(5/2))","A",5,5,21,0.2381,1,"{1960, 413, 385, 199, 208}"
2397,1,245,0,2.2817489,"\int \frac{b+2 a x}{(-b+a x) (2 b+a x) \sqrt[4]{-1+b x+a x^2}} \, dx","Int[(b + 2*a*x)/((-b + a*x)*(2*b + a*x)*(-1 + b*x + a*x^2)^(1/4)),x]","\frac{2 \sqrt[4]{4 a+b^2} \sqrt[4]{\frac{a \left(-a x^2-b x+1\right)}{4 a+b^2}} \tan ^{-1}\left(\frac{\sqrt[4]{4 a+b^2} \sqrt[4]{1-\frac{(2 a x+b)^2}{4 a+b^2}}}{\sqrt{2} \sqrt[4]{a-2 b^2}}\right)}{a \sqrt[4]{a-2 b^2} \sqrt[4]{a x^2+b x-1}}-\frac{2 \sqrt[4]{4 a+b^2} \sqrt[4]{\frac{a \left(-a x^2-b x+1\right)}{4 a+b^2}} \tanh ^{-1}\left(\frac{\sqrt[4]{4 a+b^2} \sqrt[4]{1-\frac{(2 a x+b)^2}{4 a+b^2}}}{\sqrt{2} \sqrt[4]{a-2 b^2}}\right)}{a \sqrt[4]{a-2 b^2} \sqrt[4]{a x^2+b x-1}}","\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,"(2*(4*a + b^2)^(1/4)*((a*(1 - b*x - a*x^2))/(4*a + b^2))^(1/4)*ArcTan[((4*a + b^2)^(1/4)*(1 - (b + 2*a*x)^2/(4*a + b^2))^(1/4))/(Sqrt[2]*(a - 2*b^2)^(1/4))])/(a*(a - 2*b^2)^(1/4)*(-1 + b*x + a*x^2)^(1/4)) - (2*(4*a + b^2)^(1/4)*((a*(1 - b*x - a*x^2))/(4*a + b^2))^(1/4)*ArcTanh[((4*a + b^2)^(1/4)*(1 - (b + 2*a*x)^2/(4*a + b^2))^(1/4))/(Sqrt[2]*(a - 2*b^2)^(1/4))])/(a*(a - 2*b^2)^(1/4)*(-1 + b*x + a*x^2)^(1/4))","A",30,13,39,0.3333,1,"{6742, 749, 748, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
2398,1,411,0,2.795902,"\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","Int[(-1 + a*k*x + k*x^2)/((1 + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","\frac{\sqrt{1-x^2} \left(2 \sqrt{-k}-a k\right) \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{2 \sqrt{k} (k+1) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \left(a k+2 \sqrt{-k}\right) \sqrt{1-k^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{2 \sqrt{k} (k+1) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \left(2-a \sqrt{-k}\right) \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{2 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \left(a \sqrt{-k}+2\right) \sqrt{1-k^2 x^2} \Pi \left(-k;\sin ^{-1}(x)|k^2\right)}{2 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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,"((2*Sqrt[-k] - a*k)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/(2*Sqrt[k]*(1 + k)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - ((2*Sqrt[-k] + a*k)*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTanh[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/(2*Sqrt[k]*(1 + 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)] - ((2 - a*Sqrt[-k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/(2*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - ((2 + a*Sqrt[-k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[-k, ArcSin[x], k^2])/(2*Sqrt[(1 - x^2)*(1 - k^2*x^2)])","C",16,8,43,0.1860,1,"{6719, 6725, 419, 2113, 537, 571, 93, 208}"
2399,1,416,0,0.4150296,"\int \frac{\left(-b+x^3\right) \left(b+x^3\right)}{\sqrt[3]{a x^2+x^3}} \, dx","Int[((-b + x^3)*(b + x^3))/(a*x^2 + x^3)^(1/3),x]","-\frac{364 a^6 x^{2/3} \sqrt[3]{a+x} \log (x)}{6561 \sqrt[3]{a x^2+x^3}}-\frac{364 a^6 x^{2/3} \sqrt[3]{a+x} \log \left(\frac{\sqrt[3]{a+x}}{\sqrt[3]{x}}-1\right)}{2187 \sqrt[3]{a x^2+x^3}}-\frac{728 a^6 x^{2/3} \sqrt[3]{a+x} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+x}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2187 \sqrt{3} \sqrt[3]{a x^2+x^3}}-\frac{728 a^5 \left(a x^2+x^3\right)^{2/3}}{2187 x}+\frac{182}{729} a^4 \left(a x^2+x^3\right)^{2/3}-\frac{52}{243} a^3 x \left(a x^2+x^3\right)^{2/3}+\frac{26}{135} a^2 x^2 \left(a x^2+x^3\right)^{2/3}+\frac{b^2 x^{2/3} \sqrt[3]{a+x} \log (x)}{2 \sqrt[3]{a x^2+x^3}}+\frac{3 b^2 x^{2/3} \sqrt[3]{a+x} \log \left(\frac{\sqrt[3]{a+x}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{a x^2+x^3}}+\frac{\sqrt{3} b^2 x^{2/3} \sqrt[3]{a+x} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+x}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a x^2+x^3}}-\frac{8}{45} a x^3 \left(a x^2+x^3\right)^{2/3}+\frac{1}{6} x^4 \left(a x^2+x^3\right)^{2/3}","\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,"(182*a^4*(a*x^2 + x^3)^(2/3))/729 - (728*a^5*(a*x^2 + x^3)^(2/3))/(2187*x) - (52*a^3*x*(a*x^2 + x^3)^(2/3))/243 + (26*a^2*x^2*(a*x^2 + x^3)^(2/3))/135 - (8*a*x^3*(a*x^2 + x^3)^(2/3))/45 + (x^4*(a*x^2 + x^3)^(2/3))/6 - (728*a^6*x^(2/3)*(a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2187*Sqrt[3]*(a*x^2 + x^3)^(1/3)) + (Sqrt[3]*b^2*x^(2/3)*(a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(a*x^2 + x^3)^(1/3) - (364*a^6*x^(2/3)*(a + x)^(1/3)*Log[x])/(6561*(a*x^2 + x^3)^(1/3)) + (b^2*x^(2/3)*(a + x)^(1/3)*Log[x])/(2*(a*x^2 + x^3)^(1/3)) - (364*a^6*x^(2/3)*(a + x)^(1/3)*Log[-1 + (a + x)^(1/3)/x^(1/3)])/(2187*(a*x^2 + x^3)^(1/3)) + (3*b^2*x^(2/3)*(a + x)^(1/3)*Log[-1 + (a + x)^(1/3)/x^(1/3)])/(2*(a*x^2 + x^3)^(1/3))","B",12,4,26,0.1538,1,"{2053, 2011, 59, 2024}"
2400,0,0,0,0.7490824,"\int \frac{x}{\left(1-x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[x/((1 - x^2)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{x}{\left(1-x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","\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,"-1/2*Defer[Int][1/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - Defer[Int][1/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]/2","F",0,0,0,0,-1,"{}"
2401,1,209,0,0.200491,"\int \frac{1}{\sqrt[4]{-1+x^4} \left(-1-x^4+x^8\right)} \, dx","Int[1/((-1 + x^4)^(1/4)*(-1 - x^4 + x^8)),x]","-\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)}{2 \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)}{2 \sqrt{5}}-\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)}{2 \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)}{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,"-1/2*(((3 - Sqrt[5])/2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)])/Sqrt[5] - (((3 + Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(2*Sqrt[5]) - (((3 - Sqrt[5])/2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)])/(2*Sqrt[5]) - (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(2*Sqrt[5])","A",9,5,22,0.2273,0,"{1428, 377, 212, 206, 203}"
2402,1,189,0,0.287131,"\int \frac{-1+2 x^4}{\sqrt[4]{-1+x^4} \left(-1-x^4+x^8\right)} \, dx","Int[(-1 + 2*x^4)/((-1 + x^4)^(1/4)*(-1 - x^4 + x^8)),x]","-\frac{1}{2} \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)+\frac{1}{2} \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)-\frac{1}{2} \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)+\frac{1}{2} \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)","-\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,"-1/2*(((3 - Sqrt[5])/2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)]) + (((3 + Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/2 - (((3 - Sqrt[5])/2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(-1 + x^4)^(1/4)])/2 + (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/2","A",10,5,29,0.1724,0,"{6728, 377, 212, 206, 203}"
2403,1,209,0,0.1249359,"\int \frac{1}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Int[1/((1 + x^4)^(1/4)*(-1 + x^4 + x^8)),x]","-\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)}{2 \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)}{2 \sqrt{5}}-\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)}{2 \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)}{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,"-1/2*(((3 - Sqrt[5])/2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/Sqrt[5] - (((3 + Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5]) - (((3 - Sqrt[5])/2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5]) - (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5])","A",9,5,20,0.2500,0,"{1428, 377, 212, 206, 203}"
2404,1,189,0,0.3114951,"\int \frac{-2+x^4}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Int[(-2 + x^4)/((1 + x^4)^(1/4)*(-1 + x^4 + x^8)),x]","\frac{1}{2} \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)+\frac{1}{2} \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)+\frac{1}{2} \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)+\frac{1}{2} \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)","\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])/2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/2 + (((3 - Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/2 + (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/2 + (((3 - Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/2","A",10,5,25,0.2000,1,"{6728, 377, 212, 206, 203}"
2405,1,341,0,0.6066754,"\int \frac{\sqrt[4]{b x^3+a x^4} \left(-d+c x^8\right)}{x^8} \, dx","Int[((b*x^3 + a*x^4)^(1/4)*(-d + c*x^8))/x^8,x]","\frac{3 b^2 c x^{9/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{16 a^{7/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{3 b^2 c x^{9/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{16 a^{7/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{32768 a^5 d \left(a x^4+b x^3\right)^{5/4}}{348075 b^6 x^5}+\frac{8192 a^4 d \left(a x^4+b x^3\right)^{5/4}}{69615 b^5 x^6}-\frac{1024 a^3 d \left(a x^4+b x^3\right)^{5/4}}{7735 b^4 x^7}+\frac{256 a^2 d \left(a x^4+b x^3\right)^{5/4}}{1785 b^3 x^8}-\frac{16 a d \left(a x^4+b x^3\right)^{5/4}}{105 b^2 x^9}+\frac{1}{2} c x \sqrt[4]{a x^4+b x^3}+\frac{b c \sqrt[4]{a x^4+b x^3}}{8 a}+\frac{4 d \left(a x^4+b x^3\right)^{5/4}}{25 b x^{10}}","\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,"(b*c*(b*x^3 + a*x^4)^(1/4))/(8*a) + (c*x*(b*x^3 + a*x^4)^(1/4))/2 + (4*d*(b*x^3 + a*x^4)^(5/4))/(25*b*x^10) - (16*a*d*(b*x^3 + a*x^4)^(5/4))/(105*b^2*x^9) + (256*a^2*d*(b*x^3 + a*x^4)^(5/4))/(1785*b^3*x^8) - (1024*a^3*d*(b*x^3 + a*x^4)^(5/4))/(7735*b^4*x^7) + (8192*a^4*d*(b*x^3 + a*x^4)^(5/4))/(69615*b^5*x^6) - (32768*a^5*d*(b*x^3 + a*x^4)^(5/4))/(348075*b^6*x^5) + (3*b^2*c*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(7/4)*(b*x^3 + a*x^4)^(3/4)) - (3*b^2*c*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(7/4)*(b*x^3 + a*x^4)^(3/4))","A",16,11,28,0.3929,1,"{2052, 2004, 2024, 2032, 63, 331, 298, 203, 206, 2016, 2014}"
2406,1,73,0,0.4041046,"\int \frac{x^4 \left(2+x^5\right)}{\sqrt{1+x^5} \left(-1-x^5+a x^{10}\right)} \, dx","Int[(x^4*(2 + x^5))/(Sqrt[1 + x^5]*(-1 - x^5 + a*x^10)),x]","\frac{2 \tanh ^{-1}\left(\sqrt{4 a+1}-2 \sqrt{a} \sqrt{x^5+1}\right)}{5 \sqrt{a}}-\frac{2 \tanh ^{-1}\left(2 \sqrt{a} \sqrt{x^5+1}+\sqrt{4 a+1}\right)}{5 \sqrt{a}}","\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,"(2*ArcTanh[Sqrt[1 + 4*a] - 2*Sqrt[a]*Sqrt[1 + x^5]])/(5*Sqrt[a]) - (2*ArcTanh[Sqrt[1 + 4*a] + 2*Sqrt[a]*Sqrt[1 + x^5]])/(5*Sqrt[a])","A",7,5,32,0.1562,1,"{6715, 826, 1161, 618, 206}"
2407,1,81,0,0.378708,"\int \frac{x^4 \left(-2+x^5\right)}{\sqrt{-1+x^5} \left(1-x^5+a x^{10}\right)} \, dx","Int[(x^4*(-2 + x^5))/(Sqrt[-1 + x^5]*(1 - x^5 + a*x^10)),x]","\frac{\log \left(-\sqrt{a} \left(1-x^5\right)+\sqrt{a}-\sqrt{x^5-1}\right)}{5 \sqrt{a}}-\frac{\log \left(-\sqrt{a} \left(1-x^5\right)+\sqrt{a}+\sqrt{x^5-1}\right)}{5 \sqrt{a}}","\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,"Log[Sqrt[a] - Sqrt[a]*(1 - x^5) - Sqrt[-1 + x^5]]/(5*Sqrt[a]) - Log[Sqrt[a] - Sqrt[a]*(1 - x^5) + Sqrt[-1 + x^5]]/(5*Sqrt[a])","A",5,4,32,0.1250,1,"{6715, 826, 1164, 628}"
2408,1,73,0,0.4707122,"\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","Int[(x^4*(3 + x^5))/(Sqrt[1 + x^5]*(-1 + a - (1 + 2*a)*x^5 + a*x^10)),x]","\frac{2 \tanh ^{-1}\left(\sqrt{8 a+1}-2 \sqrt{a} \sqrt{x^5+1}\right)}{5 \sqrt{a}}-\frac{2 \tanh ^{-1}\left(2 \sqrt{a} \sqrt{x^5+1}+\sqrt{8 a+1}\right)}{5 \sqrt{a}}","\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,"(2*ArcTanh[Sqrt[1 + 8*a] - 2*Sqrt[a]*Sqrt[1 + x^5]])/(5*Sqrt[a]) - (2*ArcTanh[Sqrt[1 + 8*a] + 2*Sqrt[a]*Sqrt[1 + x^5]])/(5*Sqrt[a])","A",7,5,38,0.1316,1,"{6715, 826, 1161, 618, 206}"
2409,0,0,0,1.0360769,"\int \frac{1}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[(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{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]",1,"4*a*c*Defer[Subst][Defer[Int][x/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*Defer[Subst][Defer[Int][x^3/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2410,0,0,0,0.8081725,"\int \frac{1}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])^(-1),x]","\int \frac{1}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1} c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]",1,"4*a*c*Defer[Subst][Defer[Int][x/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*Defer[Subst][Defer[Int][x^3/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2411,0,0,0,0.3794667,"\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","Int[1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)),x]","\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","\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,"Defer[Int][1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3)), x]","F",0,0,0,0,-1,"{}"
2412,0,0,0,0.2968917,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)),x]","\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","-\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,"Defer[Int][1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3)), x]","F",0,0,0,0,-1,"{}"
2413,1,81,0,0.0130902,"\int \frac{1}{\sqrt[3]{1-3 x^2} \left(-3+x^2\right)} \, dx","Int[1/((1 - 3*x^2)^(1/3)*(-3 + x^2)),x]","-\frac{1}{4} \tan ^{-1}\left(\frac{1-\sqrt[3]{1-3 x^2}}{x}\right)+\frac{\tanh ^{-1}\left(\frac{\left(1-\sqrt[3]{1-3 x^2}\right)^2}{3 \sqrt{3} x}\right)}{4 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{4 \sqrt{3}}","-\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,"-1/4*ArcTan[(1 - (1 - 3*x^2)^(1/3))/x] - ArcTanh[x/Sqrt[3]]/(4*Sqrt[3]) + ArcTanh[(1 - (1 - 3*x^2)^(1/3))^2/(3*Sqrt[3]*x)]/(4*Sqrt[3])","A",1,1,19,0.05263,1,"{395}"
2414,1,418,0,0.6525828,"\int \frac{-a+x}{\sqrt[3]{x^2 (-a+x)} \left(a^2 d-2 a d x+(-1+d) x^2\right)} \, dx","Int[(-a + x)/((x^2*(-a + x))^(1/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","-\frac{x^{2/3} \sqrt[3]{x-a} \log \left(-2 a \sqrt{d} \left(\sqrt{d}+1\right)-2 (1-d) x\right)}{4 a d^{5/6} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{x^{2/3} \sqrt[3]{x-a} \log \left(2 (1-d) x-2 a \left(1-\sqrt{d}\right) \sqrt{d}\right)}{4 a d^{5/6} \sqrt[3]{-\left(x^2 (a-x)\right)}}-\frac{3 x^{2/3} \sqrt[3]{x-a} \log \left(-\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x}\right)}{4 a d^{5/6} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{3 x^{2/3} \sqrt[3]{x-a} \log \left(\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x}\right)}{4 a d^{5/6} \sqrt[3]{-\left(x^2 (a-x)\right)}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x-a} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x}}\right)}{2 a d^{5/6} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{x-a} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 a d^{5/6} \sqrt[3]{-\left(x^2 (a-x)\right)}}","\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,"-1/2*(Sqrt[3]*x^(2/3)*(-a + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(a*d^(5/6)*(-((a - x)*x^2))^(1/3)) + (Sqrt[3]*x^(2/3)*(-a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2*a*d^(5/6)*(-((a - x)*x^2))^(1/3)) - (x^(2/3)*(-a + x)^(1/3)*Log[-2*a*(1 + Sqrt[d])*Sqrt[d] - 2*(1 - d)*x])/(4*a*d^(5/6)*(-((a - x)*x^2))^(1/3)) + (x^(2/3)*(-a + x)^(1/3)*Log[-2*a*(1 - Sqrt[d])*Sqrt[d] + 2*(1 - d)*x])/(4*a*d^(5/6)*(-((a - x)*x^2))^(1/3)) - (3*x^(2/3)*(-a + x)^(1/3)*Log[-x^(1/3) - d^(1/6)*(-a + x)^(1/3)])/(4*a*d^(5/6)*(-((a - x)*x^2))^(1/3)) + (3*x^(2/3)*(-a + x)^(1/3)*Log[-x^(1/3) + d^(1/6)*(-a + x)^(1/3)])/(4*a*d^(5/6)*(-((a - x)*x^2))^(1/3))","B",9,5,39,0.1282,1,"{6719, 911, 105, 59, 91}"
2415,1,256,0,0.4328924,"\int \frac{b-a x^4+2 x^8}{\sqrt[4]{-b+a x^4} \left(b+3 a x^4\right)} \, dx","Int[(b - a*x^4 + 2*x^8)/((-b + a*x^4)^(1/4)*(b + 3*a*x^4)),x]","\frac{b \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{12 a^{9/4}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{12 a^{9/4}}+\frac{x \left(a x^4-b\right)^{3/4}}{6 a^2}-\frac{\left(3 a^2+2 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{18 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(3 a^2+2 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{18 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}}","\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,"(x*(-b + a*x^4)^(3/4))/(6*a^2) + (b*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(12*a^(9/4)) - ((3*a^2 + 2*b)*ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(18*a^(9/4)) + ((6*a^2 + b)*ArcTan[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(9*Sqrt[2]*a^(9/4)) + (b*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(12*a^(9/4)) - ((3*a^2 + 2*b)*ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(18*a^(9/4)) + ((6*a^2 + b)*ArcTanh[(Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(9*Sqrt[2]*a^(9/4))","A",15,7,37,0.1892,1,"{6725, 240, 212, 206, 203, 321, 377}"
2416,1,196,0,0.3239713,"\int \frac{d+c x^2}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x^2)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","-\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^2 c \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{4 a^3}+\frac{c \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}{20 a^3}-\frac{b^6 c}{28 a^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}+\frac{b^4 c}{12 a^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}","\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,"-1/28*(b^6*c)/(a^3*(a*x + Sqrt[b^2 + a^2*x^2])^(7/2)) + (b^4*c)/(12*a^3*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) - (b^2*d)/(3*a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) - (b^2*c*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(4*a^3) + (d*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/a + (c*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2))/(20*a^3)","A",8,5,31,0.1613,1,"{6742, 2117, 14, 2119, 448}"
2417,1,341,0,0.7517479,"\int \frac{\sqrt[4]{b x^3+a x^4} \left(-c+d x^8\right)}{x^4} \, dx","Int[((b*x^3 + a*x^4)^(1/4)*(-c + d*x^8))/x^4,x]","\frac{1463 b^6 d x^{9/4} (a x+b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{32768 a^{23/4} \left(a x^4+b x^3\right)^{3/4}}-\frac{1463 b^6 d x^{9/4} (a x+b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{32768 a^{23/4} \left(a x^4+b x^3\right)^{3/4}}+\frac{1463 b^5 d \sqrt[4]{a x^4+b x^3}}{49152 a^5}-\frac{209 b^4 d x \sqrt[4]{a x^4+b x^3}}{12288 a^4}+\frac{19 b^3 d x^2 \sqrt[4]{a x^4+b x^3}}{1536 a^3}-\frac{19 b^2 d x^3 \sqrt[4]{a x^4+b x^3}}{1920 a^2}-\frac{16 a c \left(a x^4+b x^3\right)^{5/4}}{45 b^2 x^5}+\frac{4 c \left(a x^4+b x^3\right)^{5/4}}{9 b x^6}+\frac{b d x^4 \sqrt[4]{a x^4+b x^3}}{120 a}+\frac{1}{6} d x^5 \sqrt[4]{a x^4+b x^3}","\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,"(1463*b^5*d*(b*x^3 + a*x^4)^(1/4))/(49152*a^5) - (209*b^4*d*x*(b*x^3 + a*x^4)^(1/4))/(12288*a^4) + (19*b^3*d*x^2*(b*x^3 + a*x^4)^(1/4))/(1536*a^3) - (19*b^2*d*x^3*(b*x^3 + a*x^4)^(1/4))/(1920*a^2) + (b*d*x^4*(b*x^3 + a*x^4)^(1/4))/(120*a) + (d*x^5*(b*x^3 + a*x^4)^(1/4))/6 + (4*c*(b*x^3 + a*x^4)^(5/4))/(9*b*x^6) - (16*a*c*(b*x^3 + a*x^4)^(5/4))/(45*b^2*x^5) + (1463*b^6*d*x^(9/4)*(b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(32768*a^(23/4)*(b*x^3 + a*x^4)^(3/4)) - (1463*b^6*d*x^(9/4)*(b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(32768*a^(23/4)*(b*x^3 + a*x^4)^(3/4))","A",16,11,28,0.3929,1,"{2052, 2016, 2014, 2021, 2024, 2032, 63, 331, 298, 203, 206}"
2418,0,0,0,0.2067475,"\int \frac{\left(b^2+a x^2\right)^{5/2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[(b^2 + a*x^2)^(5/2)/Sqrt[b + Sqrt[b^2 + a*x^2]],x]","\int \frac{\left(b^2+a x^2\right)^{5/2}}{\sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\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,"Defer[Int][(b^2 + a*x^2)^(5/2)/Sqrt[b + Sqrt[b^2 + a*x^2]], x]","F",0,0,0,0,-1,"{}"
2419,0,0,0,0.1640462,"\int \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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,"Defer[Int][Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",0,0,0,0,-1,"{}"
2420,0,0,0,15.7478163,"\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","Int[((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]","\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","-\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,"(-3*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(x*Sqrt[x*C[0] + x^2*C[3] + C[4]]), x])/(Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (4*C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(-1 + 2*x*C[3] - Sqrt[1 - 4*C[3]*C[4]])), x])/(Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (2*C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(1 + 2*x*C[3] - Sqrt[1 - 4*C[3]*C[4]])), x])/(Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (4*C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(-1 + 2*x*C[3] + Sqrt[1 - 4*C[3]*C[4]])), x])/(Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (2*C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(1 + 2*x*C[3] + Sqrt[1 - 4*C[3]*C[4]])), x])/(Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]])","F",0,0,0,0,-1,"{}"
2421,0,0,0,1.4999957,"\int \frac{1+x^6}{\sqrt[3]{x+x^5} \left(-1+x^6\right)} \, dx","Int[(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,"-((x*(1 + x^4)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^4)/(1 - I*Sqrt[3]), -x^4])/(x + x^5)^(1/3)) - (x*(1 + x^4)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^4)/(1 + I*Sqrt[3]), -x^4])/(x + x^5)^(1/3) - ((I - Sqrt[3])*x^3*(1 + x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^4, (-2*x^4)/(1 - I*Sqrt[3])])/(4*(I + Sqrt[3])*(x + x^5)^(1/3)) - ((I + Sqrt[3])*x^3*(1 + x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/(4*(I - Sqrt[3])*(x + x^5)^(1/3)) + (3*x*(1 + x^4)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^4])/(2*(x + x^5)^(1/3)) + (x^(1/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x)*(1 + x^6)^(1/3)), x], x, x^(2/3)])/(3*(x + x^5)^(1/3)) - ((1 - I*Sqrt[3])*x^(1/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(2/3)])/(3*(x + x^5)^(1/3)) - ((1 + I*Sqrt[3])*x^(1/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(2/3)])/(3*(x + x^5)^(1/3))","F",0,0,0,0,-1,"{}"
2422,1,845,0,0.9062845,"\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","Int[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{\sqrt[3]{2} (x-2)^{2/3} \tan ^{-1}\left(\frac{1-2^{2/3} \sqrt[3]{x-2}}{\sqrt{3}}\right) \left(-x^2+x+1\right)}{\sqrt{3} \sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}-\frac{\sqrt{\frac{3}{5}} \sqrt[3]{\frac{1}{2} \left(3+\sqrt{5}\right)} (x-2)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\frac{2}{3+\sqrt{5}}} \sqrt[3]{x-2}}{\sqrt{3}}\right) \left(-x^2+x+1\right)}{\sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}+\frac{\sqrt{\frac{3}{5}} \sqrt[3]{\frac{1}{2} \left(3-\sqrt{5}\right)} (x-2)^{2/3} \tan ^{-1}\left(\frac{1-2^{2/3} \sqrt[3]{3+\sqrt{5}} \sqrt[3]{x-2}}{\sqrt{3}}\right) \left(-x^2+x+1\right)}{\sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}-\frac{\sqrt[3]{2} (x-2)^{2/3} \log \left(\sqrt[3]{x-2}+\sqrt[3]{2}\right) \left(-x^2+x+1\right)}{3 \sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}-\frac{\sqrt[3]{\frac{1}{2} \left(3-\sqrt{5}\right)} (x-2)^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{x-2}+\sqrt[3]{3-\sqrt{5}}\right) \left(-x^2+x+1\right)}{\sqrt{5} \sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}+\frac{\sqrt[3]{\frac{1}{2} \left(3+\sqrt{5}\right)} (x-2)^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{x-2}+\sqrt[3]{3+\sqrt{5}}\right) \left(-x^2+x+1\right)}{\sqrt{5} \sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}+\frac{(x-2)^{2/3} \log \left((x-2)^{2/3}-\sqrt[3]{2} \sqrt[3]{x-2}+2^{2/3}\right) \left(-x^2+x+1\right)}{3\ 2^{2/3} \sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}+\frac{\sqrt[3]{\frac{1}{2} \left(3-\sqrt{5}\right)} (x-2)^{2/3} \log \left(2^{2/3} (x-2)^{2/3}-\sqrt[3]{2 \left(3-\sqrt{5}\right)} \sqrt[3]{x-2}+\left(3-\sqrt{5}\right)^{2/3}\right) \left(-x^2+x+1\right)}{2 \sqrt{5} \sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}-\frac{\sqrt[3]{\frac{1}{2} \left(3+\sqrt{5}\right)} (x-2)^{2/3} \log \left(2^{2/3} (x-2)^{2/3}-\sqrt[3]{2 \left(3+\sqrt{5}\right)} \sqrt[3]{x-2}+\left(3+\sqrt{5}\right)^{2/3}\right) \left(-x^2+x+1\right)}{2 \sqrt{5} \sqrt[3]{-(2-x)^2 \left(-x^2+x+1\right)^3}}-\frac{(2-x) \left(-x^2+x+1\right)}{2 x \sqrt[3]{-(2-x)^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^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*ArcTan[(1 - 2^(2/3)*(-2 + x)^(1/3))/Sqrt[3]])/(Sqrt[3]*(-((2 - x)^2*(1 + x - x^2)^3))^(1/3)) - (Sqrt[3/5]*((3 + Sqrt[5])/2)^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*ArcTan[(1 - 2*(2/(3 + Sqrt[5]))^(1/3)*(-2 + x)^(1/3))/Sqrt[3]])/(-((2 - x)^2*(1 + x - x^2)^3))^(1/3) + (Sqrt[3/5]*((3 - Sqrt[5])/2)^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*ArcTan[(1 - 2^(2/3)*(3 + Sqrt[5])^(1/3)*(-2 + x)^(1/3))/Sqrt[3]])/(-((2 - x)^2*(1 + x - x^2)^3))^(1/3) - (2^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*Log[2^(1/3) + (-2 + x)^(1/3)])/(3*(-((2 - x)^2*(1 + x - x^2)^3))^(1/3)) - (((3 - Sqrt[5])/2)^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*Log[(3 - Sqrt[5])^(1/3) + 2^(1/3)*(-2 + x)^(1/3)])/(Sqrt[5]*(-((2 - x)^2*(1 + x - x^2)^3))^(1/3)) + (((3 + Sqrt[5])/2)^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*Log[(3 + Sqrt[5])^(1/3) + 2^(1/3)*(-2 + x)^(1/3)])/(Sqrt[5]*(-((2 - x)^2*(1 + x - x^2)^3))^(1/3)) + ((-2 + x)^(2/3)*(1 + x - x^2)*Log[2^(2/3) - 2^(1/3)*(-2 + x)^(1/3) + (-2 + x)^(2/3)])/(3*2^(2/3)*(-((2 - x)^2*(1 + x - x^2)^3))^(1/3)) + (((3 - Sqrt[5])/2)^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*Log[(3 - Sqrt[5])^(2/3) - (2*(3 - Sqrt[5]))^(1/3)*(-2 + x)^(1/3) + 2^(2/3)*(-2 + x)^(2/3)])/(2*Sqrt[5]*(-((2 - x)^2*(1 + x - x^2)^3))^(1/3)) - (((3 + Sqrt[5])/2)^(1/3)*(-2 + x)^(2/3)*(1 + x - x^2)*Log[(3 + Sqrt[5])^(2/3) - (2*(3 + Sqrt[5]))^(1/3)*(-2 + x)^(1/3) + 2^(2/3)*(-2 + x)^(2/3)])/(2*Sqrt[5]*(-((2 - x)^2*(1 + x - x^2)^3))^(1/3))","B",31,12,46,0.2609,0,"{6688, 6719, 897, 1424, 199, 200, 31, 634, 617, 204, 628, 1374}"
2423,1,101,0,0.6426185,"\int \frac{b^8+a^8 x^8}{\sqrt{b^4+a^4 x^4} \left(-b^8+a^8 x^8\right)} \, dx","Int[(b^8 + a^8*x^8)/(Sqrt[b^4 + a^4*x^4]*(-b^8 + a^8*x^8)),x]","-\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}}\right)}{4 \sqrt{2} a b}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}}\right)}{4 \sqrt{2} a b}","-\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,"-1/2*x/Sqrt[b^4 + a^4*x^4] - ArcTan[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(4*Sqrt[2]*a*b) - ArcTanh[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(4*Sqrt[2]*a*b)","A",16,10,42,0.2381,1,"{6725, 220, 1404, 414, 523, 409, 1211, 1699, 206, 203}"
2424,1,189,0,0.3069361,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(x - Sqrt[1 + x]),x]","2 \sqrt{x+\sqrt{x+1}}+2 \sqrt{\frac{2}{5} \left(\sqrt{5}-2\right)} \tan ^{-1}\left(\frac{-2 \left(2-\sqrt{5}\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)+2 \sqrt{\frac{2}{5} \left(2+\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{$\#$1}^4-8 \text{$\#$1}^3+6 \text{$\#$1}^2-40 \text{$\#$1}+25\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2+3 \text{$\#$1}-10}\&\right]+2 \sqrt{x+\sqrt{x+1}}-3 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[x + Sqrt[1 + x]] + 2*Sqrt[(2*(-2 + Sqrt[5]))/5]*ArcTan[(3 + Sqrt[5] - 2*(2 - Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[-1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])] + 3*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + 2*Sqrt[(2*(2 + Sqrt[5]))/5]*ArcTanh[(3 - Sqrt[5] - 2*(2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])]","A",10,7,27,0.2593,0,"{1019, 1076, 621, 206, 1032, 724, 204}"
2425,1,189,0,0.2290378,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x-\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(x - Sqrt[1 + x]),x]","2 \sqrt{x+\sqrt{x+1}}+2 \sqrt{\frac{2}{5} \left(\sqrt{5}-2\right)} \tan ^{-1}\left(\frac{-2 \left(2-\sqrt{5}\right) \sqrt{x+1}+\sqrt{5}+3}{4 \sqrt{\sqrt{5}-1} \sqrt{x+\sqrt{x+1}}}\right)+3 \tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)+2 \sqrt{\frac{2}{5} \left(2+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{-2 \left(2+\sqrt{5}\right) \sqrt{x+1}-\sqrt{5}+3}{4 \sqrt{1+\sqrt{5}} \sqrt{x+\sqrt{x+1}}}\right)","-4 \text{RootSum}\left[\text{$\#$1}^4-8 \text{$\#$1}^3+6 \text{$\#$1}^2-40 \text{$\#$1}+25\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+2 \text{$\#$1} \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^3-6 \text{$\#$1}^2+3 \text{$\#$1}-10}\&\right]+2 \sqrt{x+\sqrt{x+1}}-3 \log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[x + Sqrt[1 + x]] + 2*Sqrt[(2*(-2 + Sqrt[5]))/5]*ArcTan[(3 + Sqrt[5] - 2*(2 - Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[-1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])] + 3*ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + 2*Sqrt[(2*(2 + Sqrt[5]))/5]*ArcTanh[(3 - Sqrt[5] - 2*(2 + Sqrt[5])*Sqrt[1 + x])/(4*Sqrt[1 + Sqrt[5]]*Sqrt[x + Sqrt[1 + x]])]","A",10,7,27,0.2593,0,"{1019, 1076, 621, 206, 1032, 724, 204}"
2426,1,454,0,1.5095699,"\int \frac{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{-d+c x^2} \, dx","Int[((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(-d + c*x^2),x]","\frac{2 \sqrt{d} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{c^{3/4}}+\frac{2 \sqrt{d} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{c^{3/4}}-\frac{2 \sqrt{d} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{c^{3/4}}-\frac{2 \sqrt{d} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{c^{3/4}}-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-c)+2 \text{$\#$1} a^2 d+\text{$\#$1} b^2 c}\&\right]-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}",1,"-(b^2/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])) + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(3*a) + (2*Sqrt[d]*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/c^(3/4) + (2*Sqrt[d]*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/c^(3/4) - (2*Sqrt[d]*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/c^(3/4) - (2*Sqrt[d]*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/c^(3/4)","B",21,9,42,0.2143,1,"{6725, 2117, 14, 2119, 1628, 826, 1166, 208, 205}"
2427,1,454,0,1.2169475,"\int \frac{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{-d+c x^2} \, dx","Int[((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(-d + c*x^2),x]","\frac{2 \sqrt{d} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{c^{3/4}}+\frac{2 \sqrt{d} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{c^{3/4}}-\frac{2 \sqrt{d} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{c^{3/4}}-\frac{2 \sqrt{d} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{c^{3/4}}-\frac{b^2}{a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}+\frac{\left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^5 (-c)+2 \text{$\#$1} a^2 d+\text{$\#$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,"-(b^2/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])) + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(3*a) + (2*Sqrt[d]*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/c^(3/4) + (2*Sqrt[d]*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/c^(3/4) - (2*Sqrt[d]*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/c^(3/4) - (2*Sqrt[d]*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/c^(3/4)","B",21,9,42,0.2143,1,"{6725, 2117, 14, 2119, 1628, 826, 1166, 208, 205}"
2428,0,0,0,1.7105352,"\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","Int[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]","\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","\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2429,0,0,0,2.716921,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-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{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-5 \text{$\#$1}^9+8 \text{$\#$1}^7-4 \text{$\#$1}^5-\text{$\#$1}^3+\text{$\#$1}}\&\right]+\frac{8}{5} \sqrt{x+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{32}{15} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{32}{15} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(-16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + 32*Defer[Subst][Defer[Int][x^2/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 16*Defer[Subst][Defer[Int][x^4/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2430,0,0,0,2.2396168,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + x]]*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+x}} \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^{11}-5 \text{$\#$1}^9+8 \text{$\#$1}^7-4 \text{$\#$1}^5-\text{$\#$1}^3+\text{$\#$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,"(-16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + 32*Defer[Subst][Defer[Int][x^2/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 16*Defer[Subst][Defer[Int][x^4/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2431,0,0,0,0.0334707,"\int \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]],x]","\int \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","\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,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",0,0,0,0,-1,"{}"
2432,0,0,0,0.0125332,"\int \frac{2+3 x}{\sqrt[3]{4+3 x^2} \left(-12+52 x+9 x^2\right)} \, dx","Int[(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,"Defer[Int][(2 + 3*x)/((4 + 3*x^2)^(1/3)*(-12 + 52*x + 9*x^2)), x]","F",0,0,0,0,-1,"{}"
2433,1,149,0,0.0668881,"\int \left(c+b x+a x^2\right)^{5/2} \, dx","Int[(c + b*x + a*x^2)^(5/2),x]","-\frac{5 \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{2 a x+b}{2 \sqrt{a} \sqrt{a x^2+b x+c}}\right)}{1024 a^{7/2}}+\frac{5 \left(b^2-4 a c\right)^2 (2 a x+b) \sqrt{a x^2+b x+c}}{512 a^3}-\frac{5 \left(b^2-4 a c\right) (2 a x+b) \left(a x^2+b x+c\right)^{3/2}}{192 a^2}+\frac{(2 a x+b) \left(a x^2+b x+c\right)^{5/2}}{12 a}","\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,"(5*(b^2 - 4*a*c)^2*(b + 2*a*x)*Sqrt[c + b*x + a*x^2])/(512*a^3) - (5*(b^2 - 4*a*c)*(b + 2*a*x)*(c + b*x + a*x^2)^(3/2))/(192*a^2) + ((b + 2*a*x)*(c + b*x + a*x^2)^(5/2))/(12*a) - (5*(b^2 - 4*a*c)^3*ArcTanh[(b + 2*a*x)/(2*Sqrt[a]*Sqrt[c + b*x + a*x^2])])/(1024*a^(7/2))","A",5,3,14,0.2143,1,"{612, 621, 206}"
2434,1,157,0,0.5488125,"\int \frac{1-x^4+x^8}{x^2 \left(-1+x^4\right)^{3/4} \left(-1-x^4+x^8\right)} \, dx","Int[(1 - x^4 + x^8)/(x^2*(-1 + x^4)^(3/4)*(-1 - x^4 + x^8)),x]","\frac{4 \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};-\frac{1}{4},1;\frac{7}{4};x^4,\frac{2 x^4}{1-\sqrt{5}}\right)}{3 \sqrt{5} \left(1-\sqrt{5}\right) \sqrt[4]{1-x^4}}-\frac{4 \sqrt[4]{x^4-1} x^3 F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{2 x^4}{1+\sqrt{5}},x^4\right)}{3 \sqrt{5} \left(1+\sqrt{5}\right) \sqrt[4]{1-x^4}}-\frac{\sqrt[4]{x^4-1}}{x}","-\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,"-((-1 + x^4)^(1/4)/x) + (4*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, -1/4, 1, 7/4, x^4, (2*x^4)/(1 - Sqrt[5])])/(3*Sqrt[5]*(1 - Sqrt[5])*(1 - x^4)^(1/4)) - (4*x^3*(-1 + x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (2*x^4)/(1 + Sqrt[5]), x^4])/(3*Sqrt[5]*(1 + Sqrt[5])*(1 - x^4)^(1/4))","C",9,5,35,0.1429,0,"{6728, 264, 1528, 511, 510}"
2435,1,1288,0,4.3374961,"\int \frac{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{d+c x^2} \, dx","Int[((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(d + c*x^2),x]","-\frac{b^2}{a \sqrt{a x+\sqrt{b^2+a^2 x^2}}}+\frac{\left(a x+\sqrt{b^2+a^2 x^2}\right)^{3/2}}{3 a}+\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}-\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{(-c)^{5/4}}-\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}+\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{(-c)^{5/4}}-\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}-\sqrt{2} (-c)^{3/4} \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{(-c)^{3/4}}+\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a x+\sqrt{b^2+a^2 x^2}} (-c)^{3/4}+\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{(-c)^{3/4}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} (-c)^{5/4}}+\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} (-c)^{5/4}}","-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,"-(b^2/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])) + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(3*a) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] - Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(-c)^(5/4) - (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] + Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(-c)^(5/4) - (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] - Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(-c)^(3/4) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] + Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(-c)^(3/4) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(5/4)) + (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(5/4))","B",33,11,42,0.2619,1,"{6725, 2117, 14, 2119, 1628, 826, 1169, 634, 618, 204, 628}"
2436,1,1288,0,3.5686303,"\int \frac{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{d+c x^2} \, dx","Int[((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(d + c*x^2),x]","-\frac{b^2}{a \sqrt{a x+\sqrt{b^2+a^2 x^2}}}+\frac{\left(a x+\sqrt{b^2+a^2 x^2}\right)^{3/2}}{3 a}+\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}-\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{(-c)^{5/4}}-\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}+\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{(-c)^{5/4}}-\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}-\sqrt{2} (-c)^{3/4} \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{(-c)^{3/4}}+\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a x+\sqrt{b^2+a^2 x^2}} (-c)^{3/4}+\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{(-c)^{3/4}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} (-c)^{5/4}}+\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} (-c)^{5/4}}","-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,"-(b^2/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])) + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(3*a) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] - Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(-c)^(5/4) - (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] + Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(-c)^(5/4) - (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] - Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(-c)^(3/4) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] + Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(-c)^(3/4) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(5/4)) + (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*(-c)^(5/4))","B",33,11,42,0.2619,1,"{6725, 2117, 14, 2119, 1628, 826, 1169, 634, 618, 204, 628}"
2437,0,0,0,0.134705,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[x + Sqrt[1 + x^2]], x]","F",0,0,0,0,-1,"{}"
2438,1,97,0,0.0149794,"\int \frac{1}{x \sqrt[3]{4-6 x+3 x^2}} \, dx","Int[1/(x*(4 - 6*x + 3*x^2)^(1/3)),x]","\frac{\log \left(-3 \sqrt[3]{2} \sqrt[3]{3 x^2-6 x+4}-3 x+6\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} (2-x)}{\sqrt{3} \sqrt[3]{3 x^2-6 x+4}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log (x)}{2\ 2^{2/3}}","\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,"-(ArcTan[1/Sqrt[3] + (2^(2/3)*(2 - x))/(Sqrt[3]*(4 - 6*x + 3*x^2)^(1/3))]/(2^(2/3)*Sqrt[3])) - Log[x]/(2*2^(2/3)) + Log[6 - 3*x - 3*2^(1/3)*(4 - 6*x + 3*x^2)^(1/3)]/(2*2^(2/3))","A",1,1,18,0.05556,1,"{750}"
2439,1,339,0,0.4644351,"\int \frac{x^2 \sqrt[4]{b x^3+a x^4}}{-b+a x} \, dx","Int[(x^2*(b*x^3 + a*x^4)^(1/4))/(-b + a*x),x]","-\frac{155 b^3 \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{64 a^{15/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{2} b^3 \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{a^{15/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{155 b^3 \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{64 a^{15/4} x^{3/4} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{2} b^3 \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{a^{15/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{101 b^2 \sqrt[4]{a x^4+b x^3}}{96 a^3}+\frac{13 b x \sqrt[4]{a x^4+b x^3}}{24 a^2}+\frac{x^2 \sqrt[4]{a x^4+b x^3}}{3 a}","-\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,"(101*b^2*(b*x^3 + a*x^4)^(1/4))/(96*a^3) + (13*b*x*(b*x^3 + a*x^4)^(1/4))/(24*a^2) + (x^2*(b*x^3 + a*x^4)^(1/4))/(3*a) - (155*b^3*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(64*a^(15/4)*x^(3/4)*(b + a*x)^(1/4)) + (2*2^(1/4)*b^3*(b*x^3 + a*x^4)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(15/4)*x^(3/4)*(b + a*x)^(1/4)) + (155*b^3*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(64*a^(15/4)*x^(3/4)*(b + a*x)^(1/4)) - (2*2^(1/4)*b^3*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(15/4)*x^(3/4)*(b + a*x)^(1/4))","A",27,11,28,0.3929,1,"{2042, 101, 157, 50, 63, 331, 298, 203, 206, 105, 93}"
2440,0,0,0,1.5031894,"\int \frac{-1+x^6}{\sqrt[3]{x+x^5} \left(1+x^6\right)} \, dx","Int[(-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,"-((x*(1 + x^4)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^4)/(1 - I*Sqrt[3]), -x^4])/(x + x^5)^(1/3)) - (x*(1 + x^4)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^4)/(1 + I*Sqrt[3]), -x^4])/(x + x^5)^(1/3) + ((I - Sqrt[3])*x^3*(1 + x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^4, (-2*x^4)/(1 - I*Sqrt[3])])/(4*(I + Sqrt[3])*(x + x^5)^(1/3)) + ((I + Sqrt[3])*x^3*(1 + x^4)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^4, (-2*x^4)/(1 + I*Sqrt[3])])/(4*(I - Sqrt[3])*(x + x^5)^(1/3)) + (3*x*(1 + x^4)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^4])/(2*(x + x^5)^(1/3)) - (x^(1/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x)*(1 + x^6)^(1/3)), x], x, x^(2/3)])/(3*(x + x^5)^(1/3)) + ((1 + I*Sqrt[3])*x^(1/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(2/3)])/(3*(x + x^5)^(1/3)) + ((1 - I*Sqrt[3])*x^(1/3)*(1 + x^4)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(2/3)])/(3*(x + x^5)^(1/3))","F",0,0,0,0,-1,"{}"
2441,1,555,0,2.1508318,"\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","Int[(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)}{4 \sqrt[4]{a}}+\frac{\left(1-\frac{1-a b}{\sqrt{1-2 a b}}\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)}{4 \sqrt[4]{a} \left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(\frac{1-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)}{4 \sqrt[4]{a} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[4]{a}}+\frac{\left(1-\frac{1-a b}{\sqrt{1-2 a b}}\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)}{4 \sqrt[4]{a} \left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(\frac{1-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)}{4 \sqrt[4]{a} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}","\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)]/(4*a^(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))])/(4*a^(1/4)*(1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(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))])/(4*a^(1/4)*(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)]/(4*a^(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))])/(4*a^(1/4)*(1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(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))])/(4*a^(1/4)*(1 + Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4))","B",16,8,41,0.1951,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2442,1,555,0,1.5336961,"\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","Int[(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)}{4 \sqrt[4]{a}}+\frac{\left(1-\frac{1-a b}{\sqrt{1-2 a b}}\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)}{4 \sqrt[4]{a} \left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(\frac{1-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)}{4 \sqrt[4]{a} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{4 \sqrt[4]{a}}+\frac{\left(1-\frac{1-a b}{\sqrt{1-2 a b}}\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)}{4 \sqrt[4]{a} \left(1-\sqrt{1-2 a b}\right)^{3/4} \sqrt[4]{-\sqrt{1-2 a b}-2 b+1}}+\frac{\left(\frac{1-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)}{4 \sqrt[4]{a} \left(\sqrt{1-2 a b}+1\right)^{3/4} \sqrt[4]{\sqrt{1-2 a b}-2 b+1}}","\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)]/(4*a^(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))])/(4*a^(1/4)*(1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(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))])/(4*a^(1/4)*(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)]/(4*a^(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))])/(4*a^(1/4)*(1 - Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b - Sqrt[1 - 2*a*b])^(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))])/(4*a^(1/4)*(1 + Sqrt[1 - 2*a*b])^(3/4)*(1 - 2*b + Sqrt[1 - 2*a*b])^(1/4))","B",16,8,41,0.1951,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2443,1,605,0,2.9430146,"\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","Int[(-b + c*x^4 + 2*a*x^8)/((-b + a*x^4)^(1/4)*(b - c*x^4 + a*x^8)),x]","\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)}{2 \sqrt[4]{a} \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(c-\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}\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)}{2 \sqrt[4]{a} \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)}{2 \sqrt[4]{a} \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(c-\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}\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)}{2 \sqrt[4]{a} \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}+\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[\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,"ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(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))])/(2*a^(1/4)*(-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(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))])/(2*a^(1/4)*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(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))])/(2*a^(1/4)*(-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(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))])/(2*a^(1/4)*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4))","B",16,8,44,0.1818,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2444,1,605,0,2.2204008,"\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","Int[(-b + c*x^4 + 2*a*x^8)/((-b + a*x^4)^(1/4)*(b - c*x^4 + a*x^8)),x]","\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)}{2 \sqrt[4]{a} \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(c-\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}\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)}{2 \sqrt[4]{a} \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)}{2 \sqrt[4]{a} \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(c-\frac{2 a b-c^2}{\sqrt{c^2-4 a b}}\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)}{2 \sqrt[4]{a} \left(\sqrt{c^2-4 a b}+c\right)^{3/4} \sqrt[4]{\sqrt{c^2-4 a b}-2 b+c}}+\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[\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,"ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(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))])/(2*a^(1/4)*(-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(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))])/(2*a^(1/4)*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4)) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/a^(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))])/(2*a^(1/4)*(-c + Sqrt[-4*a*b + c^2])^(3/4)*(2*b - c + Sqrt[-4*a*b + c^2])^(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))])/(2*a^(1/4)*(c + Sqrt[-4*a*b + c^2])^(3/4)*(-2*b + c + Sqrt[-4*a*b + c^2])^(1/4))","B",16,8,44,0.1818,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2445,1,359,0,0.8010139,"\int \frac{\sqrt[4]{-b x^3+a x^4} \left(-d+c x^8\right)}{x^4} \, dx","Int[((-(b*x^3) + a*x^4)^(1/4)*(-d + c*x^8))/x^4,x]","\frac{1463 b^6 c x^{9/4} (a x-b)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{32768 a^{23/4} \left(a x^4-b x^3\right)^{3/4}}-\frac{1463 b^6 c x^{9/4} (a x-b)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{32768 a^{23/4} \left(a x^4-b x^3\right)^{3/4}}-\frac{1463 b^5 c \sqrt[4]{a x^4-b x^3}}{49152 a^5}-\frac{209 b^4 c x \sqrt[4]{a x^4-b x^3}}{12288 a^4}-\frac{19 b^3 c x^2 \sqrt[4]{a x^4-b x^3}}{1536 a^3}-\frac{19 b^2 c x^3 \sqrt[4]{a x^4-b x^3}}{1920 a^2}-\frac{16 a d \left(a x^4-b x^3\right)^{5/4}}{45 b^2 x^5}-\frac{b c x^4 \sqrt[4]{a x^4-b x^3}}{120 a}+\frac{1}{6} c x^5 \sqrt[4]{a x^4-b x^3}-\frac{4 d \left(a x^4-b x^3\right)^{5/4}}{9 b x^6}","\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,"(-1463*b^5*c*(-(b*x^3) + a*x^4)^(1/4))/(49152*a^5) - (209*b^4*c*x*(-(b*x^3) + a*x^4)^(1/4))/(12288*a^4) - (19*b^3*c*x^2*(-(b*x^3) + a*x^4)^(1/4))/(1536*a^3) - (19*b^2*c*x^3*(-(b*x^3) + a*x^4)^(1/4))/(1920*a^2) - (b*c*x^4*(-(b*x^3) + a*x^4)^(1/4))/(120*a) + (c*x^5*(-(b*x^3) + a*x^4)^(1/4))/6 - (4*d*(-(b*x^3) + a*x^4)^(5/4))/(9*b*x^6) - (16*a*d*(-(b*x^3) + a*x^4)^(5/4))/(45*b^2*x^5) + (1463*b^6*c*x^(9/4)*(-b + a*x)^(3/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(32768*a^(23/4)*(-(b*x^3) + a*x^4)^(3/4)) - (1463*b^6*c*x^(9/4)*(-b + a*x)^(3/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(32768*a^(23/4)*(-(b*x^3) + a*x^4)^(3/4))","A",16,11,29,0.3793,1,"{2052, 2016, 2014, 2021, 2024, 2032, 63, 331, 298, 203, 206}"
2446,0,0,0,0.1458309,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^6} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]]/x^6,x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^6} \, dx","\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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/x^6, x]","F",0,0,0,0,-1,"{}"
2447,0,0,0,0.6827883,"\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^6 \sqrt{b^2+a x^2}} \, dx","Int[Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^6*Sqrt[b^2 + a*x^2]),x]","\int \frac{\sqrt{b+\sqrt{b^2+a x^2}}}{x^6 \sqrt{b^2+a x^2}} \, dx","\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,"Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(x^6*Sqrt[b^2 + a*x^2]), x]","F",0,0,0,0,-1,"{}"
2448,1,129,0,0.1497364,"\int \sqrt{d+\sqrt{c+\sqrt{b+a x}}} \, dx","Int[Sqrt[d + Sqrt[c + Sqrt[b + a*x]]],x]","-\frac{8 \left(c-3 d^2\right) \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{5/2}}{5 a}+\frac{8 d \left(c-d^2\right) \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{3/2}}{3 a}+\frac{8 \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{9/2}}{9 a}-\frac{24 d \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{7/2}}{7 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*(c - d^2)*(d + Sqrt[c + Sqrt[b + a*x]])^(3/2))/(3*a) - (8*(c - 3*d^2)*(d + Sqrt[c + Sqrt[b + a*x]])^(5/2))/(5*a) - (24*d*(d + Sqrt[c + Sqrt[b + a*x]])^(7/2))/(7*a) + (8*(d + Sqrt[c + Sqrt[b + a*x]])^(9/2))/(9*a)","A",5,3,21,0.1429,1,"{371, 1398, 772}"
2449,1,270,0,0.3379034,"\int \frac{1}{\left(-b+a x^2\right) \sqrt[3]{-x+x^3}} \, dx","Int[1/((-b + a*x^2)*(-x + x^3)^(1/3)),x]","-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2-1}}+\sqrt[3]{b}\right)}{2 b^{2/3} \sqrt[3]{x^3-x} \sqrt[3]{a-b}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{x^{4/3} (a-b)^{2/3}}{\left(x^2-1\right)^{2/3}}-\frac{\sqrt[3]{b} x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2-1}}+b^{2/3}\right)}{4 b^{2/3} \sqrt[3]{x^3-x} \sqrt[3]{a-b}}+\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[3]{b}-\frac{2 x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2-1}}}{\sqrt{3} \sqrt[3]{b}}\right)}{2 b^{2/3} \sqrt[3]{x^3-x} \sqrt[3]{a-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,"(Sqrt[3]*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(b^(1/3) - (2*(a - b)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3))/(Sqrt[3]*b^(1/3))])/(2*(a - b)^(1/3)*b^(2/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[b^(1/3) + ((a - b)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(2*(a - b)^(1/3)*b^(2/3)*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[b^(2/3) + ((a - b)^(2/3)*x^(4/3))/(-1 + x^2)^(2/3) - ((a - b)^(1/3)*b^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(4*(a - b)^(1/3)*b^(2/3)*(-x + x^3)^(1/3))","A",10,10,23,0.4348,1,"{2056, 466, 465, 377, 200, 31, 634, 617, 204, 628}"
2450,1,728,0,0.7909216,"\int \frac{1}{x^3 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x^3*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","-\frac{\left(3-4 (-1)^{2/3}\right) (x+1)}{20 x \sqrt[3]{x^3+x^2}}-\frac{\left(3+4 \sqrt[3]{-1}\right) (x+1)}{20 x \sqrt[3]{x^3+x^2}}+\frac{x+1}{20 x \sqrt[3]{x^3+x^2}}+\frac{3 (x+1)}{8 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(5+16 i \sqrt{3}\right) (x+1)}{40 \sqrt[3]{x^3+x^2}}+\frac{\left(5-16 i \sqrt{3}\right) (x+1)}{40 \sqrt[3]{x^3+x^2}}+\frac{17 (x+1)}{40 \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log (1-x)}{6 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\sqrt[3]{-1} x+1\right)}{6 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log \left(1-(-1)^{2/3} x\right)}{6 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+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}}+\frac{3 \left(x^3+x^2\right)^{2/3} \left(9 x^2-6 x+5\right)}{40 x^4}",1,"(17*(1 + x))/(40*(x^2 + x^3)^(1/3)) + ((5 - (16*I)*Sqrt[3])*(1 + x))/(40*(x^2 + x^3)^(1/3)) + ((5 + (16*I)*Sqrt[3])*(1 + x))/(40*(x^2 + x^3)^(1/3)) + (3*(1 + x))/(8*x^2*(x^2 + x^3)^(1/3)) + (1 + x)/(20*x*(x^2 + x^3)^(1/3)) - ((3 + 4*(-1)^(1/3))*(1 + x))/(20*x*(x^2 + x^3)^(1/3)) - ((3 - 4*(-1)^(2/3))*(1 + x))/(20*x*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*Sqrt[3]*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - x])/(6*2^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 + (-1)^(1/3)*x])/(6*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - (-1)^(2/3)*x])/(6*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/2^(1/3)])/(2*2^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3)])/(2*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3)])/(2*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3))","C",18,6,22,0.2727,1,"{2056, 6725, 129, 155, 12, 91}"
2451,1,728,0,0.640055,"\int \frac{1}{x^3 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x^3*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","-\frac{\left(3-4 (-1)^{2/3}\right) (x+1)}{20 x \sqrt[3]{x^3+x^2}}-\frac{\left(3+4 \sqrt[3]{-1}\right) (x+1)}{20 x \sqrt[3]{x^3+x^2}}+\frac{x+1}{20 x \sqrt[3]{x^3+x^2}}+\frac{3 (x+1)}{8 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(5+16 i \sqrt{3}\right) (x+1)}{40 \sqrt[3]{x^3+x^2}}+\frac{\left(5-16 i \sqrt{3}\right) (x+1)}{40 \sqrt[3]{x^3+x^2}}+\frac{17 (x+1)}{40 \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log (1-x)}{6 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\sqrt[3]{-1} x+1\right)}{6 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \sqrt[3]{x+1} \log \left(1-(-1)^{2/3} x\right)}{6 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \sqrt[3]{x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+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}}+\frac{3 \left(x^3+x^2\right)^{2/3} \left(9 x^2-6 x+5\right)}{40 x^4}",1,"(17*(1 + x))/(40*(x^2 + x^3)^(1/3)) + ((5 - (16*I)*Sqrt[3])*(1 + x))/(40*(x^2 + x^3)^(1/3)) + ((5 + (16*I)*Sqrt[3])*(1 + x))/(40*(x^2 + x^3)^(1/3)) + (3*(1 + x))/(8*x^2*(x^2 + x^3)^(1/3)) + (1 + x)/(20*x*(x^2 + x^3)^(1/3)) - ((3 + 4*(-1)^(1/3))*(1 + x))/(20*x*(x^2 + x^3)^(1/3)) - ((3 - 4*(-1)^(2/3))*(1 + x))/(20*x*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*Sqrt[3]*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - x])/(6*2^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 + (-1)^(1/3)*x])/(6*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - (-1)^(2/3)*x])/(6*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/2^(1/3)])/(2*2^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3)])/(2*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3)])/(2*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3))","C",18,6,22,0.2727,1,"{2056, 6725, 129, 155, 12, 91}"
2452,1,2306,0,3.9457513,"\int \frac{1}{x^6 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^6*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x+\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{a} x\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(810 a^8-918 b^{5/3} a^{16/3}+1071 b^{10/3} a^{8/3}-1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(810 a^8-918 (-1)^{2/3} b^{5/3} a^{16/3}-1071 \sqrt[3]{-1} b^{10/3} a^{8/3}-1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(810 a^8+918 \sqrt[3]{-1} b^{5/3} a^{16/3}+1071 (-1)^{2/3} b^{10/3} a^{8/3}-1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(90 a^{16/3}-102 b^{5/3} a^{8/3}+119 b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(90 a^{16/3}-102 (-1)^{2/3} b^{5/3} a^{8/3}-119 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(90 a^{16/3}+102 \sqrt[3]{-1} b^{5/3} a^{8/3}+119 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(15 a^{8/3}-17 b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(15 a^{8/3}+17 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(15 a^{8/3}-17 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(7290 a^{15}-8262 b^{5/3} a^{37/3}+9639 b^{10/3} a^{29/3}-11781 b^5 a^7+15708 b^{20/3} a^{13/3}-26180 b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(7290 a^{15}-8262 (-1)^{2/3} b^{5/3} a^{37/3}-9639 \sqrt[3]{-1} b^{10/3} a^{29/3}-11781 b^5 a^7+15708 (-1)^{2/3} b^{20/3} a^{13/3}+26180 \sqrt[3]{-1} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(7290 a^{15}+8262 \sqrt[3]{-1} b^{5/3} a^{37/3}+9639 (-1)^{2/3} b^{10/3} a^{29/3}-11781 b^5 a^7-15708 \sqrt[3]{-1} b^{20/3} a^{13/3}-26180 (-1)^{2/3} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(2430 a^{12}-2754 b^{5/3} a^{28/3}+3213 b^{10/3} a^{20/3}-3927 b^5 a^4+5236 b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(2430 a^{12}+2754 \sqrt[3]{-1} b^{5/3} a^{28/3}+3213 (-1)^{2/3} b^{10/3} a^{20/3}-3927 b^5 a^4-5236 \sqrt[3]{-1} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(2430 a^{12}-2754 (-1)^{2/3} b^{5/3} a^{28/3}-3213 \sqrt[3]{-1} b^{10/3} a^{20/3}-3927 b^5 a^4+5236 (-1)^{2/3} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 \left(x a^3+b^2\right)}{17 b^3 x^5 \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/52360*((7290*a^15 - 8262*a^(37/3)*b^(5/3) + 9639*a^(29/3)*b^(10/3) - 11781*a^7*b^5 + 15708*a^(13/3)*b^(20/3) - 26180*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(b^13*(b^2*x^2 + a^3*x^3)^(1/3)) - ((7290*a^15 - 8262*(-1)^(2/3)*a^(37/3)*b^(5/3) - 9639*(-1)^(1/3)*a^(29/3)*b^(10/3) - 11781*a^7*b^5 + 15708*(-1)^(2/3)*a^(13/3)*b^(20/3) + 26180*(-1)^(1/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) - ((7290*a^15 + 8262*(-1)^(1/3)*a^(37/3)*b^(5/3) + 9639*(-1)^(2/3)*a^(29/3)*b^(10/3) - 11781*a^7*b^5 - 15708*(-1)^(1/3)*a^(13/3)*b^(20/3) - 26180*(-1)^(2/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*(b^2 + a^3*x))/(17*b^3*x^5*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(15*a^(8/3) - 17*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(15*a^(8/3) + 17*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(15*a^(8/3) - 17*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(90*a^(16/3) - 102*a^(8/3)*b^(5/3) + 119*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(90*a^(16/3) - 102*(-1)^(2/3)*a^(8/3)*b^(5/3) - 119*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(90*a^(16/3) + 102*(-1)^(1/3)*a^(8/3)*b^(5/3) + 119*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) - (a*(810*a^8 - 918*a^(16/3)*b^(5/3) + 1071*a^(8/3)*b^(10/3) - 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - (a*(810*a^8 - 918*(-1)^(2/3)*a^(16/3)*b^(5/3) - 1071*(-1)^(1/3)*a^(8/3)*b^(10/3) - 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - (a*(810*a^8 + 918*(-1)^(1/3)*a^(16/3)*b^(5/3) + 1071*(-1)^(2/3)*a^(8/3)*b^(10/3) - 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2430*a^12 - 2754*a^(28/3)*b^(5/3) + 3213*a^(20/3)*b^(10/3) - 3927*a^4*b^5 + 5236*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2430*a^12 + 2754*(-1)^(1/3)*a^(28/3)*b^(5/3) + 3213*(-1)^(2/3)*a^(20/3)*b^(10/3) - 3927*a^4*b^5 - 5236*(-1)^(1/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2430*a^12 - 2754*(-1)^(2/3)*a^(28/3)*b^(5/3) - 3213*(-1)^(1/3)*a^(20/3)*b^(10/3) - 3927*a^4*b^5 + 5236*(-1)^(2/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - a^(1/3)*x])/(6*b^3*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",27,6,34,0.1765,1,"{2056, 6725, 129, 155, 12, 91}"
2453,1,2306,0,3.516621,"\int \frac{1}{x^6 \left(-b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^6*(-b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-\sqrt[3]{a} x\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x+\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{a} x\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}+b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}-\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}+(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(810 a^8-918 b^{5/3} a^{16/3}+1071 b^{10/3} a^{8/3}-1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(810 a^8-918 (-1)^{2/3} b^{5/3} a^{16/3}-1071 \sqrt[3]{-1} b^{10/3} a^{8/3}-1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(810 a^8+918 \sqrt[3]{-1} b^{5/3} a^{16/3}+1071 (-1)^{2/3} b^{10/3} a^{8/3}-1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(90 a^{16/3}-102 b^{5/3} a^{8/3}+119 b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(90 a^{16/3}-102 (-1)^{2/3} b^{5/3} a^{8/3}-119 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(90 a^{16/3}+102 \sqrt[3]{-1} b^{5/3} a^{8/3}+119 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(15 a^{8/3}-17 b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(15 a^{8/3}+17 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(15 a^{8/3}-17 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(7290 a^{15}-8262 b^{5/3} a^{37/3}+9639 b^{10/3} a^{29/3}-11781 b^5 a^7+15708 b^{20/3} a^{13/3}-26180 b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(7290 a^{15}-8262 (-1)^{2/3} b^{5/3} a^{37/3}-9639 \sqrt[3]{-1} b^{10/3} a^{29/3}-11781 b^5 a^7+15708 (-1)^{2/3} b^{20/3} a^{13/3}+26180 \sqrt[3]{-1} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(7290 a^{15}+8262 \sqrt[3]{-1} b^{5/3} a^{37/3}+9639 (-1)^{2/3} b^{10/3} a^{29/3}-11781 b^5 a^7-15708 \sqrt[3]{-1} b^{20/3} a^{13/3}-26180 (-1)^{2/3} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(2430 a^{12}-2754 b^{5/3} a^{28/3}+3213 b^{10/3} a^{20/3}-3927 b^5 a^4+5236 b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(2430 a^{12}+2754 \sqrt[3]{-1} b^{5/3} a^{28/3}+3213 (-1)^{2/3} b^{10/3} a^{20/3}-3927 b^5 a^4-5236 \sqrt[3]{-1} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(2430 a^{12}-2754 (-1)^{2/3} b^{5/3} a^{28/3}-3213 \sqrt[3]{-1} b^{10/3} a^{20/3}-3927 b^5 a^4+5236 (-1)^{2/3} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 \left(x a^3+b^2\right)}{17 b^3 x^5 \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/52360*((7290*a^15 - 8262*a^(37/3)*b^(5/3) + 9639*a^(29/3)*b^(10/3) - 11781*a^7*b^5 + 15708*a^(13/3)*b^(20/3) - 26180*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(b^13*(b^2*x^2 + a^3*x^3)^(1/3)) - ((7290*a^15 - 8262*(-1)^(2/3)*a^(37/3)*b^(5/3) - 9639*(-1)^(1/3)*a^(29/3)*b^(10/3) - 11781*a^7*b^5 + 15708*(-1)^(2/3)*a^(13/3)*b^(20/3) + 26180*(-1)^(1/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) - ((7290*a^15 + 8262*(-1)^(1/3)*a^(37/3)*b^(5/3) + 9639*(-1)^(2/3)*a^(29/3)*b^(10/3) - 11781*a^7*b^5 - 15708*(-1)^(1/3)*a^(13/3)*b^(20/3) - 26180*(-1)^(2/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*(b^2 + a^3*x))/(17*b^3*x^5*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(15*a^(8/3) - 17*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(15*a^(8/3) + 17*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(1/3)*(15*a^(8/3) - 17*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(90*a^(16/3) - 102*a^(8/3)*b^(5/3) + 119*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(90*a^(16/3) - 102*(-1)^(2/3)*a^(8/3)*b^(5/3) - 119*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(2/3)*(90*a^(16/3) + 102*(-1)^(1/3)*a^(8/3)*b^(5/3) + 119*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) - (a*(810*a^8 - 918*a^(16/3)*b^(5/3) + 1071*a^(8/3)*b^(10/3) - 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - (a*(810*a^8 - 918*(-1)^(2/3)*a^(16/3)*b^(5/3) - 1071*(-1)^(1/3)*a^(8/3)*b^(10/3) - 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - (a*(810*a^8 + 918*(-1)^(1/3)*a^(16/3)*b^(5/3) + 1071*(-1)^(2/3)*a^(8/3)*b^(10/3) - 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2430*a^12 - 2754*a^(28/3)*b^(5/3) + 3213*a^(20/3)*b^(10/3) - 3927*a^4*b^5 + 5236*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2430*a^12 + 2754*(-1)^(1/3)*a^(28/3)*b^(5/3) + 3213*(-1)^(2/3)*a^(20/3)*b^(10/3) - 3927*a^4*b^5 - 5236*(-1)^(1/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2430*a^12 - 2754*(-1)^(2/3)*a^(28/3)*b^(5/3) - 3213*(-1)^(1/3)*a^(20/3)*b^(10/3) - 3927*a^4*b^5 + 5236*(-1)^(2/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - a^(1/3)*x])/(6*b^3*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) + b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) - (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) + (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",27,6,34,0.1765,1,"{2056, 6725, 129, 155, 12, 91}"
2454,0,0,0,0.9602495,"\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","Int[((-1 + x^2)*(1 + x + x^2)*Sqrt[1 + 3*x^2 + x^4])/(1 + x + x^2 + x^3 + x^4)^2,x]","\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","\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,"-2*Defer[Int][Sqrt[1 + 3*x^2 + x^4]/(1 + x + x^2 + x^3 + x^4)^2, x] - 2*Defer[Int][(x*Sqrt[1 + 3*x^2 + x^4])/(1 + x + x^2 + x^3 + x^4)^2, x] - Defer[Int][(x^2*Sqrt[1 + 3*x^2 + x^4])/(1 + x + x^2 + x^3 + x^4)^2, x] + Defer[Int][Sqrt[1 + 3*x^2 + x^4]/(1 + x + x^2 + x^3 + x^4), x]","F",0,0,0,0,-1,"{}"
2455,0,0,0,0.6163875,"\int \frac{b+a x^4}{\left(-b+a x^4\right) \sqrt[4]{b^2+c x^4+a^2 x^8}} \, dx","Int[(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,"(x*(1 + (2*a^2*x^4)/(c - Sqrt[-4*a^2*b^2 + c^2]))^(1/4)*(1 + (2*a^2*x^4)/(c + Sqrt[-4*a^2*b^2 + c^2]))^(1/4)*AppellF1[1/4, 1/4, 1/4, 5/4, (-2*a^2*x^4)/(c - Sqrt[-4*a^2*b^2 + c^2]), (-2*a^2*x^4)/(c + Sqrt[-4*a^2*b^2 + c^2])])/(b^2 + c*x^4 + a^2*x^8)^(1/4) + 2*b*Defer[Int][1/((-b + a*x^4)*(b^2 + c*x^4 + a^2*x^8)^(1/4)), x]","F",0,0,0,0,-1,"{}"
2456,1,60,0,0.4503294,"\int \frac{2 x^4-x^9}{\sqrt{-1+x^5} \left(a-a x^5+x^{10}\right)} \, dx","Int[(2*x^4 - x^9)/(Sqrt[-1 + x^5]*(a - a*x^5 + x^10)),x]","\frac{\log \left(\sqrt{a} \sqrt{x^5-1}+x^5\right)}{5 \sqrt{a}}-\frac{\log \left(x^5-\sqrt{a} \sqrt{x^5-1}\right)}{5 \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}}-\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*Log[x^5 - Sqrt[a]*Sqrt[-1 + x^5]]/Sqrt[a] + Log[x^5 + Sqrt[a]*Sqrt[-1 + x^5]]/(5*Sqrt[a])","A",6,5,34,0.1471,1,"{1593, 6715, 826, 1164, 628}"
2457,1,199,0,0.560111,"\int \frac{1+x^2}{\left(-1+x^2\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(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}}-\frac{2 \tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}+\frac{2 \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}-\frac{2 \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}+\frac{2 \tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}","\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*ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[1 + Sqrt[2]] + (2*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[-1 + Sqrt[2]] - (2*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[1 + Sqrt[2]] + (2*ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[-1 + Sqrt[2]]","A",23,12,28,0.4286,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 204, 206, 207, 203}"
2458,1,453,0,1.667454,"\int \frac{d+c x^2}{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x^2)/((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{\sqrt[4]{c} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}-\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{\sqrt[4]{c} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{\sqrt[4]{c} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{\sqrt[4]{c} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}-\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}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)+2 \text{$\#$1}^3 a^2 d+\text{$\#$1}^3 b^2 c}\&\right]-\frac{b^2}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}+\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}",1,"-1/3*b^2/(a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/a - (2*Sqrt[d]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]) - (2*Sqrt[d]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]) - (2*Sqrt[d]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]) - (2*Sqrt[d]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]])","B",23,10,42,0.2381,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 208, 205}"
2459,1,453,0,1.2933793,"\int \frac{d+c x^2}{\left(-d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x^2)/((-d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{\sqrt[4]{c} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}-\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{\sqrt[4]{c} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}\right)}{\sqrt[4]{c} \sqrt{a \sqrt{d}-\sqrt{a^2 d+b^2 c}}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{\sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}\right)}{\sqrt[4]{c} \sqrt{\sqrt{a^2 d+b^2 c}+a \sqrt{d}}}-\frac{b^2}{3 a \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}+\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x}}{a}","a d \text{RootSum}\left[\text{$\#$1}^8 c-4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{\text{$\#$1}^4 \left(-\log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)\right)-b^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{\text{$\#$1}^7 (-c)+2 \text{$\#$1}^3 a^2 d+\text{$\#$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*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/a - (2*Sqrt[d]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]) - (2*Sqrt[d]*ArcTan[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]) - (2*Sqrt[d]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] - Sqrt[b^2*c + a^2*d]]) - (2*Sqrt[d]*ArcTanh[(c^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]]])/(c^(1/4)*Sqrt[a*Sqrt[d] + Sqrt[b^2*c + a^2*d]])","B",23,10,42,0.2381,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 208, 205}"
2460,1,2325,0,3.9747689,"\int \frac{1}{x^6 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^6*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[3]{a} x-\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x-\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[3]{a} x-\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(810 a^8+918 b^{5/3} a^{16/3}+1071 b^{10/3} a^{8/3}+1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(810 a^8+918 (-1)^{2/3} b^{5/3} a^{16/3}-1071 \sqrt[3]{-1} b^{10/3} a^{8/3}+1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(810 a^8-918 \sqrt[3]{-1} b^{5/3} a^{16/3}+1071 (-1)^{2/3} b^{10/3} a^{8/3}+1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(90 a^{16/3}+102 b^{5/3} a^{8/3}+119 b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(90 a^{16/3}+102 (-1)^{2/3} b^{5/3} a^{8/3}-119 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(90 a^{16/3}-102 \sqrt[3]{-1} b^{5/3} a^{8/3}+119 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(15 a^{8/3}+17 b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(15 a^{8/3}-17 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(15 a^{8/3}+17 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(7290 a^{15}+8262 b^{5/3} a^{37/3}+9639 b^{10/3} a^{29/3}+11781 b^5 a^7+15708 b^{20/3} a^{13/3}+26180 b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(7290 a^{15}+8262 (-1)^{2/3} b^{5/3} a^{37/3}-9639 \sqrt[3]{-1} b^{10/3} a^{29/3}+11781 b^5 a^7+15708 (-1)^{2/3} b^{20/3} a^{13/3}-26180 \sqrt[3]{-1} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(7290 a^{15}-8262 \sqrt[3]{-1} b^{5/3} a^{37/3}+9639 (-1)^{2/3} b^{10/3} a^{29/3}+11781 b^5 a^7-15708 \sqrt[3]{-1} b^{20/3} a^{13/3}+26180 (-1)^{2/3} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(2430 a^{12}+2754 b^{5/3} a^{28/3}+3213 b^{10/3} a^{20/3}+3927 b^5 a^4+5236 b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(2430 a^{12}-2754 \sqrt[3]{-1} b^{5/3} a^{28/3}+3213 (-1)^{2/3} b^{10/3} a^{20/3}+3927 b^5 a^4-5236 \sqrt[3]{-1} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(2430 a^{12}+2754 (-1)^{2/3} b^{5/3} a^{28/3}-3213 \sqrt[3]{-1} b^{10/3} a^{20/3}+3927 b^5 a^4+5236 (-1)^{2/3} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 \left(x a^3+b^2\right)}{17 b^3 x^5 \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"((7290*a^15 + 8262*a^(37/3)*b^(5/3) + 9639*a^(29/3)*b^(10/3) + 11781*a^7*b^5 + 15708*a^(13/3)*b^(20/3) + 26180*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) + ((7290*a^15 + 8262*(-1)^(2/3)*a^(37/3)*b^(5/3) - 9639*(-1)^(1/3)*a^(29/3)*b^(10/3) + 11781*a^7*b^5 + 15708*(-1)^(2/3)*a^(13/3)*b^(20/3) - 26180*(-1)^(1/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) + ((7290*a^15 - 8262*(-1)^(1/3)*a^(37/3)*b^(5/3) + 9639*(-1)^(2/3)*a^(29/3)*b^(10/3) + 11781*a^7*b^5 - 15708*(-1)^(1/3)*a^(13/3)*b^(20/3) + 26180*(-1)^(2/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*(b^2 + a^3*x))/(17*b^3*x^5*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(15*a^(8/3) + 17*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(15*a^(8/3) - 17*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(15*a^(8/3) + 17*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(90*a^(16/3) + 102*a^(8/3)*b^(5/3) + 119*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(90*a^(16/3) + 102*(-1)^(2/3)*a^(8/3)*b^(5/3) - 119*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(90*a^(16/3) - 102*(-1)^(1/3)*a^(8/3)*b^(5/3) + 119*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) + (a*(810*a^8 + 918*a^(16/3)*b^(5/3) + 1071*a^(8/3)*b^(10/3) + 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + (a*(810*a^8 + 918*(-1)^(2/3)*a^(16/3)*b^(5/3) - 1071*(-1)^(1/3)*a^(8/3)*b^(10/3) + 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + (a*(810*a^8 - 918*(-1)^(1/3)*a^(16/3)*b^(5/3) + 1071*(-1)^(2/3)*a^(8/3)*b^(10/3) + 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2430*a^12 + 2754*a^(28/3)*b^(5/3) + 3213*a^(20/3)*b^(10/3) + 3927*a^4*b^5 + 5236*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2430*a^12 - 2754*(-1)^(1/3)*a^(28/3)*b^(5/3) + 3213*(-1)^(2/3)*a^(20/3)*b^(10/3) + 3927*a^4*b^5 - 5236*(-1)^(1/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2430*a^12 + 2754*(-1)^(2/3)*a^(28/3)*b^(5/3) - 3213*(-1)^(1/3)*a^(20/3)*b^(10/3) + 3927*a^4*b^5 + 5236*(-1)^(2/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - a^(1/3)*x])/(6*b^3*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",27,6,32,0.1875,1,"{2056, 6725, 129, 155, 12, 91}"
2461,1,2325,0,3.4546895,"\int \frac{1}{x^6 \left(b+a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[1/(x^6*(b + a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^{17/9}}{\sqrt{3} b^3 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[3]{a} x-\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-1} \sqrt[3]{a} x-\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[3]{a} x-\sqrt[3]{b}\right) a^{17/9}}{6 b^3 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}-b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}+\sqrt[3]{-1} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}}}-\sqrt[3]{x}\right) a^{17/9}}{2 b^3 \sqrt[3]{a^{8/3}-(-1)^{2/3} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(810 a^8+918 b^{5/3} a^{16/3}+1071 b^{10/3} a^{8/3}+1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(810 a^8+918 (-1)^{2/3} b^{5/3} a^{16/3}-1071 \sqrt[3]{-1} b^{10/3} a^{8/3}+1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(810 a^8-918 \sqrt[3]{-1} b^{5/3} a^{16/3}+1071 (-1)^{2/3} b^{10/3} a^{8/3}+1309 b^5\right) \left(x a^3+b^2\right) a}{10472 b^9 x^2 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(90 a^{16/3}+102 b^{5/3} a^{8/3}+119 b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(90 a^{16/3}+102 (-1)^{2/3} b^{5/3} a^{8/3}-119 \sqrt[3]{-1} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(90 a^{16/3}-102 \sqrt[3]{-1} b^{5/3} a^{8/3}+119 (-1)^{2/3} b^{10/3}\right) \left(x a^3+b^2\right) a^{2/3}}{1309 b^7 x^3 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(15 a^{8/3}+17 b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(15 a^{8/3}-17 \sqrt[3]{-1} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(15 a^{8/3}+17 (-1)^{2/3} b^{5/3}\right) \left(x a^3+b^2\right) \sqrt[3]{a}}{238 b^5 x^4 \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(7290 a^{15}+8262 b^{5/3} a^{37/3}+9639 b^{10/3} a^{29/3}+11781 b^5 a^7+15708 b^{20/3} a^{13/3}+26180 b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(7290 a^{15}+8262 (-1)^{2/3} b^{5/3} a^{37/3}-9639 \sqrt[3]{-1} b^{10/3} a^{29/3}+11781 b^5 a^7+15708 (-1)^{2/3} b^{20/3} a^{13/3}-26180 \sqrt[3]{-1} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(7290 a^{15}-8262 \sqrt[3]{-1} b^{5/3} a^{37/3}+9639 (-1)^{2/3} b^{10/3} a^{29/3}+11781 b^5 a^7-15708 \sqrt[3]{-1} b^{20/3} a^{13/3}+26180 (-1)^{2/3} b^{25/3} a^{5/3}\right) \left(x a^3+b^2\right)}{52360 b^{13} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(2430 a^{12}+2754 b^{5/3} a^{28/3}+3213 b^{10/3} a^{20/3}+3927 b^5 a^4+5236 b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(2430 a^{12}-2754 \sqrt[3]{-1} b^{5/3} a^{28/3}+3213 (-1)^{2/3} b^{10/3} a^{20/3}+3927 b^5 a^4-5236 \sqrt[3]{-1} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(2430 a^{12}+2754 (-1)^{2/3} b^{5/3} a^{28/3}-3213 \sqrt[3]{-1} b^{10/3} a^{20/3}+3927 b^5 a^4+5236 (-1)^{2/3} b^{20/3} a^{4/3}\right) \left(x a^3+b^2\right)}{26180 b^{11} x \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 \left(x a^3+b^2\right)}{17 b^3 x^5 \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"((7290*a^15 + 8262*a^(37/3)*b^(5/3) + 9639*a^(29/3)*b^(10/3) + 11781*a^7*b^5 + 15708*a^(13/3)*b^(20/3) + 26180*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) + ((7290*a^15 + 8262*(-1)^(2/3)*a^(37/3)*b^(5/3) - 9639*(-1)^(1/3)*a^(29/3)*b^(10/3) + 11781*a^7*b^5 + 15708*(-1)^(2/3)*a^(13/3)*b^(20/3) - 26180*(-1)^(1/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) + ((7290*a^15 - 8262*(-1)^(1/3)*a^(37/3)*b^(5/3) + 9639*(-1)^(2/3)*a^(29/3)*b^(10/3) + 11781*a^7*b^5 - 15708*(-1)^(1/3)*a^(13/3)*b^(20/3) + 26180*(-1)^(2/3)*a^(5/3)*b^(25/3))*(b^2 + a^3*x))/(52360*b^13*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*(b^2 + a^3*x))/(17*b^3*x^5*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(15*a^(8/3) + 17*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(15*a^(8/3) - 17*(-1)^(1/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(1/3)*(15*a^(8/3) + 17*(-1)^(2/3)*b^(5/3))*(b^2 + a^3*x))/(238*b^5*x^4*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(90*a^(16/3) + 102*a^(8/3)*b^(5/3) + 119*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(90*a^(16/3) + 102*(-1)^(2/3)*a^(8/3)*b^(5/3) - 119*(-1)^(1/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(2/3)*(90*a^(16/3) - 102*(-1)^(1/3)*a^(8/3)*b^(5/3) + 119*(-1)^(2/3)*b^(10/3))*(b^2 + a^3*x))/(1309*b^7*x^3*(b^2*x^2 + a^3*x^3)^(1/3)) + (a*(810*a^8 + 918*a^(16/3)*b^(5/3) + 1071*a^(8/3)*b^(10/3) + 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + (a*(810*a^8 + 918*(-1)^(2/3)*a^(16/3)*b^(5/3) - 1071*(-1)^(1/3)*a^(8/3)*b^(10/3) + 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) + (a*(810*a^8 - 918*(-1)^(1/3)*a^(16/3)*b^(5/3) + 1071*(-1)^(2/3)*a^(8/3)*b^(10/3) + 1309*b^5)*(b^2 + a^3*x))/(10472*b^9*x^2*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2430*a^12 + 2754*a^(28/3)*b^(5/3) + 3213*a^(20/3)*b^(10/3) + 3927*a^4*b^5 + 5236*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2430*a^12 - 2754*(-1)^(1/3)*a^(28/3)*b^(5/3) + 3213*(-1)^(2/3)*a^(20/3)*b^(10/3) + 3927*a^4*b^5 - 5236*(-1)^(1/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2430*a^12 + 2754*(-1)^(2/3)*a^(28/3)*b^(5/3) - 3213*(-1)^(1/3)*a^(20/3)*b^(10/3) + 3927*a^4*b^5 + 5236*(-1)^(2/3)*a^(4/3)*b^(20/3))*(b^2 + a^3*x))/(26180*b^11*x*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*b^3*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - a^(1/3)*x])/(6*b^3*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) + (-1)^(1/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*a^(1/3)*x])/(6*b^3*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) - b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) + (-1)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (a^(17/9)*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3))])/(2*b^3*(a^(8/3) - (-1)^(2/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",27,6,32,0.1875,1,"{2056, 6725, 129, 155, 12, 91}"
2462,1,1405,0,9.2790429,"\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","Int[((-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]","\frac{\sqrt{2 c^2 p q-d^2} \tan ^{-1}\left(\frac{\sqrt{2 c^2 p q-d^2} x}{c \sqrt{p^2 x^4+q^2}}\right) (b c-a d)}{c^3}-\frac{\left(d-\sqrt{d^2-4 c^2 p q}\right) \tanh ^{-1}\left(\frac{p x^2}{\sqrt{p^2 x^4+q^2}}\right) (b c-a d)}{4 c^3}-\frac{\left(d+\sqrt{d^2-4 c^2 p q}\right) \tanh ^{-1}\left(\frac{p x^2}{\sqrt{p^2 x^4+q^2}}\right) (b c-a d)}{4 c^3}+\frac{\sqrt{d^2-2 c^2 p q} \left(d+\sqrt{d^2-4 c^2 p q}\right) \sqrt{-2 p q c^2+d^2-d \sqrt{d^2-4 c^2 p q}} \tanh ^{-1}\left(\frac{p \left(4 c^2 q^2+\left(d-\sqrt{d^2-4 c^2 p q}\right)^2 x^2\right)}{2 \sqrt{2} \sqrt{d^2-2 c^2 p q} \sqrt{-2 p q c^2+d^2-d \sqrt{d^2-4 c^2 p q}} \sqrt{p^2 x^4+q^2}}\right) (b c-a d)}{4 \sqrt{2} c^5 p q}+\frac{\sqrt{d^2-2 c^2 p q} \left(d-\sqrt{d^2-4 c^2 p q}\right) \sqrt{-2 p q c^2+d^2+d \sqrt{d^2-4 c^2 p q}} \tanh ^{-1}\left(\frac{p \left(4 c^2 q^2+\left(d+\sqrt{d^2-4 c^2 p q}\right)^2 x^2\right)}{2 \sqrt{2} \sqrt{d^2-2 c^2 p q} \sqrt{-2 p q c^2+d^2+d \sqrt{d^2-4 c^2 p q}} \sqrt{p^2 x^4+q^2}}\right) (b c-a d)}{4 \sqrt{2} c^5 p q}-\frac{\left(d^2-2 c^2 p q\right) \left(d-\sqrt{d^2-4 c^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right) (b c-a d)}{4 c^4 d \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2}}+\frac{d \left(d-\sqrt{d^2-4 c^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right) (b c-a d)}{4 c^4 \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2}}-\frac{\left(d^2-2 c^2 p q\right) \left(d+\sqrt{d^2-4 c^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right) (b c-a d)}{4 c^4 d \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2}}+\frac{d \left(d+\sqrt{d^2-4 c^2 p q}\right) \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right) (b c-a d)}{4 c^4 \sqrt{p} \sqrt{q} \sqrt{p^2 x^4+q^2}}-\frac{\sqrt{p} \sqrt{q} \left(p x^2+q\right) \sqrt{\frac{p^2 x^4+q^2}{\left(p x^2+q\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{p} x}{\sqrt{q}}\right)|\frac{1}{2}\right) (b c-a d)}{c^2 \sqrt{p^2 x^4+q^2}}-\frac{\left(d-\sqrt{d^2-4 c^2 p q}\right) \sqrt{p^2 x^4+q^2} (b c-a d)}{4 c^3 q}-\frac{\left(d+\sqrt{d^2-4 c^2 p q}\right) \sqrt{p^2 x^4+q^2} (b c-a d)}{4 c^3 q}+\frac{\sqrt{p^2 x^4+q^2} (b c-a d)}{c^2 x}-\frac{a p q \tanh ^{-1}\left(\frac{p x^2}{\sqrt{p^2 x^4+q^2}}\right)}{2 c}-\frac{\left(a p q c^2+b d c-a d^2\right) \tanh ^{-1}\left(\frac{\sqrt{p^2 x^4+q^2}}{q}\right)}{2 c^3}+\frac{\left(a p q c^2+b d c-a d^2\right) \sqrt{p^2 x^4+q^2}}{2 c^3 q}+\frac{a q \sqrt{p^2 x^4+q^2}}{2 c x^2}","\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,"((b*c*d - a*d^2 + a*c^2*p*q)*Sqrt[q^2 + p^2*x^4])/(2*c^3*q) - ((b*c - a*d)*(d - Sqrt[d^2 - 4*c^2*p*q])*Sqrt[q^2 + p^2*x^4])/(4*c^3*q) - ((b*c - a*d)*(d + Sqrt[d^2 - 4*c^2*p*q])*Sqrt[q^2 + p^2*x^4])/(4*c^3*q) + (a*q*Sqrt[q^2 + p^2*x^4])/(2*c*x^2) + ((b*c - a*d)*Sqrt[q^2 + p^2*x^4])/(c^2*x) + ((b*c - a*d)*Sqrt[-d^2 + 2*c^2*p*q]*ArcTan[(Sqrt[-d^2 + 2*c^2*p*q]*x)/(c*Sqrt[q^2 + p^2*x^4])])/c^3 - (a*p*q*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]])/(2*c) - ((b*c - a*d)*(d - Sqrt[d^2 - 4*c^2*p*q])*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]])/(4*c^3) - ((b*c - a*d)*(d + Sqrt[d^2 - 4*c^2*p*q])*ArcTanh[(p*x^2)/Sqrt[q^2 + p^2*x^4]])/(4*c^3) + ((b*c - a*d)*Sqrt[d^2 - 2*c^2*p*q]*(d + Sqrt[d^2 - 4*c^2*p*q])*Sqrt[d^2 - 2*c^2*p*q - d*Sqrt[d^2 - 4*c^2*p*q]]*ArcTanh[(p*(4*c^2*q^2 + (d - Sqrt[d^2 - 4*c^2*p*q])^2*x^2))/(2*Sqrt[2]*Sqrt[d^2 - 2*c^2*p*q]*Sqrt[d^2 - 2*c^2*p*q - d*Sqrt[d^2 - 4*c^2*p*q]]*Sqrt[q^2 + p^2*x^4])])/(4*Sqrt[2]*c^5*p*q) + ((b*c - a*d)*Sqrt[d^2 - 2*c^2*p*q]*(d - Sqrt[d^2 - 4*c^2*p*q])*Sqrt[d^2 - 2*c^2*p*q + d*Sqrt[d^2 - 4*c^2*p*q]]*ArcTanh[(p*(4*c^2*q^2 + (d + Sqrt[d^2 - 4*c^2*p*q])^2*x^2))/(2*Sqrt[2]*Sqrt[d^2 - 2*c^2*p*q]*Sqrt[d^2 - 2*c^2*p*q + d*Sqrt[d^2 - 4*c^2*p*q]]*Sqrt[q^2 + p^2*x^4])])/(4*Sqrt[2]*c^5*p*q) - ((b*c*d - a*d^2 + a*c^2*p*q)*ArcTanh[Sqrt[q^2 + p^2*x^4]/q])/(2*c^3) - ((b*c - a*d)*Sqrt[p]*Sqrt[q]*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(c^2*Sqrt[q^2 + p^2*x^4]) + (d*(b*c - a*d)*(d - Sqrt[d^2 - 4*c^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*c^4*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4]) - ((b*c - a*d)*(d^2 - 2*c^2*p*q)*(d - Sqrt[d^2 - 4*c^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*c^4*d*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4]) + (d*(b*c - a*d)*(d + Sqrt[d^2 - 4*c^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*c^4*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4]) - ((b*c - a*d)*(d^2 - 2*c^2*p*q)*(d + Sqrt[d^2 - 4*c^2*p*q])*(q + p*x^2)*Sqrt[(q^2 + p^2*x^4)/(q + p*x^2)^2]*EllipticF[2*ArcTan[(Sqrt[p]*x)/Sqrt[q]], 1/2])/(4*c^4*d*Sqrt[p]*Sqrt[q]*Sqrt[q^2 + p^2*x^4])","C",46,21,56,0.3750,1,"{6728, 275, 277, 217, 206, 305, 220, 1196, 266, 50, 63, 208, 1729, 1209, 1198, 1217, 1707, 1248, 735, 844, 725}"
2463,0,0,0,0.4907839,"\int \frac{x \left(3+7 x^4\right)}{\sqrt[3]{1+x^4} \left(-4+x^3+x^7\right)} \, dx","Int[(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,"3*Defer[Int][x/((1 + x^4)^(1/3)*(-4 + x^3 + x^7)), x] + 7*Defer[Int][x^5/((1 + x^4)^(1/3)*(-4 + x^3 + x^7)), x]","F",0,0,0,0,-1,"{}"
2464,1,1359,0,5.1696068,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{b^2}{3 a \left(a x+\sqrt{b^2+a^2 x^2}\right)^{3/2}}-\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}-\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}+\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}-\sqrt{2} (-c)^{3/4} \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{-b^2} (-c)^{3/4}}-\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a x+\sqrt{b^2+a^2 x^2}} (-c)^{3/4}+\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{-b^2} (-c)^{3/4}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{a x+\sqrt{b^2+a^2 x^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*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/a - (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] - Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[-b^2]*(-c)^(5/4)) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] + Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[-b^2]*(-c)^(5/4)) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] - Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[-b^2]*(-c)^(3/4)) - (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] + Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[-b^2]*(-c)^(3/4)) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)) + (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4))","B",35,12,42,0.2857,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1169, 634, 618, 204, 628}"
2465,1,1359,0,4.5932676,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{b^2}{3 a \left(a x+\sqrt{b^2+a^2 x^2}\right)^{3/2}}-\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}-\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{-c} \left(\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}+\sqrt{2} \sqrt[4]{-c} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}\right)}{\sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}-\sqrt{2} (-c)^{3/4} \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{-b^2} (-c)^{3/4}}-\frac{\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a x+\sqrt{b^2+a^2 x^2}} (-c)^{3/4}+\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}}}{\sqrt{-c} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}}}\right)}{\sqrt{-b^2} (-c)^{3/4}}+\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{d} \log \left(\sqrt[4]{-c} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{d} a+\sqrt{-b^2} \sqrt{-c}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-c}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{3/4}}-\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{d} \log \left((-c)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{-b^2} (-c)^{3/2}+a c \sqrt{d}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-c)^{3/4}\right)}{\sqrt{2} \sqrt{-b^2} (-c)^{5/4}}+\frac{\sqrt{a x+\sqrt{b^2+a^2 x^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*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/a - (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] - Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[-b^2]*(-c)^(5/4)) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[-c]*(Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]] + Sqrt[2]*(-c)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]])/(Sqrt[-b^2]*(-c)^(5/4)) + (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] - Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[-b^2]*(-c)^(3/4)) - (Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*ArcTan[(Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]] + Sqrt[2]*(-c)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-c]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]])])/(Sqrt[-b^2]*(-c)^(3/4)) + (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(1/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-c] + a*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(3/4)) - (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4)) + (Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[d]*Log[Sqrt[-b^2]*(-c)^(3/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*(-c)^(3/2) + a*c*Sqrt[d]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-c)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(Sqrt[2]*Sqrt[-b^2]*(-c)^(5/4))","B",35,12,42,0.2857,1,"{6725, 2117, 14, 2119, 1628, 828, 826, 1169, 634, 618, 204, 628}"
2466,0,0,0,3.0732949,"\int \frac{\sqrt{-b x+a^2 x^2}}{\sqrt{a x^2+x \sqrt{-b x+a^2 x^2}}} \, dx","Int[Sqrt[-(b*x) + a^2*x^2]/Sqrt[a*x^2 + x*Sqrt[-(b*x) + a^2*x^2]],x]","\int \frac{\sqrt{-b x+a^2 x^2}}{\sqrt{a x^2+x \sqrt{-b x+a^2 x^2}}} \, dx","\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,"(2*Sqrt[-(b*x) + a^2*x^2]*Defer[Subst][Defer[Int][(x^2*Sqrt[-b + a^2*x^2])/Sqrt[a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4]], x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-b + a^2*x])","F",0,0,0,0,-1,"{}"
2467,0,0,0,0.1625284,"\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","Int[(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,"Defer[Int][(a - 2*b + x)/((a*b + (-a - b)*x + x^2)^(1/3)*(a^2 + b*d + (-2*a - d)*x + x^2)), x]","F",0,0,0,0,-1,"{}"
2468,1,191,0,1.5558737,"\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","Int[(-(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]","-\frac{3 (a-x)^2 \left(-\frac{b-x}{a-b}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};\frac{a-x}{a-b},-\frac{2 d (a-x)}{1-\sqrt{4 a d-4 b d+1}}\right)}{4 ((a-x) (b-x))^{2/3}}-\frac{3 (a-x)^2 \left(-\frac{b-x}{a-b}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};\frac{a-x}{a-b},-\frac{2 d (a-x)}{\sqrt{4 a d-4 b d+1}+1}\right)}{4 ((a-x) (b-x))^{2/3}}","-\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,"(-3*(a - x)^2*(-((b - x)/(a - b)))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, (a - x)/(a - b), (-2*d*(a - x))/(1 - Sqrt[1 + 4*a*d - 4*b*d])])/(4*((a - x)*(b - x))^(2/3)) - (3*(a - x)^2*(-((b - x)/(a - b)))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, (a - x)/(a - b), (-2*d*(a - x))/(1 + Sqrt[1 + 4*a*d - 4*b*d])])/(4*((a - x)*(b - x))^(2/3))","C",8,5,55,0.09091,0,"{6719, 1586, 6728, 137, 136}"
2469,0,0,0,3.6735603,"\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","Int[(-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,"((2 - k*(1 + Sqrt[-4 + b + 4*k]/Sqrt[b]))*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-b - 2*k - Sqrt[b]*Sqrt[-4 + b + 4*k] + 2*(b + k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3) + ((2 - k*(1 - Sqrt[-4 + b + 4*k]/Sqrt[b]))*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-b - 2*k + Sqrt[b]*Sqrt[-4 + b + 4*k] + 2*(b + k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2470,0,0,0,8.0152183,"\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","Int[(-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,"(k*(5*d + k^2)*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*k^(4/3)*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*d*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) + (k*(8*d^2 - k^2 - d*(5 - k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (2 + d)*k*x + (d + k^2)*x^2 - d*k*x^3)), x])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((2*k^4 - 2*d^2*(1 - k^2) + d*k^2*(11 + k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (2 + d)*k*x + (d + k^2)*x^2 - d*k*x^3)), x])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - (k*(8*d*k^2 + k^4 + 2*d^2*(3 + k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (2 + d)*k*x + (d + k^2)*x^2 - d*k*x^3)), x])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))","F",0,0,0,0,-1,"{}"
2471,1,213,0,0.4010739,"\int \frac{-1+2 x^4}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Int[(-1 + 2*x^4)/((1 + x^4)^(1/4)*(-1 + x^4 + x^8)),x]","\frac{\sqrt[4]{\frac{1}{2} \left(123+55 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(123-55 \sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(123+55 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} x}{\sqrt[4]{x^4+1}}\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(123-55 \sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x}{\sqrt[4]{x^4+1}}\right)}{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])/2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5]) - (((123 - 55*Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5]) + (((123 + 55*Sqrt[5])/2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5]) - (((123 - 55*Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5])","A",10,5,27,0.1852,0,"{6728, 377, 212, 206, 203}"
2472,0,0,0,54.8492435,"\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","Int[((-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,"(-3*(1 + k)*(1 + a*k)*(1 - x)*x)/((1 - k)^2*(1 - b*k)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(2 + a + b + 4*a*k + a*(1 - 2*b)*k^2 + b*k^2)*(1 - x)*x)/(2*(1 - k)^2*(1 - b*k)^2*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(1 + k)*(1 + a*k)*x^2)/(2*(1 - k)*(1 - b*k)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(2 + a + b + 4*a*k + a*(1 - 2*b)*k^2 + b*k^2)*x^2)/(2*(1 - k)*(1 - b*k)^2*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(1 + k)*(1 + a*k)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/((1 - k)^3*(1 - b*k)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(2 + a + b + 4*a*k + a*(1 - 2*b)*k^2 + b*k^2)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/(2*(1 - k)^3*(1 - b*k)^2*((1 - x)*x*(1 - k*x))^(2/3)) + ((a + b)*(3 + b + 3*k + b*k^3 + (4 + b^2*(1 - k)^2*(1 + k + k^2) + b*(5 + 2*k + 5*k^2))/(Sqrt[b]*Sqrt[4 + b*(1 - k)^2]))*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][x^(1/3)/((1 - x)^(5/3)*(1 - k*x)^(5/3)*(-(b*(1 + k)) - Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - b*k)^2*((1 - x)*x*(1 - k*x))^(2/3)) + ((a + b)*(3*(1 + k) + b*(1 + k^3) - (4 + b*(5 + 2*k + 5*k^2) + b^2*(1 - k - k^3 + k^4))/(Sqrt[b]*Sqrt[4 + b*(1 - k)^2]))*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][x^(1/3)/((1 - x)^(5/3)*(1 - k*x)^(5/3)*(-(b*(1 + k)) + Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - b*k)^2*((1 - x)*x*(1 - k*x))^(2/3))","F",0,0,0,0,-1,"{}"
2473,0,0,0,8.0451506,"\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","Int[(-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,"-((k*(5*d + k^2)*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*k^(4/3)*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*d*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) - (k*(8*d^2 - k^2 - d*(5 - k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((2*k^4 - 2*d^2*(1 - k^2) + d*k^2*(11 + k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) + (k*(8*d*k^2 + k^4 + 2*d^2*(3 + k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x])/(d^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))","F",0,0,0,0,-1,"{}"
2474,1,420,0,3.0187666,"\int \frac{\sqrt[3]{-x+x^3} \left(-b+a x^6\right)}{-d+c x^6} \, dx","Int[((-x + x^3)^(1/3)*(-b + a*x^6))/(-d + c*x^6),x]","\frac{\sqrt[3]{x^3-x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{\sqrt[3]{c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{1-x^2}}+\frac{\sqrt[3]{x^3-x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,-\frac{\sqrt[3]{-1} \sqrt[3]{c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{1-x^2}}+\frac{\sqrt[3]{x^3-x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{(-1)^{2/3} \sqrt[3]{c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{1-x^2}}+\frac{a \sqrt[3]{x^3-x} x}{2 c}+\frac{a \sqrt[3]{x^3-x} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{6 c \sqrt[3]{x^2-1} \sqrt[3]{x}}-\frac{a \sqrt[3]{x^3-x} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{12 c \sqrt[3]{x^2-1} \sqrt[3]{x}}+\frac{a \sqrt[3]{x^3-x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} c \sqrt[3]{x^2-1} \sqrt[3]{x}}","\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,"(a*x*(-x + x^3)^(1/3))/(2*c) + ((b*c - a*d)*x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, (c^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 - x^2)^(1/3)) + ((b*c - a*d)*x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, -(((-1)^(1/3)*c^(1/3)*x^2)/d^(1/3))])/(4*c*d*(1 - x^2)^(1/3)) + ((b*c - a*d)*x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, ((-1)^(2/3)*c^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 - x^2)^(1/3)) + (a*(-x + x^3)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*c*x^(1/3)*(-1 + x^2)^(1/3)) + (a*(-x + x^3)^(1/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(6*c*x^(1/3)*(-1 + x^2)^(1/3)) - (a*(-x + x^3)^(1/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(12*c*x^(1/3)*(-1 + x^2)^(1/3))","B",67,17,32,0.5312,0,"{2056, 6725, 279, 329, 275, 331, 292, 31, 634, 618, 204, 628, 959, 466, 465, 511, 510}"
2475,1,420,0,2.8638101,"\int \frac{\sqrt[3]{-x+x^3} \left(-b+a x^6\right)}{-d+c x^6} \, dx","Int[((-x + x^3)^(1/3)*(-b + a*x^6))/(-d + c*x^6),x]","\frac{\sqrt[3]{x^3-x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{\sqrt[3]{c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{1-x^2}}+\frac{\sqrt[3]{x^3-x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,-\frac{\sqrt[3]{-1} \sqrt[3]{c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{1-x^2}}+\frac{\sqrt[3]{x^3-x} x (b c-a d) F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};x^2,\frac{(-1)^{2/3} \sqrt[3]{c} x^2}{\sqrt[3]{d}}\right)}{4 c d \sqrt[3]{1-x^2}}+\frac{a \sqrt[3]{x^3-x} x}{2 c}+\frac{a \sqrt[3]{x^3-x} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{6 c \sqrt[3]{x^2-1} \sqrt[3]{x}}-\frac{a \sqrt[3]{x^3-x} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{12 c \sqrt[3]{x^2-1} \sqrt[3]{x}}+\frac{a \sqrt[3]{x^3-x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} c \sqrt[3]{x^2-1} \sqrt[3]{x}}","\frac{(b c-a d) \text{RootSum}\left[\text{$\#$1}^9 d-3 \text{$\#$1}^6 d+3 \text{$\#$1}^3 d+c-d\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3-x}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{\text{$\#$1}^3-1}\&\right]}{6 c d}+\frac{a \sqrt[3]{x^3-x} x}{2 c}+\frac{a \log \left(\sqrt[3]{x^3-x}-x\right)}{6 c}+\frac{a \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3-x}+x}\right)}{2 \sqrt{3} c}-\frac{a \log \left(\sqrt[3]{x^3-x} x+\left(x^3-x\right)^{2/3}+x^2\right)}{12 c}",1,"(a*x*(-x + x^3)^(1/3))/(2*c) + ((b*c - a*d)*x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, (c^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 - x^2)^(1/3)) + ((b*c - a*d)*x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, -(((-1)^(1/3)*c^(1/3)*x^2)/d^(1/3))])/(4*c*d*(1 - x^2)^(1/3)) + ((b*c - a*d)*x*(-x + x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, x^2, ((-1)^(2/3)*c^(1/3)*x^2)/d^(1/3)])/(4*c*d*(1 - x^2)^(1/3)) + (a*(-x + x^3)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*c*x^(1/3)*(-1 + x^2)^(1/3)) + (a*(-x + x^3)^(1/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(6*c*x^(1/3)*(-1 + x^2)^(1/3)) - (a*(-x + x^3)^(1/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(12*c*x^(1/3)*(-1 + x^2)^(1/3))","B",67,17,32,0.5312,0,"{2056, 6725, 279, 329, 275, 331, 292, 31, 634, 618, 204, 628, 959, 466, 465, 511, 510}"
2476,0,0,0,0.369981,"\int \frac{1}{1-x \sqrt{c+b x+a x^2}} \, dx","Int[(1 - x*Sqrt[c + b*x + a*x^2])^(-1),x]","\int \frac{1}{1-x \sqrt{c+b x+a x^2}} \, dx","-2 \text{RootSum}\left[\text{$\#$1}^4 \sqrt{a}-\text{$\#$1}^3 b+4 \text{$\#$1}^2 a-4 \text{$\#$1} \sqrt{a} b+\text{$\#$1} b c-\sqrt{a} c^2+b^2\&,\frac{\text{$\#$1}^2 \sqrt{a} \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1} b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{4 \text{$\#$1}^3 \sqrt{a}-3 \text{$\#$1}^2 b+8 \text{$\#$1} a-4 \sqrt{a} b+b c}\&\right]",1,"Defer[Int][(1 - c*x^2 - b*x^3 - a*x^4)^(-1), x] - Defer[Int][(x*Sqrt[c + b*x + a*x^2])/(-1 + c*x^2 + b*x^3 + a*x^4), x]","F",0,0,0,0,-1,"{}"
2477,1,870,0,1.3326078,"\int \frac{-b+a x^2}{\left(-b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(-b + a*x^2)/((-b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{b}-\sqrt{2} \sqrt{a} x\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{2} \sqrt{a} x+\sqrt{b}\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*x^(1/3))])/(4*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*x^(1/3))])/(4*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[2]*Sqrt[a]*x])/(8*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[2]*Sqrt[a]*x])/(8*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3))])/(8*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3))])/(8*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3))","B",8,5,41,0.1220,1,"{2056, 6725, 59, 912, 91}"
2478,1,870,0,1.0526063,"\int \frac{-b+a x^2}{\left(-b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(-b + a*x^2)/((-b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{b}-\sqrt{2} \sqrt{a} x\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{2} \sqrt{a} x+\sqrt{b}\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}-\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[6]{a} \sqrt[3]{a^{5/2}+\sqrt{2} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*x^(1/3))])/(4*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*x^(1/3))])/(4*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[2]*Sqrt[a]*x])/(8*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[2]*Sqrt[a]*x])/(8*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3))])/(8*a^(1/6)*(a^(5/2) - Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3))])/(8*a^(1/6)*(a^(5/2) + Sqrt[2]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3))","B",8,5,41,0.1220,1,"{2056, 6725, 59, 912, 91}"
2479,1,874,0,1.2210043,"\int \frac{b+a x^2}{\left(b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(b + a*x^2)/((b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{b}-\sqrt{2} \sqrt{-a} x\right)}{8 \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{2} \sqrt{-a} x+\sqrt{b}\right)}{8 \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(4*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(4*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[2]*Sqrt[-a]*x])/(8*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[2]*Sqrt[-a]*x])/(8*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)])/(8*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)])/(8*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3))","B",8,5,37,0.1351,1,"{2056, 6725, 59, 912, 91}"
2480,1,874,0,0.959386,"\int \frac{b+a x^2}{\left(b+2 a x^2\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(b + a*x^2)/((b + 2*a*x^2)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{b}-\sqrt{2} \sqrt{-a} x\right)}{8 \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt{2} \sqrt{-a} x+\sqrt{b}\right)}{8 \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a^3-\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{a^3+\sqrt{2} \sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(4*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))])/(4*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] - Sqrt[2]*Sqrt[-a]*x])/(8*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[Sqrt[b] + Sqrt[2]*Sqrt[-a]*x])/(8*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)])/(8*(a^3 - Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)])/(8*(a^3 + Sqrt[2]*Sqrt[-a]*b^(3/2))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a*(b^2*x^2 + a^3*x^3)^(1/3))","B",8,5,37,0.1351,1,"{2056, 6725, 59, 912, 91}"
2481,0,0,0,12.2944738,"\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","Int[(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,"(9*(a + b)*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a*b - a*(1 + b/a)*x^3 + x^6 - d*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (12*a*b*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(-(a*b) + a*(1 + b/a)*x^3 - x^6 + d*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (6*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^9/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(-(a*b) + a*(1 + b/a)*x^3 - x^6 + d*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3)","F",0,0,0,0,-1,"{}"
2482,1,715,0,2.9011425,"\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","Int[((b + a*x^4)^(1/4)*(2*b + 3*a*x^4))/(x^6*(b + a*x^8)),x]","-\frac{3 a^2 \tan ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}-\frac{3 a^2 \tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}+\frac{3 a^2 \tanh ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}+\frac{3 a^2 \tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}-\frac{a x^3 \sqrt[4]{a x^4+b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^4}{\sqrt{b}},-\frac{a x^4}{b}\right)}{3 b \sqrt[4]{\frac{a x^4}{b}+1}}-\frac{a x^3 \sqrt[4]{a x^4+b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^4}{\sqrt{b}},-\frac{a x^4}{b}\right)}{3 b \sqrt[4]{\frac{a x^4}{b}+1}}-\frac{3 a \sqrt[4]{a x^4+b}}{b x}-\frac{3 (-a)^{3/2} \tan ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}+\frac{3 (-a)^{3/2} \tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}+\frac{3 (-a)^{3/2} \tanh ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}-\frac{3 (-a)^{3/2} \tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}-\frac{2 \left(a x^4+b\right)^{5/4}}{5 b x^5}","\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,"(-3*a*(b + a*x^4)^(1/4))/(b*x) - (2*(b + a*x^4)^(5/4))/(5*b*x^5) - (a*x^3*(b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^4)/Sqrt[b]), -((a*x^4)/b)])/(3*b*(1 + (a*x^4)/b)^(1/4)) - (a*x^3*(b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^4)/Sqrt[b], -((a*x^4)/b)])/(3*b*(1 + (a*x^4)/b)^(1/4)) - (3*a^2*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*b) - (3*(-a)^(3/2)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) - (3*a^2*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*b) + (3*(-a)^(3/2)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (3*a^2*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*b) + (3*(-a)^(3/2)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (3*a^2*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*b) - (3*(-a)^(3/2)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b])","B",43,12,34,0.3529,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
2483,1,715,0,2.609216,"\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","Int[((b + a*x^4)^(1/4)*(2*b + 3*a*x^4))/(x^6*(b + a*x^8)),x]","-\frac{3 a^2 \tan ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}-\frac{3 a^2 \tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}+\frac{3 a^2 \tanh ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}+\frac{3 a^2 \tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 b \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}-\frac{a x^3 \sqrt[4]{a x^4+b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^4}{\sqrt{b}},-\frac{a x^4}{b}\right)}{3 b \sqrt[4]{\frac{a x^4}{b}+1}}-\frac{a x^3 \sqrt[4]{a x^4+b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^4}{\sqrt{b}},-\frac{a x^4}{b}\right)}{3 b \sqrt[4]{\frac{a x^4}{b}+1}}-\frac{3 a \sqrt[4]{a x^4+b}}{b x}-\frac{3 (-a)^{3/2} \tan ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}+\frac{3 (-a)^{3/2} \tan ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}+\frac{3 (-a)^{3/2} \tanh ^{-1}\left(\frac{x \sqrt[4]{a-\sqrt{-a} \sqrt{b}}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(a-\sqrt{-a} \sqrt{b}\right)^{3/4}}-\frac{3 (-a)^{3/2} \tanh ^{-1}\left(\frac{x \sqrt[4]{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{a x^4+b}}\right)}{4 \sqrt{b} \left(\sqrt{-a} \sqrt{b}+a\right)^{3/4}}-\frac{2 \left(a x^4+b\right)^{5/4}}{5 b x^5}","\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,"(-3*a*(b + a*x^4)^(1/4))/(b*x) - (2*(b + a*x^4)^(5/4))/(5*b*x^5) - (a*x^3*(b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^4)/Sqrt[b]), -((a*x^4)/b)])/(3*b*(1 + (a*x^4)/b)^(1/4)) - (a*x^3*(b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^4)/Sqrt[b], -((a*x^4)/b)])/(3*b*(1 + (a*x^4)/b)^(1/4)) - (3*a^2*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*b) - (3*(-a)^(3/2)*ArcTan[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) - (3*a^2*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*b) + (3*(-a)^(3/2)*ArcTan[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (3*a^2*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*b) + (3*(-a)^(3/2)*ArcTanh[((a - Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a - Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (3*a^2*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*b) - (3*(-a)^(3/2)*ArcTanh[((a + Sqrt[-a]*Sqrt[b])^(1/4)*x)/(b + a*x^4)^(1/4)])/(4*(a + Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b])","B",43,12,34,0.3529,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
2484,1,337,0,0.8102329,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+x^2} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(1 + x^2),x]","\frac{1}{2} i \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}{2} i \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}{2} i \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}{2} i \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{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"(I/2)*Sqrt[I + Sqrt[1 - I]]*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])] - (I/2)*Sqrt[-I + Sqrt[1 + I]]*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])] + (I/2)*Sqrt[-I + Sqrt[1 - I]]*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])] - (I/2)*Sqrt[I + Sqrt[1 + I]]*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])]","C",22,9,21,0.4286,1,"{6741, 6728, 1021, 1078, 621, 206, 1033, 724, 204}"
2485,1,337,0,0.6353572,"\int \frac{\sqrt{x+\sqrt{1+x}}}{1+x^2} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(1 + x^2),x]","\frac{1}{2} i \sqrt{i+\sqrt{1-i}} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{2} i \sqrt{\sqrt{1+i}-i} \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)+\frac{1}{2} i \sqrt{\sqrt{1-i}-i} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)-\frac{1}{2} i \sqrt{i+\sqrt{1+i}} \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)","\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"(I/2)*Sqrt[I + Sqrt[1 - I]]*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])] - (I/2)*Sqrt[-I + Sqrt[1 + I]]*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])] + (I/2)*Sqrt[-I + Sqrt[1 - I]]*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])] - (I/2)*Sqrt[I + Sqrt[1 + I]]*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])]","C",22,9,21,0.4286,1,"{6741, 6728, 1021, 1078, 621, 206, 1033, 724, 204}"
2486,0,0,0,0.3661371,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2-\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(x^2 - Sqrt[1 + x]),x]","\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2-\sqrt{1+x}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+16 \text{$\#$1}^5-8 \text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}-1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^7-12 \text{$\#$1}^5+40 \text{$\#$1}^4-16 \text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+3}\&\right]",1,"2*Defer[Subst][Defer[Int][(x*Sqrt[-1 + x + x^2])/(1 - x - 2*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2487,0,0,0,0.2729474,"\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2-\sqrt{1+x}} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(x^2 - Sqrt[1 + x]),x]","\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2-\sqrt{1+x}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+16 \text{$\#$1}^5-8 \text{$\#$1}^4-2 \text{$\#$1}^3+3 \text{$\#$1}^2+6 \text{$\#$1}-1\&,\frac{\text{$\#$1}^6 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+2 \text{$\#$1} \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{4 \text{$\#$1}^7-12 \text{$\#$1}^5+40 \text{$\#$1}^4-16 \text{$\#$1}^3-3 \text{$\#$1}^2+3 \text{$\#$1}+3}\&\right]",1,"2*Defer[Subst][Defer[Int][(x*Sqrt[-1 + x + x^2])/(1 - x - 2*x^2 + x^4), x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
2488,1,408,0,0.8316118,"\int \frac{x^2}{\left(x^2 (-a+x)\right)^{2/3} \left(-a^2+2 a x+(-1+d) x^2\right)} \, dx","Int[x^2/((x^2*(-a + x))^(2/3)*(-a^2 + 2*a*x + (-1 + d)*x^2)),x]","-\frac{x^{4/3} (x-a)^{2/3} \log \left(2 a \left(1-\sqrt{d}\right)-2 (1-d) x\right)}{4 a d^{5/6} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{x^{4/3} (x-a)^{2/3} \log \left(2 (1-d) x-2 a \left(\sqrt{d}+1\right)\right)}{4 a d^{5/6} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(-\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{x}\right)}{4 a d^{5/6} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}-\frac{3 x^{4/3} (x-a)^{2/3} \log \left(\sqrt[6]{d} \sqrt[3]{x}-\sqrt[3]{x-a}\right)}{4 a d^{5/6} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-a}}\right)}{2 a d^{5/6} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}-\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 a d^{5/6} \left(-\left(x^2 (a-x)\right)\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,"(Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*x^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*a*d^(5/6)*(-((a - x)*x^2))^(2/3)) - (Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*x^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*a*d^(5/6)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[2*a*(1 - Sqrt[d]) - 2*(1 - d)*x])/(4*a*d^(5/6)*(-((a - x)*x^2))^(2/3)) + (x^(4/3)*(-a + x)^(2/3)*Log[-2*a*(1 + Sqrt[d]) + 2*(1 - d)*x])/(4*a*d^(5/6)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[-(d^(1/6)*x^(1/3)) - (-a + x)^(1/3)])/(4*a*d^(5/6)*(-((a - x)*x^2))^(2/3)) - (3*x^(4/3)*(-a + x)^(2/3)*Log[d^(1/6)*x^(1/3) - (-a + x)^(1/3)])/(4*a*d^(5/6)*(-((a - x)*x^2))^(2/3))","A",9,5,36,0.1389,1,"{6719, 911, 105, 59, 91}"
2489,0,0,0,24.9962934,"\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","Int[((-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,"(3*(2*k^2 - a*(1 + 2*b + k^2) - b*(1 + 4*k + k^2))*(1 - x)*(1 - k*x))/(2*(b - k)^2*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(a + k)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/((1 - k)*(b - k)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(2*k^2 - a*(1 + 2*b + k^2) - b*(1 + 4*k + k^2))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/(2*(1 - k)*(b - k)^2*((1 - x)*x*(1 - k*x))^(2/3)) + ((a + b)*(1 + k^3 + 3*b*(1 + k) + (4*b^2 + (1 - k)^2*(1 + k + k^2) + b*(5 + 2*k + 5*k^2))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][1/((1 - x)^(2/3)*x^(5/3)*(1 - k*x)^(2/3)*(-1 - k - Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^2*((1 - x)*x*(1 - k*x))^(2/3)) + ((a + b)*(1 + k^3 + 3*b*(1 + k) - (1 + 4*b^2 - k - k^3 + k^4 + b*(5 + 2*k + 5*k^2))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][1/((1 - x)^(2/3)*x^(5/3)*(1 - k*x)^(2/3)*(-1 - k + Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^2*((1 - x)*x*(1 - k*x))^(2/3))","F",0,0,0,0,-1,"{}"
2490,0,0,0,11.5018668,"\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","Int[(-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,"(9*a*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-a + x^3)^(1/3))/((-b + x^3)^(2/3)*(a^2 - 2*a*x^3 + (1 + b*d)*x^6 - d*x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (6*a*b*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(-a + x^3)^(1/3))/((-b + x^3)^(2/3)*(-a^2 + 2*a*x^3 - (1 + b*d)*x^6 + d*x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (3*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-a + x^3)^(1/3))/((-b + x^3)^(2/3)*(-a^2 + 2*a*x^3 - (1 + b*d)*x^6 + d*x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3)","F",0,0,0,0,-1,"{}"
2491,1,170,0,0.0729794,"\int \frac{1}{\sqrt[3]{-8+12 x+54 x^2-135 x^3+81 x^4}} \, dx","Int[(-8 + 12*x + 54*x^2 - 135*x^3 + 81*x^4)^(-1/3),x]","\frac{(2-3 x) \sqrt[3]{3 x+1} \log (2-3 x)}{6 \sqrt[3]{3} \sqrt[3]{-(2-3 x)^3 (3 x+1)}}-\frac{(2-3 x) \sqrt[3]{3 x+1} \log \left(\sqrt[3]{3}-\sqrt[3]{3 x+1}\right)}{2 \sqrt[3]{3} \sqrt[3]{-(2-3 x)^3 (3 x+1)}}-\frac{(2-3 x) \sqrt[3]{3 x+1} \tan ^{-1}\left(\frac{2 \sqrt[3]{3 x+1}+\sqrt[3]{3}}{3^{5/6}}\right)}{3^{5/6} \sqrt[3]{-(2-3 x)^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,"-(((2 - 3*x)*(1 + 3*x)^(1/3)*ArcTan[(3^(1/3) + 2*(1 + 3*x)^(1/3))/3^(5/6)])/(3^(5/6)*(-((2 - 3*x)^3*(1 + 3*x)))^(1/3))) + ((2 - 3*x)*(1 + 3*x)^(1/3)*Log[2 - 3*x])/(6*3^(1/3)*(-((2 - 3*x)^3*(1 + 3*x)))^(1/3)) - ((2 - 3*x)*(1 + 3*x)^(1/3)*Log[3^(1/3) - (1 + 3*x)^(1/3)])/(2*3^(1/3)*(-((2 - 3*x)^3*(1 + 3*x)))^(1/3))","A",6,6,24,0.2500,1,"{6688, 6719, 55, 617, 204, 31}"
2492,0,0,0,0.425194,"\int \frac{1+x^2}{\left(-1-x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Int[(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,"(x*(1 - x^6)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^6])/(-1 + x^6)^(1/3) + (1 + Sqrt[5])*Defer[Int][1/((-1 - Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x] + (1 - Sqrt[5])*Defer[Int][1/((-1 + Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
2493,0,0,0,0.3275616,"\int \frac{1+x^2}{\left(-1-x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Int[(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,"(x*(1 - x^6)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^6])/(-1 + x^6)^(1/3) + (1 + Sqrt[5])*Defer[Int][1/((-1 - Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x] + (1 - Sqrt[5])*Defer[Int][1/((-1 + Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
2494,0,0,0,4.532041,"\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","Int[((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,"(3*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3)/(1 - x^6 + x^12 - x^15 - x^18), x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3)) - (3*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3)/(-1 + x^6 - x^12 + x^15 + x^18)^2, x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3)) + (18*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^3*(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3))/(-1 + x^6 - x^12 + x^15 + x^18)^2, x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3)) + (3*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^6*(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3))/(-1 + x^6 - x^12 + x^15 + x^18)^2, x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3)) - (12*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^9*(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3))/(-1 + x^6 - x^12 + x^15 + x^18)^2, x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3)) - (3*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^12*(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3))/(-1 + x^6 - x^12 + x^15 + x^18)^2, x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3)) + (9*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^15*(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3))/(-1 + x^6 - x^12 + x^15 + x^18)^2, x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3)) + (12*(-x + 2*x^3 - x^5 + x^6 + x^7)^(1/3)*Defer[Subst][Defer[Int][(x^3*(-1 + 2*x^6 - x^12 + x^15 + x^18)^(1/3))/(-1 + x^6 - x^12 + x^15 + x^18), x], x, x^(1/3)])/(x^(1/3)*(-1 + 2*x^2 - x^4 + x^5 + x^6)^(1/3))","F",0,0,0,0,-1,"{}"
2495,0,0,0,2.6545308,"\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","Int[(-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,"-(((1 - 2*k + Sqrt[1 + 4*b - 4*b*k])*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - k*x)^(1/3)*(-1 - 2*b - Sqrt[1 + 4*b - 4*b*k] + 2*(b + k)*x)*(x - x^2)^(1/3)), x])/((1 - x)*x*(1 - k*x))^(1/3)) - ((1 - 2*k - Sqrt[1 + 4*b - 4*b*k])*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - k*x)^(1/3)*(-1 - 2*b + Sqrt[1 + 4*b - 4*b*k] + 2*(b + k)*x)*(x - x^2)^(1/3)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2496,1,359,0,0.909307,"\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","Int[(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{c \sqrt{a^2 x^3+b^2}}{3 b^2 x^3}-\frac{2 a^2 \sqrt{a^2 x^3+b^2}}{b^2}+\frac{a^2 \sqrt{a^2 x^3+b^2}}{6 b^2 x^3}+\frac{2 a^2 \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{b}+\frac{\sqrt{a^2 x^3+b^2}}{3 x^6}-\frac{a \sqrt{a-b} (3 a b-c) \tan ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a-b}}\right)}{3 b^{5/2}}-\frac{a \sqrt{a+b} (3 a b+c) \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{a+b}}\right)}{3 b^{5/2}}+\frac{a (3 a b-c) \sqrt{a^2 x^3+b^2}}{3 b^3}+\frac{a (3 a b+c) \sqrt{a^2 x^3+b^2}}{3 b^3}+\frac{a^2 c \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{3 b^3}-\frac{a^4 \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{6 b^3}","\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,"(-2*a^2*Sqrt[b^2 + a^2*x^3])/b^2 + (a*(3*a*b - c)*Sqrt[b^2 + a^2*x^3])/(3*b^3) + (a*(3*a*b + c)*Sqrt[b^2 + a^2*x^3])/(3*b^3) + Sqrt[b^2 + a^2*x^3]/(3*x^6) + (a^2*Sqrt[b^2 + a^2*x^3])/(6*b^2*x^3) + (c*Sqrt[b^2 + a^2*x^3])/(3*b^2*x^3) - (a*Sqrt[a - b]*(3*a*b - c)*ArcTan[Sqrt[b^2 + a^2*x^3]/(Sqrt[a - b]*Sqrt[b])])/(3*b^(5/2)) - (a^4*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/(6*b^3) + (2*a^2*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/b + (a^2*c*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/(3*b^3) - (a*Sqrt[a + b]*(3*a*b + c)*ArcTanh[Sqrt[b^2 + a^2*x^3]/(Sqrt[b]*Sqrt[a + b])])/(3*b^(5/2))","A",23,9,52,0.1731,1,"{6725, 266, 47, 51, 63, 208, 50, 444, 205}"
2497,0,0,0,3.3767823,"\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","Int[(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,"(12*a*x^(4/3)*(-a + x)^(2/3)*Defer[Subst][Defer[Int][x^19/((-a + x^3)^(2/3)*(a^2 - 2*a*x^3 + x^6 - d*x^24)), x], x, x^(1/3)])/(-((a - x)*x^2))^(2/3) + (9*x^(4/3)*(-a + x)^(2/3)*Defer[Subst][Defer[Int][x^22/((-a + x^3)^(2/3)*(-a^2 + 2*a*x^3 - x^6 + d*x^24)), x], x, x^(1/3)])/(-((a - x)*x^2))^(2/3)","F",0,0,0,0,-1,"{}"
2498,0,0,0,3.5073956,"\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","Int[(-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,"((2 - k - Sqrt[1 - 4*b*(1 - k)]*k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - k*x)^(1/3)/((1 - x)^(2/3)*x^(2/3)*(-1 - 2*b*k - Sqrt[1 - 4*b + 4*b*k] + 2*(1 + b*k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3) + ((2 - (1 - Sqrt[1 - 4*b*(1 - k)])*k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - k*x)^(1/3)/((1 - x)^(2/3)*x^(2/3)*(-1 - 2*b*k + Sqrt[1 - 4*b + 4*b*k] + 2*(1 + b*k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2499,1,538,0,0.4843826,"\int \frac{1}{\sqrt[3]{-x^2+x^3} \left(-1+x^4\right)} \, dx","Int[1/((-x^2 + x^3)^(1/3)*(-1 + x^4)),x]","-\frac{3 x}{4 \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(-\sqrt[3]{x}+\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-i}}\right)}{8 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(-\sqrt[3]{x}+\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+i}}\right)}{8 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (-x-1)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (-x+i)}{8 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x+i)}{8 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1-i} \sqrt{3} \sqrt[3]{x}}\right)}{4 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1+i} \sqrt{3} \sqrt[3]{x}}\right)}{4 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3-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,"(-3*x)/(4*(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/((1 - I)^(1/3)*Sqrt[3]*x^(1/3))])/(4*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/((1 + I)^(1/3)*Sqrt[3]*x^(1/3))])/(4*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(4*2^(1/3)*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - I)^(1/3) - x^(1/3)])/(8*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + I)^(1/3) - x^(1/3)])/(8*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(8*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - x])/(8*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[I - x])/(8*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[I + x])/(8*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3))","C",10,6,21,0.2857,1,"{2056, 6725, 848, 96, 91, 912}"
2500,1,538,0,0.3504859,"\int \frac{1}{\sqrt[3]{-x^2+x^3} \left(-1+x^4\right)} \, dx","Int[1/((-x^2 + x^3)^(1/3)*(-1 + x^4)),x]","-\frac{3 x}{4 \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(-\sqrt[3]{x}+\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-i}}\right)}{8 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(-\sqrt[3]{x}+\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+i}}\right)}{8 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (-x-1)}{8 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (-x+i)}{8 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x+i)}{8 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1-i} \sqrt{3} \sqrt[3]{x}}\right)}{4 \sqrt[3]{1-i} \sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{x-1}}{\sqrt[3]{1+i} \sqrt{3} \sqrt[3]{x}}\right)}{4 \sqrt[3]{1+i} \sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3-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,"(-3*x)/(4*(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/((1 - I)^(1/3)*Sqrt[3]*x^(1/3))])/(4*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/((1 + I)^(1/3)*Sqrt[3]*x^(1/3))])/(4*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(4*2^(1/3)*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - I)^(1/3) - x^(1/3)])/(8*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + I)^(1/3) - x^(1/3)])/(8*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(8*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - x])/(8*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[I - x])/(8*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[I + x])/(8*(1 - I)^(1/3)*(-x^2 + x^3)^(1/3))","C",10,6,21,0.2857,1,"{2056, 6725, 848, 96, 91, 912}"
2501,1,370,0,0.6024357,"\int \frac{\sqrt[3]{-x^2+x^4}}{x \left(1+x^2\right)} \, dx","Int[(-x^2 + x^4)^(1/3)/(x*(1 + x^2)),x]","\frac{3 \left(\frac{x^2}{x^2+1}\right)^{2/3} \left(-\frac{1-x^2}{x^2+1}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},\frac{2}{3};\frac{7}{3};\frac{2}{x^2+1},\frac{1}{x^2+1}\right)}{4 \left(x^4-x^2\right)^{2/3}}-\frac{3^{3/4} \sqrt{2-\sqrt{3}} \left(x^2-x^4\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{x^2-x^4}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(x^2-x^4\right)^{2/3}+2^{2/3} \sqrt[3]{x^2-x^4}+1}{\left(-2^{2/3} \sqrt[3]{x^2-x^4}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{x^2-x^4}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{x^2-x^4}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2^{2/3} \left(1-2 x^2\right) \left(x^4-x^2\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{x^2-x^4}}{\left(-2^{2/3} \sqrt[3]{x^2-x^4}-\sqrt{3}+1\right)^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))^(2/3)*(-((1 - x^2)/(1 + x^2)))^(2/3)*AppellF1[4/3, 2/3, 2/3, 7/3, 2/(1 + x^2), (1 + x^2)^(-1)])/(4*(-x^2 + x^4)^(2/3)) - (3^(3/4)*Sqrt[2 - Sqrt[3]]*(x^2 - x^4)^(2/3)*(1 - 2^(2/3)*(x^2 - x^4)^(1/3))*Sqrt[(1 + 2^(2/3)*(x^2 - x^4)^(1/3) + 2*2^(1/3)*(x^2 - x^4)^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(x^2 - x^4)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(x^2 - x^4)^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(x^2 - x^4)^(1/3))], -7 + 4*Sqrt[3]])/(2^(2/3)*(1 - 2*x^2)*(-x^2 + x^4)^(2/3)*Sqrt[-((1 - 2^(2/3)*(x^2 - x^4)^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(x^2 - x^4)^(1/3))^2)])","C",9,9,24,0.3750,0,"{1311, 2013, 622, 619, 236, 219, 2034, 758, 133}"
2502,1,343,0,1.1480855,"\int \frac{b+a x^6}{x^3 \left(-b+a x^3\right) \sqrt[4]{b x+a x^4}} \, dx","Int[(b + a*x^6)/(x^3*(-b + a*x^3)*(b*x + a*x^4)^(1/4)),x]","\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4+b x}}-\frac{2^{3/4} \sqrt[4]{x} (a+b) \sqrt[4]{a x^3+b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} b \sqrt[4]{a x^4+b x}}+\frac{2 \sqrt[4]{x} \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} \sqrt[4]{a x^4+b x}}-\frac{2^{3/4} \sqrt[4]{x} (a+b) \sqrt[4]{a x^3+b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{3/4}}{\sqrt[4]{a x^3+b}}\right)}{3 \sqrt[4]{a} b \sqrt[4]{a x^4+b x}}+\frac{4 (a+b) \left(a x^3+b\right)}{9 a b x^2 \sqrt[4]{a x^4+b x}}-\frac{4 \left(a x^3+b\right)}{9 a x^2 \sqrt[4]{a x^4+b x}}","\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*(b + a*x^3))/(9*a*x^2*(b*x + a*x^4)^(1/4)) + (4*(a + b)*(b + a*x^3))/(9*a*b*x^2*(b*x + a*x^4)^(1/4)) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4)) - (2^(3/4)*(a + b)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTan[(2^(1/4)*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*b*(b*x + a*x^4)^(1/4)) + (2*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*(b*x + a*x^4)^(1/4)) - (2^(3/4)*(a + b)*x^(1/4)*(b + a*x^3)^(1/4)*ArcTanh[(2^(1/4)*a^(1/4)*x^(3/4))/(b + a*x^3)^(1/4)])/(3*a^(1/4)*b*(b*x + a*x^4)^(1/4))","A",17,13,35,0.3714,1,"{2056, 6725, 264, 329, 275, 240, 212, 206, 203, 466, 465, 494, 453}"
2503,1,198,0,1.0358927,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{x^2 \sqrt{-b+a x}} \, dx","Int[Sqrt[a*x + Sqrt[-b + a*x]]/(x^2*Sqrt[-b + a*x]),x]","-\frac{a \left(2 \sqrt{b}+1\right) \tan ^{-1}\left(\frac{\sqrt{b}-\sqrt{a x-b}}{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a x-b}+a x}}\right)}{2 \sqrt{2} b^{5/4}}-\frac{a \left(1-2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{a x-b}+\sqrt{b}}{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a x-b}+a x}}\right)}{2 \sqrt{2} b^{5/4}}+\frac{\left(\sqrt{a x-b}+a x\right)^{3/2}}{b x}-\frac{a \sqrt{\sqrt{a x-b}+a x}}{b}","\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,"-((a*Sqrt[a*x + Sqrt[-b + a*x]])/b) + (a*x + Sqrt[-b + a*x])^(3/2)/(b*x) - (a*(1 + 2*Sqrt[b])*ArcTan[(Sqrt[b] - Sqrt[-b + a*x])/(Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(2*Sqrt[2]*b^(5/4)) - (a*(1 - 2*Sqrt[b])*ArcTanh[(Sqrt[b] + Sqrt[-b + a*x])/(Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(2*Sqrt[2]*b^(5/4))","A",8,6,34,0.1765,1,"{976, 1021, 1036, 1030, 208, 205}"
2504,0,0,0,0.0114076,"\int \frac{3+x}{\sqrt[3]{-1+x^2} \left(5-x+2 x^2\right)} \, dx","Int[(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,"Defer[Int][(3 + x)/((-1 + x^2)^(1/3)*(5 - x + 2*x^2)), x]","F",0,0,0,0,-1,"{}"
2505,0,0,0,23.8531872,"\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","Int[((-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,"(3*(2*k^2 - a*(1 + 2*b + k^2) - b*(1 + 4*k + k^2))*(1 - x)*(1 - k*x))/(4*(b - k)^2*x*((1 - x)*x*(1 - k*x))^(1/3)) + (3*(1 + k)*(a + k)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(4/3)*(1 - k*x)*Hypergeometric2F1[2/3, 4/3, 5/3, (1 - x)/(1 - k*x)])/(2*(1 - k)*(b - k)*x*((1 - x)*x*(1 - k*x))^(1/3)) + (3*(1 + k)*(2*k^2 - a*(1 + 2*b + k^2) - b*(1 + 4*k + k^2))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(4/3)*(1 - k*x)*Hypergeometric2F1[2/3, 4/3, 5/3, (1 - x)/(1 - k*x)])/(4*(1 - k)*(b - k)^2*x*((1 - x)*x*(1 - k*x))^(1/3)) + ((a + b)*(1 + k^3 + 3*b*(1 + k) + (4*b^2 + (1 - k)^2*(1 + k + k^2) + b*(5 + 2*k + 5*k^2))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(7/3)*(1 - k*x)^(1/3)*(-1 - k - Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^2*((1 - x)*x*(1 - k*x))^(1/3)) + ((a + b)*(1 + k^3 + 3*b*(1 + k) - (1 + 4*b^2 - k - k^3 + k^4 + b*(5 + 2*k + 5*k^2))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(7/3)*(1 - k*x)^(1/3)*(-1 - k + Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^2*((1 - x)*x*(1 - k*x))^(1/3))","F",0,0,0,0,-1,"{}"
2506,0,0,0,6.2130522,"\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","Int[((-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,"(3*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3)) - (3*(1 - I*Sqrt[3])*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) - (3*(1 + I*Sqrt[3])*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) - ((x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/(1 + x), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 + I*Sqrt[3])*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/(-1 - I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 - I*Sqrt[3])*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/(-1 + I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 - I*Sqrt[3])^(1/3)*(1 + I*Sqrt[3])*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/((1 - I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 - I*Sqrt[3])*(1 + I*Sqrt[3])^(1/3)*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/((1 + I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 - I*Sqrt[3])^(1/3)*(1 + I*Sqrt[3])*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/((1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 - I*Sqrt[3])*(1 + I*Sqrt[3])^(1/3)*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/((1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 - I*Sqrt[3])^(1/3)*(1 + I*Sqrt[3])*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/((1 - I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) + ((1 - I*Sqrt[3])*(1 + I*Sqrt[3])^(1/3)*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6 + x^9)^(1/3)/((1 + I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + x^2 + x^3)^(1/3)) - (6*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 + x^6 + x^9)^(1/3))/(1 - x^6 + x^9), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3)) + (9*(x + x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^6*(1 + x^6 + x^9)^(1/3))/(1 - x^6 + x^9), x], x, x^(1/3)])/(x^(1/3)*(1 + x^2 + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2507,1,750,0,4.3047603,"\int \frac{\sqrt[4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/(-2*b + a*x + 2*x^2),x]","\frac{\left(-\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{-a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{a-\sqrt{a^2+16 b}} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2+16 b}} \left(-a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}+\frac{\left(\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{\sqrt{a^2+16 b}+a} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2+16 b}+a} \left(a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}-\frac{\left(-\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{-a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{a-\sqrt{a^2+16 b}} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2+16 b}} \left(-a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}-\frac{\left(\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{\sqrt{a^2+16 b}+a} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2+16 b}+a} \left(a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}-\frac{\sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}+\frac{\sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}","\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,"-((a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4))) + ((a^2 - 2*b - (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^2 - 2*b + (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + (a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) - ((a^2 - 2*b - (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^2 - 2*b + (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4))","B",17,11,30,0.3667,1,"{2056, 905, 63, 331, 298, 203, 206, 6728, 93, 205, 208}"
2508,1,750,0,3.1766137,"\int \frac{\sqrt[4]{b x^3+a x^4}}{-2 b+a x+2 x^2} \, dx","Int[(b*x^3 + a*x^4)^(1/4)/(-2*b + a*x + 2*x^2),x]","\frac{\left(-\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{-a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{a-\sqrt{a^2+16 b}} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2+16 b}} \left(-a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}+\frac{\left(\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{\sqrt{a^2+16 b}+a} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2+16 b}+a} \left(a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}-\frac{\left(-\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{-a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{a-\sqrt{a^2+16 b}} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a-\sqrt{a^2+16 b}} \left(-a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}-\frac{\left(\frac{a \left(a^2+6 b\right)}{\sqrt{a^2+16 b}}+a^2-2 b\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{a^2+16 b}+a^2-4 b}}{\sqrt[4]{\sqrt{a^2+16 b}+a} \sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{a^2+16 b}+a} \left(a \sqrt{a^2+16 b}+a^2-4 b\right)^{3/4} \sqrt[4]{a x+b}}-\frac{\sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}+\frac{\sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}","\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,"-((a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4))) + ((a^2 - 2*b - (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^2 - 2*b + (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + (a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) - ((a^2 - 2*b - (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a - Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b - a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^2 - 2*b + (a*(a^2 + 6*b))/Sqrt[a^2 + 16*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 16*b])^(1/4)*(b + a*x)^(1/4))])/((a + Sqrt[a^2 + 16*b])^(1/4)*(a^2 - 4*b + a*Sqrt[a^2 + 16*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4))","B",17,11,30,0.3667,1,"{2056, 905, 63, 331, 298, 203, 206, 6728, 93, 205, 208}"
2509,1,99,0,0.3855891,"\int \frac{\left(1+x^3\right)^{2/3} \left(-1+2 x^6\right)}{x^6 \left(-1+2 x^3\right)} \, dx","Int[((1 + x^3)^(2/3)*(-1 + 2*x^6))/(x^6*(-1 + 2*x^3)),x]","2 x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,2 x^3\right)-\log \left(\sqrt[3]{x^3+1}-x\right)+\frac{2 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3+1\right)^{5/3}}{5 x^5}-\frac{\left(x^3+1\right)^{2/3}}{x^2}","-\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 + x^3)^(2/3)/x^2) - (1 + x^3)^(5/3)/(5*x^5) + 2*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, 2*x^3] + (2*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] - Log[-x + (1 + x^3)^(1/3)]","C",6,5,29,0.1724,0,"{6725, 264, 277, 239, 429}"
2510,0,0,0,0.6269775,"\int \frac{-b+a x^4}{\left(b+a x^4\right) \sqrt[4]{b^2+c x^4+a^2 x^8}} \, dx","Int[(-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,"(x*(1 + (2*a^2*x^4)/(c - Sqrt[-4*a^2*b^2 + c^2]))^(1/4)*(1 + (2*a^2*x^4)/(c + Sqrt[-4*a^2*b^2 + c^2]))^(1/4)*AppellF1[1/4, 1/4, 1/4, 5/4, (-2*a^2*x^4)/(c - Sqrt[-4*a^2*b^2 + c^2]), (-2*a^2*x^4)/(c + Sqrt[-4*a^2*b^2 + c^2])])/(b^2 + c*x^4 + a^2*x^8)^(1/4) - 2*b*Defer[Int][1/((b + a*x^4)*(b^2 + c*x^4 + a^2*x^8)^(1/4)), x]","F",0,0,0,0,-1,"{}"
2511,1,365,0,1.0284761,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^2\right)} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(Sqrt[1 + x]*(1 + x^2)),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)}{2 \sqrt{\frac{1-i}{i+\sqrt{1-i}}}}+\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)}{2 \sqrt{-\frac{1+i}{i-\sqrt{1+i}}}}+\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)}{2 \sqrt{-\frac{1-i}{i-\sqrt{1-i}}}}-\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)}{2 \sqrt{\frac{1+i}{i+\sqrt{1+i}}}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-5 \text{$\#$1}^4 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"((-1/2*I)*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I)/(I + Sqrt[1 - I])] + ((I/2)*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 - I)/(I - Sqrt[1 + I])] + ((I/2)*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(-1 + I)/(I - Sqrt[1 - I])] - ((I/2)*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I)/(I + Sqrt[1 + I])]","C",20,8,28,0.2857,0,"{6741, 6728, 990, 621, 206, 1033, 724, 204}"
2512,1,365,0,0.8057783,"\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x} \left(1+x^2\right)} \, dx","Int[Sqrt[x + Sqrt[1 + x]]/(Sqrt[1 + x]*(1 + x^2)),x]","-\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{\frac{1-i}{i+\sqrt{1-i}}}}+\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{-\frac{1+i}{i-\sqrt{1+i}}}}+\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{-\frac{1-i}{i-\sqrt{1-i}}}}-\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)}{2 \sqrt{\frac{1+i}{i+\sqrt{1+i}}}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^5+20 \text{$\#$1}^4-48 \text{$\#$1}^3+40 \text{$\#$1}^2-8 \text{$\#$1}+1\&,\frac{2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-5 \text{$\#$1}^4 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)+5 \text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)-\log \left(\text{$\#$1}+\sqrt{x+1}-\sqrt{x+\sqrt{x+1}}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+5 \text{$\#$1}^4+10 \text{$\#$1}^3-18 \text{$\#$1}^2+10 \text{$\#$1}-1}\&\right]",1,"((-1/2*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)/(I + Sqrt[1 - I])] + ((I/2)*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)/(I - Sqrt[1 + I])] + ((I/2)*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)/(I - Sqrt[1 - I])] - ((I/2)*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)/(I + Sqrt[1 + I])]","C",20,8,28,0.2857,0,"{6741, 6728, 990, 621, 206, 1033, 724, 204}"
2513,0,0,0,1.5132173,"\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","Int[((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,"((-19 + 66*x - 30*x^2 + 9*x^3)^(1/3)*Defer[Subst][Defer[Int][((7 + 9*x)^(1/3)*(343 - 63*x + 81*x^2)^(1/3))/(-35/9 + x), x], x, -10/9 + x])/(63*3^(1/3)*(-1 + 3*x)^(1/3)*(19 - 9*x + 3*x^2)^(1/3)) - (2*(-19 + 66*x - 30*x^2 + 9*x^3)^(1/3)*Defer[Subst][Defer[Int][((7 + 9*x)^(1/3)*(343 - 63*x + 81*x^2)^(1/3))/(-7/9 + 2*x)^2, x], x, -10/9 + x])/(3*3^(1/3)*(-1 + 3*x)^(1/3)*(19 - 9*x + 3*x^2)^(1/3)) + (2*(-19 + 66*x - 30*x^2 + 9*x^3)^(1/3)*Defer[Subst][Defer[Int][((7 + 9*x)^(1/3)*(343 - 63*x + 81*x^2)^(1/3))/(-7/9 + 2*x), x], x, -10/9 + x])/(21*3^(1/3)*(-1 + 3*x)^(1/3)*(19 - 9*x + 3*x^2)^(1/3)) - (2*(2 + I*Sqrt[3])*(-19 + 66*x - 30*x^2 + 9*x^3)^(1/3)*Defer[Subst][Defer[Int][((7 + 9*x)^(1/3)*(343 - 63*x + 81*x^2)^(1/3))/((60 + 27*(-1 - I*Sqrt[3]))/27 + 2*x), x], x, -10/9 + x])/(63*3^(1/3)*(-1 + 3*x)^(1/3)*(19 - 9*x + 3*x^2)^(1/3)) - (2*(2 - I*Sqrt[3])*(-19 + 66*x - 30*x^2 + 9*x^3)^(1/3)*Defer[Subst][Defer[Int][((7 + 9*x)^(1/3)*(343 - 63*x + 81*x^2)^(1/3))/((60 + 27*(-1 + I*Sqrt[3]))/27 + 2*x), x], x, -10/9 + x])/(63*3^(1/3)*(-1 + 3*x)^(1/3)*(19 - 9*x + 3*x^2)^(1/3))","F",0,0,0,0,-1,"{}"
2514,0,0,0,1.5340057,"\int \frac{1+x^3}{\left(-1+x^3\right) \sqrt[3]{x^2+x^4}} \, dx","Int[(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,"(-2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^2)/(1 - I*Sqrt[3]), -x^2])/(x^2 + x^4)^(1/3) - (2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^2)/(1 + I*Sqrt[3]), -x^2])/(x^2 + x^4)^(1/3) - ((I - Sqrt[3])*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^2, (-2*x^2)/(1 - I*Sqrt[3])])/(2*(I + Sqrt[3])*(x^2 + x^4)^(1/3)) - ((I + Sqrt[3])*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^2, (-2*x^2)/(1 + I*Sqrt[3])])/(2*(I - Sqrt[3])*(x^2 + x^4)^(1/3)) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3) + (2*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(x^2 + x^4)^(1/3)) - (2*(1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(x^2 + x^4)^(1/3)) - (2*(1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(3*(x^2 + x^4)^(1/3))","F",0,0,0,0,-1,"{}"
2515,0,0,0,16.8110994,"\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","Int[(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,"(9*(a + b)*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a*b*d - a*(1 + b/a)*d*x^3 + d*x^6 - x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (12*a*b*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(-(a*b*d) + a*(1 + b/a)*d*x^3 - d*x^6 + x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (6*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^9/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(-(a*b*d) + a*(1 + b/a)*d*x^3 - d*x^6 + x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3)","F",0,0,0,0,-1,"{}"
2516,1,97,0,0.0439417,"\int \frac{\sqrt{b+a x^4}}{-b+a x^4} \, dx","Int[Sqrt[b + a*x^4]/(-b + a*x^4),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[4]{b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt[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)}{\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,"-1/2*ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[b + a*x^4]]/(Sqrt[2]*a^(1/4)*b^(1/4)) - ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[b + a*x^4]]/(2*Sqrt[2]*a^(1/4)*b^(1/4))","A",4,4,23,0.1739,1,"{404, 212, 206, 203}"
2517,0,0,0,0.4079454,"\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Int[(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,"(x*(1 - x^6)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^6])/(-1 + x^6)^(1/3) - (1 - Sqrt[5])*Defer[Int][1/((1 - Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x] - (1 + Sqrt[5])*Defer[Int][1/((1 + Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
2518,0,0,0,0.3207788,"\int \frac{1+x^2}{\left(-1+x+x^2\right) \sqrt[3]{-1+x^6}} \, dx","Int[(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,"(x*(1 - x^6)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, x^6])/(-1 + x^6)^(1/3) - (1 - Sqrt[5])*Defer[Int][1/((1 - Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x] - (1 + Sqrt[5])*Defer[Int][1/((1 + Sqrt[5] + 2*x)*(-1 + x^6)^(1/3)), x]","F",0,0,0,0,-1,"{}"
2519,1,4727,0,5.1546262,"\int \frac{x^3 \sqrt[3]{-x^2+x^3}}{1+x^6} \, dx","Int[(x^3*(-x^2 + x^3)^(1/3))/(1 + x^6),x]","-\frac{1}{216} \sqrt[6]{-1} \left((1+6 i)+6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} x^2+\frac{1}{216} \sqrt[6]{-1} \left((1-6 i)-6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} x^2+\frac{1}{216} (-1)^{2/3} \left(12+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} x^2+\frac{1}{216} (-1)^{2/3} \left(12-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} x^2+\frac{1}{9} \sqrt[3]{x^3-x^2} x^2-\frac{1}{162} \sqrt[6]{-1} \left((1+6 i)+6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} x+\frac{1}{24} \sqrt[3]{-1} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} x-\frac{1}{24} i \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} x+\frac{1}{24} i \left((-2-i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} x+\frac{1}{162} \sqrt[6]{-1} \left((1-6 i)-6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} x+\frac{1}{162} (-1)^{2/3} \left(12+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} x+\frac{1}{162} (-1)^{2/3} \left(12-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} x+\frac{1}{12} i \left(1-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} x-\frac{1}{54} \sqrt[3]{x^3-x^2} x-\frac{5}{486} \sqrt[6]{-1} \left((1+6 i)+6 \sqrt{3}\right) \sqrt[3]{x^3-x^2}+\frac{5}{72} \sqrt[3]{-1} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2}-\frac{1}{12} i \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2}-\left(\frac{5}{72}+\frac{5 i}{72}\right) \sqrt[3]{-1} \left(1+\sqrt{3}\right) \sqrt[3]{x^3-x^2}+\frac{5}{72} i \left((-2-i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2}+\frac{1}{12} \left((1+2 i)-i \sqrt{3}\right) \sqrt[3]{x^3-x^2}+\frac{5}{486} \sqrt[6]{-1} \left((1-6 i)-6 \sqrt{3}\right) \sqrt[3]{x^3-x^2}-\frac{1}{6} i \left(1+(-1)^{5/6}\right) \sqrt[3]{x^3-x^2}+\frac{1}{6} i \left(1-(-1)^{5/6}\right) \sqrt[3]{x^3-x^2}+\frac{5}{486} (-1)^{2/3} \left(12+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2}+\frac{5}{486} (-1)^{2/3} \left(12-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2}+\frac{5}{36} i \left(1-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2}-\frac{59}{162} \sqrt[3]{x^3-x^2}+\frac{11 i \left(3+(2+i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{108 \sqrt[3]{x-1} x^{2/3}}-\frac{5 i \left((36+3 i)+(1+12 i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{1458 \sqrt[3]{x-1} x^{2/3}}-\frac{5 i \left((-36-3 i)+(1+12 i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{1458 \sqrt[3]{x-1} x^{2/3}}-\frac{11 \left(3 i+(1+2 i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{108 \sqrt[3]{x-1} x^{2/3}}-\frac{5 \left(3 i+(1-2 i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{108 \sqrt[3]{x-1} x^{2/3}}+\frac{\left(3+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt[3]{x-1} x^{2/3}}-\frac{\left(3-\sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{6 \sqrt[3]{x-1} x^{2/3}}+\frac{i \left(3-(2-i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{18 \sqrt[3]{x-1} x^{2/3}}-\frac{5 \left((3+36 i)-(12+i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{1458 \sqrt[3]{x-1} x^{2/3}}-\frac{5 \left((-3-36 i)-(12+i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{1458 \sqrt[3]{x-1} x^{2/3}}+\frac{i \left(1+(-1)^{5/6}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}-\frac{5 i \left(1-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{18 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}-\frac{22 \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{81 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[6]{-1} \sqrt[3]{-1+i} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-i} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}-\frac{i \sqrt[3]{1+i} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1+i} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{12}-\frac{i}{12}\right) \left(3-\sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-\sqrt[6]{-1}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\left(1-\sqrt[6]{-1}\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[6]{-1} \left(-\frac{1}{1+\sqrt[6]{-1}}\right)^{2/3} \left(i+\sqrt[3]{-1}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1+\sqrt[6]{-1}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{i \sqrt[3]{\frac{1}{2} \left((-2+i)-\sqrt{3}\right)} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-(-1)^{5/6}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{12}+\frac{i}{12}\right) \left(3-\sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1+(-1)^{5/6}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\left(1+(-1)^{5/6}\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[6]{-1} \sqrt[3]{-1+i} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1-i} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{4 \sqrt[3]{x-1} x^{2/3}}-\frac{i \sqrt[3]{1+i} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1+i} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{4 \sqrt[3]{x-1} x^{2/3}}-\frac{(-1)^{5/6} \sqrt[3]{-1+\sqrt[6]{-1}} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1-\sqrt[6]{-1}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{4 \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[6]{-1} \left(-\frac{1}{1+\sqrt[6]{-1}}\right)^{2/3} \left(i+\sqrt[3]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1+\sqrt[6]{-1}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{4 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{-1} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1-(-1)^{5/6}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{8 \left(-1+(-1)^{5/6}\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{\left(-\frac{1}{1+(-1)^{5/6}}\right)^{2/3} \left((-2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1+(-1)^{5/6}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{8 \sqrt[3]{x-1} x^{2/3}}+\frac{5 \sqrt[6]{-1} \left((1+6 i)+6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{486 \sqrt[3]{x-1} x^{2/3}}-\frac{(-1)^{2/3} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{8 \sqrt[3]{x-1} x^{2/3}}-\frac{5 \sqrt[3]{-1} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{72 \sqrt[3]{x-1} x^{2/3}}+\frac{i \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{12 \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{5}{72}+\frac{5 i}{72}\right) \sqrt[3]{-1} \left(1+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{\sqrt[3]{x-1} x^{2/3}}+\frac{(-1)^{2/3} \left((-2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{8 \sqrt[3]{x-1} x^{2/3}}+\frac{i \left((-2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{12 \sqrt[3]{x-1} x^{2/3}}-\frac{5 i \left((-2-i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{72 \sqrt[3]{x-1} x^{2/3}}-\frac{5 \sqrt[6]{-1} \left((1-6 i)-6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{486 \sqrt[3]{x-1} x^{2/3}}+\frac{i \left(1+(-1)^{5/6}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{6 \sqrt[3]{x-1} x^{2/3}}-\frac{i \left(1-(-1)^{5/6}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{6 \sqrt[3]{x-1} x^{2/3}}-\frac{(-1)^{5/6} \left(i-\sqrt[3]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{4 \sqrt[3]{x-1} x^{2/3}}-\frac{5 (-1)^{2/3} \left(12+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{486 \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[6]{-1} \left(1+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{4 \sqrt[3]{x-1} x^{2/3}}-\frac{5 (-1)^{2/3} \left(12-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{486 \sqrt[3]{x-1} x^{2/3}}-\frac{5 i \left(1-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{36 \sqrt[3]{x-1} x^{2/3}}-\frac{11 \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{81 \sqrt[3]{x-1} x^{2/3}}+\frac{\left(-\frac{1}{1+(-1)^{5/6}}\right)^{2/3} \left((-2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\sqrt[6]{-1}-x\right)}{24 \sqrt[3]{x-1} x^{2/3}}+\frac{(-1)^{5/6} \sqrt[3]{-1+\sqrt[6]{-1}} \sqrt[3]{x^3-x^2} \log \left(-x-(-1)^{5/6}\right)}{12 \sqrt[3]{x-1} x^{2/3}}+\frac{5 \sqrt[6]{-1} \left((1+6 i)+6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{1458 \sqrt[3]{x-1} x^{2/3}}-\frac{(-1)^{2/3} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{24 \sqrt[3]{x-1} x^{2/3}}-\frac{5 \sqrt[3]{-1} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{216 \sqrt[3]{x-1} x^{2/3}}+\frac{11 i \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{216 \sqrt[3]{x-1} x^{2/3}}+\frac{(-1)^{2/3} \left((-2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{24 \sqrt[3]{x-1} x^{2/3}}+\frac{i \left((-2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{36 \sqrt[3]{x-1} x^{2/3}}-\frac{5 i \left((-2-i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{216 \sqrt[3]{x-1} x^{2/3}}-\frac{5 \sqrt[6]{-1} \left((1-6 i)-6 \sqrt{3}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{1458 \sqrt[3]{x-1} x^{2/3}}+\frac{i \left(1+(-1)^{5/6}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{18 \sqrt[3]{x-1} x^{2/3}}-\frac{i \left(1-(-1)^{5/6}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{18 \sqrt[3]{x-1} x^{2/3}}-\frac{(-1)^{5/6} \left(i-\sqrt[3]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{12 \sqrt[3]{x-1} x^{2/3}}-\frac{5 (-1)^{2/3} \left(12+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{1458 \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[6]{-1} \left(1+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{12 \sqrt[3]{x-1} x^{2/3}}-\frac{5 (-1)^{2/3} \left(12-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{1458 \sqrt[3]{x-1} x^{2/3}}-\frac{5 i \left(1-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{108 \sqrt[3]{x-1} x^{2/3}}-\frac{11 \sqrt[3]{x^3-x^2} \log (x-1)}{243 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[6]{-1} \left(-\frac{1}{1+\sqrt[6]{-1}}\right)^{2/3} \left(i+\sqrt[3]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{-1} x+\sqrt[6]{-1}\right)}{12 \sqrt[3]{x-1} x^{2/3}}+\frac{i \sqrt[3]{1+i} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{-1} x-(-1)^{5/6}\right)}{12 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[6]{-1} \sqrt[3]{-1+i} \sqrt[3]{x^3-x^2} \log \left(\sqrt[6]{-1}-(-1)^{2/3} x\right)}{12 \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[3]{-1} \left((2+i)+\sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(-(-1)^{2/3} x-(-1)^{5/6}\right)}{24 \left(-1+(-1)^{5/6}\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}","\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,"(-59*(-x^2 + x^3)^(1/3))/162 + ((5*I)/36)*(1 - (-1)^(1/6))*(-x^2 + x^3)^(1/3) + (5*(-1)^(2/3)*(12 - (-1)^(1/6))*(-x^2 + x^3)^(1/3))/486 + (5*(-1)^(2/3)*(12 + (-1)^(1/6))*(-x^2 + x^3)^(1/3))/486 + (I/6)*(1 - (-1)^(5/6))*(-x^2 + x^3)^(1/3) - (I/6)*(1 + (-1)^(5/6))*(-x^2 + x^3)^(1/3) + (5*(-1)^(1/6)*((1 - 6*I) - 6*Sqrt[3])*(-x^2 + x^3)^(1/3))/486 + (((1 + 2*I) - I*Sqrt[3])*(-x^2 + x^3)^(1/3))/12 + ((5*I)/72)*((-2 - I) + Sqrt[3])*(-x^2 + x^3)^(1/3) - (5/72 + (5*I)/72)*(-1)^(1/3)*(1 + Sqrt[3])*(-x^2 + x^3)^(1/3) - (I/12)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3) + (5*(-1)^(1/3)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3))/72 - (5*(-1)^(1/6)*((1 + 6*I) + 6*Sqrt[3])*(-x^2 + x^3)^(1/3))/486 - (x*(-x^2 + x^3)^(1/3))/54 + (I/12)*(1 - (-1)^(1/6))*x*(-x^2 + x^3)^(1/3) + ((-1)^(2/3)*(12 - (-1)^(1/6))*x*(-x^2 + x^3)^(1/3))/162 + ((-1)^(2/3)*(12 + (-1)^(1/6))*x*(-x^2 + x^3)^(1/3))/162 + ((-1)^(1/6)*((1 - 6*I) - 6*Sqrt[3])*x*(-x^2 + x^3)^(1/3))/162 + (I/24)*((-2 - I) + Sqrt[3])*x*(-x^2 + x^3)^(1/3) - (I/24)*((2 + I) + Sqrt[3])*x*(-x^2 + x^3)^(1/3) + ((-1)^(1/3)*((2 + I) + Sqrt[3])*x*(-x^2 + x^3)^(1/3))/24 - ((-1)^(1/6)*((1 + 6*I) + 6*Sqrt[3])*x*(-x^2 + x^3)^(1/3))/162 + (x^2*(-x^2 + x^3)^(1/3))/9 + ((-1)^(2/3)*(12 - (-1)^(1/6))*x^2*(-x^2 + x^3)^(1/3))/216 + ((-1)^(2/3)*(12 + (-1)^(1/6))*x^2*(-x^2 + x^3)^(1/3))/216 + ((-1)^(1/6)*((1 - 6*I) - 6*Sqrt[3])*x^2*(-x^2 + x^3)^(1/3))/216 - ((-1)^(1/6)*((1 + 6*I) + 6*Sqrt[3])*x^2*(-x^2 + x^3)^(1/3))/216 - (22*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(81*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) - (((5*I)/18)*(1 - (-1)^(1/6))*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + ((I/3)*(1 + (-1)^(5/6))*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) - (5*((-3 - 36*I) - (12 + I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(1458*(-1 + x)^(1/3)*x^(2/3)) - (5*((3 + 36*I) - (12 + I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(1458*(-1 + x)^(1/3)*x^(2/3)) + ((I/18)*(3 - (2 - I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3)) - ((3 - Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(6*(-1 + x)^(1/3)*x^(2/3)) + ((3 + Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(6*(-1 + x)^(1/3)*x^(2/3)) - (5*(3*I + (1 - 2*I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(108*(-1 + x)^(1/3)*x^(2/3)) - (11*(3*I + (1 + 2*I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(108*(-1 + x)^(1/3)*x^(2/3)) - (((5*I)/1458)*((-36 - 3*I) + (1 + 12*I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3)) - (((5*I)/1458)*((36 + 3*I) + (1 + 12*I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3)) + (((11*I)/108)*(3 + (2 + I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3)) + ((-1)^(1/6)*(-1 + I)^(1/3)*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 - I)^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(2*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) - ((I/2)*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + I)^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + ((1/12 - I/12)*(3 - Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 - (-1)^(1/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((1 - (-1)^(1/6))^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((-1)^(1/6)*(-(1 + (-1)^(1/6))^(-1))^(2/3)*(I + (-1)^(1/3))*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + (-1)^(1/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(2*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + ((I/2)*(((-2 + I) - Sqrt[3])/2)^(1/3)*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 - (-1)^(5/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + ((1/12 + I/12)*(3 - Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + (-1)^(5/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((1 + (-1)^(5/6))^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((-1)^(1/6)*(-1 + I)^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 - I)^(1/3)*x^(1/3)])/(4*(-1 + x)^(1/3)*x^(2/3)) - ((I/4)*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 + I)^(1/3)*x^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - ((-1)^(5/6)*(-1 + (-1)^(1/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 - (-1)^(1/6))^(1/3)*x^(1/3)])/(4*(-1 + x)^(1/3)*x^(2/3)) + ((-1)^(1/6)*(-(1 + (-1)^(1/6))^(-1))^(2/3)*(I + (-1)^(1/3))*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 + (-1)^(1/6))^(1/3)*x^(1/3)])/(4*(-1 + x)^(1/3)*x^(2/3)) - ((-1)^(1/3)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 - (-1)^(5/6))^(1/3)*x^(1/3)])/(8*(-1 + (-1)^(5/6))^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - ((-(1 + (-1)^(5/6))^(-1))^(2/3)*((-2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 + (-1)^(5/6))^(1/3)*x^(1/3)])/(8*(-1 + x)^(1/3)*x^(2/3)) - (11*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(81*(-1 + x)^(1/3)*x^(2/3)) - (((5*I)/36)*(1 - (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(2/3)*(12 - (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(486*(-1 + x)^(1/3)*x^(2/3)) + ((-1)^(1/6)*(1 + (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(4*(-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(2/3)*(12 + (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(486*(-1 + x)^(1/3)*x^(2/3)) - ((-1)^(5/6)*(I - (-1)^(1/3))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(4*(-1 + x)^(1/3)*x^(2/3)) - ((I/6)*(1 - (-1)^(5/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + ((I/6)*(1 + (-1)^(5/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(1/6)*((1 - 6*I) - 6*Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(486*(-1 + x)^(1/3)*x^(2/3)) - (((5*I)/72)*((-2 - I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + ((I/12)*((-2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + ((-1)^(2/3)*((-2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(8*(-1 + x)^(1/3)*x^(2/3)) + ((5/72 + (5*I)/72)*(-1)^(1/3)*(1 + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + ((I/12)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(1/3)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(72*(-1 + x)^(1/3)*x^(2/3)) - ((-1)^(2/3)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(8*(-1 + x)^(1/3)*x^(2/3)) + (5*(-1)^(1/6)*((1 + 6*I) + 6*Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(486*(-1 + x)^(1/3)*x^(2/3)) + ((-(1 + (-1)^(5/6))^(-1))^(2/3)*((-2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[(-1)^(1/6) - x])/(24*(-1 + x)^(1/3)*x^(2/3)) + ((-1)^(5/6)*(-1 + (-1)^(1/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1)^(5/6) - x])/(12*(-1 + x)^(1/3)*x^(2/3)) - (11*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(243*(-1 + x)^(1/3)*x^(2/3)) - (((5*I)/108)*(1 - (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(2/3)*(12 - (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(1458*(-1 + x)^(1/3)*x^(2/3)) + ((-1)^(1/6)*(1 + (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(12*(-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(2/3)*(12 + (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(1458*(-1 + x)^(1/3)*x^(2/3)) - ((-1)^(5/6)*(I - (-1)^(1/3))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(12*(-1 + x)^(1/3)*x^(2/3)) - ((I/18)*(1 - (-1)^(5/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) + ((I/18)*(1 + (-1)^(5/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(1/6)*((1 - 6*I) - 6*Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(1458*(-1 + x)^(1/3)*x^(2/3)) - (((5*I)/216)*((-2 - I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) + ((I/36)*((-2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) + ((-1)^(2/3)*((-2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(24*(-1 + x)^(1/3)*x^(2/3)) + (((11*I)/216)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) - (5*(-1)^(1/3)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(216*(-1 + x)^(1/3)*x^(2/3)) - ((-1)^(2/3)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(24*(-1 + x)^(1/3)*x^(2/3)) + (5*(-1)^(1/6)*((1 + 6*I) + 6*Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(1458*(-1 + x)^(1/3)*x^(2/3)) - ((-1)^(1/6)*(-(1 + (-1)^(1/6))^(-1))^(2/3)*(I + (-1)^(1/3))*(-x^2 + x^3)^(1/3)*Log[(-1)^(1/6) + (-1)^(1/3)*x])/(12*(-1 + x)^(1/3)*x^(2/3)) + ((I/12)*(1 + I)^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1)^(5/6) + (-1)^(1/3)*x])/((-1 + x)^(1/3)*x^(2/3)) - ((-1)^(1/6)*(-1 + I)^(1/3)*(-x^2 + x^3)^(1/3)*Log[(-1)^(1/6) - (-1)^(2/3)*x])/(12*(-1 + x)^(1/3)*x^(2/3)) + ((-1)^(1/3)*((2 + I) + Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-(-1)^(5/6) - (-1)^(2/3)*x])/(24*(-1 + (-1)^(5/6))^(2/3)*(-1 + x)^(1/3)*x^(2/3))","C",103,8,24,0.3333,0,"{2056, 6725, 101, 157, 50, 59, 105, 91}"
2520,1,611,0,2.6427377,"\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","Int[(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{\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)}{2 \sqrt[4]{a} \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-\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}\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)}{2 \sqrt[4]{a} \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)}{2 \sqrt[4]{a} \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-\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}\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)}{2 \sqrt[4]{a} \left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}+\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}}","\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)]/(2*a^(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))])/(2*a^(1/4)*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(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))])/(2*a^(1/4)*(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)]/(2*a^(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))])/(2*a^(1/4)*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(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))])/(2*a^(1/4)*(c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4))","B",16,8,46,0.1739,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2521,1,611,0,1.8987719,"\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","Int[(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{\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)}{2 \sqrt[4]{a} \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-\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}\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)}{2 \sqrt[4]{a} \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)}{2 \sqrt[4]{a} \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-\frac{12 a b-c^2}{\sqrt{16 a b+c^2}}\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)}{2 \sqrt[4]{a} \left(\sqrt{16 a b+c^2}+c\right)^{3/4} \sqrt[4]{\sqrt{16 a b+c^2}-4 b+c}}+\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}}","\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)]/(2*a^(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))])/(2*a^(1/4)*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(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))])/(2*a^(1/4)*(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)]/(2*a^(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))])/(2*a^(1/4)*(-c + Sqrt[16*a*b + c^2])^(3/4)*(4*b - c + Sqrt[16*a*b + c^2])^(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))])/(2*a^(1/4)*(c + Sqrt[16*a*b + c^2])^(3/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(1/4))","B",16,8,46,0.1739,1,"{6728, 240, 212, 206, 203, 377, 208, 205}"
2522,1,774,0,0.7831161,"\int \frac{1}{x^3 \left(1+x^3\right) \sqrt[3]{-x^2+x^3}} \, dx","Int[1/(x^3*(1 + x^3)*(-x^2 + x^3)^(1/3)),x]","-\frac{\left(3-4 (-1)^{2/3}\right) (1-x)}{20 x \sqrt[3]{x^3-x^2}}-\frac{\left(3+4 \sqrt[3]{-1}\right) (1-x)}{20 x \sqrt[3]{x^3-x^2}}+\frac{1-x}{20 x \sqrt[3]{x^3-x^2}}-\frac{3 (1-x)}{8 x^2 \sqrt[3]{x^3-x^2}}-\frac{\left(5+16 i \sqrt{3}\right) (1-x)}{40 \sqrt[3]{x^3-x^2}}-\frac{\left(5-16 i \sqrt{3}\right) (1-x)}{40 \sqrt[3]{x^3-x^2}}-\frac{17 (1-x)}{40 \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (-x-1)}{6 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(\sqrt[3]{-1} x-1\right)}{6 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log \left(-(-1)^{2/3} x-1\right)}{6 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3-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}}+\frac{3 \left(x^3-x^2\right)^{2/3} \left(9 x^2+6 x+5\right)}{40 x^4}",1,"(-17*(1 - x))/(40*(-x^2 + x^3)^(1/3)) - ((5 - (16*I)*Sqrt[3])*(1 - x))/(40*(-x^2 + x^3)^(1/3)) - ((5 + (16*I)*Sqrt[3])*(1 - x))/(40*(-x^2 + x^3)^(1/3)) - (3*(1 - x))/(8*x^2*(-x^2 + x^3)^(1/3)) + (1 - x)/(20*x*(-x^2 + x^3)^(1/3)) - ((3 + 4*(-1)^(1/3))*(1 - x))/(20*x*(-x^2 + x^3)^(1/3)) - ((3 - 4*(-1)^(2/3))*(1 - x))/(20*x*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*Sqrt[3]*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(2*2^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3) - x^(1/3)])/(2*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3) - x^(1/3)])/(2*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - x])/(6*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1)^(1/3)*x])/(6*(1 - (-1)^(1/3))^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - (-1)^(2/3)*x])/(6*(1 + (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3))","C",18,6,24,0.2500,1,"{2056, 6725, 129, 155, 12, 91}"
2523,1,1271,0,3.160671,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^3+x^4}}{1+x^2+x^4} \, dx","Int[((-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^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} 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 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4))) - ((1 + I*Sqrt[3])*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - ((1 - I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) - ((1 - I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) - ((1 + I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) - ((1 + I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4))","C",35,12,27,0.4444,1,"{2056, 6728, 906, 63, 331, 298, 203, 206, 6725, 93, 205, 208}"
2524,1,1271,0,2.8190292,"\int \frac{\left(-1+x^2\right) \sqrt[4]{x^3+x^4}}{1+x^2+x^4} \, dx","Int[((-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^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1-i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1-i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1-i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1-i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{-\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1+i \sqrt{3}\right) \sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2}+\sqrt{-1+i \sqrt{3}}} \sqrt[4]{x}}{\sqrt[8]{-1+i \sqrt{3}} \sqrt[4]{x+1}}\right)}{2 \sqrt[8]{-1+i \sqrt{3}} 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 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4))) - ((1 + I*Sqrt[3])*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) + ((1 - I*Sqrt[3])*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + ((1 + I*Sqrt[3])*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - ((1 - I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((-Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) - ((1 - I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((Sqrt[2] + Sqrt[-1 - I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 - I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 - I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) - ((1 + I*Sqrt[3])*(-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((-Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4)) - ((1 + I*Sqrt[3])*(Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((Sqrt[2] + Sqrt[-1 + I*Sqrt[3]])^(1/4)*x^(1/4))/((-1 + I*Sqrt[3])^(1/8)*(1 + x)^(1/4))])/(2*(-1 + I*Sqrt[3])^(1/8)*x^(3/4)*(1 + x)^(1/4))","C",35,12,27,0.4444,1,"{2056, 6728, 906, 63, 331, 298, 203, 206, 6725, 93, 205, 208}"
2525,1,200,0,0.6553947,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx","Int[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b - a*x^2 + x^4),x]","\frac{4 b x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{5}{4};\frac{7}{4};\frac{2 x^2}{a-\sqrt{a^2-4 b}},\frac{a x^2}{b}\right)}{3 \left(-a \sqrt{a^2-4 b}+a^2-4 b\right) \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{4 b x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{5}{4};\frac{7}{4};\frac{2 x^2}{a+\sqrt{a^2-4 b}},\frac{a x^2}{b}\right)}{3 \left(a \sqrt{a^2-4 b}+a^2-4 b\right) \sqrt[4]{1-\frac{a x^2}{b}}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \left(-a^2\right) \log (x)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)-a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a b \log (x)}{\text{$\#$1}^3 a-2 \text{$\#$1}^7}\&\right]+a^{5/4} \left(-\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)\right)+a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)",1,"(4*b*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -5/4, 7/4, (2*x^2)/(a - Sqrt[a^2 - 4*b]), (a*x^2)/b])/(3*(a^2 - a*Sqrt[a^2 - 4*b] - 4*b)*(1 - (a*x^2)/b)^(1/4)) + (4*b*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -5/4, 7/4, (2*x^2)/(a + Sqrt[a^2 - 4*b]), (a*x^2)/b])/(3*(a^2 + a*Sqrt[a^2 - 4*b] - 4*b)*(1 - (a*x^2)/b)^(1/4))","A",8,5,39,0.1282,0,"{2056, 1269, 1528, 511, 510}"
2526,1,200,0,0.5418725,"\int \frac{\left(-b+a x^2\right) \sqrt[4]{-b x^2+a x^4}}{b-a x^2+x^4} \, dx","Int[((-b + a*x^2)*(-(b*x^2) + a*x^4)^(1/4))/(b - a*x^2 + x^4),x]","\frac{4 b x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{5}{4};\frac{7}{4};\frac{2 x^2}{a-\sqrt{a^2-4 b}},\frac{a x^2}{b}\right)}{3 \left(-a \sqrt{a^2-4 b}+a^2-4 b\right) \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{4 b x \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{5}{4};\frac{7}{4};\frac{2 x^2}{a+\sqrt{a^2-4 b}},\frac{a x^2}{b}\right)}{3 \left(a \sqrt{a^2-4 b}+a^2-4 b\right) \sqrt[4]{1-\frac{a x^2}{b}}}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-\text{$\#$1}^4 a+b\&,\frac{\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 \left(-a^2\right) \log (x)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log (x)-a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a b \log (x)}{\text{$\#$1}^3 a-2 \text{$\#$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,"(4*b*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -5/4, 7/4, (2*x^2)/(a - Sqrt[a^2 - 4*b]), (a*x^2)/b])/(3*(a^2 - a*Sqrt[a^2 - 4*b] - 4*b)*(1 - (a*x^2)/b)^(1/4)) + (4*b*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -5/4, 7/4, (2*x^2)/(a + Sqrt[a^2 - 4*b]), (a*x^2)/b])/(3*(a^2 + a*Sqrt[a^2 - 4*b] - 4*b)*(1 - (a*x^2)/b)^(1/4))","A",8,5,39,0.1282,0,"{2056, 1269, 1528, 511, 510}"
2527,0,0,0,2.4804325,"\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","Int[(-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,"Defer[Int][1/Sqrt[b + Sqrt[b^2 + a*x^2]], x] - b*Defer[Int][1/((b - Sqrt[-a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] - b*Defer[Int][1/((b + Sqrt[-a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] - a*b^2*Defer[Int][1/((Sqrt[-a]*b - a*x)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] - a*b^2*Defer[Int][1/((Sqrt[-a]*b + a*x)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",0,0,0,0,-1,"{}"
2528,0,0,0,55.1334857,"\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","Int[((-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,"(-3*(1 + k)*(1 + a*k)*x)/((1 - k)*(1 - b*k)*((1 - x)*x*(1 - k*x))^(1/3)) + (3*(2 + a + b + 4*a*k + a*(1 - 2*b)*k^2 + b*k^2)*x)/((1 - k)*(1 - b*k)^2*((1 - x)*x*(1 - k*x))^(1/3)) - (3*(1 + k)*(1 + a*k)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (1 - x)/(1 - k*x)])/((1 - k)^2*(1 - b*k)*((1 - x)*x*(1 - k*x))^(1/3)) + (3*(1 + k)*(2 + a + b + 4*a*k + a*(1 - 2*b)*k^2 + b*k^2)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, (1 - x)/(1 - k*x)])/(2*(1 - k)^2*(1 - b*k)^2*((1 - x)*x*(1 - k*x))^(1/3)) + ((a + b)*(3 + b + 3*k + b*k^3 + (4 + b^2*(1 - k)^2*(1 + k + k^2) + b*(5 + 2*k + 5*k^2))/(Sqrt[b]*Sqrt[4 + b*(1 - k)^2]))*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(4/3)*x^(1/3)*(1 - k*x)^(4/3)*(-(b*(1 + k)) - Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - b*k)^2*((1 - x)*x*(1 - k*x))^(1/3)) + ((a + b)*(3*(1 + k) + b*(1 + k^3) - (4 + b*(5 + 2*k + 5*k^2) + b^2*(1 - k - k^3 + k^4))/(Sqrt[b]*Sqrt[4 + b*(1 - k)^2]))*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(4/3)*x^(1/3)*(1 - k*x)^(4/3)*(-(b*(1 + k)) + Sqrt[b]*Sqrt[4 + b - 2*b*k + b*k^2] + 2*(-1 + b*k)*x)), x])/((1 - b*k)^2*((1 - x)*x*(1 - k*x))^(1/3))","F",0,0,0,0,-1,"{}"
2529,1,171,0,0.1202288,"\int \frac{\left(b+x^3\right)^3}{\sqrt[3]{a+x^3}} \, dx","Int[(b + x^3)^3/(a + x^3)^(1/3),x]","\frac{1}{162} x \left(28 a^2-87 a b+99 b^2\right) \left(a+x^3\right)^{2/3}+\frac{1}{162} \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{\left(14 a^3-54 a^2 b+81 a b^2-81 b^3\right) \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{a+x^3}}+1}{\sqrt{3}}\right)}{81 \sqrt{3}}+\frac{1}{9} x \left(a+x^3\right)^{2/3} \left(b+x^3\right)^2-\frac{1}{54} x (7 a-15 b) \left(a+x^3\right)^{2/3} \left(b+x^3\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,"((28*a^2 - 87*a*b + 99*b^2)*x*(a + x^3)^(2/3))/162 - ((7*a - 15*b)*x*(a + x^3)^(2/3)*(b + x^3))/54 + (x*(a + x^3)^(2/3)*(b + x^3)^2)/9 - ((14*a^3 - 54*a^2*b + 81*a*b^2 - 81*b^3)*ArcTan[(1 + (2*x)/(a + x^3)^(1/3))/Sqrt[3]])/(81*Sqrt[3]) + ((14*a^3 - 54*a^2*b + 81*a*b^2 - 81*b^3)*Log[-x + (a + x^3)^(1/3)])/162","A",4,4,17,0.2353,1,"{416, 528, 388, 239}"
2530,0,0,0,0.6713114,"\int \frac{1-x^2+x^3}{\left(-1-x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[(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{$\#$1}^9-3 \text{$\#$1}^6+4 \text{$\#$1}^3-3\&,\frac{\text{$\#$1}^6 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^6 (-\log (x))-2 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{3 \text{$\#$1}^7-6 \text{$\#$1}^4+4 \text{$\#$1}}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"(Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[(1 + (2*x^(1/3))/(1 + x)^(1/3))/Sqrt[3]])/(x^2 + x^3)^(1/3) - (3*x^(2/3)*(1 + x)^(1/3)*Log[x^(1/3) - (1 + x)^(1/3)])/(2*(x^2 + x^3)^(1/3)) + (6*x^(2/3)*(1 + x)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x^3)^(1/3)*(-1 - x^6 + x^9)), x], x, x^(1/3)])/(x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
2531,0,0,0,0.5022683,"\int \frac{1-x^2+x^3}{\left(-1-x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[(1 - x^2 + x^3)/((-1 - x^2 + x^3)*(x^2 + x^3)^(1/3)),x]","\int \frac{1-x^2+x^3}{\left(-1-x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^9-3 \text{$\#$1}^6+4 \text{$\#$1}^3-3\&,\frac{\text{$\#$1}^6 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+\text{$\#$1}^6 (-\log (x))-2 \text{$\#$1}^3 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1}^3 \log (x)+\log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\log (x)}{3 \text{$\#$1}^7-6 \text{$\#$1}^4+4 \text{$\#$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,"(Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[(1 + (2*x^(1/3))/(1 + x)^(1/3))/Sqrt[3]])/(x^2 + x^3)^(1/3) - (3*x^(2/3)*(1 + x)^(1/3)*Log[x^(1/3) - (1 + x)^(1/3)])/(2*(x^2 + x^3)^(1/3)) + (6*x^(2/3)*(1 + x)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x^3)^(1/3)*(-1 - x^6 + x^9)), x], x, x^(1/3)])/(x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
2532,0,0,0,6.3223308,"\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","Int[(-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,"(x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - ((1 - 4*d)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (2 + d)*x + (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - (2*(1 + d - d*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (2 + d)*x + (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - ((1 + 4*d*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (2 + d)*x + (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3))","F",0,0,0,0,-1,"{}"
2533,1,97,0,0.3024535,"\int \frac{x^2}{\left(-b+a x^4\right) \sqrt{b+a x^4}} \, dx","Int[x^2/((-b + a*x^4)*Sqrt[b + a*x^4]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}}\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{a x^4+b}}\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}","\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,"ArcTan[(Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[b + a*x^4]]/(4*Sqrt[2]*a^(3/4)*b^(3/4)) - ArcTanh[(Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[b + a*x^4]]/(4*Sqrt[2]*a^(3/4)*b^(3/4))","A",9,6,26,0.2308,1,"{490, 1211, 220, 1699, 205, 208}"
2534,0,0,0,18.5669196,"\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","Int[((-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,"(6*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x*(1 - x^3)^(2/3)*(1 - k*x^3)^(2/3))/(x^12 - b*(-1 + x^3)^2*(-1 + k*x^3)^2), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (3*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - x^3)^(2/3)*(1 - k*x^3)^(2/3))/(-x^12 + b*(-1 + x^3)^2*(-1 + k*x^3)^2), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2535,0,0,0,3.5845373,"\int \frac{\left(-g+f x^2\right) \sqrt{c+\sqrt{b+a x}}}{e+d x^2} \, dx","Int[((-g + f*x^2)*Sqrt[c + Sqrt[b + a*x]])/(e + d*x^2),x]","\int \frac{\left(-g+f x^2\right) \sqrt{c+\sqrt{b+a x}}}{e+d x^2} \, dx","-\frac{a (d g+e f) \text{RootSum}\left[\text{$\#$1}^8 d-4 \text{$\#$1}^6 c d-2 \text{$\#$1}^4 b d+6 \text{$\#$1}^4 c^2 d+4 \text{$\#$1}^2 b c d-4 \text{$\#$1}^2 c^3 d+a^2 e+b^2 d-2 b c^2 d+c^4 d\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2 c-b+c^2}\&\right]}{2 d^2}+\frac{4 f \left(3 a x+3 b-2 c^2\right) \sqrt{\sqrt{a x+b}+c}}{15 a d}+\frac{4 c f \sqrt{a x+b} \sqrt{\sqrt{a x+b}+c}}{15 a d}",1,"(-4*c*f*(c + Sqrt[b + a*x])^(3/2))/(3*a*d) + (4*f*(c + Sqrt[b + a*x])^(5/2))/(5*a*d) + (4*a*(e*f + d*g)*Defer[Subst][Defer[Int][x^4/(-(b^2*d*(1 + (-2*b*c^2*d + c^4*d + a^2*e)/(b^2*d))) - 4*b*c*(1 - c^2/b)*d*x^2 + 2*b*(1 - (3*c^2)/b)*d*x^4 + 4*c*d*x^6 - d*x^8), x], x, Sqrt[c + Sqrt[b + a*x]]])/d + (4*a*c*(e*f + d*g)*Defer[Subst][Defer[Int][x^2/(b^2*d*(1 + (-2*b*c^2*d + c^4*d + a^2*e)/(b^2*d)) + 4*b*c*(1 - c^2/b)*d*x^2 - 2*b*(1 - (3*c^2)/b)*d*x^4 - 4*c*d*x^6 + d*x^8), x], x, Sqrt[c + Sqrt[b + a*x]]])/d","F",0,0,0,0,-1,"{}"
2536,0,0,0,26.7013647,"\int \frac{\sqrt{b^2+a^2 x^2}}{d+c x^2+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[Sqrt[b^2 + a^2*x^2]/(d + c*x^2 + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\int \frac{\sqrt{b^2+a^2 x^2}}{d+c x^2+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\frac{a \log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{c}-\frac{2 a \text{RootSum}\left[\text{$\#$1}^8 c+4 \text{$\#$1}^5 a^2+4 \text{$\#$1}^4 a^2 d-2 \text{$\#$1}^4 b^2 c+b^4 c\&,\frac{b^2 c \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+a^2 (-d) \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-\text{$\#$1} a^2 \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{-2 \text{$\#$1}^4 c-5 \text{$\#$1} a^2-4 a^2 d+2 b^2 c}\&\right]}{c}",1,"a*d*Defer[Int][(x*Sqrt[b^2 + a^2*x^2])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a*c*Defer[Int][(x^3*Sqrt[b^2 + a^2*x^2])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + b^2*Defer[Int][Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a^2*Defer[Int][(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + d^2*Defer[Int][(Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + 2*c*d*Defer[Int][(x^2*Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + c^2*Defer[Int][(x^4*Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + b^2*d*Defer[Int][(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4))^(-1), x] + b^2*c*Defer[Int][x^2/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a^2*d*Defer[Int][x^2/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a^2*c*Defer[Int][x^4/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + d^3*Defer[Int][Sqrt[b^2 + a^2*x^2]/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + 3*c*d^2*Defer[Int][(x^2*Sqrt[b^2 + a^2*x^2])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + 3*c^2*d*Defer[Int][(x^4*Sqrt[b^2 + a^2*x^2])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + c^3*Defer[Int][(x^6*Sqrt[b^2 + a^2*x^2])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a*Defer[Int][(x*Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x]","F",0,0,0,0,-1,"{}"
2537,0,0,0,25.2170651,"\int \frac{\sqrt{b^2+a^2 x^2}}{d+c x^2+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[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,"a*d*Defer[Int][(x*Sqrt[b^2 + a^2*x^2])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a*c*Defer[Int][(x^3*Sqrt[b^2 + a^2*x^2])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + b^2*Defer[Int][Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a^2*Defer[Int][(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + d^2*Defer[Int][(Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + 2*c*d*Defer[Int][(x^2*Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + c^2*Defer[Int][(x^4*Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + b^2*d*Defer[Int][(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4))^(-1), x] + b^2*c*Defer[Int][x^2/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a^2*d*Defer[Int][x^2/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a^2*c*Defer[Int][x^4/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + d^3*Defer[Int][Sqrt[b^2 + a^2*x^2]/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + 3*c*d^2*Defer[Int][(x^2*Sqrt[b^2 + a^2*x^2])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + 3*c^2*d*Defer[Int][(x^4*Sqrt[b^2 + a^2*x^2])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + c^3*Defer[Int][(x^6*Sqrt[b^2 + a^2*x^2])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x] + a*Defer[Int][(x*Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(-b^2 + (d + c*x^2)^2*(d^2 - 2*a*x + 2*c*d*x^2 + c^2*x^4)), x]","F",0,0,0,0,-1,"{}"
2538,1,94,0,0.3467553,"\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{x^2} \, dx","Int[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/x^2,x]","\frac{8}{9} \left(1-\sqrt{1-\sqrt{\frac{x-1}{x}}}\right)^{9/2}-\frac{24}{7} \left(1-\sqrt{1-\sqrt{\frac{x-1}{x}}}\right)^{7/2}+\frac{16}{5} \left(1-\sqrt{1-\sqrt{\frac{x-1}{x}}}\right)^{5/2}","\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,"(16*(1 - Sqrt[1 - Sqrt[(-1 + x)/x]])^(5/2))/5 - (24*(1 - Sqrt[1 - Sqrt[(-1 + x)/x]])^(7/2))/7 + (8*(1 - Sqrt[1 - Sqrt[(-1 + x)/x]])^(9/2))/9","A",6,4,31,0.1290,1,"{6715, 371, 1398, 772}"
2539,1,382,0,0.6757526,"\int \frac{\sqrt[3]{x^2+x^4}}{x \left(-1+x^2\right)} \, dx","Int[(x^2 + x^4)^(1/3)/(x*(-1 + x^2)),x]","\frac{3^{3/4} \sqrt{2-\sqrt{3}} \left(-x^4-x^2\right)^{2/3} \left(1-2^{2/3} \sqrt[3]{-x^2 \left(x^2+1\right)}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-x^2 \left(x^2+1\right)\right)^{2/3}+2^{2/3} \sqrt[3]{-x^2 \left(x^2+1\right)}+1}{\left(-2^{2/3} \sqrt[3]{-x^2 \left(x^2+1\right)}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-x^2 \left(x^2+1\right)}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-x^2 \left(x^2+1\right)}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2^{2/3} \left(2 x^2+1\right) \left(x^4+x^2\right)^{2/3} \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-x^2 \left(x^2+1\right)}}{\left(-2^{2/3} \sqrt[3]{-x^2 \left(x^2+1\right)}-\sqrt{3}+1\right)^2}}}-\frac{3 \left(-\frac{x^2}{1-x^2}\right)^{2/3} \left(-\frac{x^2+1}{1-x^2}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},\frac{2}{3};\frac{7}{3};\frac{1}{1-x^2},\frac{2}{1-x^2}\right)}{4 \left(x^4+x^2\right)^{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^{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/(1 - x^2)))^(2/3)*(-((1 + x^2)/(1 - x^2)))^(2/3)*AppellF1[4/3, 2/3, 2/3, 7/3, (1 - x^2)^(-1), 2/(1 - x^2)])/(4*(x^2 + x^4)^(2/3)) + (3^(3/4)*Sqrt[2 - Sqrt[3]]*(-x^2 - x^4)^(2/3)*(1 - 2^(2/3)*(-(x^2*(1 + x^2)))^(1/3))*Sqrt[(1 + 2^(2/3)*(-(x^2*(1 + x^2)))^(1/3) + 2*2^(1/3)*(-(x^2*(1 + x^2)))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-(x^2*(1 + x^2)))^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-(x^2*(1 + x^2)))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-(x^2*(1 + x^2)))^(1/3))], -7 + 4*Sqrt[3]])/(2^(2/3)*(1 + 2*x^2)*(x^2 + x^4)^(2/3)*Sqrt[-((1 - 2^(2/3)*(-(x^2*(1 + x^2)))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-(x^2*(1 + x^2)))^(1/3))^2)])","C",9,9,22,0.4091,0,"{1311, 2013, 622, 619, 236, 219, 2034, 758, 133}"
2540,0,0,0,0.8805245,"\int \frac{1}{(c+d x) \sqrt{b+a^2 x^2} \sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","Int[1/((c + d*x)*Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]]),x]","\int \frac{1}{(c+d x) \sqrt{b+a^2 x^2} \sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","\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,"Defer[Int][1/((c + d*x)*Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]]), x]","F",0,0,0,0,-1,"{}"
2541,1,432,0,3.4025384,"\int \frac{\sqrt{1+x} \sqrt{1+\sqrt{1+x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\frac{8 \left(\sqrt{\sqrt{x+1}+1}+1\right)^{3/2}}{3 \left(1-\sqrt{x+1}\right) \sqrt{\sqrt{x+1}+1}}-\frac{\left(50-17 \sqrt{\sqrt{x+1}+1}\right) \sqrt{\sqrt{\sqrt{x+1}+1}+1}}{30 \left(1-\sqrt{x+1}\right)}-\frac{24 \sqrt{\sqrt{\sqrt{x+1}+1}+1}}{5 \left(1-\sqrt{x+1}\right) \sqrt{\sqrt{x+1}+1}}-\frac{1}{30 \left(1-\sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)}+\frac{1}{30 \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}+1\right)}-\frac{1}{60} \sqrt{10961+8989 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{\sqrt{2}-1}}\right)+\frac{1}{15} \sqrt{\frac{1}{2} \left(97+113 \sqrt{2}\right)} \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}{60} \sqrt{8989 \sqrt{2}-10961} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{1+\sqrt{2}}}\right)-\frac{1}{15} \sqrt{\frac{1}{2} \left(113 \sqrt{2}-97\right)} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{x+1}+1}+1}}{\sqrt{1+\sqrt{2}}}\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,"(-24*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])/(5*(1 - Sqrt[1 + x])*Sqrt[1 + Sqrt[1 + x]]) - ((50 - 17*Sqrt[1 + Sqrt[1 + x]])*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])/(30*(1 - Sqrt[1 + x])) + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/(3*(1 - Sqrt[1 + x])*Sqrt[1 + Sqrt[1 + x]]) - 1/(30*(1 - Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])) + 1/(30*(1 + Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]])) + (Sqrt[(97 + 113*Sqrt[2])/2]*ArcTan[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[-1 + Sqrt[2]]])/15 - (Sqrt[10961 + 8989*Sqrt[2]]*ArcTan[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[-1 + Sqrt[2]]])/60 + ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - (Sqrt[(-97 + 113*Sqrt[2])/2]*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[1 + Sqrt[2]]])/15 - (Sqrt[-10961 + 8989*Sqrt[2]]*ArcTanh[Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]/Sqrt[1 + Sqrt[2]]])/60","B",19,9,43,0.2093,0,"{1586, 2102, 1594, 28, 2073, 207, 1178, 1166, 203}"
2542,0,0,0,4.1395656,"\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","Int[(-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,"((2 - k - Sqrt[1 - 4*b*(1 - k)]*k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-1 - 2*b*k - Sqrt[1 - 4*b + 4*b*k] + 2*(1 + b*k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3) + ((2 - (1 - Sqrt[1 - 4*b*(1 - k)])*k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*(-1 - 2*b*k + Sqrt[1 - 4*b + 4*b*k] + 2*(1 + b*k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2543,1,983,0,1.2805467,"\int \frac{1}{x^6 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x^6*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","-\frac{\left(8689+731 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}-\frac{\left(8689-731 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}+\frac{2099 (x+1)}{13090 x \sqrt[3]{x^3+x^2}}+\frac{\left(1151+1989 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(1151-1989 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{173 (x+1)}{5236 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(163+221 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}+\frac{\left(163-221 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}+\frac{107 (x+1)}{1309 x^3 \sqrt[3]{x^3+x^2}}-\frac{\left(15-17 (-1)^{2/3}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}-\frac{\left(15+17 \sqrt[3]{-1}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}+\frac{x+1}{119 x^4 \sqrt[3]{x^3+x^2}}+\frac{3 (x+1)}{17 x^5 \sqrt[3]{x^3+x^2}}-\frac{\left(113+23987 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}-\frac{\left(113-23987 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}+\frac{6793 (x+1)}{26180 \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log (1-x) \sqrt[3]{x+1}}{6 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(\sqrt[3]{-1} x+1\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(1-(-1)^{2/3} x\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+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}}+\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,"(6793*(1 + x))/(26180*(x^2 + x^3)^(1/3)) - ((113 - (23987*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) - ((113 + (23987*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) + (3*(1 + x))/(17*x^5*(x^2 + x^3)^(1/3)) + (1 + x)/(119*x^4*(x^2 + x^3)^(1/3)) - ((15 + 17*(-1)^(1/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) - ((15 - 17*(-1)^(2/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) + (107*(1 + x))/(1309*x^3*(x^2 + x^3)^(1/3)) + ((163 - (221*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + ((163 + (221*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + (173*(1 + x))/(5236*x^2*(x^2 + x^3)^(1/3)) + ((1151 - (1989*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) + ((1151 + (1989*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) + (2099*(1 + x))/(13090*x*(x^2 + x^3)^(1/3)) - ((8689 - (731*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) - ((8689 + (731*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*Sqrt[3]*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - x])/(6*2^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 + (-1)^(1/3)*x])/(6*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - (-1)^(2/3)*x])/(6*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/2^(1/3)])/(2*2^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3)])/(2*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3)])/(2*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3))","C",27,6,22,0.2727,1,"{2056, 6725, 129, 155, 12, 91}"
2544,1,983,0,1.0905515,"\int \frac{1}{x^6 \left(-1+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[1/(x^6*(-1 + x^3)*(x^2 + x^3)^(1/3)),x]","-\frac{\left(8689+731 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}-\frac{\left(8689-731 i \sqrt{3}\right) (x+1)}{52360 x \sqrt[3]{x^3+x^2}}+\frac{2099 (x+1)}{13090 x \sqrt[3]{x^3+x^2}}+\frac{\left(1151+1989 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(1151-1989 i \sqrt{3}\right) (x+1)}{20944 x^2 \sqrt[3]{x^3+x^2}}+\frac{173 (x+1)}{5236 x^2 \sqrt[3]{x^3+x^2}}+\frac{\left(163+221 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}+\frac{\left(163-221 i \sqrt{3}\right) (x+1)}{2618 x^3 \sqrt[3]{x^3+x^2}}+\frac{107 (x+1)}{1309 x^3 \sqrt[3]{x^3+x^2}}-\frac{\left(15-17 (-1)^{2/3}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}-\frac{\left(15+17 \sqrt[3]{-1}\right) (x+1)}{238 x^4 \sqrt[3]{x^3+x^2}}+\frac{x+1}{119 x^4 \sqrt[3]{x^3+x^2}}+\frac{3 (x+1)}{17 x^5 \sqrt[3]{x^3+x^2}}-\frac{\left(113+23987 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}-\frac{\left(113-23987 i \sqrt{3}\right) (x+1)}{104720 \sqrt[3]{x^3+x^2}}+\frac{6793 (x+1)}{26180 \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) \sqrt[3]{x+1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log (1-x) \sqrt[3]{x+1}}{6 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(\sqrt[3]{-1} x+1\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}-\frac{x^{2/3} \log \left(1-(-1)^{2/3} x\right) \sqrt[3]{x+1}}{6 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{2} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x^3+x^2}}+\frac{x^{2/3} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right) \sqrt[3]{x+1}}{2 \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x^3+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}}+\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,"(6793*(1 + x))/(26180*(x^2 + x^3)^(1/3)) - ((113 - (23987*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) - ((113 + (23987*I)*Sqrt[3])*(1 + x))/(104720*(x^2 + x^3)^(1/3)) + (3*(1 + x))/(17*x^5*(x^2 + x^3)^(1/3)) + (1 + x)/(119*x^4*(x^2 + x^3)^(1/3)) - ((15 + 17*(-1)^(1/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) - ((15 - 17*(-1)^(2/3))*(1 + x))/(238*x^4*(x^2 + x^3)^(1/3)) + (107*(1 + x))/(1309*x^3*(x^2 + x^3)^(1/3)) + ((163 - (221*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + ((163 + (221*I)*Sqrt[3])*(1 + x))/(2618*x^3*(x^2 + x^3)^(1/3)) + (173*(1 + x))/(5236*x^2*(x^2 + x^3)^(1/3)) + ((1151 - (1989*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) + ((1151 + (1989*I)*Sqrt[3])*(1 + x))/(20944*x^2*(x^2 + x^3)^(1/3)) + (2099*(1 + x))/(13090*x*(x^2 + x^3)^(1/3)) - ((8689 - (731*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) - ((8689 + (731*I)*Sqrt[3])*(1 + x))/(52360*x*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*Sqrt[3]*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - x])/(6*2^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 + (-1)^(1/3)*x])/(6*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) - (x^(2/3)*(1 + x)^(1/3)*Log[1 - (-1)^(2/3)*x])/(6*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/2^(1/3)])/(2*2^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3)])/(2*(1 - (-1)^(1/3))^(1/3)*(x^2 + x^3)^(1/3)) + (x^(2/3)*(1 + x)^(1/3)*Log[-x^(1/3) + (1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3)])/(2*(1 + (-1)^(2/3))^(1/3)*(x^2 + x^3)^(1/3))","C",27,6,22,0.2727,1,"{2056, 6725, 129, 155, 12, 91}"
2545,0,0,0,6.4074482,"\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","Int[(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,"(x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) + ((1 - 4*d)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(-1 + d + (2 + d)*x - (1 + d*k^2)*x^2 - d*k^2*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) + (2*(1 + d - d*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - ((1 + 4*d*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (2 + d)*x + (1 + d*k^2)*x^2 + d*k^2*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3))","F",0,0,0,0,-1,"{}"
2546,1,103,0,0.3857274,"\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","Int[((1 + x^3)^(2/3)*(8 - 4*x^3 + x^6))/(x^6*(2 + x^3)),x]","\frac{5}{2} x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,-\frac{x^3}{2}\right)+2 \log \left(\sqrt[3]{x^3+1}-x\right)-\frac{4 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{4 \left(x^3+1\right)^{5/3}}{5 x^5}+\frac{2 \left(x^3+1\right)^{2/3}}{x^2}","-\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,"(2*(1 + x^3)^(2/3))/x^2 - (4*(1 + x^3)^(5/3))/(5*x^5) + (5*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -1/2*x^3])/2 - (4*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] + 2*Log[-x + (1 + x^3)^(1/3)]","C",6,5,30,0.1667,0,"{6725, 264, 277, 239, 429}"
2547,1,123,0,0.392488,"\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","Int[((-1 + x^3)^(2/3)*(8 + 2*x^3 + x^6))/(x^6*(-2 + x^3)),x]","-\frac{2 x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{2}\right)}{\left(1-x^3\right)^{2/3}}+\frac{3}{2} \log \left(\sqrt[3]{x^3-1}-x\right)-\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)-\frac{4 \left(x^3-1\right)^{5/3}}{5 x^5}+\frac{3 \left(x^3-1\right)^{2/3}}{2 x^2}","-\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,"(3*(-1 + x^3)^(2/3))/(2*x^2) - (4*(-1 + x^3)^(5/3))/(5*x^5) - (2*x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/2])/(1 - x^3)^(2/3) - Sqrt[3]*ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]] + (3*Log[-x + (-1 + x^3)^(1/3)])/2","C",7,6,30,0.2000,0,"{6725, 264, 277, 239, 430, 429}"
2548,0,0,0,1.9144973,"\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","Int[((-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,"a*p^3*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6], x] - 2*a*q^3*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^9, x] - 2*b*q^2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^7, x] - 3*a*p*q^2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^6, x] - 2*c*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^5, x] - b*p*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^4, x] + c*p*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^2, x] + b*p^2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x, x]","F",0,0,0,0,-1,"{}"
2549,1,466,0,0.3428167,"\int \frac{-b+a x^2}{\sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(-b + a*x^2)/(b^2*x^2 + a^3*x^3)^(1/3),x]","\frac{b x^{2/3} \log (x) \sqrt[3]{a^3 x+b^2}}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 b x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt{3} b x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{b^4 x^{2/3} \log (x) \sqrt[3]{a^3 x+b^2}}{9 a^6 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{b^4 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{a \sqrt[3]{x}}-1\right)}{3 a^6 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{2 b^4 x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^6 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{2 b^2 \left(a^3 x^3+b^2 x^2\right)^{2/3}}{3 a^5 x}+\frac{\left(a^3 x^3+b^2 x^2\right)^{2/3}}{2 a^2}","\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,"(b^2*x^2 + a^3*x^3)^(2/3)/(2*a^2) - (2*b^2*(b^2*x^2 + a^3*x^3)^(2/3))/(3*a^5*x) + (Sqrt[3]*b*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3)) - (2*b^4*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(3*Sqrt[3]*a^6*(b^2*x^2 + a^3*x^3)^(1/3)) + (b*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3)) - (b^4*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(9*a^6*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*b*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3)) - (b^4*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(3*a^6*(b^2*x^2 + a^3*x^3)^(1/3))","B",8,4,29,0.1379,1,"{2053, 2011, 59, 2024}"
2550,1,467,0,0.3603775,"\int \frac{b+a x^2}{\sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(b + a*x^2)/(b^2*x^2 + a^3*x^3)^(1/3),x]","-\frac{b x^{2/3} \log (x) \sqrt[3]{a^3 x+b^2}}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 b x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} b x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{b^4 x^{2/3} \log (x) \sqrt[3]{a^3 x+b^2}}{9 a^6 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{b^4 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{a \sqrt[3]{x}}-1\right)}{3 a^6 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{2 b^4 x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} a^6 \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{2 b^2 \left(a^3 x^3+b^2 x^2\right)^{2/3}}{3 a^5 x}+\frac{\left(a^3 x^3+b^2 x^2\right)^{2/3}}{2 a^2}","\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,"(b^2*x^2 + a^3*x^3)^(2/3)/(2*a^2) - (2*b^2*(b^2*x^2 + a^3*x^3)^(2/3))/(3*a^5*x) - (Sqrt[3]*b*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3)) - (2*b^4*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(3*Sqrt[3]*a^6*(b^2*x^2 + a^3*x^3)^(1/3)) - (b*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3)) - (b^4*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(9*a^6*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*b*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3)) - (b^4*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(3*a^6*(b^2*x^2 + a^3*x^3)^(1/3))","B",8,4,27,0.1481,1,"{2053, 2011, 59, 2024}"
2551,0,0,0,14.6689693,"\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","Int[(-(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,"(12*b*x^(1/4)*Sqrt[-a + x]*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^6*Sqrt[-a + x^4])/((-b + x^4)^(3/4)*(-b + (1 - a^2*d)*x^4 + 2*a*d*x^8 - d*x^12)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(1/4) + (4*a*b*x^(1/4)*Sqrt[-a + x]*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^2*Sqrt[-a + x^4])/((-b + x^4)^(3/4)*(b - (1 - a^2*d)*x^4 - 2*a*d*x^8 + d*x^12)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(1/4) + (8*x^(1/4)*Sqrt[-a + x]*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^10*Sqrt[-a + x^4])/((-b + x^4)^(3/4)*(b - (1 - a^2*d)*x^4 - 2*a*d*x^8 + d*x^12)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(1/4)","F",0,0,0,0,-1,"{}"
2552,1,491,0,2.2030796,"\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","Int[((b + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(x^2*(-b + a*x^2)),x]","\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}-\frac{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}-\sqrt{b}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{x} \sqrt[4]{\sqrt{a}-\sqrt{b}}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}-\frac{2 \sqrt[8]{a} \sqrt[4]{\sqrt{a}+\sqrt{b}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{x} \sqrt[4]{\sqrt{a}+\sqrt{b}}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}","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*(b*x^3 + a*x^4)^(1/4))/x - (2*a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) + (2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) + (2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) + (2*a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) - (2*a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] - Sqrt[b])^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) - (2*a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/8)*(Sqrt[a] + Sqrt[b])^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4))","B",23,13,37,0.3514,1,"{2056, 6725, 47, 63, 331, 298, 203, 206, 908, 37, 6688, 12, 93}"
2553,0,0,0,27.4475058,"\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","Int[(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,"(-4*a*b*x^(1/4)*Sqrt[-a + x]*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^2*(-b + x^4)^(5/4))/(Sqrt[-a + x^4]*(a^2 - 2*a*(1 - (b^3*d)/(2*a))*x^4 + (1 - 3*b^2*d)*x^8 + 3*b*d*x^12 - d*x^16)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(1/4) + (4*(4*a - b)*x^(1/4)*Sqrt[-a + x]*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^6*(-b + x^4)^(5/4))/(Sqrt[-a + x^4]*(a^2 - 2*a*(1 - (b^3*d)/(2*a))*x^4 + (1 - 3*b^2*d)*x^8 + 3*b*d*x^12 - d*x^16)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(1/4) - (8*x^(1/4)*Sqrt[-a + x]*(-b + x)^(3/4)*Defer[Subst][Defer[Int][(x^10*(-b + x^4)^(5/4))/(Sqrt[-a + x^4]*(a^2 - 2*a*(1 - (b^3*d)/(2*a))*x^4 + (1 - 3*b^2*d)*x^8 + 3*b*d*x^12 - d*x^16)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(1/4)","F",0,0,0,0,-1,"{}"
2554,1,933,0,4.6741112,"\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","Int[((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8))/(x^6*(b + 2*a*x^8)),x]","-\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{2} \sqrt{-a} x^4}{\sqrt{b}},\frac{a x^4}{b}\right) x^3}{6 b \sqrt[4]{1-\frac{a x^4}{b}}}-\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{2} \sqrt{-a} x^4}{\sqrt{b}},\frac{a x^4}{b}\right) x^3}{6 b \sqrt[4]{1-\frac{a x^4}{b}}}+\frac{\sqrt{-a} c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}-\frac{\sqrt{-a} c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}-\frac{\sqrt{-a} c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}+\frac{\sqrt{-a} c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}-\frac{c \sqrt[4]{a x^4-b}}{b x}+\frac{\left(a x^4-b\right)^{5/4}}{5 b x^5}","\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,"-((c*(-b + a*x^4)^(1/4))/(b*x)) + (-b + a*x^4)^(5/4)/(5*b*x^5) - (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[2]*Sqrt[-a]*x^4)/Sqrt[b]), (a*x^4)/b])/(6*b*(1 - (a*x^4)/b)^(1/4)) - (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[2]*Sqrt[-a]*x^4)/Sqrt[b], (a*x^4)/b])/(6*b*(1 - (a*x^4)/b)^(1/4)) - (a*c*ArcTan[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) + (Sqrt[-a]*c*ArcTan[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) - (a*c*ArcTan[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) - (Sqrt[-a]*c*ArcTan[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (a*c*ArcTanh[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) - (Sqrt[-a]*c*ArcTanh[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (a*c*ArcTanh[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) + (Sqrt[-a]*c*ArcTanh[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b])","B",43,12,39,0.3077,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
2555,1,933,0,4.3420914,"\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","Int[((-b + a*x^4)^(1/4)*(b + c*x^4 + a*x^8))/(x^6*(b + 2*a*x^8)),x]","-\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{2} \sqrt{-a} x^4}{\sqrt{b}},\frac{a x^4}{b}\right) x^3}{6 b \sqrt[4]{1-\frac{a x^4}{b}}}-\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{2} \sqrt{-a} x^4}{\sqrt{b}},\frac{a x^4}{b}\right) x^3}{6 b \sqrt[4]{1-\frac{a x^4}{b}}}+\frac{\sqrt{-a} c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}-\frac{\sqrt{-a} c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a c \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}-\frac{\sqrt{-a} c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a-2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a-2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}+\frac{\sqrt{-a} c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2 \sqrt[8]{2} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a c \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{2} a+2 \sqrt{-a} \sqrt{b}} x}{\sqrt[8]{2} \sqrt[4]{a x^4-b}}\right)}{2\ 2^{5/8} \left(\sqrt{2} a+2 \sqrt{-a} \sqrt{b}\right)^{3/4} b}-\frac{c \sqrt[4]{a x^4-b}}{b x}+\frac{\left(a x^4-b\right)^{5/4}}{5 b x^5}","\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,"-((c*(-b + a*x^4)^(1/4))/(b*x)) + (-b + a*x^4)^(5/4)/(5*b*x^5) - (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[2]*Sqrt[-a]*x^4)/Sqrt[b]), (a*x^4)/b])/(6*b*(1 - (a*x^4)/b)^(1/4)) - (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[2]*Sqrt[-a]*x^4)/Sqrt[b], (a*x^4)/b])/(6*b*(1 - (a*x^4)/b)^(1/4)) - (a*c*ArcTan[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) + (Sqrt[-a]*c*ArcTan[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) - (a*c*ArcTan[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) - (Sqrt[-a]*c*ArcTan[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (a*c*ArcTanh[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) - (Sqrt[-a]*c*ArcTanh[((Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a - 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b]) + (a*c*ArcTanh[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(5/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*b) + (Sqrt[-a]*c*ArcTanh[((Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(1/4)*x)/(2^(1/8)*(-b + a*x^4)^(1/4))])/(2*2^(1/8)*(Sqrt[2]*a + 2*Sqrt[-a]*Sqrt[b])^(3/4)*Sqrt[b])","B",43,12,39,0.3077,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
2556,1,215,0,0.4987195,"\int \frac{1}{(d+c x) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[1/((d + c*x)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\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}}","\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/(c*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + (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]]])/(Sqrt[c]*Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]) + (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]]])/(Sqrt[c]*Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]])","A",8,6,31,0.1935,1,"{2119, 1628, 828, 826, 1166, 205}"
2557,0,0,0,1.8757044,"\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","Int[((-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,"2*c*p*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] - a*q^3*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^5, x] - b*q^2*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^4, x] - c*q*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^3, x] + b*p*q*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x, x] + 3*a*p^2*q*Defer[Int][x*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 2*b*p^2*Defer[Int][x^2*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 2*a*p^3*Defer[Int][x^4*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2558,1,209,0,1.6572449,"\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","Int[(-(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]","-\frac{3 (a-x)^2 \left(-\frac{b-x}{a-b}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};\frac{a-x}{a-b},-\frac{2 (a-x)}{\sqrt{d} \left(\sqrt{d}-\sqrt{4 a-4 b+d}\right)}\right)}{4 d ((a-x) (b-x))^{2/3}}-\frac{3 (a-x)^2 \left(-\frac{b-x}{a-b}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};\frac{a-x}{a-b},-\frac{2 (a-x)}{\sqrt{d} \left(\sqrt{d}+\sqrt{4 a-4 b+d}\right)}\right)}{4 d ((a-x) (b-x))^{2/3}}","-\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,"(-3*(a - x)^2*(-((b - x)/(a - b)))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, (a - x)/(a - b), (-2*(a - x))/(Sqrt[d]*(Sqrt[d] - Sqrt[4*a - 4*b + d]))])/(4*d*((a - x)*(b - x))^(2/3)) - (3*(a - x)^2*(-((b - x)/(a - b)))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, (a - x)/(a - b), (-2*(a - x))/(Sqrt[d]*(Sqrt[d] + Sqrt[4*a - 4*b + d]))])/(4*d*((a - x)*(b - x))^(2/3))","C",8,5,52,0.09615,0,"{6719, 1586, 6728, 137, 136}"
2559,0,0,0,0.1698231,"\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","Int[(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,"Defer[Int][(a - 2*b + x)/((a*b + (-a - b)*x + x^2)^(1/3)*(b + a^2*d + (-1 - 2*a*d)*x + d*x^2)), x]","F",0,0,0,0,-1,"{}"
2560,0,0,0,0.1686796,"\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","Int[(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,"Defer[Int][(a - 2*b + x)/((a*b + (-a - b)*x + x^2)^(1/3)*(b + a^2*d + (-1 - 2*a*d)*x + d*x^2)), x]","F",0,0,0,0,-1,"{}"
2561,0,0,0,3.5637668,"\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","Int[(-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,"-(((1 - 2*k + Sqrt[1 + 4*b - 4*b*k])*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - x)^(1/3)/(x^(2/3)*(1 - k*x)^(2/3)*(-1 - 2*b - Sqrt[1 + 4*b - 4*b*k] + 2*(b + k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)) - ((1 - 2*k - Sqrt[1 + 4*b - 4*b*k])*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - x)^(1/3)/(x^(2/3)*(1 - k*x)^(2/3)*(-1 - 2*b + Sqrt[1 + 4*b - 4*b*k] + 2*(b + k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2562,1,291,0,0.1046637,"\int \frac{-1+x}{(1+x) \sqrt[3]{-x^2+x^3}} \, dx","Int[(-1 + x)/((1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{\sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x+1)}{\sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-x^2}}+\frac{2^{2/3} \sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-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,"-((Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3)) + (2^(2/3)*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 + x])/(2^(1/3)*(-x^2 + x^3)^(1/3))","A",4,4,22,0.1818,1,"{2056, 105, 59, 91}"
2563,0,0,0,2.2865294,"\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","Int[((-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,"Defer[Int][(-1 + x + x^3 + x^6)^(2/3)/(-1 + x), x] + Defer[Int][(-1 + x + x^3 + x^6)^(2/3)/(1 + x), x] + 2*Defer[Int][(-1 + x + x^3 + x^6)^(2/3)/(1 - x + x^2 + x^4), x] + 3*Defer[Int][(x*(-1 + x + x^3 + x^6)^(2/3))/(1 - x + x^2 + x^4), x] + Defer[Int][(x^2*(-1 + x + x^3 + x^6)^(2/3))/(1 - x + x^2 + x^4), x] - Defer[Int][(x^3*(-1 + x + x^3 + x^6)^(2/3))/(1 - x + x^2 + x^4), x] + Defer[Int][(-1 + x + x^3 + x^6)^(2/3)/(1 - x - x^6), x] - 6*Defer[Int][(x^3*(-1 + x + x^3 + x^6)^(2/3))/(-1 + x + x^6), x] - Defer[Int][(x^4*(-1 + x + x^3 + x^6)^(2/3))/(-1 + x + x^6), x] - Defer[Int][(x^5*(-1 + x + x^3 + x^6)^(2/3))/(-1 + x + x^6), x]","F",0,0,0,0,-1,"{}"
2564,1,233,0,0.3788708,"\int \frac{-1-2 x^4+2 x^8}{\sqrt[4]{-1+x^4} \left(-1-x^4+x^8\right)} \, dx","Int[(-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)}{2 \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)}{2 \sqrt{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)}{2 \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)}{2 \sqrt{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)])/(2*Sqrt[5]) - (((3 + Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(2*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)])/(2*Sqrt[5]) - (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(-1 + x^4)^(1/4)])/(2*Sqrt[5])","A",15,7,34,0.2059,0,"{6728, 240, 212, 206, 203, 1428, 377}"
2565,1,233,0,0.3021494,"\int \frac{-1+2 x^4+2 x^8}{\sqrt[4]{1+x^4} \left(-1+x^4+x^8\right)} \, dx","Int[(-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)}{2 \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)}{2 \sqrt{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)}{2 \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)}{2 \sqrt{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)])/(2*Sqrt[5]) - (((3 + Sqrt[5])/2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*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)])/(2*Sqrt[5]) - (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x)/(1 + x^4)^(1/4)])/(2*Sqrt[5])","A",15,7,32,0.2188,0,"{6728, 240, 212, 206, 203, 1428, 377}"
2566,0,0,0,3.7010282,"\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","Int[(-(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,"((2*a - b - Sqrt[4*a^2 - 4*a*b + b^2*d]/Sqrt[d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(2*a - b*d - Sqrt[d]*Sqrt[4*a^2 - 4*a*b + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3) + ((2*a - b + Sqrt[4*a^2 - 4*a*b + b^2*d]/Sqrt[d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(2*a - b*d + Sqrt[d]*Sqrt[4*a^2 - 4*a*b + b^2*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2567,1,928,0,4.0250036,"\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","Int[((-4*b + a*x^4)*(-b + a*x^4)^(1/4))/(x^6*(-8*b + a*x^8)),x]","\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^4}{2 \sqrt{2} \sqrt{b}},\frac{a x^4}{b}\right) x^3}{96 b \sqrt[4]{1-\frac{a x^4}{b}}}+\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^4}{2 \sqrt{2} \sqrt{b}},\frac{a x^4}{b}\right) x^3}{96 b \sqrt[4]{1-\frac{a x^4}{b}}}-\frac{a^{9/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a^{13/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} b}+\frac{a^{9/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a^{13/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} b}+\frac{a^{9/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a^{13/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} b}-\frac{a^{9/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a^{13/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} b}+\frac{a \sqrt[4]{a x^4-b}}{8 b x}+\frac{\left(a x^4-b\right)^{5/4}}{10 b x^5}","\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,"(a*(-b + a*x^4)^(1/4))/(8*b*x) + (-b + a*x^4)^(5/4)/(10*b*x^5) + (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -1/2*(Sqrt[a]*x^4)/(Sqrt[2]*Sqrt[b]), (a*x^4)/b])/(96*b*(1 - (a*x^4)/b)^(1/4)) + (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^4)/(2*Sqrt[2]*Sqrt[b]), (a*x^4)/b])/(96*b*(1 - (a*x^4)/b)^(1/4)) + (a^(13/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*b) - (a^(9/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*Sqrt[b]) + (a^(13/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*b) + (a^(9/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*Sqrt[b]) - (a^(13/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*b) + (a^(9/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*Sqrt[b]) - (a^(13/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*b) - (a^(9/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*Sqrt[b])","B",43,12,37,0.3243,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
2568,1,928,0,3.7687677,"\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","Int[((-4*b + a*x^4)*(-b + a*x^4)^(1/4))/(x^6*(-8*b + a*x^8)),x]","\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^4}{2 \sqrt{2} \sqrt{b}},\frac{a x^4}{b}\right) x^3}{96 b \sqrt[4]{1-\frac{a x^4}{b}}}+\frac{a \sqrt[4]{a x^4-b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^4}{2 \sqrt{2} \sqrt{b}},\frac{a x^4}{b}\right) x^3}{96 b \sqrt[4]{1-\frac{a x^4}{b}}}-\frac{a^{9/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a^{13/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} b}+\frac{a^{9/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} \sqrt{b}}+\frac{a^{13/8} \tan ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} b}+\frac{a^{9/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a^{13/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}-\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}-\sqrt{b}\right)^{3/4} b}-\frac{a^{9/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{32\ 2^{3/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} \sqrt{b}}-\frac{a^{13/8} \tanh ^{-1}\left(\frac{\sqrt[8]{a} \sqrt[4]{2 \sqrt{2} \sqrt{a}+\sqrt{b}} x}{2^{3/8} \sqrt[4]{a x^4-b}}\right)}{8\ 2^{7/8} \left(2 \sqrt{2} \sqrt{a}+\sqrt{b}\right)^{3/4} b}+\frac{a \sqrt[4]{a x^4-b}}{8 b x}+\frac{\left(a x^4-b\right)^{5/4}}{10 b x^5}","\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,"(a*(-b + a*x^4)^(1/4))/(8*b*x) + (-b + a*x^4)^(5/4)/(10*b*x^5) + (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -1/2*(Sqrt[a]*x^4)/(Sqrt[2]*Sqrt[b]), (a*x^4)/b])/(96*b*(1 - (a*x^4)/b)^(1/4)) + (a*x^3*(-b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^4)/(2*Sqrt[2]*Sqrt[b]), (a*x^4)/b])/(96*b*(1 - (a*x^4)/b)^(1/4)) + (a^(13/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*b) - (a^(9/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*Sqrt[b]) + (a^(13/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*b) + (a^(9/8)*ArcTan[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*Sqrt[b]) - (a^(13/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*b) + (a^(9/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] - Sqrt[b])^(3/4)*Sqrt[b]) - (a^(13/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(8*2^(7/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*b) - (a^(9/8)*ArcTanh[(a^(1/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(1/4)*x)/(2^(3/8)*(-b + a*x^4)^(1/4))])/(32*2^(3/8)*(2*Sqrt[2]*Sqrt[a] + Sqrt[b])^(3/4)*Sqrt[b])","B",43,12,37,0.3243,0,"{6725, 264, 277, 331, 298, 203, 206, 1529, 511, 510, 1519, 494}"
2569,1,295,0,0.1048768,"\int \frac{x}{(1+x) \sqrt[3]{-x^2+x^3}} \, dx","Int[x/((1 + x)*(-x^2 + x^3)^(1/3)),x]","-\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3-x^2}}+\frac{3 \sqrt[3]{x-1} x^{2/3} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x)}{2 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} x^{2/3} \log (x+1)}{2 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3-x^2}}+\frac{\sqrt{3} \sqrt[3]{x-1} x^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt[3]{x^3-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,"-((Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(-x^2 + x^3)^(1/3)) + (Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2^(1/3)*(-x^2 + x^3)^(1/3)) - (3*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(2*(-x^2 + x^3)^(1/3)) + (3*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(2*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 + x])/(2*2^(1/3)*(-x^2 + x^3)^(1/3))","A",4,4,20,0.2000,1,"{2042, 105, 59, 91}"
2570,1,298,0,0.0819567,"\int \frac{\sqrt[3]{-x^2+x^3}}{-1+x^2} \, dx","Int[(-x^2 + x^3)^(1/3)/(-1 + x^2),x]","\frac{3 \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{2} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{2\ 2^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{3 \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{2 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{x^3-x^2} \log (x-1)}{2 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{x^3-x^2} \log (x+1)}{2\ 2^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{2} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{2^{2/3} \sqrt[3]{x-1} x^{2/3}}","-\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,"-((Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3))) + (Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*2^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(2^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + (3*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + 2^(1/3)*x^(1/3)])/(2*2^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - (3*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(2*(-1 + x)^(1/3)*x^(2/3)) - ((-x^2 + x^3)^(1/3)*Log[-1 + x])/(2*(-1 + x)^(1/3)*x^(2/3)) - ((-x^2 + x^3)^(1/3)*Log[1 + x])/(2*2^(2/3)*(-1 + x)^(1/3)*x^(2/3))","A",5,5,21,0.2381,1,"{2056, 848, 105, 59, 91}"
2571,0,0,0,0.6679351,"\int x^2 \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Int[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,"Defer[Int][x^2*Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
2572,0,0,0,4.1281531,"\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","Int[(-(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,"(2*Sqrt[-(b*x) + a^2*x^2]*Defer[Subst][Defer[Int][(x^4*(-b + a^2*x^2)^(3/2))/(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-b + a^2*x])","F",0,0,0,0,-1,"{}"
2573,0,0,0,7.552658,"\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","Int[(-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,"(k*x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - ((1 - 4*d)*k*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (2 + d)*k*x + (d + k^2)*x^2 - d*k*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - (2*(k^2 - d*(1 - k^2))*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (2 + d)*k*x + (d + k^2)*x^2 - d*k*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - (k*(4*d + k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (2 + d)*k*x + (d + k^2)*x^2 - d*k*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3))","F",0,0,0,0,-1,"{}"
2574,1,179,0,0.3356258,"\int \frac{a+b x}{x (-d+c x) \sqrt[4]{-x^3+x^4}} \, dx","Int[(a + b*x)/(x*(-d + c*x)*(-x^3 + x^4)^(1/4)),x]","-\frac{2 \sqrt[4]{x-1} x^{3/4} (a c+b d) \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{d-c}}{\sqrt[4]{d} \sqrt[4]{x-1}}\right)}{d^{7/4} \sqrt[4]{x^4-x^3} \sqrt[4]{d-c}}-\frac{2 \sqrt[4]{x-1} x^{3/4} (a c+b d) \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{d-c}}{\sqrt[4]{d} \sqrt[4]{x-1}}\right)}{d^{7/4} \sqrt[4]{x^4-x^3} \sqrt[4]{d-c}}+\frac{4 a (1-x)}{3 d \sqrt[4]{x^4-x^3}}","\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*a*(1 - x))/(3*d*(-x^3 + x^4)^(1/4)) - (2*(a*c + b*d)*(-1 + x)^(1/4)*x^(3/4)*ArcTan[((-c + d)^(1/4)*x^(1/4))/(d^(1/4)*(-1 + x)^(1/4))])/(d^(7/4)*(-c + d)^(1/4)*(-x^3 + x^4)^(1/4)) - (2*(a*c + b*d)*(-1 + x)^(1/4)*x^(3/4)*ArcTanh[((-c + d)^(1/4)*x^(1/4))/(d^(1/4)*(-1 + x)^(1/4))])/(d^(7/4)*(-c + d)^(1/4)*(-x^3 + x^4)^(1/4))","A",7,7,31,0.2258,1,"{2056, 155, 12, 93, 212, 208, 205}"
2575,0,0,0,3.7222526,"\int \frac{(-4+3 x) \sqrt[4]{\frac{-a+a x+b x^4}{-c+c x+d x^4}}}{(-1+x) x} \, dx","Int[((-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,"(((a - a*x - b*x^4)/(c - c*x - d*x^4))^(1/4)*(-c + c*x + d*x^4)^(1/4)*Defer[Int][(-a + a*x + b*x^4)^(1/4)/((1 - x)*(-c + c*x + d*x^4)^(1/4)), x])/(-a + a*x + b*x^4)^(1/4) + (4*((a - a*x - b*x^4)/(c - c*x - d*x^4))^(1/4)*(-c + c*x + d*x^4)^(1/4)*Defer[Int][(-a + a*x + b*x^4)^(1/4)/(x*(-c + c*x + d*x^4)^(1/4)), x])/(-a + a*x + b*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2576,0,0,0,0.7821452,"\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","Int[((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{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,"(-3*(1 + x^3)^(2/3))/(2*x^2) + (1 + x^3)^(5/3)/(5*x^5) - (20*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, -2*x^3])/3 + Sqrt[3]*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]] - (3*Log[-x + (1 + x^3)^(1/3)])/2 + Defer[Int][(1 + x^3)^(2/3)/(-1 + x), x]/9 - ((1 - I*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(1 - I*Sqrt[3] + 2*x), x])/9 - ((1 + I*Sqrt[3])*Defer[Int][(1 + x^3)^(2/3)/(1 + I*Sqrt[3] + 2*x), x])/9","F",0,0,0,0,-1,"{}"
2577,1,196,0,0.1070075,"\int \frac{2}{(3+x) \left(2-8 x+8 x^2\right)^{2/3}} \, dx","Int[2/((3 + x)*(2 - 8*x + 8*x^2)^(2/3)),x]","\frac{3 \sqrt[3]{2} (1-2 x)}{7 \left(4 x^2-4 x+1\right)^{2/3}}-\frac{(2 x-1)^{4/3} \log (x+3)}{7\ 2^{2/3} \sqrt[3]{7} \left(4 x^2-4 x+1\right)^{2/3}}+\frac{3 (2 x-1)^{4/3} \log \left(\sqrt[3]{8 x-4}+2^{2/3} \sqrt[3]{7}\right)}{7\ 2^{2/3} \sqrt[3]{7} \left(4 x^2-4 x+1\right)^{2/3}}+\frac{\sqrt[3]{\frac{2}{7}} \sqrt{3} (2 x-1)^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{2 x-1}}{\sqrt{3} \sqrt[3]{7}}\right)}{7 \left(4 x^2-4 x+1\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,"(3*2^(1/3)*(1 - 2*x))/(7*(1 - 4*x + 4*x^2)^(2/3)) + ((2/7)^(1/3)*Sqrt[3]*(-1 + 2*x)^(4/3)*ArcTan[1/Sqrt[3] - (2*(-1 + 2*x)^(1/3))/(Sqrt[3]*7^(1/3))])/(7*(1 - 4*x + 4*x^2)^(2/3)) - ((-1 + 2*x)^(4/3)*Log[3 + x])/(7*2^(2/3)*7^(1/3)*(1 - 4*x + 4*x^2)^(2/3)) + (3*(-1 + 2*x)^(4/3)*Log[2^(2/3)*7^(1/3) + (-4 + 8*x)^(1/3)])/(7*2^(2/3)*7^(1/3)*(1 - 4*x + 4*x^2)^(2/3))","A",7,7,21,0.3333,1,"{12, 646, 51, 56, 617, 204, 31}"
2578,0,0,0,13.1409768,"\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","Int[(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,"(-6*(2 - k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - x^3)^(2/3))/((1 - k*x^3)^(1/3)*(1 - 5*(1 + b/5)*x^3 + 10*(1 + (b*k)/10)*x^6 - 10*x^9 + 5*x^12 - x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (9*k*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^7*(1 - x^3)^(2/3))/((1 - k*x^3)^(1/3)*(1 - 5*(1 + b/5)*x^3 + 10*(1 + (b*k)/10)*x^6 - 10*x^9 + 5*x^12 - x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (3*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x*(1 - x^3)^(2/3))/((1 - k*x^3)^(1/3)*(-1 + 5*(1 + b/5)*x^3 - 10*(1 + (b*k)/10)*x^6 + 10*x^9 - 5*x^12 + x^15)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2579,0,0,0,22.0045969,"\int \frac{1}{x \sqrt[3]{(1+x) \left(q+2 q x+x^2\right)}} \, dx","Int[1/(x*((1 + x)*(q + 2*q*x + x^2))^(1/3)),x]","\int \frac{1}{x \sqrt[3]{(1+x) \left(q+2 q x+x^2\right)}} \, dx","-\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,"((1 + 2*q + (1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[-((-1 + q)^3*q)])^(2/3))/(1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[-((-1 + q)^3*q)])^(1/3) + 3*x)^(1/3)*(-1 + 5*q - 4*q^2 + ((1 - 4*q)^2*(1 - q)^2)/(1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) - (3*(1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))*((1 + 2*q)/3 + x))/(1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3) + 9*((1 + 2*q)/3 + x)^2)^(1/3)*Defer[Subst][Defer[Int][1/(((-1 - 2*q)/3 + x)*((1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))/(3*(1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3)) + x)^(1/3)*((-1 + 5*q - 4*q^2 + ((1 - 4*q)^2*(1 - q)^2)/(1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))/9 - ((1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))*x)/(3*(1 + 6*q - 15*q^2 + 8*q^3 - 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3)) + x^2)^(1/3)), x], x, (1 + 2*q)/3 + x])/(3*(q + 3*q*x + (1 + 2*q)*x^2 + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2580,0,0,0,3.5954885,"\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","Int[(-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,"((2 - k*(1 + Sqrt[-4 + b + 4*k]/Sqrt[b]))*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - k*x)^(1/3)/((1 - x)^(2/3)*x^(2/3)*(-b - 2*k - Sqrt[b]*Sqrt[-4 + b + 4*k] + 2*(b + k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3) + ((2 - k*(1 - Sqrt[-4 + b + 4*k]/Sqrt[b]))*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - k*x)^(1/3)/((1 - x)^(2/3)*x^(2/3)*(-b - 2*k + Sqrt[b]*Sqrt[-4 + b + 4*k] + 2*(b + k^2)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2581,0,0,0,7.2013462,"\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","Int[(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,"(k*x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - ((1 - 4*d)*k*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) + (2*(k^2 - d*(1 - k^2))*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3)) - (k*(4*d + k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (2 + d)*k*x + (d + k^2)*x^2 + d*k*x^3)), x])/(d*((1 - x^2)*(1 - k^2*x^2))^(1/3))","F",0,0,0,0,-1,"{}"
2582,0,0,0,7.9404873,"\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","Int[(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,"-(((5 + d/k^2)*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(2/3)) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*k^(2/3)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) + ((d^2 - 8*k^2 - d*(1 - 5*k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(-1 + d + (1 + 2*d)*x + (d + k^2)*x^2 - k^2*x^3)), x])/(k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((d + 2*d^2 + 2*k^2 + 11*d*k^2 - 2*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)), x])/(k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((d^2 + 2*k^2 + 8*d*k^2 + 6*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)), x])/(k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))","F",0,0,0,0,-1,"{}"
2583,1,373,0,1.3347314,"\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","Int[(((-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{\sqrt[4]{-\frac{1-x}{2 x+1}} (2 x+1) \left(1-3 \sqrt{-\frac{1-x}{2 x+1}}\right)}{6 (x+1)}-\frac{5}{9} \log \left(2 \sqrt{-\frac{1-x}{2 x+1}}-2 \sqrt[4]{-\frac{1-x}{2 x+1}}+1\right)+\frac{5}{9} \log \left(2 \sqrt{-\frac{1-x}{2 x+1}}+2 \sqrt[4]{-\frac{1-x}{2 x+1}}+1\right)-\frac{8}{9} \sqrt[4]{2} \left(1+3 \sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{1-x}{2 x+1}}}{\sqrt[4]{2}}\right)+\frac{3 \left(1+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt[4]{-\frac{1-x}{2 x+1}}}{\sqrt[4]{2}}\right)}{4\ 2^{3/4}}+\frac{2}{9} \tan ^{-1}\left(1-2 \sqrt[4]{-\frac{1-x}{2 x+1}}\right)-\frac{2}{9} \tan ^{-1}\left(2 \sqrt[4]{-\frac{1-x}{2 x+1}}+1\right)+\frac{3 \left(1-\sqrt{2}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{1-x}{2 x+1}}}{\sqrt[4]{2}}\right)}{4\ 2^{3/4}}-\frac{8}{9} \sqrt[4]{2} \left(1-3 \sqrt{2}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{-\frac{1-x}{2 x+1}}}{\sqrt[4]{2}}\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,"((-((1 - x)/(1 + 2*x)))^(1/4)*(1 + 2*x)*(1 - 3*Sqrt[-((1 - x)/(1 + 2*x))]))/(6*(1 + x)) + (3*(1 + Sqrt[2])*ArcTan[(-((1 - x)/(1 + 2*x)))^(1/4)/2^(1/4)])/(4*2^(3/4)) - (8*2^(1/4)*(1 + 3*Sqrt[2])*ArcTan[(-((1 - x)/(1 + 2*x)))^(1/4)/2^(1/4)])/9 + (2*ArcTan[1 - 2*(-((1 - x)/(1 + 2*x)))^(1/4)])/9 - (2*ArcTan[1 + 2*(-((1 - x)/(1 + 2*x)))^(1/4)])/9 - (8*2^(1/4)*(1 - 3*Sqrt[2])*ArcTanh[(-((1 - x)/(1 + 2*x)))^(1/4)/2^(1/4)])/9 + (3*(1 - Sqrt[2])*ArcTanh[(-((1 - x)/(1 + 2*x)))^(1/4)/2^(1/4)])/(4*2^(3/4)) - (5*Log[1 - 2*(-((1 - x)/(1 + 2*x)))^(1/4) + 2*Sqrt[-((1 - x)/(1 + 2*x))]])/9 + (5*Log[1 + 2*(-((1 - x)/(1 + 2*x)))^(1/4) + 2*Sqrt[-((1 - x)/(1 + 2*x))]])/9","A",18,9,51,0.1765,1,"{6725, 634, 617, 204, 628, 1179, 1167, 207, 203}"
2584,0,0,0,1.545184,"\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","Int[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(b*x^3 + a*(q + p*x^2)^3),x]","\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","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 a+6 \text{$\#$1}^4 a p q+8 \text{$\#$1}^3 b+12 \text{$\#$1}^2 a p^2 q^2+8 a p^3 q^3\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+\text{$\#$1}^4 (-\log (x))-4 \text{$\#$1}^2 p q \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+4 \text{$\#$1}^2 p q \log (x)+4 p^2 q^2 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)-4 p^2 q^2 \log (x)}{\text{$\#$1}^5 a+4 \text{$\#$1}^3 a p q+4 \text{$\#$1}^2 b+4 \text{$\#$1} a p^2 q^2}\&\right]",1,"-(q*Defer[Int][Sqrt[q^2 + p^2*x^4]/(b*x^3 + a*(q + p*x^2)^3), x]) + p*Defer[Int][(x^2*Sqrt[q^2 + p^2*x^4])/(b*x^3 + a*(q + p*x^2)^3), x]","F",0,0,0,0,-1,"{}"
2585,0,0,0,1.1906311,"\int \frac{\left(-q+p x^2\right) \sqrt{q^2+p^2 x^4}}{b x^3+a \left(q+p x^2\right)^3} \, dx","Int[((-q + p*x^2)*Sqrt[q^2 + p^2*x^4])/(b*x^3 + a*(q + p*x^2)^3),x]","\int \frac{\left(-q+p x^2\right) \sqrt{q^2+p^2 x^4}}{b x^3+a \left(q+p x^2\right)^3} \, dx","\frac{1}{3} \text{RootSum}\left[\text{$\#$1}^6 a+6 \text{$\#$1}^4 a p q+8 \text{$\#$1}^3 b+12 \text{$\#$1}^2 a p^2 q^2+8 a p^3 q^3\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+\text{$\#$1}^4 (-\log (x))-4 \text{$\#$1}^2 p q \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)+4 \text{$\#$1}^2 p q \log (x)+4 p^2 q^2 \log \left(-\text{$\#$1} x+\sqrt{p^2 x^4+q^2}+p x^2+q\right)-4 p^2 q^2 \log (x)}{\text{$\#$1}^5 a+4 \text{$\#$1}^3 a p q+4 \text{$\#$1}^2 b+4 \text{$\#$1} a p^2 q^2}\&\right]",1,"-(q*Defer[Int][Sqrt[q^2 + p^2*x^4]/(b*x^3 + a*(q + p*x^2)^3), x]) + p*Defer[Int][(x^2*Sqrt[q^2 + p^2*x^4])/(b*x^3 + a*(q + p*x^2)^3), x]","F",0,0,0,0,-1,"{}"
2586,0,0,0,3.3577838,"\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","Int[(-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,"Defer[Int][1/(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - Defer[Int][1/((I - x)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - I*Defer[Int][1/((I - x)*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - Defer[Int][1/((I + x)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - I*Defer[Int][1/((I + x)*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",0,0,0,0,-1,"{}"
2587,0,0,0,8.2978651,"\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","Int[(-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,"-(((5 + d/k^2)*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(2/3)) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*k^(2/3)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) - ((d^2 - 8*k^2 - d*(1 - 5*k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (1 + 2*d)*x - (d + k^2)*x^2 - k^2*x^3)), x])/(k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) + ((d + 2*d^2 + 2*k^2 + 11*d*k^2 - 2*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (1 + 2*d)*x - (d + k^2)*x^2 - k^2*x^3)), x])/(k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3)) - ((d^2 + 2*k^2 + 8*d*k^2 + 6*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (1 + 2*d)*x - (d + k^2)*x^2 - k^2*x^3)), x])/(k^2*((1 - x^2)*(1 - k^2*x^2))^(2/3))","F",0,0,0,0,-1,"{}"
2588,0,0,0,20.1648226,"\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","Int[(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,"(-3*(1 + k)*x*((1 - x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, ((1 - k)*x)/(1 - k*x)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][1/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(1 + 4*k + k^2)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^6/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) - (6*(b + k + k^2 + k^3)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^9/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) + (6*(1 + k)^2*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^3/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(-1 + 2*(1 + k)*x^3 - (1 + k*(4 + k))*x^6 + 2*k*(1 + k)*x^9 + b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3))","F",0,0,0,0,-1,"{}"
2589,0,0,0,1.8855776,"\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","Int[(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,"Defer[Int][1/(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((-1 - x)*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((-1 + x)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((-1 + x)*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((1 + x)^2*Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",0,0,0,0,-1,"{}"
2590,1,426,0,2.6124005,"\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","Int[((-1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/((1 + x^2)^2*Sqrt[1 + x^4]),x]","\frac{i \sqrt{1-i x^2}}{2 (-x+i)}-\frac{i \sqrt{1-i x^2}}{2 (x+i)}-\frac{i \sqrt{1+i x^2}}{2 (-x+i)}+\frac{i \sqrt{1+i x^2}}{2 (x+i)}+\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1+i} \sqrt{1-i x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{1-x}{\sqrt{1+i} \sqrt{1-i x^2}}\right)}{(1+i)^{5/2}}-\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1+i} \sqrt{1-i x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{x+1}{\sqrt{1+i} \sqrt{1-i x^2}}\right)}{(1+i)^{5/2}}+\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1-i} \sqrt{1+i x^2}}\right)+\frac{\tanh ^{-1}\left(\frac{1-x}{\sqrt{1-i} \sqrt{1+i x^2}}\right)}{(1-i)^{5/2}}-\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1-i} \sqrt{1+i x^2}}\right)-\frac{\tanh ^{-1}\left(\frac{x+1}{\sqrt{1-i} \sqrt{1+i x^2}}\right)}{(1-i)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\right)}{\sqrt{2}}","\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,"((I/2)*Sqrt[1 - I*x^2])/(I - x) - ((I/2)*Sqrt[1 - I*x^2])/(I + x) - ((I/2)*Sqrt[1 + I*x^2])/(I - x) + ((I/2)*Sqrt[1 + I*x^2])/(I + x) + ArcTanh[(1 - x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])]/(1 + I)^(5/2) + (Sqrt[1 + I]*ArcTanh[(1 - x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/2 - ArcTanh[(1 + x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])]/(1 + I)^(5/2) - (Sqrt[1 + I]*ArcTanh[(1 + x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/2 + ArcTanh[(1 - x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])]/(1 - I)^(5/2) + (Sqrt[1 - I]*ArcTanh[(1 - x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/2 - ArcTanh[(1 + x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])]/(1 - I)^(5/2) - (Sqrt[1 - I]*ArcTanh[(1 + x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/2 + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",44,7,41,0.1707,0,"{6742, 2132, 206, 2133, 731, 725, 6725}"
2591,0,0,0,2.6988377,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^9-4 \text{$\#$1}^7+4 \text{$\#$1}^5-\text{$\#$1}}\&\right]+\sqrt{x+1} \left(\frac{8}{7} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}-\frac{48}{35} \sqrt{\sqrt{\sqrt{x+1}+1}+1}\right)+\frac{32}{105} \sqrt{\sqrt{x+1}+1} \sqrt{\sqrt{\sqrt{x+1}+1}+1}+\frac{32}{105} \sqrt{\sqrt{\sqrt{x+1}+1}+1}",1,"(16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 - 32*Defer[Subst][Defer[Int][x^2/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + 48*Defer[Subst][Defer[Int][x^4/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 16*Defer[Subst][Defer[Int][x^6/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2592,0,0,0,2.329945,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]),x]","\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{1+\sqrt{1+\sqrt{1+x}}}} \, dx","-\text{RootSum}\left[\text{$\#$1}^{16}-8 \text{$\#$1}^{14}+24 \text{$\#$1}^{12}-32 \text{$\#$1}^{10}+14 \text{$\#$1}^8+8 \text{$\#$1}^6-8 \text{$\#$1}^4+2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x+1}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^9-4 \text{$\#$1}^7+4 \text{$\#$1}^5-\text{$\#$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,"(16*(1 + Sqrt[1 + Sqrt[1 + x]])^(3/2))/3 - (24*(1 + Sqrt[1 + Sqrt[1 + x]])^(5/2))/5 + (8*(1 + Sqrt[1 + Sqrt[1 + x]])^(7/2))/7 - 32*Defer[Subst][Defer[Int][x^2/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] + 48*Defer[Subst][Defer[Int][x^4/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]] - 16*Defer[Subst][Defer[Int][x^6/(2 - 8*x^4 + 8*x^6 + 14*x^8 - 32*x^10 + 24*x^12 - 8*x^14 + x^16), x], x, Sqrt[1 + Sqrt[1 + Sqrt[1 + x]]]]","F",0,0,0,0,-1,"{}"
2593,0,0,0,1.7377029,"\int \frac{(-2+x) \sqrt[3]{x-x^2+x^3}}{(-1+x) \left(-1+x+x^2\right)} \, dx","Int[((-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,"-(((x - x^2 + x^3)^(1/3)*Defer[Subst][Defer[Int][(1 - x^3 + x^6)^(1/3)/(-1 + x), x], x, x^(1/3)])/(x^(1/3)*(1 - x + x^2)^(1/3))) + ((1 - I*Sqrt[3])*(x - x^2 + x^3)^(1/3)*Defer[Subst][Defer[Int][(1 - x^3 + x^6)^(1/3)/(1 - I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(1 - x + x^2)^(1/3)) + ((1 + I*Sqrt[3])*(x - x^2 + x^3)^(1/3)*Defer[Subst][Defer[Int][(1 - x^3 + x^6)^(1/3)/(1 + I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(1 - x + x^2)^(1/3)) + (6*(x - x^2 + x^3)^(1/3)*Defer[Subst][Defer[Int][(1 - x^3 + x^6)^(1/3)/(1 - Sqrt[5] + 2*x^3), x], x, x^(1/3)])/(x^(1/3)*(1 - x + x^2)^(1/3)) + (6*(x - x^2 + x^3)^(1/3)*Defer[Subst][Defer[Int][(1 - x^3 + x^6)^(1/3)/(1 + Sqrt[5] + 2*x^3), x], x, x^(1/3)])/(x^(1/3)*(1 - x + x^2)^(1/3))","F",0,0,0,0,-1,"{}"
2594,1,369,0,1.0064439,"\int \frac{\left(1+x^2\right) \sqrt[3]{x^2+x^3}}{-1+x^2} \, dx","Int[((1 + x^2)*(x^2 + x^3)^(1/3))/(-1 + x^2),x]","\frac{1}{2} \sqrt[3]{x^3+x^2} x+\frac{1}{6} \sqrt[3]{x^3+x^2}-\frac{17 \sqrt[3]{x^3+x^2} \log \left(1-\frac{\sqrt[3]{x}}{\sqrt[3]{x+1}}\right)}{9 \sqrt[3]{x+1} x^{2/3}}+\frac{17 \sqrt[3]{x^3+x^2} \log \left(\frac{x^{2/3}}{(x+1)^{2/3}}+\frac{\sqrt[3]{x}}{\sqrt[3]{x+1}}+1\right)}{18 \sqrt[3]{x+1} x^{2/3}}+\frac{\sqrt[3]{2} \sqrt[3]{x^3+x^2} \log \left(1-\frac{\sqrt[3]{2} \sqrt[3]{x}}{\sqrt[3]{x+1}}\right)}{\sqrt[3]{x+1} x^{2/3}}-\frac{\sqrt[3]{x^3+x^2} \log \left(\frac{2^{2/3} x^{2/3}}{(x+1)^{2/3}}+\frac{\sqrt[3]{2} \sqrt[3]{x}}{\sqrt[3]{x+1}}+1\right)}{2^{2/3} \sqrt[3]{x+1} x^{2/3}}-\frac{17 \sqrt[3]{x^3+x^2} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{x}}{\sqrt[3]{x+1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{x+1} x^{2/3}}+\frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3+x^2} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{x}}{\sqrt[3]{x+1}}+1}{\sqrt{3}}\right)}{\sqrt[3]{x+1} x^{2/3}}","\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,"(x^2 + x^3)^(1/3)/6 + (x*(x^2 + x^3)^(1/3))/2 - (17*(x^2 + x^3)^(1/3)*ArcTan[(1 + (2*x^(1/3))/(1 + x)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*x^(2/3)*(1 + x)^(1/3)) + (2^(1/3)*Sqrt[3]*(x^2 + x^3)^(1/3)*ArcTan[(1 + (2*2^(1/3)*x^(1/3))/(1 + x)^(1/3))/Sqrt[3]])/(x^(2/3)*(1 + x)^(1/3)) - (17*(x^2 + x^3)^(1/3)*Log[1 - x^(1/3)/(1 + x)^(1/3)])/(9*x^(2/3)*(1 + x)^(1/3)) + (17*(x^2 + x^3)^(1/3)*Log[1 + x^(2/3)/(1 + x)^(2/3) + x^(1/3)/(1 + x)^(1/3)])/(18*x^(2/3)*(1 + x)^(1/3)) + (2^(1/3)*(x^2 + x^3)^(1/3)*Log[1 - (2^(1/3)*x^(1/3))/(1 + x)^(1/3)])/(x^(2/3)*(1 + x)^(1/3)) - ((x^2 + x^3)^(1/3)*Log[1 + (2^(2/3)*x^(2/3))/(1 + x)^(2/3) + (2^(1/3)*x^(1/3))/(1 + x)^(1/3)])/(2^(2/3)*x^(2/3)*(1 + x)^(1/3))","A",36,14,24,0.5833,1,"{2056, 1586, 6733, 6725, 331, 292, 31, 634, 618, 204, 628, 321, 494, 617}"
2595,1,131,0,0.1392689,"\int \frac{-b+a x}{x \sqrt[3]{-b^3+a^3 x^3}} \, dx","Int[(-b + a*x)/(x*(-b^3 + a^3*x^3)^(1/3)),x]","\frac{1}{2} \log \left(\sqrt[3]{a^3 x^3-b^3}+b\right)-\frac{1}{2} \log \left(\sqrt[3]{a^3 x^3-b^3}-a x\right)+\frac{\tan ^{-1}\left(\frac{\frac{2 a x}{\sqrt[3]{a^3 x^3-b^3}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{b-2 \sqrt[3]{a^3 x^3-b^3}}{\sqrt{3} b}\right)}{\sqrt{3}}-\frac{\log (x)}{2}","-\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,"ArcTan[(1 + (2*a*x)/(-b^3 + a^3*x^3)^(1/3))/Sqrt[3]]/Sqrt[3] + ArcTan[(b - 2*(-b^3 + a^3*x^3)^(1/3))/(Sqrt[3]*b)]/Sqrt[3] - Log[x]/2 + Log[b + (-b^3 + a^3*x^3)^(1/3)]/2 - Log[-(a*x) + (-b^3 + a^3*x^3)^(1/3)]/2","A",8,7,28,0.2500,1,"{1844, 239, 266, 56, 617, 204, 31}"
2596,0,0,0,6.2704133,"\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","Int[((-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,"(-3*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) + (3*(1 - I*Sqrt[3])*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) + (3*(1 + I*Sqrt[3])*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) + ((x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/(1 + x), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 + I*Sqrt[3])*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/(-1 - I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 - I*Sqrt[3])*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/(-1 + I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 - I*Sqrt[3])^(1/3)*(1 + I*Sqrt[3])*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/((1 - I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 - I*Sqrt[3])*(1 + I*Sqrt[3])^(1/3)*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/((1 + I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 - I*Sqrt[3])^(1/3)*(1 + I*Sqrt[3])*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/((1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 - I*Sqrt[3])*(1 + I*Sqrt[3])^(1/3)*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/((1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 - I*Sqrt[3])^(1/3)*(1 + I*Sqrt[3])*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/((1 - I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - ((1 - I*Sqrt[3])*(1 + I*Sqrt[3])^(1/3)*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(1 + 2*x^6 + x^9)^(1/3)/((1 + I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(1/3)])/(2*x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - (6*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 + 2*x^6 + x^9)^(1/3))/(1 + x^6 + x^9), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 + x^3)^(1/3)) - (9*(x + 2*x^3 + x^4)^(1/3)*Defer[Subst][Defer[Int][(x^6*(1 + 2*x^6 + x^9)^(1/3))/(1 + x^6 + x^9), x], x, x^(1/3)])/(x^(1/3)*(1 + 2*x^2 + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2597,1,242,0,0.2005191,"\int \frac{x^4}{\sqrt[4]{-1+x^4} \left(1-2 x^4+2 x^8\right)} \, dx","Int[x^4/((-1 + x^4)^(1/4)*(1 - 2*x^4 + 2*x^8)),x]","\frac{1}{4} (-1)^{5/8} \tan ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)+\frac{(-1)^{5/8} \tan ^{-1}\left(1-\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt{2}}-\frac{(-1)^{5/8} \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}+1\right)}{4 \sqrt{2}}+\frac{1}{4} (-1)^{5/8} \tanh ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)+\frac{(-1)^{5/8} \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)}{8 \sqrt{2}}-\frac{(-1)^{5/8} \log \left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}-\frac{(-1)^{3/4} x^2}{\sqrt{x^4-1}}+1\right)}{8 \sqrt{2}}","-\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)^(5/8)*ArcTan[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)])/4 + ((-1)^(5/8)*ArcTan[1 - ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(4*Sqrt[2]) - ((-1)^(5/8)*ArcTan[1 + ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(4*Sqrt[2]) + ((-1)^(5/8)*ArcTanh[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)])/4 + ((-1)^(5/8)*Log[(-1)^(1/4) + x^2/Sqrt[-1 + x^4] + ((-1)^(1/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2]) - ((-1)^(5/8)*Log[1 - ((-1)^(3/4)*x^2)/Sqrt[-1 + x^4] + ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2])","A",16,11,27,0.4074,1,"{1528, 377, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
2598,1,242,0,0.1915183,"\int \frac{\left(-1+x^4\right)^{3/4}}{1-2 x^4+2 x^8} \, dx","Int[(-1 + x^4)^(3/4)/(1 - 2*x^4 + 2*x^8),x]","\frac{1}{4} \sqrt[8]{-1} \tan ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)-\frac{\sqrt[8]{-1} \tan ^{-1}\left(1-\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}\right)}{4 \sqrt{2}}+\frac{\sqrt[8]{-1} \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}+1\right)}{4 \sqrt{2}}+\frac{1}{4} \sqrt[8]{-1} \tanh ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)-\frac{\sqrt[8]{-1} \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)}{8 \sqrt{2}}+\frac{\sqrt[8]{-1} \log \left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}-\frac{(-1)^{3/4} x^2}{\sqrt{x^4-1}}+1\right)}{8 \sqrt{2}}","-\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)^(1/8)*ArcTan[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)])/4 - ((-1)^(1/8)*ArcTan[1 - ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(4*Sqrt[2]) + ((-1)^(1/8)*ArcTan[1 + ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(4*Sqrt[2]) + ((-1)^(1/8)*ArcTanh[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)])/4 - ((-1)^(1/8)*Log[(-1)^(1/4) + x^2/Sqrt[-1 + x^4] + ((-1)^(1/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2]) + ((-1)^(1/8)*Log[1 - ((-1)^(3/4)*x^2)/Sqrt[-1 + x^4] + ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/(8*Sqrt[2])","A",25,13,24,0.5417,1,"{1428, 408, 240, 212, 206, 203, 377, 211, 1165, 628, 1162, 617, 204}"
2599,1,242,0,0.1794514,"\int \frac{x^4}{\sqrt[4]{1+x^4} \left(1+2 x^4+2 x^8\right)} \, dx","Int[x^4/((1 + x^4)^(1/4)*(1 + 2*x^4 + 2*x^8)),x]","-\frac{1}{4} (-1)^{5/8} \tan ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4+1}}\right)-\frac{(-1)^{5/8} \tan ^{-1}\left(1-\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt{2}}+\frac{(-1)^{5/8} \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}+1\right)}{4 \sqrt{2}}-\frac{1}{4} (-1)^{5/8} \tanh ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4+1}}\right)-\frac{(-1)^{5/8} \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)}{8 \sqrt{2}}+\frac{(-1)^{5/8} \log \left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}-\frac{(-1)^{3/4} x^2}{\sqrt{x^4+1}}+1\right)}{8 \sqrt{2}}","\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,"-1/4*((-1)^(5/8)*ArcTan[((-1)^(7/8)*x)/(1 + x^4)^(1/4)]) - ((-1)^(5/8)*ArcTan[1 - ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(4*Sqrt[2]) + ((-1)^(5/8)*ArcTan[1 + ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(4*Sqrt[2]) - ((-1)^(5/8)*ArcTanh[((-1)^(7/8)*x)/(1 + x^4)^(1/4)])/4 - ((-1)^(5/8)*Log[(-1)^(1/4) + x^2/Sqrt[1 + x^4] + ((-1)^(1/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(8*Sqrt[2]) + ((-1)^(5/8)*Log[1 - ((-1)^(3/4)*x^2)/Sqrt[1 + x^4] + ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(8*Sqrt[2])","A",16,11,27,0.4074,1,"{1528, 377, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
2600,1,242,0,0.186595,"\int \frac{\left(1+x^4\right)^{3/4}}{1+2 x^4+2 x^8} \, dx","Int[(1 + x^4)^(3/4)/(1 + 2*x^4 + 2*x^8),x]","-\frac{1}{4} \sqrt[8]{-1} \tan ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4+1}}\right)+\frac{\sqrt[8]{-1} \tan ^{-1}\left(1-\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}\right)}{4 \sqrt{2}}-\frac{\sqrt[8]{-1} \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}+1\right)}{4 \sqrt{2}}-\frac{1}{4} \sqrt[8]{-1} \tanh ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4+1}}\right)+\frac{\sqrt[8]{-1} \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)}{8 \sqrt{2}}-\frac{\sqrt[8]{-1} \log \left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4+1}}-\frac{(-1)^{3/4} x^2}{\sqrt{x^4+1}}+1\right)}{8 \sqrt{2}}","\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,"-1/4*((-1)^(1/8)*ArcTan[((-1)^(7/8)*x)/(1 + x^4)^(1/4)]) + ((-1)^(1/8)*ArcTan[1 - ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(4*Sqrt[2]) - ((-1)^(1/8)*ArcTan[1 + ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(4*Sqrt[2]) - ((-1)^(1/8)*ArcTanh[((-1)^(7/8)*x)/(1 + x^4)^(1/4)])/4 + ((-1)^(1/8)*Log[(-1)^(1/4) + x^2/Sqrt[1 + x^4] + ((-1)^(1/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(8*Sqrt[2]) - ((-1)^(1/8)*Log[1 - ((-1)^(3/4)*x^2)/Sqrt[1 + x^4] + ((-1)^(7/8)*Sqrt[2]*x)/(1 + x^4)^(1/4)])/(8*Sqrt[2])","A",25,13,24,0.5417,1,"{1428, 408, 240, 212, 206, 203, 377, 211, 1165, 628, 1162, 617, 204}"
2601,0,0,0,4.4033736,"\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","Int[(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,"(2*Sqrt[-(b*x) + a^2*x^2]*Defer[Subst][Defer[Int][(x^6*Sqrt[-b + a^2*x^2])/(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2), x], x, Sqrt[x]])/(Sqrt[x]*Sqrt[-b + a^2*x])","F",0,0,0,0,-1,"{}"
2602,1,81,0,0.1760009,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x) \sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)*Sqrt[1 + x^4]),x]","-\frac{1}{2} \sqrt{1-i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)-\frac{1}{2} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)","\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,"-1/2*(Sqrt[1 - I]*ArcTanh[(1 + I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])]) - (Sqrt[1 + I]*ArcTanh[(1 - I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/2","C",5,3,32,0.09375,0,"{2133, 725, 206}"
2603,1,1265,0,2.0842854,"\int \frac{-b+a x^2}{\left(-b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(-b + a*x^2)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-2} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{12 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-\sqrt[3]{2} \sqrt[3]{a} x\right)}{12 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a} x\right)}{12 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/9)*b^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/9)*b^(1/3)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (((-1)^(2/3)*2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/9)*b^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-2)^(1/3)*a^(1/3)*x])/(12*a^(1/9)*b^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - 2^(1/3)*a^(1/3)*x])/(12*a^(1/9)*b^(1/3)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (((-1)^(2/3)*2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*2^(1/3)*a^(1/3)*x])/(12*a^(1/9)*b^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3))])/(4*a^(1/9)*b^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3))])/(4*a^(1/9)*b^(1/3)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (((-1)^(2/3)*2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3))])/(4*a^(1/9)*b^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",6,3,41,0.07317,0,"{2056, 6725, 91}"
2604,1,1265,0,1.7478258,"\int \frac{-b+a x^2}{\left(-b+2 a x^3\right) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(-b + a*x^2)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-2} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{12 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-\sqrt[3]{2} \sqrt[3]{a} x\right)}{12 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a} x\right)}{12 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{-2} \sqrt[3]{a}+2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a}-2 \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 \sqrt[9]{a} \sqrt[3]{b} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-1/2*(((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(Sqrt[3]*a^(1/9)*b^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/9)*b^(1/3)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (((-1)^(2/3)*2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(1/9)*b^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-2)^(1/3)*a^(1/3)*x])/(12*a^(1/9)*b^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - 2^(1/3)*a^(1/3)*x])/(12*a^(1/9)*b^(1/3)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (((-1)^(2/3)*2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*2^(1/3)*a^(1/3)*x])/(12*a^(1/9)*b^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (((-2)^(1/3)*a^(1/3) + 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3))])/(4*a^(1/9)*b^(1/3)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3))])/(4*a^(1/9)*b^(1/3)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (((-1)^(2/3)*2^(1/3)*a^(1/3) - 2*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3))])/(4*a^(1/9)*b^(1/3)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",6,3,41,0.07317,0,"{2056, 6725, 91}"
2605,0,0,0,13.2582693,"\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","Int[(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,"(3*x*(1 - x/a)^(1/3)*(1 - x/b)^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, x/a, x/b])/(d*((a - x)*(b - x)*x^2)^(1/3)) + (6*a*(1 - b*d)*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a^2 - 2*a*x^3 + (1 + b*d)*x^6 - d*x^9)), x], x, x^(1/3)])/(d*((a - x)*(b - x)*x^2)^(1/3)) - (3*(1 - 3*a*d + b*d)*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a^2 - 2*a*x^3 + (1 + b*d)*x^6 - d*x^9)), x], x, x^(1/3)])/(d*((a - x)*(b - x)*x^2)^(1/3)) + (3*a^2*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][1/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(-a^2 + 2*a*x^3 - (1 + b*d)*x^6 + d*x^9)), x], x, x^(1/3)])/(d*((a - x)*(b - x)*x^2)^(1/3))","F",0,0,0,0,-1,"{}"
2606,0,0,0,0.7985764,"\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","Int[((-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,"Defer[Subst][Defer[Int][(-2 + k^2 + k^2*x)/((1 - d + (-2 + d*k^2)*x + x^2)*(1 + (-1 - k^2)*x + k^2*x^2)^(1/3)), x], x, x^2]/2","F",0,0,0,0,-1,"{}"
2607,1,496,0,0.7443668,"\int \frac{(1+2 x) \sqrt[4]{x^3+x^4}}{-1+x+x^2} \, dx","Int[((1 + 2*x)*(x^3 + x^4)^(1/4))/(-1 + x + x^2),x]","2 \sqrt[4]{x^4+x^3}+\frac{\left(1+2 \sqrt{5}\right) \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 x^{3/4} \sqrt[4]{x+1}}+\frac{\left(1-2 \sqrt{5}\right) \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 x^{3/4} \sqrt[4]{x+1}}-\frac{2^{3/4} \sqrt[4]{3+\sqrt{5}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}+\frac{2^{3/4} \sqrt[4]{3-\sqrt{5}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1+2 \sqrt{5}\right) \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 x^{3/4} \sqrt[4]{x+1}}-\frac{\left(1-2 \sqrt{5}\right) \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{2 x^{3/4} \sqrt[4]{x+1}}+\frac{2^{3/4} \sqrt[4]{3+\sqrt{5}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}-\frac{2^{3/4} \sqrt[4]{3-\sqrt{5}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{x^{3/4} \sqrt[4]{x+1}}","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 + x^4)^(1/4) + ((1 - 2*Sqrt[5])*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(2*x^(3/4)*(1 + x)^(1/4)) + ((1 + 2*Sqrt[5])*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(2*x^(3/4)*(1 + x)^(1/4)) - (2^(3/4)*(3 + Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) + (2^(3/4)*(3 - Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - ((1 - 2*Sqrt[5])*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(2*x^(3/4)*(1 + x)^(1/4)) - ((1 + 2*Sqrt[5])*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(2*x^(3/4)*(1 + x)^(1/4)) + (2^(3/4)*(3 + Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4)) - (2^(3/4)*(3 - Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(x^(3/4)*(1 + x)^(1/4))","B",25,10,25,0.4000,0,"{2056, 6728, 101, 157, 63, 331, 298, 203, 206, 93}"
2608,1,423,0,2.9119873,"\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","Int[((-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]","\frac{3 k^2 \left(1-x^2\right) \left(1-\sqrt{1-4 d k^2 \left(1-k^2\right)}\right) \left(1-k^2 x^2\right) F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 d k^4 \left(1-x^2\right)}{-2 d \left(1-k^2\right) k^2-\sqrt{1-4 d k^2 \left(1-k^2\right)}+1}\right)}{2 \left(-2 d \left(1-k^2\right) k^2-\sqrt{1-4 d k^2 \left(1-k^2\right)}+1\right) \sqrt[3]{\frac{1-k^2 x^2}{1-k^2}} \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}+\frac{3 k^2 \left(1-x^2\right) \left(\sqrt{1-4 d k^2 \left(1-k^2\right)}+1\right) \left(1-k^2 x^2\right) F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 d k^4 \left(1-x^2\right)}{-2 d \left(1-k^2\right) k^2+\sqrt{1-4 d k^2 \left(1-k^2\right)}+1}\right)}{2 \left(-2 d \left(1-k^2\right) k^2+\sqrt{1-4 d k^2 \left(1-k^2\right)}+1\right) \sqrt[3]{\frac{1-k^2 x^2}{1-k^2}} \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}","-\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,"(3*k^2*(1 - Sqrt[1 - 4*d*k^2*(1 - k^2)])*(1 - x^2)*(1 - k^2*x^2)*AppellF1[1/3, -1/3, 1, 4/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*d*k^4*(1 - x^2))/(1 - 2*d*k^2*(1 - k^2) - Sqrt[1 - 4*d*k^2*(1 - k^2)])])/(2*(1 - 2*d*k^2*(1 - k^2) - Sqrt[1 - 4*d*k^2*(1 - k^2)])*((1 - k^2*x^2)/(1 - k^2))^(1/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3)) + (3*k^2*(1 + Sqrt[1 - 4*d*k^2*(1 - k^2)])*(1 - x^2)*(1 - k^2*x^2)*AppellF1[1/3, -1/3, 1, 4/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*d*k^4*(1 - x^2))/(1 - 2*d*k^2*(1 - k^2) + Sqrt[1 - 4*d*k^2*(1 - k^2)])])/(2*(1 - 2*d*k^2*(1 - k^2) + Sqrt[1 - 4*d*k^2*(1 - k^2)])*((1 - k^2*x^2)/(1 - k^2))^(1/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))","C",10,7,73,0.09589,0,"{1594, 6715, 6719, 1586, 6728, 137, 136}"
2609,0,0,0,41.6171222,"\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","Int[((-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,"(3*(a + b)*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(-a + x^3)^(2/3)*(-b + x^3)^(2/3))/(a^2*b^2*d - 2*a^2*b*(1 + b/a)*d*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*d*x^6 - 2*a*(1 + b/a)*d*x^9 - (1 - d)*x^12), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3) + (6*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x*(-a + x^3)^(2/3)*(-b + x^3)^(2/3))/(-(a^2*b^2*d) + 2*a^2*b*(1 + b/a)*d*x^3 - a^2*(1 + (b*(4*a + b))/a^2)*d*x^6 + 2*a*(1 + b/a)*d*x^9 + (1 - d)*x^12), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2610,1,609,0,3.1564888,"\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","Int[(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{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)-\frac{\left(\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \log \left(-\sqrt{2} \sqrt{b} \sqrt{\sqrt{a^2+b^2}+b} \sqrt{a^2 x^3+b^2}+b \left(\sqrt{a^2+b^2}+b\right)+a^2 x^3\right)}{6 \sqrt{2} \sqrt{b} \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+b}}+\frac{\left(\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \log \left(\sqrt{2} \sqrt{b} \sqrt{\sqrt{a^2+b^2}+b} \sqrt{a^2 x^3+b^2}+b \left(\sqrt{a^2+b^2}+b\right)+a^2 x^3\right)}{6 \sqrt{2} \sqrt{b} \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+b}}+\frac{\left(-\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\sqrt{a^2+b^2}+b}-\sqrt{2} \sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{b-\sqrt{a^2+b^2}}}\right)}{3 \sqrt{2} \sqrt{b} \sqrt{a^2+b^2} \sqrt{b-\sqrt{a^2+b^2}}}-\frac{\left(-\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a^2 x^3+b^2}+\sqrt{b} \sqrt{\sqrt{a^2+b^2}+b}}{\sqrt{b} \sqrt{b-\sqrt{a^2+b^2}}}\right)}{3 \sqrt{2} \sqrt{b} \sqrt{a^2+b^2} \sqrt{b-\sqrt{a^2+b^2}}}","\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*Sqrt[b^2 + a^2*x^3])/3 - (4*b*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/3 + ((a^2*b + b^3 - Sqrt[a^2 + b^2]*(b^2 - c))*ArcTanh[(Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]] - Sqrt[2]*Sqrt[b^2 + a^2*x^3])/(Sqrt[b]*Sqrt[b - Sqrt[a^2 + b^2]])])/(3*Sqrt[2]*Sqrt[b]*Sqrt[a^2 + b^2]*Sqrt[b - Sqrt[a^2 + b^2]]) - ((a^2*b + b^3 - Sqrt[a^2 + b^2]*(b^2 - c))*ArcTanh[(Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]] + Sqrt[2]*Sqrt[b^2 + a^2*x^3])/(Sqrt[b]*Sqrt[b - Sqrt[a^2 + b^2]])])/(3*Sqrt[2]*Sqrt[b]*Sqrt[a^2 + b^2]*Sqrt[b - Sqrt[a^2 + b^2]]) - ((a^2*b + b^3 + Sqrt[a^2 + b^2]*(b^2 - c))*Log[b*(b + Sqrt[a^2 + b^2]) + a^2*x^3 - Sqrt[2]*Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]]*Sqrt[b^2 + a^2*x^3]])/(6*Sqrt[2]*Sqrt[b]*Sqrt[a^2 + b^2]*Sqrt[b + Sqrt[a^2 + b^2]]) + ((a^2*b + b^3 + Sqrt[a^2 + b^2]*(b^2 - c))*Log[b*(b + Sqrt[a^2 + b^2]) + a^2*x^3 + Sqrt[2]*Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]]*Sqrt[b^2 + a^2*x^3]])/(6*Sqrt[2]*Sqrt[b]*Sqrt[a^2 + b^2]*Sqrt[b + Sqrt[a^2 + b^2]])","B",18,13,50,0.2600,1,"{6725, 266, 50, 63, 208, 6715, 825, 827, 1169, 634, 618, 206, 628}"
2611,1,250,0,0.7350913,"\int \frac{\sqrt{x+x^4} \left(b+a x^6\right)}{-d+c x^6} \, dx","Int[(Sqrt[x + x^4]*(b + a*x^6))/(-d + c*x^6),x]","-\frac{\sqrt{x^4+x} \sqrt{\sqrt{c}-\sqrt{d}} (a d+b c) \tan ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{c}-\sqrt{d}}}{\sqrt[4]{d} \sqrt{x^3+1}}\right)}{3 c^{3/2} d^{3/4} \sqrt{x^3+1} \sqrt{x}}-\frac{\sqrt{x^4+x} \sqrt{\sqrt{c}+\sqrt{d}} (a d+b c) \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{c}+\sqrt{d}}}{\sqrt[4]{d} \sqrt{x^3+1}}\right)}{3 c^{3/2} d^{3/4} \sqrt{x^3+1} \sqrt{x}}+\frac{a \sqrt{x^4+x} x}{3 c}+\frac{a \sqrt{x^4+x} \sinh ^{-1}\left(x^{3/2}\right)}{3 c \sqrt{x^3+1} \sqrt{x}}","\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,"(a*x*Sqrt[x + x^4])/(3*c) + (a*Sqrt[x + x^4]*ArcSinh[x^(3/2)])/(3*c*Sqrt[x]*Sqrt[1 + x^3]) - (Sqrt[Sqrt[c] - Sqrt[d]]*(b*c + a*d)*Sqrt[x + x^4]*ArcTan[(Sqrt[Sqrt[c] - Sqrt[d]]*x^(3/2))/(d^(1/4)*Sqrt[1 + x^3])])/(3*c^(3/2)*d^(3/4)*Sqrt[x]*Sqrt[1 + x^3]) - (Sqrt[Sqrt[c] + Sqrt[d]]*(b*c + a*d)*Sqrt[x + x^4]*ArcTanh[(Sqrt[Sqrt[c] + Sqrt[d]]*x^(3/2))/(d^(1/4)*Sqrt[1 + x^3])])/(3*c^(3/2)*d^(3/4)*Sqrt[x]*Sqrt[1 + x^3])","A",15,10,28,0.3571,1,"{2056, 6715, 1693, 195, 215, 1175, 402, 377, 208, 205}"
2612,0,0,0,10.4450162,"\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","Int[(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,"(-3*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][(x^3*(1 - x^3)^(1/3)*(1 - k*x^3)^(1/3))/(-1 + 4*x^3 - 6*(1 - b/6)*x^6 + 4*(1 - (b*k)/2)*x^9 - (1 - b*k^2)*x^12), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (3*(1 - 2*k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][(x^6*(1 - x^3)^(1/3)*(1 - k*x^3)^(1/3))/(1 - 4*x^3 + 6*(1 - b/6)*x^6 - 4*(1 - (b*k)/2)*x^9 + (1 - b*k^2)*x^12), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2613,0,0,0,4.1400928,"\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","Int[(-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,"(a*x*(1 + (p*x^4)/q)^(1/3)*Hypergeometric2F1[1/4, 1/3, 5/4, -((p*x^4)/q)])/(c*(q + p*x^4)^(1/3)) - (a*(b^3*d + 4*c*q)*Defer[Int][1/((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])/c - (3*a^2*b^2*d*Defer[Int][x/((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])/c - (3*a^3*b*d*Defer[Int][x^2/((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])/c - ((a^4*d - 4*b*c*p)*Defer[Int][x^3/((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])/c","F",0,0,0,0,-1,"{}"
2614,0,0,0,3.4061757,"\int \frac{x^2}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[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{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+2 \text{$\#$1}^4 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]+x",1,"(-2*c*Sqrt[b + a*x])/a + (c + Sqrt[b + a*x])^2/a + 8*a*c*Defer[Subst][Defer[Int][x^4/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*c^2*Defer[Subst][Defer[Int][x^2/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*Defer[Subst][Defer[Int][x^6/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2615,0,0,0,2.837501,"\int \frac{x^2}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[x^2/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x^2}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+2 \text{$\#$1}^4 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{-8 \text{$\#$1}^7+24 \text{$\#$1}^5 c+8 \text{$\#$1}^3 b-24 \text{$\#$1}^3 c^2+3 \text{$\#$1}^2 a^2-8 \text{$\#$1} b c+8 \text{$\#$1} c^3-a^2 c}\&\right]+x",1,"(-2*c*Sqrt[b + a*x])/a + (c + Sqrt[b + a*x])^2/a + 8*a*c*Defer[Subst][Defer[Int][x^4/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*c^2*Defer[Subst][Defer[Int][x^2/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*Defer[Subst][Defer[Int][x^6/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2616,0,0,0,5.9224899,"\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","Int[(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,"-((x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(1/3)) - ((4 - d)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(-1 + d + (1 + 2*d)*x + (d + k^2)*x^2 - k^2*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) - (2*(1 + d - k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) - ((d + 4*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (1 + 2*d)*x - (d + k^2)*x^2 + k^2*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2617,0,0,0,5.1706381,"\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","Int[(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,"(x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(1/3) - ((4 - d)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (1 + 2*d)*x - (d + k^2)*x^2 - k^2*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) - (2*(1 + d - k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (1 + 2*d)*x - (d + k^2)*x^2 - k^2*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) + ((d + 4*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (1 + 2*d)*x - (d + k^2)*x^2 - k^2*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2618,1,508,0,1.6375739,"\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","Int[(Sqrt[-b^4 + a^4*x^4]*(b^4 + a^4*x^4))/(b^8 - c*x^4 + a^8*x^8),x]","\frac{b \left(1-\frac{2 a^4 b^4+c}{\sqrt{c^2-4 a^8 b^8}}\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}+\frac{b \left(\frac{2 a^4 b^4+c}{\sqrt{c^2-4 a^8 b^8}}+1\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{2} a^2 b^2}{\sqrt{c-\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{2} a^2 b^2}{\sqrt{c-\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{2} a^2 b^2}{\sqrt{c+\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{2} a^2 b^2}{\sqrt{c+\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \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,"(b*(1 - (2*a^4*b^4 + c)/Sqrt[-4*a^8*b^8 + c^2])*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) + (b*(1 + (2*a^4*b^4 + c)/Sqrt[-4*a^8*b^8 + c^2])*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-((Sqrt[2]*a^2*b^2)/Sqrt[c - Sqrt[-4*a^8*b^8 + c^2]]), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(Sqrt[2]*a^2*b^2)/Sqrt[c - Sqrt[-4*a^8*b^8 + c^2]], ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-((Sqrt[2]*a^2*b^2)/Sqrt[c + Sqrt[-4*a^8*b^8 + c^2]]), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(Sqrt[2]*a^2*b^2)/Sqrt[c + Sqrt[-4*a^8*b^8 + c^2]], ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4])","C",18,7,48,0.1458,1,"{6728, 406, 224, 221, 409, 1219, 1218}"
2619,1,508,0,1.2183711,"\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","Int[(-b^8 + a^8*x^8)/(Sqrt[-b^4 + a^4*x^4]*(b^8 - c*x^4 + a^8*x^8)),x]","\frac{b \left(1-\frac{2 a^4 b^4+c}{\sqrt{c^2-4 a^8 b^8}}\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}+\frac{b \left(\frac{2 a^4 b^4+c}{\sqrt{c^2-4 a^8 b^8}}+1\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{2} a^2 b^2}{\sqrt{c-\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{2} a^2 b^2}{\sqrt{c-\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{2} a^2 b^2}{\sqrt{c+\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{2} a^2 b^2}{\sqrt{c+\sqrt{c^2-4 a^8 b^8}}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \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,"(b*(1 - (2*a^4*b^4 + c)/Sqrt[-4*a^8*b^8 + c^2])*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) + (b*(1 + (2*a^4*b^4 + c)/Sqrt[-4*a^8*b^8 + c^2])*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-((Sqrt[2]*a^2*b^2)/Sqrt[c - Sqrt[-4*a^8*b^8 + c^2]]), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(Sqrt[2]*a^2*b^2)/Sqrt[c - Sqrt[-4*a^8*b^8 + c^2]], ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-((Sqrt[2]*a^2*b^2)/Sqrt[c + Sqrt[-4*a^8*b^8 + c^2]]), ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(Sqrt[2]*a^2*b^2)/Sqrt[c + Sqrt[-4*a^8*b^8 + c^2]], ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4])","C",19,8,50,0.1600,1,"{1586, 6728, 406, 224, 221, 409, 1219, 1218}"
2620,1,171,0,0.4807879,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{x^2} \, dx","Int[Sqrt[a*x + Sqrt[-b + a*x]]/x^2,x]","-\frac{a \left(2 \sqrt{b}+1\right) \tan ^{-1}\left(\frac{\sqrt{b}-\sqrt{a x-b}}{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a x-b}+a x}}\right)}{2 \sqrt{2} b^{3/4}}+\frac{a \left(1-2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{a x-b}+\sqrt{b}}{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a x-b}+a x}}\right)}{2 \sqrt{2} b^{3/4}}-\frac{\sqrt{\sqrt{a x-b}+a x}}{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,"-(Sqrt[a*x + Sqrt[-b + a*x]]/x) - (a*(1 + 2*Sqrt[b])*ArcTan[(Sqrt[b] - Sqrt[-b + a*x])/(Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(2*Sqrt[2]*b^(3/4)) + (a*(1 - 2*Sqrt[b])*ArcTanh[(Sqrt[b] + Sqrt[-b + a*x])/(Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(2*Sqrt[2]*b^(3/4))","A",7,5,23,0.2174,1,"{1014, 1036, 1030, 208, 205}"
2621,0,0,0,4.1796364,"\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","Int[(-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,"-(((1 + Sqrt[4 + b - 4*k]/Sqrt[b] - 2*k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - x)^(1/3)/(x^(2/3)*(1 - k*x)^(2/3)*(-2 - b - Sqrt[b]*Sqrt[4 + b - 4*k] + 2*(1 + b*k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)) - ((1 - Sqrt[4 + b - 4*k]/Sqrt[b] - 2*k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - x)^(1/3)/(x^(2/3)*(1 - k*x)^(2/3)*(-2 - b + Sqrt[b]*Sqrt[4 + b - 4*k] + 2*(1 + b*k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2622,0,0,0,6.3474846,"\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","Int[(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,"-1/4*((2 + 2^(1/3)*(2/(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(1/3)) - 6*x)^(1/3)*(2 + (2*2^(1/3) + (58 + 6*Sqrt[93])^(2/3))/(29 + 3*Sqrt[93])^(1/3) - 6*x)^(2/3)*(1 - (2^(2/3)*(2*2^(1/3) + 2*(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(2/3) - 6*(29 + 3*Sqrt[93])^(1/3)*x))/(6 + 3*2^(1/3)*(29 + 3*Sqrt[93])^(2/3) + 2^(1/6)*(29 + 3*Sqrt[93])^(1/3)*Sqrt[3*(4 - 2*(2/(29 + 3*Sqrt[93]))^(2/3) - 2^(1/3)*(29 + 3*Sqrt[93])^(2/3))]))^(1/3)*(1 - (2^(2/3)*(2*2^(1/3) + 2*(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(2/3) - 6*(29 + 3*Sqrt[93])^(1/3)*x))/(6 + 3*2^(1/3)*(29 + 3*Sqrt[93])^(2/3) - I*2^(1/6)*(29 + 3*Sqrt[93])^(1/3)*Sqrt[3*(-4 + 2*(2/(29 + 3*Sqrt[93]))^(2/3) + 2^(1/3)*(29 + 3*Sqrt[93])^(2/3))]))^(1/3)*AppellF1[2/3, 1/3, 1/3, 5/3, ((29 + 3*Sqrt[93])^(1/3)*(2*(2/(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(1/3)) + 2*2^(2/3)*(1 - 3*x)))/(6 + 3*2^(1/3)*(29 + 3*Sqrt[93])^(2/3) + 2^(1/6)*(29 + 3*Sqrt[93])^(1/3)*Sqrt[3*(4 - 2*(2/(29 + 3*Sqrt[93]))^(2/3) - 2^(1/3)*(29 + 3*Sqrt[93])^(2/3))]), ((29 + 3*Sqrt[93])^(1/3)*(2*(2/(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(1/3)) + 2*2^(2/3)*(1 - 3*x)))/(6 + 3*2^(1/3)*(29 + 3*Sqrt[93])^(2/3) - I*2^(1/6)*(29 + 3*Sqrt[93])^(1/3)*Sqrt[3*(-4 + 2*(2/(29 + 3*Sqrt[93]))^(2/3) + 2^(1/3)*(29 + 3*Sqrt[93])^(2/3))])])/(1 + x^2 - x^3)^(1/3) - 3*Defer[Int][1/((1 + x^2 - x^3)^(1/3)*(1 + x^2 + x^3)), x] - Defer[Int][x^2/((1 + x^2 - x^3)^(1/3)*(1 + x^2 + x^3)), x] + ((I/3)*(-2 + 2*(2/(29 + 3*Sqrt[93]))^(2/3) + 2^(1/3)*(29 + 3*Sqrt[93])^(2/3) - 2*((2/(29 + 3*Sqrt[93]))^(1/3) + ((29 + 3*Sqrt[93])/2)^(1/3))*(1 - 3*x) + 2*(1 - 3*x)^2)^(1/3)*(2 + 2^(1/3)*(2/(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(1/3)) - 6*x)^(1/3)*Defer[Subst][Defer[Int][1/(((-1/3 + I) - x)*((2/(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(1/3))/(3*2^(2/3)) - x)^(1/3)*((-2 + 2*(2/(29 + 3*Sqrt[93]))^(2/3) + 2^(1/3)*(29 + 3*Sqrt[93])^(2/3))/18 + (((2/(29 + 3*Sqrt[93]))^(1/3) + ((29 + 3*Sqrt[93])/2)^(1/3))*x)/3 + x^2)^(1/3)), x], x, -1/3 + x])/(2^(2/3)*(1 + x^2 - x^3)^(1/3)) + ((I/3)*(-2 + 2*(2/(29 + 3*Sqrt[93]))^(2/3) + 2^(1/3)*(29 + 3*Sqrt[93])^(2/3) - 2*((2/(29 + 3*Sqrt[93]))^(1/3) + ((29 + 3*Sqrt[93])/2)^(1/3))*(1 - 3*x) + 2*(1 - 3*x)^2)^(1/3)*(2 + 2^(1/3)*(2/(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(1/3)) - 6*x)^(1/3)*Defer[Subst][Defer[Int][1/(((2/(29 + 3*Sqrt[93])^(1/3) + (58 + 6*Sqrt[93])^(1/3))/(3*2^(2/3)) - x)^(1/3)*((1/3 + I) + x)*((-2 + 2*(2/(29 + 3*Sqrt[93]))^(2/3) + 2^(1/3)*(29 + 3*Sqrt[93])^(2/3))/18 + (((2/(29 + 3*Sqrt[93]))^(1/3) + ((29 + 3*Sqrt[93])/2)^(1/3))*x)/3 + x^2)^(1/3)), x], x, -1/3 + x])/(2^(2/3)*(1 + x^2 - x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2623,1,480,0,1.0477755,"\int \frac{\left(1+x^2\right) \sqrt[4]{-x^3+x^4}}{-1+x+2 x^2} \, dx","Int[((1 + x^2)*(-x^3 + x^4)^(1/4))/(-1 + x + 2*x^2),x]","-\frac{1}{4} \sqrt[4]{x^4-x^3} (1-x)-\frac{1}{16} \sqrt[4]{x^4-x^3}+\frac{5 \sqrt[4]{x^4-x^3} \log \left(\frac{\sqrt{x}}{\sqrt{x-1}}-\frac{\sqrt{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}+1\right)}{24 \sqrt{2} \sqrt[4]{x-1} x^{3/4}}-\frac{5 \sqrt[4]{x^4-x^3} \log \left(\frac{\sqrt{x}}{\sqrt{x-1}}+\frac{\sqrt{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}+1\right)}{24 \sqrt{2} \sqrt[4]{x-1} x^{3/4}}-\frac{5 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{12 \sqrt{2} \sqrt[4]{x-1} x^{3/4}}+\frac{5 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}+1\right)}{12 \sqrt{2} \sqrt[4]{x-1} x^{3/4}}+\frac{57 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{32 \sqrt[4]{x-1} x^{3/4}}+\frac{4 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}+\frac{57 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{32 \sqrt[4]{x-1} x^{3/4}}-\frac{4 \sqrt[4]{2} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{3 \sqrt[4]{x-1} x^{3/4}}","\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,"-1/16*(-x^3 + x^4)^(1/4) - ((1 - x)*(-x^3 + x^4)^(1/4))/4 - (5*(-x^3 + x^4)^(1/4)*ArcTan[1 - (Sqrt[2]*x^(1/4))/(-1 + x)^(1/4)])/(12*Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) + (5*(-x^3 + x^4)^(1/4)*ArcTan[1 + (Sqrt[2]*x^(1/4))/(-1 + x)^(1/4)])/(12*Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) + (57*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(32*(-1 + x)^(1/4)*x^(3/4)) + (4*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (57*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(32*(-1 + x)^(1/4)*x^(3/4)) - (4*2^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(2^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(3*(-1 + x)^(1/4)*x^(3/4)) + (5*(-x^3 + x^4)^(1/4)*Log[1 - (Sqrt[2]*x^(1/4))/(-1 + x)^(1/4) + Sqrt[x]/Sqrt[-1 + x]])/(24*Sqrt[2]*(-1 + x)^(1/4)*x^(3/4)) - (5*(-x^3 + x^4)^(1/4)*Log[1 + (Sqrt[2]*x^(1/4))/(-1 + x)^(1/4) + Sqrt[x]/Sqrt[-1 + x]])/(24*Sqrt[2]*(-1 + x)^(1/4)*x^(3/4))","B",40,18,29,0.6207,1,"{2056, 6728, 50, 63, 240, 212, 206, 203, 101, 157, 93, 297, 1162, 617, 204, 1165, 628, 298}"
2624,1,529,0,1.2906374,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(b+a x^4+x^8\right)}{b+a x^4} \, dx","Int[((b*x^2 + a*x^4)^(1/4)*(b + a*x^4 + x^8))/(b + a*x^4),x]","-\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{7 b^2 x \sqrt[4]{a x^4+b x^2}}{192 a^3}+\frac{b x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a^2 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{b x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a^2 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{1}{2} x \left(1-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2}+\frac{b x^3 \sqrt[4]{a x^4+b x^2}}{48 a^2}-\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{x^5 \sqrt[4]{a x^4+b x^2}}{6 a}","-\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,"(-7*b^2*x*(b*x^2 + a*x^4)^(1/4))/(192*a^3) + ((1 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4))/2 + (b*x^3*(b*x^2 + a*x^4)^(1/4))/(48*a^2) + (x^5*(b*x^2 + a*x^4)^(1/4))/(6*a) + (b*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*a^2*(1 + (a*x^2)/b)^(1/4)) + (b*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*a^2*(1 + (a*x^2)/b)^(1/4)) - ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4))","B",24,13,35,0.3714,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 321, 1270, 1529, 511, 510}"
2625,1,529,0,1.2138175,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(b+a x^4+x^8\right)}{b+a x^4} \, dx","Int[((b*x^2 + a*x^4)^(1/4)*(b + a*x^4 + x^8))/(b + a*x^4),x]","-\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{7 b^2 x \sqrt[4]{a x^4+b x^2}}{192 a^3}+\frac{b x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a^2 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{b x \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a^2 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{1}{2} x \left(1-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2}+\frac{b x^3 \sqrt[4]{a x^4+b x^2}}{48 a^2}-\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{x^5 \sqrt[4]{a x^4+b x^2}}{6 a}","-\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,"(-7*b^2*x*(b*x^2 + a*x^4)^(1/4))/(192*a^3) + ((1 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4))/2 + (b*x^3*(b*x^2 + a*x^4)^(1/4))/(48*a^2) + (x^5*(b*x^2 + a*x^4)^(1/4))/(6*a) + (b*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*a^2*(1 + (a*x^2)/b)^(1/4)) + (b*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*a^2*(1 + (a*x^2)/b)^(1/4)) - ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4))","B",24,13,35,0.3714,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 321, 1270, 1529, 511, 510}"
2626,1,136,0,0.0227667,"\int \frac{1}{\sqrt[3]{-1+x^2} \left(3+x^2\right)} \, dx","Int[1/((-1 + x^2)^(1/3)*(3 + x^2)),x]","-\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{x^2-1}+1\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{1}{2} \left(-\frac{1}{2}\right)^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{-1} x}{\sqrt[3]{2} \sqrt[3]{x^2-1}+\sqrt[3]{-1}}\right)-\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{1}{6} \left(-\frac{1}{2}\right)^{2/3} \tanh ^{-1}(x)","\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,"-1/2*((-1)^(2/3)*ArcTan[Sqrt[3]/x])/(2^(2/3)*Sqrt[3]) - ((-1)^(2/3)*ArcTan[(Sqrt[3]*(1 + (-1)^(2/3)*2^(1/3)*(-1 + x^2)^(1/3)))/x])/(2*2^(2/3)*Sqrt[3]) + ((-1/2)^(2/3)*ArcTanh[x])/6 - ((-1/2)^(2/3)*ArcTanh[((-1)^(1/3)*x)/((-1)^(1/3) + 2^(1/3)*(-1 + x^2)^(1/3))])/2","A",1,1,17,0.05882,1,"{393}"
2627,0,0,0,0.3054033,"\int \frac{1+x}{\left(1+3 x+x^2\right) \sqrt[3]{1-x^3}} \, dx","Int[(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,"((5 - Sqrt[5])*Defer[Int][1/((3 - Sqrt[5] + 2*x)*(1 - x^3)^(1/3)), x])/5 + ((5 + Sqrt[5])*Defer[Int][1/((3 + Sqrt[5] + 2*x)*(1 - x^3)^(1/3)), x])/5","F",0,0,0,0,-1,"{}"
2628,0,0,0,9.487793,"\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","Int[(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,"-((k*(5 + d*k^2)*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(2/3)) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*k^(4/3)*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) + (k*(8 - d^2*k^2 - d*(5 - k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(2/3) + ((2 - (2 + 11*d)*k^2 - d*(1 + 2*d)*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(2/3) - (k*(6 + (2 + 8*d)*k^2 + d^2*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(2/3)","F",0,0,0,0,-1,"{}"
2629,1,268,0,0.8487073,"\int \frac{\sqrt{-x+x^4} \left(b+a x^6\right)}{-d+c x^6} \, dx","Int[(Sqrt[-x + x^4]*(b + a*x^6))/(-d + c*x^6),x]","\frac{\sqrt{x^4-x} \sqrt{\sqrt{c}-\sqrt{d}} (a d+b c) \tan ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{c}-\sqrt{d}}}{\sqrt[4]{d} \sqrt{x^3-1}}\right)}{3 c^{3/2} d^{3/4} \sqrt{x^3-1} \sqrt{x}}+\frac{\sqrt{x^4-x} \sqrt{\sqrt{c}+\sqrt{d}} (a d+b c) \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{c}+\sqrt{d}}}{\sqrt[4]{d} \sqrt{x^3-1}}\right)}{3 c^{3/2} d^{3/4} \sqrt{x^3-1} \sqrt{x}}+\frac{a \sqrt{x^4-x} x}{3 c}-\frac{a \sqrt{x^4-x} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)}{3 c \sqrt{x^3-1} \sqrt{x}}","-\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,"(a*x*Sqrt[-x + x^4])/(3*c) + (Sqrt[Sqrt[c] - Sqrt[d]]*(b*c + a*d)*Sqrt[-x + x^4]*ArcTan[(Sqrt[Sqrt[c] - Sqrt[d]]*x^(3/2))/(d^(1/4)*Sqrt[-1 + x^3])])/(3*c^(3/2)*d^(3/4)*Sqrt[x]*Sqrt[-1 + x^3]) - (a*Sqrt[-x + x^4]*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]])/(3*c*Sqrt[x]*Sqrt[-1 + x^3]) + (Sqrt[Sqrt[c] + Sqrt[d]]*(b*c + a*d)*Sqrt[-x + x^4]*ArcTanh[(Sqrt[Sqrt[c] + Sqrt[d]]*x^(3/2))/(d^(1/4)*Sqrt[-1 + x^3])])/(3*c^(3/2)*d^(3/4)*Sqrt[x]*Sqrt[-1 + x^3])","A",18,11,30,0.3667,1,"{2056, 6715, 1693, 195, 217, 206, 1175, 402, 377, 205, 208}"
2630,0,0,0,4.1505771,"\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","Int[(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,"((2*a - b + Sqrt[b^2 + 4*a^2*d - 4*a*b*d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/(x^(2/3)*(-b + x)^(2/3)*(b - 2*a*d - Sqrt[b^2 + 4*a^2*d - 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(2/3) + ((2*a - b - Sqrt[b^2 + 4*a^2*d - 4*a*b*d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/(x^(2/3)*(-b + x)^(2/3)*(b - 2*a*d + Sqrt[b^2 + 4*a^2*d - 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(2/3)","F",0,0,0,0,-1,"{}"
2631,0,0,0,15.9354447,"\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","Int[(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,"(-3*(b - x)*x*(1 - x/a)^(2/3)*(1 - x/b)^(1/3)*AppellF1[1/3, 2/3, 1/3, 4/3, x/a, x/b])/(-((a - x)*(b - x)^2*x))^(2/3) + (3*b*(4*a + b)*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(2/3)*(-b + x^3)^(1/3)*(a*b^2 - 2*a*b*(1 + b/(2*a))*x^3 + a*(1 + (2*b + d)/a)*x^6 - x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(2/3) - (3*(a + 3*b + d)*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(2/3)*(-b + x^3)^(1/3)*(a*b^2 - 2*a*b*(1 + b/(2*a))*x^3 + a*(1 + (2*b + d)/a)*x^6 - x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(2/3) + (3*a*b^2*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][1/((-a + x^3)^(2/3)*(-b + x^3)^(1/3)*(-(a*b^2) + 2*a*b*(1 + b/(2*a))*x^3 - a*(1 + (2*b + d)/a)*x^6 + x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(2/3)","F",0,0,0,0,-1,"{}"
2632,0,0,0,9.0009863,"\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","Int[(-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,"-((k*(5 + d*k^2)*x*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*AppellF1[1/2, 2/3, 2/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(2/3)) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*k^(4/3)*Sqrt[(-1 - k^2 + 2*k^2*x^2)^2]*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))*Sqrt[((-1 + k^2)^(4/3) - 2^(2/3)*k^(2/3)*(-1 + k^2)^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3) + 2*2^(1/3)*k^(4/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]*EllipticF[ArcSin[((1 - Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))], -7 - 4*Sqrt[3]])/(2^(2/3)*(1 + k^2 - 2*k^2*x^2)*Sqrt[(-1 - k^2*(1 - 2*x^2))^2]*Sqrt[((-1 + k^2)^(2/3)*((-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3)))/((1 + Sqrt[3])*(-1 + k^2)^(2/3) + 2^(2/3)*k^(2/3)*((1 - x^2)*(1 - k^2*x^2))^(1/3))^2]) + (k*(8 - d^2*k^2 - d*(5 - k^2))*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][1/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (1 + 2*d)*k*x - (1 + d*k^2)*x^2 - k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(2/3) - ((2 - (2 + 11*d)*k^2 - d*(1 + 2*d)*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (1 + 2*d)*k*x - (1 + d*k^2)*x^2 - k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(2/3) - (k*(6 + (2 + 8*d)*k^2 + d^2*k^4)*(1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*Defer[Int][x^2/((1 - x^2)^(2/3)*(1 - k^2*x^2)^(2/3)*(1 - d + (1 + 2*d)*k*x - (1 + d*k^2)*x^2 - k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(2/3)","F",0,0,0,0,-1,"{}"
2633,0,0,0,1.8906459,"\int \frac{1-((-1+3 x) (3+4 x))^{3/2}}{1+((-1+3 x) (3+4 x))^{3/2}} \, dx","Int[(1 - ((-1 + 3*x)*(3 + 4*x))^(3/2))/(1 + ((-1 + 3*x)*(3 + 4*x))^(3/2)),x]","\int \frac{1-((-1+3 x) (3+4 x))^{3/2}}{1+((-1+3 x) (3+4 x))^{3/2}} \, dx","-\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,"-x + (2*Sqrt[(217 + 2*Sqrt[22753])/22753]*ArcTan[(10 - Sqrt[2*(145 + Sqrt[22753])] + 48*x)/Sqrt[2*(-145 + Sqrt[22753])]])/3 + (2*Sqrt[(217 + 2*Sqrt[22753])/22753]*ArcTan[(10 + Sqrt[2*(145 + Sqrt[22753])] + 48*x)/Sqrt[2*(-145 + Sqrt[22753])]])/3 + (4*ArcTanh[(5 + 24*x)/Sqrt[217]])/(3*Sqrt[217]) + ArcTanh[(5 + 24*x)/(4*Sqrt[3]*Sqrt[-3 + 5*x + 12*x^2])]/(3*Sqrt[3]) - (4*ArcTanh[(5 + 24*x)/(Sqrt[217]*Sqrt[-3 + 5*x + 12*x^2])])/(3*Sqrt[217]) + (Sqrt[(-217 + 2*Sqrt[22753])/22753]*Log[Sqrt[22753] - Sqrt[2*(145 + Sqrt[22753])]*(5 + 24*x) + (5 + 24*x)^2])/3 - (Sqrt[(-217 + 2*Sqrt[22753])/22753]*Log[Sqrt[22753] + Sqrt[2*(145 + Sqrt[22753])]*(5 + 24*x) + (5 + 24*x)^2])/3 + (8*Defer[Int][Sqrt[-3 + 5*x + 12*x^2]/(7 - 25*x - 35*x^2 + 120*x^3 + 144*x^4), x])/3 - (10*Defer[Int][(x*Sqrt[-3 + 5*x + 12*x^2])/(7 - 25*x - 35*x^2 + 120*x^3 + 144*x^4), x])/3 - 8*Defer[Int][(x^2*Sqrt[-3 + 5*x + 12*x^2])/(7 - 25*x - 35*x^2 + 120*x^3 + 144*x^4), x]","F",0,0,0,0,-1,"{}"
2634,0,0,0,4.564376,"\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","Int[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,"(2*Sqrt[x]*Sqrt[-b + a^2*x]*Defer[Subst][Defer[Int][1/(x^2*(-b + a^2*x^2)^(3/2)*(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2)), x], x, Sqrt[x]])/Sqrt[-(b*x) + a^2*x^2]","F",0,0,0,0,-1,"{}"
2635,0,0,0,22.3160815,"\int \frac{1}{x \sqrt[3]{(-1+x) \left(q-2 q x+x^2\right)}} \, dx","Int[1/(x*((-1 + x)*(q - 2*q*x + x^2))^(1/3)),x]","\int \frac{1}{x \sqrt[3]{(-1+x) \left(q-2 q x+x^2\right)}} \, dx","\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,"((-1 - 2*q - (1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[-((-1 + q)^3*q)])^(2/3))/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[-((-1 + q)^3*q)])^(1/3) + 3*x)^(1/3)*(-1 + 5*q - 4*q^2 + ((1 - 4*q)^2*(1 - q)^2)/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (3*(1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))*((-1 - 2*q)/3 + x))/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3) + 9*((-1 - 2*q)/3 + x)^2)^(1/3)*Defer[Subst][Defer[Int][1/(((1 + 2*q)/3 + x)*(-1/3*(1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3) + x)^(1/3)*((-1 + 5*q - 4*q^2 + ((1 - 4*q)^2*(1 - q)^2)/(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3) + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))/9 + ((1 - 5*q + 4*q^2 + (1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(2/3))*x)/(3*(1 + 6*q - 15*q^2 + 8*q^3 + 3*Sqrt[3]*Sqrt[(1 - q)^3*q])^(1/3)) + x^2)^(1/3)), x], x, (-1 - 2*q)/3 + x])/(3*(-q + 3*q*x + (-1 - 2*q)*x^2 + x^3)^(1/3))","F",0,0,0,0,-1,"{}"
2636,0,0,0,3.6889505,"\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","Int[(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,"-(((2*a - b + Sqrt[b^2 + 4*a^2*d - 4*a*b*d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(b - 2*a*d - Sqrt[b^2 + 4*a^2*d - 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3)) - ((2*a - b - Sqrt[b^2 + 4*a^2*d - 4*a*b*d])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*(b - 2*a*d + Sqrt[b^2 + 4*a^2*d - 4*a*b*d] + 2*(-1 + d)*x)), x])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2637,1,393,0,1.2831664,"\int \frac{1+x^4}{\left(-1-x^2+x^4\right) \sqrt[4]{-x^2+x^4}} \, dx","Int[(1 + x^4)/((-1 - x^2 + x^4)*(-x^2 + x^4)^(1/4)),x]","\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}+\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}","\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)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (((3 + Sqrt[5])/2)^(1/4)*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (((3 - Sqrt[5])/2)^(1/4)*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) + (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (((3 + Sqrt[5])/2)^(1/4)*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (((3 - Sqrt[5])/2)^(1/4)*Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4)","A",18,8,31,0.2581,1,"{2056, 6715, 6728, 240, 212, 206, 203, 377}"
2638,0,0,0,2.0978888,"\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","Int[(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]","\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","\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,"Defer[Int][(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]","F",0,0,0,0,-1,"{}"
2639,1,316,0,0.8025867,"\int \frac{\sqrt[3]{-x+x^3} \left(-2+x^4\right)}{x^4 \left(1+x^2\right)} \, dx","Int[((-x + x^3)^(1/3)*(-2 + x^4))/(x^4*(1 + x^2)),x]","\frac{3 \sqrt[3]{x^3-x} \left(\left(1-3 x^2\right) x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{2 x^2}{1-x^2}\right)-3 \left(x^4+x^2\right) \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};-\frac{2 x^2}{1-x^2}\right)+3 x^4-4 x^2+1\right)}{8 x^3 \left(1-x^2\right)}-\frac{3 \sqrt[3]{x^3-x}}{2 x}+\frac{3 \sqrt[3]{x^3-x} \left(1-x^2\right)}{8 x^3}-\frac{\sqrt[3]{x^3-x} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{2 \sqrt[3]{x} \sqrt[3]{x^2-1}}+\frac{\sqrt[3]{x^3-x} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{4 \sqrt[3]{x} \sqrt[3]{x^2-1}}-\frac{\sqrt{3} \sqrt[3]{x^3-x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{x} \sqrt[3]{x^2-1}}","-\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 + x^3)^(1/3))/(2*x) + (3*(1 - x^2)*(-x + x^3)^(1/3))/(8*x^3) - (Sqrt[3]*(-x + x^3)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*x^(1/3)*(-1 + x^2)^(1/3)) + (3*(-x + x^3)^(1/3)*(1 - 4*x^2 + 3*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)) - ((-x + x^3)^(1/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(2*x^(1/3)*(-1 + x^2)^(1/3)) + ((-x + x^3)^(1/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(4*x^(1/3)*(-1 + x^2)^(1/3))","C",18,17,27,0.6296,0,"{2056, 6725, 264, 277, 329, 275, 331, 292, 31, 634, 618, 204, 628, 466, 465, 511, 510}"
2640,0,0,0,3.8037133,"\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","Int[(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]","\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","-\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*b*p*Defer[Subst][Defer[Int][x/((q + p*x^2)^(1/3)*(-(b^3*d) - c*q - 3*a*b^2*d*x - (3*a^2*b*d + c*p)*x^2 - a^3*d*x^3)), x], x, x^2] + 3*a*q*Defer[Subst][Defer[Int][1/((q + p*x^2)^(1/3)*(b^3*d + c*q + 3*a*b^2*d*x + (3*a^2*b*d + c*p)*x^2 + a^3*d*x^3)), x], x, x^2] + a*p*Defer[Subst][Defer[Int][x^2/((q + p*x^2)^(1/3)*(b^3*d + c*q + 3*a*b^2*d*x + (3*a^2*b*d + c*p)*x^2 + a^3*d*x^3)), x], x, x^2]","F",0,0,0,0,-1,"{}"
2641,0,0,0,10.0282182,"\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","Int[((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,"(12*b*x^(3/4)*(-a + x)^(3/2)*(-b + x)^(9/4)*Defer[Subst][Defer[Int][x^4/(Sqrt[-a + x^4]*(-b + x^4)^(1/4)*(-(b*d) - a^2*(1 - d/a^2)*x^4 + 2*a*x^8 - x^12)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(3/4) + (4*a*b*x^(3/4)*(-a + x)^(3/2)*(-b + x)^(9/4)*Defer[Subst][Defer[Int][1/(Sqrt[-a + x^4]*(-b + x^4)^(1/4)*(b*d + a^2*(1 - d/a^2)*x^4 - 2*a*x^8 + x^12)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(3/4) + (8*x^(3/4)*(-a + x)^(3/2)*(-b + x)^(9/4)*Defer[Subst][Defer[Int][x^8/(Sqrt[-a + x^4]*(-b + x^4)^(1/4)*(b*d + a^2*(1 - d/a^2)*x^4 - 2*a*x^8 + x^12)), x], x, x^(1/4)])/(-((a - x)^2*(b - x)^3*x))^(3/4)","F",0,0,0,0,-1,"{}"
2642,0,0,0,38.4375994,"\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","Int[((-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,"(-3*(a*(1 + 2*b + k^2) + 2*b*k*(1 + 3*k + k^2) - k^2*(1 + 4*k + k^2))*(1 - x)*(1 - k*x))/(2*(b - k)^2*((1 - x)*x*(1 - k*x))^(2/3)) - (6*(1 + k)^2*(9*b*k^2 - 3*k^3 - a*(1 + 3*b - k + k^2) - b^2*(1 + 8*k + k^2))*(1 - x)*(1 - k*x))/(5*(b - k)^3*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(14 + 13*k + 14*k^2)*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(1 - k*x))/(40*(b - k)^4*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(1 - k*x))/(8*(b - k)^4*x^2*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(1 + k)*(9*b*k^2 - 3*k^3 - a*(1 + 3*b - k + k^2) - b^2*(1 + 8*k + k^2))*(1 - x)*(1 - k*x))/(5*(b - k)^3*x*((1 - x)*x*(1 - k*x))^(2/3)) - (21*(1 + k)*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(1 - k*x))/(40*(b - k)^4*x*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(a + k^2)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/((1 - k)*(b - k)*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(1 + k)*(2 + k + 2*k^2)*(9*b*k^2 - 3*k^3 - a*(1 + 3*b - k + k^2) - b^2*(1 + 8*k + k^2))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/(5*(1 - k)*(b - k)^3*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(1 + k)*(7 - 4*k + 7*k^2)*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/(20*(1 - k)*(b - k)^4*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(1 + k)*(a*(1 + 2*b + k^2) + k*(2*b*(1 + 3*k + k^2) - k*(1 + 4*k + k^2)))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, (1 - x)/(1 - k*x)])/(2*(1 - k)*(b - k)^2*((1 - x)*x*(1 - k*x))^(2/3)) + ((a + b^2)*(1 + 5*b^2 + 5*b^2*k + k^5 + 5*b*(1 + k^2) + 5*b*k*(1 + k^2) + (1 + 4*b^3 - k - k^5 + k^6 + b^2*(13 + 14*k + 13*k^2) + b*(7 + 2*k + 2*k^2 + 2*k^3 + 7*k^4))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][1/((1 - x)^(2/3)*x^(11/3)*(1 - k*x)^(2/3)*(-1 - k - Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^4*((1 - x)*x*(1 - k*x))^(2/3)) + ((a + b^2)*(1 + k^5 + 5*b^2*(1 + k) + 5*b*(1 + k + k^2 + k^3) - (1 + 4*b^3 - k - k^5 + k^6 + b^2*(13 + 14*k + 13*k^2) + b*(7 + 2*k + 2*k^2 + 2*k^3 + 7*k^4))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][1/((1 - x)^(2/3)*x^(11/3)*(1 - k*x)^(2/3)*(-1 - k + Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^4*((1 - x)*x*(1 - k*x))^(2/3))","F",0,0,0,0,-1,"{}"
2643,1,2197,0,2.6630642,"\int \frac{\left(1+x^3\right) \sqrt[3]{-x^2+x^3}}{1+x^6} \, dx","Int[((1 + x^3)*(-x^2 + x^3)^(1/3))/(1 + x^6),x]","\frac{\left((6-3 i)+(2+i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{18 \sqrt[3]{x-1} x^{2/3}}+\frac{\left((-6+3 i)+(2+i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{18 \sqrt[3]{x-1} x^{2/3}}+\frac{\left((-6-3 i)+(2-i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{18 \sqrt[3]{x-1} x^{2/3}}-\frac{i \left((-3+6 i)+(1+2 i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{18 \sqrt[3]{x-1} x^{2/3}}-\frac{4 \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-i} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{(1-i)^{2/3} \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1+i} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{(1+i)^{2/3} \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\left(3-\sqrt{3}\right) \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-\sqrt[6]{-1}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{6 \left(1-\sqrt[6]{-1}\right)^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt[6]{-1} \sqrt[3]{1+\sqrt[6]{-1}} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1+\sqrt[6]{-1}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt[3]{-1+(-1)^{5/6}} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-(-1)^{5/6}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (-1)^{5/6} \sqrt[3]{1+(-1)^{5/6}} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{1+(-1)^{5/6}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1-i} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{2 (1-i)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1+i} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{2 (1+i)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \sqrt[6]{-1} \sqrt[3]{1-\sqrt[6]{-1}} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1-\sqrt[6]{-1}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \sqrt[6]{-1} \sqrt[3]{1+\sqrt[6]{-1}} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1+\sqrt[6]{-1}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \sqrt[3]{-1+(-1)^{5/6}} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1-(-1)^{5/6}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (-1)^{5/6} \sqrt[3]{1+(-1)^{5/6}} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{1+(-1)^{5/6}} \sqrt[3]{x}-\sqrt[3]{x-1}\right)}{\sqrt[3]{x-1} x^{2/3}}+\frac{\left((2-i)+(2+i) \sqrt{3}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{12 \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{12}-\frac{i}{12}\right) (-1)^{5/6} \left(3+(-1)^{5/6}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{\sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{12}-\frac{i}{12}\right) \sqrt[6]{-1} \left(3+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{12}+\frac{i}{12}\right) \sqrt[6]{-1} \left(3-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{2 \sqrt[3]{x^3-x^2} \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}-1\right)}{3 \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{12}-\frac{i}{12}\right) (-1)^{5/6} \sqrt[3]{1+(-1)^{5/6}} \sqrt[3]{x^3-x^2} \log \left(\sqrt[6]{-1}-x\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{12}+\frac{i}{12}\right) \sqrt[6]{-1} \sqrt[3]{1-\sqrt[6]{-1}} \sqrt[3]{x^3-x^2} \log \left(-x-(-1)^{5/6}\right)}{\sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{36}-\frac{i}{36}\right) (-1)^{5/6} \left(3+(-1)^{5/6}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{36}+\frac{i}{36}\right) \sqrt[3]{-1} \left(3 i+\sqrt[3]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{\sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{36}-\frac{i}{36}\right) \sqrt[6]{-1} \left(3+\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\left(\frac{1}{36}+\frac{i}{36}\right) \sqrt[6]{-1} \left(3-\sqrt[6]{-1}\right) \sqrt[3]{x^3-x^2} \log (x-1)}{\sqrt[3]{x-1} x^{2/3}}-\frac{2 \sqrt[3]{x^3-x^2} \log (x-1)}{9 \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{12}-\frac{i}{12}\right) \sqrt[6]{-1} \sqrt[3]{1+\sqrt[6]{-1}} \sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{-1} x+\sqrt[6]{-1}\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{x^3-x^2} \log \left(\sqrt[3]{-1} x-(-1)^{5/6}\right)}{6 (1+i)^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{x^3-x^2} \log \left(\sqrt[6]{-1}-(-1)^{2/3} x\right)}{6 (1-i)^{2/3} \sqrt[3]{x-1} x^{2/3}}+\frac{\left(\frac{1}{12}-\frac{i}{12}\right) \sqrt[3]{-1+(-1)^{5/6}} \sqrt[3]{x^3-x^2} \log \left(-(-1)^{2/3} x-(-1)^{5/6}\right)}{\sqrt[3]{x-1} x^{2/3}}-\frac{1}{3} (-1)^{2/3} \sqrt[3]{x^3-x^2}+\frac{1}{3} \sqrt[3]{-1} \sqrt[3]{x^3-x^2}-\frac{1}{3} \sqrt[3]{x^3-x^2}","\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,"-1/3*(-x^2 + x^3)^(1/3) + ((-1)^(1/3)*(-x^2 + x^3)^(1/3))/3 - ((-1)^(2/3)*(-x^2 + x^3)^(1/3))/3 - (4*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(3*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) - ((I/18)*((-3 + 6*I) + (1 + 2*I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((-1 + x)^(1/3)*x^(2/3)) + (((-6 - 3*I) + (2 - I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(18*(-1 + x)^(1/3)*x^(2/3)) + (((-6 + 3*I) + (2 + I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(18*(-1 + x)^(1/3)*x^(2/3)) + (((6 - 3*I) + (2 + I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(18*(-1 + x)^(1/3)*x^(2/3)) + ((-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 - I)^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((1 - I)^(2/3)*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + ((-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + I)^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/((1 + I)^(2/3)*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + ((3 - Sqrt[3])*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 - (-1)^(1/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(6*(1 - (-1)^(1/6))^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - ((1/2 - I/2)*(-1)^(1/6)*(1 + (-1)^(1/6))^(1/3)*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + (-1)^(1/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) - ((1/2 - I/2)*(-1 + (-1)^(5/6))^(1/3)*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 - (-1)^(5/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) - ((1/2 - I/2)*(-1)^(5/6)*(1 + (-1)^(5/6))^(1/3)*(-x^2 + x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + (-1)^(5/6))^(1/3)*x^(1/3))/(Sqrt[3]*(-1 + x)^(1/3))])/(Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + ((-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 - I)^(1/3)*x^(1/3)])/(2*(1 - I)^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 + I)^(1/3)*x^(1/3)])/(2*(1 + I)^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((1/4 + I/4)*(-1)^(1/6)*(1 - (-1)^(1/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 - (-1)^(1/6))^(1/3)*x^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - ((1/4 - I/4)*(-1)^(1/6)*(1 + (-1)^(1/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 + (-1)^(1/6))^(1/3)*x^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - ((1/4 - I/4)*(-1 + (-1)^(5/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 - (-1)^(5/6))^(1/3)*x^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - ((1/4 - I/4)*(-1)^(5/6)*(1 + (-1)^(5/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1 + x)^(1/3) + (1 + (-1)^(5/6))^(1/3)*x^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) - (2*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(3*(-1 + x)^(1/3)*x^(2/3)) - ((1/12 + I/12)*(-1)^(1/6)*(3 - (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + ((1/12 - I/12)*(-1)^(1/6)*(3 + (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + ((1/12 - I/12)*(-1)^(5/6)*(3 + (-1)^(5/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + (((2 - I) + (2 + I)*Sqrt[3])*(-x^2 + x^3)^(1/3)*Log[-1 + x^(1/3)/(-1 + x)^(1/3)])/(12*(-1 + x)^(1/3)*x^(2/3)) + ((1/12 - I/12)*(-1)^(5/6)*(1 + (-1)^(5/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[(-1)^(1/6) - x])/((-1 + x)^(1/3)*x^(2/3)) - ((1/12 + I/12)*(-1)^(1/6)*(1 - (-1)^(1/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1)^(5/6) - x])/((-1 + x)^(1/3)*x^(2/3)) - (2*(-x^2 + x^3)^(1/3)*Log[-1 + x])/(9*(-1 + x)^(1/3)*x^(2/3)) - ((1/36 + I/36)*(-1)^(1/6)*(3 - (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) + ((1/36 - I/36)*(-1)^(1/6)*(3 + (-1)^(1/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) - ((1/36 + I/36)*(-1)^(1/3)*(3*I + (-1)^(1/3))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) + ((1/36 - I/36)*(-1)^(5/6)*(3 + (-1)^(5/6))*(-x^2 + x^3)^(1/3)*Log[-1 + x])/((-1 + x)^(1/3)*x^(2/3)) + ((1/12 - I/12)*(-1)^(1/6)*(1 + (-1)^(1/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[(-1)^(1/6) + (-1)^(1/3)*x])/((-1 + x)^(1/3)*x^(2/3)) - ((-x^2 + x^3)^(1/3)*Log[-(-1)^(5/6) + (-1)^(1/3)*x])/(6*(1 + I)^(2/3)*(-1 + x)^(1/3)*x^(2/3)) - ((-x^2 + x^3)^(1/3)*Log[(-1)^(1/6) - (-1)^(2/3)*x])/(6*(1 - I)^(2/3)*(-1 + x)^(1/3)*x^(2/3)) + ((1/12 - I/12)*(-1 + (-1)^(5/6))^(1/3)*(-x^2 + x^3)^(1/3)*Log[-(-1)^(5/6) - (-1)^(2/3)*x])/((-1 + x)^(1/3)*x^(2/3))","C",31,6,26,0.2308,0,"{2056, 6725, 101, 157, 59, 91}"
2644,0,0,0,2.0620468,"\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","Int[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{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c+3 i \text{$\#$1}^2 a d+\text{$\#$1} b c-i a b d}\&\right]}{\sqrt{2}}",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[d] - Sqrt[-c]*x)*Sqrt[b + a^2*x^4]), x]/(2*Sqrt[d]) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[d] + Sqrt[-c]*x)*Sqrt[b + a^2*x^4]), x]/(2*Sqrt[d])","F",0,0,0,0,-1,"{}"
2645,0,0,0,1.499183,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(d+c x^2\right) \sqrt{b+a^2 x^4}} \, dx","Int[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x^2)*Sqrt[b + a^2*x^4]),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(d+c x^2\right) \sqrt{b+a^2 x^4}} \, dx","-\frac{i \sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c+3 i \text{$\#$1}^2 a d+\text{$\#$1} b c-i a b d}\&\right]}{\sqrt{2}}",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[d] - Sqrt[-c]*x)*Sqrt[b + a^2*x^4]), x]/(2*Sqrt[d]) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[d] + Sqrt[-c]*x)*Sqrt[b + a^2*x^4]), x]/(2*Sqrt[d])","F",0,0,0,0,-1,"{}"
2646,0,0,0,1.0317365,"\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","Int[(Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(b + a^2*x^2)^(3/2),x]","\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{-\text{$\#$1}^7+3 \text{$\#$1}^5 c-3 \text{$\#$1}^3 c^2+\text{$\#$1} c^3}\&\right]}{4 a}-\frac{\sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{a^2 x \sqrt{a^2 x^2+b}+a \left(a^2 x^2+b\right)}",1,"Defer[Int][(Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(b + a^2*x^2)^(3/2), x]","F",0,0,0,0,-1,"{}"
2647,0,0,0,0.6581398,"\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","Int[(Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]])/(b + a^2*x^2)^(3/2),x]","\int \frac{\sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2}} \, dx","-\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{-\text{$\#$1}^7+3 \text{$\#$1}^5 c-3 \text{$\#$1}^3 c^2+\text{$\#$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,"Defer[Int][(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",0,0,0,0,-1,"{}"
2648,1,389,0,2.3762714,"\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","Int[(1 + a*k*x + k*x^2)/((-1 + k*x^2)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]),x]","-\frac{\sqrt{1-x^2} \left(2-a \sqrt{k}\right) \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{2 (1-k) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \left(a \sqrt{k}+2\right) \sqrt{1-k^2 x^2} \tan ^{-1}\left(\frac{\sqrt{k} \sqrt{1-x^2}}{\sqrt{1-k^2 x^2}}\right)}{2 (1-k) \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \left(2-a \sqrt{k}\right) \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{2 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}-\frac{\sqrt{1-x^2} \left(a \sqrt{k}+2\right) \sqrt{1-k^2 x^2} \Pi \left(k;\sin ^{-1}(x)|k^2\right)}{2 \sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}+\frac{\sqrt{1-x^2} \sqrt{1-k^2 x^2} F\left(\sin ^{-1}(x)|k^2\right)}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\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,"-1/2*((2 - a*Sqrt[k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/((1 - k)*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) + ((2 + a*Sqrt[k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*ArcTan[(Sqrt[k]*Sqrt[1 - x^2])/Sqrt[1 - k^2*x^2]])/(2*(1 - 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)] - ((2 - a*Sqrt[k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/(2*Sqrt[(1 - x^2)*(1 - k^2*x^2)]) - ((2 + a*Sqrt[k])*Sqrt[1 - x^2]*Sqrt[1 - k^2*x^2]*EllipticPi[k, ArcSin[x], k^2])/(2*Sqrt[(1 - x^2)*(1 - k^2*x^2)])","C",16,8,43,0.1860,1,"{6719, 6725, 419, 2113, 537, 571, 93, 205}"
2649,0,0,0,6.5062612,"\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","Int[(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,"-((k*x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(1/3)) + ((4 - d)*k*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) + (2*(1 - (1 + d)*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) - (k*(4 + d*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d - (1 + 2*d)*k*x - (1 + d*k^2)*x^2 + k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2650,0,0,0,6.1828394,"\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","Int[(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,"(k*x*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*AppellF1[1/2, 1/3, 1/3, 3/2, x^2, k^2*x^2])/((1 - x^2)*(1 - k^2*x^2))^(1/3) - ((4 - d)*k*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][1/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (1 + 2*d)*k*x - (1 + d*k^2)*x^2 - k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) + (2*(1 - (1 + d)*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (1 + 2*d)*k*x - (1 + d*k^2)*x^2 - k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3) + (k*(4 + d*k^2)*(1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*Defer[Int][x^2/((1 - x^2)^(1/3)*(1 - k^2*x^2)^(1/3)*(1 - d + (1 + 2*d)*k*x - (1 + d*k^2)*x^2 - k*x^3)), x])/((1 - x^2)*(1 - k^2*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2651,1,561,0,1.5987694,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{d+c x^2} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(d + c*x^2),x]","\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}+\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{c x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{c x^{3/4} \sqrt[4]{a x-b}}","\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*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(c*x^(3/4)*(-b + a*x)^(1/4)) + ((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4)) + ((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4)) + (2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(c*x^(3/4)*(-b + a*x)^(1/4)) - ((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4)) - ((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4))","B",17,11,26,0.4231,1,"{2056, 906, 63, 331, 298, 203, 206, 6725, 93, 205, 208}"
2652,1,561,0,1.2334267,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{d+c x^2} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(d + c*x^2),x]","\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}+\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{\sqrt[4]{a x^4-b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{-c}}}{\sqrt[8]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[8]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{c x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{c x^{3/4} \sqrt[4]{a x-b}}","\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*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(c*x^(3/4)*(-b + a*x)^(1/4)) + ((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4)) + ((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4)) + (2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(c*x^(3/4)*(-b + a*x)^(1/4)) - ((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[-c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4)) - ((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[-c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(-b + a*x)^(1/4))])/(c*d^(1/8)*x^(3/4)*(-b + a*x)^(1/4))","B",17,11,26,0.4231,1,"{2056, 906, 63, 331, 298, 203, 206, 6725, 93, 205, 208}"
2653,1,236,0,0.728256,"\int \frac{d+c x^4}{x \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x^4)/(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\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}}","\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,"(b^8*c)/(72*a^4*(a*x + Sqrt[b^2 + a^2*x^2])^(9/2)) - (b^6*c)/(20*a^4*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2)) + (2*d)/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] - (b^2*c*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2))/(12*a^4) + (c*(a*x + Sqrt[b^2 + a^2*x^2])^(7/2))/(56*a^4) + (2*d*ArcTan[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/Sqrt[b]])/Sqrt[b] - (2*d*ArcTanh[Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/Sqrt[b]])/Sqrt[b]","A",11,8,34,0.2353,1,"{6742, 2119, 453, 329, 298, 203, 206, 448}"
2654,0,0,0,0.4683926,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(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,"Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[x + Sqrt[1 + x^2]], x]","F",0,0,0,0,-1,"{}"
2655,0,0,0,0.3383043,"\int \sqrt{1+x^2} \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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,"Defer[Int][Sqrt[1 + x^2]*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",0,0,0,0,-1,"{}"
2656,1,233,0,0.2450417,"\int \frac{\sqrt[4]{-x^3+x^4}}{x (-b+a x)} \, dx","Int[(-x^3 + x^4)^(1/4)/(x*(-b + a*x)),x]","\frac{2 \sqrt[4]{x^4-x^3} \sqrt[4]{b-a} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a}}{\sqrt[4]{b} \sqrt[4]{x-1}}\right)}{a \sqrt[4]{b} \sqrt[4]{x-1} x^{3/4}}-\frac{2 \sqrt[4]{x^4-x^3} \sqrt[4]{b-a} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a}}{\sqrt[4]{b} \sqrt[4]{x-1}}\right)}{a \sqrt[4]{b} \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{a \sqrt[4]{x-1} x^{3/4}}+\frac{2 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{a \sqrt[4]{x-1} x^{3/4}}","-\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,"(2*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(a*(-1 + x)^(1/4)*x^(3/4)) + (2*(-a + b)^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((-a + b)^(1/4)*x^(1/4))/(b^(1/4)*(-1 + x)^(1/4))])/(a*b^(1/4)*(-1 + x)^(1/4)*x^(3/4)) + (2*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(a*(-1 + x)^(1/4)*x^(3/4)) - (2*(-a + b)^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((-a + b)^(1/4)*x^(1/4))/(b^(1/4)*(-1 + x)^(1/4))])/(a*b^(1/4)*(-1 + x)^(1/4)*x^(3/4))","A",11,11,26,0.4231,1,"{2042, 105, 63, 240, 212, 206, 203, 93, 298, 205, 208}"
2657,0,0,0,31.6602962,"\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","Int[(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,"(-3*(a + b)*((b*(a - x))/(a*(b - x)))^(2/3)*(b - x)*x*Hypergeometric2F1[1/3, 2/3, 4/3, -(((a - b)*x)/(a*(b - x)))])/(b*(1 - d)*((a - x)*(b - x)*x)^(2/3)) + (3*a^2*b^2*(a + b)*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][1/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((1 - d)*((a - x)*(b - x)*x)^(2/3)) - (6*a*b*(a + b)^2*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((1 - d)*((a - x)*(b - x)*x)^(2/3)) + (3*(a + b)*(a^2 + 4*a*b + b^2)*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((1 - d)*((a - x)*(b - x)*x)^(2/3)) - (6*(a^2 + b^2 + a*b*(1 + d))*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^9/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((1 - d)*((a - x)*(b - x)*x)^(2/3))","F",0,0,0,0,-1,"{}"
2658,1,1380,0,2.2789528,"\int \frac{1+2 x^6}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Int[(1 + 2*x^6)/((x + x^3)^(1/3)*(-1 + x^6)),x]","-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}-i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}+i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(x^{2/3}+1\right)}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{\sqrt[3]{x^3+x}}-\frac{\left(3 i-\sqrt{3}\right) \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3}}{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}} \sqrt[3]{x^3+x}}+\frac{\sqrt{3} \left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} x^{2/3}}{\sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(1-x^{2/3}\right)^2 \left(x^{2/3}+1\right)\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}-i \sqrt{3}+1\right) \left(2 x^{2/3}-i \sqrt{3}+1\right)^2\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}+i \sqrt{3}+1\right) \left(2 x^{2/3}+i \sqrt{3}+1\right)^2\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1-i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1+i \sqrt{3}\right)^{2/3}\right)}{4 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1+i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1-i \sqrt{3}\right)^{2/3}\right)}{4 \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1-i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1+i \sqrt{3}}\right)}{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1+i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1-i \sqrt{3}}\right)}{2 \sqrt[3]{x^3+x}}-\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-\sqrt[3]{x^2+1}\right)}{2 \sqrt[3]{x^3+x}}+\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-2^{2/3} \sqrt[3]{x^2+1}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}-i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}+i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}","\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,"-1/4*(Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(2^(1/3)*(x + x^3)^(1/3)) - (Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*(x + x^3)^(1/3)) - (Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2^(1/3)*(1 + x^(2/3)))/(1 + x^2)^(1/3))/Sqrt[3]])/(4*2^(1/3)*(x + x^3)^(1/3)) + (Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(x + x^3)^(1/3) - ((3*I - Sqrt[3])*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*x^(2/3))/(((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(1 + x^2)^(1/3)))/Sqrt[3]])/(2*2^(2/3)*(1 - I*Sqrt[3])^(1/3)*(x + x^3)^(1/3)) + (Sqrt[3]*(1 + I*Sqrt[3])^(2/3)*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - x^(2/3))^2*(1 + x^(2/3))])/(8*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3] - 2*x^(2/3))*(1 - I*Sqrt[3] + 2*x^(2/3))^2])/(8*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3] - 2*x^(2/3))*(1 + I*Sqrt[3] + 2*x^(2/3))^2])/(8*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(2/3) + ((1 - I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(4*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) + (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(2/3) + ((1 + I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(4*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(1/3) + ((1 - I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) - (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(1/3) + ((1 + I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*(x + x^3)^(1/3)) - (3*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(2*(x + x^3)^(1/3)) + (3*x^(1/3)*(1 + x^2)^(1/3)*Log[1 + x^(2/3) - 2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (3*x^(1/3)*(1 + x^2)^(1/3)*Log[1 - I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (3*x^(1/3)*(1 + x^2)^(1/3)*Log[1 + I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3))","C",28,14,24,0.5833,0,"{2056, 6715, 6725, 239, 2074, 2148, 6728, 377, 200, 31, 634, 617, 204, 628}"
2659,1,1380,0,2.0507045,"\int \frac{1+2 x^6}{\sqrt[3]{x+x^3} \left(-1+x^6\right)} \, dx","Int[(1 + 2*x^6)/((x + x^3)^(1/3)*(-1 + x^6)),x]","-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}-i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2-\frac{\sqrt[3]{2} \left(-2 x^{2/3}+i \sqrt{3}+1\right)}{\sqrt[3]{x^2+1}}}{2 \sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(x^{2/3}+1\right)}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{\sqrt[3]{x^3+x}}-\frac{\left(3 i-\sqrt{3}\right) \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 x^{2/3}}{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}} \sqrt[3]{x^3+x}}+\frac{\sqrt{3} \left(1+i \sqrt{3}\right)^{2/3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} x^{2/3}}{\sqrt[3]{x^2+1}}}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(1-x^{2/3}\right)^2 \left(x^{2/3}+1\right)\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}-i \sqrt{3}+1\right) \left(2 x^{2/3}-i \sqrt{3}+1\right)^2\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\left(-2 x^{2/3}+i \sqrt{3}+1\right) \left(2 x^{2/3}+i \sqrt{3}+1\right)^2\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1-i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1+i \sqrt{3}\right)^{2/3}\right)}{4 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\left(1+i \sqrt{3}\right)^{2/3} x^{4/3}}{\left(x^2+1\right)^{2/3}}-\frac{2^{2/3} x^{2/3}}{\sqrt[3]{x^2+1}}+\left(1-i \sqrt{3}\right)^{2/3}\right)}{4 \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1-i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1+i \sqrt{3}}\right)}{2 \sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x^3+x}}-\frac{\sqrt[3]{\frac{i+\sqrt{3}}{i-\sqrt{3}}} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{\sqrt[3]{1+i \sqrt{3}} x^{2/3}}{\sqrt[3]{x^2+1}}+\sqrt[3]{1-i \sqrt{3}}\right)}{2 \sqrt[3]{x^3+x}}-\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-\sqrt[3]{x^2+1}\right)}{2 \sqrt[3]{x^3+x}}+\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-2^{2/3} \sqrt[3]{x^2+1}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}-i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}+\frac{3 \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(-2 x^{2/3}+2\ 2^{2/3} \sqrt[3]{x^2+1}+i \sqrt{3}+1\right)}{8 \sqrt[3]{2} \sqrt[3]{x^3+x}}","\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,"-1/4*(Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 - I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(2^(1/3)*(x + x^3)^(1/3)) - (Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(2 - (2^(1/3)*(1 + I*Sqrt[3] - 2*x^(2/3)))/(1 + x^2)^(1/3))/(2*Sqrt[3])])/(4*2^(1/3)*(x + x^3)^(1/3)) - (Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2^(1/3)*(1 + x^(2/3)))/(1 + x^2)^(1/3))/Sqrt[3]])/(4*2^(1/3)*(x + x^3)^(1/3)) + (Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(x + x^3)^(1/3) - ((3*I - Sqrt[3])*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*x^(2/3))/(((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(1 + x^2)^(1/3)))/Sqrt[3]])/(2*2^(2/3)*(1 - I*Sqrt[3])^(1/3)*(x + x^3)^(1/3)) + (Sqrt[3]*(1 + I*Sqrt[3])^(2/3)*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 - (2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - x^(2/3))^2*(1 + x^(2/3))])/(8*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3] - 2*x^(2/3))*(1 - I*Sqrt[3] + 2*x^(2/3))^2])/(8*2^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3] - 2*x^(2/3))*(1 + I*Sqrt[3] + 2*x^(2/3))^2])/(8*2^(1/3)*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(2/3) + ((1 - I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(4*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) + (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(2/3) + ((1 + I*Sqrt[3])^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - (2^(2/3)*x^(2/3))/(1 + x^2)^(1/3)])/(4*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[(1 + I*Sqrt[3])^(1/3) + ((1 - I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*(x + x^3)^(1/3)) - (((I + Sqrt[3])/(I - Sqrt[3]))^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[(1 - I*Sqrt[3])^(1/3) + ((1 + I*Sqrt[3])^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*(x + x^3)^(1/3)) - (3*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(2*(x + x^3)^(1/3)) + (3*x^(1/3)*(1 + x^2)^(1/3)*Log[1 + x^(2/3) - 2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (3*x^(1/3)*(1 + x^2)^(1/3)*Log[1 - I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3)) + (3*x^(1/3)*(1 + x^2)^(1/3)*Log[1 + I*Sqrt[3] - 2*x^(2/3) + 2*2^(2/3)*(1 + x^2)^(1/3)])/(8*2^(1/3)*(x + x^3)^(1/3))","C",28,14,24,0.5833,0,"{2056, 6715, 6725, 239, 2074, 2148, 6728, 377, 200, 31, 634, 617, 204, 628}"
2660,1,226,0,0.353406,"\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","Int[((-4*b + a*x^3)*(b + a*x^3)^(1/3))/(x^5*(-2*b + a*x^3)),x]","-\frac{a^{4/3} \log \left(\sqrt[3]{2}-\frac{\sqrt[3]{3} \sqrt[3]{a} x}{\sqrt[3]{a x^3+b}}\right)}{2 \sqrt[3]{2} 3^{2/3} b}-\frac{a^{4/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a} x}{\sqrt[6]{3} \sqrt[3]{a x^3+b}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt[6]{3} b}+\frac{a^{4/3} \log \left(\frac{3^{2/3} a^{2/3} x^2}{\left(a x^3+b\right)^{2/3}}+\frac{\sqrt[3]{6} \sqrt[3]{a} x}{\sqrt[3]{a x^3+b}}+2^{2/3}\right)}{4 \sqrt[3]{2} 3^{2/3} b}-\frac{a \sqrt[3]{a x^3+b}}{b x}-\frac{\sqrt[3]{a x^3+b}}{2 x^4}","-\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,"-1/2*(b + a*x^3)^(1/3)/x^4 - (a*(b + a*x^3)^(1/3))/(b*x) - (a^(4/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*a^(1/3)*x)/(3^(1/6)*(b + a*x^3)^(1/3))])/(2*2^(1/3)*3^(1/6)*b) - (a^(4/3)*Log[2^(1/3) - (3^(1/3)*a^(1/3)*x)/(b + a*x^3)^(1/3)])/(2*2^(1/3)*3^(2/3)*b) + (a^(4/3)*Log[2^(2/3) + (3^(2/3)*a^(2/3)*x^2)/(b + a*x^3)^(2/3) + (6^(1/3)*a^(1/3)*x)/(b + a*x^3)^(1/3)])/(4*2^(1/3)*3^(2/3)*b)","A",10,10,35,0.2857,1,"{580, 583, 12, 494, 292, 31, 634, 617, 204, 628}"
2661,0,0,0,13.7566564,"\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","Int[(-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,"(9*a*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-a + x^3)^(1/3))/((-b + x^3)^(2/3)*(a^2*d - 2*a*d*x^3 + b*(1 + d/b)*x^6 - x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (6*a*b*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(-a + x^3)^(1/3))/((-b + x^3)^(2/3)*(-(a^2*d) + 2*a*d*x^3 - b*(1 + d/b)*x^6 + x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (3*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-a + x^3)^(1/3))/((-b + x^3)^(2/3)*(-(a^2*d) + 2*a*d*x^3 - b*(1 + d/b)*x^6 + x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3)","F",0,0,0,0,-1,"{}"
2662,0,0,0,32.1945539,"\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","Int[((-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,"(-3*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(1 - k*x))/(10*(b - k)^4*x^3*((1 - x)*x*(1 - k*x))^(1/3)) - (3*(1 + k)*(9*b*k^2 - 3*k^3 - a*(1 + 3*b - k + k^2) - b^2*(1 + 8*k + k^2))*(1 - x)*(1 - k*x))/(7*(b - k)^3*x^2*((1 - x)*x*(1 - k*x))^(1/3)) - (12*(1 + k)*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(1 - k*x))/(35*(b - k)^4*x^2*((1 - x)*x*(1 - k*x))^(1/3)) - (3*(a*(1 + 2*b + k^2) + 2*b*k*(1 + 3*k + k^2) - k^2*(1 + 4*k + k^2))*(1 - x)*(1 - k*x))/(4*(b - k)^2*x*((1 - x)*x*(1 - k*x))^(1/3)) - (15*(1 + k)^2*(9*b*k^2 - 3*k^3 - a*(1 + 3*b - k + k^2) - b^2*(1 + 8*k + k^2))*(1 - x)*(1 - k*x))/(28*(b - k)^3*x*((1 - x)*x*(1 - k*x))^(1/3)) - (3*(20 + 19*k + 20*k^2)*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(1 - k*x))/(140*(b - k)^4*x*((1 - x)*x*(1 - k*x))^(1/3)) + (3*(1 + k)*(a + k^2)*(1 - x)*(((1 - k)*x)/(1 - k*x))^(4/3)*(1 - k*x)*Hypergeometric2F1[2/3, 4/3, 5/3, (1 - x)/(1 - k*x)])/(2*(1 - k)*(b - k)*x*((1 - x)*x*(1 - k*x))^(1/3)) - (3*(1 + k)*(5 + 4*k + 5*k^2)*(9*b*k^2 - 3*k^3 - a*(1 + 3*b - k + k^2) - b^2*(1 + 8*k + k^2))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(4/3)*(1 - k*x)*Hypergeometric2F1[2/3, 4/3, 5/3, (1 - x)/(1 - k*x)])/(28*(1 - k)*(b - k)^3*x*((1 - x)*x*(1 - k*x))^(1/3)) - (3*(1 + k)*(4 - k + 4*k^2)*(8*b*k^3 - 2*k^4 + 4*b^3*(1 + 3*k + k^2) + b^2*(1 - 12*k^2 + k^4) + a*(1 + 2*b^2 + k^4 + 4*b*(1 + k + k^2)))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(4/3)*(1 - k*x)*Hypergeometric2F1[2/3, 4/3, 5/3, (1 - x)/(1 - k*x)])/(28*(1 - k)*(b - k)^4*x*((1 - x)*x*(1 - k*x))^(1/3)) - (3*(1 + k)*(a*(1 + 2*b + k^2) + k*(2*b*(1 + 3*k + k^2) - k*(1 + 4*k + k^2)))*(1 - x)*(((1 - k)*x)/(1 - k*x))^(4/3)*(1 - k*x)*Hypergeometric2F1[2/3, 4/3, 5/3, (1 - x)/(1 - k*x)])/(4*(1 - k)*(b - k)^2*x*((1 - x)*x*(1 - k*x))^(1/3)) + ((a + b^2)*(1 + 5*b^2 + 5*b^2*k + k^5 + 5*b*(1 + k^2) + 5*b*k*(1 + k^2) + (1 + 4*b^3 - k - k^5 + k^6 + b^2*(13 + 14*k + 13*k^2) + b*(7 + 2*k + 2*k^2 + 2*k^3 + 7*k^4))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(13/3)*(1 - k*x)^(1/3)*(-1 - k - Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^4*((1 - x)*x*(1 - k*x))^(1/3)) + ((a + b^2)*(1 + k^5 + 5*b^2*(1 + k) + 5*b*(1 + k + k^2 + k^3) - (1 + 4*b^3 - k - k^5 + k^6 + b^2*(13 + 14*k + 13*k^2) + b*(7 + 2*k + 2*k^2 + 2*k^3 + 7*k^4))/Sqrt[4*b + (-1 + k)^2])*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Int][1/((1 - x)^(1/3)*x^(13/3)*(1 - k*x)^(1/3)*(-1 - k + Sqrt[1 + 4*b - 2*k + k^2] + 2*(-b + k)*x)), x])/((b - k)^4*((1 - x)*x*(1 - k*x))^(1/3))","F",0,0,0,0,-1,"{}"
2663,1,253,0,0.6325886,"\int \frac{x^6 \sqrt{x+x^4}}{b+a x^6} \, dx","Int[(x^6*Sqrt[x + x^4])/(b + a*x^6),x]","\frac{\sqrt[4]{b} \sqrt{x^4+x} \sqrt{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{-a}+\sqrt{b}}}{\sqrt[4]{b} \sqrt{x^3+1}}\right)}{3 (-a)^{3/2} \sqrt{x^3+1} \sqrt{x}}-\frac{\sqrt[4]{b} \sqrt{x^4+x} \sqrt{\sqrt{-a} \sqrt{b}+a} \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{x^3+1}}\right)}{3 (-a)^{7/4} \sqrt{x^3+1} \sqrt{x}}+\frac{\sqrt{x^4+x} x}{3 a}+\frac{\sqrt{x^4+x} \sinh ^{-1}\left(x^{3/2}\right)}{3 a \sqrt{x^3+1} \sqrt{x}}","\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])/(3*a) + (Sqrt[x + x^4]*ArcSinh[x^(3/2)])/(3*a*Sqrt[x]*Sqrt[1 + x^3]) + (Sqrt[Sqrt[-a] + Sqrt[b]]*b^(1/4)*Sqrt[x + x^4]*ArcTanh[(Sqrt[Sqrt[-a] + Sqrt[b]]*x^(3/2))/(b^(1/4)*Sqrt[1 + x^3])])/(3*(-a)^(3/2)*Sqrt[x]*Sqrt[1 + x^3]) - (Sqrt[a + Sqrt[-a]*Sqrt[b]]*b^(1/4)*Sqrt[x + x^4]*ArcTanh[(Sqrt[a + Sqrt[-a]*Sqrt[b]]*x^(3/2))/((-a)^(1/4)*b^(1/4)*Sqrt[1 + x^3])])/(3*(-a)^(7/4)*Sqrt[x]*Sqrt[1 + x^3])","A",15,10,22,0.4545,1,"{2056, 1493, 1491, 1292, 195, 215, 1175, 402, 377, 208}"
2664,1,533,0,1.1616518,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+x^8\right)}{-b+a x^4} \, dx","Int[((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + x^8))/(-b + a*x^4),x]","-\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{7 b^2 x \sqrt[4]{a x^4+b x^2}}{192 a^3}+\frac{x \left(2-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{x \left(2-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{1}{2} x \left(1-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2}+\frac{b x^3 \sqrt[4]{a x^4+b x^2}}{48 a^2}+\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{x^5 \sqrt[4]{a x^4+b x^2}}{6 a}","\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,"(-7*b^2*x*(b*x^2 + a*x^4)^(1/4))/(192*a^3) - ((1 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4))/2 + (b*x^3*(b*x^2 + a*x^4)^(1/4))/(48*a^2) + (x^5*(b*x^2 + a*x^4)^(1/4))/(6*a) + ((2 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*(1 + (a*x^2)/b)^(1/4)) + ((2 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*(1 + (a*x^2)/b)^(1/4)) + ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4))","B",24,13,40,0.3250,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 321, 1270, 1529, 511, 510}"
2665,1,533,0,1.0671462,"\int \frac{\sqrt[4]{b x^2+a x^4} \left(-b-a x^4+x^8\right)}{-b+a x^4} \, dx","Int[((b*x^2 + a*x^4)^(1/4)*(-b - a*x^4 + x^8))/(-b + a*x^4),x]","-\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{7 b^3 \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{128 a^{15/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{7 b^2 x \sqrt[4]{a x^4+b x^2}}{192 a^3}+\frac{x \left(2-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{x \left(2-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{1}{2} x \left(1-\frac{b}{a^2}\right) \sqrt[4]{a x^4+b x^2}+\frac{b x^3 \sqrt[4]{a x^4+b x^2}}{48 a^2}+\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{b \left(a^2-b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{11/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{x^5 \sqrt[4]{a x^4+b x^2}}{6 a}","\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,"(-7*b^2*x*(b*x^2 + a*x^4)^(1/4))/(192*a^3) - ((1 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4))/2 + (b*x^3*(b*x^2 + a*x^4)^(1/4))/(48*a^2) + (x^5*(b*x^2 + a*x^4)^(1/4))/(6*a) + ((2 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*(1 + (a*x^2)/b)^(1/4)) + ((2 - b/a^2)*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*(1 + (a*x^2)/b)^(1/4)) + ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - ((a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(11/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (7*b^3*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(128*a^(15/4)*Sqrt[x]*(b + a*x^2)^(1/4))","B",24,13,40,0.3250,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 321, 1270, 1529, 511, 510}"
2666,0,0,0,2.9204845,"\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","Int[((-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,"(-21*(x - x^3 + x^5 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 - x^6 + x^12 + x^21)^(1/3))/(2 + x^6 + 2*x^12 + 2*x^21)^2, x], x, x^(1/3)])/(x^(1/3)*(1 - x^2 + x^4 + x^7)^(1/3)) - (15*(x - x^3 + x^5 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^9*(1 - x^6 + x^12 + x^21)^(1/3))/(2 + x^6 + 2*x^12 + 2*x^21)^2, x], x, x^(1/3)])/(2*x^(1/3)*(1 - x^2 + x^4 + x^7)^(1/3)) - (9*(x - x^3 + x^5 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^15*(1 - x^6 + x^12 + x^21)^(1/3))/(2 + x^6 + 2*x^12 + 2*x^21)^2, x], x, x^(1/3)])/(x^(1/3)*(1 - x^2 + x^4 + x^7)^(1/3)) + (15*(x - x^3 + x^5 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^3*(1 - x^6 + x^12 + x^21)^(1/3))/(2 + x^6 + 2*x^12 + 2*x^21), x], x, x^(1/3)])/(2*x^(1/3)*(1 - x^2 + x^4 + x^7)^(1/3))","F",0,0,0,0,-1,"{}"
2667,0,0,0,3.6683351,"\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","Int[(-b^5 + a^5*x^5)/(Sqrt[b^2*x + a^2*x^3]*(b^5 + a^5*x^5)),x]","\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","-\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,"-1/5*(Sqrt[2]*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (4*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(5*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (16*b^4*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][1/(Sqrt[b^2 + a^2*x^4]*(b^4 - a*b^3*x^2 + a^2*b^2*x^4 - a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3]) + (12*a*b^3*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][x^2/(Sqrt[b^2 + a^2*x^4]*(b^4 - a*b^3*x^2 + a^2*b^2*x^4 - a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3]) - (8*a^2*b^2*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][x^4/(Sqrt[b^2 + a^2*x^4]*(b^4 - a*b^3*x^2 + a^2*b^2*x^4 - a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3]) + (4*a^3*b*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][x^6/(Sqrt[b^2 + a^2*x^4]*(b^4 - a*b^3*x^2 + a^2*b^2*x^4 - a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3])","F",0,0,0,0,-1,"{}"
2668,0,0,0,3.3793634,"\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","Int[(b^5 + a^5*x^5)/(Sqrt[b^2*x + a^2*x^3]*(-b^5 + a^5*x^5)),x]","\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","-\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,"-1/5*(Sqrt[2]*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + (4*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(5*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (16*b^4*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][1/(Sqrt[b^2 + a^2*x^4]*(b^4 + a*b^3*x^2 + a^2*b^2*x^4 + a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3]) - (12*a*b^3*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][x^2/(Sqrt[b^2 + a^2*x^4]*(b^4 + a*b^3*x^2 + a^2*b^2*x^4 + a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3]) - (8*a^2*b^2*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][x^4/(Sqrt[b^2 + a^2*x^4]*(b^4 + a*b^3*x^2 + a^2*b^2*x^4 + a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3]) - (4*a^3*b*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*Defer[Subst][Defer[Int][x^6/(Sqrt[b^2 + a^2*x^4]*(b^4 + a*b^3*x^2 + a^2*b^2*x^4 + a^3*b*x^6 + a^4*x^8)), x], x, Sqrt[x]])/(5*Sqrt[b^2*x + a^2*x^3])","F",0,0,0,0,-1,"{}"
2669,1,346,0,0.8866594,"\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","Int[(-2*b - a*x^4 + 2*x^8)/(x^4*(-b + a*x^4)^(1/4)*(-b + 2*a*x^4)),x]","\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(1-\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}\right)}{2 \sqrt{2} a^{5/4} b}+\frac{\left(5 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a} x}{\sqrt[4]{a x^4-b}}+1\right)}{2 \sqrt{2} a^{5/4} b}-\frac{\left(5 a^2-b\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)}{4 \sqrt{2} a^{5/4} b}+\frac{\left(5 a^2-b\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)}{4 \sqrt{2} a^{5/4} b}+\frac{2 \left(a x^4-b\right)^{3/4}}{3 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,"(2*(-b + a*x^4)^(3/4))/(3*b*x^3) + ArcTan[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2*a^(5/4)) - ((5*a^2 - b)*ArcTan[1 - (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(2*Sqrt[2]*a^(5/4)*b) + ((5*a^2 - b)*ArcTan[1 + (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(2*Sqrt[2]*a^(5/4)*b) + ArcTanh[(a^(1/4)*x)/(-b + a*x^4)^(1/4)]/(2*a^(5/4)) - ((5*a^2 - b)*Log[1 + (Sqrt[a]*x^2)/Sqrt[-b + a*x^4] - (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(4*Sqrt[2]*a^(5/4)*b) + ((5*a^2 - b)*Log[1 + (Sqrt[a]*x^2)/Sqrt[-b + a*x^4] + (Sqrt[2]*a^(1/4)*x)/(-b + a*x^4)^(1/4)])/(4*Sqrt[2]*a^(5/4)*b)","A",17,13,44,0.2955,1,"{6725, 240, 212, 206, 203, 264, 377, 211, 1165, 628, 1162, 617, 204}"
2670,1,853,0,4.4446311,"\int \frac{-1+x^{16}}{\sqrt{-1+x^4} \left(1+x^8+x^{16}\right)} \, dx","Int[(-1 + x^16)/(Sqrt[-1 + x^4]*(1 + x^8 + x^16)),x]","-\frac{1}{32} \sqrt{\frac{1}{6} \left(3+i \sqrt{3}\right)} \left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1-i \sqrt{3}\right) x^2+2}{\sqrt{2 \left(3+i \sqrt{3}\right)} \sqrt{x^4-1}}\right)+\frac{1}{32} \sqrt{\frac{1}{6} \left(3+i \sqrt{3}\right)} \left(i+\sqrt{3}\right) \tan ^{-1}\left(\frac{4-\left(1+i \sqrt{3}\right)^2 x^2}{2 \sqrt{2 \left(3+i \sqrt{3}\right)} \sqrt{x^4-1}}\right)+\frac{\left(i+\sqrt{3}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \sqrt{6} \sqrt{x^4-1}}+\frac{3 \left(1+i \sqrt{3}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \sqrt{x^4-1}}+\frac{3 \left(1-i \sqrt{3}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \sqrt{2} \sqrt{x^4-1}}-\frac{\left(i-\sqrt{3}\right) \sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{8 \sqrt{6} \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{2} \left(-i-\sqrt{3}\right);\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{4}{\left(i-\sqrt{3}\right)^2};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{2} \left(i-\sqrt{3}\right);\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1-i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{2}{1-i \sqrt{3}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{1}{\sqrt{\frac{1}{2} \left(1+i \sqrt{3}\right)}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(\frac{2}{1+i \sqrt{3}};\left.\sin ^{-1}(x)\right|-1\right)}{4 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} \Pi \left(-\frac{4}{\left(i+\sqrt{3}\right)^2};\left.\sin ^{-1}(x)\right|-1\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,"-1/32*(Sqrt[(3 + I*Sqrt[3])/6]*(I + Sqrt[3])*ArcTan[(2 + (1 - I*Sqrt[3])*x^2)/(Sqrt[2*(3 + I*Sqrt[3])]*Sqrt[-1 + x^4])]) + (Sqrt[(3 + I*Sqrt[3])/6]*(I + Sqrt[3])*ArcTan[(4 - (1 + I*Sqrt[3])^2*x^2)/(2*Sqrt[2*(3 + I*Sqrt[3])]*Sqrt[-1 + x^4])])/32 - ((I - Sqrt[3])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*Sqrt[6]*Sqrt[-1 + x^4]) + (3*(1 - I*Sqrt[3])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*Sqrt[2]*Sqrt[-1 + x^4]) + (3*(1 + I*Sqrt[3])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*Sqrt[2]*Sqrt[-1 + x^4]) + ((I + Sqrt[3])*Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(8*Sqrt[6]*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[(-I - Sqrt[3])/2, ArcSin[x], -1])/(4*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-4/(I - Sqrt[3])^2, ArcSin[x], -1])/(4*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[(I - Sqrt[3])/2, ArcSin[x], -1])/(4*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[1/Sqrt[(1 - I*Sqrt[3])/2], ArcSin[x], -1])/(4*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[2/(1 - I*Sqrt[3]), ArcSin[x], -1])/(4*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[1/Sqrt[(1 + I*Sqrt[3])/2], ArcSin[x], -1])/(4*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[2/(1 + I*Sqrt[3]), ArcSin[x], -1])/(4*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticPi[-4/(I + Sqrt[3])^2, ArcSin[x], -1])/(4*Sqrt[-1 + x^4])","C",153,22,25,0.8800,0,"{1586, 6728, 1729, 1209, 1188, 222, 1185, 1215, 1457, 540, 253, 538, 537, 1248, 735, 844, 217, 206, 725, 204, 406, 409}"
2671,0,0,0,15.6900562,"\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","Int[(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,"(3*x*(1 - x/a)^(1/3)*(1 - x/b)^(1/3)*AppellF1[1/3, 1/3, 1/3, 4/3, x/a, x/b])/((a - x)*(b - x)*x^2)^(1/3) - (6*a*(b - d)*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a^2*d - 2*a*d*x^3 + b*(1 + d/b)*x^6 - x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (3*(3*a - b - d)*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^6/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a^2*d - 2*a*d*x^3 + b*(1 + d/b)*x^6 - x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (3*a^2*d*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][1/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(-(a^2*d) + 2*a*d*x^3 - b*(1 + d/b)*x^6 + x^9)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3)","F",0,0,0,0,-1,"{}"
2672,1,519,0,2.1049315,"\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","Int[((d + c*x^2)*(b*x^3 + a*x^4)^(1/4))/(x^2*(-d + c*x^2)),x]","\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}+\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}","\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*(b*x^3 + a*x^4)^(1/4))/x - (2*a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) + (2*(-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4)) + (2*(b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4)) + (2*a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) - (2*(-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4)) - (2*(b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4))","B",21,13,37,0.3514,1,"{2056, 6725, 47, 63, 331, 298, 203, 206, 908, 37, 93, 205, 208}"
2673,1,519,0,1.7632708,"\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","Int[((d + c*x^2)*(b*x^3 + a*x^4)^(1/4))/(x^2*(-d + c*x^2)),x]","\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}-b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}-\frac{2 \sqrt[4]{a x^4+b x^3} \sqrt[4]{a \sqrt{d}+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \sqrt{d}+b \sqrt{c}}}{\sqrt[8]{d} \sqrt[4]{a x+b}}\right)}{\sqrt[8]{d} x^{3/4} \sqrt[4]{a x+b}}+\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{x^{3/4} \sqrt[4]{a x+b}}","\frac{\text{RootSum}\left[\text{$\#$1}^8 (-d)+2 \text{$\#$1}^4 a d-a^2 d+b^2 c\&,\frac{-\text{$\#$1}^4 a d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)+\text{$\#$1}^4 a d \log (x)+a^2 d \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-b^2 c \log \left(\sqrt[4]{a x^4+b x^3}-\text{$\#$1} x\right)-a^2 d \log (x)+b^2 c \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{d}+\frac{4 \sqrt[4]{a x^4+b x^3}}{x}-2 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)+2 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^3}}\right)",1,"(4*(b*x^3 + a*x^4)^(1/4))/x - (2*a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) + (2*(-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4)) + (2*(b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4)) + (2*a^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(x^(3/4)*(b + a*x)^(1/4)) - (2*(-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((-(b*Sqrt[c]) + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4)) - (2*(b*Sqrt[c] + a*Sqrt[d])^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((b*Sqrt[c] + a*Sqrt[d])^(1/4)*x^(1/4))/(d^(1/8)*(b + a*x)^(1/4))])/(d^(1/8)*x^(3/4)*(b + a*x)^(1/4))","B",21,13,37,0.3514,1,"{2056, 6725, 47, 63, 331, 298, 203, 206, 908, 37, 93, 205, 208}"
2674,0,0,0,1.6290619,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(-1 + x^4)/((1 + x^4)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^2 a-2 \text{$\#$1}^2 c+8 \text{$\#$1} \sqrt{a} b+4 a^2-4 a c-2 b^2+c^2\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1} x+\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} \left(-x^2-1\right)\right)+\text{$\#$1}^2 (-\log (x))+2 a \log \left(-\text{$\#$1} x+\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} \left(-x^2-1\right)\right)-c \log \left(-\text{$\#$1} x+\sqrt{a x^4+a+b x^3+b x+c x^2}+\sqrt{a} \left(-x^2-1\right)\right)-2 a \log (x)+c \log (x)}{-\text{$\#$1}^3+2 \text{$\#$1} a+\text{$\#$1} c-2 \sqrt{a} b}\&\right]",1,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] - ((-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) - x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/2 + ((-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) - x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/2 - ((-1)^(1/4)*Defer[Int][1/(((-1)^(1/4) + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/2 + ((-1)^(3/4)*Defer[Int][1/((-(-1)^(3/4) + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/2","F",0,0,0,0,-1,"{}"
2675,0,0,0,0.8237457,"\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","Int[((-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,"Defer[Subst][Defer[Int][(-2 + k^2 + k^2*x)/((-1 + d + (-2*d + k^2)*x + d*x^2)*(1 + (-1 - k^2)*x + k^2*x^2)^(1/3)), x], x, x^2]/2","F",0,0,0,0,-1,"{}"
2676,1,451,0,2.8720886,"\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","Int[((-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]","\frac{3 k^2 \left(1-x^2\right) \left(\sqrt{d}-\sqrt{d-4 k^2 \left(1-k^2\right)}\right) \left(1-k^2 x^2\right) F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 k^4 \left(1-x^2\right)}{-2 \left(1-k^2\right) k^2+d-\sqrt{d} \sqrt{d-4 k^2 \left(1-k^2\right)}}\right)}{2 \sqrt{d} \left(-\sqrt{d} \sqrt{d-4 k^2 \left(1-k^2\right)}+d-2 \left(1-k^2\right) k^2\right) \sqrt[3]{\frac{1-k^2 x^2}{1-k^2}} \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}+\frac{3 k^2 \left(1-x^2\right) \left(\sqrt{d-4 k^2 \left(1-k^2\right)}+\sqrt{d}\right) \left(1-k^2 x^2\right) F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 k^4 \left(1-x^2\right)}{-2 \left(1-k^2\right) k^2+d+\sqrt{d} \sqrt{d-4 k^2 \left(1-k^2\right)}}\right)}{2 \sqrt{d} \left(\sqrt{d} \sqrt{d-4 k^2 \left(1-k^2\right)}+d-2 \left(1-k^2\right) k^2\right) \sqrt[3]{\frac{1-k^2 x^2}{1-k^2}} \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}","\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,"(3*k^2*(Sqrt[d] - Sqrt[d - 4*k^2*(1 - k^2)])*(1 - x^2)*(1 - k^2*x^2)*AppellF1[1/3, -1/3, 1, 4/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*k^4*(1 - x^2))/(d - 2*k^2*(1 - k^2) - Sqrt[d]*Sqrt[d - 4*k^2*(1 - k^2)])])/(2*Sqrt[d]*(d - 2*k^2*(1 - k^2) - Sqrt[d]*Sqrt[d - 4*k^2*(1 - k^2)])*((1 - k^2*x^2)/(1 - k^2))^(1/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3)) + (3*k^2*(Sqrt[d] + Sqrt[d - 4*k^2*(1 - k^2)])*(1 - x^2)*(1 - k^2*x^2)*AppellF1[1/3, -1/3, 1, 4/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*k^4*(1 - x^2))/(d - 2*k^2*(1 - k^2) + Sqrt[d]*Sqrt[d - 4*k^2*(1 - k^2)])])/(2*Sqrt[d]*(d - 2*k^2*(1 - k^2) + Sqrt[d]*Sqrt[d - 4*k^2*(1 - k^2)])*((1 - k^2*x^2)/(1 - k^2))^(1/3)*((1 - x^2)*(1 - k^2*x^2))^(2/3))","C",10,7,73,0.09589,0,"{1594, 6715, 6719, 1586, 6728, 137, 136}"
2677,0,0,0,1.3984285,"\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","Int[((-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,"x*Hypergeometric2F1[1/6, 1/4, 7/6, -x^6] - 3*Defer[Int][1/((1 + x^6)^(1/4)*(1 + 2*x^6 + x^8 + x^12)), x] + 2*Defer[Int][x^4/((1 + x^6)^(1/4)*(1 + 2*x^6 + x^8 + x^12)), x] - 3*Defer[Int][x^6/((1 + x^6)^(1/4)*(1 + 2*x^6 + x^8 + x^12)), x] - Defer[Int][x^8/((1 + x^6)^(1/4)*(1 + 2*x^6 + x^8 + x^12)), x] - Defer[Int][x^10/((1 + x^6)^(1/4)*(1 + 2*x^6 + x^8 + x^12)), x]","F",0,0,0,0,-1,"{}"
2678,0,0,0,18.8071401,"\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","Int[((-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,"(2*a*p*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x])/c - (a*q*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^3, x])/c - ((b*c - a*d)*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^2, x])/c^2 + (d*(b*c - a*d)*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x, x])/(c^3*q) - (d^2*(b*c - a*d)*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/(c*q + d*x + c*p*x^3), x])/(c^3*q) + (3*(b*c - a*d)*p*Defer[Int][(x*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(c*q + d*x + c*p*x^3), x])/c - (d*(b*c - a*d)*p*Defer[Int][(x^2*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6])/(c*q + d*x + c*p*x^3), x])/(c^2*q)","F",0,0,0,0,-1,"{}"
2679,0,0,0,0.5352594,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[(-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,"Defer[Int][1/Sqrt[x^2 + Sqrt[1 + x^4]], x] - I*Defer[Int][1/((I - x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - I*Defer[Int][1/((I + x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",0,0,0,0,-1,"{}"
2680,0,0,0,0.4560792,"\int \frac{\left(-1+x^2\right) \sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","Int[((-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,"Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]], x] - I*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(I - x), x] - I*Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(I + x), x]","F",0,0,0,0,-1,"{}"
2681,0,0,0,0.1537123,"\int \sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]],x]","\int \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(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,"Defer[Int][Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",0,0,0,0,-1,"{}"
2682,1,418,0,0.8406547,"\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","Int[(x*(-a + x))/((x^2*(-a + x))^(2/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","-\frac{x^{4/3} (x-a)^{2/3} \log \left(-2 a \sqrt{d} \left(\sqrt{d}+1\right)-2 (1-d) x\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}-\frac{x^{4/3} (x-a)^{2/3} \log \left(2 (1-d) x-2 a \left(1-\sqrt{d}\right) \sqrt{d}\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(-\sqrt[3]{x-a}-\frac{\sqrt[3]{x}}{\sqrt[6]{d}}\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[6]{d}}-\sqrt[3]{x-a}\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 a d^{2/3} \left(-\left(x^2 (a-x)\right)\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,"(Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*x^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) + (Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[-2*a*(1 + Sqrt[d])*Sqrt[d] - 2*(1 - d)*x])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[-2*a*(1 - Sqrt[d])*Sqrt[d] + 2*(1 - d)*x])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[-(x^(1/3)/d^(1/6)) - (-a + x)^(1/3)])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[x^(1/3)/d^(1/6) - (-a + x)^(1/3)])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3))","A",9,5,40,0.1250,1,"{6719, 911, 105, 59, 91}"
2683,1,418,0,0.6132852,"\int \frac{x}{\sqrt[3]{x^2 (-a+x)} \left(a^2 d-2 a d x+(-1+d) x^2\right)} \, dx","Int[x/((x^2*(-a + x))^(1/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","-\frac{x^{2/3} \sqrt[3]{x-a} \log \left(-2 a \sqrt{d} \left(\sqrt{d}+1\right)-2 (1-d) x\right)}{4 a \sqrt[3]{d} \sqrt[3]{-\left(x^2 (a-x)\right)}}-\frac{x^{2/3} \sqrt[3]{x-a} \log \left(2 (1-d) x-2 a \left(1-\sqrt{d}\right) \sqrt{d}\right)}{4 a \sqrt[3]{d} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{3 x^{2/3} \sqrt[3]{x-a} \log \left(-\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x}\right)}{4 a \sqrt[3]{d} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{3 x^{2/3} \sqrt[3]{x-a} \log \left(\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x}\right)}{4 a \sqrt[3]{d} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{x-a} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x}}\right)}{2 a \sqrt[3]{d} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{x-a} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 a \sqrt[3]{d} \sqrt[3]{-\left(x^2 (a-x)\right)}}","\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,"(Sqrt[3]*x^(2/3)*(-a + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2*a*d^(1/3)*(-((a - x)*x^2))^(1/3)) + (Sqrt[3]*x^(2/3)*(-a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2*a*d^(1/3)*(-((a - x)*x^2))^(1/3)) - (x^(2/3)*(-a + x)^(1/3)*Log[-2*a*(1 + Sqrt[d])*Sqrt[d] - 2*(1 - d)*x])/(4*a*d^(1/3)*(-((a - x)*x^2))^(1/3)) - (x^(2/3)*(-a + x)^(1/3)*Log[-2*a*(1 - Sqrt[d])*Sqrt[d] + 2*(1 - d)*x])/(4*a*d^(1/3)*(-((a - x)*x^2))^(1/3)) + (3*x^(2/3)*(-a + x)^(1/3)*Log[-x^(1/3) - d^(1/6)*(-a + x)^(1/3)])/(4*a*d^(1/3)*(-((a - x)*x^2))^(1/3)) + (3*x^(2/3)*(-a + x)^(1/3)*Log[-x^(1/3) + d^(1/6)*(-a + x)^(1/3)])/(4*a*d^(1/3)*(-((a - x)*x^2))^(1/3))","A",9,5,35,0.1429,1,"{6719, 911, 105, 59, 91}"
2684,1,418,0,0.7832847,"\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","Int[(-(a*x) + x^2)/((x^2*(-a + x))^(2/3)*(a^2*d - 2*a*d*x + (-1 + d)*x^2)),x]","-\frac{x^{4/3} (x-a)^{2/3} \log \left(-2 a \sqrt{d} \left(\sqrt{d}+1\right)-2 (1-d) x\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}-\frac{x^{4/3} (x-a)^{2/3} \log \left(2 (1-d) x-2 a \left(1-\sqrt{d}\right) \sqrt{d}\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(-\sqrt[3]{x-a}-\frac{\sqrt[3]{x}}{\sqrt[6]{d}}\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(\frac{\sqrt[3]{x}}{\sqrt[6]{d}}-\sqrt[3]{x-a}\right)}{4 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 a d^{2/3} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 a d^{2/3} \left(-\left(x^2 (a-x)\right)\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,"(Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*x^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) + (Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*x^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[-2*a*(1 + Sqrt[d])*Sqrt[d] - 2*(1 - d)*x])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[-2*a*(1 - Sqrt[d])*Sqrt[d] + 2*(1 - d)*x])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[-(x^(1/3)/d^(1/6)) - (-a + x)^(1/3)])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[x^(1/3)/d^(1/6) - (-a + x)^(1/3)])/(4*a*d^(2/3)*(-((a - x)*x^2))^(2/3))","A",10,6,42,0.1429,1,"{1593, 6719, 911, 105, 59, 91}"
2685,1,139,0,0.104076,"\int \frac{-1+x}{(1+x) \sqrt[3]{-1+x^3}} \, dx","Int[(-1 + x)/((1 + x)*(-1 + x^3)^(1/3)),x]","-\frac{1}{2} \log \left(\sqrt[3]{x^3-1}-x\right)+\frac{3 \log \left(2^{2/3} \sqrt[3]{x^3-1}-x+1\right)}{2 \sqrt[3]{2}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{x^3-1}}}{\sqrt{3}}\right)}{\sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{2 \sqrt[3]{2}}","\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,"-((Sqrt[3]*ArcTan[(1 - (2^(1/3)*(1 - x))/(-1 + x^3)^(1/3))/Sqrt[3]])/2^(1/3)) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - Log[(1 - x)*(1 + x)^2]/(2*2^(1/3)) - Log[-x + (-1 + x^3)^(1/3)]/2 + (3*Log[1 - x + 2^(2/3)*(-1 + x^3)^(1/3)])/(2*2^(1/3))","A",3,3,18,0.1667,1,"{2152, 239, 2148}"
2686,1,385,0,1.0119768,"\int \frac{\left(1+x^2\right) \sqrt[3]{-x^2+x^3}}{-1+x^2} \, dx","Int[((1 + x^2)*(-x^2 + x^3)^(1/3))/(-1 + x^2),x]","\frac{1}{2} \sqrt[3]{x^3-x^2} x-\frac{1}{6} \sqrt[3]{x^3-x^2}-\frac{17 \sqrt[3]{x^3-x^2} \log \left(1-\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}\right)}{9 \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[3]{2} \sqrt[3]{x^3-x^2} \log \left(1-\frac{\sqrt[3]{2} \sqrt[3]{x}}{\sqrt[3]{x-1}}\right)}{\sqrt[3]{x-1} x^{2/3}}+\frac{17 \sqrt[3]{x^3-x^2} \log \left(\frac{x^{2/3}}{(x-1)^{2/3}}+\frac{\sqrt[3]{x}}{\sqrt[3]{x-1}}+1\right)}{18 \sqrt[3]{x-1} x^{2/3}}-\frac{\sqrt[3]{x^3-x^2} \log \left(\frac{2^{2/3} x^{2/3}}{(x-1)^{2/3}}+\frac{\sqrt[3]{2} \sqrt[3]{x}}{\sqrt[3]{x-1}}+1\right)}{2^{2/3} \sqrt[3]{x-1} x^{2/3}}-\frac{17 \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{x}}{\sqrt[3]{x-1}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{x-1} x^{2/3}}+\frac{\sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x^2} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{x}}{\sqrt[3]{x-1}}+1}{\sqrt{3}}\right)}{\sqrt[3]{x-1} x^{2/3}}","\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,"-1/6*(-x^2 + x^3)^(1/3) + (x*(-x^2 + x^3)^(1/3))/2 - (17*(-x^2 + x^3)^(1/3)*ArcTan[(1 + (2*x^(1/3))/(-1 + x)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*(-1 + x)^(1/3)*x^(2/3)) + (2^(1/3)*Sqrt[3]*(-x^2 + x^3)^(1/3)*ArcTan[(1 + (2*2^(1/3)*x^(1/3))/(-1 + x)^(1/3))/Sqrt[3]])/((-1 + x)^(1/3)*x^(2/3)) - (17*(-x^2 + x^3)^(1/3)*Log[1 - x^(1/3)/(-1 + x)^(1/3)])/(9*(-1 + x)^(1/3)*x^(2/3)) + (2^(1/3)*(-x^2 + x^3)^(1/3)*Log[1 - (2^(1/3)*x^(1/3))/(-1 + x)^(1/3)])/((-1 + x)^(1/3)*x^(2/3)) + (17*(-x^2 + x^3)^(1/3)*Log[1 + x^(1/3)/(-1 + x)^(1/3) + x^(2/3)/(-1 + x)^(2/3)])/(18*(-1 + x)^(1/3)*x^(2/3)) - ((-x^2 + x^3)^(1/3)*Log[1 + (2^(1/3)*x^(1/3))/(-1 + x)^(1/3) + (2^(2/3)*x^(2/3))/(-1 + x)^(2/3)])/(2^(2/3)*(-1 + x)^(1/3)*x^(2/3))","A",36,14,26,0.5385,1,"{2056, 1586, 6733, 6725, 331, 292, 31, 634, 618, 204, 628, 321, 494, 617}"
2687,1,805,0,2.7683384,"\int \frac{b+a x^4}{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + a*x^4)/((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2-\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2+\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2-\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2+\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2+\sqrt{a^2+4 b} a-2 b} \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,"(a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(-(b*x^2) + a*x^4)^(1/4) - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - ((a^2 + (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + (a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(-(b*x^2) + a*x^4)^(1/4) - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - ((a^2 + (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4))","B",18,10,39,0.2564,1,"{2056, 6715, 6728, 240, 212, 206, 203, 377, 208, 205}"
2688,1,805,0,2.1906595,"\int \frac{b+a x^4}{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}} \, dx","Int[(b + a*x^4)/((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4)),x]","\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2-\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2+\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4-b x^2}}+\frac{a^{3/4} \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{\sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2-\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4-b x^2}}-\frac{\left(a^2+\frac{a^3+2 b a+2 b}{\sqrt{a^2+4 b}}\right) \sqrt{x} \sqrt[4]{a x^2-b} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt{x}}{\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^2+\sqrt{a^2+4 b} a-2 b} \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,"(a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(-(b*x^2) + a*x^4)^(1/4) - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - ((a^2 + (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) + (a^(3/4)*Sqrt[x]*(-b + a*x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(-(b*x^2) + a*x^4)^(1/4) - ((a^2 - (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4)) - ((a^2 + (a^3 + 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*Sqrt[x]*(-b + a*x^2)^(1/4)*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)*(-(b*x^2) + a*x^4)^(1/4))","B",18,10,39,0.2564,1,"{2056, 6715, 6728, 240, 212, 206, 203, 377, 208, 205}"
2689,0,0,0,0.8514191,"\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","Int[((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,"Defer[Subst][Defer[Int][(1 - 2*k^2 + k^2*x)/((1 + (-1 - k^2)*x + k^2*x^2)^(1/3)*(1 - d + (d - 2*k^2)*x + k^4*x^2)), x], x, x^2]/2","F",0,0,0,0,-1,"{}"
2690,1,251,0,2.4386807,"\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","Int[((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]","\frac{3 \left(1-x^2\right)^2 \left(\frac{1-k^2 x^2}{1-k^2}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 d \left(1-x^2\right)}{k^2-\sqrt{k^4-4 d k^2+4 d}}\right)}{8 \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}+\frac{3 \left(1-x^2\right)^2 \left(\frac{1-k^2 x^2}{1-k^2}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 d \left(1-x^2\right)}{k^2+\sqrt{k^4-4 d k^2+4 d}}\right)}{8 \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}","-\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,"(3*(1 - x^2)^2*((1 - k^2*x^2)/(1 - k^2))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*d*(1 - x^2))/(k^2 - Sqrt[4*d - 4*d*k^2 + k^4])])/(8*((1 - x^2)*(1 - k^2*x^2))^(2/3)) + (3*(1 - x^2)^2*((1 - k^2*x^2)/(1 - k^2))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*d*(1 - x^2))/(k^2 + Sqrt[4*d - 4*d*k^2 + k^4])])/(8*((1 - x^2)*(1 - k^2*x^2))^(2/3))","C",10,7,66,0.1061,0,"{1594, 6715, 6719, 1586, 6728, 137, 136}"
2691,0,0,0,0.1581781,"\int \frac{1}{x^4 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[1/(x^4*Sqrt[b + Sqrt[b^2 + a*x^2]]),x]","\int \frac{1}{x^4 \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","\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,"Defer[Int][1/(x^4*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",0,0,0,0,-1,"{}"
2692,0,0,0,7.4038857,"\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","Int[(-(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,"(-3*(a - 5*b)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^4/((a - b + x^3)^(1/3)*(a*(1 - b/a)*d + d*x^3 - x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) + (12*a*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^4/((a - b + x^3)^(1/3)*(-(a*(1 - b/a)*d) - d*x^3 + x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) + (12*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^7/((a - b + x^3)^(1/3)*(-(a*(1 - b/a)*d) - d*x^3 + x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3)","F",0,0,0,0,-1,"{}"
2693,1,271,0,0.6369098,"\int \frac{x^6 \sqrt{-x+x^4}}{b+a x^6} \, dx","Int[(x^6*Sqrt[-x + x^4])/(b + a*x^6),x]","-\frac{\sqrt[4]{b} \sqrt{x^4-x} \sqrt{\sqrt{-a}+\sqrt{b}} \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{-a}+\sqrt{b}}}{\sqrt[4]{b} \sqrt{x^3-1}}\right)}{3 (-a)^{3/2} \sqrt{x^3-1} \sqrt{x}}+\frac{\sqrt[4]{b} \sqrt{x^4-x} \sqrt{\sqrt{-a} \sqrt{b}+a} \tanh ^{-1}\left(\frac{x^{3/2} \sqrt{\sqrt{-a} \sqrt{b}+a}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{x^3-1}}\right)}{3 (-a)^{7/4} \sqrt{x^3-1} \sqrt{x}}+\frac{\sqrt{x^4-x} x}{3 a}-\frac{\sqrt{x^4-x} \tanh ^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-1}}\right)}{3 a \sqrt{x^3-1} \sqrt{x}}","-\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])/(3*a) - (Sqrt[-x + x^4]*ArcTanh[x^(3/2)/Sqrt[-1 + x^3]])/(3*a*Sqrt[x]*Sqrt[-1 + x^3]) - (Sqrt[Sqrt[-a] + Sqrt[b]]*b^(1/4)*Sqrt[-x + x^4]*ArcTanh[(Sqrt[Sqrt[-a] + Sqrt[b]]*x^(3/2))/(b^(1/4)*Sqrt[-1 + x^3])])/(3*(-a)^(3/2)*Sqrt[x]*Sqrt[-1 + x^3]) + (Sqrt[a + Sqrt[-a]*Sqrt[b]]*b^(1/4)*Sqrt[-x + x^4]*ArcTanh[(Sqrt[a + Sqrt[-a]*Sqrt[b]]*x^(3/2))/((-a)^(1/4)*b^(1/4)*Sqrt[-1 + x^3])])/(3*(-a)^(7/4)*Sqrt[x]*Sqrt[-1 + x^3])","A",18,11,24,0.4583,1,"{2056, 1493, 1491, 1292, 195, 217, 206, 1175, 402, 377, 208}"
2694,1,519,0,3.0950514,"\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","Int[(b^6 + a^6*x^6)/(Sqrt[-(b^2*x) + a^2*x^3]*(-b^6 + a^6*x^6)),x]","-\frac{x (b-a x)}{3 b \sqrt{a^2 x^3-b^2 x}}-\frac{x (a x+b)}{3 b \sqrt{a^2 x^3-b^2 x}}+\frac{4 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(-\frac{2 a}{a-\sqrt{3} \sqrt{-a^2}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{2 a}{a-\sqrt{3} \sqrt{-a^2}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(-\frac{2 a}{a+\sqrt{3} \sqrt{-a^2}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{2 a}{a+\sqrt{3} \sqrt{-a^2}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \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,"-1/3*(x*(b - a*x))/(b*Sqrt[-(b^2*x) + a^2*x^3]) - (x*(b + a*x))/(3*b*Sqrt[-(b^2*x) + a^2*x^3]) + (4*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(-2*a)/(a - Sqrt[3]*Sqrt[-a^2]), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(2*a)/(a - Sqrt[3]*Sqrt[-a^2]), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(-2*a)/(a + Sqrt[3]*Sqrt[-a^2]), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(2*a)/(a + Sqrt[3]*Sqrt[-a^2]), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3])","C",36,17,45,0.3778,1,"{2056, 6715, 6725, 224, 221, 2073, 1152, 414, 21, 423, 427, 426, 424, 253, 6728, 1219, 1218}"
2695,0,0,0,3.5167961,"\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","Int[(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,"((2*a - b + Sqrt[4*a^2 - 4*a*b + b^2*d]/Sqrt[d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/(x^(2/3)*(-b + x)^(2/3)*(-2*a + b*d - Sqrt[d]*Sqrt[4*a^2 - 4*a*b + b^2*d] + 2*(1 - d)*x)), x])/((a - x)*(b - x)*x)^(2/3) + ((2*a - b - Sqrt[4*a^2 - 4*a*b + b^2*d]/Sqrt[d])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/(x^(2/3)*(-b + x)^(2/3)*(-2*a + b*d + Sqrt[d]*Sqrt[4*a^2 - 4*a*b + b^2*d] + 2*(1 - d)*x)), x])/((a - x)*(b - x)*x)^(2/3)","F",0,0,0,0,-1,"{}"
2696,1,956,0,8.4203595,"\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","Int[(b^6 + a^6*x^6)/(Sqrt[b^2*x + a^2*x^3]*(-b^6 + a^6*x^6)),x]","-\frac{2 \sqrt{x} \sqrt{b^2+a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{-a} \sqrt{b} \sqrt{x}}{\sqrt{b^2+a^2 x^2}}\right)}{3 \sqrt{-a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{2 \sqrt{x} \sqrt{b^2+a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{b^2+a^2 x^2}}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\sqrt{x} \sqrt{b^2+a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{b^2+a^2 x^2}}\right)}{3 \sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\sqrt{x} \sqrt{b^2+a^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{b} \sqrt{x}}{\sqrt{b^2+a^2 x^2}}\right)}{3 \sqrt{2} \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{\left(3+i \sqrt{3}\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{6 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\left(1+i \sqrt{3}\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}+\frac{\left(3-i \sqrt{3}\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{6 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\left(1-i \sqrt{3}\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\left(i-\sqrt{3}\right) \sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \left(3 i-\sqrt{3}\right) \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}-\frac{\sqrt{x} (b+a x) \sqrt{\frac{b^2+a^2 x^2}{(b+a x)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)|\frac{1}{2}\right)}{3 \left(1+\sqrt[3]{-1}\right) \sqrt{a} \sqrt{b} \sqrt{a^2 x^3+b^2 x}}","-\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*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[-a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[-a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (2*Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTan[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (Sqrt[x]*Sqrt[b^2 + a^2*x^2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[x])/Sqrt[b^2 + a^2*x^2]])/(3*Sqrt[2]*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - (Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*(1 + (-1)^(1/3))*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - ((I - Sqrt[3])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*(3*I - Sqrt[3])*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - ((1 - I*Sqrt[3])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + ((3 - I*Sqrt[3])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(6*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) - ((1 + I*Sqrt[3])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(3*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3]) + ((3 + I*Sqrt[3])*Sqrt[x]*(b + a*x)*Sqrt[(b^2 + a^2*x^2)/(b + a*x)^2]*EllipticF[2*ArcTan[(Sqrt[a]*Sqrt[x])/Sqrt[b]], 1/2])/(6*Sqrt[a]*Sqrt[b]*Sqrt[b^2*x + a^2*x^3])","C",185,21,44,0.4773,1,"{2056, 1586, 6715, 6725, 1729, 1209, 1198, 220, 1196, 1211, 1699, 208, 1248, 735, 844, 217, 206, 725, 205, 1217, 1707}"
2697,0,0,0,9.5359918,"\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","Int[((2 + 5*x^7)*(-x - x^3 + x^8)^(1/3))/((-1 + x^7)*(-1 + x^2 + x^7)),x]","\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","-\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,"((-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 + x^21)^(1/3)/(-1 + x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - ((1 - I*Sqrt[3])*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 + x^21)^(1/3)/(1 - I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - ((1 + I*Sqrt[3])*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 + x^21)^(1/3)/(1 + I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + ((-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 + x^21)^(1/3)/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + (2*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x*(-1 - x^6 + x^21)^(1/3))/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + (3*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^2*(-1 - x^6 + x^21)^(1/3))/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + (4*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^3*(-1 - x^6 + x^21)^(1/3))/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - (2*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^4*(-1 - x^6 + x^21)^(1/3))/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - ((-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^5*(-1 - x^6 + x^21)^(1/3))/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + (2*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 + x^21)^(1/3)/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - (3*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + (5*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^3*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + ((-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^4*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - (7*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^5*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + (8*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^6*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - (10*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^8*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + (11*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^9*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) + ((-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^11*(-1 - x^6 + x^21)^(1/3))/(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - (6*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^3*(-1 - x^6 + x^21)^(1/3))/(-1 + x^6 + x^21), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3)) - (21*(-x - x^3 + x^8)^(1/3)*Defer[Subst][Defer[Int][(x^18*(-1 - x^6 + x^21)^(1/3))/(-1 + x^6 + x^21), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 + x^7)^(1/3))","F",0,0,0,0,-1,"{}"
2698,0,0,0,1.4167692,"\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","Int[(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,"(x^2*(1 - x^3)^(3/4)*Hypergeometric2F1[2/3, 3/4, 5/3, x^3])/(2*(-1 + x^3)^(3/4)) - Defer[Int][x/((-1 + x^3)^(3/4)*(1 - 2*x^3 + x^6 + x^8)), x] + 2*Defer[Int][x^4/((-1 + x^3)^(3/4)*(1 - 2*x^3 + x^6 + x^8)), x] - 4*Defer[Int][x^6/((-1 + x^3)^(3/4)*(1 - 2*x^3 + x^6 + x^8)), x] - Defer[Int][x^7/((-1 + x^3)^(3/4)*(1 - 2*x^3 + x^6 + x^8)), x]","F",0,0,0,0,-1,"{}"
2699,0,0,0,1.1372051,"\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","Int[(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,"(x^2*(1 - x^5)^(3/4)*Hypergeometric2F1[2/5, 3/4, 7/5, x^5])/(2*(-1 + x^5)^(3/4)) - Defer[Int][x/((-1 + x^5)^(3/4)*(1 - 2*x^5 + x^8 + x^10)), x] + 6*Defer[Int][x^6/((-1 + x^5)^(3/4)*(1 - 2*x^5 + x^8 + x^10)), x] - Defer[Int][x^9/((-1 + x^5)^(3/4)*(1 - 2*x^5 + x^8 + x^10)), x]","F",0,0,0,0,-1,"{}"
2700,1,2139,0,23.5447743,"\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","Int[(Sqrt[b + a*x]*(-g + f*x^2))/((e + d*x^2)*Sqrt[c + Sqrt[b + a*x]]),x]","\frac{4 f \left(c+\sqrt{b+a x}\right)^{5/2}}{5 a d}-\frac{8 c f \left(c+\sqrt{b+a x}\right)^{3/2}}{3 a d}+\frac{4 c^2 f \sqrt{c+\sqrt{b+a x}}}{a d}+\frac{\left(b \sqrt{-d}-a \sqrt{e}\right) (e f+d g) \tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-d} c+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}}-\sqrt{2} \sqrt[8]{-d} \sqrt{c+\sqrt{b+a x}}}{\sqrt{c \sqrt[4]{-d}-\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}}}\right)}{\sqrt{2} (-d)^{13/8} \sqrt{c \sqrt[4]{-d}-\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}} \sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}} \sqrt{e}}-\frac{\left(b \sqrt{-d}-a \sqrt{e}\right) (e f+d g) \tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-d} c+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}}+\sqrt{2} \sqrt[8]{-d} \sqrt{c+\sqrt{b+a x}}}{\sqrt{c \sqrt[4]{-d}-\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}}}\right)}{\sqrt{2} (-d)^{13/8} \sqrt{c \sqrt[4]{-d}-\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}} \sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}} \sqrt{e}}-\frac{\left(\frac{\sqrt{e} a}{\sqrt{-d}}+b\right) (e f+d g) \tanh ^{-1}\left(\frac{\sqrt{(-d)^{3/4} c+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}}-\sqrt{2} (-d)^{3/8} \sqrt{c+\sqrt{b+a x}}}{\sqrt{c (-d)^{3/4}-\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}}}\right)}{\sqrt{2} (-d)^{3/8} \sqrt{c (-d)^{3/4}-\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}} \sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)} \sqrt{e}}+\frac{\left(\frac{\sqrt{e} a}{\sqrt{-d}}+b\right) (e f+d g) \tanh ^{-1}\left(\frac{\sqrt{(-d)^{3/4} c+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}}+\sqrt{2} (-d)^{3/8} \sqrt{c+\sqrt{b+a x}}}{\sqrt{c (-d)^{3/4}-\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}}}\right)}{\sqrt{2} (-d)^{3/8} \sqrt{c (-d)^{3/4}-\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}} \sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)} \sqrt{e}}-\frac{\left(b \sqrt{-d}-a \sqrt{e}\right) (e f+d g) \log \left(\sqrt[4]{-d} \left(c+\sqrt{b+a x}\right)-\sqrt{2} \sqrt[8]{-d} \sqrt{\sqrt[4]{-d} c+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}} \sqrt{c+\sqrt{b+a x}}+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}\right)}{2 \sqrt{2} (-d)^{13/8} \sqrt{\sqrt[4]{-d} c+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}} \sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}} \sqrt{e}}+\frac{\left(b \sqrt{-d}-a \sqrt{e}\right) (e f+d g) \log \left(\sqrt[4]{-d} \left(c+\sqrt{b+a x}\right)+\sqrt{2} \sqrt[8]{-d} \sqrt{\sqrt[4]{-d} c+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}} \sqrt{c+\sqrt{b+a x}}+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}\right)}{2 \sqrt{2} (-d)^{13/8} \sqrt{\sqrt[4]{-d} c+\sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}}} \sqrt{\sqrt{-d} c^2-b \sqrt{-d}+a \sqrt{e}} \sqrt{e}}+\frac{\left(\frac{\sqrt{e} a}{\sqrt{-d}}+b\right) (e f+d g) \log \left((-d)^{3/4} \left(c+\sqrt{b+a x}\right)-\sqrt{2} (-d)^{3/8} \sqrt{(-d)^{3/4} c+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}} \sqrt{c+\sqrt{b+a x}}+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}\right)}{2 \sqrt{2} (-d)^{3/8} \sqrt{(-d)^{3/4} c+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}} \sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)} \sqrt{e}}-\frac{\left(\frac{\sqrt{e} a}{\sqrt{-d}}+b\right) (e f+d g) \log \left((-d)^{3/4} \left(c+\sqrt{b+a x}\right)+\sqrt{2} (-d)^{3/8} \sqrt{(-d)^{3/4} c+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}} \sqrt{c+\sqrt{b+a x}}+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}\right)}{2 \sqrt{2} (-d)^{3/8} \sqrt{(-d)^{3/4} c+\sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)}} \sqrt{d \left(-\sqrt{-d} c^2+b \sqrt{-d}+a \sqrt{e}\right)} \sqrt{e}}","-\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,"(4*c^2*f*Sqrt[c + Sqrt[b + a*x]])/(a*d) - (8*c*f*(c + Sqrt[b + a*x])^(3/2))/(3*a*d) + (4*f*(c + Sqrt[b + a*x])^(5/2))/(5*a*d) + ((b*Sqrt[-d] - a*Sqrt[e])*(e*f + d*g)*ArcTanh[(Sqrt[c*(-d)^(1/4) + Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]] - Sqrt[2]*(-d)^(1/8)*Sqrt[c + Sqrt[b + a*x]])/Sqrt[c*(-d)^(1/4) - Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]])/(Sqrt[2]*(-d)^(13/8)*Sqrt[c*(-d)^(1/4) - Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]*Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]*Sqrt[e]) - ((b*Sqrt[-d] - a*Sqrt[e])*(e*f + d*g)*ArcTanh[(Sqrt[c*(-d)^(1/4) + Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]] + Sqrt[2]*(-d)^(1/8)*Sqrt[c + Sqrt[b + a*x]])/Sqrt[c*(-d)^(1/4) - Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]])/(Sqrt[2]*(-d)^(13/8)*Sqrt[c*(-d)^(1/4) - Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]*Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]*Sqrt[e]) - ((b + (a*Sqrt[e])/Sqrt[-d])*(e*f + d*g)*ArcTanh[(Sqrt[c*(-d)^(3/4) + Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]] - Sqrt[2]*(-d)^(3/8)*Sqrt[c + Sqrt[b + a*x]])/Sqrt[c*(-d)^(3/4) - Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]])/(Sqrt[2]*(-d)^(3/8)*Sqrt[c*(-d)^(3/4) - Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]*Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]*Sqrt[e]) + ((b + (a*Sqrt[e])/Sqrt[-d])*(e*f + d*g)*ArcTanh[(Sqrt[c*(-d)^(3/4) + Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]] + Sqrt[2]*(-d)^(3/8)*Sqrt[c + Sqrt[b + a*x]])/Sqrt[c*(-d)^(3/4) - Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]])/(Sqrt[2]*(-d)^(3/8)*Sqrt[c*(-d)^(3/4) - Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]*Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]*Sqrt[e]) - ((b*Sqrt[-d] - a*Sqrt[e])*(e*f + d*g)*Log[Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]] - Sqrt[2]*(-d)^(1/8)*Sqrt[c*(-d)^(1/4) + Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]*Sqrt[c + Sqrt[b + a*x]] + (-d)^(1/4)*(c + Sqrt[b + a*x])])/(2*Sqrt[2]*(-d)^(13/8)*Sqrt[c*(-d)^(1/4) + Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]*Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]*Sqrt[e]) + ((b*Sqrt[-d] - a*Sqrt[e])*(e*f + d*g)*Log[Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]] + Sqrt[2]*(-d)^(1/8)*Sqrt[c*(-d)^(1/4) + Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]*Sqrt[c + Sqrt[b + a*x]] + (-d)^(1/4)*(c + Sqrt[b + a*x])])/(2*Sqrt[2]*(-d)^(13/8)*Sqrt[c*(-d)^(1/4) + Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]]*Sqrt[-(b*Sqrt[-d]) + c^2*Sqrt[-d] + a*Sqrt[e]]*Sqrt[e]) + ((b + (a*Sqrt[e])/Sqrt[-d])*(e*f + d*g)*Log[Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])] - Sqrt[2]*(-d)^(3/8)*Sqrt[c*(-d)^(3/4) + Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]*Sqrt[c + Sqrt[b + a*x]] + (-d)^(3/4)*(c + Sqrt[b + a*x])])/(2*Sqrt[2]*(-d)^(3/8)*Sqrt[c*(-d)^(3/4) + Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]*Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]*Sqrt[e]) - ((b + (a*Sqrt[e])/Sqrt[-d])*(e*f + d*g)*Log[Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])] + Sqrt[2]*(-d)^(3/8)*Sqrt[c*(-d)^(3/4) + Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]*Sqrt[c + Sqrt[b + a*x]] + (-d)^(3/4)*(c + Sqrt[b + a*x])])/(2*Sqrt[2]*(-d)^(3/8)*Sqrt[c*(-d)^(3/4) + Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]]*Sqrt[d*(b*Sqrt[-d] - c^2*Sqrt[-d] + a*Sqrt[e])]*Sqrt[e])","B",31,10,43,0.2326,0,"{6740, 194, 6688, 12, 1988, 1094, 634, 618, 206, 628}"
2701,0,0,0,0.8339909,"\int \frac{\sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}}{1+x^2} \, dx","Int[(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,"(I/2)*Defer[Int][(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(I - x), x] + (I/2)*Defer[Int][(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(I + x), x]","F",0,0,0,0,-1,"{}"
2702,0,0,0,0.9492629,"\int \frac{x}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[x/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{x}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-12 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-5 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{55} \left(15+\sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(\sqrt{5}-15\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(-2*(5 + 7*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/385 - (2*(5 - 7*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/385 + (4*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/385 + (4*Log[Sqrt[1 + x] - 4*(1 + Sqrt[1 + x])^(3/2) + 4*(1 + Sqrt[1 + x])^(5/2) - (1 + Sqrt[1 + x])^(7/2)])/7 - (12*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (36*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (48*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (8*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55","F",0,0,0,0,-1,"{}"
2703,0,0,0,0.7555551,"\int \frac{x}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[x/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{x}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-12 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-5 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{55} \left(15+\sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(\sqrt{5}-15\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(-2*(5 + 7*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/385 - (2*(5 - 7*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/385 + (4*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/385 + (4*Log[Sqrt[1 + x] - 4*(1 + Sqrt[1 + x])^(3/2) + 4*(1 + Sqrt[1 + x])^(5/2) - (1 + Sqrt[1 + x])^(7/2)])/7 - (12*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (36*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (48*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (8*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55","F",0,0,0,0,-1,"{}"
2704,0,0,0,3.7051304,"\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","Int[(Sqrt[b + a*x]*Sqrt[1 + Sqrt[b + a*x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]),x]","\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","\frac{1}{8} a \text{RootSum}\left[-\text{$\#$1}^8+4 \text{$\#$1}^6-4 \text{$\#$1}^4+b\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)-9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{\sqrt{a x+b} \sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}+\frac{\sqrt{\sqrt{a x+b}+1} \sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}-\frac{\sqrt{\sqrt{\sqrt{a x+b}+1}+1}}{x}",1,"(-376*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]])/(105*x) + (112*(1 + Sqrt[1 + Sqrt[b + a*x]])^(3/2))/(15*x) - (8*(1 + Sqrt[1 + Sqrt[b + a*x]])^(5/2))/(3*x) - (376*a*b*Defer[Subst][Defer[Int][(b - 4*x^4 + 4*x^6 - x^8)^(-2), x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/105 + (112*a*b*Defer[Subst][Defer[Int][x^2/(b - 4*x^4 + 4*x^6 - x^8)^2, x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/5 - (8*a*(144 + 175*b)*Defer[Subst][Defer[Int][x^4/(b - 4*x^4 + 4*x^6 - x^8)^2, x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/105 + (192*a*Defer[Subst][Defer[Int][x^6/(-b + 4*x^4 - 4*x^6 + x^8)^2, x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/35","F",0,0,0,0,-1,"{}"
2705,0,0,0,3.1187427,"\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","Int[(Sqrt[b + a*x]*Sqrt[1 + Sqrt[b + a*x]])/(x^2*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]),x]","\int \frac{\sqrt{b+a x} \sqrt{1+\sqrt{b+a x}}}{x^2 \sqrt{1+\sqrt{1+\sqrt{b+a x}}}} \, dx","\frac{1}{8} a \text{RootSum}\left[-\text{$\#$1}^8+4 \text{$\#$1}^6-4 \text{$\#$1}^4+b\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)-9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{a x+b}+1}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$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,"(-376*Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]])/(105*x) + (112*(1 + Sqrt[1 + Sqrt[b + a*x]])^(3/2))/(15*x) - (8*(1 + Sqrt[1 + Sqrt[b + a*x]])^(5/2))/(3*x) - (376*a*b*Defer[Subst][Defer[Int][(b - 4*x^4 + 4*x^6 - x^8)^(-2), x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/105 + (112*a*b*Defer[Subst][Defer[Int][x^2/(b - 4*x^4 + 4*x^6 - x^8)^2, x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/5 - (8*a*(144 + 175*b)*Defer[Subst][Defer[Int][x^4/(b - 4*x^4 + 4*x^6 - x^8)^2, x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/105 + (192*a*Defer[Subst][Defer[Int][x^6/(-b + 4*x^4 - 4*x^6 + x^8)^2, x], x, Sqrt[1 + Sqrt[1 + Sqrt[b + a*x]]]])/35","F",0,0,0,0,-1,"{}"
2706,1,1403,0,4.3618029,"\int \frac{x^4 \sqrt[4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx","Int[(x^4*(b*x^2 + a*x^4)^(1/4))/(b + a*x^2 + x^4),x]","\frac{1}{2} \sqrt[4]{a x^4+b x^2} x+\frac{\left(4 a^2-b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{a \left(a-\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{a \left(a+\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{\left(4 a^2-b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{a \left(a-\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{a \left(a+\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}","\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*(b*x^2 + a*x^4)^(1/4))/2 + ((4*a^2 - b)*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (a*(a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (a*(a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - ((4*a^2 - b)*(b*x^2 + a*x^4)^(1/4)*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*(a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (a*(a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4))","B",30,13,31,0.4194,1,"{2056, 1269, 1516, 459, 331, 298, 203, 206, 6728, 1528, 494, 205, 208}"
2707,1,1403,0,3.8885209,"\int \frac{x^4 \sqrt[4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx","Int[(x^4*(b*x^2 + a*x^4)^(1/4))/(b + a*x^2 + x^4),x]","\frac{1}{2} \sqrt[4]{a x^4+b x^2} x+\frac{\left(4 a^2-b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{a \left(a-\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{a \left(a+\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{\left(4 a^2-b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{a \left(a-\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a-\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2-\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}-\frac{2 \left(a^2-b\right) b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}+\frac{a \left(a+\sqrt{a^2-4 b}\right)^{3/4} \left(a^2-2 b\right) \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2-4 b} a-2 b} \sqrt{x}}{\sqrt[4]{a+\sqrt{a^2-4 b}} \sqrt[4]{a x^2+b}}\right)}{\sqrt{a^2-4 b} \left(a^2+\sqrt{a^2-4 b} a-2 b\right)^{3/4} \sqrt[4]{a x^2+b} \sqrt{x}}","\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*(b*x^2 + a*x^4)^(1/4))/2 + ((4*a^2 - b)*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (a*(a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (a*(a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - ((4*a^2 - b)*(b*x^2 + a*x^4)^(1/4)*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*(a - Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 - a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (a*(a + Sqrt[a^2 - 4*b])^(3/4)*(a^2 - 2*b)*(b*x^2 + a*x^4)^(1/4)*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))])/(Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4)) - (2*(a^2 - b)*b*(b*x^2 + a*x^4)^(1/4)*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])^(1/4)*Sqrt[a^2 - 4*b]*(a^2 + a*Sqrt[a^2 - 4*b] - 2*b)^(3/4)*Sqrt[x]*(b + a*x^2)^(1/4))","B",30,13,31,0.4194,1,"{2056, 1269, 1516, 459, 331, 298, 203, 206, 6728, 1528, 494, 205, 208}"
2708,0,0,0,6.2212492,"\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","Int[((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,"-1/2*(3^(3/4)*Sqrt[2 - Sqrt[3]]*a^2*(q^(1/3) - (q + p*x^4)^(1/3))*Sqrt[(q^(2/3) + q^(1/3)*(q + p*x^4)^(1/3) + (q + p*x^4)^(2/3))/((1 - Sqrt[3])*q^(1/3) - (q + p*x^4)^(1/3))^2]*EllipticF[ArcSin[((1 + Sqrt[3])*q^(1/3) - (q + p*x^4)^(1/3))/((1 - Sqrt[3])*q^(1/3) - (q + p*x^4)^(1/3))], -7 + 4*Sqrt[3]])/(d*p*x^2*Sqrt[-((q^(1/3)*(q^(1/3) - (q + p*x^4)^(1/3)))/((1 - Sqrt[3])*q^(1/3) - (q + p*x^4)^(1/3))^2)]) - (a*(a^4*c - 5*b*d*p)*x*(1 + (p*x^4)/q)^(2/3)*Hypergeometric2F1[1/4, 2/3, 5/4, -((p*x^4)/q)])/(d^2*p*(q + p*x^4)^(2/3)) + (a*(a^4*c*(b^3*c + d*q) - b*d*p*(5*b^3*c + 8*d*q))*Defer[Int][1/((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])/(d^2*p) + (a^2*(3*a^4*b^2*c^2 - 4*d*p*(4*b^3*c + d*q))*Defer[Int][x/((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])/(d^2*p) + (3*a^3*b*c*(a^4*c - 6*b*d*p)*Defer[Int][x^2/((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])/(d^2*p) + ((a^8*c^2 - 8*a^4*b*c*d*p + 4*b^2*d^2*p^2)*Defer[Int][x^3/((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])/(d^2*p)","F",0,0,0,0,-1,"{}"
2709,1,744,0,3.5967722,"\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","Int[(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{c \sqrt{a^2 x^3+b^2}}{3 b^2 x^3}-\frac{a^2 \sqrt{a^2 x^3+b^2}}{6 b^2 x^3}+\frac{2 a^2 \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{3 b}-\frac{\sqrt{a^2 x^3+b^2}}{3 x^6}-\frac{a^2 c \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{3 b^3}+\frac{a^2 \left(\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \log \left(-\sqrt{2} \sqrt{b} \sqrt{\sqrt{a^2+b^2}+b} \sqrt{a^2 x^3+b^2}+b \left(\sqrt{a^2+b^2}+b\right)+a^2 x^3\right)}{6 \sqrt{2} b^{5/2} \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+b}}-\frac{a^2 \left(\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \log \left(\sqrt{2} \sqrt{b} \sqrt{\sqrt{a^2+b^2}+b} \sqrt{a^2 x^3+b^2}+b \left(\sqrt{a^2+b^2}+b\right)+a^2 x^3\right)}{6 \sqrt{2} b^{5/2} \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+b}}-\frac{a^2 \left(-\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\sqrt{a^2+b^2}+b}-\sqrt{2} \sqrt{a^2 x^3+b^2}}{\sqrt{b} \sqrt{b-\sqrt{a^2+b^2}}}\right)}{3 \sqrt{2} b^{5/2} \sqrt{a^2+b^2} \sqrt{b-\sqrt{a^2+b^2}}}+\frac{a^2 \left(-\sqrt{a^2+b^2} \left(b^2-c\right)+a^2 b+b^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a^2 x^3+b^2}+\sqrt{b} \sqrt{\sqrt{a^2+b^2}+b}}{\sqrt{b} \sqrt{b-\sqrt{a^2+b^2}}}\right)}{3 \sqrt{2} b^{5/2} \sqrt{a^2+b^2} \sqrt{b-\sqrt{a^2+b^2}}}+\frac{a^4 \tanh ^{-1}\left(\frac{\sqrt{a^2 x^3+b^2}}{b}\right)}{6 b^3}","\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,"-1/3*Sqrt[b^2 + a^2*x^3]/x^6 - (a^2*Sqrt[b^2 + a^2*x^3])/(6*b^2*x^3) - (c*Sqrt[b^2 + a^2*x^3])/(3*b^2*x^3) + (a^4*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/(6*b^3) + (2*a^2*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/(3*b) - (a^2*c*ArcTanh[Sqrt[b^2 + a^2*x^3]/b])/(3*b^3) - (a^2*(a^2*b + b^3 - Sqrt[a^2 + b^2]*(b^2 - c))*ArcTanh[(Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]] - Sqrt[2]*Sqrt[b^2 + a^2*x^3])/(Sqrt[b]*Sqrt[b - Sqrt[a^2 + b^2]])])/(3*Sqrt[2]*b^(5/2)*Sqrt[a^2 + b^2]*Sqrt[b - Sqrt[a^2 + b^2]]) + (a^2*(a^2*b + b^3 - Sqrt[a^2 + b^2]*(b^2 - c))*ArcTanh[(Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]] + Sqrt[2]*Sqrt[b^2 + a^2*x^3])/(Sqrt[b]*Sqrt[b - Sqrt[a^2 + b^2]])])/(3*Sqrt[2]*b^(5/2)*Sqrt[a^2 + b^2]*Sqrt[b - Sqrt[a^2 + b^2]]) + (a^2*(a^2*b + b^3 + Sqrt[a^2 + b^2]*(b^2 - c))*Log[b*(b + Sqrt[a^2 + b^2]) + a^2*x^3 - Sqrt[2]*Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]]*Sqrt[b^2 + a^2*x^3]])/(6*Sqrt[2]*b^(5/2)*Sqrt[a^2 + b^2]*Sqrt[b + Sqrt[a^2 + b^2]]) - (a^2*(a^2*b + b^3 + Sqrt[a^2 + b^2]*(b^2 - c))*Log[b*(b + Sqrt[a^2 + b^2]) + a^2*x^3 + Sqrt[2]*Sqrt[b]*Sqrt[b + Sqrt[a^2 + b^2]]*Sqrt[b^2 + a^2*x^3]])/(6*Sqrt[2]*b^(5/2)*Sqrt[a^2 + b^2]*Sqrt[b + Sqrt[a^2 + b^2]])","B",27,15,50,0.3000,1,"{6725, 266, 47, 51, 63, 208, 50, 6715, 825, 827, 1169, 634, 618, 206, 628}"
2710,1,905,0,1.8403447,"\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","Int[((-2 + x^4)*Sqrt[2 + x^4])/((2 + x^2 + x^4)*(2 + 2*x^2 + x^4)),x]","\tan ^{-1}\left(\frac{x}{\sqrt{x^4+2}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+2}}\right)-\frac{\left(i-\sqrt{7}\right) \left(1+2 \sqrt{2}+i \sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \left(7 i+\sqrt{7}\right) \sqrt{x^4+2}}-\frac{\left(1+2 \sqrt{2}-i \sqrt{7}\right) \left(i+\sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \left(7 i-\sqrt{7}\right) \sqrt{x^4+2}}-\frac{\left(1-2 \sqrt{2}+i \sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \sqrt{x^4+2}}-\frac{\left(1-2 \sqrt{2}-i \sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \sqrt{x^4+2}}+\frac{i \left((1+i)+\sqrt{2}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{2} \sqrt{x^4+2}}-\frac{\left((-1+i)+\sqrt{2}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{2} \sqrt{x^4+2}}-\frac{\left((-1-i)+\sqrt{2}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{2} \sqrt{x^4+2}}-\frac{\left((1+i)+i \sqrt{2}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{2} \sqrt{x^4+2}}-\frac{\left(1+2 \sqrt{2}\right) \left(3 i-\sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} \Pi \left(\frac{1}{8} \left(4-\sqrt{2}\right);2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \left(7 i+3 \sqrt{7}\right) \sqrt{x^4+2}}-\frac{\left(1+2 \sqrt{2}\right) \left(3 i+\sqrt{7}\right) \left(x^2+\sqrt{2}\right) \sqrt{\frac{x^4+2}{\left(x^2+\sqrt{2}\right)^2}} \Pi \left(\frac{1}{8} \left(4-\sqrt{2}\right);2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{2}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{2} \left(7 i-3 \sqrt{7}\right) \sqrt{x^4+2}}","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,"ArcTan[x/Sqrt[2 + x^4]] - Sqrt[2]*ArcTan[(Sqrt[2]*x)/Sqrt[2 + x^4]] - (((1 + I) + I*Sqrt[2])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(2*2^(1/4)*Sqrt[2 + x^4]) - (((-1 - I) + Sqrt[2])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(2*2^(1/4)*Sqrt[2 + x^4]) - (((-1 + I) + Sqrt[2])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(2*2^(1/4)*Sqrt[2 + x^4]) + ((I/2)*((1 + I) + Sqrt[2])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(2^(1/4)*Sqrt[2 + x^4]) - ((1 - 2*Sqrt[2] - I*Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*Sqrt[2 + x^4]) - ((1 - 2*Sqrt[2] + I*Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*Sqrt[2 + x^4]) - ((1 + 2*Sqrt[2] - I*Sqrt[7])*(I + Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*(7*I - Sqrt[7])*Sqrt[2 + x^4]) - ((I - Sqrt[7])*(1 + 2*Sqrt[2] + I*Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticF[2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*(7*I + Sqrt[7])*Sqrt[2 + x^4]) - ((1 + 2*Sqrt[2])*(3*I + Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticPi[(4 - Sqrt[2])/8, 2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*(7*I - 3*Sqrt[7])*Sqrt[2 + x^4]) - ((1 + 2*Sqrt[2])*(3*I - Sqrt[7])*(Sqrt[2] + x^2)*Sqrt[(2 + x^4)/(Sqrt[2] + x^2)^2]*EllipticPi[(4 - Sqrt[2])/8, 2*ArcTan[x/2^(1/4)], 1/2])/(4*2^(1/4)*(7*I + 3*Sqrt[7])*Sqrt[2 + x^4])","C",34,7,37,0.1892,1,"{6728, 1209, 1198, 220, 1196, 1217, 1707}"
2711,0,0,0,8.718731,"\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","Int[(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,"-1/4*((-1)^(7/8)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((-2)^(1/8) - x), x])/2^(1/8) + ((-1)^(3/8)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(-((-1)^(5/8)*2^(1/8)) - x), x])/(4*2^(1/8)) - ((-1)^(7/8)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((-2)^(1/8) + x), x])/(4*2^(1/8)) + ((-1)^(3/8)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(-((-1)^(5/8)*2^(1/8)) + x), x])/(4*2^(1/8)) + Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-1 + I] - 2^(1/8)*x), x]/(2*Sqrt[-1 + I]*2^(3/4)) + Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[1 - I] - 2^(1/8)*x), x]/(2*Sqrt[1 - I]*2^(3/4)) + Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-1 + I] + 2^(1/8)*x), x]/(2*Sqrt[-1 + I]*2^(3/4)) + Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[1 - I] + 2^(1/8)*x), x]/(2*Sqrt[1 - I]*2^(3/4)) + ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 - I*Sqrt[31]]] - Sqrt[2]*x), x])/Sqrt[-31*Sqrt[1 - I*Sqrt[31]]] - ((I + Sqrt[31])*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 - I*Sqrt[31]]] - Sqrt[2]*x), x])/(2*Sqrt[-31*Sqrt[1 - I*Sqrt[31]]]) + ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 - I*Sqrt[31])^(1/4) - Sqrt[2]*x), x])/(Sqrt[31]*(1 - I*Sqrt[31])^(1/4)) - ((I/2)*(1 - I*Sqrt[31])^(3/4)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 - I*Sqrt[31])^(1/4) - Sqrt[2]*x), x])/Sqrt[31] - ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 + I*Sqrt[31]]] - Sqrt[2]*x), x])/Sqrt[-31*Sqrt[1 + I*Sqrt[31]]] + ((I - Sqrt[31])*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 + I*Sqrt[31]]] - Sqrt[2]*x), x])/(2*Sqrt[-31*Sqrt[1 + I*Sqrt[31]]]) - ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 + I*Sqrt[31])^(1/4) - Sqrt[2]*x), x])/(Sqrt[31]*(1 + I*Sqrt[31])^(1/4)) + ((I/2)*(1 + I*Sqrt[31])^(3/4)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 + I*Sqrt[31])^(1/4) - Sqrt[2]*x), x])/Sqrt[31] + ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 - I*Sqrt[31]]] + Sqrt[2]*x), x])/Sqrt[-31*Sqrt[1 - I*Sqrt[31]]] - ((I + Sqrt[31])*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 - I*Sqrt[31]]] + Sqrt[2]*x), x])/(2*Sqrt[-31*Sqrt[1 - I*Sqrt[31]]]) + ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 - I*Sqrt[31])^(1/4) + Sqrt[2]*x), x])/(Sqrt[31]*(1 - I*Sqrt[31])^(1/4)) - ((I/2)*(1 - I*Sqrt[31])^(3/4)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 - I*Sqrt[31])^(1/4) + Sqrt[2]*x), x])/Sqrt[31] - ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 + I*Sqrt[31]]] + Sqrt[2]*x), x])/Sqrt[-31*Sqrt[1 + I*Sqrt[31]]] + ((I - Sqrt[31])*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/(Sqrt[-Sqrt[1 + I*Sqrt[31]]] + Sqrt[2]*x), x])/(2*Sqrt[-31*Sqrt[1 + I*Sqrt[31]]]) - ((I/2)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 + I*Sqrt[31])^(1/4) + Sqrt[2]*x), x])/(Sqrt[31]*(1 + I*Sqrt[31])^(1/4)) + ((I/2)*(1 + I*Sqrt[31])^(3/4)*Defer[Int][(2 - 2*x^4 + x^8)^(1/4)/((1 + I*Sqrt[31])^(1/4) + Sqrt[2]*x), x])/Sqrt[31]","F",0,0,0,0,-1,"{}"
2712,1,375,0,1.0331106,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","2 \sqrt{x+\sqrt{x+1}}+\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{i+\sqrt{1-i}}}-\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{\sqrt{1+i}-i}}-\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{\sqrt{1-i}-i}}+\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{i+\sqrt{1+i}}}","32 \text{RootSum}\left[\text{$\#$1}^8-8 \text{$\#$1}^7+12 \text{$\#$1}^6-24 \text{$\#$1}^5+470 \text{$\#$1}^4-120 \text{$\#$1}^3+300 \text{$\#$1}^2-1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1}^3 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7-7 \text{$\#$1}^6+9 \text{$\#$1}^5-15 \text{$\#$1}^4+235 \text{$\#$1}^3-45 \text{$\#$1}^2+75 \text{$\#$1}-125}\&\right]+2 \sqrt{x+\sqrt{x+1}}+\log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[x + Sqrt[1 + x]] + (I*ArcTan[(2 + Sqrt[1 - I] - (1 - 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[I + Sqrt[1 - I]] - (I*ArcTan[(2 + Sqrt[1 + I] - (1 - 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[-I + Sqrt[1 + I]] - ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] - (I*ArcTanh[(2 - Sqrt[1 - I] - (1 + 2*Sqrt[1 - I])*Sqrt[1 + x])/(2*Sqrt[-I + Sqrt[1 - I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[-I + Sqrt[1 - I]] + (I*ArcTanh[(2 - Sqrt[1 + I] - (1 + 2*Sqrt[1 + I])*Sqrt[1 + x])/(2*Sqrt[I + Sqrt[1 + I]]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[I + Sqrt[1 + I]]","C",18,7,26,0.2692,1,"{6728, 640, 621, 206, 1033, 724, 204}"
2713,1,375,0,0.8162535,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[x + Sqrt[1 + x]]),x]","2 \sqrt{x+\sqrt{x+1}}+\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1-i}\right) \sqrt{x+1}\right)+\sqrt{1-i}+2}{2 \sqrt{i+\sqrt{1-i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{i+\sqrt{1-i}}}-\frac{i \tan ^{-1}\left(\frac{-\left(\left(1-2 \sqrt{1+i}\right) \sqrt{x+1}\right)+\sqrt{1+i}+2}{2 \sqrt{\sqrt{1+i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{\sqrt{1+i}-i}}-\tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)-\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1-i}\right) \sqrt{x+1}\right)-\sqrt{1-i}+2}{2 \sqrt{\sqrt{1-i}-i} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{\sqrt{1-i}-i}}+\frac{i \tanh ^{-1}\left(\frac{-\left(\left(1+2 \sqrt{1+i}\right) \sqrt{x+1}\right)-\sqrt{1+i}+2}{2 \sqrt{i+\sqrt{1+i}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{i+\sqrt{1+i}}}","32 \text{RootSum}\left[\text{$\#$1}^8-8 \text{$\#$1}^7+12 \text{$\#$1}^6-24 \text{$\#$1}^5+470 \text{$\#$1}^4-120 \text{$\#$1}^3+300 \text{$\#$1}^2-1000 \text{$\#$1}+625\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)-2 \text{$\#$1}^3 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)+5 \text{$\#$1}^2 \log \left(-\text{$\#$1}+2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)}{\text{$\#$1}^7-7 \text{$\#$1}^6+9 \text{$\#$1}^5-15 \text{$\#$1}^4+235 \text{$\#$1}^3-45 \text{$\#$1}^2+75 \text{$\#$1}-125}\&\right]+2 \sqrt{x+\sqrt{x+1}}+\log \left(2 \sqrt{x+1}-2 \sqrt{x+\sqrt{x+1}}+1\right)",1,"2*Sqrt[x + Sqrt[1 + x]] + (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[I + Sqrt[1 - I]] - (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[-I + Sqrt[1 + I]] - 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[-I + Sqrt[1 - I]] + (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[I + Sqrt[1 + I]]","C",18,7,26,0.2692,1,"{6728, 640, 621, 206, 1033, 724, 204}"
2714,0,0,0,0.3323686,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[3]{a x^2+x \sqrt{-b+a^2 x^2}}} \, dx","Int[1/(Sqrt[-b + a^2*x^2]*(a*x^2 + x*Sqrt[-b + a^2*x^2])^(1/3)),x]","\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[3]{a x^2+x \sqrt{-b+a^2 x^2}}} \, dx","-\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,"Defer[Int][1/(Sqrt[-b + a^2*x^2]*(a*x^2 + x*Sqrt[-b + a^2*x^2])^(1/3)), x]","F",0,0,0,0,-1,"{}"
2715,1,442,0,0.7081499,"\int \frac{\sqrt{-b+a x}}{1+\sqrt{a x+\sqrt{-b+a x}}} \, dx","Int[Sqrt[-b + a*x]/(1 + Sqrt[a*x + Sqrt[-b + a*x]]),x]","\frac{\sqrt{\sqrt{a x-b}+a x} \left(2 \sqrt{a x-b}+1\right)}{2 a}-\frac{2 \sqrt{a x-b}}{a}-\frac{2 \sqrt{\sqrt{a x-b}+a x}}{a}+\frac{\log \left(-\sqrt{a x-b}-a x+1\right)}{a}+\frac{2 \tanh ^{-1}\left(\sqrt{\sqrt{a x-b}+a x}\right)}{a}+\frac{2 (3-2 b) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{\sqrt{5-4 b}}\right)}{a \sqrt{5-4 b}}-\frac{(1-4 b) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{4 a}+\frac{2 (1-b) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{a}+\frac{\tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)}{a}-\frac{4 (1-b) \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{\sqrt{5-4 b} \sqrt{\sqrt{a x-b}+a x}}\right)}{a \sqrt{5-4 b}}-\frac{2 \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{\sqrt{5-4 b} \sqrt{\sqrt{a x-b}+a x}}\right)}{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,"(-2*Sqrt[-b + a*x])/a - (2*Sqrt[a*x + Sqrt[-b + a*x]])/a + (Sqrt[a*x + Sqrt[-b + a*x]]*(1 + 2*Sqrt[-b + a*x]))/(2*a) + (2*ArcTanh[Sqrt[a*x + Sqrt[-b + a*x]]])/a + (2*(3 - 2*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/Sqrt[5 - 4*b]])/(a*Sqrt[5 - 4*b]) + ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])]/a - ((1 - 4*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(4*a) + (2*(1 - b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/a - (2*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(Sqrt[5 - 4*b]*Sqrt[a*x + Sqrt[-b + a*x]])])/(a*Sqrt[5 - 4*b]) - (4*(1 - b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(Sqrt[5 - 4*b]*Sqrt[a*x + Sqrt[-b + a*x]])])/(a*Sqrt[5 - 4*b]) + Log[1 - a*x - Sqrt[-b + a*x]]/a","A",25,14,35,0.4000,1,"{6742, 634, 618, 206, 628, 612, 621, 989, 982, 1019, 1076, 1, 1025, 1024}"
2716,1,99,0,0.1084376,"\int x \sqrt{1+\sqrt{2}+\sqrt{2} x+x^2} \, dx","Int[x*Sqrt[1 + Sqrt[2] + Sqrt[2]*x + x^2],x]","\frac{1}{3} \left(x^2+\sqrt{2} x+\sqrt{2}+1\right)^{3/2}-\frac{1}{4} \left(\sqrt{2} x+1\right) \sqrt{x^2+\sqrt{2} x+\sqrt{2}+1}-\frac{1}{8} \left(4+\sqrt{2}\right) \sinh ^{-1}\left(\sqrt{\frac{1}{7} \left(2 \sqrt{2}-1\right)} \left(\sqrt{2} x+1\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,"-1/4*((1 + Sqrt[2]*x)*Sqrt[1 + Sqrt[2] + Sqrt[2]*x + x^2]) + (1 + Sqrt[2] + Sqrt[2]*x + x^2)^(3/2)/3 - ((4 + Sqrt[2])*ArcSinh[Sqrt[(-1 + 2*Sqrt[2])/7]*(1 + Sqrt[2]*x)])/8","A",4,4,23,0.1739,1,"{640, 612, 619, 215}"
2717,1,408,0,0.900432,"\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","Int[(-(a*x) + x^2)/((x^2*(-a + x))^(2/3)*(a^2 - 2*a*x + (1 - d)*x^2)),x]","-\frac{x^{4/3} (x-a)^{2/3} \log \left(2 a \left(1-\sqrt{d}\right)-2 (1-d) x\right)}{4 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}-\frac{x^{4/3} (x-a)^{2/3} \log \left(2 (1-d) x-2 a \left(\sqrt{d}+1\right)\right)}{4 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(-\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{x}\right)}{4 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{3 x^{4/3} (x-a)^{2/3} \log \left(\sqrt[6]{d} \sqrt[3]{x}-\sqrt[3]{x-a}\right)}{4 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-a}}\right)}{2 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\right)^{2/3}}+\frac{\sqrt{3} x^{4/3} (x-a)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 a \sqrt[3]{d} \left(-\left(x^2 (a-x)\right)\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,"(Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*x^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*a*d^(1/3)*(-((a - x)*x^2))^(2/3)) + (Sqrt[3]*x^(4/3)*(-a + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*x^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*a*d^(1/3)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[2*a*(1 - Sqrt[d]) - 2*(1 - d)*x])/(4*a*d^(1/3)*(-((a - x)*x^2))^(2/3)) - (x^(4/3)*(-a + x)^(2/3)*Log[-2*a*(1 + Sqrt[d]) + 2*(1 - d)*x])/(4*a*d^(1/3)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[-(d^(1/6)*x^(1/3)) - (-a + x)^(1/3)])/(4*a*d^(1/3)*(-((a - x)*x^2))^(2/3)) + (3*x^(4/3)*(-a + x)^(2/3)*Log[d^(1/6)*x^(1/3) - (-a + x)^(1/3)])/(4*a*d^(1/3)*(-((a - x)*x^2))^(2/3))","A",10,6,41,0.1463,1,"{1593, 6719, 911, 105, 59, 91}"
2718,1,408,0,0.6185375,"\int \frac{x}{\sqrt[3]{x^2 (-a+x)} \left(-a^2+2 a x+(-1+d) x^2\right)} \, dx","Int[x/((x^2*(-a + x))^(1/3)*(-a^2 + 2*a*x + (-1 + d)*x^2)),x]","\frac{x^{2/3} \sqrt[3]{x-a} \log \left(2 a \left(1-\sqrt{d}\right)-2 (1-d) x\right)}{4 a d^{2/3} \sqrt[3]{-\left(x^2 (a-x)\right)}}+\frac{x^{2/3} \sqrt[3]{x-a} \log \left(2 (1-d) x-2 a \left(\sqrt{d}+1\right)\right)}{4 a d^{2/3} \sqrt[3]{-\left(x^2 (a-x)\right)}}-\frac{3 x^{2/3} \sqrt[3]{x-a} \log \left(-\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x}\right)}{4 a d^{2/3} \sqrt[3]{-\left(x^2 (a-x)\right)}}-\frac{3 x^{2/3} \sqrt[3]{x-a} \log \left(\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x}\right)}{4 a d^{2/3} \sqrt[3]{-\left(x^2 (a-x)\right)}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x-a} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x}}\right)}{2 a d^{2/3} \sqrt[3]{-\left(x^2 (a-x)\right)}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{x-a} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 a d^{2/3} \sqrt[3]{-\left(x^2 (a-x)\right)}}","-\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,"-1/2*(Sqrt[3]*x^(2/3)*(-a + x)^(1/3)*ArcTan[1/Sqrt[3] - (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*x^(1/3))])/(a*d^(2/3)*(-((a - x)*x^2))^(1/3)) - (Sqrt[3]*x^(2/3)*(-a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*x^(1/3))])/(2*a*d^(2/3)*(-((a - x)*x^2))^(1/3)) + (x^(2/3)*(-a + x)^(1/3)*Log[2*a*(1 - Sqrt[d]) - 2*(1 - d)*x])/(4*a*d^(2/3)*(-((a - x)*x^2))^(1/3)) + (x^(2/3)*(-a + x)^(1/3)*Log[-2*a*(1 + Sqrt[d]) + 2*(1 - d)*x])/(4*a*d^(2/3)*(-((a - x)*x^2))^(1/3)) - (3*x^(2/3)*(-a + x)^(1/3)*Log[-x^(1/3) - (-a + x)^(1/3)/d^(1/6)])/(4*a*d^(2/3)*(-((a - x)*x^2))^(1/3)) - (3*x^(2/3)*(-a + x)^(1/3)*Log[-x^(1/3) + (-a + x)^(1/3)/d^(1/6)])/(4*a*d^(2/3)*(-((a - x)*x^2))^(1/3))","A",9,5,34,0.1471,1,"{6719, 911, 105, 59, 91}"
2719,0,0,0,19.2647813,"\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","Int[(-(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,"(3*a*b*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^4/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(-(a^2*b^2) + 2*a^2*b*(1 + b/a)*x^3 - a^2*(1 + (4*a*b + b^2 - d)/a^2)*x^6 + 2*a*(1 + b/a)*x^9 - x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (3*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^10/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (4*a*b + b^2 - d)/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3)","F",0,0,0,0,-1,"{}"
2720,1,244,0,0.4140554,"\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","Int[((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{(4 a+1) \sqrt{x} \sqrt[4]{\frac{\left(x^2+1\right)^4 \left(a x^2+1\right)}{x^2}} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+1}}\right)}{4 a^{3/4} \left(x^2+1\right) \sqrt[4]{a x^2+1}}+\frac{(4 a+1) \sqrt{x} \sqrt[4]{\frac{\left(x^2+1\right)^4 \left(a x^2+1\right)}{x^2}} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+1}}\right)}{4 a^{3/4} \left(x^2+1\right) \sqrt[4]{a x^2+1}}+\frac{(4 a+1) x^2 \sqrt[4]{\frac{\left(x^2+1\right)^4 \left(a x^2+1\right)}{x^2}}}{2 \left(x^2+1\right)}-\frac{2 \left(a x^2+1\right) \sqrt[4]{\frac{\left(x^2+1\right)^4 \left(a x^2+1\right)}{x^2}}}{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,"((1 + 4*a)*x^2*(((1 + x^2)^4*(1 + a*x^2))/x^2)^(1/4))/(2*(1 + x^2)) - (2*(1 + a*x^2)*(((1 + x^2)^4*(1 + a*x^2))/x^2)^(1/4))/(1 + x^2) - ((1 + 4*a)*Sqrt[x]*(((1 + x^2)^4*(1 + a*x^2))/x^2)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(1 + a*x^2)^(1/4)])/(4*a^(3/4)*(1 + x^2)*(1 + a*x^2)^(1/4)) + ((1 + 4*a)*Sqrt[x]*(((1 + x^2)^4*(1 + a*x^2))/x^2)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(1 + a*x^2)^(1/4)])/(4*a^(3/4)*(1 + x^2)*(1 + a*x^2)^(1/4))","A",9,9,60,0.1500,1,"{6688, 6718, 453, 279, 329, 331, 298, 203, 206}"
2721,1,179,0,0.0889974,"\int \frac{\sqrt[3]{2-8 x+8 x^2}}{3+x} \, dx","Int[(2 - 8*x + 8*x^2)^(1/3)/(3 + x),x]","\frac{3 \sqrt[3]{4 x^2-4 x+1}}{2^{2/3}}-\frac{\left(\frac{7}{2}\right)^{2/3} \sqrt[3]{4 x^2-4 x+1} \log (x+3)}{(2 x-1)^{2/3}}+\frac{3 \left(\frac{7}{2}\right)^{2/3} \sqrt[3]{4 x^2-4 x+1} \log \left(\sqrt[3]{8 x-4}+2^{2/3} \sqrt[3]{7}\right)}{(2 x-1)^{2/3}}+\frac{\sqrt[3]{2} \sqrt{3} 7^{2/3} \sqrt[3]{4 x^2-4 x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{2 x-1}}{\sqrt{3} \sqrt[3]{7}}\right)}{(2 x-1)^{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 - 4*x + 4*x^2)^(1/3))/2^(2/3) + (2^(1/3)*Sqrt[3]*7^(2/3)*(1 - 4*x + 4*x^2)^(1/3)*ArcTan[1/Sqrt[3] - (2*(-1 + 2*x)^(1/3))/(Sqrt[3]*7^(1/3))])/(-1 + 2*x)^(2/3) - ((7/2)^(2/3)*(1 - 4*x + 4*x^2)^(1/3)*Log[3 + x])/(-1 + 2*x)^(2/3) + (3*(7/2)^(2/3)*(1 - 4*x + 4*x^2)^(1/3)*Log[2^(2/3)*7^(1/3) + (-4 + 8*x)^(1/3)])/(-1 + 2*x)^(2/3)","A",6,6,20,0.3000,1,"{646, 50, 56, 617, 204, 31}"
2722,0,0,0,3.5746507,"\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","Int[((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,"(a*b*p*x*(1 + (p*x^3)/q)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((p*x^3)/q)])/((a^3*c + d*p)*(q + p*x^3)^(2/3)) - (a*b*(b^3*c*p + a^3*c*q + 2*d*p*q)*Defer[Int][1/((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])/(a^3*c + d*p) - (a^2*(3*b^3*c*p + a^3*c*q + d*p*q)*Defer[Int][x/((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])/(a^3*c + d*p) - (b^2*p*(2*a^3*c - d*p)*Defer[Int][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])/(a^3*c + d*p)","F",0,0,0,0,-1,"{}"
2723,0,0,0,7.4049773,"\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","Int[((-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,"(-3*((a - x)*(b - x))^(1/3)*Defer[Subst][Defer[Int][(x^6*(-a + b + x^3)^(1/3))/(a^2*(1 + (b*(-2*a + b))/a^2)*d - 2*a*(1 - b/a)*d*x^3 + d*x^6 - x^12), x], x, (a - x)^(1/3)])/((a - x)^(1/3)*(b - x)^(1/3)) - (3*a*((a - x)*(b - x))^(1/3)*Defer[Subst][Defer[Int][(x^3*(-a + b + x^3)^(1/3))/(-(a^2*(1 + (b*(-2*a + b))/a^2)*d) + 2*a*(1 - b/a)*d*x^3 - d*x^6 + x^12), x], x, (a - x)^(1/3)])/((a - x)^(1/3)*(b - x)^(1/3)) + (3*(a - 2*b)*((a - x)*(b - x))^(1/3)*Defer[Subst][Defer[Int][(x^3*(-a + b + x^3)^(1/3))/(a^2*(1 + b^2/a^2)*d + 2*b*d*x^3 - 2*a*d*(b + x^3) + x^6*(d - x^6)), x], x, (a - x)^(1/3)])/((a - x)^(1/3)*(b - x)^(1/3))","F",0,0,0,0,-1,"{}"
2724,1,89,0,0.8067361,"\int \frac{\sqrt{1+x^5} \left(2+x^5\right)}{x^6 \left(-1-x^5+a x^{10}\right)} \, dx","Int[(Sqrt[1 + x^5]*(2 + x^5))/(x^6*(-1 - x^5 + a*x^10)),x]","\frac{2}{5} \sqrt{a} \tanh ^{-1}\left(\sqrt{4 a+1}-2 \sqrt{a} \sqrt{x^5+1}\right)-\frac{2}{5} \sqrt{a} \tanh ^{-1}\left(2 \sqrt{a} \sqrt{x^5+1}+\sqrt{4 a+1}\right)+\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) + (2*Sqrt[a]*ArcTanh[Sqrt[1 + 4*a] - 2*Sqrt[a]*Sqrt[1 + x^5]])/5 - (2*Sqrt[a]*ArcTanh[Sqrt[1 + 4*a] + 2*Sqrt[a]*Sqrt[1 + x^5]])/5","A",18,12,32,0.3750,1,"{6728, 266, 47, 63, 207, 50, 6715, 824, 826, 1161, 618, 206}"
2725,1,97,0,0.7300957,"\int \frac{\left(-2+x^5\right) \sqrt{-1+x^5}}{x^6 \left(1-x^5+a x^{10}\right)} \, dx","Int[((-2 + x^5)*Sqrt[-1 + x^5])/(x^6*(1 - x^5 + a*x^10)),x]","\frac{1}{5} \sqrt{a} \log \left(-\sqrt{a} \left(1-x^5\right)+\sqrt{a}-\sqrt{x^5-1}\right)-\frac{1}{5} \sqrt{a} \log \left(-\sqrt{a} \left(1-x^5\right)+\sqrt{a}+\sqrt{x^5-1}\right)+\frac{2 \sqrt{x^5-1}}{5 x^5}","\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*Sqrt[-1 + x^5])/(5*x^5) + (Sqrt[a]*Log[Sqrt[a] - Sqrt[a]*(1 - x^5) - Sqrt[-1 + x^5]])/5 - (Sqrt[a]*Log[Sqrt[a] - Sqrt[a]*(1 - x^5) + Sqrt[-1 + x^5]])/5","A",16,11,32,0.3438,1,"{6728, 266, 47, 63, 203, 50, 6715, 824, 826, 1164, 628}"
2726,0,0,0,0.551933,"\int \frac{1}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])^(-1),x]","\int \frac{1}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{55} \left(7 \sqrt{5}-5\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(5+7 \sqrt{5}\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"(-2*(5 + 7*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 - (2*(5 - 7*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 + (4*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/55 + (136*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (32*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (116*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (56*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55","F",0,0,0,0,-1,"{}"
2727,0,0,0,0.4588813,"\int \frac{1}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]])^(-1),x]","\int \frac{1}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$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,"(-2*(5 + 7*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 - (2*(5 - 7*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 + (4*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/55 + (136*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (32*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (116*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (56*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55","F",0,0,0,0,-1,"{}"
2728,0,0,0,17.033309,"\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","Int[(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]","\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","-\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,"(-9*C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(1 + 6*x*C[3] - Sqrt[1 - 36*C[3]*C[4]])), x])/(4*Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) - (9*C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(1 + 6*x*C[3] + Sqrt[1 - 36*C[3]*C[4]])), x])/(4*Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(-1 + 2*x*C[3] - Sqrt[1 - 4*C[3]*C[4]])), x])/(4*Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(1 + 2*x*C[3] - Sqrt[1 - 4*C[3]*C[4]])), x])/(2*Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(-1 + 2*x*C[3] + Sqrt[1 - 4*C[3]*C[4]])), x])/(4*Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]]) + (C[3]*Sqrt[x*C[0] + x^2*C[3] + C[4]]*Defer[Int][Sqrt[x*C[1] + x^2*C[3] + C[4]]/(Sqrt[x*C[0] + x^2*C[3] + C[4]]*(1 + 2*x*C[3] + Sqrt[1 - 4*C[3]*C[4]])), x])/(2*Sqrt[(x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4])]*Sqrt[x*C[1] + x^2*C[3] + C[4]])","F",0,0,0,0,-1,"{}"
2729,0,0,0,0.1109939,"\int \frac{1}{\left(-b+a x^4\right)^2 \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((-b + a*x^4)^2*(-(b*x^2) + a*x^4)^(1/4)),x]","\int \frac{1}{\left(-b+a x^4\right)^2 \sqrt[4]{-b x^2+a x^4}} \, dx","\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{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-8 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+7 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+8 \text{$\#$1}^4 a \log (x)-7 \text{$\#$1}^4 b \log (x)+8 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-6 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-8 a^2 \log (x)+6 a b \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 b^2 (a-b)}",1,"(2*Sqrt[x]*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][1/((-b + a*x^4)^(1/4)*(-b + a*x^8)^2), x], x, Sqrt[x]])/(-(b*x^2) + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2730,0,0,0,0.1118571,"\int \frac{1}{\left(-b+a x^4\right)^2 \sqrt[4]{-b x^2+a x^4}} \, dx","Int[1/((-b + a*x^4)^2*(-(b*x^2) + a*x^4)^(1/4)),x]","\int \frac{1}{\left(-b+a x^4\right)^2 \sqrt[4]{-b x^2+a x^4}} \, dx","\frac{\left(-a x^2-b\right) \left(a x^4-b x^2\right)^{3/4}}{4 b^2 x (b-a) \left(b-a x^4\right)}-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-8 \text{$\#$1}^4 a \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+7 \text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+8 \text{$\#$1}^4 a \log (x)-7 \text{$\#$1}^4 b \log (x)+8 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-6 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-8 a^2 \log (x)+6 a b \log (x)}{\text{$\#$1} a-\text{$\#$1}^5}\&\right]}{32 b^2 (a-b)}",1,"(2*Sqrt[x]*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][1/((-b + a*x^4)^(1/4)*(-b + a*x^8)^2), x], x, Sqrt[x]])/(-(b*x^2) + a*x^4)^(1/4)","F",0,0,0,0,-1,"{}"
2731,0,0,0,13.9355185,"\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","Int[((-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,"(-2*a*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^5, x])/c - (2*(b*c - a*d)*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^3, x])/c^2 + (a*p*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^2, x])/c + (2*d*(b*c - a*d)*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x, x])/(c^3*q) + (3*(b*c - a*d)*p*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/(c*q + d*x^2 + c*p*x^3), x])/c - (2*d^2*(b*c - a*d)*Defer[Int][(x*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(c*q + d*x^2 + c*p*x^3), x])/(c^3*q) - (2*d*(b*c - a*d)*p*Defer[Int][(x^2*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6])/(c*q + d*x^2 + c*p*x^3), x])/(c^2*q)","F",0,0,0,0,-1,"{}"
2732,0,0,0,10.8060009,"\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","Int[-(((-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{(-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","\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,"(3*(2 - k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][(x^6*(1 - x^3)^(1/3)*(1 - k*x^3)^(1/3))/(1 - 4*k*x^3 - b*(1 - (6*k^2)/b)*x^6 + 2*b*(1 - (2*k^3)/b)*x^9 - b*(1 - k^4/b)*x^12), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (3*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][(x^3*(1 - x^3)^(1/3)*(1 - k*x^3)^(1/3))/(-1 + 4*k*x^3 + b*(1 - (6*k^2)/b)*x^6 - 2*b*(1 - (2*k^3)/b)*x^9 + b*(1 - k^4/b)*x^12), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2733,0,0,0,1.7699937,"\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","Int[((-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,"-2*a*q^5*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^13, x] - 7*a*p*q^4*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^10, x] - 8*a*p^2*q^3*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^7, x] - 2*b*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^5, x] - 2*a*p^3*q^2*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^4, x] + b*p*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^2, x] + 2*a*p^4*q*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x, x] + a*p^5*Defer[Int][x^2*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2734,0,0,0,1.2315188,"\int \frac{x^2}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[x^2/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{x^2}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+x+\frac{4}{55} \left(5+4 \sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{4}{55} \left(4 \sqrt{5}-5\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"-2*Sqrt[1 + x] + (1 + Sqrt[1 + x])^2 + (4*(5 - 4*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 + (4*(5 + 4*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 - (8*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/55 - (52*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (156*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 + (12*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 + (112*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55","F",0,0,0,0,-1,"{}"
2735,0,0,0,1.0158467,"\int \frac{x^2}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[x^2/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{x^2}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+7 \text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$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,"-2*Sqrt[1 + x] + (1 + Sqrt[1 + x])^2 + (4*(5 - 4*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 + (4*(5 + 4*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 - (8*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/55 - (52*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 - (156*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 + (12*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55 + (112*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/55","F",0,0,0,0,-1,"{}"
2736,0,0,0,0.0825937,"\int \frac{1}{x \sqrt[5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx","Int[1/(x*(1 - 4*x + 6*x^2 - 4*x^3 + x^4)^(1/5)),x]","\int \frac{1}{x \sqrt[5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx","\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,"Defer[Int][1/(x*(1 - 4*x + 6*x^2 - 4*x^3 + x^4)^(1/5)), x]","F",0,0,0,0,-1,"{}"
2737,1,127,0,0.870702,"\int \frac{1-x+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Int[(1 - x + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)),x]","\frac{3 \sqrt[3]{x^2+1} x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};x^2,-x^2\right)}{4 \sqrt[3]{x^4+x^2}}-\frac{6 \sqrt[3]{x^2+1} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};x^2,-x^2\right)}{\sqrt[3]{x^4+x^2}}+\frac{3 \sqrt[3]{x^2+1} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};-x^2\right)}{\sqrt[3]{x^4+x^2}}","\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,"(-6*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, x^2, -x^2])/(x^2 + x^4)^(1/3) + (3*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, x^2, -x^2])/(4*(x^2 + x^4)^(1/3)) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3)","C",18,8,27,0.2963,0,"{2056, 6725, 364, 959, 466, 429, 465, 510}"
2738,1,127,0,0.7571962,"\int \frac{1+x+x^2}{\left(-1+x^2\right) \sqrt[3]{x^2+x^4}} \, dx","Int[(1 + x + x^2)/((-1 + x^2)*(x^2 + x^4)^(1/3)),x]","-\frac{3 \sqrt[3]{x^2+1} x^2 F_1\left(\frac{2}{3};1,\frac{1}{3};\frac{5}{3};x^2,-x^2\right)}{4 \sqrt[3]{x^4+x^2}}-\frac{6 \sqrt[3]{x^2+1} x F_1\left(\frac{1}{6};1,\frac{1}{3};\frac{7}{6};x^2,-x^2\right)}{\sqrt[3]{x^4+x^2}}+\frac{3 \sqrt[3]{x^2+1} x \, _2F_1\left(\frac{1}{6},\frac{1}{3};\frac{7}{6};-x^2\right)}{\sqrt[3]{x^4+x^2}}","\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,"(-6*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, x^2, -x^2])/(x^2 + x^4)^(1/3) - (3*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1, 1/3, 5/3, x^2, -x^2])/(4*(x^2 + x^4)^(1/3)) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3)","C",18,8,25,0.3200,0,"{2056, 6725, 364, 959, 466, 429, 465, 510}"
2739,0,0,0,0.657052,"\int \frac{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}}{x^2 \left(1+x^2\right)} \, dx","Int[((-1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4])/(x^2*(1 + x^2)),x]","\int \frac{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}}{x^2 \left(1+x^2\right)} \, dx","\text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3+62 \text{$\#$1}^2+12 \text{$\#$1}+9\&,\frac{3 \text{$\#$1}^2 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-3 \text{$\#$1}^2 \log (x)+10 \text{$\#$1} \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-9 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-10 \text{$\#$1} \log (x)+9 \log (x)}{\text{$\#$1}^3-3 \text{$\#$1}^2+31 \text{$\#$1}+3}\&\right]+\frac{\sqrt{x^4+x^3-x^2-x+1}}{x}-\frac{1}{2} \log \left(-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)+\frac{\log (x)}{2}",1,"I*Defer[Int][Sqrt[1 - x - x^2 + x^3 + x^4]/(I - x), x] - Defer[Int][Sqrt[1 - x - x^2 + x^3 + x^4]/x^2, x] + I*Defer[Int][Sqrt[1 - x - x^2 + x^3 + x^4]/(I + x), x]","F",0,0,0,0,-1,"{}"
2740,0,0,0,0.5524342,"\int \frac{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}}{x^2 \left(1+x^2\right)} \, dx","Int[((-1 + x^2)*Sqrt[1 - x - x^2 + x^3 + x^4])/(x^2*(1 + x^2)),x]","\int \frac{\left(-1+x^2\right) \sqrt{1-x-x^2+x^3+x^4}}{x^2 \left(1+x^2\right)} \, dx","\text{RootSum}\left[\text{$\#$1}^4-4 \text{$\#$1}^3+62 \text{$\#$1}^2+12 \text{$\#$1}+9\&,\frac{3 \text{$\#$1}^2 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-3 \text{$\#$1}^2 \log (x)+10 \text{$\#$1} \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-9 \log \left(\text{$\#$1} x-2 x^2+2 \sqrt{x^4+x^3-x^2-x+1}-x+2\right)-10 \text{$\#$1} \log (x)+9 \log (x)}{\text{$\#$1}^3-3 \text{$\#$1}^2+31 \text{$\#$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,"I*Defer[Int][Sqrt[1 - x - x^2 + x^3 + x^4]/(I - x), x] - Defer[Int][Sqrt[1 - x - x^2 + x^3 + x^4]/x^2, x] + I*Defer[Int][Sqrt[1 - x - x^2 + x^3 + x^4]/(I + x), x]","F",0,0,0,0,-1,"{}"
2741,0,0,0,0.7372475,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(-2-x^3+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(4 + x^3))/(x^6*(-2 - x^3 + x^6)),x]","\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^3\right)}{x^6 \left(-2-x^3+x^6\right)} \, dx","\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,"-1/4*(-1 + x^3)^(2/3)/x^2 - (2*(-1 + x^3)^(5/3))/(5*x^5) - (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/2])/(4*(1 - x^3)^(2/3)) + ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[-x + (-1 + x^3)^(1/3)]/4 - Defer[Int][(-1 + x^3)^(2/3)/(1 + x), x]/3 + ((1 + I*Sqrt[3])*Defer[Int][(-1 + x^3)^(2/3)/(-1 - I*Sqrt[3] + 2*x), x])/3 + ((1 - I*Sqrt[3])*Defer[Int][(-1 + x^3)^(2/3)/(-1 + I*Sqrt[3] + 2*x), x])/3","F",0,0,0,0,-1,"{}"
2742,0,0,0,1.0943239,"\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","Int[(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]","\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","\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,"Defer[Int][(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]","F",0,0,0,0,-1,"{}"
2743,1,416,0,0.4539071,"\int \frac{\left(x+x^2\right) \sqrt[4]{x^3+x^4}}{-1+x+x^2} \, dx","Int[((x + x^2)*(x^3 + x^4)^(1/4))/(-1 + x + x^2),x]","\frac{1}{2} \sqrt[4]{x^4+x^3} x+\frac{1}{8} \sqrt[4]{x^4+x^3}-\frac{29 \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{16 \sqrt[4]{x+1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{3+\sqrt{5}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt{5} \sqrt[4]{x+1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{3-\sqrt{5}} \sqrt[4]{x^4+x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt{5} \sqrt[4]{x+1} x^{3/4}}+\frac{29 \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{16 \sqrt[4]{x+1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{3+\sqrt{5}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt{5} \sqrt[4]{x+1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{3-\sqrt{5}} \sqrt[4]{x^4+x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x+1}}\right)}{\sqrt{5} \sqrt[4]{x+1} x^{3/4}}","\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,"(x^3 + x^4)^(1/4)/8 + (x*(x^3 + x^4)^(1/4))/2 - (29*(x^3 + x^4)^(1/4)*ArcTan[x^(1/4)/(1 + x)^(1/4)])/(16*x^(3/4)*(1 + x)^(1/4)) + (2^(3/4)*(3 + Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(Sqrt[5]*x^(3/4)*(1 + x)^(1/4)) + (2^(3/4)*(3 - Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(Sqrt[5]*x^(3/4)*(1 + x)^(1/4)) + (29*(x^3 + x^4)^(1/4)*ArcTanh[x^(1/4)/(1 + x)^(1/4)])/(16*x^(3/4)*(1 + x)^(1/4)) - (2^(3/4)*(3 + Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(Sqrt[5]*x^(3/4)*(1 + x)^(1/4)) - (2^(3/4)*(3 - Sqrt[5])^(1/4)*(x^3 + x^4)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(1 + x)^(1/4)])/(Sqrt[5]*x^(3/4)*(1 + x)^(1/4))","A",26,12,25,0.4800,0,"{1593, 2056, 903, 50, 63, 331, 298, 203, 206, 905, 911, 93}"
2744,1,137,0,0.5159534,"\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","Int[(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{x \left(a+x^4\right) \left(b+x^4\right)}{4 \sqrt[4]{\left(a+x^4\right) \left(b+x^4\right)^4}}-\frac{(a-4 b) \sqrt[4]{a+x^4} \left(b+x^4\right) \tan ^{-1}\left(\frac{x}{\sqrt[4]{a+x^4}}\right)}{8 \sqrt[4]{\left(a+x^4\right) \left(b+x^4\right)^4}}-\frac{(a-4 b) \sqrt[4]{a+x^4} \left(b+x^4\right) \tanh ^{-1}\left(\frac{x}{\sqrt[4]{a+x^4}}\right)}{8 \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,"(x*(a + x^4)*(b + x^4))/(4*((a + x^4)*(b + x^4)^4)^(1/4)) - ((a - 4*b)*(a + x^4)^(1/4)*(b + x^4)*ArcTan[x/(a + x^4)^(1/4)])/(8*((a + x^4)*(b + x^4)^4)^(1/4)) - ((a - 4*b)*(a + x^4)^(1/4)*(b + x^4)*ArcTanh[x/(a + x^4)^(1/4)])/(8*((a + x^4)*(b + x^4)^4)^(1/4))","A",11,8,80,0.1000,1,"{6, 6688, 6719, 388, 240, 212, 206, 203}"
2745,0,0,0,2.2123621,"\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","Int[((-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,"(7*a*p^2*q*(q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6)^(3/2))/9 + 2*b*p*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] - a*q^5*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^7, x] - 2*a*p*q^4*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^4, x] - b*q*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^3, x] + 2*a*p^2*q^3*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x, x] + (14*a*p^3*q^2*Defer[Int][x*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x])/3 + a*p^3*q^2*Defer[Int][x^2*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 2*a*p^5*Defer[Int][x^8*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2746,0,0,0,13.0416996,"\int \frac{1-\sqrt{x-\sqrt{1+x^2}}}{x^4-2 x^2 \sqrt{1+x^2}} \, dx","Int[(1 - Sqrt[x - Sqrt[1 + x^2]])/(x^4 - 2*x^2*Sqrt[1 + x^2]),x]","\int \frac{1-\sqrt{x-\sqrt{1+x^2}}}{x^4-2 x^2 \sqrt{1+x^2}} \, dx","-\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) + 1/(2*x*Sqrt[x - Sqrt[1 + x^2]]) - Sqrt[x - Sqrt[1 + x^2]] - ArcTan[x/Sqrt[2*(-1 + Sqrt[2])]]/(8*Sqrt[-1 + Sqrt[2]]) + (Sqrt[-1 + Sqrt[2]]*ArcTan[(Sqrt[(-1 + Sqrt[2])/2]*x)/Sqrt[1 + x^2]])/4 + (Sqrt[-7 + 5*Sqrt[2]]*ArcTan[(Sqrt[(-1 + Sqrt[2])/2]*x)/Sqrt[1 + x^2]])/8 + ArcTan[Sqrt[x - Sqrt[1 + x^2]]]/2 + ((3*I - (2*I)*Sqrt[2] + Sqrt[2*(-7 + 5*Sqrt[2])])*ArcTan[Sqrt[x - Sqrt[1 + x^2]]/Sqrt[Sqrt[3 - 2*Sqrt[2]] - I*Sqrt[2*(-1 + Sqrt[2])]]])/(8*Sqrt[5*Sqrt[6 - 4*Sqrt[2]] - 7*Sqrt[3 - 2*Sqrt[2]] - I*(10 - 7*Sqrt[2])*Sqrt[-1 + Sqrt[2]]]) - ((3*I - (2*I)*Sqrt[2] - Sqrt[2*(-7 + 5*Sqrt[2])])*ArcTan[Sqrt[x - Sqrt[1 + x^2]]/Sqrt[Sqrt[3 - 2*Sqrt[2]] + I*Sqrt[2*(-1 + Sqrt[2])]]])/(8*Sqrt[5*Sqrt[6 - 4*Sqrt[2]] - 7*Sqrt[3 - 2*Sqrt[2]] + I*(10 - 7*Sqrt[2])*Sqrt[-1 + Sqrt[2]]]) + ((3 + 2*Sqrt[2] - Sqrt[2*(7 + 5*Sqrt[2])])*ArcTan[Sqrt[-((x - Sqrt[1 + x^2])/(Sqrt[2*(1 + Sqrt[2])] - Sqrt[3 + 2*Sqrt[2]]))]])/(8*Sqrt[(1 + Sqrt[2])*(3 + 2*Sqrt[2])*(-Sqrt[2*(1 + Sqrt[2])] + Sqrt[3 + 2*Sqrt[2]])]) - ((3 + 2*Sqrt[2] + Sqrt[2*(7 + 5*Sqrt[2])])*ArcTan[Sqrt[(x - Sqrt[1 + x^2])/(Sqrt[2*(1 + Sqrt[2])] + Sqrt[3 + 2*Sqrt[2]])]])/(8*Sqrt[(1 + Sqrt[2])*(3 + 2*Sqrt[2])*(Sqrt[2*(1 + Sqrt[2])] + Sqrt[3 + 2*Sqrt[2]])]) - ArcTanh[x/Sqrt[2*(1 + Sqrt[2])]]/(8*Sqrt[1 + Sqrt[2]]) + (Sqrt[1 + Sqrt[2]]*ArcTanh[(Sqrt[(1 + Sqrt[2])/2]*x)/Sqrt[1 + x^2]])/4 - (Sqrt[7 + 5*Sqrt[2]]*ArcTanh[(Sqrt[(1 + Sqrt[2])/2]*x)/Sqrt[1 + x^2]])/8 + ArcTanh[Sqrt[x - Sqrt[1 + x^2]]]/2 - ((3*I - (2*I)*Sqrt[2] + Sqrt[2*(-7 + 5*Sqrt[2])])*ArcTanh[Sqrt[x - Sqrt[1 + x^2]]/Sqrt[Sqrt[3 - 2*Sqrt[2]] - I*Sqrt[2*(-1 + Sqrt[2])]]])/(8*Sqrt[5*Sqrt[6 - 4*Sqrt[2]] - 7*Sqrt[3 - 2*Sqrt[2]] - I*(10 - 7*Sqrt[2])*Sqrt[-1 + Sqrt[2]]]) + ((3*I - (2*I)*Sqrt[2] - Sqrt[2*(-7 + 5*Sqrt[2])])*ArcTanh[Sqrt[x - Sqrt[1 + x^2]]/Sqrt[Sqrt[3 - 2*Sqrt[2]] + I*Sqrt[2*(-1 + Sqrt[2])]]])/(8*Sqrt[5*Sqrt[6 - 4*Sqrt[2]] - 7*Sqrt[3 - 2*Sqrt[2]] + I*(10 - 7*Sqrt[2])*Sqrt[-1 + Sqrt[2]]]) - ((3 + 2*Sqrt[2] - Sqrt[2*(7 + 5*Sqrt[2])])*ArcTanh[Sqrt[-((x - Sqrt[1 + x^2])/(Sqrt[2*(1 + Sqrt[2])] - Sqrt[3 + 2*Sqrt[2]]))]])/(8*Sqrt[(1 + Sqrt[2])*(3 + 2*Sqrt[2])*(-Sqrt[2*(1 + Sqrt[2])] + Sqrt[3 + 2*Sqrt[2]])]) + ((3 + 2*Sqrt[2] + Sqrt[2*(7 + 5*Sqrt[2])])*ArcTanh[Sqrt[(x - Sqrt[1 + x^2])/(Sqrt[2*(1 + Sqrt[2])] + Sqrt[3 + 2*Sqrt[2]])]])/(8*Sqrt[(1 + Sqrt[2])*(3 + 2*Sqrt[2])*(Sqrt[2*(1 + Sqrt[2])] + Sqrt[3 + 2*Sqrt[2]])]) - ((I/8)*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(I*Sqrt[2*(-1 + Sqrt[2])] - x), x])/Sqrt[-1 + Sqrt[2]] - (I/16)*Sqrt[-1 + Sqrt[2]]*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(I*Sqrt[2*(-1 + Sqrt[2])] - x), x] - Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(Sqrt[2*(1 + Sqrt[2])] - x), x]/(8*Sqrt[1 + Sqrt[2]]) + (Sqrt[1 + Sqrt[2]]*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(Sqrt[2*(1 + Sqrt[2])] - x), x])/16 - ((I/8)*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(I*Sqrt[2*(-1 + Sqrt[2])] + x), x])/Sqrt[-1 + Sqrt[2]] - (I/16)*Sqrt[-1 + Sqrt[2]]*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(I*Sqrt[2*(-1 + Sqrt[2])] + x), x] - Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(Sqrt[2*(1 + Sqrt[2])] + x), x]/(8*Sqrt[1 + Sqrt[2]]) + (Sqrt[1 + Sqrt[2]]*Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(Sqrt[2*(1 + Sqrt[2])] + x), x])/16","F",0,0,0,0,-1,"{}"
2747,0,0,0,0.354978,"\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[6]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)),x]","\int \frac{1}{\sqrt{-b+a^2 x^2} \sqrt[6]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","-\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,"Defer[Int][1/(Sqrt[-b + a^2*x^2]*(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)), x]","F",0,0,0,0,-1,"{}"
2748,0,0,0,0.8739481,"\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","Int[((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,"Defer[Subst][Defer[Int][(1 - 2*k^2 + k^2*x)/((1 + (-1 - k^2)*x + k^2*x^2)^(1/3)*(-1 + d + (1 - 2*d*k^2)*x + d*k^4*x^2)), x], x, x^2]/2","F",0,0,0,0,-1,"{}"
2749,1,275,0,2.5715347,"\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","Int[((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]","\frac{3 \left(1-x^2\right)^2 \left(\frac{1-k^2 x^2}{1-k^2}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 \left(1-x^2\right)}{\sqrt{d} \left(\sqrt{d} k^2-\sqrt{d k^4-4 k^2+4}\right)}\right)}{8 d \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}+\frac{3 \left(1-x^2\right)^2 \left(\frac{1-k^2 x^2}{1-k^2}\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};-\frac{k^2 \left(1-x^2\right)}{1-k^2},\frac{2 \left(1-x^2\right)}{\sqrt{d} \left(\sqrt{d} k^2+\sqrt{d k^4-4 k^2+4}\right)}\right)}{8 d \left(\left(1-x^2\right) \left(1-k^2 x^2\right)\right)^{2/3}}","\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,"(3*(1 - x^2)^2*((1 - k^2*x^2)/(1 - k^2))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*(1 - x^2))/(Sqrt[d]*(Sqrt[d]*k^2 - Sqrt[4 - 4*k^2 + d*k^4]))])/(8*d*((1 - x^2)*(1 - k^2*x^2))^(2/3)) + (3*(1 - x^2)^2*((1 - k^2*x^2)/(1 - k^2))^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, -((k^2*(1 - x^2))/(1 - k^2)), (2*(1 - x^2))/(Sqrt[d]*(Sqrt[d]*k^2 + Sqrt[4 - 4*k^2 + d*k^4]))])/(8*d*((1 - x^2)*(1 - k^2*x^2))^(2/3))","C",10,7,66,0.1061,0,"{1594, 6715, 6719, 1586, 6728, 137, 136}"
2750,1,435,0,0.805438,"\int \frac{\left(-1+x^4\right) \sqrt[4]{-x^2+x^4}}{-1-x^2+x^4} \, dx","Int[((-1 + x^4)*(-x^2 + x^4)^(1/4))/(-1 - x^2 + x^4),x]","\frac{1}{2} \sqrt[4]{x^4-x^2} x-\frac{3 \sqrt[4]{x^4-x^2} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{x^2-1} \sqrt{x}}+\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x^4-x^2} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt{5} \sqrt[4]{x^2-1} \sqrt{x}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \sqrt[4]{x^4-x^2} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt{5} \sqrt[4]{x^2-1} \sqrt{x}}+\frac{3 \sqrt[4]{x^4-x^2} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{4 \sqrt[4]{x^2-1} \sqrt{x}}-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x^4-x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt{5} \sqrt[4]{x^2-1} \sqrt{x}}-\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \sqrt[4]{x^4-x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt{5} \sqrt[4]{x^2-1} \sqrt{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 + x^4)^(1/4))/2 - (3*(-x^2 + x^4)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*Sqrt[x]*(-1 + x^2)^(1/4)) + (((3 + Sqrt[5])/2)^(1/4)*(-x^2 + x^4)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(Sqrt[5]*Sqrt[x]*(-1 + x^2)^(1/4)) + (((3 - Sqrt[5])/2)^(1/4)*(-x^2 + x^4)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(Sqrt[5]*Sqrt[x]*(-1 + x^2)^(1/4)) + (3*(-x^2 + x^4)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(4*Sqrt[x]*(-1 + x^2)^(1/4)) - (((3 + Sqrt[5])/2)^(1/4)*(-x^2 + x^4)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(Sqrt[5]*Sqrt[x]*(-1 + x^2)^(1/4)) - (((3 - Sqrt[5])/2)^(1/4)*(-x^2 + x^4)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(Sqrt[5]*Sqrt[x]*(-1 + x^2)^(1/4))","A",25,12,31,0.3871,0,"{2056, 6728, 279, 329, 331, 298, 203, 206, 1269, 1518, 1528, 494}"
2751,0,0,0,11.2783425,"\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","Int[(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,"(6*(2 - k)*(-1 + x)^(1/3)*x^(1/3)*(-1 + k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(-1 + x^3)^(2/3))/((-1 + k*x^3)^(1/3)*(-x^3 + k*x^6 - b*(-1 + x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (9*k*(-1 + x)^(1/3)*x^(1/3)*(-1 + k*x)^(1/3)*Defer[Subst][Defer[Int][(x^7*(-1 + x^3)^(2/3))/((-1 + k*x^3)^(1/3)*(-x^3 + k*x^6 - b*(-1 + x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (3*(-1 + x)^(1/3)*x^(1/3)*(-1 + k*x)^(1/3)*Defer[Subst][Defer[Int][(x*(-1 + x^3)^(2/3))/((-1 + k*x^3)^(1/3)*(x^3 - k*x^6 + b*(-1 + x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2752,1,1568,0,2.3194521,"\int \frac{x^3}{\sqrt[3]{-x^2+x^3} \left(-1+x^6\right)} \, dx","Int[x^3/((-x^2 + x^3)^(1/3)*(-1 + x^6)),x]","-\frac{x^3}{2 \sqrt[3]{x^3-x^2}}-\frac{(1-x) x^2}{2 \sqrt[3]{x^3-x^2}}-\frac{(-1)^{2/3} (1-x) x}{3 \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{-1} (1-x) x}{3 \sqrt[3]{x^3-x^2}}-\frac{5 (1-x) x}{6 \sqrt[3]{x^3-x^2}}-\frac{(-1)^{2/3} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{3 \sqrt{3} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{-1} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{3 \sqrt{3} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{3 \sqrt{3} \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{2 \sqrt[3]{2} \sqrt{3} \sqrt[3]{x^3-x^2}}+\frac{(-1)^{2/3} \left(-1+\sqrt[3]{-1}\right)^{2/3} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1-\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{2 \sqrt{3} \sqrt[3]{x^3-x^2}}-\frac{(-1)^{2/3} \sqrt[3]{-\frac{1}{1+\sqrt[3]{-1}}} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1+\sqrt[3]{-1}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{2 \sqrt{3} \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{2 \sqrt{3} \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}+\frac{(-1)^{8/9} \sqrt[3]{x-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-1}}{\sqrt{3} \sqrt[3]{1+(-1)^{2/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) x^{2/3}}{2 \sqrt{3} \sqrt[3]{x^3-x^2}}-\frac{(-1)^{2/3} \sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right) x^{2/3}}{6 \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{-1} \sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right) x^{2/3}}{6 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{x}}-1\right) x^{2/3}}{6 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{2}}-\sqrt[3]{x}\right) x^{2/3}}{4 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}+\frac{(-1)^{2/3} \left(-1+\sqrt[3]{-1}\right)^{2/3} \sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-\sqrt[3]{-1}}}-\sqrt[3]{x}\right) x^{2/3}}{4 \sqrt[3]{x^3-x^2}}-\frac{(-1)^{2/3} \sqrt[3]{-\frac{1}{1+\sqrt[3]{-1}}} \sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+\sqrt[3]{-1}}}-\sqrt[3]{x}\right) x^{2/3}}{4 \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1-(-1)^{2/3}}}-\sqrt[3]{x}\right) x^{2/3}}{4 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-x^2}}+\frac{(-1)^{8/9} \sqrt[3]{x-1} \log \left(\frac{\sqrt[3]{x-1}}{\sqrt[3]{1+(-1)^{2/3}}}-\sqrt[3]{x}\right) x^{2/3}}{4 \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{x-1} \log (-x-1) x^{2/3}}{12 \sqrt[3]{2} \sqrt[3]{x^3-x^2}}-\frac{(-1)^{2/3} \sqrt[3]{x-1} \log (x) x^{2/3}}{18 \sqrt[3]{x^3-x^2}}+\frac{\sqrt[3]{-1} \sqrt[3]{x-1} \log (x) x^{2/3}}{18 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} \log (x) x^{2/3}}{18 \sqrt[3]{x^3-x^2}}-\frac{(-1)^{2/3} \left(-1+\sqrt[3]{-1}\right)^{2/3} \sqrt[3]{x-1} \log \left(\sqrt[3]{-1} x-1\right) x^{2/3}}{12 \sqrt[3]{x^3-x^2}}+\frac{(-1)^{2/3} \sqrt[3]{-\frac{1}{1+\sqrt[3]{-1}}} \sqrt[3]{x-1} \log \left(\sqrt[3]{-1} x+1\right) x^{2/3}}{12 \sqrt[3]{x^3-x^2}}-\frac{(-1)^{8/9} \sqrt[3]{x-1} \log \left(-(-1)^{2/3} x-1\right) x^{2/3}}{12 \sqrt[3]{x^3-x^2}}-\frac{\sqrt[3]{x-1} \log \left(1-(-1)^{2/3} x\right) x^{2/3}}{12 \sqrt[3]{1-(-1)^{2/3}} \sqrt[3]{x^3-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,"(-5*(1 - x)*x)/(6*(-x^2 + x^3)^(1/3)) + ((-1)^(1/3)*(1 - x)*x)/(3*(-x^2 + x^3)^(1/3)) - ((-1)^(2/3)*(1 - x)*x)/(3*(-x^2 + x^3)^(1/3)) - ((1 - x)*x^2)/(2*(-x^2 + x^3)^(1/3)) - x^3/(2*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(3*Sqrt[3]*(-x^2 + x^3)^(1/3)) + ((-1)^(1/3)*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(3*Sqrt[3]*(-x^2 + x^3)^(1/3)) - ((-1)^(2/3)*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(3*Sqrt[3]*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2^(2/3)*(-1 + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2*2^(1/3)*Sqrt[3]*(-x^2 + x^3)^(1/3)) + ((-1)^(2/3)*(-1 + (-1)^(1/3))^(2/3)*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(1/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*(-x^2 + x^3)^(1/3)) - ((-1)^(2/3)*(-(1 + (-1)^(1/3))^(-1))^(1/3)*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(1/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1)^(8/9)*(-1 + x)^(1/3)*x^(2/3)*ArcTan[1/Sqrt[3] + (2*(-1 + x)^(1/3))/(Sqrt[3]*(1 + (-1)^(2/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(6*(-x^2 + x^3)^(1/3)) + ((-1)^(1/3)*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(6*(-x^2 + x^3)^(1/3)) - ((-1)^(2/3)*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1 + x)^(1/3)/x^(1/3)])/(6*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/2^(1/3) - x^(1/3)])/(4*2^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1)^(2/3)*(-1 + (-1)^(1/3))^(2/3)*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - (-1)^(1/3))^(1/3) - x^(1/3)])/(4*(-x^2 + x^3)^(1/3)) - ((-1)^(2/3)*(-(1 + (-1)^(1/3))^(-1))^(1/3)*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + (-1)^(1/3))^(1/3) - x^(1/3)])/(4*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 - (-1)^(2/3))^(1/3) - x^(1/3)])/(4*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3)) + ((-1)^(8/9)*(-1 + x)^(1/3)*x^(2/3)*Log[(-1 + x)^(1/3)/(1 + (-1)^(2/3))^(1/3) - x^(1/3)])/(4*(-x^2 + x^3)^(1/3)) + ((-1 + x)^(1/3)*x^(2/3)*Log[-1 - x])/(12*2^(1/3)*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[x])/(18*(-x^2 + x^3)^(1/3)) + ((-1)^(1/3)*(-1 + x)^(1/3)*x^(2/3)*Log[x])/(18*(-x^2 + x^3)^(1/3)) - ((-1)^(2/3)*(-1 + x)^(1/3)*x^(2/3)*Log[x])/(18*(-x^2 + x^3)^(1/3)) - ((-1)^(2/3)*(-1 + (-1)^(1/3))^(2/3)*(-1 + x)^(1/3)*x^(2/3)*Log[-1 + (-1)^(1/3)*x])/(12*(-x^2 + x^3)^(1/3)) + ((-1)^(2/3)*(-(1 + (-1)^(1/3))^(-1))^(1/3)*(-1 + x)^(1/3)*x^(2/3)*Log[1 + (-1)^(1/3)*x])/(12*(-x^2 + x^3)^(1/3)) - ((-1)^(8/9)*(-1 + x)^(1/3)*x^(2/3)*Log[-1 - (-1)^(2/3)*x])/(12*(-x^2 + x^3)^(1/3)) - ((-1 + x)^(1/3)*x^(2/3)*Log[1 - (-1)^(2/3)*x])/(12*(1 - (-1)^(2/3))^(1/3)*(-x^2 + x^3)^(1/3))","B",62,8,24,0.3333,0,"{2056, 6725, 21, 47, 50, 59, 105, 91}"
2753,0,0,0,1.1435603,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Int[(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{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]",1,"Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/2 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
2754,0,0,0,0.8372335,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Int[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2),x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]",1,"Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/2 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
2755,0,0,0,1.2426384,"\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","Int[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]","\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","-\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2756,0,0,0,8.0733358,"\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","Int[((-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,"(-3*(b - x)*x*(1 - x/a)^(2/3)*(1 - x/b)^(1/3)*AppellF1[1/3, 2/3, 1/3, 4/3, x/a, x/b])/(d*(-((a - x)*(b - x)^2*x))^(2/3)) + ((1 + a*d - 2*b*d + Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(2/3)*(-b + x)^(1/3)*(-1 - a*d - Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2] + 2*d*x)), x])/(d*(-((a - x)*(b - x)^2*x))^(2/3)) + ((1 + a*d - 2*b*d - Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(2/3)*(-b + x)^(1/3)*(-1 - a*d + Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2] + 2*d*x)), x])/(d*(-((a - x)*(b - x)^2*x))^(2/3))","F",0,0,0,0,-1,"{}"
2757,0,0,0,9.1064893,"\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","Int[((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,"(-3*(a - 5*b)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^9/((a - b + x^3)^(2/3)*(a*(1 - b/a)*d + d*x^3 - x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(2/3) + (12*a*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^9/((a - b + x^3)^(2/3)*(-(a*(1 - b/a)*d) - d*x^3 + x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(2/3) + (12*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^12/((a - b + x^3)^(2/3)*(-(a*(1 - b/a)*d) - d*x^3 + x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(2/3)","F",0,0,0,0,-1,"{}"
2758,1,976,0,5.2404812,"\int \frac{1-x^3 \sqrt[3]{5+4 x}-x^3 (5+4 x)^{2/3}}{1-x \sqrt{5+4 x}} \, dx","Int[(1 - x^3*(5 + 4*x)^(1/3) - x^3*(5 + 4*x)^(2/3))/(1 - x*Sqrt[5 + 4*x]),x]","\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}+\frac{1}{4} \sqrt{\frac{3}{17}} \sqrt[3]{243+59 \sqrt{17}} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\frac{2}{-1+\sqrt{17}}} \sqrt[6]{4 x+5}}{\sqrt{3}}\right)-\frac{\sqrt{\frac{3}{17}} \sqrt[3]{37+9 \sqrt{17}} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\frac{2}{-1+\sqrt{17}}} \sqrt[6]{4 x+5}}{\sqrt{3}}\right)}{2^{2/3}}+\frac{1}{4} \sqrt{\frac{3}{17}} \sqrt[3]{-243+59 \sqrt{17}} \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{2}{1+\sqrt{17}}} \sqrt[6]{4 x+5}+1}{\sqrt{3}}\right)-\frac{\sqrt{\frac{3}{17}} \sqrt[3]{-37+9 \sqrt{17}} \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{2}{1+\sqrt{17}}} \sqrt[6]{4 x+5}+1}{\sqrt{3}}\right)}{2^{2/3}}-3 \log \left(\sqrt[6]{4 x+5}+1\right)+\frac{\sqrt[3]{-243+59 \sqrt{17}} \log \left(\sqrt[3]{1+\sqrt{17}}-\sqrt[3]{2} \sqrt[6]{4 x+5}\right)}{4 \sqrt{17}}+\frac{\sqrt[3]{-37+9 \sqrt{17}} \log \left(\sqrt[3]{1+\sqrt{17}}-\sqrt[3]{2} \sqrt[6]{4 x+5}\right)}{2^{2/3} \sqrt{17}}+\frac{\sqrt[3]{243+59 \sqrt{17}} \log \left(\sqrt[3]{2} \sqrt[6]{4 x+5}+\sqrt[3]{-1+\sqrt{17}}\right)}{4 \sqrt{17}}+\frac{\sqrt[3]{37+9 \sqrt{17}} \log \left(\sqrt[3]{2} \sqrt[6]{4 x+5}+\sqrt[3]{-1+\sqrt{17}}\right)}{2^{2/3} \sqrt{17}}-\frac{\sqrt[3]{243+59 \sqrt{17}} \log \left(2^{2/3} \sqrt[3]{4 x+5}-\sqrt[3]{2 \left(-1+\sqrt{17}\right)} \sqrt[6]{4 x+5}+\left(-1+\sqrt{17}\right)^{2/3}\right)}{8 \sqrt{17}}-\frac{\sqrt[3]{37+9 \sqrt{17}} \log \left(2^{2/3} \sqrt[3]{4 x+5}-\sqrt[3]{2 \left(-1+\sqrt{17}\right)} \sqrt[6]{4 x+5}+\left(-1+\sqrt{17}\right)^{2/3}\right)}{2\ 2^{2/3} \sqrt{17}}-\frac{\sqrt[3]{-243+59 \sqrt{17}} \log \left(2^{2/3} \sqrt[3]{4 x+5}+\sqrt[3]{2 \left(1+\sqrt{17}\right)} \sqrt[6]{4 x+5}+\left(1+\sqrt{17}\right)^{2/3}\right)}{8 \sqrt{17}}-\frac{\sqrt[3]{-37+9 \sqrt{17}} \log \left(2^{2/3} \sqrt[3]{4 x+5}+\sqrt[3]{2 \left(1+\sqrt{17}\right)} \sqrt[6]{4 x+5}+\left(1+\sqrt{17}\right)^{2/3}\right)}{2\ 2^{2/3} \sqrt{17}}+\frac{1}{34} \left(17+7 \sqrt{17}\right) \log \left(-2 \sqrt{4 x+5}-\sqrt{17}+1\right)+\frac{1}{34} \left(17-7 \sqrt{17}\right) \log \left(-2 \sqrt{4 x+5}+\sqrt{17}+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 - (Sqrt[3/17]*(37 + 9*Sqrt[17])^(1/3)*ArcTan[(1 - 2*(2/(-1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6))/Sqrt[3]])/2^(2/3) + (Sqrt[3/17]*(243 + 59*Sqrt[17])^(1/3)*ArcTan[(1 - 2*(2/(-1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6))/Sqrt[3]])/4 - (Sqrt[3/17]*(-37 + 9*Sqrt[17])^(1/3)*ArcTan[(1 + 2*(2/(1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6))/Sqrt[3]])/2^(2/3) + (Sqrt[3/17]*(-243 + 59*Sqrt[17])^(1/3)*ArcTan[(1 + 2*(2/(1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6))/Sqrt[3]])/4 - 3*Log[1 + (5 + 4*x)^(1/6)] + ((-37 + 9*Sqrt[17])^(1/3)*Log[(1 + Sqrt[17])^(1/3) - 2^(1/3)*(5 + 4*x)^(1/6)])/(2^(2/3)*Sqrt[17]) + ((-243 + 59*Sqrt[17])^(1/3)*Log[(1 + Sqrt[17])^(1/3) - 2^(1/3)*(5 + 4*x)^(1/6)])/(4*Sqrt[17]) + ((37 + 9*Sqrt[17])^(1/3)*Log[(-1 + Sqrt[17])^(1/3) + 2^(1/3)*(5 + 4*x)^(1/6)])/(2^(2/3)*Sqrt[17]) + ((243 + 59*Sqrt[17])^(1/3)*Log[(-1 + Sqrt[17])^(1/3) + 2^(1/3)*(5 + 4*x)^(1/6)])/(4*Sqrt[17]) - ((37 + 9*Sqrt[17])^(1/3)*Log[(-1 + Sqrt[17])^(2/3) - (2*(-1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6) + 2^(2/3)*(5 + 4*x)^(1/3)])/(2*2^(2/3)*Sqrt[17]) - ((243 + 59*Sqrt[17])^(1/3)*Log[(-1 + Sqrt[17])^(2/3) - (2*(-1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6) + 2^(2/3)*(5 + 4*x)^(1/3)])/(8*Sqrt[17]) - ((-37 + 9*Sqrt[17])^(1/3)*Log[(1 + Sqrt[17])^(2/3) + (2*(1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6) + 2^(2/3)*(5 + 4*x)^(1/3)])/(2*2^(2/3)*Sqrt[17]) - ((-243 + 59*Sqrt[17])^(1/3)*Log[(1 + Sqrt[17])^(2/3) + (2*(1 + Sqrt[17]))^(1/3)*(5 + 4*x)^(1/6) + 2^(2/3)*(5 + 4*x)^(1/3)])/(8*Sqrt[17]) + ((17 + 7*Sqrt[17])*Log[1 - Sqrt[17] - 2*Sqrt[5 + 4*x]])/34 + ((17 - 7*Sqrt[17])*Log[1 + Sqrt[17] - 2*Sqrt[5 + 4*x]])/34","B",40,17,47,0.3617,0,"{2055, 6741, 12, 6742, 2074, 1790, 1422, 200, 31, 634, 617, 204, 628, 1468, 632, 1510, 292}"
2759,0,0,0,32.273013,"\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","Int[(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,"-1/3*(Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])]*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*Defer[Int][(x*Sqrt[x^2*C[0] + x^3*C[3] + C[4]])/((-x^2 + x^3*C[3] + C[4])*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]), x])/Sqrt[x^2*C[0] + x^3*C[3] + C[4]] + (C[3]*Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])]*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^2*C[0] + x^3*C[3] + C[4]])/((-x^2 + x^3*C[3] + C[4])*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]), x])/(2*Sqrt[x^2*C[0] + x^3*C[3] + C[4]]) + (Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])]*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*Defer[Int][(x*Sqrt[x^2*C[0] + x^3*C[3] + C[4]])/((x^2 + x^3*C[3] + C[4])*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]), x])/Sqrt[x^2*C[0] + x^3*C[3] + C[4]] + (3*C[3]*Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])]*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^2*C[0] + x^3*C[3] + C[4]])/((x^2 + x^3*C[3] + C[4])*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]), x])/(2*Sqrt[x^2*C[0] + x^3*C[3] + C[4]]) - (4*Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])]*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*Defer[Int][(x*Sqrt[x^2*C[0] + x^3*C[3] + C[4]])/(Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*(x^2 + 2*x^3*C[3] + 2*C[4])), x])/(3*Sqrt[x^2*C[0] + x^3*C[3] + C[4]]) - (4*C[3]*Sqrt[(x^2*C[0] + x^3*C[3] + C[4])/(x^2*C[1] + x^3*C[3] + C[4])]*Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^2*C[0] + x^3*C[3] + C[4]])/(Sqrt[x^2*C[1] + x^3*C[3] + C[4]]*(x^2 + 2*x^3*C[3] + 2*C[4])), x])/Sqrt[x^2*C[0] + x^3*C[3] + C[4]]","F",0,0,0,0,-1,"{}"
2760,0,0,0,41.7248451,"\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","Int[(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,"-1/2*(Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/((-x^3 + x^5*C[3] + C[4])*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]), x])/Sqrt[x^3*C[0] + x^5*C[3] + C[4]] + (5*C[3]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^4*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/((-x^3 + x^5*C[3] + C[4])*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]), x])/(6*Sqrt[x^3*C[0] + x^5*C[3] + C[4]]) + (3*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/((x^3 + x^5*C[3] + C[4])*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]), x])/(2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]]) + (5*C[3]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^4*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/((x^3 + x^5*C[3] + C[4])*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]), x])/(2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]]) - (2*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/(Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*(x^3 + 2*x^5*C[3] + 2*C[4])), x])/Sqrt[x^3*C[0] + x^5*C[3] + C[4]] - (20*C[3]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^4*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/(Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*(x^3 + 2*x^5*C[3] + 2*C[4])), x])/(3*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])","F",0,0,0,0,-1,"{}"
2761,0,0,0,1.5468527,"\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","Int[((-1 + x^2)^2*(x + x^3))/(Sqrt[1 + x^4]*(1 - 2*x^2 + 4*x^4 - 2*x^6 + x^8)),x]","\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","\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,"Defer[Subst][Defer[Int][1/(Sqrt[1 + x^2]*(1 - 2*x + 4*x^2 - 2*x^3 + x^4)), x], x, x^2]/2 - Defer[Subst][Defer[Int][x/(Sqrt[1 + x^2]*(1 - 2*x + 4*x^2 - 2*x^3 + x^4)), x], x, x^2]/2 - Defer[Subst][Defer[Int][x^2/(Sqrt[1 + x^2]*(1 - 2*x + 4*x^2 - 2*x^3 + x^4)), x], x, x^2]/2 + Defer[Subst][Defer[Int][x^3/(Sqrt[1 + x^2]*(1 - 2*x + 4*x^2 - 2*x^3 + x^4)), x], x, x^2]/2","F",0,0,0,0,-1,"{}"
2762,1,672,0,1.1485208,"\int \frac{\left(-1+x+2 x^2\right) \sqrt[4]{-x^3+x^4}}{-1-x+x^2} \, dx","Int[((-1 + x + 2*x^2)*(-x^3 + x^4)^(1/4))/(-1 - x + x^2),x]","-\sqrt[4]{x^4-x^3} (1-x)+\frac{1}{2} \left(3+\sqrt{5}\right) \sqrt[4]{x^4-x^3}+\frac{1}{2} \left(3-\sqrt{5}\right) \sqrt[4]{x^4-x^3}+\frac{3}{4} \sqrt[4]{x^4-x^3}+\frac{\left(13+7 \sqrt{5}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\left(13-7 \sqrt{5}\right) \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{3 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{8 \sqrt[4]{x-1} x^{3/4}}+\frac{\left(3+\sqrt{5}\right)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{2} \sqrt[4]{x-1} x^{3/4}}-\frac{\left(3-\sqrt{5}\right)^{5/4} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{2} \sqrt[4]{x-1} x^{3/4}}+\frac{\left(13+7 \sqrt{5}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}+\frac{\left(13-7 \sqrt{5}\right) \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{4 \sqrt[4]{x-1} x^{3/4}}-\frac{3 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{8 \sqrt[4]{x-1} x^{3/4}}-\frac{\left(3+\sqrt{5}\right)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{2} \sqrt[4]{x-1} x^{3/4}}+\frac{\left(3-\sqrt{5}\right)^{5/4} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt[4]{2} \sqrt[4]{x-1} x^{3/4}}","\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,"(3*(-x^3 + x^4)^(1/4))/4 + ((3 - Sqrt[5])*(-x^3 + x^4)^(1/4))/2 + ((3 + Sqrt[5])*(-x^3 + x^4)^(1/4))/2 - (1 - x)*(-x^3 + x^4)^(1/4) - (3*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(8*(-1 + x)^(1/4)*x^(3/4)) + ((13 - 7*Sqrt[5])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((13 + 7*Sqrt[5])*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((3 + Sqrt[5])^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2^(1/4)*(-1 + x)^(1/4)*x^(3/4)) - ((3 - Sqrt[5])^(5/4)*(-x^3 + x^4)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2^(1/4)*(-1 + x)^(1/4)*x^(3/4)) - (3*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(8*(-1 + x)^(1/4)*x^(3/4)) + ((13 - 7*Sqrt[5])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) + ((13 + 7*Sqrt[5])*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(4*(-1 + x)^(1/4)*x^(3/4)) - ((3 + Sqrt[5])^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2^(1/4)*(-1 + x)^(1/4)*x^(3/4)) + ((3 - Sqrt[5])^(5/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(2^(1/4)*(-1 + x)^(1/4)*x^(3/4))","B",34,12,32,0.3750,0,"{2056, 6728, 50, 63, 240, 212, 206, 203, 101, 157, 93, 298}"
2763,0,0,0,1.3839194,"\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","Int[((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,"(x*(1 - x^6)^(1/4)*Hypergeometric2F1[1/6, 1/4, 7/6, x^6])/(-1 + x^6)^(1/4) - 3*Defer[Int][1/((-1 + x^6)^(1/4)*(1 - 2*x^6 + x^8 + x^12)), x] + 2*Defer[Int][x^4/((-1 + x^6)^(1/4)*(1 - 2*x^6 + x^8 + x^12)), x] + 3*Defer[Int][x^6/((-1 + x^6)^(1/4)*(1 - 2*x^6 + x^8 + x^12)), x] - Defer[Int][x^8/((-1 + x^6)^(1/4)*(1 - 2*x^6 + x^8 + x^12)), x] + Defer[Int][x^10/((-1 + x^6)^(1/4)*(1 - 2*x^6 + x^8 + x^12)), x]","F",0,0,0,0,-1,"{}"
2764,1,310,0,0.6119037,"\int \frac{1}{(d+c x)^2 \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[1/((d + c*x)^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\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{2 a \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{c \left(-c \left(\sqrt{a^2 x^2+b^2}+a x\right)^2-2 a d \left(\sqrt{a^2 x^2+b^2}+a x\right)+b^2 c\right)}","-\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,"(2*a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(c*(b^2*c - 2*a*d*(a*x + Sqrt[b^2 + a^2*x^2]) - c*(a*x + Sqrt[b^2 + a^2*x^2])^2)) - (a*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]]])/(Sqrt[c]*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]) + (a*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]]])/(Sqrt[c]*Sqrt[b^2*c^2 + a^2*d^2]*Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]])","A",7,6,31,0.1935,1,"{2119, 1648, 12, 707, 1093, 205}"
2765,0,0,0,0.7212605,"\int \frac{\left(1+x^2\right)^2}{\left(-1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[(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,"Defer[Int][1/Sqrt[x^2 + Sqrt[1 + x^4]], x] + Defer[Int][1/((-1 - x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((-1 + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((-1 + x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((1 + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",0,0,0,0,-1,"{}"
2766,0,0,0,12.8976927,"\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","Int[(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,"((2*a - b - c + Sqrt[4*a^2 - 4*a*(b + c) + 2*b*c*(2 - d) + b^2*d + c^2*d]/Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(2/3)*(-c + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/((-b + x)^(2/3)*(-c + x)^(2/3)*(-2*a + b*d + c*d - Sqrt[d]*Sqrt[4*a^2 - 4*a*b - 4*a*c + 4*b*c + b^2*d - 2*b*c*d + c^2*d] + 2*(1 - d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(2/3) + ((2*a - b - c - Sqrt[4*a^2 - 4*a*(b + c) + 2*b*c*(2 - d) + b^2*d + c^2*d]/Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(2/3)*(-c + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/((-b + x)^(2/3)*(-c + x)^(2/3)*(-2*a + b*d + c*d + Sqrt[d]*Sqrt[4*a^2 - 4*a*b - 4*a*c + 4*b*c + b^2*d - 2*b*c*d + c^2*d] + 2*(1 - d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(2/3)","F",0,0,0,0,-1,"{}"
2767,0,0,0,1.3552161,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(1 + x^4)/((-1 + x^4)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","\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,"Defer[Int][1/Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4], x] - (I/2)*Defer[Int][1/((I - x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] + Defer[Int][1/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]/2 - (I/2)*Defer[Int][1/((I + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - Defer[Int][1/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]/2","F",0,0,0,0,-1,"{}"
2768,0,0,0,1.2148715,"\int \frac{\left(-1+x^2\right)^2}{\left(1+x^2\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[(-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,"Defer[Int][1/Sqrt[x^2 + Sqrt[1 + x^4]], x] - Defer[Int][1/((I - x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - I*Defer[Int][1/((I - x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - Defer[Int][1/((I + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - I*Defer[Int][1/((I + x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",0,0,0,0,-1,"{}"
2769,0,0,0,11.1983966,"\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","Int[(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,"(6*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(a*b^2 - 2*a*b*(1 + b/(2*a))*x^3 + a*(1 + (2*b + d)/a)*x^6 - x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(a*b^2) + 2*a*b*(1 + b/(2*a))*x^3 - a*(1 + (2*b + d)/a)*x^6 + x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(a*b^2) + 2*a*b*(1 + b/(2*a))*x^3 - a*(1 + (2*b + d)/a)*x^6 + x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3)","F",0,0,0,0,-1,"{}"
2770,1,163,0,0.1485458,"\int \frac{-d+c x}{x \sqrt[3]{-b+a x^3}} \, dx","Int[(-d + c*x)/(x*(-b + a*x^3)^(1/3)),x]","-\frac{c \log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{2 \sqrt[3]{a}}+\frac{c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a}}+\frac{d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{2 \sqrt[3]{b}}+\frac{d \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{d \log (x)}{2 \sqrt[3]{b}}","\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,"(c*ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*a^(1/3)) + (d*ArcTan[(b^(1/3) - 2*(-b + a*x^3)^(1/3))/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*b^(1/3)) - (d*Log[x])/(2*b^(1/3)) + (d*Log[b^(1/3) + (-b + a*x^3)^(1/3)])/(2*b^(1/3)) - (c*Log[-(a^(1/3)*x) + (-b + a*x^3)^(1/3)])/(2*a^(1/3))","A",8,7,24,0.2917,1,"{1844, 239, 266, 56, 617, 204, 31}"
2771,1,350,0,1.0768389,"\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","Int[(-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{b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{a \sqrt{a^4 x^4-b^4}}-\frac{\left(2 \sqrt{-a^4} b^2-c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{4 \sqrt{2} \left(-a^4\right)^{3/4} b^3}-\frac{\left(2 \sqrt{-a^4} b^2+c^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{4 \sqrt{2} \left(-a^4\right)^{3/4} b^3}-\frac{\left(2 a^4 b^2-\sqrt{-a^4} c^2\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a^5 b \sqrt{a^4 x^4-b^4}}-\frac{\left(2 a^4 b^2+\sqrt{-a^4} c^2\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a^5 b \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,"-1/4*((2*Sqrt[-a^4]*b^2 - c^2)*ArcTan[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]])/(Sqrt[2]*(-a^4)^(3/4)*b^3) - ((2*Sqrt[-a^4]*b^2 + c^2)*ArcTanh[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]])/(4*Sqrt[2]*(-a^4)^(3/4)*b^3) + (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(a*Sqrt[-b^4 + a^4*x^4]) - ((2*a^4*b^2 - Sqrt[-a^4]*c^2)*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(4*a^5*b*Sqrt[-b^4 + a^4*x^4]) - ((2*a^4*b^2 + Sqrt[-a^4]*c^2)*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(4*a^5*b*Sqrt[-b^4 + a^4*x^4])","C",16,7,51,0.1373,1,"{6725, 224, 221, 1211, 1699, 205, 208}"
2772,0,0,0,1.4602488,"\int \frac{x^2}{\left(1-x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[x^2/((1 - x^4)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\int \frac{x^2}{\left(1-x^4\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","\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,"(-1/4*I)*Defer[Int][1/((I - x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - Defer[Int][1/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]/4 - (I/4)*Defer[Int][1/((I + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] + Defer[Int][1/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]/4","F",0,0,0,0,-1,"{}"
2773,0,0,0,14.0563066,"\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","Int[(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,"(3*a*b*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^3*(-a + x^3)^(1/3)*(-b + x^3)^(1/3))/(-a^4 + 4*a^3*x^3 - 6*a^2*(1 - (b^2*d)/(6*a^2))*x^6 + 4*a*(1 - (b*d)/(2*a))*x^9 - (1 - d)*x^12), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(2/3) + (3*(2*a - b)*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^6*(-a + x^3)^(1/3)*(-b + x^3)^(1/3))/(a^4 - 4*a^3*x^3 + 6*a^2*(1 - (b^2*d)/(6*a^2))*x^6 - 4*a*(1 - (b*d)/(2*a))*x^9 + (1 - d)*x^12), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(2/3)","F",0,0,0,0,-1,"{}"
2774,1,173,0,0.8505445,"\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","Int[((-1 + x^3)^(2/3)*(8 - 8*x^3 + x^6))/(x^6*(-4 + x^3)*(-2 + x^3)),x]","\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{4}\right)}{16 \left(1-x^3\right)^{2/3}}-\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{2}\right)}{4 \left(1-x^3\right)^{2/3}}+\frac{1}{8} \log \left(\sqrt[3]{x^3-1}-x\right)-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3-1}}+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\left(x^3-1\right)^{5/3}}{5 x^5}+\frac{\left(x^3-1\right)^{2/3}}{8 x^2}","\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 + x^3)^(2/3)/(8*x^2) + (-1 + x^3)^(5/3)/(5*x^5) + (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/4])/(16*(1 - x^3)^(2/3)) - (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/2])/(4*(1 - x^3)^(2/3)) - ArcTan[(1 + (2*x)/(-1 + x^3)^(1/3))/Sqrt[3]]/(4*Sqrt[3]) + Log[-x + (-1 + x^3)^(1/3)]/8","C",9,6,37,0.1622,0,"{6725, 264, 277, 239, 430, 429}"
2775,0,0,0,0.3962578,"\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","Int[(c + (a*x + Sqrt[-b + a^2*x^2])^(3/4))^(4/3)/Sqrt[-b + a^2*x^2],x]","\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","\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,"Defer[Int][(c + (a*x + Sqrt[-b + a^2*x^2])^(3/4))^(4/3)/Sqrt[-b + a^2*x^2], x]","F",0,0,0,0,-1,"{}"
2776,1,134,0,0.0725906,"\int \frac{1}{(-b+a x) \sqrt[3]{b^3+a^3 x^3}} \, dx","Int[1/((-b + a*x)*(b^3 + a^3*x^3)^(1/3)),x]","\frac{3 \log \left(2^{2/3} a \sqrt[3]{a^3 x^3+b^3}-a (a x+b)\right)}{4 \sqrt[3]{2} a b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (a x+b)}{\sqrt[3]{a^3 x^3+b^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} a b}-\frac{\log \left(-(b-a x)^2 (a x+b)\right)}{4 \sqrt[3]{2} a b}","\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,"-1/2*(Sqrt[3]*ArcTan[(1 + (2^(1/3)*(b + a*x))/(b^3 + a^3*x^3)^(1/3))/Sqrt[3]])/(2^(1/3)*a*b) - Log[-((b - a*x)^2*(b + a*x))]/(4*2^(1/3)*a*b) + (3*Log[-(a*(b + a*x)) + 2^(2/3)*a*(b^3 + a^3*x^3)^(1/3)])/(4*2^(1/3)*a*b)","A",1,1,25,0.04000,1,"{2148}"
2777,0,0,0,0.496038,"\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","Int[(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]","\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","\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,"Defer[Int][(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]","F",0,0,0,0,-1,"{}"
2778,0,0,0,1.1560425,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Int[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2),x]","\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","-\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$1}^2+1}\&\right]-4 \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/2 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
2779,0,0,0,0.8444574,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","Int[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2),x]","\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^2} \, dx","-\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$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,"Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/2 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
2780,1,239,0,0.6341255,"\int \frac{-b+x}{\left((-a+x) (-b+x)^2\right)^{2/3} (b-a d+(-1+d) x)} \, dx","Int[(-b + x)/(((-a + x)*(-b + x)^2)^(2/3)*(b - a*d + (-1 + d)*x)),x]","-\frac{(x-a)^{2/3} (x-b)^{4/3} \log (-a d+b-(1-d) x)}{2 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(\frac{\sqrt[3]{x-b}}{\sqrt[3]{d}}-\sqrt[3]{x-a}\right)}{2 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\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,"(Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*(-b + x)^(1/3))/(Sqrt[3]*d^(1/3)*(-a + x)^(1/3))])/((a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[b - a*d - (1 - d)*x])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + (-b + x)^(1/3)/d^(1/3)])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3))","A",2,2,36,0.05556,1,"{6719, 91}"
2781,1,44,0,1.1481139,"\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","Int[(-(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{\tan ^{-1}\left(\frac{\sqrt{c} \left(a x^2+b\right)}{\sqrt{d} \sqrt{p x^4+q}}\right)}{2 \sqrt{c} \sqrt{d}}","-\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,"-1/2*ArcTan[(Sqrt[c]*(b + a*x^2))/(Sqrt[d]*Sqrt[q + p*x^4])]/(Sqrt[c]*Sqrt[d])","A",4,4,56,0.07143,1,"{1593, 6715, 1031, 205}"
2782,0,0,0,13.3919164,"\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","Int[((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]","\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","\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,"2*a*b^2*q*Defer[Int][1/(Sqrt[q + p*x^3]*(-(b^4*c) - 4*a*b^3*c*x - 6*a^2*b^2*c*x^2 - 4*a^3*b*c*x^3 - a^4*c*x^4 - d*(q + p*x^3)^2)), x] + 4*a^2*b*q*Defer[Int][x/(Sqrt[q + p*x^3]*(-(b^4*c) - 4*a*b^3*c*x - 6*a^2*b^2*c*x^2 - 4*a^3*b*c*x^3 - a^4*c*x^4 - d*(q + p*x^3)^2)), x] - (3*b^3*p - 2*a^3*q)*Defer[Int][x^2/(Sqrt[q + p*x^3]*(-(b^4*c) - 4*a*b^3*c*x - 6*a^2*b^2*c*x^2 - 4*a^3*b*c*x^3 - a^4*c*x^4 - d*(q + p*x^3)^2)), x] + 7*a*b^2*p*Defer[Int][x^3/(Sqrt[q + p*x^3]*(b^4*c + 4*a*b^3*c*x + 6*a^2*b^2*c*x^2 + 4*a^3*b*c*x^3 + a^4*c*x^4 + d*(q + p*x^3)^2)), x] + 5*a^2*b*p*Defer[Int][x^4/(Sqrt[q + p*x^3]*(b^4*c + 4*a*b^3*c*x + 6*a^2*b^2*c*x^2 + 4*a^3*b*c*x^3 + a^4*c*x^4 + d*(q + p*x^3)^2)), x] + a^3*p*Defer[Int][x^5/(Sqrt[q + p*x^3]*(b^4*c + 4*a*b^3*c*x + 6*a^2*b^2*c*x^2 + 4*a^3*b*c*x^3 + a^4*c*x^4 + d*(q + p*x^3)^2)), x]","F",0,0,0,0,-1,"{}"
2783,0,0,0,3.8570106,"\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","Int[((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{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{\left(x^2-1\right) \sqrt{\sqrt{x^2+1}+x}}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/2","F",0,0,0,0,-1,"{}"
2784,0,0,0,3.288772,"\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[((1 + x^2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^2\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{\left(x^2-1\right) \sqrt{\sqrt{x^2+1}+x}}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/2","F",0,0,0,0,-1,"{}"
2785,1,583,0,5.9630011,"\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","Int[(-1 + k^4*x^4)/(Sqrt[(1 - x)*x*(1 - k^2*x)]*(a + b*x^2 + a*k^4*x^4)),x]","\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{\sqrt{2} \sqrt{a}}{\sqrt{-b-\sqrt{b^2-4 a^2 k^4}}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{a \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{\sqrt{2} \sqrt{a}}{\sqrt{-b-\sqrt{b^2-4 a^2 k^4}}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{a \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(-\frac{\sqrt{2} \sqrt{a}}{\sqrt{\sqrt{b^2-4 a^2 k^4}-b}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{a \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \Pi \left(\frac{\sqrt{2} \sqrt{a}}{\sqrt{\sqrt{b^2-4 a^2 k^4}-b}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{a \sqrt{-k^2} \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{a \sqrt{(1-x) x \left(1-k^2 x\right)}}","-\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,"(2*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/(a*Sqrt[(1 - x)*x*(1 - k^2*x)]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-((Sqrt[2]*Sqrt[a])/Sqrt[-b - Sqrt[b^2 - 4*a^2*k^4]]), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(a*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(Sqrt[2]*Sqrt[a])/Sqrt[-b - Sqrt[b^2 - 4*a^2*k^4]], ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(a*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[-((Sqrt[2]*Sqrt[a])/Sqrt[-b + Sqrt[b^2 - 4*a^2*k^4]]), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(a*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) + ((1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(Sqrt[2]*Sqrt[a])/Sqrt[-b + Sqrt[b^2 - 4*a^2*k^4]], ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/(a*Sqrt[-k^2]*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",28,10,46,0.2174,0,"{6718, 6688, 6728, 714, 115, 6725, 934, 12, 168, 537}"
2786,0,0,0,2.9652674,"\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","Int[(x^5*(-4*a + 3*x))/((x^2*(-a + x))^(1/3)*(-a^2 + 2*a*x - x^2 + d*x^8)),x]","\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","-\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,"(12*a*x^(2/3)*(-a + x)^(1/3)*Defer[Subst][Defer[Int][x^15/((-a + x^3)^(1/3)*(a^2 - 2*a*x^3 + x^6 - d*x^24)), x], x, x^(1/3)])/(-((a - x)*x^2))^(1/3) + (9*x^(2/3)*(-a + x)^(1/3)*Defer[Subst][Defer[Int][x^18/((-a + x^3)^(1/3)*(-a^2 + 2*a*x^3 - x^6 + d*x^24)), x], x, x^(1/3)])/(-((a - x)*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2787,1,41,0,0.007342,"\int \frac{\sqrt{1-x}}{8 (1+x)^{7/2}} \, dx","Int[Sqrt[1 - x]/(8*(1 + x)^(7/2)),x]","-\frac{(1-x)^{3/2}}{120 (x+1)^{3/2}}-\frac{(1-x)^{3/2}}{40 (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,"-1/40*(1 - x)^(3/2)/(1 + x)^(5/2) - (1 - x)^(3/2)/(120*(1 + x)^(3/2))","A",3,3,20,0.1500,1,"{12, 45, 37}"
2788,0,0,0,15.3085416,"\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","Int[(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,"(6*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(a*b^2*d - 2*a*b*(1 + b/(2*a))*d*x^3 + (1 + (a + 2*b)*d)*x^6 - d*x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(a*b^2*d) + 2*a*b*(1 + b/(2*a))*d*x^3 - (1 + (a + 2*b)*d)*x^6 + d*x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(a*b^2*d) + 2*a*b*(1 + b/(2*a))*d*x^3 - (1 + (a + 2*b)*d)*x^6 + d*x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3)","F",0,0,0,0,-1,"{}"
2789,1,436,0,0.454091,"\int \frac{\left(-x+x^2\right) \sqrt[4]{-x^3+x^4}}{-1-x+x^2} \, dx","Int[((-x + x^2)*(-x^3 + x^4)^(1/4))/(-1 - x + x^2),x]","-\frac{1}{2} \sqrt[4]{x^4-x^3} (1-x)+\frac{3}{8} \sqrt[4]{x^4-x^3}+\frac{29 \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{16 \sqrt[4]{x-1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{3+\sqrt{5}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{5} \sqrt[4]{x-1} x^{3/4}}+\frac{2^{3/4} \sqrt[4]{3-\sqrt{5}} \sqrt[4]{x^4-x^3} \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{5} \sqrt[4]{x-1} x^{3/4}}+\frac{29 \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{x}}\right)}{16 \sqrt[4]{x-1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{3+\sqrt{5}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{2}{3+\sqrt{5}}} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{5} \sqrt[4]{x-1} x^{3/4}}-\frac{2^{3/4} \sqrt[4]{3-\sqrt{5}} \sqrt[4]{x^4-x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \sqrt[4]{x}}{\sqrt[4]{x-1}}\right)}{\sqrt{5} \sqrt[4]{x-1} x^{3/4}}","\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,"(3*(-x^3 + x^4)^(1/4))/8 - ((1 - x)*(-x^3 + x^4)^(1/4))/2 + (29*(-x^3 + x^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/x^(1/4)])/(16*(-1 + x)^(1/4)*x^(3/4)) + (2^(3/4)*(3 + Sqrt[5])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[5]*(-1 + x)^(1/4)*x^(3/4)) + (2^(3/4)*(3 - Sqrt[5])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTan[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[5]*(-1 + x)^(1/4)*x^(3/4)) + (29*(-x^3 + x^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/x^(1/4)])/(16*(-1 + x)^(1/4)*x^(3/4)) - (2^(3/4)*(3 + Sqrt[5])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[((2/(3 + Sqrt[5]))^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[5]*(-1 + x)^(1/4)*x^(3/4)) - (2^(3/4)*(3 - Sqrt[5])^(1/4)*(-x^3 + x^4)^(1/4)*ArcTanh[(((3 + Sqrt[5])/2)^(1/4)*x^(1/4))/(-1 + x)^(1/4)])/(Sqrt[5]*(-1 + x)^(1/4)*x^(3/4))","A",26,13,31,0.4194,0,"{1593, 2056, 903, 50, 63, 240, 212, 206, 203, 905, 911, 93, 298}"
2790,1,790,0,5.7174321,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Int[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","8 d^2 \sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\frac{\sqrt{b} \left(\sqrt{b}-c\right) \log \left(-\sqrt{2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\sqrt{\sqrt{a x+b}+c}+\sqrt{\sqrt{b}-c+d^2}+d\right)}{\sqrt{2} \sqrt{\sqrt{b}-c+d^2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d}}+\frac{\sqrt{b} \left(\sqrt{b}-c\right) \log \left(\sqrt{2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\sqrt{\sqrt{a x+b}+c}+\sqrt{\sqrt{b}-c+d^2}+d\right)}{\sqrt{2} \sqrt{\sqrt{b}-c+d^2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d}}+\frac{\sqrt{2} \sqrt{b} \left(\sqrt{b}-c\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{b}-c+d^2}+d}-\sqrt{2} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{\sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}\right)}{\sqrt{\sqrt{b}-c+d^2} \sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}-\frac{\sqrt{2} \sqrt{b} \left(\sqrt{b}-c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\sqrt{\sqrt{\sqrt{b}-c+d^2}+d}}{\sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}\right)}{\sqrt{\sqrt{b}-c+d^2} \sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}+\frac{8}{5} \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{5/2}-\frac{16}{3} d \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{3/2}-\frac{2 \sqrt{b} \sqrt{\sqrt{b}+c} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{\sqrt{\sqrt{\sqrt{b}+c}-d}}\right)}{\sqrt{\sqrt{\sqrt{b}+c}-d}}-\frac{2 \sqrt{b} \sqrt{\sqrt{b}+c} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{\sqrt{\sqrt{\sqrt{b}+c}+d}}\right)}{\sqrt{\sqrt{\sqrt{b}+c}+d}}","-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,"8*d^2*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - (16*d*(d + Sqrt[c + Sqrt[b + a*x]])^(3/2))/3 + (8*(d + Sqrt[c + Sqrt[b + a*x]])^(5/2))/5 - (2*Sqrt[b]*Sqrt[Sqrt[b] + c]*ArcTan[Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]/Sqrt[Sqrt[Sqrt[b] + c] - d]])/Sqrt[Sqrt[Sqrt[b] + c] - d] - (2*Sqrt[b]*Sqrt[Sqrt[b] + c]*ArcTanh[Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]/Sqrt[Sqrt[Sqrt[b] + c] + d]])/Sqrt[Sqrt[Sqrt[b] + c] + d] + (Sqrt[2]*Sqrt[b]*(Sqrt[b] - c)*ArcTanh[(Sqrt[d + Sqrt[Sqrt[b] - c + d^2]] - Sqrt[2]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]])/Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]])/(Sqrt[Sqrt[b] - c + d^2]*Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]) - (Sqrt[2]*Sqrt[b]*(Sqrt[b] - c)*ArcTanh[(Sqrt[d + Sqrt[Sqrt[b] - c + d^2]] + Sqrt[2]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]])/Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]])/(Sqrt[Sqrt[b] - c + d^2]*Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]) - (Sqrt[b]*(Sqrt[b] - c)*Log[d + Sqrt[Sqrt[b] - c + d^2] + Sqrt[c + Sqrt[b + a*x]] - Sqrt[2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/(Sqrt[2]*Sqrt[Sqrt[b] - c + d^2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]]) + (Sqrt[b]*(Sqrt[b] - c)*Log[d + Sqrt[Sqrt[b] - c + d^2] + Sqrt[c + Sqrt[b + a*x]] + Sqrt[2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/(Sqrt[2]*Sqrt[Sqrt[b] - c + d^2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]])","B",26,13,49,0.2653,1,"{1593, 6740, 194, 6688, 12, 1988, 1093, 204, 206, 1094, 634, 618, 628}"
2791,1,790,0,5.0812339,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Int[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","8 d^2 \sqrt{\sqrt{\sqrt{a x+b}+c}+d}-\frac{\sqrt{b} \left(\sqrt{b}-c\right) \log \left(-\sqrt{2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\sqrt{\sqrt{a x+b}+c}+\sqrt{\sqrt{b}-c+d^2}+d\right)}{\sqrt{2} \sqrt{\sqrt{b}-c+d^2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d}}+\frac{\sqrt{b} \left(\sqrt{b}-c\right) \log \left(\sqrt{2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\sqrt{\sqrt{a x+b}+c}+\sqrt{\sqrt{b}-c+d^2}+d\right)}{\sqrt{2} \sqrt{\sqrt{b}-c+d^2} \sqrt{\sqrt{\sqrt{b}-c+d^2}+d}}+\frac{\sqrt{2} \sqrt{b} \left(\sqrt{b}-c\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{b}-c+d^2}+d}-\sqrt{2} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{\sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}\right)}{\sqrt{\sqrt{b}-c+d^2} \sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}-\frac{\sqrt{2} \sqrt{b} \left(\sqrt{b}-c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{\sqrt{a x+b}+c}+d}+\sqrt{\sqrt{\sqrt{b}-c+d^2}+d}}{\sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}\right)}{\sqrt{\sqrt{b}-c+d^2} \sqrt{d-\sqrt{\sqrt{b}-c+d^2}}}+\frac{8}{5} \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{5/2}-\frac{16}{3} d \left(\sqrt{\sqrt{a x+b}+c}+d\right)^{3/2}-\frac{2 \sqrt{b} \sqrt{\sqrt{b}+c} \tan ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{\sqrt{\sqrt{\sqrt{b}+c}-d}}\right)}{\sqrt{\sqrt{\sqrt{b}+c}-d}}-\frac{2 \sqrt{b} \sqrt{\sqrt{b}+c} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{\sqrt{a x+b}+c}+d}}{\sqrt{\sqrt{\sqrt{b}+c}+d}}\right)}{\sqrt{\sqrt{\sqrt{b}+c}+d}}","-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,"8*d^2*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]] - (16*d*(d + Sqrt[c + Sqrt[b + a*x]])^(3/2))/3 + (8*(d + Sqrt[c + Sqrt[b + a*x]])^(5/2))/5 - (2*Sqrt[b]*Sqrt[Sqrt[b] + c]*ArcTan[Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]/Sqrt[Sqrt[Sqrt[b] + c] - d]])/Sqrt[Sqrt[Sqrt[b] + c] - d] - (2*Sqrt[b]*Sqrt[Sqrt[b] + c]*ArcTanh[Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]/Sqrt[Sqrt[Sqrt[b] + c] + d]])/Sqrt[Sqrt[Sqrt[b] + c] + d] + (Sqrt[2]*Sqrt[b]*(Sqrt[b] - c)*ArcTanh[(Sqrt[d + Sqrt[Sqrt[b] - c + d^2]] - Sqrt[2]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]])/Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]])/(Sqrt[Sqrt[b] - c + d^2]*Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]) - (Sqrt[2]*Sqrt[b]*(Sqrt[b] - c)*ArcTanh[(Sqrt[d + Sqrt[Sqrt[b] - c + d^2]] + Sqrt[2]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]])/Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]])/(Sqrt[Sqrt[b] - c + d^2]*Sqrt[d - Sqrt[Sqrt[b] - c + d^2]]) - (Sqrt[b]*(Sqrt[b] - c)*Log[d + Sqrt[Sqrt[b] - c + d^2] + Sqrt[c + Sqrt[b + a*x]] - Sqrt[2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/(Sqrt[2]*Sqrt[Sqrt[b] - c + d^2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]]) + (Sqrt[b]*(Sqrt[b] - c)*Log[d + Sqrt[Sqrt[b] - c + d^2] + Sqrt[c + Sqrt[b + a*x]] + Sqrt[2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]]*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/(Sqrt[2]*Sqrt[Sqrt[b] - c + d^2]*Sqrt[d + Sqrt[Sqrt[b] - c + d^2]])","B",26,13,49,0.2653,1,"{1593, 6740, 194, 6688, 12, 1988, 1093, 204, 206, 1094, 634, 618, 628}"
2792,0,0,0,0.0777135,"\int \frac{1}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","\int \frac{1}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","\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,"Defer[Int][1/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]], x]","F",0,0,0,0,-1,"{}"
2793,0,0,0,21.234807,"\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","Int[((-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,"(6*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][(x^3*(1 - x^3)^(1/3)*(1 - k*x^3)^(1/3))/(x^12 - b*(-1 + x^3)^2*(-1 + k*x^3)^2), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) + (3*(1 + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][(x^6*(1 - x^3)^(1/3)*(1 - k*x^3)^(1/3))/(-x^12 + b*(-1 + x^3)^2*(-1 + k*x^3)^2), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2794,0,0,0,10.2605888,"\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","Int[((-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,"(6*(2 - k)*(-1 + x)^(2/3)*x^(2/3)*(-1 + k*x)^(2/3)*Defer[Subst][Defer[Int][(x^3*(-1 + x^3)^(7/3))/((-1 + k*x^3)^(2/3)*(-x^3 + k*x^6 - b*(-1 + x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) - (9*k*(-1 + x)^(2/3)*x^(2/3)*(-1 + k*x)^(2/3)*Defer[Subst][Defer[Int][(x^6*(-1 + x^3)^(7/3))/((-1 + k*x^3)^(2/3)*(-x^3 + k*x^6 - b*(-1 + x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3) - (3*(-1 + x)^(2/3)*x^(2/3)*(-1 + k*x)^(2/3)*Defer[Subst][Defer[Int][(-1 + x^3)^(7/3)/((-1 + k*x^3)^(2/3)*(x^3 - k*x^6 + b*(-1 + x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2795,1,1308,0,8.7473268,"\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","Int[((2*b + a*x^4)^(1/4)*(-4*b + a*x^8))/(x^6*(-4*b + c*x^4 + a*x^8)),x]","\frac{a c^2 \sqrt[4]{a x^4+2 b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{2 a x^4}{c-\sqrt{c^2+16 a b}},-\frac{a x^4}{2 b}\right) x^3}{3\ 2^{3/4} b \left(16 a b+c \left(c-\sqrt{c^2+16 a b}\right)\right) \sqrt[4]{\frac{a x^4}{b}+2}}+\frac{a c^2 \sqrt[4]{a x^4+2 b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{2 a x^4}{c+\sqrt{c^2+16 a b}},-\frac{a x^4}{2 b}\right) x^3}{3\ 2^{3/4} b \left(16 a b+c \left(c+\sqrt{c^2+16 a b}\right)\right) \sqrt[4]{\frac{a x^4}{b}+2}}-\frac{\sqrt[4]{a} (2 b-c) c \left(\sqrt{c^2+16 a b}-c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{a^{5/4} c \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{\sqrt{c^2+16 a b}-c} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{\sqrt[4]{a} (2 b-c) c \left(c+\sqrt{c^2+16 a b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{a^{5/4} c \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{c+\sqrt{c^2+16 a b}} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{\sqrt[4]{a} (2 b-c) c \left(\sqrt{c^2+16 a b}-c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{a^{5/4} c \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{\sqrt{c^2+16 a b}-c} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{\sqrt[4]{a} (2 b-c) c \left(c+\sqrt{c^2+16 a b}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{a^{5/4} c \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{c+\sqrt{c^2+16 a b}} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{c \sqrt[4]{a x^4+2 b}}{4 b x}-\frac{\left(a x^4+2 b\right)^{5/4}}{10 b x^5}","\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,"-1/4*(c*(2*b + a*x^4)^(1/4))/(b*x) - (2*b + a*x^4)^(5/4)/(10*b*x^5) + (a*c^2*x^3*(2*b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-2*a*x^4)/(c - Sqrt[16*a*b + c^2]), -1/2*(a*x^4)/b])/(3*2^(3/4)*b*(16*a*b + c*(c - Sqrt[16*a*b + c^2]))*(2 + (a*x^4)/b)^(1/4)) + (a*c^2*x^3*(2*b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-2*a*x^4)/(c + Sqrt[16*a*b + c^2]), -1/2*(a*x^4)/b])/(3*2^(3/4)*b*(16*a*b + c*(c + Sqrt[16*a*b + c^2]))*(2 + (a*x^4)/b)^(1/4)) - (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) - (a^(1/4)*(2*b - c)*c*(-c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) - (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(1/4)*(2*b - c)*c*(c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(1/4)*(2*b - c)*c*(-c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4)) - (a^(1/4)*(2*b - c)*c*(c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4))","B",43,14,42,0.3333,0,"{6728, 264, 277, 331, 298, 203, 206, 1528, 511, 510, 1518, 494, 205, 208}"
2796,1,1308,0,8.2396939,"\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","Int[((2*b + a*x^4)^(1/4)*(-4*b + a*x^8))/(x^6*(-4*b + c*x^4 + a*x^8)),x]","\frac{a c^2 \sqrt[4]{a x^4+2 b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{2 a x^4}{c-\sqrt{c^2+16 a b}},-\frac{a x^4}{2 b}\right) x^3}{3\ 2^{3/4} b \left(16 a b+c \left(c-\sqrt{c^2+16 a b}\right)\right) \sqrt[4]{\frac{a x^4}{b}+2}}+\frac{a c^2 \sqrt[4]{a x^4+2 b} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{2 a x^4}{c+\sqrt{c^2+16 a b}},-\frac{a x^4}{2 b}\right) x^3}{3\ 2^{3/4} b \left(16 a b+c \left(c+\sqrt{c^2+16 a b}\right)\right) \sqrt[4]{\frac{a x^4}{b}+2}}-\frac{\sqrt[4]{a} (2 b-c) c \left(\sqrt{c^2+16 a b}-c\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{a^{5/4} c \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{\sqrt{c^2+16 a b}-c} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{\sqrt[4]{a} (2 b-c) c \left(c+\sqrt{c^2+16 a b}\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{a^{5/4} c \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{c+\sqrt{c^2+16 a b}} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{\sqrt[4]{a} (2 b-c) c \left(\sqrt{c^2+16 a b}-c\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{a^{5/4} c \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{4 b-c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{\sqrt{c^2+16 a b}-c} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{\sqrt{c^2+16 a b}-c} \left(4 b-c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{\sqrt[4]{a} (2 b-c) c \left(c+\sqrt{c^2+16 a b}\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{8 b \sqrt{c^2+16 a b} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}+\frac{a^{5/4} c \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{-4 b+c+\sqrt{c^2+16 a b}} x}{\sqrt[4]{c+\sqrt{c^2+16 a b}} \sqrt[4]{a x^4+2 b}}\right)}{\sqrt{c^2+16 a b} \sqrt[4]{c+\sqrt{c^2+16 a b}} \left(-4 b+c+\sqrt{c^2+16 a b}\right)^{3/4}}-\frac{c \sqrt[4]{a x^4+2 b}}{4 b x}-\frac{\left(a x^4+2 b\right)^{5/4}}{10 b x^5}","\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,"-1/4*(c*(2*b + a*x^4)^(1/4))/(b*x) - (2*b + a*x^4)^(5/4)/(10*b*x^5) + (a*c^2*x^3*(2*b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-2*a*x^4)/(c - Sqrt[16*a*b + c^2]), -1/2*(a*x^4)/b])/(3*2^(3/4)*b*(16*a*b + c*(c - Sqrt[16*a*b + c^2]))*(2 + (a*x^4)/b)^(1/4)) + (a*c^2*x^3*(2*b + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (-2*a*x^4)/(c + Sqrt[16*a*b + c^2]), -1/2*(a*x^4)/b])/(3*2^(3/4)*b*(16*a*b + c*(c + Sqrt[16*a*b + c^2]))*(2 + (a*x^4)/b)^(1/4)) - (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) - (a^(1/4)*(2*b - c)*c*(-c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) - (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(1/4)*(2*b - c)*c*(c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(-c + Sqrt[16*a*b + c^2])^(1/4)*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(1/4)*(2*b - c)*c*(-c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(4*b - c + Sqrt[16*a*b + c^2])^(3/4)) + (a^(5/4)*c*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)*(2*b + a*x^4)^(1/4))])/(Sqrt[16*a*b + c^2]*(c + Sqrt[16*a*b + c^2])^(1/4)*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4)) - (a^(1/4)*(2*b - c)*c*(c + Sqrt[16*a*b + c^2])^(3/4)*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)*(2*b + a*x^4)^(1/4))])/(8*b*Sqrt[16*a*b + c^2]*(-4*b + c + Sqrt[16*a*b + c^2])^(3/4))","B",43,14,42,0.3333,0,"{6728, 264, 277, 331, 298, 203, 206, 1528, 511, 510, 1518, 494, 205, 208}"
2797,1,1043,0,9.286656,"\int \frac{-b^{12}+a^{12} x^{12}}{\sqrt{-b^4+a^4 x^4} \left(b^{12}+a^{12} x^{12}\right)} \, dx","Int[(-b^12 + a^12*x^12)/(Sqrt[-b^4 + a^4*x^4]*(b^12 + a^12*x^12)),x]","-\frac{(-1)^{2/3} \left(a^2-(-1)^{2/3} \sqrt[6]{-a^{12}}\right) \left(\sqrt[3]{-1} a^8-(-1)^{2/3} \sqrt[3]{-a^{12}} a^4-\left(-a^{12}\right)^{2/3}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{6 a^{11} \sqrt{a^4 x^4-b^4}}-\frac{(-1)^{2/3} \left(a^2+(-1)^{2/3} \sqrt[6]{-a^{12}}\right) \left(\sqrt[3]{-1} a^8-(-1)^{2/3} \sqrt[3]{-a^{12}} a^4-\left(-a^{12}\right)^{2/3}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{6 a^{11} \sqrt{a^4 x^4-b^4}}+\frac{\left(a^2-\sqrt[6]{-a^{12}}\right) \left(a^8+\sqrt[3]{-a^{12}} a^4+\left(-a^{12}\right)^{2/3}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{6 a^{11} \sqrt{a^4 x^4-b^4}}+\frac{\left(a^2+\sqrt[6]{-a^{12}}\right) \left(a^8+\sqrt[3]{-a^{12}} a^4+\left(-a^{12}\right)^{2/3}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{6 a^{11} \sqrt{a^4 x^4-b^4}}-\frac{\sqrt[3]{-1} \left(a^2-\sqrt[3]{-1} \sqrt[6]{-a^{12}}\right) \left((-1)^{2/3} a^8+\left(-a^{12}\right)^{2/3}+\frac{\sqrt[3]{-1} \left(-a^{12}\right)^{4/3}}{a^8}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{6 a^{11} \sqrt{a^4 x^4-b^4}}-\frac{\sqrt[3]{-1} \left(a^2+\sqrt[3]{-1} \sqrt[6]{-a^{12}}\right) \left((-1)^{2/3} a^8+\left(-a^{12}\right)^{2/3}+\frac{\sqrt[3]{-1} \left(-a^{12}\right)^{4/3}}{a^8}\right) b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{6 a^{11} \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{a^{10}}{\left(-a^{12}\right)^{5/6}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt[3]{-1} a^{10}}{\left(-a^{12}\right)^{5/6}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{(-1)^{2/3} a^{10}}{\left(-a^{12}\right)^{5/6}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt[6]{-a^{12}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt[3]{-1} \sqrt[6]{-a^{12}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{(-1)^{2/3} \sqrt[6]{-a^{12}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \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,"-1/6*((-1)^(2/3)*(a^2 - (-1)^(2/3)*(-a^12)^(1/6))*((-1)^(1/3)*a^8 - (-1)^(2/3)*a^4*(-a^12)^(1/3) - (-a^12)^(2/3))*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(a^11*Sqrt[-b^4 + a^4*x^4]) - ((-1)^(2/3)*(a^2 + (-1)^(2/3)*(-a^12)^(1/6))*((-1)^(1/3)*a^8 - (-1)^(2/3)*a^4*(-a^12)^(1/3) - (-a^12)^(2/3))*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(6*a^11*Sqrt[-b^4 + a^4*x^4]) + ((a^2 - (-a^12)^(1/6))*(a^8 + a^4*(-a^12)^(1/3) + (-a^12)^(2/3))*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(6*a^11*Sqrt[-b^4 + a^4*x^4]) + ((a^2 + (-a^12)^(1/6))*(a^8 + a^4*(-a^12)^(1/3) + (-a^12)^(2/3))*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(6*a^11*Sqrt[-b^4 + a^4*x^4]) - ((-1)^(1/3)*(a^2 - (-1)^(1/3)*(-a^12)^(1/6))*((-1)^(2/3)*a^8 + (-a^12)^(2/3) + ((-1)^(1/3)*(-a^12)^(4/3))/a^8)*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(6*a^11*Sqrt[-b^4 + a^4*x^4]) - ((-1)^(1/3)*(a^2 + (-1)^(1/3)*(-a^12)^(1/6))*((-1)^(2/3)*a^8 + (-a^12)^(2/3) + ((-1)^(1/3)*(-a^12)^(4/3))/a^8)*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(6*a^11*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[a^10/(-a^12)^(5/6), ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[((-1)^(1/3)*a^10)/(-a^12)^(5/6), ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[((-1)^(2/3)*a^10)/(-a^12)^(5/6), ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-a^12)^(1/6)/a^2, ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[((-1)^(1/3)*(-a^12)^(1/6))/a^2, ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[((-1)^(2/3)*(-a^12)^(1/6))/a^2, ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4])","C",207,18,44,0.4091,1,"{1586, 6725, 1729, 1209, 1201, 224, 221, 1200, 1199, 424, 1219, 1218, 1248, 735, 844, 217, 206, 725}"
2798,0,0,0,0.9515261,"\int \frac{1}{1-(1+x) \sqrt{c+b x+a x^2}} \, dx","Int[(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{$\#$1}^4 \left(-\sqrt{a}\right)+2 \text{$\#$1}^3 a+\text{$\#$1}^3 b-3 \text{$\#$1}^2 \sqrt{a} b-4 \text{$\#$1}^2 a+4 \text{$\#$1} \sqrt{a} b+2 \text{$\#$1} a c+\text{$\#$1} b^2-\text{$\#$1} b c-\sqrt{a} b c+\sqrt{a} c^2-b^2\&,\frac{\text{$\#$1}^2 \sqrt{a} \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1} b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{-4 \text{$\#$1}^3 \sqrt{a}+6 \text{$\#$1}^2 a+3 \text{$\#$1}^2 b-6 \text{$\#$1} \sqrt{a} b-8 \text{$\#$1} a+4 \sqrt{a} b+2 a c+b^2-b c}\&\right]",1,"Defer[Int][(1 - c - (b + 2*c)*x - (a + 2*b + c)*x^2 - (2*a + b)*x^3 - a*x^4)^(-1), x] + Defer[Int][Sqrt[c + b*x + a*x^2]/(1 - c - (b + 2*c)*x - (a + 2*b + c)*x^2 - (2*a + b)*x^3 - a*x^4), x] + Defer[Int][(x*Sqrt[c + b*x + a*x^2])/(1 - c - (b + 2*c)*x - (a + 2*b + c)*x^2 - (2*a + b)*x^3 - a*x^4), x]","F",0,0,0,0,-1,"{}"
2799,1,597,0,2.0318533,"\int \frac{\left(1-x^4\right) \sqrt[4]{1-x-4 x^2+4 x^3+6 x^4-6 x^5-4 x^6+4 x^7+x^8-x^9}}{1+x^4} \, dx","Int[((1 - x^4)*(1 - x - 4*x^2 + 4*x^3 + 6*x^4 - 6*x^5 - 4*x^6 + 4*x^7 + x^8 - x^9)^(1/4))/(1 + x^4),x]","-\frac{4 \sqrt[4]{(1-x)^5 (x+1)^4} (1-x)^2}{13 (x+1)}+\frac{8 \sqrt[4]{(1-x)^5 (x+1)^4} (1-x)}{9 (x+1)}+\frac{\sqrt[4]{-4-(2+2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right)}{(x-1)^{5/4} (x+1)}-\frac{\sqrt[4]{-4+(2+2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{\sqrt[4]{-1}-1}}\right)}{(x-1)^{5/4} (x+1)}-\frac{\sqrt[4]{-4+(2-2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{-1-(-1)^{3/4}}}\right)}{(x-1)^{5/4} (x+1)}+\frac{\sqrt[4]{-4-(2-2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tan ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{(-1)^{3/4}-1}}\right)}{(x-1)^{5/4} (x+1)}+\frac{\sqrt[4]{-4-(2+2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{-1-\sqrt[4]{-1}}}\right)}{(x-1)^{5/4} (x+1)}-\frac{\sqrt[4]{-4+(2+2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{\sqrt[4]{-1}-1}}\right)}{(x-1)^{5/4} (x+1)}-\frac{\sqrt[4]{-4+(2-2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{-1-(-1)^{3/4}}}\right)}{(x-1)^{5/4} (x+1)}+\frac{\sqrt[4]{-4-(2-2 i) \sqrt{2}} \sqrt[4]{(1-x)^5 (x+1)^4} \tanh ^{-1}\left(\frac{\sqrt[4]{x-1}}{\sqrt[4]{(-1)^{3/4}-1}}\right)}{(x-1)^{5/4} (x+1)}","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^{16}-4 \text{$\#$1}^{12}+6 \text{$\#$1}^8-4 \text{$\#$1}^4+2\&,\frac{\text{$\#$1}^9 \left(-\log \left(x^2-1\right)\right)+\text{$\#$1}^9 \log \left(-\text{$\#$1} x^2+\text{$\#$1}+\sqrt[4]{-x^9+x^8+4 x^7-4 x^6-6 x^5+6 x^4+4 x^3-4 x^2-x+1}\right)+2 \text{$\#$1}^5 \log \left(x^2-1\right)-2 \text{$\#$1}^5 \log \left(-\text{$\#$1} x^2+\text{$\#$1}+\sqrt[4]{-x^9+x^8+4 x^7-4 x^6-6 x^5+6 x^4+4 x^3-4 x^2-x+1}\right)}{\text{$\#$1}^{12}-3 \text{$\#$1}^8+3 \text{$\#$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,"(8*(1 - x)*((1 - x)^5*(1 + x)^4)^(1/4))/(9*(1 + x)) - (4*(1 - x)^2*((1 - x)^5*(1 + x)^4)^(1/4))/(13*(1 + x)) + ((-4 - (2 + 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x)) - ((-4 + (2 + 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/(-1 + (-1)^(1/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x)) - ((-4 + (2 - 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/(-1 - (-1)^(3/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x)) + ((-4 - (2 - 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTan[(-1 + x)^(1/4)/(-1 + (-1)^(3/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x)) + ((-4 - (2 + 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/(-1 - (-1)^(1/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x)) - ((-4 + (2 + 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/(-1 + (-1)^(1/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x)) - ((-4 + (2 - 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/(-1 - (-1)^(3/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x)) + ((-4 - (2 - 2*I)*Sqrt[2])^(1/4)*((1 - x)^5*(1 + x)^4)^(1/4)*ArcTanh[(-1 + x)^(1/4)/(-1 + (-1)^(3/4))^(1/4)])/((-1 + x)^(5/4)*(1 + x))","C",27,9,62,0.1452,0,"{6688, 6719, 1731, 6740, 194, 212, 206, 203, 1972}"
2800,0,0,0,7.4820928,"\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","Int[(-(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,"(-3*(a - 5*b)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^4/((a - b + x^3)^(1/3)*(a*(1 - b/a) + x^3 - d*x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) + (12*a*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^4/((a - b + x^3)^(1/3)*(-(a*(1 - b/a)) - x^3 + d*x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) + (12*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^7/((a - b + x^3)^(1/3)*(-(a*(1 - b/a)) - x^3 + d*x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3)","F",0,0,0,0,-1,"{}"
2801,1,559,0,0.8598081,"\int \frac{1+x^8}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Int[(1 + x^8)/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","-\frac{x (x+1) \left(\frac{1-x}{x+1}\right)^{5/4} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{3}{2};\frac{2 x}{x+1}\right)}{2 (1-x) \sqrt[4]{x^4-x^2}}-\frac{x \sqrt[4]{\frac{1-x}{x+1}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{2 x}{x+1}\right)}{2 \sqrt[4]{x^4-x^2}}+\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}+\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}","\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,"(Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4)) + (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (2*x)/(1 + x)])/(2*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(5/4)*(1 + x)*Hypergeometric2F1[1/2, 5/4, 3/2, (2*x)/(1 + x)])/(2*(1 - x)*(-x^2 + x^4)^(1/4))","C",27,12,26,0.4615,1,"{2056, 6715, 6725, 240, 212, 206, 203, 2073, 1152, 380, 377, 1429}"
2802,1,559,0,0.749245,"\int \frac{1+x^8}{\sqrt[4]{-x^2+x^4} \left(-1+x^8\right)} \, dx","Int[(1 + x^8)/((-x^2 + x^4)^(1/4)*(-1 + x^8)),x]","-\frac{x (x+1) \left(\frac{1-x}{x+1}\right)^{5/4} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{3}{2};\frac{2 x}{x+1}\right)}{2 (1-x) \sqrt[4]{x^4-x^2}}-\frac{x \sqrt[4]{\frac{1-x}{x+1}} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{3}{2};\frac{2 x}{x+1}\right)}{2 \sqrt[4]{x^4-x^2}}+\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}+\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{\sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1-i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1-i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{1+i} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{1+i} \sqrt[4]{x^4-x^2}}-\frac{\sqrt{x} \sqrt[4]{x^2-1} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{x}}{\sqrt[4]{x^2-1}}\right)}{2 \sqrt[4]{2} \sqrt[4]{x^4-x^2}}","\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,"(Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTan[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4)) + (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[Sqrt[x]/(-1 + x^2)^(1/4)])/(-x^2 + x^4)^(1/4) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 - I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 - I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[((1 + I)^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*(1 + I)^(1/4)*(-x^2 + x^4)^(1/4)) - (Sqrt[x]*(-1 + x^2)^(1/4)*ArcTanh[(2^(1/4)*Sqrt[x])/(-1 + x^2)^(1/4)])/(2*2^(1/4)*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(1/4)*Hypergeometric2F1[1/4, 1/2, 3/2, (2*x)/(1 + x)])/(2*(-x^2 + x^4)^(1/4)) - (x*((1 - x)/(1 + x))^(5/4)*(1 + x)*Hypergeometric2F1[1/2, 5/4, 3/2, (2*x)/(1 + x)])/(2*(1 - x)*(-x^2 + x^4)^(1/4))","C",27,12,26,0.4615,1,"{2056, 6715, 6725, 240, 212, 206, 203, 2073, 1152, 380, 377, 1429}"
2803,1,513,0,1.128458,"\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","Int[(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{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 \left(1-\sqrt{d}\right) \left(a+b \sqrt{d}\right)-2 (1-d) x\right)}{4 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 (1-d) x-2 \left(\sqrt{d}+1\right) \left(a-b \sqrt{d}\right)\right)}{4 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(-\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{x-b}\right)}{4 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(\sqrt[6]{d} \sqrt[3]{x-b}-\sqrt[3]{x-a}\right)}{4 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}\right)}{2 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{d} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}","-\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,"(Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3)) + (Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 - Sqrt[d])*(a + b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[-2*(1 + Sqrt[d])*(a - b*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) - d^(1/6)*(-b + x)^(1/3)])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + d^(1/6)*(-b + x)^(1/3)])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(2/3))","A",10,6,61,0.09836,1,"{6719, 24, 911, 105, 59, 91}"
2804,1,309,0,1.6873359,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{\left(-1+x^4\right) \sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/((-1 + x^4)*Sqrt[1 + x^4]),x]","\frac{1}{8} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1+i} \sqrt{1-i x^2}}\right)-\frac{1}{8} \sqrt{1-i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)+\frac{1}{8} \sqrt{1-i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)-\frac{1}{8} \sqrt{1+i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1+i} \sqrt{1-i x^2}}\right)+\frac{1}{8} \sqrt{1-i} \tanh ^{-1}\left(\frac{1-x}{\sqrt{1-i} \sqrt{1+i x^2}}\right)+\frac{1}{8} \sqrt{1+i} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)-\frac{1}{8} \sqrt{1+i} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)-\frac{1}{8} \sqrt{1-i} \tanh ^{-1}\left(\frac{x+1}{\sqrt{1-i} \sqrt{1+i x^2}}\right)","\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,"(Sqrt[1 + I]*ArcTanh[(1 - x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/8 - (Sqrt[1 - I]*ArcTanh[(1 - I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])])/8 + (Sqrt[1 - I]*ArcTanh[(1 + I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])])/8 - (Sqrt[1 + I]*ArcTanh[(1 + x)/(Sqrt[1 + I]*Sqrt[1 - I*x^2])])/8 + (Sqrt[1 - I]*ArcTanh[(1 - x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/8 + (Sqrt[1 + I]*ArcTanh[(1 - I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/8 - (Sqrt[1 + I]*ArcTanh[(1 + I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/8 - (Sqrt[1 - I]*ArcTanh[(1 + x)/(Sqrt[1 - I]*Sqrt[1 + I*x^2])])/8","C",26,4,34,0.1176,0,"{6725, 2133, 725, 206}"
2805,0,0,0,2.7349022,"\int \frac{-1+x^6}{\sqrt[3]{-x^2+x^4} \left(1+x^6\right)} \, dx","Int[(-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,"((-1)^(1/18)*(1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(1/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(1/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(2/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(2/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(1/3)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(1/3)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(4/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(4/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(5/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(5/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(2/3)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 + I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(2/3)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(7/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*(1 - I*Sqrt[3])*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(7/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) - (-1)^(8/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3)) + ((-1)^(1/18)*x^(2/3)*(-1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(-1 + x^6)^(2/3)/((-1)^(1/18) + (-1)^(8/9)*x), x], x, x^(1/3)])/(6*(-x^2 + x^4)^(1/3))","F",0,0,0,0,-1,"{}"
2806,0,0,0,0.1051215,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+x} \, dx","Int[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,"Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + x), x]","F",0,0,0,0,-1,"{}"
2807,1,70,0,0.2298301,"\int \frac{b+a x^2}{\left(b-a x^2\right) \sqrt[4]{b x^3+a x^5}} \, dx","Int[(b + a*x^2)/((b - a*x^2)*(b*x^3 + a*x^5)^(1/4)),x]","\frac{4 x \left(a x^2+b\right) F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};\frac{a x^2}{b},-\frac{a x^2}{b}\right)}{b \left(\frac{a x^2}{b}+1\right)^{3/4} \sqrt[4]{a x^5+b x^3}}","\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*(b + a*x^2)*AppellF1[1/8, 1, -3/4, 9/8, (a*x^2)/b, -((a*x^2)/b)])/(b*(1 + (a*x^2)/b)^(3/4)*(b*x^3 + a*x^5)^(1/4))","C",4,4,33,0.1212,0,"{2056, 466, 430, 429}"
2808,0,0,0,1.231208,"\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","Int[((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,"4*Defer[Int][1/((1 + x^3)^(1/4)*(1 + 2*x^3 + x^6 + x^8)), x] + 5*Defer[Int][x^3/((1 + x^3)^(1/4)*(1 + 2*x^3 + x^6 + x^8)), x] + 4*Defer[Int][x^4/((1 + x^3)^(1/4)*(1 + 2*x^3 + x^6 + x^8)), x] + Defer[Int][x^6/((1 + x^3)^(1/4)*(1 + 2*x^3 + x^6 + x^8)), x] + Defer[Int][x^7/((1 + x^3)^(1/4)*(1 + 2*x^3 + x^6 + x^8)), x]","F",0,0,0,0,-1,"{}"
2809,0,0,0,1.583009,"\int \frac{x^2 \sqrt{1+x}}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[(x^2*Sqrt[1 + x])/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{x^2 \sqrt{1+x}}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-9 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$1}+1}\&\right]+\frac{2}{3} (x+1)^{3/2}+4 \sqrt{\sqrt{x+1}+1}+\frac{2}{55} \left(25+9 \sqrt{5}\right) \log \left(-2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}+1\right)-\frac{2}{55} \left(9 \sqrt{5}-25\right) \log \left(2 \sqrt{\sqrt{x+1}+1}+\sqrt{5}-1\right)",1,"2*Sqrt[1 + x] + 4*Sqrt[1 + Sqrt[1 + x]] - 2*(1 + Sqrt[1 + x])^2 + (2*(1 + Sqrt[1 + x])^3)/3 + (2*(25 - 9*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 + (2*(25 + 9*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 - (4*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/11 + (40*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/11 - (12*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/11 - (16*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/11 + (12*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/11","F",0,0,0,0,-1,"{}"
2810,0,0,0,1.2652704,"\int \frac{x^2 \sqrt{1+x}}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","Int[(x^2*Sqrt[1 + x])/(x^2 - Sqrt[1 + x]*Sqrt[1 + Sqrt[1 + x]]),x]","\int \frac{x^2 \sqrt{1+x}}{x^2-\sqrt{1+x} \sqrt{1+\sqrt{1+x}}} \, dx","-\frac{4}{11} \text{RootSum}\left[\text{$\#$1}^5+\text{$\#$1}^4-2 \text{$\#$1}^3-\text{$\#$1}^2+\text{$\#$1}-1\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1}^3 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)+\text{$\#$1} \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)-9 \log \left(\sqrt{\sqrt{x+1}+1}-\text{$\#$1}\right)}{5 \text{$\#$1}^4+4 \text{$\#$1}^3-6 \text{$\#$1}^2-2 \text{$\#$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,"2*Sqrt[1 + x] + 4*Sqrt[1 + Sqrt[1 + x]] - 2*(1 + Sqrt[1 + x])^2 + (2*(1 + Sqrt[1 + x])^3)/3 + (2*(25 - 9*Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 + (2*(25 + 9*Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + Sqrt[1 + x]]])/55 - (4*Log[2 + Sqrt[1 + x] - Sqrt[1 + Sqrt[1 + x]] + 2*(1 + Sqrt[1 + x])^(3/2) - (1 + Sqrt[1 + x])^2 - (1 + Sqrt[1 + x])^(5/2)])/11 + (40*Defer[Subst][Defer[Int][(-1 + x - x^2 - 2*x^3 + x^4 + x^5)^(-1), x], x, Sqrt[1 + Sqrt[1 + x]]])/11 - (12*Defer[Subst][Defer[Int][x/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/11 - (16*Defer[Subst][Defer[Int][x^2/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/11 + (12*Defer[Subst][Defer[Int][x^3/(-1 + x - x^2 - 2*x^3 + x^4 + x^5), x], x, Sqrt[1 + Sqrt[1 + x]]])/11","F",0,0,0,0,-1,"{}"
2811,1,707,0,1.7600441,"\int \frac{\left(-b-a x+x^4\right) \sqrt[4]{b x^3+a x^4}}{-b+a x} \, dx","Int[((-b - a*x + x^4)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x),x]","-\frac{371 b^5 \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{4096 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{371 b^5 \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{4096 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}-\frac{371 b^4 \sqrt[4]{a x^4+b x^3}}{6144 a^5}+\frac{53 b^3 x \sqrt[4]{a x^4+b x^3}}{1536 a^4}-\frac{1}{2} x \left(1-\frac{b^3}{a^4}\right) \sqrt[4]{a x^4+b x^3}+\frac{65 b^2 x^2 \sqrt[4]{a x^4+b x^3}}{192 a^3}+\frac{21 b x^3 \sqrt[4]{a x^4+b x^3}}{80 a^2}-\frac{3 b^2 \left(a^4-b^3\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{16 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{b^2 \left(2 a^4-b^3\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{2 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{3 b^2 \left(a^4-b^3\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{16 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}-\frac{b^2 \left(2 a^4-b^3\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x+b}}\right)}{2 a^{23/4} x^{3/4} \sqrt[4]{a x+b}}+\frac{4 b \left(2 a^4-b^3\right) \sqrt[4]{a x^4+b x^3} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{a x}{b},-\frac{a x}{b}\right)}{3 a^5 \sqrt[4]{\frac{a x}{b}+1}}-\frac{b \left(a^4-b^3\right) \sqrt[4]{a x^4+b x^3}}{8 a^5}-\frac{b \left(2 a^4-b^3\right) \sqrt[4]{a x^4+b x^3}}{a^5}+\frac{x^4 \sqrt[4]{a x^4+b x^3}}{5 a}","\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,"(-371*b^4*(b*x^3 + a*x^4)^(1/4))/(6144*a^5) - (b*(a^4 - b^3)*(b*x^3 + a*x^4)^(1/4))/(8*a^5) - (b*(2*a^4 - b^3)*(b*x^3 + a*x^4)^(1/4))/a^5 + (53*b^3*x*(b*x^3 + a*x^4)^(1/4))/(1536*a^4) - ((1 - b^3/a^4)*x*(b*x^3 + a*x^4)^(1/4))/2 + (65*b^2*x^2*(b*x^3 + a*x^4)^(1/4))/(192*a^3) + (21*b*x^3*(b*x^3 + a*x^4)^(1/4))/(80*a^2) + (x^4*(b*x^3 + a*x^4)^(1/4))/(5*a) + (4*b*(2*a^4 - b^3)*(b*x^3 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (a*x)/b, -((a*x)/b)])/(3*a^5*(1 + (a*x)/b)^(1/4)) - (371*b^5*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(4096*a^(23/4)*x^(3/4)*(b + a*x)^(1/4)) - (3*b^2*(a^4 - b^3)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(23/4)*x^(3/4)*(b + a*x)^(1/4)) + (b^2*(2*a^4 - b^3)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(23/4)*x^(3/4)*(b + a*x)^(1/4)) + (371*b^5*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(4096*a^(23/4)*x^(3/4)*(b + a*x)^(1/4)) + (3*b^2*(a^4 - b^3)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(23/4)*x^(3/4)*(b + a*x)^(1/4)) - (b^2*(2*a^4 - b^3)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(23/4)*x^(3/4)*(b + a*x)^(1/4))","C",41,11,36,0.3056,0,"{2056, 6733, 6725, 279, 331, 298, 203, 206, 321, 511, 510}"
2812,0,0,0,8.6339867,"\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","Int[((-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,"(9*a*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(a - b + x^3)^(5/3)/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4)*d - (1 - 4*(a - b)^3*d)*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*d*x^6 + 4*a*(1 - b/a)*d*x^9 + d*x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(2/3) + (9*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(x^3*(a - b + x^3)^(5/3))/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4)*d - (1 - 4*(a - b)^3*d)*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*d*x^6 + 4*a*(1 - b/a)*d*x^9 + d*x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(2/3) - (3*(4*a - b)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(a - b + x^3)^(5/3)/(a*(1 + (b^4*d)/a) - (1 + 4*b^3*d)*(a + x^3) + 6*b^2*d*(a + x^3)^2 - 4*b*d*(a + x^3)^3 + d*(a + x^3)^4), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(2/3)","F",0,0,0,0,-1,"{}"
2813,0,0,0,15.6370041,"\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","Int[(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,"(3*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^10/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (6*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-1 + 2*(1 + k)*x^3 - (1 + k*(4 + k))*x^6 + 2*k*(1 + k)*x^9 + b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2814,1,169,0,0.1310783,"\int \frac{1}{c+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(c + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])^(-1),x]","\frac{b^2 \log \left(\sqrt{a^2 x^2+b^2}+a x\right)}{2 a c^3}+\frac{b^2}{a 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)}{a c^3}-\frac{b^2}{2 a c \left(\sqrt{a^2 x^2+b^2}+a x\right)}+\frac{\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/(a*c*(a*x + Sqrt[b^2 + a^2*x^2])) + b^2/(a*c^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/a + (b^2*Log[a*x + Sqrt[b^2 + a^2*x^2]])/(2*a*c^3) - ((b^2 + c^4)*Log[c + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]])/(a*c^3)","A",4,3,27,0.1111,1,"{2117, 1821, 1620}"
2815,1,273,0,1.446392,"\int \frac{(-7+x) \sqrt[3]{1+x-5 x^2+3 x^3}}{(-5+x) (-1+x)^3} \, dx","Int[((-7 + x)*(1 + x - 5*x^2 + 3*x^3)^(1/3))/((-5 + x)*(-1 + x)^3),x]","-\frac{9 \sqrt[3]{3 x^3-5 x^2+x+1} (3 x+1)}{32 (1-x)^2}+\frac{3 \sqrt[3]{3 x^3-5 x^2+x+1}}{8 (1-x)}+\frac{\sqrt[3]{3 x^3-5 x^2+x+1} \log (x-5)}{8 \sqrt[3]{2} (1-x)^{2/3} \sqrt[3]{3 x+1}}-\frac{3 \sqrt[3]{3 x^3-5 x^2+x+1} \log \left(-\frac{4}{3} \sqrt[3]{1-x}-\frac{2}{3} \sqrt[3]{2} \sqrt[3]{3 x+1}\right)}{8 \sqrt[3]{2} (1-x)^{2/3} \sqrt[3]{3 x+1}}-\frac{\sqrt{3} \sqrt[3]{3 x^3-5 x^2+x+1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2\ 2^{2/3} \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{3 x+1}}\right)}{4 \sqrt[3]{2} (1-x)^{2/3} \sqrt[3]{3 x+1}}","\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 + x - 5*x^2 + 3*x^3)^(1/3))/(8*(1 - x)) - (9*(1 + 3*x)*(1 + x - 5*x^2 + 3*x^3)^(1/3))/(32*(1 - x)^2) - (Sqrt[3]*(1 + x - 5*x^2 + 3*x^3)^(1/3)*ArcTan[1/Sqrt[3] - (2*2^(2/3)*(1 - x)^(1/3))/(Sqrt[3]*(1 + 3*x)^(1/3))])/(4*2^(1/3)*(1 - x)^(2/3)*(1 + 3*x)^(1/3)) + ((1 + x - 5*x^2 + 3*x^3)^(1/3)*Log[-5 + x])/(8*2^(1/3)*(1 - x)^(2/3)*(1 + 3*x)^(1/3)) - (3*(1 + x - 5*x^2 + 3*x^3)^(1/3)*Log[(-4*(1 - x)^(1/3))/3 - (2*2^(1/3)*(1 + 3*x)^(1/3))/3])/(8*2^(1/3)*(1 - x)^(2/3)*(1 + 3*x)^(1/3))","A",22,11,31,0.3548,1,"{6742, 2081, 2077, 101, 157, 60, 91, 21, 37, 47, 50}"
2816,1,1306,0,147.5128318,"\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","Int[(b^2 + a^2*x^2)/((-b^2 + a^2*x^2)^3*(-(b*x^2) + a*x^3)^(1/3)),x]","\frac{9 x \Gamma \left(\frac{4}{3}\right) \left(1820 \, _2F_1\left(1,2;\frac{13}{3};\frac{2 a x}{b+a x}\right) b^4-2275 a x \, _2F_1\left(1,2;\frac{13}{3};\frac{2 a x}{b+a x}\right) b^3+2484 a x \, _2F_1\left(2,3;\frac{16}{3};\frac{2 a x}{b+a x}\right) b^3-585 a^2 x^2 \, _2F_1\left(1,2;\frac{13}{3};\frac{2 a x}{b+a x}\right) b^2-6534 a^2 x^2 \, _2F_1\left(2,3;\frac{16}{3};\frac{2 a x}{b+a x}\right) b^2+2457 a^3 x^3 \, _2F_1\left(1,2;\frac{13}{3};\frac{2 a x}{b+a x}\right) b+5832 a^3 x^3 \, _2F_1\left(2,3;\frac{16}{3};\frac{2 a x}{b+a x}\right) b-1053 a^4 x^4 \, _2F_1\left(1,2;\frac{13}{3};\frac{2 a x}{b+a x}\right)-1782 a^4 x^4 \, _2F_1\left(2,3;\frac{16}{3};\frac{2 a x}{b+a x}\right)+162 a x (7 b-6 a x) (b-a x)^2 \, _3F_2\left(2,2,3;1,\frac{16}{3};\frac{2 a x}{b+a x}\right)+162 a \left(b \sqrt[3]{x}-a x^{4/3}\right)^3 \, _4F_3\left(2,2,2,3;1,1,\frac{16}{3};\frac{2 a x}{b+a x}\right)\right)}{1820 b^4 (b-a x) (b+a x)^3 \sqrt[3]{a x^3-b x^2} \Gamma \left(\frac{1}{3}\right)}-\frac{9 x \Gamma \left(\frac{4}{3}\right) \left(553280 \, _2F_1\left(1,3;\frac{19}{3};\frac{2 a x}{b+a x}\right) b^6-1521520 a x \, _2F_1\left(1,3;\frac{19}{3};\frac{2 a x}{b+a x}\right) b^5+994248 a x \, _2F_1\left(2,4;\frac{22}{3};\frac{2 a x}{b+a x}\right) b^5+36450 a x \, _5F_4\left(2,2,2,2,4;1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^5+2187 a x \, _6F_5\left(2,2,2,2,2,4;1,1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^5+1482000 a^2 x^2 \, _2F_1\left(1,3;\frac{19}{3};\frac{2 a x}{b+a x}\right) b^4-4219830 a^2 x^2 \, _2F_1\left(2,4;\frac{22}{3};\frac{2 a x}{b+a x}\right) b^4-178605 a^2 x^2 \, _5F_4\left(2,2,2,2,4;1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^4-10935 a^2 x^2 \, _6F_5\left(2,2,2,2,2,4;1,1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^4+355680 a^3 x^3 \, _2F_1\left(1,3;\frac{19}{3};\frac{2 a x}{b+a x}\right) b^3+7474680 a^3 x^3 \, _2F_1\left(2,4;\frac{22}{3};\frac{2 a x}{b+a x}\right) b^3+349920 a^3 x^3 \, _5F_4\left(2,2,2,2,4;1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^3+21870 a^3 x^3 \, _6F_5\left(2,2,2,2,2,4;1,1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^3-1723680 a^4 x^4 \, _2F_1\left(1,3;\frac{19}{3};\frac{2 a x}{b+a x}\right) b^2-6828300 a^4 x^4 \, _2F_1\left(2,4;\frac{22}{3};\frac{2 a x}{b+a x}\right) b^2-342630 a^4 x^4 \, _5F_4\left(2,2,2,2,4;1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^2-21870 a^4 x^4 \, _6F_5\left(2,2,2,2,2,4;1,1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b^2+1200420 a^5 x^5 \, _2F_1\left(1,3;\frac{19}{3};\frac{2 a x}{b+a x}\right) b+3178440 a^5 x^5 \, _2F_1\left(2,4;\frac{22}{3};\frac{2 a x}{b+a x}\right) b+167670 a^5 x^5 \, _5F_4\left(2,2,2,2,4;1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b+10935 a^5 x^5 \, _6F_5\left(2,2,2,2,2,4;1,1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right) b-277020 a^6 x^6 \, _2F_1\left(1,3;\frac{19}{3};\frac{2 a x}{b+a x}\right)-599238 a^6 x^6 \, _2F_1\left(2,4;\frac{22}{3};\frac{2 a x}{b+a x}\right)+405 a x (b-a x)^2 \left(1730 b^3-4419 a x b^2+3960 a^2 x^2 b-1215 a^3 x^3\right) \, _3F_2\left(2,2,4;1,\frac{22}{3};\frac{2 a x}{b+a x}\right)+1215 a \left(b \sqrt[3]{x}-a x^{4/3}\right)^3 \left(191 b^2-336 a x b+153 a^2 x^2\right) \, _4F_3\left(2,2,2,4;1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right)-32805 a^6 x^6 \, _5F_4\left(2,2,2,2,4;1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right)-2187 a^6 x^6 \, _6F_5\left(2,2,2,2,2,4;1,1,1,1,\frac{22}{3};\frac{2 a x}{b+a x}\right)\right)}{276640 b^4 (b-a x)^2 (b+a x)^4 \sqrt[3]{a x^3-b x^2} \Gamma \left(\frac{1}{3}\right)}","-\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,"(9*x*Gamma[4/3]*(1820*b^4*Hypergeometric2F1[1, 2, 13/3, (2*a*x)/(b + a*x)] - 2275*a*b^3*x*Hypergeometric2F1[1, 2, 13/3, (2*a*x)/(b + a*x)] - 585*a^2*b^2*x^2*Hypergeometric2F1[1, 2, 13/3, (2*a*x)/(b + a*x)] + 2457*a^3*b*x^3*Hypergeometric2F1[1, 2, 13/3, (2*a*x)/(b + a*x)] - 1053*a^4*x^4*Hypergeometric2F1[1, 2, 13/3, (2*a*x)/(b + a*x)] + 2484*a*b^3*x*Hypergeometric2F1[2, 3, 16/3, (2*a*x)/(b + a*x)] - 6534*a^2*b^2*x^2*Hypergeometric2F1[2, 3, 16/3, (2*a*x)/(b + a*x)] + 5832*a^3*b*x^3*Hypergeometric2F1[2, 3, 16/3, (2*a*x)/(b + a*x)] - 1782*a^4*x^4*Hypergeometric2F1[2, 3, 16/3, (2*a*x)/(b + a*x)] + 162*a*x*(7*b - 6*a*x)*(b - a*x)^2*HypergeometricPFQ[{2, 2, 3}, {1, 16/3}, (2*a*x)/(b + a*x)] + 162*a*(b*x^(1/3) - a*x^(4/3))^3*HypergeometricPFQ[{2, 2, 2, 3}, {1, 1, 16/3}, (2*a*x)/(b + a*x)]))/(1820*b^4*(b - a*x)*(b + a*x)^3*(-(b*x^2) + a*x^3)^(1/3)*Gamma[1/3]) - (9*x*Gamma[4/3]*(553280*b^6*Hypergeometric2F1[1, 3, 19/3, (2*a*x)/(b + a*x)] - 1521520*a*b^5*x*Hypergeometric2F1[1, 3, 19/3, (2*a*x)/(b + a*x)] + 1482000*a^2*b^4*x^2*Hypergeometric2F1[1, 3, 19/3, (2*a*x)/(b + a*x)] + 355680*a^3*b^3*x^3*Hypergeometric2F1[1, 3, 19/3, (2*a*x)/(b + a*x)] - 1723680*a^4*b^2*x^4*Hypergeometric2F1[1, 3, 19/3, (2*a*x)/(b + a*x)] + 1200420*a^5*b*x^5*Hypergeometric2F1[1, 3, 19/3, (2*a*x)/(b + a*x)] - 277020*a^6*x^6*Hypergeometric2F1[1, 3, 19/3, (2*a*x)/(b + a*x)] + 994248*a*b^5*x*Hypergeometric2F1[2, 4, 22/3, (2*a*x)/(b + a*x)] - 4219830*a^2*b^4*x^2*Hypergeometric2F1[2, 4, 22/3, (2*a*x)/(b + a*x)] + 7474680*a^3*b^3*x^3*Hypergeometric2F1[2, 4, 22/3, (2*a*x)/(b + a*x)] - 6828300*a^4*b^2*x^4*Hypergeometric2F1[2, 4, 22/3, (2*a*x)/(b + a*x)] + 3178440*a^5*b*x^5*Hypergeometric2F1[2, 4, 22/3, (2*a*x)/(b + a*x)] - 599238*a^6*x^6*Hypergeometric2F1[2, 4, 22/3, (2*a*x)/(b + a*x)] + 405*a*x*(b - a*x)^2*(1730*b^3 - 4419*a*b^2*x + 3960*a^2*b*x^2 - 1215*a^3*x^3)*HypergeometricPFQ[{2, 2, 4}, {1, 22/3}, (2*a*x)/(b + a*x)] + 1215*a*(b*x^(1/3) - a*x^(4/3))^3*(191*b^2 - 336*a*b*x + 153*a^2*x^2)*HypergeometricPFQ[{2, 2, 2, 4}, {1, 1, 22/3}, (2*a*x)/(b + a*x)] + 36450*a*b^5*x*HypergeometricPFQ[{2, 2, 2, 2, 4}, {1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] - 178605*a^2*b^4*x^2*HypergeometricPFQ[{2, 2, 2, 2, 4}, {1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] + 349920*a^3*b^3*x^3*HypergeometricPFQ[{2, 2, 2, 2, 4}, {1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] - 342630*a^4*b^2*x^4*HypergeometricPFQ[{2, 2, 2, 2, 4}, {1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] + 167670*a^5*b*x^5*HypergeometricPFQ[{2, 2, 2, 2, 4}, {1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] - 32805*a^6*x^6*HypergeometricPFQ[{2, 2, 2, 2, 4}, {1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] + 2187*a*b^5*x*HypergeometricPFQ[{2, 2, 2, 2, 2, 4}, {1, 1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] - 10935*a^2*b^4*x^2*HypergeometricPFQ[{2, 2, 2, 2, 2, 4}, {1, 1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] + 21870*a^3*b^3*x^3*HypergeometricPFQ[{2, 2, 2, 2, 2, 4}, {1, 1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] - 21870*a^4*b^2*x^4*HypergeometricPFQ[{2, 2, 2, 2, 2, 4}, {1, 1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] + 10935*a^5*b*x^5*HypergeometricPFQ[{2, 2, 2, 2, 2, 4}, {1, 1, 1, 1, 22/3}, (2*a*x)/(b + a*x)] - 2187*a^6*x^6*HypergeometricPFQ[{2, 2, 2, 2, 2, 4}, {1, 1, 1, 1, 22/3}, (2*a*x)/(b + a*x)]))/(276640*b^4*(b - a*x)^2*(b + a*x)^4*(-(b*x^2) + a*x^3)^(1/3)*Gamma[1/3])","C",10,6,43,0.1395,0,"{2056, 6733, 6742, 1404, 430, 429}"
2817,1,278,0,1.0868445,"\int \frac{d+c x}{(-d+c x) \sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x)/((-d + c*x)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","-\frac{4 d \tanh ^{-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{4 d \tanh ^{-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}{c \sqrt{\sqrt{a^2 x^2+b^2}+a x}}-\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}","\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,"-1/3*b^2/(a*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) + (4*d)/(c*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]) + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/a - (4*d*ArcTanh[(Sqrt[c]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]])/(Sqrt[c]*Sqrt[a*d - Sqrt[b^2*c^2 + a^2*d^2]]) - (4*d*ArcTanh[(Sqrt[c]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]]])/(Sqrt[c]*Sqrt[a*d + Sqrt[b^2*c^2 + a^2*d^2]])","A",13,9,38,0.2368,1,"{6742, 2117, 14, 2119, 1628, 828, 826, 1166, 208}"
2818,1,753,0,2.906099,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(-d - 2*c*x + x^2),x]","\frac{\sqrt[4]{a x^4-b x^3} \left(-\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a \left(c-\sqrt{c^2+d}\right)}}{\sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b} \left(b-a \left(c-\sqrt{c^2+d}\right)\right)^{3/4}}-\frac{\sqrt[4]{a x^4-b x^3} \left(\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2+d}+c\right)-b}}{\sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b} \left(a \left(\sqrt{c^2+d}+c\right)-b\right)^{3/4}}-\frac{\sqrt[4]{a x^4-b x^3} \left(-\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a \left(c-\sqrt{c^2+d}\right)}}{\sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b} \left(b-a \left(c-\sqrt{c^2+d}\right)\right)^{3/4}}+\frac{\sqrt[4]{a x^4-b x^3} \left(\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2+d}+c\right)-b}}{\sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b} \left(a \left(\sqrt{c^2+d}+c\right)-b\right)^{3/4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{a x-b}}","\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,"(-2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(x^(3/4)*(-b + a*x)^(1/4)) + ((b - 2*a*c - (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((b - a*(c - Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((-c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((-c + Sqrt[c^2 + d])^(1/4)*(b - a*(c - Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4)) - ((b - 2*a*c + (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((-b + a*(c + Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*(c + Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4)) + (2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(x^(3/4)*(-b + a*x)^(1/4)) - ((b - 2*a*c - (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((b - a*(c - Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((-c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((-c + Sqrt[c^2 + d])^(1/4)*(b - a*(c - Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4)) + ((b - 2*a*c + (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((-b + a*(c + Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*(c + Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4))","B",17,11,30,0.3667,1,"{2056, 905, 63, 331, 298, 203, 206, 6728, 93, 205, 208}"
2819,1,753,0,1.9836477,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(-d - 2*c*x + x^2),x]","\frac{\sqrt[4]{a x^4-b x^3} \left(-\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a \left(c-\sqrt{c^2+d}\right)}}{\sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b} \left(b-a \left(c-\sqrt{c^2+d}\right)\right)^{3/4}}-\frac{\sqrt[4]{a x^4-b x^3} \left(\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2+d}+c\right)-b}}{\sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b} \left(a \left(\sqrt{c^2+d}+c\right)-b\right)^{3/4}}-\frac{\sqrt[4]{a x^4-b x^3} \left(-\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{b-a \left(c-\sqrt{c^2+d}\right)}}{\sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}-c} \sqrt[4]{a x-b} \left(b-a \left(c-\sqrt{c^2+d}\right)\right)^{3/4}}+\frac{\sqrt[4]{a x^4-b x^3} \left(\frac{b c-a \left(2 c^2+d\right)}{\sqrt{c^2+d}}-2 a c+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a \left(\sqrt{c^2+d}+c\right)-b}}{\sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{\sqrt{c^2+d}+c} \sqrt[4]{a x-b} \left(a \left(\sqrt{c^2+d}+c\right)-b\right)^{3/4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{x^{3/4} \sqrt[4]{a x-b}}","\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,"(-2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(x^(3/4)*(-b + a*x)^(1/4)) + ((b - 2*a*c - (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((b - a*(c - Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((-c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((-c + Sqrt[c^2 + d])^(1/4)*(b - a*(c - Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4)) - ((b - 2*a*c + (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((-b + a*(c + Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*(c + Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4)) + (2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(x^(3/4)*(-b + a*x)^(1/4)) - ((b - 2*a*c - (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((b - a*(c - Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((-c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((-c + Sqrt[c^2 + d])^(1/4)*(b - a*(c - Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4)) + ((b - 2*a*c + (b*c - a*(2*c^2 + d))/Sqrt[c^2 + d])*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((-b + a*(c + Sqrt[c^2 + d]))^(1/4)*x^(1/4))/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*x)^(1/4))])/((c + Sqrt[c^2 + d])^(1/4)*(-b + a*(c + Sqrt[c^2 + d]))^(3/4)*x^(3/4)*(-b + a*x)^(1/4))","B",17,11,30,0.3667,1,"{2056, 905, 63, 331, 298, 203, 206, 6728, 93, 205, 208}"
2820,0,0,0,11.7698151,"\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","Int[(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,"(-3*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - k*x^3)^(2/3))/((1 - x^3)^(1/3)*(1 - 4*x^3 + 6*(1 - b/6)*x^6 - 4*(1 - (b*k)/2)*x^9 + (1 - b*k^2)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (3*(1 - 2*k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^7*(1 - k*x^3)^(2/3))/((1 - x^3)^(1/3)*(1 - 4*x^3 + 6*(1 - b/6)*x^6 - 4*(1 - (b*k)/2)*x^9 + (1 - b*k^2)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2821,0,0,0,11.0247076,"\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","Int[(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,"(3*(-1 + x)^(1/3)*x^(1/3)*(-1 + k*x)^(1/3)*Defer[Subst][Defer[Int][(x*(-1 + k*x^3)^(2/3))/((-1 + x^3)^(1/3)*(-x^3 + x^6 - b*(-1 + k*x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (6*(1 - 2*k)*(-1 + x)^(1/3)*x^(1/3)*(-1 + k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(-1 + k*x^3)^(2/3))/((-1 + x^3)^(1/3)*(-x^3 + x^6 - b*(-1 + k*x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (9*k*(-1 + x)^(1/3)*x^(1/3)*(-1 + k*x)^(1/3)*Defer[Subst][Defer[Int][(x^7*(-1 + k*x^3)^(2/3))/((-1 + x^3)^(1/3)*(x^3 - x^6 + b*(-1 + k*x^3)^5)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2822,1,232,0,0.2257582,"\int \frac{(d+c x)^2}{\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(d + c*x)^2/Sqrt[a*x + Sqrt[b^2 + a^2*x^2]],x]","\frac{c d \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}{3 a^2}+\frac{b^4 c d}{5 a^2 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}+\frac{b^2 \left(b^2 c^2-4 a^2 d^2\right)}{12 a^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{3/2}}-\frac{\sqrt{\sqrt{a^2 x^2+b^2}+a x} \left(b^2 c^2-4 a^2 d^2\right)}{4 a^3}+\frac{c^2 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{5/2}}{20 a^3}-\frac{b^6 c^2}{28 a^3 \left(\sqrt{a^2 x^2+b^2}+a x\right)^{7/2}}","\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,"-1/28*(b^6*c^2)/(a^3*(a*x + Sqrt[b^2 + a^2*x^2])^(7/2)) + (b^4*c*d)/(5*a^2*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2)) + (b^2*(b^2*c^2 - 4*a^2*d^2))/(12*a^3*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2)) - ((b^2*c^2 - 4*a^2*d^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(4*a^3) + (c*d*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2))/(3*a^2) + (c^2*(a*x + Sqrt[b^2 + a^2*x^2])^(5/2))/(20*a^3)","A",3,2,31,0.06452,1,"{2119, 1628}"
2823,0,0,0,54.3798876,"\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","Int[(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]","\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","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 - Defer[Int][(1 - 3*x + 3*x^3 - 9*x^4 + 4*x^6 - 9*x^7 + x^9 - 3*x^10)^(-1), x] - Defer[Int][(-1 + 3*x - 3*x^3 + 9*x^4 - 4*x^6 + 9*x^7 - x^9 + 3*x^10)^(-1), x] - Defer[Int][x^4/(-1 + 3*x - 3*x^3 + 9*x^4 - 4*x^6 + 9*x^7 - x^9 + 3*x^10), x] - Defer[Int][x^6/(-1 + 3*x - 3*x^3 + 9*x^4 - 4*x^6 + 9*x^7 - x^9 + 3*x^10), x] + (10*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^2/(-3 + 28*x - 6*x^3 + 3*x^4 - 3*x^6 + 3*x^7 + x^10), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (10*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^2/(-3 + 28*x - 6*x^3 + 3*x^4 - 3*x^6 + 3*x^7 + x^10), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + (2*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^5/(-3 + 28*x - 6*x^3 + 3*x^4 - 3*x^6 + 3*x^7 + x^10), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (2*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^5/(-3 + 28*x - 6*x^3 + 3*x^4 - 3*x^6 + 3*x^7 + x^10), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + (((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^8/(-3 + 28*x - 6*x^3 + 3*x^4 - 3*x^6 + 3*x^7 + x^10), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^8/(-3 + 28*x - 6*x^3 + 3*x^4 - 3*x^6 + 3*x^7 + x^10), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + (30*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^2/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (30*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^2/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) - (280*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^3/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (560*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^3/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + (66*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^5/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (66*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^5/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) - (86*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^6/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (172*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^6/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + (45*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^8/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (45*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^8/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) - (64*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^9/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (128*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^9/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + (12*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^11/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (12*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^11/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) - (19*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^12/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (38*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^12/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) + (3*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^14/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (3*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^14/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) - (5*((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^15/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (10*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^15/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2) - (((1 - 3*x)*(1 + x^3)^3)^(1/3)*Defer[Subst][Defer[Int][x^18/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(1/3)*(1 + x^3)) - (2*((1 - 3*x)*(1 + x^3)^3)^(2/3)*Defer[Subst][Defer[Int][x^18/(9 + 84*x + 784*x^2 + 36*x^3 + 177*x^4 + 168*x^5 + 54*x^6 + 111*x^7 + 177*x^8 + 36*x^9 + 30*x^10 + 74*x^11 + 9*x^12 + 15*x^13 + 15*x^14 + 3*x^16 + 6*x^17 + x^20), x], x, (-1 + 3*x)^(1/3)])/((-1 + 3*x)^(2/3)*(1 + x^3)^2)","F",0,0,0,0,-1,"{}"
2824,0,0,0,0.4954967,"\int \frac{1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx","Int[(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,"((1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Int][(1 - k*x)^(1/3)/((1 - x)^(2/3)*x^(2/3)*(1 + (-2 + k)*x)), x])/((1 - x)*x*(1 - k*x))^(2/3)","F",0,0,0,0,-1,"{}"
2825,0,0,0,0.6142937,"\int \frac{1+x^2+x^3}{\left(-1+x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[(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{$\#$1}^3-\text{$\#$1}-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{3 \text{$\#$1}^2-1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2-\text{$\#$1}+1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)+\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)-2 \text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1} \log (x)}{6 \text{$\#$1}^5+4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}-1}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"(Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[(1 + (2*x^(1/3))/(1 + x)^(1/3))/Sqrt[3]])/(x^2 + x^3)^(1/3) - (3*x^(2/3)*(1 + x)^(1/3)*Log[x^(1/3) - (1 + x)^(1/3)])/(2*(x^2 + x^3)^(1/3)) + (6*x^(2/3)*(1 + x)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x^3)^(1/3)*(-1 + x^6 + x^9)), x], x, x^(1/3)])/(x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
2826,0,0,0,0.4353038,"\int \frac{1+x^2+x^3}{\left(-1+x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","Int[(1 + x^2 + x^3)/((-1 + x^2 + x^3)*(x^2 + x^3)^(1/3)),x]","\int \frac{1+x^2+x^3}{\left(-1+x^2+x^3\right) \sqrt[3]{x^2+x^3}} \, dx","2 \text{RootSum}\left[\text{$\#$1}^3-\text{$\#$1}-1\&,\frac{\text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1} \log (x)}{3 \text{$\#$1}^2-1}\&\right]+2 \text{RootSum}\left[\text{$\#$1}^6+\text{$\#$1}^4-2 \text{$\#$1}^3+\text{$\#$1}^2-\text{$\#$1}+1\&,\frac{2 \text{$\#$1}^4 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-2 \text{$\#$1}^4 \log (x)+\text{$\#$1}^2 \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)-\text{$\#$1}^2 \log (x)-2 \text{$\#$1} \log \left(\sqrt[3]{x^3+x^2}-\text{$\#$1} x\right)+2 \text{$\#$1} \log (x)}{6 \text{$\#$1}^5+4 \text{$\#$1}^3-6 \text{$\#$1}^2+2 \text{$\#$1}-1}\&\right]-\log \left(\sqrt[3]{x^3+x^2}-x\right)+\frac{1}{2} \log \left(x^2+\sqrt[3]{x^3+x^2} x+\left(x^3+x^2\right)^{2/3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} x}{2 \sqrt[3]{x^3+x^2}+x}\right)",1,"(Sqrt[3]*x^(2/3)*(1 + x)^(1/3)*ArcTan[(1 + (2*x^(1/3))/(1 + x)^(1/3))/Sqrt[3]])/(x^2 + x^3)^(1/3) - (3*x^(2/3)*(1 + x)^(1/3)*Log[x^(1/3) - (1 + x)^(1/3)])/(2*(x^2 + x^3)^(1/3)) + (6*x^(2/3)*(1 + x)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x^3)^(1/3)*(-1 + x^6 + x^9)), x], x, x^(1/3)])/(x^2 + x^3)^(1/3)","F",0,0,0,0,-1,"{}"
2827,1,164,0,0.7847241,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{x \sqrt{-b+a x}} \, dx","Int[Sqrt[a*x + Sqrt[-b + a*x]]/(x*Sqrt[-b + a*x]),x]","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{b}-\sqrt{a x-b}}{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt[4]{b}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x-b}+\sqrt{b}}{\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt[4]{b}}+2 \tanh ^{-1}\left(\frac{2 \sqrt{a x-b}+1}{2 \sqrt{\sqrt{a x-b}+a x}}\right)","-2 \text{RootSum}\left[\text{$\#$1}^4+4 \text{$\#$1}^3+8 \text{$\#$1}^2 b+6 \text{$\#$1}^2-16 \text{$\#$1} b+4 \text{$\#$1}+16 b^2-8 b+1\&,\frac{\text{$\#$1}^2 \left(-\log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)\right)-2 \text{$\#$1} \log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)+4 b \log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)-\log \left(\text{$\#$1}+2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+4 \text{$\#$1} b+3 \text{$\#$1}-4 b+1}\&\right]-2 \log \left(2 \sqrt{a x-b}-2 \sqrt{\sqrt{a x-b}+a x}+1\right)",1,"-((Sqrt[2]*ArcTan[(Sqrt[b] - Sqrt[-b + a*x])/(Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/b^(1/4)) - (Sqrt[2]*ArcTanh[(Sqrt[b] + Sqrt[-b + a*x])/(Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/b^(1/4) + 2*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])]","A",9,7,34,0.2059,1,"{990, 621, 206, 1036, 1030, 208, 205}"
2828,0,0,0,0.3396654,"\int \sqrt{a x+\sqrt{b+a^2 x^2}} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Int[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,"Defer[Int][Sqrt[a*x + Sqrt[b + a^2*x^2]]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]], x]","F",0,0,0,0,-1,"{}"
2829,0,0,0,0.6983597,"\int x^4 \sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}} \, dx","Int[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,"Defer[Int][x^4*Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x]","F",0,0,0,0,-1,"{}"
2830,0,0,0,1.1066523,"\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","Int[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{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1}^2 \left(-\log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1} c-\text{$\#$1}^3}\&\right]}{4 a b}+\frac{a x \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}+\sqrt{a^2 x^2+b} \sqrt{\sqrt{a^2 x^2+b}+a x} \sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}}{a^2 b x \sqrt{a^2 x^2+b}+a b \left(a^2 x^2+b\right)}",1,"Defer[Int][Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/((b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]), x]","F",0,0,0,0,-1,"{}"
2831,0,0,0,0.6800241,"\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Int[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]]/((b + a^2*x^2)^(3/2)*Sqrt[a*x + Sqrt[b + a^2*x^2]]),x]","\int \frac{\sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}}}{\left(b+a^2 x^2\right)^{3/2} \sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","\frac{\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c+6 \text{$\#$1}^4 c^2-4 \text{$\#$1}^2 c^3+b+c^4\&,\frac{\text{$\#$1}^2 \left(-\log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)\right)-c \log \left(\sqrt{\sqrt{\sqrt{a^2 x^2+b}+a x}+c}-\text{$\#$1}\right)}{\text{$\#$1} c-\text{$\#$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,"Defer[Int][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",0,0,0,0,-1,"{}"
2832,1,445,0,0.5785379,"\int \frac{x^2}{\left(b+a x^2\right) \sqrt[3]{x+x^3}} \, dx","Int[x^2/((b + a*x^2)*(x + x^3)^(1/3)),x]","\frac{\sqrt[3]{b} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{x^{4/3} (a-b)^{2/3}}{\left(x^2+1\right)^{2/3}}-\frac{\sqrt[3]{b} x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2+1}}+b^{2/3}\right)}{4 a \sqrt[3]{x^3+x} \sqrt[3]{a-b}}-\frac{\sqrt[3]{b} \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2+1}}+\sqrt[3]{b}\right)}{2 a \sqrt[3]{x^3+x} \sqrt[3]{a-b}}+\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\sqrt[3]{b}-\frac{2 x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2+1}}}{\sqrt{3} \sqrt[3]{b}}\right)}{2 a \sqrt[3]{x^3+x} \sqrt[3]{a-b}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right)}{2 a \sqrt[3]{x^3+x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right)}{4 a \sqrt[3]{x^3+x}}+\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 a \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,"(Sqrt[3]*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*a*(x + x^3)^(1/3)) + (Sqrt[3]*b^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(b^(1/3) - (2*(a - b)^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/(Sqrt[3]*b^(1/3))])/(2*a*(a - b)^(1/3)*(x + x^3)^(1/3)) - (x^(1/3)*(1 + x^2)^(1/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(2*a*(x + x^3)^(1/3)) + (x^(1/3)*(1 + x^2)^(1/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(4*a*(x + x^3)^(1/3)) - (b^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[b^(1/3) + ((a - b)^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*a*(a - b)^(1/3)*(x + x^3)^(1/3)) + (b^(1/3)*x^(1/3)*(1 + x^2)^(1/3)*Log[b^(2/3) + ((a - b)^(2/3)*x^(4/3))/(1 + x^2)^(2/3) - ((a - b)^(1/3)*b^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(4*a*(a - b)^(1/3)*(x + x^3)^(1/3))","A",17,12,22,0.5455,1,"{2042, 466, 465, 494, 481, 200, 31, 634, 618, 204, 628, 617}"
2833,0,0,0,2.4640696,"\int \frac{1+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Int[(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,"-1/6*(x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - x), x], x, x^(1/3)])/(x^2 + x^4)^(1/3) - (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(1/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(1/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(2/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(2/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(1/3)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(1/3)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(4/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(4/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(5/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(5/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(2/3)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(2/3)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(7/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(7/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 - (-1)^(8/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][(1 + x^6)^(2/3)/(1 + (-1)^(8/9)*x), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3))","F",0,0,0,0,-1,"{}"
2834,1,197,0,0.8889455,"\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","Int[(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{\left(-\sqrt{3}+i\right) \sqrt{\frac{3 \left(-\sqrt{3}+3 i\right)}{\sqrt{3}+i}} \tan ^{-1}\left(\frac{x^2}{\sqrt{\frac{-\sqrt{3}+3 i}{3 \left(\sqrt{3}+i\right)}} \sqrt{3 x^4-2}}\right)}{2 \left(-\sqrt{3}+3 i\right)}-\frac{\left(\sqrt{3}+i\right) \tanh ^{-1}\left(\frac{\sqrt{-\frac{3 \left(-\sqrt{3}+i\right)}{\sqrt{3}+3 i}} x^2}{\sqrt{3 x^4-2}}\right)}{2 \sqrt{\frac{2}{3} \left(3+i \sqrt{3}\right)}}","\frac{1}{2} \sqrt{3} \text{RootSum}\left[\text{$\#$1}^4-2 \text{$\#$1}^3+4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)-\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)-2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)}{2 \text{$\#$1}^3-3 \text{$\#$1}^2+2}\&\right]-\frac{1}{2} \sqrt{3} \text{RootSum}\left[\text{$\#$1}^4+2 \text{$\#$1}^3-4 \text{$\#$1}+4\&,\frac{\text{$\#$1}^2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)+\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)-2 \log \left(-\text{$\#$1}+\sqrt{3 x^4-2}+\sqrt{3} x^2\right)}{2 \text{$\#$1}^3+3 \text{$\#$1}^2-2}\&\right]+\frac{\sqrt{3 x^4-2}}{2 x^2}",1,"Sqrt[-2 + 3*x^4]/(2*x^2) - ((I - Sqrt[3])*Sqrt[(3*(3*I - Sqrt[3]))/(I + Sqrt[3])]*ArcTan[x^2/(Sqrt[(3*I - Sqrt[3])/(3*(I + Sqrt[3]))]*Sqrt[-2 + 3*x^4])])/(2*(3*I - Sqrt[3])) - ((I + Sqrt[3])*ArcTanh[(Sqrt[(-3*(I - Sqrt[3]))/(3*I + Sqrt[3])]*x^2)/Sqrt[-2 + 3*x^4]])/(2*Sqrt[(2*(3 + I*Sqrt[3]))/3])","C",16,11,36,0.3056,0,"{6728, 275, 277, 217, 206, 1490, 1293, 1692, 377, 205, 208}"
2835,0,0,0,4.1350772,"\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","Int[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,"(2*Sqrt[x]*Sqrt[-b + a^2*x]*Defer[Subst][Defer[Int][1/(x^4*(-b + a^2*x^2)^(5/2)*(a*x^4 + x^2*Sqrt[-(b*x^2) + a^2*x^4])^(3/2)), x], x, Sqrt[x]])/Sqrt[-(b*x) + a^2*x^2]","F",0,0,0,0,-1,"{}"
2836,0,0,0,6.6175479,"\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","Int[((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,"(3*a*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x*(a - b + x^3)^(2/3))/(-(a^2*(1 + (b*(-2*a + b))/a^2)*d) - 2*a*(1 - b/a)*d*x^3 - d*x^6 + x^12), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) + (3*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(a - b + x^3)^(2/3))/(-(a^2*(1 + (b*(-2*a + b))/a^2)*d) - 2*a*(1 - b/a)*d*x^3 - d*x^6 + x^12), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) - (3*(a - 2*b)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x*(a - b + x^3)^(2/3))/(a^2*(1 + b^2/a^2)*d - 2*b*d*x^3 + 2*a*d*(-b + x^3) + x^6*(d - x^6)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3)","F",0,0,0,0,-1,"{}"
2837,0,0,0,12.3070201,"\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","Int[((-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,"(-3*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - x^3)^(2/3))/((1 - k*x^3)^(1/3)*(1 - 4*k*x^3 - b*(1 - (6*k^2)/b)*x^6 + 2*b*(1 - (2*k^3)/b)*x^9 - b*(1 - k^4/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (3*(2 - k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^7*(1 - x^3)^(2/3))/((1 - k*x^3)^(1/3)*(1 - 4*k*x^3 - b*(1 - (6*k^2)/b)*x^6 + 2*b*(1 - (2*k^3)/b)*x^9 - b*(1 - k^4/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2838,1,109,0,0.3357675,"\int \frac{\left(-1+x^3\right)^{2/3} \left(4+x^6\right)}{x^6 \left(-4+x^6\right)} \, dx","Int[((-1 + x^3)^(2/3)*(4 + x^6))/(x^6*(-4 + x^6)),x]","-\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,-\frac{x^3}{2}\right)}{4 \left(1-x^3\right)^{2/3}}-\frac{x \left(x^3-1\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};x^3,\frac{x^3}{2}\right)}{4 \left(1-x^3\right)^{2/3}}-\frac{\left(x^3-1\right)^{5/3}}{5 x^5}","\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,"-1/5*(-1 + x^3)^(5/3)/x^5 - (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, -1/2*x^3])/(4*(1 - x^3)^(2/3)) - (x*(-1 + x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, x^3, x^3/2])/(4*(1 - x^3)^(2/3))","C",7,4,25,0.1600,0,"{6725, 264, 430, 429}"
2839,0,0,0,0.3137395,"\int \frac{\sqrt[6]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}}{\sqrt{-b+a^2 x^2}} \, dx","Int[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)/Sqrt[-b + a^2*x^2],x]","\int \frac{\sqrt[6]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}}{\sqrt{-b+a^2 x^2}} \, dx","\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,"Defer[Int][(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/6)/Sqrt[-b + a^2*x^2], x]","F",0,0,0,0,-1,"{}"
2840,0,0,0,6.1809115,"\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","Int[((-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,"(-3*(b - x)*x*(1 - x/a)^(2/3)*(1 - x/b)^(1/3)*AppellF1[1/3, 2/3, 1/3, 4/3, x/a, x/b])/(-((a - x)*(b - x)^2*x))^(2/3) + ((a - 2*b + d + Sqrt[a^2 + 2*a*d - 4*b*d + d^2])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(2/3)*(-b + x)^(1/3)*(-a - d - Sqrt[a^2 + 2*a*d - 4*b*d + d^2] + 2*x)), x])/(-((a - x)*(b - x)^2*x))^(2/3) + ((a - 2*b + d - Sqrt[a^2 + 2*a*d - 4*b*d + d^2])*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Int][1/(x^(2/3)*(-a + x)^(2/3)*(-b + x)^(1/3)*(-a - d + Sqrt[a^2 + 2*a*d - 4*b*d + d^2] + 2*x)), x])/(-((a - x)*(b - x)^2*x))^(2/3)","F",0,0,0,0,-1,"{}"
2841,1,190,0,0.1689848,"\int \frac{-d+c x^4}{x \sqrt[3]{-b+a x^3}} \, dx","Int[(-d + c*x^4)/(x*(-b + a*x^3)^(1/3)),x]","-\frac{b c \log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{6 a^{4/3}}+\frac{b c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} a^{4/3}}+\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)}{2 \sqrt[3]{b}}+\frac{d \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{d \log (x)}{2 \sqrt[3]{b}}","-\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,"(c*x*(-b + a*x^3)^(2/3))/(3*a) + (b*c*ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*a^(4/3)) + (d*ArcTan[(b^(1/3) - 2*(-b + a*x^3)^(1/3))/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*b^(1/3)) - (d*Log[x])/(2*b^(1/3)) + (d*Log[b^(1/3) + (-b + a*x^3)^(1/3)])/(2*b^(1/3)) - (b*c*Log[-(a^(1/3)*x) + (-b + a*x^3)^(1/3)])/(6*a^(4/3))","A",9,8,26,0.3077,1,"{1844, 266, 56, 617, 204, 31, 321, 239}"
2842,0,0,0,7.2471792,"\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","Int[(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,"(3*x*(1 - x/a)^(1/3)*(1 - x/b)^(2/3)*AppellF1[2/3, 1/3, 2/3, 5/3, x/a, x/b])/(2*d*(-((a - x)*(b - x)^2*x))^(1/3)) + ((1 + a*d - 2*b*d + Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*(-1 - a*d - Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2] + 2*d*x)), x])/(d*(-((a - x)*(b - x)^2*x))^(1/3)) + ((1 + a*d - 2*b*d - Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*(-1 - a*d + Sqrt[1 + 2*a*d - 4*b*d + a^2*d^2] + 2*d*x)), x])/(d*(-((a - x)*(b - x)^2*x))^(1/3))","F",0,0,0,0,-1,"{}"
2843,0,0,0,8.958305,"\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","Int[(-(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,"(3*(3*a - b)*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(a^2 - 2*a*(1 + (b^2*d)/(2*a))*x^3 + (1 + 2*b*d)*x^6 - d*x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-a^2 + 2*a*(1 + (b^2*d)/(2*a))*x^3 - (1 + 2*b*d)*x^6 + d*x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-a^2 + 2*a*(1 + (b^2*d)/(2*a))*x^3 - (1 + 2*b*d)*x^6 + d*x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3)","F",0,0,0,0,-1,"{}"
2844,0,0,0,7.4911695,"\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","Int[((-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,"(9*a*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(a - b + x^3)^(5/3)/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4) + 4*a^3*(1 - (12*a^2*b - 12*a*b^2 + 4*b^3 + d)/(4*a^3))*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*x^6 + 4*a*(1 - b/a)*x^9 + x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(2/3) + (9*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(x^3*(a - b + x^3)^(5/3))/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4) + 4*a^3*(1 - (12*a^2*b - 12*a*b^2 + 4*b^3 + d)/(4*a^3))*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*x^6 + 4*a*(1 - b/a)*x^9 + x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(2/3) - (3*(4*a - b)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(a - b + x^3)^(5/3)/(b^4*(1 + (a*d)/b^4) - (4*b^3 + d)*(a + x^3) + 6*b^2*(a + x^3)^2 - 4*b*(a + x^3)^3 + (a + x^3)^4), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(2/3)","F",0,0,0,0,-1,"{}"
2845,1,309,0,0.3981005,"\int \frac{\sqrt[4]{-b x^3+a x^4}}{x (-d+c x)} \, dx","Int[(-(b*x^3) + a*x^4)^(1/4)/(x*(-d + c*x)),x]","\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a d-b c} \tan ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a d-b c}}{\sqrt[4]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[4]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a x^4-b x^3} \sqrt[4]{a d-b c} \tanh ^{-1}\left(\frac{\sqrt[4]{x} \sqrt[4]{a d-b c}}{\sqrt[4]{d} \sqrt[4]{a x-b}}\right)}{c \sqrt[4]{d} x^{3/4} \sqrt[4]{a x-b}}-\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{c x^{3/4} \sqrt[4]{a x-b}}+\frac{2 \sqrt[4]{a} \sqrt[4]{a x^4-b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{a x-b}}\right)}{c x^{3/4} \sqrt[4]{a x-b}}","-\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,"(-2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(c*x^(3/4)*(-b + a*x)^(1/4)) + (2*(-(b*c) + a*d)^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTan[((-(b*c) + a*d)^(1/4)*x^(1/4))/(d^(1/4)*(-b + a*x)^(1/4))])/(c*d^(1/4)*x^(3/4)*(-b + a*x)^(1/4)) + (2*a^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(-b + a*x)^(1/4)])/(c*x^(3/4)*(-b + a*x)^(1/4)) - (2*(-(b*c) + a*d)^(1/4)*(-(b*x^3) + a*x^4)^(1/4)*ArcTanh[((-(b*c) + a*d)^(1/4)*x^(1/4))/(d^(1/4)*(-b + a*x)^(1/4))])/(c*d^(1/4)*x^(3/4)*(-b + a*x)^(1/4))","A",11,10,29,0.3448,1,"{2042, 105, 63, 331, 298, 203, 206, 93, 205, 208}"
2846,0,0,0,48.5355898,"\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","Int[((-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,"(3*(a + b)*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^6*(-a + x^3)^(1/3)*(-b + x^3)^(1/3))/(a^2*b^2*d - 2*a^2*b*(1 + b/a)*d*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*d*x^6 - 2*a*(1 + b/a)*d*x^9 - (1 - d)*x^12), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(2/3) + (6*a*b*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^3*(-a + x^3)^(1/3)*(-b + x^3)^(1/3))/(-(a^2*b^2*d) + 2*a^2*b*(1 + b/a)*d*x^3 - a^2*(1 + (b*(4*a + b))/a^2)*d*x^6 + 2*a*(1 + b/a)*d*x^9 + (1 - d)*x^12), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(2/3)","F",0,0,0,0,-1,"{}"
2847,-1,0,0,180.0093125,"\int \frac{1+x^3+x^6}{\sqrt[4]{x^3+x^5} \left(1-x^6\right)} \, dx","Int[(1 + x^3 + x^6)/((x^3 + x^5)^(1/4)*(1 - x^6)),x]","\text{\$Aborted}","\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,"$Aborted","F",0,0,0,0,-1,"{}"
2848,1,385,0,3.7552556,"\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","Int[(-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{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \left(-2 \sqrt{1-k^2} \left(a k^2+b\right)+2 a k^2+b \left(2-k^2\right)\right) \Pi \left(\frac{1}{1-\sqrt{1-k^2}};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\left(-k^2\right)^{3/2} \left(1-\sqrt{1-k^2}\right) \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}-\frac{(1-x) \sqrt{-x} \sqrt{x} \sqrt{1-k^2 x} \left(2 \sqrt{1-k^2} \left(a k^2+b\right)+2 a k^2+b \left(2-k^2\right)\right) \Pi \left(\frac{1}{\sqrt{1-k^2}+1};\sin ^{-1}\left(\sqrt{-k^2} \sqrt{-x}\right)|\frac{1}{k^2}\right)}{\left(-k^2\right)^{3/2} \left(\sqrt{1-k^2}+1\right) \sqrt{x-x^2} \sqrt{(1-x) x \left(1-k^2 x\right)}}+\frac{2 \sqrt{1-x} \sqrt{x} \sqrt{1-k^2 x} \left(a+\frac{b}{k^2}\right) F\left(\sin ^{-1}\left(\sqrt{x}\right)|k^2\right)}{\sqrt{(1-x) x \left(1-k^2 x\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,"(2*(a + b/k^2)*Sqrt[1 - x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticF[ArcSin[Sqrt[x]], k^2])/Sqrt[(1 - x)*x*(1 - k^2*x)] - ((2*a*k^2 + b*(2 - k^2) - 2*Sqrt[1 - k^2]*(b + a*k^2))*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(1 - Sqrt[1 - k^2])^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/((-k^2)^(3/2)*(1 - Sqrt[1 - k^2])*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2]) - ((2*a*k^2 + b*(2 - k^2) + 2*Sqrt[1 - k^2]*(b + a*k^2))*(1 - x)*Sqrt[-x]*Sqrt[x]*Sqrt[1 - k^2*x]*EllipticPi[(1 + Sqrt[1 - k^2])^(-1), ArcSin[Sqrt[-k^2]*Sqrt[-x]], k^(-2)])/((-k^2)^(3/2)*(1 + Sqrt[1 - k^2])*Sqrt[(1 - x)*x*(1 - k^2*x)]*Sqrt[x - x^2])","C",17,10,53,0.1887,0,"{6718, 6688, 6728, 6, 714, 115, 934, 12, 168, 537}"
2849,1,298,0,0.2846895,"\int \frac{1-2 x^4+x^8}{\sqrt[4]{-1+x^4} \left(1-2 x^4+2 x^8\right)} \, dx","Int[(1 - 2*x^4 + x^8)/((-1 + x^4)^(1/4)*(1 - 2*x^4 + 2*x^8)),x]","\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\left(\frac{1}{8}+\frac{i}{8}\right) \sqrt[8]{-1} \tan ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (-1)^{5/8} \tan ^{-1}\left(1-\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}\right)}{\sqrt{2}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (-1)^{5/8} \tan ^{-1}\left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}+1\right)}{\sqrt{2}}+\frac{1}{4} \tanh ^{-1}\left(\frac{x}{\sqrt[4]{x^4-1}}\right)-\left(\frac{1}{8}+\frac{i}{8}\right) \sqrt[8]{-1} \tanh ^{-1}\left(\frac{(-1)^{7/8} x}{\sqrt[4]{x^4-1}}\right)-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (-1)^{5/8} \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)}{\sqrt{2}}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (-1)^{5/8} \log \left(\frac{(-1)^{7/8} \sqrt{2} x}{\sqrt[4]{x^4-1}}-\frac{(-1)^{3/4} x^2}{\sqrt{x^4-1}}+1\right)}{\sqrt{2}}","\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,"ArcTan[x/(-1 + x^4)^(1/4)]/4 - (1/8 + I/8)*(-1)^(1/8)*ArcTan[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)] - ((1/8 + I/8)*(-1)^(5/8)*ArcTan[1 - ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/Sqrt[2] + ((1/8 + I/8)*(-1)^(5/8)*ArcTan[1 + ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/Sqrt[2] + ArcTanh[x/(-1 + x^4)^(1/4)]/4 - (1/8 + I/8)*(-1)^(1/8)*ArcTanh[((-1)^(7/8)*x)/(-1 + x^4)^(1/4)] - ((1/16 + I/16)*(-1)^(5/8)*Log[(-1)^(1/4) + x^2/Sqrt[-1 + x^4] + ((-1)^(1/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/Sqrt[2] + ((1/16 + I/16)*(-1)^(5/8)*Log[1 - ((-1)^(3/4)*x^2)/Sqrt[-1 + x^4] + ((-1)^(7/8)*Sqrt[2]*x)/(-1 + x^4)^(1/4)])/Sqrt[2]","C",28,15,34,0.4412,1,"{28, 1428, 416, 530, 240, 212, 206, 203, 377, 211, 1165, 628, 1162, 617, 204}"
2850,0,0,0,0.0748557,"\int \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Int[Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]],x]","\int \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","\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,"Defer[Int][Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]], x]","F",0,0,0,0,-1,"{}"
2851,0,0,0,1.785701,"\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","Int[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]","\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","-\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,"(3*x^(2/3)*(-a + x)^(1/3)*Defer[Subst][Defer[Int][x^9/((-a + x^3)^(1/3)*(-a^4 + 4*a^3*x^3 - 6*a^2*x^6 + 4*a*x^9 + (-1 + d)*x^12)), x], x, x^(1/3)])/(-((a - x)*x^2))^(1/3)","F",0,0,0,0,-1,"{}"
2852,0,0,0,0.4372368,"\int \frac{\sqrt{c+\sqrt{a x^2+x \sqrt{-b+a^2 x^2}}}}{\sqrt{-b+a^2 x^2}} \, dx","Int[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,"Defer[Int][Sqrt[c + Sqrt[a*x^2 + x*Sqrt[-b + a^2*x^2]]]/Sqrt[-b + a^2*x^2], x]","F",0,0,0,0,-1,"{}"
2853,0,0,0,8.9715698,"\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","Int[(-(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,"-(((2*a - b - c + Sqrt[b^2 + c^2 + 4*a^2*d - 4*a*c*d - 2*b*(c + 2*a*d - 2*c*d)])*(-a + x)^(2/3)*(-b + x)^(2/3)*(-c + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/((-b + x)^(2/3)*(-c + x)^(2/3)*(b + c - 2*a*d - Sqrt[b^2 - 2*b*c + c^2 + 4*a^2*d - 4*a*b*d - 4*a*c*d + 4*b*c*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(2/3)) - ((2*a - b - c - Sqrt[b^2 + c^2 + 4*a^2*d - 4*a*c*d - 2*b*(c + 2*a*d - 2*c*d)])*(-a + x)^(2/3)*(-b + x)^(2/3)*(-c + x)^(2/3)*Defer[Int][(-a + x)^(1/3)/((-b + x)^(2/3)*(-c + x)^(2/3)*(b + c - 2*a*d + Sqrt[b^2 - 2*b*c + c^2 + 4*a^2*d - 4*a*b*d - 4*a*c*d + 4*b*c*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(2/3)","F",0,0,0,0,-1,"{}"
2854,0,0,0,24.6826107,"\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","Int[(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,"(6*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^7/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3) - (3*(a + b)*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^10/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (b*(4*a + b))/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2855,-1,0,0,0,"\int \frac{1+x^6}{\sqrt[4]{x^3+x^5} \left(1-x^6\right)} \, dx","Int[(1 + x^6)/((x^3 + x^5)^(1/4)*(1 - x^6)),x]","\text{\$Aborted}","\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,"$Aborted","F",0,0,0,0,-1,"{}"
2856,1,506,0,1.7077884,"\int \frac{b^{16}+a^{16} x^{16}}{\sqrt{-b^4+a^4 x^4} \left(-b^{16}+a^{16} x^{16}\right)} \, dx","Int[(b^16 + a^16*x^16)/(Sqrt[-b^4 + a^4*x^4]*(-b^16 + a^16*x^16)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{8 \sqrt{2} \sqrt[4]{-a^4} b}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{8 \sqrt{2} \sqrt[4]{-a^4} b}+\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{2 a \sqrt{a^4 x^4-b^4}}-\frac{x \left(b^2-a^2 x^2\right)}{8 b^2 \sqrt{a^4 x^4-b^4}}-\frac{x \left(a^2 x^2+b^2\right)}{8 b^2 \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{a^6}{\left(-a^8\right)^{3/4}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt[4]{-a^8}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a \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,"-1/8*(x*(b^2 - a^2*x^2))/(b^2*Sqrt[-b^4 + a^4*x^4]) - (x*(b^2 + a^2*x^2))/(8*b^2*Sqrt[-b^4 + a^4*x^4]) - ArcTan[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]]/(8*Sqrt[2]*(-a^4)^(1/4)*b) - ArcTanh[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]]/(8*Sqrt[2]*(-a^4)^(1/4)*b) + (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(2*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[a^6/(-a^8)^(3/4), ArcSin[(a*x)/b], -1])/(4*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-a^8)^(1/4)/a^2, ArcSin[(a*x)/b], -1])/(4*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(Sqrt[-Sqrt[-a^8]]/a^2), ArcSin[(a*x)/b], -1])/(4*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[Sqrt[-Sqrt[-a^8]]/a^2, ArcSin[(a*x)/b], -1])/(4*a*Sqrt[-b^4 + a^4*x^4])","C",44,20,44,0.4545,1,"{6725, 224, 221, 2073, 1152, 414, 21, 423, 427, 426, 424, 253, 409, 1211, 1699, 203, 206, 1429, 1219, 1218}"
2857,1,866,0,1.3543991,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{b+a x^2} \, dx","Int[(-(b^2*x^2) + a^3*x^3)^(1/3)/(b + a*x^2),x]","-\frac{\sqrt{3} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x} a}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{b}-\sqrt{-a} x\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{-a} x+\sqrt{b}\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3 x^3-b^2 x^2} \log \left(a^3 x-b^2\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{3 \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\frac{a \sqrt[3]{x}}{\sqrt[3]{a^3 x-b^2}}-1\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}","\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,"-((Sqrt[3]*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(x^(2/3)*(-b^2 + a^3*x)^(1/3))) + (Sqrt[3]*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (Sqrt[3]*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] - Sqrt[-a]*x])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] + Sqrt[-a]*x])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-b^2 + a^3*x])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - (3*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-1 + (a*x^(1/3))/(-b^2 + a^3*x)^(1/3)])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3))","B",7,5,30,0.1667,1,"{2056, 906, 59, 6725, 91}"
2858,1,866,0,0.7865129,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{b+a x^2} \, dx","Int[(-(b^2*x^2) + a^3*x^3)^(1/3)/(b + a*x^2),x]","-\frac{\sqrt{3} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x} a}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{b}-\sqrt{-a} x\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{-a} x+\sqrt{b}\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3 x^3-b^2 x^2} \log \left(a^3 x-b^2\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{3 \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\frac{a \sqrt[3]{x}}{\sqrt[3]{a^3 x-b^2}}-1\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[3]{a^3-\sqrt{-a} b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[3]{a^3+\sqrt{-a} b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a x^{2/3} \sqrt[3]{a^3 x-b^2}}","\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,"-((Sqrt[3]*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(x^(2/3)*(-b^2 + a^3*x)^(1/3))) + (Sqrt[3]*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (Sqrt[3]*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] - Sqrt[-a]*x])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] + Sqrt[-a]*x])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-b^2 + a^3*x])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - (3*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-1 + (a*x^(1/3))/(-b^2 + a^3*x)^(1/3)])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[(a^3 - Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[(a^3 + Sqrt[-a]*b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a*x^(2/3)*(-b^2 + a^3*x)^(1/3))","B",7,5,30,0.1667,1,"{2056, 906, 59, 6725, 91}"
2859,1,338,0,0.7663588,"\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","Int[(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{1}{a^4 b^4}+2\right)}{4 \sqrt{a^4 x^4-b^4}}+\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{a \sqrt{a^4 x^4-b^4}}-\frac{\left(1-2 a^4 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{8 \sqrt{2} \left(-a^4\right)^{5/4} b^5}-\frac{\left(1-2 a^4 b^4\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{8 \sqrt{2} \left(-a^4\right)^{5/4} b^5}+\frac{\left(1-2 a^4 b^4\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a^5 b^3 \sqrt{a^4 x^4-b^4}}-\frac{\left(2 a^4 b^4+1\right) \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a^5 b^3 \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,"-1/4*((2 + 1/(a^4*b^4))*x)/Sqrt[-b^4 + a^4*x^4] - ((1 - 2*a^4*b^4)*ArcTan[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]])/(8*Sqrt[2]*(-a^4)^(5/4)*b^5) - ((1 - 2*a^4*b^4)*ArcTanh[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]])/(8*Sqrt[2]*(-a^4)^(5/4)*b^5) + (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(a*Sqrt[-b^4 + a^4*x^4]) + ((1 - 2*a^4*b^4)*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(4*a^5*b^3*Sqrt[-b^4 + a^4*x^4]) - ((1 + 2*a^4*b^4)*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(4*a^5*b^3*Sqrt[-b^4 + a^4*x^4])","C",20,11,47,0.2340,1,"{6725, 224, 221, 1455, 527, 523, 409, 1211, 1699, 203, 206}"
2860,1,839,0,1.1118906,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{-b+a x^2} \, dx","Int[(-(b^2*x^2) + a^3*x^3)^(1/3)/(-b + a*x^2),x]","-\frac{\sqrt{3} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x} a}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[6]{a} \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[6]{a} \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{b}-\sqrt{a} x\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{a} x+\sqrt{b}\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3 x^3-b^2 x^2} \log \left(a^3 x-b^2\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{3 \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\frac{a \sqrt[3]{x}}{\sqrt[3]{a^3 x-b^2}}-1\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[6]{a} \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[6]{a} \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}","\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,"-((Sqrt[3]*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(x^(2/3)*(-b^2 + a^3*x)^(1/3))) + (Sqrt[3]*(a^(5/2) - b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a^(1/6)*(a^(5/2) - b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (Sqrt[3]*(a^(5/2) + b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a^(1/6)*(a^(5/2) + b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^(5/2) - b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] - Sqrt[a]*x])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^(5/2) + b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] + Sqrt[a]*x])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-b^2 + a^3*x])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - (3*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-1 + (a*x^(1/3))/(-b^2 + a^3*x)^(1/3)])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^(5/2) - b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[a^(1/6)*(a^(5/2) - b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^(5/2) + b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[a^(1/6)*(a^(5/2) + b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3))","B",7,5,32,0.1562,1,"{2056, 906, 59, 6725, 91}"
2861,1,839,0,0.7838053,"\int \frac{\sqrt[3]{-b^2 x^2+a^3 x^3}}{-b+a x^2} \, dx","Int[(-(b^2*x^2) + a^3*x^3)^(1/3)/(-b + a*x^2),x]","-\frac{\sqrt{3} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x} a}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[6]{a} \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{\sqrt{3} \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[6]{a} \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x-b^2}}+\frac{1}{\sqrt{3}}\right)}{2 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{b}-\sqrt{a} x\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt{a} x+\sqrt{b}\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{\sqrt[3]{a^3 x^3-b^2 x^2} \log \left(a^3 x-b^2\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}-\frac{3 \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\frac{a \sqrt[3]{x}}{\sqrt[3]{a^3 x-b^2}}-1\right)}{2 x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[6]{a} \sqrt[3]{a^{5/2}-b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}+\frac{3 \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{a^3 x^3-b^2 x^2} \log \left(\sqrt[6]{a} \sqrt[3]{a^{5/2}+b^{3/2}} \sqrt[3]{x}-\sqrt[3]{a^3 x-b^2}\right)}{4 a^{5/6} x^{2/3} \sqrt[3]{a^3 x-b^2}}","\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,"-((Sqrt[3]*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(x^(2/3)*(-b^2 + a^3*x)^(1/3))) + (Sqrt[3]*(a^(5/2) - b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a^(1/6)*(a^(5/2) - b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (Sqrt[3]*(a^(5/2) + b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a^(1/6)*(a^(5/2) + b^(3/2))^(1/3)*x^(1/3))/(Sqrt[3]*(-b^2 + a^3*x)^(1/3))])/(2*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^(5/2) - b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] - Sqrt[a]*x])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((a^(5/2) + b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[Sqrt[b] + Sqrt[a]*x])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - ((-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-b^2 + a^3*x])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) - (3*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[-1 + (a*x^(1/3))/(-b^2 + a^3*x)^(1/3)])/(2*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^(5/2) - b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[a^(1/6)*(a^(5/2) - b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3)) + (3*(a^(5/2) + b^(3/2))^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)*Log[a^(1/6)*(a^(5/2) + b^(3/2))^(1/3)*x^(1/3) - (-b^2 + a^3*x)^(1/3)])/(4*a^(5/6)*x^(2/3)*(-b^2 + a^3*x)^(1/3))","B",7,5,32,0.1562,1,"{2056, 906, 59, 6725, 91}"
2862,1,240,0,0.5991238,"\int \frac{-b+x}{\left((-a+x) (-b+x)^2\right)^{2/3} (a-b d+(-1+d) x)} \, dx","Int[(-b + x)/(((-a + x)*(-b + x)^2)^(2/3)*(a - b*d + (-1 + d)*x)),x]","\frac{(x-a)^{2/3} (x-b)^{4/3} \log (a-b d-(1-d) x)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(\sqrt[3]{d} \sqrt[3]{x-b}-\sqrt[3]{x-a}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\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,"-((Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/((a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3))) + ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[a - b*d - (1 - d)*x])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + d^(1/3)*(-b + x)^(1/3)])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3))","A",2,2,36,0.05556,1,"{6719, 91}"
2863,1,391,0,1.2518148,"\int \frac{\sqrt{-b+x^2} \left(c+x^4\right) \sqrt{x+\sqrt{-b+x^2}}}{x} \, dx","Int[(Sqrt[-b + x^2]*(c + x^4)*Sqrt[x + Sqrt[-b + x^2]])/x,x]","-\frac{b^{3/4} c \log \left(\sqrt{x^2-b}-\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{x^2-b}+x}+\sqrt{b}+x\right)}{\sqrt{2}}+\frac{b^{3/4} c \log \left(\sqrt{x^2-b}+\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{x^2-b}+x}+\sqrt{b}+x\right)}{\sqrt{2}}+\sqrt{2} b^{3/4} c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sqrt{x^2-b}+x}}{\sqrt[4]{b}}\right)-\sqrt{2} b^{3/4} c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{x^2-b}+x}}{\sqrt[4]{b}}+1\right)-\frac{b^5}{144 \left(\sqrt{x^2-b}+x\right)^{9/2}}-\frac{b^4}{80 \left(\sqrt{x^2-b}+x\right)^{5/2}}+\frac{b^3}{8 \sqrt{\sqrt{x^2-b}+x}}-\frac{1}{24} b^2 \left(\sqrt{x^2-b}+x\right)^{3/2}+\frac{1}{3} c \left(\sqrt{x^2-b}+x\right)^{3/2}-\frac{b c}{\sqrt{\sqrt{x^2-b}+x}}+\frac{1}{176} \left(\sqrt{x^2-b}+x\right)^{11/2}+\frac{1}{112} b \left(\sqrt{x^2-b}+x\right)^{7/2}","\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,"-1/144*b^5/(x + Sqrt[-b + x^2])^(9/2) - b^4/(80*(x + Sqrt[-b + x^2])^(5/2)) + b^3/(8*Sqrt[x + Sqrt[-b + x^2]]) - (b*c)/Sqrt[x + Sqrt[-b + x^2]] - (b^2*(x + Sqrt[-b + x^2])^(3/2))/24 + (c*(x + Sqrt[-b + x^2])^(3/2))/3 + (b*(x + Sqrt[-b + x^2])^(7/2))/112 + (x + Sqrt[-b + x^2])^(11/2)/176 + Sqrt[2]*b^(3/4)*c*ArcTan[1 - (Sqrt[2]*Sqrt[x + Sqrt[-b + x^2]])/b^(1/4)] - Sqrt[2]*b^(3/4)*c*ArcTan[1 + (Sqrt[2]*Sqrt[x + Sqrt[-b + x^2]])/b^(1/4)] - (b^(3/4)*c*Log[Sqrt[b] + x + Sqrt[-b + x^2] - Sqrt[2]*b^(1/4)*Sqrt[x + Sqrt[-b + x^2]]])/Sqrt[2] + (b^(3/4)*c*Log[Sqrt[b] + x + Sqrt[-b + x^2] + Sqrt[2]*b^(1/4)*Sqrt[x + Sqrt[-b + x^2]]])/Sqrt[2]","A",18,12,37,0.3243,1,"{6742, 2120, 462, 459, 329, 297, 1162, 617, 204, 1165, 628, 448}"
2864,1,522,0,1.2454136,"\int \frac{x^8}{\sqrt{-b^4+a^4 x^4} \left(-b^{16}+a^{16} x^{16}\right)} \, dx","Int[x^8/(Sqrt[-b^4 + a^4*x^4]*(-b^16 + a^16*x^16)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{16 \sqrt{2} \left(-a^4\right)^{9/4} b^9}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{16 \sqrt{2} \left(-a^4\right)^{9/4} b^9}-\frac{\sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{4 a^9 b^7 \sqrt{a^4 x^4-b^4}}-\frac{x \left(b^2-a^2 x^2\right)}{16 a^8 b^{10} \sqrt{a^4 x^4-b^4}}-\frac{x \left(a^2 x^2+b^2\right)}{16 a^8 b^{10} \sqrt{a^4 x^4-b^4}}+\frac{\sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{a^6}{\left(-a^8\right)^{3/4}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{8 a^9 b^7 \sqrt{a^4 x^4-b^4}}+\frac{\sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt[4]{-a^8}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{8 a^9 b^7 \sqrt{a^4 x^4-b^4}}+\frac{\sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{8 a^9 b^7 \sqrt{a^4 x^4-b^4}}+\frac{\sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{\sqrt{-\sqrt{-a^8}}}{a^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{8 a^9 b^7 \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,"-1/16*(x*(b^2 - a^2*x^2))/(a^8*b^10*Sqrt[-b^4 + a^4*x^4]) - (x*(b^2 + a^2*x^2))/(16*a^8*b^10*Sqrt[-b^4 + a^4*x^4]) - ArcTan[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]]/(16*Sqrt[2]*(-a^4)^(9/4)*b^9) - ArcTanh[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]]/(16*Sqrt[2]*(-a^4)^(9/4)*b^9) - (Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(4*a^9*b^7*Sqrt[-b^4 + a^4*x^4]) + (Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[a^6/(-a^8)^(3/4), ArcSin[(a*x)/b], -1])/(8*a^9*b^7*Sqrt[-b^4 + a^4*x^4]) + (Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-a^8)^(1/4)/a^2, ArcSin[(a*x)/b], -1])/(8*a^9*b^7*Sqrt[-b^4 + a^4*x^4]) + (Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[-(Sqrt[-Sqrt[-a^8]]/a^2), ArcSin[(a*x)/b], -1])/(8*a^9*b^7*Sqrt[-b^4 + a^4*x^4]) + (Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[Sqrt[-Sqrt[-a^8]]/a^2, ArcSin[(a*x)/b], -1])/(8*a^9*b^7*Sqrt[-b^4 + a^4*x^4])","C",40,19,36,0.5278,1,"{6725, 1152, 414, 21, 423, 427, 426, 424, 253, 224, 221, 409, 1211, 1699, 203, 206, 1429, 1219, 1218}"
2865,1,457,0,0.5301873,"\int \frac{x^2}{\left(-b+a x^2\right) \sqrt[3]{-x+x^3}} \, dx","Int[x^2/((-b + a*x^2)*(-x + x^3)^(1/3)),x]","\frac{\sqrt[3]{b} \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{x^{4/3} (a-b)^{2/3}}{\left(x^2-1\right)^{2/3}}-\frac{\sqrt[3]{b} x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2-1}}+b^{2/3}\right)}{4 a \sqrt[3]{x^3-x} \sqrt[3]{a-b}}-\frac{\sqrt[3]{b} \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2-1}}+\sqrt[3]{b}\right)}{2 a \sqrt[3]{x^3-x} \sqrt[3]{a-b}}+\frac{\sqrt{3} \sqrt[3]{b} \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\sqrt[3]{b}-\frac{2 x^{2/3} \sqrt[3]{a-b}}{\sqrt[3]{x^2-1}}}{\sqrt{3} \sqrt[3]{b}}\right)}{2 a \sqrt[3]{x^3-x} \sqrt[3]{a-b}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right)}{2 a \sqrt[3]{x^3-x}}+\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right)}{4 a \sqrt[3]{x^3-x}}+\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 a \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,"(Sqrt[3]*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*a*(-x + x^3)^(1/3)) + (Sqrt[3]*b^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(b^(1/3) - (2*(a - b)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3))/(Sqrt[3]*b^(1/3))])/(2*a*(a - b)^(1/3)*(-x + x^3)^(1/3)) - (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(2*a*(-x + x^3)^(1/3)) + (x^(1/3)*(-1 + x^2)^(1/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(4*a*(-x + x^3)^(1/3)) - (b^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)*Log[b^(1/3) + ((a - b)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(2*a*(a - b)^(1/3)*(-x + x^3)^(1/3)) + (b^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)*Log[b^(2/3) + ((a - b)^(2/3)*x^(4/3))/(-1 + x^2)^(2/3) - ((a - b)^(1/3)*b^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(4*a*(a - b)^(1/3)*(-x + x^3)^(1/3))","A",17,12,26,0.4615,1,"{2042, 466, 465, 494, 481, 200, 31, 634, 618, 204, 628, 617}"
2866,1,343,0,0.7649727,"\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}}}{-1+x^4} \, dx","Int[((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}}+\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)-\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\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)-\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)+\sqrt{\sqrt{2}-1} \tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\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 + Sqrt[1 + Sqrt[2]]*ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]] - Sqrt[-1 + Sqrt[2]]*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^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]]] - Sqrt[1 + Sqrt[2]]*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]] + Sqrt[-1 + Sqrt[2]]*ArcTanh[Sqrt[1 + 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] + Log[1 + x + Sqrt[1 + x^2] + Sqrt[2]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[2]","A",34,18,28,0.6429,1,"{6725, 2117, 14, 2119, 1628, 826, 1166, 204, 206, 207, 203, 2122, 329, 297, 1162, 617, 1165, 628}"
2867,1,513,0,1.2265171,"\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","Int[((-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{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 \left(\sqrt{d}+1\right) \left(b-a \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 (1-d) x-2 \left(1-\sqrt{d}\right) \left(a \sqrt{d}+b\right)\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(-\sqrt[3]{x-a}-\frac{\sqrt[3]{x-b}}{\sqrt[6]{d}}\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(\frac{\sqrt[3]{x-b}}{\sqrt[6]{d}}-\sqrt[3]{x-a}\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-b}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-b}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\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,"(Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] - (2*(-b + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*(-b + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 + Sqrt[d])*(b - a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[-2*(1 - Sqrt[d])*(b + a*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) - (-b + x)^(1/3)/d^(1/6)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + (-b + x)^(1/3)/d^(1/6)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3))","A",9,5,57,0.08772,1,"{6719, 911, 105, 59, 91}"
2868,1,513,0,0.8576422,"\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","Int[(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{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 \left(\sqrt{d}+1\right) \left(b-a \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 (1-d) x-2 \left(1-\sqrt{d}\right) \left(a \sqrt{d}+b\right)\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(-\sqrt[3]{x-a}-\frac{\sqrt[3]{x-b}}{\sqrt[6]{d}}\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(\frac{\sqrt[3]{x-b}}{\sqrt[6]{d}}-\sqrt[3]{x-a}\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-b}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-b}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\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,"(Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] - (2*(-b + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*(-b + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 + Sqrt[d])*(b - a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[-2*(1 - Sqrt[d])*(b + a*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) - (-b + x)^(1/3)/d^(1/6)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + (-b + x)^(1/3)/d^(1/6)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3))","A",10,6,60,0.1000,1,"{6719, 24, 911, 105, 59, 91}"
2869,0,0,0,1.3257316,"\int \frac{x}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[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{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^7 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+3 \text{$\#$1}^5 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^3 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1}^3 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$1} c^3+a^2 c}\&\right]",1,"Log[b^2 - 2*b*(b + a*x) + (b + a*x)^2 - a^2*Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]]/2 + (a^2*c*Defer[Subst][Defer[Int][(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6))^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]])/2 + (3*a^2*Defer[Subst][Defer[Int][x^2/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]])/2","F",0,0,0,0,-1,"{}"
2870,0,0,0,1.0563857,"\int \frac{x}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[x/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^7 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)+3 \text{$\#$1}^5 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^3 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1}^3 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$1} c^3+a^2 c}\&\right]",1,"Log[b^2 - 2*b*(b + a*x) + (b + a*x)^2 - a^2*Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]]/2 + (a^2*c*Defer[Subst][Defer[Int][(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6))^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]])/2 + (3*a^2*Defer[Subst][Defer[Int][x^2/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]])/2","F",0,0,0,0,-1,"{}"
2871,0,0,0,5.6577826,"\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","Int[(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,"(3*x*(1 - x/a)^(1/3)*(1 - x/b)^(2/3)*AppellF1[2/3, 1/3, 2/3, 5/3, x/a, x/b])/(2*(-((a - x)*(b - x)^2*x))^(1/3)) + ((a - 2*b + d + Sqrt[a^2 + 2*a*d - 4*b*d + d^2])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*(-a - d - Sqrt[a^2 + 2*a*d - 4*b*d + d^2] + 2*x)), x])/(-((a - x)*(b - x)^2*x))^(1/3) + ((a - 2*b + d - Sqrt[a^2 + 2*a*d - 4*b*d + d^2])*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Int][1/(x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*(-a - d + Sqrt[a^2 + 2*a*d - 4*b*d + d^2] + 2*x)), x])/(-((a - x)*(b - x)^2*x))^(1/3)","F",0,0,0,0,-1,"{}"
2872,0,0,0,8.9195818,"\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","Int[(-(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,"(3*(3*a - b)*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(a^2*d - b^2*(1 + (2*a*d)/b^2)*x^3 + 2*b*(1 + d/(2*b))*x^6 - x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(a^2*d) + b^2*(1 + (2*a*d)/b^2)*x^3 - 2*b*(1 + d/(2*b))*x^6 + x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(a^2*d) + b^2*(1 + (2*a*d)/b^2)*x^3 - 2*b*(1 + d/(2*b))*x^6 + x^9)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3)","F",0,0,0,0,-1,"{}"
2873,1,219,0,0.2402499,"\int \frac{-d+c x^7}{x \sqrt[3]{-b+a x^3}} \, dx","Int[(-d + c*x^7)/(x*(-b + a*x^3)^(1/3)),x]","-\frac{b^2 c \log \left(\sqrt[3]{a x^3-b}-\sqrt[3]{a} x\right)}{9 a^{7/3}}+\frac{2 b^2 c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a} x}{\sqrt[3]{a x^3-b}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} a^{7/3}}+\frac{2 b c x \left(a x^3-b\right)^{2/3}}{9 a^2}+\frac{c x^4 \left(a x^3-b\right)^{2/3}}{6 a}+\frac{d \log \left(\sqrt[3]{a x^3-b}+\sqrt[3]{b}\right)}{2 \sqrt[3]{b}}+\frac{d \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a x^3-b}}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt{3} \sqrt[3]{b}}-\frac{d \log (x)}{2 \sqrt[3]{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,"(2*b*c*x*(-b + a*x^3)^(2/3))/(9*a^2) + (c*x^4*(-b + a*x^3)^(2/3))/(6*a) + (2*b^2*c*ArcTan[(1 + (2*a^(1/3)*x)/(-b + a*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*a^(7/3)) + (d*ArcTan[(b^(1/3) - 2*(-b + a*x^3)^(1/3))/(Sqrt[3]*b^(1/3))])/(Sqrt[3]*b^(1/3)) - (d*Log[x])/(2*b^(1/3)) + (d*Log[b^(1/3) + (-b + a*x^3)^(1/3)])/(2*b^(1/3)) - (b^2*c*Log[-(a^(1/3)*x) + (-b + a*x^3)^(1/3)])/(9*a^(7/3))","A",10,9,26,0.3462,1,"{1836, 1844, 266, 56, 617, 204, 31, 321, 239}"
2874,1,256,0,1.7379792,"\int \frac{\sqrt{c+\sqrt{b+a x}}}{x-\sqrt{b+a x}} \, dx","Int[Sqrt[c + Sqrt[b + a*x]]/(x - Sqrt[b + a*x]),x]","\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}}-\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 - a*(Sqrt[a^2 + 4*b] - c) - 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",6,4,31,0.1290,1,"{824, 826, 1166, 206}"
2875,1,454,0,1.0155591,"\int \frac{1+x}{(1+2 x) \sqrt[3]{27+27 x+36 x^2+28 x^3+9 x^4+x^5}} \, dx","Int[(1 + x)/((1 + 2*x)*(27 + 27*x + 36*x^2 + 28*x^3 + 9*x^4 + x^5)^(1/3)),x]","\frac{2 x (x+3) \sqrt[3]{x^2+1} F_1\left(\frac{1}{2};1,\frac{1}{3};\frac{3}{2};\frac{x^2}{9},-x^2\right)}{15 \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}+\frac{x (x+3) \sqrt[3]{x^2+1} F_1\left(\frac{1}{2};1,\frac{1}{3};\frac{3}{2};4 x^2,-x^2\right)}{5 \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}-\frac{(x+3) \sqrt[3]{x^2+1} \log \left(1-4 x^2\right)}{20 \sqrt[3]{10} \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}-\frac{(x+3) \sqrt[3]{x^2+1} \log \left(9-x^2\right)}{10 \sqrt[3]{10} \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}+\frac{3 (x+3) \sqrt[3]{x^2+1} \log \left(\sqrt[3]{10}-2 \sqrt[3]{x^2+1}\right)}{20 \sqrt[3]{10} \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}+\frac{3 (x+3) \sqrt[3]{x^2+1} \log \left(\sqrt[3]{10}-\sqrt[3]{x^2+1}\right)}{10 \sqrt[3]{10} \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}+\frac{\sqrt{3} (x+3) \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{x^2+1}+\sqrt[3]{5}}{\sqrt{3} \sqrt[3]{5}}\right)}{5 \sqrt[3]{10} \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}+\frac{\sqrt{3} (x+3) \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{2\ 2^{2/3} \sqrt[3]{x^2+1}+\sqrt[3]{5}}{\sqrt{3} \sqrt[3]{5}}\right)}{10 \sqrt[3]{10} \sqrt[3]{(x+3)^3 \left(x^2+1\right)}}","\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,"(2*x*(3 + x)*(1 + x^2)^(1/3)*AppellF1[1/2, 1, 1/3, 3/2, x^2/9, -x^2])/(15*((3 + x)^3*(1 + x^2))^(1/3)) + (x*(3 + x)*(1 + x^2)^(1/3)*AppellF1[1/2, 1, 1/3, 3/2, 4*x^2, -x^2])/(5*((3 + x)^3*(1 + x^2))^(1/3)) + (Sqrt[3]*(3 + x)*(1 + x^2)^(1/3)*ArcTan[(5^(1/3) + 2^(2/3)*(1 + x^2)^(1/3))/(Sqrt[3]*5^(1/3))])/(5*10^(1/3)*((3 + x)^3*(1 + x^2))^(1/3)) + (Sqrt[3]*(3 + x)*(1 + x^2)^(1/3)*ArcTan[(5^(1/3) + 2*2^(2/3)*(1 + x^2)^(1/3))/(Sqrt[3]*5^(1/3))])/(10*10^(1/3)*((3 + x)^3*(1 + x^2))^(1/3)) - ((3 + x)*(1 + x^2)^(1/3)*Log[1 - 4*x^2])/(20*10^(1/3)*((3 + x)^3*(1 + x^2))^(1/3)) - ((3 + x)*(1 + x^2)^(1/3)*Log[9 - x^2])/(10*10^(1/3)*((3 + x)^3*(1 + x^2))^(1/3)) + (3*(3 + x)*(1 + x^2)^(1/3)*Log[10^(1/3) - 2*(1 + x^2)^(1/3)])/(20*10^(1/3)*((3 + x)^3*(1 + x^2))^(1/3)) + (3*(3 + x)*(1 + x^2)^(1/3)*Log[10^(1/3) - (1 + x^2)^(1/3)])/(10*10^(1/3)*((3 + x)^3*(1 + x^2))^(1/3))","C",20,10,38,0.2632,0,"{6688, 6719, 6742, 757, 429, 444, 55, 617, 204, 31}"
2876,1,2011,0,2.2391145,"\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","Int[(-(b*x) + a*x^3)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-2} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-\sqrt[3]{2} \sqrt[3]{a} x\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a} x\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/2*((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-2)^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - 2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,6,42,0.1429,0,"{1593, 2056, 6725, 105, 59, 91}"
2877,1,2011,0,1.4928132,"\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","Int[(-(b*x) + a*x^3)/((-b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-2} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-\sqrt[3]{2} \sqrt[3]{a} x\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{b}-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a} x\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}+(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/2*((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) + (-2)^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - 2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b^(1/3) - (-1)^(2/3)*2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) - (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) + 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) + (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,6,42,0.1429,0,"{1593, 2056, 6725, 105, 59, 91}"
2878,1,2012,0,2.0651928,"\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","Int[(b*x + a*x^3)/((b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-2} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[3]{2} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/2*((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) + (-2)^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - 2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,6,39,0.1538,0,"{1593, 2056, 6725, 105, 59, 91}"
2879,0,0,0,12.7871879,"\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","Int[(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,"(3*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(-b + x^3)^(2/3))/((-a + x^3)^(1/3)*(-a^4 + 4*a^3*x^3 - 6*a^2*(1 - (b^2*d)/(6*a^2))*x^6 + 4*a*(1 - (b*d)/(2*a))*x^9 - (1 - d)*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3) + (3*(2*a - b)*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^7*(-b + x^3)^(2/3))/((-a + x^3)^(1/3)*(a^4 - 4*a^3*x^3 + 6*a^2*(1 - (b^2*d)/(6*a^2))*x^6 - 4*a*(1 - (b*d)/(2*a))*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2880,0,0,0,9.8506578,"\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","Int[(-(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,"((2*a - b - c + Sqrt[b^2 + c^2 + 4*a^2*d - 4*a*c*d - 2*b*(c + 2*a*d - 2*c*d)])*(-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*Defer[Int][1/((-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*(b + c - 2*a*d - Sqrt[b^2 - 2*b*c + c^2 + 4*a^2*d - 4*a*b*d - 4*a*c*d + 4*b*c*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(1/3) + ((2*a - b - c - Sqrt[b^2 + c^2 + 4*a^2*d - 4*a*c*d - 2*b*(c + 2*a*d - 2*c*d)])*(-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*Defer[Int][1/((-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*(b + c - 2*a*d + Sqrt[b^2 - 2*b*c + c^2 + 4*a^2*d - 4*a*b*d - 4*a*c*d + 4*b*c*d] + 2*(-1 + d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(1/3)","F",0,0,0,0,-1,"{}"
2881,0,0,0,15.3458155,"\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","Int[(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,"(3*a*b*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^3/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(-(a^2*b^2) + 2*a^2*b*(1 + b/a)*x^3 - a^2*(1 + (4*a*b + b^2 - d)/a^2)*x^6 + 2*a*(1 + b/a)*x^9 - x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (3*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^9/((-a + x^3)^(1/3)*(-b + x^3)^(1/3)*(a^2*b^2 - 2*a^2*b*(1 + b/a)*x^3 + a^2*(1 + (4*a*b + b^2 - d)/a^2)*x^6 - 2*a*(1 + b/a)*x^9 + x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3)","F",0,0,0,0,-1,"{}"
2882,1,1295,0,8.7513392,"\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","Int[(-b^6 + a^6*x^6)/(Sqrt[-(b^2*x) + a^2*x^3]*(b^6 + a^6*x^6)),x]","-\frac{(-1)^{2/3} \left(a-(-1)^{2/3} \sqrt[6]{-a^6}\right) \left(\sqrt[3]{-1} a^4-(-1)^{2/3} \sqrt[3]{-a^6} a^2-\left(-a^6\right)^{2/3}\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 a^{11/2} \sqrt{a^2 x^3-b^2 x}}-\frac{(-1)^{2/3} \left(a+(-1)^{2/3} \sqrt[6]{-a^6}\right) \left(\sqrt[3]{-1} a^4-(-1)^{2/3} \sqrt[3]{-a^6} a^2-\left(-a^6\right)^{2/3}\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 a^{11/2} \sqrt{a^2 x^3-b^2 x}}-\frac{\sqrt[3]{-1} \left(a-\sqrt[3]{-1} \sqrt[6]{-a^6}\right) \left(\frac{\sqrt[3]{-1} a^8}{\left(-a^6\right)^{2/3}}+(-1)^{2/3} a^4+\left(-a^6\right)^{2/3}\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 a^{11/2} \sqrt{a^2 x^3-b^2 x}}-\frac{\sqrt[3]{-1} \left(a+\sqrt[3]{-1} \sqrt[6]{-a^6}\right) \left(\frac{\sqrt[3]{-1} a^8}{\left(-a^6\right)^{2/3}}+(-1)^{2/3} a^4+\left(-a^6\right)^{2/3}\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 a^{11/2} \sqrt{a^2 x^3-b^2 x}}+\frac{\left(a-\sqrt[6]{-a^6}\right) \left(a^4+\sqrt[3]{-a^6} a^2+\left(-a^6\right)^{2/3}\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 a^{11/2} \sqrt{a^2 x^3-b^2 x}}+\frac{\left(a+\sqrt[6]{-a^6}\right) \left(a^4+\sqrt[3]{-a^6} a^2+\left(-a^6\right)^{2/3}\right) \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 a^{11/2} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{a^5}{\left(-a^6\right)^{5/6}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[3]{-1} a^5}{\left(-a^6\right)^{5/6}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{(-1)^{2/3} a^5}{\left(-a^6\right)^{5/6}};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[6]{-a^6}}{a};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{\sqrt[3]{-1} \sqrt[6]{-a^6}}{a};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{a} \sqrt{a^2 x^3-b^2 x}}-\frac{2 \sqrt{b} \sqrt{x} \sqrt{1-\frac{a^2 x^2}{b^2}} \Pi \left(\frac{(-1)^{2/3} \sqrt[6]{-a^6}}{a};\left.\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{b}}\right)\right|-1\right)}{3 \sqrt{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,"-1/3*((-1)^(2/3)*(a - (-1)^(2/3)*(-a^6)^(1/6))*((-1)^(1/3)*a^4 - (-1)^(2/3)*a^2*(-a^6)^(1/3) - (-a^6)^(2/3))*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(a^(11/2)*Sqrt[-(b^2*x) + a^2*x^3]) - ((-1)^(2/3)*(a + (-1)^(2/3)*(-a^6)^(1/6))*((-1)^(1/3)*a^4 - (-1)^(2/3)*a^2*(-a^6)^(1/3) - (-a^6)^(2/3))*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*a^(11/2)*Sqrt[-(b^2*x) + a^2*x^3]) - ((-1)^(1/3)*(a - (-1)^(1/3)*(-a^6)^(1/6))*((-1)^(2/3)*a^4 + ((-1)^(1/3)*a^8)/(-a^6)^(2/3) + (-a^6)^(2/3))*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*a^(11/2)*Sqrt[-(b^2*x) + a^2*x^3]) - ((-1)^(1/3)*(a + (-1)^(1/3)*(-a^6)^(1/6))*((-1)^(2/3)*a^4 + ((-1)^(1/3)*a^8)/(-a^6)^(2/3) + (-a^6)^(2/3))*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*a^(11/2)*Sqrt[-(b^2*x) + a^2*x^3]) + ((a - (-a^6)^(1/6))*(a^4 + a^2*(-a^6)^(1/3) + (-a^6)^(2/3))*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*a^(11/2)*Sqrt[-(b^2*x) + a^2*x^3]) + ((a + (-a^6)^(1/6))*(a^4 + a^2*(-a^6)^(1/3) + (-a^6)^(2/3))*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*a^(11/2)*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[a^5/(-a^6)^(5/6), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(1/3)*a^5)/(-a^6)^(5/6), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(2/3)*a^5)/(-a^6)^(5/6), ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[(-a^6)^(1/6)/a, ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(1/3)*(-a^6)^(1/6))/a, ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3]) - (2*Sqrt[b]*Sqrt[x]*Sqrt[1 - (a^2*x^2)/b^2]*EllipticPi[((-1)^(2/3)*(-a^6)^(1/6))/a, ArcSin[(Sqrt[a]*Sqrt[x])/Sqrt[b]], -1])/(3*Sqrt[a]*Sqrt[-(b^2*x) + a^2*x^3])","C",209,20,45,0.4444,1,"{2056, 1586, 6715, 6725, 1729, 1209, 1201, 224, 221, 1200, 1199, 424, 1219, 1218, 1248, 735, 844, 217, 206, 725}"
2883,0,0,0,1.785722,"\int \frac{\sqrt{1+x^4} \sqrt{x^2+\sqrt{1+x^4}}}{-1+x^4} \, dx","Int[(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,"(-1/4*I)*Defer[Int][(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(I - x), x] - Defer[Int][(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 - x), x]/4 - (I/4)*Defer[Int][(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(I + x), x] - Defer[Int][(Sqrt[1 + x^4]*Sqrt[x^2 + Sqrt[1 + x^4]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
2884,0,0,0,8.4837921,"\int \frac{x^4}{1-x \sqrt{1+x^2} \sqrt{x-\sqrt{1+x^2}}} \, dx","Int[x^4/(1 - x*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]]),x]","\int \frac{x^4}{1-x \sqrt{1+x^2} \sqrt{x-\sqrt{1+x^2}}} \, dx","-\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,"x^2/2 + (x*Sqrt[1 + x^2])/2 + 1/(28*(x - Sqrt[1 + x^2])^(7/2)) - 1/(4*(x - Sqrt[1 + x^2])^(3/2)) + 2/Sqrt[x - Sqrt[1 + x^2]] + (5*Sqrt[x - Sqrt[1 + x^2]])/4 - (2*(x - Sqrt[1 + x^2])^(3/2))/3 + (x - Sqrt[1 + x^2])^(5/2)/20 + ArcSinh[x]/2 - Log[-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8]/8 + Defer[Int][x/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + (3*Defer[Int][x^2/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x])/4 + Defer[Int][x^3/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x]/2 - (7*Defer[Int][x^4/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x])/4 + Defer[Int][x^5/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x]/2 - 2*Defer[Int][x^6/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + Defer[Int][Sqrt[1 + x^2]/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - 2*Defer[Int][(x^3*Sqrt[1 + x^2])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - Defer[Int][(x^4*Sqrt[1 + x^2])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - 2*Defer[Int][(x^5*Sqrt[1 + x^2])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - Defer[Int][(x^6*Sqrt[1 + x^2])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - 2*Defer[Int][Sqrt[x - Sqrt[1 + x^2]]/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + 5*Defer[Int][(x^3*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + 2*Defer[Int][(x^4*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + 4*Defer[Int][(x^5*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + 2*Defer[Int][(x^6*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - Defer[Int][(Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + Defer[Int][(x^2*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + 2*Defer[Int][(x^3*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + Defer[Int][(x^4*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - Defer[Int][(x^5*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] + Defer[Int][(x^6*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x] - 2*Defer[Int][(x^7*Sqrt[1 + x^2]*Sqrt[x - Sqrt[1 + x^2]])/(-1 + 2*x^3 + x^4 + 2*x^5 + 2*x^6 + x^8), x]","F",0,0,0,0,-1,"{}"
2885,1,125,0,0.1944725,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{(1+x)^2 \sqrt{1+x^4}} \, dx","Int[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2*Sqrt[1 + x^4]),x]","-\frac{\sqrt{1-i x^2}}{2 (x+1)}-\frac{\sqrt{1+i x^2}}{2 (x+1)}-\frac{1}{4} (1-i)^{3/2} \tanh ^{-1}\left(\frac{1+i x}{\sqrt{1-i} \sqrt{1-i x^2}}\right)-\frac{1}{4} (1+i)^{3/2} \tanh ^{-1}\left(\frac{1-i x}{\sqrt{1+i} \sqrt{1+i x^2}}\right)","\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,"-1/2*Sqrt[1 - I*x^2]/(1 + x) - Sqrt[1 + I*x^2]/(2*(1 + x)) - ((1 - I)^(3/2)*ArcTanh[(1 + I*x)/(Sqrt[1 - I]*Sqrt[1 - I*x^2])])/4 - ((1 + I)^(3/2)*ArcTanh[(1 - I*x)/(Sqrt[1 + I]*Sqrt[1 + I*x^2])])/4","C",7,4,32,0.1250,0,"{2133, 731, 725, 206}"
2886,0,0,0,13.529949,"\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","Int[((-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,"(6*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(b^2*d - 2*b*d*x^3 - a^2*(1 - d/a^2)*x^6 + 2*a*x^9 - x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(b^2*d) + 2*b*d*x^3 + a^2*(1 - d/a^2)*x^6 - 2*a*x^9 + x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-b + x^3)^(1/3))/((-a + x^3)^(1/3)*(-(b^2*d) + 2*b*d*x^3 + a^2*(1 - d/a^2)*x^6 - 2*a*x^9 + x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3)","F",0,0,0,0,-1,"{}"
2887,1,135,0,0.7128236,"\int \frac{b^8+a^8 x^8}{\sqrt{-b^4+a^4 x^4} \left(-b^8+a^8 x^8\right)} \, dx","Int[(b^8 + a^8*x^8)/(Sqrt[-b^4 + a^4*x^4]*(-b^8 + a^8*x^8)),x]","-\frac{x}{2 \sqrt{a^4 x^4-b^4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{4 \sqrt{2} \sqrt[4]{-a^4} b}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{-a^4} b x}{\sqrt{a^4 x^4-b^4}}\right)}{4 \sqrt{2} \sqrt[4]{-a^4} b}","-\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,"-1/2*x/Sqrt[-b^4 + a^4*x^4] - ArcTan[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]]/(4*Sqrt[2]*(-a^4)^(1/4)*b) - ArcTanh[(Sqrt[2]*(-a^4)^(1/4)*b*x)/Sqrt[-b^4 + a^4*x^4]]/(4*Sqrt[2]*(-a^4)^(1/4)*b)","A",20,11,44,0.2500,1,"{6725, 224, 221, 1404, 414, 523, 409, 1211, 1699, 203, 206}"
2888,1,365,0,0.5653184,"\int \frac{1}{\sqrt{-1+x^2} \left(\sqrt{x}+\sqrt{-1+x^2}\right)^2} \, dx","Int[1/(Sqrt[-1 + x^2]*(Sqrt[x] + Sqrt[-1 + x^2])^2),x]","-\frac{2 \sqrt{x^2-1} (1-2 x)}{5 \left(-x^2+x+1\right)}+\frac{2 \sqrt{x} (1-2 x)}{5 \left(-x^2+x+1\right)}-\frac{2}{5} \sqrt{\frac{1}{5} \left(5 \sqrt{5}-2\right)} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)+\sqrt{\frac{2}{5 \left(\sqrt{5}-1\right)}} \tan ^{-1}\left(\frac{2-\left(1-\sqrt{5}\right) x}{\sqrt{2 \left(\sqrt{5}-1\right)} \sqrt{x^2-1}}\right)-\frac{2}{5} \sqrt{\frac{1}{5} \left(2+5 \sqrt{5}\right)} \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{2}{5 \left(1+\sqrt{5}\right)}} \tanh ^{-1}\left(\frac{2-\left(1+\sqrt{5}\right) x}{\sqrt{2 \left(1+\sqrt{5}\right)} \sqrt{x^2-1}}\right)+\frac{1}{5} \sqrt{\frac{2}{5} \left(5 \sqrt{5}-11\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x}\right)-\frac{1}{5} \sqrt{\frac{2}{5} \left(11+5 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x}\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])/(5*(1 + x - x^2)) - (2*(1 - 2*x)*Sqrt[-1 + x^2])/(5*(1 + x - x^2)) + (Sqrt[(2*(-11 + 5*Sqrt[5]))/5]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[x]])/5 + Sqrt[2/(5*(-1 + Sqrt[5]))]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])] - (2*Sqrt[(-2 + 5*Sqrt[5])/5]*ArcTan[(2 - (1 - Sqrt[5])*x)/(Sqrt[2*(-1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5 - (Sqrt[(2*(11 + 5*Sqrt[5]))/5]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[x]])/5 + Sqrt[2/(5*(1 + Sqrt[5]))]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])] - (2*Sqrt[(2 + 5*Sqrt[5])/5]*ArcTanh[(2 - (1 + Sqrt[5])*x)/(Sqrt[2*(1 + Sqrt[5])]*Sqrt[-1 + x^2])])/5","A",18,12,27,0.4444,0,"{6742, 736, 826, 1166, 207, 203, 1018, 1034, 725, 206, 204, 985}"
2889,1,407,0,0.5241845,"\int \frac{b+a x^2}{\left(d+c x^2\right) \sqrt[3]{x+x^3}} \, dx","Int[(b + a*x^2)/((d + c*x^2)*(x + x^3)^(1/3)),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} (b c-a d) \log \left(\frac{x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2+1}}+\sqrt[3]{d}\right)}{2 c d^{2/3} \sqrt[3]{x^3+x} \sqrt[3]{c-d}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2+1} (b c-a d) \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)}{4 c d^{2/3} \sqrt[3]{x^3+x} \sqrt[3]{c-d}}-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2+1} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{d}-\frac{2 x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2+1}}}{\sqrt{3} \sqrt[3]{d}}\right)}{2 c d^{2/3} \sqrt[3]{x^3+x} \sqrt[3]{c-d}}-\frac{3 a \sqrt[3]{x} \sqrt[3]{x^2+1} \log \left(x^{2/3}-\sqrt[3]{x^2+1}\right)}{4 c \sqrt[3]{x^3+x}}+\frac{\sqrt{3} a \sqrt[3]{x} \sqrt[3]{x^2+1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right)}{2 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,"(Sqrt[3]*a*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*c*(x + x^3)^(1/3)) - (Sqrt[3]*(b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*ArcTan[(d^(1/3) - (2*(c - d)^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/(Sqrt[3]*d^(1/3))])/(2*c*(c - d)^(1/3)*d^(2/3)*(x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*Log[d^(1/3) + ((c - d)^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*c*(c - d)^(1/3)*d^(2/3)*(x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(1 + x^2)^(1/3)*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)])/(4*c*(c - d)^(1/3)*d^(2/3)*(x + x^3)^(1/3)) - (3*a*x^(1/3)*(1 + x^2)^(1/3)*Log[x^(2/3) - (1 + x^2)^(1/3)])/(4*c*(x + x^3)^(1/3))","A",15,14,26,0.5385,1,"{2056, 584, 329, 275, 239, 466, 465, 377, 200, 31, 634, 617, 204, 628}"
2890,0,0,0,19.095543,"\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","Int[(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,"(3*x^2*(1 - x/a)^(2/3)*(1 - x/b)^(2/3)*AppellF1[2/3, 2/3, 2/3, 5/3, x/a, x/b])/(d*((a - x)*(b - x)*x^2)^(2/3)) + (6*(a + b)*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^4/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a*b - a*(1 + b/a)*x^3 + x^6 - d*x^12)), x], x, x^(1/3)])/(d*((a - x)*(b - x)*x^2)^(2/3)) - (6*(1 + 2*a*b*d)*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^7/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a*b - a*(1 + b/a)*x^3 + x^6 - d*x^12)), x], x, x^(1/3)])/(d*((a - x)*(b - x)*x^2)^(2/3)) + (9*(a + b)*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^10/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a*b - a*(1 + b/a)*x^3 + x^6 - d*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (6*a*b*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(-(a*b) + a*(1 + b/a)*x^3 - x^6 + d*x^12)), x], x, x^(1/3)])/(d*((a - x)*(b - x)*x^2)^(2/3))","F",0,0,0,0,-1,"{}"
2891,1,2012,0,2.1872647,"\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","Int[(b*x + a*x^3)/((b + 2*a*x^3)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{x a^3+b^2}}{\sqrt{3} \sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} a^{4/9} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log (x)}{12 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\sqrt[3]{-2} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-\sqrt[3]{2} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(-(-1)^{2/3} \sqrt[3]{2} \sqrt[3]{a} x-\sqrt[3]{b}\right)}{12 a^{4/9} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}+\sqrt[3]{-2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}-\sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{\sqrt[9]{a} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}}}-\sqrt[3]{x}\right)}{4 a^{4/9} \sqrt[3]{a^{8/3}-(-1)^{2/3} \sqrt[3]{2} b^{5/3}} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+(-2)^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}+2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\left(\sqrt[3]{a}-\sqrt[3]{-1} 2^{2/3} \sqrt[3]{b}\right) x^{2/3} \sqrt[3]{x a^3+b^2} \log \left(\frac{\sqrt[3]{x a^3+b^2}}{a \sqrt[3]{x}}-1\right)}{4 a^{4/3} \sqrt[3]{a^3 x^3+b^2 x^2}}","\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,"-1/2*((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(2*Sqrt[3]*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((-1)^(1/3)*((-1)^(2/3)*a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*x^(1/3))])/(2*Sqrt[3]*a^(4/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(12*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) + (-2)^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - 2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b^(1/3) - (-1)^(2/3)*2^(1/3)*a^(1/3)*x])/(12*a^(4/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) + (-2)^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) - 2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3))])/(4*a^(4/9)*(a^(8/3) - (-1)^(2/3)*2^(1/3)*b^(5/3))^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + (-2)^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) + 2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - ((a^(1/3) - (-1)^(1/3)*2^(2/3)*b^(1/3))*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(4*a^(4/3)*(b^2*x^2 + a^3*x^3)^(1/3))","B",13,6,39,0.1538,0,"{1593, 2056, 6725, 105, 59, 91}"
2892,0,0,0,54.4110928,"\int \frac{1}{\sqrt{-1+2 x} (4+3 x)+(1+x) \sqrt{-3+4 x}} \, dx","Int[(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,"(-16*Sqrt[-21*(359 + (63*I)*Sqrt[15])*(16*46^(2/3) - 55*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3))]*ArcTan[(Sqrt[21]*(359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[-1 + 2*x])/Sqrt[-16*46^(2/3) + 55*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3)]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) + (4*Sqrt[-21*(359 + (63*I)*Sqrt[15])*(32*46^(2/3) - 131*(359 + (63*I)*Sqrt[15])^(1/3) + 2*46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3))]*ArcTan[(Sqrt[21]*(359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[-3 + 4*x])/Sqrt[-32*46^(2/3) + 131*(359 + (63*I)*Sqrt[15])^(1/3) - 2*46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3)]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) - (8*Sqrt[359 + (63*I)*Sqrt[15]]*((359 + (63*I)*Sqrt[15])^(1/3)*(21*46^(2/3)*(59 + (3*I)*Sqrt[15]) + 55*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]) + 46^(1/3)*(31521 + (3465*I)*Sqrt[15] - 16*46^(1/3)*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]) + (359 + (63*I)*Sqrt[15])^(2/3)*(2289 - 46^(1/3)*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))*ArcTan[(Sqrt[21*(-110*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - 2*(8*46^(2/3) - Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))] - 42*(359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[-1 + 2*x])/Sqrt[21*(110*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + 2*(8*46^(2/3) + Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))]])/((11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3))*Sqrt[(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))*(110*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + 2*(8*46^(2/3) + Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))]) + (8*Sqrt[359 + (63*I)*Sqrt[15]]*((359 + (63*I)*Sqrt[15])^(1/3)*(21*46^(2/3)*(59 + (3*I)*Sqrt[15]) + 55*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]) + 46^(1/3)*(31521 + (3465*I)*Sqrt[15] - 16*46^(1/3)*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]) + (359 + (63*I)*Sqrt[15])^(2/3)*(2289 - 46^(1/3)*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))*ArcTan[(Sqrt[21*(-110*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - 2*(8*46^(2/3) - Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))] + 42*(359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[-1 + 2*x])/Sqrt[21*(110*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + 2*(8*46^(2/3) + Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))]])/((11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3))*Sqrt[(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))*(110*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + 2*(8*46^(2/3) + Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))]) + (Sqrt[(2*(359 + (63*I)*Sqrt[15]))/((4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))*(16*46^(2/3) + 131*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]))]*((359 + (63*I)*Sqrt[15])^(1/3)*(84*46^(2/3)*(67 + (3*I)*Sqrt[15]) + 131*Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]) + 2*46^(1/3)*(70581 + (8253*I)*Sqrt[15] - 16*46^(1/3)*Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]) + (359 + (63*I)*Sqrt[15])^(2/3)*(14217 - 2*46^(1/3)*Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]))*ArcTan[(Sqrt[42*(-16*46^(2/3) - 131*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))])] - 42*(359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[-3 + 4*x])/Sqrt[42*(16*46^(2/3) + 131*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))])]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) - (Sqrt[(2*(359 + (63*I)*Sqrt[15]))/((4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))*(16*46^(2/3) + 131*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]))]*((359 + (63*I)*Sqrt[15])^(1/3)*(84*46^(2/3)*(67 + (3*I)*Sqrt[15]) + 131*Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]) + 2*46^(1/3)*(70581 + (8253*I)*Sqrt[15] - 16*46^(1/3)*Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]) + (359 + (63*I)*Sqrt[15])^(2/3)*(14217 - 2*46^(1/3)*Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]))*ArcTan[(Sqrt[42*(-16*46^(2/3) - 131*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))])] + 42*(359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[-3 + 4*x])/Sqrt[42*(16*46^(2/3) + 131*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))])]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) - (84*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]) + (16*46^(2/3) - 55*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3))*Sqrt[(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))/21])*Sqrt[-((359 + (63*I)*Sqrt[15])/((46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))*(16*46^(2/3) + 110*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - 2*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))])))]*Log[Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))] - 21*(359 + (63*I)*Sqrt[15])^(1/3)*(1 - 2*x) - (359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[21*(-110*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - 2*(8*46^(2/3) - Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))]*Sqrt[-1 + 2*x]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) + (84*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]) + (16*46^(2/3) - 55*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3))*Sqrt[(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))/21])*Sqrt[-((359 + (63*I)*Sqrt[15])/((46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))*(16*46^(2/3) + 110*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - 2*Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))])))]*Log[Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))] - 21*(359 + (63*I)*Sqrt[15])^(1/3)*(1 - 2*x) + (359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[21*(-110*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - 2*(8*46^(2/3) - Sqrt[21*(46^(2/3)*(59 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 109*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(1/3)*(1501 + (165*I)*Sqrt[15]))]))]*Sqrt[-1 + 2*x]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) + (21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]) + (32*46^(2/3) - 131*(359 + (63*I)*Sqrt[15])^(1/3) + 2*46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3))*Sqrt[(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))/21])*Sqrt[-1/2*(359 + (63*I)*Sqrt[15])/((4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))*(16*46^(2/3) + 131*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]))]*Log[Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))] - 21*(359 + (63*I)*Sqrt[15])^(1/3)*(3 - 4*x) - (359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[42*(-16*46^(2/3) - 131*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))])]*Sqrt[-3 + 4*x]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) - (21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]) + (32*46^(2/3) - 131*(359 + (63*I)*Sqrt[15])^(1/3) + 2*46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3))*Sqrt[(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))/21])*Sqrt[-1/2*(359 + (63*I)*Sqrt[15])/((4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))*(16*46^(2/3) + 131*(359 + (63*I)*Sqrt[15])^(1/3) + 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) - Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))]))]*Log[Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))] - 21*(359 + (63*I)*Sqrt[15])^(1/3)*(3 - 4*x) + (359 + (63*I)*Sqrt[15])^(1/6)*Sqrt[42*(-16*46^(2/3) - 131*(359 + (63*I)*Sqrt[15])^(1/3) - 46^(1/3)*(359 + (63*I)*Sqrt[15])^(2/3) + Sqrt[21*(4*46^(2/3)*(67 + (3*I)*Sqrt[15])*(359 + (63*I)*Sqrt[15])^(1/3) + 677*(359 + (63*I)*Sqrt[15])^(2/3) + 2*46^(1/3)*(3361 + (393*I)*Sqrt[15]))])]*Sqrt[-3 + 4*x]])/(11776*46^(1/3) + 736*(359 + (63*I)*Sqrt[15])^(2/3) + 46^(2/3)*(359 + (63*I)*Sqrt[15])^(4/3)) + 6*Defer[Subst][Defer[Int][x^2/(9 + 109*x^2 + 55*x^4 + 7*x^6), x], x, Sqrt[-1 + 2*x]] + 6*Defer[Subst][Defer[Int][x^4/(9 + 109*x^2 + 55*x^4 + 7*x^6), x], x, Sqrt[-1 + 2*x]] - 12*Defer[Subst][Defer[Int][x^2/(625 + 677*x^2 + 131*x^4 + 7*x^6), x], x, Sqrt[-3 + 4*x]] - 4*Defer[Subst][Defer[Int][x^4/(625 + 677*x^2 + 131*x^4 + 7*x^6), x], x, Sqrt[-3 + 4*x]]","F",0,0,0,0,-1,"{}"
2893,0,0,0,6.1478788,"\int \frac{f+e x}{(h+g x) \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","Int[(f + e*x)/((h + g*x)*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]),x]","\int \frac{f+e x}{(h+g x) \sqrt{d+\sqrt{c+\sqrt{b+a x}}}} \, dx","\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*d*(c - d^2)*e*Sqrt[d + Sqrt[c + Sqrt[b + a*x]]])/(a*g) - (8*(c - 3*d^2)*e*(d + Sqrt[c + Sqrt[b + a*x]])^(3/2))/(3*a*g) - (24*d*e*(d + Sqrt[c + Sqrt[b + a*x]])^(5/2))/(5*a*g) + (8*e*(d + Sqrt[c + Sqrt[b + a*x]])^(7/2))/(7*a*g) - (8*d*(c - d^2)*(f*g - e*h)*Defer[Subst][Defer[Int][(b*g*(1 - (c^2*g - 2*c*d^2*g + d^4*g + a*h)/(b*g)) - 4*c*d*(1 - d^2/c)*g*x^2 + 2*c*(1 - (3*d^2)/c)*g*x^4 + 4*d*g*x^6 - g*x^8)^(-1), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/g + (8*(c - 3*d^2)*(f*g - e*h)*Defer[Subst][Defer[Int][x^2/(b*g*(1 - (c^2*g - 2*c*d^2*g + d^4*g + a*h)/(b*g)) - 4*c*d*(1 - d^2/c)*g*x^2 + 2*c*(1 - (3*d^2)/c)*g*x^4 + 4*d*g*x^6 - g*x^8), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/g - (8*(f*g - e*h)*Defer[Subst][Defer[Int][x^6/(b*g*(1 - (c^2*g - 2*c*d^2*g + d^4*g + a*h)/(b*g)) - 4*c*d*(1 - d^2/c)*g*x^2 + 2*c*(1 - (3*d^2)/c)*g*x^4 + 4*d*g*x^6 - g*x^8), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/g - (24*d*(f*g - e*h)*Defer[Subst][Defer[Int][x^4/(-(b*g*(1 - (c^2*g - 2*c*d^2*g + d^4*g + a*h)/(b*g))) + 4*c*d*(1 - d^2/c)*g*x^2 - 2*c*(1 - (3*d^2)/c)*g*x^4 - 4*d*g*x^6 + g*x^8), x], x, Sqrt[d + Sqrt[c + Sqrt[b + a*x]]]])/g","F",0,0,0,0,-1,"{}"
2894,0,0,0,0.4294976,"\int \left(1+x^2\right)^{3/2} \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(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,"Defer[Int][(1 + x^2)^(3/2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x]","F",0,0,0,0,-1,"{}"
2895,0,0,0,8.6654932,"\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","Int[((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,"(-3*(a - 5*b)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^9/((a - b + x^3)^(2/3)*(a*(1 - b/a) + x^3 - d*x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(2/3) + (12*a*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^9/((a - b + x^3)^(2/3)*(-(a*(1 - b/a)) - x^3 + d*x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(2/3) + (12*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^12/((a - b + x^3)^(2/3)*(-(a*(1 - b/a)) - x^3 + d*x^15)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(2/3)","F",0,0,0,0,-1,"{}"
2896,0,0,0,15.7036775,"\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","Int[((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,"-(((-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/(-1 + x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3))) - (2*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/(1 + x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(1 + I*Sqrt[3])*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/(-1 - I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + ((1 - I*Sqrt[3])*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/(1 - I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(1 - I*Sqrt[3])*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/(-1 + I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + ((1 + I*Sqrt[3])*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/(1 + I*Sqrt[3] + 2*x), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/((1 - I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x], x, x^(1/3)])/((1 - I*Sqrt[3])^(2/3)*x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/((1 + I*Sqrt[3])^(1/3) + (-2)^(1/3)*x), x], x, x^(1/3)])/((1 + I*Sqrt[3])^(2/3)*x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/((1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x), x], x, x^(1/3)])/((1 - I*Sqrt[3])^(2/3)*x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/((1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x), x], x, x^(1/3)])/((1 + I*Sqrt[3])^(2/3)*x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/((1 - I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(1/3)])/((1 - I*Sqrt[3])^(2/3)*x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (2*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(-1 - x^6 - x^9 + x^15)^(1/3)/((1 + I*Sqrt[3])^(1/3) - (-1)^(2/3)*2^(1/3)*x), x], x, x^(1/3)])/((1 + I*Sqrt[3])^(2/3)*x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) - (9*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(x^6*(-1 - x^6 - x^9 + x^15)^(1/3))/(-1 - x^9 + x^15), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3)) + (15*(-x - x^3 - x^4 + x^6)^(1/3)*Defer[Subst][Defer[Int][(x^12*(-1 - x^6 - x^9 + x^15)^(1/3))/(-1 - x^9 + x^15), x], x, x^(1/3)])/(x^(1/3)*(-1 - x^2 - x^3 + x^5)^(1/3))","F",0,0,0,0,-1,"{}"
2897,1,291,0,0.1370398,"\int \frac{1}{(-b+a x) \sqrt[3]{-b^2 x^2+a^3 x^3}} \, dx","Int[1/((-b + a*x)*(-(b^2*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \sqrt[3]{a^3 x-b^2} \log (a x-b)}{2 \sqrt[3]{a} b \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b^2} \log \left(\frac{\sqrt[3]{a^3 x-b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-b}}-\sqrt[3]{x}\right)}{2 \sqrt[3]{a} b \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}}+\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2-b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a} b \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}}","-\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,"(Sqrt[3]*x^(2/3)*(-b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - b)^(1/3)*x^(1/3))])/(a^(1/3)*(a^2 - b)^(1/3)*b*(-(b^2*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[-b + a*x])/(2*a^(1/3)*(a^2 - b)^(1/3)*b*(-(b^2*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (-b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - b)^(1/3))])/(2*a^(1/3)*(a^2 - b)^(1/3)*b*(-(b^2*x^2) + a^3*x^3)^(1/3))","A",2,2,30,0.06667,1,"{2056, 91}"
2898,0,0,0,7.0755907,"\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","Int[((-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]","\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","\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,"(9*a*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(a - b + x^3)^(1/3))/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4) + 4*a^3*(1 - (12*a^2*b - 12*a*b^2 + 4*b^3 + d)/(4*a^3))*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*x^6 + 4*a*(1 - b/a)*x^9 + x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(1/3) + (9*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(a - b + x^3)^(1/3))/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4) + 4*a^3*(1 - (12*a^2*b - 12*a*b^2 + 4*b^3 + d)/(4*a^3))*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*x^6 + 4*a*(1 - b/a)*x^9 + x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(1/3) - (3*(4*a - b)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(a - b + x^3)^(1/3))/(b^4*(1 + (a*d)/b^4) - (4*b^3 + d)*(a + x^3) + 6*b^2*(a + x^3)^2 - 4*b*(a + x^3)^3 + (a + x^3)^4), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(1/3)","F",0,0,0,0,-1,"{}"
2899,1,120,0,0.0756519,"\int \frac{x^4}{\sqrt{-b^4+a^4 x^4} \left(-b^8+a^8 x^8\right)} \, dx","Int[x^4/(Sqrt[-b^4 + a^4*x^4]*(-b^8 + a^8*x^8)),x]","-\frac{x}{4 a^4 b^4 \sqrt{a^4 x^4-b^4}}+\frac{\tan ^{-1}\left(\frac{a x \left(b^2-a^2 x^2\right)}{b \sqrt{a^4 x^4-b^4}}\right)}{8 a^5 b^5}+\frac{\tanh ^{-1}\left(\frac{a x \left(a^2 x^2+b^2\right)}{b \sqrt{a^4 x^4-b^4}}\right)}{8 a^5 b^5}","-\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,"-1/4*x/(a^4*b^4*Sqrt[-b^4 + a^4*x^4]) + ArcTan[(a*x*(b^2 - a^2*x^2))/(b*Sqrt[-b^4 + a^4*x^4])]/(8*a^5*b^5) + ArcTanh[(a*x*(b^2 + a^2*x^2))/(b*Sqrt[-b^4 + a^4*x^4])]/(8*a^5*b^5)","A",4,4,36,0.1111,1,"{1479, 471, 21, 405}"
2900,0,0,0,1.2642734,"\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","Int[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]","\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","\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2901,1,710,0,3.3519325,"\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","Int[((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","-\frac{i \left(3+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}+\frac{i \left(3+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}+i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}-\frac{\left(3-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}+\frac{\left(3-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(3+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(3+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}+i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(3-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(3-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\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)-\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,"((-1/4*I)*(3 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + ((I/4)*(3 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] - ((3 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) + ((3 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) - ((1/4 - I/4)*(3 + Sqrt[5])*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 - I/4)*(3 + Sqrt[5])*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 + I/4)*(3 - Sqrt[5])*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] - ((1/4 + I/4)*(3 - Sqrt[5])*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",30,6,44,0.1364,0,"{6728, 2132, 206, 6725, 2133, 725}"
2902,1,710,0,2.5820688,"\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","Int[((1 + x^2)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","-\frac{i \left(3+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}+\frac{i \left(3+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}+i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}-\frac{\left(3-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}+\frac{\left(3-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(3+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(3+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}+i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(3-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(3-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\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)-\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,"((-1/4*I)*(3 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + ((I/4)*(3 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] - ((3 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) + ((3 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) - ((1/4 - I/4)*(3 + Sqrt[5])*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 - I/4)*(3 + Sqrt[5])*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 + I/4)*(3 - Sqrt[5])*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] - ((1/4 + I/4)*(3 - Sqrt[5])*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",30,6,44,0.1364,0,"{6728, 2132, 206, 6725, 2133, 725}"
2903,1,875,0,3.4982072,"\int \frac{x^2 \sqrt[4]{b x^3+a x^4}}{-b+a x^4} \, dx","Int[(x^2*(b*x^3 + a*x^4)^(1/4))/(-b + a*x^4),x]","-\frac{2 \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}+\frac{2 \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}","\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,"(-2*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^(3/4) - b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) + ((a^(3/4) + b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) + ((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4)) + ((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4)) + (2*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^(3/4) - b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) - ((a^(3/4) + b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) - ((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4)) - ((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4))","B",53,12,30,0.4000,1,"{2056, 6725, 904, 50, 63, 331, 298, 203, 206, 21, 906, 93}"
2904,1,875,0,2.4893579,"\int \frac{x^2 \sqrt[4]{b x^3+a x^4}}{-b+a x^4} \, dx","Int[(x^2*(b*x^3 + a*x^4)^(1/4))/(-b + a*x^4),x]","-\frac{2 \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}+\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}+\frac{2 \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}-b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[16]{a} \sqrt[4]{a^{3/4}+b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{15/16} x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a-\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}-\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a+\sqrt{-\sqrt{a}} b^{3/4}} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a x^{3/4} \sqrt[4]{b+a x}}","\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,"(-2*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^(3/4) - b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) + ((a^(3/4) + b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) + ((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4)) + ((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4)) + (2*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^(3/4) - b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) - b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) - ((a^(3/4) + b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/16)*(a^(3/4) + b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(15/16)*x^(3/4)*(b + a*x)^(1/4)) - ((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a - Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4)) - ((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a + Sqrt[-Sqrt[a]]*b^(3/4))^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a*x^(3/4)*(b + a*x)^(1/4))","B",53,12,30,0.4000,1,"{2056, 6725, 904, 50, 63, 331, 298, 203, 206, 21, 906, 93}"
2905,0,0,0,3.453588,"\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","Int[((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{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{x^2-1}",1,"Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/2 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/2","F",0,0,0,0,-1,"{}"
2906,0,0,0,2.811394,"\int \frac{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-2 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{x^2-1}",1,"Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/2 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/2","F",0,0,0,0,-1,"{}"
2907,0,0,0,52.3367989,"\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","Int[(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,"(9*a*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^12*(-b + x^3)^(2/3))/((-a + x^3)^(1/3)*(a^4 - 4*a^3*x^3 + 6*a^2*x^6 - 4*a*x^9 + (1 - b^2*d)*x^12 + 2*b*d*x^15 - d*x^18)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (6*a*b*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^9*(-b + x^3)^(2/3))/((-a + x^3)^(1/3)*(-a^4 + 4*a^3*x^3 - 6*a^2*x^6 + 4*a*x^9 - (1 - b^2*d)*x^12 - 2*b*d*x^15 + d*x^18)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3) + (3*x^(2/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^15*(-b + x^3)^(2/3))/((-a + x^3)^(1/3)*(-a^4 + 4*a^3*x^3 - 6*a^2*x^6 + 4*a*x^9 - (1 - b^2*d)*x^12 - 2*b*d*x^15 + d*x^18)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(1/3)","F",0,0,0,0,-1,"{}"
2908,1,176,0,0.5638831,"\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","Int[((1 + x^3)^(2/3)*(-1 + x^6))/(x^6*(-1 - 2*x^3 + 2*x^6)),x]","-\frac{\left(2+\sqrt{3}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\frac{2 x^3}{1-\sqrt{3}}\right)}{1-\sqrt{3}}-\frac{\left(2-\sqrt{3}\right) x F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-x^3,\frac{2 x^3}{1+\sqrt{3}}\right)}{1+\sqrt{3}}+\log \left(\sqrt[3]{x^3+1}-x\right)-\frac{2 \tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\left(x^3+1\right)^{5/3}}{5 x^5}+\frac{\left(x^3+1\right)^{2/3}}{x^2}","\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 + x^3)^(2/3)/x^2 - (1 + x^3)^(5/3)/(5*x^5) - ((2 + Sqrt[3])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (2*x^3)/(1 - Sqrt[3])])/(1 - Sqrt[3]) - ((2 - Sqrt[3])*x*AppellF1[1/3, -2/3, 1, 4/3, -x^3, (2*x^3)/(1 + Sqrt[3])])/(1 + Sqrt[3]) - (2*ArcTan[(1 + (2*x)/(1 + x^3)^(1/3))/Sqrt[3]])/Sqrt[3] + Log[-x + (1 + x^3)^(1/3)]","C",9,5,32,0.1562,0,"{6728, 264, 277, 239, 429}"
2909,1,341,0,0.8168444,"\int \frac{1+x^4}{\left(-1+x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[(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(\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{\tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}+\frac{\tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}+\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{\tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{1+\sqrt{2}}}+\frac{\tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{\sqrt{\sqrt{2}-1}}","\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]] - ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + Sqrt[2]] + ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[-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]]] - ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + Sqrt[2]] + ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[-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",36,19,28,0.6786,0,"{6725, 2117, 14, 2119, 1628, 828, 826, 1166, 204, 206, 207, 203, 2122, 329, 211, 1165, 628, 1162, 617}"
2910,1,1092,0,2.2646677,"\int \frac{(b+2 a x) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Int[((b + 2*a*x)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","\frac{\left(2 a^2-2 \sqrt{a^2+4 b} a-b\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(2 a^2-2 \sqrt{a^2+4 b} a-b\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{x^{3/4} \sqrt[4]{b+a x}}+\sqrt[4]{a x^4+b x^3} \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)-\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(b-2 a \left(a+\sqrt{a^2+4 b}\right)\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(a+\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(b-2 a \left(a+\sqrt{a^2+4 b}\right)\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(a+\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{x^{3/4} \sqrt[4]{b+a x}}+\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \sqrt[4]{a x^4+b x^3}","-\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,"(a - (a^2 - b)/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4) + (a + (a^2 - b)/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4) + ((a - (a^2 - b)/Sqrt[a^2 + 4*b])*(2*a^2 - b - 2*a*Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a + (a^2 - b)/Sqrt[a^2 + 4*b])*(b - 2*a*(a + Sqrt[a^2 + 4*b]))*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a - (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4)) - ((a + (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4)) - ((a - (a^2 - b)/Sqrt[a^2 + 4*b])*(2*a^2 - b - 2*a*Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a + (a^2 - b)/Sqrt[a^2 + 4*b])*(b - 2*a*(a + Sqrt[a^2 + 4*b]))*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a - (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4)) + ((a + (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4))","B",25,12,34,0.3529,1,"{2056, 6728, 101, 157, 63, 331, 298, 203, 206, 93, 205, 208}"
2911,1,1092,0,1.6220865,"\int \frac{(b+2 a x) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Int[((b + 2*a*x)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","\frac{\left(2 a^2-2 \sqrt{a^2+4 b} a-b\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(2 a^2-2 \sqrt{a^2+4 b} a-b\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right) \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)}{x^{3/4} \sqrt[4]{b+a x}}+\sqrt[4]{a x^4+b x^3} \left(a-\frac{a^2-b}{\sqrt{a^2+4 b}}\right)-\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(b-2 a \left(a+\sqrt{a^2+4 b}\right)\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(a+\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(b-2 a \left(a+\sqrt{a^2+4 b}\right)\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{2 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \left(a+\sqrt{a^2+4 b}\right)^{3/4} \sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{x^{3/4} \sqrt[4]{b+a x}}+\left(a+\frac{a^2-b}{\sqrt{a^2+4 b}}\right) \sqrt[4]{a x^4+b x^3}","-\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,"(a - (a^2 - b)/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4) + (a + (a^2 - b)/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4) + ((a - (a^2 - b)/Sqrt[a^2 + 4*b])*(2*a^2 - b - 2*a*Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a + (a^2 - b)/Sqrt[a^2 + 4*b])*(b - 2*a*(a + Sqrt[a^2 + 4*b]))*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a - (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4)) - ((a + (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4)) - ((a - (a^2 - b)/Sqrt[a^2 + 4*b])*(2*a^2 - b - 2*a*Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a + (a^2 - b)/Sqrt[a^2 + 4*b])*(b - 2*a*(a + Sqrt[a^2 + 4*b]))*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(2*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a - (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4)) + ((a + (a^2 - b)/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^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/(x^(3/4)*(b + a*x)^(1/4))","B",25,12,34,0.3529,1,"{2056, 6728, 101, 157, 63, 331, 298, 203, 206, 93, 205, 208}"
2912,1,160,0,2.0890603,"\int \frac{x^3}{\sqrt[3]{-x^2+x^4} \left(1+x^6\right)} \, dx","Int[x^3/((-x^2 + x^4)^(1/3)*(1 + x^6)),x]","\frac{\sqrt[3]{1-x^2} x^4 F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};x^2,-x^2\right)}{10 \sqrt[3]{x^4-x^2}}+\frac{\sqrt[3]{1-x^2} x^4 F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};x^2,\sqrt[3]{-1} x^2\right)}{10 \sqrt[3]{x^4-x^2}}+\frac{\sqrt[3]{1-x^2} x^4 F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};x^2,-(-1)^{2/3} x^2\right)}{10 \sqrt[3]{x^4-x^2}}","\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,"(x^4*(1 - x^2)^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, x^2, -x^2])/(10*(-x^2 + x^4)^(1/3)) + (x^4*(1 - x^2)^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, x^2, (-1)^(1/3)*x^2])/(10*(-x^2 + x^4)^(1/3)) + (x^4*(1 - x^2)^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, x^2, -((-1)^(2/3)*x^2)])/(10*(-x^2 + x^4)^(1/3))","C",55,7,24,0.2917,0,"{2056, 6725, 959, 466, 465, 511, 510}"
2913,0,0,0,6.4505236,"\int \frac{x^4 \sqrt{b+a^2 x^2}}{x^2-\sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","Int[(x^4*Sqrt[b + a^2*x^2])/(x^2 - Sqrt[a*x - Sqrt[b + a^2*x^2]]),x]","\int \frac{x^4 \sqrt{b+a^2 x^2}}{x^2-\sqrt{a x-\sqrt{b+a^2 x^2}}} \, dx","\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,"-(a^2*x) + (b*x*Sqrt[b + a^2*x^2])/(8*a^2) + (x^3*Sqrt[b + a^2*x^2])/4 + b^2/(6*a*(a*x - Sqrt[b + a^2*x^2])^(3/2)) - (b*Sqrt[a*x - Sqrt[b + a^2*x^2]])/a - (a*x - Sqrt[b + a^2*x^2])^(5/2)/(10*a) - (b^2*ArcTanh[(a*x)/Sqrt[b + a^2*x^2]])/(8*a^3) + a^2*b*Defer[Int][(b + 2*a*x^5 - x^8)^(-1), x] + 2*a^3*Defer[Int][x^5/(b + 2*a*x^5 - x^8), x] + b*Defer[Int][x^6/(b + 2*a*x^5 - x^8), x] - b*Defer[Int][(x^2*Sqrt[b + a^2*x^2])/(b + 2*a*x^5 - x^8), x] - a*Defer[Int][(x^7*Sqrt[b + a^2*x^2])/(b + 2*a*x^5 - x^8), x] + b*Defer[Int][(x^4*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(b + 2*a*x^5 - x^8), x] + a^2*Defer[Int][(x^6*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(b + 2*a*x^5 - x^8), x] - b*Defer[Int][(Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(b + 2*a*x^5 - x^8), x] - a*Defer[Int][(x^5*Sqrt[b + a^2*x^2]*Sqrt[a*x - Sqrt[b + a^2*x^2]])/(b + 2*a*x^5 - x^8), x]","F",0,0,0,0,-1,"{}"
2914,1,624,0,0.7666023,"\int \frac{-1+x^2}{\sqrt[4]{\frac{b+a x}{d+c x}}} \, dx","Int[(-1 + x^2)/((b + a*x)/(d + c*x))^(1/4),x]","\frac{15 (b c-a d)^3 \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{5 d (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{a}}\right)}{8 a^{9/4} c^{11/4}}-\frac{15 (b c-a d)^3 \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}}-\frac{5 d (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{a}}\right)}{8 a^{9/4} c^{11/4}}-\frac{\left(c^2-d^2\right) (b c-a d) \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{a}}\right)}{2 a^{5/4} c^{11/4}}+\frac{\left(c^2-d^2\right) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt[4]{\frac{a x+b}{c x+d}}}{\sqrt[4]{a}}\right)}{2 a^{5/4} c^{11/4}}+\frac{15 (c x+d) (b c-a d)^2 \left(\frac{a x+b}{c x+d}\right)^{3/4}}{32 a^3 c^2}-\frac{3 (b c-a d)^3 \left(\frac{a x+b}{c x+d}\right)^{3/4}}{8 a^2 c^2 \left(a-\frac{c (a x+b)}{c x+d}\right)^2}+\frac{5 d (c x+d) (b c-a d) \left(\frac{a x+b}{c x+d}\right)^{3/4}}{4 a^2 c^2}-\frac{\left(c^2-d^2\right) (c x+d) \left(\frac{a x+b}{c x+d}\right)^{3/4}}{a c^2}-\frac{(b c-a d)^3 \left(\frac{a x+b}{c x+d}\right)^{3/4}}{3 a c^2 \left(a-\frac{c (a x+b)}{c x+d}\right)^3}-\frac{d (b c-a d)^2 \left(\frac{a x+b}{c x+d}\right)^{3/4}}{a c^2 \left(a-\frac{c (a x+b)}{c x+d}\right)^2}","\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,"(5*d*(b*c - a*d)*((b + a*x)/(d + c*x))^(3/4)*(d + c*x))/(4*a^2*c^2) + (15*(b*c - a*d)^2*((b + a*x)/(d + c*x))^(3/4)*(d + c*x))/(32*a^3*c^2) - ((c^2 - d^2)*((b + a*x)/(d + c*x))^(3/4)*(d + c*x))/(a*c^2) - ((b*c - a*d)^3*((b + a*x)/(d + c*x))^(3/4))/(3*a*c^2*(a - (c*(b + a*x))/(d + c*x))^3) - (d*(b*c - a*d)^2*((b + a*x)/(d + c*x))^(3/4))/(a*c^2*(a - (c*(b + a*x))/(d + c*x))^2) - (3*(b*c - a*d)^3*((b + a*x)/(d + c*x))^(3/4))/(8*a^2*c^2*(a - (c*(b + a*x))/(d + c*x))^2) + (5*d*(b*c - a*d)^2*ArcTan[(c^(1/4)*((b + a*x)/(d + c*x))^(1/4))/a^(1/4)])/(8*a^(9/4)*c^(11/4)) + (15*(b*c - a*d)^3*ArcTan[(c^(1/4)*((b + a*x)/(d + c*x))^(1/4))/a^(1/4)])/(64*a^(13/4)*c^(11/4)) - ((b*c - a*d)*(c^2 - d^2)*ArcTan[(c^(1/4)*((b + a*x)/(d + c*x))^(1/4))/a^(1/4)])/(2*a^(5/4)*c^(11/4)) - (5*d*(b*c - a*d)^2*ArcTanh[(c^(1/4)*((b + a*x)/(d + c*x))^(1/4))/a^(1/4)])/(8*a^(9/4)*c^(11/4)) - (15*(b*c - a*d)^3*ArcTanh[(c^(1/4)*((b + a*x)/(d + c*x))^(1/4))/a^(1/4)])/(64*a^(13/4)*c^(11/4)) + ((b*c - a*d)*(c^2 - d^2)*ArcTanh[(c^(1/4)*((b + a*x)/(d + c*x))^(1/4))/a^(1/4)])/(2*a^(5/4)*c^(11/4))","A",18,6,23,0.2609,1,"{1961, 6742, 290, 298, 205, 208}"
2915,1,20,0,0.1487432,"\int \frac{-b+a x^4}{\sqrt{b+a x^4} \left(b-c^2 x^2+a x^4\right)} \, dx","Int[(-b + a*x^4)/(Sqrt[b + a*x^4]*(b - c^2*x^2 + a*x^4)),x]","-\frac{\tanh ^{-1}\left(\frac{c x}{\sqrt{a x^4+b}}\right)}{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} \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,"-(ArcTanh[(c*x)/Sqrt[b + a*x^4]]/c)","A",2,2,38,0.05263,1,"{2112, 208}"
2916,1,488,0,0.5513054,"\int \frac{\left(1+x^2\right) \sqrt[3]{-1-x^2+x^4+x^6}}{x} \, dx","Int[((1 + x^2)*(-1 - x^2 + x^4 + x^6)^(1/3))/x,x]","\frac{1}{4} \sqrt[3]{x^6+x^4-x^2-1} \left(x^2+1\right)+\frac{1}{3} \sqrt[3]{x^6+x^4-x^2-1}+\frac{\sqrt[3]{x^6+x^4-x^2-1} \log \left(x^2\right)}{4 \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}}+\frac{\sqrt[3]{x^6+x^4-x^2-1} \log \left(x^2-1\right)}{36 \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}}-\frac{3 \sqrt[3]{x^6+x^4-x^2-1} \log \left(-\sqrt[3]{x^2-1}-\sqrt[3]{x^2+1}\right)}{4 \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}}+\frac{\sqrt[3]{x^6+x^4-x^2-1} \log \left(\frac{\sqrt[3]{x^2+1}}{\sqrt[3]{x^2-1}}-1\right)}{12 \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}}-\frac{\sqrt{3} \sqrt[3]{x^6+x^4-x^2-1} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3} \sqrt[3]{x^2-1}}\right)}{2 \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}}+\frac{\sqrt{3} \sqrt[3]{x^6+x^4-x^2-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3} \sqrt[3]{x^2-1}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}}-\frac{4 \sqrt[3]{x^6+x^4-x^2-1} \tan ^{-1}\left(\frac{2 \sqrt[3]{x^2+1}}{\sqrt{3} \sqrt[3]{x^2-1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{x^2-1} \left(x^2+1\right)^{2/3}}","\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,"(-1 - x^2 + x^4 + x^6)^(1/3)/3 + ((1 + x^2)*(-1 - x^2 + x^4 + x^6)^(1/3))/4 - (Sqrt[3]*(-1 - x^2 + x^4 + x^6)^(1/3)*ArcTan[1/Sqrt[3] - (2*(1 + x^2)^(1/3))/(Sqrt[3]*(-1 + x^2)^(1/3))])/(2*(-1 + x^2)^(1/3)*(1 + x^2)^(2/3)) - (4*(-1 - x^2 + x^4 + x^6)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x^2)^(1/3))/(Sqrt[3]*(-1 + x^2)^(1/3))])/(3*Sqrt[3]*(-1 + x^2)^(1/3)*(1 + x^2)^(2/3)) + (Sqrt[3]*(-1 - x^2 + x^4 + x^6)^(1/3)*ArcTan[1/Sqrt[3] + (2*(1 + x^2)^(1/3))/(Sqrt[3]*(-1 + x^2)^(1/3))])/(2*(-1 + x^2)^(1/3)*(1 + x^2)^(2/3)) + ((-1 - x^2 + x^4 + x^6)^(1/3)*Log[x^2])/(4*(-1 + x^2)^(1/3)*(1 + x^2)^(2/3)) + ((-1 - x^2 + x^4 + x^6)^(1/3)*Log[-1 + x^2])/(36*(-1 + x^2)^(1/3)*(1 + x^2)^(2/3)) - (3*(-1 - x^2 + x^4 + x^6)^(1/3)*Log[-(-1 + x^2)^(1/3) - (1 + x^2)^(1/3)])/(4*(-1 + x^2)^(1/3)*(1 + x^2)^(2/3)) + ((-1 - x^2 + x^4 + x^6)^(1/3)*Log[-1 + (1 + x^2)^(1/3)/(-1 + x^2)^(1/3)])/(12*(-1 + x^2)^(1/3)*(1 + x^2)^(2/3))","A",9,7,26,0.2692,1,"{6719, 101, 157, 50, 59, 105, 91}"
2917,0,0,0,0.4665055,"\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","Int[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]","\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","\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2918,1,417,0,0.5464445,"\int \frac{-b+a x^2}{\left(-d+c x^2\right) \sqrt[3]{-x+x^3}} \, dx","Int[(-b + a*x^2)/((-d + c*x^2)*(-x + x^3)^(1/3)),x]","\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} (b c-a d) \log \left(\frac{x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2-1}}+\sqrt[3]{d}\right)}{2 c d^{2/3} \sqrt[3]{x^3-x} \sqrt[3]{c-d}}-\frac{\sqrt[3]{x} \sqrt[3]{x^2-1} (b c-a d) \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)}{4 c d^{2/3} \sqrt[3]{x^3-x} \sqrt[3]{c-d}}-\frac{\sqrt{3} \sqrt[3]{x} \sqrt[3]{x^2-1} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{d}-\frac{2 x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2-1}}}{\sqrt{3} \sqrt[3]{d}}\right)}{2 c d^{2/3} \sqrt[3]{x^3-x} \sqrt[3]{c-d}}-\frac{3 a \sqrt[3]{x} \sqrt[3]{x^2-1} \log \left(x^{2/3}-\sqrt[3]{x^2-1}\right)}{4 c \sqrt[3]{x^3-x}}+\frac{\sqrt{3} a \sqrt[3]{x} \sqrt[3]{x^2-1} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right)}{2 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,"(Sqrt[3]*a*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*c*(-x + x^3)^(1/3)) - (Sqrt[3]*(b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*ArcTan[(d^(1/3) - (2*(c - d)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3))/(Sqrt[3]*d^(1/3))])/(2*c*(c - d)^(1/3)*d^(2/3)*(-x + x^3)^(1/3)) + ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*Log[d^(1/3) + ((c - d)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(2*c*(c - d)^(1/3)*d^(2/3)*(-x + x^3)^(1/3)) - ((b*c - a*d)*x^(1/3)*(-1 + x^2)^(1/3)*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)])/(4*c*(c - d)^(1/3)*d^(2/3)*(-x + x^3)^(1/3)) - (3*a*x^(1/3)*(-1 + x^2)^(1/3)*Log[x^(2/3) - (-1 + x^2)^(1/3)])/(4*c*(-x + x^3)^(1/3))","A",15,14,32,0.4375,1,"{2056, 584, 329, 275, 239, 466, 465, 377, 200, 31, 634, 617, 204, 628}"
2919,1,139,0,0.0758603,"\int \frac{1}{(b+a x) \sqrt[3]{-b^3+a^3 x^3}} \, dx","Int[1/((b + a*x)*(-b^3 + a^3*x^3)^(1/3)),x]","-\frac{3 \log \left(2^{2/3} a \sqrt[3]{a^3 x^3-b^3}+a (b-a x)\right)}{4 \sqrt[3]{2} a b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} (b-a x)}{\sqrt[3]{a^3 x^3-b^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} a b}+\frac{\log \left((b-a x) (a x+b)^2\right)}{4 \sqrt[3]{2} a b}","\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,"(Sqrt[3]*ArcTan[(1 - (2^(1/3)*(b - a*x))/(-b^3 + a^3*x^3)^(1/3))/Sqrt[3]])/(2*2^(1/3)*a*b) + Log[(b - a*x)*(b + a*x)^2]/(4*2^(1/3)*a*b) - (3*Log[a*(b - a*x) + 2^(2/3)*a*(-b^3 + a^3*x^3)^(1/3)])/(4*2^(1/3)*a*b)","A",1,1,25,0.04000,1,"{2148}"
2920,1,2431,0,11.7417394,"\int \frac{-b^{12}+a^{12} x^{12}}{\sqrt{b^4+a^4 x^4} \left(b^{12}+a^{12} x^{12}\right)} \, dx","Int[(-b^12 + a^12*x^12)/(Sqrt[b^4 + a^4*x^4]*(b^12 + a^12*x^12)),x]","-\frac{2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{3 a^4-\sqrt{3} \sqrt{-a^8}} b x}{\sqrt[4]{2} \sqrt[4]{a^4-\sqrt{3} \sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right) a^{12}}{\sqrt{3} \sqrt{-a^8} \left(a^4-\sqrt{3} \sqrt{-a^8}\right)^{3/4} \left(3 a^4-\sqrt{3} \sqrt{-a^8}\right)^{3/2} b}+\frac{2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{\sqrt{3} \sqrt{-a^8}-3 a^4} b x}{\sqrt[4]{2} \sqrt[4]{a^4-\sqrt{3} \sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right) a^{12}}{\sqrt{3} \sqrt{-a^8} \left(a^4-\sqrt{3} \sqrt{-a^8}\right)^{3/4} \left(\sqrt{3} \sqrt{-a^8}-3 a^4\right)^{3/2} b}-\frac{2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{-3 a^4-\sqrt{3} \sqrt{-a^8}} b x}{\sqrt[4]{2} \sqrt[4]{a^4+\sqrt{3} \sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right) a^{12}}{\sqrt{3} \sqrt{-a^8} \left(-3 a^4-\sqrt{3} \sqrt{-a^8}\right)^{3/2} \left(a^4+\sqrt{3} \sqrt{-a^8}\right)^{3/4} b}+\frac{2 \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{3 a^4+\sqrt{3} \sqrt{-a^8}} b x}{\sqrt[4]{2} \sqrt[4]{a^4+\sqrt{3} \sqrt{-a^8}} \sqrt{b^4+a^4 x^4}}\right) a^{12}}{\sqrt{3} \sqrt{-a^8} \left(a^4+\sqrt{3} \sqrt{-a^8}\right)^{3/4} \left(3 a^4+\sqrt{3} \sqrt{-a^8}\right)^{3/2} b}+\frac{\left(1-\frac{\sqrt{2} a^2}{\sqrt{a^4-\sqrt{3} \sqrt{-a^8}}}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right) a^7}{\sqrt{3} \sqrt{-a^8} \left(3 a^4+\sqrt{3} \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4}}+\frac{\left(\frac{\sqrt{2} a^2}{\sqrt{a^4-\sqrt{3} \sqrt{-a^8}}}+1\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right) a^7}{\sqrt{3} \sqrt{-a^8} \left(3 a^4+\sqrt{3} \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4}}-\frac{\left(1-\frac{\sqrt{2} a^2}{\sqrt{a^4+\sqrt{3} \sqrt{-a^8}}}\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right) a^7}{\sqrt{3} \sqrt{-a^8} \left(3 a^4-\sqrt{3} \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4}}-\frac{\left(\frac{\sqrt{2} a^2}{\sqrt{a^4+\sqrt{3} \sqrt{-a^8}}}+1\right) \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right) a^7}{\sqrt{3} \sqrt{-a^8} \left(3 a^4-\sqrt{3} \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4}}-\frac{2 x a^4}{\sqrt{3} \left(\sqrt{3} a^4-3 \sqrt{-a^8}\right) \sqrt{b^4+a^4 x^4}}-\frac{2 x a^4}{\sqrt{3} \left(\sqrt{3} a^4+3 \sqrt{-a^8}\right) \sqrt{b^4+a^4 x^4}}-\frac{\left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right) a^3}{\sqrt{3} \left(\sqrt{3} a^4-3 \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4}}-\frac{\left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right) a^3}{\sqrt{3} \left(\sqrt{3} a^4+3 \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4}}+\frac{\left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{2 b \sqrt{b^4+a^4 x^4} a}-\frac{\left(\sqrt{2} a^2+\sqrt{a^4-\sqrt{3} \sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(-\frac{\left(\sqrt{2} a^2-\sqrt{a^4-\sqrt{3} \sqrt{-a^8}}\right)^2}{4 \sqrt{2} a^2 \sqrt{a^4-\sqrt{3} \sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 \sqrt{3} \left(\sqrt{3} a^4+3 \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4} a}-\frac{\left(\sqrt{2} a^2-\sqrt{a^4-\sqrt{3} \sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{\left(\sqrt{2} a^2+\sqrt{a^4-\sqrt{3} \sqrt{-a^8}}\right)^2}{4 \sqrt{2} a^2 \sqrt{a^4-\sqrt{3} \sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 \sqrt{3} \left(\sqrt{3} a^4+3 \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4} a}-\frac{\left(\sqrt{2} a^2+\sqrt{a^4+\sqrt{3} \sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(-\frac{\left(\sqrt{2} a^2-\sqrt{a^4+\sqrt{3} \sqrt{-a^8}}\right)^2}{4 \sqrt{2} a^2 \sqrt{a^4+\sqrt{3} \sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 \sqrt{3} \left(\sqrt{3} a^4-3 \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4} a}-\frac{\left(\sqrt{2} a^2-\sqrt{a^4+\sqrt{3} \sqrt{-a^8}}\right)^2 \left(b^2+a^2 x^2\right) \sqrt{\frac{b^4+a^4 x^4}{\left(b^2+a^2 x^2\right)^2}} \Pi \left(\frac{\left(\sqrt{2} a^2+\sqrt{a^4+\sqrt{3} \sqrt{-a^8}}\right)^2}{4 \sqrt{2} a^2 \sqrt{a^4+\sqrt{3} \sqrt{-a^8}}};2 \tan ^{-1}\left(\frac{a x}{b}\right)|\frac{1}{2}\right)}{4 \sqrt{3} \left(\sqrt{3} a^4-3 \sqrt{-a^8}\right) b \sqrt{b^4+a^4 x^4} a}","\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,"(-2*a^4*x)/(Sqrt[3]*(Sqrt[3]*a^4 - 3*Sqrt[-a^8])*Sqrt[b^4 + a^4*x^4]) - (2*a^4*x)/(Sqrt[3]*(Sqrt[3]*a^4 + 3*Sqrt[-a^8])*Sqrt[b^4 + a^4*x^4]) - (2*2^(1/4)*a^12*ArcTan[(Sqrt[3*a^4 - Sqrt[3]*Sqrt[-a^8]]*b*x)/(2^(1/4)*(a^4 - Sqrt[3]*Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(Sqrt[3]*Sqrt[-a^8]*(a^4 - Sqrt[3]*Sqrt[-a^8])^(3/4)*(3*a^4 - Sqrt[3]*Sqrt[-a^8])^(3/2)*b) + (2*2^(1/4)*a^12*ArcTan[(Sqrt[-3*a^4 + Sqrt[3]*Sqrt[-a^8]]*b*x)/(2^(1/4)*(a^4 - Sqrt[3]*Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(Sqrt[3]*Sqrt[-a^8]*(a^4 - Sqrt[3]*Sqrt[-a^8])^(3/4)*(-3*a^4 + Sqrt[3]*Sqrt[-a^8])^(3/2)*b) - (2*2^(1/4)*a^12*ArcTan[(Sqrt[-3*a^4 - Sqrt[3]*Sqrt[-a^8]]*b*x)/(2^(1/4)*(a^4 + Sqrt[3]*Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(Sqrt[3]*Sqrt[-a^8]*(-3*a^4 - Sqrt[3]*Sqrt[-a^8])^(3/2)*(a^4 + Sqrt[3]*Sqrt[-a^8])^(3/4)*b) + (2*2^(1/4)*a^12*ArcTan[(Sqrt[3*a^4 + Sqrt[3]*Sqrt[-a^8]]*b*x)/(2^(1/4)*(a^4 + Sqrt[3]*Sqrt[-a^8])^(1/4)*Sqrt[b^4 + a^4*x^4])])/(Sqrt[3]*Sqrt[-a^8]*(a^4 + Sqrt[3]*Sqrt[-a^8])^(3/4)*(3*a^4 + Sqrt[3]*Sqrt[-a^8])^(3/2)*b) + ((b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(2*a*b*Sqrt[b^4 + a^4*x^4]) - (a^3*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(Sqrt[3]*(Sqrt[3]*a^4 - 3*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) - (a^3*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(Sqrt[3]*(Sqrt[3]*a^4 + 3*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) + (a^7*(1 - (Sqrt[2]*a^2)/Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(Sqrt[3]*Sqrt[-a^8]*(3*a^4 + Sqrt[3]*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) + (a^7*(1 + (Sqrt[2]*a^2)/Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(Sqrt[3]*Sqrt[-a^8]*(3*a^4 + Sqrt[3]*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) - (a^7*(1 - (Sqrt[2]*a^2)/Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(Sqrt[3]*Sqrt[-a^8]*(3*a^4 - Sqrt[3]*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) - (a^7*(1 + (Sqrt[2]*a^2)/Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]])*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(Sqrt[3]*Sqrt[-a^8]*(3*a^4 - Sqrt[3]*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) - ((Sqrt[2]*a^2 + Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[-1/4*(Sqrt[2]*a^2 - Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]])^2/(Sqrt[2]*a^2*Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(4*Sqrt[3]*a*(Sqrt[3]*a^4 + 3*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) - ((Sqrt[2]*a^2 - Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(Sqrt[2]*a^2 + Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]])^2/(4*Sqrt[2]*a^2*Sqrt[a^4 - Sqrt[3]*Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(4*Sqrt[3]*a*(Sqrt[3]*a^4 + 3*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) - ((Sqrt[2]*a^2 + Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[-1/4*(Sqrt[2]*a^2 - Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]])^2/(Sqrt[2]*a^2*Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(4*Sqrt[3]*a*(Sqrt[3]*a^4 - 3*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4]) - ((Sqrt[2]*a^2 - Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]])^2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticPi[(Sqrt[2]*a^2 + Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]])^2/(4*Sqrt[2]*a^2*Sqrt[a^4 + Sqrt[3]*Sqrt[-a^8]]), 2*ArcTan[(a*x)/b], 1/2])/(4*Sqrt[3]*a*(Sqrt[3]*a^4 - 3*Sqrt[-a^8])*b*Sqrt[b^4 + a^4*x^4])","B",25,8,42,0.1905,0,"{6725, 220, 2073, 414, 523, 409, 1217, 1707}"
2921,1,309,0,0.3343987,"\int \frac{\left(c+b x+a x^2\right)^{5/2}}{c+b x} \, dx","Int[(c + b*x + a*x^2)^(5/2)/(c + b*x),x]","-\frac{a^{5/2} c^5 \tanh ^{-1}\left(\frac{x \left(b^2-2 a c\right)+b c}{2 \sqrt{a} c \sqrt{a x^2+b x+c}}\right)}{b^6}+\frac{\left(16 a^2 c^2+6 a b x \left(b^2-2 a c\right)-6 a b^2 c+3 b^4\right) \left(a x^2+b x+c\right)^{3/2}}{48 a b^3}+\frac{\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{a x^2+b x+c}}\right)}{256 a^{5/2} b^6}-\frac{\left(-128 a^4 c^4+32 a^3 b^2 c^3+8 a^2 b^4 c^2+2 a b x \left(b^2-2 a c\right) \left(-16 a^2 c^2-12 a b^2 c+3 b^4\right)-18 a b^6 c+3 b^8\right) \sqrt{a x^2+b x+c}}{128 a^2 b^5}+\frac{\left(a x^2+b x+c\right)^{5/2}}{5 b}","-\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,"-1/128*((3*b^8 - 18*a*b^6*c + 8*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4 + 2*a*b*(b^2 - 2*a*c)*(3*b^4 - 12*a*b^2*c - 16*a^2*c^2)*x)*Sqrt[c + b*x + a*x^2])/(a^2*b^5) + ((3*b^4 - 6*a*b^2*c + 16*a^2*c^2 + 6*a*b*(b^2 - 2*a*c)*x)*(c + b*x + a*x^2)^(3/2))/(48*a*b^3) + (c + b*x + a*x^2)^(5/2)/(5*b) + ((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 + b*x + a*x^2])])/(256*a^(5/2)*b^6) - (a^(5/2)*c^5*ArcTanh[(b*c + (b^2 - 2*a*c)*x)/(2*Sqrt[a]*c*Sqrt[c + b*x + a*x^2])])/b^6","A",8,6,22,0.2727,1,"{734, 814, 843, 621, 206, 724}"
2922,1,332,0,1.4605613,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}}{b+a x^4} \, dx","Int[((-b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4))/(b + a*x^4),x]","-\frac{b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{x \left(\frac{\sqrt{-a} a}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{x \left(\frac{(-a)^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{x \sqrt[4]{a x^4+b x^2}}{2 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(4 a^2-b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{7/4}}+\frac{\left(b-4 a^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4+b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4+b x^2}}{2 a}",1,"(x*(b*x^2 + a*x^4)^(1/4))/(2*a) - ((1 + a + (Sqrt[-a]*a)/Sqrt[b])*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*a*(1 + (a*x^2)/b)^(1/4)) - ((1 + a + (-a)^(3/2)/Sqrt[b])*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*a*(1 + (a*x^2)/b)^(1/4)) - (b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(b + a*x^2)^(1/4))","A",17,11,38,0.2895,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2923,1,332,0,1.249277,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{b x^2+a x^4}}{b+a x^4} \, dx","Int[((-b - a*x^2 + x^4)*(b*x^2 + a*x^4)^(1/4))/(b + a*x^4),x]","-\frac{b \sqrt[4]{a x^4+b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2+b}}+\frac{b \sqrt[4]{a x^4+b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2+b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2+b}}-\frac{x \left(\frac{\sqrt{-a} a}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a \sqrt[4]{\frac{a x^2}{b}+1}}-\frac{x \left(\frac{(-a)^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4+b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},-\frac{a x^2}{b}\right)}{3 a \sqrt[4]{\frac{a x^2}{b}+1}}+\frac{x \sqrt[4]{a x^4+b x^2}}{2 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4+b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$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*(b*x^2 + a*x^4)^(1/4))/(2*a) - ((1 + a + (Sqrt[-a]*a)/Sqrt[b])*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), -((a*x^2)/b)])/(3*a*(1 + (a*x^2)/b)^(1/4)) - ((1 + a + (-a)^(3/2)/Sqrt[b])*x*(b*x^2 + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], -((a*x^2)/b)])/(3*a*(1 + (a*x^2)/b)^(1/4)) - (b*(b*x^2 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(b + a*x^2)^(1/4)) + (b*(b*x^2 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(b + a*x^2)^(1/4))","A",17,11,38,0.2895,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2924,1,420,0,1.3539323,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(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{-2 \left((-2+2 i)+\sqrt{1-i}\right) \sqrt{x+1}+4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)+(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}-\frac{(1+i) \tan ^{-1}\left(\frac{2 \left((2-2 i)+\sqrt{1-i}\right) \sqrt{x+1}-4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)-(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)-(1-i)^{3/2}}}-\frac{(1-i) \tan ^{-1}\left(\frac{-2 \left((-2-2 i)+\sqrt{1+i}\right) \sqrt{x+1}+4 \sqrt{1+i}+(2+2 i)}{4 \sqrt{(1-i)+(1+i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}-\frac{(1-i) \tan ^{-1}\left(\frac{2 \left((2+2 i)+\sqrt{1+i}\right) \sqrt{x+1}-4 \sqrt{1+i}+(2+2 i)}{4 \sqrt{(1-i)-(1+i)^{3/2}} \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)","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 - 2*I) + 4*Sqrt[1 - I] - 2*((-2 + 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) + (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] - ((1 + I)*ArcTan[((2 - 2*I) - 4*Sqrt[1 - I] + 2*((2 - 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) - (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) - (1 - I)^(3/2)] - ((1 - I)*ArcTan[((2 + 2*I) + 4*Sqrt[1 + I] - 2*((-2 - 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) + (1 + I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] - ((1 - I)*ArcTan[((2 + 2*I) - 4*Sqrt[1 + I] + 2*((2 + 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) - (1 + I)^(3/2)]*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","C",19,8,33,0.2424,1,"{6728, 742, 640, 621, 206, 984, 724, 204}"
2925,1,420,0,1.0381374,"\int \frac{\sqrt{1+x} \left(-1+x^2\right)}{\left(1+x^2\right) \sqrt{x+\sqrt{1+x}}} \, dx","Int[(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{-2 \left((-2+2 i)+\sqrt{1-i}\right) \sqrt{x+1}+4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)+(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)+(1-i)^{3/2}}}-\frac{(1+i) \tan ^{-1}\left(\frac{2 \left((2-2 i)+\sqrt{1-i}\right) \sqrt{x+1}-4 \sqrt{1-i}+(2-2 i)}{4 \sqrt{(1+i)-(1-i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1+i)-(1-i)^{3/2}}}-\frac{(1-i) \tan ^{-1}\left(\frac{-2 \left((-2-2 i)+\sqrt{1+i}\right) \sqrt{x+1}+4 \sqrt{1+i}+(2+2 i)}{4 \sqrt{(1-i)+(1+i)^{3/2}} \sqrt{x+\sqrt{x+1}}}\right)}{\sqrt{(1-i)+(1+i)^{3/2}}}-\frac{(1-i) \tan ^{-1}\left(\frac{2 \left((2+2 i)+\sqrt{1+i}\right) \sqrt{x+1}-4 \sqrt{1+i}+(2+2 i)}{4 \sqrt{(1-i)-(1+i)^{3/2}} \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)","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 - 2*I) + 4*Sqrt[1 - I] - 2*((-2 + 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) + (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) + (1 - I)^(3/2)] - ((1 + I)*ArcTan[((2 - 2*I) - 4*Sqrt[1 - I] + 2*((2 - 2*I) + Sqrt[1 - I])*Sqrt[1 + x])/(4*Sqrt[(1 + I) - (1 - I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 + I) - (1 - I)^(3/2)] - ((1 - I)*ArcTan[((2 + 2*I) + 4*Sqrt[1 + I] - 2*((-2 - 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) + (1 + I)^(3/2)]*Sqrt[x + Sqrt[1 + x]])])/Sqrt[(1 - I) + (1 + I)^(3/2)] - ((1 - I)*ArcTan[((2 + 2*I) - 4*Sqrt[1 + I] + 2*((2 + 2*I) + Sqrt[1 + I])*Sqrt[1 + x])/(4*Sqrt[(1 - I) - (1 + I)^(3/2)]*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","C",19,8,33,0.2424,1,"{6728, 742, 640, 621, 206, 984, 724, 204}"
2926,1,776,0,2.518926,"\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","Int[(-x^2 + Sqrt[1 + 2*x^2] + (1 + 2*x^2)^(5/2))/(x^2 - x*(1 + 2*x^2)^(3/2)),x]","-x^2+\frac{1}{5} \log \left(x^2+1\right)+\frac{1}{40} \sqrt{1+5 \sqrt{2}} \log \left(4 x^2-2 \sqrt{2 \left(\sqrt{2}-1\right)} x+\sqrt{2}\right)-\frac{1}{40} \sqrt{1+5 \sqrt{2}} \log \left(4 x^2+2 \sqrt{2 \left(\sqrt{2}-1\right)} x+\sqrt{2}\right)+\frac{\log \left(2 \left(2 x^2+1\right)-2 \sqrt{1+\sqrt{2}} \sqrt{2 x^2+1}+\sqrt{2}\right)}{20 \sqrt{2 \left(1+\sqrt{2}\right)}}+\frac{3 \log \left(2 \left(2 x^2+1\right)-2 \sqrt{1+\sqrt{2}} \sqrt{2 x^2+1}+\sqrt{2}\right)}{40 \sqrt{1+\sqrt{2}}}-\frac{\log \left(\sqrt{2} \left(2 x^2+1\right)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{2 x^2+1}+1\right)}{20 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{3 \log \left(\sqrt{2} \left(2 x^2+1\right)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{2 x^2+1}+1\right)}{40 \sqrt{1+\sqrt{2}}}-\left(\frac{2}{5}-\frac{3 i}{10}\right) \tan ^{-1}\left(\frac{(1+i) x}{\sqrt{2 x^2+1}}\right)+\frac{1}{5} \tan ^{-1}\left(\sqrt{2 x^2+1}\right)-\frac{2}{5} \tan ^{-1}\left(4 x^2+1\right)+\frac{1}{10} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{1+\sqrt{2}}-2 \sqrt{2 x^2+1}}{\sqrt{\sqrt{2}-1}}\right)-\frac{3 \tan ^{-1}\left(\frac{\sqrt{1+\sqrt{2}}-2 \sqrt{2 x^2+1}}{\sqrt{\sqrt{2}-1}}\right)}{20 \sqrt{\sqrt{2}-1}}-\frac{1}{10} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{2 x^2+1}+\sqrt{1+\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)+\frac{3 \tan ^{-1}\left(\frac{2 \sqrt{2 x^2+1}+\sqrt{1+\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)}{20 \sqrt{\sqrt{2}-1}}+\frac{2}{5} \tanh ^{-1}\left(\frac{x}{\sqrt{2 x^2+1}}\right)-\left(\frac{3}{10}-\frac{2 i}{5}\right) \tanh ^{-1}\left(\frac{(1+i) x}{\sqrt{2 x^2+1}}\right)+\frac{3}{20} \log \left(8 x^4+4 x^2+1\right)-2 \log (x)-\frac{1}{5} \tan ^{-1}(x)-\frac{1}{20} \sqrt{5 \sqrt{2}-1} \tan ^{-1}\left(-2 \sqrt{2 \left(\sqrt{2}-1\right)} x-\sqrt{2}+1\right)+\frac{1}{20} \sqrt{5 \sqrt{2}-1} \tan ^{-1}\left(2 \sqrt{2 \left(\sqrt{2}-1\right)} x-\sqrt{2}+1\right)-\frac{\sinh ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}","\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^2 - ArcSinh[Sqrt[2]*x]/Sqrt[2] - ArcTan[x]/5 - (Sqrt[-1 + 5*Sqrt[2]]*ArcTan[1 - Sqrt[2] - 2*Sqrt[2*(-1 + Sqrt[2])]*x])/20 + (Sqrt[-1 + 5*Sqrt[2]]*ArcTan[1 - Sqrt[2] + 2*Sqrt[2*(-1 + Sqrt[2])]*x])/20 - (2/5 - (3*I)/10)*ArcTan[((1 + I)*x)/Sqrt[1 + 2*x^2]] + ArcTan[Sqrt[1 + 2*x^2]]/5 - (2*ArcTan[1 + 4*x^2])/5 - (3*ArcTan[(Sqrt[1 + Sqrt[2]] - 2*Sqrt[1 + 2*x^2])/Sqrt[-1 + Sqrt[2]]])/(20*Sqrt[-1 + Sqrt[2]]) + (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[1 + Sqrt[2]] - 2*Sqrt[1 + 2*x^2])/Sqrt[-1 + Sqrt[2]]])/10 + (3*ArcTan[(Sqrt[1 + Sqrt[2]] + 2*Sqrt[1 + 2*x^2])/Sqrt[-1 + Sqrt[2]]])/(20*Sqrt[-1 + Sqrt[2]]) - (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[1 + Sqrt[2]] + 2*Sqrt[1 + 2*x^2])/Sqrt[-1 + Sqrt[2]]])/10 + (2*ArcTanh[x/Sqrt[1 + 2*x^2]])/5 - (3/10 - (2*I)/5)*ArcTanh[((1 + I)*x)/Sqrt[1 + 2*x^2]] - 2*Log[x] + Log[1 + x^2]/5 + (Sqrt[1 + 5*Sqrt[2]]*Log[Sqrt[2] - 2*Sqrt[2*(-1 + Sqrt[2])]*x + 4*x^2])/40 - (Sqrt[1 + 5*Sqrt[2]]*Log[Sqrt[2] + 2*Sqrt[2*(-1 + Sqrt[2])]*x + 4*x^2])/40 + (3*Log[1 + 4*x^2 + 8*x^4])/20 + (3*Log[Sqrt[2] - 2*Sqrt[1 + Sqrt[2]]*Sqrt[1 + 2*x^2] + 2*(1 + 2*x^2)])/(40*Sqrt[1 + Sqrt[2]]) + Log[Sqrt[2] - 2*Sqrt[1 + Sqrt[2]]*Sqrt[1 + 2*x^2] + 2*(1 + 2*x^2)]/(20*Sqrt[2*(1 + Sqrt[2])]) - (3*Log[1 + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + 2*x^2] + Sqrt[2]*(1 + 2*x^2)])/(40*Sqrt[1 + Sqrt[2]]) - Log[1 + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + 2*x^2] + Sqrt[2]*(1 + 2*x^2)]/(20*Sqrt[2*(1 + Sqrt[2])])","C",112,37,49,0.7551,0,"{6742, 402, 215, 377, 206, 14, 444, 43, 1692, 208, 205, 1247, 634, 617, 204, 628, 1251, 773, 12, 416, 528, 523, 266, 701, 800, 203, 50, 63, 1169, 618, 699, 1127, 1161, 1164, 824, 707, 1094}"
2927,1,993,0,1.0655491,"\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","Int[((-b + x^3)*(b + x^3)*(-c + x^3))/(a*x^2 + x^3)^(1/3),x]","\frac{135850 x^{2/3} \sqrt[3]{a+x} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+x}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^9}{531441 \sqrt{3} \sqrt[3]{x^3+a x^2}}+\frac{67925 x^{2/3} \sqrt[3]{a+x} \log (x) a^9}{1594323 \sqrt[3]{x^3+a x^2}}+\frac{67925 x^{2/3} \sqrt[3]{a+x} \log \left(\frac{\sqrt[3]{a+x}}{\sqrt[3]{x}}-1\right) a^9}{531441 \sqrt[3]{x^3+a x^2}}+\frac{135850 \left(x^3+a x^2\right)^{2/3} a^8}{531441 x}-\frac{67925 \left(x^3+a x^2\right)^{2/3} a^7}{354294}+\frac{728 c x^{2/3} \sqrt[3]{a+x} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+x}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^6}{2187 \sqrt{3} \sqrt[3]{x^3+a x^2}}+\frac{364 c x^{2/3} \sqrt[3]{a+x} \log (x) a^6}{6561 \sqrt[3]{x^3+a x^2}}+\frac{364 c x^{2/3} \sqrt[3]{a+x} \log \left(\frac{\sqrt[3]{a+x}}{\sqrt[3]{x}}-1\right) a^6}{2187 \sqrt[3]{x^3+a x^2}}+\frac{67925 x \left(x^3+a x^2\right)^{2/3} a^6}{413343}-\frac{13585 x^2 \left(x^3+a x^2\right)^{2/3} a^5}{91854}+\frac{728 c \left(x^3+a x^2\right)^{2/3} a^5}{2187 x}+\frac{2090 x^3 \left(x^3+a x^2\right)^{2/3} a^4}{15309}-\frac{182}{729} c \left(x^3+a x^2\right)^{2/3} a^4-\frac{14 b^2 x^{2/3} \sqrt[3]{a+x} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+x}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right) a^3}{27 \sqrt{3} \sqrt[3]{x^3+a x^2}}-\frac{7 b^2 x^{2/3} \sqrt[3]{a+x} \log (x) a^3}{81 \sqrt[3]{x^3+a x^2}}-\frac{7 b^2 x^{2/3} \sqrt[3]{a+x} \log \left(\frac{\sqrt[3]{a+x}}{\sqrt[3]{x}}-1\right) a^3}{27 \sqrt[3]{x^3+a x^2}}-\frac{5225 x^4 \left(x^3+a x^2\right)^{2/3} a^3}{40824}+\frac{52}{243} c x \left(x^3+a x^2\right)^{2/3} a^3+\frac{275 x^5 \left(x^3+a x^2\right)^{2/3} a^2}{2268}-\frac{26}{135} c x^2 \left(x^3+a x^2\right)^{2/3} a^2-\frac{14 b^2 \left(x^3+a x^2\right)^{2/3} a^2}{27 x}-\frac{25}{216} x^6 \left(x^3+a x^2\right)^{2/3} a+\frac{8}{45} c x^3 \left(x^3+a x^2\right)^{2/3} a+\frac{7}{18} b^2 \left(x^3+a x^2\right)^{2/3} a-\frac{\sqrt{3} b^2 c x^{2/3} \sqrt[3]{a+x} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+x}}{\sqrt{3} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{x^3+a x^2}}-\frac{b^2 c x^{2/3} \sqrt[3]{a+x} \log (x)}{2 \sqrt[3]{x^3+a x^2}}-\frac{3 b^2 c x^{2/3} \sqrt[3]{a+x} \log \left(\frac{\sqrt[3]{a+x}}{\sqrt[3]{x}}-1\right)}{2 \sqrt[3]{x^3+a x^2}}+\frac{1}{9} x^7 \left(x^3+a x^2\right)^{2/3}-\frac{1}{6} c x^4 \left(x^3+a x^2\right)^{2/3}-\frac{1}{3} b^2 x \left(x^3+a x^2\right)^{2/3}","\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,"(-67925*a^7*(a*x^2 + x^3)^(2/3))/354294 + (7*a*b^2*(a*x^2 + x^3)^(2/3))/18 - (182*a^4*c*(a*x^2 + x^3)^(2/3))/729 + (135850*a^8*(a*x^2 + x^3)^(2/3))/(531441*x) - (14*a^2*b^2*(a*x^2 + x^3)^(2/3))/(27*x) + (728*a^5*c*(a*x^2 + x^3)^(2/3))/(2187*x) + (67925*a^6*x*(a*x^2 + x^3)^(2/3))/413343 - (b^2*x*(a*x^2 + x^3)^(2/3))/3 + (52*a^3*c*x*(a*x^2 + x^3)^(2/3))/243 - (13585*a^5*x^2*(a*x^2 + x^3)^(2/3))/91854 - (26*a^2*c*x^2*(a*x^2 + x^3)^(2/3))/135 + (2090*a^4*x^3*(a*x^2 + x^3)^(2/3))/15309 + (8*a*c*x^3*(a*x^2 + x^3)^(2/3))/45 - (5225*a^3*x^4*(a*x^2 + x^3)^(2/3))/40824 - (c*x^4*(a*x^2 + x^3)^(2/3))/6 + (275*a^2*x^5*(a*x^2 + x^3)^(2/3))/2268 - (25*a*x^6*(a*x^2 + x^3)^(2/3))/216 + (x^7*(a*x^2 + x^3)^(2/3))/9 + (135850*a^9*x^(2/3)*(a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(531441*Sqrt[3]*(a*x^2 + x^3)^(1/3)) - (14*a^3*b^2*x^(2/3)*(a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(27*Sqrt[3]*(a*x^2 + x^3)^(1/3)) + (728*a^6*c*x^(2/3)*(a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(2187*Sqrt[3]*(a*x^2 + x^3)^(1/3)) - (Sqrt[3]*b^2*c*x^(2/3)*(a + x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(a + x)^(1/3))/(Sqrt[3]*x^(1/3))])/(a*x^2 + x^3)^(1/3) + (67925*a^9*x^(2/3)*(a + x)^(1/3)*Log[x])/(1594323*(a*x^2 + x^3)^(1/3)) - (7*a^3*b^2*x^(2/3)*(a + x)^(1/3)*Log[x])/(81*(a*x^2 + x^3)^(1/3)) + (364*a^6*c*x^(2/3)*(a + x)^(1/3)*Log[x])/(6561*(a*x^2 + x^3)^(1/3)) - (b^2*c*x^(2/3)*(a + x)^(1/3)*Log[x])/(2*(a*x^2 + x^3)^(1/3)) + (67925*a^9*x^(2/3)*(a + x)^(1/3)*Log[-1 + (a + x)^(1/3)/x^(1/3)])/(531441*(a*x^2 + x^3)^(1/3)) - (7*a^3*b^2*x^(2/3)*(a + x)^(1/3)*Log[-1 + (a + x)^(1/3)/x^(1/3)])/(27*(a*x^2 + x^3)^(1/3)) + (364*a^6*c*x^(2/3)*(a + x)^(1/3)*Log[-1 + (a + x)^(1/3)/x^(1/3)])/(2187*(a*x^2 + x^3)^(1/3)) - (3*b^2*c*x^(2/3)*(a + x)^(1/3)*Log[-1 + (a + x)^(1/3)/x^(1/3)])/(2*(a*x^2 + x^3)^(1/3))","B",28,4,33,0.1212,1,"{2053, 2011, 59, 2024}"
2928,0,0,0,23.6432486,"\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","Int[(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,"(6*b*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(x^6*(-a + x^3)^(1/3))/((-b + x^3)^(1/3)*(b^2 - 2*b*x^3 + (1 - a^2*d)*x^6 + 2*a*d*x^9 - d*x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(2/3) + (3*a*b*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(x^3*(-a + x^3)^(1/3))/((-b + x^3)^(1/3)*(-b^2 + 2*b*x^3 - (1 - a^2*d)*x^6 - 2*a*d*x^9 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(2/3) + (3*x^(2/3)*(-a + x)^(2/3)*(-b + x)^(4/3)*Defer[Subst][Defer[Int][(x^9*(-a + x^3)^(1/3))/((-b + x^3)^(1/3)*(-b^2 + 2*b*x^3 - (1 - a^2*d)*x^6 - 2*a*d*x^9 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(2/3)","F",0,0,0,0,-1,"{}"
2929,1,345,0,1.4996336,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{b+a x^4} \, dx","Int[((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(b + a*x^4),x]","\frac{b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{x \left(\frac{\sqrt{-a} a}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{x \left(\frac{(-a)^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)-\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a b \log (x)+\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(4 a^2+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{\left(-4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}",1,"(x*(-(b*x^2) + a*x^4)^(1/4))/(2*a) - ((1 + a + (Sqrt[-a]*a)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) - ((1 + a + (-a)^(3/2)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) + (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4)) - (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4))","A",17,11,39,0.2821,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2930,1,345,0,1.2937658,"\int \frac{\left(-b-a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{b+a x^4} \, dx","Int[((-b - a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(b + a*x^4),x]","\frac{b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{x \left(\frac{\sqrt{-a} a}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{x \left(\frac{(-a)^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{-a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2+a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)-\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a b \log (x)+\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)-a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$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))/(2*a) - ((1 + a + (Sqrt[-a]*a)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[-a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) - ((1 + a + (-a)^(3/2)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[-a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) + (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4)) - (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4))","A",17,11,39,0.2821,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2931,1,1002,0,5.1106372,"\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","Int[(a*b*c - b^2*x + a^2*x^2)/(Sqrt[c + b*x + a*x^2]*(c + b*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{b+2 a x}{2 \sqrt{a} \sqrt{a x^2+b x+c}}\right) a^{3/2}}{b}+\frac{\sqrt{\sqrt{c} a^2+(1-b) b \sqrt{c} a-b \left(b \sqrt{c}-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \sqrt{b^4-a c b^3+\left(a^2 c-a \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+a^2 c b-a^3 c+a^2 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}} \tan ^{-1}\left(\frac{b \sqrt{c} \left(\sqrt{c} a^2+(1-b) b \sqrt{c} a-b^2 \sqrt{c}+b \sqrt{b^3+c b^2-2 a c b+a^2 c}\right)-\left(b^4-a \left(a-b^2\right) \left(a c-b c-\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right)\right) x}{\sqrt{2} \sqrt[4]{c} \sqrt{b^4-a c b^3+a^2 c b^2+a^2 c b-a^3 c+a \left(a-b^2\right) \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}} \sqrt{\sqrt{c} a^2+(1-b) b \sqrt{c} a-b \left(b \sqrt{c}-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \sqrt{a x^2+b x+c}}\right)}{\sqrt{2} b \sqrt[4]{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}}-\frac{\sqrt{\sqrt{c} a^2+(1-b) b \sqrt{c} a-b \left(\sqrt{c} b+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \sqrt{b^4-a c b^3+\left(c a^2+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} a\right) b^2+a^2 c b-a^2 \sqrt{c} \left(\sqrt{c} a+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \tan ^{-1}\left(\frac{b \sqrt{c} \left(\sqrt{c} a^2+(1-b) b \sqrt{c} a-b \left(\sqrt{c} b+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)\right)-\left(b^4-a \left(a-b^2\right) \left(a c-b c+\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right)\right) x}{\sqrt{2} \sqrt[4]{c} \sqrt{b^4-a c b^3+a^2 c b^2+a^2 c b-a^3 c-a \left(a-b^2\right) \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}} \sqrt{\sqrt{c} a^2+(1-b) b \sqrt{c} a-b \left(\sqrt{c} b+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \sqrt{a x^2+b x+c}}\right)}{\sqrt{2} b \sqrt[4]{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}}","\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,"(Sqrt[a^2*Sqrt[c] + a*(1 - b)*b*Sqrt[c] - b*(b*Sqrt[c] - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*Sqrt[b^4 - a^3*c + a^2*b*c - a*b^3*c + a^2*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + b^2*(a^2*c - a*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*ArcTan[(b*Sqrt[c]*(a^2*Sqrt[c] + a*(1 - b)*b*Sqrt[c] - b^2*Sqrt[c] + b*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) - (b^4 - a*(a - b^2)*(a*c - b*c - Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))*x)/(Sqrt[2]*c^(1/4)*Sqrt[b^4 - a^3*c + a^2*b*c + a^2*b^2*c - a*b^3*c + a*(a - b^2)*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]]*Sqrt[a^2*Sqrt[c] + a*(1 - b)*b*Sqrt[c] - b*(b*Sqrt[c] - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*Sqrt[c + b*x + a*x^2])])/(Sqrt[2]*b*c^(1/4)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) - (Sqrt[a^2*Sqrt[c] + a*(1 - b)*b*Sqrt[c] - b*(b*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*Sqrt[b^4 + a^2*b*c - a*b^3*c - a^2*Sqrt[c]*(a*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + b^2*(a^2*c + a*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*ArcTan[(b*Sqrt[c]*(a^2*Sqrt[c] + a*(1 - b)*b*Sqrt[c] - b*(b*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])) - (b^4 - a*(a - b^2)*(a*c - b*c + Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))*x)/(Sqrt[2]*c^(1/4)*Sqrt[b^4 - a^3*c + a^2*b*c + a^2*b^2*c - a*b^3*c - a*(a - b^2)*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]]*Sqrt[a^2*Sqrt[c] + a*(1 - b)*b*Sqrt[c] - b*(b*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*Sqrt[c + b*x + a*x^2])])/(Sqrt[2]*b*c^(1/4)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + (a^(3/2)*ArcTanh[(b + 2*a*x)/(2*Sqrt[a]*Sqrt[c + b*x + a*x^2])])/b","B",8,6,42,0.1429,1,"{1078, 621, 206, 1036, 1030, 205}"
2932,1,337,0,1.4467595,"\int \frac{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b+a x^4} \, dx","Int[((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b + a*x^4),x]","-\frac{x \left(-\frac{a^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{x \left(\frac{a^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)+a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(b-4 a^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{\left(4 a^2-b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt[4]{a x^4-b x^2}}\right)}{4 a^{7/4}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}",1,"(x*(-(b*x^2) + a*x^4)^(1/4))/(2*a) - ((1 + a - a^(3/2)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) - ((1 + a + a^(3/2)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) + (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4)) - (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4))","A",17,11,38,0.2895,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2933,1,337,0,1.2381848,"\int \frac{\left(b+a x^2+x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b+a x^4} \, dx","Int[((b + a*x^2 + x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b + a*x^4),x]","-\frac{x \left(-\frac{a^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};-\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{x \left(\frac{a^{3/2}}{\sqrt{b}}+a+1\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{\sqrt{a} x^2}{\sqrt{b}},\frac{a x^2}{b}\right)}{3 a \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 a^{7/4} \sqrt{x} \sqrt[4]{a x^2-b}}+\frac{x \sqrt[4]{a x^4-b x^2}}{2 a}","\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^4 a+a^2-a b\&,\frac{-\text{$\#$1}^4 a^2 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 a^2 \log (x)+\text{$\#$1}^4 a b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)+\text{$\#$1}^4 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-\text{$\#$1}^4 a b \log (x)-\text{$\#$1}^4 b \log (x)+a^3 \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^2 b \log \left(\sqrt[4]{a x^4-b x^2}-\text{$\#$1} x\right)-a^3 \log (x)+a^2 b \log (x)}{\text{$\#$1}^3 a-\text{$\#$1}^7}\&\right]}{4 a}+\frac{\left(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))/(2*a) - ((1 + a - a^(3/2)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, -((Sqrt[a]*x^2)/Sqrt[b]), (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) - ((1 + a + a^(3/2)/Sqrt[b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (Sqrt[a]*x^2)/Sqrt[b], (a*x^2)/b])/(3*a*(1 - (a*x^2)/b)^(1/4)) + (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4)) - (b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*a^(7/4)*Sqrt[x]*(-b + a*x^2)^(1/4))","A",17,11,38,0.2895,0,"{2056, 6725, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2934,0,0,0,10.6557776,"\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","Int[((-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,"(3*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x*(1 - x^3)^(5/3))/((1 - k*x^3)^(1/3)*(b*(-1 + x^3)^4 - x^6*(-1 + k*x^3)^2)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (3*(1 - 2*k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - x^3)^(5/3))/((1 - k*x^3)^(1/3)*(b*(-1 + x^3)^4 - x^6*(-1 + k*x^3)^2)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2935,1,150,0,0.2955301,"\int \frac{1}{(b+a x) \sqrt[4]{b^2 x+a^2 x^3}} \, dx","Int[1/((b + a*x)*(b^2*x + a^2*x^3)^(1/4)),x]","\frac{4 x \sqrt[4]{\frac{a^2 x^2}{b^2}+1} F_1\left(\frac{3}{8};1,\frac{1}{4};\frac{11}{8};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{b^2}\right)}{3 b \sqrt[4]{a^2 x^3+b^2 x}}-\frac{4 a x^2 \sqrt[4]{\frac{a^2 x^2}{b^2}+1} F_1\left(\frac{7}{8};1,\frac{1}{4};\frac{15}{8};\frac{a^2 x^2}{b^2},-\frac{a^2 x^2}{b^2}\right)}{7 b^2 \sqrt[4]{a^2 x^3+b^2 x}}","\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,"(4*x*(1 + (a^2*x^2)/b^2)^(1/4)*AppellF1[3/8, 1, 1/4, 11/8, (a^2*x^2)/b^2, -((a^2*x^2)/b^2)])/(3*b*(b^2*x + a^2*x^3)^(1/4)) - (4*a*x^2*(1 + (a^2*x^2)/b^2)^(1/4)*AppellF1[7/8, 1, 1/4, 15/8, (a^2*x^2)/b^2, -((a^2*x^2)/b^2)])/(7*b^2*(b^2*x + a^2*x^3)^(1/4))","C",8,5,25,0.2000,0,"{2056, 959, 466, 511, 510}"
2936,1,405,0,1.8292683,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b-a x^2+x^4} \, dx","Int[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b - a*x^2 + x^4),x]","-\frac{2 x \left(a^3-a^2 \sqrt{a^2+4 b}+2 a b-2 b\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{2 x^2}{a-\sqrt{a^2+4 b}},\frac{a x^2}{b}\right)}{3 \left(-a \sqrt{a^2+4 b}+a^2+4 b\right) \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{2 x \left(a^2+\frac{a^3+2 a b-2 b}{\sqrt{a^2+4 b}}\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{2 x^2}{a+\sqrt{a^2+4 b}},\frac{a x^2}{b}\right)}{3 \left(\sqrt{a^2+4 b}+a\right) \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{1}{2} a x \sqrt[4]{a x^4-b x^2}+\frac{\sqrt[4]{a} b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{\sqrt[4]{a} b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt{x} \sqrt[4]{a x^2-b}}","\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 - (2*(a^3 - 2*b + 2*a*b - a^2*Sqrt[a^2 + 4*b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (2*x^2)/(a - Sqrt[a^2 + 4*b]), (a*x^2)/b])/(3*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*(1 - (a*x^2)/b)^(1/4)) - (2*(a^2 + (a^3 - 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (2*x^2)/(a + Sqrt[a^2 + 4*b]), (a*x^2)/b])/(3*(a + Sqrt[a^2 + 4*b])*(1 - (a*x^2)/b)^(1/4)) + (a^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*Sqrt[x]*(-b + a*x^2)^(1/4)) - (a^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*Sqrt[x]*(-b + a*x^2)^(1/4))","A",17,11,41,0.2683,0,"{2056, 6728, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2937,1,405,0,1.4643789,"\int \frac{\left(-b+a x^4\right) \sqrt[4]{-b x^2+a x^4}}{-b-a x^2+x^4} \, dx","Int[((-b + a*x^4)*(-(b*x^2) + a*x^4)^(1/4))/(-b - a*x^2 + x^4),x]","-\frac{2 x \left(a^3-a^2 \sqrt{a^2+4 b}+2 a b-2 b\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{2 x^2}{a-\sqrt{a^2+4 b}},\frac{a x^2}{b}\right)}{3 \left(-a \sqrt{a^2+4 b}+a^2+4 b\right) \sqrt[4]{1-\frac{a x^2}{b}}}-\frac{2 x \left(a^2+\frac{a^3+2 a b-2 b}{\sqrt{a^2+4 b}}\right) \sqrt[4]{a x^4-b x^2} F_1\left(\frac{3}{4};1,-\frac{1}{4};\frac{7}{4};\frac{2 x^2}{a+\sqrt{a^2+4 b}},\frac{a x^2}{b}\right)}{3 \left(\sqrt{a^2+4 b}+a\right) \sqrt[4]{1-\frac{a x^2}{b}}}+\frac{1}{2} a x \sqrt[4]{a x^4-b x^2}+\frac{\sqrt[4]{a} b \sqrt[4]{a x^4-b x^2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt{x} \sqrt[4]{a x^2-b}}-\frac{\sqrt[4]{a} b \sqrt[4]{a x^4-b x^2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{x}}{\sqrt[4]{a x^2-b}}\right)}{4 \sqrt{x} \sqrt[4]{a x^2-b}}","\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 - (2*(a^3 - 2*b + 2*a*b - a^2*Sqrt[a^2 + 4*b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (2*x^2)/(a - Sqrt[a^2 + 4*b]), (a*x^2)/b])/(3*(a^2 + 4*b - a*Sqrt[a^2 + 4*b])*(1 - (a*x^2)/b)^(1/4)) - (2*(a^2 + (a^3 - 2*b + 2*a*b)/Sqrt[a^2 + 4*b])*x*(-(b*x^2) + a*x^4)^(1/4)*AppellF1[3/4, 1, -1/4, 7/4, (2*x^2)/(a + Sqrt[a^2 + 4*b]), (a*x^2)/b])/(3*(a + Sqrt[a^2 + 4*b])*(1 - (a*x^2)/b)^(1/4)) + (a^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)*ArcTan[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*Sqrt[x]*(-b + a*x^2)^(1/4)) - (a^(1/4)*b*(-(b*x^2) + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*Sqrt[x])/(-b + a*x^2)^(1/4)])/(4*Sqrt[x]*(-b + a*x^2)^(1/4))","A",17,11,41,0.2683,0,"{2056, 6728, 279, 329, 331, 298, 203, 206, 466, 511, 510}"
2938,0,0,0,7.8633735,"\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","Int[((-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,"(9*a*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(a - b + x^3)^(1/3))/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4)*d - (1 - 4*(a - b)^3*d)*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*d*x^6 + 4*a*(1 - b/a)*d*x^9 + d*x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(1/3) + (9*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(a - b + x^3)^(1/3))/(a^4*(1 + (b*(-4*a^3 + 6*a^2*b - 4*a*b^2 + b^3))/a^4)*d - (1 - 4*(a - b)^3*d)*x^3 + 6*a^2*(1 + (b*(-2*a + b))/a^2)*d*x^6 + 4*a*(1 - b/a)*d*x^9 + d*x^12), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(1/3) - (3*(4*a - b)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x*(a - b + x^3)^(1/3))/(a*(1 + (b^4*d)/a) - (1 + 4*b^3*d)*(a + x^3) + 6*b^2*d*(a + x^3)^2 - 4*b*d*(a + x^3)^3 + d*(a + x^3)^4), x], x, (-a + x)^(1/3)])/(-((a - x)*(b - x)^2))^(1/3)","F",0,0,0,0,-1,"{}"
2939,1,1370,0,3.8729178,"\int \frac{\left(d+c x^2\right) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{f+e x^2} \, dx","Int[((d + c*x^2)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(f + e*x^2),x]","-\frac{c b^2}{a e \sqrt{a x+\sqrt{b^2+a^2 x^2}}}+\frac{c \left(a x+\sqrt{b^2+a^2 x^2}\right)^{3/2}}{3 a e}+\frac{\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{-e} \left(\sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}}-\sqrt{2} \sqrt[4]{-e} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}}}\right)}{\sqrt{2} (-e)^{9/4} \sqrt{f}}-\frac{\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{-e} \left(\sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}}+\sqrt{2} \sqrt[4]{-e} \sqrt{a x+\sqrt{b^2+a^2 x^2}}\right)}{\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}}}\right)}{\sqrt{2} (-e)^{9/4} \sqrt{f}}-\frac{\sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}}-\sqrt{2} (-e)^{3/4} \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{\sqrt{-e} \sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}}}\right)}{\sqrt{2} (-e)^{7/4} \sqrt{f}}+\frac{\sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a x+\sqrt{b^2+a^2 x^2}} (-e)^{3/4}+\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}}}{\sqrt{-e} \sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}}}\right)}{\sqrt{2} (-e)^{7/4} \sqrt{f}}+\frac{\sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}} (d e-c f) \log \left(\sqrt[4]{-e} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-e}\right)}{2 \sqrt{2} (-e)^{7/4} \sqrt{f}}-\frac{\sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}} (d e-c f) \log \left(\sqrt[4]{-e} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{f} a+\sqrt{-b^2} \sqrt{-e}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} \sqrt[4]{-e}\right)}{2 \sqrt{2} (-e)^{7/4} \sqrt{f}}-\frac{\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}} (d e-c f) \log \left((-e)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)-\sqrt{2} \sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-e)^{3/4}\right)}{2 \sqrt{2} (-e)^{9/4} \sqrt{f}}+\frac{\sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}} (d e-c f) \log \left((-e)^{3/4} \left(a x+\sqrt{b^2+a^2 x^2}\right)+\sqrt{2} \sqrt{\sqrt{-b^2} (-e)^{3/2}+a e \sqrt{f}} \sqrt{a x+\sqrt{b^2+a^2 x^2}}+\sqrt{-b^2} (-e)^{3/4}\right)}{2 \sqrt{2} (-e)^{9/4} \sqrt{f}}","-\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,"-((b^2*c)/(a*e*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])) + (c*(a*x + Sqrt[b^2 + a^2*x^2])^(3/2))/(3*a*e) + (Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]*(d*e - c*f)*ArcTan[(Sqrt[-e]*(Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]] - Sqrt[2]*(-e)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]])/(Sqrt[2]*(-e)^(9/4)*Sqrt[f]) - (Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]*(d*e - c*f)*ArcTan[(Sqrt[-e]*(Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]] + Sqrt[2]*(-e)^(1/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]))/Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]])/(Sqrt[2]*(-e)^(9/4)*Sqrt[f]) - (Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]]*(d*e - c*f)*ArcTan[(Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]] - Sqrt[2]*(-e)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-e]*Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]])])/(Sqrt[2]*(-e)^(7/4)*Sqrt[f]) + (Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]]*(d*e - c*f)*ArcTan[(Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]] + Sqrt[2]*(-e)^(3/4)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(Sqrt[-e]*Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]])])/(Sqrt[2]*(-e)^(7/4)*Sqrt[f]) + (Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]]*(d*e - c*f)*Log[Sqrt[-b^2]*(-e)^(1/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-e)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*(-e)^(7/4)*Sqrt[f]) - (Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]]*(d*e - c*f)*Log[Sqrt[-b^2]*(-e)^(1/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*Sqrt[-e] + a*Sqrt[f]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-e)^(1/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*(-e)^(7/4)*Sqrt[f]) - (Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]*(d*e - c*f)*Log[Sqrt[-b^2]*(-e)^(3/4) - Sqrt[2]*Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-e)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*(-e)^(9/4)*Sqrt[f]) + (Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]*(d*e - c*f)*Log[Sqrt[-b^2]*(-e)^(3/4) + Sqrt[2]*Sqrt[Sqrt[-b^2]*(-e)^(3/2) + a*e*Sqrt[f]]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]] + (-e)^(3/4)*(a*x + Sqrt[b^2 + a^2*x^2])])/(2*Sqrt[2]*(-e)^(9/4)*Sqrt[f])","B",33,11,40,0.2750,1,"{6725, 2117, 14, 2119, 1628, 826, 1169, 634, 618, 204, 628}"
2940,1,679,0,2.6878922,"\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","Int[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","-\frac{i \left(1+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}+\frac{i \left(1+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}+i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}-\frac{\left(1-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}+\frac{\left(1-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(1+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(1+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}+i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-3 \text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+3 \text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{2 \sqrt{2}}",1,"((-1/4*I)*(1 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + ((I/4)*(1 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] - ((1 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) + ((1 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) - ((1/4 - I/4)*(1 + Sqrt[5])*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 - I/4)*(1 + Sqrt[5])*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 + I/4)*(1 - Sqrt[5])*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] - ((1/4 + I/4)*(1 - Sqrt[5])*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])]","C",26,5,42,0.1190,0,"{6728, 6725, 2133, 725, 206}"
2941,1,679,0,2.2268326,"\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","Int[((1 + x^2)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","-\frac{i \left(1+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}+\frac{i \left(1+\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}+i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}-\frac{\left(1-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}+\frac{\left(1-\sqrt{5}\right) \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{4 \sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(1+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(1+\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}+i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(1-\sqrt{5}\right) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^6-6 \text{$\#$1}^4+2 \text{$\#$1}^2+1\&,\frac{\text{$\#$1}^6 \left(-\log \left(\sqrt{x^4+1}+x^2-1\right)\right)+\text{$\#$1}^6 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-3 \text{$\#$1}^4 \log \left(\sqrt{x^4+1}+x^2-1\right)+3 \text{$\#$1}^4 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\text{$\#$1}^2 \log \left(\sqrt{x^4+1}+x^2-1\right)+\text{$\#$1}^2 \log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)-\log \left(\text{$\#$1} \sqrt{x^4+1}+\text{$\#$1} x^2-\text{$\#$1}+\sqrt{2} \sqrt{\sqrt{x^4+1}+x^2} x\right)+\log \left(\sqrt{x^4+1}+x^2-1\right)}{2 \text{$\#$1}^7-3 \text{$\#$1}^5-6 \text{$\#$1}^3+\text{$\#$1}}\&\right]}{2 \sqrt{2}}",1,"((-1/4*I)*(1 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + ((I/4)*(1 + Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] - ((1 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) + ((1 - Sqrt[5])*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(4*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) - ((1/4 - I/4)*(1 + Sqrt[5])*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 - I/4)*(1 + Sqrt[5])*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1/4 + I/4)*(1 - Sqrt[5])*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] - ((1/4 + I/4)*(1 - Sqrt[5])*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])]","C",26,5,42,0.1190,0,"{6728, 6725, 2133, 725, 206}"
2942,1,167,0,0.7610242,"\int \frac{1-x^4}{\left(1+x^2+x^4\right) \sqrt[4]{-x^3+x^5}} \, dx","Int[(1 - x^4)/((1 + x^2 + x^4)*(-x^3 + x^5)^(1/4)),x]","\frac{4 \left(\sqrt{3}+3 i\right) x \sqrt[4]{1-x^2} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};x^2,-\frac{2 x^2}{1-i \sqrt{3}}\right)}{3 \left(\sqrt{3}+i\right) \sqrt[4]{x^5-x^3}}+\frac{4 \left(-\sqrt{3}+3 i\right) x \sqrt[4]{1-x^2} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};x^2,-\frac{2 x^2}{1+i \sqrt{3}}\right)}{3 \left(-\sqrt{3}+i\right) \sqrt[4]{x^5-x^3}}","\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,"(4*(3*I + Sqrt[3])*x*(1 - x^2)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, x^2, (-2*x^2)/(1 - I*Sqrt[3])])/(3*(I + Sqrt[3])*(-x^3 + x^5)^(1/4)) + (4*(3*I - Sqrt[3])*x*(1 - x^2)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, x^2, (-2*x^2)/(1 + I*Sqrt[3])])/(3*(I - Sqrt[3])*(-x^3 + x^5)^(1/4))","C",9,6,31,0.1935,0,"{2056, 1586, 6715, 6728, 430, 429}"
2943,0,0,0,0.3129184,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt[3]{a x^2+x \sqrt{-b+a^2 x^2}}} \, dx","Int[Sqrt[-b + a^2*x^2]/(a*x^2 + x*Sqrt[-b + a^2*x^2])^(1/3),x]","\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt[3]{a x^2+x \sqrt{-b+a^2 x^2}}} \, dx","\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,"Defer[Int][Sqrt[-b + a^2*x^2]/(a*x^2 + x*Sqrt[-b + a^2*x^2])^(1/3), x]","F",0,0,0,0,-1,"{}"
2944,0,0,0,2.6192525,"\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","Int[((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{$\#$1}^4 \sqrt{a}-4 i \text{$\#$1}^3 b+2 \text{$\#$1}^2 a^{3/2} b+4 i \text{$\#$1} a b^2+a^{5/2} b^2\&,\frac{a b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-\text{$\#$1}^2 b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^3 \sqrt{a}-3 i \text{$\#$1}^2 b+\text{$\#$1} a^{3/2} b+i a b^2}\&\right]}{\sqrt{a}}",1,"ArcTanh[(Sqrt[2]*Sqrt[a]*x)/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]]/(Sqrt[2]*Sqrt[a]) - Sqrt[b]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[b] - a*x)*Sqrt[b + a^2*x^4]), x] - Sqrt[b]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[b] + a*x)*Sqrt[b + a^2*x^4]), x]","F",0,0,0,0,-1,"{}"
2945,0,0,0,2.0277445,"\int \frac{\left(b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(-b+a^2 x^2\right) \sqrt{b+a^2 x^4}} \, dx","Int[((b + a^2*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/((-b + a^2*x^2)*Sqrt[b + a^2*x^4]),x]","\int \frac{\left(b+a^2 x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\left(-b+a^2 x^2\right) \sqrt{b+a^2 x^4}} \, dx","\frac{\log \left(i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\sqrt{2} \sqrt{a}}-\frac{i \sqrt{2} \text{RootSum}\left[\text{$\#$1}^4 \sqrt{a}-4 i \text{$\#$1}^3 b+2 \text{$\#$1}^2 a^{3/2} b+4 i \text{$\#$1} a b^2+a^{5/2} b^2\&,\frac{a b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-\text{$\#$1}^2 b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^3 \sqrt{a}-3 i \text{$\#$1}^2 b+\text{$\#$1} a^{3/2} b+i a b^2}\&\right]}{\sqrt{a}}",1,"ArcTanh[(Sqrt[2]*Sqrt[a]*x)/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]]/(Sqrt[2]*Sqrt[a]) - Sqrt[b]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[b] - a*x)*Sqrt[b + a^2*x^4]), x] - Sqrt[b]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((Sqrt[b] + a*x)*Sqrt[b + a^2*x^4]), x]","F",0,0,0,0,-1,"{}"
2946,0,0,0,2.7476372,"\int \frac{x^3}{\sqrt{a+b x+c x^2+b x^3+a x^4} \left(1-x^6\right)} \, dx","Int[x^3/(Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]*(1 - x^6)),x]","\int \frac{x^3}{\sqrt{a+b x+c x^2+b x^3+a x^4} \left(1-x^6\right)} \, dx","\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,"-1/6*Defer[Int][1/((-1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x] - Defer[Int][1/((1 + x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x]/6 + ((1 + I*Sqrt[3])*Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/6 + ((1 - I*Sqrt[3])*Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/6 + ((1 - I*Sqrt[3])*Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/6 + ((1 + I*Sqrt[3])*Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]), x])/6","F",0,0,0,0,-1,"{}"
2947,0,0,0,1.7608288,"\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","Int[((-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,"2*p*(b + 5*a*p^2*q^4)*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] - a*q^7*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^9, x] - 4*a*p*q^6*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^6, x] - q*(b + 3*a*p^2*q^4)*Defer[Int][Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6]/x^3, x] + 25*a*p^4*q^3*Defer[Int][x^3*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 24*a*p^5*q^2*Defer[Int][x^6*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 11*a*p^6*q*Defer[Int][x^9*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x] + 2*a*p^7*Defer[Int][x^12*Sqrt[q^2 - 2*p*q*x^2 + 2*p*q*x^3 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2948,0,0,0,1.8225529,"\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","Int[((-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,"-2*a*q^7*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^17, x] - 11*a*p*q^6*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^14, x] - 24*a*p^2*q^5*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^11, x] - 25*a*p^3*q^4*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^8, x] - 2*q*(b + 5*a*p^4*q^2)*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^5, x] + p*(b + 3*a*p^4*q^2)*Defer[Int][Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6]/x^2, x] + 4*a*p^6*q*Defer[Int][x*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6], x] + a*p^7*Defer[Int][x^4*Sqrt[q^2 + 2*p*q*x^3 - 2*p*q*x^4 + p^2*x^6], x]","F",0,0,0,0,-1,"{}"
2949,1,247,0,0.4259237,"\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","Int[((-q + p*x^4)*Sqrt[q + p*x^4])/(b*x^4 + a*(q + p*x^4)^2),x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a} \sqrt{p x^4+q}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a} \sqrt{p x^4+q}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b}}+\frac{\log \left(-\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{p x^4+q}}+\sqrt{a}+\frac{\sqrt{b} x^2}{p x^4+q}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}-\frac{\log \left(\frac{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x}{\sqrt{p x^4+q}}+\sqrt{a}+\frac{\sqrt{b} x^2}{p x^4+q}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{b}}","\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,"ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/(a^(1/4)*Sqrt[q + p*x^4])]/(2*Sqrt[2]*a^(3/4)*b^(1/4)) - ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/(a^(1/4)*Sqrt[q + p*x^4])]/(2*Sqrt[2]*a^(3/4)*b^(1/4)) + Log[Sqrt[a] + (Sqrt[b]*x^2)/(q + p*x^4) - (Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[q + p*x^4]]/(4*Sqrt[2]*a^(3/4)*b^(1/4)) - Log[Sqrt[a] + (Sqrt[b]*x^2)/(q + p*x^4) + (Sqrt[2]*a^(1/4)*b^(1/4)*x)/Sqrt[q + p*x^4]]/(4*Sqrt[2]*a^(3/4)*b^(1/4))","A",10,7,40,0.1750,1,"{6712, 211, 1165, 628, 1162, 617, 204}"
2950,1,229,0,0.0822181,"\int \frac{-3 b+a x}{\sqrt[3]{b^2-a^2 x^2} \left(3 b^2+a^2 x^2\right)} \, dx","Int[(-3*b + a*x)/((b^2 - a^2*x^2)^(1/3)*(3*b^2 + a^2*x^2)),x]","\frac{\sqrt[3]{1-\frac{a^2 x^2}{b^2}} \log \left(a^2 x^2+3 b^2\right)}{2\ 2^{2/3} a \sqrt[3]{b^2-a^2 x^2}}-\frac{3 \sqrt[3]{1-\frac{a^2 x^2}{b^2}} \log \left(\left(\frac{a x}{b}+1\right)^{2/3}+\sqrt[3]{2} \sqrt[3]{1-\frac{a x}{b}}\right)}{2\ 2^{2/3} a \sqrt[3]{b^2-a^2 x^2}}+\frac{\sqrt{3} \sqrt[3]{1-\frac{a^2 x^2}{b^2}} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2^{2/3} \left(\frac{a x}{b}+1\right)^{2/3}}{\sqrt{3} \sqrt[3]{1-\frac{a x}{b}}}\right)}{2^{2/3} a \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,"(Sqrt[3]*(1 - (a^2*x^2)/b^2)^(1/3)*ArcTan[1/Sqrt[3] - (2^(2/3)*(1 + (a*x)/b)^(2/3))/(Sqrt[3]*(1 - (a*x)/b)^(1/3))])/(2^(2/3)*a*(b^2 - a^2*x^2)^(1/3)) + ((1 - (a^2*x^2)/b^2)^(1/3)*Log[3*b^2 + a^2*x^2])/(2*2^(2/3)*a*(b^2 - a^2*x^2)^(1/3)) - (3*(1 - (a^2*x^2)/b^2)^(1/3)*Log[2^(1/3)*(1 - (a*x)/b)^(1/3) + (1 + (a*x)/b)^(2/3)])/(2*2^(2/3)*a*(b^2 - a^2*x^2)^(1/3))","A",2,2,39,0.05128,1,"{1009, 1008}"
2951,0,0,0,9.3736991,"\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","Int[(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]","\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","\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,"-x + (Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*ArcTanh[Sqrt[1 + 2*x]])/(2*Sqrt[1 + 2*x]*(1 + x + x^2)) - Log[x]/4 + Log[4 + 7*x + 8*x^2 + 5*x^3 + 2*x^4]/16 - (Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Log[3 + 3*x + 2*x^2 - Sqrt[1 + 2*x] - x*Sqrt[1 + 2*x]])/(16*Sqrt[1 + 2*x]*(1 + x + x^2)) + (Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Log[3 + 3*x + 2*x^2 + Sqrt[1 + 2*x] + x*Sqrt[1 + 2*x]])/(16*Sqrt[1 + 2*x]*(1 + x + x^2)) + (5*Defer[Int][(4 + 7*x + 8*x^2 + 5*x^3 + 2*x^4)^(-1), x])/16 + Defer[Int][x/(4 + 7*x + 8*x^2 + 5*x^3 + 2*x^4), x] + (5*Defer[Int][x^2/(4 + 7*x + 8*x^2 + 5*x^3 + 2*x^4), x])/16 - (17*Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Defer[Subst][Defer[Int][(4 - x + x^2 - x^3 + x^4)^(-1), x], x, Sqrt[1 + 2*x]])/(16*Sqrt[1 + 2*x]*(1 + x + x^2)) + (3*Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Defer[Subst][Defer[Int][x/(4 - x + x^2 - x^3 + x^4), x], x, Sqrt[1 + 2*x]])/(8*Sqrt[1 + 2*x]*(1 + x + x^2)) - (11*Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Defer[Subst][Defer[Int][x^2/(4 - x + x^2 - x^3 + x^4), x], x, Sqrt[1 + 2*x]])/(16*Sqrt[1 + 2*x]*(1 + x + x^2)) - (17*Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Defer[Subst][Defer[Int][(4 + x + x^2 + x^3 + x^4)^(-1), x], x, Sqrt[1 + 2*x]])/(16*Sqrt[1 + 2*x]*(1 + x + x^2)) - (3*Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Defer[Subst][Defer[Int][x/(4 + x + x^2 + x^3 + x^4), x], x, Sqrt[1 + 2*x]])/(8*Sqrt[1 + 2*x]*(1 + x + x^2)) - (11*Sqrt[(1 + 2*x)*(1 + x + x^2)^2]*Defer[Subst][Defer[Int][x^2/(4 + x + x^2 + x^3 + x^4), x], x, Sqrt[1 + 2*x]])/(16*Sqrt[1 + 2*x]*(1 + x + x^2))","F",0,0,0,0,-1,"{}"
2952,0,0,0,27.6910959,"\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","Int[(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,"(3*x^2*(1 - x/a)^(2/3)*(1 - x/b)^(2/3)*AppellF1[2/3, 2/3, 2/3, 5/3, x/a, x/b])/((a - x)*(b - x)*x^2)^(2/3) + (6*(a + b)*d*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^4/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a*b*d - a*(1 + b/a)*d*x^3 + d*x^6 - x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) - (6*(2*a*b + d)*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^7/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a*b*d - a*(1 + b/a)*d*x^3 + d*x^6 - x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (9*(a + b)*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x^10/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(a*b*d - a*(1 + b/a)*d*x^3 + d*x^6 - x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3) + (6*a*b*d*x^(4/3)*(-a + x)^(2/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][x/((-a + x^3)^(2/3)*(-b + x^3)^(2/3)*(-(a*b*d) + a*(1 + b/a)*d*x^3 - d*x^6 + x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x^2)^(2/3)","F",0,0,0,0,-1,"{}"
2953,1,152,0,1.5761948,"\int \frac{x^3}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Int[x^3/((x^2 + x^4)^(1/3)*(-1 + x^6)),x]","-\frac{\sqrt[3]{x^2+1} x^4 F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};-x^2,-\sqrt[3]{-1} x^2\right)}{10 \sqrt[3]{x^4+x^2}}-\frac{\sqrt[3]{x^2+1} x^4 F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};-x^2,(-1)^{2/3} x^2\right)}{10 \sqrt[3]{x^4+x^2}}-\frac{\sqrt[3]{x^2+1} x^4 F_1\left(\frac{5}{3};1,\frac{1}{3};\frac{8}{3};x^2,-x^2\right)}{10 \sqrt[3]{x^4+x^2}}","-\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,"-1/10*(x^4*(1 + x^2)^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, -x^2, -((-1)^(1/3)*x^2)])/(x^2 + x^4)^(1/3) - (x^4*(1 + x^2)^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, -x^2, (-1)^(2/3)*x^2])/(10*(x^2 + x^4)^(1/3)) - (x^4*(1 + x^2)^(1/3)*AppellF1[5/3, 1, 1/3, 8/3, x^2, -x^2])/(10*(x^2 + x^4)^(1/3))","C",43,6,22,0.2727,0,"{2056, 6725, 959, 466, 465, 510}"
2954,0,0,0,2.2550385,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[1 + x^2]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{1+x^2}} \, dx","\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{11 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{11 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{4 \left(2 x^2+1\right) \left(x^2-1\right)+8 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]/4","F",0,0,0,0,-1,"{}"
2955,0,0,0,1.7291221,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[1 + x^2]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{1+x^2}} \, dx","\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{11 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{32} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{11 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-10 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{4 \left(2 x^2+1\right) \left(x^2-1\right)+8 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]/4","F",0,0,0,0,-1,"{}"
2956,0,0,0,1.8085778,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{2 \left(2 x^2+1\right) \left(x^2-1\right)+4 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
2957,0,0,0,1.6378176,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{\left(-3 x^2-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-3 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{2 \left(2 x^2+1\right) \left(x^2-1\right)+4 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
2958,0,0,0,1.6028131,"\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\sqrt{1+x^2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{3 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{3 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$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,"Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
2959,1,277,0,0.3170333,"\int \frac{\left(c+b x+a x^2\right)^{5/2}}{(c+b x)^2} \, dx","Int[(c + b*x + a*x^2)^(5/2)/(c + b*x)^2,x]","-\frac{5 a^{3/2} c^3 \left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{x \left(b^2-2 a c\right)+b c}{2 \sqrt{a} c \sqrt{a x^2+b x+c}}\right)}{2 b^6}+\frac{5 \left(-64 a^3 c^3+48 a^2 b^2 c^2+2 a b x \left(16 a^2 c^2-4 a b^2 c+b^4\right)-4 a b^4 c+b^6\right) \sqrt{a x^2+b x+c}}{64 a b^5}-\frac{5 \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{a x^2+b x+c}}\right)}{128 a^{3/2} b^6}+\frac{5 \left(6 a b x-8 a c+7 b^2\right) \left(a x^2+b x+c\right)^{3/2}}{24 b^3}-\frac{\left(a x^2+b x+c\right)^{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*(b^6 - 4*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3 + 2*a*b*(b^4 - 4*a*b^2*c + 16*a^2*c^2)*x)*Sqrt[c + b*x + a*x^2])/(64*a*b^5) + (5*(7*b^2 - 8*a*c + 6*a*b*x)*(c + b*x + a*x^2)^(3/2))/(24*b^3) - (c + b*x + a*x^2)^(5/2)/(b*(c + b*x)) - (5*(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 + b*x + a*x^2])])/(128*a^(3/2)*b^6) - (5*a^(3/2)*c^3*(b^2 - 2*a*c)*ArcTanh[(b*c + (b^2 - 2*a*c)*x)/(2*Sqrt[a]*c*Sqrt[c + b*x + a*x^2])])/(2*b^6)","A",8,6,22,0.2727,1,"{732, 814, 843, 621, 206, 724}"
2960,0,0,0,1.7048804,"\int \frac{\left(1+x^4\right)^2}{\left(-1+x^4\right)^2 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[(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,"Defer[Int][1/Sqrt[x^2 + Sqrt[1 + x^4]], x] - Defer[Int][1/((I - x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]/4 - (I/4)*Defer[Int][1/((I - x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x] - Defer[Int][1/((1 - x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x]/4 + Defer[Int][1/((-1 + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]/4 - Defer[Int][1/((I + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]/4 - (I/4)*Defer[Int][1/((I + x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x] + Defer[Int][1/((1 + x)^2*Sqrt[x^2 + Sqrt[1 + x^4]]), x]/4 - Defer[Int][1/((1 + x)*Sqrt[x^2 + Sqrt[1 + x^4]]), x]/4","F",0,0,0,0,-1,"{}"
2961,1,148,0,0.3049136,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{1+\sqrt{-b+a x}} \, dx","Int[Sqrt[a*x + Sqrt[-b + a*x]]/(1 + Sqrt[-b + a*x]),x]","-\frac{\sqrt{\sqrt{a x-b}+a x} \left(3-2 \sqrt{a x-b}\right)}{2 a}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a x-b}-2 b+1}{2 \sqrt{b} \sqrt{\sqrt{a x-b}+a x}}\right)}{a}+\frac{(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,"-1/2*((3 - 2*Sqrt[-b + a*x])*Sqrt[a*x + Sqrt[-b + a*x]])/a - (2*Sqrt[b]*ArcTanh[(1 - 2*b + Sqrt[-b + a*x])/(2*Sqrt[b]*Sqrt[a*x + Sqrt[-b + a*x]])])/a + ((3 + 4*b)*ArcTanh[(1 + 2*Sqrt[-b + a*x])/(2*Sqrt[a*x + Sqrt[-b + a*x]])])/(4*a)","A",7,5,35,0.1429,1,"{814, 843, 621, 206, 724}"
2962,1,1264,0,5.8188565,"\int \frac{\left(b x+a x^2\right) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Int[((b*x + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","-\frac{3 b \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(8 a^2-9 b\right)}{16 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{3 b \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(8 a^2-9 b\right)}{16 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{1}{8} \sqrt[4]{a x^4+b x^3} \left(8 a^2-9 b\right)-\frac{\left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2-\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a+\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2+\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2-\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a+\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2+\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{1}{2} a x \sqrt[4]{a x^4+b x^3}","\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,"-1/8*((8*a^2 - 9*b)*(b*x^3 + a*x^4)^(1/4)) + (a*x*(b*x^3 + a*x^4)^(1/4))/2 - (3*(8*a^2 - 9*b)*b*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a - Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a + Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + (3*(8*a^2 - 9*b)*b*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a - Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a + Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4))","B",32,15,37,0.4054,1,"{1593, 2056, 903, 80, 50, 63, 331, 298, 203, 206, 6728, 105, 93, 205, 208}"
2963,1,1264,0,4.1901883,"\int \frac{\left(b x+a x^2\right) \sqrt[4]{b x^3+a x^4}}{-b+a x+x^2} \, dx","Int[((b*x + a*x^2)*(b*x^3 + a*x^4)^(1/4))/(-b + a*x + x^2),x]","-\frac{3 b \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(8 a^2-9 b\right)}{16 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{3 b \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right) \left(8 a^2-9 b\right)}{16 a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{1}{8} \sqrt[4]{a x^4+b x^3} \left(8 a^2-9 b\right)-\frac{\left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2-\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a+\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tan ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2+\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{\left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[4]{x}}{\sqrt[4]{b+a x}}\right)}{a^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a-\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2-\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2-\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a-\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2-\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}-\frac{\left(a+\sqrt{a^2+4 b}\right)^{3/4} \left(a^4-b a^2+\frac{\left(a^4+b a^2-3 b^2\right) a}{\sqrt{a^2+4 b}}+b^2\right) \sqrt[4]{a x^4+b x^3} \tanh ^{-1}\left(\frac{\sqrt[4]{a^2+\sqrt{a^2+4 b} a-2 b} \sqrt[4]{x}}{\sqrt[4]{a+\sqrt{a^2+4 b}} \sqrt[4]{b+a x}}\right)}{\left(a^2+\sqrt{a^2+4 b} a-2 b\right)^{3/4} x^{3/4} \sqrt[4]{b+a x}}+\frac{1}{2} a x \sqrt[4]{a x^4+b x^3}","\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,"-1/8*((8*a^2 - 9*b)*(b*x^3 + a*x^4)^(1/4)) + (a*x*(b*x^3 + a*x^4)^(1/4))/2 - (3*(8*a^2 - 9*b)*b*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a - Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a + Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTan[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + (3*(8*a^2 - 9*b)*b*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(16*a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) + ((a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[(a^(1/4)*x^(1/4))/(b + a*x)^(1/4)])/(a^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a - Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 - (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a - Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b - a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4)) - ((a + Sqrt[a^2 + 4*b])^(3/4)*(a^4 - a^2*b + b^2 + (a*(a^4 + a^2*b - 3*b^2))/Sqrt[a^2 + 4*b])*(b*x^3 + a*x^4)^(1/4)*ArcTanh[((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(1/4)*x^(1/4))/((a + Sqrt[a^2 + 4*b])^(1/4)*(b + a*x)^(1/4))])/((a^2 - 2*b + a*Sqrt[a^2 + 4*b])^(3/4)*x^(3/4)*(b + a*x)^(1/4))","B",32,15,37,0.4054,1,"{1593, 2056, 903, 80, 50, 63, 331, 298, 203, 206, 6728, 105, 93, 205, 208}"
2964,0,0,0,2.7943466,"\int \frac{-b^{10}+a^{10} x^{10}}{\sqrt{b^4+a^4 x^4} \left(b^{10}+a^{10} x^{10}\right)} \, dx","Int[(-b^10 + a^10*x^10)/(Sqrt[b^4 + a^4*x^4]*(b^10 + a^10*x^10)),x]","\int \frac{-b^{10}+a^{10} x^{10}}{\sqrt{b^4+a^4 x^4} \left(b^{10}+a^{10} x^{10}\right)} \, dx","\frac{1}{5} \text{RootSum}\left[\text{$\#$1}^8-12 \text{$\#$1}^6 a^2 b^2+24 \text{$\#$1}^4 a^4 b^4-48 \text{$\#$1}^2 a^6 b^6+16 a^8 b^8\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+\text{$\#$1}^6 \log (x)-4 \text{$\#$1}^4 a^2 b^2 \log (x)+4 \text{$\#$1}^4 a^2 b^2 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 \text{$\#$1}^2 a^4 b^4 \log (x)+8 \text{$\#$1}^2 a^4 b^4 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 a^6 b^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+8 a^6 b^6 \log (x)}{-\text{$\#$1}^7+9 \text{$\#$1}^5 a^2 b^2-12 \text{$\#$1}^3 a^4 b^4+12 \text{$\#$1} a^6 b^6}\&\right]-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} a b x}{\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2}\right)}{5 a b}",1,"-1/5*ArcTan[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(Sqrt[2]*a*b) + (2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(5*a*b*Sqrt[b^4 + a^4*x^4]) - (8*b^8*Defer[Int][1/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5 + (6*a^2*b^6*Defer[Int][x^2/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5 - (4*a^4*b^4*Defer[Int][x^4/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5 + (2*a^6*b^2*Defer[Int][x^6/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5","F",0,0,0,0,-1,"{}"
2965,0,0,0,2.3143564,"\int \frac{-b^{10}+a^{10} x^{10}}{\sqrt{b^4+a^4 x^4} \left(b^{10}+a^{10} x^{10}\right)} \, dx","Int[(-b^10 + a^10*x^10)/(Sqrt[b^4 + a^4*x^4]*(b^10 + a^10*x^10)),x]","\int \frac{-b^{10}+a^{10} x^{10}}{\sqrt{b^4+a^4 x^4} \left(b^{10}+a^{10} x^{10}\right)} \, dx","\frac{1}{5} \text{RootSum}\left[\text{$\#$1}^8-12 \text{$\#$1}^6 a^2 b^2+24 \text{$\#$1}^4 a^4 b^4-48 \text{$\#$1}^2 a^6 b^6+16 a^8 b^8\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+\text{$\#$1}^6 \log (x)-4 \text{$\#$1}^4 a^2 b^2 \log (x)+4 \text{$\#$1}^4 a^2 b^2 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 \text{$\#$1}^2 a^4 b^4 \log (x)+8 \text{$\#$1}^2 a^4 b^4 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)-8 a^6 b^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4+b^4}+a^2 x^2+b^2\right)+8 a^6 b^6 \log (x)}{-\text{$\#$1}^7+9 \text{$\#$1}^5 a^2 b^2-12 \text{$\#$1}^3 a^4 b^4+12 \text{$\#$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,"-1/5*ArcTan[(Sqrt[2]*a*b*x)/Sqrt[b^4 + a^4*x^4]]/(Sqrt[2]*a*b) + (2*(b^2 + a^2*x^2)*Sqrt[(b^4 + a^4*x^4)/(b^2 + a^2*x^2)^2]*EllipticF[2*ArcTan[(a*x)/b], 1/2])/(5*a*b*Sqrt[b^4 + a^4*x^4]) - (8*b^8*Defer[Int][1/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5 + (6*a^2*b^6*Defer[Int][x^2/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5 - (4*a^4*b^4*Defer[Int][x^4/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5 + (2*a^6*b^2*Defer[Int][x^6/(Sqrt[b^4 + a^4*x^4]*(b^8 - a^2*b^6*x^2 + a^4*b^4*x^4 - a^6*b^2*x^6 + a^8*x^8)), x])/5","F",0,0,0,0,-1,"{}"
2966,1,523,0,0.864069,"\int \frac{\left(b+a x^2\right) \sqrt[3]{x+x^3}}{d+c x^2} \, dx","Int[((b + a*x^2)*(x + x^3)^(1/3))/(d + c*x^2),x]","\frac{\sqrt[3]{x^3+x} \sqrt[3]{c-d} (b c-a d) \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)}{4 c^2 \sqrt[3]{d} \sqrt[3]{x^2+1} \sqrt[3]{x}}-\frac{\sqrt[3]{x^3+x} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2+1}}\right) (a (c-3 d)+3 b c)}{6 c^2 \sqrt[3]{x^2+1} \sqrt[3]{x}}+\frac{\sqrt[3]{x^3+x} \log \left(\frac{x^{4/3}}{\left(x^2+1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2+1}}+1\right) (a (c-3 d)+3 b c)}{12 c^2 \sqrt[3]{x^2+1} \sqrt[3]{x}}-\frac{\sqrt[3]{x^3+x} \sqrt[3]{c-d} (b c-a d) \log \left(\frac{x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2+1}}+\sqrt[3]{d}\right)}{2 c^2 \sqrt[3]{d} \sqrt[3]{x^2+1} \sqrt[3]{x}}-\frac{\sqrt[3]{x^3+x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2+1}}+1}{\sqrt{3}}\right) (a (c-3 d)+3 b c)}{2 \sqrt{3} c^2 \sqrt[3]{x^2+1} \sqrt[3]{x}}-\frac{\sqrt{3} \sqrt[3]{x^3+x} \sqrt[3]{c-d} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{d}-\frac{2 x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2+1}}}{\sqrt{3} \sqrt[3]{d}}\right)}{2 c^2 \sqrt[3]{d} \sqrt[3]{x^2+1} \sqrt[3]{x}}+\frac{a \sqrt[3]{x^3+x} x}{2 c}","\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,"(a*x*(x + x^3)^(1/3))/(2*c) - ((3*b*c + a*(c - 3*d))*(x + x^3)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*c^2*x^(1/3)*(1 + x^2)^(1/3)) - (Sqrt[3]*(c - d)^(1/3)*(b*c - a*d)*(x + x^3)^(1/3)*ArcTan[(d^(1/3) - (2*(c - d)^(1/3)*x^(2/3))/(1 + x^2)^(1/3))/(Sqrt[3]*d^(1/3))])/(2*c^2*d^(1/3)*x^(1/3)*(1 + x^2)^(1/3)) - ((3*b*c + a*(c - 3*d))*(x + x^3)^(1/3)*Log[1 - x^(2/3)/(1 + x^2)^(1/3)])/(6*c^2*x^(1/3)*(1 + x^2)^(1/3)) + ((3*b*c + a*(c - 3*d))*(x + x^3)^(1/3)*Log[1 + x^(4/3)/(1 + x^2)^(2/3) + x^(2/3)/(1 + x^2)^(1/3)])/(12*c^2*x^(1/3)*(1 + x^2)^(1/3)) - ((c - d)^(1/3)*(b*c - a*d)*(x + x^3)^(1/3)*Log[d^(1/3) + ((c - d)^(1/3)*x^(2/3))/(1 + x^2)^(1/3)])/(2*c^2*d^(1/3)*x^(1/3)*(1 + x^2)^(1/3)) + ((c - d)^(1/3)*(b*c - a*d)*(x + x^3)^(1/3)*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)])/(4*c^2*d^(1/3)*x^(1/3)*(1 + x^2)^(1/3))","A",22,16,26,0.6154,1,"{2056, 581, 584, 329, 275, 331, 292, 31, 634, 618, 204, 628, 466, 465, 494, 617}"
2967,0,0,0,16.8455999,"\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","Int[(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]","\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","\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*Defer[Subst][Defer[Int][(-(b^3*c*p^3) - d*p^3*x^3 + 3*a*b^2*c*p^2*(q - x^3) - 3*a^2*b*c*p*(q - x^3)^2 + a^3*c*(q - x^3)^3)^(-1), x], x, (q + p*x^3)^(1/3)] - a*p*(b*p - a*q)*Defer[Subst][Defer[Int][x^3/(-(b^3*c*p^3) - d*p^3*x^3 - 3*a^2*b*c*p*(q - x^3)^2 + a^3*c*(q - x^3)^3 - 3*a*b^2*c*p^2*(-q + x^3)), x], x, (q + p*x^3)^(1/3)] - 2*a^2*p*Defer[Subst][Defer[Int][x^6/(-(b^3*c*p^3) - d*p^3*x^3 - 3*a^2*b*c*p*(q - x^3)^2 + a^3*c*(q - x^3)^3 - 3*a*b^2*c*p^2*(-q + x^3)), x], x, (q + p*x^3)^(1/3)]","F",0,0,0,0,-1,"{}"
2968,0,0,0,10.1491976,"\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","Int[(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,"-(((2*a - b - c + Sqrt[4*a^2 - 4*a*(b + c) + 2*b*c*(2 - d) + b^2*d + c^2*d]/Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*Defer[Int][1/((-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*(-2*a + b*d + c*d - Sqrt[d]*Sqrt[4*a^2 - 4*a*b - 4*a*c + 4*b*c + b^2*d - 2*b*c*d + c^2*d] + 2*(1 - d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(1/3)) - ((2*a - b - c - Sqrt[4*a^2 - 4*a*(b + c) + 2*b*c*(2 - d) + b^2*d + c^2*d]/Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*Defer[Int][1/((-a + x)^(1/3)*(-b + x)^(1/3)*(-c + x)^(1/3)*(-2*a + b*d + c*d + Sqrt[d]*Sqrt[4*a^2 - 4*a*b - 4*a*c + 4*b*c + b^2*d - 2*b*c*d + c^2*d] + 2*(1 - d)*x)), x])/(-((a - x)*(b - x)*(c - x)))^(1/3)","F",0,0,0,0,-1,"{}"
2969,0,0,0,4.9345987,"\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","Int[((-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,"(2*(1 - x + 2*x^2)^(1/3)*Defer[Int][(1 - x + 3*x^2)^(1/3)/(x^3*(1 - x + 2*x^2)^(1/3)), x])/(((1 - x + 2*x^2)/(1 - x + 3*x^2))^(1/3)*(1 - x + 3*x^2)^(1/3)) - ((1 - x + 2*x^2)^(1/3)*Defer[Int][(1 - x + 3*x^2)^(1/3)/(x^2*(1 - x + 2*x^2)^(1/3)), x])/(((1 - x + 2*x^2)/(1 - x + 3*x^2))^(1/3)*(1 - x + 3*x^2)^(1/3)) + (4*(1 - x + 2*x^2)^(1/3)*Defer[Int][(1 - x + 3*x^2)^(1/3)/(x*(1 - x + 2*x^2)^(1/3)), x])/(((1 - x + 2*x^2)/(1 - x + 3*x^2))^(1/3)*(1 - x + 3*x^2)^(1/3)) - (4*(1 - x + 2*x^2)^(1/3)*Defer[Int][(1 - x + 3*x^2)^(1/3)/((1 - Sqrt[5] + 2*x)*(1 - x + 2*x^2)^(1/3)), x])/(((1 - x + 2*x^2)/(1 - x + 3*x^2))^(1/3)*(1 - x + 3*x^2)^(1/3)) - (4*(1 - x + 2*x^2)^(1/3)*Defer[Int][(1 - x + 3*x^2)^(1/3)/((1 + Sqrt[5] + 2*x)*(1 - x + 2*x^2)^(1/3)), x])/(((1 - x + 2*x^2)/(1 - x + 3*x^2))^(1/3)*(1 - x + 3*x^2)^(1/3))","F",0,0,0,0,-1,"{}"
2970,0,0,0,2.3133356,"\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","Int[(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,"(20*b*x^(1/4)*(b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^14/((b + a*x^16)^(1/4)*(1 + b*x^20 + a*x^36)), x], x, x^(1/4)])/(b*x + a*x^5)^(1/4) + (36*a*x^(1/4)*(b + a*x^4)^(1/4)*Defer[Subst][Defer[Int][x^30/((b + a*x^16)^(1/4)*(1 + b*x^20 + a*x^36)), x], x, x^(1/4)])/(b*x + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
2971,0,0,0,2.0732388,"\int \frac{\sqrt{1+x^2} \left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Int[(Sqrt[1 + x^2]*(1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\int \frac{\sqrt{1+x^2} \left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+2}\&\right]+\frac{251}{128} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2560 x^3-2048 x^2-345 x-184\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2560 x^2-2048 x+935\right)+\left(-35840 x^3+3072 x^2-175104 x-282\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-35840 x^4+3072 x^3-193024 x^2+1254 x-78032\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{80640 \sqrt{x^2+1} x+40320 \left(2 x^2+1\right)}",1,"-Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + x^2], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x] - Defer[Int][(x^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[1 + x^2], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]","F",0,0,0,0,-1,"{}"
2972,0,0,0,1.5656774,"\int \frac{\sqrt{1+x^2} \left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Int[(Sqrt[1 + x^2]*(1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\int \frac{\sqrt{1+x^2} \left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","-\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$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,"-Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + x^2], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x] - Defer[Int][(x^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/Sqrt[1 + x^2], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]","F",0,0,0,0,-1,"{}"
2973,1,428,0,3.7432658,"\int \frac{b^{12}+a^{12} x^{12}}{\sqrt{-b^4+a^4 x^4} \left(-b^{12}+a^{12} x^{12}\right)} \, dx","Int[(b^12 + a^12*x^12)/(Sqrt[-b^4 + a^4*x^4]*(-b^12 + a^12*x^12)),x]","\frac{2 b \sqrt{1-\frac{a^4 x^4}{b^4}} F\left(\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{4 a^2}{\left(a+\sqrt{3} \sqrt{-a^2}\right)^2};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(-\frac{2 a}{a+\sqrt{3} \sqrt{-a^2}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{2 a^2}{a^2-\sqrt{3} \sqrt{-a^4}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{b \sqrt{1-\frac{a^4 x^4}{b^4}} \Pi \left(\frac{2 a^2}{a^2+\sqrt{3} \sqrt{-a^4}};\left.\sin ^{-1}\left(\frac{a x}{b}\right)\right|-1\right)}{3 a \sqrt{a^4 x^4-b^4}}-\frac{x \left(b^2-a^2 x^2\right)}{6 b^2 \sqrt{a^4 x^4-b^4}}-\frac{x \left(a^2 x^2+b^2\right)}{6 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{$\#$1}^8-8 i \text{$\#$1}^6 a^2 b^2+24 \text{$\#$1}^4 a^4 b^4+32 i \text{$\#$1}^2 a^6 b^6+16 a^8 b^8\&,\frac{-i \text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)+i \text{$\#$1}^6 \log (x)+2 \text{$\#$1}^4 a^2 b^2 \log (x)-2 \text{$\#$1}^4 a^2 b^2 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)+4 i \text{$\#$1}^2 a^4 b^4 \log (x)-4 i \text{$\#$1}^2 a^4 b^4 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)-8 a^6 b^6 \log \left(-\text{$\#$1} x+\sqrt{a^4 x^4-b^4}+a^2 x^2+i b^2\right)+8 a^6 b^6 \log (x)}{-i \text{$\#$1}^7-6 \text{$\#$1}^5 a^2 b^2-12 i \text{$\#$1}^3 a^4 b^4+8 \text{$\#$1} a^6 b^6}\&\right]",1,"-1/6*(x*(b^2 - a^2*x^2))/(b^2*Sqrt[-b^4 + a^4*x^4]) - (x*(b^2 + a^2*x^2))/(6*b^2*Sqrt[-b^4 + a^4*x^4]) + (2*b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticF[ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(4*a^2)/(a + Sqrt[3]*Sqrt[-a^2])^2, ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(-2*a)/(a + Sqrt[3]*Sqrt[-a^2]), ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(2*a^2)/(a^2 - Sqrt[3]*Sqrt[-a^4]), ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4]) - (b*Sqrt[1 - (a^4*x^4)/b^4]*EllipticPi[(2*a^2)/(a^2 + Sqrt[3]*Sqrt[-a^4]), ArcSin[(a*x)/b], -1])/(3*a*Sqrt[-b^4 + a^4*x^4])","A",56,19,44,0.4318,1,"{6725, 224, 221, 2073, 1152, 414, 21, 423, 427, 426, 424, 253, 6728, 1725, 1219, 1218, 1248, 725, 204}"
2974,0,0,0,4.7259616,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","Int[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[b + a^2*x^4]*(d + c*x^4)),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","-\sqrt{2} a^{3/2} \text{RootSum}\left[\text{$\#$1}^8 c-16 \text{$\#$1}^6 a^2 d+4 \text{$\#$1}^6 b c+32 \text{$\#$1}^4 a^2 b d+6 \text{$\#$1}^4 b^2 c-16 \text{$\#$1}^2 a^2 b^2 d+4 \text{$\#$1}^2 b^3 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-2 \text{$\#$1}^2 b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+b^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^6 c-12 \text{$\#$1}^4 a^2 d+3 \text{$\#$1}^4 b c+16 \text{$\#$1}^2 a^2 b d+3 \text{$\#$1}^2 b^2 c-4 a^2 b^2 d+b^3 c}\&\right]",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) - Sqrt[-Sqrt[-c]]*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4)) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) + Sqrt[-Sqrt[-c]]*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4)) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) - (-c)^(1/4)*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4)) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) + (-c)^(1/4)*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4))","F",0,0,0,0,-1,"{}"
2975,0,0,0,3.6455287,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","Int[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[b + a^2*x^4]*(d + c*x^4)),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{\sqrt{b+a^2 x^4} \left(d+c x^4\right)} \, dx","-\sqrt{2} a^{3/2} \text{RootSum}\left[\text{$\#$1}^8 c-16 \text{$\#$1}^6 a^2 d+4 \text{$\#$1}^6 b c+32 \text{$\#$1}^4 a^2 b d+6 \text{$\#$1}^4 b^2 c-16 \text{$\#$1}^2 a^2 b^2 d+4 \text{$\#$1}^2 b^3 c+b^4 c\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-2 \text{$\#$1}^2 b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+b^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^6 c-12 \text{$\#$1}^4 a^2 d+3 \text{$\#$1}^4 b c+16 \text{$\#$1}^2 a^2 b d+3 \text{$\#$1}^2 b^2 c-4 a^2 b^2 d+b^3 c}\&\right]",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) - Sqrt[-Sqrt[-c]]*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4)) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) + Sqrt[-Sqrt[-c]]*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4)) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) - (-c)^(1/4)*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4)) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d^(1/4) + (-c)^(1/4)*x)*Sqrt[b + a^2*x^4]), x]/(4*d^(3/4))","F",0,0,0,0,-1,"{}"
2976,0,0,0,1.8001447,"\int \frac{x}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[x/(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 a^3 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)-\text{$\#$1}^3 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^3 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$1} c+a c}\&\right]+\frac{4}{3} \left(3 a^2+c\right) \sqrt{\sqrt{a x+b}+c}+\sqrt{a x+b} \left(\frac{4}{3} \sqrt{\sqrt{a x+b}+c}+2 a\right)+x",1,"(2*(a^2 - c)*Sqrt[b + a*x])/a + 4*a^2*Sqrt[c + Sqrt[b + a*x]] + (4*(c + Sqrt[b + a*x])^(3/2))/3 + (c + Sqrt[b + a*x])^2/a + a*(a^2 + c)*Log[b - c^2 - a*c*Sqrt[c + Sqrt[b + a*x]] + 2*c*(c + Sqrt[b + a*x]) + a*(c + Sqrt[b + a*x])^(3/2) - (c + Sqrt[b + a*x])^2] - a^2*(4*b - c*(a^2 + 5*c))*Defer[Subst][Defer[Int][(b - c^2 - a*c*x + 2*c*x^2 + a*x^3 - x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*b*Defer[Subst][Defer[Int][x/(b - c^2 - a*c*x + 2*c*x^2 + a*x^3 - x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] + (3*a^4 + 4*b + 7*a^2*c)*Defer[Subst][Defer[Int][x^2/(-b + c^2 + a*c*x - 2*c*x^2 - a*x^3 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2977,0,0,0,1.3816085,"\int \frac{x}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[x/(x - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x}{x-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 \text{RootSum}\left[-\text{$\#$1}^4+\text{$\#$1}^3 a+2 \text{$\#$1}^2 c-\text{$\#$1} a c+b-c^2\&,\frac{\text{$\#$1}^3 a^3 \left(-\log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)\right)-\text{$\#$1}^3 a c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^3 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+a^2 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-a^2 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1} a b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{4 \text{$\#$1}^3-3 \text{$\#$1}^2 a-4 \text{$\#$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,"(2*(a^2 - c)*Sqrt[b + a*x])/a + 4*a^2*Sqrt[c + Sqrt[b + a*x]] + (4*(c + Sqrt[b + a*x])^(3/2))/3 + (c + Sqrt[b + a*x])^2/a + a*(a^2 + c)*Log[b - c^2 - a*c*Sqrt[c + Sqrt[b + a*x]] + 2*c*(c + Sqrt[b + a*x]) + a*(c + Sqrt[b + a*x])^(3/2) - (c + Sqrt[b + a*x])^2] - a^2*(4*b - c*(a^2 + 5*c))*Defer[Subst][Defer[Int][(b - c^2 - a*c*x + 2*c*x^2 + a*x^3 - x^4)^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*b*Defer[Subst][Defer[Int][x/(b - c^2 - a*c*x + 2*c*x^2 + a*x^3 - x^4), x], x, Sqrt[c + Sqrt[b + a*x]]] + (3*a^4 + 4*b + 7*a^2*c)*Defer[Subst][Defer[Int][x^2/(-b + c^2 + a*c*x - 2*c*x^2 - a*x^3 + x^4), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
2978,0,0,0,35.0269693,"\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","Int[((-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,"(-3*(1 + k)*(a + k)*x*((1 - x)/(1 - k*x))^(2/3)*(1 - k*x)*Hypergeometric2F1[1/3, 2/3, 4/3, ((1 - k)*x)/(1 - k*x)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(a + k)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][1/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) - (6*(b + k + k^2 + k^3 + a*(1 + k)^2)*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^3/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) + (3*(1 + k)*(3*b + k + k^2 + k^3 + a*(1 + 4*k + k^2))*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^6/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3)) - (3*(b*(1 + 2*a + 4*k + k^2) + k*(k + k^3 + 2*a*(1 + k + k^2)))*(1 - x)^(2/3)*x^(2/3)*(1 - k*x)^(2/3)*Defer[Subst][Defer[Int][x^9/((1 - x^3)^(2/3)*(1 - k*x^3)^(2/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((b - k^2)*((1 - x)*x*(1 - k*x))^(2/3))","F",0,0,0,0,-1,"{}"
2979,0,0,0,28.9332287,"\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","Int[((-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,"(9*(1 + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^4/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (3*(1 + 2*a + 4*k + k^2)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^7/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (3*(1 + k)*(a + k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x^10/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(1 - 2*(1 + k)*x^3 + (1 + k*(4 + k))*x^6 - 2*k*(1 + k)*x^9 - b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) + (6*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][x/((1 - x^3)^(1/3)*(1 - k*x^3)^(1/3)*(-1 + 2*(1 + k)*x^3 - (1 + k*(4 + k))*x^6 + 2*k*(1 + k)*x^9 + b*(1 - k^2/b)*x^12)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
2980,0,0,0,1.2193219,"\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","Int[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]","\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","-\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
2981,0,0,0,0.1971179,"\int \frac{x}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[x/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","\int \frac{x}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","\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,"Defer[Int][x/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]], x]","F",0,0,0,0,-1,"{}"
2982,1,869,0,1.7413688,"\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","Int[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(-b + a^2*x^2)^(3/2),x]","\frac{4 c \left(a x+\sqrt{a^2 x^2-b}\right)^{5/4}}{5 a^3}+\frac{2 b c \left(a x+\sqrt{a^2 x^2-b}\right)^{5/4}}{a^3 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)}+\frac{2 d \left(a x+\sqrt{a^2 x^2-b}\right)^{5/4}}{a \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)}-\frac{5 b^{5/8} c \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{2 a^3}-\frac{5 d \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{2 a b^{3/8}}-\frac{5 b^{5/8} c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{2 \sqrt{2} a^3}-\frac{5 d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{2 \sqrt{2} a b^{3/8}}+\frac{5 b^{5/8} c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right)}{2 \sqrt{2} a^3}+\frac{5 d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right)}{2 \sqrt{2} a b^{3/8}}-\frac{5 b^{5/8} c \tanh ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{2 a^3}-\frac{5 d \tanh ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{2 a b^{3/8}}-\frac{5 b^{5/8} c \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)}{4 \sqrt{2} a^3}-\frac{5 d \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)}{4 \sqrt{2} a b^{3/8}}+\frac{5 b^{5/8} c \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)}{4 \sqrt{2} a^3}+\frac{5 d \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)}{4 \sqrt{2} a b^{3/8}}","\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,"(4*c*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(5*a^3) + (2*b*c*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(a^3*(b - (a*x + Sqrt[-b + a^2*x^2])^2)) + (2*d*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(a*(b - (a*x + Sqrt[-b + a^2*x^2])^2)) - (5*b^(5/8)*c*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(2*a^3) - (5*d*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(2*a*b^(3/8)) - (5*b^(5/8)*c*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(2*Sqrt[2]*a^3) - (5*d*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(2*Sqrt[2]*a*b^(3/8)) + (5*b^(5/8)*c*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(2*Sqrt[2]*a^3) + (5*d*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(2*Sqrt[2]*a*b^(3/8)) - (5*b^(5/8)*c*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(2*a^3) - (5*d*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(2*a*b^(3/8)) - (5*b^(5/8)*c*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]]])/(4*Sqrt[2]*a^3) - (5*d*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]]])/(4*Sqrt[2]*a*b^(3/8)) + (5*b^(5/8)*c*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]]])/(4*Sqrt[2]*a^3) + (5*d*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]]])/(4*Sqrt[2]*a*b^(3/8))","B",35,17,46,0.3696,1,"{6742, 2122, 288, 329, 301, 211, 1165, 628, 1162, 617, 204, 212, 206, 203, 2120, 463, 459}"
2983,1,537,0,0.8774665,"\int \frac{\left(-b+a x^2\right) \sqrt[3]{-x+x^3}}{-d+c x^2} \, dx","Int[((-b + a*x^2)*(-x + x^3)^(1/3))/(-d + c*x^2),x]","-\frac{\sqrt[3]{x^3-x} \sqrt[3]{c-d} (b c-a d) \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)}{4 c^2 \sqrt[3]{d} \sqrt[3]{x^2-1} \sqrt[3]{x}}+\frac{\sqrt[3]{x^3-x} \log \left(1-\frac{x^{2/3}}{\sqrt[3]{x^2-1}}\right) (a (c-3 d)+3 b c)}{6 c^2 \sqrt[3]{x^2-1} \sqrt[3]{x}}-\frac{\sqrt[3]{x^3-x} \log \left(\frac{x^{4/3}}{\left(x^2-1\right)^{2/3}}+\frac{x^{2/3}}{\sqrt[3]{x^2-1}}+1\right) (a (c-3 d)+3 b c)}{12 c^2 \sqrt[3]{x^2-1} \sqrt[3]{x}}+\frac{\sqrt[3]{x^3-x} \sqrt[3]{c-d} (b c-a d) \log \left(\frac{x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2-1}}+\sqrt[3]{d}\right)}{2 c^2 \sqrt[3]{d} \sqrt[3]{x^2-1} \sqrt[3]{x}}+\frac{\sqrt[3]{x^3-x} \tan ^{-1}\left(\frac{\frac{2 x^{2/3}}{\sqrt[3]{x^2-1}}+1}{\sqrt{3}}\right) (a (c-3 d)+3 b c)}{2 \sqrt{3} c^2 \sqrt[3]{x^2-1} \sqrt[3]{x}}+\frac{\sqrt{3} \sqrt[3]{x^3-x} \sqrt[3]{c-d} (b c-a d) \tan ^{-1}\left(\frac{\sqrt[3]{d}-\frac{2 x^{2/3} \sqrt[3]{c-d}}{\sqrt[3]{x^2-1}}}{\sqrt{3} \sqrt[3]{d}}\right)}{2 c^2 \sqrt[3]{d} \sqrt[3]{x^2-1} \sqrt[3]{x}}+\frac{a \sqrt[3]{x^3-x} x}{2 c}","-\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,"(a*x*(-x + x^3)^(1/3))/(2*c) + ((3*b*c + a*(c - 3*d))*(-x + x^3)^(1/3)*ArcTan[(1 + (2*x^(2/3))/(-1 + x^2)^(1/3))/Sqrt[3]])/(2*Sqrt[3]*c^2*x^(1/3)*(-1 + x^2)^(1/3)) + (Sqrt[3]*(c - d)^(1/3)*(b*c - a*d)*(-x + x^3)^(1/3)*ArcTan[(d^(1/3) - (2*(c - d)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3))/(Sqrt[3]*d^(1/3))])/(2*c^2*d^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)) + ((3*b*c + a*(c - 3*d))*(-x + x^3)^(1/3)*Log[1 - x^(2/3)/(-1 + x^2)^(1/3)])/(6*c^2*x^(1/3)*(-1 + x^2)^(1/3)) - ((3*b*c + a*(c - 3*d))*(-x + x^3)^(1/3)*Log[1 + x^(4/3)/(-1 + x^2)^(2/3) + x^(2/3)/(-1 + x^2)^(1/3)])/(12*c^2*x^(1/3)*(-1 + x^2)^(1/3)) + ((c - d)^(1/3)*(b*c - a*d)*(-x + x^3)^(1/3)*Log[d^(1/3) + ((c - d)^(1/3)*x^(2/3))/(-1 + x^2)^(1/3)])/(2*c^2*d^(1/3)*x^(1/3)*(-1 + x^2)^(1/3)) - ((c - d)^(1/3)*(b*c - a*d)*(-x + x^3)^(1/3)*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)])/(4*c^2*d^(1/3)*x^(1/3)*(-1 + x^2)^(1/3))","A",22,16,32,0.5000,1,"{2056, 581, 584, 329, 275, 331, 292, 31, 634, 618, 204, 628, 466, 465, 494, 617}"
2984,0,0,0,13.2324528,"\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","Int[((-(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,"(3*(2*a - b)*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(-a + x^3)^(5/3))/((-b + x^3)^(1/3)*(a^4*d - 4*a^3*d*x^3 - b^2*(1 - (6*a^2*d)/b^2)*x^6 + 2*b*(1 - (2*a*d)/b)*x^9 - (1 - d)*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3) + (3*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][(x*(-a + x^3)^(5/3))/((-b + x^3)^(1/3)*(-(a^4*d) + 4*a^3*d*x^3 + b^2*(1 - (6*a^2*d)/b^2)*x^6 - 2*b*(1 - (2*a*d)/b)*x^9 + (1 - d)*x^12)), x], x, x^(1/3)])/((a - x)*(b - x)*x)^(1/3)","F",0,0,0,0,-1,"{}"
2985,1,397,0,0.5784848,"\int \frac{b+d x}{x^4 \sqrt[4]{\frac{b+a x}{d+c x}}} \, dx","Int[(b + d*x)/(x^4*((b + a*x)/(d + c*x))^(1/4)),x]","-\frac{\left(2 b c d (5 a-6 d)+5 a d^2 (3 a-4 d)+7 b^2 c^2\right) (b c-a d) \left(\frac{a x+b}{c x+d}\right)^{3/4}}{32 b^2 d^2 \left(b-\frac{d (a x+b)}{c x+d}\right)}+\frac{\left(2 b c d (5 a-6 d)+5 a d^2 (3 a-4 d)+7 b^2 c^2\right) (b c-a d) \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(2 b c d (5 a-6 d)+5 a d^2 (3 a-4 d)+7 b^2 c^2\right) (b c-a d) \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}}+\frac{(d (9 a-4 d)+7 b c) (b c-a d)^2 \left(\frac{a x+b}{c x+d}\right)^{3/4}}{24 b d^2 \left(b-\frac{d (a x+b)}{c x+d}\right)^2}-\frac{(b+d x) (b c-a d)^3 \left(\frac{a x+b}{c x+d}\right)^{3/4}}{3 b d (c x+d) \left(b-\frac{d (a x+b)}{c x+d}\right)^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,"-1/3*((b*c - a*d)^3*((b + a*x)/(d + c*x))^(3/4)*(b + d*x))/(b*d*(d + c*x)*(b - (d*(b + a*x))/(d + c*x))^3) + ((b*c - a*d)^2*(7*b*c + (9*a - 4*d)*d)*((b + a*x)/(d + c*x))^(3/4))/(24*b*d^2*(b - (d*(b + a*x))/(d + c*x))^2) - ((b*c - a*d)*(7*b^2*c^2 + 2*b*c*(5*a - 6*d)*d + 5*a*(3*a - 4*d)*d^2)*((b + a*x)/(d + c*x))^(3/4))/(32*b^2*d^2*(b - (d*(b + a*x))/(d + c*x))) + ((b*c - a*d)*(7*b^2*c^2 + 2*b*c*(5*a - 6*d)*d + 5*a*(3*a - 4*d)*d^2)*ArcTan[(d^(1/4)*((b + a*x)/(d + c*x))^(1/4))/b^(1/4)])/(64*b^(9/4)*d^(11/4)) - ((b*c - a*d)*(7*b^2*c^2 + 2*b*c*(5*a - 6*d)*d + 5*a*(3*a - 4*d)*d^2)*ArcTanh[(d^(1/4)*((b + a*x)/(d + c*x))^(1/4))/b^(1/4)])/(64*b^(9/4)*d^(11/4))","A",7,7,26,0.2692,1,"{1962, 577, 457, 290, 298, 205, 208}"
2986,0,0,0,13.8108574,"\int \frac{f+e x}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","Int[(f + e*x)/(d + c*x + Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]),x]","\int \frac{f+e x}{d+c x+\sqrt{a x+\sqrt{b^2+a^2 x^2}}} \, dx","\frac{2 \text{RootSum}\left[\text{$\#$1}^4 (-c)-2 \text{$\#$1}^3 a-2 \text{$\#$1}^2 a d+b^2 c\&,\frac{\text{$\#$1}^3 c^2 f \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-\text{$\#$1}^3 c d e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1}^3 a e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1}^2 a c f \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)+\text{$\#$1} a c d f \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-b^2 c e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)-\text{$\#$1} a d^2 e \log \left(\sqrt{\sqrt{a^2 x^2+b^2}+a x}-\text{$\#$1}\right)}{2 \text{$\#$1}^3 c+3 \text{$\#$1}^2 a+2 \text{$\#$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,"(e*x)/c + ((a - c*d)*e*Log[b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4])/(4*c^3) + (f*Log[b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4])/(4*c) - ((2*b^2*c^2 + a*d^2*(a - 3*c*d))*e*Defer[Int][(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4)^(-1), x])/(2*c^3) - (a*d^2*f*Defer[Int][(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4)^(-1), x])/(2*c) - (a*d*(2*a - 3*c*d)*e*Defer[Int][x/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x])/c^2 - a*d*f*Defer[Int][x/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] - (3*a*(a - c*d)*e*Defer[Int][x^2/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x])/(2*c) - (a*c*f*Defer[Int][x^2/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x])/2 + d*f*Defer[Int][Sqrt[b^2 + a^2*x^2]/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + d*e*Defer[Int][(x*Sqrt[b^2 + a^2*x^2])/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + c*f*Defer[Int][(x*Sqrt[b^2 + a^2*x^2])/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + c*e*Defer[Int][(x^2*Sqrt[b^2 + a^2*x^2])/(-b^2 + d^4 - 2*d^2*(a - 2*c*d)*x - 2*c*d*(2*a - 3*c*d)*x^2 - 2*c^2*(a - 2*c*d)*x^3 + c^4*x^4), x] + d^2*f*Defer[Int][Sqrt[a*x + Sqrt[b^2 + a^2*x^2]]/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + d^2*e*Defer[Int][(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] - (a - 2*c*d)*f*Defer[Int][(x*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] - (a - 2*c*d)*e*Defer[Int][(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + c^2*f*Defer[Int][(x^2*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + c^2*e*Defer[Int][(x^3*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + f*Defer[Int][(Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x] + e*Defer[Int][(x*Sqrt[b^2 + a^2*x^2]*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(b^2 - d^4 + 2*d^2*(a - 2*c*d)*x + 2*c*d*(2*a - 3*c*d)*x^2 + 2*c^2*(a - 2*c*d)*x^3 - c^4*x^4), x]","F",0,0,0,0,-1,"{}"
2987,-1,0,0,180.0040368,"\int \frac{1+x^6}{\sqrt[4]{-x^3+x^5} \left(1-x^6\right)} \, dx","Int[(1 + x^6)/((-x^3 + x^5)^(1/4)*(1 - x^6)),x]","\text{\$Aborted}","\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,"$Aborted","F",0,0,0,0,-1,"{}"
2988,1,433,0,1.9743686,"\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","Int[(Sqrt[-b + a^2*x^2]*(d + c*x^4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/x^2,x]","2 a d \sqrt{\sqrt{a^2 x^2-b}+a x}+\frac{2 a b d \sqrt{\sqrt{a^2 x^2-b}+a x}}{\left(\sqrt{a^2 x^2-b}+a x\right)^2+b}+\frac{a \sqrt[4]{b} d \log \left(\sqrt{a^2 x^2-b}-\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a^2 x^2-b}+a x}+a x+\sqrt{b}\right)}{2 \sqrt{2}}-\frac{a \sqrt[4]{b} d \log \left(\sqrt{a^2 x^2-b}+\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a^2 x^2-b}+a x}+a x+\sqrt{b}\right)}{2 \sqrt{2}}+\frac{a \sqrt[4]{b} d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt[4]{b}}\right)}{\sqrt{2}}-\frac{a \sqrt[4]{b} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2}}-\frac{b^4 c}{56 a^3 \left(\sqrt{a^2 x^2-b}+a x\right)^{7/2}}-\frac{b^2 c \sqrt{\sqrt{a^2 x^2-b}+a x}}{4 a^3}+\frac{c \left(\sqrt{a^2 x^2-b}+a x\right)^{9/2}}{72 a^3}","\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,"-1/56*(b^4*c)/(a^3*(a*x + Sqrt[-b + a^2*x^2])^(7/2)) - (b^2*c*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/(4*a^3) + 2*a*d*Sqrt[a*x + Sqrt[-b + a^2*x^2]] + (c*(a*x + Sqrt[-b + a^2*x^2])^(9/2))/(72*a^3) + (2*a*b*d*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/(b + (a*x + Sqrt[-b + a^2*x^2])^2) + (a*b^(1/4)*d*ArcTan[1 - (Sqrt[2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/b^(1/4)])/Sqrt[2] - (a*b^(1/4)*d*ArcTan[1 + (Sqrt[2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/b^(1/4)])/Sqrt[2] + (a*b^(1/4)*d*Log[Sqrt[b] + a*x + Sqrt[-b + a^2*x^2] - Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]]])/(2*Sqrt[2]) - (a*b^(1/4)*d*Log[Sqrt[b] + a*x + Sqrt[-b + a^2*x^2] + Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]]])/(2*Sqrt[2])","A",20,14,49,0.2857,1,"{6742, 2120, 463, 12, 321, 329, 211, 1165, 628, 1162, 617, 204, 259, 270}"
2989,0,0,0,2.3538231,"\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\left(8 x^4-7 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+\sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^3-11 x\right)}{\left(2 x^2+1\right) \left(x^2-1\right)+2 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
2990,0,0,0,1.7500267,"\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\left(8 x^4-7 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}+\sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(8 x^3-11 x\right)}{\left(2 x^2+1\right) \left(x^2-1\right)+2 x \sqrt{x^2+1} \left(x^2-1\right)}",1,"Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
2991,0,0,0,1.7219622,"\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^{3/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{5 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{8} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{5 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$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,"Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][((1 + x^2)^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
2992,1,621,0,3.0064809,"\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","Int[((1 + x^2 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","-\frac{i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}+\frac{i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}+i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}-\frac{\tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}+\frac{\tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}-\frac{(1-i) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{(1-i) \tanh ^{-1}\left(\frac{\sqrt{2}+i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{(1+i) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}-\frac{(1+i) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\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)-\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,"((-I)*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + (I*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] - ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])]/Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])] + ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])]/Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])] - ((1 - I)*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1 - I)*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1 + I)*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] - ((1 + I)*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",30,6,45,0.1333,0,"{6728, 2132, 206, 6725, 2133, 725}"
2993,1,621,0,2.4237123,"\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","Int[((1 + x^2 + x^4)*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)),x]","-\frac{i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}+\frac{i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}+i \sqrt{\sqrt{5}-1} x\right)}{\sqrt{2 \left(\sqrt{5}+(-1-2 i)\right)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(-2+i)\right)}}-\frac{\tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}+\frac{\tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{-2 \sqrt{5}+(-2-4 i)} \sqrt{1+i x^2}}\right)}{\sqrt{(-5-5 i) \left(\sqrt{5}+(2-i)\right)}}-\frac{(1-i) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{(1-i) \tanh ^{-1}\left(\frac{\sqrt{2}+i \sqrt{\sqrt{5}-1} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(-2-i)\right)}}+\frac{(1+i) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}-\frac{(1+i) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{(10+10 i) \left(\sqrt{5}+(2+i)\right)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{\sqrt{x^4+1}+x^2}}\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)-\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,"((-I)*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + (I*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] - ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])]/Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])] + ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])]/Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])] - ((1 - I)*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1 - I)*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((-2 - I) + Sqrt[5])] + ((1 + I)*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] - ((1 + I)*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(10 + 10*I)*((2 + I) + Sqrt[5])] + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",30,6,45,0.1333,0,"{6728, 2132, 206, 6725, 2133, 725}"
2994,1,499,0,1.7227442,"\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","Int[(Sqrt[-b + a^2*x^2]*(d + c*x^4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/x,x]","-\frac{b^{3/4} d \log \left(\sqrt{a^2 x^2-b}-\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a^2 x^2-b}+a x}+a x+\sqrt{b}\right)}{\sqrt{2}}+\frac{b^{3/4} d \log \left(\sqrt{a^2 x^2-b}+\sqrt{2} \sqrt[4]{b} \sqrt{\sqrt{a^2 x^2-b}+a x}+a x+\sqrt{b}\right)}{\sqrt{2}}+\sqrt{2} b^{3/4} d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt[4]{b}}\right)-\sqrt{2} b^{3/4} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sqrt{a^2 x^2-b}+a x}}{\sqrt[4]{b}}+1\right)+\frac{1}{3} d \left(\sqrt{a^2 x^2-b}+a x\right)^{3/2}-\frac{b d}{\sqrt{\sqrt{a^2 x^2-b}+a x}}-\frac{b^5 c}{144 a^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{9/2}}-\frac{b^4 c}{80 a^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/2}}+\frac{b^3 c}{8 a^4 \sqrt{\sqrt{a^2 x^2-b}+a x}}-\frac{b^2 c \left(\sqrt{a^2 x^2-b}+a x\right)^{3/2}}{24 a^4}+\frac{c \left(\sqrt{a^2 x^2-b}+a x\right)^{11/2}}{176 a^4}+\frac{b c \left(\sqrt{a^2 x^2-b}+a x\right)^{7/2}}{112 a^4}","\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,"-1/144*(b^5*c)/(a^4*(a*x + Sqrt[-b + a^2*x^2])^(9/2)) - (b^4*c)/(80*a^4*(a*x + Sqrt[-b + a^2*x^2])^(5/2)) + (b^3*c)/(8*a^4*Sqrt[a*x + Sqrt[-b + a^2*x^2]]) - (b*d)/Sqrt[a*x + Sqrt[-b + a^2*x^2]] - (b^2*c*(a*x + Sqrt[-b + a^2*x^2])^(3/2))/(24*a^4) + (d*(a*x + Sqrt[-b + a^2*x^2])^(3/2))/3 + (b*c*(a*x + Sqrt[-b + a^2*x^2])^(7/2))/(112*a^4) + (c*(a*x + Sqrt[-b + a^2*x^2])^(11/2))/(176*a^4) + Sqrt[2]*b^(3/4)*d*ArcTan[1 - (Sqrt[2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/b^(1/4)] - Sqrt[2]*b^(3/4)*d*ArcTan[1 + (Sqrt[2]*Sqrt[a*x + Sqrt[-b + a^2*x^2]])/b^(1/4)] - (b^(3/4)*d*Log[Sqrt[b] + a*x + Sqrt[-b + a^2*x^2] - Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]]])/Sqrt[2] + (b^(3/4)*d*Log[Sqrt[b] + a*x + Sqrt[-b + a^2*x^2] + Sqrt[2]*b^(1/4)*Sqrt[a*x + Sqrt[-b + a^2*x^2]]])/Sqrt[2]","A",18,12,49,0.2449,1,"{6742, 2120, 462, 459, 329, 297, 1162, 617, 204, 1165, 628, 448}"
2995,0,0,0,0.5890092,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Int[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{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 (-a) d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+2 i \text{$\#$1} b c \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+a b d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{i \text{$\#$1}^3 c-3 \text{$\#$1}^2 a d+i \text{$\#$1} b c+a b d}\&\right]}{\sqrt{2} c}",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] - Sqrt[-c]*x), x]/(2*Sqrt[d]) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] + Sqrt[-c]*x), x]/(2*Sqrt[d])","F",0,0,0,0,-1,"{}"
2996,0,0,0,0.4410292,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Int[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(d + c*x^2),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","\frac{\sqrt{a} \log \left(i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\sqrt{2} c}-\frac{\sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 i \text{$\#$1}^3 a d+2 \text{$\#$1}^2 b c-4 i \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 (-a) d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+2 i \text{$\#$1} b c \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)+a b d \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{i \text{$\#$1}^3 c-3 \text{$\#$1}^2 a d+i \text{$\#$1} b c+a b d}\&\right]}{\sqrt{2} c}",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] - Sqrt[-c]*x), x]/(2*Sqrt[d]) + Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] + Sqrt[-c]*x), x]/(2*Sqrt[d])","F",0,0,0,0,-1,"{}"
2997,0,0,0,2.4164296,"\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","Int[(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,"(28*b*x^(3/4)*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^20/((b + a*x^12)^(1/4)*(1 + b*x^28 + a*x^40)), x], x, x^(1/4)])/(b*x^3 + a*x^6)^(1/4) + (40*a*x^(3/4)*(b + a*x^3)^(1/4)*Defer[Subst][Defer[Int][x^32/((b + a*x^12)^(1/4)*(1 + b*x^28 + a*x^40)), x], x, x^(1/4)])/(b*x^3 + a*x^6)^(1/4)","F",0,0,0,0,-1,"{}"
2998,0,0,0,2.3331016,"\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","Int[(x^4*(-2*q + p*x^3)*Sqrt[q + p*x^3])/(b*x^8 + a*(q + p*x^3)^4),x]","\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","-\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,"-2*q*Defer[Int][(x^4*Sqrt[q + p*x^3])/(b*x^8 + a*(q + p*x^3)^4), x] + p*Defer[Int][(x^7*Sqrt[q + p*x^3])/(b*x^8 + a*(q + p*x^3)^4), x]","F",0,0,0,0,-1,"{}"
2999,0,0,0,2.1834651,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2} \, dx","Int[(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{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-16 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2-x-1\right)+\left(26 x^2+x+5\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3-x^2-2 x-1\right)+\left(26 x^3+x^2+18 x+1\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}",1,"-1/4*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x)^2, x] + (I/4)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x), x] - Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x)^2, x]/4 + (I/4)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x), x]","F",0,0,0,0,-1,"{}"
3000,0,0,0,1.6043725,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2} \, dx","Int[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x^2)^2,x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2} \, dx","\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-16 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2-x-1\right)+\left(26 x^2+x+5\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3-x^2-2 x-1\right)+\left(26 x^3+x^2+18 x+1\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}",1,"-1/4*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x)^2, x] + (I/4)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x), x] - Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x)^2, x]/4 + (I/4)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x), x]","F",0,0,0,0,-1,"{}"
3001,0,0,0,1.9877507,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{2 \left(x^2-1\right)}",1,"Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
3002,0,0,0,1.6935671,"\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+3 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{2 \left(x^2-1\right)}",1,"Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
3003,0,0,0,2.0101088,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2+5 x-1\right)+\left(2 x^2-x+1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3+5 x^2-2 x-3\right)+\left(2 x^3-x^2+2 x-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}-\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-24 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]",1,"-1/4*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)^2*Sqrt[x + Sqrt[1 + x^2]]), x] + (I/4)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)*Sqrt[x + Sqrt[1 + x^2]]), x] - Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + (I/4)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",0,0,0,0,-1,"{}"
3004,0,0,0,1.7298401,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^2+5 x-1\right)+\left(2 x^2-x+1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-2 x^3+5 x^2-2 x-3\right)+\left(2 x^3-x^2+2 x-1\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{16 \left(2 x^4+3 x^2+1\right)+16 \sqrt{x^2+1} \left(2 x^3+2 x\right)}-\frac{1}{64} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-24 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]",1,"-1/4*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)^2*Sqrt[x + Sqrt[1 + x^2]]), x] + (I/4)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)*Sqrt[x + Sqrt[1 + x^2]]), x] - Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + (I/4)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)*Sqrt[x + Sqrt[1 + x^2]]), x]","F",0,0,0,0,-1,"{}"
3005,0,0,0,11.4026764,"\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","Int[((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,"(3*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x*(1 - k*x^3)^(5/3))/((1 - x^3)^(1/3)*(-(x^6*(-1 + x^3)^2) + b*(-1 + k*x^3)^4)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3) - (3*(2 - k)*(1 - x)^(1/3)*x^(1/3)*(1 - k*x)^(1/3)*Defer[Subst][Defer[Int][(x^4*(1 - k*x^3)^(5/3))/((1 - x^3)^(1/3)*(-(x^6*(-1 + x^3)^2) + b*(-1 + k*x^3)^4)), x], x, x^(1/3)])/((1 - x)*x*(1 - k*x))^(1/3)","F",0,0,0,0,-1,"{}"
3006,0,0,0,2.1706106,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[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{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} x}{2 \left(x^2-1\right) \sqrt{\sqrt{x^2+1}+x}}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x]/4","F",0,0,0,0,-1,"{}"
3007,0,0,0,1.7216937,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{16} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+7 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$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,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x]/4","F",0,0,0,0,-1,"{}"
3008,0,0,0,9.1064932,"\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","Int[((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,"(-3*(a - 2*b)*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^7/((a - b + x^3)^(1/3)*(a^2*(1 + (b*(-2*a + b))/a^2) + (2*a - 2*b)*x^3 + x^6 - d*x^12)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) - (3*a*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^7/((a - b + x^3)^(1/3)*(a^2*(1 + (b*(-2*a + b))/a^2) + 2*a*(1 - b/a)*x^3 + x^6 - d*x^12)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3) - (3*(-a + x)^(1/3)*(-b + x)^(1/3)*Defer[Subst][Defer[Int][x^10/((a - b + x^3)^(1/3)*(a^2*(1 + (b*(-2*a + b))/a^2) + 2*a*(1 - b/a)*x^3 + x^6 - d*x^12)), x], x, (-a + x)^(1/3)])/((a - x)*(b - x))^(1/3)","F",0,0,0,0,-1,"{}"
3009,0,0,0,2.9341389,"\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","Int[((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{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (2-16 x)+\sqrt{x^2+1} \left((-32 x-3) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-16 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-32 x^2-3 x-8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(\sqrt{x^2+1}+x\right)^{3/2}}+\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[x + Sqrt[1 + x^2]], x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2 + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2","F",0,0,0,0,-1,"{}"
3010,0,0,0,2.425202,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^4)*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^4\right) \sqrt{x+\sqrt{1+x^2}}} \, dx","-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]+\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+3 \text{$\#$1}^2-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$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,"-Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[x + Sqrt[1 + x^2]], x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I - x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2 + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((I + x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x]/2","F",0,0,0,0,-1,"{}"
3011,1,255,0,4.6521112,"\int \frac{\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}}{x-\sqrt{b+a x}} \, dx","Int[(Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]])/(x - Sqrt[b + a*x]),x]","-\frac{2 \sqrt{2} \left(a^2-\frac{a^3+a^2 c+3 a b+2 b c}{\sqrt{a^2+4 b}}+a c+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{-\sqrt{a^2+4 b}+a+2 c}}-\frac{2 \sqrt{2} \left(a^2+\frac{a^3+a^2 c+3 a b+2 b c}{\sqrt{a^2+4 b}}+a c+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{\sqrt{a^2+4 b}+a+2 c}}+\frac{4}{3} \left(\sqrt{a x+b}+c\right)^{3/2}+4 a \sqrt{\sqrt{a x+b}+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{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,"4*a*Sqrt[c + Sqrt[b + a*x]] + (4*(c + Sqrt[b + a*x])^(3/2))/3 - (2*Sqrt[2]*(a^2 + b + a*c - (a^3 + 3*a*b + a^2*c + 2*b*c)/Sqrt[a^2 + 4*b])*ArcTanh[(Sqrt[2]*Sqrt[c + Sqrt[b + a*x]])/Sqrt[a - Sqrt[a^2 + 4*b] + 2*c]])/Sqrt[a - Sqrt[a^2 + 4*b] + 2*c] - (2*Sqrt[2]*(a^2 + b + a*c + (a^3 + 3*a*b + a^2*c + 2*b*c)/Sqrt[a^2 + 4*b])*ArcTanh[(Sqrt[2]*Sqrt[c + Sqrt[b + a*x]])/Sqrt[a + Sqrt[a^2 + 4*b] + 2*c]])/Sqrt[a + Sqrt[a^2 + 4*b] + 2*c]","A",7,4,40,0.1000,1,"{897, 1287, 1166, 206}"
3012,1,425,0,1.1818763,"\int \frac{1+x}{(1-a x) \sqrt[4]{\frac{1-b x}{c+x}}} \, dx","Int[(1 + x)/((1 - a*x)*((1 - b*x)/(c + x))^(1/4)),x]","\frac{(a b (c+4)+a+4 b) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{\frac{1-b x}{c+x}}+\sqrt{\frac{1-b x}{c+x}}+\sqrt{b}\right)}{4 \sqrt{2} a^2 b^{5/4}}-\frac{(a b (c+4)+a+4 b) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{\frac{1-b x}{c+x}}+\sqrt{\frac{1-b x}{c+x}}+\sqrt{b}\right)}{4 \sqrt{2} a^2 b^{5/4}}-\frac{(a b (c+4)+a+4 b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\frac{1-b x}{c+x}}}{\sqrt[4]{b}}\right)}{2 \sqrt{2} a^2 b^{5/4}}+\frac{(a b (c+4)+a+4 b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\frac{1-b x}{c+x}}}{\sqrt[4]{b}}+1\right)}{2 \sqrt{2} a^2 b^{5/4}}-\frac{2 (a+1) \sqrt[4]{a c+1} \tan ^{-1}\left(\frac{\sqrt[4]{a c+1} \sqrt[4]{\frac{1-b x}{c+x}}}{\sqrt[4]{a-b}}\right)}{a^2 \sqrt[4]{a-b}}+\frac{2 (a+1) \sqrt[4]{a c+1} \tanh ^{-1}\left(\frac{\sqrt[4]{a c+1} \sqrt[4]{\frac{1-b x}{c+x}}}{\sqrt[4]{a-b}}\right)}{a^2 \sqrt[4]{a-b}}+\frac{(c+x) \left(\frac{1-b x}{c+x}\right)^{3/4}}{a b}","-\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,"((c + x)*((1 - b*x)/(c + x))^(3/4))/(a*b) - (2*(1 + a)*(1 + a*c)^(1/4)*ArcTan[((1 + a*c)^(1/4)*((1 - b*x)/(c + x))^(1/4))/(a - b)^(1/4)])/(a^2*(a - b)^(1/4)) - ((a + 4*b + a*b*(4 + c))*ArcTan[1 - (Sqrt[2]*((1 - b*x)/(c + x))^(1/4))/b^(1/4)])/(2*Sqrt[2]*a^2*b^(5/4)) + ((a + 4*b + a*b*(4 + c))*ArcTan[1 + (Sqrt[2]*((1 - b*x)/(c + x))^(1/4))/b^(1/4)])/(2*Sqrt[2]*a^2*b^(5/4)) + (2*(1 + a)*(1 + a*c)^(1/4)*ArcTanh[((1 + a*c)^(1/4)*((1 - b*x)/(c + x))^(1/4))/(a - b)^(1/4)])/(a^2*(a - b)^(1/4)) + ((a + 4*b + a*b*(4 + c))*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*((1 - b*x)/(c + x))^(1/4) + Sqrt[(1 - b*x)/(c + x)]])/(4*Sqrt[2]*a^2*b^(5/4)) - ((a + 4*b + a*b*(4 + c))*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*((1 - b*x)/(c + x))^(1/4) + Sqrt[(1 - b*x)/(c + x)]])/(4*Sqrt[2]*a^2*b^(5/4))","A",17,12,28,0.4286,1,"{1977, 579, 584, 297, 1162, 617, 204, 1165, 628, 298, 205, 208}"
3013,0,0,0,2.7085866,"\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","Int[(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,"(28*b*x^(3/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^20/((-b + a*x^8)^(1/4)*(-1 + b*x^28 - a*x^36)), x], x, x^(1/4)])/(-(b*x^3) + a*x^5)^(1/4) + (36*a*x^(3/4)*(-b + a*x^2)^(1/4)*Defer[Subst][Defer[Int][x^28/((-b + a*x^8)^(1/4)*(1 - b*x^28 + a*x^36)), x], x, x^(1/4)])/(-(b*x^3) + a*x^5)^(1/4)","F",0,0,0,0,-1,"{}"
3014,1,22,0,0.1540797,"\int \frac{b+a x^4}{\sqrt{-b+a x^4} \left(-b+c^2 x^2+a x^4\right)} \, dx","Int[(b + a*x^4)/(Sqrt[-b + a*x^4]*(-b + c^2*x^2 + a*x^4)),x]","-\frac{\tan ^{-1}\left(\frac{c x}{\sqrt{a x^4-b}}\right)}{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} \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,"-(ArcTan[(c*x)/Sqrt[-b + a*x^4]]/c)","A",2,2,39,0.05128,1,"{2112, 205}"
3015,0,0,0,17.5353338,"\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","Int[(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,"(6*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^7*(-a + x^3)^(2/3))/((-b + x^3)^(2/3)*(b^2 - 2*b*x^3 + (1 - a^2*d)*x^6 + 2*a*d*x^9 - d*x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*a*b*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^4*(-a + x^3)^(2/3))/((-b + x^3)^(2/3)*(-b^2 + 2*b*x^3 - (1 - a^2*d)*x^6 - 2*a*d*x^9 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3) + (3*x^(1/3)*(-a + x)^(1/3)*(-b + x)^(2/3)*Defer[Subst][Defer[Int][(x^10*(-a + x^3)^(2/3))/((-b + x^3)^(2/3)*(-b^2 + 2*b*x^3 - (1 - a^2*d)*x^6 - 2*a*d*x^9 + d*x^12)), x], x, x^(1/3)])/(-((a - x)*(b - x)^2*x))^(1/3)","F",0,0,0,0,-1,"{}"
3016,1,453,0,0.2207842,"\int \frac{b+a x}{(-b+a x) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(b + a*x)/((-b + a*x)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \log (x) \sqrt[3]{a^3 x+b^2}}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log (a x-b)}{\sqrt[3]{a} \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+b}}-\sqrt[3]{x}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{2 \sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2+b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-((Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3))) + (2*Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + b)^(1/3)*x^(1/3))])/(a^(1/3)*(a^2 + b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-b + a*x])/(a^(1/3)*(a^2 + b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + b)^(1/3))])/(a^(1/3)*(a^2 + b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3))","A",4,4,34,0.1176,1,"{2056, 157, 59, 91}"
3017,0,0,0,4.0985014,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{-b+a^2 x^4} \, dx","Int[(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{$\#$1}^8+20 \text{$\#$1}^6 a b-26 \text{$\#$1}^4 a^2 b^2+20 \text{$\#$1}^2 a^3 b^3+a^4 b^4\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-2 \text{$\#$1}^2 a b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)+a^2 b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^6+15 \text{$\#$1}^4 a b-13 \text{$\#$1}^2 a^2 b^2+5 a^3 b^3}\&\right]",1,"-1/4*Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) - Sqrt[-a]*x), x]/b^(3/4) - Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) + Sqrt[-a]*x), x]/(4*b^(3/4)) - Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) - Sqrt[a]*x), x]/(4*b^(3/4)) - Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) + Sqrt[a]*x), x]/(4*b^(3/4))","F",0,0,0,0,-1,"{}"
3018,0,0,0,3.1622152,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{-b+a^2 x^4} \, dx","Int[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(-b + a^2*x^4),x]","\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{-b+a^2 x^4} \, dx","\frac{\log \left(i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\sqrt{2} \sqrt{a}}-2 \sqrt{2} \sqrt{a} b \text{RootSum}\left[\text{$\#$1}^8+20 \text{$\#$1}^6 a b-26 \text{$\#$1}^4 a^2 b^2+20 \text{$\#$1}^2 a^3 b^3+a^4 b^4\&,\frac{\text{$\#$1}^4 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)-2 \text{$\#$1}^2 a b \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)+a^2 b^2 \log \left(-\text{$\#$1}+i a^{3/2} x^2+i \sqrt{a} \sqrt{a^2 x^4+b}+i \sqrt{2} a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}\right)}{\text{$\#$1}^6+15 \text{$\#$1}^4 a b-13 \text{$\#$1}^2 a^2 b^2+5 a^3 b^3}\&\right]",1,"-1/4*Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) - Sqrt[-a]*x), x]/b^(3/4) - Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) + Sqrt[-a]*x), x]/(4*b^(3/4)) - Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) - Sqrt[a]*x), x]/(4*b^(3/4)) - Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(b^(1/4) + Sqrt[a]*x), x]/(4*b^(3/4))","F",0,0,0,0,-1,"{}"
3019,1,376,0,0.6807409,"\int \frac{1}{\sqrt[3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx","Int[1/(((-a + x)*(-b + x)^2)^(1/3)*(b - a*d + (-1 + d)*x)),x]","-\frac{\left((a-b)^2 (b-x)\right)^{2/3} \sqrt[3]{(a-b)^2 (x-a)} \log (-a d+b+(d-1) x)}{2 d^{2/3} (a-b)^3 \sqrt[3]{-a b^2+x^2 (-a-2 b)+b x (2 a+b)+x^3}}+\frac{3 \left((a-b)^2 (b-x)\right)^{2/3} \sqrt[3]{(a-b)^2 (x-a)} \log \left(-\sqrt[3]{\frac{2}{3}} \sqrt[3]{d} \sqrt[3]{(a-b)^2 (x-a)}-\sqrt[3]{\frac{2}{3}} \sqrt[3]{(a-b)^2 (b-x)}\right)}{2 d^{2/3} (a-b)^3 \sqrt[3]{-a b^2+x^2 (-a-2 b)+b x (2 a+b)+x^3}}+\frac{\sqrt{3} \left((a-b)^2 (b-x)\right)^{2/3} \sqrt[3]{(a-b)^2 (x-a)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{d} \sqrt[3]{(a-b)^2 (x-a)}}{\sqrt{3} \sqrt[3]{(a-b)^2 (b-x)}}\right)}{d^{2/3} (a-b)^3 \sqrt[3]{-a b^2+x^2 (-a-2 b)+b x (2 a+b)+x^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 (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,"(Sqrt[3]*((a - b)^2*(b - x))^(2/3)*((a - b)^2*(-a + x))^(1/3)*ArcTan[1/Sqrt[3] - (2*d^(1/3)*((a - b)^2*(-a + x))^(1/3))/(Sqrt[3]*((a - b)^2*(b - x))^(1/3))])/((a - b)^3*d^(2/3)*(-(a*b^2) + b*(2*a + b)*x + (-a - 2*b)*x^2 + x^3)^(1/3)) - (((a - b)^2*(b - x))^(2/3)*((a - b)^2*(-a + x))^(1/3)*Log[b - a*d + (-1 + d)*x])/(2*(a - b)^3*d^(2/3)*(-(a*b^2) + b*(2*a + b)*x + (-a - 2*b)*x^2 + x^3)^(1/3)) + (3*((a - b)^2*(b - x))^(2/3)*((a - b)^2*(-a + x))^(1/3)*Log[-((2/3)^(1/3)*((a - b)^2*(b - x))^(1/3)) - (2/3)^(1/3)*d^(1/3)*((a - b)^2*(-a + x))^(1/3)])/(2*(a - b)^3*d^(2/3)*(-(a*b^2) + b*(2*a + b)*x + (-a - 2*b)*x^2 + x^3)^(1/3))","A",3,3,31,0.09677,1,"{2081, 2077, 91}"
3020,0,0,0,10.0321788,"\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","Int[((-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,"(-2*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(1 + x - x^2 + 2*x^4)^(1/3)/((-1 + x)*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3) + (4*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(1 + x - x^2 + 2*x^4)^(1/3)/(x^5*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3) + (3*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(1 + x - x^2 + 2*x^4)^(1/3)/(x^4*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3) - (2*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(1 + x - x^2 + 2*x^4)^(1/3)/(x^3*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3) + (8*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(1 + x - x^2 + 2*x^4)^(1/3)/(x*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3) - (4*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(1 + x - x^2 + 2*x^4)^(1/3)/((1 + 2*x + x^2 + x^3)*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3) - (4*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(x*(1 + x - x^2 + 2*x^4)^(1/3))/((1 + 2*x + x^2 + x^3)*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3) - (6*((1 + x - x^2 + 2*x^4)/(1 + x - x^2 + 3*x^4))^(1/3)*(1 + x - x^2 + 3*x^4)^(1/3)*Defer[Int][(x^2*(1 + x - x^2 + 2*x^4)^(1/3))/((1 + 2*x + x^2 + x^3)*(1 + x - x^2 + 3*x^4)^(1/3)), x])/(1 + x - x^2 + 2*x^4)^(1/3)","F",0,0,0,0,-1,"{}"
3021,1,477,0,0.2318483,"\int \frac{-b+a x}{(b+a x) \sqrt[3]{-b^2 x^2+a^3 x^3}} \, dx","Int[(-b + a*x)/((b + a*x)*(-(b^2*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \log (x) \sqrt[3]{a^3 x-b^2}}{2 a \sqrt[3]{a^3 x^3-b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b^2} \log \left(\frac{\sqrt[3]{a^3 x-b^2}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3-b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3-b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b^2} \log (a x+b)}{\sqrt[3]{a} \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3-b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b^2} \log \left(\frac{\sqrt[3]{a^3 x-b^2}}{\sqrt[3]{a} \sqrt[3]{a^2+b}}-\sqrt[3]{x}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3-b^2 x^2}}+\frac{2 \sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2+b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3-b^2 x^2}}","-\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,"-((Sqrt[3]*x^(2/3)*(-b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(-(b^2*x^2) + a^3*x^3)^(1/3))) + (2*Sqrt[3]*x^(2/3)*(-b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 + b)^(1/3)*x^(1/3))])/(a^(1/3)*(a^2 + b)^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[x])/(2*a*(-(b^2*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[b + a*x])/(a^(1/3)*(a^2 + b)^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (-b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 + b)^(1/3))])/(a^(1/3)*(a^2 + b)^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[-1 + (-b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(-(b^2*x^2) + a^3*x^3)^(1/3))","A",4,4,35,0.1143,1,"{2056, 157, 59, 91}"
3022,0,0,0,1.7021902,"\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","Int[((-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]","\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","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8 a-8 \text{$\#$1}^6 a \sqrt{p} \sqrt{q}+4 \text{$\#$1}^6 b+24 \text{$\#$1}^4 a p q-16 \text{$\#$1}^4 b \sqrt{p} \sqrt{q}+16 \text{$\#$1}^4 c-32 \text{$\#$1}^2 a p^{3/2} q^{3/2}+16 \text{$\#$1}^2 b p q+16 a p^2 q^2\&,\frac{-\text{$\#$1}^6 \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)+\text{$\#$1}^6 \log (x)+2 \text{$\#$1}^4 \sqrt{p} \sqrt{q} \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)-2 \text{$\#$1}^4 \sqrt{p} \sqrt{q} \log (x)+4 \text{$\#$1}^2 p q \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)-4 \text{$\#$1}^2 p q \log (x)-8 p^{3/2} q^{3/2} \log \left(-\text{$\#$1} x+\sqrt{p x^4+q}-\sqrt{p} x^2-\sqrt{q}\right)+8 p^{3/2} q^{3/2} \log (x)}{\text{$\#$1}^7 (-a)+6 \text{$\#$1}^5 a \sqrt{p} \sqrt{q}-3 \text{$\#$1}^5 b-12 \text{$\#$1}^3 a p q+8 \text{$\#$1}^3 b \sqrt{p} \sqrt{q}-8 \text{$\#$1}^3 c+8 \text{$\#$1} a p^{3/2} q^{3/2}-4 \text{$\#$1} b p q}\&\right]",1,"q*Defer[Int][Sqrt[q + p*x^4]/(-(c*x^4) - b*x^2*(q + p*x^4) - a*(q + p*x^4)^2), x] + p*Defer[Int][(x^4*Sqrt[q + p*x^4])/(c*x^4 + b*x^2*(q + p*x^4) + a*(q + p*x^4)^2), x]","F",0,0,0,0,-1,"{}"
3023,0,0,0,2.0398334,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \left(1-x^4\right)} \, dx","Int[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(Sqrt[1 + x^2]*(1 - x^4)),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \left(1-x^4\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+16 \text{$\#$1}^4+1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+18 \text{$\#$1}^5+20 \text{$\#$1}^4+8 \text{$\#$1}^3}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$1}^2+1}\&\right]+\frac{\left(-4 x^2-5\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-4 x \sqrt{x^2+1} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{x^2+\sqrt{x^2+1} x+1}+4 \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2), x] - Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + x^2], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]/2","F",0,0,0,0,-1,"{}"
3024,0,0,0,1.6516127,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \left(1-x^4\right)} \, dx","Int[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(Sqrt[1 + x^2]*(1 - x^4)),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\sqrt{1+x^2} \left(1-x^4\right)} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+16 \text{$\#$1}^4+1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^7+7 \text{$\#$1}^6+18 \text{$\#$1}^5+20 \text{$\#$1}^4+8 \text{$\#$1}^3}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+14 \text{$\#$1}^4-8 \text{$\#$1}^3-8 \text{$\#$1}^2-1\&,\frac{\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^3+3 \text{$\#$1}^2+\text{$\#$1}-1}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+24 \text{$\#$1}^6+32 \text{$\#$1}^5+18 \text{$\#$1}^4+8 \text{$\#$1}^3+8 \text{$\#$1}^2-1\&,\frac{\text{$\#$1} \log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)+\log \left(-\text{$\#$1}+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-1\right)}{\text{$\#$1}^4+4 \text{$\#$1}^3+4 \text{$\#$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,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(3/2), x] - Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[1 + x^2], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x]/2 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[1 + x^2]), x]/2","F",0,0,0,0,-1,"{}"
3025,0,0,0,2.5451435,"\int \frac{1-x^3+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Int[(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,"(-2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^2)/(1 - I*Sqrt[3]), -x^2])/(x^2 + x^4)^(1/3) - (2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^2)/(1 + I*Sqrt[3]), -x^2])/(x^2 + x^4)^(1/3) + ((I - Sqrt[3])*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^2, (-2*x^2)/(1 - I*Sqrt[3])])/(4*(I + Sqrt[3])*(x^2 + x^4)^(1/3)) + ((I + Sqrt[3])*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^2, (-2*x^2)/(1 + I*Sqrt[3])])/(4*(I - Sqrt[3])*(x^2 + x^4)^(1/3)) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3) + (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(2*(x^2 + x^4)^(1/3)) + ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(2*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) + ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(2*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3))","F",0,0,0,0,-1,"{}"
3026,0,0,0,2.1775783,"\int \frac{1+x^3+x^6}{\sqrt[3]{x^2+x^4} \left(-1+x^6\right)} \, dx","Int[(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,"(-2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^2)/(1 - I*Sqrt[3]), -x^2])/(x^2 + x^4)^(1/3) - (2*x*(1 + x^2)^(1/3)*AppellF1[1/6, 1, 1/3, 7/6, (-2*x^2)/(1 + I*Sqrt[3]), -x^2])/(x^2 + x^4)^(1/3) - ((I - Sqrt[3])*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^2, (-2*x^2)/(1 - I*Sqrt[3])])/(4*(I + Sqrt[3])*(x^2 + x^4)^(1/3)) - ((I + Sqrt[3])*x^2*(1 + x^2)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -x^2, (-2*x^2)/(1 + I*Sqrt[3])])/(4*(I - Sqrt[3])*(x^2 + x^4)^(1/3)) + (3*x*(1 + x^2)^(1/3)*Hypergeometric2F1[1/6, 1/3, 7/6, -x^2])/(x^2 + x^4)^(1/3) + (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(2*(x^2 + x^4)^(1/3)) - (x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 + x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) + ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 - I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(2*(x^2 + x^4)^(1/3)) + ((1 - I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(6*(x^2 + x^4)^(1/3)) - ((1 + I*Sqrt[3])*x^(2/3)*(1 + x^2)^(1/3)*Defer[Subst][Defer[Int][1/((1 + I*Sqrt[3] + 2*x)*(1 + x^6)^(1/3)), x], x, x^(1/3)])/(2*(x^2 + x^4)^(1/3))","F",0,0,0,0,-1,"{}"
3027,0,0,0,1.0920288,"\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","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]]],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,"Defer[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]]], x]","F",0,0,0,0,-1,"{}"
3028,1,160,0,0.3836541,"\int \frac{\left(-1+a x^8\right) \left(1+a x^8\right)^{3/4}}{1+x^8+a^2 x^{16}} \, dx","Int[((-1 + a*x^8)*(1 + a*x^8)^(3/4))/(1 + x^8 + a^2*x^16),x]","\frac{a \left(1-\frac{2 a+1}{\sqrt{1-4 a^2}}\right) x F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-a x^8,-\frac{2 a^2 x^8}{1-\sqrt{1-4 a^2}}\right)}{1-\sqrt{1-4 a^2}}+\frac{a \left(\frac{2 a+1}{\sqrt{1-4 a^2}}+1\right) x F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};-a x^8,-\frac{2 a^2 x^8}{\sqrt{1-4 a^2}+1}\right)}{\sqrt{1-4 a^2}+1}","\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,"(a*(1 - (1 + 2*a)/Sqrt[1 - 4*a^2])*x*AppellF1[1/8, -3/4, 1, 9/8, -(a*x^8), (-2*a^2*x^8)/(1 - Sqrt[1 - 4*a^2])])/(1 - Sqrt[1 - 4*a^2]) + (a*(1 + (1 + 2*a)/Sqrt[1 - 4*a^2])*x*AppellF1[1/8, -3/4, 1, 9/8, -(a*x^8), (-2*a^2*x^8)/(1 + Sqrt[1 - 4*a^2])])/(1 + Sqrt[1 - 4*a^2])","C",4,2,33,0.06061,0,"{6728, 429}"
3029,1,461,0,0.2372652,"\int \frac{-b+a x}{(b+a x) \sqrt[3]{b^2 x^2+a^3 x^3}} \, dx","Int[(-b + a*x)/((b + a*x)*(b^2*x^2 + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \log (x) \sqrt[3]{a^3 x+b^2}}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3+b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x+b^2} \log (a x+b)}{\sqrt[3]{a} \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x+b^2} \log \left(\frac{\sqrt[3]{a^3 x+b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-b}}-\sqrt[3]{x}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2}}+\frac{2 \sqrt{3} x^{2/3} \sqrt[3]{a^3 x+b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x+b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2-b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2}}","-\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,"-((Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(b^2*x^2 + a^3*x^3)^(1/3))) + (2*Sqrt[3]*x^(2/3)*(b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - b)^(1/3)*x^(1/3))])/(a^(1/3)*(a^2 - b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[x])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3)) - (x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[b + a*x])/(a^(1/3)*(a^2 - b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) + (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - b)^(1/3))])/(a^(1/3)*(a^2 - b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)) - (3*x^(2/3)*(b^2 + a^3*x)^(1/3)*Log[-1 + (b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(b^2*x^2 + a^3*x^3)^(1/3))","A",4,4,34,0.1176,1,"{2056, 157, 59, 91}"
3030,1,463,0,0.7964839,"\int \frac{1}{\left(-1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[1/((-1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\frac{\sqrt{\sqrt{x^2+1}+x}}{2 \left(-\left(\sqrt{x^2+1}+x\right)^2-2 \left(\sqrt{x^2+1}+x\right)+1\right)}+\frac{\sqrt{\sqrt{x^2+1}+x}}{2 \left(-\left(\sqrt{x^2+1}+x\right)^2+2 \left(\sqrt{x^2+1}+x\right)+1\right)}+\frac{\tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{2 \sqrt{1+\sqrt{2}}}+\frac{1}{4} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)+\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)-\frac{\tan ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{2 \sqrt{\sqrt{2}-1}}+\frac{\tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)}{2 \sqrt{1+\sqrt{2}}}+\frac{1}{4} \sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tanh ^{-1}\left(\sqrt{\sqrt{2}-1} \sqrt{\sqrt{x^2+1}+x}\right)+\frac{1}{4} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)-\frac{\tanh ^{-1}\left(\sqrt{1+\sqrt{2}} \sqrt{\sqrt{x^2+1}+x}\right)}{2 \sqrt{\sqrt{2}-1}}","\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,"Sqrt[x + Sqrt[1 + x^2]]/(2*(1 - 2*(x + Sqrt[1 + x^2]) - (x + Sqrt[1 + x^2])^2)) + Sqrt[x + Sqrt[1 + x^2]]/(2*(1 + 2*(x + Sqrt[1 + x^2]) - (x + Sqrt[1 + x^2])^2)) + (Sqrt[(-1 + Sqrt[2])/2]*ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/4 + ArcTan[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/(2*Sqrt[1 + Sqrt[2]]) - ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/(2*Sqrt[-1 + Sqrt[2]]) + (Sqrt[(1 + Sqrt[2])/2]*ArcTan[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/4 + (Sqrt[(-1 + Sqrt[2])/2]*ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/4 + ArcTanh[Sqrt[-1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/(2*Sqrt[1 + Sqrt[2]]) - ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]]/(2*Sqrt[-1 + Sqrt[2]]) + (Sqrt[(1 + Sqrt[2])/2]*ArcTanh[Sqrt[1 + Sqrt[2]]*Sqrt[x + Sqrt[1 + x^2]]])/4","A",34,15,23,0.6522,0,"{6742, 2119, 1648, 12, 707, 1093, 204, 206, 207, 203, 6725, 1628, 828, 826, 1166}"
3031,0,0,0,0.9921616,"\int \frac{\left(c+b x+a x^2\right)^{3/2}}{1-x \sqrt{c+b x+a x^2}} \, dx","Int[(c + b*x + a*x^2)^(3/2)/(1 - x*Sqrt[c + b*x + a*x^2]),x]","\int \frac{\left(c+b x+a x^2\right)^{3/2}}{1-x \sqrt{c+b x+a x^2}} \, dx","-2 \text{RootSum}\left[\text{$\#$1}^4 \sqrt{a}-\text{$\#$1}^3 b+4 \text{$\#$1}^2 a-4 \text{$\#$1} \sqrt{a} b+\text{$\#$1} b c-\sqrt{a} c^2+b^2\&,\frac{\text{$\#$1}^3 \sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\text{$\#$1}^2 \sqrt{a} b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1}^2 b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 \text{$\#$1} a^{3/2} \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-\text{$\#$1} b^2 \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+\text{$\#$1} \sqrt{a} c^2 \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 \text{$\#$1} a c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-a b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{4 \text{$\#$1}^3 \sqrt{a}-3 \text{$\#$1}^2 b+8 \text{$\#$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,"-(b*x) - (a*x^2)/2 - (c*Log[-1 + c*x^2 + b*x^3 + a*x^4])/4 + Defer[Int][(c + b*x + a*x^2)^(3/2)/(1 - c*x^2 - b*x^3 - a*x^4), x] - b*Defer[Int][(-1 + c*x^2 + b*x^3 + a*x^4)^(-1), x] - ((2*a + c^2)*Defer[Int][x/(-1 + c*x^2 + b*x^3 + a*x^4), x])/2 - (b*c*Defer[Int][x^2/(-1 + c*x^2 + b*x^3 + a*x^4), x])/4","F",0,0,0,0,-1,"{}"
3032,1,513,0,1.3201882,"\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","Int[(-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{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 \left(1-\sqrt{d}\right) \left(a+b \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{(x-a)^{2/3} (x-b)^{4/3} \log \left(2 (1-d) x-2 \left(\sqrt{d}+1\right) \left(a-b \sqrt{d}\right)\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(-\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{x-b}\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{3 (x-a)^{2/3} (x-b)^{4/3} \log \left(\sqrt[6]{d} \sqrt[3]{x-b}-\sqrt[3]{x-a}\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}\right)}{2 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\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,"(Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) - (Sqrt[3]*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) - ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 - Sqrt[d])*(a + b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) + ((-a + x)^(2/3)*(-b + x)^(4/3)*Log[-2*(1 + Sqrt[d])*(a - b*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) - d^(1/6)*(-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) - (3*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + d^(1/6)*(-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3))","A",9,5,54,0.09259,1,"{6719, 911, 105, 59, 91}"
3033,1,489,0,0.2369657,"\int \frac{b+a x}{(-b+a x) \sqrt[3]{-b^2 x^2+a^3 x^3}} \, dx","Int[(b + a*x)/((-b + a*x)*(-(b^2*x^2) + a^3*x^3)^(1/3)),x]","-\frac{x^{2/3} \log (x) \sqrt[3]{a^3 x-b^2}}{2 a \sqrt[3]{a^3 x^3-b^2 x^2}}-\frac{3 x^{2/3} \sqrt[3]{a^3 x-b^2} \log \left(\frac{\sqrt[3]{a^3 x-b^2}}{a \sqrt[3]{x}}-1\right)}{2 a \sqrt[3]{a^3 x^3-b^2 x^2}}-\frac{\sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b^2}}{\sqrt{3} a \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{a \sqrt[3]{a^3 x^3-b^2 x^2}}-\frac{x^{2/3} \sqrt[3]{a^3 x-b^2} \log (a x-b)}{\sqrt[3]{a} \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}}+\frac{3 x^{2/3} \sqrt[3]{a^3 x-b^2} \log \left(\frac{\sqrt[3]{a^3 x-b^2}}{\sqrt[3]{a} \sqrt[3]{a^2-b}}-\sqrt[3]{x}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}}+\frac{2 \sqrt{3} x^{2/3} \sqrt[3]{a^3 x-b^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a^3 x-b^2}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2-b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{a} \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3-b^2 x^2}}","-\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,"-((Sqrt[3]*x^(2/3)*(-b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b^2 + a^3*x)^(1/3))/(Sqrt[3]*a*x^(1/3))])/(a*(-(b^2*x^2) + a^3*x^3)^(1/3))) + (2*Sqrt[3]*x^(2/3)*(-b^2 + a^3*x)^(1/3)*ArcTan[1/Sqrt[3] + (2*(-b^2 + a^3*x)^(1/3))/(Sqrt[3]*a^(1/3)*(a^2 - b)^(1/3)*x^(1/3))])/(a^(1/3)*(a^2 - b)^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[x])/(2*a*(-(b^2*x^2) + a^3*x^3)^(1/3)) - (x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[-b + a*x])/(a^(1/3)*(a^2 - b)^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)) + (3*x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[-x^(1/3) + (-b^2 + a^3*x)^(1/3)/(a^(1/3)*(a^2 - b)^(1/3))])/(a^(1/3)*(a^2 - b)^(1/3)*(-(b^2*x^2) + a^3*x^3)^(1/3)) - (3*x^(2/3)*(-b^2 + a^3*x)^(1/3)*Log[-1 + (-b^2 + a^3*x)^(1/3)/(a*x^(1/3))])/(2*a*(-(b^2*x^2) + a^3*x^3)^(1/3))","A",4,4,35,0.1143,1,"{2056, 157, 59, 91}"
3034,0,0,0,0.3764657,"\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","Int[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]","\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","-\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
3035,1,409,0,0.7097551,"\int \frac{x^4}{\sqrt[4]{-b+a x^4} \left(-b+2 a x^4+x^8\right)} \, dx","Int[x^4/((-b + a*x^4)^(1/4)*(-b + 2*a*x^4 + x^8)),x]","-\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)}{4 \sqrt{a^2+b} \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)}{4 \sqrt{a^2+b} \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)}{4 \sqrt{a^2+b} \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)}{4 \sqrt{a^2+b} \sqrt[4]{a \sqrt{a^2+b}+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,"-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))])/(Sqrt[a^2 + b]*(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))])/(4*Sqrt[a^2 + b]*(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))])/(4*Sqrt[a^2 + b]*(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))])/(4*Sqrt[a^2 + b]*(a^2 + b + a*Sqrt[a^2 + b])^(1/4))","A",10,5,32,0.1562,1,"{1528, 377, 212, 208, 205}"
3036,1,1077,0,1.86983,"\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","Int[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(-b + a^2*x^2)^(5/2),x]","-\frac{11 c \left(a x+\sqrt{a^2 x^2-b}\right)^{11/4}}{6 a^3 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^2}+\frac{8 b c \left(a x+\sqrt{a^2 x^2-b}\right)^{11/4}}{3 a^3 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^3}+\frac{8 d \left(a x+\sqrt{a^2 x^2-b}\right)^{11/4}}{3 a \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^3}+\frac{41 c \left(a x+\sqrt{a^2 x^2-b}\right)^{3/4}}{48 a^3 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)}+\frac{11 d \left(a x+\sqrt{a^2 x^2-b}\right)^{3/4}}{16 a b \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)}-\frac{11 d \left(a x+\sqrt{a^2 x^2-b}\right)^{3/4}}{6 a \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^2}+\frac{41 c \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 a^3 b^{5/8}}-\frac{55 d \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 a b^{13/8}}+\frac{41 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 \sqrt{2} a^3 b^{5/8}}-\frac{55 d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 \sqrt{2} a b^{13/8}}-\frac{41 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right)}{64 \sqrt{2} a^3 b^{5/8}}+\frac{55 d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right)}{64 \sqrt{2} a b^{13/8}}-\frac{41 c \tanh ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 a^3 b^{5/8}}+\frac{55 d \tanh ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 a b^{13/8}}-\frac{41 c \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)}{128 \sqrt{2} a^3 b^{5/8}}+\frac{55 d \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)}{128 \sqrt{2} a b^{13/8}}+\frac{41 c \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)}{128 \sqrt{2} a^3 b^{5/8}}-\frac{55 d \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)}{128 \sqrt{2} a b^{13/8}}","\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,"(8*b*c*(a*x + Sqrt[-b + a^2*x^2])^(11/4))/(3*a^3*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^3) + (8*d*(a*x + Sqrt[-b + a^2*x^2])^(11/4))/(3*a*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^3) - (11*d*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(6*a*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^2) - (11*c*(a*x + Sqrt[-b + a^2*x^2])^(11/4))/(6*a^3*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^2) + (41*c*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(48*a^3*(b - (a*x + Sqrt[-b + a^2*x^2])^2)) + (11*d*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(16*a*b*(b - (a*x + Sqrt[-b + a^2*x^2])^2)) + (41*c*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*a^3*b^(5/8)) - (55*d*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*a*b^(13/8)) + (41*c*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*a^3*b^(5/8)) - (55*d*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*a*b^(13/8)) - (41*c*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*a^3*b^(5/8)) + (55*d*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*a*b^(13/8)) - (41*c*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*a^3*b^(5/8)) + (55*d*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*a*b^(13/8)) - (41*c*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]]])/(128*Sqrt[2]*a^3*b^(5/8)) + (55*d*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]]])/(128*Sqrt[2]*a*b^(13/8)) + (41*c*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]]])/(128*Sqrt[2]*a^3*b^(5/8)) - (55*d*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]]])/(128*Sqrt[2]*a*b^(13/8))","B",38,18,46,0.3913,1,"{6742, 2122, 288, 290, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 203, 206, 2120, 463, 457}"
3037,1,50,0,0.1576784,"\int \frac{x^2}{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Int[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^6-x^2}}","-\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 + x^6)^(1/4))","C",4,4,24,0.1667,0,"{2042, 466, 511, 510}"
3038,1,50,0,0.1586619,"\int \frac{x^2}{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Int[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^6-x^2}}","-\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 + x^6)^(1/4))","C",4,4,24,0.1667,0,"{2042, 466, 511, 510}"
3039,1,46,0,0.1121141,"\int \frac{-1+x^4}{\left(1+x^4\right) \sqrt[4]{-x^2+x^6}} \, dx","Int[(-1 + x^4)/((1 + x^4)*(-x^2 + x^6)^(1/4)),x]","-\frac{2 x \sqrt[4]{1-x^4} 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{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*(1 - x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, x^4, -x^4])/(-x^2 + x^6)^(1/4)","C",4,4,26,0.1538,0,"{2056, 466, 430, 429}"
3040,1,409,0,0.5201387,"\int \frac{\left(-b+a x^4\right)^{3/4}}{-b+2 a x^4+x^8} \, dx","Int[(-b + a*x^4)^(3/4)/(-b + 2*a*x^4 + x^8),x]","-\frac{\left(-a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(a-\sqrt{a^2+b}\right)^{3/4}}+\frac{\left(a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(\sqrt{a^2+b}+a\right)^{3/4}}-\frac{\left(-a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(a-\sqrt{a^2+b}\right)^{3/4}}+\frac{\left(a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(\sqrt{a^2+b}+a\right)^{3/4}}","\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,"-1/4*((a^2 + b - a*Sqrt[a^2 + b])^(3/4)*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))])/(Sqrt[a^2 + b]*(a - Sqrt[a^2 + b])^(3/4)) + ((a^2 + b + a*Sqrt[a^2 + b])^(3/4)*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))])/(4*Sqrt[a^2 + b]*(a + Sqrt[a^2 + b])^(3/4)) - ((a^2 + b - a*Sqrt[a^2 + b])^(3/4)*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))])/(4*Sqrt[a^2 + b]*(a - Sqrt[a^2 + b])^(3/4)) + ((a^2 + b + a*Sqrt[a^2 + b])^(3/4)*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))])/(4*Sqrt[a^2 + b]*(a + Sqrt[a^2 + b])^(3/4))","A",19,9,29,0.3103,1,"{1428, 408, 240, 212, 206, 203, 377, 208, 205}"
3041,0,0,0,0.1417881,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{5/2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(5/2),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{5/2}} \, dx","\frac{1}{256} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{2 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+40 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^4+30 x^3-17 x^2-166 x-1\right)+\left(24 x^4+8 x^3+22 x^2+4 x+2\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^5+30 x^4-27 x^3-151 x^2-7 x-117\right)+\left(24 x^5+8 x^4+34 x^3+8 x^2+10 x\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{192 \left(4 x^6+9 x^4+6 x^2+1\right)+192 \sqrt{x^2+1} \left(4 x^5+7 x^3+3 x\right)}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(5/2), x]","F",0,0,0,0,-1,"{}"
3042,0,0,0,0.1114515,"\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{5/2}} \, dx","Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(5/2),x]","\int \frac{\sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1+x^2\right)^{5/2}} \, dx","\frac{1}{256} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{2 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-7 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+8 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+40 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+3 \text{$\#$1}^3-\text{$\#$1}}\&\right]+\frac{\sqrt{x^2+1} \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^4+30 x^3-17 x^2-166 x-1\right)+\left(24 x^4+8 x^3+22 x^2+4 x+2\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(-20 x^5+30 x^4-27 x^3-151 x^2-7 x-117\right)+\left(24 x^5+8 x^4+34 x^3+8 x^2+10 x\right) \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{192 \left(4 x^6+9 x^4+6 x^2+1\right)+192 \sqrt{x^2+1} \left(4 x^5+7 x^3+3 x\right)}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x^2)^(5/2), x]","F",0,0,0,0,-1,"{}"
3043,0,0,0,5.0765398,"\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[(x^2*Sqrt[b + a*x])/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 (-c) \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+3 \text{$\#$1}^4 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 \text{$\#$1}^4 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^2 c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+4 \text{$\#$1}^2 b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+c^4 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 b c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$1} c^3+a^2 c}\&\right]+4 a \sqrt{\sqrt{a x+b}+c}+\frac{2 (a x+b)^{3/2}}{3 a}",1,"(2*c^2*Sqrt[b + a*x])/a + 4*a*Sqrt[c + Sqrt[b + a*x]] - (2*c*(c + Sqrt[b + a*x])^2)/a + (2*(c + Sqrt[b + a*x])^3)/(3*a) - 4*a^3*Defer[Subst][Defer[Int][x^3/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*c*Defer[Subst][Defer[Int][x^6/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*(b - c^2)^2*Defer[Subst][Defer[Int][(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6))^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a^3*c*Defer[Subst][Defer[Int][x/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*c*(4*b - 3*c^2)*Defer[Subst][Defer[Int][x^2/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*(2*b - 3*c^2)*Defer[Subst][Defer[Int][x^4/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
3044,0,0,0,4.2365082,"\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","Int[(x^2*Sqrt[b + a*x])/(x^2 - Sqrt[b + a*x]*Sqrt[c + Sqrt[b + a*x]]),x]","\int \frac{x^2 \sqrt{b+a x}}{x^2-\sqrt{b+a x} \sqrt{c+\sqrt{b+a x}}} \, dx","-4 a \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6 c-2 \text{$\#$1}^4 b+6 \text{$\#$1}^4 c^2-\text{$\#$1}^3 a^2+4 \text{$\#$1}^2 b c-4 \text{$\#$1}^2 c^3+\text{$\#$1} a^2 c+b^2-2 b c^2+c^4\&,\frac{\text{$\#$1}^6 (-c) \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+3 \text{$\#$1}^4 c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 \text{$\#$1}^4 b \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-\text{$\#$1}^3 a^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-3 \text{$\#$1}^2 c^3 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+4 \text{$\#$1}^2 b c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+\text{$\#$1} a^2 c \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+b^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)+c^4 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)-2 b c^2 \log \left(\sqrt{\sqrt{a x+b}+c}-\text{$\#$1}\right)}{8 \text{$\#$1}^7-24 \text{$\#$1}^5 c-8 \text{$\#$1}^3 b+24 \text{$\#$1}^3 c^2-3 \text{$\#$1}^2 a^2+8 \text{$\#$1} b c-8 \text{$\#$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,"(2*c^2*Sqrt[b + a*x])/a + 4*a*Sqrt[c + Sqrt[b + a*x]] - (2*c*(c + Sqrt[b + a*x])^2)/a + (2*(c + Sqrt[b + a*x])^3)/(3*a) - 4*a^3*Defer[Subst][Defer[Int][x^3/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*c*Defer[Subst][Defer[Int][x^6/(-b^2 + 2*b*(c - x^2)^2 - (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*(b - c^2)^2*Defer[Subst][Defer[Int][(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6))^(-1), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a^3*c*Defer[Subst][Defer[Int][x/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] - 4*a*c*(4*b - 3*c^2)*Defer[Subst][Defer[Int][x^2/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]] + 4*a*(2*b - 3*c^2)*Defer[Subst][Defer[Int][x^4/(b^2 - 2*b*(c - x^2)^2 + (c - x^2)*(c^3 + a^2*x - 3*c^2*x^2 + 3*c*x^4 - x^6)), x], x, Sqrt[c + Sqrt[b + a*x]]]","F",0,0,0,0,-1,"{}"
3045,0,0,0,0.8897805,"\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","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]]],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,"Defer[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]]], x]","F",0,0,0,0,-1,"{}"
3046,1,457,0,0.7682866,"\int \frac{x^4}{\sqrt[4]{b+a x^4} \left(b+2 a x^4+2 x^8\right)} \, dx","Int[x^4/((b + a*x^4)^(1/4)*(b + 2*a*x^4 + 2*x^8)),x]","-\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)}{4 \sqrt{a^2-2 b} \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)}{4 \sqrt{a^2-2 b} \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)}{4 \sqrt{a^2-2 b} \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)}{4 \sqrt{a^2-2 b} \sqrt[4]{a \sqrt{a^2-2 b}+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,"-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))])/(Sqrt[a^2 - 2*b]*(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))])/(4*Sqrt[a^2 - 2*b]*(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))])/(4*Sqrt[a^2 - 2*b]*(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))])/(4*Sqrt[a^2 - 2*b]*(a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4))","A",10,5,30,0.1667,1,"{1528, 377, 212, 208, 205}"
3047,0,0,0,2.6239635,"\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","Int[(x^4*(-q + p*x^4)*Sqrt[q + p*x^4])/(b*x^8 + a*(q + p*x^4)^4),x]","\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","-\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,"q*Defer[Int][(x^4*Sqrt[q + p*x^4])/(-(b*x^8) - a*(q + p*x^4)^4), x] + p*Defer[Int][(x^8*Sqrt[q + p*x^4])/(b*x^8 + a*(q + p*x^4)^4), x]","F",0,0,0,0,-1,"{}"
3048,1,1245,0,1.047227,"\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","Int[(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) \tan ^{-1}\left(\frac{1-\sqrt[3]{2} \sqrt[3]{3 x-1}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}-\frac{i \left(1-3 i \sqrt{3}\right)^{2/3} \sqrt[3]{3 x-1} \left(x^3+1\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{3 x-1}}{\sqrt[3]{1-3 i \sqrt{3}}}+1}{\sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}+\frac{5 i \sqrt[3]{2} \sqrt[3]{3 x-1} \left(x^3+1\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{3 x-1}}{\sqrt[3]{1-3 i \sqrt{3}}}+1}{\sqrt{3}}\right)}{9 \sqrt[3]{1-3 i \sqrt{3}} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}+\frac{i \left(1+3 i \sqrt{3}\right)^{2/3} \sqrt[3]{3 x-1} \left(x^3+1\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{3 x-1}}{\sqrt[3]{1+3 i \sqrt{3}}}+1}{\sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}-\frac{5 i \sqrt[3]{2} \sqrt[3]{3 x-1} \left(x^3+1\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{3 x-1}}{\sqrt[3]{1+3 i \sqrt{3}}}+1}{\sqrt{3}}\right)}{9 \sqrt[3]{1+3 i \sqrt{3}} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}+\frac{i \left(1-3 i \sqrt{3}\right)^{2/3} \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(-2 x-i \sqrt{3}+1\right)}{18\ 2^{2/3} \sqrt{3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}-\frac{5 i \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(-2 x-i \sqrt{3}+1\right)}{9\ 2^{2/3} \sqrt{3} \sqrt[3]{1-3 i \sqrt{3}} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}-\frac{i \left(1+3 i \sqrt{3}\right)^{2/3} \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(-2 x+i \sqrt{3}+1\right)}{18\ 2^{2/3} \sqrt{3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}+\frac{5 i \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(-2 x+i \sqrt{3}+1\right)}{9\ 2^{2/3} \sqrt{3} \sqrt[3]{1+3 i \sqrt{3}} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}+\frac{\sqrt[3]{3 x-1} \left(x^3+1\right) \log (x+1)}{6\ 2^{2/3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}-\frac{\sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(\sqrt[3]{3 x-1}+2^{2/3}\right)}{2\ 2^{2/3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}-\frac{i \left(1-3 i \sqrt{3}\right)^{2/3} \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(\sqrt[3]{1-3 i \sqrt{3}}-\sqrt[3]{2} \sqrt[3]{3 x-1}\right)}{6\ 2^{2/3} \sqrt{3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}+\frac{5 i \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(\sqrt[3]{1-3 i \sqrt{3}}-\sqrt[3]{2} \sqrt[3]{3 x-1}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1-3 i \sqrt{3}} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}+\frac{i \left(1+3 i \sqrt{3}\right)^{2/3} \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(\sqrt[3]{1+3 i \sqrt{3}}-\sqrt[3]{2} \sqrt[3]{3 x-1}\right)}{6\ 2^{2/3} \sqrt{3} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}-\frac{5 i \sqrt[3]{3 x-1} \left(x^3+1\right) \log \left(\sqrt[3]{1+3 i \sqrt{3}}-\sqrt[3]{2} \sqrt[3]{3 x-1}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1+3 i \sqrt{3}} \sqrt[3]{(1-3 x) \left(x^3+1\right)^3}}","\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)*ArcTan[(1 - 2^(1/3)*(-1 + 3*x)^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*((1 - 3*x)*(1 + x^3)^3)^(1/3))) + (((5*I)/9)*2^(1/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*ArcTan[(1 + (2*2^(1/3)*(-1 + 3*x)^(1/3))/(1 - (3*I)*Sqrt[3])^(1/3))/Sqrt[3]])/((1 - (3*I)*Sqrt[3])^(1/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) - ((I/9)*(1 - (3*I)*Sqrt[3])^(2/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*ArcTan[(1 + (2*2^(1/3)*(-1 + 3*x)^(1/3))/(1 - (3*I)*Sqrt[3])^(1/3))/Sqrt[3]])/(2^(2/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) - (((5*I)/9)*2^(1/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*ArcTan[(1 + (2*2^(1/3)*(-1 + 3*x)^(1/3))/(1 + (3*I)*Sqrt[3])^(1/3))/Sqrt[3]])/((1 + (3*I)*Sqrt[3])^(1/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) + ((I/9)*(1 + (3*I)*Sqrt[3])^(2/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*ArcTan[(1 + (2*2^(1/3)*(-1 + 3*x)^(1/3))/(1 + (3*I)*Sqrt[3])^(1/3))/Sqrt[3]])/(2^(2/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) - (((5*I)/9)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[1 - I*Sqrt[3] - 2*x])/(2^(2/3)*Sqrt[3]*(1 - (3*I)*Sqrt[3])^(1/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) + ((I/18)*(1 - (3*I)*Sqrt[3])^(2/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[1 - I*Sqrt[3] - 2*x])/(2^(2/3)*Sqrt[3]*((1 - 3*x)*(1 + x^3)^3)^(1/3)) + (((5*I)/9)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[1 + I*Sqrt[3] - 2*x])/(2^(2/3)*Sqrt[3]*(1 + (3*I)*Sqrt[3])^(1/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) - ((I/18)*(1 + (3*I)*Sqrt[3])^(2/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[1 + I*Sqrt[3] - 2*x])/(2^(2/3)*Sqrt[3]*((1 - 3*x)*(1 + x^3)^3)^(1/3)) + ((-1 + 3*x)^(1/3)*(1 + x^3)*Log[1 + x])/(6*2^(2/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) - ((-1 + 3*x)^(1/3)*(1 + x^3)*Log[2^(2/3) + (-1 + 3*x)^(1/3)])/(2*2^(2/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) + (((5*I)/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[(1 - (3*I)*Sqrt[3])^(1/3) - 2^(1/3)*(-1 + 3*x)^(1/3)])/(2^(2/3)*Sqrt[3]*(1 - (3*I)*Sqrt[3])^(1/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) - ((I/6)*(1 - (3*I)*Sqrt[3])^(2/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[(1 - (3*I)*Sqrt[3])^(1/3) - 2^(1/3)*(-1 + 3*x)^(1/3)])/(2^(2/3)*Sqrt[3]*((1 - 3*x)*(1 + x^3)^3)^(1/3)) - (((5*I)/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[(1 + (3*I)*Sqrt[3])^(1/3) - 2^(1/3)*(-1 + 3*x)^(1/3)])/(2^(2/3)*Sqrt[3]*(1 + (3*I)*Sqrt[3])^(1/3)*((1 - 3*x)*(1 + x^3)^3)^(1/3)) + ((I/6)*(1 + (3*I)*Sqrt[3])^(2/3)*(-1 + 3*x)^(1/3)*(1 + x^3)*Log[(1 + (3*I)*Sqrt[3])^(1/3) - 2^(1/3)*(-1 + 3*x)^(1/3)])/(2^(2/3)*Sqrt[3]*((1 - 3*x)*(1 + x^3)^3)^(1/3))","C",31,11,37,0.2973,1,"{6688, 6719, 2074, 56, 617, 204, 31, 843, 711, 50, 55}"
3049,1,457,0,0.5856937,"\int \frac{\left(b+a x^4\right)^{3/4}}{b+2 a x^4+2 x^8} \, dx","Int[(b + a*x^4)^(3/4)/(b + 2*a*x^4 + 2*x^8),x]","-\frac{\left(-a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(a-\sqrt{a^2-2 b}\right)^{3/4} \sqrt{a^2-2 b}}+\frac{\left(a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(\sqrt{a^2-2 b}+a\right)^{3/4} \sqrt{a^2-2 b}}-\frac{\left(-a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(a-\sqrt{a^2-2 b}\right)^{3/4} \sqrt{a^2-2 b}}+\frac{\left(a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(\sqrt{a^2-2 b}+a\right)^{3/4} \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 \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,"-1/4*((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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 - Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b]) + ((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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))])/(4*(a + Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b]) - ((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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))])/(4*(a - Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b]) + ((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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))])/(4*(a + Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b])","A",19,9,27,0.3333,1,"{1428, 408, 240, 212, 206, 203, 377, 208, 205}"
3050,0,0,0,0.5872667,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x) \sqrt{b+a^2 x^4}} \, dx","Int[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{$\#$1}^4 c^2-4 i \text{$\#$1}^3 a d^2+2 \text{$\#$1}^2 b c^2+4 i \text{$\#$1} a b d^2+b^2 c^2\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c^2-3 i \text{$\#$1}^2 a d^2+\text{$\#$1} b c^2+i a b d^2}\&\right]}{\sqrt{2}}-\frac{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}+\frac{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)*Sqrt[b + a^2*x^4]), x]","F",0,0,0,0,-1,"{}"
3051,0,0,0,0.4070454,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x) \sqrt{b+a^2 x^4}} \, dx","Int[Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)*Sqrt[b + a^2*x^4]),x]","\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x) \sqrt{b+a^2 x^4}} \, dx","\frac{i \sqrt{a} d \text{RootSum}\left[\text{$\#$1}^4 c^2-4 i \text{$\#$1}^3 a d^2+2 \text{$\#$1}^2 b c^2+4 i \text{$\#$1} a b d^2+b^2 c^2\&,\frac{b \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)-\text{$\#$1}^2 \log \left(-\text{$\#$1}+i \sqrt{a^2 x^4+b}+i \sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+i a x^2\right)}{\text{$\#$1}^3 c^2-3 i \text{$\#$1}^2 a d^2+\text{$\#$1} b c^2+i a b d^2}\&\right]}{\sqrt{2}}-\frac{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{-\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}+\frac{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2} \tan ^{-1}\left(\frac{c \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{\sqrt{a^2 d^4+b c^4}-a d^2}}\right)}{\sqrt{a^2 d^4+b c^4}}",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)*Sqrt[b + a^2*x^4]), x]","F",0,0,0,0,-1,"{}"
3052,1,518,0,2.4679586,"\int \frac{1}{\sqrt{c+b x+a x^2} \left(c^3+a^3 b^3 x^3\right)} \, dx","Int[1/(Sqrt[c + b*x + a*x^2]*(c^3 + a^3*b^3*x^3)),x]","\frac{\sqrt{2 \left(\sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}+c\right)+(1-a) b^2} \tanh ^{-1}\left(\frac{(a+1) b c-a x \left(-\sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}+a b^2-c\right)}{\sqrt{a} \sqrt{c} \sqrt{2 \left(\sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}+c\right)+(1-a) b^2} \sqrt{a x^2+b x+c}}\right)}{3 \sqrt{a} c^{5/2} \sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}}-\frac{\sqrt{-2 \sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}+(1-a) b^2+2 c} \tanh ^{-1}\left(\frac{(a+1) b c-a x \left(\sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}+a b^2-c\right)}{\sqrt{a} \sqrt{c} \sqrt{-2 \sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}+(1-a) b^2+2 c} \sqrt{a x^2+b x+c}}\right)}{3 \sqrt{a} c^{5/2} \sqrt{\left(a^2+a+1\right) b^4+b^2 (c-a c)+c^2}}-\frac{\tan ^{-1}\left(\frac{(1-2 a) b c-a x \left(b^2-2 c\right)}{2 \sqrt{a} \sqrt{c} \sqrt{(1-a) b^2-c} \sqrt{a x^2+b x+c}}\right)}{3 \sqrt{a} c^{5/2} \sqrt{(1-a) b^2-c}}","\frac{2 \tanh ^{-1}\left(-\frac{\sqrt{a} b \sqrt{a x^2+b x+c}}{\sqrt{c} \sqrt{a b^2-b^2+c}}+\frac{a b x}{\sqrt{c} \sqrt{a b^2-b^2+c}}+\frac{\sqrt{c}}{\sqrt{a b^2-b^2+c}}\right)}{3 \sqrt{a} c^{5/2} \sqrt{a b^2-b^2+c}}-\frac{\text{RootSum}\left[\text{$\#$1}^4 a^2 b^2+2 \text{$\#$1}^3 a^{3/2} b c-2 \text{$\#$1}^2 a^2 b^2 c-\text{$\#$1}^2 a b^2 c+4 \text{$\#$1}^2 a c^2-2 \text{$\#$1} a^{3/2} b c^2-4 \text{$\#$1} \sqrt{a} b c^2+a^2 b^2 c^2+a b^2 c^2+b^2 c^2\&,\frac{\text{$\#$1}^2 (-a) b \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)-4 \text{$\#$1} \sqrt{a} c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+a b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)+2 b c \log \left(-\text{$\#$1}+\sqrt{a x^2+b x+c}-\sqrt{a} x\right)}{-2 \text{$\#$1}^3 a^{3/2} b^2-3 \text{$\#$1}^2 a b c+2 \text{$\#$1} a^{3/2} b^2 c+\text{$\#$1} \sqrt{a} b^2 c-4 \text{$\#$1} \sqrt{a} c^2+a b c^2+2 b c^2}\&\right]}{3 \sqrt{a} c^2}",1,"-1/3*ArcTan[((1 - 2*a)*b*c - a*(b^2 - 2*c)*x)/(2*Sqrt[a]*Sqrt[(1 - a)*b^2 - c]*Sqrt[c]*Sqrt[c + b*x + a*x^2])]/(Sqrt[a]*Sqrt[(1 - a)*b^2 - c]*c^(5/2)) + (Sqrt[(1 - a)*b^2 + 2*(c + Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)])]*ArcTanh[((1 + a)*b*c - a*(a*b^2 - c - Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)])*x)/(Sqrt[a]*Sqrt[c]*Sqrt[(1 - a)*b^2 + 2*(c + Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)])]*Sqrt[c + b*x + a*x^2])])/(3*Sqrt[a]*c^(5/2)*Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)]) - (Sqrt[(1 - a)*b^2 + 2*c - 2*Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)]]*ArcTanh[((1 + a)*b*c - a*(a*b^2 - c + Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)])*x)/(Sqrt[a]*Sqrt[c]*Sqrt[(1 - a)*b^2 + 2*c - 2*Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)]]*Sqrt[c + b*x + a*x^2])])/(3*Sqrt[a]*c^(5/2)*Sqrt[(1 + a + a^2)*b^4 + c^2 + b^2*(c - a*c)])","A",9,6,31,0.1935,1,"{2074, 724, 204, 1035, 1029, 208}"
3053,0,0,0,0.951254,"\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Int[((-d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2),x]","\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","\frac{\sqrt{2} \sqrt{a} d \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)-2 \text{$\#$1} b c \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$1} b c+a b d}\&\right]}{c}-\frac{\sqrt{2} \sqrt{a} d \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{c}+\frac{1}{2} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{2} \sqrt{a}}",1,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x] - Sqrt[d]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] - Sqrt[-c]*x), x] - Sqrt[d]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] + Sqrt[-c]*x), x]","F",0,0,0,0,-1,"{}"
3054,0,0,0,0.7275156,"\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Int[((-d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2),x]","\int \frac{\left(-d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","\frac{\sqrt{2} \sqrt{a} d \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)-2 \text{$\#$1} b c \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$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,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x] - Sqrt[d]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] - Sqrt[-c]*x), x] - Sqrt[d]*Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/(Sqrt[d] + Sqrt[-c]*x), x]","F",0,0,0,0,-1,"{}"
3055,0,0,0,0.0645926,"\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","Int[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]","\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","\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,"Defer[Int][Sqrt[((-1 + a*x)*(1 + x^2)^2)/((1 + a*x)*(-1 + x^2)^2)], x]","F",0,0,0,0,-1,"{}"
3056,1,191,0,0.0739555,"\int \frac{1+x}{\left(-3+x^2\right) \sqrt[3]{1+x^2}} \, dx","Int[(1 + x)/((-3 + x^2)*(1 + x^2)^(1/3)),x]","-\frac{\log \left(3-x^2\right)}{4\ 2^{2/3}}+\frac{3 \log \left(2^{2/3}-\sqrt[3]{x^2+1}\right)}{4\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{x^2+1}+1}\right)}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2} \sqrt[3]{x^2+1}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{x^2+1}\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}(x)}{6\ 2^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{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(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,"ArcTan[x]/(6*2^(2/3)) - ArcTan[x/(1 + 2^(1/3)*(1 + x^2)^(1/3))]/(2*2^(2/3)) + (Sqrt[3]*ArcTan[(1 + 2^(1/3)*(1 + x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)) + ArcTanh[Sqrt[3]/x]/(2*2^(2/3)*Sqrt[3]) + ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*(1 + x^2)^(1/3)))/x]/(2*2^(2/3)*Sqrt[3]) - Log[3 - x^2]/(4*2^(2/3)) + (3*Log[2^(2/3) - (1 + x^2)^(1/3)])/(4*2^(2/3))","A",7,7,20,0.3500,1,"{1010, 392, 444, 55, 617, 204, 31}"
3057,1,101,0,0.6527652,"\int \frac{1-x^4}{\left(1+x^4\right) \sqrt[4]{-x^3+x^5}} \, dx","Int[(1 - x^4)/((1 + x^4)*(-x^3 + x^5)^(1/4)),x]","\frac{(2-2 i) x \sqrt[4]{1-x^2} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};x^2,i x^2\right)}{\sqrt[4]{x^5-x^3}}+\frac{(2+2 i) x \sqrt[4]{1-x^2} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};-i x^2,x^2\right)}{\sqrt[4]{x^5-x^3}}","\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,"((2 - 2*I)*x*(1 - x^2)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, x^2, I*x^2])/(-x^3 + x^5)^(1/4) + ((2 + 2*I)*x*(1 - x^2)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, (-I)*x^2, x^2])/(-x^3 + x^5)^(1/4)","C",9,6,28,0.2143,0,"{2056, 1586, 6715, 6725, 430, 429}"
3058,1,101,0,0.5634937,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^6} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((-x^2 + x^6)^(1/4)*(1 + x^8)),x]","-\frac{(1-i) x \sqrt[4]{1-x^4} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};x^4,i x^4\right)}{\sqrt[4]{x^6-x^2}}-\frac{(1+i) x \sqrt[4]{1-x^4} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};-i x^4,x^4\right)}{\sqrt[4]{x^6-x^2}}","\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,"((-1 + I)*x*(1 - x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, x^4, I*x^4])/(-x^2 + x^6)^(1/4) - ((1 + I)*x*(1 - x^4)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, (-I)*x^4, x^4])/(-x^2 + x^6)^(1/4)","C",9,6,26,0.2308,0,"{2056, 1586, 6715, 6725, 430, 429}"
3059,1,101,0,0.4839657,"\int \frac{-1+x^8}{\sqrt[4]{-x^2+x^6} \left(1+x^8\right)} \, dx","Int[(-1 + x^8)/((-x^2 + x^6)^(1/4)*(1 + x^8)),x]","-\frac{(1-i) x \sqrt[4]{1-x^4} F_1\left(\frac{1}{8};-\frac{3}{4},1;\frac{9}{8};x^4,i x^4\right)}{\sqrt[4]{x^6-x^2}}-\frac{(1+i) x \sqrt[4]{1-x^4} F_1\left(\frac{1}{8};1,-\frac{3}{4};\frac{9}{8};-i x^4,x^4\right)}{\sqrt[4]{x^6-x^2}}","\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,"((-1 + I)*x*(1 - x^4)^(1/4)*AppellF1[1/8, -3/4, 1, 9/8, x^4, I*x^4])/(-x^2 + x^6)^(1/4) - ((1 + I)*x*(1 - x^4)^(1/4)*AppellF1[1/8, 1, -3/4, 9/8, (-I)*x^4, x^4])/(-x^2 + x^6)^(1/4)","C",9,6,26,0.2308,0,"{2056, 1586, 6715, 6725, 430, 429}"
3060,0,0,0,0.313297,"\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","Int[(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,"Defer[Int][(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",0,0,0,0,-1,"{}"
3061,0,0,0,0.668523,"\int \frac{b^2+a x}{\left(-b^2+a x\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[(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,"Defer[Int][1/Sqrt[b + Sqrt[b^2 + a*x^2]], x] - 2*b^2*Defer[Int][1/((b^2 - a*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",0,0,0,0,-1,"{}"
3062,1,465,0,0.601634,"\int \frac{\left(-b+a x^4\right)^{3/4}}{b-2 a x^4+2 x^8} \, dx","Int[(-b + a*x^4)^(3/4)/(b - 2*a*x^4 + 2*x^8),x]","\frac{\left(-a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(a-\sqrt{a^2-2 b}\right)^{3/4} \sqrt{a^2-2 b}}-\frac{\left(a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(\sqrt{a^2-2 b}+a\right)^{3/4} \sqrt{a^2-2 b}}+\frac{\left(-a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(a-\sqrt{a^2-2 b}\right)^{3/4} \sqrt{a^2-2 b}}-\frac{\left(a \sqrt{a^2-2 b}+a^2-2 b\right)^{3/4} \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)}{4 \left(\sqrt{a^2-2 b}+a\right)^{3/4} \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 \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,"((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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))])/(4*(a - Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b]) - ((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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))])/(4*(a + Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b]) + ((a^2 - a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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))])/(4*(a - Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b]) - ((a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(3/4)*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))])/(4*(a + Sqrt[a^2 - 2*b])^(3/4)*Sqrt[a^2 - 2*b])","A",19,9,29,0.3103,1,"{1428, 408, 240, 212, 206, 203, 377, 208, 205}"
3063,0,0,0,1.0421095,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Int[(-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{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+2 \text{$\#$1} a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$1} b c+a b d}\&\right]}{\sqrt{a} c}+\frac{2 \sqrt{2} \sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{x}{2 \sqrt{\sqrt{a^2 x^4+b}+a x^2}}+\frac{\log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{2 \sqrt{2} \sqrt{a}}",1,"Defer[Int][1/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x] - Sqrt[d]*Defer[Int][1/((Sqrt[d] - Sqrt[-c]*x)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]), x] - Sqrt[d]*Defer[Int][1/((Sqrt[d] + Sqrt[-c]*x)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]), x]","F",0,0,0,0,-1,"{}"
3064,0,0,0,0.8023159,"\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","Int[(-d + c*x^2)/((d + c*x^2)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]),x]","\int \frac{-d+c x^2}{\left(d+c x^2\right) \sqrt{a x^2+\sqrt{b+a^2 x^4}}} \, dx","-\frac{\sqrt{2} \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 a c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a b c d \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+2 \text{$\#$1} a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 c+3 \text{$\#$1}^2 a d-\text{$\#$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,"Defer[Int][1/Sqrt[a*x^2 + Sqrt[b + a^2*x^4]], x] - Sqrt[d]*Defer[Int][1/((Sqrt[d] - Sqrt[-c]*x)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]), x] - Sqrt[d]*Defer[Int][1/((Sqrt[d] + Sqrt[-c]*x)*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]), x]","F",0,0,0,0,-1,"{}"
3065,1,465,0,0.3842617,"\int \frac{x^4}{\sqrt[4]{-b+a x^4} \left(b-2 a x^4+2 x^8\right)} \, dx","Int[x^4/((-b + a*x^4)^(1/4)*(b - 2*a*x^4 + 2*x^8)),x]","\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)}{4 \sqrt{a^2-2 b} \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)}{4 \sqrt{a^2-2 b} \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)}{4 \sqrt{a^2-2 b} \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)}{4 \sqrt{a^2-2 b} \sqrt[4]{a \sqrt{a^2-2 b}+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))])/(4*Sqrt[a^2 - 2*b]*(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))])/(4*Sqrt[a^2 - 2*b]*(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))])/(4*Sqrt[a^2 - 2*b]*(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))])/(4*Sqrt[a^2 - 2*b]*(a^2 + a*Sqrt[a^2 - 2*b] - 2*b)^(1/4))","A",10,5,32,0.1562,1,"{1528, 377, 212, 208, 205}"
3066,0,0,0,3.004708,"\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","Int[(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,"(20*b*x^(1/4)*(-b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^14/((-b + a*x^4)^(1/4)*(-c + b*x^20 - a*x^24)), x], x, x^(1/4)])/(-(b*x) + a*x^2)^(1/4) + (24*a*x^(1/4)*(-b + a*x)^(1/4)*Defer[Subst][Defer[Int][x^18/((-b + a*x^4)^(1/4)*(c - b*x^20 + a*x^24)), x], x, x^(1/4)])/(-(b*x) + a*x^2)^(1/4)","F",0,0,0,0,-1,"{}"
3067,1,513,0,1.0572336,"\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","Int[(-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{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 \left(\sqrt{d}+1\right) \left(b-a \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 (1-d) x-2 \left(1-\sqrt{d}\right) \left(a \sqrt{d}+b\right)\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(-\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x-b}\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x-b}\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x-b}}\right)}{2 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{2 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","\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,"-1/2*(Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*(-b + x)^(1/3))])/((a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) + (Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*(-b + x)^(1/3))])/(2*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) - ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 + Sqrt[d])*(b - a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) + ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[-2*(1 - Sqrt[d])*(b + a*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[-(d^(1/6)*(-a + x)^(1/3)) - (-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) + (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[d^(1/6)*(-a + x)^(1/3) - (-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3))","A",9,5,52,0.09615,1,"{6719, 911, 105, 59, 91}"
3068,1,451,0,1.0450835,"\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","Int[(b - a*x^4 + 2*x^8)/((b + a*x^4)^(1/4)*(-b - 2*a*x^4 + x^8)),x]","\frac{3 \left(-a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(a-\sqrt{a^2+b}\right)^{3/4}}-\frac{3 \left(a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(\sqrt{a^2+b}+a\right)^{3/4}}+\frac{3 \left(-a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(a-\sqrt{a^2+b}\right)^{3/4}}-\frac{3 \left(a \sqrt{a^2+b}+a^2+b\right)^{3/4} \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)}{4 \sqrt{a^2+b} \left(\sqrt{a^2+b}+a\right)^{3/4}}+\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 \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,"ArcTan[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (3*(a^2 + b - a*Sqrt[a^2 + b])^(3/4)*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))])/(4*Sqrt[a^2 + b]*(a - Sqrt[a^2 + b])^(3/4)) - (3*(a^2 + b + a*Sqrt[a^2 + b])^(3/4)*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))])/(4*Sqrt[a^2 + b]*(a + Sqrt[a^2 + b])^(3/4)) + ArcTanh[(a^(1/4)*x)/(b + a*x^4)^(1/4)]/a^(1/4) + (3*(a^2 + b - a*Sqrt[a^2 + b])^(3/4)*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))])/(4*Sqrt[a^2 + b]*(a - Sqrt[a^2 + b])^(3/4)) - (3*(a^2 + b + a*Sqrt[a^2 + b])^(3/4)*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))])/(4*Sqrt[a^2 + b]*(a + Sqrt[a^2 + b])^(3/4))","A",25,10,40,0.2500,1,"{6728, 240, 212, 206, 203, 1428, 408, 377, 208, 205}"
3069,0,0,0,0.3319865,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[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{c+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","-\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,"Defer[Int][Sqrt[-b + a^2*x^2]/Sqrt[c + Sqrt[a*x + Sqrt[-b + a^2*x^2]]], x]","F",0,0,0,0,-1,"{}"
3070,0,0,0,0.3439874,"\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","Int[(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,"((1 + x^2)^(1/3)*(3 + 7*x + 2*x^2)*Defer[Int][(1 + x)/((1 + x^2)^(1/3)*(3 + 7*x + 2*x^2)), x])/((1 + x^2)*(3 + 7*x + 2*x^2)^3)^(1/3)","F",0,0,0,0,-1,"{}"
3071,1,45,0,0.1550479,"\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","Int[(-1 + k^2*x^4)/(Sqrt[(1 - x^2)*(1 - k^2*x^2)]*(1 + k^2*x^4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{k^2+1} x}{\sqrt{\left(1-x^2\right) \left(1-k^2 x^2\right)}}\right)}{\sqrt{k^2+1}}","\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,"-(ArcTan[(Sqrt[1 + k^2]*x)/Sqrt[(1 - x^2)*(1 - k^2*x^2)]]/Sqrt[1 + k^2])","A",2,2,43,0.04651,1,"{2112, 203}"
3072,1,213,0,0.0889989,"\int \frac{1+2 x}{\sqrt[3]{-1+x^2} \left(3+x^2\right)} \, dx","Int[(1 + 2*x)/((-1 + x^2)^(1/3)*(3 + x^2)),x]","\frac{\log \left(x^2+3\right)}{2\ 2^{2/3}}-\frac{3 \log \left(\sqrt[3]{x^2-1}+2^{2/3}\right)}{2\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\sqrt[3]{2} \sqrt[3]{x^2-1}}{\sqrt{3}}\right)}{2^{2/3}}-\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left((-1)^{2/3} \sqrt[3]{2} \sqrt[3]{x^2-1}+1\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{1}{2} \left(-\frac{1}{2}\right)^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{-1} x}{\sqrt[3]{2} \sqrt[3]{x^2-1}+\sqrt[3]{-1}}\right)-\frac{(-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{1}{6} \left(-\frac{1}{2}\right)^{2/3} \tanh ^{-1}(x)","\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,"-1/2*((-1)^(2/3)*ArcTan[Sqrt[3]/x])/(2^(2/3)*Sqrt[3]) - (Sqrt[3]*ArcTan[(1 - 2^(1/3)*(-1 + x^2)^(1/3))/Sqrt[3]])/2^(2/3) - ((-1)^(2/3)*ArcTan[(Sqrt[3]*(1 + (-1)^(2/3)*2^(1/3)*(-1 + x^2)^(1/3)))/x])/(2*2^(2/3)*Sqrt[3]) + ((-1/2)^(2/3)*ArcTanh[x])/6 - ((-1/2)^(2/3)*ArcTanh[((-1)^(1/3)*x)/((-1)^(1/3) + 2^(1/3)*(-1 + x^2)^(1/3))])/2 + Log[3 + x^2]/(2*2^(2/3)) - (3*Log[2^(2/3) + (-1 + x^2)^(1/3)])/(2*2^(2/3))","A",7,7,22,0.3182,1,"{1010, 393, 444, 56, 617, 204, 31}"
3073,1,758,0,1.4969661,"\int \frac{x}{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}} \, dx","Int[x/Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]],x]","-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(\sqrt{1-\sqrt{1-\frac{1}{x}}}+1\right)}{8 \left(\sqrt{1-\frac{1}{x}}+1\right)}-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(\sqrt{1-\sqrt{1-\frac{1}{x}}}+1\right)}{8 \left(\sqrt{1-\frac{1}{x}}+1\right)^2}+\frac{59}{256 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)}-\frac{59}{256 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)}-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(11 \sqrt{1-\sqrt{1-\frac{1}{x}}}+12\right)}{64 \left(\sqrt{1-\frac{1}{x}}+1\right)}+\frac{23}{256 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^2}-\frac{23}{256 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^2}+\frac{5}{192 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^3}-\frac{5}{192 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^3}+\frac{1}{128 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^4}-\frac{1}{128 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^4}-\frac{1}{128} \sqrt{527+373 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{\sqrt{2}-1}}\right)-\frac{\left(1+\sqrt{2}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{\sqrt{2}-1}}\right)}{16 \sqrt{2}}+\frac{59}{128} \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)+\frac{1}{128} \sqrt{373 \sqrt{2}-527} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)+\frac{\left(\sqrt{2}-1\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)}{16 \sqrt{2}}","\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,"1/(128*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^4) + 5/(192*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^3) + 23/(256*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^2) + 59/(256*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])) - 1/(128*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^4) - 5/(192*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^3) - 23/(256*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^2) - 59/(256*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(1 + Sqrt[1 - Sqrt[1 - x^(-1)]]))/(8*(1 + Sqrt[1 - x^(-1)])^2) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(1 + Sqrt[1 - Sqrt[1 - x^(-1)]]))/(8*(1 + Sqrt[1 - x^(-1)])) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(12 + 11*Sqrt[1 - Sqrt[1 - x^(-1)]]))/(64*(1 + Sqrt[1 - x^(-1)])) - ((1 + Sqrt[2])^(3/2)*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[-1 + Sqrt[2]]])/(16*Sqrt[2]) - (Sqrt[527 + 373*Sqrt[2]]*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[-1 + Sqrt[2]]])/128 + (59*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]])/128 + ((-1 + Sqrt[2])^(3/2)*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[1 + Sqrt[2]]])/(16*Sqrt[2]) + (Sqrt[-527 + 373*Sqrt[2]]*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[1 + Sqrt[2]]])/128","A",16,6,29,0.2069,0,"{1586, 1692, 207, 1178, 1166, 203}"
3074,1,131,0,0.5478639,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1-x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Int[((-x^2 + x^6)^(1/4)*(1 - x^4 + x^8))/(x^4*(1 + x^4)),x]","-\frac{6 \sqrt[4]{x^6-x^2} F_1\left(-\frac{5}{8};-\frac{1}{4},1;\frac{3}{8};x^4,-x^4\right)}{5 \sqrt[4]{1-x^4} x^3}+\frac{4 \sqrt[4]{x^6-x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};x^4\right)}{5 \sqrt[4]{1-x^4}}+\frac{2}{5} \sqrt[4]{x^6-x^2} x+\frac{4 \sqrt[4]{x^6-x^2}}{5 x^3}","-\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,"(4*(-x^2 + x^6)^(1/4))/(5*x^3) + (2*x*(-x^2 + x^6)^(1/4))/5 - (6*(-x^2 + x^6)^(1/4)*AppellF1[-5/8, -1/4, 1, 3/8, x^4, -x^4])/(5*x^3*(1 - x^4)^(1/4)) + (4*x*(-x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, x^4])/(5*(1 - x^4)^(1/4))","C",14,10,34,0.2941,0,"{2056, 6725, 277, 329, 365, 364, 279, 466, 511, 510}"
3075,1,131,0,0.4541532,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1-x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Int[((-x^2 + x^6)^(1/4)*(1 - x^4 + x^8))/(x^4*(1 + x^4)),x]","-\frac{6 \sqrt[4]{x^6-x^2} F_1\left(-\frac{5}{8};-\frac{1}{4},1;\frac{3}{8};x^4,-x^4\right)}{5 \sqrt[4]{1-x^4} x^3}+\frac{4 \sqrt[4]{x^6-x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};x^4\right)}{5 \sqrt[4]{1-x^4}}+\frac{2}{5} \sqrt[4]{x^6-x^2} x+\frac{4 \sqrt[4]{x^6-x^2}}{5 x^3}","-\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,"(4*(-x^2 + x^6)^(1/4))/(5*x^3) + (2*x*(-x^2 + x^6)^(1/4))/5 - (6*(-x^2 + x^6)^(1/4)*AppellF1[-5/8, -1/4, 1, 3/8, x^4, -x^4])/(5*x^3*(1 - x^4)^(1/4)) + (4*x*(-x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, x^4])/(5*(1 - x^4)^(1/4))","C",14,10,34,0.2941,0,"{2056, 6725, 277, 329, 365, 364, 279, 466, 511, 510}"
3076,1,111,0,0.4416876,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1+x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Int[((-x^2 + x^6)^(1/4)*(1 + x^4 + x^8))/(x^4*(1 + x^4)),x]","-\frac{2 \sqrt[4]{x^6-x^2} F_1\left(-\frac{5}{8};-\frac{1}{4},1;\frac{3}{8};x^4,-x^4\right)}{5 \sqrt[4]{1-x^4} x^3}+\frac{4 \sqrt[4]{x^6-x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};x^4\right)}{15 \sqrt[4]{1-x^4}}+\frac{2}{5} \sqrt[4]{x^6-x^2} x","-\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*(-x^2 + x^6)^(1/4))/5 - (2*(-x^2 + x^6)^(1/4)*AppellF1[-5/8, -1/4, 1, 3/8, x^4, -x^4])/(5*x^3*(1 - x^4)^(1/4)) + (4*x*(-x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, x^4])/(15*(1 - x^4)^(1/4))","C",10,9,32,0.2812,0,"{2056, 6725, 279, 329, 365, 364, 466, 511, 510}"
3077,1,111,0,0.3978301,"\int \frac{\sqrt[4]{-x^2+x^6} \left(1+x^4+x^8\right)}{x^4 \left(1+x^4\right)} \, dx","Int[((-x^2 + x^6)^(1/4)*(1 + x^4 + x^8))/(x^4*(1 + x^4)),x]","-\frac{2 \sqrt[4]{x^6-x^2} F_1\left(-\frac{5}{8};-\frac{1}{4},1;\frac{3}{8};x^4,-x^4\right)}{5 \sqrt[4]{1-x^4} x^3}+\frac{4 \sqrt[4]{x^6-x^2} x \, _2F_1\left(\frac{3}{8},\frac{3}{4};\frac{11}{8};x^4\right)}{15 \sqrt[4]{1-x^4}}+\frac{2}{5} \sqrt[4]{x^6-x^2} x","-\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*(-x^2 + x^6)^(1/4))/5 - (2*(-x^2 + x^6)^(1/4)*AppellF1[-5/8, -1/4, 1, 3/8, x^4, -x^4])/(5*x^3*(1 - x^4)^(1/4)) + (4*x*(-x^2 + x^6)^(1/4)*Hypergeometric2F1[3/8, 3/4, 11/8, x^4])/(15*(1 - x^4)^(1/4))","C",10,9,32,0.2812,0,"{2056, 6725, 279, 329, 365, 364, 466, 511, 510}"
3078,1,510,0,0.2681574,"\int \frac{\sqrt[3]{b^2 x^2+a^3 x^3}}{-b+a x} \, dx","Int[(b^2*x^2 + a^3*x^3)^(1/3)/(-b + a*x),x]","\frac{\sqrt[3]{a^3 x^3+b^2 x^2}}{a}-\frac{b \left(3 a^2+b\right) \sqrt[3]{a^3 x^3+b^2 x^2} \log \left(a^3 x+b^2\right)}{6 a^3 x^{2/3} \sqrt[3]{a^3 x+b^2}}-\frac{b \left(3 a^2+b\right) \sqrt[3]{a^3 x^3+b^2 x^2} \log \left(\frac{a \sqrt[3]{x}}{\sqrt[3]{a^3 x+b^2}}-1\right)}{2 a^3 x^{2/3} \sqrt[3]{a^3 x+b^2}}-\frac{b \left(3 a^2+b\right) \sqrt[3]{a^3 x^3+b^2 x^2} \tan ^{-1}\left(\frac{2 a \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x+b^2}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} a^3 x^{2/3} \sqrt[3]{a^3 x+b^2}}-\frac{b \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2} \log (a x-b)}{2 a^{5/3} x^{2/3} \sqrt[3]{a^3 x+b^2}}+\frac{3 b \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2} \log \left(\sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2+b}-\sqrt[3]{a^3 x+b^2}\right)}{2 a^{5/3} x^{2/3} \sqrt[3]{a^3 x+b^2}}+\frac{\sqrt{3} b \sqrt[3]{a^2+b} \sqrt[3]{a^3 x^3+b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2+b}}{\sqrt{3} \sqrt[3]{a^3 x+b^2}}+\frac{1}{\sqrt{3}}\right)}{a^{5/3} x^{2/3} \sqrt[3]{a^3 x+b^2}}","\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,"(b^2*x^2 + a^3*x^3)^(1/3)/a - (b*(3*a^2 + b)*(b^2*x^2 + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a*x^(1/3))/(Sqrt[3]*(b^2 + a^3*x)^(1/3))])/(Sqrt[3]*a^3*x^(2/3)*(b^2 + a^3*x)^(1/3)) + (Sqrt[3]*b*(a^2 + b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a^(1/3)*(a^2 + b)^(1/3)*x^(1/3))/(Sqrt[3]*(b^2 + a^3*x)^(1/3))])/(a^(5/3)*x^(2/3)*(b^2 + a^3*x)^(1/3)) - (b*(a^2 + b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)*Log[-b + a*x])/(2*a^(5/3)*x^(2/3)*(b^2 + a^3*x)^(1/3)) - (b*(3*a^2 + b)*(b^2*x^2 + a^3*x^3)^(1/3)*Log[b^2 + a^3*x])/(6*a^3*x^(2/3)*(b^2 + a^3*x)^(1/3)) - (b*(3*a^2 + b)*(b^2*x^2 + a^3*x^3)^(1/3)*Log[-1 + (a*x^(1/3))/(b^2 + a^3*x)^(1/3)])/(2*a^3*x^(2/3)*(b^2 + a^3*x)^(1/3)) + (3*b*(a^2 + b)^(1/3)*(b^2*x^2 + a^3*x^3)^(1/3)*Log[a^(1/3)*(a^2 + b)^(1/3)*x^(1/3) - (b^2 + a^3*x)^(1/3)])/(2*a^(5/3)*x^(2/3)*(b^2 + a^3*x)^(1/3))","A",5,5,29,0.1724,1,"{2056, 101, 157, 59, 91}"
3079,0,0,0,1.2104711,"\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","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]]]),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,"Defer[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]]]), x]","F",0,0,0,0,-1,"{}"
3080,0,0,0,5.3840881,"\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","Int[((-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,"(-3*(-a + a*x^2 + b*x^3)^(1/4)*Defer[Int][(-c + c*x^2 + d*x^3)^(1/4)/(x^10*(-a + a*x^2 + b*x^3)^(1/4)), x])/(((a - a*x^2 - b*x^3)/(c - c*x^2 - d*x^3))^(1/4)*(-c + c*x^2 + d*x^3)^(1/4)) + (7*(-a + a*x^2 + b*x^3)^(1/4)*Defer[Int][(-c + c*x^2 + d*x^3)^(1/4)/(x^8*(-a + a*x^2 + b*x^3)^(1/4)), x])/(((a - a*x^2 - b*x^3)/(c - c*x^2 - d*x^3))^(1/4)*(-c + c*x^2 + d*x^3)^(1/4)) - (5*(-a + a*x^2 + b*x^3)^(1/4)*Defer[Int][(-c + c*x^2 + d*x^3)^(1/4)/(x^6*(-a + a*x^2 + b*x^3)^(1/4)), x])/(((a - a*x^2 - b*x^3)/(c - c*x^2 - d*x^3))^(1/4)*(-c + c*x^2 + d*x^3)^(1/4)) - (2*(-a + a*x^2 + b*x^3)^(1/4)*Defer[Int][(-c + c*x^2 + d*x^3)^(1/4)/(x^4*(-a + a*x^2 + b*x^3)^(1/4)), x])/(((a - a*x^2 - b*x^3)/(c - c*x^2 - d*x^3))^(1/4)*(-c + c*x^2 + d*x^3)^(1/4)) + ((-a + a*x^2 + b*x^3)^(1/4)*Defer[Int][(-c + c*x^2 + d*x^3)^(1/4)/(x^2*(-a + a*x^2 + b*x^3)^(1/4)), x])/(((a - a*x^2 - b*x^3)/(c - c*x^2 - d*x^3))^(1/4)*(-c + c*x^2 + d*x^3)^(1/4))","F",0,0,0,0,-1,"{}"
3081,0,0,0,3.0522107,"\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","Int[((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{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (-6 x-16)+\sqrt{x^2+1} \left((8-60 x) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-6 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-60 x^2+8 x+75\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{105 \sqrt{\sqrt{x^2+1}+x}}+\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-Defer[Int][Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x] + (I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/2 + (I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
3082,0,0,0,2.4236807,"\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Int[((1 + x^4)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\int \frac{\left(1+x^4\right) \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^2-1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^5-3 \text{$\#$1}^3+2 \text{$\#$1}}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^5 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$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,"-Defer[Int][Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x] + (I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I - x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/2 + (I/2)*Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(I + x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
3083,0,0,0,0.3097707,"\int \sqrt{b+a^2 x^2} \sqrt{c+\sqrt{a x+\sqrt{b+a^2 x^2}}} \, dx","Int[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{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)}{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,"Defer[Int][Sqrt[b + a^2*x^2]*Sqrt[c + Sqrt[a*x + Sqrt[b + a^2*x^2]]], x]","F",0,0,0,0,-1,"{}"
3084,1,459,0,0.9349873,"\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","Int[Sqrt[(-81 + 27*x + 135*x^2 - 150*x^3 + 65*x^4 - 13*x^5 + x^6)^3]/(-1 + x),x]","-\frac{\left(-x^2+x+1\right) \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3} (1-x)^4}{9 (3-x)^6}-\frac{229 \left(-x^2+x+1\right) \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3} (1-x)^3}{144 (3-x)^6}-\frac{19927 \left(-x^2+x+1\right) \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3} (1-x)^2}{2016 (3-x)^6}-\frac{281233 \left(-x^2+x+1\right) \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3} (1-x)}{8064 (3-x)^6}-\frac{6158183 \left(-x^2+x+1\right) \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3}}{80640 (3-x)^6}+\frac{(5567931-6941558 x) \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3}}{32768 (3-x)^6 \left(-x^2+x+1\right)}+\frac{(903871-1283454 x) \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3}}{12288 (3-x)^6}-\frac{64 \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3} \tan ^{-1}\left(\frac{3-x}{2 \sqrt{x^2-x-1}}\right)}{(3-x)^6 \left(x^2-x-1\right)^{3/2}}+\frac{19451047 \sqrt{-(3-x)^{12} \left(-x^2+x+1\right)^3} \tanh ^{-1}\left(\frac{1-2 x}{2 \sqrt{x^2-x-1}}\right)}{65536 (3-x)^6 \left(x^2-x-1\right)^{3/2}}","-\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,"((903871 - 1283454*x)*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)])/(12288*(3 - x)^6) + ((5567931 - 6941558*x)*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)])/(32768*(3 - x)^6*(1 + x - x^2)) - (6158183*(1 + x - x^2)*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)])/(80640*(3 - x)^6) - (281233*(1 - x)*(1 + x - x^2)*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)])/(8064*(3 - x)^6) - (19927*(1 - x)^2*(1 + x - x^2)*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)])/(2016*(3 - x)^6) - (229*(1 - x)^3*(1 + x - x^2)*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)])/(144*(3 - x)^6) - ((1 - x)^4*(1 + x - x^2)*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)])/(9*(3 - x)^6) - (64*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)]*ArcTan[(3 - x)/(2*Sqrt[-1 - x + x^2])])/((3 - x)^6*(-1 - x + x^2)^(3/2)) + (19451047*Sqrt[-((3 - x)^12*(1 + x - x^2)^3)]*ArcTanh[(1 - 2*x)/(2*Sqrt[-1 - x + x^2])])/(65536*(3 - x)^6*(-1 - x + x^2)^(3/2))","A",14,9,40,0.2250,1,"{6688, 6719, 1653, 814, 843, 621, 206, 724, 204}"
3085,1,2475,0,11.2752072,"\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","Int[((1 + x^2 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)^2),x]","-\frac{6 i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{-1+\sqrt{5}} x\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((-2+i)+\sqrt{5}\right)}}-\frac{2 i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{-1+\sqrt{5}} x\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \left(1-\sqrt{5}\right) \sqrt{(3+i)-(1+i) \sqrt{5}}}+\frac{6 i \tan ^{-1}\left(\frac{(1+i) \left(i \sqrt{-1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((-2+i)+\sqrt{5}\right)}}+\frac{2 i \tan ^{-1}\left(\frac{(1+i) \left(i \sqrt{-1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \left(1-\sqrt{5}\right) \sqrt{(3+i)-(1+i) \sqrt{5}}}+\frac{2 i \sqrt{\frac{2}{-1+\sqrt{5}}} \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(2-i \sqrt{2 \left(-1+\sqrt{5}\right)} x\right)}{\sqrt{(-1-2 i)+\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((-1-2 i)+\sqrt{5}\right)^{3/2}}-\frac{2 i \sqrt{\frac{2}{-1+\sqrt{5}}} \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \sqrt{2 \left(-1+\sqrt{5}\right)} x+2\right)}{\sqrt{(-1-2 i)+\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((-1-2 i)+\sqrt{5}\right)^{3/2}}+\frac{2 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left(1+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}-\frac{6 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((2-i)+\sqrt{5}\right)}}-\frac{2 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left(1+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}+\frac{6 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((2-i)+\sqrt{5}\right)}}+\frac{2 \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(2-\sqrt{2 \left(1+\sqrt{5}\right)} x\right)}{\sqrt{(-1-2 i)-\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((1+2 i)+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}-\frac{2 \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{2 \left(1+\sqrt{5}\right)} x+2\right)}{\sqrt{(-1-2 i)-\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((1+2 i)+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}-\frac{\left(\frac{3}{5}-\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{-1+\sqrt{5}} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((-2-i)+\sqrt{5}\right)}}-\frac{i \sqrt{(2+2 i) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{-1+\sqrt{5}} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)-(15+5 i) \sqrt{5}}+\frac{\left(\frac{3}{5}-\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{i \sqrt{-1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((-2-i)+\sqrt{5}\right)}}+\frac{i \sqrt{(2+2 i) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{i \sqrt{-1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)-(15+5 i) \sqrt{5}}+\frac{\left(\frac{1}{25}-\frac{3 i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{2-i \sqrt{2 \left(-1+\sqrt{5}\right)} x}{\sqrt{(4+2 i)-2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3-\sqrt{5}}-\frac{\left(\frac{1}{25}-\frac{3 i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{i \sqrt{2 \left(-1+\sqrt{5}\right)} x+2}{\sqrt{(4+2 i)-2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3-\sqrt{5}}-\frac{\sqrt{(2+2 i) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)+(15+5 i) \sqrt{5}}+\frac{\left(\frac{3}{5}+\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((2+i)+\sqrt{5}\right)}}+\frac{\sqrt{(2+2 i) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)+(15+5 i) \sqrt{5}}-\frac{\left(\frac{3}{5}+\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((2+i)+\sqrt{5}\right)}}-\frac{\left(\frac{3}{25}+\frac{i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{2-\sqrt{2 \left(1+\sqrt{5}\right)} x}{\sqrt{(4+2 i)+2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3+\sqrt{5}}+\frac{\left(\frac{3}{25}+\frac{i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{5}\right)} x+2}{\sqrt{(4+2 i)+2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3+\sqrt{5}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2+\sqrt{x^4+1}}}\right)}{\sqrt{2}}+\frac{16 i \sqrt{1-i x^2}}{5 \left((16+8 i)-8 \sqrt{5}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}+\frac{2 i \sqrt{1-i x^2}}{5 \left((2+i)+\sqrt{5}\right) \left(i \sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}+\frac{2 i \sqrt{1-i x^2}}{5 \left((-2-i)+\sqrt{5}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}-\frac{2 i \sqrt{1-i x^2}}{5 \left((2+i)+\sqrt{5}\right) \left(2 x+i \sqrt{2 \left(1+\sqrt{5}\right)}\right)}+\frac{2 i \sqrt{i x^2+1}}{5 \left((-2+i)+\sqrt{5}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}-\frac{2 i \sqrt{i x^2+1}}{5 \left((2-i)+\sqrt{5}\right) \left(i \sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}-\frac{2 i \sqrt{i x^2+1}}{5 \left((-2+i)+\sqrt{5}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}+\frac{2 i \sqrt{i x^2+1}}{5 \left((2-i)+\sqrt{5}\right) \left(2 x+i \sqrt{2 \left(1+\sqrt{5}\right)}\right)}","-\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,"(((16*I)/5)*Sqrt[1 - I*x^2])/(((16 + 8*I) - 8*Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x)) + (((2*I)/5)*Sqrt[1 - I*x^2])/(((2 + I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] - 2*x)) + (((2*I)/5)*Sqrt[1 - I*x^2])/(((-2 - I) + Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x)) - (((2*I)/5)*Sqrt[1 - I*x^2])/(((2 + I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] + 2*x)) + (((2*I)/5)*Sqrt[1 + I*x^2])/(((-2 + I) + Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x)) - (((2*I)/5)*Sqrt[1 + I*x^2])/(((2 - I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] - 2*x)) - (((2*I)/5)*Sqrt[1 + I*x^2])/(((-2 + I) + Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x)) + (((2*I)/5)*Sqrt[1 + I*x^2])/(((2 - I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] + 2*x)) - (((2*I)/5)*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/((1 - Sqrt[5])*Sqrt[(3 + I) - (1 + I)*Sqrt[5]]) - (((6*I)/5)*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + (((2*I)/5)*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/((1 - Sqrt[5])*Sqrt[(3 + I) - (1 + I)*Sqrt[5]]) + (((6*I)/5)*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + (((2*I)/5)*Sqrt[2/(-1 + Sqrt[5])]*ArcTan[((1/2 + I/2)*(2 - I*Sqrt[2*(-1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) + Sqrt[5]]*Sqrt[1 + I*x^2])])/((-1 - 2*I) + Sqrt[5])^(3/2) - (((2*I)/5)*Sqrt[2/(-1 + Sqrt[5])]*ArcTan[((1/2 + I/2)*(2 + I*Sqrt[2*(-1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) + Sqrt[5]]*Sqrt[1 + I*x^2])])/((-1 - 2*I) + Sqrt[5])^(3/2) - (6*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) + (2*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*(1 + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) + (6*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) - (2*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*(1 + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) + (2*ArcTan[((1/2 + I/2)*(2 - Sqrt[2*(1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) - Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*((1 + 2*I) + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) - (2*ArcTan[((1/2 + I/2)*(2 + Sqrt[2*(1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) - Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*((1 + 2*I) + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) - (I*Sqrt[(2 + 2*I)*((-2 - I) + Sqrt[5])]*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) - (15 + 5*I)*Sqrt[5]) - ((3/5 - (3*I)/5)*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((-2 - I) + Sqrt[5])] + (I*Sqrt[(2 + 2*I)*((-2 - I) + Sqrt[5])]*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) - (15 + 5*I)*Sqrt[5]) + ((3/5 - (3*I)/5)*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((-2 - I) + Sqrt[5])] + ((1/25 - (3*I)/25)*Sqrt[(1/2 + I/2)*((-2 - I) + Sqrt[5])]*ArcTanh[(2 - I*Sqrt[2*(-1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) - (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 - Sqrt[5]) - ((1/25 - (3*I)/25)*Sqrt[(1/2 + I/2)*((-2 - I) + Sqrt[5])]*ArcTanh[(2 + I*Sqrt[2*(-1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) - (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 - Sqrt[5]) + ((3/5 + (3*I)/5)*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((2 + I) + Sqrt[5])] - (Sqrt[(2 + 2*I)*((2 + I) + Sqrt[5])]*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) + (15 + 5*I)*Sqrt[5]) - ((3/5 + (3*I)/5)*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((2 + I) + Sqrt[5])] + (Sqrt[(2 + 2*I)*((2 + I) + Sqrt[5])]*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) + (15 + 5*I)*Sqrt[5]) - ((3/25 + I/25)*Sqrt[(1/2 + I/2)*((2 + I) + Sqrt[5])]*ArcTanh[(2 - Sqrt[2*(1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) + (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 + Sqrt[5]) + ((3/25 + I/25)*Sqrt[(1/2 + I/2)*((2 + I) + Sqrt[5])]*ArcTanh[(2 + Sqrt[2*(1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) + (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 + Sqrt[5]) + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",112,8,47,0.1702,0,"{6742, 2132, 206, 2133, 731, 725, 6725, 6728}"
3086,1,2475,0,9.5414707,"\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","Int[((1 + x^2 + x^4)^2*Sqrt[x^2 + Sqrt[1 + x^4]])/(Sqrt[1 + x^4]*(-1 + x^2 + x^4)^2),x]","-\frac{6 i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{-1+\sqrt{5}} x\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((-2+i)+\sqrt{5}\right)}}-\frac{2 i \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-i \sqrt{-1+\sqrt{5}} x\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \left(1-\sqrt{5}\right) \sqrt{(3+i)-(1+i) \sqrt{5}}}+\frac{6 i \tan ^{-1}\left(\frac{(1+i) \left(i \sqrt{-1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((-2+i)+\sqrt{5}\right)}}+\frac{2 i \tan ^{-1}\left(\frac{(1+i) \left(i \sqrt{-1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{2 \left((-1-2 i)+\sqrt{5}\right)} \sqrt{i x^2+1}}\right)}{5 \left(1-\sqrt{5}\right) \sqrt{(3+i)-(1+i) \sqrt{5}}}+\frac{2 i \sqrt{\frac{2}{-1+\sqrt{5}}} \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(2-i \sqrt{2 \left(-1+\sqrt{5}\right)} x\right)}{\sqrt{(-1-2 i)+\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((-1-2 i)+\sqrt{5}\right)^{3/2}}-\frac{2 i \sqrt{\frac{2}{-1+\sqrt{5}}} \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \sqrt{2 \left(-1+\sqrt{5}\right)} x+2\right)}{\sqrt{(-1-2 i)+\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((-1-2 i)+\sqrt{5}\right)^{3/2}}+\frac{2 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left(1+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}-\frac{6 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{2}-\sqrt{1+\sqrt{5}} x\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((2-i)+\sqrt{5}\right)}}-\frac{2 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left(1+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}+\frac{6 \tan ^{-1}\left(\frac{(1+i) \left(\sqrt{1+\sqrt{5}} x+\sqrt{2}\right)}{\sqrt{(-2-4 i)-2 \sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \sqrt{(-5-5 i) \left((2-i)+\sqrt{5}\right)}}+\frac{2 \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(2-\sqrt{2 \left(1+\sqrt{5}\right)} x\right)}{\sqrt{(-1-2 i)-\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((1+2 i)+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}-\frac{2 \tan ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{2 \left(1+\sqrt{5}\right)} x+2\right)}{\sqrt{(-1-2 i)-\sqrt{5}} \sqrt{i x^2+1}}\right)}{5 \left((1+2 i)+\sqrt{5}\right) \sqrt{(-1-i) \left((2-i)+\sqrt{5}\right)}}-\frac{\left(\frac{3}{5}-\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{-1+\sqrt{5}} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((-2-i)+\sqrt{5}\right)}}-\frac{i \sqrt{(2+2 i) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{2}-i \sqrt{-1+\sqrt{5}} x}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)-(15+5 i) \sqrt{5}}+\frac{\left(\frac{3}{5}-\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{i \sqrt{-1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((-2-i)+\sqrt{5}\right)}}+\frac{i \sqrt{(2+2 i) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{i \sqrt{-1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)-i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)-(15+5 i) \sqrt{5}}+\frac{\left(\frac{1}{25}-\frac{3 i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{2-i \sqrt{2 \left(-1+\sqrt{5}\right)} x}{\sqrt{(4+2 i)-2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3-\sqrt{5}}-\frac{\left(\frac{1}{25}-\frac{3 i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((-2-i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{i \sqrt{2 \left(-1+\sqrt{5}\right)} x+2}{\sqrt{(4+2 i)-2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3-\sqrt{5}}-\frac{\sqrt{(2+2 i) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)+(15+5 i) \sqrt{5}}+\frac{\left(\frac{3}{5}+\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{\sqrt{2}-\sqrt{1+\sqrt{5}} x}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((2+i)+\sqrt{5}\right)}}+\frac{\sqrt{(2+2 i) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{(35+5 i)+(15+5 i) \sqrt{5}}-\frac{\left(\frac{3}{5}+\frac{3 i}{5}\right) \tanh ^{-1}\left(\frac{\sqrt{1+\sqrt{5}} x+\sqrt{2}}{\sqrt{(2+i)+i \sqrt{5}} \sqrt{1-i x^2}}\right)}{\sqrt{\left(\frac{5}{2}+\frac{5 i}{2}\right) \left((2+i)+\sqrt{5}\right)}}-\frac{\left(\frac{3}{25}+\frac{i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{2-\sqrt{2 \left(1+\sqrt{5}\right)} x}{\sqrt{(4+2 i)+2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3+\sqrt{5}}+\frac{\left(\frac{3}{25}+\frac{i}{25}\right) \sqrt{\left(\frac{1}{2}+\frac{i}{2}\right) \left((2+i)+\sqrt{5}\right)} \tanh ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{5}\right)} x+2}{\sqrt{(4+2 i)+2 i \sqrt{5}} \sqrt{1-i x^2}}\right)}{3+\sqrt{5}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2+\sqrt{x^4+1}}}\right)}{\sqrt{2}}+\frac{16 i \sqrt{1-i x^2}}{5 \left((16+8 i)-8 \sqrt{5}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}+\frac{2 i \sqrt{1-i x^2}}{5 \left((2+i)+\sqrt{5}\right) \left(i \sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}+\frac{2 i \sqrt{1-i x^2}}{5 \left((-2-i)+\sqrt{5}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}-\frac{2 i \sqrt{1-i x^2}}{5 \left((2+i)+\sqrt{5}\right) \left(2 x+i \sqrt{2 \left(1+\sqrt{5}\right)}\right)}+\frac{2 i \sqrt{i x^2+1}}{5 \left((-2+i)+\sqrt{5}\right) \left(\sqrt{2 \left(-1+\sqrt{5}\right)}-2 x\right)}-\frac{2 i \sqrt{i x^2+1}}{5 \left((2-i)+\sqrt{5}\right) \left(i \sqrt{2 \left(1+\sqrt{5}\right)}-2 x\right)}-\frac{2 i \sqrt{i x^2+1}}{5 \left((-2+i)+\sqrt{5}\right) \left(2 x+\sqrt{2 \left(-1+\sqrt{5}\right)}\right)}+\frac{2 i \sqrt{i x^2+1}}{5 \left((2-i)+\sqrt{5}\right) \left(2 x+i \sqrt{2 \left(1+\sqrt{5}\right)}\right)}","-\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,"(((16*I)/5)*Sqrt[1 - I*x^2])/(((16 + 8*I) - 8*Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x)) + (((2*I)/5)*Sqrt[1 - I*x^2])/(((2 + I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] - 2*x)) + (((2*I)/5)*Sqrt[1 - I*x^2])/(((-2 - I) + Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x)) - (((2*I)/5)*Sqrt[1 - I*x^2])/(((2 + I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] + 2*x)) + (((2*I)/5)*Sqrt[1 + I*x^2])/(((-2 + I) + Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] - 2*x)) - (((2*I)/5)*Sqrt[1 + I*x^2])/(((2 - I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] - 2*x)) - (((2*I)/5)*Sqrt[1 + I*x^2])/(((-2 + I) + Sqrt[5])*(Sqrt[2*(-1 + Sqrt[5])] + 2*x)) + (((2*I)/5)*Sqrt[1 + I*x^2])/(((2 - I) + Sqrt[5])*(I*Sqrt[2*(1 + Sqrt[5])] + 2*x)) - (((2*I)/5)*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/((1 - Sqrt[5])*Sqrt[(3 + I) - (1 + I)*Sqrt[5]]) - (((6*I)/5)*ArcTan[((1 + I)*(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + (((2*I)/5)*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/((1 - Sqrt[5])*Sqrt[(3 + I) - (1 + I)*Sqrt[5]]) + (((6*I)/5)*ArcTan[((1 + I)*(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x))/(Sqrt[2*((-1 - 2*I) + Sqrt[5])]*Sqrt[1 + I*x^2])])/Sqrt[(-5 - 5*I)*((-2 + I) + Sqrt[5])] + (((2*I)/5)*Sqrt[2/(-1 + Sqrt[5])]*ArcTan[((1/2 + I/2)*(2 - I*Sqrt[2*(-1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) + Sqrt[5]]*Sqrt[1 + I*x^2])])/((-1 - 2*I) + Sqrt[5])^(3/2) - (((2*I)/5)*Sqrt[2/(-1 + Sqrt[5])]*ArcTan[((1/2 + I/2)*(2 + I*Sqrt[2*(-1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) + Sqrt[5]]*Sqrt[1 + I*x^2])])/((-1 - 2*I) + Sqrt[5])^(3/2) - (6*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) + (2*ArcTan[((1 + I)*(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*(1 + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) + (6*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*Sqrt[(-5 - 5*I)*((2 - I) + Sqrt[5])]) - (2*ArcTan[((1 + I)*(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x))/(Sqrt[(-2 - 4*I) - 2*Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*(1 + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) + (2*ArcTan[((1/2 + I/2)*(2 - Sqrt[2*(1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) - Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*((1 + 2*I) + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) - (2*ArcTan[((1/2 + I/2)*(2 + Sqrt[2*(1 + Sqrt[5])]*x))/(Sqrt[(-1 - 2*I) - Sqrt[5]]*Sqrt[1 + I*x^2])])/(5*((1 + 2*I) + Sqrt[5])*Sqrt[(-1 - I)*((2 - I) + Sqrt[5])]) - (I*Sqrt[(2 + 2*I)*((-2 - I) + Sqrt[5])]*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) - (15 + 5*I)*Sqrt[5]) - ((3/5 - (3*I)/5)*ArcTanh[(Sqrt[2] - I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((-2 - I) + Sqrt[5])] + (I*Sqrt[(2 + 2*I)*((-2 - I) + Sqrt[5])]*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) - (15 + 5*I)*Sqrt[5]) + ((3/5 - (3*I)/5)*ArcTanh[(Sqrt[2] + I*Sqrt[-1 + Sqrt[5]]*x)/(Sqrt[(2 + I) - I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((-2 - I) + Sqrt[5])] + ((1/25 - (3*I)/25)*Sqrt[(1/2 + I/2)*((-2 - I) + Sqrt[5])]*ArcTanh[(2 - I*Sqrt[2*(-1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) - (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 - Sqrt[5]) - ((1/25 - (3*I)/25)*Sqrt[(1/2 + I/2)*((-2 - I) + Sqrt[5])]*ArcTanh[(2 + I*Sqrt[2*(-1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) - (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 - Sqrt[5]) + ((3/5 + (3*I)/5)*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((2 + I) + Sqrt[5])] - (Sqrt[(2 + 2*I)*((2 + I) + Sqrt[5])]*ArcTanh[(Sqrt[2] - Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) + (15 + 5*I)*Sqrt[5]) - ((3/5 + (3*I)/5)*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/Sqrt[(5/2 + (5*I)/2)*((2 + I) + Sqrt[5])] + (Sqrt[(2 + 2*I)*((2 + I) + Sqrt[5])]*ArcTanh[(Sqrt[2] + Sqrt[1 + Sqrt[5]]*x)/(Sqrt[(2 + I) + I*Sqrt[5]]*Sqrt[1 - I*x^2])])/((35 + 5*I) + (15 + 5*I)*Sqrt[5]) - ((3/25 + I/25)*Sqrt[(1/2 + I/2)*((2 + I) + Sqrt[5])]*ArcTanh[(2 - Sqrt[2*(1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) + (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 + Sqrt[5]) + ((3/25 + I/25)*Sqrt[(1/2 + I/2)*((2 + I) + Sqrt[5])]*ArcTanh[(2 + Sqrt[2*(1 + Sqrt[5])]*x)/(Sqrt[(4 + 2*I) + (2*I)*Sqrt[5]]*Sqrt[1 - I*x^2])])/(3 + Sqrt[5]) + ArcTanh[(Sqrt[2]*x)/Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[2]","C",112,8,47,0.1702,0,"{6742, 2132, 206, 2133, 731, 725, 6725, 6728}"
3087,1,1029,0,3.467542,"\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","Int[((-q + p*x^4)*Sqrt[q + p*x^4])/(x^2*(a*q + b*x^2 + a*p*x^4)),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a} \sqrt{p x^4+q}}\right)}{a^{3/2}}-\frac{\left(-2 \sqrt{p} \sqrt{q} a+b-\sqrt{b^2-4 a^2 p q}\right) \left(\sqrt{p} x^2+\sqrt{q}\right) \sqrt{\frac{p x^4+q}{\left(\sqrt{p} x^2+\sqrt{q}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{p} x}{\sqrt[4]{q}}\right)|\frac{1}{2}\right)}{4 a^2 \sqrt[4]{p} \sqrt[4]{q} \sqrt{p x^4+q}}-\frac{\left(-2 \sqrt{p} \sqrt{q} a+b+\sqrt{b^2-4 a^2 p q}\right) \left(\sqrt{p} x^2+\sqrt{q}\right) \sqrt{\frac{p x^4+q}{\left(\sqrt{p} x^2+\sqrt{q}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{p} x}{\sqrt[4]{q}}\right)|\frac{1}{2}\right)}{4 a^2 \sqrt[4]{p} \sqrt[4]{q} \sqrt{p x^4+q}}-\frac{\sqrt[4]{p} \sqrt[4]{q} \left(\sqrt{p} x^2+\sqrt{q}\right) \sqrt{\frac{p x^4+q}{\left(\sqrt{p} x^2+\sqrt{q}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{p} x}{\sqrt[4]{q}}\right)|\frac{1}{2}\right)}{a \sqrt{p x^4+q}}+\frac{b \left(b-\sqrt{b^2-4 a^2 p q}\right) \left(\sqrt{p} x^2+\sqrt{q}\right) \sqrt{\frac{p x^4+q}{\left(\sqrt{p} x^2+\sqrt{q}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{p} x}{\sqrt[4]{q}}\right)|\frac{1}{2}\right)}{2 a^2 \sqrt[4]{p} \sqrt[4]{q} \left(-2 \sqrt{p} \sqrt{q} a+b-\sqrt{b^2-4 a^2 p q}\right) \sqrt{p x^4+q}}+\frac{b \left(b+\sqrt{b^2-4 a^2 p q}\right) \left(\sqrt{p} x^2+\sqrt{q}\right) \sqrt{\frac{p x^4+q}{\left(\sqrt{p} x^2+\sqrt{q}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{p} x}{\sqrt[4]{q}}\right)|\frac{1}{2}\right)}{2 a^2 \sqrt[4]{p} \sqrt[4]{q} \left(-2 \sqrt{p} \sqrt{q} a+b+\sqrt{b^2-4 a^2 p q}\right) \sqrt{p x^4+q}}-\frac{b \left(2 \sqrt{p} \sqrt{q} a+b-\sqrt{b^2-4 a^2 p q}\right) \left(\sqrt{p} x^2+\sqrt{q}\right) \sqrt{\frac{p x^4+q}{\left(\sqrt{p} x^2+\sqrt{q}\right)^2}} \Pi \left(\frac{1}{4} \left(2-\frac{b}{a \sqrt{p} \sqrt{q}}\right);2 \tan ^{-1}\left(\frac{\sqrt[4]{p} x}{\sqrt[4]{q}}\right)|\frac{1}{2}\right)}{4 a^2 \sqrt[4]{p} \sqrt[4]{q} \left(-2 \sqrt{p} \sqrt{q} a+b-\sqrt{b^2-4 a^2 p q}\right) \sqrt{p x^4+q}}-\frac{b \left(2 \sqrt{p} \sqrt{q} a+b+\sqrt{b^2-4 a^2 p q}\right) \left(\sqrt{p} x^2+\sqrt{q}\right) \sqrt{\frac{p x^4+q}{\left(\sqrt{p} x^2+\sqrt{q}\right)^2}} \Pi \left(\frac{1}{4} \left(2-\frac{b}{a \sqrt{p} \sqrt{q}}\right);2 \tan ^{-1}\left(\frac{\sqrt[4]{p} x}{\sqrt[4]{q}}\right)|\frac{1}{2}\right)}{4 a^2 \sqrt[4]{p} \sqrt[4]{q} \left(-2 \sqrt{p} \sqrt{q} a+b+\sqrt{b^2-4 a^2 p q}\right) \sqrt{p x^4+q}}+\frac{\sqrt{p x^4+q}}{a x}","\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,"Sqrt[q + p*x^4]/(a*x) + (Sqrt[b]*ArcTan[(Sqrt[b]*x)/(Sqrt[a]*Sqrt[q + p*x^4])])/a^(3/2) - (p^(1/4)*q^(1/4)*(Sqrt[q] + Sqrt[p]*x^2)*Sqrt[(q + p*x^4)/(Sqrt[q] + Sqrt[p]*x^2)^2]*EllipticF[2*ArcTan[(p^(1/4)*x)/q^(1/4)], 1/2])/(a*Sqrt[q + p*x^4]) + (b*(b - Sqrt[b^2 - 4*a^2*p*q])*(Sqrt[q] + Sqrt[p]*x^2)*Sqrt[(q + p*x^4)/(Sqrt[q] + Sqrt[p]*x^2)^2]*EllipticF[2*ArcTan[(p^(1/4)*x)/q^(1/4)], 1/2])/(2*a^2*p^(1/4)*q^(1/4)*(b - 2*a*Sqrt[p]*Sqrt[q] - Sqrt[b^2 - 4*a^2*p*q])*Sqrt[q + p*x^4]) - ((b - 2*a*Sqrt[p]*Sqrt[q] - Sqrt[b^2 - 4*a^2*p*q])*(Sqrt[q] + Sqrt[p]*x^2)*Sqrt[(q + p*x^4)/(Sqrt[q] + Sqrt[p]*x^2)^2]*EllipticF[2*ArcTan[(p^(1/4)*x)/q^(1/4)], 1/2])/(4*a^2*p^(1/4)*q^(1/4)*Sqrt[q + p*x^4]) + (b*(b + Sqrt[b^2 - 4*a^2*p*q])*(Sqrt[q] + Sqrt[p]*x^2)*Sqrt[(q + p*x^4)/(Sqrt[q] + Sqrt[p]*x^2)^2]*EllipticF[2*ArcTan[(p^(1/4)*x)/q^(1/4)], 1/2])/(2*a^2*p^(1/4)*q^(1/4)*(b - 2*a*Sqrt[p]*Sqrt[q] + Sqrt[b^2 - 4*a^2*p*q])*Sqrt[q + p*x^4]) - ((b - 2*a*Sqrt[p]*Sqrt[q] + Sqrt[b^2 - 4*a^2*p*q])*(Sqrt[q] + Sqrt[p]*x^2)*Sqrt[(q + p*x^4)/(Sqrt[q] + Sqrt[p]*x^2)^2]*EllipticF[2*ArcTan[(p^(1/4)*x)/q^(1/4)], 1/2])/(4*a^2*p^(1/4)*q^(1/4)*Sqrt[q + p*x^4]) - (b*(b + 2*a*Sqrt[p]*Sqrt[q] - Sqrt[b^2 - 4*a^2*p*q])*(Sqrt[q] + Sqrt[p]*x^2)*Sqrt[(q + p*x^4)/(Sqrt[q] + Sqrt[p]*x^2)^2]*EllipticPi[(2 - b/(a*Sqrt[p]*Sqrt[q]))/4, 2*ArcTan[(p^(1/4)*x)/q^(1/4)], 1/2])/(4*a^2*p^(1/4)*q^(1/4)*(b - 2*a*Sqrt[p]*Sqrt[q] - Sqrt[b^2 - 4*a^2*p*q])*Sqrt[q + p*x^4]) - (b*(b + 2*a*Sqrt[p]*Sqrt[q] + Sqrt[b^2 - 4*a^2*p*q])*(Sqrt[q] + Sqrt[p]*x^2)*Sqrt[(q + p*x^4)/(Sqrt[q] + Sqrt[p]*x^2)^2]*EllipticPi[(2 - b/(a*Sqrt[p]*Sqrt[q]))/4, 2*ArcTan[(p^(1/4)*x)/q^(1/4)], 1/2])/(4*a^2*p^(1/4)*q^(1/4)*(b - 2*a*Sqrt[p]*Sqrt[q] + Sqrt[b^2 - 4*a^2*p*q])*Sqrt[q + p*x^4])","C",22,9,41,0.2195,1,"{6728, 277, 305, 220, 1196, 1209, 1198, 1217, 1707}"
3088,1,524,0,0.2691427,"\int \frac{\sqrt[3]{b^2 x^2+a^3 x^3}}{b+a x} \, dx","Int[(b^2*x^2 + a^3*x^3)^(1/3)/(b + a*x),x]","\frac{\sqrt[3]{a^3 x^3+b^2 x^2}}{a}+\frac{b \left(3 a^2-b\right) \sqrt[3]{a^3 x^3+b^2 x^2} \log \left(a^3 x+b^2\right)}{6 a^3 x^{2/3} \sqrt[3]{a^3 x+b^2}}+\frac{b \left(3 a^2-b\right) \sqrt[3]{a^3 x^3+b^2 x^2} \log \left(\frac{a \sqrt[3]{x}}{\sqrt[3]{a^3 x+b^2}}-1\right)}{2 a^3 x^{2/3} \sqrt[3]{a^3 x+b^2}}+\frac{b \left(3 a^2-b\right) \sqrt[3]{a^3 x^3+b^2 x^2} \tan ^{-1}\left(\frac{2 a \sqrt[3]{x}}{\sqrt{3} \sqrt[3]{a^3 x+b^2}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3} a^3 x^{2/3} \sqrt[3]{a^3 x+b^2}}+\frac{b \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2} \log (a x+b)}{2 a^{5/3} x^{2/3} \sqrt[3]{a^3 x+b^2}}-\frac{3 b \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2} \log \left(\sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2-b}-\sqrt[3]{a^3 x+b^2}\right)}{2 a^{5/3} x^{2/3} \sqrt[3]{a^3 x+b^2}}-\frac{\sqrt{3} b \sqrt[3]{a^2-b} \sqrt[3]{a^3 x^3+b^2 x^2} \tan ^{-1}\left(\frac{2 \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{a^2-b}}{\sqrt{3} \sqrt[3]{a^3 x+b^2}}+\frac{1}{\sqrt{3}}\right)}{a^{5/3} x^{2/3} \sqrt[3]{a^3 x+b^2}}","\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,"(b^2*x^2 + a^3*x^3)^(1/3)/a + ((3*a^2 - b)*b*(b^2*x^2 + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a*x^(1/3))/(Sqrt[3]*(b^2 + a^3*x)^(1/3))])/(Sqrt[3]*a^3*x^(2/3)*(b^2 + a^3*x)^(1/3)) - (Sqrt[3]*(a^2 - b)^(1/3)*b*(b^2*x^2 + a^3*x^3)^(1/3)*ArcTan[1/Sqrt[3] + (2*a^(1/3)*(a^2 - b)^(1/3)*x^(1/3))/(Sqrt[3]*(b^2 + a^3*x)^(1/3))])/(a^(5/3)*x^(2/3)*(b^2 + a^3*x)^(1/3)) + ((a^2 - b)^(1/3)*b*(b^2*x^2 + a^3*x^3)^(1/3)*Log[b + a*x])/(2*a^(5/3)*x^(2/3)*(b^2 + a^3*x)^(1/3)) + ((3*a^2 - b)*b*(b^2*x^2 + a^3*x^3)^(1/3)*Log[b^2 + a^3*x])/(6*a^3*x^(2/3)*(b^2 + a^3*x)^(1/3)) + ((3*a^2 - b)*b*(b^2*x^2 + a^3*x^3)^(1/3)*Log[-1 + (a*x^(1/3))/(b^2 + a^3*x)^(1/3)])/(2*a^3*x^(2/3)*(b^2 + a^3*x)^(1/3)) - (3*(a^2 - b)^(1/3)*b*(b^2*x^2 + a^3*x^3)^(1/3)*Log[a^(1/3)*(a^2 - b)^(1/3)*x^(1/3) - (b^2 + a^3*x)^(1/3)])/(2*a^(5/3)*x^(2/3)*(b^2 + a^3*x)^(1/3))","A",5,5,27,0.1852,1,"{2056, 101, 157, 59, 91}"
3089,1,468,0,0.656665,"\int \frac{\left(-b+a^2 x^2\right)^{3/2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x} \, dx","Int[((-b + a^2*x^2)^(3/2)*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/x,x]","-\frac{b^3}{22 \left(\sqrt{a^2 x^2-b}+a x\right)^{11/4}}+\frac{5 b^2}{6 \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}}+\frac{1}{26} \left(\sqrt{a^2 x^2-b}+a x\right)^{13/4}-\frac{1}{2} b \left(\sqrt{a^2 x^2-b}+a x\right)^{5/4}-\frac{(-b)^{13/8} \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{\sqrt{2}}+\frac{(-b)^{13/8} \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{\sqrt{2}}-2 (-b)^{13/8} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)-\sqrt{2} (-b)^{13/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)+\sqrt{2} (-b)^{13/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}+1\right)-2 (-b)^{13/8} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)","\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,"-1/22*b^3/(a*x + Sqrt[-b + a^2*x^2])^(11/4) + (5*b^2)/(6*(a*x + Sqrt[-b + a^2*x^2])^(3/4)) - (b*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/2 + (a*x + Sqrt[-b + a^2*x^2])^(13/4)/26 - 2*(-b)^(13/8)*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)] - Sqrt[2]*(-b)^(13/8)*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)] + Sqrt[2]*(-b)^(13/8)*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)] - 2*(-b)^(13/8)*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)] - ((-b)^(13/8)*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)^(13/8)*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",17,13,42,0.3095,1,"{2120, 466, 461, 301, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
3090,0,0,0,0.9196104,"\int \frac{\left(b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}}{-b^2+a x^2} \, dx","Int[((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,"(2*a*x^3)/(3*(b + Sqrt[b^2 + a*x^2])^(3/2)) + (2*b*x)/Sqrt[b + Sqrt[b^2 + a*x^2]] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[a]*x), x] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[a]*x), x]","F",0,0,0,0,-1,"{}"
3091,1,490,0,2.1058474,"\int \frac{d+c x^4}{x \sqrt{-b+a^2 x^2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Int[(d + c*x^4)/(x*Sqrt[-b + a^2*x^2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4)),x]","-\frac{d \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{\sqrt{2} (-b)^{5/8}}+\frac{d \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{\sqrt{2} (-b)^{5/8}}+\frac{2 d \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{(-b)^{5/8}}+\frac{\sqrt{2} d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{(-b)^{5/8}}-\frac{\sqrt{2} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}+1\right)}{(-b)^{5/8}}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{(-b)^{5/8}}-\frac{b^3 c}{26 a^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{13/4}}-\frac{3 b^2 c}{10 a^4 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/4}}+\frac{b c \left(\sqrt{a^2 x^2-b}+a x\right)^{3/4}}{2 a^4}+\frac{c \left(\sqrt{a^2 x^2-b}+a x\right)^{11/4}}{22 a^4}","\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,"-1/26*(b^3*c)/(a^4*(a*x + Sqrt[-b + a^2*x^2])^(13/4)) - (3*b^2*c)/(10*a^4*(a*x + Sqrt[-b + a^2*x^2])^(5/4)) + (b*c*(a*x + Sqrt[-b + a^2*x^2])^(3/4))/(2*a^4) + (c*(a*x + Sqrt[-b + a^2*x^2])^(11/4))/(22*a^4) + (2*d*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(-b)^(5/8) + (Sqrt[2]*d*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(-b)^(5/8) - (Sqrt[2]*d*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(-b)^(5/8) - (2*d*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(-b)^(5/8) - (d*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)^(5/8)) + (d*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)^(5/8))","A",20,14,49,0.2857,1,"{6742, 2120, 329, 300, 297, 1162, 617, 204, 1165, 628, 298, 203, 206, 270}"
3092,1,539,0,0.7002069,"\int \frac{\left(-b+a^2 x^2\right)^{3/2} \sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x^2} \, dx","Int[((-b + a^2*x^2)^(3/2)*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/x^2,x]","-\frac{11 a b^2}{28 \left(\sqrt{a^2 x^2-b}+a x\right)^{7/4}}+\frac{a \left(b-\left(\sqrt{a^2 x^2-b}+a x\right)^2\right)^3}{4 \left(\sqrt{a^2 x^2-b}+a x\right)^{7/4} \left(\left(\sqrt{a^2 x^2-b}+a x\right)^2+b\right)}+\frac{13}{36} a \left(\sqrt{a^2 x^2-b}+a x\right)^{9/4}-7 a b \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\frac{a (-b)^{9/8} \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{4 \sqrt{2}}-\frac{a (-b)^{9/8} \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{4 \sqrt{2}}-\frac{1}{2} a (-b)^{9/8} \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)+\frac{a (-b)^{9/8} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{2 \sqrt{2}}-\frac{a (-b)^{9/8} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}+1\right)}{2 \sqrt{2}}-\frac{1}{2} a (-b)^{9/8} \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)","\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,"(-11*a*b^2)/(28*(a*x + Sqrt[-b + a^2*x^2])^(7/4)) - 7*a*b*(a*x + Sqrt[-b + a^2*x^2])^(1/4) + (13*a*(a*x + Sqrt[-b + a^2*x^2])^(9/4))/36 + (a*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^3)/(4*(a*x + Sqrt[-b + a^2*x^2])^(7/4)*(b + (a*x + Sqrt[-b + a^2*x^2])^2)) - (a*(-b)^(9/8)*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/2 + (a*(-b)^(9/8)*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(2*Sqrt[2]) - (a*(-b)^(9/8)*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(2*Sqrt[2]) - (a*(-b)^(9/8)*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/2 + (a*(-b)^(9/8)*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]]])/(4*Sqrt[2]) - (a*(-b)^(9/8)*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]]])/(4*Sqrt[2])","A",18,14,42,0.3333,1,"{2120, 466, 468, 570, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
3093,1,513,0,1.0786304,"\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","Int[(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{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 \left(1-\sqrt{d}\right) \left(a+b \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 (1-d) x-2 \left(\sqrt{d}+1\right) \left(a-b \sqrt{d}\right)\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(-\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x-b}\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x-b}\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-b}}\right)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","\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,"-1/2*(Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-b + x)^(1/3))])/((a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-b + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) + ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 - Sqrt[d])*(a + b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) + ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[-2*(1 + Sqrt[d])*(a - b*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[-((-a + x)^(1/3)/d^(1/6)) - (-b + x)^(1/3)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[(-a + x)^(1/3)/d^(1/6) - (-b + x)^(1/3)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3))","A",10,6,53,0.1132,1,"{6719, 21, 911, 105, 59, 91}"
3094,1,513,0,0.9615901,"\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","Int[(-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{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 \left(1-\sqrt{d}\right) \left(a+b \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 (1-d) x-2 \left(\sqrt{d}+1\right) \left(a-b \sqrt{d}\right)\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(-\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x-b}\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x-b}\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-b}}\right)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","\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,"-1/2*(Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-b + x)^(1/3))])/((a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-b + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) + ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 - Sqrt[d])*(a + b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) + ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[-2*(1 + Sqrt[d])*(a - b*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[-((-a + x)^(1/3)/d^(1/6)) - (-b + x)^(1/3)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[(-a + x)^(1/3)/d^(1/6) - (-b + x)^(1/3)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3))","A",9,5,52,0.09615,1,"{6719, 911, 105, 59, 91}"
3095,0,0,0,0.9678078,"\int \frac{b^2+a x^2}{\left(-b^2+a x^2\right) \sqrt{b+\sqrt{b^2+a x^2}}} \, dx","Int[(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,"Defer[Int][1/Sqrt[b + Sqrt[b^2 + a*x^2]], x] - b*Defer[Int][1/((b - Sqrt[a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] - b*Defer[Int][1/((b + Sqrt[a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",0,0,0,0,-1,"{}"
3096,1,377,0,0.6729682,"\int \frac{1}{\sqrt[3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx","Int[1/(((-a + x)*(-b + x)^2)^(1/3)*(a - b*d + (-1 + d)*x)),x]","\frac{\left((a-b)^2 (b-x)\right)^{2/3} \sqrt[3]{(a-b)^2 (x-a)} \log (a-b d+(d-1) x)}{2 \sqrt[3]{d} (a-b)^3 \sqrt[3]{-a b^2+x^2 (-a-2 b)+b x (2 a+b)+x^3}}-\frac{3 \left((a-b)^2 (b-x)\right)^{2/3} \sqrt[3]{(a-b)^2 (x-a)} \log \left(-\frac{\sqrt[3]{\frac{2}{3}} \sqrt[3]{(a-b)^2 (x-a)}}{\sqrt[3]{d}}-\sqrt[3]{\frac{2}{3}} \sqrt[3]{(a-b)^2 (b-x)}\right)}{2 \sqrt[3]{d} (a-b)^3 \sqrt[3]{-a b^2+x^2 (-a-2 b)+b x (2 a+b)+x^3}}-\frac{\sqrt{3} \left((a-b)^2 (b-x)\right)^{2/3} \sqrt[3]{(a-b)^2 (x-a)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{(a-b)^2 (x-a)}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{(a-b)^2 (b-x)}}\right)}{\sqrt[3]{d} (a-b)^3 \sqrt[3]{-a b^2+x^2 (-a-2 b)+b x (2 a+b)+x^3}}","\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,"-((Sqrt[3]*((a - b)^2*(b - x))^(2/3)*((a - b)^2*(-a + x))^(1/3)*ArcTan[1/Sqrt[3] - (2*((a - b)^2*(-a + x))^(1/3))/(Sqrt[3]*d^(1/3)*((a - b)^2*(b - x))^(1/3))])/((a - b)^3*d^(1/3)*(-(a*b^2) + b*(2*a + b)*x + (-a - 2*b)*x^2 + x^3)^(1/3))) + (((a - b)^2*(b - x))^(2/3)*((a - b)^2*(-a + x))^(1/3)*Log[a - b*d + (-1 + d)*x])/(2*(a - b)^3*d^(1/3)*(-(a*b^2) + b*(2*a + b)*x + (-a - 2*b)*x^2 + x^3)^(1/3)) - (3*((a - b)^2*(b - x))^(2/3)*((a - b)^2*(-a + x))^(1/3)*Log[-((2/3)^(1/3)*((a - b)^2*(b - x))^(1/3)) - ((2/3)^(1/3)*((a - b)^2*(-a + x))^(1/3))/d^(1/3)])/(2*(a - b)^3*d^(1/3)*(-(a*b^2) + b*(2*a + b)*x + (-a - 2*b)*x^2 + x^3)^(1/3))","A",3,3,31,0.09677,1,"{2081, 2077, 91}"
3097,0,0,0,1.7902249,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Int[(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{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 b c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+\text{$\#$1}^2 a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+b^2 c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a^2 b d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 (-c)-3 \text{$\#$1}^2 a d+\text{$\#$1} b c-a b d}\&\right]}{\sqrt{2} c^2}+\frac{a x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{2 c}-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a^2 x^4+b}}{\sqrt{b}}+\frac{\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}}{\sqrt{b}}+\frac{a x^2}{\sqrt{b}}\right)}{\sqrt{2} c}-\frac{a^{3/2} d \log \left(\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\sqrt{2} c^2}",1,"Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(Sqrt[d] - Sqrt[-c]*x), x]/(2*Sqrt[d]) + Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(Sqrt[d] + Sqrt[-c]*x), x]/(2*Sqrt[d])","F",0,0,0,0,-1,"{}"
3098,0,0,0,1.2908331,"\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","Int[(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(d + c*x^2),x]","\int \frac{\sqrt{b+a^2 x^4} \sqrt{a x^2+\sqrt{b+a^2 x^4}}}{d+c x^2} \, dx","-\frac{\sqrt{a} \text{RootSum}\left[\text{$\#$1}^4 c+4 \text{$\#$1}^3 a d-2 \text{$\#$1}^2 b c+4 \text{$\#$1} a b d+b^2 c\&,\frac{\text{$\#$1}^2 b c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+\text{$\#$1}^2 a^2 d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+b^2 c^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)+a^2 b d^2 \log \left(-\text{$\#$1}+\sqrt{a^2 x^4+b}+\sqrt{2} \sqrt{a} x \sqrt{\sqrt{a^2 x^4+b}+a x^2}+a x^2\right)}{\text{$\#$1}^3 (-c)-3 \text{$\#$1}^2 a d+\text{$\#$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,"Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(Sqrt[d] - Sqrt[-c]*x), x]/(2*Sqrt[d]) + Defer[Int][(Sqrt[b + a^2*x^4]*Sqrt[a*x^2 + Sqrt[b + a^2*x^4]])/(Sqrt[d] + Sqrt[-c]*x), x]/(2*Sqrt[d])","F",0,0,0,0,-1,"{}"
3099,0,0,0,0.1031734,"\int \frac{\sqrt{x^2+\sqrt{1+x^4}}}{1+a x} \, dx","Int[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,"Defer[Int][Sqrt[x^2 + Sqrt[1 + x^4]]/(1 + a*x), x]","F",0,0,0,0,-1,"{}"
3100,1,561,0,5.6693356,"\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","Int[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 \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{c_3 c_6-c_2 c_7} \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)}{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} \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)}{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{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]]*C[7]) + (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]]*C[7]) - (2*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[6] - C[2]*C[7]])/(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]]]) - (2*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[6] - C[2]*C[7]])/(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",11,4,41,0.09756,1,"{6741, 6728, 1166, 208}"
3101,1,513,0,1.0509759,"\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","Int[(-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{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 \left(\sqrt{d}+1\right) \left(b-a \sqrt{d}\right)-2 (1-d) x\right)}{4 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt[3]{x-a} (x-b)^{2/3} \log \left(2 (1-d) x-2 \left(1-\sqrt{d}\right) \left(a \sqrt{d}+b\right)\right)}{4 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(-\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x-b}\right)}{4 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \log \left(\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x-b}\right)}{4 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x-b}}\right)}{2 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","-\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,"(Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*(-b + x)^(1/3))])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3)) + (Sqrt[3]*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*(-b + x)^(1/3))])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3)) - ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 + Sqrt[d])*(b - a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3)) - ((-a + x)^(1/3)*(-b + x)^(2/3)*Log[-2*(1 - Sqrt[d])*(b + a*Sqrt[d]) + 2*(1 - d)*x])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3)) + (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[-(d^(1/6)*(-a + x)^(1/3)) - (-b + x)^(1/3)])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3)) + (3*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[d^(1/6)*(-a + x)^(1/3) - (-b + x)^(1/3)])/(4*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3))","A",9,5,52,0.09615,1,"{6719, 911, 105, 59, 91}"
3102,0,0,0,2.329761,"\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","Int[(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,"Defer[Int][1/Sqrt[b + Sqrt[b^2 + a*x^2]], x] - b*Defer[Int][1/((b - Sqrt[a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] - b*Defer[Int][1/((b + Sqrt[a]*x)*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] + a*b^2*Defer[Int][1/((Sqrt[a]*b - a*x)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]), x] + a*b^2*Defer[Int][1/((Sqrt[a]*b + a*x)^2*Sqrt[b + Sqrt[b^2 + a*x^2]]), x]","F",0,0,0,0,-1,"{}"
3103,1,590,0,1.9141486,"\int \frac{\sqrt{a x+\sqrt{-b+a x}}}{\sqrt{-b+a x} \left(1+a^2 x^2\right)} \, dx","Int[Sqrt[a*x + Sqrt[-b + a*x]]/(Sqrt[-b + a*x]*(1 + a^2*x^2)),x]","-\frac{\sqrt{-i b+\sqrt{b-(1-i)}+(1+i)} \tan ^{-1}\left(\frac{\left(b+i \sqrt{b-(1-i)}-(1-i)\right) \sqrt{a x-b}+\sqrt{b-(1-i)} (b+i)}{\sqrt{2} \sqrt{1-i b} \sqrt{-i b+\sqrt{b-(1-i)}+(1+i)} \sqrt[4]{b-(1-i)} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt{2} a \sqrt{1-i b} \sqrt[4]{b-(1-i)}}+\frac{i \sqrt{i-\sqrt{-b+i}} \tanh ^{-1}\left(\frac{\left(1-2 \sqrt{-b+i}\right) \left(-\sqrt{a x-b}\right)-2 b+\sqrt{-b+i}}{2 \sqrt{i-\sqrt{-b+i}} \sqrt{\sqrt{a x-b}+a x}}\right)}{2 a \sqrt{-b+i}}+\frac{i \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)}{2 a \sqrt{-b+i}}+\frac{i \sqrt{b-i \sqrt{b-(1-i)}-(1-i)} \tanh ^{-1}\left(\frac{\left(-b+i \sqrt{b-(1-i)}+(1-i)\right) \sqrt{a x-b}+\sqrt{b-(1-i)} (b+i)}{\sqrt{2} \sqrt{-b-i} \sqrt[4]{b-(1-i)} \sqrt{b-i \sqrt{b-(1-i)}-(1-i)} \sqrt{\sqrt{a x-b}+a x}}\right)}{\sqrt{2} a \sqrt{-b-i} \sqrt[4]{b-(1-i)}}","-\frac{\text{RootSum}\left[\text{$\#$1}^8+4 \text{$\#$1}^6 b-8 \text{$\#$1}^5 b+6 \text{$\#$1}^4 b^2+2 \text{$\#$1}^4 b+16 \text{$\#$1}^4-16 \text{$\#$1}^3 b^2-32 \text{$\#$1}^3+4 \text{$\#$1}^2 b^3+20 \text{$\#$1}^2 b^2+24 \text{$\#$1}^2-8 \text{$\#$1} b^3-8 \text{$\#$1} b^2-8 \text{$\#$1}+b^4+2 b^3+b^2+1\&,\frac{2 \text{$\#$1}^5 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-5 \text{$\#$1}^4 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+4 \text{$\#$1}^3 b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+4 \text{$\#$1}^3 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-6 \text{$\#$1}^2 b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-\text{$\#$1}^2 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+2 \text{$\#$1} b^2 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)-b^2 \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)+2 \text{$\#$1} b \log \left(\text{$\#$1}+\sqrt{a x-b}-\sqrt{\sqrt{a x-b}+a x}\right)}{\text{$\#$1}^7+3 \text{$\#$1}^5 b-5 \text{$\#$1}^4 b+3 \text{$\#$1}^3 b^2+\text{$\#$1}^3 b+8 \text{$\#$1}^3-6 \text{$\#$1}^2 b^2-12 \text{$\#$1}^2+\text{$\#$1} b^3+5 \text{$\#$1} b^2+6 \text{$\#$1}-b^3-b^2-1}\&\right]}{2 a}",1,"-((Sqrt[(1 + I) + Sqrt[(-1 + I) + b] - I*b]*ArcTan[(Sqrt[(-1 + I) + b]*(I + b) + ((-1 + I) + I*Sqrt[(-1 + I) + b] + b)*Sqrt[-b + a*x])/(Sqrt[2]*Sqrt[1 - I*b]*Sqrt[(1 + I) + Sqrt[(-1 + I) + b] - I*b]*((-1 + I) + b)^(1/4)*Sqrt[a*x + Sqrt[-b + a*x]])])/(Sqrt[2]*a*Sqrt[1 - I*b]*((-1 + I) + b)^(1/4))) + ((I/2)*Sqrt[I - Sqrt[I - b]]*ArcTanh[(Sqrt[I - b] - 2*b - (1 - 2*Sqrt[I - b])*Sqrt[-b + a*x])/(2*Sqrt[I - Sqrt[I - b]]*Sqrt[a*x + Sqrt[-b + a*x]])])/(a*Sqrt[I - b]) + ((I/2)*Sqrt[I + Sqrt[I - b]]*ArcTanh[(Sqrt[I - b] + 2*b + (1 + 2*Sqrt[I - b])*Sqrt[-b + a*x])/(2*Sqrt[I + Sqrt[I - b]]*Sqrt[a*x + Sqrt[-b + a*x]])])/(a*Sqrt[I - b]) + (I*Sqrt[(-1 + I) - I*Sqrt[(-1 + I) + b] + b]*ArcTanh[(Sqrt[(-1 + I) + b]*(I + b) + ((1 - I) + I*Sqrt[(-1 + I) + b] - b)*Sqrt[-b + a*x])/(Sqrt[2]*Sqrt[-I - b]*((-1 + I) + b)^(1/4)*Sqrt[(-1 + I) - I*Sqrt[(-1 + I) + b] + b]*Sqrt[a*x + Sqrt[-b + a*x]])])/(Sqrt[2]*a*Sqrt[-I - b]*((-1 + I) + b)^(1/4))","C",19,10,42,0.2381,1,"{6728, 990, 621, 206, 1033, 724, 1036, 1030, 205, 208}"
3104,0,0,0,1.0662641,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Int[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (15-8 x)+\sqrt{x^2+1} \left((16-48 x) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-8 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-48 x^2+16 x+6\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{60 \sqrt{x^2+1}+60 x}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I - x), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 - x), x]/2 + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I + x), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
3105,0,0,0,0.9046106,"\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","Int[((1 + x^4)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^4),x]","\int \frac{\left(1+x^4\right) \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{1-x^4} \, dx","\text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+6 \text{$\#$1}^4-4 \text{$\#$1}^2+2\&,\frac{\text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^4-2 \text{$\#$1}^2+1}\&\right]-\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{2} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{\text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-4 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+6 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} (15-8 x)+\sqrt{x^2+1} \left((16-48 x) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-8 \sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(-48 x^2+16 x+6\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{60 \sqrt{x^2+1}+60 x}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)",1,"-Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x] + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I - x), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 - x), x]/2 + (I/2)*Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(I + x), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/(1 + x), x]/2","F",0,0,0,0,-1,"{}"
3106,0,0,0,2.3081064,"\int \frac{\left(1+x^2\right)^{5/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^{5/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{2299}{128} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(10240 x^7+8192 x^6-3740 x^5-1680 x^4-8025 x^3-6328 x^2+1525 x-184\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(10240 x^6+8192 x^5-8860 x^4-5776 x^3-2315 x^2-2416 x+935\right)+\left(143360 x^7-12288 x^6+5789696 x^5+7272 x^4-3989088 x^3+5298 x^2-3314848 x-282\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(143360 x^8-12288 x^7+5861376 x^6+1128 x^5-1112160 x^4+10470 x^3-6024144 x^2+690 x-803792\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{40320 \left(x^2-1\right) \left(8 x^4+8 x^2+1\right)+40320 \left(x^2-1\right) \sqrt{x^2+1} \left(8 x^3+4 x\right)}",1,"Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
3107,0,0,0,1.748889,"\int \frac{\left(1+x^2\right)^{5/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^{5/2} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{13 \text{$\#$1}^3 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1} \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^6-3 \text{$\#$1}^4+4 \text{$\#$1}^2-2}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{13 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-14 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$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,"Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4","F",0,0,0,0,-1,"{}"
3108,0,0,0,0.3361713,"\int \frac{\sqrt{1+x^4}}{(1+x)^3 \sqrt{x^2+\sqrt{1+x^4}}} \, dx","Int[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,"Defer[Int][Sqrt[1 + x^4]/((1 + x)^3*Sqrt[x^2 + Sqrt[1 + x^4]]), x]","F",0,0,0,0,-1,"{}"
3109,1,1229,0,2.0304705,"\int \frac{x^2}{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}} \, dx","Int[x^2/Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]],x]","-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(\sqrt{1-\sqrt{1-\frac{1}{x}}}+1\right)}{16 \left(\sqrt{1-\frac{1}{x}}+1\right)}-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(\sqrt{1-\sqrt{1-\frac{1}{x}}}+1\right)}{16 \left(\sqrt{1-\frac{1}{x}}+1\right)^2}-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(\sqrt{1-\sqrt{1-\frac{1}{x}}}+1\right)}{24 \left(\sqrt{1-\frac{1}{x}}+1\right)^3}-\frac{\sqrt{\frac{1}{2} \left(12049+8521 \sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{-1+\sqrt{2}}}\right)}{1024}-\frac{1}{256} \sqrt{527+373 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{-1+\sqrt{2}}}\right)-\frac{\left(1+\sqrt{2}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{-1+\sqrt{2}}}\right)}{32 \sqrt{2}}+\frac{703 \tanh ^{-1}\left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)}{2048}+\frac{\sqrt{\frac{1}{2} \left(-12049+8521 \sqrt{2}\right)} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)}{1024}+\frac{1}{256} \sqrt{-527+373 \sqrt{2}} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)+\frac{\left(-1+\sqrt{2}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{\sqrt{1+\sqrt{2}}}\right)}{32 \sqrt{2}}+\frac{703}{4096 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)}-\frac{703}{4096 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)}-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(11 \sqrt{1-\sqrt{1-\frac{1}{x}}}+12\right)}{128 \left(\sqrt{1-\frac{1}{x}}+1\right)}-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(108 \sqrt{1-\sqrt{1-\frac{1}{x}}}+121\right)}{1536 \left(\sqrt{1-\frac{1}{x}}+1\right)}+\frac{289}{4096 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^2}-\frac{289}{4096 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^2}-\frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}} \left(19 \sqrt{1-\sqrt{1-\frac{1}{x}}}+20\right)}{384 \left(\sqrt{1-\frac{1}{x}}+1\right)^2}+\frac{41}{1536 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^3}-\frac{41}{1536 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^3}+\frac{11}{1024 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^4}-\frac{11}{1024 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^4}+\frac{7}{2560 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^5}-\frac{7}{2560 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^5}+\frac{1}{1536 \left(1-\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}\right)^6}-\frac{1}{1536 \left(\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}+1\right)^6}","\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,"1/(1536*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^6) + 7/(2560*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^5) + 11/(1024*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^4) + 41/(1536*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^3) + 289/(4096*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^2) + 703/(4096*(1 - Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])) - 1/(1536*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^6) - 7/(2560*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^5) - 11/(1024*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^4) - 41/(1536*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^3) - 289/(4096*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])^2) - 703/(4096*(1 + Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]])) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(1 + Sqrt[1 - Sqrt[1 - x^(-1)]]))/(24*(1 + Sqrt[1 - x^(-1)])^3) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(1 + Sqrt[1 - Sqrt[1 - x^(-1)]]))/(16*(1 + Sqrt[1 - x^(-1)])^2) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(20 + 19*Sqrt[1 - Sqrt[1 - x^(-1)]]))/(384*(1 + Sqrt[1 - x^(-1)])^2) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(1 + Sqrt[1 - Sqrt[1 - x^(-1)]]))/(16*(1 + Sqrt[1 - x^(-1)])) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(12 + 11*Sqrt[1 - Sqrt[1 - x^(-1)]]))/(128*(1 + Sqrt[1 - x^(-1)])) - (Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]*(121 + 108*Sqrt[1 - Sqrt[1 - x^(-1)]]))/(1536*(1 + Sqrt[1 - x^(-1)])) - ((1 + Sqrt[2])^(3/2)*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[-1 + Sqrt[2]]])/(32*Sqrt[2]) - (Sqrt[527 + 373*Sqrt[2]]*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[-1 + Sqrt[2]]])/256 - (Sqrt[(12049 + 8521*Sqrt[2])/2]*ArcTan[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[-1 + Sqrt[2]]])/1024 + (703*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]])/2048 + ((-1 + Sqrt[2])^(3/2)*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[1 + Sqrt[2]]])/(32*Sqrt[2]) + (Sqrt[-527 + 373*Sqrt[2]]*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[1 + Sqrt[2]]])/256 + (Sqrt[(-12049 + 8521*Sqrt[2])/2]*ArcTanh[Sqrt[1 - Sqrt[1 - Sqrt[1 - x^(-1)]]]/Sqrt[1 + Sqrt[2]]])/1024","A",22,6,31,0.1935,0,"{1586, 1692, 207, 1178, 1166, 203}"
3110,0,0,0,13.2605025,"\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","Int[((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,"(a*(-1 + x^2 - x*C[0])^(1/3)*Defer[Int][(-1 + x^2 - x*C[1])^(1/3)/(-1 + x^2 - x*C[0])^(1/3), x])/(c*(-1 + x^2 - x*C[1])^(1/3)*((1 - x^2 + x*C[0])/(1 - x^2 + x*C[1]))^(1/3)) + (a*(-1 + x^2 - x*C[0])^(1/3)*Defer[Int][(-1 + x^2 - x*C[1])^(1/3)/(x^2*(-1 + x^2 - x*C[0])^(1/3)), x])/(c*(-1 + x^2 - x*C[1])^(1/3)*((1 - x^2 + x*C[0])/(1 - x^2 + x*C[1]))^(1/3)) + ((b*c + a*d)*(-1 + x^2 - x*C[0])^(1/3)*Defer[Int][(-1 + x^2 - x*C[1])^(1/3)/(x*(-1 + x^2 - x*C[0])^(1/3)), x])/(c^2*(-1 + x^2 - x*C[1])^(1/3)*((1 - x^2 + x*C[0])/(1 - x^2 + x*C[1]))^(1/3)) - (2*(b*c + a*d)*(-1 + x^2 - x*C[0])^(1/3)*Defer[Int][(-1 + x^2 - x*C[1])^(1/3)/((d - Sqrt[4*c^2 + d^2] + 2*c*x)*(-1 + x^2 - x*C[0])^(1/3)), x])/(c*(-1 + x^2 - x*C[1])^(1/3)*((1 - x^2 + x*C[0])/(1 - x^2 + x*C[1]))^(1/3)) - (2*(b*c + a*d)*(-1 + x^2 - x*C[0])^(1/3)*Defer[Int][(-1 + x^2 - x*C[1])^(1/3)/((d + Sqrt[4*c^2 + d^2] + 2*c*x)*(-1 + x^2 - x*C[0])^(1/3)), x])/(c*(-1 + x^2 - x*C[1])^(1/3)*((1 - x^2 + x*C[0])/(1 - x^2 + x*C[1]))^(1/3))","F",0,0,0,0,-1,"{}"
3111,0,0,0,2.3964806,"\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","Int[((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{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^5-4 x^4-16 x^3+2 x^2-48 x+2\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^4-4 x^3-48 x^2+4 x-16\right)+\left(128 x^5+12 x^4-272 x^3-9 x^2-96 x-3\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(128 x^6+12 x^5-208 x^4-3 x^3-248 x^2-9 x-8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(x^2-1\right) \left(\sqrt{x^2+1}+x\right)^{7/2}}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[x + Sqrt[1 + x^2]], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((-1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((-1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((-1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",0,0,0,0,-1,"{}"
3112,0,0,0,1.8585092,"\int \frac{\left(1+x^2\right)^2 \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","Int[((1 + x^2)^2*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]","\int \frac{\left(1+x^2\right)^2 \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2 \sqrt{x+\sqrt{1+x^2}}} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]-\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{4 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-8 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+9 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\frac{1}{8} \tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^5-4 x^4-16 x^3+2 x^2-48 x+2\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(64 x^4-4 x^3-48 x^2+4 x-16\right)+\left(128 x^5+12 x^4-272 x^3-9 x^2-96 x-3\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(128 x^6+12 x^5-208 x^4-3 x^3-248 x^2-9 x-8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{24 \left(x^2-1\right) \left(\sqrt{x^2+1}+x\right)^{7/2}}",1,"Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/Sqrt[x + Sqrt[1 + x^2]], x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((-1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((-1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((-1 + x)*Sqrt[x + Sqrt[1 + x^2]]), x] + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]","F",0,0,0,0,-1,"{}"
3113,0,0,0,1.8688775,"\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+13 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$1}}\&\right]-\tanh ^{-1}\left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\frac{\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(24 x^5+32 x^4-6 x^3-16 x^2-18 x-16\right)+\sqrt{x^2+1} \left(\sqrt{\sqrt{x^2+1}+x} \sqrt{\sqrt{\sqrt{x^2+1}+x}+1} \left(24 x^4+32 x^3-18 x^2-32 x-6\right)+\left(240 x^5-32 x^4-1170 x^3+24 x^2-120 x+8\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}\right)+\left(240 x^6-32 x^5-1050 x^4+8 x^3-735 x^2+24 x+75\right) \sqrt{\sqrt{\sqrt{x^2+1}+x}+1}}{105 \left(x^2-1\right) \left(\sqrt{x^2+1}+x\right)^{5/2}}",1,"Defer[Int][Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 - x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x)^2, x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]","F",0,0,0,0,-1,"{}"
3114,0,0,0,1.7164984,"\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","Int[((1 + x^2)^2*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]","\int \frac{\left(1+x^2\right)^2 \sqrt{x+\sqrt{1+x^2}} \sqrt{1+\sqrt{x+\sqrt{1+x^2}}}}{\left(1-x^2\right)^2} \, dx","\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+4 \text{$\#$1}^4-2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+13 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+2 \text{$\#$1}^3}\&\right]+\frac{1}{4} \text{RootSum}\left[\text{$\#$1}^8-4 \text{$\#$1}^6+8 \text{$\#$1}^4-8 \text{$\#$1}^2+2\&,\frac{7 \text{$\#$1}^6 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-15 \text{$\#$1}^4 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)+5 \text{$\#$1}^2 \log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)-\log \left(\sqrt{\sqrt{\sqrt{x^2+1}+x}+1}-\text{$\#$1}\right)}{\text{$\#$1}^7-3 \text{$\#$1}^5+4 \text{$\#$1}^3-2 \text{$\#$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,"Defer[Int][Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]], x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 - x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x)^2, x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x), x] + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]","F",0,0,0,0,-1,"{}"
3115,0,0,0,0.281788,"\int \frac{x^2}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[x^2/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]],x]","\int \frac{x^2}{\sqrt{1+\sqrt{a x+\sqrt{-b+a^2 x^2}}}} \, dx","\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,"Defer[Int][x^2/Sqrt[1 + Sqrt[a*x + Sqrt[-b + a^2*x^2]]], x]","F",0,0,0,0,-1,"{}"
3116,1,473,0,0.2000021,"\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","Int[(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{\left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log (1-x)}{4 \sqrt[3]{a+1} \sqrt[3]{x}}-\frac{\left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log (x+1)}{4 \sqrt[3]{a-1} \sqrt[3]{x}}+\frac{3 \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log \left(\frac{\sqrt[3]{a x+1}}{\sqrt[3]{a-1}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a-1} \sqrt[3]{x}}-\frac{3 \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log \left(\frac{\sqrt[3]{a x+1}}{\sqrt[3]{a+1}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a+1} \sqrt[3]{x}}+\frac{\sqrt{3} \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x+1}}{\sqrt{3} \sqrt[3]{a-1} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{a-1} \sqrt[3]{x}}-\frac{\sqrt{3} \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x+1}}{\sqrt{3} \sqrt[3]{a+1} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{a+1} \sqrt[3]{x}}","\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,"(Sqrt[3]*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*ArcTan[1/Sqrt[3] + (2*(1 + a*x)^(1/3))/(Sqrt[3]*(-1 + a)^(1/3)*x^(1/3))])/(2*(-1 + a)^(1/3)*x^(1/3)) - (Sqrt[3]*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*ArcTan[1/Sqrt[3] + (2*(1 + a*x)^(1/3))/(Sqrt[3]*(1 + a)^(1/3)*x^(1/3))])/(2*(1 + a)^(1/3)*x^(1/3)) + ((1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[1 - x])/(4*(1 + a)^(1/3)*x^(1/3)) - ((1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[1 + x])/(4*(-1 + a)^(1/3)*x^(1/3)) + (3*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[-x^(1/3) + (1 + a*x)^(1/3)/(-1 + a)^(1/3)])/(4*(-1 + a)^(1/3)*x^(1/3)) - (3*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[-x^(1/3) + (1 + a*x)^(1/3)/(1 + a)^(1/3)])/(4*(1 + a)^(1/3)*x^(1/3))","A",10,6,44,0.1364,1,"{6688, 6718, 912, 105, 59, 91}"
3117,0,0,0,1.0508293,"\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","Int[(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,"Defer[Int][(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",0,0,0,0,-1,"{}"
3118,1,760,0,1.2557326,"\int \frac{\sqrt[6]{a x+\sqrt{-b+a^2 x^2}}}{x^3 \sqrt{-b+a^2 x^2}} \, dx","Int[(a*x + Sqrt[-b + a^2*x^2])^(1/6)/(x^3*Sqrt[-b + a^2*x^2]),x]","\frac{7 a^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{7/6}}{6 b \left(\left(\sqrt{a^2 x^2-b}+a x\right)^2+b\right)}-\frac{2 a^2 \left(\sqrt{a^2 x^2-b}+a x\right)^{7/6}}{\left(\left(\sqrt{a^2 x^2-b}+a x\right)^2+b\right)^2}-\frac{35 a^2 \log \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}-\sqrt[12]{-b} \sqrt[6]{\sqrt{a^2 x^2-b}+a x}+\sqrt[6]{-b}\right)}{144 (-b)^{17/12}}+\frac{35 a^2 \log \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+\sqrt[12]{-b} \sqrt[6]{\sqrt{a^2 x^2-b}+a x}+\sqrt[6]{-b}\right)}{144 (-b)^{17/12}}+\frac{35 a^2 \log \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}-\sqrt{3} \sqrt[12]{-b} \sqrt[6]{\sqrt{a^2 x^2-b}+a x}+\sqrt[6]{-b}\right)}{48 \sqrt{3} (-b)^{17/12}}-\frac{35 a^2 \log \left(\sqrt[3]{\sqrt{a^2 x^2-b}+a x}+\sqrt{3} \sqrt[12]{-b} \sqrt[6]{\sqrt{a^2 x^2-b}+a x}+\sqrt[6]{-b}\right)}{48 \sqrt{3} (-b)^{17/12}}-\frac{35 a^2 \tan ^{-1}\left(\frac{\sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[12]{-b}}\right)}{36 (-b)^{17/12}}-\frac{35 a^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[12]{-b}}}{\sqrt{3}}\right)}{24 \sqrt{3} (-b)^{17/12}}+\frac{35 a^2 \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[12]{-b}}\right)}{72 (-b)^{17/12}}+\frac{35 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[12]{-b}}+1}{\sqrt{3}}\right)}{24 \sqrt{3} (-b)^{17/12}}-\frac{35 a^2 \tan ^{-1}\left(\frac{2 \sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[12]{-b}}+\sqrt{3}\right)}{72 (-b)^{17/12}}+\frac{35 a^2 \tanh ^{-1}\left(\frac{\sqrt[6]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[12]{-b}}\right)}{36 (-b)^{17/12}}","-\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,"(-2*a^2*(a*x + Sqrt[-b + a^2*x^2])^(7/6))/(b + (a*x + Sqrt[-b + a^2*x^2])^2)^2 + (7*a^2*(a*x + Sqrt[-b + a^2*x^2])^(7/6))/(6*b*(b + (a*x + Sqrt[-b + a^2*x^2])^2)) - (35*a^2*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/6)/(-b)^(1/12)])/(36*(-b)^(17/12)) - (35*a^2*ArcTan[(1 - (2*(a*x + Sqrt[-b + a^2*x^2])^(1/6))/(-b)^(1/12))/Sqrt[3]])/(24*Sqrt[3]*(-b)^(17/12)) + (35*a^2*ArcTan[Sqrt[3] - (2*(a*x + Sqrt[-b + a^2*x^2])^(1/6))/(-b)^(1/12)])/(72*(-b)^(17/12)) + (35*a^2*ArcTan[(1 + (2*(a*x + Sqrt[-b + a^2*x^2])^(1/6))/(-b)^(1/12))/Sqrt[3]])/(24*Sqrt[3]*(-b)^(17/12)) - (35*a^2*ArcTan[Sqrt[3] + (2*(a*x + Sqrt[-b + a^2*x^2])^(1/6))/(-b)^(1/12)])/(72*(-b)^(17/12)) + (35*a^2*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/6)/(-b)^(1/12)])/(36*(-b)^(17/12)) - (35*a^2*Log[(-b)^(1/6) - (-b)^(1/12)*(a*x + Sqrt[-b + a^2*x^2])^(1/6) + (a*x + Sqrt[-b + a^2*x^2])^(1/3)])/(144*(-b)^(17/12)) + (35*a^2*Log[(-b)^(1/6) + (-b)^(1/12)*(a*x + Sqrt[-b + a^2*x^2])^(1/6) + (a*x + Sqrt[-b + a^2*x^2])^(1/3)])/(144*(-b)^(17/12)) + (35*a^2*Log[(-b)^(1/6) - Sqrt[3]*(-b)^(1/12)*(a*x + Sqrt[-b + a^2*x^2])^(1/6) + (a*x + Sqrt[-b + a^2*x^2])^(1/3)])/(48*Sqrt[3]*(-b)^(17/12)) - (35*a^2*Log[(-b)^(1/6) + Sqrt[3]*(-b)^(1/12)*(a*x + Sqrt[-b + a^2*x^2])^(1/6) + (a*x + Sqrt[-b + a^2*x^2])^(1/3)])/(48*Sqrt[3]*(-b)^(17/12))","A",25,13,42,0.3095,1,"{2120, 288, 290, 329, 301, 209, 634, 618, 204, 628, 203, 210, 206}"
3119,0,0,0,30.4783668,"\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","Int[(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,"(C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(-1 + 2*x*C[3] - Sqrt[1 - 4*C[3]*C[4]])), x])/(2*(x*C[0] + x^2*C[3] + C[4])^(1/4)) - (C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(1 + 2*x*C[3] - Sqrt[1 - 4*C[3]*C[4]])), x])/(2*(x*C[0] + x^2*C[3] + C[4])^(1/4)) + (C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(-1 + 2*x*C[3] + Sqrt[1 - 4*C[3]*C[4]])), x])/(2*(x*C[0] + x^2*C[3] + C[4])^(1/4)) - (C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(1 + 2*x*C[3] + Sqrt[1 - 4*C[3]*C[4]])), x])/(2*(x*C[0] + x^2*C[3] + C[4])^(1/4)) + (C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*(1 + Sqrt[1 + 4*C[3]*C[4]])*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(-(Sqrt[2]*x*C[3]) + Sqrt[-1 - 2*C[3]*C[4] - Sqrt[1 + 4*C[3]*C[4]]])), x])/(4*(x*C[0] + x^2*C[3] + C[4])^(1/4)*Sqrt[-1 - 2*C[3]*C[4] - Sqrt[1 + 4*C[3]*C[4]]]) + (C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*(1 + Sqrt[1 + 4*C[3]*C[4]])*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(Sqrt[2]*x*C[3] + Sqrt[-1 - 2*C[3]*C[4] - Sqrt[1 + 4*C[3]*C[4]]])), x])/(4*(x*C[0] + x^2*C[3] + C[4])^(1/4)*Sqrt[-1 - 2*C[3]*C[4] - Sqrt[1 + 4*C[3]*C[4]]]) + (C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*(1 - Sqrt[1 + 4*C[3]*C[4]])*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(-(Sqrt[2]*x*C[3]) + Sqrt[-1 - 2*C[3]*C[4] + Sqrt[1 + 4*C[3]*C[4]]])), x])/(4*(x*C[0] + x^2*C[3] + C[4])^(1/4)*Sqrt[-1 - 2*C[3]*C[4] + Sqrt[1 + 4*C[3]*C[4]]]) + (C[3]*((x*C[0] + x^2*C[3] + C[4])/(x*C[1] + x^2*C[3] + C[4]))^(1/4)*(x*C[1] + x^2*C[3] + C[4])^(1/4)*(1 - Sqrt[1 + 4*C[3]*C[4]])*Defer[Int][(x*C[0] + x^2*C[3] + C[4])^(1/4)/((x*C[1] + x^2*C[3] + C[4])^(1/4)*(Sqrt[2]*x*C[3] + Sqrt[-1 - 2*C[3]*C[4] + Sqrt[1 + 4*C[3]*C[4]]])), x])/(4*(x*C[0] + x^2*C[3] + C[4])^(1/4)*Sqrt[-1 - 2*C[3]*C[4] + Sqrt[1 + 4*C[3]*C[4]]])","F",0,0,0,0,-1,"{}"
3120,0,0,0,0.3552844,"\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","Int[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]","\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","\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,"Defer[Int][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]","F",0,0,0,0,-1,"{}"
3121,0,0,0,0.0526305,"\int \frac{1}{\sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(-1/3),x]","\int \frac{1}{\sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","-\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,"Defer[Int][(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(-1/3), x]","F",0,0,0,0,-1,"{}"
3122,1,471,0,0.4050337,"\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","Int[((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{(a x+1) (5 b-3 a c) (c-b x) \sqrt[4]{-\frac{\left(1-x^2\right)^4 (a x+1)}{c-b x}}}{8 a^2 b^2 \left(1-x^2\right)}+\frac{\left(\left(7-32 a^2\right) b^2+15 a^2 c^2-10 a b c\right) (c-b x) \sqrt[4]{-\frac{\left(1-x^2\right)^4 (a x+1)}{c-b x}}}{32 a^2 b^3 \left(1-x^2\right)}+\frac{(a x+1)^2 (c-b x) \sqrt[4]{-\frac{\left(1-x^2\right)^4 (a x+1)}{c-b x}}}{3 a^2 b \left(1-x^2\right)}-\frac{(a c+b) \left(\left(7-32 a^2\right) b^2+15 a^2 c^2-10 a b c\right) \sqrt[4]{b x-c} \sqrt[4]{-\frac{\left(1-x^2\right)^4 (a x+1)}{c-b x}} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{a x+1}}{\sqrt[4]{a} \sqrt[4]{b x-c}}\right)}{64 a^{11/4} b^{13/4} \left(1-x^2\right) \sqrt[4]{a x+1}}-\frac{(a c+b) \left(\left(7-32 a^2\right) b^2+15 a^2 c^2-10 a b c\right) \sqrt[4]{b x-c} \sqrt[4]{-\frac{\left(1-x^2\right)^4 (a x+1)}{c-b x}} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt[4]{a x+1}}{\sqrt[4]{a} \sqrt[4]{b x-c}}\right)}{64 a^{11/4} b^{13/4} \left(1-x^2\right) \sqrt[4]{a x+1}}","\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,"(((7 - 32*a^2)*b^2 - 10*a*b*c + 15*a^2*c^2)*(c - b*x)*(-(((1 + a*x)*(1 - x^2)^4)/(c - b*x)))^(1/4))/(32*a^2*b^3*(1 - x^2)) - ((5*b - 3*a*c)*(1 + a*x)*(c - b*x)*(-(((1 + a*x)*(1 - x^2)^4)/(c - b*x)))^(1/4))/(8*a^2*b^2*(1 - x^2)) + ((1 + a*x)^2*(c - b*x)*(-(((1 + a*x)*(1 - x^2)^4)/(c - b*x)))^(1/4))/(3*a^2*b*(1 - x^2)) - ((b + a*c)*((7 - 32*a^2)*b^2 - 10*a*b*c + 15*a^2*c^2)*(-c + b*x)^(1/4)*(-(((1 + a*x)*(1 - x^2)^4)/(c - b*x)))^(1/4)*ArcTan[(b^(1/4)*(1 + a*x)^(1/4))/(a^(1/4)*(-c + b*x)^(1/4))])/(64*a^(11/4)*b^(13/4)*(1 + a*x)^(1/4)*(1 - x^2)) - ((b + a*c)*((7 - 32*a^2)*b^2 - 10*a*b*c + 15*a^2*c^2)*(-c + b*x)^(1/4)*(-(((1 + a*x)*(1 - x^2)^4)/(c - b*x)))^(1/4)*ArcTanh[(b^(1/4)*(1 + a*x)^(1/4))/(a^(1/4)*(-c + b*x)^(1/4))])/(64*a^(11/4)*b^(13/4)*(1 + a*x)^(1/4)*(1 - x^2))","A",10,10,60,0.1667,1,"{6688, 6718, 952, 80, 50, 63, 240, 212, 208, 205}"
3123,0,0,0,0.052621,"\int \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","Int[(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3),x]","\int \sqrt[3]{c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}} \, dx","\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,"Defer[Int][(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(1/3), x]","F",0,0,0,0,-1,"{}"
3124,1,746,0,0.9115966,"\int \frac{\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x \left(-b+a^2 x^2\right)^{3/2}} \, dx","Int[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(x*(-b + a^2*x^2)^(3/2)),x]","-\frac{\log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt{2} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{b}\right)}{4 \sqrt{2} b^{11/8}}+\frac{\log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+\sqrt{2} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{b}\right)}{4 \sqrt{2} b^{11/8}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}\right)}{2 b^{11/8}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}\right)}{2 \sqrt{2} b^{11/8}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}+1\right)}{2 \sqrt{2} 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{2 \left(\sqrt{a^2 x^2-b}+a x\right)^{5/4}}{b \left(b-\left(\sqrt{a^2 x^2-b}+a x\right)^2\right)}-\frac{\log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{\sqrt{2} (-b)^{11/8}}+\frac{\log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{\sqrt{2} (-b)^{11/8}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{(-b)^{11/8}}-\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{(-b)^{11/8}}+\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}+1\right)}{(-b)^{11/8}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{(-b)^{11/8}}","-\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,"(2*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(b*(b - (a*x + Sqrt[-b + a^2*x^2])^2)) - (2*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(-b)^(11/8) - ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)]/(2*b^(11/8)) - (Sqrt[2]*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(-b)^(11/8) + (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(-b)^(11/8) - ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)]/(2*Sqrt[2]*b^(11/8)) + ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)]/(2*Sqrt[2]*b^(11/8)) - (2*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(-b)^(11/8) - ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)]/(2*b^(11/8)) - 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)^(11/8)) + 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)^(11/8)) - 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]]]/(4*Sqrt[2]*b^(11/8)) + 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]]]/(4*Sqrt[2]*b^(11/8))","A",31,14,42,0.3333,1,"{2120, 466, 471, 584, 301, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
3125,0,0,0,27.7794502,"\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","Int[(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,"((x*C[0] + x^3*C[3] + C[4])^(1/3)*Defer[Int][(x*C[1] + x^3*C[3] + C[4])^(1/3)/((x - x^3*C[3] - C[4])*(x*C[0] + x^3*C[3] + C[4])^(1/3)), x])/(3*((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x*C[1] + x^3*C[3] + C[4])^(1/3)) + (C[3]*(x*C[0] + x^3*C[3] + C[4])^(1/3)*Defer[Int][(x^2*(x*C[1] + x^3*C[3] + C[4])^(1/3))/((-x + x^3*C[3] + C[4])*(x*C[0] + x^3*C[3] + C[4])^(1/3)), x])/(((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x*C[1] + x^3*C[3] + C[4])^(1/3)) + (C[4]*(x*C[0] + x^3*C[3] + C[4])^(1/3)*Defer[Int][(x*C[1] + x^3*C[3] + C[4])^(1/3)/((x*C[0] + 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])/(3*((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x*C[1] + x^3*C[3] + C[4])^(1/3)) - ((x*C[0] + x^3*C[3] + C[4])^(1/3)*Defer[Int][(x*(x*C[1] + x^3*C[3] + C[4])^(1/3))/((x*C[0] + 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])/(3*((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x*C[1] + x^3*C[3] + C[4])^(1/3)) - (C[3]*C[4]*(x*C[0] + x^3*C[3] + C[4])^(1/3)*Defer[Int][(x^2*(x*C[1] + x^3*C[3] + C[4])^(1/3))/((x*C[0] + 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])/(((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x*C[1] + x^3*C[3] + C[4])^(1/3)) - (5*C[3]*(x*C[0] + x^3*C[3] + C[4])^(1/3)*Defer[Int][(x^3*(x*C[1] + x^3*C[3] + C[4])^(1/3))/((x*C[0] + 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])/(3*((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x*C[1] + x^3*C[3] + C[4])^(1/3)) - (C[3]^2*(x*C[0] + x^3*C[3] + C[4])^(1/3)*Defer[Int][(x^5*(x*C[1] + x^3*C[3] + C[4])^(1/3))/((x*C[0] + 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])/(((x*C[0] + x^3*C[3] + C[4])/(x*C[1] + x^3*C[3] + C[4]))^(1/3)*(x*C[1] + x^3*C[3] + C[4])^(1/3))","F",0,0,0,0,-1,"{}"
3126,1,279,0,0.8913214,"\int \frac{(-d+c x) \sqrt{a x+\sqrt{b^2+a^2 x^2}}}{d+c x} \, dx","Int[((-d + c*x)*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/(d + c*x),x]","\frac{4 d \sqrt{a d-\sqrt{a^2 d^2+b^2 c^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}}+\frac{4 d \sqrt{\sqrt{a^2 d^2+b^2 c^2}+a 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)}{c^{3/2}}-\frac{4 d \sqrt{\sqrt{a^2 x^2+b^2}+a x}}{c}-\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}","-\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/(a*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])) - (4*d*Sqrt[a*x + Sqrt[b^2 + a^2*x^2]])/c + (a*x + Sqrt[b^2 + a^2*x^2])^(3/2)/(3*a) + (4*d*Sqrt[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) + (4*d*Sqrt[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)","A",12,8,38,0.2105,1,"{6742, 2117, 14, 2119, 1628, 826, 1166, 205}"
3127,1,609,0,0.539334,"\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","Int[(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 (5-3 a) \left(1-x^2\right) (a x+1) \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}}}{20 x}+\frac{3 (3 a+5) \left(1-x^2\right) (a x+1) \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}}}{20 x}-\frac{3 \left(1-x^2\right) (a x+1) \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}}}{5 x^2}+\frac{\left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log (1-x)}{4 \sqrt[3]{a+1} \sqrt[3]{x}}+\frac{\left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log (x+1)}{4 \sqrt[3]{a-1} \sqrt[3]{x}}-\frac{3 \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log \left(\frac{\sqrt[3]{a x+1}}{\sqrt[3]{a-1}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a-1} \sqrt[3]{x}}-\frac{3 \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \log \left(\frac{\sqrt[3]{a x+1}}{\sqrt[3]{a+1}}-\sqrt[3]{x}\right)}{4 \sqrt[3]{a+1} \sqrt[3]{x}}-\frac{\sqrt{3} \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x+1}}{\sqrt{3} \sqrt[3]{a-1} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{a-1} \sqrt[3]{x}}-\frac{\sqrt{3} \left(1-x^2\right) \sqrt[3]{a x+1} \sqrt[3]{-\frac{x}{\left(1-x^2\right)^3 (a x+1)}} \tan ^{-1}\left(\frac{2 \sqrt[3]{a x+1}}{\sqrt{3} \sqrt[3]{a+1} \sqrt[3]{x}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt[3]{a+1} \sqrt[3]{x}}","-\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*(1 + a*x)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2))/(5*x^2) - (3*(5 - 3*a)*(1 + a*x)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2))/(20*x) + (3*(5 + 3*a)*(1 + a*x)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2))/(20*x) - (Sqrt[3]*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*ArcTan[1/Sqrt[3] + (2*(1 + a*x)^(1/3))/(Sqrt[3]*(-1 + a)^(1/3)*x^(1/3))])/(2*(-1 + a)^(1/3)*x^(1/3)) - (Sqrt[3]*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*ArcTan[1/Sqrt[3] + (2*(1 + a*x)^(1/3))/(Sqrt[3]*(1 + a)^(1/3)*x^(1/3))])/(2*(1 + a)^(1/3)*x^(1/3)) + ((1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[1 - x])/(4*(1 + a)^(1/3)*x^(1/3)) + ((1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[1 + x])/(4*(-1 + a)^(1/3)*x^(1/3)) - (3*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[-x^(1/3) + (1 + a*x)^(1/3)/(-1 + a)^(1/3)])/(4*(-1 + a)^(1/3)*x^(1/3)) - (3*(1 + a*x)^(1/3)*(-(x/((1 + a*x)*(1 - x^2)^3)))^(1/3)*(1 - x^2)*Log[-x^(1/3) + (1 + a*x)^(1/3)/(1 + a)^(1/3)])/(4*(1 + a)^(1/3)*x^(1/3))","A",12,7,48,0.1458,1,"{6688, 6718, 912, 129, 155, 12, 91}"
3128,0,0,0,6.282881,"\int \frac{1}{a b c-(c+a b x)^2 \sqrt{c+b x+a x^2}} \, dx","Int[(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,"a*b*c*Defer[Int][(a^2*b^2*c^2*(1 - c^3/(a^2*b^2)) - (1 + 4*a)*b*c^4*x - 4*a*b^2*c^3*(1 + (6*a + c/b^2)/4)*x^2 - 6*a^2*b^3*c^2*(1 + (2*(a*b^2 + c))/(3*b^2))*x^3 - 4*a^3*b^4*c*(1 + (a + (6*c)/b^2)/4)*x^4 - a^4*b^5*(1 + (4*c)/b^2)*x^5 - a^5*b^4*x^6)^(-1), x] + c^2*Defer[Int][Sqrt[c + b*x + a*x^2]/(a^2*b^2*c^2*(1 - c^3/(a^2*b^2)) - (1 + 4*a)*b*c^4*x - 4*a*b^2*c^3*(1 + (6*a + c/b^2)/4)*x^2 - 6*a^2*b^3*c^2*(1 + (2*(a*b^2 + c))/(3*b^2))*x^3 - 4*a^3*b^4*c*(1 + (a + (6*c)/b^2)/4)*x^4 - a^4*b^5*(1 + (4*c)/b^2)*x^5 - a^5*b^4*x^6), x] + 2*a*b*c*Defer[Int][(x*Sqrt[c + b*x + a*x^2])/(a^2*b^2*c^2*(1 - c^3/(a^2*b^2)) - (1 + 4*a)*b*c^4*x - 4*a*b^2*c^3*(1 + (6*a + c/b^2)/4)*x^2 - 6*a^2*b^3*c^2*(1 + (2*(a*b^2 + c))/(3*b^2))*x^3 - 4*a^3*b^4*c*(1 + (a + (6*c)/b^2)/4)*x^4 - a^4*b^5*(1 + (4*c)/b^2)*x^5 - a^5*b^4*x^6), x] + a^2*b^2*Defer[Int][(x^2*Sqrt[c + b*x + a*x^2])/(a^2*b^2*c^2*(1 - c^3/(a^2*b^2)) - (1 + 4*a)*b*c^4*x - 4*a*b^2*c^3*(1 + (6*a + c/b^2)/4)*x^2 - 6*a^2*b^3*c^2*(1 + (2*(a*b^2 + c))/(3*b^2))*x^3 - 4*a^3*b^4*c*(1 + (a + (6*c)/b^2)/4)*x^4 - a^4*b^5*(1 + (4*c)/b^2)*x^5 - a^5*b^4*x^6), x]","F",0,0,0,0,-1,"{}"
3129,1,772,0,0.8730825,"\int \frac{\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}}{x^2 \left(-b+a^2 x^2\right)^{3/2}} \, dx","Int[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(x^2*(-b + a^2*x^2)^(3/2)),x]","\frac{a \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt{2} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{b}\right)}{4 \sqrt{2} b^{15/8}}-\frac{a \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+\sqrt{2} \sqrt[8]{b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{b}\right)}{4 \sqrt{2} b^{15/8}}-\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{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}\right)}{2 \sqrt{2} b^{15/8}}-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{b}}+1\right)}{2 \sqrt{2} 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{4 a \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{b^2-\left(\sqrt{a^2 x^2-b}+a x\right)^4}+\frac{a \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}-\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{4 \sqrt{2} (-b)^{15/8}}-\frac{a \log \left(\sqrt{\sqrt{a^2 x^2-b}+a x}+\sqrt{2} \sqrt[8]{-b} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}+\sqrt[4]{-b}\right)}{4 \sqrt{2} (-b)^{15/8}}-\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{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}\right)}{2 \sqrt{2} (-b)^{15/8}}-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{\sqrt{a^2 x^2-b}+a x}}{\sqrt[8]{-b}}+1\right)}{2 \sqrt{2} (-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 \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,"(4*a*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(b^2 - (a*x + Sqrt[-b + a^2*x^2])^4) - (a*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(2*(-b)^(15/8)) - (a*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(2*b^(15/8)) + (a*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(2*Sqrt[2]*(-b)^(15/8)) - (a*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(2*Sqrt[2]*(-b)^(15/8)) + (a*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(2*Sqrt[2]*b^(15/8)) - (a*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(2*Sqrt[2]*b^(15/8)) - (a*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(2*(-b)^(15/8)) - (a*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(2*b^(15/8)) + (a*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]]])/(4*Sqrt[2]*(-b)^(15/8)) - (a*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]]])/(4*Sqrt[2]*(-b)^(15/8)) + (a*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]]])/(4*Sqrt[2]*b^(15/8)) - (a*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]]])/(4*Sqrt[2]*b^(15/8))","A",31,14,42,0.3333,1,"{2120, 259, 288, 329, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
3130,0,0,0,26.0205471,"\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","Int[((-1 + x^2)*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/(1 + x^2),x]","\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","\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,"(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[1]*C[2] - C[0]*C[3])*C[5])/(2*Sqrt[C[1]]*C[3]^(5/4)*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[1]*C[2] - C[0]*C[3])*C[5])/(2*Sqrt[C[1]]*C[3]^(5/4)*Sqrt[Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5]]) + ((C[2] + x*C[3])*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]])/C[3] + 8*(C[1]*C[2] - C[0]*C[3])*C[5]^2*Defer[Subst][Defer[Int][x^4/(-(x^8*C[2]^2*(1 + C[3]^2/C[2]^2)) + 4*x^6*C[2]^2*(1 + C[3]^2/C[2]^2)*C[4] + 4*x^2*C[2]^2*C[4]^3*(1 + (C[3]^2 - ((C[0]*C[2] + C[1]*C[3])*C[5]^2)/C[4]^2)/C[2]^2) - 6*x^4*C[2]^2*C[4]^2*(1 + (3*C[3]^2 - ((C[0]*C[2] + C[1]*C[3])*C[5]^2)/C[4]^2)/(3*C[2]^2)) - C[2]^2*C[4]^4*(1 + (C[3]^2 + (C[5]^2*(-2*C[0]*C[2]*C[4]^2 + C[0]^2*C[5]^2 + C[1]*(-2*C[3]*C[4]^2 + C[1]*C[5]^2)))/C[4]^4)/C[2]^2)), x], x, Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]] + 8*(C[1]*C[2] - C[0]*C[3])*C[4]*C[5]^2*Defer[Subst][Defer[Int][x^2/(x^8*C[2]^2*(1 + C[3]^2/C[2]^2) - 4*x^6*C[2]^2*(1 + C[3]^2/C[2]^2)*C[4] - 4*x^2*C[2]^2*C[4]^3*(1 + (C[3]^2 - ((C[0]*C[2] + C[1]*C[3])*C[5]^2)/C[4]^2)/C[2]^2) + 6*x^4*C[2]^2*C[4]^2*(1 + (3*C[3]^2 - ((C[0]*C[2] + C[1]*C[3])*C[5]^2)/C[4]^2)/(3*C[2]^2)) + C[2]^2*C[4]^4*(1 + (C[3]^2 + (C[5]^2*(-2*C[0]*C[2]*C[4]^2 + C[0]^2*C[5]^2 + C[1]*(-2*C[3]*C[4]^2 + C[1]*C[5]^2)))/C[4]^4)/C[2]^2)), x], x, Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]]","F",0,0,0,0,-1,"{}"
3131,0,0,0,0.3325449,"\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","Int[Sqrt[-b + a^2*x^2]/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4),x]","\int \frac{\sqrt{-b+a^2 x^2}}{\sqrt[4]{c+\sqrt[3]{a x+\sqrt{-b+a^2 x^2}}}} \, dx","\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,"Defer[Int][Sqrt[-b + a^2*x^2]/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/3))^(1/4), x]","F",0,0,0,0,-1,"{}"
3132,0,0,0,1.1322729,"\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","Int[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{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,"Defer[Int][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",0,0,0,0,-1,"{}"
3133,1,908,0,5.5700935,"\int \frac{\left(b+a x^4\right) \sqrt{-b-c x^2+a x^4}}{\left(-b+a x^4\right)^2} \, dx","Int[((b + a*x^4)*Sqrt[-b - c*x^2 + a*x^4])/(-b + a*x^4)^2,x]","\frac{\sqrt{a x^4-c x^2-b} x}{4 \sqrt{b} \left(\sqrt{b}-\sqrt{a} x^2\right)}+\frac{\sqrt{a x^4-c x^2-b} x}{4 \sqrt{b} \left(\sqrt{a} x^2+\sqrt{b}\right)}+\frac{\left(c+2 \sqrt{a} \sqrt{b}-\sqrt{c^2+4 a b}\right) \sqrt{c+\sqrt{c^2+4 a b}} \sqrt{1-\frac{2 a x^2}{c-\sqrt{c^2+4 a b}}} \sqrt{1-\frac{2 a x^2}{c+\sqrt{c^2+4 a b}}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x}{\sqrt{c+\sqrt{c^2+4 a b}}}\right)|\frac{c+\sqrt{c^2+4 a b}}{c-\sqrt{c^2+4 a b}}\right)}{8 \sqrt{2} a \sqrt{b} \sqrt{a x^4-c x^2-b}}+\frac{\left(-c+2 \sqrt{a} \sqrt{b}+\sqrt{c^2+4 a b}\right) \sqrt{c+\sqrt{c^2+4 a b}} \sqrt{1-\frac{2 a x^2}{c-\sqrt{c^2+4 a b}}} \sqrt{1-\frac{2 a x^2}{c+\sqrt{c^2+4 a b}}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x}{\sqrt{c+\sqrt{c^2+4 a b}}}\right)|\frac{c+\sqrt{c^2+4 a b}}{c-\sqrt{c^2+4 a b}}\right)}{8 \sqrt{2} a \sqrt{b} \sqrt{a x^4-c x^2-b}}-\frac{\sqrt{c+\sqrt{c^2+4 a b}} \sqrt{1-\frac{2 a x^2}{c-\sqrt{c^2+4 a b}}} \sqrt{1-\frac{2 a x^2}{c+\sqrt{c^2+4 a b}}} \Pi \left(-\frac{c+\sqrt{c^2+4 a b}}{2 \sqrt{a} \sqrt{b}};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x}{\sqrt{c+\sqrt{c^2+4 a b}}}\right)|\frac{c+\sqrt{c^2+4 a b}}{c-\sqrt{c^2+4 a b}}\right)}{2 \sqrt{2} \sqrt{a} \sqrt{a x^4-c x^2-b}}-\frac{\sqrt{c+\sqrt{c^2+4 a b}} \sqrt{1-\frac{2 a x^2}{c-\sqrt{c^2+4 a b}}} \sqrt{1-\frac{2 a x^2}{c+\sqrt{c^2+4 a b}}} \Pi \left(\frac{c+\sqrt{c^2+4 a b}}{2 \sqrt{a} \sqrt{b}};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x}{\sqrt{c+\sqrt{c^2+4 a b}}}\right)|\frac{c+\sqrt{c^2+4 a b}}{c-\sqrt{c^2+4 a b}}\right)}{2 \sqrt{2} \sqrt{a} \sqrt{a x^4-c x^2-b}}","\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,"(x*Sqrt[-b - c*x^2 + a*x^4])/(4*Sqrt[b]*(Sqrt[b] - Sqrt[a]*x^2)) + (x*Sqrt[-b - c*x^2 + a*x^4])/(4*Sqrt[b]*(Sqrt[b] + Sqrt[a]*x^2)) + ((2*Sqrt[a]*Sqrt[b] + c - Sqrt[4*a*b + c^2])*Sqrt[c + Sqrt[4*a*b + c^2]]*Sqrt[1 - (2*a*x^2)/(c - Sqrt[4*a*b + c^2])]*Sqrt[1 - (2*a*x^2)/(c + Sqrt[4*a*b + c^2])]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[a]*x)/Sqrt[c + Sqrt[4*a*b + c^2]]], (c + Sqrt[4*a*b + c^2])/(c - Sqrt[4*a*b + c^2])])/(8*Sqrt[2]*a*Sqrt[b]*Sqrt[-b - c*x^2 + a*x^4]) + ((2*Sqrt[a]*Sqrt[b] - c + Sqrt[4*a*b + c^2])*Sqrt[c + Sqrt[4*a*b + c^2]]*Sqrt[1 - (2*a*x^2)/(c - Sqrt[4*a*b + c^2])]*Sqrt[1 - (2*a*x^2)/(c + Sqrt[4*a*b + c^2])]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[a]*x)/Sqrt[c + Sqrt[4*a*b + c^2]]], (c + Sqrt[4*a*b + c^2])/(c - Sqrt[4*a*b + c^2])])/(8*Sqrt[2]*a*Sqrt[b]*Sqrt[-b - c*x^2 + a*x^4]) - (Sqrt[c + Sqrt[4*a*b + c^2]]*Sqrt[1 - (2*a*x^2)/(c - Sqrt[4*a*b + c^2])]*Sqrt[1 - (2*a*x^2)/(c + Sqrt[4*a*b + c^2])]*EllipticPi[-1/2*(c + Sqrt[4*a*b + c^2])/(Sqrt[a]*Sqrt[b]), ArcSin[(Sqrt[2]*Sqrt[a]*x)/Sqrt[c + Sqrt[4*a*b + c^2]]], (c + Sqrt[4*a*b + c^2])/(c - Sqrt[4*a*b + c^2])])/(2*Sqrt[2]*Sqrt[a]*Sqrt[-b - c*x^2 + a*x^4]) - (Sqrt[c + Sqrt[4*a*b + c^2]]*Sqrt[1 - (2*a*x^2)/(c - Sqrt[4*a*b + c^2])]*Sqrt[1 - (2*a*x^2)/(c + Sqrt[4*a*b + c^2])]*EllipticPi[(c + Sqrt[4*a*b + c^2])/(2*Sqrt[a]*Sqrt[b]), ArcSin[(Sqrt[2]*Sqrt[a]*x)/Sqrt[c + Sqrt[4*a*b + c^2]]], (c + Sqrt[4*a*b + c^2])/(c - Sqrt[4*a*b + c^2])])/(2*Sqrt[2]*Sqrt[a]*Sqrt[-b - c*x^2 + a*x^4])","C",50,10,38,0.2632,1,"{6742, 1226, 1202, 524, 424, 419, 1220, 537, 6725, 1208}"
3134,1,286,0,0.8763007,"\int \frac{-a-b c+(1+c) x}{\left((-a+x) (-b+x)^2\right)^{2/3} (a-b d+(-1+d) x)} \, dx","Int[(-a - b*c + (1 + c)*x)/(((-a + x)*(-b + x)^2)^(2/3)*(a - b*d + (-1 + d)*x)),x]","\frac{(x-a)^{2/3} (x-b)^{4/3} (c+d) \log (a-b d-(1-d) x)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{3 (x-a)^{2/3} (x-b)^{4/3} (c+d) \log \left(\sqrt[3]{d} \sqrt[3]{x-b}-\sqrt[3]{x-a}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} (c+d) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{3 (a-x) (b-x)}{(a-b) \left(-\left((a-x) (b-x)^2\right)\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*(a - x)*(b - x))/((a - b)*(-((a - x)*(b - x)^2))^(2/3)) - (Sqrt[3]*(c + d)*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/((a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + ((c + d)*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[a - b*d - (1 - d)*x])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - (3*(c + d)*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + d^(1/3)*(-b + x)^(1/3)])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3))","A",4,4,44,0.09091,1,"{6719, 155, 12, 91}"
3135,1,283,0,1.4440232,"\int \frac{-a-b c+(1+c) x}{(-b+x) \sqrt[3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx","Int[(-a - b*c + (1 + c)*x)/((-b + x)*((-a + x)*(-b + x)^2)^(1/3)*(a - b*d + (-1 + d)*x)),x]","\frac{\sqrt[3]{x-a} (x-b)^{2/3} (c+d) \log (a-b d-(1-d) x)}{2 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} (c+d) \log \left(\frac{\sqrt[3]{x-a}}{\sqrt[3]{d}}-\sqrt[3]{x-b}\right)}{2 \sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} (c+d) \tan ^{-1}\left(\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{d} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{\sqrt[3]{d} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{3 (a-x)}{2 (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","\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*(a - b)*(-((a - x)*(b - x)^2))^(1/3)) - (Sqrt[3]*(c + d)*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/3)*(-b + x)^(1/3))])/((a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3)) + ((c + d)*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[a - b*d - (1 - d)*x])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(c + d)*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[(-a + x)^(1/3)/d^(1/3) - (-b + x)^(1/3)])/(2*(a - b)*d^(1/3)*(-((a - x)*(b - x)^2))^(1/3))","A",4,4,51,0.07843,1,"{6719, 155, 12, 91}"
3136,1,1407,0,3.1901408,"\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","Int[((d + c*x^2)*(a*x + Sqrt[-b + a^2*x^2])^(5/4))/(x*(-b + a^2*x^2)^(5/2)),x]","\frac{8 c \left(a x+\sqrt{a^2 x^2-b}\right)^{17/4}}{3 a^2 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^3}-\frac{5 c \left(a x+\sqrt{a^2 x^2-b}\right)^{9/4}}{6 a^2 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^2}+\frac{8 d \left(a x+\sqrt{a^2 x^2-b}\right)^{9/4}}{3 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^3}+\frac{15 c \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{16 a^2 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)}+\frac{39 d \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{16 b \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)}-\frac{7 d \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{2 \left(b-\left(a x+\sqrt{a^2 x^2-b}\right)^2\right)^2}-\frac{2 d \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{-b}}\right)}{(-b)^{15/8}}-\frac{15 c \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 a^2 b^{7/8}}+\frac{145 d \tan ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 b^{15/8}}+\frac{\sqrt{2} d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{-b}}\right)}{(-b)^{15/8}}-\frac{\sqrt{2} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{-b}}+1\right)}{(-b)^{15/8}}+\frac{15 c \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 \sqrt{2} a^2 b^{7/8}}-\frac{145 d \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 \sqrt{2} b^{15/8}}-\frac{15 c \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right)}{64 \sqrt{2} a^2 b^{7/8}}+\frac{145 d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}+1\right)}{64 \sqrt{2} b^{15/8}}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{-b}}\right)}{(-b)^{15/8}}-\frac{15 c \tanh ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 a^2 b^{7/8}}+\frac{145 d \tanh ^{-1}\left(\frac{\sqrt[4]{a x+\sqrt{a^2 x^2-b}}}{\sqrt[8]{b}}\right)}{64 b^{15/8}}+\frac{d \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)^{15/8}}-\frac{d \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)^{15/8}}+\frac{15 c \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)}{128 \sqrt{2} a^2 b^{7/8}}-\frac{145 d \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)}{128 \sqrt{2} b^{15/8}}-\frac{15 c \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)}{128 \sqrt{2} a^2 b^{7/8}}+\frac{145 d \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)}{128 \sqrt{2} b^{15/8}}","\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,"(8*d*(a*x + Sqrt[-b + a^2*x^2])^(9/4))/(3*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^3) + (8*c*(a*x + Sqrt[-b + a^2*x^2])^(17/4))/(3*a^2*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^3) - (7*d*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(2*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^2) - (5*c*(a*x + Sqrt[-b + a^2*x^2])^(9/4))/(6*a^2*(b - (a*x + Sqrt[-b + a^2*x^2])^2)^2) + (15*c*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(16*a^2*(b - (a*x + Sqrt[-b + a^2*x^2])^2)) + (39*d*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(16*b*(b - (a*x + Sqrt[-b + a^2*x^2])^2)) - (2*d*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(-b)^(15/8) - (15*c*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*a^2*b^(7/8)) + (145*d*ArcTan[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*b^(15/8)) + (Sqrt[2]*d*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(-b)^(15/8) - (Sqrt[2]*d*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/(-b)^(1/8)])/(-b)^(15/8) + (15*c*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*a^2*b^(7/8)) - (145*d*ArcTan[1 - (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*b^(15/8)) - (15*c*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*a^2*b^(7/8)) + (145*d*ArcTan[1 + (Sqrt[2]*(a*x + Sqrt[-b + a^2*x^2])^(1/4))/b^(1/8)])/(64*Sqrt[2]*b^(15/8)) - (2*d*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/(-b)^(1/8)])/(-b)^(15/8) - (15*c*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*a^2*b^(7/8)) + (145*d*ArcTanh[(a*x + Sqrt[-b + a^2*x^2])^(1/4)/b^(1/8)])/(64*b^(15/8)) + (d*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)^(15/8)) - (d*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)^(15/8)) + (15*c*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]]])/(128*Sqrt[2]*a^2*b^(7/8)) - (145*d*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]]])/(128*Sqrt[2]*b^(15/8)) - (15*c*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]]])/(128*Sqrt[2]*a^2*b^(7/8)) + (145*d*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]]])/(128*Sqrt[2]*b^(15/8))","A",52,20,49,0.4082,0,"{6742, 2120, 466, 470, 578, 527, 522, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204, 457, 288, 329}"
3137,1,711,0,4.6389199,"\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","Int[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_3 x+c_2) \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4} \left(c_4-c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}\right)}{\left(c_5{}^2 (c_1 c_6-c_0 c_7)-c_4{}^2 (c_3 c_6-c_2 c_7)\right) (c_7 x+c_6)}+\frac{(c_1 c_2-c_0 c_3) c_5 \left(\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_4+c_1 c_5 c_6-c_0 c_5 c_7\right) \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)}{2 (c_1 c_6-c_0 c_7) \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} \left(c_5{}^2 (c_1 c_6-c_0 c_7)-c_4{}^2 (c_3 c_6-c_2 c_7)\right)}+\frac{(c_1 c_2-c_0 c_3) c_5 \left(-\sqrt{c_1 c_6-c_0 c_7} \sqrt{c_3 c_6-c_2 c_7} c_4+c_1 c_5 c_6-c_0 c_5 c_7\right) \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)}{2 (c_1 c_6-c_0 c_7) \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} \left(c_5{}^2 (c_1 c_6-c_0 c_7)-c_4{}^2 (c_3 c_6-c_2 c_7)\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[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[6] + x*C[7])*(C[5]^2*(C[1]*C[6] - C[0]*C[7]) - C[4]^2*(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]]]]*(C[1]*C[2] - C[0]*C[3])*C[5]*(C[1]*C[5]*C[6] - C[0]*C[5]*C[7] + C[4]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]))/(2*(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[5]^2*(C[1]*C[6] - C[0]*C[7]) - C[4]^2*(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]]]]*(C[1]*C[2] - C[0]*C[3])*C[5]*(C[1]*C[5]*C[6] - C[0]*C[5]*C[7] - C[4]*Sqrt[C[1]*C[6] - C[0]*C[7]]*Sqrt[C[3]*C[6] - C[2]*C[7]]))/(2*(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[5]^2*(C[1]*C[6] - C[0]*C[7]) - C[4]^2*(C[3]*C[6] - C[2]*C[7])))","A",6,4,41,0.09756,1,"{823, 827, 1166, 208}"
3138,1,1549,0,5.2799805,"\int \frac{\sqrt[6]{\frac{1-b x}{c+x}} \left(1+d x^2\right)}{(1+b x) (1+c x)} \, dx","Int[(((1 - b*x)/(c + x))^(1/6)*(1 + d*x^2))/((1 + b*x)*(1 + c*x)),x]","\frac{d \sqrt[6]{\frac{1-b x}{c+x}} (c+x)}{b c}+\frac{5 (b c+1) d \tan ^{-1}\left(\frac{\sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}\right)}{3 b^{11/6} c}-\frac{2 \left(b c^2+2 c+b\right) d \tan ^{-1}\left(\frac{\sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}\right)}{b^{11/6} c^2}-\frac{2 \sqrt[6]{2} \left(b^2+d\right) \tan ^{-1}\left(\frac{\sqrt[6]{1-b c} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{2} \sqrt[6]{b}}\right)}{b^{11/6} (b-c) \sqrt[6]{1-b c}}+\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)}{(b-c) c^2 \sqrt[6]{1-c^2}}-\frac{5 (b c+1) d \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}\right)}{6 b^{11/6} c}+\frac{\left(b c^2+2 c+b\right) d \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}\right)}{b^{11/6} c^2}+\frac{5 (b c+1) d \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}+\sqrt{3}\right)}{6 b^{11/6} c}-\frac{\left(b c^2+2 c+b\right) d \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}+\sqrt{3}\right)}{b^{11/6} c^2}+\frac{\sqrt[6]{2} \left(b^2+d\right) \tan ^{-1}\left(\sqrt{3}-\frac{2^{5/6} \sqrt[6]{1-b c} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}\right)}{b^{11/6} (b-c) \sqrt[6]{1-b c}}-\frac{\sqrt[6]{2} \left(b^2+d\right) \tan ^{-1}\left(\frac{2^{5/6} \sqrt[6]{1-b c} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b}}+\sqrt{3}\right)}{b^{11/6} (b-c) \sqrt[6]{1-b c}}-\frac{\sqrt[6]{b+c} \left(c^2+d\right) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-c^2} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b+c}}\right)}{(b-c) c^2 \sqrt[6]{1-c^2}}+\frac{\sqrt[6]{b+c} \left(c^2+d\right) \tan ^{-1}\left(\frac{2 \sqrt[6]{1-c^2} \sqrt[6]{\frac{1-b x}{c+x}}}{\sqrt[6]{b+c}}+\sqrt{3}\right)}{(b-c) c^2 \sqrt[6]{1-c^2}}-\frac{5 (b c+1) d \log \left(\sqrt[3]{b}-\sqrt{3} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b}+\sqrt[3]{\frac{1-b x}{c+x}}\right)}{4 \sqrt{3} b^{11/6} c}+\frac{\sqrt{3} \left(b c^2+2 c+b\right) d \log \left(\sqrt[3]{b}-\sqrt{3} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b}+\sqrt[3]{\frac{1-b x}{c+x}}\right)}{2 b^{11/6} c^2}+\frac{5 (b c+1) d \log \left(\sqrt[3]{b}+\sqrt{3} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b}+\sqrt[3]{\frac{1-b x}{c+x}}\right)}{4 \sqrt{3} b^{11/6} c}-\frac{\sqrt{3} \left(b c^2+2 c+b\right) d \log \left(\sqrt[3]{b}+\sqrt{3} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b}+\sqrt[3]{\frac{1-b x}{c+x}}\right)}{2 b^{11/6} c^2}+\frac{\sqrt{3} \left(b^2+d\right) \log \left(\sqrt[3]{2} \sqrt[3]{b}-\sqrt[6]{2} \sqrt{3} \sqrt[6]{1-b c} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b}+\sqrt[3]{1-b c} \sqrt[3]{\frac{1-b x}{c+x}}\right)}{2^{5/6} b^{11/6} (b-c) \sqrt[6]{1-b c}}-\frac{\sqrt{3} \left(b^2+d\right) \log \left(\sqrt[3]{2} \sqrt[3]{b}+\sqrt[6]{2} \sqrt{3} \sqrt[6]{1-b c} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b}+\sqrt[3]{1-b c} \sqrt[3]{\frac{1-b x}{c+x}}\right)}{2^{5/6} b^{11/6} (b-c) \sqrt[6]{1-b c}}-\frac{\sqrt{3} \sqrt[6]{b+c} \left(c^2+d\right) \log \left(\sqrt[3]{b+c}-\sqrt{3} \sqrt[6]{1-c^2} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b+c}+\sqrt[3]{1-c^2} \sqrt[3]{\frac{1-b x}{c+x}}\right)}{2 (b-c) c^2 \sqrt[6]{1-c^2}}+\frac{\sqrt{3} \sqrt[6]{b+c} \left(c^2+d\right) \log \left(\sqrt[3]{b+c}+\sqrt{3} \sqrt[6]{1-c^2} \sqrt[6]{\frac{1-b x}{c+x}} \sqrt[6]{b+c}+\sqrt[3]{1-c^2} \sqrt[3]{\frac{1-b x}{c+x}}\right)}{2 (b-c) c^2 \sqrt[6]{1-c^2}}","\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,"(d*(c + x)*((1 - b*x)/(c + x))^(1/6))/(b*c) + (5*(1 + b*c)*d*ArcTan[((1 - b*x)/(c + x))^(1/6)/b^(1/6)])/(3*b^(11/6)*c) - (2*(b + 2*c + b*c^2)*d*ArcTan[((1 - b*x)/(c + x))^(1/6)/b^(1/6)])/(b^(11/6)*c^2) - (2*2^(1/6)*(b^2 + d)*ArcTan[((1 - b*c)^(1/6)*((1 - b*x)/(c + x))^(1/6))/(2^(1/6)*b^(1/6))])/(b^(11/6)*(b - c)*(1 - b*c)^(1/6)) + (2*(b + c)^(1/6)*(c^2 + d)*ArcTan[((1 - c^2)^(1/6)*((1 - b*x)/(c + x))^(1/6))/(b + c)^(1/6)])/((b - c)*c^2*(1 - c^2)^(1/6)) - (5*(1 + b*c)*d*ArcTan[Sqrt[3] - (2*((1 - b*x)/(c + x))^(1/6))/b^(1/6)])/(6*b^(11/6)*c) + ((b + 2*c + b*c^2)*d*ArcTan[Sqrt[3] - (2*((1 - b*x)/(c + x))^(1/6))/b^(1/6)])/(b^(11/6)*c^2) + (5*(1 + b*c)*d*ArcTan[Sqrt[3] + (2*((1 - b*x)/(c + x))^(1/6))/b^(1/6)])/(6*b^(11/6)*c) - ((b + 2*c + b*c^2)*d*ArcTan[Sqrt[3] + (2*((1 - b*x)/(c + x))^(1/6))/b^(1/6)])/(b^(11/6)*c^2) + (2^(1/6)*(b^2 + d)*ArcTan[Sqrt[3] - (2^(5/6)*(1 - b*c)^(1/6)*((1 - b*x)/(c + x))^(1/6))/b^(1/6)])/(b^(11/6)*(b - c)*(1 - b*c)^(1/6)) - (2^(1/6)*(b^2 + d)*ArcTan[Sqrt[3] + (2^(5/6)*(1 - b*c)^(1/6)*((1 - b*x)/(c + x))^(1/6))/b^(1/6)])/(b^(11/6)*(b - c)*(1 - b*c)^(1/6)) - ((b + c)^(1/6)*(c^2 + d)*ArcTan[Sqrt[3] - (2*(1 - c^2)^(1/6)*((1 - b*x)/(c + x))^(1/6))/(b + c)^(1/6)])/((b - c)*c^2*(1 - c^2)^(1/6)) + ((b + c)^(1/6)*(c^2 + d)*ArcTan[Sqrt[3] + (2*(1 - c^2)^(1/6)*((1 - b*x)/(c + x))^(1/6))/(b + c)^(1/6)])/((b - c)*c^2*(1 - c^2)^(1/6)) - (5*(1 + b*c)*d*Log[b^(1/3) - Sqrt[3]*b^(1/6)*((1 - b*x)/(c + x))^(1/6) + ((1 - b*x)/(c + x))^(1/3)])/(4*Sqrt[3]*b^(11/6)*c) + (Sqrt[3]*(b + 2*c + b*c^2)*d*Log[b^(1/3) - Sqrt[3]*b^(1/6)*((1 - b*x)/(c + x))^(1/6) + ((1 - b*x)/(c + x))^(1/3)])/(2*b^(11/6)*c^2) + (5*(1 + b*c)*d*Log[b^(1/3) + Sqrt[3]*b^(1/6)*((1 - b*x)/(c + x))^(1/6) + ((1 - b*x)/(c + x))^(1/3)])/(4*Sqrt[3]*b^(11/6)*c) - (Sqrt[3]*(b + 2*c + b*c^2)*d*Log[b^(1/3) + Sqrt[3]*b^(1/6)*((1 - b*x)/(c + x))^(1/6) + ((1 - b*x)/(c + x))^(1/3)])/(2*b^(11/6)*c^2) + (Sqrt[3]*(b^2 + d)*Log[2^(1/3)*b^(1/3) - 2^(1/6)*Sqrt[3]*b^(1/6)*(1 - b*c)^(1/6)*((1 - b*x)/(c + x))^(1/6) + (1 - b*c)^(1/3)*((1 - b*x)/(c + x))^(1/3)])/(2^(5/6)*b^(11/6)*(b - c)*(1 - b*c)^(1/6)) - (Sqrt[3]*(b^2 + d)*Log[2^(1/3)*b^(1/3) + 2^(1/6)*Sqrt[3]*b^(1/6)*(1 - b*c)^(1/6)*((1 - b*x)/(c + x))^(1/6) + (1 - b*c)^(1/3)*((1 - b*x)/(c + x))^(1/3)])/(2^(5/6)*b^(11/6)*(b - c)*(1 - b*c)^(1/6)) - (Sqrt[3]*(b + c)^(1/6)*(c^2 + d)*Log[(b + c)^(1/3) - Sqrt[3]*(b + c)^(1/6)*(1 - c^2)^(1/6)*((1 - b*x)/(c + x))^(1/6) + (1 - c^2)^(1/3)*((1 - b*x)/(c + x))^(1/3)])/(2*(b - c)*c^2*(1 - c^2)^(1/6)) + (Sqrt[3]*(b + c)^(1/6)*(c^2 + d)*Log[(b + c)^(1/3) + Sqrt[3]*(b + c)^(1/6)*(1 - c^2)^(1/6)*((1 - b*x)/(c + x))^(1/6) + (1 - c^2)^(1/3)*((1 - b*x)/(c + x))^(1/3)])/(2*(b - c)*c^2*(1 - c^2)^(1/6))","A",45,10,38,0.2632,1,"{6, 6725, 199, 209, 634, 618, 204, 628, 203, 205}"
3139,0,0,0,1.1278485,"\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","Int[(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,"Defer[Int][(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",0,0,0,0,-1,"{}"
3140,1,750,0,2.5349396,"\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","Int[(C[6] + x*C[7])/Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]],x]","\frac{c_7 (c_1 c_2-c_0 c_3){}^2 \left(c_4-c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}\right) \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4}}{2 c_3 \left(c_3 c_4{}^2-c_1 c_5{}^2\right) \left(c_1-\frac{c_3 (c_1 x+c_0)}{c_3 x+c_2}\right){}^2}-\frac{(c_3 x+c_2) \sqrt{c_5 \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}+c_4} \left(c_3 c_5 \left(c_0 c_3 c_7 c_4{}^2-\frac{c_1{}^2 c_5{}^2 (8 c_3 c_6-3 c_2 c_7)}{c_3}+c_1 \left(8 c_3 c_4{}^2 c_6-\left(9 c_2 c_4{}^2-5 c_0 c_5{}^2\right) c_7\right)\right) \sqrt{\frac{c_1 x+c_0}{c_3 x+c_2}}-2 c_1 c_4 \left(4 c_3{}^2 c_6 c_4{}^2+c_1 c_2 c_5{}^2 c_7-c_3 \left(4 c_1 c_6 c_5{}^2+\left(4 c_2 c_4{}^2-3 c_0 c_5{}^2\right) c_7\right)\right)\right)}{8 c_1 c_3 \left(c_3 c_4{}^2-c_1 c_5{}^2\right){}^2}-\frac{c_5 \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 c_2-c_0 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)}{16 c_1{}^{3/2} c_3{}^{7/4} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^{5/2}}+\frac{c_5 \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 c_2-c_0 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)}{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) \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,"((C[1]*C[2] - C[0]*C[3])^2*(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[7])/(2*C[3]*(C[1] - ((C[0] + x*C[1])*C[3])/(C[2] + x*C[3]))^2*(C[3]*C[4]^2 - C[1]*C[5]^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[1]*C[2] - C[0]*C[3])*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])))/(16*C[1]^(3/2)*C[3]^(7/4)*(Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5])^(5/2)) + (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[1]*C[2] - C[0]*C[3])*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])))/(16*C[1]^(3/2)*C[3]^(7/4)*(Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5])^(5/2)) - ((C[2] + x*C[3])*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*(C[3]*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]*(C[0]*C[3]*C[4]^2*C[7] - (C[1]^2*C[5]^2*(8*C[3]*C[6] - 3*C[2]*C[7]))/C[3] + C[1]*(8*C[3]*C[4]^2*C[6] - (9*C[2]*C[4]^2 - 5*C[0]*C[5]^2)*C[7])) - 2*C[1]*C[4]*(4*C[3]^2*C[4]^2*C[6] + C[1]*C[2]*C[5]^2*C[7] - C[3]*(4*C[1]*C[5]^2*C[6] + (4*C[2]*C[4]^2 - 3*C[0]*C[5]^2)*C[7]))))/(8*C[1]*C[3]*(C[3]*C[4]^2 - C[1]*C[5]^2)^2)","A",7,5,39,0.1282,1,"{1649, 823, 827, 1166, 208}"
3141,0,0,0,0.2966274,"\int \frac{\sqrt{-b+a^2 x^2}}{\left(c+\sqrt[4]{a x+\sqrt{-b+a^2 x^2}}\right)^{2/3}} \, dx","Int[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,"Defer[Int][Sqrt[-b + a^2*x^2]/(c + (a*x + Sqrt[-b + a^2*x^2])^(1/4))^(2/3), x]","F",0,0,0,0,-1,"{}"
3142,0,0,0,0.8787228,"\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","Int[(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,"Defer[Int][(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",0,0,0,0,-1,"{}"
3143,0,0,0,0.9460875,"\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","Int[(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]","\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","-\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,"Defer[Int][(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]","F",0,0,0,0,-1,"{}"
3144,1,3187,0,43.6338144,"\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","Int[(a*b*c - b^2*x + a^2*x^2)/(Sqrt[c + b*x + a*x^2]*(c + b*x^2)^2),x]","-\frac{\sqrt{a x^2+b x+c} \left(b \left(a^2+(1-b) b a-b^2\right) c+\left(b^4+a (a-b) c b^2-a^2 (a-b) c\right) x\right)}{2 \left(c b^3+(a c-b c)^2\right) \left(b x^2+c\right)}-\frac{\sqrt{2 c b^5-\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b^4+a c \left(3 b^3+c b^2-2 c b+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b+2 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+a^2 c \left(-6 c b^2+b^2+7 c b+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b-3 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-a^4 c^2-a^3 \left(-5 b^2 c^2+4 b c^2+\sqrt{b^3+c b^2-2 a c b+a^2 c} c^{3/2}\right)} \sqrt{b^6-(4 a c+c) b^5+\left(2 c a^2-\left(2 c^2+2 c+3 \sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right) a-\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^4+\left(a^2 c (8 c+3)-a \sqrt{c} (2 c+1) \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^3+a^2 \sqrt{c} \left(-2 c^{3/2}+6 \sqrt{b^3+c b^2-2 a c b+a^2 c} c+2 a (1-5 c) \sqrt{c}-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+2 a^2 c^{3/2} \left(2 \sqrt{c} a^2+2 \sqrt{c} a-2 \sqrt{b^3+c b^2-2 a c b+a^2 c} a-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-2 a^3 c^{3/2} \left(a \sqrt{c}-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \tanh ^{-1}\left(\frac{\sqrt{b} \left(b c \left(b^4+a (3 b+2 c+1) b^3+a^2 (-6 c b+b+2 c) b-2 a^3 (1-2 b) c\right)-\left(b^4-a c b^3-a (a+2) c b^2+3 a^2 c b+a^3 c\right) \left(a c-b c+\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right)+\left(\left(b^4-a c b^3-a (a+2) c b^2+3 a^2 c b+a^3 c\right) b^2+\left(b^4+a (3 b+2 c+1) b^3+a^2 (-6 c b+b+2 c) b-2 a^3 (1-2 b) c\right) \left(a c-b c-\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right)\right) x\right)}{\sqrt{2} \sqrt{2 c b^5-\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b^4+a c \left(3 b^3+c b^2-2 c b+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b+2 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+a^2 c \left(-6 c b^2+b^2+7 c b+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b-3 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-a^4 c^2-a^3 \left(-5 b^2 c^2+4 b c^2+\sqrt{b^3+c b^2-2 a c b+a^2 c} c^{3/2}\right)} \sqrt{b^6-(4 a c+c) b^5+\left(2 c a^2-\left(2 c^2+2 c+3 \sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right) a-\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^4+\left(a^2 c (8 c+3)-a \sqrt{c} (2 c+1) \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^3+a^2 \sqrt{c} \left(-2 c^{3/2}+6 \sqrt{b^3+c b^2-2 a c b+a^2 c} c+2 a (1-5 c) \sqrt{c}-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+2 a^2 c^{3/2} \left(2 \sqrt{c} a^2+2 \sqrt{c} a-2 \sqrt{b^3+c b^2-2 a c b+a^2 c} a-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-2 a^3 c^{3/2} \left(a \sqrt{c}-\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \sqrt{a x^2+b x+c}}\right)}{4 \sqrt{2} \sqrt{b} c^{3/2} \left(b^3+c b^2-2 a c b+a^2 c\right)^{3/2}}+\frac{\sqrt{b^6-(4 a c+c) b^5+\left(2 c a^2-\left(2 c^2+2 c-3 \sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right) a+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^4+\left(c (8 c+3) a^2+\sqrt{c} (2 c+1) \sqrt{b^3+c b^2-2 a c b+a^2 c} a\right) b^3+a^2 \sqrt{c} \left(-2 c^{3/2}-6 \sqrt{b^3+c b^2-2 a c b+a^2 c} c+2 a (1-5 c) \sqrt{c}+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+2 a^2 c^{3/2} \left(2 \sqrt{c} a^2+2 \left(\sqrt{c}+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) a+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-2 a^3 c^{3/2} \left(\sqrt{c} a+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \sqrt{2 c b^5+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b^4+a c \left(3 b^3+c b^2-\left(2 c+\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right) b-2 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+a^2 c \left(-6 c b^2+b^2+7 c b-\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b+3 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-a^4 c^2-a^3 \left(-5 b^2 c^2+4 b c^2-\sqrt{b^3+c b^2-2 a c b+a^2 c} c^{3/2}\right)} \tanh ^{-1}\left(\frac{\sqrt{b} \left(b c \left(b^4+a (3 b+2 c+1) b^3+a^2 (-6 c b+b+2 c) b-2 a^3 (1-2 b) c\right)-\left(b^4-a c b^3-a (a+2) c b^2+3 a^2 c b+a^3 c\right) \left(a c-b c-\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right)+\left(\left(b^4-a c b^3-a (a+2) c b^2+3 a^2 c b+a^3 c\right) b^2+\left(b^4+a (3 b+2 c+1) b^3+a^2 (-6 c b+b+2 c) b-2 a^3 (1-2 b) c\right) \left(a c-b c+\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right)\right) x\right)}{\sqrt{2} \sqrt{b^6-(4 a c+c) b^5+\left(2 c a^2-\left(2 c^2+2 c-3 \sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right) a+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^4+\left(c (8 c+3) a^2+\sqrt{c} (2 c+1) \sqrt{b^3+c b^2-2 a c b+a^2 c} a\right) b^3+a^2 \sqrt{c} \left(-2 c^{3/2}-6 \sqrt{b^3+c b^2-2 a c b+a^2 c} c+2 a (1-5 c) \sqrt{c}+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+2 a^2 c^{3/2} \left(2 \sqrt{c} a^2+2 \left(\sqrt{c}+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) a+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-2 a^3 c^{3/2} \left(\sqrt{c} a+\sqrt{b^3+c b^2-2 a c b+a^2 c}\right)} \sqrt{2 c b^5+\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b^4+a c \left(3 b^3+c b^2-\left(2 c+\sqrt{b^3+c b^2-2 a c b+a^2 c} \sqrt{c}\right) b-2 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b^2+a^2 c \left(-6 c b^2+b^2+7 c b-\sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c} b+3 \sqrt{c} \sqrt{b^3+c b^2-2 a c b+a^2 c}\right) b-a^4 c^2-a^3 \left(-5 b^2 c^2+4 b c^2-\sqrt{b^3+c b^2-2 a c b+a^2 c} c^{3/2}\right)} \sqrt{a x^2+b x+c}}\right)}{4 \sqrt{2} \sqrt{b} c^{3/2} \left(b^3+c b^2-2 a c b+a^2 c\right)^{3/2}}","\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,"-1/2*((b*(a^2 + a*(1 - b)*b - b^2)*c + (b^4 - a^2*(a - b)*c + a*(a - b)*b^2*c)*x)*Sqrt[c + b*x + a*x^2])/((b^3*c + (a*c - b*c)^2)*(c + b*x^2)) - (Sqrt[2*b^5*c - a^4*c^2 - b^4*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + a^2*b*c*(b^2 + 7*b*c - 6*b^2*c - 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + b*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a*b^2*c*(3*b^3 - 2*b*c + b^2*c + 2*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + b*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) - a^3*(4*b*c^2 - 5*b^2*c^2 + c^(3/2)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*Sqrt[b^6 - b^5*(c + 4*a*c) - 2*a^3*c^(3/2)*(a*Sqrt[c] - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + 2*a^2*b*c^(3/2)*(2*a*Sqrt[c] + 2*a^2*Sqrt[c] - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - 2*a*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a^2*b^2*Sqrt[c]*(2*a*(1 - 5*c)*Sqrt[c] - 2*c^(3/2) - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + 6*c*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + b^3*(a^2*c*(3 + 8*c) - a*Sqrt[c]*(1 + 2*c)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + b^4*(2*a^2*c - Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - a*(2*c + 2*c^2 + 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))]*ArcTanh[(Sqrt[b]*(b*c*(b^4 - 2*a^3*(1 - 2*b)*c + a*b^3*(1 + 3*b + 2*c) + a^2*b*(b + 2*c - 6*b*c)) - (b^4 + a^3*c + 3*a^2*b*c - a*(2 + a)*b^2*c - a*b^3*c)*(a*c - b*c + Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + (b^2*(b^4 + a^3*c + 3*a^2*b*c - a*(2 + a)*b^2*c - a*b^3*c) + (b^4 - 2*a^3*(1 - 2*b)*c + a*b^3*(1 + 3*b + 2*c) + a^2*b*(b + 2*c - 6*b*c))*(a*c - b*c - Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))*x))/(Sqrt[2]*Sqrt[2*b^5*c - a^4*c^2 - b^4*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + a^2*b*c*(b^2 + 7*b*c - 6*b^2*c - 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + b*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a*b^2*c*(3*b^3 - 2*b*c + b^2*c + 2*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + b*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) - a^3*(4*b*c^2 - 5*b^2*c^2 + c^(3/2)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])]*Sqrt[b^6 - b^5*(c + 4*a*c) - 2*a^3*c^(3/2)*(a*Sqrt[c] - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + 2*a^2*b*c^(3/2)*(2*a*Sqrt[c] + 2*a^2*Sqrt[c] - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - 2*a*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a^2*b^2*Sqrt[c]*(2*a*(1 - 5*c)*Sqrt[c] - 2*c^(3/2) - Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + 6*c*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + b^3*(a^2*c*(3 + 8*c) - a*Sqrt[c]*(1 + 2*c)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + b^4*(2*a^2*c - Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - a*(2*c + 2*c^2 + 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))]*Sqrt[c + b*x + a*x^2])])/(4*Sqrt[2]*Sqrt[b]*c^(3/2)*(b^3 + a^2*c - 2*a*b*c + b^2*c)^(3/2)) + (Sqrt[b^6 - b^5*(c + 4*a*c) - 2*a^3*c^(3/2)*(a*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a^2*b^2*Sqrt[c]*(2*a*(1 - 5*c)*Sqrt[c] - 2*c^(3/2) + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - 6*c*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + b^3*(a^2*c*(3 + 8*c) + a*Sqrt[c]*(1 + 2*c)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + 2*a^2*b*c^(3/2)*(2*a^2*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + 2*a*(Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])) + b^4*(2*a^2*c + Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - a*(2*c + 2*c^2 - 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))]*Sqrt[2*b^5*c - a^4*c^2 + b^4*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + a^2*b*c*(b^2 + 7*b*c - 6*b^2*c + 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - b*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) - a^3*(4*b*c^2 - 5*b^2*c^2 - c^(3/2)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a*b^2*c*(3*b^3 + b^2*c - 2*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - b*(2*c + Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))]*ArcTanh[(Sqrt[b]*(b*c*(b^4 - 2*a^3*(1 - 2*b)*c + a*b^3*(1 + 3*b + 2*c) + a^2*b*(b + 2*c - 6*b*c)) - (b^4 + a^3*c + 3*a^2*b*c - a*(2 + a)*b^2*c - a*b^3*c)*(a*c - b*c - Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + (b^2*(b^4 + a^3*c + 3*a^2*b*c - a*(2 + a)*b^2*c - a*b^3*c) + (b^4 - 2*a^3*(1 - 2*b)*c + a*b^3*(1 + 3*b + 2*c) + a^2*b*(b + 2*c - 6*b*c))*(a*c - b*c + Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))*x))/(Sqrt[2]*Sqrt[b^6 - b^5*(c + 4*a*c) - 2*a^3*c^(3/2)*(a*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a^2*b^2*Sqrt[c]*(2*a*(1 - 5*c)*Sqrt[c] - 2*c^(3/2) + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - 6*c*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + b^3*(a^2*c*(3 + 8*c) + a*Sqrt[c]*(1 + 2*c)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + 2*a^2*b*c^(3/2)*(2*a^2*Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + 2*a*(Sqrt[c] + Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c])) + b^4*(2*a^2*c + Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - a*(2*c + 2*c^2 - 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))]*Sqrt[2*b^5*c - a^4*c^2 + b^4*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] + a^2*b*c*(b^2 + 7*b*c - 6*b^2*c + 3*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - b*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) - a^3*(4*b*c^2 - 5*b^2*c^2 - c^(3/2)*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]) + a*b^2*c*(3*b^3 + b^2*c - 2*Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c] - b*(2*c + Sqrt[c]*Sqrt[b^3 + a^2*c - 2*a*b*c + b^2*c]))]*Sqrt[c + b*x + a*x^2])])/(4*Sqrt[2]*Sqrt[b]*c^(3/2)*(b^3 + a^2*c - 2*a*b*c + b^2*c)^(3/2))","B",6,4,42,0.09524,1,"{1062, 1036, 1030, 208}"
3145,0,0,0,2.0668446,"\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","Int[((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,"(2*a*x^3)/(3*(b + Sqrt[b^2 + a*x^2])^(3/2)) + (2*b*x)/Sqrt[b + Sqrt[b^2 + a*x^2]] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b - Sqrt[a]*x), x] - b*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(b + Sqrt[a]*x), x] + a*b^2*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[a]*b - a*x)^2, x] + a*b^2*Defer[Int][Sqrt[b + Sqrt[b^2 + a*x^2]]/(Sqrt[a]*b + a*x)^2, x]","F",0,0,0,0,-1,"{}"
3146,0,0,0,0.6278317,"\int \frac{\sqrt{a x^2+\sqrt{b+a^2 x^4}}}{(d+c x)^2 \sqrt{b+a^2 x^4}} \, dx","Int[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,"Defer[Int][Sqrt[a*x^2 + Sqrt[b + a^2*x^4]]/((d + c*x)^2*Sqrt[b + a^2*x^4]), x]","F",0,0,0,0,-1,"{}"
3147,1,280,0,1.4710896,"\int \frac{-b-a c+(1+c) x}{(-a+x) \sqrt[3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx","Int[(-b - a*c + (1 + c)*x)/((-a + x)*((-a + x)*(-b + x)^2)^(1/3)*(b - a*d + (-1 + d)*x)),x]","-\frac{\sqrt[3]{x-a} (x-b)^{2/3} (c+d) \log (-a d+b-(1-d) x)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} (c+d) \log \left(\sqrt[3]{d} \sqrt[3]{x-a}-\sqrt[3]{x-b}\right)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} (c+d) \tan ^{-1}\left(\frac{2 \sqrt[3]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 (b-x)}{(a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","\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))/((a - b)*(-((a - x)*(b - x)^2))^(1/3)) + (Sqrt[3]*(c + d)*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*d^(1/3)*(-a + x)^(1/3))/(Sqrt[3]*(-b + x)^(1/3))])/((a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - ((c + d)*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[b - a*d - (1 - d)*x])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) + (3*(c + d)*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[d^(1/3)*(-a + x)^(1/3) - (-b + x)^(1/3)])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3))","A",4,4,51,0.07843,1,"{6719, 155, 12, 91}"
3148,1,561,0,1.9640083,"\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","Int[(-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{\sqrt[3]{x-a} (x-b)^{2/3} \left(c+\sqrt{d}\right) \log \left(2 \left(\sqrt{d}+1\right) \left(a-b \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt[3]{x-a} (x-b)^{2/3} \left(c-\sqrt{d}\right) \log \left(2 \left(1-\sqrt{d}\right) \left(a+b \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \left(c-\sqrt{d}\right) \log \left(-\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x-b}\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \left(c+\sqrt{d}\right) \log \left(\frac{\sqrt[3]{x-a}}{\sqrt[6]{d}}-\sqrt[3]{x-b}\right)}{4 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \left(c-\sqrt{d}\right) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-b}}\right)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \left(c+\sqrt{d}\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{x-a}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{2 d^{2/3} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","\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,"-1/2*(Sqrt[3]*(c - Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-b + x)^(1/3))])/((a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (Sqrt[3]*(c + Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*(-a + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-b + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) + ((c + Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 + Sqrt[d])*(a - b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) + ((c - Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 - Sqrt[d])*(a + b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(c - Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[-((-a + x)^(1/3)/d^(1/6)) - (-b + x)^(1/3)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(c + Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[(-a + x)^(1/3)/d^(1/6) - (-b + x)^(1/3)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(1/3))","A",5,3,60,0.05000,1,"{6719, 6728, 91}"
3149,1,561,0,1.8723487,"\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","Int[(-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{\sqrt[3]{x-a} (x-b)^{2/3} \left(c+\sqrt{d}\right) \log \left(2 \left(\sqrt{d}+1\right) \left(b-a \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt[3]{x-a} (x-b)^{2/3} \left(c-\sqrt{d}\right) \log \left(2 \left(1-\sqrt{d}\right) \left(a \sqrt{d}+b\right)-2 (1-d) x\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \left(c-\sqrt{d}\right) \log \left(-\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x-b}\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{3 \sqrt[3]{x-a} (x-b)^{2/3} \left(c+\sqrt{d}\right) \log \left(\sqrt[6]{d} \sqrt[3]{x-a}-\sqrt[3]{x-b}\right)}{4 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}-\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \left(c-\sqrt{d}\right) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x-b}}\right)}{2 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}+\frac{\sqrt{3} \sqrt[3]{x-a} (x-b)^{2/3} \left(c+\sqrt{d}\right) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-a}}{\sqrt{3} \sqrt[3]{x-b}}+\frac{1}{\sqrt{3}}\right)}{2 d^{5/6} (a-b) \sqrt[3]{-\left((a-x) (b-x)^2\right)}}","\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,"-1/2*(Sqrt[3]*(c - Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*(-b + x)^(1/3))])/((a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) + (Sqrt[3]*(c + Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-a + x)^(1/3))/(Sqrt[3]*(-b + x)^(1/3))])/(2*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) - ((c + Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 + Sqrt[d])*(b - a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) + ((c - Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[2*(1 - Sqrt[d])*(b + a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) - (3*(c - Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[-(d^(1/6)*(-a + x)^(1/3)) - (-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3)) + (3*(c + Sqrt[d])*(-a + x)^(1/3)*(-b + x)^(2/3)*Log[d^(1/6)*(-a + x)^(1/3) - (-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(1/3))","A",5,3,60,0.05000,1,"{6719, 6728, 91}"
3150,1,944,0,33.9440133,"\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","Int[(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]","\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_9}{\left(c_3 c_4{}^2-c_1 c_5{}^2\right) c_7}-\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_1 c_2-c_0 c_3) c_5 c_9}{2 \sqrt{c_1} c_3{}^{3/4} \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right){}^{3/2} c_7}+\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_1 c_2-c_0 c_3) c_5 c_9}{2 \sqrt{c_1} c_3{}^{3/4} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^{3/2} c_7}-\frac{2 \tanh ^{-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_7 c_8-c_6 c_9)}{c_7{}^2 \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{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_7 c_8-c_6 c_9)}{c_7{}^2 \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_7 c_8-c_6 c_9)}{\sqrt{\sqrt{c_3} c_4-\sqrt{c_1} c_5} c_7{}^2}+\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_7 c_8-c_6 c_9)}{\sqrt{\sqrt{c_3} c_4+\sqrt{c_1} c_5} c_7{}^2}","\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,"-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[1]*C[2] - C[0]*C[3])*C[5]*C[9])/(Sqrt[C[1]]*C[3]^(3/4)*(Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5])^(3/2)*C[7]) + (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[1]*C[2] - C[0]*C[3])*C[5]*C[9])/(2*Sqrt[C[1]]*C[3]^(3/4)*(Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5])^(3/2)*C[7]) + ((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[9])/((C[3]*C[4]^2 - C[1]*C[5]^2)*C[7]) + (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)*(C[7]*C[8] - C[6]*C[9]))/(Sqrt[Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5]]*C[7]^2) + (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)*(C[7]*C[8] - C[6]*C[9]))/(Sqrt[Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5]]*C[7]^2) - (2*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[6] - C[2]*C[7]]*(C[7]*C[8] - C[6]*C[9]))/(C[7]^2*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]]]) - (2*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[6] - C[2]*C[7]]*(C[7]*C[8] - C[6]*C[9]))/(C[7]^2*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",15,5,48,0.1042,1,"{6741, 6728, 1178, 1166, 208}"
3151,1,561,0,2.2845312,"\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","Int[((-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{(x-a)^{2/3} (x-b)^{4/3} \left(c+\sqrt{d}\right) \log \left(2 \left(\sqrt{d}+1\right) \left(a-b \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{(x-a)^{2/3} (x-b)^{4/3} \left(c-\sqrt{d}\right) \log \left(2 \left(1-\sqrt{d}\right) \left(a+b \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \left(c-\sqrt{d}\right) \log \left(-\sqrt[3]{x-a}-\sqrt[6]{d} \sqrt[3]{x-b}\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{3 (x-a)^{2/3} (x-b)^{4/3} \left(c+\sqrt{d}\right) \log \left(\sqrt[6]{d} \sqrt[3]{x-b}-\sqrt[3]{x-a}\right)}{4 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \left(c-\sqrt{d}\right) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[6]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}\right)}{2 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \left(c+\sqrt{d}\right) \tan ^{-1}\left(\frac{2 \sqrt[6]{d} \sqrt[3]{x-b}}{\sqrt{3} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 d^{5/6} (a-b) \left(-\left((a-x) (b-x)^2\right)\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,"(Sqrt[3]*(c - Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] - (2*d^(1/6)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) - (Sqrt[3]*(c + Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*d^(1/6)*(-b + x)^(1/3))/(Sqrt[3]*(-a + x)^(1/3))])/(2*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) + ((c + Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 + Sqrt[d])*(a - b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) - ((c - Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 - Sqrt[d])*(a + b*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(c - Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) - d^(1/6)*(-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3)) - (3*(c + Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + d^(1/6)*(-b + x)^(1/3)])/(4*(a - b)*d^(5/6)*(-((a - x)*(b - x)^2))^(2/3))","A",5,3,65,0.04615,1,"{6719, 6728, 91}"
3152,1,561,0,2.1604779,"\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","Int[((-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{(x-a)^{2/3} (x-b)^{4/3} \left(c+\sqrt{d}\right) \log \left(2 \left(\sqrt{d}+1\right) \left(b-a \sqrt{d}\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}-\frac{(x-a)^{2/3} (x-b)^{4/3} \left(c-\sqrt{d}\right) \log \left(2 \left(1-\sqrt{d}\right) \left(a \sqrt{d}+b\right)-2 (1-d) x\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \left(c-\sqrt{d}\right) \log \left(-\sqrt[3]{x-a}-\frac{\sqrt[3]{x-b}}{\sqrt[6]{d}}\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{3 (x-a)^{2/3} (x-b)^{4/3} \left(c+\sqrt{d}\right) \log \left(\frac{\sqrt[3]{x-b}}{\sqrt[6]{d}}-\sqrt[3]{x-a}\right)}{4 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \left(c-\sqrt{d}\right) \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{x-b}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\right)^{2/3}}+\frac{\sqrt{3} (x-a)^{2/3} (x-b)^{4/3} \left(c+\sqrt{d}\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{x-b}}{\sqrt{3} \sqrt[6]{d} \sqrt[3]{x-a}}+\frac{1}{\sqrt{3}}\right)}{2 d^{2/3} (a-b) \left(-\left((a-x) (b-x)^2\right)\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,"(Sqrt[3]*(c - Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] - (2*(-b + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (Sqrt[3]*(c + Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*ArcTan[1/Sqrt[3] + (2*(-b + x)^(1/3))/(Sqrt[3]*d^(1/6)*(-a + x)^(1/3))])/(2*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((c + Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 + Sqrt[d])*(b - a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) - ((c - Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[2*(1 - Sqrt[d])*(b + a*Sqrt[d]) - 2*(1 - d)*x])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(c - Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) - (-b + x)^(1/3)/d^(1/6)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3)) + (3*(c + Sqrt[d])*(-a + x)^(2/3)*(-b + x)^(4/3)*Log[-(-a + x)^(1/3) + (-b + x)^(1/3)/d^(1/6)])/(4*(a - b)*d^(2/3)*(-((a - x)*(b - x)^2))^(2/3))","A",5,3,65,0.04615,1,"{6719, 6728, 91}"
3153,1,1063,0,4.6782667,"\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","Int[(x^2 - c*x^2*((b + a*x)/(d + c*x))^(3/2))/(a - b*Sqrt[(b + a*x)/(d + c*x)]),x]","-\frac{\left(a (a b-c)+\left(a^2-b\right) c \sqrt{\frac{b+a x}{d+c x}}\right) (b c-a d)^3}{3 a c^3 \left(b^2-a c\right) \left(a-\frac{c (b+a x)}{d+c x}\right)^3}+\frac{\left(5 c^2 b^9+a c \left(15 c^2+2 b d\right) b^7+a^2 \left(-5 c^4+b^3 c^2-18 b d c^2+b^2 d^2\right) b^5-a^3 c \left(-2 d b^4+9 c^2 b^3+5 d^2 b^2+18 c^2 d b-c^4\right) b^3-a^4 \left(-5 d^2 b^4+10 c^2 d b^3+9 c^4 b^2-15 c^2 d^2 b-2 c^4 d\right) b^2+5 a^6 c^2 d \left(2 c^2+7 b d\right) b+a^5 c \left(b c^4+5 d^2 c^2+30 b^2 d c^2-21 b^3 d^2\right) b-35 a^7 c^3 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{b+a x}{d+c x}}}{\sqrt{a}}\right) (b c-a d)}{8 a^{7/2} c^{5/2} \left(b^2-a c\right)^4}-\frac{b \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(\frac{1}{d+c x}\right) (b c-a d)}{a^3 c^3 \left(b^2-a c\right)^4}+\frac{2 \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) (b c-a d)}{a^3 b \left(b^2-a c\right)^4}+\frac{(d+c x) \left(8 a \left(-\left(\left(c^3+2 a^2 d c\right) b^6\right)+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)-c \left(5 c^2 b^7+2 a c \left(2 c^2+b d\right) b^5+a^2 \left(-c^4+b^3 c^2-16 b d c^2+b^2 d^2\right) b^3-2 a^3 c \left(-d b^3+4 c^2 b^2+2 d^2 b+c^2 d\right) b^2+2 a^5 c d \left(11 c^2+16 b d\right) b-a^4 \left(b c^4-11 d^2 c^2+8 b^2 d c^2+11 b^3 d^2\right) b-29 a^6 c^2 d^2\right) \sqrt{\frac{b+a x}{d+c x}}\right)}{8 a^3 c^3 \left(b^2-a c\right)^3}+\frac{6 a \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) (b c-a d)^2+c \left(19 c d a^4-b \left(7 c^2+13 b d\right) a^3+b c \left(b^2-13 d\right) a^2+b^2 \left(c^2+7 b d\right) a+5 b^4 c\right) \sqrt{\frac{b+a x}{d+c x}} (b c-a d)^2}{12 a^2 c^3 \left(b^2-a c\right)^2 \left(a-\frac{c (b+a x)}{d+c x}\right)^2}","\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,"((d + c*x)*(8*a*(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)) - c*(5*b^7*c^2 - 29*a^6*c^2*d^2 + 2*a*b^5*c*(2*c^2 + b*d) + 2*a^5*b*c*d*(11*c^2 + 16*b*d) - 2*a^3*b^2*c*(4*b^2*c^2 - b^3*d + c^2*d + 2*b*d^2) + a^2*b^3*(b^3*c^2 - c^4 - 16*b*c^2*d + b^2*d^2) - a^4*b*(b*c^4 + 8*b^2*c^2*d + 11*b^3*d^2 - 11*c^2*d^2))*Sqrt[(b + a*x)/(d + c*x)]))/(8*a^3*c^3*(b^2 - a*c)^3) - ((b*c - a*d)^3*(a*(a*b - c) + (a^2 - b)*c*Sqrt[(b + a*x)/(d + c*x)]))/(3*a*c^3*(b^2 - a*c)*(a - (c*(b + a*x))/(d + c*x))^3) + (6*a*(b*c - a*d)^2*(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)) + c*(b*c - a*d)^2*(5*b^4*c + a^2*b*c*(b^2 - 13*d) + 19*a^4*c*d + a*b^2*(c^2 + 7*b*d) - a^3*b*(7*c^2 + 13*b*d))*Sqrt[(b + a*x)/(d + c*x)])/(12*a^2*c^3*(b^2 - a*c)^2*(a - (c*(b + a*x))/(d + c*x))^2) + ((b*c - a*d)*(5*b^9*c^2 - 35*a^7*c^3*d^2 + a*b^7*c*(15*c^2 + 2*b*d) + 5*a^6*b*c^2*d*(2*c^2 + 7*b*d) + a^2*b^5*(b^3*c^2 - 5*c^4 - 18*b*c^2*d + b^2*d^2) - a^3*b^3*c*(9*b^3*c^2 - c^4 - 2*b^4*d + 18*b*c^2*d + 5*b^2*d^2) + a^5*b*c*(b*c^4 + 30*b^2*c^2*d - 21*b^3*d^2 + 5*c^2*d^2) - a^4*b^2*(9*b^2*c^4 + 10*b^3*c^2*d - 2*c^4*d - 5*b^4*d^2 - 15*b*c^2*d^2))*ArcTanh[(Sqrt[c]*Sqrt[(b + a*x)/(d + c*x)])/Sqrt[a]])/(8*a^(7/2)*c^(5/2)*(b^2 - a*c)^4) - (b*(b*c - a*d)*(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[(d + c*x)^(-1)])/(a^3*c^3*(b^2 - a*c)^4) + (2*(b^3 - a^3*c)*(b*c - a*d)*(b^3 - a^2*d)^2*Log[a - b*Sqrt[(b + a*x)/(d + c*x)]])/(a^3*b*(b^2 - a*c)^4)","A",9,5,52,0.09615,1,"{1647, 1629, 635, 208, 260}"
3154,1,1806,0,20.9391551,"\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","Int[(C[6] + x*C[7])^2/Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]],x]","\frac{\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_7{}^2 (c_1 c_2-c_0 c_3){}^3}{3 c_3{}^2 \left(c_1-\frac{(c_0+x c_1) c_3}{c_2+x c_3}\right){}^3 \left(c_3 c_4{}^2-c_1 c_5{}^2\right)}-\frac{\sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} c_7 \left(\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5 \left(c_0 c_3{}^2 c_7 c_4{}^2-3 c_1{}^2 c_5{}^2 (8 c_3 c_6-5 c_2 c_7)+c_1 c_3 \left(24 c_3 c_4{}^2 c_6-\left(25 c_2 c_4{}^2-9 c_0 c_5{}^2\right) c_7\right)\right)-2 c_1 c_4 \left(12 c_3{}^2 c_6 c_4{}^2+7 c_1 c_2 c_5{}^2 c_7-c_3 \left(12 c_1 c_6 c_5{}^2+\left(12 c_2 c_4{}^2-5 c_0 c_5{}^2\right) c_7\right)\right)\right) (c_1 c_2-c_0 c_3){}^2}{24 c_1 c_3{}^2 \left(c_1-\frac{(c_0+x c_1) c_3}{c_2+x c_3}\right){}^2 \left(c_3 c_4{}^2-c_1 c_5{}^2\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) c_5 \left(c_5{}^2 \left(32 c_3{}^2 c_6{}^2-24 c_2 c_3 c_7 c_6+7 c_2{}^2 c_7{}^2\right) c_1{}^3-2 \sqrt{c_3} c_4 c_5 \left(32 c_3{}^2 c_6{}^2-36 c_2 c_3 c_7 c_6+11 c_2{}^2 c_7{}^2\right) c_1{}^{5/2}+2 c_3 \left(16 c_3{}^2 c_4{}^2 c_6{}^2-4 c_3 \left(6 c_2 c_4{}^2+5 c_0 c_5{}^2\right) c_7 c_6+5 c_2 \left(2 c_2 c_4{}^2+c_0 c_5{}^2\right) c_7{}^2\right) c_1{}^2+28 c_0 c_3{}^{3/2} c_4 c_5 c_7 (2 c_3 c_6-c_2 c_7) c_1{}^{3/2}-c_0 c_3{}^2 c_7 \left(16 c_3 c_4{}^2 c_6-\left(8 c_2 c_4{}^2+15 c_0 c_5{}^2\right) c_7\right) c_1-14 c_0{}^2 c_3{}^{5/2} c_4 c_5 c_7{}^2 \sqrt{c_1}+4 c_0{}^2 c_3{}^3 c_4{}^2 c_7{}^2\right) (c_1 c_2-c_0 c_3)}{64 c_1{}^{5/2} c_3{}^{11/4} \left(\sqrt{c_3} c_4-\sqrt{c_1} c_5\right){}^{7/2}}+\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_5 \left(c_5{}^2 \left(32 c_3{}^2 c_6{}^2-24 c_2 c_3 c_7 c_6+7 c_2{}^2 c_7{}^2\right) c_1{}^3+2 \sqrt{c_3} c_4 c_5 \left(32 c_3{}^2 c_6{}^2-36 c_2 c_3 c_7 c_6+11 c_2{}^2 c_7{}^2\right) c_1{}^{5/2}+2 c_3 \left(16 c_3{}^2 c_4{}^2 c_6{}^2-4 c_3 \left(6 c_2 c_4{}^2+5 c_0 c_5{}^2\right) c_7 c_6+5 c_2 \left(2 c_2 c_4{}^2+c_0 c_5{}^2\right) c_7{}^2\right) c_1{}^2-28 c_0 c_3{}^{3/2} c_4 c_5 c_7 (2 c_3 c_6-c_2 c_7) c_1{}^{3/2}-c_0 c_3{}^2 c_7 \left(16 c_3 c_4{}^2 c_6-\left(8 c_2 c_4{}^2+15 c_0 c_5{}^2\right) c_7\right) c_1+14 c_0{}^2 c_3{}^{5/2} c_4 c_5 c_7{}^2 \sqrt{c_1}+4 c_0{}^2 c_3{}^3 c_4{}^2 c_7{}^2\right) (c_1 c_2-c_0 c_3)}{64 c_1{}^{5/2} c_3{}^{11/4} \left(\sqrt{c_3} c_4+\sqrt{c_1} c_5\right){}^{7/2}}+\frac{(c_2+x c_3) \sqrt{c_4+\sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5} \left(3 \sqrt{\frac{c_0+x c_1}{c_2+x c_3}} c_5 \left(2 c_0{}^2 c_3{}^4 c_7{}^2 c_4{}^4-c_0 c_1 c_3{}^3 c_7 \left(8 c_3 c_4{}^2 c_6-\left(4 c_2 c_4{}^2-7 c_0 c_5{}^2\right) c_7\right) c_4{}^2-c_1{}^4 c_5{}^4 \left(32 c_3{}^2 c_6{}^2-24 c_2 c_3 c_7 c_6+7 c_2{}^2 c_7{}^2\right)+c_1{}^3 c_3 c_5{}^2 \left(64 c_3{}^2 c_4{}^2 c_6{}^2-8 c_3 \left(12 c_2 c_4{}^2-5 c_0 c_5{}^2\right) c_7 c_6+5 c_2 \left(5 c_2 c_4{}^2-2 c_0 c_5{}^2\right) c_7{}^2\right)-c_1{}^2 c_3{}^2 \left(32 c_3{}^2 c_6{}^2 c_4{}^4-8 c_3 \left(9 c_2 c_4{}^2-4 c_0 c_5{}^2\right) c_6 c_7 c_4{}^2+\left(38 c_2{}^2 c_4{}^4-46 c_0 c_2 c_5{}^2 c_4{}^2+15 c_0{}^2 c_5{}^4\right) c_7{}^2\right)\right)-c_1 c_4 \left(-c_1{}^3 \left(96 c_3{}^2 c_6{}^2-48 c_2 c_3 c_7 c_6+13 c_2{}^2 c_7{}^2\right) c_5{}^4+c_0{}^2 c_3{}^3 c_4{}^2 c_7{}^2 c_5{}^2+c_1{}^2 c_3 \left(192 c_3{}^2 c_4{}^2 c_6{}^2-48 c_3 \left(5 c_2 c_4{}^2-3 c_0 c_5{}^2\right) c_7 c_6+c_2 \left(49 c_2 c_4{}^2-22 c_0 c_5{}^2\right) c_7{}^2\right) c_5{}^2-c_1 c_3{}^2 \left(96 c_3{}^2 c_6{}^2 c_4{}^4-48 c_3 \left(4 c_2 c_4{}^2-3 c_0 c_5{}^2\right) c_6 c_7 c_4{}^2+\left(96 c_2{}^2 c_4{}^4-142 c_0 c_2 c_5{}^2 c_4{}^2+61 c_0{}^2 c_5{}^4\right) c_7{}^2\right)\right)\right)}{96 c_1{}^2 c_3{}^2 \left(c_3 c_4{}^2-c_1 c_5{}^2\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) (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,"((C[1]*C[2] - C[0]*C[3])^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[7]^2)/(3*C[3]^2*(C[1] - ((C[0] + x*C[1])*C[3])/(C[2] + x*C[3]))^3*(C[3]*C[4]^2 - C[1]*C[5]^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[1]*C[2] - C[0]*C[3])*C[5]*(4*C[0]^2*C[3]^3*C[4]^2*C[7]^2 - 14*C[0]^2*Sqrt[C[1]]*C[3]^(5/2)*C[4]*C[5]*C[7]^2 + 28*C[0]*C[1]^(3/2)*C[3]^(3/2)*C[4]*C[5]*C[7]*(2*C[3]*C[6] - C[2]*C[7]) - C[0]*C[1]*C[3]^2*C[7]*(16*C[3]*C[4]^2*C[6] - (8*C[2]*C[4]^2 + 15*C[0]*C[5]^2)*C[7]) + C[1]^3*C[5]^2*(32*C[3]^2*C[6]^2 - 24*C[2]*C[3]*C[6]*C[7] + 7*C[2]^2*C[7]^2) - 2*C[1]^(5/2)*Sqrt[C[3]]*C[4]*C[5]*(32*C[3]^2*C[6]^2 - 36*C[2]*C[3]*C[6]*C[7] + 11*C[2]^2*C[7]^2) + 2*C[1]^2*C[3]*(16*C[3]^2*C[4]^2*C[6]^2 - 4*C[3]*(6*C[2]*C[4]^2 + 5*C[0]*C[5]^2)*C[6]*C[7] + 5*C[2]*(2*C[2]*C[4]^2 + C[0]*C[5]^2)*C[7]^2)))/(64*C[1]^(5/2)*C[3]^(11/4)*(Sqrt[C[3]]*C[4] - Sqrt[C[1]]*C[5])^(7/2)) + (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[1]*C[2] - C[0]*C[3])*C[5]*(4*C[0]^2*C[3]^3*C[4]^2*C[7]^2 + 14*C[0]^2*Sqrt[C[1]]*C[3]^(5/2)*C[4]*C[5]*C[7]^2 - 28*C[0]*C[1]^(3/2)*C[3]^(3/2)*C[4]*C[5]*C[7]*(2*C[3]*C[6] - C[2]*C[7]) - C[0]*C[1]*C[3]^2*C[7]*(16*C[3]*C[4]^2*C[6] - (8*C[2]*C[4]^2 + 15*C[0]*C[5]^2)*C[7]) + C[1]^3*C[5]^2*(32*C[3]^2*C[6]^2 - 24*C[2]*C[3]*C[6]*C[7] + 7*C[2]^2*C[7]^2) + 2*C[1]^(5/2)*Sqrt[C[3]]*C[4]*C[5]*(32*C[3]^2*C[6]^2 - 36*C[2]*C[3]*C[6]*C[7] + 11*C[2]^2*C[7]^2) + 2*C[1]^2*C[3]*(16*C[3]^2*C[4]^2*C[6]^2 - 4*C[3]*(6*C[2]*C[4]^2 + 5*C[0]*C[5]^2)*C[6]*C[7] + 5*C[2]*(2*C[2]*C[4]^2 + C[0]*C[5]^2)*C[7]^2)))/(64*C[1]^(5/2)*C[3]^(11/4)*(Sqrt[C[3]]*C[4] + Sqrt[C[1]]*C[5])^(7/2)) - ((C[1]*C[2] - C[0]*C[3])^2*Sqrt[C[4] + Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]]*C[7]*(Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]*(C[0]*C[3]^2*C[4]^2*C[7] - 3*C[1]^2*C[5]^2*(8*C[3]*C[6] - 5*C[2]*C[7]) + C[1]*C[3]*(24*C[3]*C[4]^2*C[6] - (25*C[2]*C[4]^2 - 9*C[0]*C[5]^2)*C[7])) - 2*C[1]*C[4]*(12*C[3]^2*C[4]^2*C[6] + 7*C[1]*C[2]*C[5]^2*C[7] - C[3]*(12*C[1]*C[5]^2*C[6] + (12*C[2]*C[4]^2 - 5*C[0]*C[5]^2)*C[7]))))/(24*C[1]*C[3]^2*(C[1] - ((C[0] + x*C[1])*C[3])/(C[2] + x*C[3]))^2*(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]]*(3*Sqrt[(C[0] + x*C[1])/(C[2] + x*C[3])]*C[5]*(2*C[0]^2*C[3]^4*C[4]^4*C[7]^2 - C[0]*C[1]*C[3]^3*C[4]^2*C[7]*(8*C[3]*C[4]^2*C[6] - (4*C[2]*C[4]^2 - 7*C[0]*C[5]^2)*C[7]) - C[1]^4*C[5]^4*(32*C[3]^2*C[6]^2 - 24*C[2]*C[3]*C[6]*C[7] + 7*C[2]^2*C[7]^2) + C[1]^3*C[3]*C[5]^2*(64*C[3]^2*C[4]^2*C[6]^2 - 8*C[3]*(12*C[2]*C[4]^2 - 5*C[0]*C[5]^2)*C[6]*C[7] + 5*C[2]*(5*C[2]*C[4]^2 - 2*C[0]*C[5]^2)*C[7]^2) - C[1]^2*C[3]^2*(32*C[3]^2*C[4]^4*C[6]^2 - 8*C[3]*C[4]^2*(9*C[2]*C[4]^2 - 4*C[0]*C[5]^2)*C[6]*C[7] + (38*C[2]^2*C[4]^4 - 46*C[0]*C[2]*C[4]^2*C[5]^2 + 15*C[0]^2*C[5]^4)*C[7]^2)) - C[1]*C[4]*(C[0]^2*C[3]^3*C[4]^2*C[5]^2*C[7]^2 - C[1]^3*C[5]^4*(96*C[3]^2*C[6]^2 - 48*C[2]*C[3]*C[6]*C[7] + 13*C[2]^2*C[7]^2) + C[1]^2*C[3]*C[5]^2*(192*C[3]^2*C[4]^2*C[6]^2 - 48*C[3]*(5*C[2]*C[4]^2 - 3*C[0]*C[5]^2)*C[6]*C[7] + C[2]*(49*C[2]*C[4]^2 - 22*C[0]*C[5]^2)*C[7]^2) - C[1]*C[3]^2*(96*C[3]^2*C[4]^4*C[6]^2 - 48*C[3]*C[4]^2*(4*C[2]*C[4]^2 - 3*C[0]*C[5]^2)*C[6]*C[7] + (96*C[2]^2*C[4]^4 - 142*C[0]*C[2]*C[4]^2*C[5]^2 + 61*C[0]^2*C[5]^4)*C[7]^2))))/(96*C[1]^2*C[3]^2*(C[3]*C[4]^2 - C[1]*C[5]^2)^3)","A",8,5,41,0.1220,1,"{1649, 823, 827, 1166, 208}"