1,1,9,0,0.487020," ","integrate(x/(x^2-1)^(3/4),x, algorithm=""giac"")","2 \, {\left(x^{2} - 1\right)}^{\frac{1}{4}}"," ",0,"2*(x^2 - 1)^(1/4)","A",0
2,1,10,0,0.405393," ","integrate((3*x^2+1)/(x^3+x-1)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x^{3} + x - 1}"," ",0,"2*sqrt(x^3 + x - 1)","A",0
3,1,10,0,0.553811," ","integrate((x^8-1)/(x^4-1)^(1/2)/(x^8-2*x^4+1),x, algorithm=""giac"")","-\frac{x}{\sqrt{x^{4} - 1}}"," ",0,"-x/sqrt(x^4 - 1)","A",0
4,1,9,0,0.634496," ","integrate(x/(x^2-1)^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, {\left(x^{2} - 1\right)}^{\frac{2}{3}}"," ",0,"3/4*(x^2 - 1)^(2/3)","A",0
5,1,9,0,0.418564," ","integrate(x/(x^2-1)^(1/4),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x^{2} - 1\right)}^{\frac{3}{4}}"," ",0,"2/3*(x^2 - 1)^(3/4)","A",0
6,1,9,0,0.453712," ","integrate(x*(x^2-1)^(1/4),x, algorithm=""giac"")","\frac{2}{5} \, {\left(x^{2} - 1\right)}^{\frac{5}{4}}"," ",0,"2/5*(x^2 - 1)^(5/4)","A",0
7,1,9,0,0.440115," ","integrate(x*(x^2-1)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(x^{2} - 1\right)}^{\frac{4}{3}}"," ",0,"3/8*(x^2 - 1)^(4/3)","A",0
8,1,9,0,0.282319," ","integrate(x*(x^2-1)^(2/3),x, algorithm=""giac"")","\frac{3}{10} \, {\left(x^{2} - 1\right)}^{\frac{5}{3}}"," ",0,"3/10*(x^2 - 1)^(5/3)","A",0
9,1,9,0,0.303800," ","integrate(x*(x^2-1)^(3/4),x, algorithm=""giac"")","\frac{2}{7} \, {\left(x^{2} - 1\right)}^{\frac{7}{4}}"," ",0,"2/7*(x^2 - 1)^(7/4)","A",0
10,1,9,0,0.406580," ","integrate(x/(x^2+1)^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, {\left(x^{2} + 1\right)}^{\frac{2}{3}}"," ",0,"3/4*(x^2 + 1)^(2/3)","A",0
11,1,9,0,0.259318," ","integrate(x/(x^2+1)^(1/4),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x^{2} + 1\right)}^{\frac{3}{4}}"," ",0,"2/3*(x^2 + 1)^(3/4)","A",0
12,1,9,0,0.328112," ","integrate(x*(x^2+1)^(1/4),x, algorithm=""giac"")","\frac{2}{5} \, {\left(x^{2} + 1\right)}^{\frac{5}{4}}"," ",0,"2/5*(x^2 + 1)^(5/4)","A",0
13,1,9,0,0.662986," ","integrate(x*(x^2+1)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(x^{2} + 1\right)}^{\frac{4}{3}}"," ",0,"3/8*(x^2 + 1)^(4/3)","A",0
14,1,9,0,0.361134," ","integrate(x*(x^2+1)^(3/4),x, algorithm=""giac"")","\frac{2}{7} \, {\left(x^{2} + 1\right)}^{\frac{7}{4}}"," ",0,"2/7*(x^2 + 1)^(7/4)","A",0
15,1,9,0,0.380889," ","integrate(x^2/(x^3-1)^(1/4),x, algorithm=""giac"")","\frac{4}{9} \, {\left(x^{3} - 1\right)}^{\frac{3}{4}}"," ",0,"4/9*(x^3 - 1)^(3/4)","A",0
16,1,9,0,0.358726," ","integrate(x^2*(x^3-1)^(1/4),x, algorithm=""giac"")","\frac{4}{15} \, {\left(x^{3} - 1\right)}^{\frac{5}{4}}"," ",0,"4/15*(x^3 - 1)^(5/4)","A",0
17,1,9,0,0.436340," ","integrate(x^2*(x^3-1)^(3/4),x, algorithm=""giac"")","\frac{4}{21} \, {\left(x^{3} - 1\right)}^{\frac{7}{4}}"," ",0,"4/21*(x^3 - 1)^(7/4)","A",0
18,1,9,0,0.747617," ","integrate(x^2/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} + 1}"," ",0,"2/3*sqrt(x^3 + 1)","A",0
19,1,9,0,0.360582," ","integrate(x^2/(x^3+1)^(1/4),x, algorithm=""giac"")","\frac{4}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{4}}"," ",0,"4/9*(x^3 + 1)^(3/4)","A",0
20,1,9,0,0.355128," ","integrate(x^2*(x^3+1)^(1/4),x, algorithm=""giac"")","\frac{4}{15} \, {\left(x^{3} + 1\right)}^{\frac{5}{4}}"," ",0,"4/15*(x^3 + 1)^(5/4)","A",0
21,1,9,0,0.443589," ","integrate(x^2*(x^3+1)^(1/3),x, algorithm=""giac"")","\frac{1}{4} \, {\left(x^{3} + 1\right)}^{\frac{4}{3}}"," ",0,"1/4*(x^3 + 1)^(4/3)","A",0
22,1,9,0,0.438010," ","integrate(x^2*(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{2}}"," ",0,"2/9*(x^3 + 1)^(3/2)","A",0
23,1,9,0,0.588429," ","integrate(x^2*(x^3+1)^(2/3),x, algorithm=""giac"")","\frac{1}{5} \, {\left(x^{3} + 1\right)}^{\frac{5}{3}}"," ",0,"1/5*(x^3 + 1)^(5/3)","A",0
24,1,9,0,0.501610," ","integrate(x^2*(x^3+1)^(3/4),x, algorithm=""giac"")","\frac{4}{21} \, {\left(x^{3} + 1\right)}^{\frac{7}{4}}"," ",0,"4/21*(x^3 + 1)^(7/4)","A",0
25,1,9,0,0.294337," ","integrate((3*x^2+1)*(x^3+x)^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, {\left(x^{3} + x\right)}^{\frac{4}{3}}"," ",0,"3/4*(x^3 + x)^(4/3)","A",0
26,0,0,0,0.000000," ","integrate(1/x^2/(x^4-1)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^4 - 1)^(3/4)*x^2), x)","F",0
27,1,9,0,0.694025," ","integrate(x^3/(x^4-1)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(x^{4} - 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(x^4 - 1)^(2/3)","A",0
28,1,9,0,0.424482," ","integrate(x^3*(x^4-1)^(1/3),x, algorithm=""giac"")","\frac{3}{16} \, {\left(x^{4} - 1\right)}^{\frac{4}{3}}"," ",0,"3/16*(x^4 - 1)^(4/3)","A",0
29,1,9,0,0.277081," ","integrate(x^3*(x^4-1)^(2/3),x, algorithm=""giac"")","\frac{3}{20} \, {\left(x^{4} - 1\right)}^{\frac{5}{3}}"," ",0,"3/20*(x^4 - 1)^(5/3)","A",0
30,1,9,0,0.293706," ","integrate(x^3*(x^4-1)^(3/4),x, algorithm=""giac"")","\frac{1}{7} \, {\left(x^{4} - 1\right)}^{\frac{7}{4}}"," ",0,"1/7*(x^4 - 1)^(7/4)","A",0
31,0,0,0,0.000000," ","integrate((x^4-1)/x^2/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{\sqrt{x^{4} + 1} x^{2}}\,{d x}"," ",0,"integrate((x^4 - 1)/(sqrt(x^4 + 1)*x^2), x)","F",0
32,1,9,0,0.605700," ","integrate(x^3/(x^4+1)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(x^{4} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(x^4 + 1)^(2/3)","A",0
33,1,9,0,0.277667," ","integrate(x^3*(x^4+1)^(1/4),x, algorithm=""giac"")","\frac{1}{5} \, {\left(x^{4} + 1\right)}^{\frac{5}{4}}"," ",0,"1/5*(x^4 + 1)^(5/4)","A",0
34,1,9,0,0.372713," ","integrate(x^3*(x^4+1)^(1/3),x, algorithm=""giac"")","\frac{3}{16} \, {\left(x^{4} + 1\right)}^{\frac{4}{3}}"," ",0,"3/16*(x^4 + 1)^(4/3)","A",0
35,1,9,0,0.407264," ","integrate(x^3*(x^4+1)^(2/3),x, algorithm=""giac"")","\frac{3}{20} \, {\left(x^{4} + 1\right)}^{\frac{5}{3}}"," ",0,"3/20*(x^4 + 1)^(5/3)","A",0
36,1,9,0,0.439085," ","integrate(x^4*(x^5-1)^(2/3),x, algorithm=""giac"")","\frac{3}{25} \, {\left(x^{5} - 1\right)}^{\frac{5}{3}}"," ",0,"3/25*(x^5 - 1)^(5/3)","A",0
37,1,9,0,0.425402," ","integrate(x^4*(x^5+1)^(2/3),x, algorithm=""giac"")","\frac{3}{25} \, {\left(x^{5} + 1\right)}^{\frac{5}{3}}"," ",0,"3/25*(x^5 + 1)^(5/3)","A",0
38,1,9,0,0.276841," ","integrate(x^5/(x^6-1)^(1/3),x, algorithm=""giac"")","\frac{1}{4} \, {\left(x^{6} - 1\right)}^{\frac{2}{3}}"," ",0,"1/4*(x^6 - 1)^(2/3)","A",0
39,1,9,0,0.377077," ","integrate(x^5*(x^6-1)^(1/4),x, algorithm=""giac"")","\frac{2}{15} \, {\left(x^{6} - 1\right)}^{\frac{5}{4}}"," ",0,"2/15*(x^6 - 1)^(5/4)","A",0
40,1,9,0,0.319960," ","integrate(x^5*(x^6-1)^(1/3),x, algorithm=""giac"")","\frac{1}{8} \, {\left(x^{6} - 1\right)}^{\frac{4}{3}}"," ",0,"1/8*(x^6 - 1)^(4/3)","A",0
41,1,9,0,0.511140," ","integrate(x^5*(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{1}{9} \, {\left(x^{6} - 1\right)}^{\frac{3}{2}}"," ",0,"1/9*(x^6 - 1)^(3/2)","A",0
42,1,9,0,0.416934," ","integrate(x^5*(x^6-1)^(3/4),x, algorithm=""giac"")","\frac{2}{21} \, {\left(x^{6} - 1\right)}^{\frac{7}{4}}"," ",0,"2/21*(x^6 - 1)^(7/4)","A",0
43,0,0,0,0.000000," ","integrate((x^6-2)/x^3/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6} - 2}{\sqrt{x^{6} + 1} x^{3}}\,{d x}"," ",0,"integrate((x^6 - 2)/(sqrt(x^6 + 1)*x^3), x)","F",0
44,1,9,0,0.342918," ","integrate(x^5/(x^6+1)^(1/3),x, algorithm=""giac"")","\frac{1}{4} \, {\left(x^{6} + 1\right)}^{\frac{2}{3}}"," ",0,"1/4*(x^6 + 1)^(2/3)","A",0
45,1,9,0,0.314993," ","integrate(x^5*(x^6+1)^(1/4),x, algorithm=""giac"")","\frac{2}{15} \, {\left(x^{6} + 1\right)}^{\frac{5}{4}}"," ",0,"2/15*(x^6 + 1)^(5/4)","A",0
46,1,9,0,0.354490," ","integrate(x^5*(x^6+1)^(1/3),x, algorithm=""giac"")","\frac{1}{8} \, {\left(x^{6} + 1\right)}^{\frac{4}{3}}"," ",0,"1/8*(x^6 + 1)^(4/3)","A",0
47,0,0,0,0.000000," ","integrate((x^3-4)/x^2/(x^3-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{3} - 4}{{\left(x^{3} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^3 - 4)/((x^3 - 1)^(3/4)*x^2), x)","F",0
48,1,26,0,0.336801," ","integrate(1/x/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(abs(sqrt(x^3 + 1) - 1))","B",0
49,0,0,0,0.000000," ","integrate((x^3+4)/x^2/(x^3+1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{3} + 4}{{\left(x^{3} + 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^3 + 4)/((x^3 + 1)^(3/4)*x^2), x)","F",0
50,1,12,0,0.419696," ","integrate((3*x^2+2)*(x^3+x)^(1/3)/(x^2+1),x, algorithm=""giac"")","\frac{3}{2} \, x^{2} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}"," ",0,"3/2*x^2*(1/x^2 + 1)^(1/3)","A",0
51,0,0,0,0.000000," ","integrate((-2+x)/(-1+x)/(x^3-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x - 2}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{4}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x - 2)/((x^3 - x^2)^(1/4)*(x - 1)), x)","F",0
52,1,11,0,0.446290," ","integrate((2+x)/(1+x)/(x^3+x^2)^(1/4),x, algorithm=""giac"")","\frac{4}{{\left(\frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{4}}}"," ",0,"4/(1/x + 1/x^2)^(1/4)","A",0
53,0,0,0,0.000000," ","integrate(1/x^2/(x^4+1)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(3/4)*x^2), x)","F",0
54,1,12,0,0.572592," ","integrate((x^4+3)/x^4/(x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\frac{1}{x^{4}} + 1}}{x}"," ",0,"-sqrt(1/x^4 + 1)/x","A",0
55,1,12,0,0.439137," ","integrate((4*x^3-1)/(2*x^4-2*x-1)^(1/2),x, algorithm=""giac"")","\sqrt{2 \, x^{4} - 2 \, x - 1}"," ",0,"sqrt(2*x^4 - 2*x - 1)","A",0
56,0,0,0,0.000000," ","integrate((x^5-4)/x^2/(x^5+1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{5} - 4}{{\left(x^{5} + 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^5 - 4)/((x^5 + 1)^(3/4)*x^2), x)","F",0
57,0,0,0,0.000000," ","integrate((x^5+4)/x^2/(x^5-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{5} + 4}{{\left(x^{5} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^5 + 4)/((x^5 - 1)^(3/4)*x^2), x)","F",0
58,0,0,0,0.000000," ","integrate((5*x^3+2)/(x^3+1)^(1/2)/(x^5+x^2+1),x, algorithm=""giac"")","\int \frac{5 \, x^{3} + 2}{{\left(x^{5} + x^{2} + 1\right)} \sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate((5*x^3 + 2)/((x^5 + x^2 + 1)*sqrt(x^3 + 1)), x)","F",0
59,1,10,0,0.459337," ","integrate(1/x/(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/3*arctan(sqrt(x^6 - 1))","A",0
60,0,0,0,0.000000," ","integrate((x^6-2)/x^2/(x^6+1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6} - 2}{{\left(x^{6} + 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^6 - 2)/((x^6 + 1)^(3/4)*x^2), x)","F",0
61,1,25,0,0.311707," ","integrate(1/x/(x^6+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, \log\left(\sqrt{x^{6} + 1} + 1\right) + \frac{1}{6} \, \log\left(\sqrt{x^{6} + 1} - 1\right)"," ",0,"-1/6*log(sqrt(x^6 + 1) + 1) + 1/6*log(sqrt(x^6 + 1) - 1)","B",0
62,0,0,0,0.000000," ","integrate((x^6+2)/x^2/(x^6-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6} + 2}{{\left(x^{6} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^6 + 2)/((x^6 - 1)^(3/4)*x^2), x)","F",0
63,0,0,0,0.000000," ","integrate((2*x^6-1)/(x^6+1)^(1/2)/(x^6-x^2+1),x, algorithm=""giac"")","\int \frac{2 \, x^{6} - 1}{{\left(x^{6} - x^{2} + 1\right)} \sqrt{x^{6} + 1}}\,{d x}"," ",0,"integrate((2*x^6 - 1)/((x^6 - x^2 + 1)*sqrt(x^6 + 1)), x)","F",0
64,0,0,0,0.000000," ","integrate((2*x^6+1)/(x^6-1)^(1/2)/(x^6+x^2-1),x, algorithm=""giac"")","\int \frac{2 \, x^{6} + 1}{{\left(x^{6} + x^{2} - 1\right)} \sqrt{x^{6} - 1}}\,{d x}"," ",0,"integrate((2*x^6 + 1)/((x^6 + x^2 - 1)*sqrt(x^6 - 1)), x)","F",0
65,1,11,0,0.286018," ","integrate((3*x^2-1)/(x^3-x)^(1/3),x, algorithm=""giac"")","\frac{3}{2} \, {\left(x^{3} - x\right)}^{\frac{2}{3}}"," ",0,"3/2*(x^3 - x)^(2/3)","A",0
66,1,11,0,0.311910," ","integrate((3*x^2-1)*(x^3-x)^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, {\left(x^{3} - x\right)}^{\frac{4}{3}}"," ",0,"3/4*(x^3 - x)^(4/3)","A",0
67,0,0,0,0.000000," ","integrate((-x^3+x+2)/(x^3+x+1)^(1/2)/(x^3-x^2+x+1),x, algorithm=""giac"")","\int -\frac{x^{3} - x - 2}{{\left(x^{3} - x^{2} + x + 1\right)} \sqrt{x^{3} + x + 1}}\,{d x}"," ",0,"integrate(-(x^3 - x - 2)/((x^3 - x^2 + x + 1)*sqrt(x^3 + x + 1)), x)","F",0
68,0,0,0,0.000000," ","integrate((x^4+1)/(-x^4+1)/(x^4+x^2-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{4} + 1}{\sqrt{x^{4} + x^{2} - 1} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^4 + 1)/(sqrt(x^4 + x^2 - 1)*(x^4 - 1)), x)","F",0
69,1,12,0,0.356387," ","integrate((x^3-4)/x^4/(x^3-1)^(1/4),x, algorithm=""giac"")","-\frac{4 \, {\left(x^{3} - 1\right)}^{\frac{3}{4}}}{3 \, x^{3}}"," ",0,"-4/3*(x^3 - 1)^(3/4)/x^3","A",0
70,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)/x^5,x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{5}}\,{d x}"," ",0,"integrate((x^3 - 1)^(1/3)/x^5, x)","F",0
71,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)/x^6, x)","F",0
72,0,0,0,0.000000," ","integrate((x^3+1)^(1/3)/x^5,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}}}{x^{5}}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)/x^5, x)","F",0
73,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)/x^6, x)","F",0
74,1,27,0,0.497307," ","integrate((x^3-2)*(x^3+1)^(3/2)/x^6,x, algorithm=""giac"")","\frac{2}{5} \, \sqrt{x^{3} + 1} x + \frac{2}{5} \, \sqrt{\frac{1}{x} + \frac{1}{x^{4}}} {\left(\frac{1}{x^{3}} + 2\right)}"," ",0,"2/5*sqrt(x^3 + 1)*x + 2/5*sqrt(1/x + 1/x^4)*(1/x^3 + 2)","B",0
75,1,12,0,0.305590," ","integrate((x^3+4)/x^4/(x^3+1)^(1/4),x, algorithm=""giac"")","-\frac{4 \, {\left(x^{3} + 1\right)}^{\frac{3}{4}}}{3 \, x^{3}}"," ",0,"-4/3*(x^3 + 1)^(3/4)/x^3","A",0
76,1,9,0,0.505402," ","integrate(1/x^2/(x^3+x)^(1/3),x, algorithm=""giac"")","-\frac{3}{4} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/4*(1/x^2 + 1)^(2/3)","A",0
77,1,11,0,0.415074," ","integrate((x^2+1)*(x^2+3)/x^6/(x^3+x)^(1/4),x, algorithm=""giac"")","-\frac{4}{7} \, {\left(\frac{1}{x} + \frac{1}{x^{3}}\right)}^{\frac{7}{4}}"," ",0,"-4/7*(1/x + 1/x^3)^(7/4)","A",0
78,1,9,0,0.517095," ","integrate((x^3+x)^(1/3)/x^4,x, algorithm=""giac"")","-\frac{3}{8} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}}"," ",0,"-3/8*(1/x^2 + 1)^(4/3)","A",0
79,0,0,0,0.000000," ","integrate(1/x^4/(x^4-1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} - 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((x^4 - 1)^(1/4)*x^4), x)","F",0
80,0,0,0,0.000000," ","integrate((x^4-1)^(3/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)}^{\frac{3}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((x^4 - 1)^(3/4)/x^8, x)","F",0
81,1,21,0,0.411257," ","integrate((x^4-1)/x^2/(x^3+x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} + x} + \frac{2}{3} \, \sqrt{\frac{1}{x} + \frac{1}{x^{3}}}"," ",0,"2/3*sqrt(x^3 + x) + 2/3*sqrt(1/x + 1/x^3)","A",0
82,0,0,0,0.000000," ","integrate(1/x^4/(x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(1/4)*x^4), x)","F",0
83,1,22,0,0.270583," ","integrate((x^4-3)*(x^4+1)^(1/3)/x^5,x, algorithm=""giac"")","\frac{3}{4} \, {\left(x^{4} + 1\right)}^{\frac{1}{3}} + \frac{3 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}}}{4 \, x^{4}}"," ",0,"3/4*(x^4 + 1)^(1/3) + 3/4*(x^4 + 1)^(1/3)/x^4","A",0
84,1,23,0,0.501540," ","integrate((x^2-1)*(x^2+1)*(x^4+1)^(1/2)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} + 1} x + \frac{\sqrt{\frac{1}{x^{4}} + 1}}{3 \, x}"," ",0,"1/3*sqrt(x^4 + 1)*x + 1/3*sqrt(1/x^4 + 1)/x","A",0
85,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(2/3)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{x^{6}}\,{d x}"," ",0,"integrate((x^4 + 1)^(2/3)*(x^4 - 3)/x^6, x)","F",0
86,0,0,0,0.000000," ","integrate((x^4+1)^(3/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{3}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((x^4 + 1)^(3/4)/x^8, x)","F",0
87,0,0,0,0.000000," ","integrate((x^4-1)^(2/3)*(x^4+3)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((x^4 + 3)*(x^4 - 1)^(2/3)/x^6, x)","F",0
88,1,12,0,0.545143," ","integrate((x^4+1)^(1/3)*(x^4+3)/x^9,x, algorithm=""giac"")","-\frac{3 \, {\left(x^{4} + 1\right)}^{\frac{4}{3}}}{8 \, x^{8}}"," ",0,"-3/8*(x^4 + 1)^(4/3)/x^8","A",0
89,1,9,0,0.393275," ","integrate(1/x^2/(x^4+x)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{\frac{1}{x^{3}} + 1}"," ",0,"-2/3*sqrt(1/x^3 + 1)","A",0
90,1,9,0,0.472332," ","integrate((x^3+1)/x^6/(x^4+x)^(1/4),x, algorithm=""giac"")","-\frac{4}{21} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}}"," ",0,"-4/21*(1/x^3 + 1)^(7/4)","A",0
91,0,0,0,0.000000," ","integrate((x^3-2)*(x^4+x)^(1/3)/(x^3+1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x\right)}^{\frac{1}{3}} {\left(x^{3} - 2\right)}}{{\left(x^{3} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^4 + x)^(1/3)*(x^3 - 2)/(x^3 + 1)^2, x)","F",0
92,1,9,0,0.341867," ","integrate((x^4+x^2)^(1/4)/x^2/(x^2+1),x, algorithm=""giac"")","-2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}"," ",0,"-2*(1/x^2 + 1)^(1/4)","A",0
93,1,12,0,0.431139," ","integrate((x^5-6)*(x^5-1)^(2/3)/x^11,x, algorithm=""giac"")","-\frac{3 \, {\left(x^{5} - 1\right)}^{\frac{5}{3}}}{5 \, x^{10}}"," ",0,"-3/5*(x^5 - 1)^(5/3)/x^10","A",0
94,0,0,0,0.000000," ","integrate((x^5-4)*(x^5+1)^(3/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{5} + 1\right)}^{\frac{3}{4}} {\left(x^{5} - 4\right)}}{x^{8}}\,{d x}"," ",0,"integrate((x^5 + 1)^(3/4)*(x^5 - 4)/x^8, x)","F",0
95,0,0,0,0.000000," ","integrate((x^5-1)^(3/4)*(x^5+4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{5} + 4\right)} {\left(x^{5} - 1\right)}^{\frac{3}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((x^5 + 4)*(x^5 - 1)^(3/4)/x^8, x)","F",0
96,1,12,0,0.741239," ","integrate((x^5+1)^(2/3)*(x^5+6)/x^11,x, algorithm=""giac"")","-\frac{3 \, {\left(x^{5} + 1\right)}^{\frac{5}{3}}}{5 \, x^{10}}"," ",0,"-3/5*(x^5 + 1)^(5/3)/x^10","A",0
97,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)/x^6/(x^5+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)} {\left(x^{4} - 3\right)}}{{\left(x^{5} + x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 + 1)*(x^4 - 3)/((x^5 + x)^(1/4)*x^6), x)","F",0
98,0,0,0,0.000000," ","integrate((x^2-1)*(x^5+x^3)^(1/4)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^5 + x^3)^(1/4)*(x^2 - 1)/((x^2 + 1)*x^2), x)","F",0
99,0,0,0,0.000000," ","integrate((3*a*x^5-2*b)/(a*x^5+b)^(1/2)/(a*x^5+x^2+b),x, algorithm=""giac"")","\int \frac{3 \, a x^{5} - 2 \, b}{{\left(a x^{5} + x^{2} + b\right)} \sqrt{a x^{5} + b}}\,{d x}"," ",0,"integrate((3*a*x^5 - 2*b)/((a*x^5 + x^2 + b)*sqrt(a*x^5 + b)), x)","F",0
100,1,20,0,0.356272," ","integrate(1/x^4/(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{-\frac{1}{x^{6}} + 1}}{3 \, \mathrm{sgn}\left(x\right)} - \frac{1}{3} \, \mathrm{sgn}\left(x\right)"," ",0,"1/3*sqrt(-1/x^6 + 1)/sgn(x) - 1/3*sgn(x)","A",0
101,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)/x^9,x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((x^6 - 1)^(1/3)/x^9, x)","F",0
102,1,20,0,0.616914," ","integrate((x^6-1)^(1/2)/x^10,x, algorithm=""giac"")","\frac{{\left(-\frac{1}{x^{6}} + 1\right)}^{\frac{3}{2}}}{9 \, \mathrm{sgn}\left(x\right)} - \frac{1}{9} \, \mathrm{sgn}\left(x\right)"," ",0,"1/9*(-1/x^6 + 1)^(3/2)/sgn(x) - 1/9*sgn(x)","A",0
103,1,18,0,0.369610," ","integrate(1/x^4/(x^6+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\frac{1}{x^{6}} + 1}}{3 \, \mathrm{sgn}\left(x\right)} + \frac{1}{3} \, \mathrm{sgn}\left(x\right)"," ",0,"-1/3*sqrt(1/x^6 + 1)/sgn(x) + 1/3*sgn(x)","A",0
104,0,0,0,0.000000," ","integrate(1/x^5/(x^6+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 1\right)}^{\frac{1}{3}} x^{5}}\,{d x}"," ",0,"integrate(1/((x^6 + 1)^(1/3)*x^5), x)","F",0
105,0,0,0,0.000000," ","integrate((x^6-2)/x^4/(x^6+1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{6} - 2}{{\left(x^{6} + 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^6 - 2)/((x^6 + 1)^(1/4)*x^4), x)","F",0
106,1,18,0,0.446733," ","integrate((x^6+1)^(1/2)/x^10,x, algorithm=""giac"")","-\frac{{\left(\frac{1}{x^{6}} + 1\right)}^{\frac{3}{2}}}{9 \, \mathrm{sgn}\left(x\right)} + \frac{1}{9} \, \mathrm{sgn}\left(x\right)"," ",0,"-1/9*(1/x^6 + 1)^(3/2)/sgn(x) + 1/9*sgn(x)","A",0
107,0,0,0,0.000000," ","integrate((x^6-2)*(x^6+1)^(3/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)}^{\frac{3}{4}} {\left(x^{6} - 2\right)}}{x^{8}}\,{d x}"," ",0,"integrate((x^6 + 1)^(3/4)*(x^6 - 2)/x^8, x)","F",0
108,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(x^6+1)/x^5,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{5}}\,{d x}"," ",0,"integrate((x^6 + 1)*(x^6 - 1)^(1/3)/x^5, x)","F",0
109,0,0,0,0.000000," ","integrate((x^6+2)/x^4/(x^6-1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{6} + 2}{{\left(x^{6} - 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^6 + 2)/((x^6 - 1)^(1/4)*x^4), x)","F",0
110,0,0,0,0.000000," ","integrate((x^6-1)^(3/4)*(x^6+2)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2\right)} {\left(x^{6} - 1\right)}^{\frac{3}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((x^6 + 2)*(x^6 - 1)^(3/4)/x^8, x)","F",0
111,0,0,0,0.000000," ","integrate((2*x^5-3)/x^3/(x^6+x)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, x^{5} - 3}{{\left(x^{6} + x\right)}^{\frac{1}{4}} x^{3}}\,{d x}"," ",0,"integrate((2*x^5 - 3)/((x^6 + x)^(1/4)*x^3), x)","F",0
112,0,0,0,0.000000," ","integrate((x^4+x)^(1/3)*(x^6-x^3-2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{3} - 2\right)} {\left(x^{4} + x\right)}^{\frac{1}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^3 - 2)*(x^4 + x)^(1/3)/x^6, x)","F",0
113,0,0,0,0.000000," ","integrate(x*(x^6+2)/(x^6-1)^(1/2)/(x^6-x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2\right)} x}{{\left(x^{6} - x^{4} - 1\right)} \sqrt{x^{6} - 1}}\,{d x}"," ",0,"integrate((x^6 + 2)*x/((x^6 - x^4 - 1)*sqrt(x^6 - 1)), x)","F",0
114,1,25,0,0.648198," ","integrate((x^8-1)/x^4/(x^4-1)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} - 1} x - \frac{\sqrt{-\frac{1}{x^{4}} + 1}}{3 \, x}"," ",0,"1/3*sqrt(x^4 - 1)*x - 1/3*sqrt(-1/x^4 + 1)/x","B",0
115,1,25,0,0.685753," ","integrate((x^8-1)*(x^8+1)^(1/2)/x^7,x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{x^{8} + 1} x^{2} + \frac{\sqrt{\frac{1}{x^{8}} + 1}}{6 \, x^{2}}"," ",0,"1/6*sqrt(x^8 + 1)*x^2 + 1/6*sqrt(1/x^8 + 1)/x^2","B",0
116,0,0,0,0.000000," ","integrate((2*x^2+x+2)/(-1+2*x)/(x^4+x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} + x + 2}{\sqrt{x^{4} + x} {\left(2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 + x + 2)/(sqrt(x^4 + x)*(2*x - 1)), x)","F",0
117,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^4 + x^2 + 1)*(x^2 + 1)), x)","F",0
118,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/(sqrt(x^4 + x^2 + 1)*(x^4 + 1)), x)","F",0
119,0,0,0,0.000000," ","integrate((2*x^4+2*x^2-1)/(2*x^2+1)/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} + 2 \, x^{2} - 1}{\sqrt{x^{6} - 1} {\left(2 \, x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 + 2*x^2 - 1)/(sqrt(x^6 - 1)*(2*x^2 + 1)), x)","F",0
120,1,19,0,0.285227," ","integrate(x^3/(x^2-1)^(3/4),x, algorithm=""giac"")","\frac{2}{5} \, {\left(x^{2} - 1\right)}^{\frac{5}{4}} + 2 \, {\left(x^{2} - 1\right)}^{\frac{1}{4}}"," ",0,"2/5*(x^2 - 1)^(5/4) + 2*(x^2 - 1)^(1/4)","A",0
121,0,0,0,0.000000," ","integrate((3+x)/(-1+x)^2/(x^2-1)^(1/3),x, algorithm=""giac"")","\int \frac{x + 3}{{\left(x^{2} - 1\right)}^{\frac{1}{3}} {\left(x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((x + 3)/((x^2 - 1)^(1/3)*(x - 1)^2), x)","F",0
122,1,19,0,0.289732," ","integrate(x^3/(x^2+1)^(2/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(x^{2} + 1\right)}^{\frac{4}{3}} - \frac{3}{2} \, {\left(x^{2} + 1\right)}^{\frac{1}{3}}"," ",0,"3/8*(x^2 + 1)^(4/3) - 3/2*(x^2 + 1)^(1/3)","A",0
123,1,11,0,0.425805," ","integrate(1/x^2/(x^3-x)^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}"," ",0,"3/4*(-1/x^2 + 1)^(2/3)","A",0
124,1,11,0,0.329106," ","integrate((x^3-x)^(1/3)/x^4,x, algorithm=""giac"")","\frac{3}{8} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}}"," ",0,"3/8*(-1/x^2 + 1)^(4/3)","A",0
125,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^3+x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{3} + x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^3 + x)*(x^2 + 1)), x)","F",0
126,1,9,0,0.382514," ","integrate(1/x/(x^3+x^2)^(1/3),x, algorithm=""giac"")","-\frac{3}{2} \, {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/2*(1/x + 1)^(2/3)","A",0
127,1,11,0,0.411662," ","integrate((2+x)/x^2/(x^3+x^2)^(1/4),x, algorithm=""giac"")","-\frac{4}{3} \, {\left(\frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{3}{4}}"," ",0,"-4/3*(1/x + 1/x^2)^(3/4)","A",0
128,1,34,0,0.308692," ","integrate((a*x^3-2*b)*(a*x^3+b)^(1/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(\sqrt{a x^{3} + b} a^{2} + \frac{\sqrt{a x^{3} + b} a b}{x^{3}}\right)}}{3 \, a}"," ",0,"2/3*(sqrt(a*x^3 + b)*a^2 + sqrt(a*x^3 + b)*a*b/x^3)/a","B",0
129,1,27,0,0.445166," ","integrate((x^2+x+1)/(-1+x)^2/(x^4-1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{\frac{4}{x - 1} + \frac{6}{{\left(x - 1\right)}^{2}} + \frac{4}{{\left(x - 1\right)}^{3}} + 1}"," ",0,"-1/2*sqrt(4/(x - 1) + 6/(x - 1)^2 + 4/(x - 1)^3 + 1)","A",0
130,1,25,0,0.538385," ","integrate((x^4-1)/x^2/(x^3-x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} - x} - \frac{2}{3} \, \sqrt{\frac{1}{x} - \frac{1}{x^{3}}}"," ",0,"2/3*sqrt(x^3 - x) - 2/3*sqrt(1/x - 1/x^3)","A",0
131,1,11,0,0.577006," ","integrate(1/x^2/(x^4-x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{-\frac{1}{x^{3}} + 1}"," ",0,"2/3*sqrt(-1/x^3 + 1)","A",0
132,1,11,0,0.472097," ","integrate(1/x^3/(x^4-x)^(1/4),x, algorithm=""giac"")","-\frac{4}{9} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/9*(-1/x^3 + 1)^(3/4)","A",0
133,1,11,0,0.503670," ","integrate((x^3-1)/x^6/(x^4-x)^(1/4),x, algorithm=""giac"")","-\frac{4}{21} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}}"," ",0,"-4/21*(-1/x^3 + 1)^(7/4)","A",0
134,1,11,0,0.506362," ","integrate((x^4-x)^(1/4)/x^5,x, algorithm=""giac"")","-\frac{4}{15} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{5}{4}}"," ",0,"-4/15*(-1/x^3 + 1)^(5/4)","A",0
135,0,0,0,0.000000," ","integrate((x^3+2)*(x^4-x)^(1/3)/(x^3-1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x\right)}^{\frac{1}{3}} {\left(x^{3} + 2\right)}}{{\left(x^{3} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^4 - x)^(1/3)*(x^3 + 2)/(x^3 - 1)^2, x)","F",0
136,1,11,0,0.380438," ","integrate((x^4-x)^(1/2)/x^6,x, algorithm=""giac"")","\frac{2}{9} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{2}}"," ",0,"2/9*(-1/x^3 + 1)^(3/2)","A",0
137,1,26,0,0.352513," ","integrate(x/(x^4+x)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{3} \, \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/3*log(sqrt(1/x^3 + 1) + 1) - 1/3*log(abs(sqrt(1/x^3 + 1) - 1))","A",0
138,0,0,0,0.000000," ","integrate((x^3-2)/(x^3+1)/(x^4+x)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} - 2}{{\left(x^{4} + x\right)}^{\frac{1}{3}} {\left(x^{3} + 1\right)}}\,{d x}"," ",0,"integrate((x^3 - 2)/((x^4 + x)^(1/3)*(x^3 + 1)), x)","F",0
139,0,0,0,0.000000," ","integrate((x^2-1)/x/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^4 + x^2)^(1/3)*x), x)","F",0
140,1,9,0,0.352748," ","integrate(1/x^2/(x^4+x^2)^(1/4),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}"," ",0,"-2/3*(1/x^2 + 1)^(3/4)","A",0
141,1,9,0,0.297883," ","integrate((x^4+x^2)^(1/4)/x^4,x, algorithm=""giac"")","-\frac{2}{5} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}}"," ",0,"-2/5*(1/x^2 + 1)^(5/4)","A",0
142,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+x^2)^(1/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} - 1\right)}}{x^{3}}\,{d x}"," ",0,"integrate((x^4 + x^2)^(1/3)*(x^2 - 1)/x^3, x)","F",0
143,1,9,0,0.577493," ","integrate(1/x/(x^4+x^3)^(1/4),x, algorithm=""giac"")","-\frac{4}{3} \, {\left(\frac{1}{x} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/3*(1/x + 1)^(3/4)","A",0
144,1,9,0,1.000216," ","integrate((1+x)*(x^4+x^3)^(1/4)/x^4,x, algorithm=""giac"")","-\frac{4}{9} \, {\left(\frac{1}{x} + 1\right)}^{\frac{9}{4}}"," ",0,"-4/9*(1/x + 1)^(9/4)","A",0
145,0,0,0,0.000000," ","integrate((2*x^4-x-2)/(x^4+x+1)/(x^4+x^2+x+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - x - 2}{\sqrt{x^{4} + x^{2} + x + 1} {\left(x^{4} + x + 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 - x - 2)/(sqrt(x^4 + x^2 + x + 1)*(x^4 + x + 1)), x)","F",0
146,0,0,0,0.000000," ","integrate((x^4+3)/x^3/(x^5-x)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} + 3}{{\left(x^{5} - x\right)}^{\frac{1}{4}} x^{3}}\,{d x}"," ",0,"integrate((x^4 + 3)/((x^5 - x)^(1/4)*x^3), x)","F",0
147,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+3)/x^6/(x^5-x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}}{{\left(x^{5} - x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 + 3)*(x^4 - 1)/((x^5 - x)^(1/4)*x^6), x)","F",0
148,0,0,0,0.000000," ","integrate((x^4-3)/(x^4+1)/(x^5+x)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 3}{{\left(x^{5} + x\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 3)/((x^5 + x)^(1/4)*(x^4 + 1)), x)","F",0
149,0,0,0,0.000000," ","integrate((2*x^3-1)*(x^5+x^2)^(1/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{2}\right)}^{\frac{1}{3}} {\left(2 \, x^{3} - 1\right)}}{x^{3}}\,{d x}"," ",0,"integrate((x^5 + x^2)^(1/3)*(2*x^3 - 1)/x^3, x)","F",0
150,0,0,0,0.000000," ","integrate((x^2-1)/x/(x^5+x^3)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^5 + x^3)^(1/4)*x), x)","F",0
151,0,0,0,0.000000," ","integrate((x^4-1)*(x^5+x^3)^(1/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{4}}\,{d x}"," ",0,"integrate((x^5 + x^3)^(1/4)*(x^4 - 1)/x^4, x)","F",0
152,1,17,0,0.396405," ","integrate(x^2/(x^6-1)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left({\left| -x^{3} + \sqrt{x^{6} - 1} \right|}\right)"," ",0,"-1/3*log(abs(-x^3 + sqrt(x^6 - 1)))","A",0
153,1,16,0,0.447932," ","integrate(x^2/(x^6+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(-x^{3} + \sqrt{x^{6} + 1}\right)"," ",0,"-1/3*log(-x^3 + sqrt(x^6 + 1))","A",0
154,0,0,0,0.000000," ","integrate((x^5-1)*(2*x^5+3)/x^6/(x^6-x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} + 3\right)} {\left(x^{5} - 1\right)}}{{\left(x^{6} - x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((2*x^5 + 3)*(x^5 - 1)/((x^6 - x)^(1/4)*x^6), x)","F",0
155,1,9,0,0.609602," ","integrate(1/x^3/(x^6+x^2)^(1/3),x, algorithm=""giac"")","-\frac{3}{8} \, {\left(\frac{1}{x^{4}} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/8*(1/x^4 + 1)^(2/3)","A",0
156,0,0,0,0.000000," ","integrate((x^4-1)/x^2/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^6 + x^2)^(1/4)*x^2), x)","F",0
157,0,0,0,0.000000," ","integrate((x^4-1)*(x^6+x^2)^(1/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{4}}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^4 - 1)/x^4, x)","F",0
158,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x^{2} + 1} + 1}}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 1) + 1)/sqrt(x^2 + 1), x)","F",0
159,0,0,0,0.000000," ","integrate((x^2-2*x-2)/(x^2+x+1)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 2 \, x - 2}{\sqrt{x^{3} - 1} {\left(x^{2} + x + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 2*x - 2)/(sqrt(x^3 - 1)*(x^2 + x + 1)), x)","F",0
160,0,0,0,0.000000," ","integrate((a*x^2+b)/x/(a*x^3-b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{\sqrt{a x^{3} - b x} x}\,{d x}"," ",0,"integrate((a*x^2 + b)/(sqrt(a*x^3 - b*x)*x), x)","F",0
161,0,0,0,0.000000," ","integrate((2*x^2-2*x-1)/(2*x^2+1)/(x^4+x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - 2 \, x - 1}{\sqrt{x^{4} + x} {\left(2 \, x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 - 2*x - 1)/(sqrt(x^4 + x)*(2*x^2 + 1)), x)","F",0
162,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(x^4-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{\sqrt{x^{4} - x^{2} - 1} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/(sqrt(x^4 - x^2 - 1)*(x^4 - 1)), x)","F",0
163,0,0,0,0.000000," ","integrate(x/(x^4-4*x^3+6*x^2-4*x+1)^(1/5),x, algorithm=""giac"")","\int \frac{x}{{\left(x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right)}^{\frac{1}{5}}}\,{d x}"," ",0,"integrate(x/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1)^(1/5), x)","F",0
164,0,0,0,0.000000," ","integrate((x^6-2)/x^4/(x^6+x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{6} - 2}{{\left(x^{6} + x^{4} + 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^6 - 2)/((x^6 + x^4 + 1)^(1/4)*x^4), x)","F",0
165,0,0,0,0.000000," ","integrate((x^8+1)/x^4/(x^8+x^4-1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{8} + 1}{{\left(x^{8} + x^{4} - 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^8 + 1)/((x^8 + x^4 - 1)^(1/4)*x^4), x)","F",0
166,0,0,0,0.000000," ","integrate((x^8-1)/x^4/(x^8+x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + x^{4} + 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + x^4 + 1)^(1/4)*x^4), x)","F",0
167,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{3} - x} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(x^3 - x)*(x^2 - 1)), x)","F",0
168,1,9,0,0.302113," ","integrate(1/(x^2+1)/(x^3+x)^(1/3),x, algorithm=""giac"")","\frac{3}{2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}"," ",0,"3/2/(1/x^2 + 1)^(1/3)","A",0
169,1,11,0,0.279927," ","integrate(1/x/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{2} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"3/2*(-1/x + 1)^(2/3)","A",0
170,1,16,0,0.280257," ","integrate(x^2/(a*x^3-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a x^{3} - b}}{3 \, a}"," ",0,"2/3*sqrt(a*x^3 - b)/a","A",0
171,1,16,0,0.192922," ","integrate(x^2*(a*x^3-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(a x^{3} - b\right)}^{\frac{3}{2}}}{9 \, a}"," ",0,"2/9*(a*x^3 - b)^(3/2)/a","A",0
172,1,39,0,0.607952," ","integrate((a*x^3-b)^(1/2)*(a*x^3+2*b)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(\sqrt{a x^{3} - b} a^{2} - \frac{\sqrt{a x^{3} - b} a b}{x^{3}}\right)}}{3 \, a}"," ",0,"2/3*(sqrt(a*x^3 - b)*a^2 - sqrt(a*x^3 - b)*a*b/x^3)/a","B",0
173,1,11,0,0.358971," ","integrate(1/x^2/(x^4-x^2)^(1/4),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}"," ",0,"-2/3*(-1/x^2 + 1)^(3/4)","A",0
174,1,11,0,0.293166," ","integrate((x^4-x^2)^(1/4)/x^4,x, algorithm=""giac"")","-\frac{2}{5} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}}"," ",0,"-2/5*(-1/x^2 + 1)^(5/4)","A",0
175,0,0,0,0.000000," ","integrate((x^2+1)*(x^4-x^2)^(1/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + 1\right)}}{x^{3}}\,{d x}"," ",0,"integrate((x^4 - x^2)^(1/3)*(x^2 + 1)/x^3, x)","F",0
176,1,11,0,0.671387," ","integrate(1/x/(x^4-x^3)^(1/4),x, algorithm=""giac"")","-\frac{4}{3} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/3*(-1/x + 1)^(3/4)","A",0
177,1,18,0,0.228485," ","integrate((-1+x)*(x^4-x^3)^(1/4)/x^4,x, algorithm=""giac"")","-\frac{4}{9} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}"," ",0,"-4/9*(1/x - 1)^2*(-1/x + 1)^(1/4)","A",0
178,1,11,0,0.250119," ","integrate((x^4-x^3)^(1/4)/x^3,x, algorithm=""giac"")","-\frac{4}{5} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}}"," ",0,"-4/5*(-1/x + 1)^(5/4)","A",0
179,1,16,0,0.264273," ","integrate(x*(2*x^2+1)*(2*x^4+2*x^2-1)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(2 \, x^{4} + 2 \, x^{2} - 1\right)}^{\frac{3}{2}}"," ",0,"1/6*(2*x^4 + 2*x^2 - 1)^(3/2)","A",0
180,0,0,0,0.000000," ","integrate((2*x^3+1)*(x^5-x^2)^(1/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{5} - x^{2}\right)}^{\frac{1}{3}} {\left(2 \, x^{3} + 1\right)}}{x^{3}}\,{d x}"," ",0,"integrate((x^5 - x^2)^(1/3)*(2*x^3 + 1)/x^3, x)","F",0
181,0,0,0,0.000000," ","integrate((x^4-1)/x^2/(x^5-x^3)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{5} - x^{3}\right)}^{\frac{1}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^5 - x^3)^(1/4)*x^2), x)","F",0
182,0,0,0,0.000000," ","integrate((x^4-1)*(x^5-x^3)^(1/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(x^{5} - x^{3}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{4}}\,{d x}"," ",0,"integrate((x^5 - x^3)^(1/4)*(x^4 - 1)/x^4, x)","F",0
183,0,0,0,0.000000," ","integrate((2*x^4-2*x^2-1)/x^2/(x^2+1)/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 2 \, x^{2} - 1}{\sqrt{x^{6} + 1} {\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^4 - 2*x^2 - 1)/(sqrt(x^6 + 1)*(x^2 + 1)*x^2), x)","F",0
184,1,11,0,0.426786," ","integrate(1/x^3/(x^6-x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(-\frac{1}{x^{4}} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(-1/x^4 + 1)^(2/3)","A",0
185,0,0,0,0.000000," ","integrate((x^4+1)/x^2/(x^6-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^6 - x^2)^(1/4)*x^2), x)","F",0
186,0,0,0,0.000000," ","integrate((x^4+1)*(x^6-x^2)^(1/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}{x^{4}}\,{d x}"," ",0,"integrate((x^6 - x^2)^(1/4)*(x^4 + 1)/x^4, x)","F",0
187,0,0,0,0.000000," ","integrate((x^8-1)/x^4/(x^6-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^6 - x^2)^(1/4)*x^4), x)","F",0
188,0,0,0,0.000000," ","integrate((x^8+1)/(-x^8+1)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{8} + 1}{{\left(x^{8} - 1\right)} {\left(-x^{8} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 + 1)/((x^8 - 1)*(-x^8 + 1)^(1/4)), x)","F",0
189,-2,0,0,0.000000," ","integrate(1/(x^8-x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -atan(i)/3*sign(x)+1/3*atan(sqrt(x^6-1))/sign(x)","F(-2)",0
190,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x^{2} + 1} + 1}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 1) + 1)/(x^2 + 1), x)","F",0
191,0,0,0,0.000000," ","integrate((-1+x)/(2+x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x^{3} - 1} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate((x - 1)/(sqrt(x^3 - 1)*(x + 2)), x)","F",0
192,0,0,0,0.000000," ","integrate((x^2-2*x-2)/(x^2+2)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 2 \, x - 2}{\sqrt{x^{3} - 1} {\left(x^{2} + 2\right)}}\,{d x}"," ",0,"integrate((x^2 - 2*x - 2)/(sqrt(x^3 - 1)*(x^2 + 2)), x)","F",0
193,0,0,0,0.000000," ","integrate((x^2-2*x-2)/(x^2+2*x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 2 \, x - 2}{\sqrt{x^{3} - 1} {\left(x^{2} + 2 \, x\right)}}\,{d x}"," ",0,"integrate((x^2 - 2*x - 2)/(sqrt(x^3 - 1)*(x^2 + 2*x)), x)","F",0
194,0,0,0,0.000000," ","integrate((2*x^2+2*x-1)/(-1+x)/x/(x^4-x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} + 2 \, x - 1}{\sqrt{x^{4} - x} {\left(x - 1\right)} x}\,{d x}"," ",0,"integrate((2*x^2 + 2*x - 1)/(sqrt(x^4 - x)*(x - 1)*x), x)","F",0
195,0,0,0,0.000000," ","integrate((2*x^2+2*x-1)/(2*x^2+1)/(x^4-x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} + 2 \, x - 1}{\sqrt{x^{4} - x} {\left(2 \, x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 + 2*x - 1)/(sqrt(x^4 - x)*(2*x^2 + 1)), x)","F",0
196,0,0,0,0.000000," ","integrate((2*x^2-2*x-1)/(-1+2*x)/(x^4+x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - 2 \, x - 1}{\sqrt{x^{4} + x} {\left(2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 - 2*x - 1)/(sqrt(x^4 + x)*(2*x - 1)), x)","F",0
197,0,0,0,0.000000," ","integrate((2*x^2-2*x-1)/(x^2-x+1)/(x^4+x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - 2 \, x - 1}{\sqrt{x^{4} + x} {\left(x^{2} - x + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 - 2*x - 1)/(sqrt(x^4 + x)*(x^2 - x + 1)), x)","F",0
198,1,9,0,0.622070," ","integrate(1/(1+x)/(x^4+x^3)^(1/4),x, algorithm=""giac"")","\frac{4}{{\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}"," ",0,"4/(1/x + 1)^(1/4)","A",0
199,0,0,0,0.000000," ","integrate((2*x^4+1)/(2*x^4-1)/(2*x^4-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} + 1}{\sqrt{2 \, x^{4} - x^{2} - 1} {\left(2 \, x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 + 1)/(sqrt(2*x^4 - x^2 - 1)*(2*x^4 - 1)), x)","F",0
200,0,0,0,0.000000," ","integrate((2*x^4-1)/(2*x^4+2*x^2+1)/(2*x^4+3*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 1}{\sqrt{2 \, x^{4} + 3 \, x^{2} + 1} {\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 - 1)/(sqrt(2*x^4 + 3*x^2 + 1)*(2*x^4 + 2*x^2 + 1)), x)","F",0
201,0,0,0,0.000000," ","integrate((-x^5+x^4-1)^(1/4)*(x^5-4)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{5} - 4\right)} {\left(-x^{5} + x^{4} - 1\right)}^{\frac{1}{4}}}{x^{6}}\,{d x}"," ",0,"integrate((x^5 - 4)*(-x^5 + x^4 - 1)^(1/4)/x^6, x)","F",0
202,0,0,0,0.000000," ","integrate((x^8+1)*(x^8-2*x^4-1)^(1/2)/x^7,x, algorithm=""giac"")","\int \frac{\sqrt{x^{8} - 2 \, x^{4} - 1} {\left(x^{8} + 1\right)}}{x^{7}}\,{d x}"," ",0,"integrate(sqrt(x^8 - 2*x^4 - 1)*(x^8 + 1)/x^7, x)","F",0
203,1,67,0,0.318993," ","integrate(x^2*(x^3-2)*(x^3+1)^(1/2)/(4*x^9+13*x^6+12*x^3+4),x, algorithm=""giac"")","-\frac{1}{3} \, \arctan\left(2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(\sqrt{14} \left(\frac{1}{4}\right)^{\frac{1}{4}} + 4 \, \sqrt{x^{3} + 1}\right)}\right) - \frac{1}{3} \, \arctan\left(-2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(\sqrt{14} \left(\frac{1}{4}\right)^{\frac{1}{4}} - 4 \, \sqrt{x^{3} + 1}\right)}\right) + \frac{1}{3} \, \arctan\left(\sqrt{x^{3} + 1}\right)"," ",0,"-1/3*arctan(2*sqrt(2)*(1/4)^(3/4)*(sqrt(14)*(1/4)^(1/4) + 4*sqrt(x^3 + 1))) - 1/3*arctan(-2*sqrt(2)*(1/4)^(3/4)*(sqrt(14)*(1/4)^(1/4) - 4*sqrt(x^3 + 1))) + 1/3*arctan(sqrt(x^3 + 1))","B",0
204,1,11,0,0.643411," ","integrate(1/(x^2-1)/(x^3-x)^(1/3),x, algorithm=""giac"")","-\frac{3}{2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}"," ",0,"-3/2/(-1/x^2 + 1)^(1/3)","A",0
205,1,11,0,0.389007," ","integrate(1/(x^3-1)/(x^4-x)^(1/4),x, algorithm=""giac"")","\frac{4}{3 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}}"," ",0,"4/3/(-1/x^3 + 1)^(1/4)","A",0
206,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{\sqrt{a x^{2} + b^{2}}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/sqrt(a*x^2 + b^2), x)","F",0
207,1,33,0,0.367266," ","integrate(1/x/(x^2+1)^(1/4),x, algorithm=""giac"")","\arctan\left({\left(x^{2} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"arctan((x^2 + 1)^(1/4)) - 1/2*log((x^2 + 1)^(1/4) + 1) + 1/2*log((x^2 + 1)^(1/4) - 1)","A",0
208,0,0,0,0.000000," ","integrate((-5+2*x)/(x^2-4*x+4)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, x - 5}{{\left(x^{2} - 4 \, x + 4\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x - 5)/(x^2 - 4*x + 4)^(1/4), x)","F",0
209,1,19,0,0.616813," ","integrate(x^5*(x^3+1)^(1/3),x, algorithm=""giac"")","\frac{1}{7} \, {\left(x^{3} + 1\right)}^{\frac{7}{3}} - \frac{1}{4} \, {\left(x^{3} + 1\right)}^{\frac{4}{3}}"," ",0,"1/7*(x^3 + 1)^(7/3) - 1/4*(x^3 + 1)^(4/3)","A",0
210,1,26,0,0.295914," ","integrate((3*x^2+1)*(x^3-x)^(1/3)/x^2,x, algorithm=""giac"")","\frac{3}{2} \, x^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - \frac{3}{2} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}"," ",0,"3/2*x^2*(-1/x^2 + 1)^(1/3) - 3/2*(-1/x^2 + 1)^(1/3)","A",0
211,1,11,0,0.274692," ","integrate(1/(-1+x)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\frac{3}{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}"," ",0,"-3/(-1/x + 1)^(1/3)","A",0
212,1,19,0,0.491936," ","integrate(1/x^2/(x^3+x^2)^(1/3),x, algorithm=""giac"")","-\frac{3}{5} \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{3}} + \frac{3}{2} \, {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/5*(1/x + 1)^(5/3) + 3/2*(1/x + 1)^(2/3)","A",0
213,1,13,0,0.311156," ","integrate((2*x^2+3)*(2*x^3+x)^(1/2)/(2*x^2+1)^2,x, algorithm=""giac"")","\frac{2}{\sqrt{\frac{2}{x} + \frac{1}{x^{3}}}}"," ",0,"2/sqrt(2/x + 1/x^3)","A",0
214,0,0,0,0.000000," ","integrate(1/x^6/(x^4-1)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} - 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate(1/((x^4 - 1)^(3/4)*x^6), x)","F",0
215,0,0,0,0.000000," ","integrate(1/x^4/(x^4+1)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{5}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(5/4)*x^4), x)","F",0
216,0,0,0,0.000000," ","integrate(1/x^6/(x^4+1)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(3/4)*x^6), x)","F",0
217,0,0,0,0.000000," ","integrate((x^4-1)/x^6/(x^4+1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{4} + 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^4 + 1)^(3/4)*x^6), x)","F",0
218,0,0,0,0.000000," ","integrate((x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} + 1}{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 1)/(sqrt(x^4 + 1)*(x^2 - 1)), x)","F",0
219,0,0,0,0.000000," ","integrate((2*x^2+2*x-1)/(1+2*x)/(x^4-x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} + 2 \, x - 1}{\sqrt{x^{4} - x} {\left(2 \, x + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 + 2*x - 1)/(sqrt(x^4 - x)*(2*x + 1)), x)","F",0
220,1,19,0,0.585818," ","integrate(1/x^5/(x^4+x)^(1/2),x, algorithm=""giac"")","-\frac{2}{9} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{\frac{1}{x^{3}} + 1}"," ",0,"-2/9*(1/x^3 + 1)^(3/2) + 2/3*sqrt(1/x^3 + 1)","A",0
221,1,19,0,0.418024," ","integrate((x^3-1)/x^6/(x^4+x)^(1/4),x, algorithm=""giac"")","\frac{4}{21} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} - \frac{8}{9} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}}"," ",0,"4/21*(1/x^3 + 1)^(7/4) - 8/9*(1/x^3 + 1)^(3/4)","A",0
222,1,19,0,0.415833," ","integrate((2*x^3+1)/x^6/(x^4+x)^(1/4),x, algorithm=""giac"")","-\frac{4}{21} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} - \frac{4}{9} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/21*(1/x^3 + 1)^(7/4) - 4/9*(1/x^3 + 1)^(3/4)","A",0
223,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^4 + x^2)^(1/3)*(x^2 + 1)), x)","F",0
224,1,9,0,0.228804," ","integrate(1/(x^2+1)/(x^4+x^2)^(1/4),x, algorithm=""giac"")","\frac{2}{{\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"2/(1/x^2 + 1)^(1/4)","A",0
225,1,11,0,0.323773," ","integrate(1/(-1+x)/(x^4-x^3)^(1/4),x, algorithm=""giac"")","\frac{4}{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}"," ",0,"4/(-1/x + 1)^(1/4)","A",0
226,1,19,0,0.367585," ","integrate(1/x/(x^4+x^3)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(\frac{1}{x} + 1\right)}^{\frac{3}{2}} + 2 \, \sqrt{\frac{1}{x} + 1}"," ",0,"-2/3*(1/x + 1)^(3/2) + 2*sqrt(1/x + 1)","A",0
227,1,19,0,0.322876," ","integrate(1/x^2/(x^4+x^3)^(1/4),x, algorithm=""giac"")","-\frac{4}{7} \, {\left(\frac{1}{x} + 1\right)}^{\frac{7}{4}} + \frac{4}{3} \, {\left(\frac{1}{x} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/7*(1/x + 1)^(7/4) + 4/3*(1/x + 1)^(3/4)","A",0
228,1,23,0,0.396449," ","integrate((1+2*x)/(x^4+2*x^3+x^2+3)^(1/2),x, algorithm=""giac"")","-\log\left(-x^{2} - x + \sqrt{{\left(x^{2} + x\right)}^{2} + 3}\right)"," ",0,"-log(-x^2 - x + sqrt((x^2 + x)^2 + 3))","A",0
229,0,0,0,0.000000," ","integrate((2*x^4-1)/x^8/(x^4-1)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 1}{{\left(x^{4} - 1\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate((2*x^4 - 1)/((x^4 - 1)^(1/4)*x^8), x)","F",0
230,0,0,0,0.000000," ","integrate((2*x^4+1)/x^4/(x^4+1)^(5/4),x, algorithm=""giac"")","\int \frac{2 \, x^{4} + 1}{{\left(x^{4} + 1\right)}^{\frac{5}{4}} x^{4}}\,{d x}"," ",0,"integrate((2*x^4 + 1)/((x^4 + 1)^(5/4)*x^4), x)","F",0
231,1,19,0,0.272065," ","integrate((4*x^3+1)*(2*x^4+2*x+1)/(x^4+x)^(1/2),x, algorithm=""giac"")","\frac{4}{3} \, {\left(x^{4} + x\right)}^{\frac{3}{2}} + 2 \, \sqrt{x^{4} + x}"," ",0,"4/3*(x^4 + x)^(3/2) + 2*sqrt(x^4 + x)","A",0
232,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^5+x^3)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^5 + x^3)^(1/4)*(x^2 + 1)), x)","F",0
233,-2,0,0,0.000000," ","integrate(1/x^10/(x^6-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
234,-2,0,0,0.000000," ","integrate((x^6+1)/x^10/(x^6-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
235,0,0,0,0.000000," ","integrate((3*x^4-1)/(x^4+1)/(x^6+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x^{4} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((3*x^4 - 1)/((x^6 + x^2)^(1/3)*(x^4 + 1)), x)","F",0
236,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^6 + x^2)^(1/4)*(x^4 + 1)), x)","F",0
237,0,0,0,0.000000," ","integrate(x^2*(2*x^2+3)*(2*x^6+x^2+1)/(x^2+1)^2/(x^6+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{2} + 1\right)} {\left(2 \, x^{2} + 3\right)} x^{2}}{\sqrt{x^{6} + x^{2} + 1} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((2*x^6 + x^2 + 1)*(2*x^2 + 3)*x^2/(sqrt(x^6 + x^2 + 1)*(x^2 + 1)^2), x)","F",0
238,1,34,0,0.338432," ","integrate(1/(x^3+x^2-5*x+3)^(1/2),x, algorithm=""giac"")","-\frac{\log\left(\sqrt{x + 3} + 2\right)}{2 \, \mathrm{sgn}\left(x - 1\right)} + \frac{\log\left({\left| \sqrt{x + 3} - 2 \right|}\right)}{2 \, \mathrm{sgn}\left(x - 1\right)}"," ",0,"-1/2*log(sqrt(x + 3) + 2)/sgn(x - 1) + 1/2*log(abs(sqrt(x + 3) - 2))/sgn(x - 1)","A",0
239,0,0,0,0.000000," ","integrate((-1+x)/(1+x)/(x^3+x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x^{3} + x^{2} + x} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x - 1)/(sqrt(x^3 + x^2 + x)*(x + 1)), x)","F",0
240,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^3+x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{3} + x^{2} + x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^3 + x^2 + x)*(x^2 + 1)), x)","F",0
241,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{4} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^4 + 1)*(x^2 + 1)), x)","F",0
242,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(x^4 + 1)*(x^2 - 1)), x)","F",0
243,0,0,0,0.000000," ","integrate((-3*x^5+2)/(x^5+1)^(1/2)/(x^5-a*x^2+1),x, algorithm=""giac"")","\int -\frac{3 \, x^{5} - 2}{{\left(x^{5} - a x^{2} + 1\right)} \sqrt{x^{5} + 1}}\,{d x}"," ",0,"integrate(-(3*x^5 - 2)/((x^5 - a*x^2 + 1)*sqrt(x^5 + 1)), x)","F",0
244,0,0,0,0.000000," ","integrate((3*x^5+2)/(x^5-1)^(1/2)/(x^5-a*x^2-1),x, algorithm=""giac"")","\int \frac{3 \, x^{5} + 2}{{\left(x^{5} - a x^{2} - 1\right)} \sqrt{x^{5} - 1}}\,{d x}"," ",0,"integrate((3*x^5 + 2)/((x^5 - a*x^2 - 1)*sqrt(x^5 - 1)), x)","F",0
245,0,0,0,0.000000," ","integrate((3*x^5+2)/(x^5-1)^(1/2)/(a*x^5-x^2-a),x, algorithm=""giac"")","\int \frac{3 \, x^{5} + 2}{{\left(a x^{5} - x^{2} - a\right)} \sqrt{x^{5} - 1}}\,{d x}"," ",0,"integrate((3*x^5 + 2)/((a*x^5 - x^2 - a)*sqrt(x^5 - 1)), x)","F",0
246,0,0,0,0.000000," ","integrate((3*x^5-2)/(x^5+1)^(1/2)/(a*x^5-x^2+a),x, algorithm=""giac"")","\int \frac{3 \, x^{5} - 2}{{\left(a x^{5} - x^{2} + a\right)} \sqrt{x^{5} + 1}}\,{d x}"," ",0,"integrate((3*x^5 - 2)/((a*x^5 - x^2 + a)*sqrt(x^5 + 1)), x)","F",0
247,0,0,0,0.000000," ","integrate((2*x^4-2*x^2-1)/(x^4-x^2+1)/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 2 \, x^{2} - 1}{\sqrt{x^{6} + 1} {\left(x^{4} - x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 - 2*x^2 - 1)/(sqrt(x^6 + 1)*(x^4 - x^2 + 1)), x)","F",0
248,0,0,0,0.000000," ","integrate((4*x^5-1)/(x^5-a*x+1)/(x^6+x)^(1/2),x, algorithm=""giac"")","\int \frac{4 \, x^{5} - 1}{\sqrt{x^{6} + x} {\left(x^{5} - a x + 1\right)}}\,{d x}"," ",0,"integrate((4*x^5 - 1)/(sqrt(x^6 + x)*(x^5 - a*x + 1)), x)","F",0
249,0,0,0,0.000000," ","integrate((4*x^5-1)/(a*x^5+a-x)/(x^6+x)^(1/2),x, algorithm=""giac"")","\int \frac{4 \, x^{5} - 1}{{\left(a x^{5} + a - x\right)} \sqrt{x^{6} + x}}\,{d x}"," ",0,"integrate((4*x^5 - 1)/((a*x^5 + a - x)*sqrt(x^6 + x)), x)","F",0
250,1,19,0,0.293967," ","integrate(x^3*(x^2-1)^(2/3),x, algorithm=""giac"")","\frac{3}{16} \, {\left(x^{2} - 1\right)}^{\frac{8}{3}} + \frac{3}{10} \, {\left(x^{2} - 1\right)}^{\frac{5}{3}}"," ",0,"3/16*(x^2 - 1)^(8/3) + 3/10*(x^2 - 1)^(5/3)","A",0
251,1,19,0,0.525331," ","integrate(x^3*(x^2-1)^(3/4),x, algorithm=""giac"")","\frac{2}{11} \, {\left(x^{2} - 1\right)}^{\frac{11}{4}} + \frac{2}{7} \, {\left(x^{2} - 1\right)}^{\frac{7}{4}}"," ",0,"2/11*(x^2 - 1)^(11/4) + 2/7*(x^2 - 1)^(7/4)","A",0
252,1,35,0,0.444643," ","integrate(1/x/(x^2+1)^(3/4),x, algorithm=""giac"")","-\arctan\left({\left(x^{2} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"-arctan((x^2 + 1)^(1/4)) - 1/2*log((x^2 + 1)^(1/4) + 1) + 1/2*log((x^2 + 1)^(1/4) - 1)","A",0
253,1,19,0,0.434588," ","integrate(x^3*(x^2+1)^(3/4),x, algorithm=""giac"")","\frac{2}{11} \, {\left(x^{2} + 1\right)}^{\frac{11}{4}} - \frac{2}{7} \, {\left(x^{2} + 1\right)}^{\frac{7}{4}}"," ",0,"2/11*(x^2 + 1)^(11/4) - 2/7*(x^2 + 1)^(7/4)","A",0
254,1,19,0,0.276467," ","integrate(x^5*(x^3-1)^(1/3),x, algorithm=""giac"")","\frac{1}{7} \, {\left(x^{3} - 1\right)}^{\frac{7}{3}} + \frac{1}{4} \, {\left(x^{3} - 1\right)}^{\frac{4}{3}}"," ",0,"1/7*(x^3 - 1)^(7/3) + 1/4*(x^3 - 1)^(4/3)","A",0
255,1,19,0,0.612703," ","integrate(x^5*(x^3-1)^(3/4),x, algorithm=""giac"")","\frac{4}{33} \, {\left(x^{3} - 1\right)}^{\frac{11}{4}} + \frac{4}{21} \, {\left(x^{3} - 1\right)}^{\frac{7}{4}}"," ",0,"4/33*(x^3 - 1)^(11/4) + 4/21*(x^3 - 1)^(7/4)","A",0
256,1,28,0,0.520981," ","integrate(x^8/(x^3+1)^(1/4),x, algorithm=""giac"")","\frac{4}{33} \, {\left(x^{3} + 1\right)}^{\frac{11}{4}} - \frac{8}{21} \, {\left(x^{3} + 1\right)}^{\frac{7}{4}} + \frac{4}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{4}}"," ",0,"4/33*(x^3 + 1)^(11/4) - 8/21*(x^3 + 1)^(7/4) + 4/9*(x^3 + 1)^(3/4)","A",0
257,1,19,0,0.406381," ","integrate(x^5*(x^3+1)^(2/3),x, algorithm=""giac"")","\frac{1}{8} \, {\left(x^{3} + 1\right)}^{\frac{8}{3}} - \frac{1}{5} \, {\left(x^{3} + 1\right)}^{\frac{5}{3}}"," ",0,"1/8*(x^3 + 1)^(8/3) - 1/5*(x^3 + 1)^(5/3)","A",0
258,1,23,0,0.467732," ","integrate(1/x^2/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\frac{3}{5} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{3}} + \frac{3}{2} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/5*(-1/x + 1)^(5/3) + 3/2*(-1/x + 1)^(2/3)","A",0
259,1,19,0,0.454372," ","integrate(x^7*(x^4+1)^(2/3),x, algorithm=""giac"")","\frac{3}{32} \, {\left(x^{4} + 1\right)}^{\frac{8}{3}} - \frac{3}{20} \, {\left(x^{4} + 1\right)}^{\frac{5}{3}}"," ",0,"3/32*(x^4 + 1)^(8/3) - 3/20*(x^4 + 1)^(5/3)","A",0
260,1,23,0,0.396225," ","integrate(1/x^5/(x^4-x)^(1/2),x, algorithm=""giac"")","-\frac{2}{9} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{-\frac{1}{x^{3}} + 1}"," ",0,"-2/9*(-1/x^3 + 1)^(3/2) + 2/3*sqrt(-1/x^3 + 1)","A",0
261,1,23,0,0.550151," ","integrate((x^3+1)/x^6/(x^4-x)^(1/4),x, algorithm=""giac"")","\frac{4}{21} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} - \frac{8}{9} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}}"," ",0,"4/21*(-1/x^3 + 1)^(7/4) - 8/9*(-1/x^3 + 1)^(3/4)","A",0
262,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^4-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{4} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^4 - x^2)^(1/3)*(x^2 - 1)), x)","F",0
263,1,11,0,0.330617," ","integrate(1/(x^2-1)/(x^4-x^2)^(1/4),x, algorithm=""giac"")","\frac{2}{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"2/(-1/x^2 + 1)^(1/4)","A",0
264,1,19,0,0.302367," ","integrate(1/x^4/(x^4+x^2)^(1/4),x, algorithm=""giac"")","-\frac{2}{7} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{7}{4}} + \frac{2}{3} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}"," ",0,"-2/7*(1/x^2 + 1)^(7/4) + 2/3*(1/x^2 + 1)^(3/4)","A",0
265,1,24,0,0.406937," ","integrate((-1+2*x)/(x^4-2*x^3+x^2-3)^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x^{2} + x + \sqrt{{\left(x^{2} - x\right)}^{2} - 3} \right|}\right)"," ",0,"-log(abs(-x^2 + x + sqrt((x^2 - x)^2 - 3)))","A",0
266,1,23,0,0.681617," ","integrate((-1+2*x)/(x^4-2*x^3+x^2+4)^(1/2),x, algorithm=""giac"")","-\log\left(-x^{2} + x + \sqrt{{\left(x^{2} - x\right)}^{2} + 4}\right)"," ",0,"-log(-x^2 + x + sqrt((x^2 - x)^2 + 4))","A",0
267,1,23,0,0.296144," ","integrate((-1+2*x)/(x^4-2*x^3+x^2+13)^(1/2),x, algorithm=""giac"")","-\log\left(-x^{2} + x + \sqrt{{\left(x^{2} - x\right)}^{2} + 13}\right)"," ",0,"-log(-x^2 + x + sqrt((x^2 - x)^2 + 13))","A",0
268,1,23,0,0.371232," ","integrate(1/x^2/(x^4-x^3)^(1/4),x, algorithm=""giac"")","\frac{4}{7} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{7}{4}} - \frac{4}{3} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{4}}"," ",0,"4/7*(-1/x + 1)^(7/4) - 4/3*(-1/x + 1)^(3/4)","A",0
269,0,0,0,0.000000," ","integrate((x^4-1)/x^8/(2*x^4-1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate((x^4 - 1)/((2*x^4 - 1)^(1/4)*x^8), x)","F",0
270,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^5-x^3)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{5} - x^{3}\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^5 - x^3)^(1/4)*(x^2 - 1)), x)","F",0
271,0,0,0,0.000000," ","integrate((3*x^4+1)/(x^4-1)/(x^6-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x^{4} + 1}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((3*x^4 + 1)/((x^6 - x^2)^(1/3)*(x^4 - 1)), x)","F",0
272,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(x^6-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^6 - x^2)^(1/4)*(x^4 - 1)), x)","F",0
273,1,19,0,0.493250," ","integrate(1/x^7/(x^6+x^2)^(1/3),x, algorithm=""giac"")","-\frac{3}{20} \, {\left(\frac{1}{x^{4}} + 1\right)}^{\frac{5}{3}} + \frac{3}{8} \, {\left(\frac{1}{x^{4}} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/20*(1/x^4 + 1)^(5/3) + 3/8*(1/x^4 + 1)^(2/3)","A",0
274,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{8}}\,{d x}"," ",0,"integrate((x^3 - 1)^(1/3)/x^8, x)","F",0
275,0,0,0,0.000000," ","integrate((a*x^2+b)/(a*x^2-b)/(a*x^3-b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{\sqrt{a x^{3} - b x} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/(sqrt(a*x^3 - b*x)*(a*x^2 - b)), x)","F",0
276,0,0,0,0.000000," ","integrate((a*x^3-2*b)/(a*x^3+b)^(1/2)/(a*x^3-c*x^2+b),x, algorithm=""giac"")","\int \frac{a x^{3} - 2 \, b}{{\left(a x^{3} - c x^{2} + b\right)} \sqrt{a x^{3} + b}}\,{d x}"," ",0,"integrate((a*x^3 - 2*b)/((a*x^3 - c*x^2 + b)*sqrt(a*x^3 + b)), x)","F",0
277,0,0,0,0.000000," ","integrate((a*x^3-2*b)/(a*x^3+b)^(1/2)/(a*x^3+c*x^2+b),x, algorithm=""giac"")","\int \frac{a x^{3} - 2 \, b}{{\left(a x^{3} + c x^{2} + b\right)} \sqrt{a x^{3} + b}}\,{d x}"," ",0,"integrate((a*x^3 - 2*b)/((a*x^3 + c*x^2 + b)*sqrt(a*x^3 + b)), x)","F",0
278,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^2+2)/(x^4-3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{4} - 3} {\left(x^{2} + 2\right)} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(x^4 - 3)*(x^2 + 2)*(x^2 - 1)), x)","F",0
279,0,0,0,0.000000," ","integrate((x^4-4)*(x^4+1)^(3/4)/x^12,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{3}{4}} {\left(x^{4} - 4\right)}}{x^{12}}\,{d x}"," ",0,"integrate((x^4 + 1)^(3/4)*(x^4 - 4)/x^12, x)","F",0
280,0,0,0,0.000000," ","integrate((x^4-1)^(1/2)*(x^4+1)/x^2/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)} \sqrt{x^{4} - 1}}{{\left(x^{4} + x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^4 + 1)*sqrt(x^4 - 1)/((x^4 + x^2 - 1)*x^2), x)","F",0
281,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+x^2+1)/x^4/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} + 1\right)} {\left(x^{4} - 1\right)}}{\sqrt{x^{4} + 1} x^{4}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)*(x^4 - 1)/(sqrt(x^4 + 1)*x^4), x)","F",0
282,0,0,0,0.000000," ","integrate((x^3-4)*(x^4+x^3-1)/x^6/(x^3-1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} - 1\right)} {\left(x^{3} - 4\right)}}{{\left(x^{3} - 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^3 - 1)*(x^3 - 4)/((x^3 - 1)^(3/4)*x^6), x)","F",0
283,0,0,0,0.000000," ","integrate((3*x^4+1)/(x^4-a*x-1)/(x^5-x)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{4} + 1}{\sqrt{x^{5} - x} {\left(x^{4} - a x - 1\right)}}\,{d x}"," ",0,"integrate((3*x^4 + 1)/(sqrt(x^5 - x)*(x^4 - a*x - 1)), x)","F",0
284,0,0,0,0.000000," ","integrate((3*x^4+1)/(a*x^4-a-x)/(x^5-x)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{4} + 1}{{\left(a x^{4} - a - x\right)} \sqrt{x^{5} - x}}\,{d x}"," ",0,"integrate((3*x^4 + 1)/((a*x^4 - a - x)*sqrt(x^5 - x)), x)","F",0
285,0,0,0,0.000000," ","integrate((x^5+4)*(x^5+x^4-1)/x^6/(x^5-1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{4} - 1\right)} {\left(x^{5} + 4\right)}}{{\left(x^{5} - 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^5 + x^4 - 1)*(x^5 + 4)/((x^5 - 1)^(3/4)*x^6), x)","F",0
286,0,0,0,0.000000," ","integrate((x^5-4)*(x^5+x^4+1)/x^6/(x^5+1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{4} + 1\right)} {\left(x^{5} - 4\right)}}{{\left(x^{5} + 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^5 + x^4 + 1)*(x^5 - 4)/((x^5 + 1)^(3/4)*x^6), x)","F",0
287,1,41,0,0.420364," ","integrate((x^6-1)^(1/2)/x^16,x, algorithm=""giac"")","-\frac{3 \, {\left(\frac{1}{x^{6}} - 1\right)}^{2} \sqrt{-\frac{1}{x^{6}} + 1} - 5 \, {\left(-\frac{1}{x^{6}} + 1\right)}^{\frac{3}{2}}}{45 \, \mathrm{sgn}\left(x\right)} - \frac{2}{45} \, \mathrm{sgn}\left(x\right)"," ",0,"-1/45*(3*(1/x^6 - 1)^2*sqrt(-1/x^6 + 1) - 5*(-1/x^6 + 1)^(3/2))/sgn(x) - 2/45*sgn(x)","A",0
288,0,0,0,0.000000," ","integrate((2*x^4-2*x^2-1)/(2*x^4+1)/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 2 \, x^{2} - 1}{\sqrt{x^{6} + 1} {\left(2 \, x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 - 2*x^2 - 1)/(sqrt(x^6 + 1)*(2*x^4 + 1)), x)","F",0
289,0,0,0,0.000000," ","integrate((4*x^5+1)/(x^5-a*x-1)/(x^6-x)^(1/2),x, algorithm=""giac"")","\int \frac{4 \, x^{5} + 1}{\sqrt{x^{6} - x} {\left(x^{5} - a x - 1\right)}}\,{d x}"," ",0,"integrate((4*x^5 + 1)/(sqrt(x^6 - x)*(x^5 - a*x - 1)), x)","F",0
290,0,0,0,0.000000," ","integrate((4*x^5+1)/(a*x^5-a-x)/(x^6-x)^(1/2),x, algorithm=""giac"")","\int \frac{4 \, x^{5} + 1}{{\left(a x^{5} - a - x\right)} \sqrt{x^{6} - x}}\,{d x}"," ",0,"integrate((4*x^5 + 1)/((a*x^5 - a - x)*sqrt(x^6 - x)), x)","F",0
291,0,0,0,0.000000," ","integrate((x^6+2)*(x^6-x^4-1)/x^6/(x^6-1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} - 1\right)} {\left(x^{6} + 2\right)}}{{\left(x^{6} - 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^4 - 1)*(x^6 + 2)/((x^6 - 1)^(3/4)*x^6), x)","F",0
292,0,0,0,0.000000," ","integrate((x^6-2)*(x^6-x^4+1)/x^6/(x^6+1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} + 1\right)} {\left(x^{6} - 2\right)}}{{\left(x^{6} + 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^4 + 1)*(x^6 - 2)/((x^6 + 1)^(3/4)*x^6), x)","F",0
293,0,0,0,0.000000," ","integrate((x^6-1)^(1/2)*(2*x^6+1)/x^2/(x^6+x^2-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + 1\right)} \sqrt{x^{6} - 1}}{{\left(x^{6} + x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^6 + 1)*sqrt(x^6 - 1)/((x^6 + x^2 - 1)*x^2), x)","F",0
294,0,0,0,0.000000," ","integrate((-2*x^7-x^5+x^3-1)^(2/3)*(2*x^7+x^5-x^3+1)*(8*x^7+2*x^5-3)/x^9,x, algorithm=""giac"")","\int \frac{{\left(8 \, x^{7} + 2 \, x^{5} - 3\right)} {\left(2 \, x^{7} + x^{5} - x^{3} + 1\right)} {\left(-2 \, x^{7} - x^{5} + x^{3} - 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((8*x^7 + 2*x^5 - 3)*(2*x^7 + x^5 - x^3 + 1)*(-2*x^7 - x^5 + x^3 - 1)^(2/3)/x^9, x)","F",0
295,0,0,0,0.000000," ","integrate(x^4*(4*x^5+9)/(x^6+x)^(1/2)/(x^9-a*x^5-a),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{5} + 9\right)} x^{4}}{{\left(x^{9} - a x^{5} - a\right)} \sqrt{x^{6} + x}}\,{d x}"," ",0,"integrate((4*x^5 + 9)*x^4/((x^9 - a*x^5 - a)*sqrt(x^6 + x)), x)","F",0
296,0,0,0,0.000000," ","integrate(x^4*(5*x^4+9)/(x^5+x)^(1/2)/(a*x^9-x^4-1),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{4} + 9\right)} x^{4}}{{\left(a x^{9} - x^{4} - 1\right)} \sqrt{x^{5} + x}}\,{d x}"," ",0,"integrate((5*x^4 + 9)*x^4/((a*x^9 - x^4 - 1)*sqrt(x^5 + x)), x)","F",0
297,0,0,0,0.000000," ","integrate(x^4*(4*x^5+9)/(x^6+x)^(1/2)/(a*x^9-x^5-1),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{5} + 9\right)} x^{4}}{{\left(a x^{9} - x^{5} - 1\right)} \sqrt{x^{6} + x}}\,{d x}"," ",0,"integrate((4*x^5 + 9)*x^4/((a*x^9 - x^5 - 1)*sqrt(x^6 + x)), x)","F",0
298,1,32,0,0.306475," ","integrate(x^5*(-2*x^3+1)^(1/2),x, algorithm=""giac"")","\frac{1}{30} \, {\left(2 \, x^{3} - 1\right)}^{2} \sqrt{-2 \, x^{3} + 1} - \frac{1}{18} \, {\left(-2 \, x^{3} + 1\right)}^{\frac{3}{2}}"," ",0,"1/30*(2*x^3 - 1)^2*sqrt(-2*x^3 + 1) - 1/18*(-2*x^3 + 1)^(3/2)","A",0
299,0,0,0,0.000000," ","integrate((2+x)/(-1+x)/(x^3+3*x-1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 2}{\sqrt{x^{3} + 3 \, x - 1} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 2)/(sqrt(x^3 + 3*x - 1)*(x - 1)), x)","F",0
300,0,0,0,0.000000," ","integrate((-1+2*x)/(1+x)/(x^3-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x - 1}{\sqrt{x^{3} - x^{2} - x} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((2*x - 1)/(sqrt(x^3 - x^2 - x)*(x + 1)), x)","F",0
301,1,30,0,0.588213," ","integrate(x^5/(a*x^3+b)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(a x^{3} + b\right)}^{\frac{3}{2}}}{9 \, a^{2}} - \frac{2 \, \sqrt{a x^{3} + b} b}{3 \, a^{2}}"," ",0,"2/9*(a*x^3 + b)^(3/2)/a^2 - 2/3*sqrt(a*x^3 + b)*b/a^2","A",0
302,1,23,0,0.420523," ","integrate(1/x^4/(x^4-x^2)^(1/4),x, algorithm=""giac"")","\frac{2}{7} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{7}{4}} - \frac{2}{3} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}"," ",0,"2/7*(-1/x^2 + 1)^(7/4) - 2/3*(-1/x^2 + 1)^(3/4)","A",0
303,1,23,0,0.359380," ","integrate(1/x/(a*x^4+b)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{2 \, \sqrt{-b}}"," ",0,"1/2*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b)","A",0
304,1,23,0,0.325080," ","integrate(1/x^7/(x^6-x^2)^(1/3),x, algorithm=""giac"")","-\frac{3}{20} \, {\left(-\frac{1}{x^{4}} + 1\right)}^{\frac{5}{3}} + \frac{3}{8} \, {\left(-\frac{1}{x^{4}} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/20*(-1/x^4 + 1)^(5/3) + 3/8*(-1/x^4 + 1)^(2/3)","A",0
305,1,20,0,0.645263," ","integrate((x^3-1)^(1/2)/x,x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} - 1} - \frac{2}{3} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"2/3*sqrt(x^3 - 1) - 2/3*arctan(sqrt(x^3 - 1))","A",0
306,0,0,0,0.000000," ","integrate((x^3-1)*(x^3+1)^(1/3)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}{x^{8}}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)*(x^3 - 1)/x^8, x)","F",0
307,1,35,0,0.226036," ","integrate((x^3+1)^(1/2)/x,x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} + 1} - \frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(abs(sqrt(x^3 + 1) - 1))","A",0
308,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)*(x^3+1)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{8}}\,{d x}"," ",0,"integrate((x^3 + 1)*(x^3 - 1)^(1/3)/x^8, x)","F",0
309,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^9,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/x^9, x)","F",0
310,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+2)/x^9,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 + 1)^(2/3)/x^9, x)","F",0
311,1,28,0,0.373290," ","integrate(1/x^6/(x^3+x)^(1/3),x, algorithm=""giac"")","-\frac{3}{16} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{8}{3}} + \frac{3}{5} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{3}} - \frac{3}{4} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/16*(1/x^2 + 1)^(8/3) + 3/5*(1/x^2 + 1)^(5/3) - 3/4*(1/x^2 + 1)^(2/3)","A",0
312,0,0,0,0.000000," ","integrate((2*x^2-x-2)/(-1+x)/x/(x^3-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - x - 2}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{4}} {\left(x - 1\right)} x}\,{d x}"," ",0,"integrate((2*x^2 - x - 2)/((x^3 - x^2)^(1/4)*(x - 1)*x), x)","F",0
313,0,0,0,0.000000," ","integrate((2+x)/(-1+x)/(x^3-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{x + 2}{\sqrt{x^{3} - x^{2} - x} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 2)/(sqrt(x^3 - x^2 - x)*(x - 1)), x)","F",0
314,1,23,0,0.563162," ","integrate((x^2+3)*(x^3+x^2+1)/x^6/(x^3+x)^(1/4),x, algorithm=""giac"")","-\frac{4}{7} \, {\left(\frac{1}{x} + \frac{1}{x^{3}}\right)}^{\frac{7}{4}} - \frac{4}{3} \, {\left(\frac{1}{x} + \frac{1}{x^{3}}\right)}^{\frac{3}{4}}"," ",0,"-4/7*(1/x + 1/x^3)^(7/4) - 4/3*(1/x + 1/x^3)^(3/4)","A",0
315,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)*(2*x^3-1)/x^11,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{11}}\,{d x}"," ",0,"integrate((2*x^3 - 1)*(x^3 - 1)^(1/3)/x^11, x)","F",0
316,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)*(2*x^3-1)/x^8,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{8}}\,{d x}"," ",0,"integrate((2*x^3 - 1)*(x^3 - 1)^(1/3)/x^8, x)","F",0
317,1,23,0,0.571550," ","integrate((x^2+3)*(2*x^3-x^2-1)/x^6/(x^3+x)^(1/4),x, algorithm=""giac"")","\frac{4}{7} \, {\left(\frac{1}{x} + \frac{1}{x^{3}}\right)}^{\frac{7}{4}} - \frac{8}{3} \, {\left(\frac{1}{x} + \frac{1}{x^{3}}\right)}^{\frac{3}{4}}"," ",0,"4/7*(1/x + 1/x^3)^(7/4) - 8/3*(1/x + 1/x^3)^(3/4)","A",0
318,0,0,0,0.000000," ","integrate((a*x^3+2*b)/(a*x^3-b)^(1/2)/(a*x^3+x^2-b),x, algorithm=""giac"")","\int \frac{a x^{3} + 2 \, b}{{\left(a x^{3} + x^{2} - b\right)} \sqrt{a x^{3} - b}}\,{d x}"," ",0,"integrate((a*x^3 + 2*b)/((a*x^3 + x^2 - b)*sqrt(a*x^3 - b)), x)","F",0
319,0,0,0,0.000000," ","integrate((x^4-4)*(x^4-1)^(3/4)/x^12,x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)}^{\frac{3}{4}} {\left(x^{4} - 4\right)}}{x^{12}}\,{d x}"," ",0,"integrate((x^4 - 1)^(3/4)*(x^4 - 4)/x^12, x)","F",0
320,1,34,0,0.685680," ","integrate((x^4+1)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} + 1} - \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} - 1\right)"," ",0,"1/2*sqrt(x^4 + 1) - 1/4*log(sqrt(x^4 + 1) + 1) + 1/4*log(sqrt(x^4 + 1) - 1)","A",0
321,1,30,0,0.385287," ","integrate((x^4-x)^(1/4)/x^8,x, algorithm=""giac"")","\frac{4}{27} \, {\left(\frac{1}{x^{3}} - 1\right)}^{2} {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} - \frac{4}{15} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{5}{4}}"," ",0,"4/27*(1/x^3 - 1)^2*(-1/x^3 + 1)^(1/4) - 4/15*(-1/x^3 + 1)^(5/4)","A",0
322,1,19,0,0.259594," ","integrate((x^4+x)^(1/4)/x^8,x, algorithm=""giac"")","-\frac{4}{27} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{9}{4}} + \frac{4}{15} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{5}{4}}"," ",0,"-4/27*(1/x^3 + 1)^(9/4) + 4/15*(1/x^3 + 1)^(5/4)","A",0
323,0,0,0,0.000000," ","integrate((x^2+2)/(x^2-1)/(x^4-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2}{\sqrt{x^{4} - x^{2} - 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 2)/(sqrt(x^4 - x^2 - 1)*(x^2 - 1)), x)","F",0
324,0,0,0,0.000000," ","integrate((x^3+4)*(x^4-x^3-1)/x^6/(x^3+1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} - 1\right)} {\left(x^{3} + 4\right)}}{{\left(x^{3} + 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 - x^3 - 1)*(x^3 + 4)/((x^3 + 1)^(3/4)*x^6), x)","F",0
325,0,0,0,0.000000," ","integrate((x^3+4)*(x^4-x^3-1)/x^8/(x^3+1)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} - 1\right)} {\left(x^{3} + 4\right)}}{{\left(x^{3} + 1\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate((x^4 - x^3 - 1)*(x^3 + 4)/((x^3 + 1)^(1/4)*x^8), x)","F",0
326,0,0,0,0.000000," ","integrate((x^3-4)*(x^4-x^3+1)/x^8/(x^3-1)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} + 1\right)} {\left(x^{3} - 4\right)}}{{\left(x^{3} - 1\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate((x^4 - x^3 + 1)*(x^3 - 4)/((x^3 - 1)^(1/4)*x^8), x)","F",0
327,1,24,0,0.367832," ","integrate(x/(x^4+x^3)^(1/2),x, algorithm=""giac"")","\log\left(\sqrt{\frac{1}{x} + 1} + 1\right) - \log\left({\left| \sqrt{\frac{1}{x} + 1} - 1 \right|}\right)"," ",0,"log(sqrt(1/x + 1) + 1) - log(abs(sqrt(1/x + 1) - 1))","A",0
328,1,19,0,0.655006," ","integrate(1/x/(1+x)/(x^4+x^3)^(1/4),x, algorithm=""giac"")","-\frac{4}{3} \, {\left(\frac{1}{x} + 1\right)}^{\frac{3}{4}} - \frac{4}{{\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}"," ",0,"-4/3*(1/x + 1)^(3/4) - 4/(1/x + 1)^(1/4)","A",0
329,0,0,0,0.000000," ","integrate((x^3+4)*(2*x^4-x^3-1)/x^6/(x^3+1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x^{3} - 1\right)} {\left(x^{3} + 4\right)}}{{\left(x^{3} + 1\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((2*x^4 - x^3 - 1)*(x^3 + 4)/((x^3 + 1)^(3/4)*x^6), x)","F",0
330,0,0,0,0.000000," ","integrate((x^4-3)*(x^4-x^3+1)/x^6/(x^5+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} + 1\right)} {\left(x^{4} - 3\right)}}{{\left(x^{5} + x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 - x^3 + 1)*(x^4 - 3)/((x^5 + x)^(1/4)*x^6), x)","F",0
331,1,20,0,0.355581," ","integrate((x^6-1)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{6} - 1} - \frac{1}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/3*sqrt(x^6 - 1) - 1/3*arctan(sqrt(x^6 - 1))","A",0
332,1,34,0,0.291158," ","integrate((x^6-1)/x/(x^6+1)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{6} + 1} + \frac{1}{6} \, \log\left(\sqrt{x^{6} + 1} + 1\right) - \frac{1}{6} \, \log\left(\sqrt{x^{6} + 1} - 1\right)"," ",0,"1/3*sqrt(x^6 + 1) + 1/6*log(sqrt(x^6 + 1) + 1) - 1/6*log(sqrt(x^6 + 1) - 1)","A",0
333,1,34,0,0.442667," ","integrate((x^6+1)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{6} + 1} - \frac{1}{6} \, \log\left(\sqrt{x^{6} + 1} + 1\right) + \frac{1}{6} \, \log\left(\sqrt{x^{6} + 1} - 1\right)"," ",0,"1/3*sqrt(x^6 + 1) - 1/6*log(sqrt(x^6 + 1) + 1) + 1/6*log(sqrt(x^6 + 1) - 1)","A",0
334,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(x^6+1)/x^15,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{15}}\,{d x}"," ",0,"integrate((x^6 + 1)*(x^6 - 1)^(1/3)/x^15, x)","F",0
335,0,0,0,0.000000," ","integrate((x^5-x^3+1)*(2*x^5-3)/x^6/(x^6+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 3\right)} {\left(x^{5} - x^{3} + 1\right)}}{{\left(x^{6} + x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((2*x^5 - 3)*(x^5 - x^3 + 1)/((x^6 + x)^(1/4)*x^6), x)","F",0
336,0,0,0,0.000000," ","integrate((x^6-2)*(x^6-x^4+1)/x^8/(x^6+1)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} + 1\right)} {\left(x^{6} - 2\right)}}{{\left(x^{6} + 1\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate((x^6 - x^4 + 1)*(x^6 - 2)/((x^6 + 1)^(1/4)*x^8), x)","F",0
337,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(2*x^6-1)/x^15,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{15}}\,{d x}"," ",0,"integrate((2*x^6 - 1)*(x^6 - 1)^(1/3)/x^15, x)","F",0
338,1,58,0,0.287315," ","integrate(x^2*(x^3-2)*(x^3+1)^(1/2)/(x^9+3*x^3+1),x, algorithm=""giac"")","-\frac{1}{9} \, \sqrt{3} \log\left({\left| \sqrt{3} {\left(x^{3} + 1\right)} + {\left(x^{3} + 1\right)}^{\frac{3}{2}} - \sqrt{3} \right|}\right) + \frac{1}{9} \, \sqrt{3} \log\left({\left| -\sqrt{3} {\left(x^{3} + 1\right)} + {\left(x^{3} + 1\right)}^{\frac{3}{2}} + \sqrt{3} \right|}\right)"," ",0,"-1/9*sqrt(3)*log(abs(sqrt(3)*(x^3 + 1) + (x^3 + 1)^(3/2) - sqrt(3))) + 1/9*sqrt(3)*log(abs(-sqrt(3)*(x^3 + 1) + (x^3 + 1)^(3/2) + sqrt(3)))","B",0
339,0,0,0,0.000000," ","integrate(x^4*(4*x^5-9)/(x^6-x)^(1/2)/(x^9-a*x^5+a),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{5} - 9\right)} x^{4}}{{\left(x^{9} - a x^{5} + a\right)} \sqrt{x^{6} - x}}\,{d x}"," ",0,"integrate((4*x^5 - 9)*x^4/((x^9 - a*x^5 + a)*sqrt(x^6 - x)), x)","F",0
340,0,0,0,0.000000," ","integrate(x^4*(5*x^4-9)/(x^5-x)^(1/2)/(a*x^9-x^4+1),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{4} - 9\right)} x^{4}}{{\left(a x^{9} - x^{4} + 1\right)} \sqrt{x^{5} - x}}\,{d x}"," ",0,"integrate((5*x^4 - 9)*x^4/((a*x^9 - x^4 + 1)*sqrt(x^5 - x)), x)","F",0
341,0,0,0,0.000000," ","integrate(x^4*(4*x^5-9)/(x^6-x)^(1/2)/(a*x^9-x^5+1),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{5} - 9\right)} x^{4}}{{\left(a x^{9} - x^{5} + 1\right)} \sqrt{x^{6} - x}}\,{d x}"," ",0,"integrate((4*x^5 - 9)*x^4/((a*x^9 - x^5 + 1)*sqrt(x^6 - x)), x)","F",0
342,-2,0,0,0.000000," ","integrate((x^12+1)/x^16/(x^6-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
343,0,0,0,0.000000," ","integrate((-1+x)/(-3+x)/(1+x)/(x^2-2*x-2)^(1/4),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{2} - 2 \, x - 2\right)}^{\frac{1}{4}} {\left(x + 1\right)} {\left(x - 3\right)}}\,{d x}"," ",0,"integrate((x - 1)/((x^2 - 2*x - 2)^(1/4)*(x + 1)*(x - 3)), x)","F",0
344,0,0,0,0.000000," ","integrate(1/(-1+x)/(x^2-2*x+2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 2 \, x + 2\right)}^{\frac{1}{4}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 - 2*x + 2)^(1/4)*(x - 1)), x)","F",0
345,0,0,0,0.000000," ","integrate(1/(1+x)/(x^2+2*x+2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 2 \, x + 2\right)}^{\frac{1}{4}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + 2*x + 2)^(1/4)*(x + 1)), x)","F",0
346,1,36,0,0.364324," ","integrate(1/x/(x^3+1)^(1/4),x, algorithm=""giac"")","\frac{2}{3} \, \arctan\left({\left(x^{3} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{3} \, \log\left({\left(x^{3} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2/3*arctan((x^3 + 1)^(1/4)) - 1/3*log((x^3 + 1)^(1/4) + 1) + 1/3*log(abs((x^3 + 1)^(1/4) - 1))","A",0
347,1,21,0,0.532714," ","integrate(1/x/(a*x^3-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{a x^{3} - b}}{\sqrt{b}}\right)}{3 \, \sqrt{b}}"," ",0,"2/3*arctan(sqrt(a*x^3 - b)/sqrt(b))/sqrt(b)","A",0
348,1,34,0,0.411847," ","integrate(x^5/(a*x^3-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(a x^{3} - b\right)}^{\frac{3}{2}}}{9 \, a^{2}} + \frac{2 \, \sqrt{a x^{3} - b} b}{3 \, a^{2}}"," ",0,"2/9*(a*x^3 - b)^(3/2)/a^2 + 2/3*sqrt(a*x^3 - b)*b/a^2","A",0
349,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(x^4-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{4} - x^{2} + 1} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^4 - x^2 + 1)*(x - 1)), x)","F",0
350,1,26,0,0.422864," ","integrate((x^4-1)*(x^4+1)/(x^4+x^2+1)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(3 \, x^{2} + 2\right)} x^{2} + 3\right)} x}{3 \, {\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}}}"," ",0,"-1/3*((3*x^2 + 2)*x^2 + 3)*x/(x^4 + x^2 + 1)^(3/2)","A",0
351,0,0,0,0.000000," ","integrate(x^2*(x^3-4)/(x^3-1)^(3/4)/(x^4-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 4\right)} x^{2}}{{\left(x^{4} - x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((x^3 - 4)*x^2/((x^4 - x^3 + 1)*(x^3 - 1)^(3/4)), x)","F",0
352,1,33,0,0.384909," ","integrate((1+2*x)/(x^4+2*x^3-3*x^2-4*x-4)^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x^{2} - x + \sqrt{{\left(x^{2} + x\right)}^{2} - 4 \, x^{2} - 4 \, x - 4} + 2 \right|}\right)"," ",0,"-log(abs(-x^2 - x + sqrt((x^2 + x)^2 - 4*x^2 - 4*x - 4) + 2))","A",0
353,1,21,0,0.287063," ","integrate(1/x/(a*x^4-b)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{a x^{4} - b}}{\sqrt{b}}\right)}{2 \, \sqrt{b}}"," ",0,"1/2*arctan(sqrt(a*x^4 - b)/sqrt(b))/sqrt(b)","A",0
354,0,0,0,0.000000," ","integrate((2*x^6-1)/(x^6+1)/(x^6-2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{6} - 1}{\sqrt{x^{6} - 2 \, x^{2} + 1} {\left(x^{6} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^6 - 1)/(sqrt(x^6 - 2*x^2 + 1)*(x^6 + 1)), x)","F",0
355,0,0,0,0.000000," ","integrate((2*x^6+1)/(x^6-1)/(x^6-2*x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{6} + 1}{\sqrt{x^{6} - 2 \, x^{2} - 1} {\left(x^{6} - 1\right)}}\,{d x}"," ",0,"integrate((2*x^6 + 1)/(sqrt(x^6 - 2*x^2 - 1)*(x^6 - 1)), x)","F",0
356,1,28,0,0.277203," ","integrate(x^8*(x^3-1)^(1/3),x, algorithm=""giac"")","\frac{1}{10} \, {\left(x^{3} - 1\right)}^{\frac{10}{3}} + \frac{2}{7} \, {\left(x^{3} - 1\right)}^{\frac{7}{3}} + \frac{1}{4} \, {\left(x^{3} - 1\right)}^{\frac{4}{3}}"," ",0,"1/10*(x^3 - 1)^(10/3) + 2/7*(x^3 - 1)^(7/3) + 1/4*(x^3 - 1)^(4/3)","A",0
357,1,28,0,0.448644," ","integrate(x^8*(x^3+1)^(1/4),x, algorithm=""giac"")","\frac{4}{39} \, {\left(x^{3} + 1\right)}^{\frac{13}{4}} - \frac{8}{27} \, {\left(x^{3} + 1\right)}^{\frac{9}{4}} + \frac{4}{15} \, {\left(x^{3} + 1\right)}^{\frac{5}{4}}"," ",0,"4/39*(x^3 + 1)^(13/4) - 8/27*(x^3 + 1)^(9/4) + 4/15*(x^3 + 1)^(5/4)","A",0
358,1,41,0,0.444698," ","integrate(1/x^6/(x^3-x)^(1/3),x, algorithm=""giac"")","\frac{3}{16} \, {\left(\frac{1}{x^{2}} - 1\right)}^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} - \frac{3}{5} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{5}{3}} + \frac{3}{4} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}"," ",0,"3/16*(1/x^2 - 1)^2*(-1/x^2 + 1)^(2/3) - 3/5*(-1/x^2 + 1)^(5/3) + 3/4*(-1/x^2 + 1)^(2/3)","A",0
359,1,41,0,0.727298," ","integrate(1/x^3/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} - \frac{6}{5} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{3}} + \frac{3}{2} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(1/x - 1)^2*(-1/x + 1)^(2/3) - 6/5*(-1/x + 1)^(5/3) + 3/2*(-1/x + 1)^(2/3)","A",0
360,0,0,0,0.000000," ","integrate((x^2-3)*(x^3-x^2+1)/x^6/(x^3-x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2} + 1\right)} {\left(x^{2} - 3\right)}}{{\left(x^{3} - x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^3 - x^2 + 1)*(x^2 - 3)/((x^3 - x)^(1/4)*x^6), x)","F",0
361,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^3-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{3} - x^{2} - x} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(x^3 - x^2 - x)*(x^2 - 1)), x)","F",0
362,1,19,0,0.447053," ","integrate((x^3-1)/x^3/(x^3+1)/(x^4+x)^(1/4),x, algorithm=""giac"")","\frac{4}{9} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}} + \frac{8}{3 \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}}"," ",0,"4/9*(1/x^3 + 1)^(3/4) + 8/3/(1/x^3 + 1)^(1/4)","A",0
363,1,30,0,0.427844," ","integrate((x^4-x^2)^(1/4)/x^6,x, algorithm=""giac"")","\frac{2}{9} \, {\left(\frac{1}{x^{2}} - 1\right)}^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - \frac{2}{5} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}}"," ",0,"2/9*(1/x^2 - 1)^2*(-1/x^2 + 1)^(1/4) - 2/5*(-1/x^2 + 1)^(5/4)","A",0
364,1,34,0,0.317378," ","integrate((-1+2*x)/(x^4-2*x^3+x+1)^(1/2),x, algorithm=""giac"")","-\log\left(-2 \, x^{2} + 2 \, x + 2 \, \sqrt{{\left(x^{2} - x\right)}^{2} - x^{2} + x + 1} + 1\right)"," ",0,"-log(-2*x^2 + 2*x + 2*sqrt((x^2 - x)^2 - x^2 + x + 1) + 1)","A",0
365,1,23,0,0.767521," ","integrate((1+x)/(-1+x)/x/(x^4-x^3)^(1/4),x, algorithm=""giac"")","\frac{4}{3} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{4}} + \frac{8}{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}"," ",0,"4/3*(-1/x + 1)^(3/4) + 8/(-1/x + 1)^(1/4)","A",0
366,0,0,0,0.000000," ","integrate((x^4+3)*(x^4-x^3-1)/x^6/(x^5-x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} - 1\right)} {\left(x^{4} + 3\right)}}{{\left(x^{5} - x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 - x^3 - 1)*(x^4 + 3)/((x^5 - x)^(1/4)*x^6), x)","F",0
367,0,0,0,0.000000," ","integrate((x^4+3)*(x^4+x^3-1)/x^6/(x^5-x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} - 1\right)} {\left(x^{4} + 3\right)}}{{\left(x^{5} - x\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^3 - 1)*(x^4 + 3)/((x^5 - x)^(1/4)*x^6), x)","F",0
368,0,0,0,0.000000," ","integrate((3*x^4-1)/(x^4-a*x+1)/(x^5+x)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{4} - 1}{\sqrt{x^{5} + x} {\left(x^{4} - a x + 1\right)}}\,{d x}"," ",0,"integrate((3*x^4 - 1)/(sqrt(x^5 + x)*(x^4 - a*x + 1)), x)","F",0
369,0,0,0,0.000000," ","integrate((3*x^4-1)/(a*x^4+a-x)/(x^5+x)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{4} - 1}{{\left(a x^{4} + a - x\right)} \sqrt{x^{5} + x}}\,{d x}"," ",0,"integrate((3*x^4 - 1)/((a*x^4 + a - x)*sqrt(x^5 + x)), x)","F",0
370,0,0,0,0.000000," ","integrate((x^6-1)^(1/2)*(x^6+2)/x^3/(x^6-x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2\right)} \sqrt{x^{6} - 1}}{{\left(x^{6} - x^{4} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^6 + 2)*sqrt(x^6 - 1)/((x^6 - x^4 - 1)*x^3), x)","F",0
371,0,0,0,0.000000," ","integrate((-x^6+1)^(1/2)*(2*x^6+1)/x^2/(x^6-x^2-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + 1\right)} \sqrt{-x^{6} + 1}}{{\left(x^{6} - x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^6 + 1)*sqrt(-x^6 + 1)/((x^6 - x^2 - 1)*x^2), x)","F",0
372,1,23,0,0.233799," ","integrate(1/x^4/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{x^{3} - 1}}{3 \, x^{3}} + \frac{1}{3} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"1/3*sqrt(x^3 - 1)/x^3 + 1/3*arctan(sqrt(x^3 - 1))","A",0
373,0,0,0,0.000000," ","integrate((x^2-2*x-2)/(x^2-x+3)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 2 \, x - 2}{\sqrt{x^{3} - 1} {\left(x^{2} - x + 3\right)}}\,{d x}"," ",0,"integrate((x^2 - 2*x - 2)/(sqrt(x^3 - 1)*(x^2 - x + 3)), x)","F",0
374,0,0,0,0.000000," ","integrate((x^2-2*x-2)/(x^2+3*x-1)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 2 \, x - 2}{\sqrt{x^{3} - 1} {\left(x^{2} + 3 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 2*x - 2)/(sqrt(x^3 - 1)*(x^2 + 3*x - 1)), x)","F",0
375,1,23,0,0.233401," ","integrate((x^3-1)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{\sqrt{x^{3} - 1}}{3 \, x^{3}} + \frac{1}{3} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"-1/3*sqrt(x^3 - 1)/x^3 + 1/3*arctan(sqrt(x^3 - 1))","A",0
376,1,38,0,0.244770," ","integrate(1/x^4/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{x^{3} + 1}}{3 \, x^{3}} + \frac{1}{6} \, \log\left(\sqrt{x^{3} + 1} + 1\right) - \frac{1}{6} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/3*sqrt(x^3 + 1)/x^3 + 1/6*log(sqrt(x^3 + 1) + 1) - 1/6*log(abs(sqrt(x^3 + 1) - 1))","A",0
377,0,0,0,0.000000," ","integrate((1+x)/(-2+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{3} + 1} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^3 + 1)*(x - 2)), x)","F",0
378,1,38,0,0.388592," ","integrate((x^3+1)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{\sqrt{x^{3} + 1}}{3 \, x^{3}} - \frac{1}{6} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{6} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/3*sqrt(x^3 + 1)/x^3 - 1/6*log(sqrt(x^3 + 1) + 1) + 1/6*log(abs(sqrt(x^3 + 1) - 1))","A",0
379,0,0,0,0.000000," ","integrate((1+x)/(-1+2*x)/(x^4+x)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{4} + x} {\left(2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^4 + x)*(2*x - 1)), x)","F",0
380,1,26,0,0.463701," ","integrate((-1+x)/(x^4-4*x^3+4*x^2-5)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| -x^{2} + 2 \, x + \sqrt{{\left(x^{2} - 2 \, x\right)}^{2} - 5} \right|}\right)"," ",0,"-1/2*log(abs(-x^2 + 2*x + sqrt((x^2 - 2*x)^2 - 5)))","A",0
381,1,25,0,0.659836," ","integrate((2+x)/(x^4+8*x^3+16*x^2+13)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(-x^{2} - 4 \, x + \sqrt{{\left(x^{2} + 4 \, x\right)}^{2} + 13}\right)"," ",0,"-1/2*log(-x^2 - 4*x + sqrt((x^2 + 4*x)^2 + 13))","A",0
382,1,25,0,0.507799," ","integrate(x/(a*x^4+b)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{2 \, \sqrt{a}}"," ",0,"-1/2*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/sqrt(a)","A",0
383,1,23,0,0.256174," ","integrate(1/x^7/(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{x^{6} - 1}}{6 \, x^{6}} + \frac{1}{6} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/6*sqrt(x^6 - 1)/x^6 + 1/6*arctan(sqrt(x^6 - 1))","A",0
384,1,23,0,0.282872," ","integrate((x^6-1)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{\sqrt{x^{6} - 1}}{6 \, x^{6}} + \frac{1}{6} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"-1/6*sqrt(x^6 - 1)/x^6 + 1/6*arctan(sqrt(x^6 - 1))","A",0
385,1,37,0,0.317622," ","integrate((x^6-1)/x^7/(x^6+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{x^{6} + 1}}{6 \, x^{6}} - \frac{1}{4} \, \log\left(\sqrt{x^{6} + 1} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{x^{6} + 1} - 1\right)"," ",0,"1/6*sqrt(x^6 + 1)/x^6 - 1/4*log(sqrt(x^6 + 1) + 1) + 1/4*log(sqrt(x^6 + 1) - 1)","A",0
386,1,37,0,0.230551," ","integrate((x^6+1)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{\sqrt{x^{6} + 1}}{6 \, x^{6}} - \frac{1}{12} \, \log\left(\sqrt{x^{6} + 1} + 1\right) + \frac{1}{12} \, \log\left(\sqrt{x^{6} + 1} - 1\right)"," ",0,"-1/6*sqrt(x^6 + 1)/x^6 - 1/12*log(sqrt(x^6 + 1) + 1) + 1/12*log(sqrt(x^6 + 1) - 1)","A",0
387,0,0,0,0.000000," ","integrate((x^6+2)*(x^12+x^8-2*x^6+1)/x^10/(x^6-1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{12} + x^{8} - 2 \, x^{6} + 1\right)} {\left(x^{6} + 2\right)}}{{\left(x^{6} - 1\right)}^{\frac{3}{4}} x^{10}}\,{d x}"," ",0,"integrate((x^12 + x^8 - 2*x^6 + 1)*(x^6 + 2)/((x^6 - 1)^(3/4)*x^10), x)","F",0
388,0,0,0,0.000000," ","integrate((2*x^2+2*x-1)/(3*x^2-x+1)/(x^4-x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} + 2 \, x - 1}{\sqrt{x^{4} - x} {\left(3 \, x^{2} - x + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 + 2*x - 1)/(sqrt(x^4 - x)*(3*x^2 - x + 1)), x)","F",0
389,1,23,0,0.321973," ","integrate((x^3+1)/x^3/(x^3-1)/(x^4-x)^(1/4),x, algorithm=""giac"")","\frac{4}{9} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}} + \frac{8}{3 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}}"," ",0,"4/9*(-1/x^3 + 1)^(3/4) + 8/3/(-1/x^3 + 1)^(1/4)","A",0
390,0,0,0,0.000000," ","integrate((2*x^2-2*x-1)/(x^2+3*x-1)/(x^4+x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - 2 \, x - 1}{\sqrt{x^{4} + x} {\left(x^{2} + 3 \, x - 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 - 2*x - 1)/(sqrt(x^4 + x)*(x^2 + 3*x - 1)), x)","F",0
391,1,19,0,0.363322," ","integrate((x^2-1)/x^2/(x^2+1)/(x^4+x^2)^(1/4),x, algorithm=""giac"")","\frac{2}{3} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}} + \frac{4}{{\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"2/3*(1/x^2 + 1)^(3/4) + 4/(1/x^2 + 1)^(1/4)","A",0
392,1,33,0,0.727494," ","integrate((-1+2*x)/(x^4-2*x^3+9*x^2-8*x)^(1/2),x, algorithm=""giac"")","-\log\left(x^{2} - x - \sqrt{{\left(x^{2} - x\right)}^{2} + 8 \, x^{2} - 8 \, x} + 4\right)"," ",0,"-log(x^2 - x - sqrt((x^2 - x)^2 + 8*x^2 - 8*x) + 4)","A",0
393,1,46,0,0.421813," ","integrate((-a+2*x)/(-a*x+x^2+b-1)/(-a*x+x^2+b)^(1/4),x, algorithm=""giac"")","2 \, \arctan\left({\left(-a x + x^{2} + b\right)}^{\frac{1}{4}}\right) - \log\left({\left(-a x + x^{2} + b\right)}^{\frac{1}{4}} + 1\right) + \log\left({\left| {\left(-a x + x^{2} + b\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2*arctan((-a*x + x^2 + b)^(1/4)) - log((-a*x + x^2 + b)^(1/4) + 1) + log(abs((-a*x + x^2 + b)^(1/4) - 1))","A",0
394,0,0,0,0.000000," ","integrate((x^3-4)*(x^3-1)^(2/3)/x^12,x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{3} - 4\right)}}{x^{12}}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)*(x^3 - 4)/x^12, x)","F",0
395,0,0,0,0.000000," ","integrate((x^2+2*x-2)/(x^2-3*x-1)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2 \, x - 2}{\sqrt{x^{3} + 1} {\left(x^{2} - 3 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 2*x - 2)/(sqrt(x^3 + 1)*(x^2 - 3*x - 1)), x)","F",0
396,0,0,0,0.000000," ","integrate((x^2+2*x-2)/(2*x^2-x+3)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2 \, x - 2}{\sqrt{x^{3} + 1} {\left(2 \, x^{2} - x + 3\right)}}\,{d x}"," ",0,"integrate((x^2 + 2*x - 2)/(sqrt(x^3 + 1)*(2*x^2 - x + 3)), x)","F",0
397,0,0,0,0.000000," ","integrate((x^2+2*x-2)/(3*x^2-4*x+2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2 \, x - 2}{\sqrt{x^{3} + 1} {\left(3 \, x^{2} - 4 \, x + 2\right)}}\,{d x}"," ",0,"integrate((x^2 + 2*x - 2)/(sqrt(x^3 + 1)*(3*x^2 - 4*x + 2)), x)","F",0
398,0,0,0,0.000000," ","integrate((x^3-1)*(x^3+1)^(1/3)/x^11,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}{x^{11}}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)*(x^3 - 1)/x^11, x)","F",0
399,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)*(x^3+1)/x^11,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{11}}\,{d x}"," ",0,"integrate((x^3 + 1)*(x^3 - 1)^(1/3)/x^11, x)","F",0
400,0,0,0,0.000000," ","integrate((3*x^3+x^2-2*x-1)/(x^3-3*x^2+3*x-1)^(1/4),x, algorithm=""giac"")","\int \frac{3 \, x^{3} + x^{2} - 2 \, x - 1}{{\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((3*x^3 + x^2 - 2*x - 1)/(x^3 - 3*x^2 + 3*x - 1)^(1/4), x)","F",0
401,0,0,0,0.000000," ","integrate((x^3-3*x^2+3*x-1)^(1/4)*(3*x^3+x^2-2*x-1),x, algorithm=""giac"")","\int {\left(3 \, x^{3} + x^{2} - 2 \, x - 1\right)} {\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}^{\frac{1}{4}}\,{d x}"," ",0,"integrate((3*x^3 + x^2 - 2*x - 1)*(x^3 - 3*x^2 + 3*x - 1)^(1/4), x)","F",0
402,0,0,0,0.000000," ","integrate((a*x^3-2*b)*(a*x^3+b)^(1/2)/x^2/(a*x^3-x^2+b),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3} + b} {\left(a x^{3} - 2 \, b\right)}}{{\left(a x^{3} - x^{2} + b\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^3 + b)*(a*x^3 - 2*b)/((a*x^3 - x^2 + b)*x^2), x)","F",0
403,1,47,0,0.350291," ","integrate(1/(x^4+1)^(1/4),x, algorithm=""giac"")","-\frac{1}{2} \, \arctan\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{4} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{1}{4} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} - 1\right)"," ",0,"-1/2*arctan((x^4 + 1)^(1/4)/x) + 1/4*log((x^4 + 1)^(1/4)/x + 1) - 1/4*log((x^4 + 1)^(1/4)/x - 1)","A",0
404,0,0,0,0.000000," ","integrate((2*x^2-2*x-1)/(4*x^2+2*x+1)/(x^4+x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - 2 \, x - 1}{\sqrt{x^{4} + x} {\left(4 \, x^{2} + 2 \, x + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 - 2*x - 1)/(sqrt(x^4 + x)*(4*x^2 + 2*x + 1)), x)","F",0
405,1,36,0,0.502985," ","integrate((x^4+x)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} + x} x + \frac{1}{6} \, \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{6} \, \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/3*sqrt(x^4 + x)*x + 1/6*log(sqrt(1/x^3 + 1) + 1) - 1/6*log(abs(sqrt(1/x^3 + 1) - 1))","A",0
406,1,41,0,0.351099," ","integrate(1/(x^4-x^2)^(1/4),x, algorithm=""giac"")","\arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"arctan((-1/x^2 + 1)^(1/4)) - 1/2*log((-1/x^2 + 1)^(1/4) + 1) + 1/2*log(-(-1/x^2 + 1)^(1/4) + 1)","A",0
407,0,0,0,0.000000," ","integrate((a*x^2+2*b)/(a*x^2+b)^(1/4)/(x^4-a*x^2-b),x, algorithm=""giac"")","\int \frac{a x^{2} + 2 \, b}{{\left(x^{4} - a x^{2} - b\right)} {\left(a x^{2} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^2 + 2*b)/((x^4 - a*x^2 - b)*(a*x^2 + b)^(1/4)), x)","F",0
408,1,34,0,0.389342," ","integrate((-1+2*x)/(x^4-2*x^3+3*x^2-2*x-2)^(1/2),x, algorithm=""giac"")","-\log\left(x^{2} - x - \sqrt{{\left(x^{2} - x\right)}^{2} + 2 \, x^{2} - 2 \, x - 2} + 1\right)"," ",0,"-log(x^2 - x - sqrt((x^2 - x)^2 + 2*x^2 - 2*x - 2) + 1)","A",0
409,1,34,0,0.387162," ","integrate((-1+2*x)/(x^4-2*x^3+5*x^2-4*x-4)^(1/2),x, algorithm=""giac"")","-\log\left(x^{2} - x - \sqrt{{\left(x^{2} - x\right)}^{2} + 4 \, x^{2} - 4 \, x - 4} + 2\right)"," ",0,"-log(x^2 - x - sqrt((x^2 - x)^2 + 4*x^2 - 4*x - 4) + 2)","A",0
410,1,37,0,0.306117," ","integrate(1/x^4/(x^4+x^3)^(1/4),x, algorithm=""giac"")","-\frac{4}{15} \, {\left(\frac{1}{x} + 1\right)}^{\frac{15}{4}} + \frac{12}{11} \, {\left(\frac{1}{x} + 1\right)}^{\frac{11}{4}} - \frac{12}{7} \, {\left(\frac{1}{x} + 1\right)}^{\frac{7}{4}} + \frac{4}{3} \, {\left(\frac{1}{x} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/15*(1/x + 1)^(15/4) + 12/11*(1/x + 1)^(11/4) - 12/7*(1/x + 1)^(7/4) + 4/3*(1/x + 1)^(3/4)","A",0
411,1,27,0,0.294827," ","integrate(x/(a*x^4-b)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} - b} \right|}\right)}{2 \, \sqrt{a}}"," ",0,"-1/2*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 - b)))/sqrt(a)","A",0
412,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6-x^3+1)/x^12,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{x^{12}}\,{d x}"," ",0,"integrate((2*x^6 - x^3 + 1)*(x^3 + 1)^(2/3)/x^12, x)","F",0
413,0,0,0,0.000000," ","integrate((x^4+3)*(-x^5+x)^(1/2)/(x^8-x^6-2*x^4+1),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{5} + x} {\left(x^{4} + 3\right)}}{x^{8} - x^{6} - 2 \, x^{4} + 1}\,{d x}"," ",0,"integrate(sqrt(-x^5 + x)*(x^4 + 3)/(x^8 - x^6 - 2*x^4 + 1), x)","F",0
414,1,39,0,0.428199," ","integrate((x^16-1)/x^8/(x^4-1)^(1/2),x, algorithm=""giac"")","\frac{1}{21} \, {\left(3 \, x^{4} + 5\right)} \sqrt{x^{4} - 1} x - \frac{{\left(\frac{3}{x^{4}} + 5\right)} \sqrt{-\frac{1}{x^{4}} + 1}}{21 \, x}"," ",0,"1/21*(3*x^4 + 5)*sqrt(x^4 - 1)*x - 1/21*(3/x^4 + 5)*sqrt(-1/x^4 + 1)/x","A",0
415,1,15,0,0.392648," ","integrate(((-1+x)^(3/2)+(1+x)^(3/2))/(-1+x)^(3/2)/(1+x)^(3/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{x + 1}} - \frac{2}{\sqrt{x - 1}}"," ",0,"-2/sqrt(x + 1) - 2/sqrt(x - 1)","A",0
416,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(x^3+x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{3} + x^{2} + x} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^3 + x^2 + x)*(x - 1)), x)","F",0
417,0,0,0,0.000000," ","integrate((x^2-1)/(x^2-x+1)/(x^3+x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{3} + x^{2} + x} {\left(x^{2} - x + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^3 + x^2 + x)*(x^2 - x + 1)), x)","F",0
418,0,0,0,0.000000," ","integrate((-1+x)/(1+x)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x^{4} + 1} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x - 1)/(sqrt(x^4 + 1)*(x + 1)), x)","F",0
419,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{4} + 1} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^4 + 1)*(x - 1)), x)","F",0
420,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{4} + x^{2} + 1} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^4 + x^2 + 1)*(x - 1)), x)","F",0
421,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^4+x^3-x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^2 - 1)), x)","F",0
422,0,0,0,0.000000," ","integrate(x/(x^4+2*x^3-3*x^2-11*x+11)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{4} + 2 \, x^{3} - 3 \, x^{2} - 11 \, x + 11}}\,{d x}"," ",0,"integrate(x/sqrt(x^4 + 2*x^3 - 3*x^2 - 11*x + 11), x)","F",0
423,0,0,0,0.000000," ","integrate((1+x)/(x^4+2*x^3-3*x^2-5*x+2)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{4} + 2 \, x^{3} - 3 \, x^{2} - 5 \, x + 2}}\,{d x}"," ",0,"integrate((x + 1)/sqrt(x^4 + 2*x^3 - 3*x^2 - 5*x + 2), x)","F",0
424,0,0,0,0.000000," ","integrate(x/(x^4+2*x^3-3*x^2+3*x-3)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{4} + 2 \, x^{3} - 3 \, x^{2} + 3 \, x - 3}}\,{d x}"," ",0,"integrate(x/sqrt(x^4 + 2*x^3 - 3*x^2 + 3*x - 3), x)","F",0
425,0,0,0,0.000000," ","integrate((-x^6+1)^(1/2)*(x^6+2)/x^3/(x^6+x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2\right)} \sqrt{-x^{6} + 1}}{{\left(x^{6} + x^{4} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^6 + 2)*sqrt(-x^6 + 1)/((x^6 + x^4 - 1)*x^3), x)","F",0
426,0,0,0,0.000000," ","integrate(x^(1/2)/(x^2-2)^(3/4),x, algorithm=""giac"")","\int \frac{\sqrt{x}}{{\left(x^{2} - 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(sqrt(x)/(x^2 - 2)^(3/4), x)","F",0
427,1,60,0,0.462404," ","integrate((a+x)/(2*a*x+x^2+2*b-1)/(2*a*x+x^2+2*b)^(1/4),x, algorithm=""giac"")","\arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(a x + \frac{1}{2} \, x^{2} + b\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left(\left(\frac{1}{2}\right)^{\frac{1}{4}} + {\left(a x + \frac{1}{2} \, x^{2} + b\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \, \log\left({\left| -\left(\frac{1}{2}\right)^{\frac{1}{4}} + {\left(a x + \frac{1}{2} \, x^{2} + b\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"arctan(2*(1/2)^(3/4)*(a*x + 1/2*x^2 + b)^(1/4)) - 1/2*log((1/2)^(1/4) + (a*x + 1/2*x^2 + b)^(1/4)) + 1/2*log(abs(-(1/2)^(1/4) + (a*x + 1/2*x^2 + b)^(1/4)))","A",0
428,1,36,0,0.638308," ","integrate(1/(a*x^2+b*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x + c}\right)} \sqrt{a} - b \right|}\right)}{\sqrt{a}}"," ",0,"-log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x + c))*sqrt(a) - b))/sqrt(a)","A",0
429,1,37,0,0.372864," ","integrate(x^11*(x^3-1)^(1/3),x, algorithm=""giac"")","\frac{1}{13} \, {\left(x^{3} - 1\right)}^{\frac{13}{3}} + \frac{3}{10} \, {\left(x^{3} - 1\right)}^{\frac{10}{3}} + \frac{3}{7} \, {\left(x^{3} - 1\right)}^{\frac{7}{3}} + \frac{1}{4} \, {\left(x^{3} - 1\right)}^{\frac{4}{3}}"," ",0,"1/13*(x^3 - 1)^(13/3) + 3/10*(x^3 - 1)^(10/3) + 3/7*(x^3 - 1)^(7/3) + 1/4*(x^3 - 1)^(4/3)","A",0
430,0,0,0,0.000000," ","integrate((x^2-2*x-1)/(3*x^2+2*x+1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 2 \, x - 1}{\sqrt{x^{3} - x} {\left(3 \, x^{2} + 2 \, x + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 2*x - 1)/(sqrt(x^3 - x)*(3*x^2 + 2*x + 1)), x)","F",0
431,0,0,0,0.000000," ","integrate((x^2-1)*(-x^4-4*x^3-5*x^2-4*x-1)^(1/2)/(x^2+x+1)/(x^2+3*x+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-x^{4} - 4 \, x^{3} - 5 \, x^{2} - 4 \, x - 1} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 3 \, x + 1\right)}^{2} {\left(x^{2} + x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-x^4 - 4*x^3 - 5*x^2 - 4*x - 1)*(x^2 - 1)/((x^2 + 3*x + 1)^2*(x^2 + x + 1)), x)","F",0
432,1,38,0,0.308683," ","integrate((x^4-1)/x^3/(x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{{\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1} - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"-1/((x^2 - sqrt(x^4 + 1))^2 - 1) - 1/2*log(-x^2 + sqrt(x^4 + 1))","A",0
433,1,28,0,0.347470," ","integrate((x^3-1)/x^6/(x^3+1)/(x^4+x)^(1/4),x, algorithm=""giac"")","\frac{4}{21} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} - \frac{4}{3} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}} - \frac{8}{3 \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}}"," ",0,"4/21*(1/x^3 + 1)^(7/4) - 4/3*(1/x^3 + 1)^(3/4) - 8/3/(1/x^3 + 1)^(1/4)","A",0
434,1,35,0,0.262758," ","integrate((x^4+x)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{\frac{1}{x^{3}} + 1} + \frac{1}{3} \, \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{3} \, \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"-2/3*sqrt(1/x^3 + 1) + 1/3*log(sqrt(1/x^3 + 1) + 1) - 1/3*log(abs(sqrt(1/x^3 + 1) - 1))","A",0
435,1,37,0,0.799481," ","integrate(1/x^8/(x^4+x^2)^(1/4),x, algorithm=""giac"")","-\frac{2}{15} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{15}{4}} + \frac{6}{11} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{11}{4}} - \frac{6}{7} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{7}{4}} + \frac{2}{3} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}"," ",0,"-2/15*(1/x^2 + 1)^(15/4) + 6/11*(1/x^2 + 1)^(11/4) - 6/7*(1/x^2 + 1)^(7/4) + 2/3*(1/x^2 + 1)^(3/4)","A",0
436,1,35,0,0.461108," ","integrate((1-2*x)/(x^4-2*x^3-4*x^2+5*x+5)^(1/2),x, algorithm=""giac"")","\log\left({\left| -2 \, x^{2} + 2 \, x + 2 \, \sqrt{{\left(x^{2} - x\right)}^{2} - 5 \, x^{2} + 5 \, x + 5} + 5 \right|}\right)"," ",0,"log(abs(-2*x^2 + 2*x + 2*sqrt((x^2 - x)^2 - 5*x^2 + 5*x + 5) + 5))","A",0
437,1,59,0,0.269688," ","integrate(1/x^4/(x^4-x^3)^(1/4),x, algorithm=""giac"")","-\frac{4}{15} \, {\left(\frac{1}{x} - 1\right)}^{3} {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{4}} - \frac{12}{11} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{4}} + \frac{12}{7} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{7}{4}} - \frac{4}{3} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/15*(1/x - 1)^3*(-1/x + 1)^(3/4) - 12/11*(1/x - 1)^2*(-1/x + 1)^(3/4) + 12/7*(-1/x + 1)^(7/4) - 4/3*(-1/x + 1)^(3/4)","A",0
438,1,35,0,0.730105," ","integrate((1+2*x)/(x^4+2*x^3-2*x^2-3*x-4)^(1/2),x, algorithm=""giac"")","-\log\left({\left| -2 \, x^{2} - 2 \, x + 2 \, \sqrt{{\left(x^{2} + x\right)}^{2} - 3 \, x^{2} - 3 \, x - 4} + 3 \right|}\right)"," ",0,"-log(abs(-2*x^2 - 2*x + 2*sqrt((x^2 + x)^2 - 3*x^2 - 3*x - 4) + 3))","A",0
439,0,0,0,0.000000," ","integrate((a*x^3+4*b)/(a*x^3+b)^(1/4)/(-a*x^3+x^4-b),x, algorithm=""giac"")","\int -\frac{a x^{3} + 4 \, b}{{\left(a x^{3} - x^{4} + b\right)} {\left(a x^{3} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(a*x^3 + 4*b)/((a*x^3 - x^4 + b)*(a*x^3 + b)^(1/4)), x)","F",0
440,0,0,0,0.000000," ","integrate(x^8/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{x^{6} - 1}}\,{d x}"," ",0,"integrate(x^8/sqrt(x^6 - 1), x)","F",0
441,1,46,0,0.287594," ","integrate((x^6-1)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{2 \, \sqrt{-\frac{1}{x^{6}} + 1} - \log\left(\sqrt{-\frac{1}{x^{6}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{x^{6}} + 1} + 1\right)}{6 \, \mathrm{sgn}\left(x\right)}"," ",0,"-1/6*(2*sqrt(-1/x^6 + 1) - log(sqrt(-1/x^6 + 1) + 1) + log(-sqrt(-1/x^6 + 1) + 1))/sgn(x)","A",0
442,1,30,0,0.294350," ","integrate(x^2*(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{x^{6} - 1} x^{3} + \frac{1}{6} \, \log\left({\left| -x^{3} + \sqrt{x^{6} - 1} \right|}\right)"," ",0,"1/6*sqrt(x^6 - 1)*x^3 + 1/6*log(abs(-x^3 + sqrt(x^6 - 1)))","A",0
443,0,0,0,0.000000," ","integrate(x^8/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{x^{6} + 1}}\,{d x}"," ",0,"integrate(x^8/sqrt(x^6 + 1), x)","F",0
444,1,38,0,0.310304," ","integrate((x^6+1)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{2 \, \sqrt{\frac{1}{x^{6}} + 1} - \log\left(\sqrt{\frac{1}{x^{6}} + 1} + 1\right) + \log\left(\sqrt{\frac{1}{x^{6}} + 1} - 1\right)}{6 \, \mathrm{sgn}\left(x\right)}"," ",0,"-1/6*(2*sqrt(1/x^6 + 1) - log(sqrt(1/x^6 + 1) + 1) + log(sqrt(1/x^6 + 1) - 1))/sgn(x)","A",0
445,1,28,0,0.275726," ","integrate((x^6+1)/x^6/(x^3+1)/(x^4+x)^(1/4),x, algorithm=""giac"")","-\frac{4}{21} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} + \frac{8}{9} \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}} + \frac{8}{3 \, {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}}"," ",0,"-4/21*(1/x^3 + 1)^(7/4) + 8/9*(1/x^3 + 1)^(3/4) + 8/3/(1/x^3 + 1)^(1/4)","A",0
446,0,0,0,0.000000," ","integrate(x*(x^6+x)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{6} + x} x\,{d x}"," ",0,"integrate(sqrt(x^6 + x)*x, x)","F",0
447,0,0,0,0.000000," ","integrate((a*c*x^6-2*b*c)/(a*x^6+b)^(1/4)/(-c^4*x^4+a*x^6+b),x, algorithm=""giac"")","\int -\frac{a c x^{6} - 2 \, b c}{{\left(c^{4} x^{4} - a x^{6} - b\right)} {\left(a x^{6} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(a*c*x^6 - 2*b*c)/((c^4*x^4 - a*x^6 - b)*(a*x^6 + b)^(1/4)), x)","F",0
448,0,0,0,0.000000," ","integrate(1/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(1/sqrt(x + sqrt(x^2 + 1)), x)","F",0
449,1,44,0,0.335981," ","integrate((x^2+1)^(1/4)/x,x, algorithm=""giac"")","2 \, {\left(x^{2} + 1\right)}^{\frac{1}{4}} - \arctan\left({\left(x^{2} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2*(x^2 + 1)^(1/4) - arctan((x^2 + 1)^(1/4)) - 1/2*log((x^2 + 1)^(1/4) + 1) + 1/2*log((x^2 + 1)^(1/4) - 1)","A",0
450,1,63,0,0.299138," ","integrate((x^3-1)^(1/2)/x^7,x, algorithm=""giac"")","\frac{1}{48} \, \pi + \frac{\sqrt{x^{3} - 1} - \frac{1}{\sqrt{x^{3} - 1}}}{12 \, {\left({\left(\sqrt{x^{3} - 1} - \frac{1}{\sqrt{x^{3} - 1}}\right)}^{2} + 4\right)}} + \frac{1}{24} \, \arctan\left(\frac{x^{3} - 2}{2 \, \sqrt{x^{3} - 1}}\right)"," ",0,"1/48*pi + 1/12*(sqrt(x^3 - 1) - 1/sqrt(x^3 - 1))/((sqrt(x^3 - 1) - 1/sqrt(x^3 - 1))^2 + 4) + 1/24*arctan(1/2*(x^3 - 2)/sqrt(x^3 - 1))","B",0
451,0,0,0,0.000000," ","integrate((a*x^2-b)/(a*x^2+c*x+b)/(a*x^3+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{\sqrt{a x^{3} + b x} {\left(a x^{2} + c x + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/(sqrt(a*x^3 + b*x)*(a*x^2 + c*x + b)), x)","F",0
452,0,0,0,0.000000," ","integrate((-1+x)/(x^4-4*x^3+6*x^2-x-2)^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x^{4} - 4 \, x^{3} + 6 \, x^{2} - x - 2}}\,{d x}"," ",0,"integrate((x - 1)/sqrt(x^4 - 4*x^3 + 6*x^2 - x - 2), x)","F",0
453,1,63,0,0.211518," ","integrate((x^6-1)^(1/2)/x^13,x, algorithm=""giac"")","\frac{1}{96} \, \pi + \frac{\sqrt{x^{6} - 1} - \frac{1}{\sqrt{x^{6} - 1}}}{24 \, {\left({\left(\sqrt{x^{6} - 1} - \frac{1}{\sqrt{x^{6} - 1}}\right)}^{2} + 4\right)}} + \frac{1}{48} \, \arctan\left(\frac{x^{6} - 2}{2 \, \sqrt{x^{6} - 1}}\right)"," ",0,"1/96*pi + 1/24*(sqrt(x^6 - 1) - 1/sqrt(x^6 - 1))/((sqrt(x^6 - 1) - 1/sqrt(x^6 - 1))^2 + 4) + 1/48*arctan(1/2*(x^6 - 2)/sqrt(x^6 - 1))","B",0
454,0,0,0,0.000000," ","integrate((2*x^4-2*x^2-1)/(x^4-3*x^2+2)/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 2 \, x^{2} - 1}{\sqrt{x^{6} + 1} {\left(x^{4} - 3 \, x^{2} + 2\right)}}\,{d x}"," ",0,"integrate((2*x^4 - 2*x^2 - 1)/(sqrt(x^6 + 1)*(x^4 - 3*x^2 + 2)), x)","F",0
455,0,0,0,0.000000," ","integrate((k*x-1)/(k*x+1)/((1-x)*x*(-k^2*x+1))^(1/2),x, algorithm=""giac"")","\int \frac{k x - 1}{\sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x} {\left(k x + 1\right)}}\,{d x}"," ",0,"integrate((k*x - 1)/(sqrt((k^2*x - 1)*(x - 1)*x)*(k*x + 1)), x)","F",0
456,0,0,0,0.000000," ","integrate((k*x+1)/(k*x-1)/((1-x)*x*(-k^2*x+1))^(1/2),x, algorithm=""giac"")","\int \frac{k x + 1}{\sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x} {\left(k x - 1\right)}}\,{d x}"," ",0,"integrate((k*x + 1)/(sqrt((k^2*x - 1)*(x - 1)*x)*(k*x - 1)), x)","F",0
457,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+1)^(1/2)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*(x^2 - 1)/((x^2 + 1)*x^2), x)","F",0
458,1,34,0,0.702610," ","integrate((x^3+1)/x^6/(x^3-1)/(x^4-x)^(1/4),x, algorithm=""giac"")","-\frac{4}{21} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} + \frac{4}{3} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}} + \frac{8}{3 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}}"," ",0,"-4/21*(-1/x^3 + 1)^(7/4) + 4/3*(-1/x^3 + 1)^(3/4) + 8/3/(-1/x^3 + 1)^(1/4)","A",0
459,1,42,0,0.321869," ","integrate((x^4-x)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} - x} x - \frac{1}{6} \, \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right) + \frac{1}{6} \, \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/3*sqrt(x^4 - x)*x - 1/6*log(sqrt(-1/x^3 + 1) + 1) + 1/6*log(abs(sqrt(-1/x^3 + 1) - 1))","A",0
460,1,59,0,0.316327," ","integrate(1/x^8/(x^4-x^2)^(1/4),x, algorithm=""giac"")","-\frac{2}{15} \, {\left(\frac{1}{x^{2}} - 1\right)}^{3} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}} - \frac{6}{11} \, {\left(\frac{1}{x^{2}} - 1\right)}^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}} + \frac{6}{7} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{7}{4}} - \frac{2}{3} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}"," ",0,"-2/15*(1/x^2 - 1)^3*(-1/x^2 + 1)^(3/4) - 6/11*(1/x^2 - 1)^2*(-1/x^2 + 1)^(3/4) + 6/7*(-1/x^2 + 1)^(7/4) - 2/3*(-1/x^2 + 1)^(3/4)","A",0
461,1,35,0,0.340595," ","integrate((-1+x)/(x^4-4*x^3+2*x^2+4*x-1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| -x^{2} + 2 \, x + \sqrt{{\left(x^{2} - 2 \, x\right)}^{2} - 2 \, x^{2} + 4 \, x - 1} + 1 \right|}\right)"," ",0,"-1/2*log(abs(-x^2 + 2*x + sqrt((x^2 - 2*x)^2 - 2*x^2 + 4*x - 1) + 1))","A",0
462,1,40,0,0.305779," ","integrate((x^4-x^3)^(1/4)/(-1+x)/x,x, algorithm=""giac"")","-2 \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-2*arctan((-1/x + 1)^(1/4)) - log((-1/x + 1)^(1/4) + 1) + log(abs((-1/x + 1)^(1/4) - 1))","A",0
463,0,0,0,0.000000," ","integrate((x^3-2)/x/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3} - 2}{\sqrt{x^{6} - 1} x}\,{d x}"," ",0,"integrate((x^3 - 2)/(sqrt(x^6 - 1)*x), x)","F",0
464,0,0,0,0.000000," ","integrate((x^3+1)/x/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3} + 1}{\sqrt{x^{6} - 1} x}\,{d x}"," ",0,"integrate((x^3 + 1)/(sqrt(x^6 - 1)*x), x)","F",0
465,0,0,0,0.000000," ","integrate((2*x^3-1)/x/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{3} - 1}{\sqrt{x^{6} - 1} x}\,{d x}"," ",0,"integrate((2*x^3 - 1)/(sqrt(x^6 - 1)*x), x)","F",0
466,0,0,0,0.000000," ","integrate((2*x^3+1)/x/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{3} + 1}{\sqrt{x^{6} - 1} x}\,{d x}"," ",0,"integrate((2*x^3 + 1)/(sqrt(x^6 - 1)*x), x)","F",0
467,0,0,0,0.000000," ","integrate((4*x^3+1)/x/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{4 \, x^{3} + 1}{\sqrt{x^{6} - 1} x}\,{d x}"," ",0,"integrate((4*x^3 + 1)/(sqrt(x^6 - 1)*x), x)","F",0
468,1,34,0,0.856856," ","integrate((x^6+1)/x^6/(x^3-1)/(x^4-x)^(1/4),x, algorithm=""giac"")","-\frac{4}{21} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} + \frac{8}{9} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{4}} + \frac{8}{3 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}}"," ",0,"-4/21*(-1/x^3 + 1)^(7/4) + 8/9*(-1/x^3 + 1)^(3/4) + 8/3/(-1/x^3 + 1)^(1/4)","A",0
469,0,0,0,0.000000," ","integrate(x*(5*a*x^3+8*b)/(a*x^3+b)^(1/4)/(x^8-a*x^3-b),x, algorithm=""giac"")","\int \frac{{\left(5 \, a x^{3} + 8 \, b\right)} x}{{\left(x^{8} - a x^{3} - b\right)} {\left(a x^{3} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((5*a*x^3 + 8*b)*x/((x^8 - a*x^3 - b)*(a*x^3 + b)^(1/4)), x)","F",0
470,0,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x + \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(x + sqrt(x^2 + 1)), x)","F",0
471,0,0,0,0.000000," ","integrate((a*b-x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a*b-(a+b+d)*x+x^2),x, algorithm=""giac"")","\int \frac{a b - x^{2}}{\sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(a b - {\left(a + b + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate((a*b - x^2)/(sqrt((a - x)*(b - x)*x)*(a*b - (a + b + d)*x + x^2)), x)","F",0
472,0,0,0,0.000000," ","integrate((a*b-x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a b - x^{2}}{{\left(a b d + d x^{2} - {\left(a d + b d + 1\right)} x\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate((a*b - x^2)/((a*b*d + d*x^2 - (a*d + b*d + 1)*x)*sqrt((a - x)*(b - x)*x)), x)","F",0
473,0,0,0,0.000000," ","integrate((k*x^2-1)/(k*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{k x^{2} - 1}{{\left(k x^{2} + 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((k*x^2 - 1)/((k*x^2 + 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
474,0,0,0,0.000000," ","integrate((k*x^2+1)/(k*x^2-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{k x^{2} + 1}{{\left(k x^{2} - 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((k*x^2 + 1)/((k*x^2 - 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
475,0,0,0,0.000000," ","integrate((k^2*x^2-2*k^2*x+1)/x/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x-1),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} - 2 \, k^{2} x + 1}{{\left(k^{2} x - 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x} x}\,{d x}"," ",0,"integrate((k^2*x^2 - 2*k^2*x + 1)/((k^2*x - 1)*sqrt((k^2*x - 1)*(x - 1)*x)*x), x)","F",0
476,1,35,0,0.324045," ","integrate(1/x^7/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{x^{3} - 1}}{12 \, x^{6}} + \frac{1}{4} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"1/12*(3*(x^3 - 1)^(3/2) + 5*sqrt(x^3 - 1))/x^6 + 1/4*arctan(sqrt(x^3 - 1))","A",0
477,1,50,0,0.308414," ","integrate(1/x^7/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{x^{3} + 1}}{12 \, x^{6}} - \frac{1}{8} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{8} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"1/12*(3*(x^3 + 1)^(3/2) - 5*sqrt(x^3 + 1))/x^6 - 1/8*log(sqrt(x^3 + 1) + 1) + 1/8*log(abs(sqrt(x^3 + 1) - 1))","A",0
478,1,78,0,0.332476," ","integrate((x^3+1)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{\sqrt{x^{3} + 1} + \frac{1}{\sqrt{x^{3} + 1}}}{12 \, {\left({\left(\sqrt{x^{3} + 1} + \frac{1}{\sqrt{x^{3} + 1}}\right)}^{2} - 4\right)}} + \frac{1}{48} \, \log\left(\sqrt{x^{3} + 1} + \frac{1}{\sqrt{x^{3} + 1}} + 2\right) - \frac{1}{48} \, \log\left({\left| \sqrt{x^{3} + 1} + \frac{1}{\sqrt{x^{3} + 1}} - 2 \right|}\right)"," ",0,"-1/12*(sqrt(x^3 + 1) + 1/sqrt(x^3 + 1))/((sqrt(x^3 + 1) + 1/sqrt(x^3 + 1))^2 - 4) + 1/48*log(sqrt(x^3 + 1) + 1/sqrt(x^3 + 1) + 2) - 1/48*log(abs(sqrt(x^3 + 1) + 1/sqrt(x^3 + 1) - 2))","B",0
479,1,35,0,0.310651," ","integrate((x^3+1)/x^7/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{7 \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + 9 \, \sqrt{x^{3} - 1}}{12 \, x^{6}} + \frac{7}{12} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"1/12*(7*(x^3 - 1)^(3/2) + 9*sqrt(x^3 - 1))/x^6 + 7/12*arctan(sqrt(x^3 - 1))","A",0
480,0,0,0,0.000000," ","integrate((x^3-1)^(1/2)*(x^3+2)/x^2/(2*x^3-4*x^2-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} \sqrt{x^{3} - 1}}{2 \, {\left(x^{3} - 2 \, x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate(1/2*(x^3 + 2)*sqrt(x^3 - 1)/((x^3 - 2*x^2 - 1)*x^2), x)","F",0
481,1,29,0,0.360763," ","integrate(x^5*(a*x^3+b)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(a x^{3} + b\right)}^{\frac{5}{2}} - 5 \, {\left(a x^{3} + b\right)}^{\frac{3}{2}} b\right)}}{45 \, a^{2}}"," ",0,"2/45*(3*(a*x^3 + b)^(5/2) - 5*(a*x^3 + b)^(3/2)*b)/a^2","A",0
482,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(1/3)*(x^4+x^3+1)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{3}} {\left(x^{4} - 3\right)}}{x^{8}}\,{d x}"," ",0,"integrate((x^4 + x^3 + 1)*(x^4 + 1)^(1/3)*(x^4 - 3)/x^8, x)","F",0
483,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(2/3)*(x^4+x^3+1)/x^9,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{x^{9}}\,{d x}"," ",0,"integrate((x^4 + x^3 + 1)*(x^4 + 1)^(2/3)*(x^4 - 3)/x^9, x)","F",0
484,0,0,0,0.000000," ","integrate((x^4-1)^(2/3)*(x^4+3)*(2*x^4-x^3-2)/x^9,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x^{3} - 2\right)} {\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((2*x^4 - x^3 - 2)*(x^4 + 3)*(x^4 - 1)^(2/3)/x^9, x)","F",0
485,0,0,0,0.000000," ","integrate((x^5-1)^(3/4)*(x^5+4)*(x^5-x^4-1)/x^12,x, algorithm=""giac"")","\int \frac{{\left(x^{5} - x^{4} - 1\right)} {\left(x^{5} + 4\right)} {\left(x^{5} - 1\right)}^{\frac{3}{4}}}{x^{12}}\,{d x}"," ",0,"integrate((x^5 - x^4 - 1)*(x^5 + 4)*(x^5 - 1)^(3/4)/x^12, x)","F",0
486,0,0,0,0.000000," ","integrate((x^5+1)^(2/3)*(x^5+x^3+1)*(2*x^5-3)/x^9,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 3\right)} {\left(x^{5} + x^{3} + 1\right)} {\left(x^{5} + 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((2*x^5 - 3)*(x^5 + x^3 + 1)*(x^5 + 1)^(2/3)/x^9, x)","F",0
487,0,0,0,0.000000," ","integrate((x^5-1)^(2/3)*(x^5+x^3-1)*(2*x^5+3)/x^9,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} + 3\right)} {\left(x^{5} + x^{3} - 1\right)} {\left(x^{5} - 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((2*x^5 + 3)*(x^5 + x^3 - 1)*(x^5 - 1)^(2/3)/x^9, x)","F",0
488,0,0,0,0.000000," ","integrate((x^5-4)*(x^5+1)^(3/4)*(2*x^5-x^4+2)/x^12,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - x^{4} + 2\right)} {\left(x^{5} + 1\right)}^{\frac{3}{4}} {\left(x^{5} - 4\right)}}{x^{12}}\,{d x}"," ",0,"integrate((2*x^5 - x^4 + 2)*(x^5 + 1)^(3/4)*(x^5 - 4)/x^12, x)","F",0
489,0,0,0,0.000000," ","integrate((x^5+1)^(2/3)*(2*x^5-3)*(4*x^5+3*x^3+4)/x^9,x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{5} + 3 \, x^{3} + 4\right)} {\left(2 \, x^{5} - 3\right)} {\left(x^{5} + 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((4*x^5 + 3*x^3 + 4)*(2*x^5 - 3)*(x^5 + 1)^(2/3)/x^9, x)","F",0
490,1,35,0,0.252030," ","integrate(1/x^13/(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x^{6} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{x^{6} - 1}}{24 \, x^{12}} + \frac{1}{8} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/24*(3*(x^6 - 1)^(3/2) + 5*sqrt(x^6 - 1))/x^12 + 1/8*arctan(sqrt(x^6 - 1))","A",0
491,1,49,0,0.317702," ","integrate((x^6-1)/x^13/(x^6+1)^(1/2),x, algorithm=""giac"")","-\frac{7 \, {\left(x^{6} + 1\right)}^{\frac{3}{2}} - 9 \, \sqrt{x^{6} + 1}}{24 \, x^{12}} + \frac{7}{48} \, \log\left(\sqrt{x^{6} + 1} + 1\right) - \frac{7}{48} \, \log\left(\sqrt{x^{6} + 1} - 1\right)"," ",0,"-1/24*(7*(x^6 + 1)^(3/2) - 9*sqrt(x^6 + 1))/x^12 + 7/48*log(sqrt(x^6 + 1) + 1) - 7/48*log(sqrt(x^6 + 1) - 1)","A",0
492,1,77,0,0.420928," ","integrate((x^6+1)^(1/2)/x^13,x, algorithm=""giac"")","-\frac{\sqrt{x^{6} + 1} + \frac{1}{\sqrt{x^{6} + 1}}}{24 \, {\left({\left(\sqrt{x^{6} + 1} + \frac{1}{\sqrt{x^{6} + 1}}\right)}^{2} - 4\right)}} + \frac{1}{96} \, \log\left(\sqrt{x^{6} + 1} + \frac{1}{\sqrt{x^{6} + 1}} + 2\right) - \frac{1}{96} \, \log\left(\sqrt{x^{6} + 1} + \frac{1}{\sqrt{x^{6} + 1}} - 2\right)"," ",0,"-1/24*(sqrt(x^6 + 1) + 1/sqrt(x^6 + 1))/((sqrt(x^6 + 1) + 1/sqrt(x^6 + 1))^2 - 4) + 1/96*log(sqrt(x^6 + 1) + 1/sqrt(x^6 + 1) + 2) - 1/96*log(sqrt(x^6 + 1) + 1/sqrt(x^6 + 1) - 2)","B",0
493,1,35,0,0.275866," ","integrate((x^6+1)/x^13/(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{7 \, {\left(x^{6} - 1\right)}^{\frac{3}{2}} + 9 \, \sqrt{x^{6} - 1}}{24 \, x^{12}} + \frac{7}{24} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/24*(7*(x^6 - 1)^(3/2) + 9*sqrt(x^6 - 1))/x^12 + 7/24*arctan(sqrt(x^6 - 1))","A",0
494,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(x^6+1)*(x^6+x^3-1)/x^8,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} - 1\right)} {\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{8}}\,{d x}"," ",0,"integrate((x^6 + x^3 - 1)*(x^6 + 1)*(x^6 - 1)^(1/3)/x^8, x)","F",0
495,0,0,0,0.000000," ","integrate((x^6-1)^(3/4)*(x^6+2)*(x^6-x^4-1)/x^12,x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} - 1\right)} {\left(x^{6} + 2\right)} {\left(x^{6} - 1\right)}^{\frac{3}{4}}}{x^{12}}\,{d x}"," ",0,"integrate((x^6 - x^4 - 1)*(x^6 + 2)*(x^6 - 1)^(3/4)/x^12, x)","F",0
496,0,0,0,0.000000," ","integrate((x^6-2)*(x^6+1)^(3/4)*(x^6-x^4+1)/x^12,x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} + 1\right)} {\left(x^{6} + 1\right)}^{\frac{3}{4}} {\left(x^{6} - 2\right)}}{x^{12}}\,{d x}"," ",0,"integrate((x^6 - x^4 + 1)*(x^6 + 1)^(3/4)*(x^6 - 2)/x^12, x)","F",0
497,1,38,0,0.689832," ","integrate((3*x^2-2*x)/(x^6-2*x^5+x^4+4*x^3-4*x^2+5)^(1/2),x, algorithm=""giac"")","-\log\left(-x^{3} + x^{2} + \sqrt{4 \, x^{3} + {\left(x^{3} - x^{2}\right)}^{2} - 4 \, x^{2} + 5} - 2\right)"," ",0,"-log(-x^3 + x^2 + sqrt(4*x^3 + (x^3 - x^2)^2 - 4*x^2 + 5) - 2)","A",0
498,1,29,0,0.360964," ","integrate((5*x^6-2)/x/(x^6-1)^(1/2)/(x^6+2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) - \frac{1}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(x^6 - 1)) - 1/3*arctan(sqrt(x^6 - 1))","A",0
499,1,29,0,0.306486," ","integrate((10*x^6-1)/x/(x^6-1)^(1/2)/(4*x^6-1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) + \frac{1}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/3*sqrt(3)*arctan(2/3*sqrt(3)*sqrt(x^6 - 1)) + 1/3*arctan(sqrt(x^6 - 1))","A",0
500,0,0,0,0.000000," ","integrate((x^2+x+2)/x^2/(x^2+1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2} + x + 2}{{\left(x^{2} + 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^2 + x + 2)/((x^2 + 1)^(3/4)*x^2), x)","F",0
501,0,0,0,0.000000," ","integrate((-3+2*x)/(x^2-x)^(1/4)/(x^3-x+1),x, algorithm=""giac"")","\int \frac{2 \, x - 3}{{\left(x^{3} - x + 1\right)} {\left(x^{2} - x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x - 3)/((x^3 - x + 1)*(x^2 - x)^(1/4)), x)","F",0
502,0,0,0,0.000000," ","integrate((x^2-1)*(x^3+x)^(1/2)/(x^2+1)/(x^2+x+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{3} + x} {\left(x^{2} - 1\right)}}{{\left(x^{2} + x + 1\right)}^{2} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^3 + x)*(x^2 - 1)/((x^2 + x + 1)^2*(x^2 + 1)), x)","F",0
503,0,0,0,0.000000," ","integrate((x^3-2)*(2*x^3+x^2+2)^(1/2)/(x^3+1)/(x^3+x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{3} + x^{2} + 2} {\left(x^{3} - 2\right)}}{{\left(x^{3} + x^{2} + 1\right)} {\left(x^{3} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(2*x^3 + x^2 + 2)*(x^3 - 2)/((x^3 + x^2 + 1)*(x^3 + 1)), x)","F",0
504,0,0,0,0.000000," ","integrate((a*x^2+b)/(a*x^2+c*x-b)/(a*x^3-b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{\sqrt{a x^{3} - b x} {\left(a x^{2} + c x - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/(sqrt(a*x^3 - b*x)*(a*x^2 + c*x - b)), x)","F",0
505,1,29,0,0.299139," ","integrate(x*(x^4-1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{4} - 1} x^{2} + \frac{1}{4} \, \log\left(x^{2} - \sqrt{x^{4} - 1}\right)"," ",0,"1/4*sqrt(x^4 - 1)*x^2 + 1/4*log(x^2 - sqrt(x^4 - 1))","A",0
506,1,41,0,0.258212," ","integrate((x^4-x)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{-\frac{1}{x^{3}} + 1} + \frac{1}{3} \, \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{3} \, \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"-2/3*sqrt(-1/x^3 + 1) + 1/3*log(sqrt(-1/x^3 + 1) + 1) - 1/3*log(abs(sqrt(-1/x^3 + 1) - 1))","A",0
507,1,43,0,0.341259," ","integrate(x^3*(x^4+x)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{x^{4} + x} {\left(2 \, x^{3} + 1\right)} x - \frac{1}{24} \, \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) + \frac{1}{24} \, \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/12*sqrt(x^4 + x)*(2*x^3 + 1)*x - 1/24*log(sqrt(1/x^3 + 1) + 1) + 1/24*log(abs(sqrt(1/x^3 + 1) - 1))","A",0
508,1,46,0,0.397443," ","integrate((1+x)/(x^4+4*x^3+13*x^2+18*x+16)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\sqrt{2} {\left(\sqrt{2} {\left(x^{2} + 2 \, x\right)} - 2 \, \sqrt{\frac{1}{2} \, {\left(x^{2} + 2 \, x\right)}^{2} + \frac{9}{2} \, x^{2} + 9 \, x + 8}\right)} + 9\right)"," ",0,"-1/2*log(sqrt(2)*(sqrt(2)*(x^2 + 2*x) - 2*sqrt(1/2*(x^2 + 2*x)^2 + 9/2*x^2 + 9*x + 8)) + 9)","A",0
509,0,0,0,0.000000," ","integrate((x^5-1)^(1/2)*(3*x^5+2)/x^2/(x^5-a*x^2-1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{5} + 2\right)} \sqrt{x^{5} - 1}}{{\left(x^{5} - a x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((3*x^5 + 2)*sqrt(x^5 - 1)/((x^5 - a*x^2 - 1)*x^2), x)","F",0
510,0,0,0,0.000000," ","integrate(x*(x^6-x)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{6} - x} x\,{d x}"," ",0,"integrate(sqrt(x^6 - x)*x, x)","F",0
511,0,0,0,0.000000," ","integrate((x^5+1)*(4*x^5-1)/x/(x^5-a*x+1)/(x^6+x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{5} - 1\right)} {\left(x^{5} + 1\right)}}{\sqrt{x^{6} + x} {\left(x^{5} - a x + 1\right)} x}\,{d x}"," ",0,"integrate((4*x^5 - 1)*(x^5 + 1)/(sqrt(x^6 + x)*(x^5 - a*x + 1)*x), x)","F",0
512,0,0,0,0.000000," ","integrate(1/(x-(x^2-1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x - \sqrt{x^{2} - 1}}}\,{d x}"," ",0,"integrate(1/sqrt(x - sqrt(x^2 - 1)), x)","F",0
513,0,0,0,0.000000," ","integrate((x^2+1)/(x^2+2*x-1)/(x^3-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{3} - x^{2} - x} {\left(x^{2} + 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(x^3 - x^2 - x)*(x^2 + 2*x - 1)), x)","F",0
514,0,0,0,0.000000," ","integrate((x^3+2)*(x^3+x^2-1)^(1/2)/(x^3-1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{3} + x^{2} - 1} {\left(x^{3} + 2\right)}}{{\left(x^{3} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^3 + x^2 - 1)*(x^3 + 2)/(x^3 - 1)^2, x)","F",0
515,0,0,0,0.000000," ","integrate((x^2+2)/(x^2-2)/(x^3+2*x^2-2*x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2}{\sqrt{x^{3} + 2 \, x^{2} - 2 \, x} {\left(x^{2} - 2\right)}}\,{d x}"," ",0,"integrate((x^2 + 2)/(sqrt(x^3 + 2*x^2 - 2*x)*(x^2 - 2)), x)","F",0
516,0,0,0,0.000000," ","integrate((2+x)/(-1+x)/(a*x^2+x^3+3*x-1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 2}{\sqrt{a x^{2} + x^{3} + 3 \, x - 1} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 2)/(sqrt(a*x^2 + x^3 + 3*x - 1)*(x - 1)), x)","F",0
517,0,0,0,0.000000," ","integrate((-2+x)/(1+x)/(a*x^2+x^3+3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x - 2}{\sqrt{a x^{2} + x^{3} + 3 \, x + 1} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x - 2)/(sqrt(a*x^2 + x^3 + 3*x + 1)*(x + 1)), x)","F",0
518,0,0,0,0.000000," ","integrate(x*(3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(-a*b*d+(a+b)*d*x-d*x^2+x^3),x, algorithm=""giac"")","\int -\frac{{\left(3 \, a b - 2 \, {\left(a + b\right)} x + x^{2}\right)} x}{{\left(a b d - {\left(a + b\right)} d x + d x^{2} - x^{3}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate(-(3*a*b - 2*(a + b)*x + x^2)*x/((a*b*d - (a + b)*d*x + d*x^2 - x^3)*sqrt((a - x)*(b - x)*x)), x)","F",0
519,0,0,0,0.000000," ","integrate((3*a*b*x-2*(a+b)*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a*b+(a+b)*x-x^2+d*x^3),x, algorithm=""giac"")","\int \frac{3 \, a b x - 2 \, {\left(a + b\right)} x^{2} + x^{3}}{{\left(d x^{3} - a b + {\left(a + b\right)} x - x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate((3*a*b*x - 2*(a + b)*x^2 + x^3)/((d*x^3 - a*b + (a + b)*x - x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
520,1,34,0,0.268843," ","integrate((x^2-1)*((x^2+1)^2)^(1/2)/(x^2+1)/(x^4+1),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{4} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"-1/4*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/4*sqrt(2)*log(x^2 - sqrt(2)*x + 1)","A",0
521,0,0,0,0.000000," ","integrate((-1+x)/(x^4-12*x^3+14*x^2+4*x-7)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
522,0,0,0,0.000000," ","integrate((k^2*x^4-2*k^2*x^2+1)/x^2/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^2-1),x, algorithm=""giac"")","\int \frac{k^{2} x^{4} - 2 \, k^{2} x^{2} + 1}{{\left(k^{2} x^{2} - 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}} x^{2}}\,{d x}"," ",0,"integrate((k^2*x^4 - 2*k^2*x^2 + 1)/((k^2*x^2 - 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))*x^2), x)","F",0
523,1,29,0,0.267822," ","integrate((x^6-2)/x/(x^6-1)^(1/2)/(x^6+2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) - \frac{1}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(x^6 - 1)) - 1/3*arctan(sqrt(x^6 - 1))","A",0
524,1,53,0,0.338321," ","integrate((x^3+2)*(x^6+x^3+1)/x/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(x^{3} + 1\right)}^{\frac{5}{2}} + \frac{2}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} + 1} - \frac{2}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{2}{3} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"2/15*(x^3 + 1)^(5/2) + 2/9*(x^3 + 1)^(3/2) + 2/3*sqrt(x^3 + 1) - 2/3*log(sqrt(x^3 + 1) + 1) + 2/3*log(abs(sqrt(x^3 + 1) - 1))","A",0
525,1,41,0,0.352535," ","integrate((3*x^2+4*x)/(x^6+4*x^5+4*x^4+2*x^3+4*x^2-5)^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x^{3} - 2 \, x^{2} + \sqrt{2 \, x^{3} + {\left(x^{3} + 2 \, x^{2}\right)}^{2} + 4 \, x^{2} - 5} - 1 \right|}\right)"," ",0,"-log(abs(-x^3 - 2*x^2 + sqrt(2*x^3 + (x^3 + 2*x^2)^2 + 4*x^2 - 5) - 1))","A",0
526,0,0,0,0.000000," ","integrate(x^2*(p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(b*x^6+a*(p*x^5+q)^3),x, algorithm=""giac"")","\int \frac{{\left(3 \, p x^{5} - 2 \, q\right)} \sqrt{p x^{5} + q} x^{2}}{b x^{6} + {\left(p x^{5} + q\right)}^{3} a}\,{d x}"," ",0,"integrate((3*p*x^5 - 2*q)*sqrt(p*x^5 + q)*x^2/(b*x^6 + (p*x^5 + q)^3*a), x)","F",0
527,1,53,0,0.298697," ","integrate(x^8/(a*x^3-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a x^{3} - b} b^{2}}{3 \, a^{3}} + \frac{2 \, {\left(3 \, {\left(a x^{3} - b\right)}^{\frac{5}{2}} + 10 \, {\left(a x^{3} - b\right)}^{\frac{3}{2}} b\right)}}{45 \, a^{3}}"," ",0,"2/3*sqrt(a*x^3 - b)*b^2/a^3 + 2/45*(3*(a*x^3 - b)^(5/2) + 10*(a*x^3 - b)^(3/2)*b)/a^3","A",0
528,1,33,0,0.337836," ","integrate(x^5*(a*x^3-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(a x^{3} - b\right)}^{\frac{5}{2}} + 5 \, {\left(a x^{3} - b\right)}^{\frac{3}{2}} b\right)}}{45 \, a^{2}}"," ",0,"2/45*(3*(a*x^3 - b)^(5/2) + 5*(a*x^3 - b)^(3/2)*b)/a^2","A",0
529,0,0,0,0.000000," ","integrate((a*x^3+2*b)/(a*x^3-b)^(1/2)/(2*a*x^3-3*x^2-2*b),x, algorithm=""giac"")","\int \frac{a x^{3} + 2 \, b}{{\left(2 \, a x^{3} - 3 \, x^{2} - 2 \, b\right)} \sqrt{a x^{3} - b}}\,{d x}"," ",0,"integrate((a*x^3 + 2*b)/((2*a*x^3 - 3*x^2 - 2*b)*sqrt(a*x^3 - b)), x)","F",0
530,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+1)^(1/2)*(x^4+x^2+1)/x^4/(x^4-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} + 1\right)} \sqrt{x^{4} + 1} {\left(x^{4} - 1\right)}}{{\left(x^{4} - x^{2} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)*sqrt(x^4 + 1)*(x^4 - 1)/((x^4 - x^2 + 1)*x^4), x)","F",0
531,-1,0,0,0.000000," ","integrate((2*a*x^2+3*b*x+4*c)/(a*x^2+b*x+c)^(1/4)/(x^4-a*x^2-b*x-c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,1,56,0,0.395709," ","integrate((x^3+2)*(x^6+x^3+1)/x^4/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{x^{3} + 1} - \frac{2 \, \sqrt{x^{3} + 1}}{3 \, x^{3}} - \frac{2}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{2}{3} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"2/9*(x^3 + 1)^(3/2) + 4/3*sqrt(x^3 + 1) - 2/3*sqrt(x^3 + 1)/x^3 - 2/3*log(sqrt(x^3 + 1) + 1) + 2/3*log(abs(sqrt(x^3 + 1) - 1))","A",0
533,1,44,0,0.640882," ","integrate((x^3-1)^(1/2)*(2*x^6+x^3-2)/x^10,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, {\left(x^{3} - 1\right)}^{\frac{5}{2}} + 7 \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + 3 \, \sqrt{x^{3} - 1}\right)}}{9 \, x^{9}} + \frac{2}{3} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"-2/9*(3*(x^3 - 1)^(5/2) + 7*(x^3 - 1)^(3/2) + 3*sqrt(x^3 - 1))/x^9 + 2/3*arctan(sqrt(x^3 - 1))","A",0
534,1,29,0,0.323632," ","integrate((13*x^6-4)/x/(x^6-1)^(1/2)/(4*x^6-1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) + \frac{4}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"-1/6*sqrt(3)*arctan(2/3*sqrt(3)*sqrt(x^6 - 1)) + 4/3*arctan(sqrt(x^6 - 1))","A",0
535,0,0,0,0.000000," ","integrate((2*a*x^3-b)/(a*x^3+b-x)/(a*x^6+b*x^3)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{3} - b}{{\left(a x^{6} + b x^{3}\right)}^{\frac{1}{4}} {\left(a x^{3} + b - x\right)}}\,{d x}"," ",0,"integrate((2*a*x^3 - b)/((a*x^6 + b*x^3)^(1/4)*(a*x^3 + b - x)), x)","F",0
536,0,0,0,0.000000," ","integrate(x^3*(2*a*x^5+b)/(a*x^6+b*x)^(1/4)/(a*x^10+b*x^5-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, a x^{5} + b\right)} x^{3}}{{\left(a x^{10} + b x^{5} - 1\right)} {\left(a x^{6} + b x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^5 + b)*x^3/((a*x^10 + b*x^5 - 1)*(a*x^6 + b*x)^(1/4)), x)","F",0
537,1,45,0,0.331868," ","integrate((x^3+1)^(1/4)/x,x, algorithm=""giac"")","\frac{4}{3} \, {\left(x^{3} + 1\right)}^{\frac{1}{4}} - \frac{2}{3} \, \arctan\left({\left(x^{3} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{3} \, \log\left({\left(x^{3} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"4/3*(x^3 + 1)^(1/4) - 2/3*arctan((x^3 + 1)^(1/4)) - 1/3*log((x^3 + 1)^(1/4) + 1) + 1/3*log(abs((x^3 + 1)^(1/4) - 1))","A",0
538,-1,0,0,0.000000," ","integrate((a*p*x^3+3*b*p*x^2-2*a*q)/(p*x^3+q)^(1/2)/(a^2*c*x^2+d*p*x^3+2*a*b*c*x+b^2*c+d*q),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,0,0,0,0.000000," ","integrate((x^3-1)*(x^6-1)^(1/2)/x^7/(x^3+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} - 1\right)}}{{\left(x^{3} + 1\right)} x^{7}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 - 1)/((x^3 + 1)*x^7), x)","F",0
540,0,0,0,0.000000," ","integrate((x^3+1)*(x^6-1)^(1/2)/x^7/(x^3-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} + 1\right)}}{{\left(x^{3} - 1\right)} x^{7}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 + 1)/((x^3 - 1)*x^7), x)","F",0
541,1,44,0,1.930821," ","integrate((x^6+1)^(1/4)/x,x, algorithm=""giac"")","\frac{2}{3} \, {\left(x^{6} + 1\right)}^{\frac{1}{4}} - \frac{1}{3} \, \arctan\left({\left(x^{6} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{6} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{6} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/3*(x^6 + 1)^(1/4) - 1/3*arctan((x^6 + 1)^(1/4)) - 1/6*log((x^6 + 1)^(1/4) + 1) + 1/6*log((x^6 + 1)^(1/4) - 1)","A",0
542,0,0,0,0.000000," ","integrate((x^12+1)/x^4/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{12} + 1}{\sqrt{x^{6} - 1} x^{4}}\,{d x}"," ",0,"integrate((x^12 + 1)/(sqrt(x^6 - 1)*x^4), x)","F",0
543,1,59,0,0.301923," ","integrate(1/x^10/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{15 \, {\left(x^{3} + 1\right)}^{\frac{5}{2}} - 40 \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{x^{3} + 1}}{72 \, x^{9}} + \frac{5}{48} \, \log\left(\sqrt{x^{3} + 1} + 1\right) - \frac{5}{48} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/72*(15*(x^3 + 1)^(5/2) - 40*(x^3 + 1)^(3/2) + 33*sqrt(x^3 + 1))/x^9 + 5/48*log(sqrt(x^3 + 1) + 1) - 5/48*log(abs(sqrt(x^3 + 1) - 1))","A",0
544,1,55,0,0.454505," ","integrate((x^3-1)/x^6/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{17} \, {\left(\frac{1}{x} + 1\right)}^{\frac{17}{3}} - \frac{15}{14} \, {\left(\frac{1}{x} + 1\right)}^{\frac{14}{3}} + \frac{30}{11} \, {\left(\frac{1}{x} + 1\right)}^{\frac{11}{3}} - \frac{33}{8} \, {\left(\frac{1}{x} + 1\right)}^{\frac{8}{3}} + \frac{21}{5} \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{3}} - 3 \, {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"3/17*(1/x + 1)^(17/3) - 15/14*(1/x + 1)^(14/3) + 30/11*(1/x + 1)^(11/3) - 33/8*(1/x + 1)^(8/3) + 21/5*(1/x + 1)^(5/3) - 3*(1/x + 1)^(2/3)","A",0
545,0,0,0,0.000000," ","integrate((x^3-2)*(x^3+1)^(1/2)*(2*x^3+x^2+2)/x^4/(x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + x^{2} + 2\right)} \sqrt{x^{3} + 1} {\left(x^{3} - 2\right)}}{{\left(x^{3} + x^{2} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((2*x^3 + x^2 + 2)*sqrt(x^3 + 1)*(x^3 - 2)/((x^3 + x^2 + 1)*x^4), x)","F",0
546,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+x^2+1)^(1/2)/(x^4+1)/(x^4-x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{2} + 1} {\left(x^{4} - 1\right)}}{{\left(x^{4} - x^{2} + 1\right)} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)*(x^4 - 1)/((x^4 - x^2 + 1)*(x^4 + 1)), x)","F",0
547,0,0,0,0.000000," ","integrate((x^4+x^2+x+1)^(1/2)*(2*x^4-x-2)/(x^4+x+1)^2,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x - 2\right)} \sqrt{x^{4} + x^{2} + x + 1}}{{\left(x^{4} + x + 1\right)}^{2}}\,{d x}"," ",0,"integrate((2*x^4 - x - 2)*sqrt(x^4 + x^2 + x + 1)/(x^4 + x + 1)^2, x)","F",0
548,0,0,0,0.000000," ","integrate((x^4-1)*(3*x^4+1)/x/(x^4-a*x-1)/(x^5-x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{4} + 1\right)} {\left(x^{4} - 1\right)}}{\sqrt{x^{5} - x} {\left(x^{4} - a x - 1\right)} x}\,{d x}"," ",0,"integrate((3*x^4 + 1)*(x^4 - 1)/(sqrt(x^5 - x)*(x^4 - a*x - 1)*x), x)","F",0
549,1,44,0,0.360296," ","integrate(1/x^19/(x^6-1)^(1/2),x, algorithm=""giac"")","\frac{15 \, {\left(x^{6} - 1\right)}^{\frac{5}{2}} + 40 \, {\left(x^{6} - 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{x^{6} - 1}}{144 \, x^{18}} + \frac{5}{48} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/144*(15*(x^6 - 1)^(5/2) + 40*(x^6 - 1)^(3/2) + 33*sqrt(x^6 - 1))/x^18 + 5/48*arctan(sqrt(x^6 - 1))","A",0
550,0,0,0,0.000000," ","integrate(x^14/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{14}}{\sqrt{x^{6} - 1}}\,{d x}"," ",0,"integrate(x^14/sqrt(x^6 - 1), x)","F",0
551,1,44,0,0.344640," ","integrate((x^6-1)^(1/2)/x^19,x, algorithm=""giac"")","\frac{3 \, {\left(x^{6} - 1\right)}^{\frac{5}{2}} + 8 \, {\left(x^{6} - 1\right)}^{\frac{3}{2}} - 3 \, \sqrt{x^{6} - 1}}{144 \, x^{18}} + \frac{1}{48} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/144*(3*(x^6 - 1)^(5/2) + 8*(x^6 - 1)^(3/2) - 3*sqrt(x^6 - 1))/x^18 + 1/48*arctan(sqrt(x^6 - 1))","A",0
552,0,0,0,0.000000," ","integrate(x^8*(x^6-1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{6} - 1} x^{8}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*x^8, x)","F",0
553,0,0,0,0.000000," ","integrate((x^6-1)/(x^4+1)^(1/2)/(x^6+1),x, algorithm=""giac"")","\int \frac{x^{6} - 1}{{\left(x^{6} + 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^6 - 1)/((x^6 + 1)*sqrt(x^4 + 1)), x)","F",0
554,0,0,0,0.000000," ","integrate(x^14/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{14}}{\sqrt{x^{6} + 1}}\,{d x}"," ",0,"integrate(x^14/sqrt(x^6 + 1), x)","F",0
555,1,58,0,0.321521," ","integrate((x^6-1)/x^19/(x^6+1)^(1/2),x, algorithm=""giac"")","\frac{33 \, {\left(x^{6} + 1\right)}^{\frac{5}{2}} - 88 \, {\left(x^{6} + 1\right)}^{\frac{3}{2}} + 63 \, \sqrt{x^{6} + 1}}{144 \, x^{18}} - \frac{11}{96} \, \log\left(\sqrt{x^{6} + 1} + 1\right) + \frac{11}{96} \, \log\left(\sqrt{x^{6} + 1} - 1\right)"," ",0,"1/144*(33*(x^6 + 1)^(5/2) - 88*(x^6 + 1)^(3/2) + 63*sqrt(x^6 + 1))/x^18 - 11/96*log(sqrt(x^6 + 1) + 1) + 11/96*log(sqrt(x^6 + 1) - 1)","A",0
556,0,0,0,0.000000," ","integrate((x^6+1)/(x^4+1)^(1/2)/(-x^6+1),x, algorithm=""giac"")","\int -\frac{x^{6} + 1}{{\left(x^{6} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(-(x^6 + 1)/((x^6 - 1)*sqrt(x^4 + 1)), x)","F",0
557,0,0,0,0.000000," ","integrate((x^6+1)/(x^4+1)^(1/2)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{6} + 1}{{\left(x^{6} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^6 + 1)/((x^6 - 1)*sqrt(x^4 + 1)), x)","F",0
558,0,0,0,0.000000," ","integrate((x^5-1)*(4*x^5+1)/x/(x^5-a*x-1)/(x^6-x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{5} + 1\right)} {\left(x^{5} - 1\right)}}{\sqrt{x^{6} - x} {\left(x^{5} - a x - 1\right)} x}\,{d x}"," ",0,"integrate((4*x^5 + 1)*(x^5 - 1)/(sqrt(x^6 - x)*(x^5 - a*x - 1)*x), x)","F",0
559,1,59,0,0.339723," ","integrate((x^3+2)*(x^6+x^3+1)/x^7/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} + 1} - \frac{3 \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} - \sqrt{x^{3} + 1}}{6 \, x^{6}} - \frac{3}{4} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{3}{4} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"2/3*sqrt(x^3 + 1) - 1/6*(3*(x^3 + 1)^(3/2) - sqrt(x^3 + 1))/x^6 - 3/4*log(sqrt(x^3 + 1) + 1) + 3/4*log(abs(sqrt(x^3 + 1) - 1))","A",0
560,-1,0,0,0.000000," ","integrate((4*x^6-x)/(x^5+1)/(a*x^5+a-x)/(x^6+x)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,0,0,0,0.000000," ","integrate((x^6+x^3+2)/x/(x^6+1)^(1/4)/(x^9-4*x^6+5*x^3-4),x, algorithm=""giac"")","\int \frac{x^{6} + x^{3} + 2}{{\left(x^{9} - 4 \, x^{6} + 5 \, x^{3} - 4\right)} {\left(x^{6} + 1\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((x^6 + x^3 + 2)/((x^9 - 4*x^6 + 5*x^3 - 4)*(x^6 + 1)^(1/4)*x), x)","F",0
562,0,0,0,0.000000," ","integrate((1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/5),x, algorithm=""giac"")","\int {\left(1024 \, x^{10} - 16640 \, x^{9} + 112000 \, x^{8} - 401440 \, x^{7} + 820340 \, x^{6} - 954733 \, x^{5} + 615255 \, x^{4} - 225810 \, x^{3} + 47250 \, x^{2} - 5265 \, x + 243\right)}^{\frac{1}{5}}\,{d x}"," ",0,"integrate((1024*x^10 - 16640*x^9 + 112000*x^8 - 401440*x^7 + 820340*x^6 - 954733*x^5 + 615255*x^4 - 225810*x^3 + 47250*x^2 - 5265*x + 243)^(1/5), x)","F",0
563,0,0,0,0.000000," ","integrate((2*a*x^8-b*x^3)/(a*x^6-b*x)^(1/4)/(a*x^10-b*x^5-1),x, algorithm=""giac"")","\int \frac{2 \, a x^{8} - b x^{3}}{{\left(a x^{10} - b x^{5} - 1\right)} {\left(a x^{6} - b x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^8 - b*x^3)/((a*x^10 - b*x^5 - 1)*(a*x^6 - b*x)^(1/4)), x)","F",0
564,0,0,0,0.000000," ","integrate(x^5*(10*a*x^3-7*b)/(a*x^6-b*x^3)^(1/4)/(a*x^10-b*x^7-1),x, algorithm=""giac"")","\int \frac{{\left(10 \, a x^{3} - 7 \, b\right)} x^{5}}{{\left(a x^{10} - b x^{7} - 1\right)} {\left(a x^{6} - b x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((10*a*x^3 - 7*b)*x^5/((a*x^10 - b*x^7 - 1)*(a*x^6 - b*x^3)^(1/4)), x)","F",0
565,0,0,0,0.000000," ","integrate(1/x/(-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x} \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} x}\,{d x}"," ",0,"integrate(1/(sqrt(a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)*sqrt(a^2*x^2/b^2 - a/b^2)*x), x)","F",0
566,0,0,0,0.000000," ","integrate((a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a*d-(b+d)*x+x^2),x, algorithm=""giac"")","\int \frac{a b - 2 \, a x + x^{2}}{\sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(a d - {\left(b + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate((a*b - 2*a*x + x^2)/(sqrt((a - x)*(b - x)*x)*(a*d - (b + d)*x + x^2)), x)","F",0
567,0,0,0,0.000000," ","integrate((a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a-(b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a b - 2 \, a x + x^{2}}{\sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(d x^{2} - {\left(b d + 1\right)} x + a\right)}}\,{d x}"," ",0,"integrate((a*b - 2*a*x + x^2)/(sqrt((a - x)*(b - x)*x)*(d*x^2 - (b*d + 1)*x + a)), x)","F",0
568,0,0,0,0.000000," ","integrate((x^3-2)*(x^3-x^2+1)^(1/2)/(x^3+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{3} - x^{2} + 1} {\left(x^{3} - 2\right)}}{{\left(x^{3} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^3 - x^2 + 1)*(x^3 - 2)/(x^3 + 1)^2, x)","F",0
569,0,0,0,0.000000," ","integrate((a^2*b-a*(2*a-b)*x-(-a+2*b)*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^3+(3*a^2+b*d)*x-(3*a+d)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{a^{2} b - {\left(2 \, a - b\right)} a x + {\left(a - 2 \, b\right)} x^{2} + x^{3}}{{\left(a^{3} + {\left(3 \, a + d\right)} x^{2} - x^{3} - {\left(3 \, a^{2} + b d\right)} x\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate(-(a^2*b - (2*a - b)*a*x + (a - 2*b)*x^2 + x^3)/((a^3 + (3*a + d)*x^2 - x^3 - (3*a^2 + b*d)*x)*sqrt((a - x)*(b - x)*x)), x)","F",0
570,0,0,0,0.000000," ","integrate((a^2*b-a*(2*a-b)*x-(-a+2*b)*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^3*d+(3*a^2*d+b)*x-(3*a*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int -\frac{a^{2} b - {\left(2 \, a - b\right)} a x + {\left(a - 2 \, b\right)} x^{2} + x^{3}}{{\left(a^{3} d - d x^{3} + {\left(3 \, a d + 1\right)} x^{2} - {\left(3 \, a^{2} d + b\right)} x\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate(-(a^2*b - (2*a - b)*a*x + (a - 2*b)*x^2 + x^3)/((a^3*d - d*x^3 + (3*a*d + 1)*x^2 - (3*a^2*d + b)*x)*sqrt((a - x)*(b - x)*x)), x)","F",0
571,0,0,0,0.000000," ","integrate((2*x^2-3*x)/(x^3+2*x-2)/(3*x^4+2*x^2-2*x)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - 3 \, x}{\sqrt{3 \, x^{4} + 2 \, x^{2} - 2 \, x} {\left(x^{3} + 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((2*x^2 - 3*x)/(sqrt(3*x^4 + 2*x^2 - 2*x)*(x^3 + 2*x - 2)), x)","F",0
572,-1,0,0,0.000000," ","integrate((a*p*x^4-3*b*p*x^2+4*a*q*x)/(p*x^3+q)^(1/2)/(a^2*c*x^4+2*a*b*c*x^2+d*p*x^3+b^2*c+d*q),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,1,59,0,0.417600," ","integrate((x^12+1)/x^10/(x^6-1)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(-\frac{1}{x^{6}} + 1\right)}^{\frac{3}{2}} - 6 \, \sqrt{-\frac{1}{x^{6}} + 1} - 3 \, \log\left(\sqrt{-\frac{1}{x^{6}} + 1} + 1\right) + 3 \, \log\left(-\sqrt{-\frac{1}{x^{6}} + 1} + 1\right)}{18 \, \mathrm{sgn}\left(x\right)}"," ",0,"-1/18*(2*(-1/x^6 + 1)^(3/2) - 6*sqrt(-1/x^6 + 1) - 3*log(sqrt(-1/x^6 + 1) + 1) + 3*log(-sqrt(-1/x^6 + 1) + 1))/sgn(x)","A",0
574,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^20+5*x^16+10*x^12+10*x^8+5*x^4+1)^(1/10),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{20} + 5 \, x^{16} + 10 \, x^{12} + 10 \, x^{8} + 5 \, x^{4} + 1\right)}^{\frac{1}{10}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^20 + 5*x^16 + 10*x^12 + 10*x^8 + 5*x^4 + 1)^(1/10)*(x^2 + 1)), x)","F",0
575,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2),x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{a x^{2} + b^{2}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2), x)","F",0
576,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/sqrt(x^4 + 1), x)","F",0
577,1,47,0,0.344646," ","integrate(1/x^3/(x^2+1)^(3/4),x, algorithm=""giac"")","-\frac{{\left(x^{2} + 1\right)}^{\frac{1}{4}}}{2 \, x^{2}} + \frac{3}{4} \, \arctan\left({\left(x^{2} + 1\right)}^{\frac{1}{4}}\right) + \frac{3}{8} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{3}{8} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"-1/2*(x^2 + 1)^(1/4)/x^2 + 3/4*arctan((x^2 + 1)^(1/4)) + 3/8*log((x^2 + 1)^(1/4) + 1) - 3/8*log((x^2 + 1)^(1/4) - 1)","A",0
578,1,48,0,0.167839," ","integrate(1/x^4/(x^3+1)^(1/4),x, algorithm=""giac"")","-\frac{{\left(x^{3} + 1\right)}^{\frac{3}{4}}}{3 \, x^{3}} - \frac{1}{6} \, \arctan\left({\left(x^{3} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{12} \, \log\left({\left(x^{3} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{12} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/3*(x^3 + 1)^(3/4)/x^3 - 1/6*arctan((x^3 + 1)^(1/4)) + 1/12*log((x^3 + 1)^(1/4) + 1) - 1/12*log(abs((x^3 + 1)^(1/4) - 1))","A",0
579,1,48,0,0.222593," ","integrate((x^3+1)^(1/4)/x^4,x, algorithm=""giac"")","-\frac{{\left(x^{3} + 1\right)}^{\frac{1}{4}}}{3 \, x^{3}} - \frac{1}{6} \, \arctan\left({\left(x^{3} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{12} \, \log\left({\left(x^{3} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{12} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/3*(x^3 + 1)^(1/4)/x^3 - 1/6*arctan((x^3 + 1)^(1/4)) - 1/12*log((x^3 + 1)^(1/4) + 1) + 1/12*log(abs((x^3 + 1)^(1/4) - 1))","A",0
580,1,49,0,0.196694," ","integrate(x^3*(x^4-x)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{x^{4} - x} {\left(2 \, x^{3} - 1\right)} x - \frac{1}{24} \, \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right) + \frac{1}{24} \, \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/12*sqrt(x^4 - x)*(2*x^3 - 1)*x - 1/24*log(sqrt(-1/x^3 + 1) + 1) + 1/24*log(abs(sqrt(-1/x^3 + 1) - 1))","A",0
581,0,0,0,0.000000," ","integrate((x^4+1)*(3*x^4-1)/x/(x^4-a*x+1)/(x^5+x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{4} - 1\right)} {\left(x^{4} + 1\right)}}{\sqrt{x^{5} + x} {\left(x^{4} - a x + 1\right)} x}\,{d x}"," ",0,"integrate((3*x^4 - 1)*(x^4 + 1)/(sqrt(x^5 + x)*(x^4 - a*x + 1)*x), x)","F",0
582,0,0,0,0.000000," ","integrate((x^5+x^2+1)^(1/2)*(3*x^5-2)/(x^5+1)/(x^5-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{5} - 2\right)} \sqrt{x^{5} + x^{2} + 1}}{{\left(x^{5} - x^{2} + 1\right)} {\left(x^{5} + 1\right)}}\,{d x}"," ",0,"integrate((3*x^5 - 2)*sqrt(x^5 + x^2 + 1)/((x^5 - x^2 + 1)*(x^5 + 1)), x)","F",0
583,1,47,0,0.208647," ","integrate((x^6+1)^(1/4)/x^7,x, algorithm=""giac"")","-\frac{{\left(x^{6} + 1\right)}^{\frac{1}{4}}}{6 \, x^{6}} - \frac{1}{12} \, \arctan\left({\left(x^{6} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{24} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{24} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"-1/6*(x^6 + 1)^(1/4)/x^6 - 1/12*arctan((x^6 + 1)^(1/4)) - 1/24*log((x^6 + 1)^(1/4) + 1) + 1/24*log((x^6 + 1)^(1/4) - 1)","A",0
584,0,0,0,0.000000," ","integrate((-1+x)^2*(5*x^3+5*x^2-8*x-10)/((1+x)/(x^2-2))^(3/4)/(x^2-2)/(x^6-4*x^5+4*x^4+4*x^3-11*x^2+7*x-3),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{3} + 5 \, x^{2} - 8 \, x - 10\right)} {\left(x - 1\right)}^{2}}{{\left(x^{6} - 4 \, x^{5} + 4 \, x^{4} + 4 \, x^{3} - 11 \, x^{2} + 7 \, x - 3\right)} {\left(x^{2} - 2\right)} \left(\frac{x + 1}{x^{2} - 2}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((5*x^3 + 5*x^2 - 8*x - 10)*(x - 1)^2/((x^6 - 4*x^5 + 4*x^4 + 4*x^3 - 11*x^2 + 7*x - 3)*(x^2 - 2)*((x + 1)/(x^2 - 2))^(3/4)), x)","F",0
585,0,0,0,0.000000," ","integrate(x^2*(9*a*x+10*b)/(a*x^3+b*x^2)^(1/4)/(x^10-a*x-b),x, algorithm=""giac"")","\int \frac{{\left(9 \, a x + 10 \, b\right)} x^{2}}{{\left(x^{10} - a x - b\right)} {\left(a x^{3} + b x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((9*a*x + 10*b)*x^2/((x^10 - a*x - b)*(a*x^3 + b*x^2)^(1/4)), x)","F",0
586,0,0,0,0.000000," ","integrate((x^16-1)/(x^4+1)^(1/2)/(x^16+1),x, algorithm=""giac"")","\int \frac{x^{16} - 1}{{\left(x^{16} + 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^16 - 1)/((x^16 + 1)*sqrt(x^4 + 1)), x)","F",0
587,0,0,0,0.000000," ","integrate((x^16-1)/(x^4-1)^(1/2)/(x^16-x^8+1),x, algorithm=""giac"")","\int \frac{x^{16} - 1}{{\left(x^{16} - x^{8} + 1\right)} \sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate((x^16 - 1)/((x^16 - x^8 + 1)*sqrt(x^4 - 1)), x)","F",0
588,0,0,0,0.000000," ","integrate((x^2+x*(x^2-1)^(1/2))^(1/2)/x/(x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{2} - 1} x}}{\sqrt{x^{2} - 1} x}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^2 - 1)*x)/(sqrt(x^2 - 1)*x), x)","F",0
589,1,50,0,0.202505," ","integrate(x^6*(x^4+x)^(1/2),x, algorithm=""giac"")","\frac{1}{72} \, {\left(2 \, {\left(4 \, x^{3} + 1\right)} x^{3} - 3\right)} \sqrt{x^{4} + x} x + \frac{1}{48} \, \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{48} \, \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/72*(2*(4*x^3 + 1)*x^3 - 3)*sqrt(x^4 + x)*x + 1/48*log(sqrt(1/x^3 + 1) + 1) - 1/48*log(abs(sqrt(1/x^3 + 1) - 1))","A",0
590,0,0,0,0.000000," ","integrate((-1+x)*(1+x)^3/(x^2+1)^2/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x + 1\right)}^{3} {\left(x - 1\right)}}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((x + 1)^3*(x - 1)/(sqrt(x^4 + x^2 + 1)*(x^2 + 1)^2), x)","F",0
591,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^4-x^3-x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{4} - x^{3} - x^{2} - x + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^4 - x^3 - x^2 - x + 1)*(x^2 + 1)), x)","F",0
592,1,46,0,0.225404," ","integrate((3*x^2-2*x-1)/(x^6-2*x^5-x^4+4*x^3-x^2-2*x-3)^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x^{3} + x^{2} + x + \sqrt{2 \, x^{3} + {\left(x^{3} - x^{2} - x\right)}^{2} - 2 \, x^{2} - 2 \, x - 3} - 1 \right|}\right)"," ",0,"-log(abs(-x^3 + x^2 + x + sqrt(2*x^3 + (x^3 - x^2 - x)^2 - 2*x^2 - 2*x - 3) - 1))","A",0
593,1,42,0,0.166632," ","integrate((x^2-x)/(x^6-2*x^5+x^4-2*x^3+4*x^2-2*x)^(1/2),x, algorithm=""giac"")","\frac{\log\left(\sqrt{-\frac{2}{x^{3}} + 1} + 1\right) - \log\left({\left| \sqrt{-\frac{2}{x^{3}} + 1} - 1 \right|}\right)}{3 \, \mathrm{sgn}\left(\frac{1}{x^{3}} - \frac{1}{x^{4}}\right)}"," ",0,"1/3*(log(sqrt(-2/x^3 + 1) + 1) - log(abs(sqrt(-2/x^3 + 1) - 1)))/sgn(1/x^3 - 1/x^4)","A",0
594,1,59,0,0.208280," ","integrate((x^4-1)^(1/4)/x^2,x, algorithm=""giac"")","\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} - \frac{1}{2} \, \arctan\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) - \frac{1}{4} \, \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right) + \frac{1}{4} \, \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right)"," ",0,"(x^4 - 1)^(1/4)/x - 1/2*arctan((x^4 - 1)^(1/4)/x) - 1/4*log((x^4 - 1)^(1/4)/x + 1) + 1/4*log(-(x^4 - 1)^(1/4)/x + 1)","A",0
595,1,53,0,0.291693," ","integrate((x^4-1)*(x^4+1)^(1/4)/x,x, algorithm=""giac"")","\frac{1}{5} \, {\left(x^{4} + 1\right)}^{\frac{5}{4}} - {\left(x^{4} + 1\right)}^{\frac{1}{4}} + \frac{1}{2} \, \arctan\left({\left(x^{4} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{4} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/5*(x^4 + 1)^(5/4) - (x^4 + 1)^(1/4) + 1/2*arctan((x^4 + 1)^(1/4)) + 1/4*log((x^4 + 1)^(1/4) + 1) - 1/4*log((x^4 + 1)^(1/4) - 1)","A",0
596,1,61,0,0.478030," ","integrate(1/(x^4+4*x+3)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{6} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{6} + 2 \, \sqrt{x^{2} - 2 \, x + 3} - 2 \right|}}{{\left| -2 \, x + 2 \, \sqrt{6} + 2 \, \sqrt{x^{2} - 2 \, x + 3} - 2 \right|}}\right)}{6 \, \mathrm{sgn}\left(x + 1\right)}"," ",0,"1/6*sqrt(6)*log(abs(-2*x - 2*sqrt(6) + 2*sqrt(x^2 - 2*x + 3) - 2)/abs(-2*x + 2*sqrt(6) + 2*sqrt(x^2 - 2*x + 3) - 2))/sgn(x + 1)","A",0
597,0,0,0,0.000000," ","integrate((x^4+1)*(x^4+2*x^2-1)^(1/2)/(x^4-1)/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 2 \, x^{2} - 1} {\left(x^{4} + 1\right)}}{{\left(x^{4} + x^{2} - 1\right)} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 2*x^2 - 1)*(x^4 + 1)/((x^4 + x^2 - 1)*(x^4 - 1)), x)","F",0
598,0,0,0,0.000000," ","integrate((x^4-x^2+x-1)^(1/2)*(2*x^4-x+2)/(x^4+x-1)^2,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x + 2\right)} \sqrt{x^{4} - x^{2} + x - 1}}{{\left(x^{4} + x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((2*x^4 - x + 2)*sqrt(x^4 - x^2 + x - 1)/(x^4 + x - 1)^2, x)","F",0
599,0,0,0,0.000000," ","integrate((3*x^5+x)/(x^4-1)/(a*x^4-a-x)/(x^5-x)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{5} + x}{{\left(a x^{4} - a - x\right)} \sqrt{x^{5} - x} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((3*x^5 + x)/((a*x^4 - a - x)*sqrt(x^5 - x)*(x^4 - 1)), x)","F",0
600,0,0,0,0.000000," ","integrate((x^6+x^2+1)^(1/2)*(2*x^6-1)/(x^6+1)/(2*x^6-x^2+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 1\right)} \sqrt{x^{6} + x^{2} + 1}}{{\left(2 \, x^{6} - x^{2} + 2\right)} {\left(x^{6} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^6 - 1)*sqrt(x^6 + x^2 + 1)/((2*x^6 - x^2 + 2)*(x^6 + 1)), x)","F",0
601,-1,0,0,0.000000," ","integrate((4*x^6+x)/(x^5-1)/(a*x^5-a-x)/(x^6-x)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,0,0,0,0.000000," ","integrate((6*x^4-1)*(2*x^5+x)^(1/2)/(2*x^4+1)/(4*x^8+4*x^4-x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{5} + x} {\left(6 \, x^{4} - 1\right)}}{{\left(4 \, x^{8} + 4 \, x^{4} - x^{2} + 1\right)} {\left(2 \, x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(2*x^5 + x)*(6*x^4 - 1)/((4*x^8 + 4*x^4 - x^2 + 1)*(2*x^4 + 1)), x)","F",0
603,1,23,0,0.228682," ","integrate((1+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4}{5} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{5}{2}} - \frac{4}{3} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{3}{2}}"," ",0,"4/5*(sqrt(x + 1) + 1)^(5/2) - 4/3*(sqrt(x + 1) + 1)^(3/2)","C",0
604,1,56,0,0.430948," ","integrate((1+(x^2+1)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{\sqrt{x^{2} + 1} + 1}}{\sqrt{2} + \sqrt{\sqrt{x^{2} + 1} + 1}}\right) + 2 \, \sqrt{\sqrt{x^{2} + 1} + 1}"," ",0,"1/2*sqrt(2)*log(-(sqrt(2) - sqrt(sqrt(x^2 + 1) + 1))/(sqrt(2) + sqrt(sqrt(x^2 + 1) + 1))) + 2*sqrt(sqrt(x^2 + 1) + 1)","A",0
605,0,0,0,0.000000," ","integrate(1/(1+(x^2-6*x+9)^(1/4)),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 6 \, x + 9\right)}^{\frac{1}{4}} + 1}\,{d x}"," ",0,"integrate(1/((x^2 - 6*x + 9)^(1/4) + 1), x)","F",0
606,0,0,0,0.000000," ","integrate(x^2/(x^2-2)/(x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{2} - 1\right)}^{\frac{3}{4}} {\left(x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^2/((x^2 - 1)^(3/4)*(x^2 - 2)), x)","F",0
607,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+1)^(1/2)/(x^2+1)^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*(x^2 - 1)/(x^2 + 1)^3, x)","F",0
608,0,0,0,0.000000," ","integrate((5*x^2-46*x+77)/(-23*x^2+82*x-23)/(x^4-3*x^3-21*x^2+83*x-60)^(1/2),x, algorithm=""giac"")","\int -\frac{5 \, x^{2} - 46 \, x + 77}{\sqrt{x^{4} - 3 \, x^{3} - 21 \, x^{2} + 83 \, x - 60} {\left(23 \, x^{2} - 82 \, x + 23\right)}}\,{d x}"," ",0,"integrate(-(5*x^2 - 46*x + 77)/(sqrt(x^4 - 3*x^3 - 21*x^2 + 83*x - 60)*(23*x^2 - 82*x + 23)), x)","F",0
609,1,45,0,0.388067," ","integrate((-1+x)*(x^4+x^3)^(1/4)/x/(1+x),x, algorithm=""giac"")","x {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \frac{7}{2} \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{7}{4} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{7}{4} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"x*(1/x + 1)^(1/4) - 7/2*arctan((1/x + 1)^(1/4)) - 7/4*log((1/x + 1)^(1/4) + 1) + 7/4*log(abs((1/x + 1)^(1/4) - 1))","A",0
610,1,46,0,0.360097," ","integrate((x^4-1)*(x^4+x^3)^(1/4)/x^8,x, algorithm=""giac"")","\frac{4}{25} \, {\left(\frac{1}{x} + 1\right)}^{\frac{25}{4}} - \frac{20}{21} \, {\left(\frac{1}{x} + 1\right)}^{\frac{21}{4}} + \frac{40}{17} \, {\left(\frac{1}{x} + 1\right)}^{\frac{17}{4}} - \frac{40}{13} \, {\left(\frac{1}{x} + 1\right)}^{\frac{13}{4}} + \frac{16}{9} \, {\left(\frac{1}{x} + 1\right)}^{\frac{9}{4}}"," ",0,"4/25*(1/x + 1)^(25/4) - 20/21*(1/x + 1)^(21/4) + 40/17*(1/x + 1)^(17/4) - 40/13*(1/x + 1)^(13/4) + 16/9*(1/x + 1)^(9/4)","A",0
611,0,0,0,0.000000," ","integrate((4*x^4-4*x^2+4*x-1)/((-2*x^2+1)/(2*x^2+1))^(1/2)/(2*x^2+1)/(4*x^4-8*x^3+12*x^2-4*x-1),x, algorithm=""giac"")","\int \frac{4 \, x^{4} - 4 \, x^{2} + 4 \, x - 1}{{\left(4 \, x^{4} - 8 \, x^{3} + 12 \, x^{2} - 4 \, x - 1\right)} {\left(2 \, x^{2} + 1\right)} \sqrt{-\frac{2 \, x^{2} - 1}{2 \, x^{2} + 1}}}\,{d x}"," ",0,"integrate((4*x^4 - 4*x^2 + 4*x - 1)/((4*x^4 - 8*x^3 + 12*x^2 - 4*x - 1)*(2*x^2 + 1)*sqrt(-(2*x^2 - 1)/(2*x^2 + 1))), x)","F",0
612,0,0,0,0.000000," ","integrate((x^4-3)*(x^4-2*x^3+1)*(x^4-x^3+1)/x^6/(x^4+1)/(x^5+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} + 1\right)} {\left(x^{4} - 2 \, x^{3} + 1\right)} {\left(x^{4} - 3\right)}}{{\left(x^{5} + x\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 - x^3 + 1)*(x^4 - 2*x^3 + 1)*(x^4 - 3)/((x^5 + x)^(1/4)*(x^4 + 1)*x^6), x)","F",0
613,0,0,0,0.000000," ","integrate(x^20/(x^6-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{20}}{\sqrt{x^{6} - 1}}\,{d x}"," ",0,"integrate(x^20/sqrt(x^6 - 1), x)","F",0
614,0,0,0,0.000000," ","integrate(x^14*(x^6-1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{6} - 1} x^{14}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*x^14, x)","F",0
615,0,0,0,0.000000," ","integrate(x^20/(x^6+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{20}}{\sqrt{x^{6} + 1}}\,{d x}"," ",0,"integrate(x^20/sqrt(x^6 + 1), x)","F",0
616,0,0,0,0.000000," ","integrate((-4*x^6+x)/(x^6+x)^(1/2)/(x^10+2*x^5-a*x^2+1),x, algorithm=""giac"")","\int -\frac{4 \, x^{6} - x}{{\left(x^{10} + 2 \, x^{5} - a x^{2} + 1\right)} \sqrt{x^{6} + x}}\,{d x}"," ",0,"integrate(-(4*x^6 - x)/((x^10 + 2*x^5 - a*x^2 + 1)*sqrt(x^6 + x)), x)","F",0
617,0,0,0,0.000000," ","integrate((4*x^6-x)/(x^6+x)^(1/2)/(a*x^10+2*a*x^5-x^2+a),x, algorithm=""giac"")","\int \frac{4 \, x^{6} - x}{{\left(a x^{10} + 2 \, a x^{5} - x^{2} + a\right)} \sqrt{x^{6} + x}}\,{d x}"," ",0,"integrate((4*x^6 - x)/((a*x^10 + 2*a*x^5 - x^2 + a)*sqrt(x^6 + x)), x)","F",0
618,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,0,0,0,0.000000," ","integrate((2*a*x-3*b)/(a*x^2-b*x)^(1/4)/(x^3-a*x+b),x, algorithm=""giac"")","\int \frac{2 \, a x - 3 \, b}{{\left(a x^{2} - b x\right)}^{\frac{1}{4}} {\left(x^{3} - a x + b\right)}}\,{d x}"," ",0,"integrate((2*a*x - 3*b)/((a*x^2 - b*x)^(1/4)*(x^3 - a*x + b)), x)","F",0
620,0,0,0,0.000000," ","integrate((x^3-4)*(x^3-x^2+2)^(1/2)/(x^3+2)/(x^3+x^2+2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{3} - x^{2} + 2} {\left(x^{3} - 4\right)}}{{\left(x^{3} + x^{2} + 2\right)} {\left(x^{3} + 2\right)}}\,{d x}"," ",0,"integrate(sqrt(x^3 - x^2 + 2)*(x^3 - 4)/((x^3 + x^2 + 2)*(x^3 + 2)), x)","F",0
621,1,60,0,0.192402," ","integrate(x^2*(x^4-1)^(1/4),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(x^{4} - 1\right)}^{\frac{1}{4}} x^{3} + \frac{1}{8} \, \arctan\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{16} \, \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{1}{16} \, \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right)"," ",0,"-1/4*(x^4 - 1)^(1/4)*x^3 + 1/8*arctan((x^4 - 1)^(1/4)/x) + 1/16*log((x^4 - 1)^(1/4)/x + 1) - 1/16*log(-(x^4 - 1)^(1/4)/x + 1)","A",0
622,1,59,0,0.509721," ","integrate(x^2*(x^4+1)^(1/4),x, algorithm=""giac"")","\frac{1}{4} \, {\left(x^{4} + 1\right)}^{\frac{1}{4}} x^{3} + \frac{1}{8} \, \arctan\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{16} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{1}{16} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} - 1\right)"," ",0,"1/4*(x^4 + 1)^(1/4)*x^3 + 1/8*arctan((x^4 + 1)^(1/4)/x) + 1/16*log((x^4 + 1)^(1/4)/x + 1) - 1/16*log((x^4 + 1)^(1/4)/x - 1)","A",0
623,1,57,0,0.354691," ","integrate((a*x^3-b)*(x^4+x)^(1/2)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} + x} a x + \frac{1}{6} \, {\left(a - 2 \, b\right)} \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{6} \, {\left(a - 2 \, b\right)} \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right) + \frac{2}{3} \, b \sqrt{\frac{1}{x^{3}} + 1}"," ",0,"1/3*sqrt(x^4 + x)*a*x + 1/6*(a - 2*b)*log(sqrt(1/x^3 + 1) + 1) - 1/6*(a - 2*b)*log(abs(sqrt(1/x^3 + 1) - 1)) + 2/3*b*sqrt(1/x^3 + 1)","A",0
624,-2,0,0,0.000000," ","integrate(1/(x^4-2)/(x^4+x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
625,0,0,0,0.000000," ","integrate((a*x^3-4*b)/(a*x^3-b)^(1/4)/(-a*x^3+x^4+b),x, algorithm=""giac"")","\int -\frac{a x^{3} - 4 \, b}{{\left(a x^{3} - x^{4} - b\right)} {\left(a x^{3} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(a*x^3 - 4*b)/((a*x^3 - x^4 - b)*(a*x^3 - b)^(1/4)), x)","F",0
626,0,0,0,0.000000," ","integrate((3*x^5-x)/(x^4+1)/(a*x^4+a-x)/(x^5+x)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{5} - x}{{\left(a x^{4} + a - x\right)} \sqrt{x^{5} + x} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((3*x^5 - x)/((a*x^4 + a - x)*sqrt(x^5 + x)*(x^4 + 1)), x)","F",0
627,0,0,0,0.000000," ","integrate((x^3-1)*(x^6-1)^(1/2)/x^10,x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} - 1\right)}}{x^{10}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 - 1)/x^10, x)","F",0
628,0,0,0,0.000000," ","integrate((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+x^3+1),x, algorithm=""giac"")","\int -\frac{x^{6} + 1}{{\left(x^{6} - x^{3} - 1\right)} {\left(x^{5} - x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(x^6 + 1)/((x^6 - x^3 - 1)*(x^5 - x^3)^(1/4)), x)","F",0
629,0,0,0,0.000000," ","integrate((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+x^3+1),x, algorithm=""giac"")","\int -\frac{x^{6} + 1}{{\left(x^{6} - x^{3} - 1\right)} {\left(x^{5} - x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(x^6 + 1)/((x^6 - x^3 - 1)*(x^5 - x^3)^(1/4)), x)","F",0
630,0,0,0,0.000000," ","integrate(x*(5*a*x+6*b)/(a*x^3+b*x^2)^(1/4)/(x^6-a*x-b),x, algorithm=""giac"")","\int \frac{{\left(5 \, a x + 6 \, b\right)} x}{{\left(x^{6} - a x - b\right)} {\left(a x^{3} + b x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((5*a*x + 6*b)*x/((x^6 - a*x - b)*(a*x^3 + b*x^2)^(1/4)), x)","F",0
631,0,0,0,0.000000," ","integrate((x^5-1)^(1/2)*(3*x^5+2)/(x^10-a*x^4-2*x^5+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{5} + 2\right)} \sqrt{x^{5} - 1}}{x^{10} - a x^{4} - 2 \, x^{5} + 1}\,{d x}"," ",0,"integrate((3*x^5 + 2)*sqrt(x^5 - 1)/(x^10 - a*x^4 - 2*x^5 + 1), x)","F",0
632,0,0,0,0.000000," ","integrate((x^5-1)^(1/2)*(3*x^5+2)/(a*x^10-2*a*x^5-x^4+a),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{5} + 2\right)} \sqrt{x^{5} - 1}}{a x^{10} - 2 \, a x^{5} - x^{4} + a}\,{d x}"," ",0,"integrate((3*x^5 + 2)*sqrt(x^5 - 1)/(a*x^10 - 2*a*x^5 - x^4 + a), x)","F",0
633,0,0,0,0.000000," ","integrate((x^5+1)^(1/2)*(3*x^5-2)/(a*x^10+2*a*x^5-x^4+a),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{5} - 2\right)} \sqrt{x^{5} + 1}}{a x^{10} + 2 \, a x^{5} - x^{4} + a}\,{d x}"," ",0,"integrate((3*x^5 - 2)*sqrt(x^5 + 1)/(a*x^10 + 2*a*x^5 - x^4 + a), x)","F",0
634,0,0,0,0.000000," ","integrate(1/(1+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\sqrt{x^{2} + 1} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(sqrt(x^2 + 1) + 1), x)","F",0
635,1,56,0,0.198924," ","integrate(x^6*(x^4-x)^(1/2),x, algorithm=""giac"")","\frac{1}{72} \, {\left(2 \, {\left(4 \, x^{3} - 1\right)} x^{3} - 3\right)} \sqrt{x^{4} - x} x - \frac{1}{48} \, \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right) + \frac{1}{48} \, \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/72*(2*(4*x^3 - 1)*x^3 - 3)*sqrt(x^4 - x)*x - 1/48*log(sqrt(-1/x^3 + 1) + 1) + 1/48*log(abs(sqrt(-1/x^3 + 1) - 1))","A",0
636,1,91,0,0.205163," ","integrate((x^2-1)*(x^4-x^3)^(1/4)/x^8,x, algorithm=""giac"")","-\frac{4}{25} \, {\left(\frac{1}{x} - 1\right)}^{6} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \frac{20}{21} \, {\left(\frac{1}{x} - 1\right)}^{5} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \frac{36}{17} \, {\left(\frac{1}{x} - 1\right)}^{4} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \frac{28}{13} \, {\left(\frac{1}{x} - 1\right)}^{3} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \frac{8}{9} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}"," ",0,"-4/25*(1/x - 1)^6*(-1/x + 1)^(1/4) - 20/21*(1/x - 1)^5*(-1/x + 1)^(1/4) - 36/17*(1/x - 1)^4*(-1/x + 1)^(1/4) - 28/13*(1/x - 1)^3*(-1/x + 1)^(1/4) - 8/9*(1/x - 1)^2*(-1/x + 1)^(1/4)","A",0
637,0,0,0,0.000000," ","integrate((x^3-1)*(x^6-1)^(1/2)/x/(x^3+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} - 1\right)}}{{\left(x^{3} + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 - 1)/((x^3 + 1)*x), x)","F",0
638,0,0,0,0.000000," ","integrate((x^3+1)*(x^6-1)^(1/2)/x/(x^3-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} + 1\right)}}{{\left(x^{3} - 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 + 1)/((x^3 - 1)*x), x)","F",0
639,0,0,0,0.000000," ","integrate((a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x, algorithm=""giac"")","\int \frac{a x^{4} + 2 \, b}{{\left(x^{8} - 2 \, a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 + 2*b)/((x^8 - 2*a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
640,0,0,0,0.000000," ","integrate((a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x, algorithm=""giac"")","\int \frac{a x^{4} + 2 \, b}{{\left(x^{8} - 2 \, a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 + 2*b)/((x^8 - 2*a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
641,0,0,0,0.000000," ","integrate((x^6-1)*(x^6+1)/(x^7-x^4+x)^(1/4)/(x^12+3*x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}}{{\left(x^{12} + 3 \, x^{6} + 1\right)} {\left(x^{7} - x^{4} + x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^6 + 1)*(x^6 - 1)/((x^12 + 3*x^6 + 1)*(x^7 - x^4 + x)^(1/4)), x)","F",0
642,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{x^{2} + 1} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 1) + 1), x)","F",0
643,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x^{2} + 1} + 1}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 1) + 1)/x^2, x)","F",0
644,1,186,0,0.500514," ","integrate(1/x/(a*x^2+b)^(3/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{2 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{2 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right)}{4 \, b} + \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right)}{4 \, b}"," ",0,"-1/2*sqrt(2)*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^2 + b)^(1/4))/(-b)^(1/4))/b - 1/2*sqrt(2)*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^2 + b)^(1/4))/(-b)^(1/4))/b - 1/4*sqrt(2)*(-b)^(1/4)*log(sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b))/b + 1/4*sqrt(2)*(-b)^(1/4)*log(-sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b))/b","B",0
645,0,0,0,0.000000," ","integrate((-7+x)/(-11+5*x)/(x^4-3*x^3-21*x^2+83*x-60)^(1/2),x, algorithm=""giac"")","\int \frac{x - 7}{\sqrt{x^{4} - 3 \, x^{3} - 21 \, x^{2} + 83 \, x - 60} {\left(5 \, x - 11\right)}}\,{d x}"," ",0,"integrate((x - 7)/(sqrt(x^4 - 3*x^3 - 21*x^2 + 83*x - 60)*(5*x - 11)), x)","F",0
646,1,38,0,0.181542," ","integrate((x^6-2)*(x^6-1)^(1/2)/x/(x^6+2),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) + \frac{1}{3} \, \sqrt{x^{6} - 1} + \frac{1}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(x^6 - 1)) + 1/3*sqrt(x^6 - 1) + 1/3*arctan(sqrt(x^6 - 1))","A",0
647,0,0,0,0.000000," ","integrate((x^6-x^2-1)^(1/2)*(2*x^6+1)/(x^6-1)/(2*x^6+x^2-2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + 1\right)} \sqrt{x^{6} - x^{2} - 1}}{{\left(2 \, x^{6} + x^{2} - 2\right)} {\left(x^{6} - 1\right)}}\,{d x}"," ",0,"integrate((2*x^6 + 1)*sqrt(x^6 - x^2 - 1)/((2*x^6 + x^2 - 2)*(x^6 - 1)), x)","F",0
648,0,0,0,0.000000," ","integrate(x*(5*a*x^3-8*b)/(a*x^3-b)^(1/4)/(x^8-a*x^3+b),x, algorithm=""giac"")","\int \frac{{\left(5 \, a x^{3} - 8 \, b\right)} x}{{\left(x^{8} - a x^{3} + b\right)} {\left(a x^{3} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((5*a*x^3 - 8*b)*x/((x^8 - a*x^3 + b)*(a*x^3 - b)^(1/4)), x)","F",0
649,0,0,0,0.000000," ","integrate((-9*x^3-x^2+16*x+2)/((1+x)/(x^2-2))^(1/4)/(x^2-2)/(x^9-x^8-5*x^7+5*x^6+9*x^5-9*x^4-7*x^3+7*x^2+2*x-3),x, algorithm=""giac"")","\int -\frac{9 \, x^{3} + x^{2} - 16 \, x - 2}{{\left(x^{9} - x^{8} - 5 \, x^{7} + 5 \, x^{6} + 9 \, x^{5} - 9 \, x^{4} - 7 \, x^{3} + 7 \, x^{2} + 2 \, x - 3\right)} {\left(x^{2} - 2\right)} \left(\frac{x + 1}{x^{2} - 2}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(9*x^3 + x^2 - 16*x - 2)/((x^9 - x^8 - 5*x^7 + 5*x^6 + 9*x^5 - 9*x^4 - 7*x^3 + 7*x^2 + 2*x - 3)*(x^2 - 2)*((x + 1)/(x^2 - 2))^(1/4)), x)","F",0
650,0,0,0,0.000000," ","integrate((7*x^8-1)/(x^8+1)/(3*x^16-x^9+6*x^8+x^2-x+3)^(1/2),x, algorithm=""giac"")","\int \frac{7 \, x^{8} - 1}{\sqrt{3 \, x^{16} - x^{9} + 6 \, x^{8} + x^{2} - x + 3} {\left(x^{8} + 1\right)}}\,{d x}"," ",0,"integrate((7*x^8 - 1)/(sqrt(3*x^16 - x^9 + 6*x^8 + x^2 - x + 3)*(x^8 + 1)), x)","F",0
651,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))^(1/2)/x^2/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x^{2} + 1} + 1}}{\sqrt{x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 1) + 1)/(sqrt(x^2 + 1)*x^2), x)","F",0
652,1,71,0,0.182410," ","integrate(x/(x+(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","{\left(\sqrt{x + 1} + 1\right)}^{2} - \frac{4}{5} \, \sqrt{5} \log\left(-\frac{\sqrt{5} - 2 \, \sqrt{\sqrt{x + 1} + 1} - 1}{\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} + 1}\right) - 2 \, \sqrt{x + 1} - 4 \, \sqrt{\sqrt{x + 1} + 1} - 2"," ",0,"(sqrt(x + 1) + 1)^2 - 4/5*sqrt(5)*log(-(sqrt(5) - 2*sqrt(sqrt(x + 1) + 1) - 1)/(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) + 1)) - 2*sqrt(x + 1) - 4*sqrt(sqrt(x + 1) + 1) - 2","A",0
653,1,65,0,0.304230," ","integrate((a+2*x)/(a*x+x^2+b)^(1/4)/(2*a*x+2*x^2+2*b-1),x, algorithm=""giac"")","\frac{1}{4} \cdot 8^{\frac{3}{4}} \arctan\left(2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(a x + x^{2} + b\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 8^{\frac{3}{4}} \log\left(\left(\frac{1}{2}\right)^{\frac{1}{4}} + {\left(a x + x^{2} + b\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 8^{\frac{3}{4}} \log\left({\left| -\left(\frac{1}{2}\right)^{\frac{1}{4}} + {\left(a x + x^{2} + b\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"1/4*8^(3/4)*arctan(2*(1/2)^(3/4)*(a*x + x^2 + b)^(1/4)) - 1/8*8^(3/4)*log((1/2)^(1/4) + (a*x + x^2 + b)^(1/4)) + 1/8*8^(3/4)*log(abs(-(1/2)^(1/4) + (a*x + x^2 + b)^(1/4)))","A",0
654,1,60,0,0.215234," ","integrate(1/x^7/(x^3+1)^(1/4),x, algorithm=""giac"")","\frac{5 \, {\left(x^{3} + 1\right)}^{\frac{7}{4}} - 9 \, {\left(x^{3} + 1\right)}^{\frac{3}{4}}}{24 \, x^{6}} + \frac{5}{48} \, \arctan\left({\left(x^{3} + 1\right)}^{\frac{1}{4}}\right) - \frac{5}{96} \, \log\left({\left(x^{3} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{5}{96} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/24*(5*(x^3 + 1)^(7/4) - 9*(x^3 + 1)^(3/4))/x^6 + 5/48*arctan((x^3 + 1)^(1/4)) - 5/96*log((x^3 + 1)^(1/4) + 1) + 5/96*log(abs((x^3 + 1)^(1/4) - 1))","A",0
655,1,58,0,0.200840," ","integrate((x^3+1)^(1/4)/x^7,x, algorithm=""giac"")","-\frac{{\left(x^{3} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(x^{3} + 1\right)}^{\frac{1}{4}}}{24 \, x^{6}} + \frac{1}{16} \, \arctan\left({\left(x^{3} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{32} \, \log\left({\left(x^{3} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{32} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/24*((x^3 + 1)^(5/4) + 3*(x^3 + 1)^(1/4))/x^6 + 1/16*arctan((x^3 + 1)^(1/4)) + 1/32*log((x^3 + 1)^(1/4) + 1) - 1/32*log(abs((x^3 + 1)^(1/4) - 1))","A",0
656,1,50,0,0.139201," ","integrate((a*x^3+b)^(1/2)*(a*x^3+2*b)/x,x, algorithm=""giac"")","\frac{4 \, b^{2} \arctan\left(\frac{\sqrt{a x^{3} + b}}{\sqrt{-b}}\right)}{3 \, \sqrt{-b}} + \frac{2}{9} \, {\left(a x^{3} + b\right)}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{a x^{3} + b} b"," ",0,"4/3*b^2*arctan(sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b) + 2/9*(a*x^3 + b)^(3/2) + 4/3*sqrt(a*x^3 + b)*b","A",0
657,0,0,0,0.000000," ","integrate((x^3+1)*(x^6-1)^(1/2)/x^13/(x^3-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} + 1\right)}}{{\left(x^{3} - 1\right)} x^{13}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 + 1)/((x^3 - 1)*x^13), x)","F",0
658,1,49,0,0.397136," ","integrate((x^4+x)^(1/2)*(a*x^6-b)/x^6,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} + x} a x + \frac{2}{9} \, b {\left(\frac{1}{x^{3}} + 1\right)}^{\frac{3}{2}} + \frac{1}{6} \, a \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{6} \, a \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/3*sqrt(x^4 + x)*a*x + 2/9*b*(1/x^3 + 1)^(3/2) + 1/6*a*log(sqrt(1/x^3 + 1) + 1) - 1/6*a*log(abs(sqrt(1/x^3 + 1) - 1))","A",0
659,0,0,0,0.000000," ","integrate((5*a*x^3-7*b*x)/(a*x^3-b*x)^(1/4)/(x^7-a*x^2+b),x, algorithm=""giac"")","\int \frac{5 \, a x^{3} - 7 \, b x}{{\left(x^{7} - a x^{2} + b\right)} {\left(a x^{3} - b x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((5*a*x^3 - 7*b*x)/((x^7 - a*x^2 + b)*(a*x^3 - b*x)^(1/4)), x)","F",0
660,0,0,0,0.000000," ","integrate((3*x^5+x)/(x^5-x)^(1/2)/(x^8-2*x^4-a*x^2+1),x, algorithm=""giac"")","\int \frac{3 \, x^{5} + x}{{\left(x^{8} - 2 \, x^{4} - a x^{2} + 1\right)} \sqrt{x^{5} - x}}\,{d x}"," ",0,"integrate((3*x^5 + x)/((x^8 - 2*x^4 - a*x^2 + 1)*sqrt(x^5 - x)), x)","F",0
661,0,0,0,0.000000," ","integrate((3*x^5+x)/(x^5-x)^(1/2)/(a*x^8-2*a*x^4-x^2+a),x, algorithm=""giac"")","\int \frac{3 \, x^{5} + x}{{\left(a x^{8} - 2 \, a x^{4} - x^{2} + a\right)} \sqrt{x^{5} - x}}\,{d x}"," ",0,"integrate((3*x^5 + x)/((a*x^8 - 2*a*x^4 - x^2 + a)*sqrt(x^5 - x)), x)","F",0
662,0,0,0,0.000000," ","integrate((4*x^6+x)/(x^6-x)^(1/2)/(x^10-2*x^5-a*x^2+1),x, algorithm=""giac"")","\int \frac{4 \, x^{6} + x}{{\left(x^{10} - 2 \, x^{5} - a x^{2} + 1\right)} \sqrt{x^{6} - x}}\,{d x}"," ",0,"integrate((4*x^6 + x)/((x^10 - 2*x^5 - a*x^2 + 1)*sqrt(x^6 - x)), x)","F",0
663,0,0,0,0.000000," ","integrate((4*x^6+x)/(x^6-x)^(1/2)/(a*x^10-2*a*x^5-x^2+a),x, algorithm=""giac"")","\int \frac{4 \, x^{6} + x}{{\left(a x^{10} - 2 \, a x^{5} - x^{2} + a\right)} \sqrt{x^{6} - x}}\,{d x}"," ",0,"integrate((4*x^6 + x)/((a*x^10 - 2*a*x^5 - x^2 + a)*sqrt(x^6 - x)), x)","F",0
664,0,0,0,0.000000," ","integrate(1/(-5+2*x)^2/(x^2-4*x+4)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 4 \, x + 4\right)}^{\frac{1}{4}} {\left(2 \, x - 5\right)}^{2}}\,{d x}"," ",0,"integrate(1/((x^2 - 4*x + 4)^(1/4)*(2*x - 5)^2), x)","F",0
665,0,0,0,0.000000," ","integrate((x^3-2)*(x^3+1)^(1/2)*(2*x^3-x^2+2)/x^4/(x^3-3*x^2+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} - x^{2} + 2\right)} \sqrt{x^{3} + 1} {\left(x^{3} - 2\right)}}{{\left(x^{3} - 3 \, x^{2} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((2*x^3 - x^2 + 2)*sqrt(x^3 + 1)*(x^3 - 2)/((x^3 - 3*x^2 + 1)*x^4), x)","F",0
666,1,50,0,0.185440," ","integrate((a*x^3-b)*(a*x^3+b)^(1/2)/x,x, algorithm=""giac"")","-\frac{2 \, b^{2} \arctan\left(\frac{\sqrt{a x^{3} + b}}{\sqrt{-b}}\right)}{3 \, \sqrt{-b}} + \frac{2}{9} \, {\left(a x^{3} + b\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{a x^{3} + b} b"," ",0,"-2/3*b^2*arctan(sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b) + 2/9*(a*x^3 + b)^(3/2) - 2/3*sqrt(a*x^3 + b)*b","A",0
667,0,0,0,0.000000," ","integrate(x^2/(x^4-1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{4} + 1} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(x^4 + 1)*(x^4 - 1)), x)","F",0
668,0,0,0,0.000000," ","integrate((x^4+1)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1}}{x^{4} - 1}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)/(x^4 - 1), x)","F",0
669,1,53,0,0.279480," ","integrate((a*x^3+b)*(x^4+x)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, a x^{3} + a + 4 \, b\right)} \sqrt{x^{4} + x} x - \frac{1}{24} \, {\left(a - 4 \, b\right)} {\left(\log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right) - \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)\right)}"," ",0,"1/12*(2*a*x^3 + a + 4*b)*sqrt(x^4 + x)*x - 1/24*(a - 4*b)*(log(sqrt(1/x^3 + 1) + 1) - log(abs(sqrt(1/x^3 + 1) - 1)))","A",0
670,1,47,0,0.153776," ","integrate((x^4+x^2)^(1/4),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + \frac{1}{4} \, \arctan\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{8} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/2*x^2*(1/x^2 + 1)^(1/4) + 1/4*arctan((1/x^2 + 1)^(1/4)) + 1/8*log((1/x^2 + 1)^(1/4) + 1) - 1/8*log((1/x^2 + 1)^(1/4) - 1)","A",0
671,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+1)^(1/2)/(x^4+3*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} {\left(x^{4} - 1\right)}}{{\left(x^{4} + 3 \, x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*(x^4 - 1)/(x^4 + 3*x^2 + 1)^2, x)","F",0
672,1,73,0,0.351850," ","integrate(1/x^8/(x^4+x^3)^(1/4),x, algorithm=""giac"")","-\frac{4}{31} \, {\left(\frac{1}{x} + 1\right)}^{\frac{31}{4}} + \frac{28}{27} \, {\left(\frac{1}{x} + 1\right)}^{\frac{27}{4}} - \frac{84}{23} \, {\left(\frac{1}{x} + 1\right)}^{\frac{23}{4}} + \frac{140}{19} \, {\left(\frac{1}{x} + 1\right)}^{\frac{19}{4}} - \frac{28}{3} \, {\left(\frac{1}{x} + 1\right)}^{\frac{15}{4}} + \frac{84}{11} \, {\left(\frac{1}{x} + 1\right)}^{\frac{11}{4}} - 4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{7}{4}} + \frac{4}{3} \, {\left(\frac{1}{x} + 1\right)}^{\frac{3}{4}}"," ",0,"-4/31*(1/x + 1)^(31/4) + 28/27*(1/x + 1)^(27/4) - 84/23*(1/x + 1)^(23/4) + 140/19*(1/x + 1)^(19/4) - 28/3*(1/x + 1)^(15/4) + 84/11*(1/x + 1)^(11/4) - 4*(1/x + 1)^(7/4) + 4/3*(1/x + 1)^(3/4)","A",0
673,0,0,0,0.000000," ","integrate((1+4*x)/(x^4+2*x^3+3*x^2-2*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{4 \, x + 1}{\sqrt{x^{4} + 2 \, x^{3} + 3 \, x^{2} - 2 \, x + 1}}\,{d x}"," ",0,"integrate((4*x + 1)/sqrt(x^4 + 2*x^3 + 3*x^2 - 2*x + 1), x)","F",0
674,0,0,0,0.000000," ","integrate(1/(x^4-1)^(1/4)/(3*x^4+1),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((3*x^4 + 1)*(x^4 - 1)^(1/4)), x)","F",0
675,0,0,0,0.000000," ","integrate((a*x^4-3*b)/(a*x^4-x^3+b)/(a*x^5+b*x)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} - 3 \, b}{{\left(a x^{5} + b x\right)}^{\frac{1}{4}} {\left(a x^{4} - x^{3} + b\right)}}\,{d x}"," ",0,"integrate((a*x^4 - 3*b)/((a*x^5 + b*x)^(1/4)*(a*x^4 - x^3 + b)), x)","F",0
676,0,0,0,0.000000," ","integrate(x^20*(x^6-1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{6} - 1} x^{20}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*x^20, x)","F",0
677,0,0,0,0.000000," ","integrate((x^3-1)*(x^6-1)^(1/2)/x^4/(x^3+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} - 1\right)}}{{\left(x^{3} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 - 1)/((x^3 + 1)*x^4), x)","F",0
678,0,0,0,0.000000," ","integrate((x^6+1)/(x^4-x^2+1)^(1/2)/(-x^6+1),x, algorithm=""giac"")","\int -\frac{x^{6} + 1}{{\left(x^{6} - 1\right)} \sqrt{x^{4} - x^{2} + 1}}\,{d x}"," ",0,"integrate(-(x^6 + 1)/((x^6 - 1)*sqrt(x^4 - x^2 + 1)), x)","F",0
679,1,41,0,0.142022," ","integrate((x^6-2)*(x^6-1)^(1/2)/x^7/(x^6+2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) + \frac{\sqrt{x^{6} - 1}}{6 \, x^{6}} - \frac{1}{2} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(x^6 - 1)) + 1/6*sqrt(x^6 - 1)/x^6 - 1/2*arctan(sqrt(x^6 - 1))","A",0
680,0,0,0,0.000000," ","integrate(x*(5*a*x-6*b)/(a*x^3-b*x^2)^(1/4)/(x^6-a*x+b),x, algorithm=""giac"")","\int \frac{{\left(5 \, a x - 6 \, b\right)} x}{{\left(x^{6} - a x + b\right)} {\left(a x^{3} - b x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((5*a*x - 6*b)*x/((x^6 - a*x + b)*(a*x^3 - b*x^2)^(1/4)), x)","F",0
681,1,72,0,0.135956," ","integrate((x^3+1)^(1/2)*(x^6+2*x^3+2)/x/(x^6-1),x, algorithm=""giac"")","\frac{5}{6} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{x^{3} + 1} \right|}}{2 \, {\left(\sqrt{2} + \sqrt{x^{3} + 1}\right)}}\right) + \frac{2}{3} \, \sqrt{x^{3} + 1} + \frac{2}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) - \frac{2}{3} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"5/6*sqrt(2)*log(1/2*abs(-2*sqrt(2) + 2*sqrt(x^3 + 1))/(sqrt(2) + sqrt(x^3 + 1))) + 2/3*sqrt(x^3 + 1) + 2/3*log(sqrt(x^3 + 1) + 1) - 2/3*log(abs(sqrt(x^3 + 1) - 1))","A",0
682,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+1)^(1/2)/(x^8+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} {\left(x^{4} - 1\right)}}{x^{8} + 1}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*(x^4 - 1)/(x^8 + 1), x)","F",0
683,0,0,0,0.000000," ","integrate((x^8-1)/(x^4+1)^(1/2)/(x^8+1),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + 1)*sqrt(x^4 + 1)), x)","F",0
684,-2,0,0,0.000000," ","integrate((x^4-2)^(1/2)*(x^4+2)/(x^8-6*x^4+4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
685,0,0,0,0.000000," ","integrate((a*x^4-2*b)/(a*x^4-b)^(1/4)/(2*x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(2 \, x^{8} + a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((2*x^8 + a*x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
686,0,0,0,0.000000," ","integrate(1/x^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x + \sqrt{x^{2} + 1}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x + sqrt(x^2 + 1))*x^2), x)","F",0
687,0,0,0,0.000000," ","integrate((-1+k^(1/2)*x)/(1+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{k} x - 1}{\sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}} {\left(\sqrt{k} x + 1\right)}}\,{d x}"," ",0,"integrate((sqrt(k)*x - 1)/(sqrt((k^2*x^2 - 1)*(x^2 - 1))*(sqrt(k)*x + 1)), x)","F",0
688,0,0,0,0.000000," ","integrate((1+k^(1/2)*x)/(-1+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{k} x + 1}{\sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}} {\left(\sqrt{k} x - 1\right)}}\,{d x}"," ",0,"integrate((sqrt(k)*x + 1)/(sqrt((k^2*x^2 - 1)*(x^2 - 1))*(sqrt(k)*x - 1)), x)","F",0
689,0,0,0,0.000000," ","integrate((2+x)/(-1+x)/(-a*x^2+x^3+3*x-1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 2}{\sqrt{-a x^{2} + x^{3} + 3 \, x - 1} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 2)/(sqrt(-a*x^2 + x^3 + 3*x - 1)*(x - 1)), x)","F",0
690,0,0,0,0.000000," ","integrate((-2+x)/(1+x)/(-a*x^2+x^3+3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x - 2}{\sqrt{-a x^{2} + x^{3} + 3 \, x + 1} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x - 2)/(sqrt(-a*x^2 + x^3 + 3*x + 1)*(x + 1)), x)","F",0
691,1,70,0,0.179212," ","integrate((x^4-1)*(x^4+1)^(1/4)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(x^{4} + 1\right)}^{\frac{1}{4}} x^{3} + \frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} - \frac{3}{8} \, \arctan\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) - \frac{3}{16} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} + 1\right) + \frac{3}{16} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} - 1\right)"," ",0,"1/4*(x^4 + 1)^(1/4)*x^3 + (x^4 + 1)^(1/4)/x - 3/8*arctan((x^4 + 1)^(1/4)/x) - 3/16*log((x^4 + 1)^(1/4)/x + 1) + 3/16*log((x^4 + 1)^(1/4)/x - 1)","A",0
692,0,0,0,0.000000," ","integrate((a*x^2+2*b)/(a*x^2+b)^(1/4)/(x^4-2*a*x^2-2*b),x, algorithm=""giac"")","\int \frac{a x^{2} + 2 \, b}{{\left(x^{4} - 2 \, a x^{2} - 2 \, b\right)} {\left(a x^{2} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^2 + 2*b)/((x^4 - 2*a*x^2 - 2*b)*(a*x^2 + b)^(1/4)), x)","F",0
693,1,54,0,0.197954," ","integrate((x^4-x^3)^(1/4)/x,x, algorithm=""giac"")","-x {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \frac{1}{2} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{4} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-x*(-1/x + 1)^(1/4) + 1/2*arctan((-1/x + 1)^(1/4)) + 1/4*log((-1/x + 1)^(1/4) + 1) - 1/4*log(abs((-1/x + 1)^(1/4) - 1))","A",0
694,0,0,0,0.000000," ","integrate((x^3-1)*(x^6-1)^(1/2)/x^13,x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} - 1\right)}}{x^{13}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 - 1)/x^13, x)","F",0
695,0,0,0,0.000000," ","integrate((x^3+2)*(-x^4+x)^(1/3)/(x^6-x^5-x^4-2*x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(-x^{4} + x\right)}^{\frac{1}{3}} {\left(x^{3} + 2\right)}}{x^{6} - x^{5} - x^{4} - 2 \, x^{3} + x^{2} + 1}\,{d x}"," ",0,"integrate((-x^4 + x)^(1/3)*(x^3 + 2)/(x^6 - x^5 - x^4 - 2*x^3 + x^2 + 1), x)","F",0
696,0,0,0,0.000000," ","integrate((x^3+2)*(-x^4+x)^(1/3)/(x^6-x^5-x^4-2*x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(-x^{4} + x\right)}^{\frac{1}{3}} {\left(x^{3} + 2\right)}}{x^{6} - x^{5} - x^{4} - 2 \, x^{3} + x^{2} + 1}\,{d x}"," ",0,"integrate((-x^4 + x)^(1/3)*(x^3 + 2)/(x^6 - x^5 - x^4 - 2*x^3 + x^2 + 1), x)","F",0
697,0,0,0,0.000000," ","integrate(1/(x^8+2*x^4+1)^(1/8),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} + 2 \, x^{4} + 1\right)}^{\frac{1}{8}}}\,{d x}"," ",0,"integrate((x^8 + 2*x^4 + 1)^(-1/8), x)","F",0
698,0,0,0,0.000000," ","integrate(1/x/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x + \sqrt{x^{2} + 1}} x}\,{d x}"," ",0,"integrate(1/(sqrt(x + sqrt(x^2 + 1))*x), x)","F",0
699,0,0,0,0.000000," ","integrate((k^2*x^2-2*x+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(-1+2*x+(k^2-2)*x^2),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} - 2 \, x + 1}{\sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x} {\left({\left(k^{2} - 2\right)} x^{2} + 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((k^2*x^2 - 2*x + 1)/(sqrt((k^2*x - 1)*(x - 1)*x)*((k^2 - 2)*x^2 + 2*x - 1)), x)","F",0
700,1,186,0,0.134137," ","integrate(1/x/(a*x^3+b)^(3/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{3 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{3 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{6 \, b} + \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{6 \, b}"," ",0,"-1/3*sqrt(2)*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/b - 1/3*sqrt(2)*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/b - 1/6*sqrt(2)*(-b)^(1/4)*log(sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/b + 1/6*sqrt(2)*(-b)^(1/4)*log(-sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/b","B",0
701,1,61,0,0.188308," ","integrate((a*x^3-b)*(a*x^3+b)^(1/2)/x^4,x, algorithm=""giac"")","\frac{\frac{a^{2} b \arctan\left(\frac{\sqrt{a x^{3} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 2 \, \sqrt{a x^{3} + b} a^{2} + \frac{\sqrt{a x^{3} + b} a b}{x^{3}}}{3 \, a}"," ",0,"1/3*(a^2*b*arctan(sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b) + 2*sqrt(a*x^3 + b)*a^2 + sqrt(a*x^3 + b)*a*b/x^3)/a","A",0
702,0,0,0,0.000000," ","integrate((k^2*x^2-2*x+1)/(k^2*x^2-2*x^2+2*x-1)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} - 2 \, x + 1}{\sqrt{k^{2} x^{3} - k^{2} x^{2} - x^{2} + x} {\left(k^{2} x^{2} - 2 \, x^{2} + 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((k^2*x^2 - 2*x + 1)/(sqrt(k^2*x^3 - k^2*x^2 - x^2 + x)*(k^2*x^2 - 2*x^2 + 2*x - 1)), x)","F",0
703,0,0,0,0.000000," ","integrate((2+x)/x/(x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{x + 2}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((x + 2)/((x^4 + 1)^(1/4)*x), x)","F",0
704,1,81,0,0.167313," ","integrate(x^6*(x^4+1)^(1/4),x, algorithm=""giac"")","\frac{1}{32} \, x^{8} {\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} + 1\right)}}{x} + \frac{3 \, {\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right)} - \frac{3}{64} \, \arctan\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) - \frac{3}{128} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} + 1\right) + \frac{3}{128} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} - 1\right)"," ",0,"1/32*x^8*((x^4 + 1)^(1/4)*(1/x^4 + 1)/x + 3*(x^4 + 1)^(1/4)/x) - 3/64*arctan((x^4 + 1)^(1/4)/x) - 3/128*log((x^4 + 1)^(1/4)/x + 1) + 3/128*log((x^4 + 1)^(1/4)/x - 1)","A",0
705,1,53,0,0.240543," ","integrate((x^4-x)^(1/4)/x^2,x, algorithm=""giac"")","\frac{4}{3} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} - \frac{2}{3} \, \arctan\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{3} \, \log\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"4/3*(-1/x^3 + 1)^(1/4) - 2/3*arctan((-1/x^3 + 1)^(1/4)) - 1/3*log((-1/x^3 + 1)^(1/4) + 1) + 1/3*log(abs((-1/x^3 + 1)^(1/4) - 1))","A",0
706,1,56,0,0.509891," ","integrate(x*(x^4-x)^(1/4),x, algorithm=""giac"")","-\frac{1}{3} \, x^{3} {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} + \frac{1}{6} \, \arctan\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{12} \, \log\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{12} \, \log\left({\left| {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/3*x^3*(-1/x^3 + 1)^(1/4) + 1/6*arctan((-1/x^3 + 1)^(1/4)) + 1/12*log((-1/x^3 + 1)^(1/4) + 1) - 1/12*log(abs((-1/x^3 + 1)^(1/4) - 1))","A",0
707,1,65,0,0.230254," ","integrate((a*x^3-b)*(x^4-x)^(1/2)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} - x} a x - \frac{1}{6} \, {\left(a + 2 \, b\right)} \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right) + \frac{1}{6} \, {\left(a + 2 \, b\right)} \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right) + \frac{2}{3} \, b \sqrt{-\frac{1}{x^{3}} + 1}"," ",0,"1/3*sqrt(x^4 - x)*a*x - 1/6*(a + 2*b)*log(sqrt(-1/x^3 + 1) + 1) + 1/6*(a + 2*b)*log(abs(sqrt(-1/x^3 + 1) - 1)) + 2/3*b*sqrt(-1/x^3 + 1)","A",0
708,1,51,0,0.193241," ","integrate((x^4-x^3)^(1/4)/x^2,x, algorithm=""giac"")","4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 2 \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"4*(-1/x + 1)^(1/4) - 2*arctan((-1/x + 1)^(1/4)) - log((-1/x + 1)^(1/4) + 1) + log(abs((-1/x + 1)^(1/4) - 1))","A",0
709,0,0,0,0.000000," ","integrate(x/(x^4+6*x^3-11*x^2+18*x-17)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{4} + 6 \, x^{3} - 11 \, x^{2} + 18 \, x - 17}}\,{d x}"," ",0,"integrate(x/sqrt(x^4 + 6*x^3 - 11*x^2 + 18*x - 17), x)","F",0
710,0,0,0,0.000000," ","integrate((x^4-x^2-x-1)^(1/2)*(2*x^4+x+2)/(x^4-x-1)/(x^4+x^2-x-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + x + 2\right)} \sqrt{x^{4} - x^{2} - x - 1}}{{\left(x^{4} + x^{2} - x - 1\right)} {\left(x^{4} - x - 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 + x + 2)*sqrt(x^4 - x^2 - x - 1)/((x^4 + x^2 - x - 1)*(x^4 - x - 1)), x)","F",0
711,1,186,0,0.176609," ","integrate(1/x/(a*x^4+b)^(3/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{4 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{4 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{8 \, b} + \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{8 \, b}"," ",0,"-1/4*sqrt(2)*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/b - 1/4*sqrt(2)*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/b - 1/8*sqrt(2)*(-b)^(1/4)*log(sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/b + 1/8*sqrt(2)*(-b)^(1/4)*log(-sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/b","B",0
712,1,186,0,0.170804," ","integrate(1/x/(a*x^4+b)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{4 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{4 \, b} + \frac{\sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{8 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{8 \, b}"," ",0,"-1/4*sqrt(2)*(-b)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/b - 1/4*sqrt(2)*(-b)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/b + 1/8*sqrt(2)*(-b)^(3/4)*log(sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/b - 1/8*sqrt(2)*(-b)^(3/4)*log(-sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/b","B",0
713,1,186,0,0.198935," ","integrate(1/x/(a*x^5+b)^(3/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{5 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{5 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{10 \, b} + \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{10 \, b}"," ",0,"-1/5*sqrt(2)*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/b - 1/5*sqrt(2)*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/b - 1/10*sqrt(2)*(-b)^(1/4)*log(sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/b + 1/10*sqrt(2)*(-b)^(1/4)*log(-sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/b","B",0
714,0,0,0,0.000000," ","integrate((2*x^3+1)*(x^6-1)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(2 \, x^{3} + 1\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(2*x^3 + 1)/x, x)","F",0
715,0,0,0,0.000000," ","integrate((x^3-2)*(x^4+x^3+x)^(1/3)/(x^6+x^5+x^4+2*x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{3} - 2\right)}}{x^{6} + x^{5} + x^{4} + 2 \, x^{3} + x^{2} + 1}\,{d x}"," ",0,"integrate((x^4 + x^3 + x)^(1/3)*(x^3 - 2)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1), x)","F",0
716,0,0,0,0.000000," ","integrate((x^3-2)*(x^4+x^3+x)^(1/3)/(x^6+x^5+x^4+2*x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{3} - 2\right)}}{x^{6} + x^{5} + x^{4} + 2 \, x^{3} + x^{2} + 1}\,{d x}"," ",0,"integrate((x^4 + x^3 + x)^(1/3)*(x^3 - 2)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1), x)","F",0
717,1,186,0,0.142040," ","integrate(1/x/(a*x^6+b)^(3/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{6 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{6 \, b} - \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right)}{12 \, b} + \frac{\sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right)}{12 \, b}"," ",0,"-1/6*sqrt(2)*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^6 + b)^(1/4))/(-b)^(1/4))/b - 1/6*sqrt(2)*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^6 + b)^(1/4))/(-b)^(1/4))/b - 1/12*sqrt(2)*(-b)^(1/4)*log(sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b))/b + 1/12*sqrt(2)*(-b)^(1/4)*log(-sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b))/b","B",0
718,0,0,0,0.000000," ","integrate((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
719,0,0,0,0.000000," ","integrate((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
720,0,0,0,0.000000," ","integrate(x^2/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a^{2} x^{8} + b^{2}\right)} {\left(a x^{4} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((a^2*x^8 + b^2)*(a*x^4 + b)^(3/4)), x)","F",0
721,1,74,0,0.511296," ","integrate(1/(-1+x)/(-x^(1/2)+x)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{2 \, {\left(\sqrt{2} - \sqrt{x - \sqrt{x}} + \sqrt{x} + 1\right)}}{{\left| 2 \, \sqrt{2} + 2 \, \sqrt{x - \sqrt{x}} - 2 \, \sqrt{x} - 2 \right|}}\right) - \frac{2}{\sqrt{x - \sqrt{x}} - \sqrt{x} + 1}"," ",0,"1/2*sqrt(2)*log(2*(sqrt(2) - sqrt(x - sqrt(x)) + sqrt(x) + 1)/abs(2*sqrt(2) + 2*sqrt(x - sqrt(x)) - 2*sqrt(x) - 2)) - 2/(sqrt(x - sqrt(x)) - sqrt(x) + 1)","A",0
722,0,0,0,0.000000," ","integrate(1/(1+2*x)/(2*x^2+2*x+1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, x^{2} + 2 \, x + 1\right)}^{\frac{1}{4}} {\left(2 \, x + 1\right)}}\,{d x}"," ",0,"integrate(1/((2*x^2 + 2*x + 1)^(1/4)*(2*x + 1)), x)","F",0
723,1,62,0,0.189100," ","integrate((a*x^3+b)^(1/2)*(a*x^3+2*b)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, a^{2} b \arctan\left(\frac{\sqrt{a x^{3} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + \sqrt{a x^{3} + b} a^{2} - \frac{\sqrt{a x^{3} + b} a b}{x^{3}}\right)}}{3 \, a}"," ",0,"2/3*(2*a^2*b*arctan(sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b) + sqrt(a*x^3 + b)*a^2 - sqrt(a*x^3 + b)*a*b/x^3)/a","A",0
724,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p*x^3+q)^(1/2)/x^2/(a*p*x^3+b*x^2+a*q),x, algorithm=""giac"")","\int \frac{\sqrt{p x^{3} + q} {\left(p x^{3} - 2 \, q\right)}}{{\left(a p x^{3} + b x^{2} + a q\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(p*x^3 + q)*(p*x^3 - 2*q)/((a*p*x^3 + b*x^2 + a*q)*x^2), x)","F",0
725,0,0,0,0.000000," ","integrate((-1+2*x)/(x^4-10*x^3-3*x^2+4*x-8)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x - 1}{\sqrt{x^{4} - 10 \, x^{3} - 3 \, x^{2} + 4 \, x - 8}}\,{d x}"," ",0,"integrate((2*x - 1)/sqrt(x^4 - 10*x^3 - 3*x^2 + 4*x - 8), x)","F",0
726,0,0,0,0.000000," ","integrate((-1+x)/(x^4-8*x^3+12*x^2-16*x+4)^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x^{4} - 8 \, x^{3} + 12 \, x^{2} - 16 \, x + 4}}\,{d x}"," ",0,"integrate((x - 1)/sqrt(x^4 - 8*x^3 + 12*x^2 - 16*x + 4), x)","F",0
727,0,0,0,0.000000," ","integrate((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/x^2/(a*p*x^5+b*x^2+a*q),x, algorithm=""giac"")","\int \frac{{\left(3 \, p x^{5} - 2 \, q\right)} \sqrt{p x^{5} + q}}{{\left(a p x^{5} + b x^{2} + a q\right)} x^{2}}\,{d x}"," ",0,"integrate((3*p*x^5 - 2*q)*sqrt(p*x^5 + q)/((a*p*x^5 + b*x^2 + a*q)*x^2), x)","F",0
728,-1,0,0,0.000000," ","integrate(x^2*(4*x^5-1)/(x^5+1)^2/(a*x^5+a-x)/(x^6+x)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,1,57,0,0.380850," ","integrate((x^4-x)^(1/2)*(a*x^6-b)/x^6,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{4} - x} a x - \frac{2}{9} \, b {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{3}{2}} - \frac{1}{6} \, a \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right) + \frac{1}{6} \, a \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)"," ",0,"1/3*sqrt(x^4 - x)*a*x - 2/9*b*(-1/x^3 + 1)^(3/2) - 1/6*a*log(sqrt(-1/x^3 + 1) + 1) + 1/6*a*log(abs(sqrt(-1/x^3 + 1) - 1))","A",0
730,0,0,0,0.000000," ","integrate((p*x^6-2*q)*(p*x^6+q)^(1/2)/x^3/(a*p*x^6+b*x^4+a*q),x, algorithm=""giac"")","\int \frac{\sqrt{p x^{6} + q} {\left(p x^{6} - 2 \, q\right)}}{{\left(a p x^{6} + b x^{4} + a q\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(p*x^6 + q)*(p*x^6 - 2*q)/((a*p*x^6 + b*x^4 + a*q)*x^3), x)","F",0
731,1,65,0,0.663587," ","integrate(2*(p*x^6-2*q)*(p*x^6+q)^(1/2)*(a*p*x^6+b*x^4+a*q)/x^11,x, algorithm=""giac"")","\frac{2}{15} \, \sqrt{p x^{6} + q} {\left(3 \, a p^{2} x^{2} + 5 \, b p\right)} + \frac{2}{15} \, {\left(6 \, a p q + \frac{5 \, b q + \frac{3 \, a q^{2}}{x^{4}}}{x^{2}}\right)} \sqrt{\frac{p}{x^{2}} + \frac{q}{x^{8}}}"," ",0,"2/15*sqrt(p*x^6 + q)*(3*a*p^2*x^2 + 5*b*p) + 2/15*(6*a*p*q + (5*b*q + 3*a*q^2/x^4)/x^2)*sqrt(p/x^2 + q/x^8)","A",0
732,0,0,0,0.000000," ","integrate(1/x^3/(x^8-16*x^6+96*x^4-256*x^2+256)^(1/8),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256\right)}^{\frac{1}{8}} x^{3}}\,{d x}"," ",0,"integrate(1/((x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)^(1/8)*x^3), x)","F",0
733,0,0,0,0.000000," ","integrate(x^3*(8*a*x^3+5*b)/(a*x^4+b*x)^(1/4)/(a*x^8+b*x^5-2),x, algorithm=""giac"")","\int \frac{{\left(8 \, a x^{3} + 5 \, b\right)} x^{3}}{{\left(a x^{8} + b x^{5} - 2\right)} {\left(a x^{4} + b x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((8*a*x^3 + 5*b)*x^3/((a*x^8 + b*x^5 - 2)*(a*x^4 + b*x)^(1/4)), x)","F",0
734,1,37,0,0.202408," ","integrate((-y^4-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(y^{4} - 1\right)} \arcsin\left(\frac{x}{\sqrt{-y^{4} + 1}}\right) + \frac{1}{2} \, \sqrt{-y^{4} - x^{2} + 1} x"," ",0,"-1/2*(y^4 - 1)*arcsin(x/sqrt(-y^4 + 1)) + 1/2*sqrt(-y^4 - x^2 + 1)*x","A",0
735,0,0,0,0.000000," ","integrate((k^2*x^2-2*k^2*x+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(-a-b*x+(a*k^2+b*k^2)*x^2),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} - 2 \, k^{2} x + 1}{\sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x} {\left({\left(a k^{2} + b k^{2}\right)} x^{2} - b x - a\right)}}\,{d x}"," ",0,"integrate((k^2*x^2 - 2*k^2*x + 1)/(sqrt((k^2*x - 1)*(x - 1)*x)*((a*k^2 + b*k^2)*x^2 - b*x - a)), x)","F",0
736,0,0,0,0.000000," ","integrate((a*b*c-(a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(-a*b*c*d+(a*b*d+a*c*d+b*c*d-1)*x-(a+b+c)*d*x^2+d*x^3),x, algorithm=""giac"")","\int -\frac{a b c - {\left(a + b + c\right)} x^{2} + 2 \, x^{3}}{{\left(a b c d + {\left(a + b + c\right)} d x^{2} - d x^{3} - {\left(a b d + a c d + b c d - 1\right)} x\right)} \sqrt{-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)} x}}\,{d x}"," ",0,"integrate(-(a*b*c - (a + b + c)*x^2 + 2*x^3)/((a*b*c*d + (a + b + c)*d*x^2 - d*x^3 - (a*b*d + a*c*d + b*c*d - 1)*x)*sqrt(-(a - x)*(b - x)*(c - x)*x)), x)","F",0
737,1,82,0,0.301488," ","integrate(x^6*(x^4-1)^(1/4),x, algorithm=""giac"")","\frac{1}{32} \, x^{8} {\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 1\right)}}{x} - \frac{3 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)} + \frac{3}{64} \, \arctan\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{3}{128} \, \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{3}{128} \, \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right)"," ",0,"1/32*x^8*((x^4 - 1)^(1/4)*(1/x^4 - 1)/x - 3*(x^4 - 1)^(1/4)/x) + 3/64*arctan((x^4 - 1)^(1/4)/x) + 3/128*log((x^4 - 1)^(1/4)/x + 1) - 3/128*log(-(x^4 - 1)^(1/4)/x + 1)","A",0
738,1,60,0,0.584916," ","integrate((-1+2*x)*(x^4+x^3)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(3 \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{4}} - 7 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{2} - \frac{7}{8} \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{7}{16} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{7}{16} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/4*(3*(1/x + 1)^(5/4) - 7*(1/x + 1)^(1/4))*x^2 - 7/8*arctan((1/x + 1)^(1/4)) - 7/16*log((1/x + 1)^(1/4) + 1) + 7/16*log(abs((1/x + 1)^(1/4) - 1))","A",0
739,0,0,0,0.000000," ","integrate((x^4-2*x^3+x^2-1)^(1/2)*(x^4-x^3+1)/(x^4-2*x^3-1)/(2*x^4-4*x^3-x^2-2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} + 1\right)} \sqrt{x^{4} - 2 \, x^{3} + x^{2} - 1}}{{\left(2 \, x^{4} - 4 \, x^{3} - x^{2} - 2\right)} {\left(x^{4} - 2 \, x^{3} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 - x^3 + 1)*sqrt(x^4 - 2*x^3 + x^2 - 1)/((2*x^4 - 4*x^3 - x^2 - 2)*(x^4 - 2*x^3 - 1)), x)","F",0
740,0,0,0,0.000000," ","integrate(x^2/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a x^{4} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/(a*x^4 + b)^(3/4), x)","F",0
741,0,0,0,0.000000," ","integrate(1/(a*x^4+b)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{8} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((a*x^8 - b)*(a*x^4 + b)^(1/4)), x)","F",0
742,0,0,0,0.000000," ","integrate((a*x^8-b)/(a*x^8+b)^(1/4)/(a*x^8-c*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{8} - b}{{\left(a x^{8} - c x^{4} + b\right)} {\left(a x^{8} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^8 - b)/((a*x^8 - c*x^4 + b)*(a*x^8 + b)^(1/4)), x)","F",0
743,0,0,0,0.000000," ","integrate((2*x^5-3)*(x^10+x^6+2*x^5+1)/x^6/(x^5-x^3+1)/(x^6+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{10} + x^{6} + 2 \, x^{5} + 1\right)} {\left(2 \, x^{5} - 3\right)}}{{\left(x^{6} + x\right)}^{\frac{1}{4}} {\left(x^{5} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^10 + x^6 + 2*x^5 + 1)*(2*x^5 - 3)/((x^6 + x)^(1/4)*(x^5 - x^3 + 1)*x^6), x)","F",0
744,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{2} + \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1)), x)","F",0
745,0,0,0,0.000000," ","integrate((x^2-x-1)/(x^2+1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - x - 1}{\sqrt{x^{3} - x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - x - 1)/(sqrt(x^3 - x)*(x^2 + 1)), x)","F",0
746,0,0,0,0.000000," ","integrate((x^2+x-1)/(x^2+1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + x - 1}{\sqrt{x^{3} - x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 + x - 1)/(sqrt(x^3 - x)*(x^2 + 1)), x)","F",0
747,0,0,0,0.000000," ","integrate((7*x^2+x-7)/(x^2+1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{7 \, x^{2} + x - 7}{\sqrt{x^{3} - x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((7*x^2 + x - 7)/(sqrt(x^3 - x)*(x^2 + 1)), x)","F",0
748,0,0,0,0.000000," ","integrate(1/(-2+x)/(x^3-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{4}} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(1/((x^3 - x^2)^(1/4)*(x - 2)), x)","F",0
749,1,61,0,0.384429," ","integrate((a*x^3+b)*(x^4-x)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, a x^{3} - a + 4 \, b\right)} \sqrt{x^{4} - x} x - \frac{1}{24} \, {\left(a + 4 \, b\right)} {\left(\log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right) - \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)\right)}"," ",0,"1/12*(2*a*x^3 - a + 4*b)*sqrt(x^4 - x)*x - 1/24*(a + 4*b)*(log(sqrt(-1/x^3 + 1) + 1) - log(abs(sqrt(-1/x^3 + 1) - 1)))","A",0
750,0,0,0,0.000000," ","integrate((2*x^2-x-2)/(x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - x - 2}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 - x - 2)/(sqrt(x^4 + x^2 + 1)*(x^2 + 1)), x)","F",0
751,0,0,0,0.000000," ","integrate(x^3*(9*a*x^4-5*b)/(a*x^5-b*x)^(1/4)/(a*x^9-b*x^5-2),x, algorithm=""giac"")","\int \frac{{\left(9 \, a x^{4} - 5 \, b\right)} x^{3}}{{\left(a x^{9} - b x^{5} - 2\right)} {\left(a x^{5} - b x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((9*a*x^4 - 5*b)*x^3/((a*x^9 - b*x^5 - 2)*(a*x^5 - b*x)^(1/4)), x)","F",0
752,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^3+x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{3} + x^{2} + x} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(x^3 + x^2 + x)*(x^2 - 1)), x)","F",0
753,0,0,0,0.000000," ","integrate((a*b*c-(a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(-a*b*c+(a*b+a*c+b*c-d)*x-(a+b+c)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{a b c - {\left(a + b + c\right)} x^{2} + 2 \, x^{3}}{\sqrt{-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)} x} {\left(a b c + {\left(a + b + c\right)} x^{2} - x^{3} - {\left(a b + a c + b c - d\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b*c - (a + b + c)*x^2 + 2*x^3)/(sqrt(-(a - x)*(b - x)*(c - x)*x)*(a*b*c + (a + b + c)*x^2 - x^3 - (a*b + a*c + b*c - d)*x)), x)","F",0
754,1,70,0,0.471348," ","integrate((a*x^3-b)*(a*x^3+b)^(1/2)/x^7,x, algorithm=""giac"")","\frac{\frac{5 \, a^{3} \arctan\left(\frac{\sqrt{a x^{3} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{3 \, {\left(a x^{3} + b\right)}^{\frac{3}{2}} a^{3} - 5 \, \sqrt{a x^{3} + b} a^{3} b}{a^{2} x^{6}}}{12 \, a}"," ",0,"1/12*(5*a^3*arctan(sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b) - (3*(a*x^3 + b)^(3/2)*a^3 - 5*sqrt(a*x^3 + b)*a^3*b)/(a^2*x^6))/a","A",0
755,1,69,0,0.282970," ","integrate((a*x^3+b)^(1/2)*(a*x^3+2*b)/x^7,x, algorithm=""giac"")","\frac{\frac{a^{3} \arctan\left(\frac{\sqrt{a x^{3} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{3 \, {\left(a x^{3} + b\right)}^{\frac{3}{2}} a^{3} - \sqrt{a x^{3} + b} a^{3} b}{a^{2} x^{6}}}{6 \, a}"," ",0,"1/6*(a^3*arctan(sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b) - (3*(a*x^3 + b)^(3/2)*a^3 - sqrt(a*x^3 + b)*a^3*b)/(a^2*x^6))/a","A",0
756,1,62,0,4.217229," ","integrate((3*a*b*c*x-2*(a*b+a*c+b*c)*x^2+(a+b+c)*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(a*b*c-(a*b+a*c+b*c)*x+(a+b+c)*x^2+(-1+d)*x^3),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{\sqrt{-\frac{a b c}{x^{3}} + \frac{a b}{x^{2}} + \frac{a c}{x^{2}} + \frac{b c}{x^{2}} - \frac{a}{x} - \frac{b}{x} - \frac{c}{x} + 1}}{\sqrt{-d}}\right)}{\sqrt{-d}}"," ",0,"-2*arctan(sqrt(-a*b*c/x^3 + a*b/x^2 + a*c/x^2 + b*c/x^2 - a/x - b/x - c/x + 1)/sqrt(-d))/sqrt(-d)","A",0
757,1,69,0,4.029276," ","integrate(x*(3*a*b*c-2*(a*b+a*c+b*c)*x+(a+b+c)*x^2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(-a*b*c*d+(a*b+a*c+b*c)*d*x-(a+b+c)*d*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\frac{2 \, {\left| d \right|} \arctan\left(\frac{\sqrt{-\frac{a b c}{x^{3}} + \frac{a b}{x^{2}} + \frac{a c}{x^{2}} + \frac{b c}{x^{2}} - \frac{a}{x} - \frac{b}{x} - \frac{c}{x} + 1}}{\sqrt{-\frac{1}{d}}}\right)}{\sqrt{-d} d}"," ",0,"2*abs(d)*arctan(sqrt(-a*b*c/x^3 + a*b/x^2 + a*c/x^2 + b*c/x^2 - a/x - b/x - c/x + 1)/sqrt(-1/d))/(sqrt(-d)*d)","A",0
758,1,57,0,0.261148," ","integrate((x^4-x^2)^(1/4),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + \frac{1}{4} \, \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{8} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"-1/2*x^2*(-1/x^2 + 1)^(1/4) + 1/4*arctan((-1/x^2 + 1)^(1/4)) + 1/8*log((-1/x^2 + 1)^(1/4) + 1) - 1/8*log(-(-1/x^2 + 1)^(1/4) + 1)","A",0
759,1,57,0,0.290986," ","integrate(x^2*(x^4+x^2)^(1/4),x, algorithm=""giac"")","\frac{1}{16} \, {\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right)} x^{4} - \frac{3}{32} \, \arctan\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{3}{64} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{3}{64} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/16*((1/x^2 + 1)^(5/4) + 3*(1/x^2 + 1)^(1/4))*x^4 - 3/32*arctan((1/x^2 + 1)^(1/4)) - 3/64*log((1/x^2 + 1)^(1/4) + 1) + 3/64*log((1/x^2 + 1)^(1/4) - 1)","A",0
760,0,0,0,0.000000," ","integrate((2*x^4-1)*(2*x^4+3*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} + 3 \, x^{2} + 1} {\left(2 \, x^{4} - 1\right)}}{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(2*x^4 + 3*x^2 + 1)*(2*x^4 - 1)/(2*x^4 + 2*x^2 + 1)^2, x)","F",0
761,0,0,0,0.000000," ","integrate((2*x^4-2*x^3+x^2-2)^(1/2)*(2*x^4-x^3+2)/(x^4-x^3-1)/(2*x^4-2*x^3-x^2-2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x^{3} + 2\right)} \sqrt{2 \, x^{4} - 2 \, x^{3} + x^{2} - 2}}{{\left(2 \, x^{4} - 2 \, x^{3} - x^{2} - 2\right)} {\left(x^{4} - x^{3} - 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 - x^3 + 2)*sqrt(2*x^4 - 2*x^3 + x^2 - 2)/((2*x^4 - 2*x^3 - x^2 - 2)*(x^4 - x^3 - 1)), x)","F",0
762,0,0,0,0.000000," ","integrate((a*x^2-b)/(a*x^2+b)/(a^2*x^4+b^2)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{\sqrt{a^{2} x^{4} + b^{2}} {\left(a x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/(sqrt(a^2*x^4 + b^2)*(a*x^2 + b)), x)","F",0
763,0,0,0,0.000000," ","integrate((a*x^4+3*b)/(a*x^4-x^3-b)/(a*x^5-b*x)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + 3 \, b}{{\left(a x^{5} - b x\right)}^{\frac{1}{4}} {\left(a x^{4} - x^{3} - b\right)}}\,{d x}"," ",0,"integrate((a*x^4 + 3*b)/((a*x^5 - b*x)^(1/4)*(a*x^4 - x^3 - b)), x)","F",0
764,0,0,0,0.000000," ","integrate((x^3-1)*(x^6-1)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} - 1\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 - 1)/x, x)","F",0
765,0,0,0,0.000000," ","integrate(x*(3+4*x)*(x^3-2*x-1)^(1/3)/(x^6-8*x^2-8*x-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 2 \, x - 1\right)}^{\frac{1}{3}} {\left(4 \, x + 3\right)} x}{x^{6} - 8 \, x^{2} - 8 \, x - 2}\,{d x}"," ",0,"integrate((x^3 - 2*x - 1)^(1/3)*(4*x + 3)*x/(x^6 - 8*x^2 - 8*x - 2), x)","F",0
766,0,0,0,0.000000," ","integrate(x*(3+4*x)*(x^3-2*x-1)^(1/3)/(x^6-8*x^2-8*x-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 2 \, x - 1\right)}^{\frac{1}{3}} {\left(4 \, x + 3\right)} x}{x^{6} - 8 \, x^{2} - 8 \, x - 2}\,{d x}"," ",0,"integrate((x^3 - 2*x - 1)^(1/3)*(4*x + 3)*x/(x^6 - 8*x^2 - 8*x - 2), x)","F",0
767,0,0,0,0.000000," ","integrate((3+2*x)*(x^3+x+1)^(2/3)/(x^6+x^4+x^3+x^2+2*x+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x + 1\right)}^{\frac{2}{3}} {\left(2 \, x + 3\right)}}{x^{6} + x^{4} + x^{3} + x^{2} + 2 \, x + 1}\,{d x}"," ",0,"integrate((x^3 + x + 1)^(2/3)*(2*x + 3)/(x^6 + x^4 + x^3 + x^2 + 2*x + 1), x)","F",0
768,0,0,0,0.000000," ","integrate((3+2*x)*(x^3+x+1)^(2/3)/(x^6+x^4+x^3+x^2+2*x+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x + 1\right)}^{\frac{2}{3}} {\left(2 \, x + 3\right)}}{x^{6} + x^{4} + x^{3} + x^{2} + 2 \, x + 1}\,{d x}"," ",0,"integrate((x^3 + x + 1)^(2/3)*(2*x + 3)/(x^6 + x^4 + x^3 + x^2 + 2*x + 1), x)","F",0
769,0,0,0,0.000000," ","integrate((x^3+2)*(-x^4+x^3+x)^(1/3)/(x^6-x^5+x^4-2*x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(-x^{4} + x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{3} + 2\right)}}{x^{6} - x^{5} + x^{4} - 2 \, x^{3} + x^{2} + 1}\,{d x}"," ",0,"integrate((-x^4 + x^3 + x)^(1/3)*(x^3 + 2)/(x^6 - x^5 + x^4 - 2*x^3 + x^2 + 1), x)","F",0
770,0,0,0,0.000000," ","integrate((x^3+2)*(-x^4+x^3+x)^(1/3)/(x^6-x^5+x^4-2*x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(-x^{4} + x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{3} + 2\right)}}{x^{6} - x^{5} + x^{4} - 2 \, x^{3} + x^{2} + 1}\,{d x}"," ",0,"integrate((-x^4 + x^3 + x)^(1/3)*(x^3 + 2)/(x^6 - x^5 + x^4 - 2*x^3 + x^2 + 1), x)","F",0
771,0,0,0,0.000000," ","integrate((x^2+3)*(x^3+x^2+1)^(2/3)/(x^6+x^5-x^4+x^3-2*x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x^{2} + 1\right)}^{\frac{2}{3}} {\left(x^{2} + 3\right)}}{x^{6} + x^{5} - x^{4} + x^{3} - 2 \, x^{2} - 1}\,{d x}"," ",0,"integrate((x^3 + x^2 + 1)^(2/3)*(x^2 + 3)/(x^6 + x^5 - x^4 + x^3 - 2*x^2 - 1), x)","F",0
772,0,0,0,0.000000," ","integrate((x^2+3)*(x^3+x^2+1)^(2/3)/(x^6+x^5-x^4+x^3-2*x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x^{2} + 1\right)}^{\frac{2}{3}} {\left(x^{2} + 3\right)}}{x^{6} + x^{5} - x^{4} + x^{3} - 2 \, x^{2} - 1}\,{d x}"," ",0,"integrate((x^3 + x^2 + 1)^(2/3)*(x^2 + 3)/(x^6 + x^5 - x^4 + x^3 - 2*x^2 - 1), x)","F",0
773,0,0,0,0.000000," ","integrate((a*x^8+b)/(-a*x^8+b)^(1/4)/(a*x^8+c*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{8} + b}{{\left(a x^{8} + c x^{4} - b\right)} {\left(-a x^{8} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^8 + b)/((a*x^8 + c*x^4 - b)*(-a*x^8 + b)^(1/4)), x)","F",0
774,0,0,0,0.000000," ","integrate(x*(x^8-x^3+2)^(1/3)*(5*x^8-6)/(x^16+4*x^8+x^6+4),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{8} - 6\right)} {\left(x^{8} - x^{3} + 2\right)}^{\frac{1}{3}} x}{x^{16} + 4 \, x^{8} + x^{6} + 4}\,{d x}"," ",0,"integrate((5*x^8 - 6)*(x^8 - x^3 + 2)^(1/3)*x/(x^16 + 4*x^8 + x^6 + 4), x)","F",0
775,0,0,0,0.000000," ","integrate((a*b+a*c-2*a*x-b*c+x^2)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(b*c+a*d-(b+c+d)*x+x^2),x, algorithm=""giac"")","\int \frac{a b + a c - b c - 2 \, a x + x^{2}}{\sqrt{-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}} {\left(b c + a d - {\left(b + c + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate((a*b + a*c - b*c - 2*a*x + x^2)/(sqrt(-(a - x)*(b - x)*(c - x))*(b*c + a*d - (b + c + d)*x + x^2)), x)","F",0
776,0,0,0,0.000000," ","integrate((a*b+a*c-2*a*x-b*c+x^2)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(a+b*c*d-(b*d+c*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a b + a c - b c - 2 \, a x + x^{2}}{\sqrt{-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}} {\left(b c d + d x^{2} - {\left(b d + c d + 1\right)} x + a\right)}}\,{d x}"," ",0,"integrate((a*b + a*c - b*c - 2*a*x + x^2)/(sqrt(-(a - x)*(b - x)*(c - x))*(b*c*d + d*x^2 - (b*d + c*d + 1)*x + a)), x)","F",0
777,0,0,0,0.000000," ","integrate((k^2*x^2-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2+1),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} - 1}{{\left(k^{2} x^{2} + 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^2*x^2 - 1)/((k^2*x^2 + 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
778,-1,0,0,0.000000," ","integrate((a*(a*b+a*c-3*b*c)+(-2*a^2+a*b+a*c+3*b*c)*x+(a-2*b-2*c)*x^2+x^3)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(-a^3-b*c*d+(3*a^2+b*d+c*d)*x-(3*a+d)*x^2+x^3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
779,0,0,0,0.000000," ","integrate((a*x^3-2*c)*(a*x^3+b*x^2+c)^(1/2)/(a*x^3+c)^2,x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3} + b x^{2} + c} {\left(a x^{3} - 2 \, c\right)}}{{\left(a x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^3 + b*x^2 + c)*(a*x^3 - 2*c)/(a*x^3 + c)^2, x)","F",0
780,0,0,0,0.000000," ","integrate((a^2*x^2-b)/(a^2*x^2+2*a*b*x+b)/(a^2*x^3+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a^{2} x^{2} - b}{\sqrt{a^{2} x^{3} + b x} {\left(a^{2} x^{2} + 2 \, a b x + b\right)}}\,{d x}"," ",0,"integrate((a^2*x^2 - b)/(sqrt(a^2*x^3 + b*x)*(a^2*x^2 + 2*a*b*x + b)), x)","F",0
781,-2,0,0,0.000000," ","integrate((a*(a*b+a*c-3*b*c)+(-2*a^2+a*b+a*c+3*b*c)*x+(a-2*b-2*c)*x^2+x^3)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(-b*c-a^3*d+(3*a^2*d+b+c)*x-(3*a*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 27.35Not invertible Error: Bad Argument Value","F(-2)",0
782,1,118,0,0.705333," ","integrate((x^2-1)*(x^4+1)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{{\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{3} - 2 \, {\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} + x^{2} - \sqrt{x^{4} + 1} + 2}{2 \, {\left({\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1\right)}^{2}} - \frac{1}{4} \, \log\left(x^{2} - \sqrt{x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 1} + 1\right) - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"-1/2*((x^2 - sqrt(x^4 + 1))^3 - 2*(x^2 - sqrt(x^4 + 1))^2 + x^2 - sqrt(x^4 + 1) + 2)/((x^2 - sqrt(x^4 + 1))^2 - 1)^2 - 1/4*log(x^2 - sqrt(x^4 + 1) + 1) + 1/4*log(-x^2 + sqrt(x^4 + 1) + 1) - 1/2*log(-x^2 + sqrt(x^4 + 1))","B",0
783,1,81,0,0.348936," ","integrate((x^2-1)*(x^4+1)^(1/2)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} + 1} - \frac{1}{{\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1} + \frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{4} + 1} + 1\right) - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1} + 1\right) + \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"1/2*sqrt(x^4 + 1) - 1/((x^2 - sqrt(x^4 + 1))^2 - 1) + 1/2*log(x^2 - sqrt(x^4 + 1) + 1) - 1/2*log(-x^2 + sqrt(x^4 + 1) + 1) + 1/2*log(-x^2 + sqrt(x^4 + 1))","A",0
784,0,0,0,0.000000," ","integrate((2*x^3+1)*(x^6-1)^(1/2)/x^7,x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(2 \, x^{3} + 1\right)}}{x^{7}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(2*x^3 + 1)/x^7, x)","F",0
785,0,0,0,0.000000," ","integrate((2*x^3+1)*(x^6-1)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(2 \, x^{3} + 1\right)}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(2*x^3 + 1)/x^4, x)","F",0
786,0,0,0,0.000000," ","integrate((a^6*x^6+b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6-b^6+c*x^3),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} + b^{6}}{{\left(a^{6} x^{6} - b^{6} + c x^{3}\right)} \sqrt{a^{2} x^{3} - b^{2} x}}\,{d x}"," ",0,"integrate((a^6*x^6 + b^6)/((a^6*x^6 - b^6 + c*x^3)*sqrt(a^2*x^3 - b^2*x)), x)","F",0
787,0,0,0,0.000000," ","integrate((a^6*x^6+b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6-b^6+c*x^3),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} + b^{6}}{{\left(a^{6} x^{6} - b^{6} + c x^{3}\right)} \sqrt{a^{2} x^{3} - b^{2} x}}\,{d x}"," ",0,"integrate((a^6*x^6 + b^6)/((a^6*x^6 - b^6 + c*x^3)*sqrt(a^2*x^3 - b^2*x)), x)","F",0
788,0,0,0,0.000000," ","integrate((-3*x^5+x)/(x^5+x)^(1/2)/(x^8+2*x^4-a*x^2+1),x, algorithm=""giac"")","\int -\frac{3 \, x^{5} - x}{{\left(x^{8} + 2 \, x^{4} - a x^{2} + 1\right)} \sqrt{x^{5} + x}}\,{d x}"," ",0,"integrate(-(3*x^5 - x)/((x^8 + 2*x^4 - a*x^2 + 1)*sqrt(x^5 + x)), x)","F",0
789,0,0,0,0.000000," ","integrate((-2*x^8+1)^(1/2)*(2*x^8-1)*(2*x^8+1)/x^7/(2*x^8+x^4-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{8} + 1\right)} {\left(2 \, x^{8} - 1\right)} \sqrt{-2 \, x^{8} + 1}}{{\left(2 \, x^{8} + x^{4} - 1\right)} x^{7}}\,{d x}"," ",0,"integrate((2*x^8 + 1)*(2*x^8 - 1)*sqrt(-2*x^8 + 1)/((2*x^8 + x^4 - 1)*x^7), x)","F",0
790,0,0,0,0.000000," ","integrate((3*x^5-x)/(x^5+x)^(1/2)/(a*x^8+2*a*x^4-x^2+a),x, algorithm=""giac"")","\int \frac{3 \, x^{5} - x}{{\left(a x^{8} + 2 \, a x^{4} - x^{2} + a\right)} \sqrt{x^{5} + x}}\,{d x}"," ",0,"integrate((3*x^5 - x)/((a*x^8 + 2*a*x^4 - x^2 + a)*sqrt(x^5 + x)), x)","F",0
791,0,0,0,0.000000," ","integrate(x^5*(9*a*x^2+7*b)/(a*x^5+b*x^3)^(1/4)/(a*x^9+b*x^7-2),x, algorithm=""giac"")","\int \frac{{\left(9 \, a x^{2} + 7 \, b\right)} x^{5}}{{\left(a x^{9} + b x^{7} - 2\right)} {\left(a x^{5} + b x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((9*a*x^2 + 7*b)*x^5/((a*x^9 + b*x^7 - 2)*(a*x^5 + b*x^3)^(1/4)), x)","F",0
792,0,0,0,0.000000," ","integrate(x^2/(x^2+1)/(1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/5),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(1024 \, x^{10} - 16640 \, x^{9} + 112000 \, x^{8} - 401440 \, x^{7} + 820340 \, x^{6} - 954733 \, x^{5} + 615255 \, x^{4} - 225810 \, x^{3} + 47250 \, x^{2} - 5265 \, x + 243\right)}^{\frac{1}{5}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/((1024*x^10 - 16640*x^9 + 112000*x^8 - 401440*x^7 + 820340*x^6 - 954733*x^5 + 615255*x^4 - 225810*x^3 + 47250*x^2 - 5265*x + 243)^(1/5)*(x^2 + 1)), x)","F",0
793,0,0,0,0.000000," ","integrate((x^2-2*x+1)^(1/3)/(x^2+2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - 2 \, x + 1\right)}^{\frac{1}{3}}}{x^{2} + 2}\,{d x}"," ",0,"integrate((x^2 - 2*x + 1)^(1/3)/(x^2 + 2), x)","F",0
794,0,0,0,0.000000," ","integrate((x^2+2*x+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 2 \, x + 1\right)}^{\frac{1}{3}}}{x^{2} + 3}\,{d x}"," ",0,"integrate((x^2 + 2*x + 1)^(1/3)/(x^2 + 3), x)","F",0
795,0,0,0,0.000000," ","integrate(1/(-1+x)/(x^3+x)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + x\right)}^{\frac{1}{4}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^3 + x)^(1/4)*(x - 1)), x)","F",0
796,0,0,0,0.000000," ","integrate((x^4-1)/(x^3+x)^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{4} + 1\right)} \sqrt{x^{3} + x}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^4 + 1)*sqrt(x^3 + x)), x)","F",0
797,0,0,0,0.000000," ","integrate((x^3+1)/(x^3-1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3} + 1}{\sqrt{x^{4} + 1} {\left(x^{3} - 1\right)}}\,{d x}"," ",0,"integrate((x^3 + 1)/(sqrt(x^4 + 1)*(x^3 - 1)), x)","F",0
798,0,0,0,0.000000," ","integrate((-1+x)/x/(x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((x - 1)/((x^4 + 1)^(1/4)*x), x)","F",0
799,0,0,0,0.000000," ","integrate(x^2/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a x^{4} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/(a*x^4 - b)^(3/4), x)","F",0
800,0,0,0,0.000000," ","integrate((x^4+6)*(x^5+x^4-2*x)^(1/2)/(x^4-2)/(x^4-x^3-2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{5} + x^{4} - 2 \, x} {\left(x^{4} + 6\right)}}{{\left(x^{4} - x^{3} - 2\right)} {\left(x^{4} - 2\right)}}\,{d x}"," ",0,"integrate(sqrt(x^5 + x^4 - 2*x)*(x^4 + 6)/((x^4 - x^3 - 2)*(x^4 - 2)), x)","F",0
801,0,0,0,0.000000," ","integrate((x^2-3)*(x^3-x^2+1)^(2/3)/(x^6+x^5+x^4-x^3-2*x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2} + 1\right)}^{\frac{2}{3}} {\left(x^{2} - 3\right)}}{x^{6} + x^{5} + x^{4} - x^{3} - 2 \, x^{2} + 1}\,{d x}"," ",0,"integrate((x^3 - x^2 + 1)^(2/3)*(x^2 - 3)/(x^6 + x^5 + x^4 - x^3 - 2*x^2 + 1), x)","F",0
802,0,0,0,0.000000," ","integrate((x^2-3)*(x^3-x^2+1)^(2/3)/(x^6+x^5+x^4-x^3-2*x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2} + 1\right)}^{\frac{2}{3}} {\left(x^{2} - 3\right)}}{x^{6} + x^{5} + x^{4} - x^{3} - 2 \, x^{2} + 1}\,{d x}"," ",0,"integrate((x^3 - x^2 + 1)^(2/3)*(x^2 - 3)/(x^6 + x^5 + x^4 - x^3 - 2*x^2 + 1), x)","F",0
803,1,47,0,0.283859," ","integrate((x^6-1)^(1/2)*(2*x^6-1)^2/x/(4*x^6-1),x, algorithm=""giac"")","\frac{1}{9} \, {\left(x^{6} - 1\right)}^{\frac{3}{2}} - \frac{1}{24} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) - \frac{1}{4} \, \sqrt{x^{6} - 1} + \frac{1}{3} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"1/9*(x^6 - 1)^(3/2) - 1/24*sqrt(3)*arctan(2/3*sqrt(3)*sqrt(x^6 - 1)) - 1/4*sqrt(x^6 - 1) + 1/3*arctan(sqrt(x^6 - 1))","A",0
804,0,0,0,0.000000," ","integrate(1/(x^3+x)^(1/3)/(a*x^6+b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{6} + b\right)} {\left(x^{3} + x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a*x^6 + b)*(x^3 + x)^(1/3)), x)","F",0
805,0,0,0,0.000000," ","integrate(1/(x^3+x)^(1/3)/(a*x^6+b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{6} + b\right)} {\left(x^{3} + x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a*x^6 + b)*(x^3 + x)^(1/3)), x)","F",0
806,0,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4-2*x^2+b)/(a*x^6+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} - b}{{\left(a x^{6} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^4 - b)/((a*x^6 + b*x^2)^(1/4)*(a*x^4 - 2*x^2 + b)), x)","F",0
807,0,0,0,0.000000," ","integrate((x^5+4)*(x^10+x^8-2*x^5+1)^(1/2)/x^9,x, algorithm=""giac"")","\int \frac{\sqrt{x^{10} + x^{8} - 2 \, x^{5} + 1} {\left(x^{5} + 4\right)}}{x^{9}}\,{d x}"," ",0,"integrate(sqrt(x^10 + x^8 - 2*x^5 + 1)*(x^5 + 4)/x^9, x)","F",0
808,0,0,0,0.000000," ","integrate((x^6+1)*(x^6+x^3-1)^(2/3)/(x^12-x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{6} + 1\right)}}{x^{12} - x^{6} + 1}\,{d x}"," ",0,"integrate((x^6 + x^3 - 1)^(2/3)*(x^6 + 1)/(x^12 - x^6 + 1), x)","F",0
809,0,0,0,0.000000," ","integrate((x^6+1)*(x^6+x^3-1)^(2/3)/(x^12-x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{6} + 1\right)}}{x^{12} - x^{6} + 1}\,{d x}"," ",0,"integrate((x^6 + x^3 - 1)^(2/3)*(x^6 + 1)/(x^12 - x^6 + 1), x)","F",0
810,0,0,0,0.000000," ","integrate((5*x^7-2)*(2*x^8+x^3+2*x)^(1/3)/(4*x^14+8*x^7+x^4+4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{8} + x^{3} + 2 \, x\right)}^{\frac{1}{3}} {\left(5 \, x^{7} - 2\right)}}{4 \, x^{14} + 8 \, x^{7} + x^{4} + 4}\,{d x}"," ",0,"integrate((2*x^8 + x^3 + 2*x)^(1/3)*(5*x^7 - 2)/(4*x^14 + 8*x^7 + x^4 + 4), x)","F",0
811,0,0,0,0.000000," ","integrate((5*x^7-2)*(2*x^8+x^3+2*x)^(1/3)/(4*x^14+8*x^7+x^4+4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{8} + x^{3} + 2 \, x\right)}^{\frac{1}{3}} {\left(5 \, x^{7} - 2\right)}}{4 \, x^{14} + 8 \, x^{7} + x^{4} + 4}\,{d x}"," ",0,"integrate((2*x^8 + x^3 + 2*x)^(1/3)*(5*x^7 - 2)/(4*x^14 + 8*x^7 + x^4 + 4), x)","F",0
812,0,0,0,0.000000," ","integrate(1/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(1/sqrt(a*x + sqrt(a^2*x^2 + b^2)), x)","F",0
813,1,105,0,0.287973," ","integrate(x^10*(x^4-1)^(1/4),x, algorithm=""giac"")","\frac{1}{384} \, x^{12} {\left(\frac{18 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 1\right)}}{x} - \frac{21 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + \frac{7 \, {\left(x^{8} - 2 \, x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x^{9}}\right)} + \frac{7}{256} \, \arctan\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{7}{512} \, \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{7}{512} \, \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right)"," ",0,"1/384*x^12*(18*(x^4 - 1)^(1/4)*(1/x^4 - 1)/x - 21*(x^4 - 1)^(1/4)/x + 7*(x^8 - 2*x^4 + 1)*(x^4 - 1)^(1/4)/x^9) + 7/256*arctan((x^4 - 1)^(1/4)/x) + 7/512*log((x^4 - 1)^(1/4)/x + 1) - 7/512*log(-(x^4 - 1)^(1/4)/x + 1)","B",0
814,1,104,0,0.269400," ","integrate(x^10*(x^4+1)^(1/4),x, algorithm=""giac"")","\frac{1}{384} \, x^{12} {\left(\frac{18 \, {\left(x^{4} + 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} + 1\right)}}{x} + \frac{21 \, {\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} - \frac{7 \, {\left(x^{8} + 2 \, x^{4} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x^{9}}\right)} + \frac{7}{256} \, \arctan\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{7}{512} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{7}{512} \, \log\left(\frac{{\left(x^{4} + 1\right)}^{\frac{1}{4}}}{x} - 1\right)"," ",0,"1/384*x^12*(18*(x^4 + 1)^(1/4)*(1/x^4 + 1)/x + 21*(x^4 + 1)^(1/4)/x - 7*(x^8 + 2*x^4 + 1)*(x^4 + 1)^(1/4)/x^9) + 7/256*arctan((x^4 + 1)^(1/4)/x) + 7/512*log((x^4 + 1)^(1/4)/x + 1) - 7/512*log((x^4 + 1)^(1/4)/x - 1)","B",0
815,0,0,0,0.000000," ","integrate((x^2+1)/(x^4-x^2+1)/(x^4+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^4 + x^2)^(1/4)*(x^4 - x^2 + 1)), x)","F",0
816,0,0,0,0.000000," ","integrate(1/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
817,0,0,0,0.000000," ","integrate(1/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
818,0,0,0,0.000000," ","integrate((-x^2+1)/x/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 1}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} x}\,{d x}"," ",0,"integrate(-(x^2 - 1)/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*x), x)","F",0
819,0,0,0,0.000000," ","integrate(x^2*(3*x^4-1)/(x^4+1)^2/(a*x^4+a-x)/(x^5+x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{4} - 1\right)} x^{2}}{{\left(a x^{4} + a - x\right)} \sqrt{x^{5} + x} {\left(x^{4} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((3*x^4 - 1)*x^2/((a*x^4 + a - x)*sqrt(x^5 + x)*(x^4 + 1)^2), x)","F",0
820,0,0,0,0.000000," ","integrate((x^4-3)*(x^8-x^7-x^6+2*x^4-x^3+1)/x^6/(x^4-x^3+1)/(x^5+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - x^{7} - x^{6} + 2 \, x^{4} - x^{3} + 1\right)} {\left(x^{4} - 3\right)}}{{\left(x^{5} + x\right)}^{\frac{1}{4}} {\left(x^{4} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^8 - x^7 - x^6 + 2*x^4 - x^3 + 1)*(x^4 - 3)/((x^5 + x)^(1/4)*(x^4 - x^3 + 1)*x^6), x)","F",0
821,1,67,0,0.146029," ","integrate((x^2+1)/(1+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4}{11} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{11}{2}} - \frac{20}{9} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{9}{2}} + \frac{32}{7} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{7}{2}} - \frac{16}{5} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{5}{2}} + \frac{4}{3} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{3}{2}} - 4 \, \sqrt{\sqrt{x + 1} + 1}"," ",0,"4/11*(sqrt(x + 1) + 1)^(11/2) - 20/9*(sqrt(x + 1) + 1)^(9/2) + 32/7*(sqrt(x + 1) + 1)^(7/2) - 16/5*(sqrt(x + 1) + 1)^(5/2) + 4/3*(sqrt(x + 1) + 1)^(3/2) - 4*sqrt(sqrt(x + 1) + 1)","A",0
822,0,0,0,0.000000," ","integrate((-1+2*x)/(1+x)/(-a^2*x^2+(1+x)^6)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x - 1}{\sqrt{{\left(x + 1\right)}^{6} - a^{2} x^{2}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((2*x - 1)/(sqrt((x + 1)^6 - a^2*x^2)*(x + 1)), x)","F",0
823,-1,0,0,0.000000," ","integrate(x/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
824,0,0,0,0.000000," ","integrate((a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}\,{d x}"," ",0,"integrate(sqrt(a*x + sqrt(a^2*x^2 + b^2)), x)","F",0
825,1,76,0,0.858070," ","integrate(1/(1+x^(1/2))/(-x^(1/2)+x)^(1/2),x, algorithm=""giac"")","-\sqrt{2} \log\left(\frac{2 \, {\left(\sqrt{2} - \sqrt{x - \sqrt{x}} + \sqrt{x} + 1\right)}}{{\left| 2 \, \sqrt{2} + 2 \, \sqrt{x - \sqrt{x}} - 2 \, \sqrt{x} - 2 \right|}}\right) - 2 \, \log\left({\left| 2 \, \sqrt{x - \sqrt{x}} - 2 \, \sqrt{x} + 1 \right|}\right)"," ",0,"-sqrt(2)*log(2*(sqrt(2) - sqrt(x - sqrt(x)) + sqrt(x) + 1)/abs(2*sqrt(2) + 2*sqrt(x - sqrt(x)) - 2*sqrt(x) - 2)) - 2*log(abs(2*sqrt(x - sqrt(x)) - 2*sqrt(x) + 1))","A",0
826,0,0,0,0.000000," ","integrate(x/(x^2-1)/(x^3+x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} + x^{2} + x} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^3 + x^2 + x)*(x^2 - 1)), x)","F",0
827,0,0,0,0.000000," ","integrate((-a*b*c+2*a*(b+c)*x-(3*a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(a*d+(b*c-d)*x-(b+c)*x^2+x^3),x, algorithm=""giac"")","\int \frac{a b c - 2 \, a {\left(b + c\right)} x + {\left(3 \, a + b + c\right)} x^{2} - 2 \, x^{3}}{\sqrt{-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)} x} {\left({\left(b + c\right)} x^{2} - x^{3} - a d - {\left(b c - d\right)} x\right)}}\,{d x}"," ",0,"integrate((a*b*c - 2*a*(b + c)*x + (3*a + b + c)*x^2 - 2*x^3)/(sqrt(-(a - x)*(b - x)*(c - x)*x)*((b + c)*x^2 - x^3 - a*d - (b*c - d)*x)), x)","F",0
828,1,54,0,0.133854," ","integrate((a*x^3+3*b)/x/(a*x^3-b)/(a*x^3+b)^(1/2),x, algorithm=""giac"")","\frac{4 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{a x^{3} + b}}{2 \, \sqrt{-b}}\right)}{3 \, \sqrt{-b}} - \frac{2 \, \arctan\left(\frac{\sqrt{a x^{3} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}}"," ",0,"4/3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b) - 2*arctan(sqrt(a*x^3 + b)/sqrt(-b))/sqrt(-b)","A",0
829,0,0,0,0.000000," ","integrate((-a*x^3+2*c)*(a*x^3+b*x^2+c)^(1/2)/(c+(-3+b)*x^2+a*x^3)/(c+(-2+b)*x^2+a*x^3),x, algorithm=""giac"")","\int -\frac{\sqrt{a x^{3} + b x^{2} + c} {\left(a x^{3} - 2 \, c\right)}}{{\left(a x^{3} + {\left(b - 2\right)} x^{2} + c\right)} {\left(a x^{3} + {\left(b - 3\right)} x^{2} + c\right)}}\,{d x}"," ",0,"integrate(-sqrt(a*x^3 + b*x^2 + c)*(a*x^3 - 2*c)/((a*x^3 + (b - 2)*x^2 + c)*(a*x^3 + (b - 3)*x^2 + c)), x)","F",0
830,0,0,0,0.000000," ","integrate((-a*b*c+2*a*(b+c)*x-(3*a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(a+(b*c*d-1)*x-(b+c)*d*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{a b c - 2 \, a {\left(b + c\right)} x + {\left(3 \, a + b + c\right)} x^{2} - 2 \, x^{3}}{\sqrt{-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)} x} {\left({\left(b + c\right)} d x^{2} - d x^{3} - {\left(b c d - 1\right)} x - a\right)}}\,{d x}"," ",0,"integrate((a*b*c - 2*a*(b + c)*x + (3*a + b + c)*x^2 - 2*x^3)/(sqrt(-(a - x)*(b - x)*(c - x)*x)*((b + c)*d*x^2 - d*x^3 - (b*c*d - 1)*x - a)), x)","F",0
831,0,0,0,0.000000," ","integrate((x^3-1)/(x^3+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3} - 1}{\sqrt{x^{4} + 1} {\left(x^{3} + 1\right)}}\,{d x}"," ",0,"integrate((x^3 - 1)/(sqrt(x^4 + 1)*(x^3 + 1)), x)","F",0
832,1,68,0,0.241762," ","integrate(x^4*(x^4-x)^(1/4),x, algorithm=""giac"")","-\frac{1}{24} \, {\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right)} x^{6} + \frac{1}{16} \, \arctan\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{32} \, \log\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{32} \, \log\left({\left| {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/24*((-1/x^3 + 1)^(5/4) + 3*(-1/x^3 + 1)^(1/4))*x^6 + 1/16*arctan((-1/x^3 + 1)^(1/4)) + 1/32*log((-1/x^3 + 1)^(1/4) + 1) - 1/32*log(abs((-1/x^3 + 1)^(1/4) - 1))","A",0
833,1,68,0,0.147141," ","integrate((x^4-x^3)^(1/4),x, algorithm=""giac"")","-\frac{1}{8} \, {\left({\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{2} + \frac{3}{16} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{3}{32} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{3}{32} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/8*((-1/x + 1)^(5/4) + 3*(-1/x + 1)^(1/4))*x^2 + 3/16*arctan((-1/x + 1)^(1/4)) + 3/32*log((-1/x + 1)^(1/4) + 1) - 3/32*log(abs((-1/x + 1)^(1/4) - 1))","A",0
834,0,0,0,0.000000," ","integrate((-x^4-x^3+2)^(1/2)*(2*x^4+x^3+4)/(x^4+x^3-3*x^2-2)/(x^4+x^3-x^2-2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + x^{3} + 4\right)} \sqrt{-x^{4} - x^{3} + 2}}{{\left(x^{4} + x^{3} - x^{2} - 2\right)} {\left(x^{4} + x^{3} - 3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate((2*x^4 + x^3 + 4)*sqrt(-x^4 - x^3 + 2)/((x^4 + x^3 - x^2 - 2)*(x^4 + x^3 - 3*x^2 - 2)), x)","F",0
835,0,0,0,0.000000," ","integrate((a*x^4+b*x^3)^(1/4)/x/(a*x+x^2+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{3}\right)}^{\frac{1}{4}}}{{\left(a x + x^{2} + b\right)} x}\,{d x}"," ",0,"integrate((a*x^4 + b*x^3)^(1/4)/((a*x + x^2 + b)*x), x)","F",0
836,0,0,0,0.000000," ","integrate((a*x^4+b*x^3)^(1/4)/x/(a*x+x^2+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{3}\right)}^{\frac{1}{4}}}{{\left(a x + x^{2} + b\right)} x}\,{d x}"," ",0,"integrate((a*x^4 + b*x^3)^(1/4)/((a*x + x^2 + b)*x), x)","F",0
837,1,72,0,0.202252," ","integrate(x^2*(x^6-4)/(x^6-1)^(1/2)/(x^6+2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{6} \log\left(\frac{{\left(x^{3} - \sqrt{x^{6} - 1}\right)}^{2} - 2 \, \sqrt{6} + 5}{{\left(x^{3} - \sqrt{x^{6} - 1}\right)}^{2} + 2 \, \sqrt{6} + 5}\right) - \frac{1}{6} \, \log\left({\left(x^{3} - \sqrt{x^{6} - 1}\right)}^{2}\right)"," ",0,"1/6*sqrt(6)*log(((x^3 - sqrt(x^6 - 1))^2 - 2*sqrt(6) + 5)/((x^3 - sqrt(x^6 - 1))^2 + 2*sqrt(6) + 5)) - 1/6*log((x^3 - sqrt(x^6 - 1))^2)","A",0
838,0,0,0,0.000000," ","integrate((x^5-1)*(x^5+x^3-1)*(2*x^5+3)/x^6/(x^5-x^3-1)/(x^6-x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} + 3\right)} {\left(x^{5} + x^{3} - 1\right)} {\left(x^{5} - 1\right)}}{{\left(x^{6} - x\right)}^{\frac{1}{4}} {\left(x^{5} - x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^5 + 3)*(x^5 + x^3 - 1)*(x^5 - 1)/((x^6 - x)^(1/4)*(x^5 - x^3 - 1)*x^6), x)","F",0
839,1,87,0,0.189386," ","integrate((x^3+1)^(1/2)*(x^6+2*x^3+2)/x^7/(x^6-1),x, algorithm=""giac"")","\frac{5}{6} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{x^{3} + 1} \right|}}{2 \, {\left(\sqrt{2} + \sqrt{x^{3} + 1}\right)}}\right) + \frac{5 \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} - 3 \, \sqrt{x^{3} + 1}}{6 \, x^{6}} + \frac{5}{4} \, \log\left(\sqrt{x^{3} + 1} + 1\right) - \frac{5}{4} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"5/6*sqrt(2)*log(1/2*abs(-2*sqrt(2) + 2*sqrt(x^3 + 1))/(sqrt(2) + sqrt(x^3 + 1))) + 1/6*(5*(x^3 + 1)^(3/2) - 3*sqrt(x^3 + 1))/x^6 + 5/4*log(sqrt(x^3 + 1) + 1) - 5/4*log(abs(sqrt(x^3 + 1) - 1))","A",0
840,0,0,0,0.000000," ","integrate((x^5+x^2-1)^(1/2)*(3*x^5+2)/(x^10-2*x^5+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{5} + 2\right)} \sqrt{x^{5} + x^{2} - 1}}{x^{10} - 2 \, x^{5} + x^{4} + 1}\,{d x}"," ",0,"integrate((3*x^5 + 2)*sqrt(x^5 + x^2 - 1)/(x^10 - 2*x^5 + x^4 + 1), x)","F",0
841,0,0,0,0.000000," ","integrate(1/x/(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + \sqrt{x^{2} + x} x} \sqrt{x^{2} + x} x}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + sqrt(x^2 + x)*x)*sqrt(x^2 + x)*x), x)","F",0
842,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{b + \sqrt{a x^{2} + b^{2}}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2)), x)","F",0
843,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,0,0,0,0.000000," ","integrate((a*x-b)/(a*x+b)/(a^2*x^3+b^2*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x - b}{\sqrt{a^{2} x^{3} + b^{2} x} {\left(a x + b\right)}}\,{d x}"," ",0,"integrate((a*x - b)/(sqrt(a^2*x^3 + b^2*x)*(a*x + b)), x)","F",0
845,0,0,0,0.000000," ","integrate((a*x+b)/(a*x-b)/(a^2*x^3+b^2*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x + b}{\sqrt{a^{2} x^{3} + b^{2} x} {\left(a x - b\right)}}\,{d x}"," ",0,"integrate((a*x + b)/(sqrt(a^2*x^3 + b^2*x)*(a*x - b)), x)","F",0
846,0,0,0,0.000000," ","integrate((a*x^3-b*x^2)/(a*x^3+b*x^2)/(a^2*x^3+b^2*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{3} - b x^{2}}{\sqrt{a^{2} x^{3} + b^{2} x} {\left(a x^{3} + b x^{2}\right)}}\,{d x}"," ",0,"integrate((a*x^3 - b*x^2)/(sqrt(a^2*x^3 + b^2*x)*(a*x^3 + b*x^2)), x)","F",0
847,0,0,0,0.000000," ","integrate((2+5*x)/(x^4+2*x^3+5*x^2+20*x-12)^(1/2),x, algorithm=""giac"")","\int \frac{5 \, x + 2}{\sqrt{x^{4} + 2 \, x^{3} + 5 \, x^{2} + 20 \, x - 12}}\,{d x}"," ",0,"integrate((5*x + 2)/sqrt(x^4 + 2*x^3 + 5*x^2 + 20*x - 12), x)","F",0
848,0,0,0,0.000000," ","integrate((x^3-1)*(x^6-1)^(1/2)/x^7,x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - 1} {\left(x^{3} - 1\right)}}{x^{7}}\,{d x}"," ",0,"integrate(sqrt(x^6 - 1)*(x^3 - 1)/x^7, x)","F",0
849,1,50,0,0.416099," ","integrate((x^6-1)^(1/2)*(2*x^6-1)^2/x^7/(4*x^6-1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \sqrt{x^{6} - 1}\right) + \frac{1}{3} \, \sqrt{x^{6} - 1} + \frac{\sqrt{x^{6} - 1}}{6 \, x^{6}} - \frac{1}{6} \, \arctan\left(\sqrt{x^{6} - 1}\right)"," ",0,"-1/6*sqrt(3)*arctan(2/3*sqrt(3)*sqrt(x^6 - 1)) + 1/3*sqrt(x^6 - 1) + 1/6*sqrt(x^6 - 1)/x^6 - 1/6*arctan(sqrt(x^6 - 1))","A",0
850,0,0,0,0.000000," ","integrate((x^4-2)/(x^4+1)^(1/4)/(2*x^8+x^4-1),x, algorithm=""giac"")","\int \frac{x^{4} - 2}{{\left(2 \, x^{8} + x^{4} - 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 - 2)/((2*x^8 + x^4 - 1)*(x^4 + 1)^(1/4)), x)","F",0
851,-2,0,0,0.000000," ","integrate((10*x^8-x^2)/(x^6-1)^(1/2)/(4*x^6-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:rootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Unable to cancel step at 0 of -5/12*ln(-sqrt(-x^6+1)+1)+5/12*ln(sqrt(-x^6+1)+1)+1/2/sqrt(3)*atan(sqrt(-x^6+1)/sqrt(3))-5/12*ln(-sqrt(-x^6+1)+1)-5/12*ln(sqrt(-x^6+1)+1)-1/2/sqrt(3)*atan(sqrt(-x^6+1)/sqrt(3))Done","F(-2)",0
852,1,83,0,0.349655," ","integrate((x^2+1)/(x^2-1)/(2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{1}{18} \, \sqrt{6} \sqrt{2} \log\left(\frac{{\left| 2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} - 4 \, \sqrt{6} - 10 \right|}}{{\left| 2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} + 4 \, \sqrt{6} - 10 \right|}}\right) - \frac{x}{3 \, \sqrt{2 \, x^{2} + 1}}"," ",0,"-1/18*sqrt(6)*sqrt(2)*log(abs(2*(sqrt(2)*x - sqrt(2*x^2 + 1))^2 - 4*sqrt(6) - 10)/abs(2*(sqrt(2)*x - sqrt(2*x^2 + 1))^2 + 4*sqrt(6) - 10)) - 1/3*x/sqrt(2*x^2 + 1)","A",0
853,1,185,0,0.360260," ","integrate((a*x^2+b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) - \frac{1}{2} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) + \frac{1}{4} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right) - \frac{1}{4} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right) + \frac{2}{3} \, {\left(a x^{2} + b\right)}^{\frac{3}{4}}"," ",0,"-1/2*sqrt(2)*(-b)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^2 + b)^(1/4))/(-b)^(1/4)) - 1/2*sqrt(2)*(-b)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^2 + b)^(1/4))/(-b)^(1/4)) + 1/4*sqrt(2)*(-b)^(3/4)*log(sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b)) - 1/4*sqrt(2)*(-b)^(3/4)*log(-sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b)) + 2/3*(a*x^2 + b)^(3/4)","B",0
854,0,0,0,0.000000," ","integrate((x^2-x+1)/(x^2-1)/(x^3+x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - x + 1}{\sqrt{x^{3} + x} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 - x + 1)/(sqrt(x^3 + x)*(x^2 - 1)), x)","F",0
855,0,0,0,0.000000," ","integrate((2*x^2-1)/(x^2+1)/(x^4-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - 1}{\sqrt{x^{4} - x^{2} - 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((2*x^2 - 1)/(sqrt(x^4 - x^2 - 1)*(x^2 + 1)), x)","F",0
856,0,0,0,0.000000," ","integrate(1/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - 2*b)), x)","F",0
857,0,0,0,0.000000," ","integrate(1/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - 2*b)), x)","F",0
858,0,0,0,0.000000," ","integrate((c*x^2-2*b)/(c*x^2-b)/(a*x^4+c*x^2-b)^(1/4),x, algorithm=""giac"")","\int \frac{c x^{2} - 2 \, b}{{\left(a x^{4} + c x^{2} - b\right)}^{\frac{1}{4}} {\left(c x^{2} - b\right)}}\,{d x}"," ",0,"integrate((c*x^2 - 2*b)/((a*x^4 + c*x^2 - b)^(1/4)*(c*x^2 - b)), x)","F",0
859,0,0,0,0.000000," ","integrate((a*x^3-4*b)/(a*x^3-b)/(c*x^4-a*x^3+b)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{3} - 4 \, b}{{\left(c x^{4} - a x^{3} + b\right)}^{\frac{1}{4}} {\left(a x^{3} - b\right)}}\,{d x}"," ",0,"integrate((a*x^3 - 4*b)/((c*x^4 - a*x^3 + b)^(1/4)*(a*x^3 - b)), x)","F",0
860,0,0,0,0.000000," ","integrate((a*x^6-b)/(a*x^6+b)/(a*x^6+a^3*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{6} - b}{{\left(a x^{6} + a^{3} x^{3} - b\right)}^{\frac{1}{3}} {\left(a x^{6} + b\right)}}\,{d x}"," ",0,"integrate((a*x^6 - b)/((a*x^6 + a^3*x^3 - b)^(1/3)*(a*x^6 + b)), x)","F",0
861,0,0,0,0.000000," ","integrate((a*x^6-b)/(a*x^6+b)/(a*x^6+a^3*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{6} - b}{{\left(a x^{6} + a^{3} x^{3} - b\right)}^{\frac{1}{3}} {\left(a x^{6} + b\right)}}\,{d x}"," ",0,"integrate((a*x^6 - b)/((a*x^6 + a^3*x^3 - b)^(1/3)*(a*x^6 + b)), x)","F",0
862,0,0,0,0.000000," ","integrate((-x^4+1)^(1/2)*(x^4+1)/(4*x^8-7*x^4+4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)} \sqrt{-x^{4} + 1}}{4 \, x^{8} - 7 \, x^{4} + 4}\,{d x}"," ",0,"integrate((x^4 + 1)*sqrt(-x^4 + 1)/(4*x^8 - 7*x^4 + 4), x)","F",0
863,0,0,0,0.000000," ","integrate(x^4/(a*x^4-b)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a x^{8} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((a*x^8 - b)*(a*x^4 - b)^(1/4)), x)","F",0
864,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,1,50,0,0.258344," ","integrate((a*x^3-b)^(1/2)/x/(a*x^3+2*b),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{a x^{3} - b}}{3 \, \sqrt{b}}\right)}{3 \, \sqrt{b}} - \frac{\arctan\left(\frac{\sqrt{a x^{3} - b}}{\sqrt{b}}\right)}{3 \, \sqrt{b}}"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(a*x^3 - b)/sqrt(b))/sqrt(b) - 1/3*arctan(sqrt(a*x^3 - b)/sqrt(b))/sqrt(b)","A",0
867,1,49,0,0.995591," ","integrate((4*a*x^3-b)/x/(a*x^3-b)^(1/2)/(a*x^3+2*b),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{a x^{3} - b}}{3 \, \sqrt{b}}\right)}{\sqrt{b}} - \frac{\arctan\left(\frac{\sqrt{a x^{3} - b}}{\sqrt{b}}\right)}{3 \, \sqrt{b}}"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*sqrt(a*x^3 - b)/sqrt(b))/sqrt(b) - 1/3*arctan(sqrt(a*x^3 - b)/sqrt(b))/sqrt(b)","A",0
868,0,0,0,0.000000," ","integrate((x^4+6*x^2+1)^(1/2)/(-1+x)/(1+x)^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 6 \, x^{2} + 1}}{{\left(x + 1\right)}^{3} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 6*x^2 + 1)/((x + 1)^3*(x - 1)), x)","F",0
869,1,183,0,0.869824," ","integrate((a*x^4+b)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) - \frac{1}{8} \, \sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right) + \frac{1}{8} \, \sqrt{2} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right) + {\left(a x^{4} + b\right)}^{\frac{1}{4}}"," ",0,"-1/4*sqrt(2)*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^4 + b)^(1/4))/(-b)^(1/4)) - 1/4*sqrt(2)*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^4 + b)^(1/4))/(-b)^(1/4)) - 1/8*sqrt(2)*(-b)^(1/4)*log(sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b)) + 1/8*sqrt(2)*(-b)^(1/4)*log(-sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b)) + (a*x^4 + b)^(1/4)","B",0
870,0,0,0,0.000000," ","integrate(1/(a*x^4-2*b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - 2*b)), x)","F",0
871,0,0,0,0.000000," ","integrate(1/(a*x^4-2*b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - 2*b)), x)","F",0
872,0,0,0,0.000000," ","integrate(x^6/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(a^{2} x^{8} + b^{2}\right)} {\left(a x^{4} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^6/((a^2*x^8 + b^2)*(a*x^4 + b)^(3/4)), x)","F",0
873,0,0,0,0.000000," ","integrate((x^3+x^2*(x^2-1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{3} + \sqrt{x^{2} - 1} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^3 + sqrt(x^2 - 1)*x^2), x)","F",0
874,0,0,0,0.000000," ","integrate((-a+x)*(-b+x)*(-a*b+x^2)/x/(x*(-a+x)*(-b+x))^(1/2)/(a*b-(a+b+d)*x+x^2),x, algorithm=""giac"")","\int -\frac{{\left(a b - x^{2}\right)} {\left(a - x\right)} {\left(b - x\right)}}{\sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(a b - {\left(a + b + d\right)} x + x^{2}\right)} x}\,{d x}"," ",0,"integrate(-(a*b - x^2)*(a - x)*(b - x)/(sqrt((a - x)*(b - x)*x)*(a*b - (a + b + d)*x + x^2)*x), x)","F",0
875,0,0,0,0.000000," ","integrate(1/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} + b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 + b)), x)","F",0
876,0,0,0,0.000000," ","integrate(1/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} + b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 + b)), x)","F",0
877,0,0,0,0.000000," ","integrate((x^4-1)^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} - 1}}{x^{4} + 1}\,{d x}"," ",0,"integrate(sqrt(x^4 - 1)/(x^4 + 1), x)","F",0
878,1,69,0,0.196089," ","integrate(x^2*(x^4-x^2)^(1/4),x, algorithm=""giac"")","-\frac{1}{16} \, {\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right)} x^{4} + \frac{3}{32} \, \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{3}{64} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{3}{64} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"-1/16*((-1/x^2 + 1)^(5/4) + 3*(-1/x^2 + 1)^(1/4))*x^4 + 3/32*arctan((-1/x^2 + 1)^(1/4)) + 3/64*log((-1/x^2 + 1)^(1/4) + 1) - 3/64*log(-(-1/x^2 + 1)^(1/4) + 1)","A",0
879,0,0,0,0.000000," ","integrate(x/(x^4-2*x^3+3*x^2+4*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{4} - 2 \, x^{3} + 3 \, x^{2} + 4 \, x + 1}}\,{d x}"," ",0,"integrate(x/sqrt(x^4 - 2*x^3 + 3*x^2 + 4*x + 1), x)","F",0
880,0,0,0,0.000000," ","integrate(x/(x^4+2*x^3+3*x^2-4*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{4} + 2 \, x^{3} + 3 \, x^{2} - 4 \, x + 1}}\,{d x}"," ",0,"integrate(x/sqrt(x^4 + 2*x^3 + 3*x^2 - 4*x + 1), x)","F",0
881,0,0,0,0.000000," ","integrate((2*x^4-3*x^2+3)/(x^2-1)^(1/4)/(x^4-3*x^2+2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 3 \, x^{2} + 3}{{\left(x^{4} - 3 \, x^{2} + 2\right)} {\left(x^{2} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^4 - 3*x^2 + 3)/((x^4 - 3*x^2 + 2)*(x^2 - 1)^(1/4)), x)","F",0
882,0,0,0,0.000000," ","integrate(x^2/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate(x^2/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
883,0,0,0,0.000000," ","integrate(x^2/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate(x^2/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
884,0,0,0,0.000000," ","integrate((x^3+4*b)/(x^3+b)/(a*x^4-x^3-b)^(1/4),x, algorithm=""giac"")","\int \frac{x^{3} + 4 \, b}{{\left(a x^{4} - x^{3} - b\right)}^{\frac{1}{4}} {\left(x^{3} + b\right)}}\,{d x}"," ",0,"integrate((x^3 + 4*b)/((a*x^4 - x^3 - b)^(1/4)*(x^3 + b)), x)","F",0
885,0,0,0,0.000000," ","integrate((a*x^5+4*b)/(a*x^5-b)/(a*x^5+c*x^4-b)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{5} + 4 \, b}{{\left(a x^{5} + c x^{4} - b\right)}^{\frac{1}{4}} {\left(a x^{5} - b\right)}}\,{d x}"," ",0,"integrate((a*x^5 + 4*b)/((a*x^5 + c*x^4 - b)^(1/4)*(a*x^5 - b)), x)","F",0
886,0,0,0,0.000000," ","integrate((-2*x^6+x^2+1)^(1/2)*(4*x^6+1)/(2*x^6-4*x^2-1)/(2*x^6-2*x^2-1),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{6} + 1\right)} \sqrt{-2 \, x^{6} + x^{2} + 1}}{{\left(2 \, x^{6} - 2 \, x^{2} - 1\right)} {\left(2 \, x^{6} - 4 \, x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((4*x^6 + 1)*sqrt(-2*x^6 + x^2 + 1)/((2*x^6 - 2*x^2 - 1)*(2*x^6 - 4*x^2 - 1)), x)","F",0
887,0,0,0,0.000000," ","integrate(x^4/(x^4-1)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{8} - 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((x^8 - 1)*(x^4 - 1)^(1/4)), x)","F",0
888,0,0,0,0.000000," ","integrate(1/(x^4+1)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^8 - 1)*(x^4 + 1)^(1/4)), x)","F",0
889,0,0,0,0.000000," ","integrate((2*x^4-1)/(x^4-1)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 1}{{\left(x^{8} - 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^4 - 1)/((x^8 - 1)*(x^4 - 1)^(1/4)), x)","F",0
890,0,0,0,0.000000," ","integrate((x^8+1)/(x^4+1)^(1/2)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{8} + 1}{{\left(x^{8} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^8 + 1)/((x^8 - 1)*sqrt(x^4 + 1)), x)","F",0
891,0,0,0,0.000000," ","integrate((x^12-1)/(x^4+1)^(1/2)/(x^12+1),x, algorithm=""giac"")","\int \frac{x^{12} - 1}{{\left(x^{12} + 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^12 - 1)/((x^12 + 1)*sqrt(x^4 + 1)), x)","F",0
892,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{2} + 1} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^2 + 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
893,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(x + sqrt(x^2 + 1)), x)","F",0
894,0,0,0,0.000000," ","integrate(1/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} - b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 - b)), x)","F",0
895,0,0,0,0.000000," ","integrate(1/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} - b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 - b)), x)","F",0
896,0,0,0,0.000000," ","integrate(1/(a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{2} + b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^2 + b)), x)","F",0
897,0,0,0,0.000000," ","integrate(1/(a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{2} + b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^2 + b)), x)","F",0
898,1,88,0,0.237377," ","integrate(x^7*(x^4-x)^(1/4),x, algorithm=""giac"")","\frac{1}{288} \, {\left(7 \, {\left(\frac{1}{x^{3}} - 1\right)}^{2} {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} - 18 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{5}{4}} - 21 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right)} x^{9} + \frac{7}{192} \, \arctan\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right) + \frac{7}{384} \, \log\left({\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{7}{384} \, \log\left({\left| {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/288*(7*(1/x^3 - 1)^2*(-1/x^3 + 1)^(1/4) - 18*(-1/x^3 + 1)^(5/4) - 21*(-1/x^3 + 1)^(1/4))*x^9 + 7/192*arctan((-1/x^3 + 1)^(1/4)) + 7/384*log((-1/x^3 + 1)^(1/4) + 1) - 7/384*log(abs((-1/x^3 + 1)^(1/4) - 1))","A",0
899,0,0,0,0.000000," ","integrate((x^2+2)*(x^4-x^2-1)^(1/4)*(x^4+x^2+1)/x^6/(x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} + 1\right)} {\left(x^{4} - x^{2} - 1\right)}^{\frac{1}{4}} {\left(x^{2} + 2\right)}}{{\left(x^{2} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)*(x^4 - x^2 - 1)^(1/4)*(x^2 + 2)/((x^2 + 1)*x^6), x)","F",0
900,1,65,0,0.198131," ","integrate((x^4+x^3)^(1/4)/x^2/(x^2-1),x, algorithm=""giac"")","-2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + 4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}"," ",0,"-2^(1/4)*arctan(1/2*2^(3/4)*(1/x + 1)^(1/4)) - 1/2*2^(1/4)*log(2^(1/4) + (1/x + 1)^(1/4)) + 1/2*2^(1/4)*log(abs(-2^(1/4) + (1/x + 1)^(1/4))) + 4*(1/x + 1)^(1/4)","A",0
901,0,0,0,0.000000," ","integrate((2*a*x^4+b)/x^2/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} + b}{{\left(a x^{4} + b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((2*a*x^4 + b)/((a*x^4 + b)^(3/4)*x^2), x)","F",0
902,0,0,0,0.000000," ","integrate((x^2+1)*(x^6+x^2)^(1/4)/x^2/(x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{2} + 1\right)}}{{\left(x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^2 + 1)/((x^2 - 1)*x^2), x)","F",0
903,1,62,0,0.193550," ","integrate((x^3-1)^(1/2)*(x^6-x^3+1)/x^10/(x^3+2),x, algorithm=""giac"")","-\frac{7}{24} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} \sqrt{x^{3} - 1}\right) - \frac{12 \, {\left(x^{3} - 1\right)}^{\frac{5}{2}} + 19 \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + 9 \, \sqrt{x^{3} - 1}}{36 \, x^{9}} + \frac{13}{24} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"-7/24*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(x^3 - 1)) - 1/36*(12*(x^3 - 1)^(5/2) + 19*(x^3 - 1)^(3/2) + 9*sqrt(x^3 - 1))/x^9 + 13/24*arctan(sqrt(x^3 - 1))","A",0
904,0,0,0,0.000000," ","integrate((x^2+x*(x^2+x)^(1/2))^(1/2)/x/(x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{2} + x} x}}{\sqrt{x^{2} + x} x}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^2 + x)*x)/(sqrt(x^2 + x)*x), x)","F",0
905,0,0,0,0.000000," ","integrate(1/(a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^2 - b)), x)","F",0
906,0,0,0,0.000000," ","integrate(1/(a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^2 - b)), x)","F",0
907,0,0,0,0.000000," ","integrate((-a+x)*(-b+x)*(3*a*b-2*(a+b)*x+x^2)/x^2/(x*(-a+x)*(-b+x))^(1/2)/(-a*b+(a+b)*x-x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(3 \, a b - 2 \, {\left(a + b\right)} x + x^{2}\right)} {\left(a - x\right)} {\left(b - x\right)}}{{\left(d x^{3} - a b + {\left(a + b\right)} x - x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x} x^{2}}\,{d x}"," ",0,"integrate((3*a*b - 2*(a + b)*x + x^2)*(a - x)*(b - x)/((d*x^3 - a*b + (a + b)*x - x^2)*sqrt((a - x)*(b - x)*x)*x^2), x)","F",0
908,1,62,0,0.342046," ","integrate(1/(x^3+1)/(x^4-x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{6} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{6} \cdot 2^{\frac{3}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"1/3*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^3 + 1)^(1/4)) - 1/6*2^(3/4)*log(2^(1/4) + (-1/x^3 + 1)^(1/4)) + 1/6*2^(3/4)*log(abs(-2^(1/4) + (-1/x^3 + 1)^(1/4)))","A",0
909,1,119,0,0.490386," ","integrate(x*(x^4-x^2)^(1/2)/(2*x^2-3),x, algorithm=""giac"")","-\frac{1}{24} \, \sqrt{3} {\left(-2 i \, \sqrt{3} \pi - 3 \, \log\left(-\frac{\sqrt{3} + 3}{\sqrt{3} - 3}\right)\right)} \mathrm{sgn}\left(x\right) + \frac{1}{4} \, \sqrt{x^{2} - 1} x \mathrm{sgn}\left(x\right) - \frac{1}{8} \, \sqrt{3} \log\left(\frac{{\left| 2 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{2} - 2 \, \sqrt{3} - 4 \right|}}{{\left| 2 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 2 \, \sqrt{3} - 4 \right|}}\right) \mathrm{sgn}\left(x\right) - \frac{1}{4} \, \log\left({\left(x - \sqrt{x^{2} - 1}\right)}^{2}\right) \mathrm{sgn}\left(x\right)"," ",0,"-1/24*sqrt(3)*(-2*I*sqrt(3)*pi - 3*log(-(sqrt(3) + 3)/(sqrt(3) - 3)))*sgn(x) + 1/4*sqrt(x^2 - 1)*x*sgn(x) - 1/8*sqrt(3)*log(abs(2*(x - sqrt(x^2 - 1))^2 - 2*sqrt(3) - 4)/abs(2*(x - sqrt(x^2 - 1))^2 + 2*sqrt(3) - 4))*sgn(x) - 1/4*log((x - sqrt(x^2 - 1))^2)*sgn(x)","C",0
910,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+1)*(x^4-x^2-1)^(1/2)/(2*x^4-x^2-2)^2/(2*x^4+x^2-2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} - x^{2} - 1} {\left(x^{4} + 1\right)} {\left(x^{4} - 1\right)}}{{\left(2 \, x^{4} + x^{2} - 2\right)} {\left(2 \, x^{4} - x^{2} - 2\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 - x^2 - 1)*(x^4 + 1)*(x^4 - 1)/((2*x^4 + x^2 - 2)*(2*x^4 - x^2 - 2)^2), x)","F",0
911,0,0,0,0.000000," ","integrate((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + a x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/((a*x^4 + b*x^2)^(1/4)*(x^4 + a*x^2 + b)), x)","F",0
912,0,0,0,0.000000," ","integrate((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + a x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/((a*x^4 + b*x^2)^(1/4)*(x^4 + a*x^2 + b)), x)","F",0
913,0,0,0,0.000000," ","integrate((a*x^2-b)*(a^2*x^4+b^2)^(1/2)/x^2/(a*x^2+b),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{4} + b^{2}} {\left(a x^{2} - b\right)}}{{\left(a x^{2} + b\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^4 + b^2)*(a*x^2 - b)/((a*x^2 + b)*x^2), x)","F",0
914,0,0,0,0.000000," ","integrate((a*x^3+4*b)/(a*x^3+b)/(c*x^4-a*x^3-b)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{3} + 4 \, b}{{\left(c x^{4} - a x^{3} - b\right)}^{\frac{1}{4}} {\left(a x^{3} + b\right)}}\,{d x}"," ",0,"integrate((a*x^3 + 4*b)/((c*x^4 - a*x^3 - b)^(1/4)*(a*x^3 + b)), x)","F",0
915,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)*(x^4+x^3+1)/x^6/(x^4-x^3+1)/(x^5+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{4} + 1\right)} {\left(x^{4} - 3\right)}}{{\left(x^{5} + x\right)}^{\frac{1}{4}} {\left(x^{4} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^3 + 1)*(x^4 + 1)*(x^4 - 3)/((x^5 + x)^(1/4)*(x^4 - x^3 + 1)*x^6), x)","F",0
916,0,0,0,0.000000," ","integrate((x^4-3)*(x^8+x^6+2*x^4+1)/x^6/(x^4-x^3+1)/(x^5+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{6} + 2 \, x^{4} + 1\right)} {\left(x^{4} - 3\right)}}{{\left(x^{5} + x\right)}^{\frac{1}{4}} {\left(x^{4} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^8 + x^6 + 2*x^4 + 1)*(x^4 - 3)/((x^5 + x)^(1/4)*(x^4 - x^3 + 1)*x^6), x)","F",0
917,1,185,0,0.752494," ","integrate((a*x^3+b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) - \frac{1}{3} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right) - \frac{1}{6} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right) + \frac{4}{9} \, {\left(a x^{3} + b\right)}^{\frac{3}{4}}"," ",0,"-1/3*sqrt(2)*(-b)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^3 + b)^(1/4))/(-b)^(1/4)) - 1/3*sqrt(2)*(-b)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^3 + b)^(1/4))/(-b)^(1/4)) + 1/6*sqrt(2)*(-b)^(3/4)*log(sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b)) - 1/6*sqrt(2)*(-b)^(3/4)*log(-sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b)) + 4/9*(a*x^3 + b)^(3/4)","B",0
918,0,0,0,0.000000," ","integrate((3*x^4+3*x+1)/x/(x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{3 \, x^{4} + 3 \, x + 1}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((3*x^4 + 3*x + 1)/((x^4 + 1)^(1/4)*x), x)","F",0
919,1,185,0,0.271870," ","integrate((a*x^4+b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) + \frac{1}{8} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right) - \frac{1}{8} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right) + \frac{1}{3} \, {\left(a x^{4} + b\right)}^{\frac{3}{4}}"," ",0,"-1/4*sqrt(2)*(-b)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^4 + b)^(1/4))/(-b)^(1/4)) - 1/4*sqrt(2)*(-b)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^4 + b)^(1/4))/(-b)^(1/4)) + 1/8*sqrt(2)*(-b)^(3/4)*log(sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b)) - 1/8*sqrt(2)*(-b)^(3/4)*log(-sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b)) + 1/3*(a*x^4 + b)^(3/4)","B",0
920,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*(x^2 + 1)), x)","F",0
921,0,0,0,0.000000," ","integrate((a*x^2+b)*(a^2*x^4+b^2)^(1/2)/x^2/(a*x^2-b),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{4} + b^{2}} {\left(a x^{2} + b\right)}}{{\left(a x^{2} - b\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^4 + b^2)*(a*x^2 + b)/((a*x^2 - b)*x^2), x)","F",0
922,1,185,0,0.272875," ","integrate((a*x^5+b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{5} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) - \frac{1}{5} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) + \frac{1}{10} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right) - \frac{1}{10} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right) + \frac{4}{15} \, {\left(a x^{5} + b\right)}^{\frac{3}{4}}"," ",0,"-1/5*sqrt(2)*(-b)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^5 + b)^(1/4))/(-b)^(1/4)) - 1/5*sqrt(2)*(-b)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^5 + b)^(1/4))/(-b)^(1/4)) + 1/10*sqrt(2)*(-b)^(3/4)*log(sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b)) - 1/10*sqrt(2)*(-b)^(3/4)*log(-sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b)) + 4/15*(a*x^5 + b)^(3/4)","B",0
923,0,0,0,0.000000," ","integrate((2*x^5+3)*(-x^6-2*x^4+x)^(1/2)/(x^5-1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-x^{6} - 2 \, x^{4} + x} {\left(2 \, x^{5} + 3\right)}}{{\left(x^{5} - 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-x^6 - 2*x^4 + x)*(2*x^5 + 3)/(x^5 - 1)^2, x)","F",0
924,0,0,0,0.000000," ","integrate((x^6-2)*(x^6+1)*(x^6-x^4+1)^(1/4)/x^6/(x^6-2*x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} + 1\right)}^{\frac{1}{4}} {\left(x^{6} + 1\right)} {\left(x^{6} - 2\right)}}{{\left(x^{6} - 2 \, x^{4} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^4 + 1)^(1/4)*(x^6 + 1)*(x^6 - 2)/((x^6 - 2*x^4 + 1)*x^6), x)","F",0
925,1,185,0,0.282727," ","integrate((a*x^6+b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right) + \frac{1}{12} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right) - \frac{1}{12} \, \sqrt{2} \left(-b\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right) + \frac{2}{9} \, {\left(a x^{6} + b\right)}^{\frac{3}{4}}"," ",0,"-1/6*sqrt(2)*(-b)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^6 + b)^(1/4))/(-b)^(1/4)) - 1/6*sqrt(2)*(-b)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^6 + b)^(1/4))/(-b)^(1/4)) + 1/12*sqrt(2)*(-b)^(3/4)*log(sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b)) - 1/12*sqrt(2)*(-b)^(3/4)*log(-sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b)) + 2/9*(a*x^6 + b)^(3/4)","B",0
926,1,44,0,0.361656," ","integrate((1+x)^(1/2)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} - 3\right)} - \frac{7}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) - 3) - 7/4*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
927,1,44,0,0.264829," ","integrate((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} + 1\right)} + \frac{5}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) + 1) + 5/4*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
928,0,0,0,0.000000," ","integrate((x^2-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - 1\right)} \sqrt{\sqrt{x^{2} + 1} + 1}}{x^{2} + 1}\,{d x}"," ",0,"integrate((x^2 - 1)*sqrt(sqrt(x^2 + 1) + 1)/(x^2 + 1), x)","F",0
929,0,0,0,0.000000," ","integrate(1/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}\,{d x}"," ",0,"integrate(1/sqrt(x^2 + sqrt(x^4 + 1)), x)","F",0
930,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/x^2, x)","F",0
931,1,132,0,0.620221," ","integrate(1/((-1+x)^(1/2)+2*x^(1/2))^2/(-1+x)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} {\left(\pi - 2 \, \arctan\left(-\frac{\sqrt{3} {\left({\left(\sqrt{x - 1} - \sqrt{x}\right)}^{2} + 1\right)}}{2 \, {\left(\sqrt{x - 1} - \sqrt{x}\right)}}\right)\right)} + \frac{4}{9} \, \sqrt{3} \arctan\left(\frac{1}{2} \, \sqrt{3} \sqrt{x - 1}\right) - \frac{8 \, {\left(\sqrt{x - 1} - \sqrt{x} + \frac{1}{\sqrt{x - 1} - \sqrt{x}}\right)}}{3 \, {\left(3 \, {\left(\sqrt{x - 1} - \sqrt{x} + \frac{1}{\sqrt{x - 1} - \sqrt{x}}\right)}^{2} + 4\right)}} - \frac{2 \, \sqrt{x - 1}}{3 \, {\left(3 \, x + 1\right)}}"," ",0,"2/9*sqrt(3)*(pi - 2*arctan(-1/2*sqrt(3)*((sqrt(x - 1) - sqrt(x))^2 + 1)/(sqrt(x - 1) - sqrt(x)))) + 4/9*sqrt(3)*arctan(1/2*sqrt(3)*sqrt(x - 1)) - 8/3*(sqrt(x - 1) - sqrt(x) + 1/(sqrt(x - 1) - sqrt(x)))/(3*(sqrt(x - 1) - sqrt(x) + 1/(sqrt(x - 1) - sqrt(x)))^2 + 4) - 2/3*sqrt(x - 1)/(3*x + 1)","B",0
932,1,94,0,0.321099," ","integrate(1/(x^2-1)^(1/2)/(3*x^2-4)^2,x, algorithm=""giac"")","\frac{5 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{2} - 3}{4 \, {\left(3 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{4} - 10 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 3\right)}} - \frac{5}{32} \, \log\left({\left| 3 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{2} - 1 \right|}\right) + \frac{5}{32} \, \log\left({\left| {\left(x - \sqrt{x^{2} - 1}\right)}^{2} - 3 \right|}\right)"," ",0,"1/4*(5*(x - sqrt(x^2 - 1))^2 - 3)/(3*(x - sqrt(x^2 - 1))^4 - 10*(x - sqrt(x^2 - 1))^2 + 3) - 5/32*log(abs(3*(x - sqrt(x^2 - 1))^2 - 1)) + 5/32*log(abs((x - sqrt(x^2 - 1))^2 - 3))","A",0
933,1,55,0,0.288476," ","integrate(1/x/(x^3+1)^(1/3),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{6} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) - 1/6*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) + 1/3*log(abs((x^3 + 1)^(1/3) - 1))","A",0
934,1,264,0,1.415580," ","integrate(x^2*(3-2*(1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(-1+(1+k)*x-k*x^2+d*x^3),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-d\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-d\right)^{\frac{1}{4}} + 2 \, {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-d\right)^{\frac{1}{4}}}\right)}{d} - \frac{\sqrt{2} \left(-d\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-d\right)^{\frac{1}{4}} - 2 \, {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-d\right)^{\frac{1}{4}}}\right)}{d} - \frac{\sqrt{2} \left(-d\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-d\right)^{\frac{1}{4}} {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-d} + \sqrt{\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}}\right)}{2 \, d} + \frac{\sqrt{2} \left(-d\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-d\right)^{\frac{1}{4}} {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-d} + \sqrt{\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}}\right)}{2 \, d}"," ",0,"-sqrt(2)*(-d)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-d)^(1/4) + 2*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4))/(-d)^(1/4))/d - sqrt(2)*(-d)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-d)^(1/4) - 2*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4))/(-d)^(1/4))/d - 1/2*sqrt(2)*(-d)^(1/4)*log(sqrt(2)*(-d)^(1/4)*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4) + sqrt(-d) + sqrt(k/x - k/x^2 - 1/x^2 + 1/x^3))/d + 1/2*sqrt(2)*(-d)^(1/4)*log(-sqrt(2)*(-d)^(1/4)*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4) + sqrt(-d) + sqrt(k/x - k/x^2 - 1/x^2 + 1/x^3))/d","B",0
935,0,0,0,0.000000," ","integrate((a*x^2-b)/(x^4+a*x^2-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a*x^4 - b*x^2)^(1/4)*(x^4 + a*x^2 - b)), x)","F",0
936,0,0,0,0.000000," ","integrate((a*x^2-b)/(x^4+a*x^2-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a*x^4 - b*x^2)^(1/4)*(x^4 + a*x^2 - b)), x)","F",0
937,0,0,0,0.000000," ","integrate((x^3-x)^(1/3)/(a*x^6+b),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x\right)}^{\frac{1}{3}}}{a x^{6} + b}\,{d x}"," ",0,"integrate((x^3 - x)^(1/3)/(a*x^6 + b), x)","F",0
938,0,0,0,0.000000," ","integrate((x^3-x)^(1/3)/(a*x^6+b),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x\right)}^{\frac{1}{3}}}{a x^{6} + b}\,{d x}"," ",0,"integrate((x^3 - x)^(1/3)/(a*x^6 + b), x)","F",0
939,0,0,0,0.000000," ","integrate((a*x^6-2*b)*(a*x^6+b)^(3/4)/x^4/(a*x^6-c*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} + b\right)}^{\frac{3}{4}} {\left(a x^{6} - 2 \, b\right)}}{{\left(a x^{6} - c x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^6 + b)^(3/4)*(a*x^6 - 2*b)/((a*x^6 - c*x^4 + b)*x^4), x)","F",0
940,0,0,0,0.000000," ","integrate((a*x^8+b)/(a*x^8-b)/(a*x^8+c*x^4-b)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{8} + b}{{\left(a x^{8} + c x^{4} - b\right)}^{\frac{1}{4}} {\left(a x^{8} - b\right)}}\,{d x}"," ",0,"integrate((a*x^8 + b)/((a*x^8 + c*x^4 - b)^(1/4)*(a*x^8 - b)), x)","F",0
941,0,0,0,0.000000," ","integrate((x^5+1)^(1/2)*(3*x^5-2)/(x^10+2*x^5+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{5} - 2\right)} \sqrt{x^{5} + 1}}{x^{10} + 2 \, x^{5} + x^{4} + 1}\,{d x}"," ",0,"integrate((3*x^5 - 2)*sqrt(x^5 + 1)/(x^10 + 2*x^5 + x^4 + 1), x)","F",0
942,1,177,0,0.223701," ","integrate(1/(2*x+(x^2+1)^(1/2))^2,x, algorithm=""giac"")","\frac{1}{18} \, \sqrt{3} \log\left(\frac{{\left| 6 \, x - 2 \, \sqrt{3} \right|}}{{\left| 6 \, x + 2 \, \sqrt{3} \right|}}\right) - \frac{1}{18} \, \sqrt{3} \log\left(-\frac{{\left| -6 \, x - 8 \, \sqrt{3} + 6 \, \sqrt{x^{2} + 1} - \frac{6}{x - \sqrt{x^{2} + 1}} \right|}}{2 \, {\left(3 \, x - 4 \, \sqrt{3} - 3 \, \sqrt{x^{2} + 1} + \frac{3}{x - \sqrt{x^{2} + 1}}\right)}}\right) - \frac{4 \, {\left(x - \sqrt{x^{2} + 1} + \frac{1}{x - \sqrt{x^{2} + 1}}\right)}}{3 \, {\left(3 \, {\left(x - \sqrt{x^{2} + 1} + \frac{1}{x - \sqrt{x^{2} + 1}}\right)}^{2} - 16\right)}} - \frac{4 \, x}{3 \, {\left(3 \, x^{2} - 1\right)}}"," ",0,"1/18*sqrt(3)*log(abs(6*x - 2*sqrt(3))/abs(6*x + 2*sqrt(3))) - 1/18*sqrt(3)*log(-1/2*abs(-6*x - 8*sqrt(3) + 6*sqrt(x^2 + 1) - 6/(x - sqrt(x^2 + 1)))/(3*x - 4*sqrt(3) - 3*sqrt(x^2 + 1) + 3/(x - sqrt(x^2 + 1)))) - 4/3*(x - sqrt(x^2 + 1) + 1/(x - sqrt(x^2 + 1)))/(3*(x - sqrt(x^2 + 1) + 1/(x - sqrt(x^2 + 1)))^2 - 16) - 4/3*x/(3*x^2 - 1)","B",0
943,0,0,0,0.000000," ","integrate((a*x^2+x*(a^2*x^2-b)^(1/2))^(1/2)/x/(a^2*x^2-b)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{2} - b} x}}{\sqrt{a^{2} x^{2} - b} x}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^2 - b)*x)/(sqrt(a^2*x^2 - b)*x), x)","F",0
944,0,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x + \sqrt{x^{2} + 1}} + 1}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^2 + 1), x)","F",0
945,0,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x + \sqrt{x^{2} + 1}} + 1}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^2 + 1), x)","F",0
946,0,0,0,0.000000," ","integrate((x^2+2*x+1)^(1/3)/(x^3+x^2+x+4),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 2 \, x + 1\right)}^{\frac{1}{3}}}{x^{3} + x^{2} + x + 4}\,{d x}"," ",0,"integrate((x^2 + 2*x + 1)^(1/3)/(x^3 + x^2 + x + 4), x)","F",0
947,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+1)^(1/2)/(x^2-x+1)/(x^2+x+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}{{\left(x^{2} + x + 1\right)}^{2} {\left(x^{2} - x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*(x^2 - 1)/((x^2 + x + 1)^2*(x^2 - x + 1)), x)","F",0
948,1,89,0,0.295844," ","integrate(x^4*(x^4-x^2)^(1/4),x, algorithm=""giac"")","\frac{1}{192} \, {\left(7 \, {\left(\frac{1}{x^{2}} - 1\right)}^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 18 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}} - 21 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right)} x^{6} + \frac{7}{128} \, \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{7}{256} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{7}{256} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"1/192*(7*(1/x^2 - 1)^2*(-1/x^2 + 1)^(1/4) - 18*(-1/x^2 + 1)^(5/4) - 21*(-1/x^2 + 1)^(1/4))*x^6 + 7/128*arctan((-1/x^2 + 1)^(1/4)) + 7/256*log((-1/x^2 + 1)^(1/4) + 1) - 7/256*log(-(-1/x^2 + 1)^(1/4) + 1)","A",0
949,1,87,0,0.316274," ","integrate(x^4*(x^4+x^3)^(1/4)/(1+x),x, algorithm=""giac"")","\frac{1}{10240} \, {\left(7315 \, {\left(\frac{1}{x} + 1\right)}^{\frac{17}{4}} - 33440 \, {\left(\frac{1}{x} + 1\right)}^{\frac{13}{4}} + 59470 \, {\left(\frac{1}{x} + 1\right)}^{\frac{9}{4}} - 50312 \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 19015 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{5} - \frac{4389}{4096} \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{4389}{8192} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{4389}{8192} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/10240*(7315*(1/x + 1)^(17/4) - 33440*(1/x + 1)^(13/4) + 59470*(1/x + 1)^(9/4) - 50312*(1/x + 1)^(5/4) + 19015*(1/x + 1)^(1/4))*x^5 - 4389/4096*arctan((1/x + 1)^(1/4)) - 4389/8192*log((1/x + 1)^(1/4) + 1) + 4389/8192*log(abs((1/x + 1)^(1/4) - 1))","A",0
950,0,0,0,0.000000," ","integrate((a*x^3+4*b)*(-a*x^3+x^4-b)/x^4/(a*x^3+b)^(1/4)/(-a*x^3+2*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{3} - x^{4} + b\right)} {\left(a x^{3} + 4 \, b\right)}}{{\left(a x^{3} - 2 \, x^{4} + b\right)} {\left(a x^{3} + b\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((a*x^3 - x^4 + b)*(a*x^3 + 4*b)/((a*x^3 - 2*x^4 + b)*(a*x^3 + b)^(1/4)*x^4), x)","F",0
951,0,0,0,0.000000," ","integrate((a*x^2+b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)), x)","F",0
952,0,0,0,0.000000," ","integrate((a*x^2+b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)), x)","F",0
953,1,90,0,0.530869," ","integrate((1-x)/(x^6+2*x^5+x^4-4*x^3-5*x^2+2*x+3)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \log\left(-\frac{{\left| -2 \, \sqrt{3} - 2 \, \sqrt{2} + 2 \, \sqrt{\frac{2}{x} + \frac{3}{x^{2}} + 1} - \frac{2 \, \sqrt{3}}{x} \right|}}{2 \, {\left(\sqrt{3} - \sqrt{2} - \sqrt{\frac{2}{x} + \frac{3}{x^{2}} + 1} + \frac{\sqrt{3}}{x}\right)}}\right)}{2 \, \mathrm{sgn}\left(-\frac{1}{x^{3}} + \frac{1}{x^{5}}\right)}"," ",0,"-1/2*sqrt(2)*log(-1/2*abs(-2*sqrt(3) - 2*sqrt(2) + 2*sqrt(2/x + 3/x^2 + 1) - 2*sqrt(3)/x)/(sqrt(3) - sqrt(2) - sqrt(2/x + 3/x^2 + 1) + sqrt(3)/x))/sgn(-1/x^3 + 1/x^5)","A",0
954,0,0,0,0.000000," ","integrate((3*x^4-1)*(x^8+2*x^4+x^2+1)^(1/2)/(x^4-x+1)^2/(x^4+x+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{8} + 2 \, x^{4} + x^{2} + 1} {\left(3 \, x^{4} - 1\right)}}{{\left(x^{4} + x + 1\right)} {\left(x^{4} - x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^8 + 2*x^4 + x^2 + 1)*(3*x^4 - 1)/((x^4 + x + 1)*(x^4 - x + 1)^2), x)","F",0
955,1,68,0,0.382712," ","integrate((a*x^2+b*x+c)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{a x^{2} + b x + c} {\left(2 \, x + \frac{b}{a}\right)} + \frac{{\left(b^{2} - 4 \, a c\right)} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x + c}\right)} \sqrt{a} - b \right|}\right)}{8 \, a^{\frac{3}{2}}}"," ",0,"1/4*sqrt(a*x^2 + b*x + c)*(2*x + b/a) + 1/8*(b^2 - 4*a*c)*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x + c))*sqrt(a) - b))/a^(3/2)","A",0
956,0,0,0,0.000000," ","integrate((-1+x)/(x^2-2*x-1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x^{3} - x} {\left(x^{2} - 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x - 1)/(sqrt(x^3 - x)*(x^2 - 2*x - 1)), x)","F",0
957,0,0,0,0.000000," ","integrate((x^2+3*x-2)/(x^2-2*x-1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 3 \, x - 2}{\sqrt{x^{3} - x} {\left(x^{2} - 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 3*x - 2)/(sqrt(x^3 - x)*(x^2 - 2*x - 1)), x)","F",0
958,0,0,0,0.000000," ","integrate(x*(x^2-3)/(x^2-1)^(2/3)/(x^3-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - 3\right)} x}{{\left(x^{3} - x^{2} + 1\right)} {\left(x^{2} - 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((x^2 - 3)*x/((x^3 - x^2 + 1)*(x^2 - 1)^(2/3)), x)","F",0
959,1,106,0,0.585006," ","integrate(x^2*(x^4-x^3)^(1/4),x, algorithm=""giac"")","\frac{1}{1536} \, {\left(77 \, {\left(\frac{1}{x} - 1\right)}^{3} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 275 \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 351 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} - 231 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{4} + \frac{77}{1024} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{77}{2048} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{77}{2048} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/1536*(77*(1/x - 1)^3*(-1/x + 1)^(1/4) + 275*(1/x - 1)^2*(-1/x + 1)^(1/4) - 351*(-1/x + 1)^(5/4) - 231*(-1/x + 1)^(1/4))*x^4 + 77/1024*arctan((-1/x + 1)^(1/4)) + 77/2048*log((-1/x + 1)^(1/4) + 1) - 77/2048*log(abs((-1/x + 1)^(1/4) - 1))","A",0
960,0,0,0,0.000000," ","integrate((x^4+3)*(-x^5+x^4+x)^(1/2)/(x^4-1)/(x^4+x^3-1),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{5} + x^{4} + x} {\left(x^{4} + 3\right)}}{{\left(x^{4} + x^{3} - 1\right)} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-x^5 + x^4 + x)*(x^4 + 3)/((x^4 + x^3 - 1)*(x^4 - 1)), x)","F",0
961,0,0,0,0.000000," ","integrate((a*x^2-b)*(a*x^3+b*x)^(1/2)/(b^2*x+2*(a*b-1)*x^3+a^2*x^5),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3} + b x} {\left(a x^{2} - b\right)}}{a^{2} x^{5} + 2 \, {\left(a b - 1\right)} x^{3} + b^{2} x}\,{d x}"," ",0,"integrate(sqrt(a*x^3 + b*x)*(a*x^2 - b)/(a^2*x^5 + 2*(a*b - 1)*x^3 + b^2*x), x)","F",0
962,0,0,0,0.000000," ","integrate((x^3-2)*(x^3+1)^(2/3)/x^3/(x^6+x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)}}{{\left(x^{6} + x^{3} + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*(x^3 - 2)/((x^6 + x^3 + 2)*x^3), x)","F",0
963,0,0,0,0.000000," ","integrate((x^3-2)*(x^3+1)^(2/3)/x^3/(x^6+x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)}}{{\left(x^{6} + x^{3} + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*(x^3 - 2)/((x^6 + x^3 + 2)*x^3), x)","F",0
964,0,0,0,0.000000," ","integrate((2*x^5-3)*(x^6+2*x^4+x)^(1/2)/(x^5+1)/(x^5+x^3+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} + 2 \, x^{4} + x} {\left(2 \, x^{5} - 3\right)}}{{\left(x^{5} + x^{3} + 1\right)} {\left(x^{5} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^6 + 2*x^4 + x)*(2*x^5 - 3)/((x^5 + x^3 + 1)*(x^5 + 1)), x)","F",0
965,0,0,0,0.000000," ","integrate((x^6+x^4+x^2-1)^(1/2)*(2*x^6+x^4+1)/(x^12+2*x^10+x^8-2*x^6-x^4+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{4} + 1\right)} \sqrt{x^{6} + x^{4} + x^{2} - 1}}{x^{12} + 2 \, x^{10} + x^{8} - 2 \, x^{6} - x^{4} + 1}\,{d x}"," ",0,"integrate((2*x^6 + x^4 + 1)*sqrt(x^6 + x^4 + x^2 - 1)/(x^12 + 2*x^10 + x^8 - 2*x^6 - x^4 + 1), x)","F",0
966,0,0,0,0.000000," ","integrate((x^2-x*(x^2-x)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} - \sqrt{x^{2} - x} x}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(x^2 - sqrt(x^2 - x)*x)/x^3, x)","F",0
967,1,54,0,0.339039," ","integrate(1/x/(x^2+1)^(2/3),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{4} \, \log\left({\left(x^{2} + 1\right)}^{\frac{2}{3}} + {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 + 1)^(1/3) + 1)) - 1/4*log((x^2 + 1)^(2/3) + (x^2 + 1)^(1/3) + 1) + 1/2*log((x^2 + 1)^(1/3) - 1)","A",0
968,1,54,0,0.434093," ","integrate(1/x/(x^2+1)^(1/3),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{4} \, \log\left({\left(x^{2} + 1\right)}^{\frac{2}{3}} + {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 + 1)^(1/3) + 1)) - 1/4*log((x^2 + 1)^(2/3) + (x^2 + 1)^(1/3) + 1) + 1/2*log((x^2 + 1)^(1/3) - 1)","A",0
969,0,0,0,0.000000," ","integrate(1/(x^3-1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^3 - x^2)^(1/3)*(x^3 - 1)), x)","F",0
970,0,0,0,0.000000," ","integrate(1/(x^3-1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^3 - x^2)^(1/3)*(x^3 - 1)), x)","F",0
971,0,0,0,0.000000," ","integrate((x^3-1)^(1/2)*(x^3+2)*(x^3-x^2-1)^2/x^6/(2*x^3-3*x^2-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2} - 1\right)}^{2} {\left(x^{3} + 2\right)} \sqrt{x^{3} - 1}}{{\left(2 \, x^{3} - 3 \, x^{2} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 - x^2 - 1)^2*(x^3 + 2)*sqrt(x^3 - 1)/((2*x^3 - 3*x^2 - 2)*x^6), x)","F",0
972,0,0,0,0.000000," ","integrate((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}^{\frac{1}{4}}}{3 \, x^{3} + x^{2} - 2 \, x - 1}\,{d x}"," ",0,"integrate((x^3 - 3*x^2 + 3*x - 1)^(1/4)/(3*x^3 + x^2 - 2*x - 1), x)","F",0
973,0,0,0,0.000000," ","integrate((x^2+x+1)*(x^2+2*x)*(-x^4+x^2+2*x+1)^(1/2)/(1+x)^4,x, algorithm=""giac"")","\int \frac{\sqrt{-x^{4} + x^{2} + 2 \, x + 1} {\left(x^{2} + 2 \, x\right)} {\left(x^{2} + x + 1\right)}}{{\left(x + 1\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2*x + 1)*(x^2 + 2*x)*(x^2 + x + 1)/(x + 1)^4, x)","F",0
974,0,0,0,0.000000," ","integrate((x^4-x-1)/x/(x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - x - 1}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((x^4 - x - 1)/((x^4 + 1)^(1/4)*x), x)","F",0
975,1,72,0,0.429823," ","integrate((x^4-x^3)^(1/4)/x^2/(x^2-1),x, algorithm=""giac"")","2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}"," ",0,"2^(1/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 1/2*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) - 1/2*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4))) - 4*(-1/x + 1)^(1/4)","A",0
976,0,0,0,0.000000," ","integrate((x^4-3)/(x^4+1)^(1/3)/(x^4-x^3+1),x, algorithm=""giac"")","\int \frac{x^{4} - 3}{{\left(x^{4} - x^{3} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^4 - 3)/((x^4 - x^3 + 1)*(x^4 + 1)^(1/3)), x)","F",0
977,-2,0,0,0.000000," ","integrate((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-7,-21]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-57,-32]Evaluation time: 5.12Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
978,-2,0,0,0.000000," ","integrate((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-7,-21]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-57,-32]Evaluation time: 4.85Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
979,0,0,0,0.000000," ","integrate((2*a*x^4-b)/x^2/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(a x^{4} - b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((a*x^4 - b)^(3/4)*x^2), x)","F",0
980,1,54,0,0.495398," ","integrate(1/x/(x^6+1)^(1/3),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{12} \, \log\left({\left(x^{6} + 1\right)}^{\frac{2}{3}} + {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 + 1)^(1/3) + 1)) - 1/12*log((x^6 + 1)^(2/3) + (x^6 + 1)^(1/3) + 1) + 1/6*log((x^6 + 1)^(1/3) - 1)","A",0
981,1,44,0,0.545909," ","integrate((2*x^6-9*x^4+3)/x/(x^2+1)^2/(2*x^2-1)/((-2*x^2+1)/(2*x^2+1))^(1/2)/(2*x^2+1),x, algorithm=""giac"")","-\frac{32}{3 \, {\left(\frac{{\left(\sqrt{-4 \, x^{4} + 1} - 1\right)}^{3}}{x^{6}} + 8\right)}} - \frac{3}{2} \, \log\left(-\frac{\sqrt{-4 \, x^{4} + 1} - 1}{2 \, x^{2}}\right) + \frac{2}{3}"," ",0,"-32/3/((sqrt(-4*x^4 + 1) - 1)^3/x^6 + 8) - 3/2*log(-1/2*(sqrt(-4*x^4 + 1) - 1)/x^2) + 2/3","A",0
982,1,108,0,0.439647," ","integrate((2*x^4-1)^(1/4)*(x^8-2)/x^6/(x^4-1)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 2\right)}}{5 \, x} - \frac{4 \, {\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x} + \frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{4 \, x {\left(\frac{1}{x^{4}} - 1\right)}} + \frac{15}{8} \, \arctan\left(\frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{15}{16} \, \log\left(\frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{15}{16} \, \log\left({\left| \frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x} - 1 \right|}\right)"," ",0,"-2/5*(2*x^4 - 1)^(1/4)*(1/x^4 - 2)/x - 4*(2*x^4 - 1)^(1/4)/x + 1/4*(2*x^4 - 1)^(1/4)/(x*(1/x^4 - 1)) + 15/8*arctan((2*x^4 - 1)^(1/4)/x) + 15/16*log((2*x^4 - 1)^(1/4)/x + 1) - 15/16*log(abs((2*x^4 - 1)^(1/4)/x - 1))","A",0
983,1,209,0,0.310728," ","integrate((a*x^2+b)^(3/4)/x^3,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right)}{b} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{2} + b\right)}^{\frac{3}{4}} a}{x^{2}}}{16 \, a}"," ",0,"1/16*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^2 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^2 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 3*sqrt(2)*a^2*(-b)^(3/4)*log(sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b))/b + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b))/(-b)^(1/4) - 8*(a*x^2 + b)^(3/4)*a/x^2)/a","B",0
984,1,288,0,0.682968," ","integrate((3-2*(1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-d+d*(1+k)*x-d*k*x^2+x^3),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{1}{d}\right)^{\frac{1}{4}} + 2 \, {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{1}{d}\right)^{\frac{1}{4}}}\right)}{d^{3}} - \frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{1}{d}\right)^{\frac{1}{4}} - 2 \, {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{1}{d}\right)^{\frac{1}{4}}}\right)}{d^{3}} + \frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}} \left(-\frac{1}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}} + \sqrt{-\frac{1}{d}}\right)}{2 \, d^{3}} - \frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}} \left(-\frac{1}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}} + \sqrt{-\frac{1}{d}}\right)}{2 \, d^{3}}"," ",0,"-sqrt(2)*(-d^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-1/d)^(1/4) + 2*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4))/(-1/d)^(1/4))/d^3 - sqrt(2)*(-d^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-1/d)^(1/4) - 2*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4))/(-1/d)^(1/4))/d^3 + 1/2*sqrt(2)*(-d^3)^(3/4)*log(sqrt(2)*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4)*(-1/d)^(1/4) + sqrt(k/x - k/x^2 - 1/x^2 + 1/x^3) + sqrt(-1/d))/d^3 - 1/2*sqrt(2)*(-d^3)^(3/4)*log(-sqrt(2)*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4)*(-1/d)^(1/4) + sqrt(k/x - k/x^2 - 1/x^2 + 1/x^3) + sqrt(-1/d))/d^3","B",0
985,0,0,0,0.000000," ","integrate(1/(x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{3} + x^{2} - 2 \, x - 1\right)} {\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((3*x^3 + x^2 - 2*x - 1)*(x^3 - 3*x^2 + 3*x - 1)^(1/4)), x)","F",0
986,1,209,0,0.612592," ","integrate((a*x^3+b)^(3/4)/x^4,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{b} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{3} + b\right)}^{\frac{3}{4}} a}{x^{3}}}{24 \, a}"," ",0,"1/24*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 3*sqrt(2)*a^2*(-b)^(3/4)*log(sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/b + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/(-b)^(1/4) - 8*(a*x^3 + b)^(3/4)*a/x^3)/a","B",0
987,1,65,0,0.336894," ","integrate((x^4+x^2)^(1/4)/x^4/(x^4-1),x, algorithm=""giac"")","\frac{2}{5} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"2/5*(1/x^2 + 1)^(5/4) - 1/2*2^(1/4)*arctan(1/2*2^(3/4)*(1/x^2 + 1)^(1/4)) - 1/4*2^(1/4)*log(2^(1/4) + (1/x^2 + 1)^(1/4)) + 1/4*2^(1/4)*log(abs(-2^(1/4) + (1/x^2 + 1)^(1/4)))","A",0
988,0,0,0,0.000000," ","integrate(x*(x^4-3)/(x^4+1)^(2/3)/(x^4+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 3\right)} x}{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((x^4 - 3)*x/((x^4 + x^3 + 1)*(x^4 + 1)^(2/3)), x)","F",0
989,0,0,0,0.000000," ","integrate((-4*x^4-x^2+2)^(1/2)*(2*x^4+1)/(2*x^4-1)/(2*x^4-x^2-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + 1\right)} \sqrt{-4 \, x^{4} - x^{2} + 2}}{{\left(2 \, x^{4} - x^{2} - 1\right)} {\left(2 \, x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 + 1)*sqrt(-4*x^4 - x^2 + 2)/((2*x^4 - x^2 - 1)*(2*x^4 - 1)), x)","F",0
990,0,0,0,0.000000," ","integrate((a*x^4+b)^(3/4),x, algorithm=""giac"")","\int {\left(a x^{4} + b\right)}^{\frac{3}{4}}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4), x)","F",0
991,0,0,0,0.000000," ","integrate((a*x^4+b)^(3/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b\right)}^{\frac{3}{4}}}{x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)/x^4, x)","F",0
992,1,209,0,0.306868," ","integrate((a*x^5+b)^(3/4)/x^6,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{b} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{5} + b\right)}^{\frac{3}{4}} a}{x^{5}}}{40 \, a}"," ",0,"1/40*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 3*sqrt(2)*a^2*(-b)^(3/4)*log(sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/b + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/(-b)^(1/4) - 8*(a*x^5 + b)^(3/4)*a/x^5)/a","B",0
993,0,0,0,0.000000," ","integrate((-3*x^5+2)/(x^5-x^2+1)/(x^6+x)^(1/3),x, algorithm=""giac"")","\int -\frac{3 \, x^{5} - 2}{{\left(x^{6} + x\right)}^{\frac{1}{3}} {\left(x^{5} - x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(-(3*x^5 - 2)/((x^6 + x)^(1/3)*(x^5 - x^2 + 1)), x)","F",0
994,1,209,0,0.434942," ","integrate((a*x^6+b)^(3/4)/x^7,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right)}{b} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{6} + b\right)}^{\frac{3}{4}} a}{x^{6}}}{48 \, a}"," ",0,"1/48*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^6 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^6 + b)^(1/4))/(-b)^(1/4))/(-b)^(1/4) + 3*sqrt(2)*a^2*(-b)^(3/4)*log(sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b))/b + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b))/(-b)^(1/4) - 8*(a*x^6 + b)^(3/4)*a/x^6)/a","B",0
995,0,0,0,0.000000," ","integrate((a*x^6+2*b)/(a*x^6-b)^(1/4)/(a*x^6-2*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{6} + 2 \, b}{{\left(a x^{6} - 2 \, x^{4} - b\right)} {\left(a x^{6} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^6 + 2*b)/((a*x^6 - 2*x^4 - b)*(a*x^6 - b)^(1/4)), x)","F",0
996,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+1)^(1/2)/(x^8+3*x^4+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} {\left(x^{4} - 1\right)}}{x^{8} + 3 \, x^{4} + 1}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*(x^4 - 1)/(x^8 + 3*x^4 + 1), x)","F",0
997,0,0,0,0.000000," ","integrate((k^2*x^2-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(a*k^2*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} - 1}{{\left(a k^{2} x^{2} + b x + a\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^2*x^2 - 1)/((a*k^2*x^2 + b*x + a)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
998,1,57,0,0.447310," ","integrate(1/x/(x^4-1)^(1/3),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{1}{8} \, \log\left({\left(x^{4} - 1\right)}^{\frac{2}{3}} - {\left(x^{4} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{4} \, \log\left({\left| {\left(x^{4} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 - 1)^(1/3) - 1)) + 1/8*log((x^4 - 1)^(2/3) - (x^4 - 1)^(1/3) + 1) - 1/4*log(abs((x^4 - 1)^(1/3) + 1))","A",0
999,0,0,0,0.000000," ","integrate(x^2*(a*x^2-2*b)/(a*x^2-b)^(3/4)/(x^4-4*a*x^2+4*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} - 2 \, b\right)} x^{2}}{{\left(x^{4} - 4 \, a x^{2} + 4 \, b\right)} {\left(a x^{2} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^2 - 2*b)*x^2/((x^4 - 4*a*x^2 + 4*b)*(a*x^2 - b)^(3/4)), x)","F",0
1000,0,0,0,0.000000," ","integrate((-a*b*x+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(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, algorithm=""giac"")","\int -\frac{a b x - x^{3}}{{\left(a^{2} b^{2} - 2 \, {\left(a + b\right)} a b x - 2 \, {\left(a + b\right)} x^{3} + x^{4} + {\left(a^{2} + 4 \, a b + b^{2} - d\right)} x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate(-(a*b*x - x^3)/((a^2*b^2 - 2*(a + b)*a*b*x - 2*(a + b)*x^3 + x^4 + (a^2 + 4*a*b + b^2 - d)*x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
1001,0,0,0,0.000000," ","integrate((-x^4-1)^(1/4)*(x^4-1)/x^6/(2*x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)} {\left(-x^{4} - 1\right)}^{\frac{1}{4}}}{{\left(2 \, x^{4} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 - 1)*(-x^4 - 1)^(1/4)/((2*x^4 + 1)*x^6), x)","F",0
1002,0,0,0,0.000000," ","integrate((a*b*x-x^3)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2*d+4*a*b*d+b^2*d-1)*x^2-2*(a+b)*d*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{a b x - x^{3}}{{\left(a^{2} b^{2} d - 2 \, {\left(a + b\right)} a b d x - 2 \, {\left(a + b\right)} d x^{3} + d x^{4} + {\left(a^{2} d + 4 \, a b d + b^{2} d - 1\right)} x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate((a*b*x - x^3)/((a^2*b^2*d - 2*(a + b)*a*b*d*x - 2*(a + b)*d*x^3 + d*x^4 + (a^2*d + 4*a*b*d + b^2*d - 1)*x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
1003,0,0,0,0.000000," ","integrate((-a*b*x+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2*d+4*a*b*d+b^2*d-1)*x^2-2*(a+b)*d*x^3+d*x^4),x, algorithm=""giac"")","\int -\frac{a b x - x^{3}}{{\left(a^{2} b^{2} d - 2 \, {\left(a + b\right)} a b d x - 2 \, {\left(a + b\right)} d x^{3} + d x^{4} + {\left(a^{2} d + 4 \, a b d + b^{2} d - 1\right)} x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate(-(a*b*x - x^3)/((a^2*b^2*d - 2*(a + b)*a*b*d*x - 2*(a + b)*d*x^3 + d*x^4 + (a^2*d + 4*a*b*d + b^2*d - 1)*x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
1004,1,57,0,0.257413," ","integrate(1/x/(x^6-1)^(1/3),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{1}{12} \, \log\left({\left(x^{6} - 1\right)}^{\frac{2}{3}} - {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{6} \, \log\left({\left| {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 - 1)^(1/3) - 1)) + 1/12*log((x^6 - 1)^(2/3) - (x^6 - 1)^(1/3) + 1) - 1/6*log(abs((x^6 - 1)^(1/3) + 1))","A",0
1005,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6+x^3+2)/x^6/(x^6+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 + x^3 + 2)*(x^3 + 1)^(2/3)/((x^6 + x^3 + 1)*x^6), x)","F",0
1006,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6+x^3+2)/x^6/(x^6+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 + x^3 + 2)*(x^3 + 1)^(2/3)/((x^6 + x^3 + 1)*x^6), x)","F",0
1007,0,0,0,0.000000," ","integrate((x^4-1)*(x^4-x^2+1)*(4*x^4-x^2+4)^(1/2)/(x^4+1)/(4*x^8+7*x^4+4),x, algorithm=""giac"")","\int \frac{\sqrt{4 \, x^{4} - x^{2} + 4} {\left(x^{4} - x^{2} + 1\right)} {\left(x^{4} - 1\right)}}{{\left(4 \, x^{8} + 7 \, x^{4} + 4\right)} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(4*x^4 - x^2 + 4)*(x^4 - x^2 + 1)*(x^4 - 1)/((4*x^8 + 7*x^4 + 4)*(x^4 + 1)), x)","F",0
1008,0,0,0,0.000000," ","integrate((-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3),x, algorithm=""giac"")","\int {\left(-3 \, x^{10} + x^{9} - 9 \, x^{7} + 3 \, x^{6} - 9 \, x^{4} + 3 \, x^{3} - 3 \, x + 1\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((-3*x^10 + x^9 - 9*x^7 + 3*x^6 - 9*x^4 + 3*x^3 - 3*x + 1)^(1/3), x)","F",0
1009,0,0,0,0.000000," ","integrate(x*(-b+x)*(a*b-2*a*x+x^2)/(-a+x)/(x*(-a+x)*(-b+x))^(1/2)/(a*d+(-b-d)*x+x^2),x, algorithm=""giac"")","\int \frac{{\left(a b - 2 \, a x + x^{2}\right)} {\left(b - x\right)} x}{\sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(a d - {\left(b + d\right)} x + x^{2}\right)} {\left(a - x\right)}}\,{d x}"," ",0,"integrate((a*b - 2*a*x + x^2)*(b - x)*x/(sqrt((a - x)*(b - x)*x)*(a*d - (b + d)*x + x^2)*(a - x)), x)","F",0
1010,0,0,0,0.000000," ","integrate((k^2*x^2+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-1),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} + 1}{{\left(k^{2} x^{2} - 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^2*x^2 + 1)/((k^2*x^2 - 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
1011,0,0,0,0.000000," ","integrate(1/(x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 + 1)^(-1/3), x)","F",0
1012,0,0,0,0.000000," ","integrate((x^2+x)/(x^2-2*x-1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + x}{\sqrt{x^{3} - x} {\left(x^{2} - 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + x)/(sqrt(x^3 - x)*(x^2 - 2*x - 1)), x)","F",0
1013,0,0,0,0.000000," ","integrate(x^2*(3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x-x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(3 \, a b - 2 \, {\left(a + b\right)} x + x^{2}\right)} x^{2}}{{\left(d x^{3} - a b + {\left(a + b\right)} x - x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((3*a*b - 2*(a + b)*x + x^2)*x^2/((d*x^3 - a*b + (a + b)*x - x^2)*((a - x)*(b - x)*x)^(3/4)), x)","F",0
1014,1,102,0,0.213684," ","integrate(1/x/(x^4-1)^(1/4),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{8} \, \sqrt{2} \log\left(\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{4} - 1} + 1\right) + \frac{1}{8} \, \sqrt{2} \log\left(-\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{4} - 1} + 1\right)"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^4 - 1)^(1/4))) + 1/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^4 - 1)^(1/4))) - 1/8*sqrt(2)*log(sqrt(2)*(x^4 - 1)^(1/4) + sqrt(x^4 - 1) + 1) + 1/8*sqrt(2)*log(-sqrt(2)*(x^4 - 1)^(1/4) + sqrt(x^4 - 1) + 1)","A",0
1015,0,0,0,0.000000," ","integrate((-a+x)*(-b+x)*(-a*b+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(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, algorithm=""giac"")","\int -\frac{{\left(a b - x^{2}\right)} {\left(a - x\right)} {\left(b - x\right)}}{{\left(a^{2} b^{2} - 2 \, {\left(a + b\right)} a b x - 2 \, {\left(a + b\right)} x^{3} + x^{4} + {\left(a^{2} + 4 \, a b + b^{2} - d\right)} x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate(-(a*b - x^2)*(a - x)*(b - x)/((a^2*b^2 - 2*(a + b)*a*b*x - 2*(a + b)*x^3 + x^4 + (a^2 + 4*a*b + b^2 - d)*x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
1016,0,0,0,0.000000," ","integrate(x^2*(a*x^4-b)/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b\right)} x^{2}}{{\left(a x^{4} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - b)*x^2/(a*x^4 + b)^(3/4), x)","F",0
1017,1,186,0,0.294878," ","integrate(1/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a","B",0
1018,0,0,0,0.000000," ","integrate((-a+x)*(-b+x)*(-a*b+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2*d+4*a*b*d+b^2*d-1)*x^2-2*(a+b)*d*x^3+d*x^4),x, algorithm=""giac"")","\int -\frac{{\left(a b - x^{2}\right)} {\left(a - x\right)} {\left(b - x\right)}}{{\left(a^{2} b^{2} d - 2 \, {\left(a + b\right)} a b d x - 2 \, {\left(a + b\right)} d x^{3} + d x^{4} + {\left(a^{2} d + 4 \, a b d + b^{2} d - 1\right)} x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate(-(a*b - x^2)*(a - x)*(b - x)/((a^2*b^2*d - 2*(a + b)*a*b*d*x - 2*(a + b)*d*x^3 + d*x^4 + (a^2*d + 4*a*b*d + b^2*d - 1)*x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
1019,1,102,0,0.252435," ","integrate(1/x/(x^6-1)^(1/4),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(x^{6} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{6} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(x^{6} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{12} \, \sqrt{2} \log\left(\sqrt{2} {\left(x^{6} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{6} - 1} + 1\right) + \frac{1}{12} \, \sqrt{2} \log\left(-\sqrt{2} {\left(x^{6} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{6} - 1} + 1\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^6 - 1)^(1/4))) + 1/6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^6 - 1)^(1/4))) - 1/12*sqrt(2)*log(sqrt(2)*(x^6 - 1)^(1/4) + sqrt(x^6 - 1) + 1) + 1/12*sqrt(2)*log(-sqrt(2)*(x^6 - 1)^(1/4) + sqrt(x^6 - 1) + 1)","A",0
1020,-1,0,0,0.000000," ","integrate(1/(a*x^3-b*x)^(1/3)/(c*x^6+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1021,-1,0,0,0.000000," ","integrate(1/(a*x^3-b*x)^(1/3)/(c*x^6+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1022,1,52,0,0.446421," ","integrate((x^2-1)*(-1+x*(-x^4+3*x^2-1)^(1/2)),x, algorithm=""giac"")","-\frac{1}{3} \, x^{3} + \frac{1}{48} \, \sqrt{-x^{4} + 3 \, x^{2} - 1} {\left(2 \, {\left(4 \, x^{2} - 9\right)} x^{2} - 1\right)} + x + \frac{5}{32} \, \arcsin\left(\frac{1}{5} \, \sqrt{5} {\left(2 \, x^{2} - 3\right)}\right)"," ",0,"-1/3*x^3 + 1/48*sqrt(-x^4 + 3*x^2 - 1)*(2*(4*x^2 - 9)*x^2 - 1) + x + 5/32*arcsin(1/5*sqrt(5)*(2*x^2 - 3))","A",0
1023,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1024,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,-1,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,1,84,0,0.379075," ","integrate((x^2-1)^(1/2)/(-I+x)^2,x, algorithm=""giac"")","i \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(x - \sqrt{x^{2} - 1} - i\right)}\right) + \frac{2 \, {\left(i \, x - i \, \sqrt{x^{2} - 1} - 1\right)}}{{\left(x - \sqrt{x^{2} - 1}\right)}^{2} - 2 i \, x + 2 i \, \sqrt{x^{2} - 1} + 1} - \log\left({\left| -x + \sqrt{x^{2} - 1} \right|}\right)"," ",0,"I*sqrt(2)*arctan(-1/2*sqrt(2)*(x - sqrt(x^2 - 1) - I)) + 2*(I*x - I*sqrt(x^2 - 1) - 1)/((x - sqrt(x^2 - 1))^2 - 2*I*x + 2*I*sqrt(x^2 - 1) + 1) - log(abs(-x + sqrt(x^2 - 1)))","A",0
1027,1,221,0,0.360725," ","integrate(1/x^3/(a*x^2+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{2} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{2} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b} - \frac{8 \, {\left(a x^{2} + b\right)}^{\frac{1}{4}} a}{b x^{2}}}{16 \, a}"," ",0,"1/16*(6*sqrt(2)*a^2*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^2 + b)^(1/4))/(-b)^(1/4))/b^2 + 6*sqrt(2)*a^2*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^2 + b)^(1/4))/(-b)^(1/4))/b^2 + 3*sqrt(2)*a^2*(-b)^(1/4)*log(sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b))/b^2 + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^2 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^2 + b) + sqrt(-b))/((-b)^(3/4)*b) - 8*(a*x^2 + b)^(1/4)*a/(b*x^2))/a","B",0
1028,0,0,0,0.000000," ","integrate((3*x^3+x^2-2*x-1)^4/(x^3-3*x^2+3*x-1)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} + x^{2} - 2 \, x - 1\right)}^{4}}{{\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((3*x^3 + x^2 - 2*x - 1)^4/(x^3 - 3*x^2 + 3*x - 1)^(1/4), x)","F",0
1029,1,221,0,0.966225," ","integrate(1/x^4/(a*x^3+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b} - \frac{8 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}} a}{b x^{3}}}{24 \, a}"," ",0,"1/24*(6*sqrt(2)*a^2*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/b^2 + 6*sqrt(2)*a^2*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/b^2 + 3*sqrt(2)*a^2*(-b)^(1/4)*log(sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/b^2 + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/((-b)^(3/4)*b) - 8*(a*x^3 + b)^(1/4)*a/(b*x^3))/a","B",0
1030,0,0,0,0.000000," ","integrate(x/(x^4+10*x^2-96*x-71)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{4} + 10 \, x^{2} - 96 \, x - 71}}\,{d x}"," ",0,"integrate(x/sqrt(x^4 + 10*x^2 - 96*x - 71), x)","F",0
1031,0,0,0,0.000000," ","integrate((8+3*x)*(2*x^4-x-2)^(1/4)/x^2/(x^4+x+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x - 2\right)}^{\frac{1}{4}} {\left(3 \, x + 8\right)}}{{\left(x^{4} + x + 2\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^4 - x - 2)^(1/4)*(3*x + 8)/((x^4 + x + 2)*x^2), x)","F",0
1032,1,221,0,0.461315," ","integrate(1/x^5/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b} - \frac{8 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}} a}{b x^{4}}}{32 \, a}"," ",0,"1/32*(6*sqrt(2)*a^2*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/b^2 + 6*sqrt(2)*a^2*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/b^2 + 3*sqrt(2)*a^2*(-b)^(1/4)*log(sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/b^2 + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/((-b)^(3/4)*b) - 8*(a*x^4 + b)^(1/4)*a/(b*x^4))/a","B",0
1033,1,221,0,0.983578," ","integrate(1/x^6/(a*x^5+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b} - \frac{8 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}} a}{b x^{5}}}{40 \, a}"," ",0,"1/40*(6*sqrt(2)*a^2*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/b^2 + 6*sqrt(2)*a^2*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/b^2 + 3*sqrt(2)*a^2*(-b)^(1/4)*log(sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/b^2 + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/((-b)^(3/4)*b) - 8*(a*x^5 + b)^(1/4)*a/(b*x^5))/a","B",0
1034,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 1)*(x^3 - 1)^(2/3)/((x^6 - x^3 + 1)*x^6), x)","F",0
1035,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 1)*(x^3 - 1)^(2/3)/((x^6 - x^3 + 1)*x^6), x)","F",0
1036,1,221,0,0.298301," ","integrate(1/x^7/(a*x^6+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{6 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \left(-b\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right)}{b^{2}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{6} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{6} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b} - \frac{8 \, {\left(a x^{6} + b\right)}^{\frac{1}{4}} a}{b x^{6}}}{48 \, a}"," ",0,"1/48*(6*sqrt(2)*a^2*(-b)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^6 + b)^(1/4))/(-b)^(1/4))/b^2 + 6*sqrt(2)*a^2*(-b)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^6 + b)^(1/4))/(-b)^(1/4))/b^2 + 3*sqrt(2)*a^2*(-b)^(1/4)*log(sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b))/b^2 + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^6 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^6 + b) + sqrt(-b))/((-b)^(3/4)*b) - 8*(a*x^6 + b)^(1/4)*a/(b*x^6))/a","B",0
1037,1,290,0,0.573410," ","integrate((x^4-1)^(1/4)*(x^8-1)/x^6/(x^8+1),x, algorithm=""giac"")","-\frac{1}{144115188075855872} i \, \left(8 i + 8\right)^{\frac{63}{4}} \log\left(\left(-281474976710656 i + 281474976710656\right)^{\frac{1}{4}} - \frac{4096 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{144115188075855872} i \, \left(8 i + 8\right)^{\frac{63}{4}} \log\left(-\left(-281474976710656 i + 281474976710656\right)^{\frac{1}{4}} - \frac{4096 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{536870912} \, \left(8 i + 8\right)^{\frac{31}{4}} \log\left(i \, \left(-16777216 i + 16777216\right)^{\frac{1}{4}} - \frac{64 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) - \frac{1}{536870912} \, \left(8 i + 8\right)^{\frac{31}{4}} \log\left(-i \, \left(-16777216 i + 16777216\right)^{\frac{1}{4}} - \frac{64 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) - \frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 1\right)}}{5 \, x} + \frac{i \, \left(8 i + 8\right)^{\frac{15}{4}} \log\left(\left(16777216 i + 16777216\right)^{\frac{1}{4}} - \frac{64 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{256 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{7}} - \frac{\left(8 i + 8\right)^{\frac{15}{4}} \log\left(i \, \left(16777216 i + 16777216\right)^{\frac{1}{4}} - \frac{64 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{256 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{7}} + \frac{\left(8 i + 8\right)^{\frac{15}{4}} \log\left(-i \, \left(16777216 i + 16777216\right)^{\frac{1}{4}} - \frac{64 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{256 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{7}} - \frac{i \, \left(8 i + 8\right)^{\frac{15}{4}} \log\left(-\left(16777216 i + 16777216\right)^{\frac{1}{4}} - \frac{64 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{256 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{7}}"," ",0,"-1/144115188075855872*I*(8*I + 8)^(63/4)*log((-281474976710656*I + 281474976710656)^(1/4) - 4096*(x^4 - 1)^(1/4)/x) + 1/144115188075855872*I*(8*I + 8)^(63/4)*log(-(-281474976710656*I + 281474976710656)^(1/4) - 4096*(x^4 - 1)^(1/4)/x) + 1/536870912*(8*I + 8)^(31/4)*log(I*(-16777216*I + 16777216)^(1/4) - 64*(x^4 - 1)^(1/4)/x) - 1/536870912*(8*I + 8)^(31/4)*log(-I*(-16777216*I + 16777216)^(1/4) - 64*(x^4 - 1)^(1/4)/x) - 1/5*(x^4 - 1)^(1/4)*(1/x^4 - 1)/x + 1/256*I*(8*I + 8)^(15/4)*log((16777216*I + 16777216)^(1/4) - 64*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^7 - 1/256*(8*I + 8)^(15/4)*log(I*(16777216*I + 16777216)^(1/4) - 64*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^7 + 1/256*(8*I + 8)^(15/4)*log(-I*(16777216*I + 16777216)^(1/4) - 64*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^7 - 1/256*I*(8*I + 8)^(15/4)*log(-(16777216*I + 16777216)^(1/4) - 64*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^7","B",0
1038,0,0,0,0.000000," ","integrate((x^8-1)/(x^4+1)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + 1)*(x^4 + 1)^(1/4)), x)","F",0
1039,0,0,0,0.000000," ","integrate((x^8-1)/(x^4+1)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + 1)*(x^4 + 1)^(1/4)), x)","F",0
1040,0,0,0,0.000000," ","integrate((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{{\left(2 \, x^{8} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^8 - x^4 + 1)*(x^4 - 1)^(1/4)/((2*x^8 + 1)*x^6), x)","F",0
1041,0,0,0,0.000000," ","integrate((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{{\left(2 \, x^{8} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^8 - x^4 + 1)*(x^4 - 1)^(1/4)/((2*x^8 + 1)*x^6), x)","F",0
1042,1,86,0,0.321664," ","integrate((2*x^4+1)*(2*x^8+1)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2 \, x^{8} + 1} {\left(x^{4} + 1\right)} - \frac{1}{8} \, \sqrt{2} \log\left(-\sqrt{2} x^{4} + \sqrt{2 \, x^{8} + 1}\right) + \frac{1}{4} \, \log\left(\sqrt{2} x^{4} - \sqrt{2 \, x^{8} + 1} + 1\right) - \frac{1}{4} \, \log\left(-\sqrt{2} x^{4} + \sqrt{2 \, x^{8} + 1} + 1\right)"," ",0,"1/4*sqrt(2*x^8 + 1)*(x^4 + 1) - 1/8*sqrt(2)*log(-sqrt(2)*x^4 + sqrt(2*x^8 + 1)) + 1/4*log(sqrt(2)*x^4 - sqrt(2*x^8 + 1) + 1) - 1/4*log(-sqrt(2)*x^4 + sqrt(2*x^8 + 1) + 1)","A",0
1043,1,53,0,0.286085," ","integrate((x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, \sqrt{x + 1} {\left(4 \, \sqrt{x + 1} + 1\right)} - 11\right)} \sqrt{x + \sqrt{x + 1}} - \frac{5}{8} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/12*(2*sqrt(x + 1)*(4*sqrt(x + 1) + 1) - 11)*sqrt(x + sqrt(x + 1)) - 5/8*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
1044,1,69,0,0.348345," ","integrate((a*x^2+2*b)/x/(a^2*x^2+b^2)^(3/4),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{{\left(a^{2} x^{2} + b^{2}\right)}^{\frac{1}{4}}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{2 \, \arctan\left(\frac{{\left(a^{2} x^{2} + b^{2}\right)}^{\frac{1}{4}}}{\sqrt{b}}\right)}{\sqrt{b}} + \frac{2 \, {\left(a^{2} x^{2} + b^{2}\right)}^{\frac{1}{4}}}{a}"," ",0,"2*arctan((a^2*x^2 + b^2)^(1/4)/sqrt(-b))/sqrt(-b) - 2*arctan((a^2*x^2 + b^2)^(1/4)/sqrt(b))/sqrt(b) + 2*(a^2*x^2 + b^2)^(1/4)/a","A",0
1045,0,0,0,0.000000," ","integrate((-a*b*x+x^3)/(-a+x)/(-b+x)/(x*(-a+x)*(-b+x))^(1/2)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int -\frac{a b x - x^{3}}{{\left(a b d + d x^{2} - {\left(a d + b d + 1\right)} x\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(a - x\right)} {\left(b - x\right)}}\,{d x}"," ",0,"integrate(-(a*b*x - x^3)/((a*b*d + d*x^2 - (a*d + b*d + 1)*x)*sqrt((a - x)*(b - x)*x)*(a - x)*(b - x)), x)","F",0
1046,0,0,0,0.000000," ","integrate((-1+2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-1+(3+d)*x-(d*k+3)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{k x^{2} + 2 \, {\left(k - 1\right)} x - 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{4}} {\left({\left(d k + 3\right)} x^{2} - x^{3} - {\left(d + 3\right)} x + 1\right)}}\,{d x}"," ",0,"integrate(-(k*x^2 + 2*(k - 1)*x - 1)/(((k*x - 1)*(x - 1)*x)^(1/4)*((d*k + 3)*x^2 - x^3 - (d + 3)*x + 1)), x)","F",0
1047,0,0,0,0.000000," ","integrate((x^4+1)/(x^3-x)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{4} - 1\right)} \sqrt{x^{3} - x}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^4 - 1)*sqrt(x^3 - x)), x)","F",0
1048,0,0,0,0.000000," ","integrate((x^2+2)*(x^4-5*x^2+4)^(1/2)/x^2/(x^2+2*x-2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} - 5 \, x^{2} + 4} {\left(x^{2} + 2\right)}}{{\left(x^{2} + 2 \, x - 2\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 - 5*x^2 + 4)*(x^2 + 2)/((x^2 + 2*x - 2)*x^2), x)","F",0
1049,1,63,0,0.506028," ","integrate(x^2/(x^4-1)/(x^4+x^2)^(1/4),x, algorithm=""giac"")","\frac{1}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right) + \frac{1}{{\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"1/4*2^(3/4)*arctan(1/2*2^(3/4)*(1/x^2 + 1)^(1/4)) - 1/8*2^(3/4)*log(2^(1/4) + (1/x^2 + 1)^(1/4)) + 1/8*2^(3/4)*log(abs(-2^(1/4) + (1/x^2 + 1)^(1/4))) + 1/(1/x^2 + 1)^(1/4)","A",0
1050,1,97,0,0.307025," ","integrate((x^6-2)*(x^6-1)^(1/2)/x^4/(x^6+2),x, algorithm=""giac"")","\frac{\sqrt{6} \log\left(\frac{\sqrt{6} - 2 \, \sqrt{-\frac{1}{x^{6}} + 1}}{\sqrt{6} + 2 \, \sqrt{-\frac{1}{x^{6}} + 1}}\right)}{6 \, \mathrm{sgn}\left(x\right)} + \frac{\log\left(\sqrt{-\frac{1}{x^{6}} + 1} + 1\right)}{6 \, \mathrm{sgn}\left(x\right)} - \frac{\log\left(-\sqrt{-\frac{1}{x^{6}} + 1} + 1\right)}{6 \, \mathrm{sgn}\left(x\right)} + \frac{\sqrt{-\frac{1}{x^{6}} + 1}}{3 \, \mathrm{sgn}\left(x\right)}"," ",0,"1/6*sqrt(6)*log((sqrt(6) - 2*sqrt(-1/x^6 + 1))/(sqrt(6) + 2*sqrt(-1/x^6 + 1)))/sgn(x) + 1/6*log(sqrt(-1/x^6 + 1) + 1)/sgn(x) - 1/6*log(-sqrt(-1/x^6 + 1) + 1)/sgn(x) + 1/3*sqrt(-1/x^6 + 1)/sgn(x)","A",0
1051,0,0,0,0.000000," ","integrate((x^6-4)*(x^6-x^4+2)^(5/2)/x^7/(x^6+2)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} + 2\right)}^{\frac{5}{2}} {\left(x^{6} - 4\right)}}{{\left(x^{6} + 2\right)}^{2} x^{7}}\,{d x}"," ",0,"integrate((x^6 - x^4 + 2)^(5/2)*(x^6 - 4)/((x^6 + 2)^2*x^7), x)","F",0
1052,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(2*x^6+x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} + x^{3} + 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((2*x^6 + x^3 + 2)*x^6), x)","F",0
1053,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(2*x^6+x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} + x^{3} + 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((2*x^6 + x^3 + 2)*x^6), x)","F",0
1054,0,0,0,0.000000," ","integrate((x^7+x)/(x^6-1)^(2/3)/(x^6+x^3-1),x, algorithm=""giac"")","\int \frac{x^{7} + x}{{\left(x^{6} + x^{3} - 1\right)} {\left(x^{6} - 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((x^7 + x)/((x^6 + x^3 - 1)*(x^6 - 1)^(2/3)), x)","F",0
1055,0,0,0,0.000000," ","integrate((-x^6+1)^(1/2)*(2*x^6+1)/(x^12-2*x^6+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + 1\right)} \sqrt{-x^{6} + 1}}{x^{12} - 2 \, x^{6} + x^{4} + 1}\,{d x}"," ",0,"integrate((2*x^6 + 1)*sqrt(-x^6 + 1)/(x^12 - 2*x^6 + x^4 + 1), x)","F",0
1056,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(1+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{\sqrt{x^{2} + 1} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(sqrt(x^2 + 1) + 1), x)","F",0
1057,0,0,0,0.000000," ","integrate((x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^2 + 1)/sqrt(x + sqrt(x^2 + 1)), x)","F",0
1058,0,0,0,0.000000," ","integrate(x^2/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}\,{d x}"," ",0,"integrate(x^2/sqrt(x^2 + sqrt(x^4 + 1)), x)","F",0
1059,0,0,0,0.000000," ","integrate((x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1}}{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)/sqrt(x^2 + sqrt(x^4 + 1)), x)","F",0
1060,0,0,0,0.000000," ","integrate((x^2-3)/(x^2-1)^(1/3)/(x^3+x^2-1),x, algorithm=""giac"")","\int \frac{x^{2} - 3}{{\left(x^{3} + x^{2} - 1\right)} {\left(x^{2} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^2 - 3)/((x^3 + x^2 - 1)*(x^2 - 1)^(1/3)), x)","F",0
1061,0,0,0,0.000000," ","integrate((-a^2*b+a*(2*a+b)*x-3*a*x^2+x^3)/x/(-b+x)/(x*(-a+x)*(-b+x))^(1/2)/(a-(b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a^{2} b - {\left(2 \, a + b\right)} a x + 3 \, a x^{2} - x^{3}}{\sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(d x^{2} - {\left(b d + 1\right)} x + a\right)} {\left(b - x\right)} x}\,{d x}"," ",0,"integrate((a^2*b - (2*a + b)*a*x + 3*a*x^2 - x^3)/(sqrt((a - x)*(b - x)*x)*(d*x^2 - (b*d + 1)*x + a)*(b - x)*x), x)","F",0
1062,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{3} + b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^3 + b)), x)","F",0
1063,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{3} + b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^3 + b)), x)","F",0
1064,0,0,0,0.000000," ","integrate(x^2*(x^3-4)/(x^3-1)^(3/4)/(x^4+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 4\right)} x^{2}}{{\left(x^{4} + x^{3} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((x^3 - 4)*x^2/((x^4 + x^3 - 1)*(x^3 - 1)^(3/4)), x)","F",0
1065,0,0,0,0.000000," ","integrate(x^6/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(a x^{4} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^6/(a*x^4 + b)^(3/4), x)","F",0
1066,1,185,0,0.371619," ","integrate((a*x^4+b*x^2)^(1/4)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}"," ",0,"1/2*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) + 1/2*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) + 1/4*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) - 1/4*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) - 2*(a + b/x^2)^(1/4)","B",0
1067,-2,0,0,0.000000," ","integrate((x^4+2)^(1/4)*(x^8-4)/x^6/(x^8-2*x^4-4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1068,-2,0,0,0.000000," ","integrate((x^4+2)^(1/4)*(x^8-4)/x^6/(x^8-2*x^4-4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1069,1,372,0,0.422195," ","integrate((x^4-1)^(1/4)*(2*x^8+x^4-1)/x^6/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{8} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{8} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{8} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{8} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{16} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} + \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) + \frac{1}{16} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} + \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) - \frac{1}{16} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} - \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) + \frac{1}{16} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} - \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) - \frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 1\right)}}{5 \, x}"," ",0,"-1/8*(sqrt(6) - 3*sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) + sqrt(2))) - 1/8*(sqrt(6) - 3*sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) + sqrt(2))) - 1/8*(sqrt(6) + 3*sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) - sqrt(2))) - 1/8*(sqrt(6) + 3*sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) - sqrt(2))) - 1/16*(sqrt(6) - 3*sqrt(2))*log(1/2*(x^4 - 1)^(1/4)*(sqrt(6) + sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) + 1/16*(sqrt(6) - 3*sqrt(2))*log(-1/2*(x^4 - 1)^(1/4)*(sqrt(6) + sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) - 1/16*(sqrt(6) + 3*sqrt(2))*log(1/2*(x^4 - 1)^(1/4)*(sqrt(6) - sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) + 1/16*(sqrt(6) + 3*sqrt(2))*log(-1/2*(x^4 - 1)^(1/4)*(sqrt(6) - sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) - 1/5*(x^4 - 1)^(1/4)*(1/x^4 - 1)/x","B",0
1070,1,372,0,0.298401," ","integrate((x^4-1)^(1/4)*(2*x^8+x^4-1)/x^6/(x^8-x^4+1),x, algorithm=""giac"")","-\frac{1}{8} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{8} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{8} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{8} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - \frac{4 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{16} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} + \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) + \frac{1}{16} \, {\left(\sqrt{6} - 3 \, \sqrt{2}\right)} \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} + \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) - \frac{1}{16} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} - \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) + \frac{1}{16} \, {\left(\sqrt{6} + 3 \, \sqrt{2}\right)} \log\left(-\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{6} - \sqrt{2}\right)}}{2 \, x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) - \frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 1\right)}}{5 \, x}"," ",0,"-1/8*(sqrt(6) - 3*sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) + sqrt(2))) - 1/8*(sqrt(6) - 3*sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) + sqrt(2))) - 1/8*(sqrt(6) + 3*sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) - sqrt(2))) - 1/8*(sqrt(6) + 3*sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(x^4 - 1)^(1/4)/x)/(sqrt(6) - sqrt(2))) - 1/16*(sqrt(6) - 3*sqrt(2))*log(1/2*(x^4 - 1)^(1/4)*(sqrt(6) + sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) + 1/16*(sqrt(6) - 3*sqrt(2))*log(-1/2*(x^4 - 1)^(1/4)*(sqrt(6) + sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) - 1/16*(sqrt(6) + 3*sqrt(2))*log(1/2*(x^4 - 1)^(1/4)*(sqrt(6) - sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) + 1/16*(sqrt(6) + 3*sqrt(2))*log(-1/2*(x^4 - 1)^(1/4)*(sqrt(6) - sqrt(2))/x + sqrt(x^4 - 1)/x^2 + 1) - 1/5*(x^4 - 1)^(1/4)*(1/x^4 - 1)/x","B",0
1071,0,0,0,0.000000," ","integrate((-2*a*b+(a+b)*x)/(x^2*(-a+x)*(-b+x))^(1/4)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{2 \, a b - {\left(a + b\right)} x}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{4}} {\left(a b d - {\left(a + b\right)} d x + {\left(d - 1\right)} x^{2}\right)}}\,{d x}"," ",0,"integrate(-(2*a*b - (a + b)*x)/(((a - x)*(b - x)*x^2)^(1/4)*(a*b*d - (a + b)*d*x + (d - 1)*x^2)), x)","F",0
1072,1,62,0,0.303407," ","integrate((x^3+1)^(1/3)/x,x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + {\left(x^{3} + 1\right)}^{\frac{1}{3}} - \frac{1}{6} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) + (x^3 + 1)^(1/3) - 1/6*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) + 1/3*log(abs((x^3 + 1)^(1/3) - 1))","A",0
1073,0,0,0,0.000000," ","integrate((3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/4)/(-a*b*d+(a+b)*d*x-d*x^2+x^3),x, algorithm=""giac"")","\int -\frac{3 \, a b - 2 \, {\left(a + b\right)} x + x^{2}}{{\left(a b d - {\left(a + b\right)} d x + d x^{2} - x^{3}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(3*a*b - 2*(a + b)*x + x^2)/((a*b*d - (a + b)*d*x + d*x^2 - x^3)*((a - x)*(b - x)*x)^(1/4)), x)","F",0
1074,0,0,0,0.000000," ","integrate(1/(a^3*x^3-b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{3} - b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^3 - b)), x)","F",0
1075,0,0,0,0.000000," ","integrate(1/(a^3*x^3-b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{3} - b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^3 - b)), x)","F",0
1076,0,0,0,0.000000," ","integrate((-2*a*b*x^2+(a+b)*x^3)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{2 \, a b x^{2} - {\left(a + b\right)} x^{3}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{3}{4}} {\left({\left(d - 1\right)} x^{2} - a b + {\left(a + b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(2*a*b*x^2 - (a + b)*x^3)/(((a - x)*(b - x)*x^2)^(3/4)*((d - 1)*x^2 - a*b + (a + b)*x)), x)","F",0
1077,0,0,0,0.000000," ","integrate((x^4-1)^(3/4)/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)}^{\frac{3}{4}}}{x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - 1)^(3/4)/(x^4 + 1), x)","F",0
1078,1,72,0,1.143145," ","integrate((x^4-x^2)^(1/4)/x^4/(x^4-1),x, algorithm=""giac"")","\frac{2}{5} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}} - \frac{1}{2} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right)"," ",0,"2/5*(-1/x^2 + 1)^(5/4) - 1/2*2^(1/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) - 1/4*2^(1/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) + 1/4*2^(1/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4))","A",0
1079,0,0,0,0.000000," ","integrate((-x^2+1)^2/(x^2+1)/(x^4+6*x^2+1)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - 1\right)}^{2}}{{\left(x^{4} + 6 \, x^{2} + 1\right)}^{\frac{3}{4}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)^2/((x^4 + 6*x^2 + 1)^(3/4)*(x^2 + 1)), x)","F",0
1080,0,0,0,0.000000," ","integrate(1/(1+x)/(x^4+6*x^2+1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 6 \, x^{2} + 1\right)}^{\frac{1}{4}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^4 + 6*x^2 + 1)^(1/4)*(x + 1)), x)","F",0
1081,1,183,0,0.460211," ","integrate((1+x)/(x^4-12*x^3+14*x^2+4*x-7)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{7} \, \sqrt{7} {\left(\sqrt{2} + \frac{3 \, {\left(\sqrt{7} \sqrt{-\frac{10}{x} - \frac{7}{x^{2}} + 1} - 4 \, \sqrt{2}\right)}}{\frac{7}{x} + 5}\right)}\right)}{\mathrm{sgn}\left(-\frac{1}{x^{2}} + \frac{1}{x^{3}}\right)} - \frac{\log\left({\left| 10 \, \sqrt{7} + 40 \, \sqrt{2} + \frac{50 \, {\left(\sqrt{7} \sqrt{-\frac{10}{x} - \frac{7}{x^{2}} + 1} - 4 \, \sqrt{2}\right)}}{\frac{7}{x} + 5} \right|}\right)}{\mathrm{sgn}\left(-\frac{1}{x^{2}} + \frac{1}{x^{3}}\right)} + \frac{\log\left({\left| -2 \, \sqrt{7} + 8 \, \sqrt{2} + \frac{10 \, {\left(\sqrt{7} \sqrt{-\frac{10}{x} - \frac{7}{x^{2}} + 1} - 4 \, \sqrt{2}\right)}}{\frac{7}{x} + 5} \right|}\right)}{\mathrm{sgn}\left(-\frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}"," ",0,"-arctan(1/7*sqrt(7)*(sqrt(2) + 3*(sqrt(7)*sqrt(-10/x - 7/x^2 + 1) - 4*sqrt(2))/(7/x + 5)))/sgn(-1/x^2 + 1/x^3) - log(abs(10*sqrt(7) + 40*sqrt(2) + 50*(sqrt(7)*sqrt(-10/x - 7/x^2 + 1) - 4*sqrt(2))/(7/x + 5)))/sgn(-1/x^2 + 1/x^3) + log(abs(-2*sqrt(7) + 8*sqrt(2) + 10*(sqrt(7)*sqrt(-10/x - 7/x^2 + 1) - 4*sqrt(2))/(7/x + 5)))/sgn(-1/x^2 + 1/x^3)","B",0
1082,0,0,0,0.000000," ","integrate((x^4+3)/(x^4-1)^(1/3)/(x^4-8*x^3-1),x, algorithm=""giac"")","\int \frac{x^{4} + 3}{{\left(x^{4} - 8 \, x^{3} - 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^4 + 3)/((x^4 - 8*x^3 - 1)*(x^4 - 1)^(1/3)), x)","F",0
1083,0,0,0,0.000000," ","integrate((-3+2*x)*(3*x^4+2*x^2-2*x)^(1/2)/(x^3+2*x-2)^2,x, algorithm=""giac"")","\int \frac{\sqrt{3 \, x^{4} + 2 \, x^{2} - 2 \, x} {\left(2 \, x - 3\right)}}{{\left(x^{3} + 2 \, x - 2\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(3*x^4 + 2*x^2 - 2*x)*(2*x - 3)/(x^3 + 2*x - 2)^2, x)","F",0
1084,0,0,0,0.000000," ","integrate((a*x^4-2*b)/x^4/(a*x^4-b)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(a x^{4} - b\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((a*x^4 - b)^(1/4)*x^4), x)","F",0
1085,0,0,0,0.000000," ","integrate((a*x^4-b)^(3/4),x, algorithm=""giac"")","\int {\left(a x^{4} - b\right)}^{\frac{3}{4}}\,{d x}"," ",0,"integrate((a*x^4 - b)^(3/4), x)","F",0
1086,0,0,0,0.000000," ","integrate((a*x^4-b)^(3/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b\right)}^{\frac{3}{4}}}{x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - b)^(3/4)/x^4, x)","F",0
1087,-1,0,0,0.000000," ","integrate(1/(a*x^3-b*x^2)^(1/3)/(a*x^4+b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,-1,0,0,0.000000," ","integrate(1/(a*x^3-b*x^2)^(1/3)/(a*x^4+b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1089,1,183,0,0.422582," ","integrate((a*x^4+b*x^3)^(1/4)/x^2,x, algorithm=""giac"")","\sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) - \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) - 4 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}"," ",0,"sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4)) + sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4)) + 1/2*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) - 1/2*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) - 4*(a + b/x)^(1/4)","B",0
1090,0,0,0,0.000000," ","integrate((x^6+x^4-x^3+1)^(3/4)*(2*x^6+x^3-4)/(x^6-x^3+1)^2,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{3} - 4\right)} {\left(x^{6} + x^{4} - x^{3} + 1\right)}^{\frac{3}{4}}}{{\left(x^{6} - x^{3} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((2*x^6 + x^3 - 4)*(x^6 + x^4 - x^3 + 1)^(3/4)/(x^6 - x^3 + 1)^2, x)","F",0
1091,0,0,0,0.000000," ","integrate((2*x^4+1)/(x^4+1)^(1/4)/(x^8-x^4-2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} + 1}{{\left(x^{8} - x^{4} - 2\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^4 + 1)/((x^8 - x^4 - 2)*(x^4 + 1)^(1/4)), x)","F",0
1092,-2,0,0,0.000000," ","integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1093,-2,0,0,0.000000," ","integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1094,0,0,0,0.000000," ","integrate((a^4*x^4-b^4)*(a^4*x^4+b^4)^(1/2)/(a^8*x^8+b^8),x, algorithm=""giac"")","\int \frac{\sqrt{a^{4} x^{4} + b^{4}} {\left(a^{4} x^{4} - b^{4}\right)}}{a^{8} x^{8} + b^{8}}\,{d x}"," ",0,"integrate(sqrt(a^4*x^4 + b^4)*(a^4*x^4 - b^4)/(a^8*x^8 + b^8), x)","F",0
1095,0,0,0,0.000000," ","integrate((a^8*x^8-b^8)/(a^4*x^4+b^4)^(1/2)/(a^8*x^8+b^8),x, algorithm=""giac"")","\int \frac{a^{8} x^{8} - b^{8}}{{\left(a^{8} x^{8} + b^{8}\right)} \sqrt{a^{4} x^{4} + b^{4}}}\,{d x}"," ",0,"integrate((a^8*x^8 - b^8)/((a^8*x^8 + b^8)*sqrt(a^4*x^4 + b^4)), x)","F",0
1096,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{{\left(a x^{2} + b^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2)^(3/2), x)","F",0
1097,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/sqrt(a^2*x^4 + b), x)","F",0
1098,0,0,0,0.000000," ","integrate(1/(a*x^3-b*x^2)^(1/3)/(a*x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b\right)} {\left(a x^{3} - b x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b)*(a*x^3 - b*x^2)^(1/3)), x)","F",0
1099,0,0,0,0.000000," ","integrate(1/(a*x^3-b*x^2)^(1/3)/(a*x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b\right)} {\left(a x^{3} - b x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b)*(a*x^3 - b*x^2)^(1/3)), x)","F",0
1100,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/x/(a*x^3+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{3}\right)}^{\frac{1}{4}}}{{\left(a x^{3} + b\right)} x}\,{d x}"," ",0,"integrate((a*x^4 - b*x^3)^(1/4)/((a*x^3 + b)*x), x)","F",0
1101,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/x/(a*x^3+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{3}\right)}^{\frac{1}{4}}}{{\left(a x^{3} + b\right)} x}\,{d x}"," ",0,"integrate((a*x^4 - b*x^3)^(1/4)/((a*x^3 + b)*x), x)","F",0
1102,1,211,0,0.205897," ","integrate((a*x^4+b*x^3)^(1/4)/x,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{2 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a} + \frac{\sqrt{2} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}}} + 8 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} b x}{8 \, b}"," ",0,"1/8*(2*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/a + 2*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/a + sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a + sqrt(2)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/(-a)^(3/4) + 8*(a + b/x)^(1/4)*b*x)/b","B",0
1103,1,207,0,0.381335," ","integrate((a*x-b)*(a*x^4+b*x^3)^(1/4)/x/(a*x+b),x, algorithm=""giac"")","\frac{\frac{14 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{14 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{7 \, \sqrt{2} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{7 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a} + 8 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} b x}{8 \, b}"," ",0,"1/8*(14*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 14*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 7*sqrt(2)*b^2*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/(-a)^(3/4) + 7*sqrt(2)*(-a)^(1/4)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a + 8*(a + b/x)^(1/4)*b*x)/b","B",0
1104,0,0,0,0.000000," ","integrate((3*x^4-1)/(x^4-x+1)/(x^6+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x^{4} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{4} - x + 1\right)}}\,{d x}"," ",0,"integrate((3*x^4 - 1)/((x^6 + x^2)^(1/3)*(x^4 - x + 1)), x)","F",0
1105,-2,0,0,0.000000," ","integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1106,-2,0,0,0.000000," ","integrate(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1107,0,0,0,0.000000," ","integrate((a*x^8-b)/x^2/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{a x^{8} - b}{{\left(a x^{4} + b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a*x^8 - b)/((a*x^4 + b)^(3/4)*x^2), x)","F",0
1108,-1,0,0,0.000000," ","integrate(x^5*(5*a*x^2-4*b)/(a*x^2-b)^(1/4)/(a*x^10-b*x^8+b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1109,1,55,0,3.027161," ","integrate(1/(x^3+x^2)^(1/3),x, algorithm=""giac"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{2} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) + 1/2*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) - log(abs((1/x + 1)^(1/3) - 1))","A",0
1110,0,0,0,0.000000," ","integrate((a-3*b+2*x)/((-a+x)*(-b+x))^(1/4)/(-a^3+b*d-(-3*a^2+d)*x-3*a*x^2+x^3),x, algorithm=""giac"")","\int -\frac{a - 3 \, b + 2 \, x}{{\left(a^{3} + 3 \, a x^{2} - x^{3} - b d - {\left(3 \, a^{2} - d\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(a - 3*b + 2*x)/((a^3 + 3*a*x^2 - x^3 - b*d - (3*a^2 - d)*x)*((a - x)*(b - x))^(1/4)), x)","F",0
1111,0,0,0,0.000000," ","integrate((a-3*b+2*x)*(a^2-2*a*x+x^2)/((-a+x)*(-b+x))^(3/4)/(-b+a^3*d+(-3*a^2*d+1)*x+3*a*d*x^2-d*x^3),x, algorithm=""giac"")","\int \frac{{\left(a^{2} - 2 \, a x + x^{2}\right)} {\left(a - 3 \, b + 2 \, x\right)}}{{\left(a^{3} d + 3 \, a d x^{2} - d x^{3} - {\left(3 \, a^{2} d - 1\right)} x - b\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a^2 - 2*a*x + x^2)*(a - 3*b + 2*x)/((a^3*d + 3*a*d*x^2 - d*x^3 - (3*a^2*d - 1)*x - b)*((a - x)*(b - x))^(3/4)), x)","F",0
1112,0,0,0,0.000000," ","integrate((-1-2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-1+(d+3*k)*x-(3*k^2+d)*x^2+k^3*x^3),x, algorithm=""giac"")","\int \frac{k x^{2} - 2 \, {\left(k - 1\right)} x - 1}{{\left(k^{3} x^{3} - {\left(3 \, k^{2} + d\right)} x^{2} + {\left(d + 3 \, k\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((k*x^2 - 2*(k - 1)*x - 1)/((k^3*x^3 - (3*k^2 + d)*x^2 + (d + 3*k)*x - 1)*((k*x - 1)*(x - 1)*x)^(1/4)), x)","F",0
1113,1,91,0,0.181318," ","integrate((x^4+6*x^2+1)^(1/2)/x/(x^2+1),x, algorithm=""giac"")","2 \, \arctan\left(-\frac{1}{2} \, x^{2} + \frac{1}{2} \, \sqrt{x^{4} + 6 \, x^{2} + 1} - \frac{1}{2}\right) - \frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{4} + 6 \, x^{2} + 1} + 3\right) - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 6 \, x^{2} + 1} + 1\right) + \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 6 \, x^{2} + 1} - 1\right)"," ",0,"2*arctan(-1/2*x^2 + 1/2*sqrt(x^4 + 6*x^2 + 1) - 1/2) - 1/2*log(x^2 - sqrt(x^4 + 6*x^2 + 1) + 3) - 1/2*log(-x^2 + sqrt(x^4 + 6*x^2 + 1) + 1) + 1/2*log(-x^2 + sqrt(x^4 + 6*x^2 + 1) - 1)","A",0
1114,0,0,0,0.000000," ","integrate((x^2-1)*(2*x^4+2*x^2-1)^(1/4)/x^2/(2*x^2-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + 2 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}{{\left(2 \, x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^4 + 2*x^2 - 1)^(1/4)*(x^2 - 1)/((2*x^2 - 1)*x^2), x)","F",0
1115,0,0,0,0.000000," ","integrate(1/(a*x^4+b)^(1/4)/(a*x^4+2*b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} + 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((a*x^4 + 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
1116,1,192,0,0.185711," ","integrate((a*x^4-b*x^2)^(1/4)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right) - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}"," ",0,"1/2*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^2)^(1/4))/(-a)^(1/4)) + 1/2*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^2)^(1/4))/(-a)^(1/4)) + 1/4*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2)) - 1/4*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2)) - 2*(a - b/x^2)^(1/4)","B",0
1117,0,0,0,0.000000," ","integrate(1/(a*x^4-b*x^2)^(1/4)/(b*x^8+a),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{8} + a\right)} {\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((b*x^8 + a)*(a*x^4 - b*x^2)^(1/4)), x)","F",0
1118,0,0,0,0.000000," ","integrate(1/(a*x^4-b*x^2)^(1/4)/(b*x^8+a),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{8} + a\right)} {\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((b*x^8 + a)*(a*x^4 - b*x^2)^(1/4)), x)","F",0
1119,1,82,0,0.353774," ","integrate((-1+x)*(x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, {\left(4 \, \sqrt{x + 1} {\left(6 \, \sqrt{x + 1} + 1\right)} - 65\right)} \sqrt{x + 1} + 19\right)} \sqrt{x + \sqrt{x + 1}} - \frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} + 1\right)} - \frac{115}{64} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/96*(2*(4*sqrt(x + 1)*(6*sqrt(x + 1) + 1) - 65)*sqrt(x + 1) + 19)*sqrt(x + sqrt(x + 1)) - 1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) + 1) - 115/64*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
1120,1,62,0,0.147550," ","integrate(x*(x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, {\left(4 \, \sqrt{x + 1} {\left(6 \, \sqrt{x + 1} + 1\right)} - 65\right)} \sqrt{x + 1} + 19\right)} \sqrt{x + \sqrt{x + 1}} - \frac{35}{64} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/96*(2*(4*sqrt(x + 1)*(6*sqrt(x + 1) + 1) - 65)*sqrt(x + 1) + 19)*sqrt(x + sqrt(x + 1)) - 35/64*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
1121,1,82,0,0.157990," ","integrate((1+x)^(1/2)*(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, {\left(4 \, \sqrt{x + 1} {\left(6 \, \sqrt{x + 1} + 1\right)} - 65\right)} \sqrt{x + 1} + 19\right)} \sqrt{x + \sqrt{x + 1}} + \frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} + 1\right)} + \frac{45}{64} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/96*(2*(4*sqrt(x + 1)*(6*sqrt(x + 1) + 1) - 65)*sqrt(x + 1) + 19)*sqrt(x + sqrt(x + 1)) + 1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) + 1) + 45/64*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
1122,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1} + 1}{\sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((sqrt(x^2 + 1) + 1)/sqrt(x + sqrt(x^2 + 1)), x)","F",0
1123,1,349,0,0.395855," ","integrate(((x^2-4*x+1)^(1/2)+(x^2-4*x+1)^(3/2))/((x^2-4*x+1)^(1/2)+(x^2-4*x+1)^(3/2)-(x^2-4*x+1)^(5/2)),x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}^{2} + 4 \, \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 6\right)} \log\left(x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}{2 \, {\left(2 \, {\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}^{3} + 12 \, {\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}^{2} + 17 \, \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 32\right)}} - \frac{{\left({\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 2\right)}^{2} - 4 \, \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 6\right)} \log\left(x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}{2 \, {\left(2 \, {\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 2\right)}^{3} - 12 \, {\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 2\right)}^{2} + 17 \, \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 32\right)}} + \frac{{\left({\left(\sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}^{2} + 4 \, \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 6\right)} \log\left(x + \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}{2 \, {\left(2 \, {\left(\sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}^{3} + 12 \, {\left(\sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}^{2} + 17 \, \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 32\right)}} - \frac{{\left({\left(\sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 2\right)}^{2} - 4 \, \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 6\right)} \log\left(x - \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} - 2\right)}{2 \, {\left(2 \, {\left(\sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 2\right)}^{3} - 12 \, {\left(\sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 2\right)}^{2} + 17 \, \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{7}{2}} + 32\right)}}"," ",0,"1/2*((sqrt(1/2*sqrt(5) + 7/2) - 2)^2 + 4*sqrt(1/2*sqrt(5) + 7/2) - 6)*log(x + sqrt(1/2*sqrt(5) + 7/2) - 2)/(2*(sqrt(1/2*sqrt(5) + 7/2) - 2)^3 + 12*(sqrt(1/2*sqrt(5) + 7/2) - 2)^2 + 17*sqrt(1/2*sqrt(5) + 7/2) - 32) - 1/2*((sqrt(1/2*sqrt(5) + 7/2) + 2)^2 - 4*sqrt(1/2*sqrt(5) + 7/2) - 6)*log(x - sqrt(1/2*sqrt(5) + 7/2) - 2)/(2*(sqrt(1/2*sqrt(5) + 7/2) + 2)^3 - 12*(sqrt(1/2*sqrt(5) + 7/2) + 2)^2 + 17*sqrt(1/2*sqrt(5) + 7/2) + 32) + 1/2*((sqrt(-1/2*sqrt(5) + 7/2) - 2)^2 + 4*sqrt(-1/2*sqrt(5) + 7/2) - 6)*log(x + sqrt(-1/2*sqrt(5) + 7/2) - 2)/(2*(sqrt(-1/2*sqrt(5) + 7/2) - 2)^3 + 12*(sqrt(-1/2*sqrt(5) + 7/2) - 2)^2 + 17*sqrt(-1/2*sqrt(5) + 7/2) - 32) - 1/2*((sqrt(-1/2*sqrt(5) + 7/2) + 2)^2 - 4*sqrt(-1/2*sqrt(5) + 7/2) - 6)*log(x - sqrt(-1/2*sqrt(5) + 7/2) - 2)/(2*(sqrt(-1/2*sqrt(5) + 7/2) + 2)^3 - 12*(sqrt(-1/2*sqrt(5) + 7/2) + 2)^2 + 17*sqrt(-1/2*sqrt(5) + 7/2) + 32)","B",0
1124,0,0,0,0.000000," ","integrate(x^2/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{a^{2} x^{2} - b x} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(sqrt(a^2*x^2 - b*x)*(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2)), x)","F",0
1125,0,0,0,0.000000," ","integrate((a^2*b-a*(2*a+b)*x+3*a*x^2-x^3)/x/(-b+x)/(x*(-a+x)*(-b+x))^(1/2)/(a+(-b*d-1)*x+d*x^2),x, algorithm=""giac"")","\int -\frac{a^{2} b - {\left(2 \, a + b\right)} a x + 3 \, a x^{2} - x^{3}}{\sqrt{{\left(a - x\right)} {\left(b - x\right)} x} {\left(d x^{2} - {\left(b d + 1\right)} x + a\right)} {\left(b - x\right)} x}\,{d x}"," ",0,"integrate(-(a^2*b - (2*a + b)*a*x + 3*a*x^2 - x^3)/(sqrt((a - x)*(b - x)*x)*(d*x^2 - (b*d + 1)*x + a)*(b - x)*x), x)","F",0
1126,1,64,0,0.210333," ","integrate((x^3+1)^(2/3)/x,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{2} \, {\left(x^{3} + 1\right)}^{\frac{2}{3}} - \frac{1}{6} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) + 1/2*(x^3 + 1)^(2/3) - 1/6*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) + 1/3*log(abs((x^3 + 1)^(1/3) - 1))","A",0
1127,1,209,0,0.194030," ","integrate((2*a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^2+b),x, algorithm=""giac"")","\frac{8 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} b x^{2} + \frac{10 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{10 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{5 \, \sqrt{2} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{5 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{a}}{8 \, b}"," ",0,"1/8*(8*(a + b/x^2)^(1/4)*b*x^2 + 10*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 10*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 5*sqrt(2)*b^2*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/(-a)^(3/4) + 5*sqrt(2)*(-a)^(1/4)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/a)/b","B",0
1128,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+x^2+1)^(1/2)*(x^8+x^6+3*x^4+x^2+1)/(x^4+1)^3/(x^4-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{6} + 3 \, x^{4} + x^{2} + 1\right)} \sqrt{x^{4} + x^{2} + 1} {\left(x^{4} - 1\right)}}{{\left(x^{4} - x^{2} + 1\right)} {\left(x^{4} + 1\right)}^{3}}\,{d x}"," ",0,"integrate((x^8 + x^6 + 3*x^4 + x^2 + 1)*sqrt(x^4 + x^2 + 1)*(x^4 - 1)/((x^4 - x^2 + 1)*(x^4 + 1)^3), x)","F",0
1129,0,0,0,0.000000," ","integrate((x^6+1)*(x^6+x^3-1)*(x^12+1)^(1/2)/x^7/(x^6-x^3-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{12} + 1} {\left(x^{6} + x^{3} - 1\right)} {\left(x^{6} + 1\right)}}{{\left(x^{6} - x^{3} - 1\right)} x^{7}}\,{d x}"," ",0,"integrate(sqrt(x^12 + 1)*(x^6 + x^3 - 1)*(x^6 + 1)/((x^6 - x^3 - 1)*x^7), x)","F",0
1130,1,99,0,0.224805," ","integrate((d+c*(a*x+b)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{5 \, {\left({\left(\sqrt{a x + b} c + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{a x + b} c + d} d\right)} d}{c} + \frac{3 \, {\left(\sqrt{a x + b} c + d\right)}^{\frac{5}{2}} - 10 \, {\left(\sqrt{a x + b} c + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{\sqrt{a x + b} c + d} d^{2}}{c}\right)}}{15 \, a c}"," ",0,"4/15*(5*((sqrt(a*x + b)*c + d)^(3/2) - 3*sqrt(sqrt(a*x + b)*c + d)*d)*d/c + (3*(sqrt(a*x + b)*c + d)^(5/2) - 10*(sqrt(a*x + b)*c + d)^(3/2)*d + 15*sqrt(sqrt(a*x + b)*c + d)*d^2)/c)/(a*c)","A",0
1131,1,63,0,0.244313," ","integrate((2*x^2+1)/x/(x^2+1)^(2/3),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + 3 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} - \frac{1}{4} \, \log\left({\left(x^{2} + 1\right)}^{\frac{2}{3}} + {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 + 1)^(1/3) + 1)) + 3*(x^2 + 1)^(1/3) - 1/4*log((x^2 + 1)^(2/3) + (x^2 + 1)^(1/3) + 1) + 1/2*log((x^2 + 1)^(1/3) - 1)","A",0
1132,0,0,0,0.000000," ","integrate(x/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-1),x, algorithm=""giac"")","\int \frac{x}{{\left(k^{2} x^{2} - 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate(x/((k^2*x^2 - 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
1133,0,0,0,0.000000," ","integrate((1+x)/(x^2+2*x-1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{3} - x} {\left(x^{2} + 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^3 - x)*(x^2 + 2*x - 1)), x)","F",0
1134,0,0,0,0.000000," ","integrate((x^2-x)/(x^2+2*x-1)/(x^3-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - x}{\sqrt{x^{3} - x} {\left(x^{2} + 2 \, x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 - x)/(sqrt(x^3 - x)*(x^2 + 2*x - 1)), x)","F",0
1135,0,0,0,0.000000," ","integrate((x^2+3)/(x^2+1)^(1/3)/(x^3+x^2+1),x, algorithm=""giac"")","\int \frac{x^{2} + 3}{{\left(x^{3} + x^{2} + 1\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^2 + 3)/((x^3 + x^2 + 1)*(x^2 + 1)^(1/3)), x)","F",0
1136,0,0,0,0.000000," ","integrate(x/(x^3-1)/(2*x^3-1)^(2/3),x, algorithm=""giac"")","\int \frac{x}{{\left(2 \, x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{3} - 1\right)}}\,{d x}"," ",0,"integrate(x/((2*x^3 - 1)^(2/3)*(x^3 - 1)), x)","F",0
1137,0,0,0,0.000000," ","integrate((-1-2*(-1+k)*x+k*x^2)*(k^2*x^2-2*k*x+1)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(3*d*k+1)*x-(3*d*k^2+1)*x^2+d*k^3*x^3),x, algorithm=""giac"")","\int \frac{{\left(k^{2} x^{2} - 2 \, k x + 1\right)} {\left(k x^{2} - 2 \, {\left(k - 1\right)} x - 1\right)}}{{\left(d k^{3} x^{3} - {\left(3 \, d k^{2} + 1\right)} x^{2} + {\left(3 \, d k + 1\right)} x - d\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((k^2*x^2 - 2*k*x + 1)*(k*x^2 - 2*(k - 1)*x - 1)/((d*k^3*x^3 - (3*d*k^2 + 1)*x^2 + (3*d*k + 1)*x - d)*((k*x - 1)*(x - 1)*x)^(3/4)), x)","F",0
1138,0,0,0,0.000000," ","integrate((x^4-1)/(x^3-x)^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{4} + 1\right)} \sqrt{x^{3} - x}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^4 + 1)*sqrt(x^3 - x)), x)","F",0
1139,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+x+1)/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + x + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^4 + x^2)^(1/3)*(x^2 + x + 1)), x)","F",0
1140,0,0,0,0.000000," ","integrate((a*x^4-2*b)*(a*x^4+b)^(3/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b\right)}^{\frac{3}{4}} {\left(a x^{4} - 2 \, b\right)}}{x^{8}}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)*(a*x^4 - 2*b)/x^8, x)","F",0
1141,0,0,0,0.000000," ","integrate((a*x^4-b)^(3/4)*(2*a*x^4-b)/x^8,x, algorithm=""giac"")","\int \frac{{\left(2 \, a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{3}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)*(a*x^4 - b)^(3/4)/x^8, x)","F",0
1142,0,0,0,0.000000," ","integrate((p*x^2-q)*(a*p*x^2+a*q+b*x)*(p^2*x^4+q^2)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{4} + q^{2}} {\left(a p x^{2} + a q + b x\right)} {\left(p x^{2} - q\right)}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^4 + q^2)*(a*p*x^2 + a*q + b*x)*(p*x^2 - q)/x^4, x)","F",0
1143,0,0,0,0.000000," ","integrate((2*x^3-1)/(x^3+x+1)/(x^5+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{2 \, x^{3} - 1}{{\left(x^{5} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} + x + 1\right)}}\,{d x}"," ",0,"integrate((2*x^3 - 1)/((x^5 + x^2)^(1/3)*(x^3 + x + 1)), x)","F",0
1144,0,0,0,0.000000," ","integrate((3*x^5+2)/(x^5+x^2-1)/(x^6-x)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x^{5} + 2}{{\left(x^{6} - x\right)}^{\frac{1}{3}} {\left(x^{5} + x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((3*x^5 + 2)/((x^6 - x)^(1/3)*(x^5 + x^2 - 1)), x)","F",0
1145,-2,0,0,0.000000," ","integrate((x^6-1)^(1/2)*(2*x^6-1)^2/x^4/(4*x^6-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:rootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument Valuerootof minimal polynomial must be unitary Error: Bad Argument ValueDone","F(-2)",0
1146,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{8} + x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^8 + x^4 + 1)*(x^4 - 1)^(1/4)), x)","F",0
1147,-2,0,0,0.000000," ","integrate((2*x^4-1)/(x^4-1)^(1/4)/(2*x^8-x^4-2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1148,0,0,0,0.000000," ","integrate((2*x^8+x^4-1)/(x^4-1)^(1/4)/(x^8-x^4+1),x, algorithm=""giac"")","\int \frac{2 \, x^{8} + x^{4} - 1}{{\left(x^{8} - x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 + x^4 - 1)/((x^8 - x^4 + 1)*(x^4 - 1)^(1/4)), x)","F",0
1149,-2,0,0,0.000000," ","integrate(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 82.77Not invertible Error: Bad Argument Value","F(-2)",0
1150,-2,0,0,0.000000," ","integrate(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 82.98Not invertible Error: Bad Argument Value","F(-2)",0
1151,0,0,0,0.000000," ","integrate((x^5+4)*(2*x^5+x^4-2)^(1/4)*(2*x^10+x^8-4*x^5+2)/x^10/(x^5-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{10} + x^{8} - 4 \, x^{5} + 2\right)} {\left(2 \, x^{5} + x^{4} - 2\right)}^{\frac{1}{4}} {\left(x^{5} + 4\right)}}{{\left(x^{5} - 1\right)} x^{10}}\,{d x}"," ",0,"integrate((2*x^10 + x^8 - 4*x^5 + 2)*(2*x^5 + x^4 - 2)^(1/4)*(x^5 + 4)/((x^5 - 1)*x^10), x)","F",0
1152,0,0,0,0.000000," ","integrate((x^12+1)/(x^4+1)^(1/2)/(x^12-1),x, algorithm=""giac"")","\int \frac{x^{12} + 1}{{\left(x^{12} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^12 + 1)/((x^12 - 1)*sqrt(x^4 + 1)), x)","F",0
1153,0,0,0,0.000000," ","integrate((-x^6+1)^(1/2)*(2*x^6+1)*(x^12-x^8-2*x^6-x^4+x^2+1)/(x^6-1)/(x^18-3*x^12+2*x^6-1),x, algorithm=""giac"")","\int \frac{{\left(x^{12} - x^{8} - 2 \, x^{6} - x^{4} + x^{2} + 1\right)} {\left(2 \, x^{6} + 1\right)} \sqrt{-x^{6} + 1}}{{\left(x^{18} - 3 \, x^{12} + 2 \, x^{6} - 1\right)} {\left(x^{6} - 1\right)}}\,{d x}"," ",0,"integrate((x^12 - x^8 - 2*x^6 - x^4 + x^2 + 1)*(2*x^6 + 1)*sqrt(-x^6 + 1)/((x^18 - 3*x^12 + 2*x^6 - 1)*(x^6 - 1)), x)","F",0
1154,0,0,0,0.000000," ","integrate((x^2-(x^2+1)^(1/2))/(1+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - \sqrt{x^{2} + 1}}{\sqrt{\sqrt{x^{2} + 1} + 1}}\,{d x}"," ",0,"integrate((x^2 - sqrt(x^2 + 1))/sqrt(sqrt(x^2 + 1) + 1), x)","F",0
1155,0,0,0,0.000000," ","integrate(1/(-1+x)/(x^2-2*x+2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 2 \, x + 2\right)}^{\frac{1}{3}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 - 2*x + 2)^(1/3)*(x - 1)), x)","F",0
1156,0,0,0,0.000000," ","integrate(1/(1+x)/(x^2+2*x+2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 2 \, x + 2\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + 2*x + 2)^(1/3)*(x + 1)), x)","F",0
1157,1,66,0,0.412634," ","integrate((x^3-1)^(2/3)/x,x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{1}{2} \, {\left(x^{3} - 1\right)}^{\frac{2}{3}} - \frac{1}{6} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) + 1/2*(x^3 - 1)^(2/3) - 1/6*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 1/3*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1158,0,0,0,0.000000," ","integrate((x^2+3)/(x^2+1)^(1/3)/(x^3-x^2-1),x, algorithm=""giac"")","\int \frac{x^{2} + 3}{{\left(x^{3} - x^{2} - 1\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^2 + 3)/((x^3 - x^2 - 1)*(x^2 + 1)^(1/3)), x)","F",0
1159,0,0,0,0.000000," ","integrate((-2-(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d-(3+d)*x-(d*k^2+3)*x^2+(d*k^2-1)*x^3),x, algorithm=""giac"")","\int \frac{2 \, k^{2} x^{2} - {\left(k + 1\right)} {\left(k - 1\right)} x - 2}{{\left({\left(d k^{2} - 1\right)} x^{3} - {\left(d k^{2} + 3\right)} x^{2} - {\left(d + 3\right)} x + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*k^2*x^2 - (k + 1)*(k - 1)*x - 2)/(((d*k^2 - 1)*x^3 - (d*k^2 + 3)*x^2 - (d + 3)*x + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/4)), x)","F",0
1160,0,0,0,0.000000," ","integrate((-2+(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(1-d-(3+d)*x+(d*k^2+3)*x^2+(d*k^2-1)*x^3),x, algorithm=""giac"")","\int \frac{2 \, k^{2} x^{2} + {\left(k + 1\right)} {\left(k - 1\right)} x - 2}{{\left({\left(d k^{2} - 1\right)} x^{3} + {\left(d k^{2} + 3\right)} x^{2} - {\left(d + 3\right)} x - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*k^2*x^2 + (k + 1)*(k - 1)*x - 2)/(((d*k^2 - 1)*x^3 + (d*k^2 + 3)*x^2 - (d + 3)*x - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/4)), x)","F",0
1161,1,109,0,0.160246," ","integrate((x^4-1)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{8} \, \sqrt{2} \log\left(\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{4} - 1} + 1\right) + \frac{1}{8} \, \sqrt{2} \log\left(-\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{4} - 1} + 1\right) + {\left(x^{4} - 1\right)}^{\frac{1}{4}}"," ",0,"-1/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^4 - 1)^(1/4))) - 1/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^4 - 1)^(1/4))) - 1/8*sqrt(2)*log(sqrt(2)*(x^4 - 1)^(1/4) + sqrt(x^4 - 1) + 1) + 1/8*sqrt(2)*log(-sqrt(2)*(x^4 - 1)^(1/4) + sqrt(x^4 - 1) + 1) + (x^4 - 1)^(1/4)","A",0
1162,1,80,0,0.297132," ","integrate((x^4-x)^(1/2)/(a*x^3-b),x, algorithm=""giac"")","-\frac{2 \, {\left(a - b\right)} \arctan\left(\frac{b \sqrt{-\frac{1}{x^{3}} + 1}}{\sqrt{a b - b^{2}}}\right)}{3 \, \sqrt{a b - b^{2}} a} + \frac{\log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right)}{3 \, a} - \frac{\log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)}{3 \, a}"," ",0,"-2/3*(a - b)*arctan(b*sqrt(-1/x^3 + 1)/sqrt(a*b - b^2))/(sqrt(a*b - b^2)*a) + 1/3*log(sqrt(-1/x^3 + 1) + 1)/a - 1/3*log(abs(sqrt(-1/x^3 + 1) - 1))/a","A",0
1163,1,70,0,0.234831," ","integrate(1/(x^4-1)/(x^4-x^2)^(1/4),x, algorithm=""giac"")","-\frac{1}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"-1/4*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) + 1/8*2^(3/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) - 1/8*2^(3/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4)) + 1/(-1/x^2 + 1)^(1/4)","A",0
1164,-2,0,0,0.000000," ","integrate((x^4-x^3)^(1/4)/(x^2-2*x-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1165,-2,0,0,0.000000," ","integrate((x^4-x^3)^(1/4)/(x^2-2*x-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1166,0,0,0,0.000000," ","integrate(x^6/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(a x^{4} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^6/(a*x^4 - b)^(3/4), x)","F",0
1167,0,0,0,0.000000," ","integrate((a*x^4-b)*(a*x^4+b)^(1/4)/x^2,x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}{x^{2}}\,{d x}"," ",0,"integrate((a*x^4 + b)^(1/4)*(a*x^4 - b)/x^2, x)","F",0
1168,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6-2*x^3-4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 2 \, x^{3} - 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 - 2*x^3 - 4)*x^6), x)","F",0
1169,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6-2*x^3-4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 2 \, x^{3} - 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 - 2*x^3 - 4)*x^6), x)","F",0
1170,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-2*x^3+4)/x^6/(x^6+4*x^3-8),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 4 \, x^{3} - 8\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 4)*(x^3 - 1)^(2/3)/((x^6 + 4*x^3 - 8)*x^6), x)","F",0
1171,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-2*x^3+4)/x^6/(x^6+4*x^3-8),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 4 \, x^{3} - 8\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 4)*(x^3 - 1)^(2/3)/((x^6 + 4*x^3 - 8)*x^6), x)","F",0
1172,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-2*x^3+2)/x^6/(x^6+4*x^3-4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 4 \, x^{3} - 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 + 4*x^3 - 4)*x^6), x)","F",0
1173,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-2*x^3+2)/x^6/(x^6+4*x^3-4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 4 \, x^{3} - 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 + 4*x^3 - 4)*x^6), x)","F",0
1174,0,0,0,0.000000," ","integrate((x^4+2)/(x^4-1)^(1/4)/(x^8-2),x, algorithm=""giac"")","\int \frac{x^{4} + 2}{{\left(x^{8} - 2\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 + 2)/((x^8 - 2)*(x^4 - 1)^(1/4)), x)","F",0
1175,0,0,0,0.000000," ","integrate((a*x^8-b)/x^6/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{a x^{8} - b}{{\left(a x^{4} + b\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate((a*x^8 - b)/((a*x^4 + b)^(3/4)*x^6), x)","F",0
1176,1,96,0,0.858321," ","integrate(x^(1/2)/(-1+x)/(-x^(1/2)+x)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\frac{2 \, {\left(\sqrt{2} - \sqrt{x - \sqrt{x}} + \sqrt{x} + 1\right)}}{{\left| 2 \, \sqrt{2} + 2 \, \sqrt{x - \sqrt{x}} - 2 \, \sqrt{x} - 2 \right|}}\right) - \frac{2}{\sqrt{x - \sqrt{x}} - \sqrt{x} + 1} - 2 \, \log\left({\left| 2 \, \sqrt{x - \sqrt{x}} - 2 \, \sqrt{x} + 1 \right|}\right)"," ",0,"-1/2*sqrt(2)*log(2*(sqrt(2) - sqrt(x - sqrt(x)) + sqrt(x) + 1)/abs(2*sqrt(2) + 2*sqrt(x - sqrt(x)) - 2*sqrt(x) - 2)) - 2/(sqrt(x - sqrt(x)) - sqrt(x) + 1) - 2*log(abs(2*sqrt(x - sqrt(x)) - 2*sqrt(x) + 1))","A",0
1177,1,66,0,0.293378," ","integrate(1/x^3/(x^2+1)^(2/3),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{2} + 1\right)}^{\frac{1}{3}}}{2 \, x^{2}} + \frac{1}{6} \, \log\left({\left(x^{2} + 1\right)}^{\frac{2}{3}} + {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{3} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 + 1)^(1/3) + 1)) - 1/2*(x^2 + 1)^(1/3)/x^2 + 1/6*log((x^2 + 1)^(2/3) + (x^2 + 1)^(1/3) + 1) - 1/3*log((x^2 + 1)^(1/3) - 1)","A",0
1178,1,66,0,0.347794," ","integrate((x^2+1)^(2/3)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{2} + 1\right)}^{\frac{2}{3}}}{2 \, x^{2}} - \frac{1}{6} \, \log\left({\left(x^{2} + 1\right)}^{\frac{2}{3}} + {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 + 1)^(1/3) + 1)) - 1/2*(x^2 + 1)^(2/3)/x^2 - 1/6*log((x^2 + 1)^(2/3) + (x^2 + 1)^(1/3) + 1) + 1/3*log((x^2 + 1)^(1/3) - 1)","A",0
1179,1,63,0,0.217746," ","integrate((x^2+1)^(2/3)/x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{3}{4} \, {\left(x^{2} + 1\right)}^{\frac{2}{3}} - \frac{1}{4} \, \log\left({\left(x^{2} + 1\right)}^{\frac{2}{3}} + {\left(x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{2} \, \log\left({\left(x^{2} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 + 1)^(1/3) + 1)) + 3/4*(x^2 + 1)^(2/3) - 1/4*log((x^2 + 1)^(2/3) + (x^2 + 1)^(1/3) + 1) + 1/2*log((x^2 + 1)^(1/3) - 1)","A",0
1180,0,0,0,0.000000," ","integrate((3+4*x)*(-2*x^4+2*x^2+x)^(1/2)/(1+2*x)/(x^3+2*x+1),x, algorithm=""giac"")","\int \frac{\sqrt{-2 \, x^{4} + 2 \, x^{2} + x} {\left(4 \, x + 3\right)}}{{\left(x^{3} + 2 \, x + 1\right)} {\left(2 \, x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-2*x^4 + 2*x^2 + x)*(4*x + 3)/((x^3 + 2*x + 1)*(2*x + 1)), x)","F",0
1181,1,63,0,0.255682," ","integrate((x^4+1)^(2/3)/x,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{3}{8} \, {\left(x^{4} + 1\right)}^{\frac{2}{3}} - \frac{1}{8} \, \log\left({\left(x^{4} + 1\right)}^{\frac{2}{3}} + {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{4} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 + 1)^(1/3) + 1)) + 3/8*(x^4 + 1)^(2/3) - 1/8*log((x^4 + 1)^(2/3) + (x^4 + 1)^(1/3) + 1) + 1/4*log((x^4 + 1)^(1/3) - 1)","A",0
1182,0,0,0,0.000000," ","integrate((x^4-1)^(1/3)*(x^4+3)/x^2/(x^4-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{1}{3}}}{{\left(x^{4} - x^{3} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^4 + 3)*(x^4 - 1)^(1/3)/((x^4 - x^3 - 1)*x^2), x)","F",0
1183,0,0,0,0.000000," ","integrate(x^2*(x^3+4)/(x^3+1)^(3/4)/(x^4+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 4\right)} x^{2}}{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((x^3 + 4)*x^2/((x^4 + x^3 + 1)*(x^3 + 1)^(3/4)), x)","F",0
1184,0,0,0,0.000000," ","integrate(x^2/(a*x^4-b)^(3/4)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((a*x^4 + b)*(a*x^4 - b)^(3/4)), x)","F",0
1185,0,0,0,0.000000," ","integrate(1/(a*x^4-b)^(1/4)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((a*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
1186,0,0,0,0.000000," ","integrate((-a^2*b+a*(2*a+b)*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2+2*a*x+(b^2*d-1)*x^2-2*b*d*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{a^{2} b - {\left(2 \, a + b\right)} a x + 3 \, a x^{2} - x^{3}}{{\left(2 \, b d x^{3} - d x^{4} - {\left(b^{2} d - 1\right)} x^{2} + a^{2} - 2 \, a x\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate((a^2*b - (2*a + b)*a*x + 3*a*x^2 - x^3)/((2*b*d*x^3 - d*x^4 - (b^2*d - 1)*x^2 + a^2 - 2*a*x)*sqrt((a - x)*(b - x)*x)), x)","F",0
1187,0,0,0,0.000000," ","integrate((k^2*x^4+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4-1),x, algorithm=""giac"")","\int \frac{k^{2} x^{4} + 1}{{\left(k^{2} x^{4} - 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((k^2*x^4 + 1)/((k^2*x^4 - 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
1188,0,0,0,0.000000," ","integrate(x*(k*x-1)*(-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(4-c)*x+(c*k+b+2*c-6)*x^2+(-2*b*k-2*c*k-c+4)*x^3+(b*k^2+c*k-1)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(2 \, k - 1\right)} x - 1\right)} {\left(k x - 1\right)} x}{{\left({\left(b k^{2} + c k - 1\right)} x^{4} - {\left(2 \, b k + 2 \, c k + c - 4\right)} x^{3} + {\left(c k + b + 2 \, c - 6\right)} x^{2} - {\left(c - 4\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((2*k - 1)*x - 1)*(k*x - 1)*x/(((b*k^2 + c*k - 1)*x^4 - (2*b*k + 2*c*k + c - 4)*x^3 + (c*k + b + 2*c - 6)*x^2 - (c - 4)*x - 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
1189,1,64,0,0.173805," ","integrate((x^5+1)^(2/3)/x,x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{5} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{3}{10} \, {\left(x^{5} + 1\right)}^{\frac{2}{3}} - \frac{1}{10} \, \log\left({\left(x^{5} + 1\right)}^{\frac{2}{3}} + {\left(x^{5} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{5} \, \log\left({\left| {\left(x^{5} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/5*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^5 + 1)^(1/3) + 1)) + 3/10*(x^5 + 1)^(2/3) - 1/10*log((x^5 + 1)^(2/3) + (x^5 + 1)^(1/3) + 1) + 1/5*log(abs((x^5 + 1)^(1/3) - 1))","A",0
1190,1,63,0,0.284506," ","integrate((x^6+1)^(2/3)/x,x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{4} \, {\left(x^{6} + 1\right)}^{\frac{2}{3}} - \frac{1}{12} \, \log\left({\left(x^{6} + 1\right)}^{\frac{2}{3}} + {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 + 1)^(1/3) + 1)) + 1/4*(x^6 + 1)^(2/3) - 1/12*log((x^6 + 1)^(2/3) + (x^6 + 1)^(1/3) + 1) + 1/6*log((x^6 + 1)^(1/3) - 1)","A",0
1191,0,0,0,0.000000," ","integrate((2*x^4-x^2+1)*(-x^6-x^4-x^2+1)^(1/2)/(x^2-1)/(x^2+1)/(x^6+x^4-1),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{6} - x^{4} - x^{2} + 1} {\left(2 \, x^{4} - x^{2} + 1\right)}}{{\left(x^{6} + x^{4} - 1\right)} {\left(x^{2} + 1\right)} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-x^6 - x^4 - x^2 + 1)*(2*x^4 - x^2 + 1)/((x^6 + x^4 - 1)*(x^2 + 1)*(x^2 - 1)), x)","F",0
1192,0,0,0,0.000000," ","integrate((x^8-1)^(1/3)*(5*x^8+3)/x^2/(x^8-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{8} + 3\right)} {\left(x^{8} - 1\right)}^{\frac{1}{3}}}{{\left(x^{8} - x^{3} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((5*x^8 + 3)*(x^8 - 1)^(1/3)/((x^8 - x^3 - 1)*x^2), x)","F",0
1193,1,126,0,0.178454," ","integrate((x^8+2)*(x^16-2*x^8+4)^(1/2)/x^9,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{16} - 2 \, x^{8} + 4} - \frac{x^{8} - \sqrt{x^{16} - 2 \, x^{8} + 4} - 4}{2 \, {\left({\left(x^{8} - \sqrt{x^{16} - 2 \, x^{8} + 4}\right)}^{2} - 4\right)}} + \frac{1}{8} \, \log\left(x^{8} - \sqrt{x^{16} - 2 \, x^{8} + 4} + 2\right) - \frac{1}{8} \, \log\left(-x^{8} + \sqrt{x^{16} - 2 \, x^{8} + 4} + 2\right) - \frac{1}{8} \, \log\left(-x^{8} + \sqrt{x^{16} - 2 \, x^{8} + 4} + 1\right)"," ",0,"1/8*sqrt(x^16 - 2*x^8 + 4) - 1/2*(x^8 - sqrt(x^16 - 2*x^8 + 4) - 4)/((x^8 - sqrt(x^16 - 2*x^8 + 4))^2 - 4) + 1/8*log(x^8 - sqrt(x^16 - 2*x^8 + 4) + 2) - 1/8*log(-x^8 + sqrt(x^16 - 2*x^8 + 4) + 2) - 1/8*log(-x^8 + sqrt(x^16 - 2*x^8 + 4) + 1)","A",0
1194,1,87,0,0.610243," ","integrate((x+(1+x)^(1/2))^(1/2)/(1-(1+x)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} + 5\right)} + \frac{7}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right) + 2 \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} + 2 \right|}\right) - 2 \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} \right|}\right)"," ",0,"-1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) + 5) + 7/4*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1) + 2*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) + 2)) - 2*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)))","A",0
1195,1,82,0,0.161412," ","integrate((c+(a*x+b)^(1/2))^(1/2)/(d-(a*x+b)^(1/2)),x, algorithm=""giac"")","-\frac{4 \, {\left(c d + d^{2}\right)} \arctan\left(\frac{\sqrt{c + \sqrt{a x + b}}}{\sqrt{-c - d}}\right)}{a \sqrt{-c - d}} - \frac{4 \, {\left(a^{2} {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}} + 3 \, a^{2} \sqrt{c + \sqrt{a x + b}} d\right)}}{3 \, a^{3}}"," ",0,"-4*(c*d + d^2)*arctan(sqrt(c + sqrt(a*x + b))/sqrt(-c - d))/(a*sqrt(-c - d)) - 4/3*(a^2*(c + sqrt(a*x + b))^(3/2) + 3*a^2*sqrt(c + sqrt(a*x + b))*d)/a^3","A",0
1196,0,0,0,0.000000," ","integrate((a*x^2+b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int {\left(a x^{2} + b^{2}\right)} \sqrt{b + \sqrt{a x^{2} + b^{2}}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)*sqrt(b + sqrt(a*x^2 + b^2)), x)","F",0
1197,0,0,0,0.000000," ","integrate(1/(x+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{x + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(1/(x + sqrt(x + sqrt(x^2 + 1))), x)","F",0
1198,0,0,0,0.000000," ","integrate(1/(x+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{x + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(1/(x + sqrt(x + sqrt(x^2 + 1))), x)","F",0
1199,0,0,0,0.000000," ","integrate(1/(-2+x)/(x^2-4*x-4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 4 \, x - 4\right)}^{\frac{1}{3}} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(1/((x^2 - 4*x - 4)^(1/3)*(x - 2)), x)","F",0
1200,0,0,0,0.000000," ","integrate((k*x^2-1)/(b*x+a)/((1-x)*x*(-k*x+1))^(1/2)/(a*k*x+b),x, algorithm=""giac"")","\int \frac{k x^{2} - 1}{{\left(a k x + b\right)} \sqrt{{\left(k x - 1\right)} {\left(x - 1\right)} x} {\left(b x + a\right)}}\,{d x}"," ",0,"integrate((k*x^2 - 1)/((a*k*x + b)*sqrt((k*x - 1)*(x - 1)*x)*(b*x + a)), x)","F",0
1201,0,0,0,0.000000," ","integrate(x*(-b+x)*(a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2+2*a*x+(b^2*d-1)*x^2-2*b*d*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{{\left(a b - 2 \, a x + x^{2}\right)} {\left(b - x\right)} x}{{\left(2 \, b d x^{3} - d x^{4} - {\left(b^{2} d - 1\right)} x^{2} + a^{2} - 2 \, a x\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate((a*b - 2*a*x + x^2)*(b - x)*x/((2*b*d*x^3 - d*x^4 - (b^2*d - 1)*x^2 + a^2 - 2*a*x)*sqrt((a - x)*(b - x)*x)), x)","F",0
1202,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-x^2-1)/(x^5-x)^(1/3),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{5} - x\right)}^{\frac{1}{3}} {\left(x^{4} - x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^5 - x)^(1/3)*(x^4 - x^2 - 1)), x)","F",0
1203,0,0,0,0.000000," ","integrate(x^3/(x^6-1)^(2/3),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(x^{6} - 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^3/(x^6 - 1)^(2/3), x)","F",0
1204,0,0,0,0.000000," ","integrate(x/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x}{{\left(x^{6} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x/(x^6 - 1)^(1/3), x)","F",0
1205,0,0,0,0.000000," ","integrate(x^3/(x^6+1)^(2/3),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(x^{6} + 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^3/(x^6 + 1)^(2/3), x)","F",0
1206,0,0,0,0.000000," ","integrate(x/(x^6+1)^(1/3),x, algorithm=""giac"")","\int \frac{x}{{\left(x^{6} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x/(x^6 + 1)^(1/3), x)","F",0
1207,0,0,0,0.000000," ","integrate((a*x^8-b)/x^2/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\int \frac{a x^{8} - b}{{\left(a x^{4} - b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a*x^8 - b)/((a*x^4 - b)^(3/4)*x^2), x)","F",0
1208,0,0,0,0.000000," ","integrate((2*a*x^8-3*b)/x^8/(a*x^4-b)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{8} - 3 \, b}{{\left(a x^{4} - b\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate((2*a*x^8 - 3*b)/((a*x^4 - b)^(1/4)*x^8), x)","F",0
1209,0,0,0,0.000000," ","integrate((a^2*x^8-b^2)/x^2/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x, algorithm=""giac"")","\int \frac{a^{2} x^{8} - b^{2}}{{\left(a^{2} x^{8} + b^{2}\right)} {\left(a x^{4} + b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a^2*x^8 - b^2)/((a^2*x^8 + b^2)*(a*x^4 + b)^(3/4)*x^2), x)","F",0
1210,0,0,0,0.000000," ","integrate((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2)/x/(-a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} x}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)/(sqrt(a^2*x^2/b^2 - a/b^2)*x), x)","F",0
1211,1,66,0,0.350053," ","integrate((x^2-1)^(2/3)/x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{3}{4} \, {\left(x^{2} - 1\right)}^{\frac{2}{3}} - \frac{1}{4} \, \log\left({\left(x^{2} - 1\right)}^{\frac{2}{3}} - {\left(x^{2} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{2} \, \log\left({\left| {\left(x^{2} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"-1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 - 1)^(1/3) - 1)) + 3/4*(x^2 - 1)^(2/3) - 1/4*log((x^2 - 1)^(2/3) - (x^2 - 1)^(1/3) + 1) + 1/2*log(abs((x^2 - 1)^(1/3) + 1))","A",0
1212,0,0,0,0.000000," ","integrate((-3+x)/(x^2-1)^(1/3)/(x^2+x+2),x, algorithm=""giac"")","\int \frac{x - 3}{{\left(x^{2} + x + 2\right)} {\left(x^{2} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x - 3)/((x^2 + x + 2)*(x^2 - 1)^(1/3)), x)","F",0
1213,0,0,0,0.000000," ","integrate((x^2+2)/(x^2-2*x-2)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2}{\sqrt{x^{3} - 1} {\left(x^{2} - 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x^2 + 2)/(sqrt(x^3 - 1)*(x^2 - 2*x - 2)), x)","F",0
1214,1,73,0,0.289675," ","integrate((x^3-1)*(x^3+1)^(1/3)/x,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{4} \, {\left(x^{3} + 1\right)}^{\frac{4}{3}} - {\left(x^{3} + 1\right)}^{\frac{1}{3}} + \frac{1}{6} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{3} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) + 1/4*(x^3 + 1)^(4/3) - (x^3 + 1)^(1/3) + 1/6*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) - 1/3*log(abs((x^3 + 1)^(1/3) - 1))","A",0
1215,0,0,0,0.000000," ","integrate((-a*b+2*(a-b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/4)/(-a^3+(3*a^2+b*d)*x-(3*a+d)*x^2+x^3),x, algorithm=""giac"")","\int \frac{a b - 2 \, {\left(a - b\right)} x - x^{2}}{{\left(a^{3} + {\left(3 \, a + d\right)} x^{2} - x^{3} - {\left(3 \, a^{2} + b d\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*b - 2*(a - b)*x - x^2)/((a^3 + (3*a + d)*x^2 - x^3 - (3*a^2 + b*d)*x)*((a - x)*(b - x)*x)^(1/4)), x)","F",0
1216,0,0,0,0.000000," ","integrate((x^2-2*x+1)*(-1+2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(1+3*d)*x-(3*d+k)*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(k x^{2} + 2 \, {\left(k - 1\right)} x - 1\right)} {\left(x^{2} - 2 \, x + 1\right)}}{{\left(d x^{3} - {\left(3 \, d + k\right)} x^{2} + {\left(3 \, d + 1\right)} x - d\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((k*x^2 + 2*(k - 1)*x - 1)*(x^2 - 2*x + 1)/((d*x^3 - (3*d + k)*x^2 + (3*d + 1)*x - d)*((k*x - 1)*(x - 1)*x)^(3/4)), x)","F",0
1217,0,0,0,0.000000," ","integrate(x^2/(x^3+x^2+x)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{4} - 1\right)} \sqrt{x^{3} + x^{2} + x}}\,{d x}"," ",0,"integrate(x^2/((x^4 - 1)*sqrt(x^3 + x^2 + x)), x)","F",0
1218,0,0,0,0.000000," ","integrate((x^3+x^2+x)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{3} + x^{2} + x}}{x^{4} - 1}\,{d x}"," ",0,"integrate(sqrt(x^3 + x^2 + x)/(x^4 - 1), x)","F",0
1219,1,66,0,0.132501," ","integrate((x^4-1)^(2/3)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{3}{8} \, {\left(x^{4} - 1\right)}^{\frac{2}{3}} - \frac{1}{8} \, \log\left({\left(x^{4} - 1\right)}^{\frac{2}{3}} - {\left(x^{4} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{4} \, \log\left({\left| {\left(x^{4} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"-1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 - 1)^(1/3) - 1)) + 3/8*(x^4 - 1)^(2/3) - 1/8*log((x^4 - 1)^(2/3) - (x^4 - 1)^(1/3) + 1) + 1/4*log(abs((x^4 - 1)^(1/3) + 1))","A",0
1220,0,0,0,0.000000," ","integrate((x^4-x^2+1)/(x^3+x^2+x)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{x^{4} - x^{2} + 1}{{\left(x^{4} - 1\right)} \sqrt{x^{3} + x^{2} + x}}\,{d x}"," ",0,"integrate((x^4 - x^2 + 1)/((x^4 - 1)*sqrt(x^3 + x^2 + x)), x)","F",0
1221,0,0,0,0.000000," ","integrate((x^2-x+1)/(x^2-1)/(x^4-x^3+x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - x + 1}{\sqrt{x^{4} - x^{3} + x^{2} - x + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 - x + 1)/(sqrt(x^4 - x^3 + x^2 - x + 1)*(x^2 - 1)), x)","F",0
1222,0,0,0,0.000000," ","integrate((-1+x)^2*(2*x^3-2*x^2+x)/(-1+2*x)/((1-2*x)/(2*x^2+1))^(1/2)/(2*x^4-4*x^3+3*x^2+4*x-2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} - 2 \, x^{2} + x\right)} {\left(x - 1\right)}^{2}}{{\left(2 \, x^{4} - 4 \, x^{3} + 3 \, x^{2} + 4 \, x - 2\right)} {\left(2 \, x - 1\right)} \sqrt{-\frac{2 \, x - 1}{2 \, x^{2} + 1}}}\,{d x}"," ",0,"integrate((2*x^3 - 2*x^2 + x)*(x - 1)^2/((2*x^4 - 4*x^3 + 3*x^2 + 4*x - 2)*(2*x - 1)*sqrt(-(2*x - 1)/(2*x^2 + 1))), x)","F",0
1223,1,66,0,0.295994," ","integrate((x^5-1)^(2/3)/x,x, algorithm=""giac"")","-\frac{1}{5} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{5} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{3}{10} \, {\left(x^{5} - 1\right)}^{\frac{2}{3}} - \frac{1}{10} \, \log\left({\left(x^{5} - 1\right)}^{\frac{2}{3}} - {\left(x^{5} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{5} \, \log\left({\left| {\left(x^{5} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"-1/5*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^5 - 1)^(1/3) - 1)) + 3/10*(x^5 - 1)^(2/3) - 1/10*log((x^5 - 1)^(2/3) - (x^5 - 1)^(1/3) + 1) + 1/5*log(abs((x^5 - 1)^(1/3) + 1))","A",0
1224,1,66,0,0.337298," ","integrate((x^6-1)^(2/3)/x,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{1}{4} \, {\left(x^{6} - 1\right)}^{\frac{2}{3}} - \frac{1}{12} \, \log\left({\left(x^{6} - 1\right)}^{\frac{2}{3}} - {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \log\left({\left| {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 - 1)^(1/3) - 1)) + 1/4*(x^6 - 1)^(2/3) - 1/12*log((x^6 - 1)^(2/3) - (x^6 - 1)^(1/3) + 1) + 1/6*log(abs((x^6 - 1)^(1/3) + 1))","A",0
1225,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b)), x)","F",0
1226,1,69,0,0.447776," ","integrate((x^2-1)^(2/3)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{2} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) - \frac{{\left(x^{2} - 1\right)}^{\frac{2}{3}}}{2 \, x^{2}} + \frac{1}{6} \, \log\left({\left(x^{2} - 1\right)}^{\frac{2}{3}} - {\left(x^{2} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{3} \, \log\left({\left| {\left(x^{2} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^2 - 1)^(1/3) - 1)) - 1/2*(x^2 - 1)^(2/3)/x^2 + 1/6*log((x^2 - 1)^(2/3) - (x^2 - 1)^(1/3) + 1) - 1/3*log(abs((x^2 - 1)^(1/3) + 1))","A",0
1227,0,0,0,0.000000," ","integrate((x^2+x-2)/x^2/(x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2} + x - 2}{{\left(x^{2} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^2 + x - 2)/((x^2 - 1)^(3/4)*x^2), x)","F",0
1228,1,67,0,0.155127," ","integrate((x^3+1)^(1/3)/x^4,x, algorithm=""giac"")","-\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x^{3}} - \frac{1}{18} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{9} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) - 1/3*(x^3 + 1)^(1/3)/x^3 - 1/18*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) + 1/9*log(abs((x^3 + 1)^(1/3) - 1))","A",0
1229,1,67,0,0.163654," ","integrate((x^3+1)^(2/3)/x^4,x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}}}{3 \, x^{3}} - \frac{1}{9} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{2}{9} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) - 1/3*(x^3 + 1)^(2/3)/x^3 - 1/9*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) + 2/9*log(abs((x^3 + 1)^(1/3) - 1))","A",0
1230,0,0,0,0.000000," ","integrate((-2*k-(-1+k)*(1+k)*x+2*k*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(3+d)*k*x-(3*k^2+d)*x^2+k*(k^2-d)*x^3),x, algorithm=""giac"")","\int -\frac{{\left(k + 1\right)} {\left(k - 1\right)} x - 2 \, k x^{2} + 2 \, k}{{\left({\left(k^{2} - d\right)} k x^{3} + {\left(d + 3\right)} k x - {\left(3 \, k^{2} + d\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-((k + 1)*(k - 1)*x - 2*k*x^2 + 2*k)/(((k^2 - d)*k*x^3 + (d + 3)*k*x - (3*k^2 + d)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/4)), x)","F",0
1231,0,0,0,0.000000," ","integrate((-2*k+(-1+k)*(1+k)*x+2*k*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(1-d+(3+d)*k*x+(3*k^2+d)*x^2+k*(k^2-d)*x^3),x, algorithm=""giac"")","\int \frac{{\left(k + 1\right)} {\left(k - 1\right)} x + 2 \, k x^{2} - 2 \, k}{{\left({\left(k^{2} - d\right)} k x^{3} + {\left(d + 3\right)} k x + {\left(3 \, k^{2} + d\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(((k + 1)*(k - 1)*x + 2*k*x^2 - 2*k)/(((k^2 - d)*k*x^3 + (d + 3)*k*x + (3*k^2 + d)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/4)), x)","F",0
1232,1,148,0,0.252487," ","integrate((x^2+1)*(-2*x^4+1)^(1/2)/x^5,x, algorithm=""giac"")","\frac{x^{4} {\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{-2 \, x^{4} + 1} - \sqrt{2}\right)}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{2} \sqrt{-2 \, x^{4} + 1} - \sqrt{2}\right)}^{2}} - \frac{1}{2} \, \sqrt{2} \arcsin\left(\sqrt{2} x^{2}\right) - \frac{\sqrt{2} {\left(\sqrt{2} \sqrt{-2 \, x^{4} + 1} - \sqrt{2}\right)}}{8 \, x^{2}} + \frac{{\left(\sqrt{2} \sqrt{-2 \, x^{4} + 1} - \sqrt{2}\right)}^{2}}{32 \, x^{4}} - \frac{1}{2} \, \log\left(-\frac{\sqrt{2} \sqrt{-2 \, x^{4} + 1} - \sqrt{2}}{2 \, x^{2}}\right)"," ",0,"1/2*x^4*(sqrt(2)*(sqrt(2)*sqrt(-2*x^4 + 1) - sqrt(2))/x^2 - 1)/(sqrt(2)*sqrt(-2*x^4 + 1) - sqrt(2))^2 - 1/2*sqrt(2)*arcsin(sqrt(2)*x^2) - 1/8*sqrt(2)*(sqrt(2)*sqrt(-2*x^4 + 1) - sqrt(2))/x^2 + 1/32*(sqrt(2)*sqrt(-2*x^4 + 1) - sqrt(2))^2/x^4 - 1/2*log(-1/2*(sqrt(2)*sqrt(-2*x^4 + 1) - sqrt(2))/x^2)","B",0
1233,1,66,0,0.327888," ","integrate((x^4+1)^(2/3)/x^5,x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{4} + 1\right)}^{\frac{2}{3}}}{4 \, x^{4}} - \frac{1}{12} \, \log\left({\left(x^{4} + 1\right)}^{\frac{2}{3}} + {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 + 1)^(1/3) + 1)) - 1/4*(x^4 + 1)^(2/3)/x^4 - 1/12*log((x^4 + 1)^(2/3) + (x^4 + 1)^(1/3) + 1) + 1/6*log((x^4 + 1)^(1/3) - 1)","A",0
1234,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(2/3)/x^3/(x^4-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{{\left(x^{4} - x^{3} + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^4 + 1)^(2/3)*(x^4 - 3)/((x^4 - x^3 + 1)*x^3), x)","F",0
1235,0,0,0,0.000000," ","integrate((x^4-1)^(1/3)*(x^4+3)/x^2/(x^4+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{1}{3}}}{{\left(x^{4} + x^{3} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^4 + 3)*(x^4 - 1)^(1/3)/((x^4 + x^3 - 1)*x^2), x)","F",0
1236,0,0,0,0.000000," ","integrate((x^4-1)^(2/3)*(x^4+3)/x^3/(x^4+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{2}{3}}}{{\left(x^{4} + x^{3} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^4 + 3)*(x^4 - 1)^(2/3)/((x^4 + x^3 - 1)*x^3), x)","F",0
1237,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(1/3)/x^2/(x^4+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{1}{3}} {\left(x^{4} - 3\right)}}{{\left(x^{4} + x^{3} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^4 + 1)^(1/3)*(x^4 - 3)/((x^4 + x^3 + 1)*x^2), x)","F",0
1238,0,0,0,0.000000," ","integrate((4+3*x)*(x^4-x-1)*(2*x^4-x-1)^(1/4)/x^6/(x^4+x+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x - 1\right)}^{\frac{1}{4}} {\left(x^{4} - x - 1\right)} {\left(3 \, x + 4\right)}}{{\left(x^{4} + x + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^4 - x - 1)^(1/4)*(x^4 - x - 1)*(3*x + 4)/((x^4 + x + 1)*x^6), x)","F",0
1239,0,0,0,0.000000," ","integrate((3*x^4+1)^(1/2)/(3*x^4-1),x, algorithm=""giac"")","\int \frac{\sqrt{3 \, x^{4} + 1}}{3 \, x^{4} - 1}\,{d x}"," ",0,"integrate(sqrt(3*x^4 + 1)/(3*x^4 - 1), x)","F",0
1240,1,222,0,0.349429," ","integrate((a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^2-b),x, algorithm=""giac"")","\frac{8 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} b x^{2} + \frac{14 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{14 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{7 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{a} + \frac{7 \, \sqrt{2} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{\left(-a\right)^{\frac{3}{4}}}}{16 \, b}"," ",0,"1/16*(8*(a - b/x^2)^(1/4)*b*x^2 + 14*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/a + 14*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/a + 7*sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2))/a + 7*sqrt(2)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2))/(-a)^(3/4))/b","B",0
1241,1,195,0,0.215255," ","integrate((2*a*x^2-b)/(a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{2 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{2 \, a} - \frac{6}{{\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}}"," ",0,"sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a + sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a - 1/2*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/a + 1/2*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/a - 6/(a + b/x^2)^(1/4)","B",0
1242,1,67,0,0.157884," ","integrate((x^5+1)^(2/3)/x^6,x, algorithm=""giac"")","\frac{2}{15} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{5} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{5} + 1\right)}^{\frac{2}{3}}}{5 \, x^{5}} - \frac{1}{15} \, \log\left({\left(x^{5} + 1\right)}^{\frac{2}{3}} + {\left(x^{5} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{2}{15} \, \log\left({\left| {\left(x^{5} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"2/15*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^5 + 1)^(1/3) + 1)) - 1/5*(x^5 + 1)^(2/3)/x^5 - 1/15*log((x^5 + 1)^(2/3) + (x^5 + 1)^(1/3) + 1) + 2/15*log(abs((x^5 + 1)^(1/3) - 1))","A",0
1243,0,0,0,0.000000," ","integrate((x^5+1)^(2/3)*(2*x^5-3)/x^3/(x^5-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 3\right)} {\left(x^{5} + 1\right)}^{\frac{2}{3}}}{{\left(x^{5} - x^{3} + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((2*x^5 - 3)*(x^5 + 1)^(2/3)/((x^5 - x^3 + 1)*x^3), x)","F",0
1244,0,0,0,0.000000," ","integrate((x^5-1)^(2/3)*(2*x^5+3)/x^3/(x^5-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} + 3\right)} {\left(x^{5} - 1\right)}^{\frac{2}{3}}}{{\left(x^{5} - x^{3} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((2*x^5 + 3)*(x^5 - 1)^(2/3)/((x^5 - x^3 - 1)*x^3), x)","F",0
1245,1,111,0,0.157037," ","integrate((x^6-1)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(x^{6} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{6} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(x^{6} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{12} \, \sqrt{2} \log\left(\sqrt{2} {\left(x^{6} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{6} - 1} + 1\right) + \frac{1}{12} \, \sqrt{2} \log\left(-\sqrt{2} {\left(x^{6} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{6} - 1} + 1\right) + \frac{2}{3} \, {\left(x^{6} - 1\right)}^{\frac{1}{4}}"," ",0,"-1/6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^6 - 1)^(1/4))) - 1/6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^6 - 1)^(1/4))) - 1/12*sqrt(2)*log(sqrt(2)*(x^6 - 1)^(1/4) + sqrt(x^6 - 1) + 1) + 1/12*sqrt(2)*log(-sqrt(2)*(x^6 - 1)^(1/4) + sqrt(x^6 - 1) + 1) + 2/3*(x^6 - 1)^(1/4)","A",0
1246,1,66,0,0.306409," ","integrate(1/x^7/(x^6+1)^(1/3),x, algorithm=""giac"")","-\frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{6} + 1\right)}^{\frac{2}{3}}}{6 \, x^{6}} + \frac{1}{36} \, \log\left({\left(x^{6} + 1\right)}^{\frac{2}{3}} + {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{18} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 + 1)^(1/3) + 1)) - 1/6*(x^6 + 1)^(2/3)/x^6 + 1/36*log((x^6 + 1)^(2/3) + (x^6 + 1)^(1/3) + 1) - 1/18*log((x^6 + 1)^(1/3) - 1)","A",0
1247,1,66,0,0.158176," ","integrate((x^6+1)^(2/3)/x^7,x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{6} + 1\right)}^{\frac{2}{3}}}{6 \, x^{6}} - \frac{1}{18} \, \log\left({\left(x^{6} + 1\right)}^{\frac{2}{3}} + {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{9} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 + 1)^(1/3) + 1)) - 1/6*(x^6 + 1)^(2/3)/x^6 - 1/18*log((x^6 + 1)^(2/3) + (x^6 + 1)^(1/3) + 1) + 1/9*log((x^6 + 1)^(1/3) - 1)","A",0
1248,0,0,0,0.000000," ","integrate(((k^2-3)*x+2*k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(-d*k^2+3)*x^2-3*x^4+x^6),x, algorithm=""giac"")","\int \frac{2 \, k^{2} x^{3} + {\left(k^{2} - 3\right)} x}{{\left(x^{6} - 3 \, x^{4} - {\left(d k^{2} - 3\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*k^2*x^3 + (k^2 - 3)*x)/((x^6 - 3*x^4 - (d*k^2 - 3)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/4)), x)","F",0
1249,0,0,0,0.000000," ","integrate((x^7-1)^(2/3)*(4*x^7+3)/x^3/(x^7+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{7} + 3\right)} {\left(x^{7} - 1\right)}^{\frac{2}{3}}}{{\left(x^{7} + x^{3} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((4*x^7 + 3)*(x^7 - 1)^(2/3)/((x^7 + x^3 - 1)*x^3), x)","F",0
1250,0,0,0,0.000000," ","integrate(x/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{a^{2} x^{2} - b x} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(sqrt(a^2*x^2 - b*x)*(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2)), x)","F",0
1251,0,0,0,0.000000," ","integrate((-(a*b)^(1/2)+x)/(x*(a+x)*(b+x))^(1/2)/((a*b)^(1/2)+x),x, algorithm=""giac"")","\int \frac{x - \sqrt{a b}}{\sqrt{{\left(a + x\right)} {\left(b + x\right)} x} {\left(x + \sqrt{a b}\right)}}\,{d x}"," ",0,"integrate((x - sqrt(a*b))/(sqrt((a + x)*(b + x)*x)*(x + sqrt(a*b))), x)","F",0
1252,1,63,0,0.179005," ","integrate(1/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
1253,0,0,0,0.000000," ","integrate((-x^2+3)/(-x^2+1)/(x^4-6*x^2+1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} - 3}{{\left(x^{4} - 6 \, x^{2} + 1\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 3)/((x^4 - 6*x^2 + 1)^(1/4)*(x^2 - 1)), x)","F",0
1254,0,0,0,0.000000," ","integrate((x^4-3)/(x^4+1)/(-3*x^5+4*x^4-3*x)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 3}{{\left(-3 \, x^{5} + 4 \, x^{4} - 3 \, x\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 3)/((-3*x^5 + 4*x^4 - 3*x)^(1/4)*(x^4 + 1)), x)","F",0
1255,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(x^6+1)/x^2/(x^6+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{{\left(x^{6} + x^{3} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^6 + 1)*(x^6 - 1)^(1/3)/((x^6 + x^3 - 1)*x^2), x)","F",0
1256,-2,0,0,0.000000," ","integrate((x^4-1)*(x^4+1)^(1/2)/(x^8+x^6+3*x^4+x^2+1),x, algorithm=""giac"")","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError >> type","F(-2)",0
1257,0,0,0,0.000000," ","integrate((2*x^8-1)/(x^4+1)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - 1}{{\left(x^{8} - 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - 1)/((x^8 - 1)*(x^4 + 1)^(1/4)), x)","F",0
1258,1,213,0,0.293762," ","integrate((a*x^8+b*x^5)^(1/4),x, algorithm=""giac"")","\frac{8 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} b x^{3} + \frac{2 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{2 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{a} + \frac{\sqrt{2} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{\left(-a\right)^{\frac{3}{4}}}}{24 \, b}"," ",0,"1/24*(8*(a + b/x^3)^(1/4)*b*x^3 + 2*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a + 2*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a + sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a + sqrt(2)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/(-a)^(3/4))/b","B",0
1259,0,0,0,0.000000," ","integrate((x-(x^2+1)^(1/2))^(1/2)/(1-(x^2+1)^(1/2)),x, algorithm=""giac"")","\int -\frac{\sqrt{x - \sqrt{x^{2} + 1}}}{\sqrt{x^{2} + 1} - 1}\,{d x}"," ",0,"integrate(-sqrt(x - sqrt(x^2 + 1))/(sqrt(x^2 + 1) - 1), x)","F",0
1260,0,0,0,0.000000," ","integrate((-1+x)*(3+x)/(x^2-1)^(2/3)/(x^2-x+2),x, algorithm=""giac"")","\int \frac{{\left(x + 3\right)} {\left(x - 1\right)}}{{\left(x^{2} - x + 2\right)} {\left(x^{2} - 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((x + 3)*(x - 1)/((x^2 - x + 2)*(x^2 - 1)^(2/3)), x)","F",0
1261,1,69,0,0.350608," ","integrate((x^3-1)^(1/3)/x^4,x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) - \frac{{\left(x^{3} - 1\right)}^{\frac{1}{3}}}{3 \, x^{3}} - \frac{1}{18} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{9} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) - 1/3*(x^3 - 1)^(1/3)/x^3 - 1/18*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 1/9*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1262,1,69,0,0.280202," ","integrate((x^3-1)^(2/3)/x^4,x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) - \frac{{\left(x^{3} - 1\right)}^{\frac{2}{3}}}{3 \, x^{3}} + \frac{1}{9} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{2}{9} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) - 1/3*(x^3 - 1)^(2/3)/x^3 + 1/9*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) - 2/9*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1263,0,0,0,0.000000," ","integrate((x^3+1)^(1/3)/x^2,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)/x^2, x)","F",0
1264,0,0,0,0.000000," ","integrate((-1+x)/(1+x)/(x^3+2)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} + 2\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x - 1)/((x^3 + 2)^(1/3)*(x + 1)), x)","F",0
1265,1,244,0,0.239327," ","integrate(1/x^7/(a*x^3+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{42 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{21 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{21 \, \sqrt{2} a^{3} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{3} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{3} + b} + \sqrt{-b}\right)}{b^{3}} + \frac{8 \, {\left(7 \, {\left(a x^{3} + b\right)}^{\frac{5}{4}} a^{3} - 11 \, {\left(a x^{3} + b\right)}^{\frac{1}{4}} a^{3} b\right)}}{a^{2} b^{2} x^{6}}}{192 \, a}"," ",0,"1/192*(42*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/((-b)^(3/4)*b^2) + 42*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^3 + b)^(1/4))/(-b)^(1/4))/((-b)^(3/4)*b^2) + 21*sqrt(2)*a^3*log(sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/((-b)^(3/4)*b^2) + 21*sqrt(2)*a^3*(-b)^(1/4)*log(-sqrt(2)*(a*x^3 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^3 + b) + sqrt(-b))/b^3 + 8*(7*(a*x^3 + b)^(5/4)*a^3 - 11*(a*x^3 + b)^(1/4)*a^3*b)/(a^2*b^2*x^6))/a","B",0
1266,0,0,0,0.000000," ","integrate((x^2+2*x+1)*(-2-(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d-(1+3*d)*x-(k^2+3*d)*x^2+(k^2-d)*x^3),x, algorithm=""giac"")","\int \frac{{\left(2 \, k^{2} x^{2} - {\left(k + 1\right)} {\left(k - 1\right)} x - 2\right)} {\left(x^{2} + 2 \, x + 1\right)}}{{\left({\left(k^{2} - d\right)} x^{3} - {\left(k^{2} + 3 \, d\right)} x^{2} - {\left(3 \, d + 1\right)} x - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((2*k^2*x^2 - (k + 1)*(k - 1)*x - 2)*(x^2 + 2*x + 1)/(((k^2 - d)*x^3 - (k^2 + 3*d)*x^2 - (3*d + 1)*x - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(3/4)), x)","F",0
1267,1,69,0,0.434025," ","integrate(1/x^5/(x^4-1)^(1/3),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{{\left(x^{4} - 1\right)}^{\frac{2}{3}}}{4 \, x^{4}} + \frac{1}{24} \, \log\left({\left(x^{4} - 1\right)}^{\frac{2}{3}} - {\left(x^{4} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{12} \, \log\left({\left| {\left(x^{4} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 - 1)^(1/3) - 1)) + 1/4*(x^4 - 1)^(2/3)/x^4 + 1/24*log((x^4 - 1)^(2/3) - (x^4 - 1)^(1/3) + 1) - 1/12*log(abs((x^4 - 1)^(1/3) + 1))","A",0
1268,0,0,0,0.000000," ","integrate(x*(-b+x)*(a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2*d+2*a*d*x+(b^2-d)*x^2-2*b*x^3+x^4),x, algorithm=""giac"")","\int \frac{{\left(a b - 2 \, a x + x^{2}\right)} {\left(b - x\right)} x}{{\left(2 \, b x^{3} - x^{4} + a^{2} d - 2 \, a d x - {\left(b^{2} - d\right)} x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate((a*b - 2*a*x + x^2)*(b - x)*x/((2*b*x^3 - x^4 + a^2*d - 2*a*d*x - (b^2 - d)*x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
1269,1,244,0,0.179409," ","integrate(1/x^9/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{42 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{21 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{21 \, \sqrt{2} a^{3} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{4} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{4} + b} + \sqrt{-b}\right)}{b^{3}} + \frac{8 \, {\left(7 \, {\left(a x^{4} + b\right)}^{\frac{5}{4}} a^{3} - 11 \, {\left(a x^{4} + b\right)}^{\frac{1}{4}} a^{3} b\right)}}{a^{2} b^{2} x^{8}}}{256 \, a}"," ",0,"1/256*(42*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/((-b)^(3/4)*b^2) + 42*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^4 + b)^(1/4))/(-b)^(1/4))/((-b)^(3/4)*b^2) + 21*sqrt(2)*a^3*log(sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/((-b)^(3/4)*b^2) + 21*sqrt(2)*a^3*(-b)^(1/4)*log(-sqrt(2)*(a*x^4 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^4 + b) + sqrt(-b))/b^3 + 8*(7*(a*x^4 + b)^(5/4)*a^3 - 11*(a*x^4 + b)^(1/4)*a^3*b)/(a^2*b^2*x^8))/a","B",0
1270,0,0,0,0.000000," ","integrate(x^4*(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int {\left(a x^{4} + b\right)}^{\frac{3}{4}} x^{4}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)*x^4, x)","F",0
1271,-2,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/x/(c*x+x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{201326592,[1,14,10,12,0,4]%%%}+%%%{-218103808,[1,14,10,11,0,6]%%%}+%%%{88080384,[1,14,10,10,0,8]%%%}+%%%{-15728640,[1,14,10,9,0,10]%%%}+%%%{1048576,[1,14,10,8,0,12]%%%}+%%%{1610612736,[1,13,10,13,1,3]%%%}+%%%{-1811939328,[1,13,10,12,1,5]%%%}+%%%{754974720,[1,13,10,11,1,7]%%%}+%%%{-138412032,[1,13,10,10,1,9]%%%}+%%%{9437184,[1,13,10,9,1,11]%%%}+%%%{4831838208,[1,12,10,14,2,2]%%%}+%%%{-5838471168,[1,12,10,13,2,4]%%%}+%%%{2566914048,[1,12,10,12,2,6]%%%}+%%%{-490733568,[1,12,10,11,2,8]%%%}+%%%{34603008,[1,12,10,10,2,10]%%%}+%%%{-18446744062972133376,[1,11,10,15,3,1]%%%}+%%%{-9126805504,[1,11,10,14,3,3]%%%}+%%%{4429185024,[1,11,10,13,3,5]%%%}+%%%{-905969664,[1,11,10,12,3,7]%%%}+%%%{67108864,[1,11,10,11,3,9]%%%}+%%%{32768,[1,11,6,12,0,3]%%%}+%%%{-8192,[1,11,6,11,0,5]%%%}+%%%{3221225472,[1,10,10,16,4,0]%%%}+%%%{-7247757312,[1,10,10,15,4,2]%%%}+%%%{4227858432,[1,10,10,14,4,4]%%%}+%%%{-956301312,[1,10,10,13,4,6]%%%}+%%%{75497472,[1,10,10,12,4,8]%%%}+%%%{196608,[1,10,6,13,1,2]%%%}+%%%{-49152,[1,10,6,12,1,4]%%%}+%%%{-3221225472,[1,9,10,16,5,1]%%%}+%%%{2415919104,[1,9,10,15,5,3]%%%}+%%%{-603979776,[1,9,10,14,5,5]%%%}+%%%{50331648,[1,9,10,13,5,7]%%%}+%%%{393216,[1,9,6,14,2,1]%%%}+%%%{-98304,[1,9,6,13,2,3]%%%}+%%%{-1073741824,[1,8,10,17,6,0]%%%}+%%%{805306368,[1,8,10,16,6,2]%%%}+%%%{-201326592,[1,8,10,15,6,4]%%%}+%%%{16777216,[1,8,10,14,6,6]%%%}+%%%{262144,[1,8,6,15,3,0]%%%}+%%%{-65536,[1,8,6,14,3,2]%%%}+%%%{1073741824,[0,15,11,12,0,4]%%%}+%%%{-1073741824,[0,15,11,11,0,6]%%%}+%%%{402653184,[0,15,11,10,0,8]%%%}+%%%{-67108864,[0,15,11,9,0,10]%%%}+%%%{4194304,[0,15,11,8,0,12]%%%}+%%%{8589934592,[0,14,11,13,1,3]%%%}+%%%{-7516192768,[0,14,11,12,1,5]%%%}+%%%{2147483648,[0,14,11,11,1,7]%%%}+%%%{-134217728,[0,14,11,10,1,9]%%%}+%%%{-33554432,[0,14,11,9,1,11]%%%}+%%%{4194304,[0,14,11,8,1,13]%%%}+%%%{25769803776,[0,13,11,14,2,2]%%%}+%%%{-16106127360,[0,13,11,13,2,4]%%%}+%%%{2013265920,[0,13,11,11,2,8]%%%}+%%%{-503316480,[0,13,11,10,2,10]%%%}+%%%{37748736,[0,13,11,9,2,12]%%%}+%%%{34359738368,[0,12,11,15,3,1]%%%}+%%%{-21474836480,[0,12,11,13,3,5]%%%}+%%%{10737418240,[0,12,11,12,3,7]%%%}+%%%{-2013265920,[0,12,11,11,3,9]%%%}+%%%{134217728,[0,12,11,10,3,11]%%%}+%%%{262144,[0,12,7,12,0,3]%%%}+%%%{-131072,[0,12,7,11,0,5]%%%}+%%%{16384,[0,12,7,10,0,7]%%%}+%%%{17179869184,[0,11,11,16,4,0]%%%}+%%%{42949672960,[0,11,11,15,4,2]%%%}+%%%{-53687091200,[0,11,11,14,4,4]%%%}+%%%{21474836480,[0,11,11,13,4,6]%%%}+%%%{-3690987520,[0,11,11,12,4,8]%%%}+%%%{234881024,[0,11,11,11,4,10]%%%}+%%%{1572864,[0,11,7,13,1,2]%%%}+%%%{-786432,[0,11,7,12,1,4]%%%}+%%%{98304,[0,11,7,11,1,6]%%%}+%%%{51539607552,[0,10,11,16,5,1]%%%}+%%%{-51539607552,[0,10,11,15,5,3]%%%}+%%%{19327352832,[0,10,11,14,5,5]%%%}+%%%{-3221225472,[0,10,11,13,5,7]%%%}+%%%{201326592,[0,10,11,12,5,9]%%%}+%%%{3145728,[0,10,7,14,2,1]%%%}+%%%{-1572864,[0,10,7,13,2,3]%%%}+%%%{196608,[0,10,7,12,2,5]%%%}+%%%{17179869184,[0,9,11,17,6,0]%%%}+%%%{-17179869184,[0,9,11,16,6,2]%%%}+%%%{6442450944,[0,9,11,15,6,4]%%%}+%%%{-1073741824,[0,9,11,14,6,6]%%%}+%%%{67108864,[0,9,11,13,6,8]%%%}+%%%{2097152,[0,9,7,15,3,0]%%%}+%%%{-1048576,[0,9,7,14,3,2]%%%}+%%%{131072,[0,9,7,13,3,4]%%%} / %%%{-4096,[0,5,5,5,0,3]%%%}+%%%{1024,[0,5,5,4,0,5]%%%}+%%%{-24576,[0,4,5,6,1,2]%%%}+%%%{6144,[0,4,5,5,1,4]%%%}+%%%{-49152,[0,3,5,7,2,1]%%%}+%%%{12288,[0,3,5,6,2,3]%%%}+%%%{-32768,[0,2,5,8,3,0]%%%}+%%%{8192,[0,2,5,7,3,2]%%%} Error: Bad Argument Value","F(-2)",0
1272,-2,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/x/(c*x+x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{201326592,[1,14,10,12,0,4]%%%}+%%%{-218103808,[1,14,10,11,0,6]%%%}+%%%{88080384,[1,14,10,10,0,8]%%%}+%%%{-15728640,[1,14,10,9,0,10]%%%}+%%%{1048576,[1,14,10,8,0,12]%%%}+%%%{1610612736,[1,13,10,13,1,3]%%%}+%%%{-1811939328,[1,13,10,12,1,5]%%%}+%%%{754974720,[1,13,10,11,1,7]%%%}+%%%{-138412032,[1,13,10,10,1,9]%%%}+%%%{9437184,[1,13,10,9,1,11]%%%}+%%%{4831838208,[1,12,10,14,2,2]%%%}+%%%{-5838471168,[1,12,10,13,2,4]%%%}+%%%{2566914048,[1,12,10,12,2,6]%%%}+%%%{-490733568,[1,12,10,11,2,8]%%%}+%%%{34603008,[1,12,10,10,2,10]%%%}+%%%{-18446744062972133376,[1,11,10,15,3,1]%%%}+%%%{-9126805504,[1,11,10,14,3,3]%%%}+%%%{4429185024,[1,11,10,13,3,5]%%%}+%%%{-905969664,[1,11,10,12,3,7]%%%}+%%%{67108864,[1,11,10,11,3,9]%%%}+%%%{32768,[1,11,6,12,0,3]%%%}+%%%{-8192,[1,11,6,11,0,5]%%%}+%%%{3221225472,[1,10,10,16,4,0]%%%}+%%%{-7247757312,[1,10,10,15,4,2]%%%}+%%%{4227858432,[1,10,10,14,4,4]%%%}+%%%{-956301312,[1,10,10,13,4,6]%%%}+%%%{75497472,[1,10,10,12,4,8]%%%}+%%%{196608,[1,10,6,13,1,2]%%%}+%%%{-49152,[1,10,6,12,1,4]%%%}+%%%{-3221225472,[1,9,10,16,5,1]%%%}+%%%{2415919104,[1,9,10,15,5,3]%%%}+%%%{-603979776,[1,9,10,14,5,5]%%%}+%%%{50331648,[1,9,10,13,5,7]%%%}+%%%{393216,[1,9,6,14,2,1]%%%}+%%%{-98304,[1,9,6,13,2,3]%%%}+%%%{-1073741824,[1,8,10,17,6,0]%%%}+%%%{805306368,[1,8,10,16,6,2]%%%}+%%%{-201326592,[1,8,10,15,6,4]%%%}+%%%{16777216,[1,8,10,14,6,6]%%%}+%%%{262144,[1,8,6,15,3,0]%%%}+%%%{-65536,[1,8,6,14,3,2]%%%}+%%%{1073741824,[0,15,11,12,0,4]%%%}+%%%{-1073741824,[0,15,11,11,0,6]%%%}+%%%{402653184,[0,15,11,10,0,8]%%%}+%%%{-67108864,[0,15,11,9,0,10]%%%}+%%%{4194304,[0,15,11,8,0,12]%%%}+%%%{8589934592,[0,14,11,13,1,3]%%%}+%%%{-7516192768,[0,14,11,12,1,5]%%%}+%%%{2147483648,[0,14,11,11,1,7]%%%}+%%%{-134217728,[0,14,11,10,1,9]%%%}+%%%{-33554432,[0,14,11,9,1,11]%%%}+%%%{4194304,[0,14,11,8,1,13]%%%}+%%%{25769803776,[0,13,11,14,2,2]%%%}+%%%{-16106127360,[0,13,11,13,2,4]%%%}+%%%{2013265920,[0,13,11,11,2,8]%%%}+%%%{-503316480,[0,13,11,10,2,10]%%%}+%%%{37748736,[0,13,11,9,2,12]%%%}+%%%{34359738368,[0,12,11,15,3,1]%%%}+%%%{-21474836480,[0,12,11,13,3,5]%%%}+%%%{10737418240,[0,12,11,12,3,7]%%%}+%%%{-2013265920,[0,12,11,11,3,9]%%%}+%%%{134217728,[0,12,11,10,3,11]%%%}+%%%{262144,[0,12,7,12,0,3]%%%}+%%%{-131072,[0,12,7,11,0,5]%%%}+%%%{16384,[0,12,7,10,0,7]%%%}+%%%{17179869184,[0,11,11,16,4,0]%%%}+%%%{42949672960,[0,11,11,15,4,2]%%%}+%%%{-53687091200,[0,11,11,14,4,4]%%%}+%%%{21474836480,[0,11,11,13,4,6]%%%}+%%%{-3690987520,[0,11,11,12,4,8]%%%}+%%%{234881024,[0,11,11,11,4,10]%%%}+%%%{1572864,[0,11,7,13,1,2]%%%}+%%%{-786432,[0,11,7,12,1,4]%%%}+%%%{98304,[0,11,7,11,1,6]%%%}+%%%{51539607552,[0,10,11,16,5,1]%%%}+%%%{-51539607552,[0,10,11,15,5,3]%%%}+%%%{19327352832,[0,10,11,14,5,5]%%%}+%%%{-3221225472,[0,10,11,13,5,7]%%%}+%%%{201326592,[0,10,11,12,5,9]%%%}+%%%{3145728,[0,10,7,14,2,1]%%%}+%%%{-1572864,[0,10,7,13,2,3]%%%}+%%%{196608,[0,10,7,12,2,5]%%%}+%%%{17179869184,[0,9,11,17,6,0]%%%}+%%%{-17179869184,[0,9,11,16,6,2]%%%}+%%%{6442450944,[0,9,11,15,6,4]%%%}+%%%{-1073741824,[0,9,11,14,6,6]%%%}+%%%{67108864,[0,9,11,13,6,8]%%%}+%%%{2097152,[0,9,7,15,3,0]%%%}+%%%{-1048576,[0,9,7,14,3,2]%%%}+%%%{131072,[0,9,7,13,3,4]%%%} / %%%{-4096,[0,5,5,5,0,3]%%%}+%%%{1024,[0,5,5,4,0,5]%%%}+%%%{-24576,[0,4,5,6,1,2]%%%}+%%%{6144,[0,4,5,5,1,4]%%%}+%%%{-49152,[0,3,5,7,2,1]%%%}+%%%{12288,[0,3,5,6,2,3]%%%}+%%%{-32768,[0,2,5,8,3,0]%%%}+%%%{8192,[0,2,5,7,3,2]%%%} Error: Bad Argument Value","F(-2)",0
1273,1,69,0,0.299201," ","integrate((x^5-1)^(2/3)/x^6,x, algorithm=""giac"")","\frac{2}{15} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{5} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) - \frac{{\left(x^{5} - 1\right)}^{\frac{2}{3}}}{5 \, x^{5}} + \frac{1}{15} \, \log\left({\left(x^{5} - 1\right)}^{\frac{2}{3}} - {\left(x^{5} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{2}{15} \, \log\left({\left| {\left(x^{5} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"2/15*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^5 - 1)^(1/3) - 1)) - 1/5*(x^5 - 1)^(2/3)/x^5 + 1/15*log((x^5 - 1)^(2/3) - (x^5 - 1)^(1/3) + 1) - 2/15*log(abs((x^5 - 1)^(1/3) + 1))","A",0
1274,1,244,0,0.246985," ","integrate(1/x^11/(a*x^5+b)^(3/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} + 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{42 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-b\right)^{\frac{1}{4}} - 2 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-b\right)^{\frac{1}{4}}}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{21 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{\left(-b\right)^{\frac{3}{4}} b^{2}} + \frac{21 \, \sqrt{2} a^{3} \left(-b\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{5} + b\right)}^{\frac{1}{4}} \left(-b\right)^{\frac{1}{4}} + \sqrt{a x^{5} + b} + \sqrt{-b}\right)}{b^{3}} + \frac{8 \, {\left(7 \, {\left(a x^{5} + b\right)}^{\frac{5}{4}} a^{3} - 11 \, {\left(a x^{5} + b\right)}^{\frac{1}{4}} a^{3} b\right)}}{a^{2} b^{2} x^{10}}}{320 \, a}"," ",0,"1/320*(42*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) + 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/((-b)^(3/4)*b^2) + 42*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b)^(1/4) - 2*(a*x^5 + b)^(1/4))/(-b)^(1/4))/((-b)^(3/4)*b^2) + 21*sqrt(2)*a^3*log(sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/((-b)^(3/4)*b^2) + 21*sqrt(2)*a^3*(-b)^(1/4)*log(-sqrt(2)*(a*x^5 + b)^(1/4)*(-b)^(1/4) + sqrt(a*x^5 + b) + sqrt(-b))/b^3 + 8*(7*(a*x^5 + b)^(5/4)*a^3 - 11*(a*x^5 + b)^(1/4)*a^3*b)/(a^2*b^2*x^10))/a","B",0
1275,1,69,0,0.145320," ","integrate(1/x^7/(x^6-1)^(1/3),x, algorithm=""giac"")","\frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{{\left(x^{6} - 1\right)}^{\frac{2}{3}}}{6 \, x^{6}} + \frac{1}{36} \, \log\left({\left(x^{6} - 1\right)}^{\frac{2}{3}} - {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{18} \, \log\left({\left| {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 - 1)^(1/3) - 1)) + 1/6*(x^6 - 1)^(2/3)/x^6 + 1/36*log((x^6 - 1)^(2/3) - (x^6 - 1)^(1/3) + 1) - 1/18*log(abs((x^6 - 1)^(1/3) + 1))","A",0
1276,1,69,0,0.165085," ","integrate((x^6-1)^(2/3)/x^7,x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) - \frac{{\left(x^{6} - 1\right)}^{\frac{2}{3}}}{6 \, x^{6}} + \frac{1}{18} \, \log\left({\left(x^{6} - 1\right)}^{\frac{2}{3}} - {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{9} \, \log\left({\left| {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 - 1)^(1/3) - 1)) - 1/6*(x^6 - 1)^(2/3)/x^6 + 1/18*log((x^6 - 1)^(2/3) - (x^6 - 1)^(1/3) + 1) - 1/9*log(abs((x^6 - 1)^(1/3) + 1))","A",0
1277,0,0,0,0.000000," ","integrate((2*x^6+x^4-1)*(x^7+x^5+x)^(1/3)/(x^6+x^4+1)/(x^6+x^4-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{7} + x^{5} + x\right)}^{\frac{1}{3}} {\left(2 \, x^{6} + x^{4} - 1\right)}}{{\left(x^{6} + x^{4} - x^{2} + 1\right)} {\left(x^{6} + x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^7 + x^5 + x)^(1/3)*(2*x^6 + x^4 - 1)/((x^6 + x^4 - x^2 + 1)*(x^6 + x^4 + 1)), x)","F",0
1278,1,136,0,0.556703," ","integrate((1+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x, algorithm=""giac"")","\frac{3}{5} \, \sqrt{5} \log\left(-\frac{\sqrt{5} - 2 \, \sqrt{\sqrt{x + 1} + 1} - 1}{\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} + 1}\right) + \frac{3}{5} \, \sqrt{5} \log\left(\frac{{\left| -\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} - 1 \right|}}{{\left| \sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} - 1 \right|}}\right) + 4 \, \sqrt{\sqrt{x + 1} + 1} - \log\left(\sqrt{x + 1} + \sqrt{\sqrt{x + 1} + 1}\right) + \log\left({\left| \sqrt{x + 1} - \sqrt{\sqrt{x + 1} + 1} \right|}\right)"," ",0,"3/5*sqrt(5)*log(-(sqrt(5) - 2*sqrt(sqrt(x + 1) + 1) - 1)/(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) + 1)) + 3/5*sqrt(5)*log(abs(-sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) - 1)/abs(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) - 1)) + 4*sqrt(sqrt(x + 1) + 1) - log(sqrt(x + 1) + sqrt(sqrt(x + 1) + 1)) + log(abs(sqrt(x + 1) - sqrt(sqrt(x + 1) + 1)))","A",0
1279,1,114,0,0.279552," ","integrate(1/x^3/(x^2-1)^(3/4),x, algorithm=""giac"")","\frac{3}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{3}{8} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{3}{16} \, \sqrt{2} \log\left(\sqrt{2} {\left(x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{2} - 1} + 1\right) - \frac{3}{16} \, \sqrt{2} \log\left(-\sqrt{2} {\left(x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{2} - 1} + 1\right) + \frac{{\left(x^{2} - 1\right)}^{\frac{1}{4}}}{2 \, x^{2}}"," ",0,"3/8*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^2 - 1)^(1/4))) + 3/8*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^2 - 1)^(1/4))) + 3/16*sqrt(2)*log(sqrt(2)*(x^2 - 1)^(1/4) + sqrt(x^2 - 1) + 1) - 3/16*sqrt(2)*log(-sqrt(2)*(x^2 - 1)^(1/4) + sqrt(x^2 - 1) + 1) + 1/2*(x^2 - 1)^(1/4)/x^2","A",0
1280,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{2}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)/x^3, x)","F",0
1281,0,0,0,0.000000," ","integrate((x^2+2)/(x^2+2*x-2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2}{\sqrt{x^{3} + 1} {\left(x^{2} + 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x^2 + 2)/(sqrt(x^3 + 1)*(x^2 + 2*x - 2)), x)","F",0
1282,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)/x^3, x)","F",0
1283,0,0,0,0.000000," ","integrate((2*a*b*x+(-3*a+b)*x^2)/(x^2*(-a+x)*(-b+x))^(1/4)/(a^3-3*a^2*x+(-b*d+3*a)*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int \frac{2 \, a b x - {\left(3 \, a - b\right)} x^{2}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{4}} {\left({\left(d - 1\right)} x^{3} + a^{3} - 3 \, a^{2} x - {\left(b d - 3 \, a\right)} x^{2}\right)}}\,{d x}"," ",0,"integrate((2*a*b*x - (3*a - b)*x^2)/(((a - x)*(b - x)*x^2)^(1/4)*((d - 1)*x^3 + a^3 - 3*a^2*x - (b*d - 3*a)*x^2)), x)","F",0
1284,1,114,0,0.167928," ","integrate((x^4-1)^(1/4)/x^5,x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{16} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{32} \, \sqrt{2} \log\left(\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{4} - 1} + 1\right) - \frac{1}{32} \, \sqrt{2} \log\left(-\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{4} - 1} + 1\right) - \frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{4 \, x^{4}}"," ",0,"1/16*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^4 - 1)^(1/4))) + 1/16*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^4 - 1)^(1/4))) + 1/32*sqrt(2)*log(sqrt(2)*(x^4 - 1)^(1/4) + sqrt(x^4 - 1) + 1) - 1/32*sqrt(2)*log(-sqrt(2)*(x^4 - 1)^(1/4) + sqrt(x^4 - 1) + 1) - 1/4*(x^4 - 1)^(1/4)/x^4","A",0
1285,0,0,0,0.000000," ","integrate((x^2+1)/(x^2+x-1)/(x^4-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{4} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^4 - x^2)^(1/3)*(x^2 + x - 1)), x)","F",0
1286,1,100,0,0.348259," ","integrate((-1+2*x)*(x^2-x+2)*(x^4-2*x^3+x^2-2)^(1/2)/(2*x^2-2*x+3),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{{\left(x^{2} - x\right)}^{2} - 2} {\left(x^{2} - x + 1\right)} + \frac{1}{8} \, \log\left(x^{2} - x - \sqrt{{\left(x^{2} - x\right)}^{2} - 2} + 2\right) - \frac{1}{8} \, \log\left(x^{2} - x - \sqrt{{\left(x^{2} - x\right)}^{2} - 2} + 1\right) + \frac{7}{8} \, \log\left({\left| -x^{2} + x + \sqrt{{\left(x^{2} - x\right)}^{2} - 2} \right|}\right)"," ",0,"1/4*sqrt((x^2 - x)^2 - 2)*(x^2 - x + 1) + 1/8*log(x^2 - x - sqrt((x^2 - x)^2 - 2) + 2) - 1/8*log(x^2 - x - sqrt((x^2 - x)^2 - 2) + 1) + 7/8*log(abs(-x^2 + x + sqrt((x^2 - x)^2 - 2)))","A",0
1287,1,100,0,0.231650," ","integrate((x^4-x^3)^(1/4)/x/(1+x),x, algorithm=""giac"")","2 \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - 2 \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2*2^(1/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) - 2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4))) - 2*arctan((-1/x + 1)^(1/4)) - log((-1/x + 1)^(1/4) + 1) + log(abs((-1/x + 1)^(1/4) - 1))","A",0
1288,0,0,0,0.000000," ","integrate((2*x^3+1)/(x^3+x-1)/(x^5-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{2 \, x^{3} + 1}{{\left(x^{5} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} + x - 1\right)}}\,{d x}"," ",0,"integrate((2*x^3 + 1)/((x^5 - x^2)^(1/3)*(x^3 + x - 1)), x)","F",0
1289,1,114,0,0.197041," ","integrate((x^6-1)^(1/4)/x^7,x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(x^{6} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(x^{6} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \, \sqrt{2} \log\left(\sqrt{2} {\left(x^{6} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{6} - 1} + 1\right) - \frac{1}{48} \, \sqrt{2} \log\left(-\sqrt{2} {\left(x^{6} - 1\right)}^{\frac{1}{4}} + \sqrt{x^{6} - 1} + 1\right) - \frac{{\left(x^{6} - 1\right)}^{\frac{1}{4}}}{6 \, x^{6}}"," ",0,"1/24*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^6 - 1)^(1/4))) + 1/24*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^6 - 1)^(1/4))) + 1/48*sqrt(2)*log(sqrt(2)*(x^6 - 1)^(1/4) + sqrt(x^6 - 1) + 1) - 1/48*sqrt(2)*log(-sqrt(2)*(x^6 - 1)^(1/4) + sqrt(x^6 - 1) + 1) - 1/6*(x^6 - 1)^(1/4)/x^6","A",0
1290,0,0,0,0.000000," ","integrate((3*x^4+1)/(x^4+x-1)/(x^6-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x^{4} + 1}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{4} + x - 1\right)}}\,{d x}"," ",0,"integrate((3*x^4 + 1)/((x^6 - x^2)^(1/3)*(x^4 + x - 1)), x)","F",0
1291,0,0,0,0.000000," ","integrate((x^3+2)*(x^3-x^2-1)^(1/2)/(x^6+x^5-x^4-2*x^3-x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{3} - x^{2} - 1} {\left(x^{3} + 2\right)}}{x^{6} + x^{5} - x^{4} - 2 \, x^{3} - x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(x^3 - x^2 - 1)*(x^3 + 2)/(x^6 + x^5 - x^4 - 2*x^3 - x^2 + 1), x)","F",0
1292,0,0,0,0.000000," ","integrate((x^4+1)*(x^4-x^2-1)^(1/2)/(x^8+x^6-3*x^4-x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} - x^{2} - 1} {\left(x^{4} + 1\right)}}{x^{8} + x^{6} - 3 \, x^{4} - x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(x^4 - x^2 - 1)*(x^4 + 1)/(x^8 + x^6 - 3*x^4 - x^2 + 1), x)","F",0
1293,1,80,0,0.162730," ","integrate(x^2*(x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\frac{1}{3840} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, \sqrt{x + 1} {\left(10 \, \sqrt{x + 1} + 1\right)} - 269\right)} \sqrt{x + 1} + 9\right)} \sqrt{x + 1} + 2487\right)} \sqrt{x + 1} + 363\right)} \sqrt{x + \sqrt{x + 1}} + \frac{385}{512} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/3840*(2*(4*(2*(8*sqrt(x + 1)*(10*sqrt(x + 1) + 1) - 269)*sqrt(x + 1) + 9)*sqrt(x + 1) + 2487)*sqrt(x + 1) + 363)*sqrt(x + sqrt(x + 1)) + 385/512*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
1294,0,0,0,0.000000," ","integrate((x^3-1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3), x)","F",0
1295,0,0,0,0.000000," ","integrate((x^3+1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{3} + 1\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3), x)","F",0
1296,0,0,0,0.000000," ","integrate((x^3-1)/(x^3+2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} - 1}{{\left(x^{3} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 - 1)/(x^3 + 2)^(1/3), x)","F",0
1297,1,67,0,0.358838," ","integrate((x^3+x)^(1/3),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{12} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{6} \, \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/2*x^2*(1/x^2 + 1)^(1/3) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) + 1/12*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - 1/6*log(abs((1/x^2 + 1)^(1/3) - 1))","A",0
1298,0,0,0,0.000000," ","integrate((-2*k+(-1+k)*(1+k)*x+2*k*x^2)*(k^2*x^2+2*k*x+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(-1+d+(1+3*d)*k*x+(3*d*k^2+1)*x^2+k*(d*k^2-1)*x^3),x, algorithm=""giac"")","\int \frac{{\left(k^{2} x^{2} + 2 \, k x + 1\right)} {\left({\left(k + 1\right)} {\left(k - 1\right)} x + 2 \, k x^{2} - 2 \, k\right)}}{{\left({\left(d k^{2} - 1\right)} k x^{3} + {\left(3 \, d + 1\right)} k x + {\left(3 \, d k^{2} + 1\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((k^2*x^2 + 2*k*x + 1)*((k + 1)*(k - 1)*x + 2*k*x^2 - 2*k)/(((d*k^2 - 1)*k*x^3 + (3*d + 1)*k*x + (3*d*k^2 + 1)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(3/4)), x)","F",0
1299,0,0,0,0.000000," ","integrate((x^4-1)^(3/4)*(x^4+4)/x^8/(x^4-4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 4\right)} {\left(x^{4} - 1\right)}^{\frac{3}{4}}}{{\left(x^{4} - 4\right)} x^{8}}\,{d x}"," ",0,"integrate((x^4 + 4)*(x^4 - 1)^(3/4)/((x^4 - 4)*x^8), x)","F",0
1300,0,0,0,0.000000," ","integrate((a*x^3+4*b)/(a*x^3+b)^(1/4)/(a*x^3+x^4+b),x, algorithm=""giac"")","\int \frac{a x^{3} + 4 \, b}{{\left(a x^{3} + x^{4} + b\right)} {\left(a x^{3} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^3 + 4*b)/((a*x^3 + x^4 + b)*(a*x^3 + b)^(1/4)), x)","F",0
1301,0,0,0,0.000000," ","integrate((-a^2*b+a*(2*a+b)*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2*d+2*a*d*x+(b^2-d)*x^2-2*b*x^3+x^4),x, algorithm=""giac"")","\int \frac{a^{2} b - {\left(2 \, a + b\right)} a x + 3 \, a x^{2} - x^{3}}{{\left(2 \, b x^{3} - x^{4} + a^{2} d - 2 \, a d x - {\left(b^{2} - d\right)} x^{2}\right)} \sqrt{{\left(a - x\right)} {\left(b - x\right)} x}}\,{d x}"," ",0,"integrate((a^2*b - (2*a + b)*a*x + 3*a*x^2 - x^3)/((2*b*x^3 - x^4 + a^2*d - 2*a*d*x - (b^2 - d)*x^2)*sqrt((a - x)*(b - x)*x)), x)","F",0
1302,1,209,0,0.224563," ","integrate((a*x^4-2*b)/x^4/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) + \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) + \frac{4 \, {\left(3 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{7}{4}} b^{6} - 7 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{21 \, b^{7}}"," ",0,"1/2*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) + 1/2*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) + 1/4*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) + 4/21*(3*(a + b/x^2)^(7/4)*b^6 - 7*(a + b/x^2)^(3/4)*a*b^6)/b^7","B",0
1303,1,209,0,0.230168," ","integrate((a*x^4+2*b)/x^4/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) + \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) - \frac{4 \, {\left(3 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{7}{4}} b^{6} - 7 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{21 \, b^{7}}"," ",0,"1/2*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) + 1/2*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) + 1/4*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) - 4/21*(3*(a + b/x^2)^(7/4)*b^6 - 7*(a + b/x^2)^(3/4)*a*b^6)/b^7","B",0
1304,-1,0,0,0.000000," ","integrate((-1+x)/(1+x)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1305,-1,0,0,0.000000," ","integrate((1+x)/(-1+x)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1306,0,0,0,0.000000," ","integrate(x^2/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4-1),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(k^{2} x^{4} - 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate(x^2/((k^2*x^4 - 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
1307,0,0,0,0.000000," ","integrate((x^6-1)^(2/3)*(x^6+1)/x^3/(x^6-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - x^{3} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^6 + 1)*(x^6 - 1)^(2/3)/((x^6 - x^3 - 1)*x^3), x)","F",0
1308,0,0,0,0.000000," ","integrate((x^6-1)*(x^6+1)^(2/3)/x^3/(x^6-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)}^{\frac{2}{3}} {\left(x^{6} - 1\right)}}{{\left(x^{6} - x^{3} + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^6 + 1)^(2/3)*(x^6 - 1)/((x^6 - x^3 + 1)*x^3), x)","F",0
1309,-2,0,0,0.000000," ","integrate((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument Value","F(-2)",0
1310,-2,0,0,0.000000," ","integrate((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Invalid _EXT in replace_ext Error: Bad Argument ValueInvalid _EXT in replace_ext Error: Bad Argument Value","F(-2)",0
1311,0,0,0,0.000000," ","integrate((x^8+3*x^4+1)/x^2/(x^4+1)^(3/4)/(3*x^8+3*x^4+1),x, algorithm=""giac"")","\int \frac{x^{8} + 3 \, x^{4} + 1}{{\left(3 \, x^{8} + 3 \, x^{4} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^8 + 3*x^4 + 1)/((3*x^8 + 3*x^4 + 1)*(x^4 + 1)^(3/4)*x^2), x)","F",0
1312,-2,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(4*a^2*x^2-4*a*x+4*b+1)]schur row 3 1.47052e-08Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [21,-68,89]Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [71,-84,-83]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Evaluation time: 22.79Conj Error: Bad Argument Type","F(-2)",0
1313,-2,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(4*a^2*x^2-4*a*x+4*b+1)]schur row 3 1.47052e-08Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [21,-68,89]Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [71,-84,-83]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming 0=[0]Evaluation time: 23.11Conj Error: Bad Argument Type","F(-2)",0
1314,0,0,0,0.000000," ","integrate((-1+x)/x^4/(x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} + 1\right)}^{\frac{1}{3}} x^{4}}\,{d x}"," ",0,"integrate((x - 1)/((x^3 + 1)^(1/3)*x^4), x)","F",0
1315,0,0,0,0.000000," ","integrate((3+2*x)*(x^3+x+1)^(1/3)/x^2/(1+x),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x + 1\right)}^{\frac{1}{3}} {\left(2 \, x + 3\right)}}{{\left(x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^3 + x + 1)^(1/3)*(2*x + 3)/((x + 1)*x^2), x)","F",0
1316,0,0,0,0.000000," ","integrate((a^2-2*a*x+x^2)*(-a*b+2*(a-b)*x+x^2)/(x*(-a+x)*(-b+x))^(3/4)/(-a^3*d+(3*a^2*d+b)*x-(3*a*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(a^{2} - 2 \, a x + x^{2}\right)} {\left(a b - 2 \, {\left(a - b\right)} x - x^{2}\right)}}{{\left(a^{3} d - d x^{3} + {\left(3 \, a d + 1\right)} x^{2} - {\left(3 \, a^{2} d + b\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a^2 - 2*a*x + x^2)*(a*b - 2*(a - b)*x - x^2)/((a^3*d - d*x^3 + (3*a*d + 1)*x^2 - (3*a^2*d + b)*x)*((a - x)*(b - x)*x)^(3/4)), x)","F",0
1317,0,0,0,0.000000," ","integrate((x^2+1)^2/(-x^2+1)/(x^4-6*x^2+1)^(3/4),x, algorithm=""giac"")","\int -\frac{{\left(x^{2} + 1\right)}^{2}}{{\left(x^{4} - 6 \, x^{2} + 1\right)}^{\frac{3}{4}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 1)^2/((x^4 - 6*x^2 + 1)^(3/4)*(x^2 - 1)), x)","F",0
1318,0,0,0,0.000000," ","integrate((x^3-4)*(x^4-x^3+1)/x^2/(x^3-1)^(3/4)/(x^4+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} + 1\right)} {\left(x^{3} - 4\right)}}{{\left(x^{4} + x^{3} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^4 - x^3 + 1)*(x^3 - 4)/((x^4 + x^3 - 1)*(x^3 - 1)^(3/4)*x^2), x)","F",0
1319,0,0,0,0.000000," ","integrate((x^4-1)*(x^4+3)*(x^4-x^3-1)/x^6/(x^4-2*x^3-1)/(x^5-x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} - 1\right)} {\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}}{{\left(x^{5} - x\right)}^{\frac{1}{4}} {\left(x^{4} - 2 \, x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 - x^3 - 1)*(x^4 + 3)*(x^4 - 1)/((x^5 - x)^(1/4)*(x^4 - 2*x^3 - 1)*x^6), x)","F",0
1320,0,0,0,0.000000," ","integrate((a*x^5+4*b)*(a*x^5+c*x^4-b)/x^2/(a*x^5-b)^(3/4)/(a*x^5-c*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} + c x^{4} - b\right)} {\left(a x^{5} + 4 \, b\right)}}{{\left(a x^{5} - c x^{4} - b\right)} {\left(a x^{5} - b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a*x^5 + c*x^4 - b)*(a*x^5 + 4*b)/((a*x^5 - c*x^4 - b)*(a*x^5 - b)^(3/4)*x^2), x)","F",0
1321,0,0,0,0.000000," ","integrate((x^6-2)*(x^6-x^4+1)/x^4/(x^6+1)^(1/4)/(x^6+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} + 1\right)} {\left(x^{6} - 2\right)}}{{\left(x^{6} + x^{4} + 1\right)} {\left(x^{6} + 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^6 - x^4 + 1)*(x^6 - 2)/((x^6 + x^4 + 1)*(x^6 + 1)^(1/4)*x^4), x)","F",0
1322,0,0,0,0.000000," ","integrate(x^4*(a*x^6+2*b)/(a*x^6-b)^(1/4)/(a*x^6-x^4-b)^2,x, algorithm=""giac"")","\int \frac{{\left(a x^{6} + 2 \, b\right)} x^{4}}{{\left(a x^{6} - x^{4} - b\right)}^{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^6 + 2*b)*x^4/((a*x^6 - x^4 - b)^2*(a*x^6 - b)^(1/4)), x)","F",0
1323,0,0,0,0.000000," ","integrate((a*x^6+2*b)*(a*x^6-x^4-b)/x^4/(a*x^6-b)^(1/4)/(a*x^6-2*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} - x^{4} - b\right)} {\left(a x^{6} + 2 \, b\right)}}{{\left(a x^{6} - 2 \, x^{4} - b\right)} {\left(a x^{6} - b\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((a*x^6 - x^4 - b)*(a*x^6 + 2*b)/((a*x^6 - 2*x^4 - b)*(a*x^6 - b)^(1/4)*x^4), x)","F",0
1324,0,0,0,0.000000," ","integrate((-x^8-2*x^3-2*x^2-1)^(1/2)*(3*x^8+x^3-1)/(x^8+2*x^3+1)/(x^8+2*x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{8} + x^{3} - 1\right)} \sqrt{-x^{8} - 2 \, x^{3} - 2 \, x^{2} - 1}}{{\left(x^{8} + 2 \, x^{3} + x^{2} + 1\right)} {\left(x^{8} + 2 \, x^{3} + 1\right)}}\,{d x}"," ",0,"integrate((3*x^8 + x^3 - 1)*sqrt(-x^8 - 2*x^3 - 2*x^2 - 1)/((x^8 + 2*x^3 + x^2 + 1)*(x^8 + 2*x^3 + 1)), x)","F",0
1325,0,0,0,0.000000," ","integrate((x^6+1)*(x^6-x^2-2)^(1/2)/(x^12-4*x^6-3*x^4+4),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - x^{2} - 2} {\left(x^{6} + 1\right)}}{x^{12} - 4 \, x^{6} - 3 \, x^{4} + 4}\,{d x}"," ",0,"integrate(sqrt(x^6 - x^2 - 2)*(x^6 + 1)/(x^12 - 4*x^6 - 3*x^4 + 4), x)","F",0
1326,0,0,0,0.000000," ","integrate(x*(x^3-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{1}{3}} x\,{d x}"," ",0,"integrate((x^3 - 1)^(1/3)*x, x)","F",0
1327,0,0,0,0.000000," ","integrate(x*(x^3+1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} + 1\right)}^{\frac{1}{3}} x\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)*x, x)","F",0
1328,1,64,0,0.190043," ","integrate((x^3+x)^(1/3)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{3}{2} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + \frac{1}{4} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{2} \, \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) - 3/2*(1/x^2 + 1)^(1/3) + 1/4*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - 1/2*log(abs((1/x^2 + 1)^(1/3) - 1))","A",0
1329,0,0,0,0.000000," ","integrate((-1+x)*(k*x-1)*(3-2*(1+k)*x+k*x^2)/x/((1-x)*x*(-k*x+1))^(3/4)/(-1+(1+k)*x-k*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(k x^{2} - 2 \, {\left(k + 1\right)} x + 3\right)} {\left(k x - 1\right)} {\left(x - 1\right)}}{{\left(d x^{3} - k x^{2} + {\left(k + 1\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{3}{4}} x}\,{d x}"," ",0,"integrate((k*x^2 - 2*(k + 1)*x + 3)*(k*x - 1)*(x - 1)/((d*x^3 - k*x^2 + (k + 1)*x - 1)*((k*x - 1)*(x - 1)*x)^(3/4)*x), x)","F",0
1330,0,0,0,0.000000," ","integrate((x^2-2*x+1)*(-2+(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(-1+d-(1+3*d)*x+(k^2+3*d)*x^2+(k^2-d)*x^3),x, algorithm=""giac"")","\int \frac{{\left(2 \, k^{2} x^{2} + {\left(k + 1\right)} {\left(k - 1\right)} x - 2\right)} {\left(x^{2} - 2 \, x + 1\right)}}{{\left({\left(k^{2} - d\right)} x^{3} + {\left(k^{2} + 3 \, d\right)} x^{2} - {\left(3 \, d + 1\right)} x + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((2*k^2*x^2 + (k + 1)*(k - 1)*x - 2)*(x^2 - 2*x + 1)/(((k^2 - d)*x^3 + (k^2 + 3*d)*x^2 - (3*d + 1)*x + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(3/4)), x)","F",0
1331,1,207,0,0.222251," ","integrate(x^2/(a*x^2-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{2 \, a^{2}} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{2 \, a^{2}} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{4 \, a^{2}} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{4 \, a^{2}} - \frac{2}{{\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} a}"," ",0,"1/2*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/a^2 + 1/2*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/a^2 - 1/4*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2))/a^2 + 1/4*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2))/a^2 - 2/((a - b/x^2)^(1/4)*a)","B",0
1332,0,0,0,0.000000," ","integrate((p*x^5+q)^(1/2)*(3*p*x^5-2*q)*(a*p*x^5+b*x^2+a*q)/x^4/(c*p*x^5+d*x^2+c*q),x, algorithm=""giac"")","\int \frac{{\left(a p x^{5} + b x^{2} + a q\right)} {\left(3 \, p x^{5} - 2 \, q\right)} \sqrt{p x^{5} + q}}{{\left(c p x^{5} + d x^{2} + c q\right)} x^{4}}\,{d x}"," ",0,"integrate((a*p*x^5 + b*x^2 + a*q)*(3*p*x^5 - 2*q)*sqrt(p*x^5 + q)/((c*p*x^5 + d*x^2 + c*q)*x^4), x)","F",0
1333,1,55,0,0.156248," ","integrate(x/(x^6+x^2)^(1/3),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{4}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{8} \, \log\left({\left(\frac{1}{x^{4}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{4}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{4} \, \log\left({\left| {\left(\frac{1}{x^{4}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^4 + 1)^(1/3) + 1)) + 1/8*log((1/x^4 + 1)^(2/3) + (1/x^4 + 1)^(1/3) + 1) - 1/4*log(abs((1/x^4 + 1)^(1/3) - 1))","A",0
1334,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+x^2+1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^6 + x^2)^(1/4)*(x^4 + x^2 + 1)), x)","F",0
1335,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+x^2+1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^6 + x^2)^(1/4)*(x^4 + x^2 + 1)), x)","F",0
1336,0,0,0,0.000000," ","integrate(x^2*(a*x^6+2*b)/(a*x^6-b)^(3/4)/(a*x^6-2*c*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} + 2 \, b\right)} x^{2}}{{\left(a x^{6} - 2 \, c x^{4} - b\right)} {\left(a x^{6} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^6 + 2*b)*x^2/((a*x^6 - 2*c*x^4 - b)*(a*x^6 - b)^(3/4)), x)","F",0
1337,0,0,0,0.000000," ","integrate(1/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - 2 \, a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^8 - 2*a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
1338,0,0,0,0.000000," ","integrate(1/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - 2 \, a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^8 - 2*a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
1339,0,0,0,0.000000," ","integrate((a*x^4-2*b)/(a*x^4+b)^(1/4)/(2*x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(2 \, x^{8} - a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((2*x^8 - a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1340,0,0,0,0.000000," ","integrate((k^2*x^2+b*x+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-1),x, algorithm=""giac"")","\int \frac{k^{2} x^{2} + b x + 1}{{\left(k^{2} x^{2} - 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^2*x^2 + b*x + 1)/((k^2*x^2 - 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
1341,1,79,0,0.162095," ","integrate((x^3-1)^(1/3)/x^7,x, algorithm=""giac"")","\frac{1}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{{\left(x^{3} - 1\right)}^{\frac{4}{3}} - 2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{18 \, x^{6}} - \frac{1}{54} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{27} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) + 1/18*((x^3 - 1)^(4/3) - 2*(x^3 - 1)^(1/3))/x^6 - 1/54*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 1/27*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1342,1,77,0,0.157152," ","integrate((x^3+1)^(1/3)/x^7,x, algorithm=""giac"")","\frac{1}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{3} + 1\right)}^{\frac{4}{3}} + 2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}}}{18 \, x^{6}} + \frac{1}{54} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{27} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) - 1/18*((x^3 + 1)^(4/3) + 2*(x^3 + 1)^(1/3))/x^6 + 1/54*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) - 1/27*log(abs((x^3 + 1)^(1/3) - 1))","A",0
1343,1,74,0,0.175411," ","integrate((x^3-1)*(x^3+1)^(1/3)/x^4,x, algorithm=""giac"")","-\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x^{3}} - \frac{1}{9} \, \log\left({\left(x^{3} + 1\right)}^{\frac{2}{3}} + {\left(x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{2}{9} \, \log\left({\left| {\left(x^{3} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 1)^(1/3) + 1)) + (x^3 + 1)^(1/3) + 1/3*(x^3 + 1)^(1/3)/x^3 - 1/9*log((x^3 + 1)^(2/3) + (x^3 + 1)^(1/3) + 1) + 2/9*log(abs((x^3 + 1)^(1/3) - 1))","A",0
1344,0,0,0,0.000000," ","integrate((1+x)/(x^3-x-1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((x^3 - x^2)^(1/3)*(x^3 - x - 1)), x)","F",0
1345,0,0,0,0.000000," ","integrate((1+x)/(x^3-x-1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((x^3 - x^2)^(1/3)*(x^3 - x - 1)), x)","F",0
1346,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^3-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{3} - x^{2} - x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^3 - x^2 - x)*(x^2 + 1)), x)","F",0
1347,1,64,0,0.328614," ","integrate((x^3+x^2)^(1/3)/x,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + x {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + \frac{1}{6} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{3} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) + x*(1/x + 1)^(1/3) + 1/6*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) - 1/3*log(abs((1/x + 1)^(1/3) - 1))","A",0
1348,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+2)/x^6/(2*x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 + 1)^(2/3)/((2*x^3 + 1)*x^6), x)","F",0
1349,1,76,0,0.236117," ","integrate((x^4-3)*(x^4+1)^(1/3)/x^9,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{4} + 1\right)}^{\frac{4}{3}} - 4 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}}}{8 \, x^{8}} - \frac{1}{12} \, \log\left({\left(x^{4} + 1\right)}^{\frac{2}{3}} + {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 + 1)^(1/3) + 1)) - 1/8*((x^4 + 1)^(4/3) - 4*(x^4 + 1)^(1/3))/x^8 - 1/12*log((x^4 + 1)^(2/3) + (x^4 + 1)^(1/3) + 1) + 1/6*log((x^4 + 1)^(1/3) - 1)","A",0
1350,1,185,0,0.225516," ","integrate((a*x^3-b)/x^3/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) + \frac{4}{9} \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) + 4/9*(a + b/x^3)^(3/4)","B",0
1351,1,185,0,0.221285," ","integrate((a*x^3+b)/x^3/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) - \frac{4}{9} \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) - 4/9*(a + b/x^3)^(3/4)","B",0
1352,1,78,0,0.180790," ","integrate(1/x^13/(x^6+1)^(1/3),x, algorithm=""giac"")","\frac{1}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{4 \, {\left(x^{6} + 1\right)}^{\frac{5}{3}} - 7 \, {\left(x^{6} + 1\right)}^{\frac{2}{3}}}{36 \, x^{12}} - \frac{1}{54} \, \log\left({\left(x^{6} + 1\right)}^{\frac{2}{3}} + {\left(x^{6} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{27} \, \log\left({\left(x^{6} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"1/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 + 1)^(1/3) + 1)) + 1/36*(4*(x^6 + 1)^(5/3) - 7*(x^6 + 1)^(2/3))/x^12 - 1/54*log((x^6 + 1)^(2/3) + (x^6 + 1)^(1/3) + 1) + 1/27*log((x^6 + 1)^(1/3) - 1)","A",0
1353,0,0,0,0.000000," ","integrate((5*x^8-3)/(x^8+1)/(x^8-x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{5 \, x^{8} - 3}{{\left(x^{8} - x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{8} + 1\right)}}\,{d x}"," ",0,"integrate((5*x^8 - 3)/((x^8 - x^3 + 1)^(1/3)*(x^8 + 1)), x)","F",0
1354,1,65,0,0.167230," ","integrate((x+(1+x)^(1/2))^(1/2)/(1+(1+x)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} - 3\right)} + 4 \, \arctan\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} - 1\right) + \frac{1}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) - 3) + 4*arctan(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) - 1) + 1/4*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
1355,0,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))/(1+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x + \sqrt{x^{2} + 1}}{\sqrt{x + \sqrt{x^{2} + 1}} + 1}\,{d x}"," ",0,"integrate((x + sqrt(x^2 + 1))/(sqrt(x + sqrt(x^2 + 1)) + 1), x)","F",0
1356,0,0,0,0.000000," ","integrate(x^2/(a*x^2-2*b)/(a*x^2-b)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a x^{2} - b\right)}^{\frac{3}{4}} {\left(a x^{2} - 2 \, b\right)}}\,{d x}"," ",0,"integrate(x^2/((a*x^2 - b)^(3/4)*(a*x^2 - 2*b)), x)","F",0
1357,0,0,0,0.000000," ","integrate((-2*k-(-1+k)*(1+k)*x+2*k*x^2)*(k^2*x^2-2*k*x+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d+(1+3*d)*k*x-(3*d*k^2+1)*x^2+k*(d*k^2-1)*x^3),x, algorithm=""giac"")","\int -\frac{{\left(k^{2} x^{2} - 2 \, k x + 1\right)} {\left({\left(k + 1\right)} {\left(k - 1\right)} x - 2 \, k x^{2} + 2 \, k\right)}}{{\left({\left(d k^{2} - 1\right)} k x^{3} + {\left(3 \, d + 1\right)} k x - {\left(3 \, d k^{2} + 1\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-(k^2*x^2 - 2*k*x + 1)*((k + 1)*(k - 1)*x - 2*k*x^2 + 2*k)/(((d*k^2 - 1)*k*x^3 + (3*d + 1)*k*x - (3*d*k^2 + 1)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(3/4)), x)","F",0
1358,0,0,0,0.000000," ","integrate((x^2-1)*(x^2+1)*(x^4+3*x^2+1)^(1/2)/x^2/(x^2+x+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 1} {\left(x^{2} + 1\right)} {\left(x^{2} - 1\right)}}{{\left(x^{2} + x + 1\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 1)*(x^2 + 1)*(x^2 - 1)/((x^2 + x + 1)^2*x^2), x)","F",0
1359,0,0,0,0.000000," ","integrate((x^2+2)*(2*x^2+x-4)*(2*x^4-7*x^2+8)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} - 7 \, x^{2} + 8} {\left(2 \, x^{2} + x - 4\right)} {\left(x^{2} + 2\right)}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(2*x^4 - 7*x^2 + 8)*(2*x^2 + x - 4)*(x^2 + 2)/x^4, x)","F",0
1360,0,0,0,0.000000," ","integrate(x^4*(a*x^4-b)^(3/4),x, algorithm=""giac"")","\int {\left(a x^{4} - b\right)}^{\frac{3}{4}} x^{4}\,{d x}"," ",0,"integrate((a*x^4 - b)^(3/4)*x^4, x)","F",0
1361,1,221,0,0.198876," ","integrate((a*x^2-2*b)*(a*x^4+b*x^2)^(1/4)/x^2,x, algorithm=""giac"")","\frac{8 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} a b x^{2} - 14 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - 14 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - 7 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) + 7 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) + 64 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} b^{2}}{16 \, b}"," ",0,"1/16*(8*(a + b/x^2)^(1/4)*a*b*x^2 - 14*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) - 14*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) - 7*sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) + 7*sqrt(2)*(-a)^(1/4)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) + 64*(a + b/x^2)^(1/4)*b^2)/b","B",0
1362,1,221,0,0.182625," ","integrate((a*x^2+2*b)*(a*x^4+b*x^2)^(1/4)/x^2,x, algorithm=""giac"")","\frac{8 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} a b x^{2} + 18 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + 18 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + 9 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) - 9 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right) - 64 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} b^{2}}{16 \, b}"," ",0,"1/16*(8*(a + b/x^2)^(1/4)*a*b*x^2 + 18*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) + 18*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4)) + 9*sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) - 9*sqrt(2)*(-a)^(1/4)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2)) - 64*(a + b/x^2)^(1/4)*b^2)/b","B",0
1363,0,0,0,0.000000," ","integrate(((-3*k^2+1)*x+2*k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(3*k^2-d)*x^2-3*k^4*x^4+k^6*x^6),x, algorithm=""giac"")","\int \frac{2 \, k^{2} x^{3} - {\left(3 \, k^{2} - 1\right)} x}{{\left(k^{6} x^{6} - 3 \, k^{4} x^{4} + {\left(3 \, k^{2} - d\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*k^2*x^3 - (3*k^2 - 1)*x)/((k^6*x^6 - 3*k^4*x^4 + (3*k^2 - d)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/4)), x)","F",0
1364,0,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{4} - b}{{\left(x^{8} - a x^{4} + b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - b)/((x^8 - a*x^4 + b)*(a*x^4 + b)^(1/4)), x)","F",0
1365,0,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{4} - b}{{\left(x^{8} - a x^{4} + b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - b)/((x^8 - a*x^4 + b)*(a*x^4 + b)^(1/4)), x)","F",0
1366,0,0,0,0.000000," ","integrate((x^5+4)*(x^10+x^9+x^8-2*x^5-x^4+1)/x^2/(x^5-1)^(3/4)/(x^10-x^9-x^8-2*x^5+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{10} + x^{9} + x^{8} - 2 \, x^{5} - x^{4} + 1\right)} {\left(x^{5} + 4\right)}}{{\left(x^{10} - x^{9} - x^{8} - 2 \, x^{5} + x^{4} + 1\right)} {\left(x^{5} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^10 + x^9 + x^8 - 2*x^5 - x^4 + 1)*(x^5 + 4)/((x^10 - x^9 - x^8 - 2*x^5 + x^4 + 1)*(x^5 - 1)^(3/4)*x^2), x)","F",0
1367,0,0,0,0.000000," ","integrate((x^5+4)*(x^10+x^9+x^8-2*x^5-x^4+1)/x^2/(x^5-1)^(3/4)/(x^10-x^9-x^8-2*x^5+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{10} + x^{9} + x^{8} - 2 \, x^{5} - x^{4} + 1\right)} {\left(x^{5} + 4\right)}}{{\left(x^{10} - x^{9} - x^{8} - 2 \, x^{5} + x^{4} + 1\right)} {\left(x^{5} - 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^10 + x^9 + x^8 - 2*x^5 - x^4 + 1)*(x^5 + 4)/((x^10 - x^9 - x^8 - 2*x^5 + x^4 + 1)*(x^5 - 1)^(3/4)*x^2), x)","F",0
1368,0,0,0,0.000000," ","integrate(1/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}\,{d x}"," ",0,"integrate(1/sqrt(a*x^2 + sqrt(a^2*x^4 + b)), x)","F",0
1369,1,97,0,0.295316," ","integrate((2*a*x^2-3*b)*(a^2*x^2+b^2)^(3/4)/x,x, algorithm=""giac"")","-\frac{3 \, b^{3} \arctan\left(\frac{{\left(a^{2} x^{2} + b^{2}\right)}^{\frac{1}{4}}}{\sqrt{-b}}\right)}{\sqrt{-b}} - 3 \, b^{\frac{5}{2}} \arctan\left(\frac{{\left(a^{2} x^{2} + b^{2}\right)}^{\frac{1}{4}}}{\sqrt{b}}\right) - \frac{2 \, {\left(7 \, {\left(a^{2} x^{2} + b^{2}\right)}^{\frac{3}{4}} a^{7} b - 2 \, {\left(a^{2} x^{2} + b^{2}\right)}^{\frac{7}{4}} a^{6}\right)}}{7 \, a^{7}}"," ",0,"-3*b^3*arctan((a^2*x^2 + b^2)^(1/4)/sqrt(-b))/sqrt(-b) - 3*b^(5/2)*arctan((a^2*x^2 + b^2)^(1/4)/sqrt(b)) - 2/7*(7*(a^2*x^2 + b^2)^(3/4)*a^7*b - 2*(a^2*x^2 + b^2)^(7/4)*a^6)/a^7","A",0
1370,0,0,0,0.000000," ","integrate((-1+x)/(x^2-2*x-2)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x^{3} - 1} {\left(x^{2} - 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x - 1)/(sqrt(x^3 - 1)*(x^2 - 2*x - 2)), x)","F",0
1371,0,0,0,0.000000," ","integrate((x^2-x+3)/(x^2-2*x-2)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - x + 3}{\sqrt{x^{3} - 1} {\left(x^{2} - 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x^2 - x + 3)/(sqrt(x^3 - 1)*(x^2 - 2*x - 2)), x)","F",0
1372,0,0,0,0.000000," ","integrate((x^2+2*x)/(x^2-2*x-2)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 2 \, x}{\sqrt{x^{3} - 1} {\left(x^{2} - 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x^2 + 2*x)/(sqrt(x^3 - 1)*(x^2 - 2*x - 2)), x)","F",0
1373,1,81,0,0.178688," ","integrate((x^3-1)^(1/3)*(x^3+1)/x^7,x, algorithm=""giac"")","\frac{4}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) - \frac{5 \, {\left(x^{3} - 1\right)}^{\frac{4}{3}} + 8 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{18 \, x^{6}} - \frac{2}{27} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{4}{27} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"4/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) - 1/18*(5*(x^3 - 1)^(4/3) + 8*(x^3 - 1)^(1/3))/x^6 - 2/27*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 4/27*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1374,1,81,0,0.176908," ","integrate((x^3-1)^(1/3)*(2*x^3-1)/x^7,x, algorithm=""giac"")","\frac{5}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) - \frac{13 \, {\left(x^{3} - 1\right)}^{\frac{4}{3}} + 10 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{18 \, x^{6}} - \frac{5}{54} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{5}{27} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"5/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) - 1/18*(13*(x^3 - 1)^(4/3) + 10*(x^3 - 1)^(1/3))/x^6 - 5/54*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 5/27*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1375,0,0,0,0.000000," ","integrate((a^2-2*a*x+x^2)*(-2*a*b*x+(3*a-b)*x^2)/(x^2*(-a+x)*(-b+x))^(3/4)/(a^3*d-3*a^2*d*x+(3*a*d-b)*x^2+(1-d)*x^3),x, algorithm=""giac"")","\int -\frac{{\left(2 \, a b x - {\left(3 \, a - b\right)} x^{2}\right)} {\left(a^{2} - 2 \, a x + x^{2}\right)}}{{\left(a^{3} d - 3 \, a^{2} d x - {\left(d - 1\right)} x^{3} + {\left(3 \, a d - b\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-(2*a*b*x - (3*a - b)*x^2)*(a^2 - 2*a*x + x^2)/((a^3*d - 3*a^2*d*x - (d - 1)*x^3 + (3*a*d - b)*x^2)*((a - x)*(b - x)*x^2)^(3/4)), x)","F",0
1376,0,0,0,0.000000," ","integrate((x^2+1)/((2*x^2-x-2)/(x^2+x-1))^(1/2)/(x^4-x^2+1),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{4} - x^{2} + 1\right)} \sqrt{\frac{2 \, x^{2} - x - 2}{x^{2} + x - 1}}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^4 - x^2 + 1)*sqrt((2*x^2 - x - 2)/(x^2 + x - 1))), x)","F",0
1377,0,0,0,0.000000," ","integrate((a*x^4-2*b)/x^4/(a*x^4+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((a*x^4 - b*x^2)^(1/4)*(a*x^4 + b)*x^4), x)","F",0
1378,0,0,0,0.000000," ","integrate((a*x^4-2*b)/x^4/(a*x^4+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((a*x^4 - b*x^2)^(1/4)*(a*x^4 + b)*x^4), x)","F",0
1379,1,243,0,0.192454," ","integrate((a*x^4+b*x^3)^(1/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{6 \, \sqrt{2} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{3 \, \sqrt{2} b^{3} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a^{2}} + \frac{8 \, {\left({\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} b^{3} + 3 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a b^{3}\right)} x^{2}}{a b^{2}}}{64 \, b}"," ",0,"1/64*(6*sqrt(2)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + 6*sqrt(2)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + 3*sqrt(2)*b^3*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a) + 3*sqrt(2)*(-a)^(1/4)*b^3*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^2 + 8*((a + b/x)^(5/4)*b^3 + 3*(a + b/x)^(1/4)*a*b^3)*x^2/(a*b^2))/b","B",0
1380,1,81,0,0.159879," ","integrate(1/x^13/(x^6-1)^(1/3),x, algorithm=""giac"")","\frac{1}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{4 \, {\left(x^{6} - 1\right)}^{\frac{5}{3}} + 7 \, {\left(x^{6} - 1\right)}^{\frac{2}{3}}}{36 \, x^{12}} + \frac{1}{54} \, \log\left({\left(x^{6} - 1\right)}^{\frac{2}{3}} - {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{27} \, \log\left({\left| {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 - 1)^(1/3) - 1)) + 1/36*(4*(x^6 - 1)^(5/3) + 7*(x^6 - 1)^(2/3))/x^12 + 1/54*log((x^6 - 1)^(2/3) - (x^6 - 1)^(1/3) + 1) - 1/27*log(abs((x^6 - 1)^(1/3) + 1))","A",0
1381,0,0,0,0.000000," ","integrate((2*a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} + b}{{\left(x^{8} - a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^4 + b)/((x^8 - a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
1382,0,0,0,0.000000," ","integrate((a*x^4+2*b)/(a*x^4+b*x^2)^(1/4)/(2*x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} + 2 \, b}{{\left(2 \, x^{8} - a x^{4} - b\right)} {\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 + 2*b)/((2*x^8 - a*x^4 - b)*(a*x^4 + b*x^2)^(1/4)), x)","F",0
1383,0,0,0,0.000000," ","integrate((a*x^4+2*b)/(a*x^4+b*x^2)^(1/4)/(2*x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} + 2 \, b}{{\left(2 \, x^{8} - a x^{4} - b\right)} {\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 + 2*b)/((2*x^8 - a*x^4 - b)*(a*x^4 + b*x^2)^(1/4)), x)","F",0
1384,0,0,0,0.000000," ","integrate((2*x^2-1)*(4*x^4-4*x^2+4*x-1)/((-2*x^2+1)/(2*x^2+1))^(1/2)/(2*x^2+1)/(8*x^8-32*x^7+56*x^6-64*x^5+46*x^4-40*x^3+32*x^2-8*x-1),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{4} - 4 \, x^{2} + 4 \, x - 1\right)} {\left(2 \, x^{2} - 1\right)}}{{\left(8 \, x^{8} - 32 \, x^{7} + 56 \, x^{6} - 64 \, x^{5} + 46 \, x^{4} - 40 \, x^{3} + 32 \, x^{2} - 8 \, x - 1\right)} {\left(2 \, x^{2} + 1\right)} \sqrt{-\frac{2 \, x^{2} - 1}{2 \, x^{2} + 1}}}\,{d x}"," ",0,"integrate((4*x^4 - 4*x^2 + 4*x - 1)*(2*x^2 - 1)/((8*x^8 - 32*x^7 + 56*x^6 - 64*x^5 + 46*x^4 - 40*x^3 + 32*x^2 - 8*x - 1)*(2*x^2 + 1)*sqrt(-(2*x^2 - 1)/(2*x^2 + 1))), x)","F",0
1385,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{x^{2} + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/(x^2 + sqrt(x + sqrt(x^2 + 1))), x)","F",0
1386,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{x^{2} + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/(x^2 + sqrt(x + sqrt(x^2 + 1))), x)","F",0
1387,0,0,0,0.000000," ","integrate((k*x^2+1)/(c*k*x+k*x^2-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{k x^{2} + 1}{{\left(c k x + k x^{2} - 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((k*x^2 + 1)/((c*k*x + k*x^2 - 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
1388,0,0,0,0.000000," ","integrate((k*x^2-1)/(c*k*x+k*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{k x^{2} - 1}{{\left(c k x + k x^{2} + 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((k*x^2 - 1)/((c*k*x + k*x^2 + 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
1389,1,77,0,0.323393," ","integrate(x^2*(x^3+x)^(1/3),x, algorithm=""giac"")","\frac{1}{12} \, {\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)} x^{4} - \frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{36} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{18} \, \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/12*((1/x^2 + 1)^(4/3) + 2*(1/x^2 + 1)^(1/3))*x^4 - 1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) - 1/36*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) + 1/18*log(abs((1/x^2 + 1)^(1/3) - 1))","A",0
1390,0,0,0,0.000000," ","integrate((x^2+2*x+6)/(x^2+2)^(1/3)/(x^3-2*x^2+3*x+1),x, algorithm=""giac"")","\int \frac{x^{2} + 2 \, x + 6}{{\left(x^{3} - 2 \, x^{2} + 3 \, x + 1\right)} {\left(x^{2} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^2 + 2*x + 6)/((x^3 - 2*x^2 + 3*x + 1)*(x^2 + 2)^(1/3)), x)","F",0
1391,1,63,0,0.316107," ","integrate((x^3+x^2)^(1/3)/x^2,x, algorithm=""giac"")","\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - 3 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + \frac{1}{2} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) - 3*(1/x + 1)^(1/3) + 1/2*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) - log(abs((1/x + 1)^(1/3) - 1))","A",0
1392,1,85,0,0.159111," ","integrate((x^4+1)^(1/3)*(x^4+3)/x^13,x, algorithm=""giac"")","-\frac{1}{54} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{{\left(x^{4} + 1\right)}^{\frac{7}{3}} - 8 \, {\left(x^{4} + 1\right)}^{\frac{4}{3}} - 2 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}}}{36 \, x^{12}} - \frac{1}{108} \, \log\left({\left(x^{4} + 1\right)}^{\frac{2}{3}} + {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{54} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-1/54*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 + 1)^(1/3) + 1)) + 1/36*((x^4 + 1)^(7/3) - 8*(x^4 + 1)^(4/3) - 2*(x^4 + 1)^(1/3))/x^12 - 1/108*log((x^4 + 1)^(2/3) + (x^4 + 1)^(1/3) + 1) + 1/54*log((x^4 + 1)^(1/3) - 1)","A",0
1393,0,0,0,0.000000," ","integrate((x^4-1)^(2/3)*(x^4+3)*(x^4+x^3-1)/x^6/(x^4-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} - 1\right)} {\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{2}{3}}}{{\left(x^{4} - x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^3 - 1)*(x^4 + 3)*(x^4 - 1)^(2/3)/((x^4 - x^3 - 1)*x^6), x)","F",0
1394,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(2/3)*(x^4+x^3+1)/x^6/(x^4-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{{\left(x^{4} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^3 + 1)*(x^4 + 1)^(2/3)*(x^4 - 3)/((x^4 - x^3 + 1)*x^6), x)","F",0
1395,-2,0,0,0.000000," ","integrate((a*x^2-b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 2.58Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1396,-2,0,0,0.000000," ","integrate((a*x^2-b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 2.61Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1397,0,0,0,0.000000," ","integrate((x^3-1)*(x^3+1)^(2/3)/x^3/(x^6-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 1\right)}}{{\left(x^{6} - x^{3} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*(x^3 - 1)/((x^6 - x^3 - 1)*x^3), x)","F",0
1398,0,0,0,0.000000," ","integrate((x^3-1)*(x^3+1)^(2/3)/x^3/(x^6-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 1\right)}}{{\left(x^{6} - x^{3} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*(x^3 - 1)/((x^6 - x^3 - 1)*x^3), x)","F",0
1399,0,0,0,0.000000," ","integrate((2*x^7+1)^(1/3)*(8*x^7-3)/x^2/(2*x^7+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(8 \, x^{7} - 3\right)} {\left(2 \, x^{7} + 1\right)}^{\frac{1}{3}}}{{\left(2 \, x^{7} + x^{3} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((8*x^7 - 3)*(2*x^7 + 1)^(1/3)/((2*x^7 + x^3 + 1)*x^2), x)","F",0
1400,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1401,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1402,0,0,0,0.000000," ","integrate((3*x^4-1)*(x^8+x^5+2*x^4+x+1)^(1/2)/x^2/(4*x^4+x+4),x, algorithm=""giac"")","\int \frac{\sqrt{x^{8} + x^{5} + 2 \, x^{4} + x + 1} {\left(3 \, x^{4} - 1\right)}}{{\left(4 \, x^{4} + x + 4\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^8 + x^5 + 2*x^4 + x + 1)*(3*x^4 - 1)/((4*x^4 + x + 4)*x^2), x)","F",0
1403,0,0,0,0.000000," ","integrate((a*x^8+c*x^4-b)/x^2/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\int \frac{a x^{8} + c x^{4} - b}{{\left(a x^{4} - b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a*x^8 + c*x^4 - b)/((a*x^4 - b)^(3/4)*x^2), x)","F",0
1404,0,0,0,0.000000," ","integrate(1/(1+x)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x + \sqrt{x^{2} + 1}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x + sqrt(x^2 + 1))*(x + 1)), x)","F",0
1405,0,0,0,0.000000," ","integrate(1/x/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}} x}\,{d x}"," ",0,"integrate(1/(sqrt(a*x + sqrt(a^2*x^2 + b^2))*x), x)","F",0
1406,1,92,0,0.179679," ","integrate((-3+x)^6*(x^2-x-1)^(3/2)/(-1+x),x, algorithm=""giac"")","\frac{1}{10321920} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, {\left(16 \, x - 325\right)} x + 38869\right)} x - 711617\right)} x + 18004133\right)} x - 168785303\right)} x - 63504203\right)} x + 2211602549\right)} x - 1245336401\right)} \sqrt{x^{2} - x - 1} + 128 \, \arctan\left(-x + \sqrt{x^{2} - x - 1} + 1\right) + \frac{19451047}{65536} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1 \right|}\right)"," ",0,"1/10321920*(2*(4*(2*(8*(10*(4*(14*(16*x - 325)*x + 38869)*x - 711617)*x + 18004133)*x - 168785303)*x - 63504203)*x + 2211602549)*x - 1245336401)*sqrt(x^2 - x - 1) + 128*arctan(-x + sqrt(x^2 - x - 1) + 1) + 19451047/65536*log(abs(-2*x + 2*sqrt(x^2 - x - 1) + 1))","A",0
1407,0,0,0,0.000000," ","integrate((x^3-1)*(x^3+1)^(1/3)/x^5,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}{x^{5}}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)*(x^3 - 1)/x^5, x)","F",0
1408,0,0,0,0.000000," ","integrate((x^3-1)*(x^3+1)^(1/3)/x^2,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}{x^{2}}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)*(x^3 - 1)/x^2, x)","F",0
1409,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)*(x^3+1)/x^5,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{5}}\,{d x}"," ",0,"integrate((x^3 + 1)*(x^3 - 1)^(1/3)/x^5, x)","F",0
1410,0,0,0,0.000000," ","integrate(x/(x^2+1)/(x^3-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} - x^{2} - x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^3 - x^2 - x)*(x^2 + 1)), x)","F",0
1411,0,0,0,0.000000," ","integrate((x^2+x-1)/(x^2+1)/(x^3-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + x - 1}{\sqrt{x^{3} - x^{2} - x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 + x - 1)/(sqrt(x^3 - x^2 - x)*(x^2 + 1)), x)","F",0
1412,1,64,0,0.234349," ","integrate(x/(x^3+x^2)^(1/3),x, algorithm=""giac"")","x {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{6} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"x*(1/x + 1)^(2/3) + 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) - 1/6*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) + 1/3*log(abs((1/x + 1)^(1/3) - 1))","A",0
1413,0,0,0,0.000000," ","integrate(1/x^6/(x^3+1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate(1/((x^3 + x^2)^(1/3)*(x^3 + 1)*x^6), x)","F",0
1414,0,0,0,0.000000," ","integrate(1/x^6/(x^3+1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate(1/((x^3 + x^2)^(1/3)*(x^3 + 1)*x^6), x)","F",0
1415,0,0,0,0.000000," ","integrate((x^3-1)^(1/3)*(2*x^3-1)/x^5,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{x^{5}}\,{d x}"," ",0,"integrate((2*x^3 - 1)*(x^3 - 1)^(1/3)/x^5, x)","F",0
1416,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(3*x^3-1)/x^6/(2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((3*x^3 - 1)*(x^3 - 1)^(2/3)/((2*x^3 - 1)*x^6), x)","F",0
1417,1,81,0,0.355276," ","integrate(x^4/(x^4-1)^2/(x^4+x^2)^(1/4),x, algorithm=""giac"")","\frac{1}{64} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{128} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{128} \cdot 2^{\frac{3}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right) + \frac{{\left(\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}}{16 \, {\left(\frac{1}{x^{2}} - 1\right)}} - \frac{1}{10 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}}}"," ",0,"1/64*2^(3/4)*arctan(1/2*2^(3/4)*(1/x^2 + 1)^(1/4)) - 1/128*2^(3/4)*log(2^(1/4) + (1/x^2 + 1)^(1/4)) + 1/128*2^(3/4)*log(abs(-2^(1/4) + (1/x^2 + 1)^(1/4))) + 1/16*(1/x^2 + 1)^(3/4)/(1/x^2 - 1) - 1/10/(1/x^2 + 1)^(5/4)","A",0
1418,1,97,0,0.256228," ","integrate((x^2+1)*(x^4+x^3)^(1/4)/x^2/(x^2-1),x, algorithm=""giac"")","-2 \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + 4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 2 \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-2*2^(1/4)*arctan(1/2*2^(3/4)*(1/x + 1)^(1/4)) - 2^(1/4)*log(2^(1/4) + (1/x + 1)^(1/4)) + 2^(1/4)*log(abs(-2^(1/4) + (1/x + 1)^(1/4))) + 4*(1/x + 1)^(1/4) + 2*arctan((1/x + 1)^(1/4)) + log((1/x + 1)^(1/4) + 1) - log(abs((1/x + 1)^(1/4) - 1))","A",0
1419,0,0,0,0.000000," ","integrate((x^3+4)*(x^4-x^3-1)/x^2/(x^3+1)^(3/4)/(x^4+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} - 1\right)} {\left(x^{3} + 4\right)}}{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((x^4 - x^3 - 1)*(x^3 + 4)/((x^4 + x^3 + 1)*(x^3 + 1)^(3/4)*x^2), x)","F",0
1420,0,0,0,0.000000," ","integrate((2*x^4+x^2+1)/(x^2+1)^(1/4)/(x^4+3*x^2+2),x, algorithm=""giac"")","\int \frac{2 \, x^{4} + x^{2} + 1}{{\left(x^{4} + 3 \, x^{2} + 2\right)} {\left(x^{2} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^4 + x^2 + 1)/((x^4 + 3*x^2 + 2)*(x^2 + 1)^(1/4)), x)","F",0
1421,1,229,0,0.196983," ","integrate((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/x^2,x, algorithm=""giac"")","\frac{8 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} a b x^{2} - 10 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - 10 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - 5 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right) + 5 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right) + 32 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} b^{2}}{16 \, b}"," ",0,"1/16*(8*(a - b/x^2)^(1/4)*a*b*x^2 - 10*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^2)^(1/4))/(-a)^(1/4)) - 10*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^2)^(1/4))/(-a)^(1/4)) - 5*sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2)) + 5*sqrt(2)*(-a)^(1/4)*b^2*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2)) + 32*(a - b/x^2)^(1/4)*b^2)/b","B",0
1422,0,0,0,0.000000," ","integrate((a*x^4+b)/x^4/(a*x^4+2*b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + 2 \, b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + 2*b)*x^4), x)","F",0
1423,0,0,0,0.000000," ","integrate((a*x^4+b)/x^4/(a*x^4+2*b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + 2 \, b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + 2*b)*x^4), x)","F",0
1424,0,0,0,0.000000," ","integrate((-x^4+1)/x^2/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{4} - 1}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} x^{2}}\,{d x}"," ",0,"integrate(-(x^4 - 1)/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*x^2), x)","F",0
1425,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^6 + x^2)^(1/4)*(x^2 + 1)), x)","F",0
1426,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^6 + x^2)^(1/4)*(x^2 + 1)), x)","F",0
1427,1,171,0,0.267847," ","integrate((x^4-x^3)^(1/4)*(x^8-1)/x^4,x, algorithm=""giac"")","\frac{1}{245760} \, {\left(7315 \, {\left(\frac{1}{x} - 1\right)}^{5} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 40755 \, {\left(\frac{1}{x} - 1\right)}^{4} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 92910 \, {\left(\frac{1}{x} - 1\right)}^{3} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 109782 \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 69327 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} - 21945 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{6} - \frac{4}{9} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \frac{4}{5} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} + \frac{1463}{32768} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1463}{65536} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1463}{65536} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/245760*(7315*(1/x - 1)^5*(-1/x + 1)^(1/4) + 40755*(1/x - 1)^4*(-1/x + 1)^(1/4) + 92910*(1/x - 1)^3*(-1/x + 1)^(1/4) + 109782*(1/x - 1)^2*(-1/x + 1)^(1/4) - 69327*(-1/x + 1)^(5/4) - 21945*(-1/x + 1)^(1/4))*x^6 - 4/9*(1/x - 1)^2*(-1/x + 1)^(1/4) + 4/5*(-1/x + 1)^(5/4) + 1463/32768*arctan((-1/x + 1)^(1/4)) + 1463/65536*log((-1/x + 1)^(1/4) + 1) - 1463/65536*log(abs((-1/x + 1)^(1/4) - 1))","A",0
1428,-2,0,0,0.000000," ","integrate((x^4+1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1429,-2,0,0,0.000000," ","integrate((x^4+1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1430,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(a x^{8} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((a*x^8 - b)*(a*x^4 - b)^(1/4)), x)","F",0
1431,0,0,0,0.000000," ","integrate((2*x^6+1)^(1/2)*(4*x^6-1)/(8*x^12+8*x^6+x^4+2),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{6} - 1\right)} \sqrt{2 \, x^{6} + 1}}{8 \, x^{12} + 8 \, x^{6} + x^{4} + 2}\,{d x}"," ",0,"integrate((4*x^6 - 1)*sqrt(2*x^6 + 1)/(8*x^12 + 8*x^6 + x^4 + 2), x)","F",0
1432,0,0,0,0.000000," ","integrate((x^2-1)*(1+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1433,0,0,0,0.000000," ","integrate((x^2-1)*(1+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1434,0,0,0,0.000000," ","integrate(x^2*(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{2} + \sqrt{x^{4} + 1}} x^{2}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*x^2, x)","F",0
1435,0,0,0,0.000000," ","integrate((x^4-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^4 - 1)*sqrt(x^2 + sqrt(x^4 + 1))/sqrt(x^4 + 1), x)","F",0
1436,0,0,0,0.000000," ","integrate((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 1} \sqrt{x^{2} + \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*sqrt(x^2 + sqrt(x^4 + 1)), x)","F",0
1437,0,0,0,0.000000," ","integrate(x^3*(x^3-1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{2}{3}} x^{3}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)*x^3, x)","F",0
1438,0,0,0,0.000000," ","integrate(x^4*(x^3+1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} + 1\right)}^{\frac{1}{3}} x^{4}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)*x^4, x)","F",0
1439,0,0,0,0.000000," ","integrate(x^3*(x^3+1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{3} + 1\right)}^{\frac{2}{3}} x^{3}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*x^3, x)","F",0
1440,0,0,0,0.000000," ","integrate((x^3-2)^(2/3)*(x^3+4)/x^6/(x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 4\right)} {\left(x^{3} - 2\right)}^{\frac{2}{3}}}{{\left(x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 4)*(x^3 - 2)^(2/3)/((x^3 - 1)*x^6), x)","F",0
1441,0,0,0,0.000000," ","integrate((a*x^2+3*b)/(a*x^2+x^3+b)/(a*x^3+b*x)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} + 3 \, b}{{\left(a x^{3} + b x\right)}^{\frac{1}{4}} {\left(a x^{2} + x^{3} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + 3*b)/((a*x^3 + b*x)^(1/4)*(a*x^2 + x^3 + b)), x)","F",0
1442,1,87,0,0.267397," ","integrate((x^4-3)*(x^4+1)^(1/3)/x^13,x, algorithm=""giac"")","\frac{2}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{4 \, {\left(x^{4} + 1\right)}^{\frac{7}{3}} - 5 \, {\left(x^{4} + 1\right)}^{\frac{4}{3}} - 8 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}}}{36 \, x^{12}} + \frac{1}{27} \, \log\left({\left(x^{4} + 1\right)}^{\frac{2}{3}} + {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{2}{27} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"2/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 + 1)^(1/3) + 1)) - 1/36*(4*(x^4 + 1)^(7/3) - 5*(x^4 + 1)^(4/3) - 8*(x^4 + 1)^(1/3))/x^12 + 1/27*log((x^4 + 1)^(2/3) + (x^4 + 1)^(1/3) + 1) - 2/27*log((x^4 + 1)^(1/3) - 1)","A",0
1443,0,0,0,0.000000," ","integrate((a*x^2-2*b)/(a*x^2-b)^(1/4)/(x^4+a*x^2-b),x, algorithm=""giac"")","\int \frac{a x^{2} - 2 \, b}{{\left(x^{4} + a x^{2} - b\right)} {\left(a x^{2} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^2 - 2*b)/((x^4 + a*x^2 - b)*(a*x^2 - b)^(1/4)), x)","F",0
1444,0,0,0,0.000000," ","integrate((a*x^3-4*b)/(a*x^3-b)^(1/4)/(a*x^3+x^4-b),x, algorithm=""giac"")","\int \frac{a x^{3} - 4 \, b}{{\left(a x^{3} + x^{4} - b\right)} {\left(a x^{3} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^3 - 4*b)/((a*x^3 + x^4 - b)*(a*x^3 - b)^(1/4)), x)","F",0
1445,-2,0,0,0.000000," ","integrate((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 2.58Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1446,-2,0,0,0.000000," ","integrate((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 2.59Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1447,0,0,0,0.000000," ","integrate((a*x^4+b)/x^4/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - 2*b)*x^4), x)","F",0
1448,0,0,0,0.000000," ","integrate((a*x^4+b)/x^4/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - 2*b)*x^4), x)","F",0
1449,0,0,0,0.000000," ","integrate((x^3-1)*(x^3+1)^3*(x^6+1)^(2/3)/x^6/(x^6-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)}^{\frac{2}{3}} {\left(x^{3} + 1\right)}^{3} {\left(x^{3} - 1\right)}}{{\left(x^{6} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 1)^(2/3)*(x^3 + 1)^3*(x^3 - 1)/((x^6 - x^3 + 1)*x^6), x)","F",0
1450,0,0,0,0.000000," ","integrate((x^6-1)^(2/3)*(x^6+1)*(2*x^6+x^3-2)/x^6/(x^6-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{3} - 2\right)} {\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 + x^3 - 2)*(x^6 + 1)*(x^6 - 1)^(2/3)/((x^6 - x^3 - 1)*x^6), x)","F",0
1451,0,0,0,0.000000," ","integrate(1/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1452,0,0,0,0.000000," ","integrate(1/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1453,-2,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4-b*x^2)^(1/4)/(2*x^8+2*a*x^4-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.76Unable to divide, perhaps due to rounding 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/ %%%{-134217728,[0,17,10,9]%%%}+%%%{402653184,[0,16,11,9]%%%}+%%%{65536,[0,16,10,5]%%%}+%%%{-536870912,[0,15,12,9]%%%}+%%%{-805306368,[0,15,11,9]%%%}+%%%{-163840,[0,15,11,5]%%%}+%%%{-8,[0,15,10,1]%%%}+%%%{536870912,[0,14,13,9]%%%}+%%%{2415919104,[0,14,12,9]%%%}+%%%{65536,[0,14,12,5]%%%}+%%%{393216,[0,14,11,5]%%%}+%%%{24,[0,14,11,1]%%%}+%%%{-3221225472,[0,13,13,9]%%%}+%%%{-1610612736,[0,13,12,9]%%%}+%%%{-1048576,[0,13,12,5]%%%}+%%%{-16,[0,13,12,1]%%%}+%%%{-48,[0,13,11,1]%%%}+%%%{4294967296,[0,12,14,9]%%%}+%%%{4831838208,[0,12,13,9]%%%}+%%%{327680,[0,12,13,5]%%%}+%%%{786432,[0,12,12,5]%%%}+%%%{160,[0,12,12,1]%%%}+%%%{-5905580032,[0,11,14,9]%%%}+%%%{-1073741824,[0,11,13,9]%%%}+%%%{-2359296,[0,11,13,5]%%%}+%%%{-112,[0,11,13,1]%%%}+%%%{-96,[0,11,12,1]%%%}+%%%{13421772800,[0,10,15,9]%%%}+%%%{3221225472,[0,10,14,9]%%%}+%%%{262144,[0,10,14,5]%%%}+%%%{524288,[0,10,13,5]%%%}+%%%{384,[0,10,13,1]%%%}+%%%{-1073741824,[0,9,15,9]%%%}+%%%{-2097152,[0,9,14,5]%%%}+%%%{-288,[0,9,14,1]%%%}+%%%{-64,[0,9,13,1]%%%}+%%%{20401094656,[0,8,16,9]%%%}+%%%{-1048576,[0,8,15,5]%%%}+%%%{384,[0,8,14,1]%%%}+%%%{6442450944,[0,7,16,9]%%%}+%%%{-524288,[0,7,15,5]%%%}+%%%{-320,[0,7,15,1]%%%}+%%%{15032385536,[0,6,17,9]%%%}+%%%{-2097152,[0,6,16,5]%%%}+%%%{128,[0,6,15,1]%%%}+%%%{4294967296,[0,5,17,9]%%%}+%%%{-128,[0,5,16,1]%%%}+%%%{4294967296,[0,4,18,9]%%%}+%%%{-1048576,[0,4,17,5]%%%} Error: Bad Argument Value","F(-2)",0
1454,-2,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4-b*x^2)^(1/4)/(2*x^8+2*a*x^4-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.84Unable to divide, perhaps due to rounding 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/ %%%{-134217728,[0,17,10,9]%%%}+%%%{402653184,[0,16,11,9]%%%}+%%%{65536,[0,16,10,5]%%%}+%%%{-536870912,[0,15,12,9]%%%}+%%%{-805306368,[0,15,11,9]%%%}+%%%{-163840,[0,15,11,5]%%%}+%%%{-8,[0,15,10,1]%%%}+%%%{536870912,[0,14,13,9]%%%}+%%%{2415919104,[0,14,12,9]%%%}+%%%{65536,[0,14,12,5]%%%}+%%%{393216,[0,14,11,5]%%%}+%%%{24,[0,14,11,1]%%%}+%%%{-3221225472,[0,13,13,9]%%%}+%%%{-1610612736,[0,13,12,9]%%%}+%%%{-1048576,[0,13,12,5]%%%}+%%%{-16,[0,13,12,1]%%%}+%%%{-48,[0,13,11,1]%%%}+%%%{4294967296,[0,12,14,9]%%%}+%%%{4831838208,[0,12,13,9]%%%}+%%%{327680,[0,12,13,5]%%%}+%%%{786432,[0,12,12,5]%%%}+%%%{160,[0,12,12,1]%%%}+%%%{-5905580032,[0,11,14,9]%%%}+%%%{-1073741824,[0,11,13,9]%%%}+%%%{-2359296,[0,11,13,5]%%%}+%%%{-112,[0,11,13,1]%%%}+%%%{-96,[0,11,12,1]%%%}+%%%{13421772800,[0,10,15,9]%%%}+%%%{3221225472,[0,10,14,9]%%%}+%%%{262144,[0,10,14,5]%%%}+%%%{524288,[0,10,13,5]%%%}+%%%{384,[0,10,13,1]%%%}+%%%{-1073741824,[0,9,15,9]%%%}+%%%{-2097152,[0,9,14,5]%%%}+%%%{-288,[0,9,14,1]%%%}+%%%{-64,[0,9,13,1]%%%}+%%%{20401094656,[0,8,16,9]%%%}+%%%{-1048576,[0,8,15,5]%%%}+%%%{384,[0,8,14,1]%%%}+%%%{6442450944,[0,7,16,9]%%%}+%%%{-524288,[0,7,15,5]%%%}+%%%{-320,[0,7,15,1]%%%}+%%%{15032385536,[0,6,17,9]%%%}+%%%{-2097152,[0,6,16,5]%%%}+%%%{128,[0,6,15,1]%%%}+%%%{4294967296,[0,5,17,9]%%%}+%%%{-128,[0,5,16,1]%%%}+%%%{4294967296,[0,4,18,9]%%%}+%%%{-1048576,[0,4,17,5]%%%} Error: Bad Argument Value","F(-2)",0
1455,0,0,0,0.000000," ","integrate((c*x^2-x*(a*x^2-b*x)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} - \sqrt{a x^{2} - b x} x}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 - sqrt(a*x^2 - b*x)*x)/x^3, x)","F",0
1456,0,0,0,0.000000," ","integrate(x/(x+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(x/(x + sqrt(x + sqrt(x^2 + 1))), x)","F",0
1457,0,0,0,0.000000," ","integrate(x/(x+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(x/(x + sqrt(x + sqrt(x^2 + 1))), x)","F",0
1458,0,0,0,0.000000," ","integrate((1+x)/(x^2+2*x-2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{3} + 1} {\left(x^{2} + 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^3 + 1)*(x^2 + 2*x - 2)), x)","F",0
1459,0,0,0,0.000000," ","integrate((x^2+x+3)/(x^2+2*x-2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + x + 3}{\sqrt{x^{3} + 1} {\left(x^{2} + 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x^2 + x + 3)/(sqrt(x^3 + 1)*(x^2 + 2*x - 2)), x)","F",0
1460,0,0,0,0.000000," ","integrate((2*x^2-x+3)/(x^2+2*x-2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x^{2} - x + 3}{\sqrt{x^{3} + 1} {\left(x^{2} + 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((2*x^2 - x + 3)/(sqrt(x^3 + 1)*(x^2 + 2*x - 2)), x)","F",0
1461,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+1)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)*(x^3 - 1)^(2/3)/x^3, x)","F",0
1462,0,0,0,0.000000," ","integrate(x^8*(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int {\left(a x^{4} + b\right)}^{\frac{3}{4}} x^{8}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)*x^8, x)","F",0
1463,1,203,0,0.418543," ","integrate(1/(a*x^3-b)/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","-\frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a b} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a b} - \frac{2^{\frac{1}{4}} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, \left(-a\right)^{\frac{1}{4}} b} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a b}"," ",0,"-1/3*2^(1/4)*(-a)^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(a*b) - 1/3*2^(1/4)*(-a)^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(a*b) - 1/6*2^(1/4)*log(2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/((-a)^(1/4)*b) - 1/6*2^(1/4)*(-a)^(3/4)*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/(a*b)","B",0
1464,0,0,0,0.000000," ","integrate((x^3-2)*(x^3+1)^(2/3)/x^3/(2*x^6+x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)}}{{\left(2 \, x^{6} + x^{3} - 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*(x^3 - 2)/((2*x^6 + x^3 - 2)*x^3), x)","F",0
1465,0,0,0,0.000000," ","integrate((x^3-2)*(x^3+1)^(2/3)/x^3/(2*x^6+x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)}}{{\left(2 \, x^{6} + x^{3} - 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*(x^3 - 2)/((2*x^6 + x^3 - 2)*x^3), x)","F",0
1466,-2,0,0,0.000000," ","integrate(x^2*(x^4-2)/(x^5-x)^(1/3)/(x^8+x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1467,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(x^{8} - a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((x^8 - a*x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
1468,0,0,0,0.000000," ","integrate((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x, algorithm=""giac"")","\int \frac{a x^{4} - 2 \, b}{{\left(x^{8} + a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - 2*b)/((x^8 + a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
1469,0,0,0,0.000000," ","integrate(1/x^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a*x + sqrt(a^2*x^2 + b^2))*x^2), x)","F",0
1470,1,90,0,0.239146," ","integrate((x^3-1)^(1/3)/x^10,x, algorithm=""giac"")","\frac{5}{243} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{5 \, {\left(x^{3} - 1\right)}^{\frac{7}{3}} + 13 \, {\left(x^{3} - 1\right)}^{\frac{4}{3}} - 10 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{162 \, x^{9}} - \frac{5}{486} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{5}{243} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"5/243*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) + 1/162*(5*(x^3 - 1)^(7/3) + 13*(x^3 - 1)^(4/3) - 10*(x^3 - 1)^(1/3))/x^9 - 5/486*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 5/243*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1471,0,0,0,0.000000," ","integrate(x^4*(x^3-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{1}{3}} x^{4}\,{d x}"," ",0,"integrate((x^3 - 1)^(1/3)*x^4, x)","F",0
1472,1,77,0,0.343562," ","integrate((x^3-x)^(1/3),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{12} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/2*x^2*(-1/x^2 + 1)^(1/3) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) - 1/12*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) + 1/6*log(abs((-1/x^2 + 1)^(1/3) - 1))","A",0
1473,1,90,0,0.176008," ","integrate((x^3-1)^(1/3)*(2*x^3-1)/x^10,x, algorithm=""giac"")","\frac{13}{243} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{13 \, {\left(x^{3} - 1\right)}^{\frac{7}{3}} - 31 \, {\left(x^{3} - 1\right)}^{\frac{4}{3}} - 26 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{162 \, x^{9}} - \frac{13}{486} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{13}{243} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"13/243*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) + 1/162*(13*(x^3 - 1)^(7/3) - 31*(x^3 - 1)^(4/3) - 26*(x^3 - 1)^(1/3))/x^9 - 13/486*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 13/243*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1474,0,0,0,0.000000," ","integrate((k^3*x^3+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^3*x^3-1),x, algorithm=""giac"")","\int \frac{k^{3} x^{3} + 1}{{\left(k^{3} x^{3} - 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^3*x^3 + 1)/((k^3*x^3 - 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
1475,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(2/3)*(x^4+2*x^3+1)/x^6/(x^4-x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 2 \, x^{3} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{{\left(x^{4} - x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + 2*x^3 + 1)*(x^4 + 1)^(2/3)*(x^4 - 3)/((x^4 - x^3 + 1)*x^6), x)","F",0
1476,0,0,0,0.000000," ","integrate((a*x^4+b)^(3/4)/x^4/(a*x^4+2*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b\right)}^{\frac{3}{4}}}{{\left(a x^{4} + 2 \, b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)/((a*x^4 + 2*b)*x^4), x)","F",0
1477,1,192,0,0.213755," ","integrate((a*x^3-b)/x^3/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) - \frac{4}{9} \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) - 4/9*(a - b/x^3)^(3/4)","B",0
1478,1,192,0,0.300771," ","integrate((a*x^3+b)/x^3/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) + \frac{4}{9} \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) + 4/9*(a - b/x^3)^(3/4)","B",0
1479,1,192,0,0.321404," ","integrate((a*x^4-b*x)^(1/4)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) - \frac{4}{3} \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}"," ",0,"1/3*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) + 1/6*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) - 1/6*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) - 4/3*(a - b/x^3)^(1/4)","B",0
1480,-2,0,0,0.000000," ","integrate(1/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[83,-68]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-17,52]Evaluation time: 2.69Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1481,-2,0,0,0.000000," ","integrate(1/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[83,-68]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-17,52]Evaluation time: 2.62Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1482,0,0,0,0.000000," ","integrate((a*x^4-b)/x^4/(2*a*x^4-b)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} - b}{{\left(2 \, a x^{4} - b\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - b)/((2*a*x^4 - b)^(1/4)*x^4), x)","F",0
1483,0,0,0,0.000000," ","integrate(x^4*(a*x^5+4*b)/(a*x^5-b)^2/(a*x^5+c*x^4-b)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} + 4 \, b\right)} x^{4}}{{\left(a x^{5} + c x^{4} - b\right)}^{\frac{1}{4}} {\left(a x^{5} - b\right)}^{2}}\,{d x}"," ",0,"integrate((a*x^5 + 4*b)*x^4/((a*x^5 + c*x^4 - b)^(1/4)*(a*x^5 - b)^2), x)","F",0
1484,1,90,0,0.347715," ","integrate(1/x^19/(x^6-1)^(1/3),x, algorithm=""giac"")","\frac{7}{243} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{6} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{28 \, {\left(x^{6} - 1\right)}^{\frac{8}{3}} + 77 \, {\left(x^{6} - 1\right)}^{\frac{5}{3}} + 67 \, {\left(x^{6} - 1\right)}^{\frac{2}{3}}}{324 \, x^{18}} + \frac{7}{486} \, \log\left({\left(x^{6} - 1\right)}^{\frac{2}{3}} - {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{7}{243} \, \log\left({\left| {\left(x^{6} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"7/243*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^6 - 1)^(1/3) - 1)) + 1/324*(28*(x^6 - 1)^(8/3) + 77*(x^6 - 1)^(5/3) + 67*(x^6 - 1)^(2/3))/x^18 + 7/486*log((x^6 - 1)^(2/3) - (x^6 - 1)^(1/3) + 1) - 7/243*log(abs((x^6 - 1)^(1/3) + 1))","A",0
1485,0,0,0,0.000000," ","integrate(x^7/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(x^{6} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^7/(x^6 - 1)^(1/3), x)","F",0
1486,0,0,0,0.000000," ","integrate(x^3*(x^6-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{6} - 1\right)}^{\frac{1}{3}} x^{3}\,{d x}"," ",0,"integrate((x^6 - 1)^(1/3)*x^3, x)","F",0
1487,0,0,0,0.000000," ","integrate(x*(x^6-1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{6} - 1\right)}^{\frac{2}{3}} x\,{d x}"," ",0,"integrate((x^6 - 1)^(2/3)*x, x)","F",0
1488,0,0,0,0.000000," ","integrate(x^7/(x^6+1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(x^{6} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^7/(x^6 + 1)^(1/3), x)","F",0
1489,0,0,0,0.000000," ","integrate(x^3*(x^6+1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{6} + 1\right)}^{\frac{1}{3}} x^{3}\,{d x}"," ",0,"integrate((x^6 + 1)^(1/3)*x^3, x)","F",0
1490,0,0,0,0.000000," ","integrate(x*(x^6+1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{6} + 1\right)}^{\frac{2}{3}} x\,{d x}"," ",0,"integrate((x^6 + 1)^(2/3)*x, x)","F",0
1491,0,0,0,0.000000," ","integrate((x^5-x^3+1)*(2*x^5-3)/x^3/(x^5+x^3+1)/(x^6+x)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 3\right)} {\left(x^{5} - x^{3} + 1\right)}}{{\left(x^{6} + x\right)}^{\frac{1}{4}} {\left(x^{5} + x^{3} + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((2*x^5 - 3)*(x^5 - x^3 + 1)/((x^6 + x)^(1/4)*(x^5 + x^3 + 1)*x^3), x)","F",0
1492,1,63,0,0.174157," ","integrate(x/(x^6-x^2)^(1/3),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{4}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{8} \, \log\left({\left(-\frac{1}{x^{4}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{4}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{4} \, \log\left({\left| {\left(-\frac{1}{x^{4}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^4 + 1)^(1/3) + 1)) + 1/8*log((-1/x^4 + 1)^(2/3) + (-1/x^4 + 1)^(1/3) + 1) - 1/4*log(abs((-1/x^4 + 1)^(1/3) - 1))","A",0
1493,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^3/(x^6+x^3-4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + x^{3} - 4\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 + x^3 - 4)*x^3), x)","F",0
1494,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^3/(x^6+x^3-4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + x^{3} - 4\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 + x^3 - 4)*x^3), x)","F",0
1495,0,0,0,0.000000," ","integrate((-3+2*x)*(x^3-x+1)^(2/3)/(2*x^6-2*x^4+2*x^3+x^2-2*x+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x + 1\right)}^{\frac{2}{3}} {\left(2 \, x - 3\right)}}{2 \, x^{6} - 2 \, x^{4} + 2 \, x^{3} + x^{2} - 2 \, x + 1}\,{d x}"," ",0,"integrate((x^3 - x + 1)^(2/3)*(2*x - 3)/(2*x^6 - 2*x^4 + 2*x^3 + x^2 - 2*x + 1), x)","F",0
1496,0,0,0,0.000000," ","integrate((x^6-2)*(x^6+4)*(x^6+2*x^4-2)^(1/4)/x^6/(2*x^6-x^4-4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2 \, x^{4} - 2\right)}^{\frac{1}{4}} {\left(x^{6} + 4\right)} {\left(x^{6} - 2\right)}}{{\left(2 \, x^{6} - x^{4} - 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 2*x^4 - 2)^(1/4)*(x^6 + 4)*(x^6 - 2)/((2*x^6 - x^4 - 4)*x^6), x)","F",0
1497,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(3*x^6-1)/x^9/(2*x^3+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{6} - 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{3} + 1\right)} x^{9}}\,{d x}"," ",0,"integrate((3*x^6 - 1)*(x^3 + 1)^(2/3)/((2*x^3 + 1)*x^9), x)","F",0
1498,0,0,0,0.000000," ","integrate((-x^4+1)^(1/2)*(x^4+1)/(x^8-x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)} \sqrt{-x^{4} + 1}}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)*sqrt(-x^4 + 1)/(x^8 - x^4 + 1), x)","F",0
1499,0,0,0,0.000000," ","integrate(x^2/(a*x^4+b)^(3/4)/(a^2*x^8-b^2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a^{2} x^{8} - b^{2}\right)} {\left(a x^{4} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((a^2*x^8 - b^2)*(a*x^4 + b)^(3/4)), x)","F",0
1500,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))^(1/2)/(x+(x^2+1)^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x^{2} + 1} + 1}}{x + \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 1) + 1)/(x + sqrt(x^2 + 1)), x)","F",0
1501,0,0,0,0.000000," ","integrate((2+x)^2/x/(x^2-2*x+4)/(x^2+x+1)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(x + 2\right)}^{2}}{{\left(x^{2} + x + 1\right)}^{\frac{1}{3}} {\left(x^{2} - 2 \, x + 4\right)} x}\,{d x}"," ",0,"integrate((x + 2)^2/((x^2 + x + 1)^(1/3)*(x^2 - 2*x + 4)*x), x)","F",0
1502,0,0,0,0.000000," ","integrate(1/(a*x^2-2*b)/(a*x^2-b)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{2} - b\right)}^{\frac{1}{4}} {\left(a x^{2} - 2 \, b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^2 - b)^(1/4)*(a*x^2 - 2*b)), x)","F",0
1503,0,0,0,0.000000," ","integrate((-1+x)/x^7/(x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} + 1\right)}^{\frac{1}{3}} x^{7}}\,{d x}"," ",0,"integrate((x - 1)/((x^3 + 1)^(1/3)*x^7), x)","F",0
1504,0,0,0,0.000000," ","integrate((a*x^2+2*b*x+3*c)/(a*x^2+b*x+c)^(1/3)/(a*x^2+x^3+b*x+c),x, algorithm=""giac"")","\int \frac{a x^{2} + 2 \, b x + 3 \, c}{{\left(a x^{2} + x^{3} + b x + c\right)} {\left(a x^{2} + b x + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x^2 + 2*b*x + 3*c)/((a*x^2 + x^3 + b*x + c)*(a*x^2 + b*x + c)^(1/3)), x)","F",0
1505,0,0,0,0.000000," ","integrate((a*x^2-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)), x)","F",0
1506,0,0,0,0.000000," ","integrate((a*x^2-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)), x)","F",0
1507,0,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}{{\left(a x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b*x^2)^(1/4)/((a*x^4 + b)*x^4), x)","F",0
1508,0,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}{{\left(a x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b*x^2)^(1/4)/((a*x^4 + b)*x^4), x)","F",0
1509,0,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}{{\left(a x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b*x^2)^(1/4)/((a*x^4 + b)*x^4), x)","F",0
1510,0,0,0,0.000000," ","integrate(x*(5*x^2+3)/(x^2+1)^(1/3)/(x^5+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 3\right)} x}{{\left(x^{5} + x^{3} - 1\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((5*x^2 + 3)*x/((x^5 + x^3 - 1)*(x^2 + 1)^(1/3)), x)","F",0
1511,0,0,0,0.000000," ","integrate((x^5-1)^(2/3)*(2*x^5+3)*(2*x^5+x^3-2)/x^6/(x^5+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} + x^{3} - 2\right)} {\left(2 \, x^{5} + 3\right)} {\left(x^{5} - 1\right)}^{\frac{2}{3}}}{{\left(x^{5} + x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^5 + x^3 - 2)*(2*x^5 + 3)*(x^5 - 1)^(2/3)/((x^5 + x^3 - 1)*x^6), x)","F",0
1512,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^6+x^3-2)/x^9,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} - 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((x^6 + x^3 - 2)*(x^3 + 1)^(2/3)/x^9, x)","F",0
1513,0,0,0,0.000000," ","integrate((x^6-1)^(2/3)*(x^6+1)*(x^6-x^3-1)/x^6/(x^6+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{3} - 1\right)} {\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^3 - 1)*(x^6 + 1)*(x^6 - 1)^(2/3)/((x^6 + x^3 - 1)*x^6), x)","F",0
1514,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+2*x^3-2)/x^9,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2 \, x^{3} - 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((x^6 + 2*x^3 - 2)*(x^3 - 1)^(2/3)/x^9, x)","F",0
1515,0,0,0,0.000000," ","integrate((x^4-2)/(x^4+1)^(1/4)/(x^8+x^4-2),x, algorithm=""giac"")","\int \frac{x^{4} - 2}{{\left(x^{8} + x^{4} - 2\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 - 2)/((x^8 + x^4 - 2)*(x^4 + 1)^(1/4)), x)","F",0
1516,1,396,0,0.350954," ","integrate((x^4-1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4+2),x, algorithm=""giac"")","\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(i \, \left(37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} - \frac{\left(12369505812480 i - 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} - \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(i \, \left(37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} + \frac{\left(12369505812480 i - 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} + \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(-i \, \left(-37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} + \frac{\left(12369505812480 i + 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} - \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(-i \, \left(-37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} - \frac{\left(12369505812480 i + 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} + \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(-i \, \left(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} + \frac{\left(4427218577690292387840 i + 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}} - \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(-i \, \left(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} - \frac{\left(4427218577690292387840 i + 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}} - \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(i \, \left(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} - \frac{\left(4427218577690292387840 i - 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}} + \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(i \, \left(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} + \frac{\left(4427218577690292387840 i - 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}}"," ",0,"(x^4 - 1)^(1/4)/x + 1/32768*(8*I + 8)^(33/4)*(I + 2)^(1/4)*log(I*(37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) - (12369505812480*I - 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 - 1/32768*(8*I + 8)^(33/4)*(I + 2)^(1/4)*log(I*(37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) + (12369505812480*I - 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 + 1/32768*(8*I + 8)^(33/4)*(2*I + 1)^(1/4)*log(-I*(-37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) + (12369505812480*I + 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 - 1/32768*(8*I + 8)^(33/4)*(2*I + 1)^(1/4)*log(-I*(-37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) - (12369505812480*I + 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 + 1/134217728*I*(8*I + 8)^(65/4)*(I + 2)^(1/4)*log(-I*(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) + (4427218577690292387840*I + 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33 - 1/134217728*I*(8*I + 8)^(65/4)*(I + 2)^(1/4)*log(-I*(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) - (4427218577690292387840*I + 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33 - 1/134217728*I*(8*I + 8)^(65/4)*(2*I + 1)^(1/4)*log(I*(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) - (4427218577690292387840*I - 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33 + 1/134217728*I*(8*I + 8)^(65/4)*(2*I + 1)^(1/4)*log(I*(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) + (4427218577690292387840*I - 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33","B",0
1517,1,396,0,0.500835," ","integrate((x^4-1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4+2),x, algorithm=""giac"")","\frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(i \, \left(37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} - \frac{\left(12369505812480 i - 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} - \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(i \, \left(37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} + \frac{\left(12369505812480 i - 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} + \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(-i \, \left(-37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} + \frac{\left(12369505812480 i + 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} - \frac{\left(8 i + 8\right)^{\frac{33}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(-i \, \left(-37572295510484393868859378145757959465275804876800000 i + 26011589199566118832287261793217048860575557222400000\right)^{\frac{1}{4}} - \frac{\left(12369505812480 i + 4123168604160\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{32768 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{17}} + \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(-i \, \left(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} + \frac{\left(4427218577690292387840 i + 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}} - \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(i + 2\right)^{\frac{1}{4}} \log\left(-i \, \left(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} - \frac{\left(4427218577690292387840 i + 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}} - \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(i \, \left(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} - \frac{\left(4427218577690292387840 i - 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}} + \frac{i \, \left(8 i + 8\right)^{\frac{65}{4}} \left(2 i + 1\right)^{\frac{1}{4}} \log\left(i \, \left(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000 i + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000\right)^{\frac{1}{4}} + \frac{\left(4427218577690292387840 i - 13281655733070877163520\right) \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}{134217728 \, {\left(\sqrt{\sqrt{2} + 2} + i \, \sqrt{-\sqrt{2} + 2}\right)}^{33}}"," ",0,"(x^4 - 1)^(1/4)/x + 1/32768*(8*I + 8)^(33/4)*(I + 2)^(1/4)*log(I*(37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) - (12369505812480*I - 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 - 1/32768*(8*I + 8)^(33/4)*(I + 2)^(1/4)*log(I*(37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) + (12369505812480*I - 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 + 1/32768*(8*I + 8)^(33/4)*(2*I + 1)^(1/4)*log(-I*(-37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) + (12369505812480*I + 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 - 1/32768*(8*I + 8)^(33/4)*(2*I + 1)^(1/4)*log(-I*(-37572295510484393868859378145757959465275804876800000*I + 26011589199566118832287261793217048860575557222400000)^(1/4) - (12369505812480*I + 4123168604160)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^17 + 1/134217728*I*(8*I + 8)^(65/4)*(I + 2)^(1/4)*log(-I*(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) + (4427218577690292387840*I + 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33 - 1/134217728*I*(8*I + 8)^(65/4)*(I + 2)^(1/4)*log(-I*(49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) - (4427218577690292387840*I + 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33 - 1/134217728*I*(8*I + 8)^(65/4)*(2*I + 1)^(1/4)*log(I*(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) - (4427218577690292387840*I - 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33 + 1/134217728*I*(8*I + 8)^(65/4)*(2*I + 1)^(1/4)*log(I*(-49942147058439763468705893258915171110704453162155832907181603209352202449245228236800000*I + 34575332578919836247565618410018195384333852189184807397279571452628447849477465702400000)^(1/4) + (4427218577690292387840*I - 13281655733070877163520)*(x^4 - 1)^(1/4)/x)/(sqrt(sqrt(2) + 2) + I*sqrt(-sqrt(2) + 2))^33","B",0
1518,0,0,0,0.000000," ","integrate((x^8-2*a*x^4-2*b)/x^4/(a*x^4+b)^(1/4),x, algorithm=""giac"")","\int \frac{x^{8} - 2 \, a x^{4} - 2 \, b}{{\left(a x^{4} + b\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^8 - 2*a*x^4 - 2*b)/((a*x^4 + b)^(1/4)*x^4), x)","F",0
1519,0,0,0,0.000000," ","integrate((2*x^8-2*x^4+1)/(x^4+1)^(1/4)/(x^8-x^4-2),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - 2 \, x^{4} + 1}{{\left(x^{8} - x^{4} - 2\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - 2*x^4 + 1)/((x^8 - x^4 - 2)*(x^4 + 1)^(1/4)), x)","F",0
1520,0,0,0,0.000000," ","integrate((x^8+x^3+1)^(2/3)*(5*x^8-3)/x^3/(x^8+1),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{8} - 3\right)} {\left(x^{8} + x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{8} + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((5*x^8 - 3)*(x^8 + x^3 + 1)^(2/3)/((x^8 + 1)*x^3), x)","F",0
1521,0,0,0,0.000000," ","integrate((2*a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\int \frac{2 \, a x^{8} - b}{{\left(a x^{8} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^8 - b)/((a*x^8 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1522,0,0,0,0.000000," ","integrate((x^6-x^2-1)^(1/2)*(2*x^6+1)/(8*x^12-16*x^6-x^4+8),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + 1\right)} \sqrt{x^{6} - x^{2} - 1}}{8 \, x^{12} - 16 \, x^{6} - x^{4} + 8}\,{d x}"," ",0,"integrate((2*x^6 + 1)*sqrt(x^6 - x^2 - 1)/(8*x^12 - 16*x^6 - x^4 + 8), x)","F",0
1523,0,0,0,0.000000," ","integrate(1/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(1/((x^2 + 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
1524,0,0,0,0.000000," ","integrate((x-(x^2+1)^(1/2))^(1/2)/(x^2+(x^2+1)^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x - \sqrt{x^{2} + 1}}}{x^{2} + \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(x - sqrt(x^2 + 1))/(x^2 + sqrt(x^2 + 1)), x)","F",0
1525,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/x^2, x)","F",0
1526,-2,0,0,0.000000," ","integrate((-1+x)/(1+x)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1]%%%}+%%%{-4,[0]%%%},%%%{-4,[1]%%%}+%%%{-4,[0]%%%},%%%{1,[2]%%%}+%%%{-1,[1]%%%}+%%%{-1,[0]%%%}] at parameters values [-23]Warning, choosing root of [1,0,%%%{-2,[1]%%%}+%%%{-4,[0]%%%},%%%{-4,[1]%%%}+%%%{-4,[0]%%%},%%%{1,[2]%%%}+%%%{-1,[1]%%%}+%%%{-1,[0]%%%}] at parameters values [65]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [x]=[95]8/7*sqrt(sqrt(sqrt(x+1)+1)+1)*(sqrt(sqrt(x+1)+1)+1)^3-24/5*sqrt(sqrt(sqrt(x+1)+1)+1)*(sqrt(sqrt(x+1)+1)+1)^2+16/3*sqrt(sqrt(sqrt(x+1)+1)+1)*(sqrt(sqrt(x+1)+1)+1)+8/sqrt(sqrt(sqrt(x+1)+1)+1)-4/sqrt(2)*ln(abs(2*sqrt(sqrt(sqrt(x+1)+1)+1)-2*sqrt(2))/(2*sqrt(sqrt(sqrt(x+1)+1)+1)+2*sqrt(2)))","F(-2)",0
1527,0,0,0,0.000000," ","integrate(1/(-2+x)/(x^2+2*x+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 2 \, x + 1\right)}^{\frac{1}{3}} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + 2*x + 1)^(1/3)*(x - 2)), x)","F",0
1528,1,74,0,0.190638," ","integrate((x^3-x)^(1/3)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{3}{2} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + \frac{1}{4} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{2} \, \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) - 3/2*(-1/x^2 + 1)^(1/3) + 1/4*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) - 1/2*log(abs((-1/x^2 + 1)^(1/3) - 1))","A",0
1529,1,74,0,0.144000," ","integrate((x^3-x^2)^(1/3)/x,x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + x {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - \frac{1}{6} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) + x*(-1/x + 1)^(1/3) - 1/6*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) + 1/3*log(abs((-1/x + 1)^(1/3) - 1))","A",0
1530,0,0,0,0.000000," ","integrate((a*x^2-3*b)/(a*x^2+x^3-b)/(a*x^3-b*x)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} - 3 \, b}{{\left(a x^{3} - b x\right)}^{\frac{1}{4}} {\left(a x^{2} + x^{3} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - 3*b)/((a*x^3 - b*x)^(1/4)*(a*x^2 + x^3 - b)), x)","F",0
1531,0,0,0,0.000000," ","integrate(1/(a*x-2*b)/(a*x^3-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{3} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x - 2 \, b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^3 - b*x^2)^(1/4)*(a*x - 2*b)), x)","F",0
1532,0,0,0,0.000000," ","integrate((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/x^4/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}{{\left(a x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)/((a*x^4 + b)*x^4), x)","F",0
1533,0,0,0,0.000000," ","integrate((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/x^4/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}{{\left(a x^{4} + b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)/((a*x^4 + b)*x^4), x)","F",0
1534,-2,0,0,0.000000," ","integrate((a*x^2-b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 3.22Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1535,-2,0,0,0.000000," ","integrate((a*x^2-b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 3.16Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1536,0,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}{{\left(a x^{4} - b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b*x^2)^(1/4)/((a*x^4 - b)*x^4), x)","F",0
1537,0,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}{{\left(a x^{4} - b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 + b*x^2)^(1/4)/((a*x^4 - b)*x^4), x)","F",0
1538,0,0,0,0.000000," ","integrate((a^3*x^3+b^3)/(a^3*x^3-b^3)/(a^4*x^4+b^4)^(1/2),x, algorithm=""giac"")","\int \frac{a^{3} x^{3} + b^{3}}{\sqrt{a^{4} x^{4} + b^{4}} {\left(a^{3} x^{3} - b^{3}\right)}}\,{d x}"," ",0,"integrate((a^3*x^3 + b^3)/(sqrt(a^4*x^4 + b^4)*(a^3*x^3 - b^3)), x)","F",0
1539,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6+x^3+1)/x^6/(2*x^6-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 + x^3 + 1)*(x^3 + 1)^(2/3)/((2*x^6 - 1)*x^6), x)","F",0
1540,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6+x^3+1)/x^6/(2*x^6-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 + x^3 + 1)*(x^3 + 1)^(2/3)/((2*x^6 - 1)*x^6), x)","F",0
1541,0,0,0,0.000000," ","integrate((x^6+1)*(2*x^6-1)*(2*x^6+x^4-1)^(5/4)/x^10/(2*x^6-x^4-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + x^{4} - 1\right)}^{\frac{5}{4}} {\left(2 \, x^{6} - 1\right)} {\left(x^{6} + 1\right)}}{{\left(2 \, x^{6} - x^{4} - 1\right)} x^{10}}\,{d x}"," ",0,"integrate((2*x^6 + x^4 - 1)^(5/4)*(2*x^6 - 1)*(x^6 + 1)/((2*x^6 - x^4 - 1)*x^10), x)","F",0
1542,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} + b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 + b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1543,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} + b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 + b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1544,0,0,0,0.000000," ","integrate(((-3*k^2+1)*x+2*k^2*x^3)*(k^4*x^4-2*k^2*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d+(3*d*k^2-1)*x^2-3*d*k^4*x^4+d*k^6*x^6),x, algorithm=""giac"")","\int \frac{{\left(k^{4} x^{4} - 2 \, k^{2} x^{2} + 1\right)} {\left(2 \, k^{2} x^{3} - {\left(3 \, k^{2} - 1\right)} x\right)}}{{\left(d k^{6} x^{6} - 3 \, d k^{4} x^{4} + {\left(3 \, d k^{2} - 1\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((k^4*x^4 - 2*k^2*x^2 + 1)*(2*k^2*x^3 - (3*k^2 - 1)*x)/((d*k^6*x^6 - 3*d*k^4*x^4 + (3*d*k^2 - 1)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(3/4)), x)","F",0
1545,1,143,0,0.220008," ","integrate((2*x^4-1)^(1/4)*(x^8+x^4-1)/x^6/(x^4-1),x, algorithm=""giac"")","-\frac{1}{2} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{2 \, x}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + \frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} - \frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 2\right)}}{5 \, x} + \frac{1}{2} \, \arctan\left(\frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{4} \, \log\left(\frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x} + 1\right) - \frac{1}{4} \, \log\left({\left| \frac{{\left(2 \, x^{4} - 1\right)}^{\frac{1}{4}}}{x} - 1 \right|}\right)"," ",0,"-1/2*2^(1/4)*arctan(1/2*2^(3/4)*(2*x^4 - 1)^(1/4)/x) - 1/4*2^(1/4)*log(2^(1/4) + (2*x^4 - 1)^(1/4)/x) + 1/4*2^(1/4)*log(2^(1/4) - (2*x^4 - 1)^(1/4)/x) + 1/5*(2*x^4 - 1)^(1/4)*(1/x^4 - 2)/x + 1/2*arctan((2*x^4 - 1)^(1/4)/x) + 1/4*log((2*x^4 - 1)^(1/4)/x + 1) - 1/4*log(abs((2*x^4 - 1)^(1/4)/x - 1))","A",0
1546,0,0,0,0.000000," ","integrate(1/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^8 - a*x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
1547,0,0,0,0.000000," ","integrate(1/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^8 - a*x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
1548,0,0,0,0.000000," ","integrate(x^6*(x^3-1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{2}{3}} x^{6}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)*x^6, x)","F",0
1549,0,0,0,0.000000," ","integrate(x^6*(x^3+1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{3} + 1\right)}^{\frac{2}{3}} x^{6}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*x^6, x)","F",0
1550,1,88,0,0.411504," ","integrate(x^4*(x^3+x)^(1/3),x, algorithm=""giac"")","-\frac{1}{108} \, {\left(5 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{7}{3}} - 13 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} - 10 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)} x^{6} + \frac{5}{162} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{5}{324} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{5}{162} \, \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/108*(5*(1/x^2 + 1)^(7/3) - 13*(1/x^2 + 1)^(4/3) - 10*(1/x^2 + 1)^(1/3))*x^6 + 5/162*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) + 5/324*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - 5/162*log(abs((1/x^2 + 1)^(1/3) - 1))","A",0
1551,0,0,0,0.000000," ","integrate(x^2*(3*a*b^2-2*b*(2*a+b)*x+(a+2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(3/4)/(a*b^2-b*(2*a+b)*x+(a+2*b)*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int \frac{{\left(3 \, a b^{2} - 2 \, {\left(2 \, a + b\right)} b x + {\left(a + 2 \, b\right)} x^{2}\right)} x^{2}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{3}{4}} {\left({\left(d - 1\right)} x^{3} + a b^{2} - {\left(2 \, a + b\right)} b x + {\left(a + 2 \, b\right)} x^{2}\right)}}\,{d x}"," ",0,"integrate((3*a*b^2 - 2*(2*a + b)*b*x + (a + 2*b)*x^2)*x^2/((-(a - x)*(b - x)^2*x)^(3/4)*((d - 1)*x^3 + a*b^2 - (2*a + b)*b*x + (a + 2*b)*x^2)), x)","F",0
1552,1,96,0,0.132004," ","integrate((x^4+1)^(1/3)*(x^4+3)/x^17,x, algorithm=""giac"")","\frac{5}{324} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{10 \, {\left(x^{4} + 1\right)}^{\frac{10}{3}} - 36 \, {\left(x^{4} + 1\right)}^{\frac{7}{3}} + 87 \, {\left(x^{4} + 1\right)}^{\frac{4}{3}} + 20 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}}}{432 \, x^{16}} + \frac{5}{648} \, \log\left({\left(x^{4} + 1\right)}^{\frac{2}{3}} + {\left(x^{4} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{5}{324} \, \log\left({\left(x^{4} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"5/324*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^4 + 1)^(1/3) + 1)) - 1/432*(10*(x^4 + 1)^(10/3) - 36*(x^4 + 1)^(7/3) + 87*(x^4 + 1)^(4/3) + 20*(x^4 + 1)^(1/3))/x^16 + 5/648*log((x^4 + 1)^(2/3) + (x^4 + 1)^(1/3) + 1) - 5/324*log((x^4 + 1)^(1/3) - 1)","A",0
1553,0,0,0,0.000000," ","integrate((x^2-2)*(x^3+x)^(1/3)/x^2/(x^4-2*x^2+4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{2} - 2\right)}}{{\left(x^{4} - 2 \, x^{2} + 4\right)} x^{2}}\,{d x}"," ",0,"integrate((x^3 + x)^(1/3)*(x^2 - 2)/((x^4 - 2*x^2 + 4)*x^2), x)","F",0
1554,0,0,0,0.000000," ","integrate((x^2-2)*(x^3+x)^(1/3)/x^2/(x^4-2*x^2+4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{2} - 2\right)}}{{\left(x^{4} - 2 \, x^{2} + 4\right)} x^{2}}\,{d x}"," ",0,"integrate((x^3 + x)^(1/3)*(x^2 - 2)/((x^4 - 2*x^2 + 4)*x^2), x)","F",0
1555,1,104,0,0.316584," ","integrate(1/(x^4-1)^2/(x^4-x^2)^(1/4),x, algorithm=""giac"")","\frac{15}{64} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{15}{128} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{15}{128} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{\frac{10}{x^{2}} - 9}{10 \, {\left(\frac{1}{x^{2}} - 1\right)} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}} + \frac{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}}{16 \, {\left(\frac{1}{x^{2}} + 1\right)}}"," ",0,"15/64*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) - 15/128*2^(3/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) + 15/128*2^(3/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4)) - 1/10*(10/x^2 - 9)/((1/x^2 - 1)*(-1/x^2 + 1)^(1/4)) + 1/16*(-1/x^2 + 1)^(3/4)/(1/x^2 + 1)","A",0
1556,0,0,0,0.000000," ","integrate((x^2-1)*(x^4-x^3+x^2-x+1)/(x^2-x+1)^2/(x^2+x+1)/(x^4+3*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} + x^{2} - x + 1\right)} {\left(x^{2} - 1\right)}}{\sqrt{x^{4} + 3 \, x^{2} + 1} {\left(x^{2} + x + 1\right)} {\left(x^{2} - x + 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^4 - x^3 + x^2 - x + 1)*(x^2 - 1)/(sqrt(x^4 + 3*x^2 + 1)*(x^2 + x + 1)*(x^2 - x + 1)^2), x)","F",0
1557,1,201,0,0.278463," ","integrate((a*x^3+b)*(2*a*x^3+b)/x^6/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{2}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) - \frac{4}{21} \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{4}} - \frac{8}{9} \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a"," ",0,"2/3*sqrt(2)*(-a)^(3/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) + 2/3*sqrt(2)*(-a)^(3/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) - 1/3*sqrt(2)*(-a)^(3/4)*a*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) + 1/3*sqrt(2)*(-a)^(3/4)*a*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) - 4/21*(a + b/x^3)^(7/4) - 8/9*(a + b/x^3)^(3/4)*a","B",0
1558,0,0,0,0.000000," ","integrate((a^3*x^3-b^3)/(a^3*x^3+b^3)/(a^4*x^4+b^4)^(1/2),x, algorithm=""giac"")","\int \frac{a^{3} x^{3} - b^{3}}{\sqrt{a^{4} x^{4} + b^{4}} {\left(a^{3} x^{3} + b^{3}\right)}}\,{d x}"," ",0,"integrate((a^3*x^3 - b^3)/(sqrt(a^4*x^4 + b^4)*(a^3*x^3 + b^3)), x)","F",0
1559,0,0,0,0.000000," ","integrate(x^4*(a*x^2-2*b)/(a*x^2-b)^2/(c*x^4+a*x^2-b)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} - 2 \, b\right)} x^{4}}{{\left(c x^{4} + a x^{2} - b\right)}^{\frac{1}{4}} {\left(a x^{2} - b\right)}^{2}}\,{d x}"," ",0,"integrate((a*x^2 - 2*b)*x^4/((c*x^4 + a*x^2 - b)^(1/4)*(a*x^2 - b)^2), x)","F",0
1560,0,0,0,0.000000," ","integrate((x^2-2*x-1)*(x^2+2*x-1)/(x^4+x^3+2*x^2-x+1)/(x^5-x)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 2 \, x - 1\right)} {\left(x^{2} - 2 \, x - 1\right)}}{{\left(x^{5} - x\right)}^{\frac{1}{3}} {\left(x^{4} + x^{3} + 2 \, x^{2} - x + 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 2*x - 1)*(x^2 - 2*x - 1)/((x^5 - x)^(1/3)*(x^4 + x^3 + 2*x^2 - x + 1)), x)","F",0
1561,1,191,0,0.189770," ","integrate((x^6-a*x^3-b)/x^6/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, \left(-a\right)^{\frac{1}{4}}} - \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, \left(-a\right)^{\frac{1}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, \left(-a\right)^{\frac{1}{4}}} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a} + \frac{4 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{4}}}{21 \, b}"," ",0,"-1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(-a)^(1/4) - 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(-a)^(1/4) + 1/6*sqrt(2)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/(-a)^(1/4) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a + 4/21*(a + b/x^3)^(7/4)/b","B",0
1562,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} - b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 - b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1563,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} - b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 - b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1564,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6-b),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, a^{6} x^{6} - b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((2*a^6*x^6 - b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1565,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6-b),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, a^{6} x^{6} - b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((2*a^6*x^6 - b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1566,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6+b),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, a^{6} x^{6} + b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((2*a^6*x^6 + b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1567,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6+b),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, a^{6} x^{6} + b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((2*a^6*x^6 + b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1568,0,0,0,0.000000," ","integrate(x^4*(x^3-4)/(x^3-1)^(1/4)/(x^8-x^6+2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 4\right)} x^{4}}{{\left(x^{8} - x^{6} + 2 \, x^{3} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^3 - 4)*x^4/((x^8 - x^6 + 2*x^3 - 1)*(x^3 - 1)^(1/4)), x)","F",0
1569,0,0,0,0.000000," ","integrate(x^6/(a*x^4+b)^(3/4)/(a^2*x^8-b^2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(a^{2} x^{8} - b^{2}\right)} {\left(a x^{4} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^6/((a^2*x^8 - b^2)*(a*x^4 + b)^(3/4)), x)","F",0
1570,0,0,0,0.000000," ","integrate((a*x^2-b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} - b^{2}\right)} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}{a x^{2} + b^{2}}\,{d x}"," ",0,"integrate((a*x^2 - b^2)*sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2), x)","F",0
1571,1,77,0,0.175635," ","integrate((x^3+x^2)^(1/3),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(\frac{1}{x} + 1\right)}^{\frac{4}{3}} + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)} x^{2} - \frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{18} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{9} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/6*((1/x + 1)^(4/3) + 2*(1/x + 1)^(1/3))*x^2 - 1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) - 1/18*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) + 1/9*log(abs((1/x + 1)^(1/3) - 1))","A",0
1572,0,0,0,0.000000," ","integrate((k^3*x^3-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^3*x^3+1),x, algorithm=""giac"")","\int \frac{k^{3} x^{3} - 1}{{\left(k^{3} x^{3} + 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^3*x^3 - 1)/((k^3*x^3 + 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
1573,-2,0,0,0.000000," ","integrate((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 4.14Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1574,-2,0,0,0.000000," ","integrate((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-59,28]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[7,11]Evaluation time: 4.99Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1575,0,0,0,0.000000," ","integrate((c*k^2*x^4+b*x^2+c)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4-1),x, algorithm=""giac"")","\int \frac{c k^{2} x^{4} + b x^{2} + c}{{\left(k^{2} x^{4} - 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((c*k^2*x^4 + b*x^2 + c)/((k^2*x^4 - 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
1576,0,0,0,0.000000," ","integrate((a*x^4+3*b)/(a*x^4+x^3-b)/(a*x^5-b*x)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + 3 \, b}{{\left(a x^{5} - b x\right)}^{\frac{1}{4}} {\left(a x^{4} + x^{3} - b\right)}}\,{d x}"," ",0,"integrate((a*x^4 + 3*b)/((a*x^5 - b*x)^(1/4)*(a*x^4 + x^3 - b)), x)","F",0
1577,1,82,0,0.390841," ","integrate((x^6-1)/x^6/(x^3+x)^(1/3),x, algorithm=""giac"")","\frac{3}{16} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{8}{3}} - \frac{3}{5} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{3}} - \frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{3}{4} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + \frac{1}{4} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{2} \, \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"3/16*(1/x^2 + 1)^(8/3) - 3/5*(1/x^2 + 1)^(5/3) - 1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) + 3/4*(1/x^2 + 1)^(2/3) + 1/4*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - 1/2*log(abs((1/x^2 + 1)^(1/3) - 1))","A",0
1578,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((x^6 + 2)*(x^3 - 1)^(2/3)/x^6, x)","F",0
1579,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+x^3-2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} - 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((x^6 + x^3 - 2)*(x^3 - 1)^(2/3)/x^6, x)","F",0
1580,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6+1)/x^6,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((2*x^6 + 1)*(x^3 + 1)^(2/3)/x^6, x)","F",0
1581,0,0,0,0.000000," ","integrate((2*a*x^5+3*b)/(a*x^5+x^3-b)/(a*x^6-b*x)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{5} + 3 \, b}{{\left(a x^{6} - b x\right)}^{\frac{1}{4}} {\left(a x^{5} + x^{3} - b\right)}}\,{d x}"," ",0,"integrate((2*a*x^5 + 3*b)/((a*x^6 - b*x)^(1/4)*(a*x^5 + x^3 - b)), x)","F",0
1582,-2,0,0,0.000000," ","integrate((x^4-1)^(1/4)*(x^8+x^4+1)/x^6/(2*x^8-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1583,-2,0,0,0.000000," ","integrate((x^4-1)^(1/4)*(x^8+x^4+1)/x^6/(2*x^8-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1584,0,0,0,0.000000," ","integrate((a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} - b x}}{{\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 - b*x)/(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2), x)","F",0
1585,0,0,0,0.000000," ","integrate(x^7*(x^3-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{1}{3}} x^{7}\,{d x}"," ",0,"integrate((x^3 - 1)^(1/3)*x^7, x)","F",0
1586,0,0,0,0.000000," ","integrate(x^7*(x^3+1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} + 1\right)}^{\frac{1}{3}} x^{7}\,{d x}"," ",0,"integrate((x^3 + 1)^(1/3)*x^7, x)","F",0
1587,1,99,0,0.352749," ","integrate((x^3-1)^(1/3)*(x^3+1)/x^13,x, algorithm=""giac"")","\frac{25}{729} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{50 \, {\left(x^{3} - 1\right)}^{\frac{10}{3}} + 180 \, {\left(x^{3} - 1\right)}^{\frac{7}{3}} + 111 \, {\left(x^{3} - 1\right)}^{\frac{4}{3}} - 100 \, {\left(x^{3} - 1\right)}^{\frac{1}{3}}}{972 \, x^{12}} - \frac{25}{1458} \, \log\left({\left(x^{3} - 1\right)}^{\frac{2}{3}} - {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{25}{729} \, \log\left({\left| {\left(x^{3} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"25/729*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 - 1)^(1/3) - 1)) + 1/972*(50*(x^3 - 1)^(10/3) + 180*(x^3 - 1)^(7/3) + 111*(x^3 - 1)^(4/3) - 100*(x^3 - 1)^(1/3))/x^12 - 25/1458*log((x^3 - 1)^(2/3) - (x^3 - 1)^(1/3) + 1) + 25/729*log(abs((x^3 - 1)^(1/3) + 1))","A",0
1588,0,0,0,0.000000," ","integrate((-b+x)*(a-3*b+2*x)/(-a+x)/((-a+x)*(-b+x))^(3/4)/(b-a^3*d-(-3*a^2*d+1)*x-3*a*d*x^2+d*x^3),x, algorithm=""giac"")","\int -\frac{{\left(a - 3 \, b + 2 \, x\right)} {\left(b - x\right)}}{{\left(a^{3} d + 3 \, a d x^{2} - d x^{3} - {\left(3 \, a^{2} d - 1\right)} x - b\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{3}{4}} {\left(a - x\right)}}\,{d x}"," ",0,"integrate(-(a - 3*b + 2*x)*(b - x)/((a^3*d + 3*a*d*x^2 - d*x^3 - (3*a^2*d - 1)*x - b)*((a - x)*(b - x))^(3/4)*(a - x)), x)","F",0
1589,0,0,0,0.000000," ","integrate(x^8*(a*x^4-b)^(3/4),x, algorithm=""giac"")","\int {\left(a x^{4} - b\right)}^{\frac{3}{4}} x^{8}\,{d x}"," ",0,"integrate((a*x^4 - b)^(3/4)*x^8, x)","F",0
1590,1,209,0,0.238022," ","integrate(1/(a*x^3+b)/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a b} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a b} + \frac{2^{\frac{1}{4}} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{6 \, \left(-a\right)^{\frac{1}{4}} b} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{6 \, a b}"," ",0,"1/3*2^(1/4)*(-a)^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/(a*b) + 1/3*2^(1/4)*(-a)^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/(a*b) + 1/6*2^(1/4)*log(2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/((-a)^(1/4)*b) + 1/6*2^(1/4)*(-a)^(3/4)*log(-2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/(a*b)","B",0
1591,0,0,0,0.000000," ","integrate((a*x^4-b*x^2)^(1/4)/x^4/(a*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}}}{{\left(a x^{4} - b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)/((a*x^4 - b)*x^4), x)","F",0
1592,0,0,0,0.000000," ","integrate((a*x^4-b*x^2)^(1/4)/x^4/(a*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}}}{{\left(a x^{4} - b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)/((a*x^4 - b)*x^4), x)","F",0
1593,0,0,0,0.000000," ","integrate((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(1-2*(1+k)*x+(k^2+c+4*k+1)*x^2-(c*k+2*k^2+c+2*k)*x^3+(c*k+k^2-b)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(a + k\right)} x^{2} - {\left(k + 1\right)} x + 1\right)} {\left({\left(k + 1\right)} x - 2\right)}}{{\left({\left(c k + k^{2} - b\right)} x^{4} - {\left(c k + 2 \, k^{2} + c + 2 \, k\right)} x^{3} + {\left(k^{2} + c + 4 \, k + 1\right)} x^{2} - 2 \, {\left(k + 1\right)} x + 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((a + k)*x^2 - (k + 1)*x + 1)*((k + 1)*x - 2)/(((c*k + k^2 - b)*x^4 - (c*k + 2*k^2 + c + 2*k)*x^3 + (k^2 + c + 4*k + 1)*x^2 - 2*(k + 1)*x + 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
1594,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(x^6+1)/x^3,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((x^6 + 1)*(x^6 - 1)^(1/3)/x^3, x)","F",0
1595,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 1)*(x^3 + 1)^(2/3)/((x^6 - 2)*x^6), x)","F",0
1596,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 2 \, x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 2*x^3 + 1)*(x^3 + 1)^(2/3)/((x^6 - 2)*x^6), x)","F",0
1597,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(2*x^6-1)/x^9,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((2*x^6 - 1)*(x^6 - 1)^(1/3)/x^9, x)","F",0
1598,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-1)/x^6/(2*x^6+x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} + x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 1)*(x^3 - 1)^(2/3)/((2*x^6 + x^3 - 2)*x^6), x)","F",0
1599,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-1)/x^6/(2*x^6+x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} + x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 1)*(x^3 - 1)^(2/3)/((2*x^6 + x^3 - 2)*x^6), x)","F",0
1600,1,172,0,0.344663," ","integrate((x^4-1)^(1/4)*(2*x^8-x^4+2)/x^10/(2*x^4-1),x, algorithm=""giac"")","2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)}\right) + \sqrt{2} \log\left(\frac{\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) - \sqrt{2} \log\left(-\frac{\sqrt{2} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} + \frac{\sqrt{x^{4} - 1}}{x^{2}} + 1\right) - \frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} - 1\right)}}{x} - \frac{8 \, {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x} - \frac{2 \, {\left(x^{8} - 2 \, x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{9 \, x^{9}}"," ",0,"2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(x^4 - 1)^(1/4)/x)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(x^4 - 1)^(1/4)/x)) + sqrt(2)*log(sqrt(2)*(x^4 - 1)^(1/4)/x + sqrt(x^4 - 1)/x^2 + 1) - sqrt(2)*log(-sqrt(2)*(x^4 - 1)^(1/4)/x + sqrt(x^4 - 1)/x^2 + 1) - (x^4 - 1)^(1/4)*(1/x^4 - 1)/x - 8*(x^4 - 1)^(1/4)/x - 2/9*(x^8 - 2*x^4 + 1)*(x^4 - 1)^(1/4)/x^9","A",0
1601,0,0,0,0.000000," ","integrate((x^6+2)*(x^12+x^8-2*x^6+1)/x^8/(x^6-1)^(1/4)/(x^6+x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{12} + x^{8} - 2 \, x^{6} + 1\right)} {\left(x^{6} + 2\right)}}{{\left(x^{6} + x^{4} - 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate((x^12 + x^8 - 2*x^6 + 1)*(x^6 + 2)/((x^6 + x^4 - 1)*(x^6 - 1)^(1/4)*x^8), x)","F",0
1602,0,0,0,0.000000," ","integrate((x^2+x)^(1/2)/x/(x^2+x*(x^2+x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + x}}{\sqrt{x^{2} + \sqrt{x^{2} + x} x} x}\,{d x}"," ",0,"integrate(sqrt(x^2 + x)/(sqrt(x^2 + sqrt(x^2 + x)*x)*x), x)","F",0
1603,0,0,0,0.000000," ","integrate((x^2+x*(x^2+x)^(1/2))^(1/2)/(x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{2} + x} x}}{\sqrt{x^{2} + x}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^2 + x)*x)/sqrt(x^2 + x), x)","F",0
1604,0,0,0,0.000000," ","integrate(1/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(1/sqrt(b + sqrt(a*x^2 + b^2)), x)","F",0
1605,0,0,0,0.000000," ","integrate((a*x^2+b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int {\left(a x^{2} + b^{2}\right)}^{2} \sqrt{b + \sqrt{a x^{2} + b^{2}}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)^2*sqrt(b + sqrt(a*x^2 + b^2)), x)","F",0
1606,0,0,0,0.000000," ","integrate(1/(1-3*x)/(x^3-x)^(1/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(x^{3} - x\right)}^{\frac{1}{3}} {\left(3 \, x - 1\right)}}\,{d x}"," ",0,"integrate(-1/((x^3 - x)^(1/3)*(3*x - 1)), x)","F",0
1607,0,0,0,0.000000," ","integrate(1/(1+3*x)/(x^3-x)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} - x\right)}^{\frac{1}{3}} {\left(3 \, x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^3 - x)^(1/3)*(3*x + 1)), x)","F",0
1608,1,74,0,0.170213," ","integrate(x/(x^3-x^2)^(1/3),x, algorithm=""giac"")","x {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{6} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{3} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"x*(-1/x + 1)^(2/3) - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) + 1/6*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - 1/3*log(abs((-1/x + 1)^(1/3) - 1))","A",0
1609,0,0,0,0.000000," ","integrate((-x^3+1)^(2/3)*(x^3-1)/x^6/(2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 - 1)*(-x^3 + 1)^(2/3)/((2*x^3 - 1)*x^6), x)","F",0
1610,0,0,0,0.000000," ","integrate((a*x+2*b)/(a*x+x^2+b)/(a*x^3+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x + 2 \, b}{{\left(a x^{3} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x + x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x + 2*b)/((a*x^3 + b*x^2)^(1/4)*(a*x + x^2 + b)), x)","F",0
1611,1,101,0,0.328927," ","integrate(x^3*(x^4+x)^(1/2)/(a*x^3-b),x, algorithm=""giac"")","\frac{\sqrt{x^{4} + x} x}{3 \, a} + \frac{{\left(a + 2 \, b\right)} \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right)}{6 \, a^{2}} - \frac{{\left(a + 2 \, b\right)} \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)}{6 \, a^{2}} + \frac{2 \, {\left(a b + b^{2}\right)} \arctan\left(\frac{b \sqrt{\frac{1}{x^{3}} + 1}}{\sqrt{-a b - b^{2}}}\right)}{3 \, \sqrt{-a b - b^{2}} a^{2}}"," ",0,"1/3*sqrt(x^4 + x)*x/a + 1/6*(a + 2*b)*log(sqrt(1/x^3 + 1) + 1)/a^2 - 1/6*(a + 2*b)*log(abs(sqrt(1/x^3 + 1) - 1))/a^2 + 2/3*(a*b + b^2)*arctan(b*sqrt(1/x^3 + 1)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*a^2)","A",0
1612,0,0,0,0.000000," ","integrate(x^9*(x^6+1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{6} + 1\right)}^{\frac{1}{3}} x^{9}\,{d x}"," ",0,"integrate((x^6 + 1)^(1/3)*x^9, x)","F",0
1613,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6+4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 + 4)*x^6), x)","F",0
1614,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6+4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 - 1)^(2/3)/((x^6 + 4)*x^6), x)","F",0
1615,1,212,0,0.281922," ","integrate((x^6-a*x^3+b)/x^6/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, \left(-a\right)^{\frac{1}{4}}} - \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, \left(-a\right)^{\frac{1}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, \left(-a\right)^{\frac{1}{4}}} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a} - \frac{4 \, {\left(3 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{6} - 14 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{63 \, b^{7}}"," ",0,"-1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(-a)^(1/4) - 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(-a)^(1/4) + 1/6*sqrt(2)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/(-a)^(1/4) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a - 4/63*(3*(a + b/x^3)^(7/4)*b^6 - 14*(a + b/x^3)^(3/4)*a*b^6)/b^7","B",0
1616,1,209,0,0.249347," ","integrate((a*x^6-b)/x^6/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) + \frac{4 \, {\left(3 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{6} - 7 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{63 \, b^{7}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) + 4/63*(3*(a + b/x^3)^(7/4)*b^6 - 7*(a + b/x^3)^(3/4)*a*b^6)/b^7","B",0
1617,1,209,0,0.285218," ","integrate((a*x^6+b)/x^6/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right) - \frac{4 \, {\left(3 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{6} - 7 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{63 \, b^{7}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3)) - 4/63*(3*(a + b/x^3)^(7/4)*b^6 - 7*(a + b/x^3)^(3/4)*a*b^6)/b^7","B",0
1618,0,0,0,0.000000," ","integrate((2*a*x^5-3*b)/(2*a*x^5+x^3+2*b)/(a*x^6+b*x)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{5} - 3 \, b}{{\left(a x^{6} + b x\right)}^{\frac{1}{4}} {\left(2 \, a x^{5} + x^{3} + 2 \, b\right)}}\,{d x}"," ",0,"integrate((2*a*x^5 - 3*b)/((a*x^6 + b*x)^(1/4)*(2*a*x^5 + x^3 + 2*b)), x)","F",0
1619,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+2*b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} + 2 \, b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 + 2*b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1620,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+2*b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} + 2 \, b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 + 2*b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1621,0,0,0,0.000000," ","integrate((x^4-1)*(x^8+x^6+3*x^4+x^2+1)/(x^4+x^2+1)^(3/2)/(x^8+3*x^6+5*x^4+3*x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{6} + 3 \, x^{4} + x^{2} + 1\right)} {\left(x^{4} - 1\right)}}{{\left(x^{8} + 3 \, x^{6} + 5 \, x^{4} + 3 \, x^{2} + 1\right)} {\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^8 + x^6 + 3*x^4 + x^2 + 1)*(x^4 - 1)/((x^8 + 3*x^6 + 5*x^4 + 3*x^2 + 1)*(x^4 + x^2 + 1)^(3/2)), x)","F",0
1622,0,0,0,0.000000," ","integrate((a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8+b),x, algorithm=""giac"")","\int \frac{a x^{8} - b}{{\left(a x^{8} + b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^8 - b)/((a*x^8 + b)*(a*x^4 + b)^(1/4)), x)","F",0
1623,0,0,0,0.000000," ","integrate((a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8+b),x, algorithm=""giac"")","\int \frac{a x^{8} - b}{{\left(a x^{8} + b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^8 - b)/((a*x^8 + b)*(a*x^4 + b)^(1/4)), x)","F",0
1624,0,0,0,0.000000," ","integrate((2*x^5+2*x-3)*(x^6-x^2+x)^(1/2)/(x^10-x^8-3*x^6+2*x^5+x^4-x^3+x^2-2*x+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{6} - x^{2} + x} {\left(2 \, x^{5} + 2 \, x - 3\right)}}{x^{10} - x^{8} - 3 \, x^{6} + 2 \, x^{5} + x^{4} - x^{3} + x^{2} - 2 \, x + 1}\,{d x}"," ",0,"integrate(sqrt(x^6 - x^2 + x)*(2*x^5 + 2*x - 3)/(x^10 - x^8 - 3*x^6 + 2*x^5 + x^4 - x^3 + x^2 - 2*x + 1), x)","F",0
1625,1,188,0,0.425428," ","integrate((x+(1+x)^(1/2))^(1/2)/x^2/(1+x)^(1/2),x, algorithm=""giac"")","-\frac{{\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{3} - 2 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{2} + 5 \, \sqrt{x + \sqrt{x + 1}} - 5 \, \sqrt{x + 1} + 1}{{\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{4} - 2 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{2} + 4 \, \sqrt{x + \sqrt{x + 1}} - 4 \, \sqrt{x + 1}} - \frac{3}{2} \, \arctan\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} - 1\right) - \frac{1}{4} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} + 2 \right|}\right) + \frac{1}{4} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} \right|}\right)"," ",0,"-((sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^3 - 2*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^2 + 5*sqrt(x + sqrt(x + 1)) - 5*sqrt(x + 1) + 1)/((sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^4 - 2*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^2 + 4*sqrt(x + sqrt(x + 1)) - 4*sqrt(x + 1)) - 3/2*arctan(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) - 1) - 1/4*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) + 2)) + 1/4*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)))","B",0
1626,1,86,0,0.430089," ","integrate((x+(1+x)^(1/2))^(1/2)/x/(1+x)^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} - 1\right) - 2 \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right) - \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} + 2 \right|}\right) + \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} \right|}\right)"," ",0,"2*arctan(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) - 1) - 2*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1) - log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) + 2)) + log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)))","A",0
1627,1,74,0,0.756662," ","integrate((a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, b - 1\right)} \log\left({\left| -2 \, \sqrt{a x - b} + 2 \, \sqrt{a x + \sqrt{a x - b}} - 1 \right|}\right) - 2 \, \sqrt{a x + \sqrt{a x - b}} {\left(2 \, \sqrt{a x - b} + 1\right)}}{4 \, a}"," ",0,"-1/4*((4*b - 1)*log(abs(-2*sqrt(a*x - b) + 2*sqrt(a*x + sqrt(a*x - b)) - 1)) - 2*sqrt(a*x + sqrt(a*x - b))*(2*sqrt(a*x - b) + 1))/a","A",0
1628,1,100,0,0.361303," ","integrate((1-a*x+b*(b*x+a)^(1/2))/(b*x+a)^(1/2)/(x+a*b*(b*x+a)^(1/2)),x, algorithm=""giac"")","{\left(a^{2} b + b\right)} \log\left(\sqrt{b x + a} a b^{2} + b x\right) - \frac{2 \, {\left(a^{3} b^{3} + a b^{3} - 2\right)} \arctan\left(\frac{a b^{2} + 2 \, \sqrt{b x + a}}{\sqrt{-a^{2} b^{4} - 4 \, a}}\right)}{\sqrt{-a^{2} b^{4} - 4 \, a}} - \frac{2 \, \sqrt{b x + a} a}{b}"," ",0,"(a^2*b + b)*log(sqrt(b*x + a)*a*b^2 + b*x) - 2*(a^3*b^3 + a*b^3 - 2)*arctan((a*b^2 + 2*sqrt(b*x + a))/sqrt(-a^2*b^4 - 4*a))/sqrt(-a^2*b^4 - 4*a) - 2*sqrt(b*x + a)*a/b","A",0
1629,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/x^2, x)","F",0
1630,0,0,0,0.000000," ","integrate(1/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a^{2} x^{2} - b x} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*x^2 - b*x)*(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2)), x)","F",0
1631,0,0,0,0.000000," ","integrate(1/(1+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x + \sqrt{x^{2} + 1}} + 1}\,{d x}"," ",0,"integrate(1/(sqrt(x + sqrt(x^2 + 1)) + 1), x)","F",0
1632,0,0,0,0.000000," ","integrate((-2+x)/(x^2+2)/(2*x^2+x-1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 2}{{\left(2 \, x^{2} + x - 1\right)}^{\frac{1}{3}} {\left(x^{2} + 2\right)}}\,{d x}"," ",0,"integrate((x - 2)/((2*x^2 + x - 1)^(1/3)*(x^2 + 2)), x)","F",0
1633,0,0,0,0.000000," ","integrate((-a+x)*(-b+x)*(-2*a*b+(a+b)*x)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, a b - {\left(a + b\right)} x\right)} {\left(a - x\right)} {\left(b - x\right)}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{3}{4}} {\left({\left(d - 1\right)} x^{2} - a b + {\left(a + b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(2*a*b - (a + b)*x)*(a - x)*(b - x)/(((a - x)*(b - x)*x^2)^(3/4)*((d - 1)*x^2 - a*b + (a + b)*x)), x)","F",0
1634,0,0,0,0.000000," ","integrate((x^2-x+1)/(x^2+2*x-2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - x + 1}{\sqrt{x^{3} + 1} {\left(x^{2} + 2 \, x - 2\right)}}\,{d x}"," ",0,"integrate((x^2 - x + 1)/(sqrt(x^3 + 1)*(x^2 + 2*x - 2)), x)","F",0
1635,1,74,0,0.211631," ","integrate((-1+x)/x/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{3}{2} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) - 3/2*(-1/x + 1)^(2/3) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
1636,1,74,0,0.181164," ","integrate((1+x)/x/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{3}{2} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) + 3/2*(-1/x + 1)^(2/3) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
1637,1,79,0,0.198086," ","integrate(x^2/(x^3+x^2)^(1/3),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{3}} - 7 \, {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right)} x^{2} - \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{9} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{2}{9} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/6*(4*(1/x + 1)^(5/3) - 7*(1/x + 1)^(2/3))*x^2 - 2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) + 1/9*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) - 2/9*log(abs((1/x + 1)^(1/3) - 1))","A",0
1638,0,0,0,0.000000," ","integrate((a-3*b+2*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/(-b+x)/((-a+x)*(-b+x))^(1/4)/(-a^3+b*d-(-3*a^2+d)*x-3*a*x^2+x^3),x, algorithm=""giac"")","\int -\frac{{\left(a^{3} - 3 \, a^{2} x + 3 \, a x^{2} - x^{3}\right)} {\left(a - 3 \, b + 2 \, x\right)}}{{\left(a^{3} + 3 \, a x^{2} - x^{3} - b d - {\left(3 \, a^{2} - d\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{4}} {\left(b - x\right)}}\,{d x}"," ",0,"integrate(-(a^3 - 3*a^2*x + 3*a*x^2 - x^3)*(a - 3*b + 2*x)/((a^3 + 3*a*x^2 - x^3 - b*d - (3*a^2 - d)*x)*((a - x)*(b - x))^(1/4)*(b - x)), x)","F",0
1639,1,312,0,0.382217," ","integrate(x^3*(3-2*(1+k)*x+k*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(1/4)/(k*x-1)/(-d+d*(1+k)*x-d*k*x^2+x^3),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{1}{d}\right)^{\frac{1}{4}} + 2 \, {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{1}{d}\right)^{\frac{1}{4}}}\right)}{d^{2}} - \frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{1}{d}\right)^{\frac{1}{4}} - 2 \, {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{1}{d}\right)^{\frac{1}{4}}}\right)}{d^{2}} + \frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}} \left(-\frac{1}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}} + \sqrt{-\frac{1}{d}}\right)}{2 \, d^{2}} - \frac{\sqrt{2} \left(-d^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}} \left(-\frac{1}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}} + \sqrt{-\frac{1}{d}}\right)}{2 \, d^{2}} + \frac{4}{{\left(\frac{k}{x} - \frac{k}{x^{2}} - \frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}^{\frac{1}{4}}}"," ",0,"-sqrt(2)*(-d^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-1/d)^(1/4) + 2*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4))/(-1/d)^(1/4))/d^2 - sqrt(2)*(-d^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-1/d)^(1/4) - 2*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4))/(-1/d)^(1/4))/d^2 + 1/2*sqrt(2)*(-d^3)^(3/4)*log(sqrt(2)*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4)*(-1/d)^(1/4) + sqrt(k/x - k/x^2 - 1/x^2 + 1/x^3) + sqrt(-1/d))/d^2 - 1/2*sqrt(2)*(-d^3)^(3/4)*log(-sqrt(2)*(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4)*(-1/d)^(1/4) + sqrt(k/x - k/x^2 - 1/x^2 + 1/x^3) + sqrt(-1/d))/d^2 + 4/(k/x - k/x^2 - 1/x^2 + 1/x^3)^(1/4)","B",0
1640,0,0,0,0.000000," ","integrate((x^3+2)*(2*x^3+1)^(2/3)/x^6/(x^3+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} + 2\right)}}{{\left(x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^3 + 1)^(2/3)*(x^3 + 2)/((x^3 + 1)*x^6), x)","F",0
1641,0,0,0,0.000000," ","integrate((3*a*b^2-2*b*(2*a+b)*x+(a+2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-a*b^2*d+b*(2*a+b)*d*x-(a+2*b)*d*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int -\frac{3 \, a b^{2} - 2 \, {\left(2 \, a + b\right)} b x + {\left(a + 2 \, b\right)} x^{2}}{{\left(a b^{2} d - {\left(2 \, a + b\right)} b d x + {\left(a + 2 \, b\right)} d x^{2} - {\left(d - 1\right)} x^{3}\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(3*a*b^2 - 2*(2*a + b)*b*x + (a + 2*b)*x^2)/((a*b^2*d - (2*a + b)*b*d*x + (a + 2*b)*d*x^2 - (d - 1)*x^3)*(-(a - x)*(b - x)^2*x)^(1/4)), x)","F",0
1642,1,257,0,0.215312," ","integrate((c*x+d)*(a*x^4-b*x^3)^(1/4)/x^2,x, algorithm=""giac"")","\frac{8 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} b c x - 32 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} b d + \frac{2 \, \sqrt{2} {\left(b^{2} c - 4 \, a b d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c - 4 \, a b d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c - 4 \, a b d\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c - 4 \, a b d\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}}}}{8 \, b}"," ",0,"1/8*(8*(a - b/x)^(1/4)*b*c*x - 32*(a - b/x)^(1/4)*b*d + 2*sqrt(2)*(b^2*c - 4*a*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 2*sqrt(2)*(b^2*c - 4*a*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + sqrt(2)*(b^2*c - 4*a*b*d)*log(sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/(-a)^(3/4) - sqrt(2)*(b^2*c - 4*a*b*d)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/(-a)^(3/4))/b","B",0
1643,0,0,0,0.000000," ","integrate((x^5+3)*(x^5+x^3-2)^(1/3)/x^2/(x^5-2),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{3} - 2\right)}^{\frac{1}{3}} {\left(x^{5} + 3\right)}}{{\left(x^{5} - 2\right)} x^{2}}\,{d x}"," ",0,"integrate((x^5 + x^3 - 2)^(1/3)*(x^5 + 3)/((x^5 - 2)*x^2), x)","F",0
1644,0,0,0,0.000000," ","integrate((x^5-3)*(x^5+x^3+2)^(2/3)/x^3/(x^5+2),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{3} + 2\right)}^{\frac{2}{3}} {\left(x^{5} - 3\right)}}{{\left(x^{5} + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^5 + x^3 + 2)^(2/3)*(x^5 - 3)/((x^5 + 2)*x^3), x)","F",0
1645,0,0,0,0.000000," ","integrate((x^6-1)^(1/3)*(x^6+1)/x^9,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((x^6 + 1)*(x^6 - 1)^(1/3)/x^9, x)","F",0
1646,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-2*b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} - 2 \, b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 - 2*b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1647,0,0,0,0.000000," ","integrate(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-2*b),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{6} x^{6} - 2 \, b\right)} {\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((a^6*x^6 - 2*b)*(a^3*x^3 + b^2*x^2)^(1/3)), x)","F",0
1648,1,65,0,0.351290," ","integrate(1/(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4),x, algorithm=""giac"")","\frac{1}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{3}{4}} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}{2 \, x}\right) - \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + \frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - \frac{{\left(x^{4} - 1\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"1/4*2^(3/4)*arctan(1/2*2^(3/4)*(x^4 - 1)^(1/4)/x) - 1/8*2^(3/4)*log(2^(1/4) + (x^4 - 1)^(1/4)/x) + 1/8*2^(3/4)*log(2^(1/4) - (x^4 - 1)^(1/4)/x)","A",0
1649,1,160,0,0.180001," ","integrate((x^2+1)/(a*x+b)^(1/2)/(c+(a*x+b)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(35 \, {\left(c + \sqrt{a x + b}\right)}^{\frac{9}{2}} - 180 \, {\left(c + \sqrt{a x + b}\right)}^{\frac{7}{2}} c + 378 \, {\left(c + \sqrt{a x + b}\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{c + \sqrt{a x + b}} c^{4} + 315 \, a^{2} \sqrt{c + \sqrt{a x + b}} + 315 \, b^{2} \sqrt{c + \sqrt{a x + b}} - 42 \, {\left(3 \, {\left(c + \sqrt{a x + b}\right)}^{\frac{5}{2}} - 10 \, {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}} c + 15 \, \sqrt{c + \sqrt{a x + b}} c^{2}\right)} b\right)}}{315 \, a^{3}}"," ",0,"4/315*(35*(c + sqrt(a*x + b))^(9/2) - 180*(c + sqrt(a*x + b))^(7/2)*c + 378*(c + sqrt(a*x + b))^(5/2)*c^2 - 420*(c + sqrt(a*x + b))^(3/2)*c^3 + 315*sqrt(c + sqrt(a*x + b))*c^4 + 315*a^2*sqrt(c + sqrt(a*x + b)) + 315*b^2*sqrt(c + sqrt(a*x + b)) - 42*(3*(c + sqrt(a*x + b))^(5/2) - 10*(c + sqrt(a*x + b))^(3/2)*c + 15*sqrt(c + sqrt(a*x + b))*c^2)*b)/a^3","A",0
1650,-1,0,0,0.000000," ","integrate(x^2/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1651,1,89,0,2.008396," ","integrate(x^2*(x^3-x)^(1/3),x, algorithm=""giac"")","\frac{1}{12} \, {\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)} x^{4} - \frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{36} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{18} \, \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/12*((-1/x^2 + 1)^(4/3) + 2*(-1/x^2 + 1)^(1/3))*x^4 - 1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) - 1/36*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) + 1/18*log(abs((-1/x^2 + 1)^(1/3) - 1))","A",0
1652,1,97,0,1.002704," ","integrate(x^6*(x^3+x)^(1/3),x, algorithm=""giac"")","\frac{1}{648} \, {\left(20 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{10}{3}} - 72 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{7}{3}} + 93 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} + 40 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)} x^{8} - \frac{5}{243} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{5}{486} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{5}{243} \, \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/648*(20*(1/x^2 + 1)^(10/3) - 72*(1/x^2 + 1)^(7/3) + 93*(1/x^2 + 1)^(4/3) + 40*(1/x^2 + 1)^(1/3))*x^8 - 5/243*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) - 5/486*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) + 5/243*log(abs((1/x^2 + 1)^(1/3) - 1))","A",0
1653,0,0,0,0.000000," ","integrate((-3+2*x)/x/(x^4-1)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, x - 3}{{\left(x^{4} - 1\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((2*x - 3)/((x^4 - 1)^(1/4)*x), x)","F",0
1654,0,0,0,0.000000," ","integrate((-x^4+x^3-1)^(1/3)*(x^4-3)/x^2/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 3\right)} {\left(-x^{4} + x^{3} - 1\right)}^{\frac{1}{3}}}{{\left(x^{4} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^4 - 3)*(-x^4 + x^3 - 1)^(1/3)/((x^4 + 1)*x^2), x)","F",0
1655,1,100,0,0.561347," ","integrate(x^3*(x^4-x)^(1/2)/(a*x^3-b),x, algorithm=""giac"")","\frac{\sqrt{x^{4} - x} x}{3 \, a} - \frac{{\left(a - 2 \, b\right)} \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right)}{6 \, a^{2}} + \frac{{\left(a - 2 \, b\right)} \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)}{6 \, a^{2}} - \frac{2 \, \sqrt{a b - b^{2}} \arctan\left(\frac{b \sqrt{-\frac{1}{x^{3}} + 1}}{\sqrt{a b - b^{2}}}\right)}{3 \, a^{2}}"," ",0,"1/3*sqrt(x^4 - x)*x/a - 1/6*(a - 2*b)*log(sqrt(-1/x^3 + 1) + 1)/a^2 + 1/6*(a - 2*b)*log(abs(sqrt(-1/x^3 + 1) - 1))/a^2 - 2/3*sqrt(a*b - b^2)*arctan(b*sqrt(-1/x^3 + 1)/sqrt(a*b - b^2))/a^2","A",0
1656,1,97,0,0.437322," ","integrate((2*x^4+1)/(x^4-1)/(x^4+x^2)^(1/4),x, algorithm=""giac"")","\frac{3}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{3}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{3}{8} \cdot 2^{\frac{3}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{3}{{\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}} - 2 \, \arctan\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) - \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"3/4*2^(3/4)*arctan(1/2*2^(3/4)*(1/x^2 + 1)^(1/4)) - 3/8*2^(3/4)*log(2^(1/4) + (1/x^2 + 1)^(1/4)) + 3/8*2^(3/4)*log(abs(-2^(1/4) + (1/x^2 + 1)^(1/4))) - 3/(1/x^2 + 1)^(1/4) - 2*arctan((1/x^2 + 1)^(1/4)) + log((1/x^2 + 1)^(1/4) + 1) - log((1/x^2 + 1)^(1/4) - 1)","A",0
1657,1,208,0,0.377066," ","integrate((a*x^2+b)/x^2/(a*x^2-b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","-\frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{b} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{b} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{2 \, b} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{2 \, b} + \frac{2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{3}{4}}}{3 \, b}"," ",0,"-2^(1/4)*(-a)^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/b - 2^(1/4)*(-a)^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/b + 1/2*2^(1/4)*(-a)^(3/4)*log(2^(3/4)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^2))/b - 1/2*2^(1/4)*(-a)^(3/4)*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^2))/b + 2/3*(a + b/x^2)^(3/4)/b","B",0
1658,1,261,0,0.376089," ","integrate(x*(a*x^4+b*x^3)^(1/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{4} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{42 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{4} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{21 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{4} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a^{3}} + \frac{21 \, \sqrt{2} b^{4} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{2}} - \frac{8 \, {\left(7 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} b^{4} - 18 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a b^{4} - 21 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{2} b^{4}\right)} x^{3}}{a^{2} b^{3}}}{768 \, b}"," ",0,"1/768*(42*sqrt(2)*(-a)^(1/4)*b^4*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^3 + 42*sqrt(2)*(-a)^(1/4)*b^4*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^3 + 21*sqrt(2)*(-a)^(1/4)*b^4*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^3 + 21*sqrt(2)*b^4*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^2) - 8*(7*(a + b/x)^(9/4)*b^4 - 18*(a + b/x)^(5/4)*a*b^4 - 21*(a + b/x)^(1/4)*a^2*b^4)*x^3/(a^2*b^3))/b","B",0
1659,0,0,0,0.000000," ","integrate((a*x^3-2*b)/(a*x^3+x^2+b)/(a*x^5+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{3} - 2 \, b}{{\left(a x^{5} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{3} + x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^3 - 2*b)/((a*x^5 + b*x^2)^(1/4)*(a*x^3 + x^2 + b)), x)","F",0
1660,0,0,0,0.000000," ","integrate((a*x^2-b)/(a*x^2+b+x)/(a*x^5+b*x^3)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a x^{5} + b x^{3}\right)}^{\frac{1}{4}} {\left(a x^{2} + b + x\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a*x^5 + b*x^3)^(1/4)*(a*x^2 + b + x)), x)","F",0
1661,0,0,0,0.000000," ","integrate(x^13/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(x^{6} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^13/(x^6 - 1)^(1/3), x)","F",0
1662,0,0,0,0.000000," ","integrate(x^9*(x^6-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{6} - 1\right)}^{\frac{1}{3}} x^{9}\,{d x}"," ",0,"integrate((x^6 - 1)^(1/3)*x^9, x)","F",0
1663,0,0,0,0.000000," ","integrate(x^7*(x^6-1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{6} - 1\right)}^{\frac{2}{3}} x^{7}\,{d x}"," ",0,"integrate((x^6 - 1)^(2/3)*x^7, x)","F",0
1664,0,0,0,0.000000," ","integrate(x^13/(x^6+1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(x^{6} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^13/(x^6 + 1)^(1/3), x)","F",0
1665,0,0,0,0.000000," ","integrate(x^7*(x^6+1)^(2/3),x, algorithm=""giac"")","\int {\left(x^{6} + 1\right)}^{\frac{2}{3}} x^{7}\,{d x}"," ",0,"integrate((x^6 + 1)^(2/3)*x^7, x)","F",0
1666,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+4)/x^6/(x^6-4*x^3+8),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 4\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 4 \, x^{3} + 8\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 4)*(x^3 + 1)^(2/3)/((x^6 - 4*x^3 + 8)*x^6), x)","F",0
1667,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+4)/x^6/(x^6-4*x^3+8),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 4\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 4 \, x^{3} + 8\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 4)*(x^3 + 1)^(2/3)/((x^6 - 4*x^3 + 8)*x^6), x)","F",0
1668,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+2)*(3*x^3+4)/x^6/(x^6+2*x^3+4),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} + 4\right)} {\left(x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 2 \, x^{3} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((3*x^3 + 4)*(x^3 + 2)*(x^3 + 1)^(2/3)/((x^6 + 2*x^3 + 4)*x^6), x)","F",0
1669,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+2)*(3*x^3+4)/x^6/(x^6+2*x^3+4),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} + 4\right)} {\left(x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 2 \, x^{3} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((3*x^3 + 4)*(x^3 + 2)*(x^3 + 1)^(2/3)/((x^6 + 2*x^3 + 4)*x^6), x)","F",0
1670,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6+2*x^3+4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 2 \, x^{3} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 4)*(x^3 - 1)^(2/3)/((x^6 + 2*x^3 + 4)*x^6), x)","F",0
1671,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6+2*x^3+4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} + 2 \, x^{3} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 4)*(x^3 - 1)^(2/3)/((x^6 + 2*x^3 + 4)*x^6), x)","F",0
1672,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-x^3+1)/x^6/(2*x^6-x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} - x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^3 + 1)*(x^3 - 1)^(2/3)/((2*x^6 - x^3 - 2)*x^6), x)","F",0
1673,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-x^3+1)/x^6/(2*x^6-x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} - x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^3 + 1)*(x^3 - 1)^(2/3)/((2*x^6 - x^3 - 2)*x^6), x)","F",0
1674,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(3*x^6+6*x^3+4)/x^6/(3*x^6+6*x^3+8),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{6} + 6 \, x^{3} + 4\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(3 \, x^{6} + 6 \, x^{3} + 8\right)} x^{6}}\,{d x}"," ",0,"integrate((3*x^6 + 6*x^3 + 4)*(x^3 + 1)^(2/3)/((3*x^6 + 6*x^3 + 8)*x^6), x)","F",0
1675,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(3*x^6+6*x^3+4)/x^6/(3*x^6+6*x^3+8),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{6} + 6 \, x^{3} + 4\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(3 \, x^{6} + 6 \, x^{3} + 8\right)} x^{6}}\,{d x}"," ",0,"integrate((3*x^6 + 6*x^3 + 4)*(x^3 + 1)^(2/3)/((3*x^6 + 6*x^3 + 8)*x^6), x)","F",0
1676,0,0,0,0.000000," ","integrate((x^8+2*x^3-1)^(1/3)*(5*x^8+3)/x^2/(x^8+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{8} + 3\right)} {\left(x^{8} + 2 \, x^{3} - 1\right)}^{\frac{1}{3}}}{{\left(x^{8} + x^{3} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((5*x^8 + 3)*(x^8 + 2*x^3 - 1)^(1/3)/((x^8 + x^3 - 1)*x^2), x)","F",0
1677,0,0,0,0.000000," ","integrate((x^4-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)} \sqrt{\sqrt{x^{2} + 1} + 1}}{x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - 1)*sqrt(sqrt(x^2 + 1) + 1)/(x^4 + 1), x)","F",0
1678,0,0,0,0.000000," ","integrate((x^4-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)} \sqrt{\sqrt{x^{2} + 1} + 1}}{x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - 1)*sqrt(sqrt(x^2 + 1) + 1)/(x^4 + 1), x)","F",0
1679,0,0,0,0.000000," ","integrate((a^2*x^2+b^2)^(1/2)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} + b^{2}}}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + b^2)/sqrt(a*x + sqrt(a^2*x^2 + b^2)), x)","F",0
1680,0,0,0,0.000000," ","integrate((-2*a+b+x)/((-a+x)*(-b+x)^2)^(1/4)/(b^2+a*d-(2*b+d)*x+x^2),x, algorithm=""giac"")","\int -\frac{2 \, a - b - x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{4}} {\left(b^{2} + a d - {\left(2 \, b + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate(-(2*a - b - x)/((-(a - x)*(b - x)^2)^(1/4)*(b^2 + a*d - (2*b + d)*x + x^2)), x)","F",0
1681,1,88,0,0.182150," ","integrate(x*(x^3+x^2)^(1/3),x, algorithm=""giac"")","-\frac{1}{54} \, {\left(5 \, {\left(\frac{1}{x} + 1\right)}^{\frac{7}{3}} - 13 \, {\left(\frac{1}{x} + 1\right)}^{\frac{4}{3}} - 10 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)} x^{3} + \frac{5}{81} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{5}{162} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{5}{81} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/54*(5*(1/x + 1)^(7/3) - 13*(1/x + 1)^(4/3) - 10*(1/x + 1)^(1/3))*x^3 + 5/81*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) + 5/162*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) - 5/81*log(abs((1/x + 1)^(1/3) - 1))","A",0
1682,0,0,0,0.000000," ","integrate((-(2*a-3*b)*b+2*(a-2*b)*x+x^2)/((-a+x)*(-b+x)^2)^(1/4)/(-a^3-b^2*d+(3*a^2+2*b*d)*x-(3*a+d)*x^2+x^3),x, algorithm=""giac"")","\int \frac{{\left(2 \, a - 3 \, b\right)} b - 2 \, {\left(a - 2 \, b\right)} x - x^{2}}{{\left(a^{3} + b^{2} d + {\left(3 \, a + d\right)} x^{2} - x^{3} - {\left(3 \, a^{2} + 2 \, b d\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(((2*a - 3*b)*b - 2*(a - 2*b)*x - x^2)/((a^3 + b^2*d + (3*a + d)*x^2 - x^3 - (3*a^2 + 2*b*d)*x)*(-(a - x)*(b - x)^2)^(1/4)), x)","F",0
1683,0,0,0,0.000000," ","integrate((-1+x)^3*(-1+2*(-1+k)*x+k*x^2)/x/((1-x)*x*(-k*x+1))^(1/4)/(k*x-1)/(-1+(3+d)*x-(d*k+3)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{{\left(k x^{2} + 2 \, {\left(k - 1\right)} x - 1\right)} {\left(x - 1\right)}^{3}}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{4}} {\left({\left(d k + 3\right)} x^{2} - x^{3} - {\left(d + 3\right)} x + 1\right)} {\left(k x - 1\right)} x}\,{d x}"," ",0,"integrate(-(k*x^2 + 2*(k - 1)*x - 1)*(x - 1)^3/(((k*x - 1)*(x - 1)*x)^(1/4)*((d*k + 3)*x^2 - x^3 - (d + 3)*x + 1)*(k*x - 1)*x), x)","F",0
1684,0,0,0,0.000000," ","integrate((a*x^2+b)/(a*x^2-b)/(a*x^3+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{\sqrt{a x^{3} + b x} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/(sqrt(a*x^3 + b*x)*(a*x^2 - b)), x)","F",0
1685,0,0,0,0.000000," ","integrate((a^2-2*a*x+x^2)*(-(2*a-3*b)*b+2*(a-2*b)*x+x^2)/((-a+x)*(-b+x)^2)^(3/4)/(-b^2-a^3*d+(3*a^2*d+2*b)*x-(3*a*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(a^{2} - 2 \, a x + x^{2}\right)} {\left({\left(2 \, a - 3 \, b\right)} b - 2 \, {\left(a - 2 \, b\right)} x - x^{2}\right)}}{{\left(a^{3} d - d x^{3} + {\left(3 \, a d + 1\right)} x^{2} + b^{2} - {\left(3 \, a^{2} d + 2 \, b\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a^2 - 2*a*x + x^2)*((2*a - 3*b)*b - 2*(a - 2*b)*x - x^2)/((a^3*d - d*x^3 + (3*a*d + 1)*x^2 + b^2 - (3*a^2*d + 2*b)*x)*(-(a - x)*(b - x)^2)^(3/4)), x)","F",0
1686,1,57,0,0.195899," ","integrate((x^3-1)*(x^4+x^3)^(1/4)/(x^3+1),x, algorithm=""giac"")","\frac{1}{8} \, {\left({\left(\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{2} - \frac{3}{16} \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{3}{32} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{3}{32} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/8*((1/x + 1)^(5/4) + 3*(1/x + 1)^(1/4))*x^2 - 3/16*arctan((1/x + 1)^(1/4)) - 3/32*log((1/x + 1)^(1/4) + 1) + 3/32*log((1/x + 1)^(1/4) - 1)","B",0
1687,1,213,0,0.208773," ","integrate((a*x^2-b)/x^2/(a*x^2+b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{b} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{b} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{2 \, b} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{2 \, b} - \frac{2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{3}{4}}}{3 \, b}"," ",0,"2^(1/4)*(-a)^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/b + 2^(1/4)*(-a)^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/b - 1/2*2^(1/4)*(-a)^(3/4)*log(2^(3/4)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^2))/b + 1/2*2^(1/4)*(-a)^(3/4)*log(-2^(3/4)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^2))/b - 2/3*(a - b/x^2)^(3/4)/b","B",0
1688,0,0,0,0.000000," ","integrate((-b+x)*(-6*a+b+5*x)/((-a+x)*(-b+x)^2)^(1/4)/(b^6+a*d-(6*b^5+d)*x+15*b^4*x^2-20*b^3*x^3+15*b^2*x^4-6*b*x^5+x^6),x, algorithm=""giac"")","\int \frac{{\left(6 \, a - b - 5 \, x\right)} {\left(b - x\right)}}{{\left(b^{6} + 15 \, b^{4} x^{2} - 20 \, b^{3} x^{3} + 15 \, b^{2} x^{4} - 6 \, b x^{5} + x^{6} + a d - {\left(6 \, b^{5} + d\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((6*a - b - 5*x)*(b - x)/((b^6 + 15*b^4*x^2 - 20*b^3*x^3 + 15*b^2*x^4 - 6*b*x^5 + x^6 + a*d - (6*b^5 + d)*x)*(-(a - x)*(b - x)^2)^(1/4)), x)","F",0
1689,0,0,0,0.000000," ","integrate((-6*a+b+5*x)*(-b^5+5*b^4*x-10*b^3*x^2+10*b^2*x^3-5*b*x^4+x^5)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^6*d-(6*b^5*d+1)*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, algorithm=""giac"")","\int \frac{{\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(6 \, a - b - 5 \, x\right)}}{{\left(b^{6} d + 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} - {\left(6 \, b^{5} d + 1\right)} x + a\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((b^5 - 5*b^4*x + 10*b^3*x^2 - 10*b^2*x^3 + 5*b*x^4 - x^5)*(6*a - b - 5*x)/((b^6*d + 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 - (6*b^5*d + 1)*x + a)*(-(a - x)*(b - x)^2)^(3/4)), x)","F",0
1690,1,218,0,0.211330," ","integrate(x^4*(x^4+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","-\frac{1}{4} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - 8 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(\left(-4722366482869645213696 i + 4722366482869645213696\right)^{\frac{1}{4}} - 262144 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + 8 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(-\left(-4722366482869645213696 i + 4722366482869645213696\right)^{\frac{1}{4}} - 262144 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(\left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-\left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(-68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(-68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"-1/4*2^(1/4)*arctan(1/2*2^(3/4)*(1/x^2 + 1)^(1/4)) - 8*I*(-1/16777216*I + 1/16777216)^(1/4)*log((-4722366482869645213696*I + 4722366482869645213696)^(1/4) - 262144*(1/x^2 + 1)^(1/4)) + 8*I*(-1/16777216*I + 1/16777216)^(1/4)*log(-(-4722366482869645213696*I + 4722366482869645213696)^(1/4) - 262144*(1/x^2 + 1)^(1/4)) + I*(1/4096*I + 1/4096)^(1/4)*log((68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - (1/4096*I + 1/4096)^(1/4)*log(I*(68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) + (1/4096*I + 1/4096)^(1/4)*log(-I*(68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - I*(1/4096*I + 1/4096)^(1/4)*log(-(68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) + (-1/4096*I + 1/4096)^(1/4)*log(I*(-68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - (-1/4096*I + 1/4096)^(1/4)*log(-I*(-68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - 1/8*2^(1/4)*log(2^(1/4) + (1/x^2 + 1)^(1/4)) + 1/8*2^(1/4)*log(abs(-2^(1/4) + (1/x^2 + 1)^(1/4)))","B",0
1691,1,218,0,0.225122," ","integrate(x^4*(x^4+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","-\frac{1}{4} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - 8 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(\left(-4722366482869645213696 i + 4722366482869645213696\right)^{\frac{1}{4}} - 262144 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + 8 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(-\left(-4722366482869645213696 i + 4722366482869645213696\right)^{\frac{1}{4}} - 262144 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(\left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-\left(68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(-68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(-68719476736 i + 68719476736\right)^{\frac{1}{4}} - 512 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"-1/4*2^(1/4)*arctan(1/2*2^(3/4)*(1/x^2 + 1)^(1/4)) - 8*I*(-1/16777216*I + 1/16777216)^(1/4)*log((-4722366482869645213696*I + 4722366482869645213696)^(1/4) - 262144*(1/x^2 + 1)^(1/4)) + 8*I*(-1/16777216*I + 1/16777216)^(1/4)*log(-(-4722366482869645213696*I + 4722366482869645213696)^(1/4) - 262144*(1/x^2 + 1)^(1/4)) + I*(1/4096*I + 1/4096)^(1/4)*log((68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - (1/4096*I + 1/4096)^(1/4)*log(I*(68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) + (1/4096*I + 1/4096)^(1/4)*log(-I*(68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - I*(1/4096*I + 1/4096)^(1/4)*log(-(68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) + (-1/4096*I + 1/4096)^(1/4)*log(I*(-68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - (-1/4096*I + 1/4096)^(1/4)*log(-I*(-68719476736*I + 68719476736)^(1/4) - 512*(1/x^2 + 1)^(1/4)) - 1/8*2^(1/4)*log(2^(1/4) + (1/x^2 + 1)^(1/4)) + 1/8*2^(1/4)*log(abs(-2^(1/4) + (1/x^2 + 1)^(1/4)))","B",0
1692,0,0,0,0.000000," ","integrate(x^4/(x^4+x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{8} + x^{4} + 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((x^8 + x^4 + 1)*(x^4 + x^2)^(1/4)), x)","F",0
1693,0,0,0,0.000000," ","integrate(x^4/(x^4+x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{8} + x^{4} + 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((x^8 + x^4 + 1)*(x^4 + x^2)^(1/4)), x)","F",0
1694,0,0,0,0.000000," ","integrate(x^6*(x^3+4)/(x^3+1)^(3/4)/(x^8-x^6-2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 4\right)} x^{6}}{{\left(x^{8} - x^{6} - 2 \, x^{3} - 1\right)} {\left(x^{3} + 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((x^3 + 4)*x^6/((x^8 - x^6 - 2*x^3 - 1)*(x^3 + 1)^(3/4)), x)","F",0
1695,0,0,0,0.000000," ","integrate(x^10*(x^3-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{1}{3}} x^{10}\,{d x}"," ",0,"integrate((x^3 - 1)^(1/3)*x^10, x)","F",0
1696,1,74,0,0.245897," ","integrate(x/(-1+x)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{3}{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}} + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) - 3/(-1/x + 1)^(1/3) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
1697,1,74,0,0.155137," ","integrate((1+x)/(-1+x)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{6}{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}} + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) - 6/(-1/x + 1)^(1/3) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
1698,0,0,0,0.000000," ","integrate((a*x-2*b)/(a*x+x^2-b)/(a*x^3-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x - 2 \, b}{{\left(a x^{3} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x + x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x - 2*b)/((a*x^3 - b*x^2)^(1/4)*(a*x + x^2 - b)), x)","F",0
1699,0,0,0,0.000000," ","integrate((x^2+1)*(2*x^3-x)^(1/3)/x^2/(x^4+1),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
1700,0,0,0,0.000000," ","integrate((-1+x)/(x^2+x+1)/(x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} {\left(x^{2} + x + 1\right)}}\,{d x}"," ",0,"integrate((x - 1)/((x^4 + 1)^(1/4)*(x^2 + x + 1)), x)","F",0
1701,1,123,0,0.527522," ","integrate(x^2*(x^4+x^3)^(1/4)/(-1+x),x, algorithm=""giac"")","\frac{1}{96} \, {\left(101 \, {\left(\frac{1}{x} + 1\right)}^{\frac{9}{4}} - 150 \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 81 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{3} - 2 \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + \frac{155}{64} \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{155}{128} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{155}{128} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/96*(101*(1/x + 1)^(9/4) - 150*(1/x + 1)^(5/4) + 81*(1/x + 1)^(1/4))*x^3 - 2*2^(1/4)*arctan(1/2*2^(3/4)*(1/x + 1)^(1/4)) - 2^(1/4)*log(2^(1/4) + (1/x + 1)^(1/4)) + 2^(1/4)*log(abs(-2^(1/4) + (1/x + 1)^(1/4))) + 155/64*arctan((1/x + 1)^(1/4)) + 155/128*log((1/x + 1)^(1/4) + 1) - 155/128*log(abs((1/x + 1)^(1/4) - 1))","A",0
1702,1,209,0,0.303270," ","integrate((a*x^3-b)*(2*a*x^3-b)/x^6/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{2}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} a \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) - \frac{4}{21} \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{7}{4}} - \frac{8}{9} \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a"," ",0,"2/3*sqrt(2)*(-a)^(3/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) + 2/3*sqrt(2)*(-a)^(3/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) - 1/3*sqrt(2)*(-a)^(3/4)*a*log(sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) + 1/3*sqrt(2)*(-a)^(3/4)*a*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) - 4/21*(a - b/x^3)^(7/4) - 8/9*(a - b/x^3)^(3/4)*a","B",0
1703,0,0,0,0.000000," ","integrate((x^8+a*x^4-b)/x^8/(a*x^4-b)/(a*x^4+b)^(1/4),x, algorithm=""giac"")","\int \frac{x^{8} + a x^{4} - b}{{\left(a x^{4} + b\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)} x^{8}}\,{d x}"," ",0,"integrate((x^8 + a*x^4 - b)/((a*x^4 + b)^(1/4)*(a*x^4 - b)*x^8), x)","F",0
1704,0,0,0,0.000000," ","integrate((x^4+1)/x^4/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{\sqrt{x + \sqrt{x^{2} + 1}} x^{4}}\,{d x}"," ",0,"integrate((x^4 + 1)/(sqrt(x + sqrt(x^2 + 1))*x^4), x)","F",0
1705,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/x^2/(a*x^2+b^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{\sqrt{a x^{2} + b^{2}} x^{2}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(sqrt(a*x^2 + b^2)*x^2), x)","F",0
1706,0,0,0,0.000000," ","integrate((x^2+2)/x/(x^2-2*x+2)/(x^2-x+1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 2}{{\left(x^{2} - x + 1\right)}^{\frac{1}{3}} {\left(x^{2} - 2 \, x + 2\right)} x}\,{d x}"," ",0,"integrate((x^2 + 2)/((x^2 - x + 1)^(1/3)*(x^2 - 2*x + 2)*x), x)","F",0
1707,0,0,0,0.000000," ","integrate((-1+x)/x^10/(x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} + 1\right)}^{\frac{1}{3}} x^{10}}\,{d x}"," ",0,"integrate((x - 1)/((x^3 + 1)^(1/3)*x^10), x)","F",0
1708,1,87,0,0.685711," ","integrate(1/x/(a*x^3+b)^(1/3),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(a x^{3} + b\right)}^{\frac{1}{3}} + b^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{3 \, b^{\frac{1}{3}}} - \frac{\log\left({\left(a x^{3} + b\right)}^{\frac{2}{3}} + {\left(a x^{3} + b\right)}^{\frac{1}{3}} b^{\frac{1}{3}} + b^{\frac{2}{3}}\right)}{6 \, b^{\frac{1}{3}}} + \frac{\log\left({\left| {\left(a x^{3} + b\right)}^{\frac{1}{3}} - b^{\frac{1}{3}} \right|}\right)}{3 \, b^{\frac{1}{3}}}"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(a*x^3 + b)^(1/3) + b^(1/3))/b^(1/3))/b^(1/3) - 1/6*log((a*x^3 + b)^(2/3) + (a*x^3 + b)^(1/3)*b^(1/3) + b^(2/3))/b^(1/3) + 1/3*log(abs((a*x^3 + b)^(1/3) - b^(1/3)))/b^(1/3)","A",0
1709,0,0,0,0.000000," ","integrate((-1-2*(-1+k)*x+k*x^2)*(k^3*x^3-3*k^2*x^2+3*k*x-1)/(-1+x)/x/((1-x)*x*(-k*x+1))^(1/4)/(-1+(d+3*k)*x-(3*k^2+d)*x^2+k^3*x^3),x, algorithm=""giac"")","\int \frac{{\left(k^{3} x^{3} - 3 \, k^{2} x^{2} + 3 \, k x - 1\right)} {\left(k x^{2} - 2 \, {\left(k - 1\right)} x - 1\right)}}{{\left(k^{3} x^{3} - {\left(3 \, k^{2} + d\right)} x^{2} + {\left(d + 3 \, k\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{4}} {\left(x - 1\right)} x}\,{d x}"," ",0,"integrate((k^3*x^3 - 3*k^2*x^2 + 3*k*x - 1)*(k*x^2 - 2*(k - 1)*x - 1)/((k^3*x^3 - (3*k^2 + d)*x^2 + (d + 3*k)*x - 1)*((k*x - 1)*(x - 1)*x)^(1/4)*(x - 1)*x), x)","F",0
1710,0,0,0,0.000000," ","integrate((x^4+3)*(x^4-x^3-1)^(2/3)/x^3/(x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{4} + 3\right)}}{{\left(x^{4} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^4 - x^3 - 1)^(2/3)*(x^4 + 3)/((x^4 - 1)*x^3), x)","F",0
1711,0,0,0,0.000000," ","integrate((2*x^2+1)*(2*x^3+x)^(1/3)/x^4/(2*x^4+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + x\right)}^{\frac{1}{3}} {\left(2 \, x^{2} + 1\right)}}{{\left(2 \, x^{4} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((2*x^3 + x)^(1/3)*(2*x^2 + 1)/((2*x^4 + 1)*x^4), x)","F",0
1712,0,0,0,0.000000," ","integrate(1/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int -\frac{1}{\sqrt{a x + b} \sqrt{c + \sqrt{a x + b}} - x}\,{d x}"," ",0,"integrate(-1/(sqrt(a*x + b)*sqrt(c + sqrt(a*x + b)) - x), x)","F",0
1713,0,0,0,0.000000," ","integrate(1/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int -\frac{1}{\sqrt{a x + b} \sqrt{c + \sqrt{a x + b}} - x}\,{d x}"," ",0,"integrate(-1/(sqrt(a*x + b)*sqrt(c + sqrt(a*x + b)) - x), x)","F",0
1714,0,0,0,0.000000," ","integrate((x^2-x+2)/(x^2-1)^(1/3)/(x^2+4*x+3),x, algorithm=""giac"")","\int \frac{x^{2} - x + 2}{{\left(x^{2} + 4 \, x + 3\right)} {\left(x^{2} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^2 - x + 2)/((x^2 + 4*x + 3)*(x^2 - 1)^(1/3)), x)","F",0
1715,0,0,0,0.000000," ","integrate(x*(k*x-1)*(-1+2*(-1+k)*x+k*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(1+3*d)*x-(3*d+k)*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(k x^{2} + 2 \, {\left(k - 1\right)} x - 1\right)} {\left(k x - 1\right)} x}{{\left(d x^{3} - {\left(3 \, d + k\right)} x^{2} + {\left(3 \, d + 1\right)} x - d\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{3}{4}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((k*x^2 + 2*(k - 1)*x - 1)*(k*x - 1)*x/((d*x^3 - (3*d + k)*x^2 + (3*d + 1)*x - d)*((k*x - 1)*(x - 1)*x)^(3/4)*(x - 1)), x)","F",0
1716,0,0,0,0.000000," ","integrate((-1+x)*x*(-1-2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(k*x-1)/(-d+(3*d*k+1)*x-(3*d*k^2+1)*x^2+d*k^3*x^3),x, algorithm=""giac"")","\int \frac{{\left(k x^{2} - 2 \, {\left(k - 1\right)} x - 1\right)} {\left(x - 1\right)} x}{{\left(d k^{3} x^{3} - {\left(3 \, d k^{2} + 1\right)} x^{2} + {\left(3 \, d k + 1\right)} x - d\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{3}{4}} {\left(k x - 1\right)}}\,{d x}"," ",0,"integrate((k*x^2 - 2*(k - 1)*x - 1)*(x - 1)*x/((d*k^3*x^3 - (3*d*k^2 + 1)*x^2 + (3*d*k + 1)*x - d)*((k*x - 1)*(x - 1)*x)^(3/4)*(k*x - 1)), x)","F",0
1717,0,0,0,0.000000," ","integrate((x^2+4)*(x^3-2*x)^(1/3)/x^4/(x^4-4*x^2-4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 2 \, x\right)}^{\frac{1}{3}} {\left(x^{2} + 4\right)}}{{\left(x^{4} - 4 \, x^{2} - 4\right)} x^{4}}\,{d x}"," ",0,"integrate((x^3 - 2*x)^(1/3)*(x^2 + 4)/((x^4 - 4*x^2 - 4)*x^4), x)","F",0
1718,0,0,0,0.000000," ","integrate((x^2+4)*(x^3-2*x)^(1/3)/x^4/(x^4-4*x^2-4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 2 \, x\right)}^{\frac{1}{3}} {\left(x^{2} + 4\right)}}{{\left(x^{4} - 4 \, x^{2} - 4\right)} x^{4}}\,{d x}"," ",0,"integrate((x^3 - 2*x)^(1/3)*(x^2 + 4)/((x^4 - 4*x^2 - 4)*x^4), x)","F",0
1719,0,0,0,0.000000," ","integrate((a*x^3+2*b)/(a*x^3+x^2-b)/(a*x^5-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{3} + 2 \, b}{{\left(a x^{5} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{3} + x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^3 + 2*b)/((a*x^5 - b*x^2)^(1/4)*(a*x^3 + x^2 - b)), x)","F",0
1720,0,0,0,0.000000," ","integrate((a*x^2+b)/(a*x^2-b+x)/(a*x^5-b*x^3)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{{\left(a x^{5} - b x^{3}\right)}^{\frac{1}{4}} {\left(a x^{2} - b + x\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/((a*x^5 - b*x^3)^(1/4)*(a*x^2 - b + x)), x)","F",0
1721,0,0,0,0.000000," ","integrate((a*x^4+b)/(a*x^4+x^2-b)/(a*x^6-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{6} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^6 - b*x^2)^(1/4)*(a*x^4 + x^2 - b)), x)","F",0
1722,0,0,0,0.000000," ","integrate((2*a*x^3+b)/(a*x^3-b+x)/(a*x^6-b*x^3)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{3} + b}{{\left(a x^{6} - b x^{3}\right)}^{\frac{1}{4}} {\left(a x^{3} - b + x\right)}}\,{d x}"," ",0,"integrate((2*a*x^3 + b)/((a*x^6 - b*x^3)^(1/4)*(a*x^3 - b + x)), x)","F",0
1723,0,0,0,0.000000," ","integrate(1/(a*x^4-b)^(1/4)/(a*x^8-x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{8} - x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((a*x^8 - x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
1724,0,0,0,0.000000," ","integrate(1/(a*x^4-b)^(1/4)/(a*x^8-x^4-b),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{8} - x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((a*x^8 - x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
1725,0,0,0,0.000000," ","integrate((a*x^4+b)/(a*x^4-b)^(1/4)/(a*x^8+c*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{8} + c x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^8 + c*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
1726,0,0,0,0.000000," ","integrate((a*x^4+b)/(a*x^4-b)^(1/4)/(a*x^8+c*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{8} + c x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^8 + c*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
1727,0,0,0,0.000000," ","integrate((x^5+1)*(x^5+x^3+1)^(1/3)*(2*x^5-3)/x^2/(2*x^10-2*x^8-x^6+4*x^5-2*x^3+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 3\right)} {\left(x^{5} + x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{5} + 1\right)}}{{\left(2 \, x^{10} - 2 \, x^{8} - x^{6} + 4 \, x^{5} - 2 \, x^{3} + 2\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^5 - 3)*(x^5 + x^3 + 1)^(1/3)*(x^5 + 1)/((2*x^10 - 2*x^8 - x^6 + 4*x^5 - 2*x^3 + 2)*x^2), x)","F",0
1728,0,0,0,0.000000," ","integrate((x^5+1)*(x^5+x^3+1)^(1/3)*(2*x^5-3)/x^2/(2*x^10-2*x^8-x^6+4*x^5-2*x^3+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 3\right)} {\left(x^{5} + x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{5} + 1\right)}}{{\left(2 \, x^{10} - 2 \, x^{8} - x^{6} + 4 \, x^{5} - 2 \, x^{3} + 2\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^5 - 3)*(x^5 + x^3 + 1)^(1/3)*(x^5 + 1)/((2*x^10 - 2*x^8 - x^6 + 4*x^5 - 2*x^3 + 2)*x^2), x)","F",0
1729,1,109,0,0.184816," ","integrate(x^4*(x^3-x)^(1/3),x, algorithm=""giac"")","-\frac{1}{108} \, {\left(5 \, {\left(\frac{1}{x^{2}} - 1\right)}^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 13 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} - 10 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)} x^{6} - \frac{5}{162} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{5}{324} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{5}{162} \, \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/108*(5*(1/x^2 - 1)^2*(-1/x^2 + 1)^(1/3) - 13*(-1/x^2 + 1)^(4/3) - 10*(-1/x^2 + 1)^(1/3))*x^6 - 5/162*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) - 5/324*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) + 5/162*log(abs((-1/x^2 + 1)^(1/3) - 1))","A",0
1730,0,0,0,0.000000," ","integrate(x/(a*x^2-b)/(a*x^3+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{a x^{3} + b x} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(a*x^3 + b*x)*(a*x^2 - b)), x)","F",0
1731,0,0,0,0.000000," ","integrate((a*x^3+b*x)^(1/2)/(a^2*x^4-b^2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3} + b x}}{a^{2} x^{4} - b^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^3 + b*x)/(a^2*x^4 - b^2), x)","F",0
1732,0,0,0,0.000000," ","integrate(x^19/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{19}}{{\left(x^{6} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^19/(x^6 - 1)^(1/3), x)","F",0
1733,0,0,0,0.000000," ","integrate(x^15*(x^6-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{6} - 1\right)}^{\frac{1}{3}} x^{15}\,{d x}"," ",0,"integrate((x^6 - 1)^(1/3)*x^15, x)","F",0
1734,0,0,0,0.000000," ","integrate(x^19/(x^6+1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{19}}{{\left(x^{6} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^19/(x^6 + 1)^(1/3), x)","F",0
1735,0,0,0,0.000000," ","integrate(x^15*(x^6+1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{6} + 1\right)}^{\frac{1}{3}} x^{15}\,{d x}"," ",0,"integrate((x^6 + 1)^(1/3)*x^15, x)","F",0
1736,1,220,0,0.311173," ","integrate((x^6-a*x^3-b)/x^6/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, \left(-a\right)^{\frac{1}{4}}} - \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, \left(-a\right)^{\frac{1}{4}}} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{6 \, a} - \frac{\sqrt{2} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{6 \, \left(-a\right)^{\frac{1}{4}}} + \frac{4 \, {\left(3 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{6} - 14 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{63 \, b^{7}}"," ",0,"-1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/(-a)^(1/4) - 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/(-a)^(1/4) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3))/a - 1/6*sqrt(2)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3))/(-a)^(1/4) + 4/63*(3*(a - b/x^3)^(7/4)*b^6 - 14*(a - b/x^3)^(3/4)*a*b^6)/b^7","B",0
1737,0,0,0,0.000000," ","integrate((3*x^6-x^4-3)/(x^6-x^4+1)/(x^6-x^4-x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x^{6} - x^{4} - 3}{{\left(x^{6} - x^{4} - x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{6} - x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((3*x^6 - x^4 - 3)/((x^6 - x^4 - x^3 + 1)^(1/3)*(x^6 - x^4 + 1)), x)","F",0
1738,1,217,0,0.353541," ","integrate((a*x^6-b)/x^6/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) + \frac{4 \, {\left(3 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{6} - 7 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{63 \, b^{7}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) + 4/63*(3*(a - b/x^3)^(7/4)*b^6 - 7*(a - b/x^3)^(3/4)*a*b^6)/b^7","B",0
1739,1,217,0,0.289725," ","integrate((a*x^6+b)/x^6/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{3} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) + \frac{1}{6} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right) - \frac{4 \, {\left(3 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{6} - 7 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{6}\right)}}{63 \, b^{7}}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4)) - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(-a) + sqrt(a - b/x^3)) - 4/63*(3*(a - b/x^3)^(7/4)*b^6 - 7*(a - b/x^3)^(3/4)*a*b^6)/b^7","B",0
1740,1,123,0,0.199136," ","integrate((x^4+x^2)^(1/4)*(x^8-x^4-1)/(x^4-1),x, algorithm=""giac"")","-\frac{1}{192} \, {\left(7 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{9}{4}} - 18 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{4}} - 21 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right)} x^{6} + \frac{1}{2} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right) + \frac{7}{128} \, \arctan\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{7}{256} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{7}{256} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"-1/192*(7*(1/x^2 + 1)^(9/4) - 18*(1/x^2 + 1)^(5/4) - 21*(1/x^2 + 1)^(1/4))*x^6 + 1/2*2^(1/4)*arctan(1/2*2^(3/4)*(1/x^2 + 1)^(1/4)) + 1/4*2^(1/4)*log(2^(1/4) + (1/x^2 + 1)^(1/4)) - 1/4*2^(1/4)*log(abs(-2^(1/4) + (1/x^2 + 1)^(1/4))) + 7/128*arctan((1/x^2 + 1)^(1/4)) + 7/256*log((1/x^2 + 1)^(1/4) + 1) - 7/256*log((1/x^2 + 1)^(1/4) - 1)","A",0
1741,0,0,0,0.000000," ","integrate((2*x^8-a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} - b}{{\left(x^{8} - a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 - b)/((x^8 - a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1742,0,0,0,0.000000," ","integrate((2*x^8-a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} - b}{{\left(x^{8} - a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 - b)/((x^8 - a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1743,0,0,0,0.000000," ","integrate((c*x^2-x*(a*x^2-b*x)^(1/2))^(1/2)/x^3/(a*x^2-b*x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} - \sqrt{a x^{2} - b x} x}}{\sqrt{a x^{2} - b x} x^{3}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 - sqrt(a*x^2 - b*x)*x)/(sqrt(a*x^2 - b*x)*x^3), x)","F",0
1744,0,0,0,0.000000," ","integrate((x^3+b)/(x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} + b}{{\left(x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 + b)/(x^3 + a)^(1/3), x)","F",0
1745,1,83,0,0.243434," ","integrate((a*x^2+b)/(x^3+x)^(1/3),x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + \frac{1}{6} \, \sqrt{3} {\left(a - 3 \, b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{12} \, {\left(a - 3 \, b\right)} \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, {\left(a - 3 \, b\right)} \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/2*a*x^2*(1/x^2 + 1)^(2/3) + 1/6*sqrt(3)*(a - 3*b)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) - 1/12*(a - 3*b)*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) + 1/6*(a - 3*b)*log(abs((1/x^2 + 1)^(1/3) - 1))","A",0
1746,1,89,0,0.177206," ","integrate((x^3-x^2)^(1/3),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(-\frac{1}{x} + 1\right)}^{\frac{4}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)} x^{2} - \frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{18} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{9} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/6*((-1/x + 1)^(4/3) + 2*(-1/x + 1)^(1/3))*x^2 - 1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) - 1/18*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) + 1/9*log(abs((-1/x + 1)^(1/3) - 1))","A",0
1747,1,97,0,0.188059," ","integrate(x^2*(x^3+x^2)^(1/3),x, algorithm=""giac"")","\frac{1}{324} \, {\left(20 \, {\left(\frac{1}{x} + 1\right)}^{\frac{10}{3}} - 72 \, {\left(\frac{1}{x} + 1\right)}^{\frac{7}{3}} + 93 \, {\left(\frac{1}{x} + 1\right)}^{\frac{4}{3}} + 40 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)} x^{4} - \frac{10}{243} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{5}{243} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{10}{243} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/324*(20*(1/x + 1)^(10/3) - 72*(1/x + 1)^(7/3) + 93*(1/x + 1)^(4/3) + 40*(1/x + 1)^(1/3))*x^4 - 10/243*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) - 5/243*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) + 10/243*log(abs((1/x + 1)^(1/3) - 1))","A",0
1748,1,193,0,0.269159," ","integrate(x^4/(x^4+1)^2/(x^4+x^2)^(1/4),x, algorithm=""giac"")","-\frac{1}{2} i \, \left(-\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(\left(248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4722366482869645213696 i\right) + \frac{1}{2} i \, \left(-\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(-\left(248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4722366482869645213696 i\right) + \frac{1}{2} i \, \left(\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(\left(-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4722366482869645213696 i\right) - \frac{1}{2} i \, \left(\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(-\left(-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4722366482869645213696 i\right) - \frac{1}{8} \, \left(-\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(i \, \left(187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4398046511104 i\right) + \frac{1}{8} \, \left(-\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(-i \, \left(187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4398046511104 i\right) + \frac{1}{8} \, \left(\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(i \, \left(-187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4398046511104 i\right) - \frac{1}{8} \, \left(\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(-i \, \left(-187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4398046511104 i\right) - \frac{{\left(\frac{1}{x^{2}} + 1\right)}^{\frac{7}{4}} - 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}}{8 \, {\left({\left(\frac{1}{x^{2}} + 1\right)}^{2} - \frac{2}{x^{2}}\right)}}"," ",0,"-1/2*I*(-1/524288*I - 1/524288)^(1/4)*log((248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) + 4722366482869645213696*I) + 1/2*I*(-1/524288*I - 1/524288)^(1/4)*log(-(248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) + 4722366482869645213696*I) + 1/2*I*(1/524288*I - 1/524288)^(1/4)*log((-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) - 4722366482869645213696*I) - 1/2*I*(1/524288*I - 1/524288)^(1/4)*log(-(-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) - 4722366482869645213696*I) - 1/8*(-1/2048*I - 1/2048)^(1/4)*log(I*(187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) - 4398046511104*I) + 1/8*(-1/2048*I - 1/2048)^(1/4)*log(-I*(187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) - 4398046511104*I) + 1/8*(1/2048*I - 1/2048)^(1/4)*log(I*(-187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) + 4398046511104*I) - 1/8*(1/2048*I - 1/2048)^(1/4)*log(-I*(-187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) + 4398046511104*I) - 1/8*((1/x^2 + 1)^(7/4) - 2*(1/x^2 + 1)^(3/4))/((1/x^2 + 1)^2 - 2/x^2)","B",0
1749,1,193,0,0.364688," ","integrate(x^4/(x^4+1)^2/(x^4+x^2)^(1/4),x, algorithm=""giac"")","-\frac{1}{2} i \, \left(-\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(\left(248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4722366482869645213696 i\right) + \frac{1}{2} i \, \left(-\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(-\left(248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4722366482869645213696 i\right) + \frac{1}{2} i \, \left(\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(\left(-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4722366482869645213696 i\right) - \frac{1}{2} i \, \left(\frac{1}{524288} i - \frac{1}{524288}\right)^{\frac{1}{4}} \log\left(-\left(-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 i + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4722366482869645213696 i\right) - \frac{1}{8} \, \left(-\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(i \, \left(187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4398046511104 i\right) + \frac{1}{8} \, \left(-\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(-i \, \left(187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 4398046511104 i\right) + \frac{1}{8} \, \left(\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(i \, \left(-187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4398046511104 i\right) - \frac{1}{8} \, \left(\frac{1}{2048} i - \frac{1}{2048}\right)^{\frac{1}{4}} \log\left(-i \, \left(-187072209578355573530071658587684226515959365500928 i + 187072209578355573530071658587684226515959365500928\right)^{\frac{1}{4}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 4398046511104 i\right) - \frac{{\left(\frac{1}{x^{2}} + 1\right)}^{\frac{7}{4}} - 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{3}{4}}}{8 \, {\left({\left(\frac{1}{x^{2}} + 1\right)}^{2} - \frac{2}{x^{2}}\right)}}"," ",0,"-1/2*I*(-1/524288*I - 1/524288)^(1/4)*log((248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) + 4722366482869645213696*I) + 1/2*I*(-1/524288*I - 1/524288)^(1/4)*log(-(248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) + 4722366482869645213696*I) + 1/2*I*(1/524288*I - 1/524288)^(1/4)*log((-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) - 4722366482869645213696*I) - 1/2*I*(1/524288*I - 1/524288)^(1/4)*log(-(-248661618204893321077691124073410420050228075398673858720231988446579748506266687766528*I + 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528)^(1/4)*(1/x^2 + 1)^(1/4) - 4722366482869645213696*I) - 1/8*(-1/2048*I - 1/2048)^(1/4)*log(I*(187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) - 4398046511104*I) + 1/8*(-1/2048*I - 1/2048)^(1/4)*log(-I*(187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) - 4398046511104*I) + 1/8*(1/2048*I - 1/2048)^(1/4)*log(I*(-187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) + 4398046511104*I) - 1/8*(1/2048*I - 1/2048)^(1/4)*log(-I*(-187072209578355573530071658587684226515959365500928*I + 187072209578355573530071658587684226515959365500928)^(1/4)*(1/x^2 + 1)^(1/4) + 4398046511104*I) - 1/8*((1/x^2 + 1)^(7/4) - 2*(1/x^2 + 1)^(3/4))/((1/x^2 + 1)^2 - 2/x^2)","B",0
1750,0,0,0,0.000000," ","integrate((x^4-3)*(x^4-x^3+1)*(x^4+x^3+1)^(2/3)/x^6/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - x^{3} + 1\right)} {\left(x^{4} - 3\right)}}{{\left(x^{4} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^3 + 1)^(2/3)*(x^4 - x^3 + 1)*(x^4 - 3)/((x^4 + 1)*x^6), x)","F",0
1751,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)), x)","F",0
1752,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)), x)","F",0
1753,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^5+x)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{5} + x\right)}^{\frac{1}{3}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^5 + x)^(1/3)*(x^2 - 1)), x)","F",0
1754,0,0,0,0.000000," ","integrate((x^2-1)*(x^6+x^2)^(1/4)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^2 - 1)/((x^2 + 1)*x^2), x)","F",0
1755,0,0,0,0.000000," ","integrate((x^2-1)*(x^6+x^2)^(1/4)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^2 - 1)/((x^2 + 1)*x^2), x)","F",0
1756,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(4*x^6-5*x^3+1)/x^6/(2*x^3-1)^2,x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{6} - 5 \, x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{3} - 1\right)}^{2} x^{6}}\,{d x}"," ",0,"integrate((4*x^6 - 5*x^3 + 1)*(x^3 - 1)^(2/3)/((2*x^3 - 1)^2*x^6), x)","F",0
1757,1,149,0,1.706546," ","integrate((1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x, algorithm=""giac"")","\frac{4}{3} \, {\left(\sqrt{x + 1} + 1\right)}^{\frac{3}{2}} + \frac{4}{5} \, \sqrt{5} \log\left(-\frac{\sqrt{5} - 2 \, \sqrt{\sqrt{x + 1} + 1} - 1}{\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} + 1}\right) + \frac{4}{5} \, \sqrt{5} \log\left(\frac{{\left| -\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} - 1 \right|}}{{\left| \sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} - 1 \right|}}\right) + 4 \, \sqrt{\sqrt{x + 1} + 1} - 2 \, \log\left(\sqrt{x + 1} + \sqrt{\sqrt{x + 1} + 1}\right) + 2 \, \log\left({\left| \sqrt{x + 1} - \sqrt{\sqrt{x + 1} + 1} \right|}\right)"," ",0,"4/3*(sqrt(x + 1) + 1)^(3/2) + 4/5*sqrt(5)*log(-(sqrt(5) - 2*sqrt(sqrt(x + 1) + 1) - 1)/(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) + 1)) + 4/5*sqrt(5)*log(abs(-sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) - 1)/abs(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) - 1)) + 4*sqrt(sqrt(x + 1) + 1) - 2*log(sqrt(x + 1) + sqrt(sqrt(x + 1) + 1)) + 2*log(abs(sqrt(x + 1) - sqrt(sqrt(x + 1) + 1)))","A",0
1758,-1,0,0,0.000000," ","integrate((a*x+b)^(1/2)/(a*b*x+(a*x+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1759,-1,0,0,0.000000," ","integrate((a^2*x^4+b)^(1/2)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1760,-2,0,0,0.000000," ","integrate(1/(e*x+f)/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-d)]Unable to divide, perhaps due to rounding error%%%{-1073741824,[2,10,18,5,4,2,0,0]%%%}+%%%{2147483648,[2,10,18,3,5,2,0,0]%%%}+%%%{1073741824,[2,10,18,3,3,3,0,0]%%%}+%%%{-1073741824,[2,10,18,1,6,2,0,0]%%%}+%%%{-1073741824,[2,10,18,1,4,3,0,0]%%%}+%%%{2147483648,[2,10,17,5,4,1,1,1]%%%}+%%%{-4294967296,[2,10,17,3,5,1,1,1]%%%}+%%%{-3221225472,[2,10,17,3,3,2,1,1]%%%}+%%%{2147483648,[2,10,17,1,6,1,1,1]%%%}+%%%{3221225472,[2,10,17,1,4,2,1,1]%%%}+%%%{-1073741824,[2,10,16,5,4,0,2,2]%%%}+%%%{2147483648,[2,10,16,3,5,0,2,2]%%%}+%%%{3221225472,[2,10,16,3,3,1,2,2]%%%}+%%%{-1073741824,[2,10,16,1,6,0,2,2]%%%}+%%%{-3221225472,[2,10,16,1,4,1,2,2]%%%}+%%%{-1073741824,[2,10,15,3,3,0,3,3]%%%}+%%%{1073741824,[2,10,15,1,4,0,3,3]%%%}+%%%{33554432,[2,8,16,4,3,1,0,0]%%%}+%%%{-50331648,[2,8,16,2,4,1,0,0]%%%}+%%%{16777216,[2,8,16,0,5,1,0,0]%%%}+%%%{-33554432,[2,8,15,4,3,0,1,1]%%%}+%%%{50331648,[2,8,15,2,4,0,1,1]%%%}+%%%{-16777216,[2,8,15,0,5,0,1,1]%%%}+%%%{-262144,[2,6,14,3,2,0,0,0]%%%}+%%%{262144,[2,6,14,1,3,0,0,0]%%%}+%%%{-134217728,[1,9,17,4,3,2,0,0]%%%}+%%%{402653184,[1,9,17,2,4,2,0,0]%%%}+%%%{-268435456,[1,9,17,0,5,2,0,0]%%%}+%%%{268435456,[1,9,16,4,3,1,1,1]%%%}+%%%{-805306368,[1,9,16,2,4,1,1,1]%%%}+%%%{536870912,[1,9,16,0,5,1,1,1]%%%}+%%%{-134217728,[1,9,15,4,3,0,2,2]%%%}+%%%{402653184,[1,9,15,2,4,0,2,2]%%%}+%%%{-268435456,[1,9,15,0,5,0,2,2]%%%}+%%%{2097152,[1,7,15,3,2,1,0,0]%%%}+%%%{-2097152,[1,7,15,1,3,1,0,0]%%%}+%%%{-2097152,[1,7,14,3,2,0,1,1]%%%}+%%%{2097152,[1,7,14,1,3,0,1,1]%%%}+%%%{1073741824,[0,10,18,6,4,2,0,0]%%%}+%%%{-3221225472,[0,10,18,4,5,2,0,0]%%%}+%%%{3221225472,[0,10,18,2,6,2,0,0]%%%}+%%%{-1073741824,[0,10,18,2,4,3,0,0]%%%}+%%%{-1073741824,[0,10,18,0,7,2,0,0]%%%}+%%%{1073741824,[0,10,18,0,5,3,0,0]%%%}+%%%{-2147483648,[0,10,17,6,4,1,1,1]%%%}+%%%{6442450944,[0,10,17,4,5,1,1,1]%%%}+%%%{-6442450944,[0,10,17,2,6,1,1,1]%%%}+%%%{3221225472,[0,10,17,2,4,2,1,1]%%%}+%%%{2147483648,[0,10,17,0,7,1,1,1]%%%}+%%%{-3221225472,[0,10,17,0,5,2,1,1]%%%}+%%%{1073741824,[0,10,16,6,4,0,2,2]%%%}+%%%{-3221225472,[0,10,16,4,5,0,2,2]%%%}+%%%{3221225472,[0,10,16,2,6,0,2,2]%%%}+%%%{-3221225472,[0,10,16,2,4,1,2,2]%%%}+%%%{-1073741824,[0,10,16,0,7,0,2,2]%%%}+%%%{3221225472,[0,10,16,0,5,1,2,2]%%%}+%%%{1073741824,[0,10,15,2,4,0,3,3]%%%}+%%%{-1073741824,[0,10,15,0,5,0,3,3]%%%}+%%%{-33554432,[0,8,16,5,3,1,0,0]%%%}+%%%{67108864,[0,8,16,3,4,1,0,0]%%%}+%%%{-33554432,[0,8,16,1,5,1,0,0]%%%}+%%%{33554432,[0,8,15,5,3,0,1,1]%%%}+%%%{-67108864,[0,8,15,3,4,0,1,1]%%%}+%%%{33554432,[0,8,15,1,5,0,1,1]%%%}+%%%{262144,[0,6,14,4,2,0,0,0]%%%}+%%%{-262144,[0,6,14,2,3,0,0,0]%%%} / %%%{4096,[0,4,7,2,2,0,0,0]%%%}+%%%{-4096,[0,4,7,0,3,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
1761,0,0,0,0.000000," ","integrate((-a*b+(-a+2*b)*x)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-b^2+(-a*d+2*b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{a b + {\left(a - 2 \, b\right)} x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{4}} {\left({\left(d - 1\right)} x^{2} - b^{2} - {\left(a d - 2 \, b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b + (a - 2*b)*x)/((-(a - x)*(b - x)^2*x)^(1/4)*((d - 1)*x^2 - b^2 - (a*d - 2*b)*x)), x)","F",0
1762,0,0,0,0.000000," ","integrate(x^13*(x^3-1)^(1/3),x, algorithm=""giac"")","\int {\left(x^{3} - 1\right)}^{\frac{1}{3}} x^{13}\,{d x}"," ",0,"integrate((x^3 - 1)^(1/3)*x^13, x)","F",0
1763,0,0,0,0.000000," ","integrate((a*b^2-2*(2*a-b)*b*x+(3*a-2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(1/4)/(a^3+(b^2*d-3*a^2)*x+(-2*b*d+3*a)*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int \frac{a b^{2} - 2 \, {\left(2 \, a - b\right)} b x + {\left(3 \, a - 2 \, b\right)} x^{2}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{4}} {\left({\left(d - 1\right)} x^{3} + a^{3} - {\left(2 \, b d - 3 \, a\right)} x^{2} + {\left(b^{2} d - 3 \, a^{2}\right)} x\right)}}\,{d x}"," ",0,"integrate((a*b^2 - 2*(2*a - b)*b*x + (3*a - 2*b)*x^2)/((-(a - x)*(b - x)^2*x)^(1/4)*((d - 1)*x^3 + a^3 - (2*b*d - 3*a)*x^2 + (b^2*d - 3*a^2)*x)), x)","F",0
1764,0,0,0,0.000000," ","integrate((2*x^3+x)^(1/3)*(x^4-1)/x^4/(x^4-x^2+2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)} {\left(2 \, x^{3} + x\right)}^{\frac{1}{3}}}{{\left(x^{4} - x^{2} + 2\right)} x^{4}}\,{d x}"," ",0,"integrate((x^4 - 1)*(2*x^3 + x)^(1/3)/((x^4 - x^2 + 2)*x^4), x)","F",0
1765,0,0,0,0.000000," ","integrate((2*a*x^4+b)/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate((2*a*x^4 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
1766,0,0,0,0.000000," ","integrate((2*a*x^4+b)/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} + b}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate((2*a*x^4 + b)/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
1767,0,0,0,0.000000," ","integrate((x^6+1)*(x^6-x^3-1)^(2/3)/x^3/(x^6-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{6} + 1\right)}}{{\left(x^{6} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^6 - x^3 - 1)^(2/3)*(x^6 + 1)/((x^6 - 1)*x^3), x)","F",0
1768,0,0,0,0.000000," ","integrate((x^6+4)*(x^6-x^4-2)^(1/4)/x^2/(x^6-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} - 2\right)}^{\frac{1}{4}} {\left(x^{6} + 4\right)}}{{\left(x^{6} - 2\right)} x^{2}}\,{d x}"," ",0,"integrate((x^6 - x^4 - 2)^(1/4)*(x^6 + 4)/((x^6 - 2)*x^2), x)","F",0
1769,1,261,0,0.337714," ","integrate((a*x^8+b*x^7)^(1/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{4} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{42 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{4} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{21 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{4} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a^{3}} + \frac{21 \, \sqrt{2} b^{4} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{2}} - \frac{8 \, {\left(7 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} b^{4} - 18 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a b^{4} - 21 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{2} b^{4}\right)} x^{3}}{a^{2} b^{3}}}{768 \, b}"," ",0,"1/768*(42*sqrt(2)*(-a)^(1/4)*b^4*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^3 + 42*sqrt(2)*(-a)^(1/4)*b^4*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^3 + 21*sqrt(2)*(-a)^(1/4)*b^4*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^3 + 21*sqrt(2)*b^4*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^2) - 8*(7*(a + b/x)^(9/4)*b^4 - 18*(a + b/x)^(5/4)*a*b^4 - 21*(a + b/x)^(1/4)*a^2*b^4)*x^3/(a^2*b^3))/b","B",0
1770,0,0,0,0.000000," ","integrate((x^10-1)/(x^4+1)^(1/2)/(x^10+1),x, algorithm=""giac"")","\int \frac{x^{10} - 1}{{\left(x^{10} + 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^10 - 1)/((x^10 + 1)*sqrt(x^4 + 1)), x)","F",0
1771,0,0,0,0.000000," ","integrate((x^10+1)/(x^4+1)^(1/2)/(x^10-1),x, algorithm=""giac"")","\int \frac{x^{10} + 1}{{\left(x^{10} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^10 + 1)/((x^10 - 1)*sqrt(x^4 + 1)), x)","F",0
1772,0,0,0,0.000000," ","integrate((x^16+1)/(x^4+1)^(1/2)/(x^16-1),x, algorithm=""giac"")","\int \frac{x^{16} + 1}{{\left(x^{16} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^16 + 1)/((x^16 - 1)*sqrt(x^4 + 1)), x)","F",0
1773,1,107,0,0.151839," ","integrate((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/(1-(a*x+b)^(1/2)),x, algorithm=""giac"")","-\frac{4 \, {\left(c + 1\right)} \arctan\left(\frac{\sqrt{c + \sqrt{a x + b}}}{\sqrt{-c - 1}}\right)}{a \sqrt{-c - 1}} - \frac{4 \, {\left(3 \, a^{4} {\left(c + \sqrt{a x + b}\right)}^{\frac{5}{2}} - 5 \, a^{4} {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}} c + 5 \, a^{4} {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}} + 15 \, a^{4} \sqrt{c + \sqrt{a x + b}}\right)}}{15 \, a^{5}}"," ",0,"-4*(c + 1)*arctan(sqrt(c + sqrt(a*x + b))/sqrt(-c - 1))/(a*sqrt(-c - 1)) - 4/15*(3*a^4*(c + sqrt(a*x + b))^(5/2) - 5*a^4*(c + sqrt(a*x + b))^(3/2)*c + 5*a^4*(c + sqrt(a*x + b))^(3/2) + 15*a^4*sqrt(c + sqrt(a*x + b)))/a^5","A",0
1774,0,0,0,0.000000," ","integrate(x*(x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{2} + \sqrt{x^{2} - 1} x} \sqrt{x^{2} - 1} x\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^2 - 1)*x)*sqrt(x^2 - 1)*x, x)","F",0
1775,0,0,0,0.000000," ","integrate((p*x^2-q)*(p^2*x^4+q^2)^(1/2)*(b*x^3+a*(p*x^2+q)^3)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{4} + q^{2}} {\left({\left(p x^{2} + q\right)}^{3} a + b x^{3}\right)} {\left(p x^{2} - q\right)}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^4 + q^2)*((p*x^2 + q)^3*a + b*x^3)*(p*x^2 - q)/x^6, x)","F",0
1776,0,0,0,0.000000," ","integrate((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} - 1\right)}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 - 1)/sqrt(x^4 + 1), x)","F",0
1777,1,102,0,0.161100," ","integrate(x*(1+x)^(1/2)/(x+(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\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)}^{\frac{3}{2}} - \frac{2}{5} \, \sqrt{5} \log\left(-\frac{\sqrt{5} - 2 \, \sqrt{\sqrt{x + 1} + 1} - 1}{\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} + 1}\right) + 2 \, \sqrt{x + 1} + 2 \, \log\left(\sqrt{x + 1} + \sqrt{\sqrt{x + 1} + 1}\right) + 2"," ",0,"2/3*(sqrt(x + 1) + 1)^3 - 2*(sqrt(x + 1) + 1)^2 - 4/3*(sqrt(x + 1) + 1)^(3/2) - 2/5*sqrt(5)*log(-(sqrt(5) - 2*sqrt(sqrt(x + 1) + 1) - 1)/(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) + 1)) + 2*sqrt(x + 1) + 2*log(sqrt(x + 1) + sqrt(sqrt(x + 1) + 1)) + 2","A",0
1778,0,0,0,0.000000," ","integrate((x^3-x)^(1/3)*(x^4-10*x^2+8)/x^4/(x^4-2*x^2+4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 10 \, x^{2} + 8\right)} {\left(x^{3} - x\right)}^{\frac{1}{3}}}{{\left(x^{4} - 2 \, x^{2} + 4\right)} x^{4}}\,{d x}"," ",0,"integrate((x^4 - 10*x^2 + 8)*(x^3 - x)^(1/3)/((x^4 - 2*x^2 + 4)*x^4), x)","F",0
1779,0,0,0,0.000000," ","integrate((x^3-x)^(1/3)*(x^4-10*x^2+8)/x^4/(x^4-2*x^2+4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 10 \, x^{2} + 8\right)} {\left(x^{3} - x\right)}^{\frac{1}{3}}}{{\left(x^{4} - 2 \, x^{2} + 4\right)} x^{4}}\,{d x}"," ",0,"integrate((x^4 - 10*x^2 + 8)*(x^3 - x)^(1/3)/((x^4 - 2*x^2 + 4)*x^4), x)","F",0
1780,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^4+x^3-x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^2 + 1)), x)","F",0
1781,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^4+x^3-x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^2 + 1)), x)","F",0
1782,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(x^4+x^3-x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^4 + 1)), x)","F",0
1783,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(x^4+x^3-x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^4 + 1)), x)","F",0
1784,0,0,0,0.000000," ","integrate((a*x^8+b)/x^6/(a*x^4-b)/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{a x^{8} + b}{{\left(a x^{4} + b\right)}^{\frac{3}{4}} {\left(a x^{4} - b\right)} x^{6}}\,{d x}"," ",0,"integrate((a*x^8 + b)/((a*x^4 + b)^(3/4)*(a*x^4 - b)*x^6), x)","F",0
1785,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(2 \, a x^{8} - c x^{4} - 2 \, b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((2*a*x^8 - c*x^4 - 2*b)*(a*x^4 - b)^(1/4)), x)","F",0
1786,0,0,0,0.000000," ","integrate((2*a*x^4-b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - b}{{\left(2 \, a x^{8} - c x^{4} - 2 \, b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^4 - b)/((2*a*x^8 - c*x^4 - 2*b)*(a*x^4 - b)^(1/4)), x)","F",0
1787,0,0,0,0.000000," ","integrate((-a*b-a*c+3*b*c+2*(a-b-c)*x+x^2)/((-a+x)*(-b+x)*(-c+x))^(1/4)/(-a^3-b*c*d+(3*a^2+b*d+c*d)*x-(3*a+d)*x^2+x^3),x, algorithm=""giac"")","\int \frac{a b + a c - 3 \, b c - 2 \, {\left(a - b - c\right)} x - x^{2}}{{\left(a^{3} + b c d + {\left(3 \, a + d\right)} x^{2} - x^{3} - {\left(3 \, a^{2} + b d + c d\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*b + a*c - 3*b*c - 2*(a - b - c)*x - x^2)/((a^3 + b*c*d + (3*a + d)*x^2 - x^3 - (3*a^2 + b*d + c*d)*x)*(-(a - x)*(b - x)*(c - x))^(1/4)), x)","F",0
1788,0,0,0,0.000000," ","integrate(1/(a*x-b)/(a^2*x^3+b^2*x)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{3} + b^{2} x\right)}^{\frac{1}{4}} {\left(a x - b\right)}}\,{d x}"," ",0,"integrate(1/((a^2*x^3 + b^2*x)^(1/4)*(a*x - b)), x)","F",0
1789,0,0,0,0.000000," ","integrate((x^2+2)*(x^2-2*x-2)*(x^4-3*x^2+4)^(1/2)/x^2/(x^2-2)/(2*x^2+x-4),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} - 3 \, x^{2} + 4} {\left(x^{2} - 2 \, x - 2\right)} {\left(x^{2} + 2\right)}}{{\left(2 \, x^{2} + x - 4\right)} {\left(x^{2} - 2\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 - 3*x^2 + 4)*(x^2 - 2*x - 2)*(x^2 + 2)/((2*x^2 + x - 4)*(x^2 - 2)*x^2), x)","F",0
1790,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((x^4 + x^2)^(1/3)*(x - 1)), x)","F",0
1791,0,0,0,0.000000," ","integrate((a^4*x^4-b^2)/(a^2*x^3+b*x)^(1/2)/(a^4*x^4+b^2),x, algorithm=""giac"")","\int \frac{a^{4} x^{4} - b^{2}}{{\left(a^{4} x^{4} + b^{2}\right)} \sqrt{a^{2} x^{3} + b x}}\,{d x}"," ",0,"integrate((a^4*x^4 - b^2)/((a^4*x^4 + b^2)*sqrt(a^2*x^3 + b*x)), x)","F",0
1792,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^5+x)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{5} + x\right)}^{\frac{1}{3}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^5 + x)^(1/3)*(x^2 + 1)), x)","F",0
1793,0,0,0,0.000000," ","integrate((x^4+1)*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}{x^{8} + x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - x^2)^(1/4)*(x^4 + 1)/(x^8 + x^4 + 1), x)","F",0
1794,0,0,0,0.000000," ","integrate((x^4+1)*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}{x^{8} + x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - x^2)^(1/4)*(x^4 + 1)/(x^8 + x^4 + 1), x)","F",0
1795,-2,0,0,0.000000," ","integrate((2*x^8-2*x^4+1)/(x^4-1)^(1/4)/(2*x^8-x^4-2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1796,0,0,0,0.000000," ","integrate((x^2-x)^(1/2)*(x^2-x*(x^2-x)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} - \sqrt{x^{2} - x} x} \sqrt{x^{2} - x}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(x^2 - sqrt(x^2 - x)*x)*sqrt(x^2 - x)/x^3, x)","F",0
1797,1,202,0,0.407482," ","integrate((2*a*x+b)/(a*x^2+b*x+c)^(1/4)/(4*a*x^2+4*b*x+5*c),x, algorithm=""giac"")","\frac{4^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(\sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, {\left(a x^{2} + b x + c\right)}^{\frac{1}{4}}\right)}}{c^{\frac{1}{4}}}\right)}{8 \, c^{\frac{1}{4}}} + \frac{4^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(\sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, {\left(a x^{2} + b x + c\right)}^{\frac{1}{4}}\right)}}{c^{\frac{1}{4}}}\right)}{8 \, c^{\frac{1}{4}}} - \frac{4^{\frac{3}{4}} \sqrt{2} \log\left(\sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}} {\left(a x^{2} + b x + c\right)}^{\frac{1}{4}} c^{\frac{1}{4}} + \sqrt{a x^{2} + b x + c} + \frac{1}{2} \, \sqrt{c}\right)}{16 \, c^{\frac{1}{4}}} + \frac{4^{\frac{3}{4}} \sqrt{2} \log\left(-\sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}} {\left(a x^{2} + b x + c\right)}^{\frac{1}{4}} c^{\frac{1}{4}} + \sqrt{a x^{2} + b x + c} + \frac{1}{2} \, \sqrt{c}\right)}{16 \, c^{\frac{1}{4}}}"," ",0,"1/8*4^(3/4)*sqrt(2)*arctan(2*sqrt(2)*(1/4)^(3/4)*(sqrt(2)*(1/4)^(1/4)*c^(1/4) + 2*(a*x^2 + b*x + c)^(1/4))/c^(1/4))/c^(1/4) + 1/8*4^(3/4)*sqrt(2)*arctan(-2*sqrt(2)*(1/4)^(3/4)*(sqrt(2)*(1/4)^(1/4)*c^(1/4) - 2*(a*x^2 + b*x + c)^(1/4))/c^(1/4))/c^(1/4) - 1/16*4^(3/4)*sqrt(2)*log(sqrt(2)*(1/4)^(1/4)*(a*x^2 + b*x + c)^(1/4)*c^(1/4) + sqrt(a*x^2 + b*x + c) + 1/2*sqrt(c))/c^(1/4) + 1/16*4^(3/4)*sqrt(2)*log(-sqrt(2)*(1/4)^(1/4)*(a*x^2 + b*x + c)^(1/4)*c^(1/4) + sqrt(a*x^2 + b*x + c) + 1/2*sqrt(c))/c^(1/4)","B",0
1798,1,127,0,0.194537," ","integrate(x^6*(x^3-x)^(1/3),x, algorithm=""giac"")","-\frac{1}{648} \, {\left(20 \, {\left(\frac{1}{x^{2}} - 1\right)}^{3} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 72 \, {\left(\frac{1}{x^{2}} - 1\right)}^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 93 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} - 40 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)} x^{8} - \frac{5}{243} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{5}{486} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{5}{243} \, \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/648*(20*(1/x^2 - 1)^3*(-1/x^2 + 1)^(1/3) + 72*(1/x^2 - 1)^2*(-1/x^2 + 1)^(1/3) - 93*(-1/x^2 + 1)^(4/3) - 40*(-1/x^2 + 1)^(1/3))*x^8 - 5/243*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) - 5/486*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) + 5/243*log(abs((-1/x^2 + 1)^(1/3) - 1))","A",0
1799,0,0,0,0.000000," ","integrate(1/(x^3+x^2-x-1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + x^{2} - x - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 + x^2 - x - 1)^(-1/3), x)","F",0
1800,1,112,0,0.357461," ","integrate((2*x^4+1)/(x^4-1)/(x^4-x^2)^(1/4),x, algorithm=""giac"")","-\frac{3}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{3}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{3}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{3}{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}} + 2 \, \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) + \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"-3/4*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) + 3/8*2^(3/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) - 3/8*2^(3/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4)) + 3/(-1/x^2 + 1)^(1/4) + 2*arctan((-1/x^2 + 1)^(1/4)) - log((-1/x^2 + 1)^(1/4) + 1) + log(-(-1/x^2 + 1)^(1/4) + 1)","A",0
1801,1,277,0,0.381224," ","integrate((a*x^4-b)*(a*x^4+b*x^2)^(1/4)/x^2,x, algorithm=""giac"")","\frac{\frac{8 \, {\left({\left(a + \frac{b}{x^{2}}\right)}^{\frac{5}{4}} b^{3} + 3 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} a b^{3}\right)} x^{4}}{b^{2}} + 256 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} b^{2} + \frac{2 \, \sqrt{2} {\left(32 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} {\left(32 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(32 \, a b^{2} + 3 \, b^{3}\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{\left(-a\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(32 \, a b^{2} + 3 \, b^{3}\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{\left(-a\right)^{\frac{3}{4}}}}{128 \, b}"," ",0,"1/128*(8*((a + b/x^2)^(5/4)*b^3 + 3*(a + b/x^2)^(1/4)*a*b^3)*x^4/b^2 + 256*(a + b/x^2)^(1/4)*b^2 + 2*sqrt(2)*(32*a*b^2 + 3*b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 2*sqrt(2)*(32*a*b^2 + 3*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + sqrt(2)*(32*a*b^2 + 3*b^3)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/(-a)^(3/4) - sqrt(2)*(32*a*b^2 + 3*b^3)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/(-a)^(3/4))/b","B",0
1802,1,277,0,0.300508," ","integrate((a*x^4+b)*(a*x^4+b*x^2)^(1/4)/x^2,x, algorithm=""giac"")","\frac{\frac{8 \, {\left({\left(a + \frac{b}{x^{2}}\right)}^{\frac{5}{4}} b^{3} + 3 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} a b^{3}\right)} x^{4}}{b^{2}} - 256 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} b^{2} - \frac{2 \, \sqrt{2} {\left(32 \, a b^{2} - 3 \, b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} - \frac{2 \, \sqrt{2} {\left(32 \, a b^{2} - 3 \, b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(32 \, a b^{2} - 3 \, b^{3}\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(32 \, a b^{2} - 3 \, b^{3}\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{\left(-a\right)^{\frac{3}{4}}}}{128 \, b}"," ",0,"1/128*(8*((a + b/x^2)^(5/4)*b^3 + 3*(a + b/x^2)^(1/4)*a*b^3)*x^4/b^2 - 256*(a + b/x^2)^(1/4)*b^2 - 2*sqrt(2)*(32*a*b^2 - 3*b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) - 2*sqrt(2)*(32*a*b^2 - 3*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) - sqrt(2)*(32*a*b^2 - 3*b^3)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/(-a)^(3/4) + sqrt(2)*(32*a*b^2 - 3*b^3)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/(-a)^(3/4))/b","B",0
1803,0,0,0,0.000000," ","integrate((2*a*x^4+b)/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} + b}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate((2*a*x^4 + b)/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
1804,0,0,0,0.000000," ","integrate((2*a*x^4+b)/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} + b}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate((2*a*x^4 + b)/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)), x)","F",0
1805,0,0,0,0.000000," ","integrate((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - 2 \, a x^{4} - b}{{\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - 2*a*x^4 - b)/(a*x^4 - b)^(1/4), x)","F",0
1806,1,84,0,0.296418," ","integrate((-1+x)/(x^2-2*x-4)/(x^2-2*x-2)^(1/3),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{2} \, x^{2} - x - 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{8} \cdot 2^{\frac{2}{3}} \log\left({\left(\frac{1}{2} \, x^{2} - x - 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{2} \, x^{2} - x - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{4} \cdot 2^{\frac{2}{3}} \log\left({\left| {\left(\frac{1}{2} \, x^{2} - x - 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/4*sqrt(3)*2^(2/3)*arctan(1/3*sqrt(3)*(2*(1/2*x^2 - x - 1)^(1/3) + 1)) - 1/8*2^(2/3)*log((1/2*x^2 - x - 1)^(2/3) + (1/2*x^2 - x - 1)^(1/3) + 1) + 1/4*2^(2/3)*log(abs((1/2*x^2 - x - 1)^(1/3) - 1))","A",0
1807,0,0,0,0.000000," ","integrate(1/(1+x)/(x^2+2*x+3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 2 \, x + 3\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + 2*x + 3)^(1/3)*(x + 1)), x)","F",0
1808,1,162,0,0.171100," ","integrate(1/x/(a*x^2-b)^(3/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{2 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{2 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{4 \, b^{\frac{3}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{4 \, b^{\frac{3}{4}}}"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/4*sqrt(2)*log(sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(3/4) - 1/4*sqrt(2)*log(-sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(3/4)","A",0
1809,1,120,0,2.056075," ","integrate(1/x/(a*x^3-b)^(1/3),x, algorithm=""giac"")","-\frac{\sqrt{3} \left(-b\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(a x^{3} - b\right)}^{\frac{1}{3}} + \left(-b\right)^{\frac{1}{3}}\right)}}{3 \, \left(-b\right)^{\frac{1}{3}}}\right)}{3 \, b} + \frac{\left(-b\right)^{\frac{2}{3}} \log\left({\left(a x^{3} - b\right)}^{\frac{2}{3}} + {\left(a x^{3} - b\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} + \left(-b\right)^{\frac{2}{3}}\right)}{6 \, b} - \frac{\left(-b\right)^{\frac{2}{3}} \log\left({\left| {\left(a x^{3} - b\right)}^{\frac{1}{3}} - \left(-b\right)^{\frac{1}{3}} \right|}\right)}{3 \, b}"," ",0,"-1/3*sqrt(3)*(-b)^(2/3)*arctan(1/3*sqrt(3)*(2*(a*x^3 - b)^(1/3) + (-b)^(1/3))/(-b)^(1/3))/b + 1/6*(-b)^(2/3)*log((a*x^3 - b)^(2/3) + (a*x^3 - b)^(1/3)*(-b)^(1/3) + (-b)^(2/3))/b - 1/3*(-b)^(2/3)*log(abs((a*x^3 - b)^(1/3) - (-b)^(1/3)))/b","A",0
1810,0,0,0,0.000000," ","integrate((a^3*x^3-b^3)/(a^2*x^3+b^2*x)^(1/2)/(a^3*x^3+b^3),x, algorithm=""giac"")","\int \frac{a^{3} x^{3} - b^{3}}{{\left(a^{3} x^{3} + b^{3}\right)} \sqrt{a^{2} x^{3} + b^{2} x}}\,{d x}"," ",0,"integrate((a^3*x^3 - b^3)/((a^3*x^3 + b^3)*sqrt(a^2*x^3 + b^2*x)), x)","F",0
1811,0,0,0,0.000000," ","integrate((a^3*x^3+b^3)/(a^2*x^3+b^2*x)^(1/2)/(a^3*x^3-b^3),x, algorithm=""giac"")","\int \frac{a^{3} x^{3} + b^{3}}{{\left(a^{3} x^{3} - b^{3}\right)} \sqrt{a^{2} x^{3} + b^{2} x}}\,{d x}"," ",0,"integrate((a^3*x^3 + b^3)/((a^3*x^3 - b^3)*sqrt(a^2*x^3 + b^2*x)), x)","F",0
1812,-2,0,0,0.000000," ","integrate((x^4+x^3)^(1/4)/(2*x^2+x-2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1813,0,0,0,0.000000," ","integrate((a*x^3-4*b)*(-a*x^3+x^4+b)/x^4/(a*x^3-b)^(1/4)/(a*x^3+x^4-b),x, algorithm=""giac"")","\int -\frac{{\left(a x^{3} - x^{4} - b\right)} {\left(a x^{3} - 4 \, b\right)}}{{\left(a x^{3} + x^{4} - b\right)} {\left(a x^{3} - b\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate(-(a*x^3 - x^4 - b)*(a*x^3 - 4*b)/((a*x^3 + x^4 - b)*(a*x^3 - b)^(1/4)*x^4), x)","F",0
1814,0,0,0,0.000000," ","integrate((x^2-2)*(x^2-1)*(x^4+x^2-1)^(1/4)/x^6/(2*x^4+x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} - 1\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)} {\left(x^{2} - 2\right)}}{{\left(2 \, x^{4} + x^{2} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^2 - 1)^(1/4)*(x^2 - 1)*(x^2 - 2)/((2*x^4 + x^2 - 1)*x^6), x)","F",0
1815,1,278,0,0.266972," ","integrate(x^2*(a*x^4+b*x^3)^(1/4),x, algorithm=""giac"")","\frac{\frac{462 \, \sqrt{2} b^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{3}} + \frac{462 \, \sqrt{2} b^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{3}} + \frac{231 \, \sqrt{2} b^{5} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{3}} + \frac{231 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{5} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a^{4}} + \frac{8 \, {\left(77 \, {\left(a + \frac{b}{x}\right)}^{\frac{13}{4}} b^{5} - 275 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} a b^{5} + 351 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a^{2} b^{5} + 231 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{3} b^{5}\right)} x^{4}}{a^{3} b^{4}}}{12288 \, b}"," ",0,"1/12288*(462*sqrt(2)*b^5*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^3) + 462*sqrt(2)*b^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^3) + 231*sqrt(2)*b^5*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^3) + 231*sqrt(2)*(-a)^(1/4)*b^5*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^4 + 8*(77*(a + b/x)^(13/4)*b^5 - 275*(a + b/x)^(9/4)*a*b^5 + 351*(a + b/x)^(5/4)*a^2*b^5 + 231*(a + b/x)^(1/4)*a^3*b^5)*x^4/(a^3*b^4))/b","B",0
1816,0,0,0,0.000000," ","integrate((x^6+1)/(x^3+x^2+x)^(1/2)/(-x^6+1),x, algorithm=""giac"")","\int -\frac{x^{6} + 1}{{\left(x^{6} - 1\right)} \sqrt{x^{3} + x^{2} + x}}\,{d x}"," ",0,"integrate(-(x^6 + 1)/((x^6 - 1)*sqrt(x^3 + x^2 + x)), x)","F",0
1817,1,125,0,0.238180," ","integrate((3*x^6-3*x^3+1)/x^6/(2*x^3-1)/(x^4-x)^(1/4),x, algorithm=""giac"")","-\frac{4}{21} \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{7}{4}} - \frac{1}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{3} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{6} \, \sqrt{2} \log\left(\sqrt{2} {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x^{3}} + 1} + 1\right) - \frac{1}{6} \, \sqrt{2} \log\left(-\sqrt{2} {\left(-\frac{1}{x^{3}} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x^{3}} + 1} + 1\right)"," ",0,"-4/21*(-1/x^3 + 1)^(7/4) - 1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(-1/x^3 + 1)^(1/4))) - 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(-1/x^3 + 1)^(1/4))) + 1/6*sqrt(2)*log(sqrt(2)*(-1/x^3 + 1)^(1/4) + sqrt(-1/x^3 + 1) + 1) - 1/6*sqrt(2)*log(-sqrt(2)*(-1/x^3 + 1)^(1/4) + sqrt(-1/x^3 + 1) + 1)","A",0
1818,1,217,0,0.389459," ","integrate((a*x^6+b)/x^3/(a*x^3+b)/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a} - \frac{4 \, {\left(a + b\right)}}{3 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} b} - \frac{4 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}}}{9 \, b}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a - 4/3*(a + b)/((a + b/x^3)^(1/4)*b) - 4/9*(a + b/x^3)^(3/4)/b","B",0
1819,0,0,0,0.000000," ","integrate((x^4-x^2-x-1)*(2*x^4+x+2)/(x^4-x-1)^(1/2)/(4*x^8+x^6-8*x^5-7*x^4-x^3+3*x^2+8*x+4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + x + 2\right)} {\left(x^{4} - x^{2} - x - 1\right)}}{{\left(4 \, x^{8} + x^{6} - 8 \, x^{5} - 7 \, x^{4} - x^{3} + 3 \, x^{2} + 8 \, x + 4\right)} \sqrt{x^{4} - x - 1}}\,{d x}"," ",0,"integrate((2*x^4 + x + 2)*(x^4 - x^2 - x - 1)/((4*x^8 + x^6 - 8*x^5 - 7*x^4 - x^3 + 3*x^2 + 8*x + 4)*sqrt(x^4 - x - 1)), x)","F",0
1820,0,0,0,0.000000," ","integrate((x^6+1)^2*(2*x^6-1)/(x^6-x^2+1)^(3/2)/(x^12-x^8+2*x^6-x^4-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 1\right)} {\left(x^{6} + 1\right)}^{2}}{{\left(x^{12} - x^{8} + 2 \, x^{6} - x^{4} - x^{2} + 1\right)} {\left(x^{6} - x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*x^6 - 1)*(x^6 + 1)^2/((x^12 - x^8 + 2*x^6 - x^4 - x^2 + 1)*(x^6 - x^2 + 1)^(3/2)), x)","F",0
1821,-2,0,0,0.000000," ","integrate(1/(2*x^(1/2)+(1+x)^(1/2))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-4,[1]%%%}+%%%{-2,[0]%%%},0,1] at parameters values [-89]Warning, choosing root of [1,0,%%%{-4,[1]%%%}+%%%{-2,[0]%%%},0,1] at parameters values [63]2*((-5*(x+1)+4)/6/(3*(x+1)-4)+5/18*ln(abs(3*(x+1)-4))+2*(1/9*ln((sqrt(x)-sqrt(x+1))^2)+5/36*ln(abs((sqrt(x)-sqrt(x+1))^2-3))-5/36*ln(abs(3*(sqrt(x)-sqrt(x+1))^2-1))-(10*(sqrt(x)-sqrt(x+1))^2-6)/9/(3*(sqrt(x)-sqrt(x+1))^4-10*(sqrt(x)-sqrt(x+1))^2+3)))","F(-2)",0
1822,0,0,0,0.000000," ","integrate(1/x^3/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)*x^3), x)","F",0
1823,1,162,0,0.179798," ","integrate(1/x/(a*x^2-b)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{2 \, b^{\frac{1}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{2 \, b^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{4 \, b^{\frac{1}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{4 \, b^{\frac{1}{4}}}"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(1/4) + 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(1/4) - 1/4*sqrt(2)*log(sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(1/4) + 1/4*sqrt(2)*log(-sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(1/4)","A",0
1824,-2,0,0,0.000000," ","integrate((1+k^(3/2)*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(-1+k^(3/2)*x^3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1825,1,322,0,0.217065," ","integrate((2*c*x-d)*(a*x^4+b*x^3)^(1/4)/x,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} {\left(3 \, b^{3} c + 4 \, a b^{2} d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{2 \, \sqrt{2} {\left(3 \, b^{3} c + 4 \, a b^{2} d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{\sqrt{2} {\left(3 \, b^{3} c + 4 \, a b^{2} d\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a} - \frac{\sqrt{2} {\left(3 \, b^{3} c + 4 \, a b^{2} d\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{8 \, {\left({\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} b^{3} c + 3 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a b^{3} c - 4 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a b^{2} d + 4 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{2} b^{2} d\right)} x^{2}}{a b^{2}}}{32 \, b}"," ",0,"1/32*(2*sqrt(2)*(3*b^3*c + 4*a*b^2*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + 2*sqrt(2)*(3*b^3*c + 4*a*b^2*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + sqrt(2)*(3*b^3*c + 4*a*b^2*d)*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a) - sqrt(2)*(3*b^3*c + 4*a*b^2*d)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a) + 8*((a + b/x)^(5/4)*b^3*c + 3*(a + b/x)^(1/4)*a*b^3*c - 4*(a + b/x)^(5/4)*a*b^2*d + 4*(a + b/x)^(1/4)*a^2*b^2*d)*x^2/(a*b^2))/b","B",0
1826,0,0,0,0.000000," ","integrate((x^6-1)/(x^6+1)/(a^3*x^3+x^6+1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{6} - 1}{{\left(a^{3} x^{3} + x^{6} + 1\right)}^{\frac{1}{3}} {\left(x^{6} + 1\right)}}\,{d x}"," ",0,"integrate((x^6 - 1)/((a^3*x^3 + x^6 + 1)^(1/3)*(x^6 + 1)), x)","F",0
1827,0,0,0,0.000000," ","integrate((4*x^6+x^3+2)*(-x^7-x^4+2*x^3+x)^(1/3)/(x^6+x^3-2*x^2-1)/(x^6+x^3-x^2-1),x, algorithm=""giac"")","\int \frac{{\left(-x^{7} - x^{4} + 2 \, x^{3} + x\right)}^{\frac{1}{3}} {\left(4 \, x^{6} + x^{3} + 2\right)}}{{\left(x^{6} + x^{3} - x^{2} - 1\right)} {\left(x^{6} + x^{3} - 2 \, x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((-x^7 - x^4 + 2*x^3 + x)^(1/3)*(4*x^6 + x^3 + 2)/((x^6 + x^3 - x^2 - 1)*(x^6 + x^3 - 2*x^2 - 1)), x)","F",0
1828,0,0,0,0.000000," ","integrate(x^2/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}\,{d x}"," ",0,"integrate(x^2/sqrt(a*x^2 + sqrt(a^2*x^4 + b)), x)","F",0
1829,0,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x + \sqrt{x^{2} + 1}} + 1}}{{\left(x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^2 + 1)^(3/2), x)","F",0
1830,0,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x + \sqrt{x^{2} + 1}} + 1}}{{\left(x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^2 + 1)^(3/2), x)","F",0
1831,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1832,0,0,0,0.000000," ","integrate(1/(-1+x)/(x^2-2*x-3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 2 \, x - 3\right)}^{\frac{1}{3}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 - 2*x - 3)^(1/3)*(x - 1)), x)","F",0
1833,0,0,0,0.000000," ","integrate(1/(-1+x)/(x^2-2*x-1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 2 \, x - 1\right)}^{\frac{1}{3}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 - 2*x - 1)^(1/3)*(x - 1)), x)","F",0
1834,0,0,0,0.000000," ","integrate(1/(1+x)/(x^2+2*x-1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 2 \, x - 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + 2*x - 1)^(1/3)*(x + 1)), x)","F",0
1835,0,0,0,0.000000," ","integrate((-2*a*b*x^2+(a+b)*x^3)/(-a+x)/(-b+x)/(x^2*(-a+x)*(-b+x))^(1/4)/(-a*b*d+(a+b)*d*x+(1-d)*x^2),x, algorithm=""giac"")","\int \frac{2 \, a b x^{2} - {\left(a + b\right)} x^{3}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{4}} {\left(a b d - {\left(a + b\right)} d x + {\left(d - 1\right)} x^{2}\right)} {\left(a - x\right)} {\left(b - x\right)}}\,{d x}"," ",0,"integrate((2*a*b*x^2 - (a + b)*x^3)/(((a - x)*(b - x)*x^2)^(1/4)*(a*b*d - (a + b)*d*x + (d - 1)*x^2)*(a - x)*(b - x)), x)","F",0
1836,0,0,0,0.000000," ","integrate((a^2-2*a*x+x^2)*(a*b^2-2*(2*a-b)*b*x+(3*a-2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(3/4)/(a^3*d+(-3*a^2*d+b^2)*x+(3*a*d-2*b)*x^2+(1-d)*x^3),x, algorithm=""giac"")","\int \frac{{\left(a b^{2} - 2 \, {\left(2 \, a - b\right)} b x + {\left(3 \, a - 2 \, b\right)} x^{2}\right)} {\left(a^{2} - 2 \, a x + x^{2}\right)}}{{\left(a^{3} d - {\left(d - 1\right)} x^{3} + {\left(3 \, a d - 2 \, b\right)} x^{2} - {\left(3 \, a^{2} d - b^{2}\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*b^2 - 2*(2*a - b)*b*x + (3*a - 2*b)*x^2)*(a^2 - 2*a*x + x^2)/((a^3*d - (d - 1)*x^3 + (3*a*d - 2*b)*x^2 - (3*a^2*d - b^2)*x)*(-(a - x)*(b - x)^2*x)^(3/4)), x)","F",0
1837,-2,0,0,0.000000," ","integrate((-1+k^(3/2)*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(1+k^(3/2)*x^3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1838,0,0,0,0.000000," ","integrate((x^3-x^2-x)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{3} - x^{2} - x}}{x^{4} - 1}\,{d x}"," ",0,"integrate(sqrt(x^3 - x^2 - x)/(x^4 - 1), x)","F",0
1839,1,128,0,0.571605," ","integrate((a*x^3+b)*(x^4+x)^(1/2)/(c*x^3-d),x, algorithm=""giac"")","\frac{\sqrt{x^{4} + x} a x}{3 \, c} + \frac{{\left(a c + 2 \, b c + 2 \, a d\right)} \log\left(\sqrt{\frac{1}{x^{3}} + 1} + 1\right)}{6 \, c^{2}} - \frac{{\left(a c + 2 \, b c + 2 \, a d\right)} \log\left({\left| \sqrt{\frac{1}{x^{3}} + 1} - 1 \right|}\right)}{6 \, c^{2}} + \frac{2 \, {\left(b c^{2} + a c d + b c d + a d^{2}\right)} \arctan\left(\frac{d \sqrt{\frac{1}{x^{3}} + 1}}{\sqrt{-c d - d^{2}}}\right)}{3 \, \sqrt{-c d - d^{2}} c^{2}}"," ",0,"1/3*sqrt(x^4 + x)*a*x/c + 1/6*(a*c + 2*b*c + 2*a*d)*log(sqrt(1/x^3 + 1) + 1)/c^2 - 1/6*(a*c + 2*b*c + 2*a*d)*log(abs(sqrt(1/x^3 + 1) - 1))/c^2 + 2/3*(b*c^2 + a*c*d + b*c*d + a*d^2)*arctan(d*sqrt(1/x^3 + 1)/sqrt(-c*d - d^2))/(sqrt(-c*d - d^2)*c^2)","A",0
1840,0,0,0,0.000000," ","integrate((2*x^4-2*x+1)/x/(x^4-1)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, x^{4} - 2 \, x + 1}{{\left(x^{4} - 1\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"integrate((2*x^4 - 2*x + 1)/((x^4 - 1)^(1/4)*x), x)","F",0
1841,0,0,0,0.000000," ","integrate(x^2*(a*x^5-4*b)/(a*x^5+b)^(3/4)/(a*x^5+c*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} - 4 \, b\right)} x^{2}}{{\left(a x^{5} + c x^{4} + b\right)} {\left(a x^{5} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^5 - 4*b)*x^2/((a*x^5 + c*x^4 + b)*(a*x^5 + b)^(3/4)), x)","F",0
1842,0,0,0,0.000000," ","integrate(1/(x^6+2*x^5-x^4-4*x^3-x^2+2*x+1)^(1/6),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 2 \, x^{5} - x^{4} - 4 \, x^{3} - x^{2} + 2 \, x + 1\right)}^{\frac{1}{6}}}\,{d x}"," ",0,"integrate((x^6 + 2*x^5 - x^4 - 4*x^3 - x^2 + 2*x + 1)^(-1/6), x)","F",0
1843,0,0,0,0.000000," ","integrate(x^2*(a*x^6-2*b)/(a*x^6+b)^(3/4)/(a*x^6+c*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} - 2 \, b\right)} x^{2}}{{\left(a x^{6} + c x^{4} + b\right)} {\left(a x^{6} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^6 - 2*b)*x^2/((a*x^6 + c*x^4 + b)*(a*x^6 + b)^(3/4)), x)","F",0
1844,0,0,0,0.000000," ","integrate((x^3+4)*(x^8+x^6+2*x^3+1)/x^4/(x^3+1)^(1/4)/(x^8-x^6-2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{6} + 2 \, x^{3} + 1\right)} {\left(x^{3} + 4\right)}}{{\left(x^{8} - x^{6} - 2 \, x^{3} - 1\right)} {\left(x^{3} + 1\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((x^8 + x^6 + 2*x^3 + 1)*(x^3 + 4)/((x^8 - x^6 - 2*x^3 - 1)*(x^3 + 1)^(1/4)*x^4), x)","F",0
1845,0,0,0,0.000000," ","integrate((2*x^8-x^4+2)/(x^4+1)^(1/4)/(x^8+x^4-2),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - x^{4} + 2}{{\left(x^{8} + x^{4} - 2\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - x^4 + 2)/((x^8 + x^4 - 2)*(x^4 + 1)^(1/4)), x)","F",0
1846,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^2,x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{{\left(a x^{2} + b^{2}\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2)^2, x)","F",0
1847,1,136,0,0.717549," ","integrate((a*x^3+b)*(x^4-x)^(1/2)/(c*x^3-d),x, algorithm=""giac"")","\frac{\sqrt{x^{4} - x} a x}{3 \, c} - \frac{{\left(a c - 2 \, b c - 2 \, a d\right)} \log\left(\sqrt{-\frac{1}{x^{3}} + 1} + 1\right)}{6 \, c^{2}} + \frac{{\left(a c - 2 \, b c - 2 \, a d\right)} \log\left({\left| \sqrt{-\frac{1}{x^{3}} + 1} - 1 \right|}\right)}{6 \, c^{2}} - \frac{2 \, {\left(b c^{2} + a c d - b c d - a d^{2}\right)} \arctan\left(\frac{d \sqrt{-\frac{1}{x^{3}} + 1}}{\sqrt{c d - d^{2}}}\right)}{3 \, \sqrt{c d - d^{2}} c^{2}}"," ",0,"1/3*sqrt(x^4 - x)*a*x/c - 1/6*(a*c - 2*b*c - 2*a*d)*log(sqrt(-1/x^3 + 1) + 1)/c^2 + 1/6*(a*c - 2*b*c - 2*a*d)*log(abs(sqrt(-1/x^3 + 1) - 1))/c^2 - 2/3*(b*c^2 + a*c*d - b*c*d - a*d^2)*arctan(d*sqrt(-1/x^3 + 1)/sqrt(c*d - d^2))/(sqrt(c*d - d^2)*c^2)","A",0
1848,1,208,0,0.399547," ","integrate((a*x^3+b)/x^3/(a*x^3-b)/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","-\frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b} - \frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{3 \, b} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{3 \, b} + \frac{4 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}}}{9 \, b}"," ",0,"-2/3*2^(1/4)*(-a)^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/b - 2/3*2^(1/4)*(-a)^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/b + 1/3*2^(1/4)*(-a)^(3/4)*log(2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/b - 1/3*2^(1/4)*(-a)^(3/4)*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/b + 4/9*(a + b/x^3)^(3/4)/b","B",0
1849,0,0,0,0.000000," ","integrate((2*x^6+1)*(-x^7+x^3+x)^(1/3)/(x^6-1)^2,x, algorithm=""giac"")","\int \frac{{\left(-x^{7} + x^{3} + x\right)}^{\frac{1}{3}} {\left(2 \, x^{6} + 1\right)}}{{\left(x^{6} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((-x^7 + x^3 + x)^(1/3)*(2*x^6 + 1)/(x^6 - 1)^2, x)","F",0
1850,0,0,0,0.000000," ","integrate((-(2*a-b)*b^2+(4*a-b)*b*x-(2*a+b)*x^2+x^3)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^2*d-(2*b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, a - b\right)} b^{2} - {\left(4 \, a - b\right)} b x + {\left(2 \, a + b\right)} x^{2} - x^{3}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{3}{4}} {\left(b^{2} d + d x^{2} - {\left(2 \, b d + 1\right)} x + a\right)}}\,{d x}"," ",0,"integrate(-((2*a - b)*b^2 - (4*a - b)*b*x + (2*a + b)*x^2 - x^3)/((-(a - x)*(b - x)^2)^(3/4)*(b^2*d + d*x^2 - (2*b*d + 1)*x + a)), x)","F",0
1851,0,0,0,0.000000," ","integrate((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x, algorithm=""giac"")","\int \frac{x^{4} + 2}{{\left(2 \, x^{8} - x^{4} - 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 + 2)/((2*x^8 - x^4 - 1)*(x^4 + x^2)^(1/4)), x)","F",0
1852,0,0,0,0.000000," ","integrate((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x, algorithm=""giac"")","\int \frac{x^{4} + 2}{{\left(2 \, x^{8} - x^{4} - 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 + 2)/((2*x^8 - x^4 - 1)*(x^4 + x^2)^(1/4)), x)","F",0
1853,1,188,0,1.025021," ","integrate((x+(1+x)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{3} - 3 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{2} - \sqrt{x + \sqrt{x + 1}} + \sqrt{x + 1} + 1}{{\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{4} - 2 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{2} + 4 \, \sqrt{x + \sqrt{x + 1}} - 4 \, \sqrt{x + 1}} + \frac{1}{2} \, \arctan\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} - 1\right) - \frac{3}{4} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} + 2 \right|}\right) + \frac{3}{4} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} \right|}\right)"," ",0,"-(2*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^3 - 3*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^2 - sqrt(x + sqrt(x + 1)) + sqrt(x + 1) + 1)/((sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^4 - 2*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^2 + 4*sqrt(x + sqrt(x + 1)) - 4*sqrt(x + 1)) + 1/2*arctan(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) - 1) - 3/4*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) + 2)) + 3/4*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)))","A",0
1854,0,0,0,0.000000," ","integrate((-1+x)*(x+(x^2+1)^(1/2))^(1/2)/(1+x),x, algorithm=""giac"")","\int \frac{\sqrt{x + \sqrt{x^{2} + 1}} {\left(x - 1\right)}}{x + 1}\,{d x}"," ",0,"integrate(sqrt(x + sqrt(x^2 + 1))*(x - 1)/(x + 1), x)","F",0
1855,0,0,0,0.000000," ","integrate((1+x)*(x+(x^2+1)^(1/2))^(1/2)/(-1+x),x, algorithm=""giac"")","\int \frac{\sqrt{x + \sqrt{x^{2} + 1}} {\left(x + 1\right)}}{x - 1}\,{d x}"," ",0,"integrate(sqrt(x + sqrt(x^2 + 1))*(x + 1)/(x - 1), x)","F",0
1856,0,0,0,0.000000," ","integrate((x^2+2*x+6)/(1+x)/(x^2+x+2)^(1/3)/(2*x^2-x+2),x, algorithm=""giac"")","\int \frac{x^{2} + 2 \, x + 6}{{\left(2 \, x^{2} - x + 2\right)} {\left(x^{2} + x + 2\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 2*x + 6)/((2*x^2 - x + 2)*(x^2 + x + 2)^(1/3)*(x + 1)), x)","F",0
1857,1,162,0,0.322012," ","integrate(1/x/(a*x^3-b)^(3/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{3 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{3 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{6 \, b^{\frac{3}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{6 \, b^{\frac{3}{4}}}"," ",0,"1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/6*sqrt(2)*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(3/4) - 1/6*sqrt(2)*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(3/4)","A",0
1858,1,162,0,0.332917," ","integrate(1/x/(a*x^3-b)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{3 \, b^{\frac{1}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{3 \, b^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{6 \, b^{\frac{1}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{6 \, b^{\frac{1}{4}}}"," ",0,"1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(1/4) + 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(1/4) - 1/6*sqrt(2)*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(1/4) + 1/6*sqrt(2)*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(1/4)","A",0
1859,0,0,0,0.000000," ","integrate((a*x^2-3*b)*(-a*x^2+x^3+b)/x^3/(a*x^2+x^3-b)/(a*x^3-b*x)^(1/4),x, algorithm=""giac"")","\int -\frac{{\left(a x^{2} - x^{3} - b\right)} {\left(a x^{2} - 3 \, b\right)}}{{\left(a x^{3} - b x\right)}^{\frac{1}{4}} {\left(a x^{2} + x^{3} - b\right)} x^{3}}\,{d x}"," ",0,"integrate(-(a*x^2 - x^3 - b)*(a*x^2 - 3*b)/((a*x^3 - b*x)^(1/4)*(a*x^2 + x^3 - b)*x^3), x)","F",0
1860,1,162,0,0.278044," ","integrate(1/x/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{4 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{4 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{8 \, b^{\frac{3}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{8 \, b^{\frac{3}{4}}}"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/8*sqrt(2)*log(sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(3/4) - 1/8*sqrt(2)*log(-sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(3/4)","A",0
1861,1,162,0,0.370121," ","integrate(1/x/(a*x^4-b)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{4 \, b^{\frac{1}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{4 \, b^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{8 \, b^{\frac{1}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{8 \, b^{\frac{1}{4}}}"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(1/4) + 1/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(1/4) - 1/8*sqrt(2)*log(sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(1/4) + 1/8*sqrt(2)*log(-sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(1/4)","A",0
1862,0,0,0,0.000000," ","integrate((-x^5+1)/(b*x+a)^(1/2)/(x^5+1),x, algorithm=""giac"")","\int -\frac{x^{5} - 1}{{\left(x^{5} + 1\right)} \sqrt{b x + a}}\,{d x}"," ",0,"integrate(-(x^5 - 1)/((x^5 + 1)*sqrt(b*x + a)), x)","F",0
1863,1,162,0,0.324956," ","integrate(1/x/(a*x^5-b)^(3/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{5 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{5 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{10 \, b^{\frac{3}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{10 \, b^{\frac{3}{4}}}"," ",0,"1/5*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/5*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/10*sqrt(2)*log(sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(3/4) - 1/10*sqrt(2)*log(-sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(3/4)","A",0
1864,1,162,0,0.383837," ","integrate(1/x/(a*x^6-b)^(3/4),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{6 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{6 \, b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right)}{12 \, b^{\frac{3}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right)}{12 \, b^{\frac{3}{4}}}"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^6 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^6 - b)^(1/4))/b^(1/4))/b^(3/4) + 1/12*sqrt(2)*log(sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b))/b^(3/4) - 1/12*sqrt(2)*log(-sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b))/b^(3/4)","A",0
1865,0,0,0,0.000000," ","integrate((x^4+1)*(x^4+x^2-1)^(3/2)/(x^4-1)/(x^8-x^6-x^4+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} - 1\right)}^{\frac{3}{2}} {\left(x^{4} + 1\right)}}{{\left(x^{8} - x^{6} - x^{4} + x^{2} + 1\right)} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + x^2 - 1)^(3/2)*(x^4 + 1)/((x^8 - x^6 - x^4 + x^2 + 1)*(x^4 - 1)), x)","F",0
1866,0,0,0,0.000000," ","integrate((x^6-1)*(x^6+x^3+1)^(2/3)/(x^12+x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{6} - 1\right)}}{x^{12} + x^{6} + 1}\,{d x}"," ",0,"integrate((x^6 + x^3 + 1)^(2/3)*(x^6 - 1)/(x^12 + x^6 + 1), x)","F",0
1867,0,0,0,0.000000," ","integrate((x^3-1)^3*(x^3+1)*(2*x^12+3*x^6+2)^(1/2)/x^7/(x^6+1),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{12} + 3 \, x^{6} + 2} {\left(x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{3}}{{\left(x^{6} + 1\right)} x^{7}}\,{d x}"," ",0,"integrate(sqrt(2*x^12 + 3*x^6 + 2)*(x^3 + 1)*(x^3 - 1)^3/((x^6 + 1)*x^7), x)","F",0
1868,0,0,0,0.000000," ","integrate((a*x-(a^2*x^2+b)^(1/2))^(1/2)/(a^2*x^2+(a^2*x^2+b)^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a x - \sqrt{a^{2} x^{2} + b}}}{a^{2} x^{2} + \sqrt{a^{2} x^{2} + b}}\,{d x}"," ",0,"integrate(sqrt(a*x - sqrt(a^2*x^2 + b))/(a^2*x^2 + sqrt(a^2*x^2 + b)), x)","F",0
1869,0,0,0,0.000000," ","integrate((c*x+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x + d}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((c*x + d)/sqrt(a*x + sqrt(a^2*x^2 + b^2)), x)","F",0
1870,1,79,0,1.318056," ","integrate(1/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(15 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{7}{2}} - 63 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{5}{2}} + 70 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{3}{2}}\right)}}{105 \, \mathrm{sgn}\left(4 \, {\left(\sqrt{x + 1} + 1\right)}^{2} - 8 \, \sqrt{x + 1} - 7\right) \mathrm{sgn}\left(4 \, x + 1\right)}"," ",0,"8/105*(15*(sqrt(sqrt(x + 1) + 1) + 1)^(7/2) - 63*(sqrt(sqrt(x + 1) + 1) + 1)^(5/2) + 70*(sqrt(sqrt(x + 1) + 1) + 1)^(3/2))/(sgn(4*(sqrt(x + 1) + 1)^2 - 8*sqrt(x + 1) - 7)*sgn(4*x + 1))","C",0
1871,1,93,0,0.482476," ","integrate((a*x^2-b)*(x^3+x)^(1/3)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + \frac{1}{6} \, \sqrt{3} {\left(a - 3 \, b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{12} \, {\left(a - 3 \, b\right)} \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{6} \, {\left(a - 3 \, b\right)} \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right) + \frac{3}{2} \, b {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}"," ",0,"1/2*a*x^2*(1/x^2 + 1)^(1/3) + 1/6*sqrt(3)*(a - 3*b)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) + 1/12*(a - 3*b)*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - 1/6*(a - 3*b)*log(abs((1/x^2 + 1)^(1/3) - 1)) + 3/2*b*(1/x^2 + 1)^(1/3)","A",0
1872,-1,0,0,0.000000," ","integrate(1/x^3/(a*x^3-b*x^2)^(1/3)/(c*x^3+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1873,0,0,0,0.000000," ","integrate((x^4-1)/(x^3-x^2-x)^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{4} + 1\right)} \sqrt{x^{3} - x^{2} - x}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^4 + 1)*sqrt(x^3 - x^2 - x)), x)","F",0
1874,1,97,0,0.302094," ","integrate((x^6+9*x^5+16*x^4-27*x^3-36*x^2-11*x-1)^(1/2),x, algorithm=""giac"")","\frac{325}{128} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1 \right|}\right) \mathrm{sgn}\left(x^{2} + 5 \, x + 1\right) + \frac{1}{64} \, {\left(2 \, {\left(4 \, {\left(2 \, x \mathrm{sgn}\left(x^{2} + 5 \, x + 1\right) + 13 \, \mathrm{sgn}\left(x^{2} + 5 \, x + 1\right)\right)} x - 3 \, \mathrm{sgn}\left(x^{2} + 5 \, x + 1\right)\right)} x - 185 \, \mathrm{sgn}\left(x^{2} + 5 \, x + 1\right)\right)} \sqrt{x^{2} - x - 1}"," ",0,"325/128*log(abs(-2*x + 2*sqrt(x^2 - x - 1) + 1))*sgn(x^2 + 5*x + 1) + 1/64*(2*(4*(2*x*sgn(x^2 + 5*x + 1) + 13*sgn(x^2 + 5*x + 1))*x - 3*sgn(x^2 + 5*x + 1))*x - 185*sgn(x^2 + 5*x + 1))*sqrt(x^2 - x - 1)","A",0
1875,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(a*p*x^3+a*q+b*x)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left(a p x^{3} + a q + b x\right)} {\left(2 \, p x^{3} - q\right)}}{x^{4}}\,{d x}"," ",0,"integrate(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)*(2*p*x^3 - q)/x^4, x)","F",0
1876,0,0,0,0.000000," ","integrate((2*x^8-x^4-2)/(x^4-1)^(1/4)/(x^8-x^4-2),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - x^{4} - 2}{{\left(x^{8} - x^{4} - 2\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - x^4 - 2)/((x^8 - x^4 - 2)*(x^4 - 1)^(1/4)), x)","F",0
1877,0,0,0,0.000000," ","integrate((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1878,0,0,0,0.000000," ","integrate((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1879,0,0,0,0.000000," ","integrate((a*x^2+b)*(a*x^3+b*x)^(1/2)/x^2/(a*x^2-b),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3} + b x} {\left(a x^{2} + b\right)}}{{\left(a x^{2} - b\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^3 + b*x)*(a*x^2 + b)/((a*x^2 - b)*x^2), x)","F",0
1880,0,0,0,0.000000," ","integrate((-2*a*b+(3*a-b)*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/x/(-b+x)/(x^2*(-a+x)*(-b+x))^(1/4)/(a^3-3*a^2*x+(-b*d+3*a)*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int -\frac{{\left(a^{3} - 3 \, a^{2} x + 3 \, a x^{2} - x^{3}\right)} {\left(2 \, a b - {\left(3 \, a - b\right)} x\right)}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{4}} {\left({\left(d - 1\right)} x^{3} + a^{3} - 3 \, a^{2} x - {\left(b d - 3 \, a\right)} x^{2}\right)} {\left(b - x\right)} x}\,{d x}"," ",0,"integrate(-(a^3 - 3*a^2*x + 3*a*x^2 - x^3)*(2*a*b - (3*a - b)*x)/(((a - x)*(b - x)*x^2)^(1/4)*((d - 1)*x^3 + a^3 - 3*a^2*x - (b*d - 3*a)*x^2)*(b - x)*x), x)","F",0
1881,0,0,0,0.000000," ","integrate((a*x^2+2*b)/(a*x^2+b)^(1/4)/(2*x^4+1881*a*x^2+1881*b),x, algorithm=""giac"")","\int \frac{a x^{2} + 2 \, b}{{\left(2 \, x^{4} + 1881 \, a x^{2} + 1881 \, b\right)} {\left(a x^{2} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^2 + 2*b)/((2*x^4 + 1881*a*x^2 + 1881*b)*(a*x^2 + b)^(1/4)), x)","F",0
1882,0,0,0,0.000000," ","integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1883,0,0,0,0.000000," ","integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1884,0,0,0,0.000000," ","integrate((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^4+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1885,0,0,0,0.000000," ","integrate((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^4+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1886,0,0,0,0.000000," ","integrate((a*x^2+1)/(a*x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + 1}{{\left(a x^{2} - 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((a*x^2 + 1)/((a*x^2 - 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
1887,0,0,0,0.000000," ","integrate(x*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + x} x}{\sqrt{x^{2} + \sqrt{x^{2} + x} x}}\,{d x}"," ",0,"integrate(sqrt(x^2 + x)*x/sqrt(x^2 + sqrt(x^2 + x)*x), x)","F",0
1888,1,157,0,0.733508," ","integrate((1+x)^(1/2)/(1+(x+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} - 3\right)} - 2 \, \sqrt{x + 1} - \frac{8}{3} \, \log\left(-\sqrt{x + \sqrt{x + 1}} + \sqrt{x + 1} + 3\right) + \frac{8}{3} \, \log\left(-\sqrt{x + \sqrt{x + 1}} + \sqrt{x + 1} + 1\right) - \frac{15}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right) + \frac{8}{3} \, \log\left(\sqrt{x + 1} + 2\right) - \frac{2}{3} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} + 2 \right|}\right) + \frac{2}{3} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} \right|}\right) - \frac{2}{3} \, \log\left({\left| \sqrt{x + 1} - 1 \right|}\right)"," ",0,"1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) - 3) - 2*sqrt(x + 1) - 8/3*log(-sqrt(x + sqrt(x + 1)) + sqrt(x + 1) + 3) + 8/3*log(-sqrt(x + sqrt(x + 1)) + sqrt(x + 1) + 1) - 15/4*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1) + 8/3*log(sqrt(x + 1) + 2) - 2/3*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) + 2)) + 2/3*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))) - 2/3*log(abs(sqrt(x + 1) - 1))","A",0
1889,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(1+2*x)/(3*x^2-1)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{3}} {\left(2 \, x + 1\right)} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((3*x^2 - 1)^(1/3)*(2*x + 1)*(x - 1)), x)","F",0
1890,1,78,0,0.241826," ","integrate((a*x^2-b)/x^2/(x^3-x)^(1/3),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{3} a \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{4} \, a \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{2} \, a \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right) - \frac{3}{4} \, b {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}"," ",0,"-1/2*sqrt(3)*a*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) + 1/4*a*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) - 1/2*a*log(abs((-1/x^2 + 1)^(1/3) - 1)) - 3/4*b*(-1/x^2 + 1)^(2/3)","A",0
1891,0,0,0,0.000000," ","integrate((x^4+1)/(x^3-x^2-x)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{4} - 1\right)} \sqrt{x^{3} - x^{2} - x}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^4 - 1)*sqrt(x^3 - x^2 - x)), x)","F",0
1892,0,0,0,0.000000," ","integrate((x^3-1)*(x^6+1)^(1/3)/x^2/(x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}{{\left(x^{3} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^6 + 1)^(1/3)*(x^3 - 1)/((x^3 + 1)*x^2), x)","F",0
1893,0,0,0,0.000000," ","integrate((x^6-2)*(x^6+2)^(1/3)/x^2/(x^6+2*x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2\right)}^{\frac{1}{3}} {\left(x^{6} - 2\right)}}{{\left(x^{6} + 2 \, x^{3} + 2\right)} x^{2}}\,{d x}"," ",0,"integrate((x^6 + 2)^(1/3)*(x^6 - 2)/((x^6 + 2*x^3 + 2)*x^2), x)","F",0
1894,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6-2*x^3-1)/x^6/(2*x^6+x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 2 \, x^{3} - 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} + x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 - 2*x^3 - 1)*(x^3 + 1)^(2/3)/((2*x^6 + x^3 - 1)*x^6), x)","F",0
1895,1,207,0,0.351535," ","integrate((x^3+1)*(-x^4+x)^(1/2)/(3*x^6+4*x^3+2),x, algorithm=""giac"")","-\frac{1}{36} \, \sqrt{18 \, \sqrt{2} + 16} \arctan\left(\frac{2 \, \left(\frac{9}{2}\right)^{\frac{3}{4}} {\left(\left(\frac{9}{2}\right)^{\frac{1}{4}} {\left(\sqrt{6} - 2 \, \sqrt{3}\right)} + 6 \, \sqrt{\frac{1}{x^{3}} - 1}\right)}}{9 \, {\left(\sqrt{6} + 2 \, \sqrt{3}\right)}}\right) + \frac{1}{36} \, \sqrt{18 \, \sqrt{2} + 16} \arctan\left(\frac{2 \, \left(\frac{9}{2}\right)^{\frac{3}{4}} {\left(\left(\frac{9}{2}\right)^{\frac{1}{4}} {\left(\sqrt{6} - 2 \, \sqrt{3}\right)} - 6 \, \sqrt{\frac{1}{x^{3}} - 1}\right)}}{9 \, {\left(\sqrt{6} + 2 \, \sqrt{3}\right)}}\right) - \frac{1}{72} \, \sqrt{18 \, \sqrt{2} - 16} \log\left(\frac{1}{3} \, {\left(\sqrt{6} \left(\frac{9}{2}\right)^{\frac{1}{4}} - 2 \, \left(\frac{9}{2}\right)^{\frac{1}{4}} \sqrt{3}\right)} \sqrt{\frac{1}{x^{3}} - 1} + 3 \, \sqrt{\frac{1}{2}} + \frac{1}{x^{3}} - 1\right) + \frac{1}{72} \, \sqrt{18 \, \sqrt{2} - 16} \log\left(-\frac{1}{3} \, {\left(\sqrt{6} \left(\frac{9}{2}\right)^{\frac{1}{4}} - 2 \, \left(\frac{9}{2}\right)^{\frac{1}{4}} \sqrt{3}\right)} \sqrt{\frac{1}{x^{3}} - 1} + 3 \, \sqrt{\frac{1}{2}} + \frac{1}{x^{3}} - 1\right) + \frac{2}{9} \, \arctan\left(\sqrt{\frac{1}{x^{3}} - 1}\right)"," ",0,"-1/36*sqrt(18*sqrt(2) + 16)*arctan(2/9*(9/2)^(3/4)*((9/2)^(1/4)*(sqrt(6) - 2*sqrt(3)) + 6*sqrt(1/x^3 - 1))/(sqrt(6) + 2*sqrt(3))) + 1/36*sqrt(18*sqrt(2) + 16)*arctan(2/9*(9/2)^(3/4)*((9/2)^(1/4)*(sqrt(6) - 2*sqrt(3)) - 6*sqrt(1/x^3 - 1))/(sqrt(6) + 2*sqrt(3))) - 1/72*sqrt(18*sqrt(2) - 16)*log(1/3*(sqrt(6)*(9/2)^(1/4) - 2*(9/2)^(1/4)*sqrt(3))*sqrt(1/x^3 - 1) + 3*sqrt(1/2) + 1/x^3 - 1) + 1/72*sqrt(18*sqrt(2) - 16)*log(-1/3*(sqrt(6)*(9/2)^(1/4) - 2*(9/2)^(1/4)*sqrt(3))*sqrt(1/x^3 - 1) + 3*sqrt(1/2) + 1/x^3 - 1) + 2/9*arctan(sqrt(1/x^3 - 1))","B",0
1896,0,0,0,0.000000," ","integrate((a*x^4-2)/(a*x^4+b)^(1/4)/(2*x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} - 2}{{\left(2 \, x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - 2)/((2*x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1897,0,0,0,0.000000," ","integrate((-1+x)/(1+x)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x - 1}{\sqrt{x + \sqrt{x^{2} + 1}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x - 1)/(sqrt(x + sqrt(x^2 + 1))*(x + 1)), x)","F",0
1898,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x + \sqrt{x^{2} + 1}} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x + sqrt(x^2 + 1))*(x - 1)), x)","F",0
1899,0,0,0,0.000000," ","integrate((x^2-x)^(1/2)/(x^2-x*(x^2-x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} - x}}{\sqrt{x^{2} - \sqrt{x^{2} - x} x}}\,{d x}"," ",0,"integrate(sqrt(x^2 - x)/sqrt(x^2 - sqrt(x^2 - x)*x), x)","F",0
1900,0,0,0,0.000000," ","integrate((x^2+2*x+6)/(2+x)/(x^2+2)/(x^2+x+2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 2 \, x + 6}{{\left(x^{2} + x + 2\right)}^{\frac{1}{3}} {\left(x^{2} + 2\right)} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate((x^2 + 2*x + 6)/((x^2 + x + 2)^(1/3)*(x^2 + 2)*(x + 2)), x)","F",0
1901,0,0,0,0.000000," ","integrate((-1+x)/x/(x^3+2*x^2+2*x+1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} + 2 \, x^{2} + 2 \, x + 1\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((x - 1)/((x^3 + 2*x^2 + 2*x + 1)^(1/3)*x), x)","F",0
1902,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(a*p*x^3+b*x^2+a*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^7,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(a p x^{3} + b x^{2} + a q\right)} {\left(p x^{3} - 2 \, q\right)}}{x^{7}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(a*p*x^3 + b*x^2 + a*q)*(p*x^3 - 2*q)/x^7, x)","F",0
1903,0,0,0,0.000000," ","integrate(x^2/(x^2+1)/(1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/10),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(1024 \, x^{10} - 16640 \, x^{9} + 112000 \, x^{8} - 401440 \, x^{7} + 820340 \, x^{6} - 954733 \, x^{5} + 615255 \, x^{4} - 225810 \, x^{3} + 47250 \, x^{2} - 5265 \, x + 243\right)}^{\frac{1}{10}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/((1024*x^10 - 16640*x^9 + 112000*x^8 - 401440*x^7 + 820340*x^6 - 954733*x^5 + 615255*x^4 - 225810*x^3 + 47250*x^2 - 5265*x + 243)^(1/10)*(x^2 + 1)), x)","F",0
1904,0,0,0,0.000000," ","integrate(1/x/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a^{2} x^{2} - b x} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*x^2 - b*x)*(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2)*x), x)","F",0
1905,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(x^2-1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(sqrt(x^4 + 1)*(x^2 - 1)), x)","F",0
1906,0,0,0,0.000000," ","integrate(1/(1+2*x)/(4*x^2+4*x-1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(4 \, x^{2} + 4 \, x - 1\right)}^{\frac{1}{3}} {\left(2 \, x + 1\right)}}\,{d x}"," ",0,"integrate(1/((4*x^2 + 4*x - 1)^(1/3)*(2*x + 1)), x)","F",0
1907,0,0,0,0.000000," ","integrate(1/x^3/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{3} - b\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^3 - b)*x^3), x)","F",0
1908,0,0,0,0.000000," ","integrate(1/x^3/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{3} - b\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^3 - b)*x^3), x)","F",0
1909,0,0,0,0.000000," ","integrate(x^3*(-b+x)*(-2*a*b+(3*a-b)*x)/(-a+x)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a^3*d+3*a^2*d*x+(-3*a*d+b)*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int \frac{{\left(2 \, a b - {\left(3 \, a - b\right)} x\right)} {\left(b - x\right)} x^{3}}{{\left(a^{3} d - 3 \, a^{2} d x - {\left(d - 1\right)} x^{3} + {\left(3 \, a d - b\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{3}{4}} {\left(a - x\right)}}\,{d x}"," ",0,"integrate((2*a*b - (3*a - b)*x)*(b - x)*x^3/((a^3*d - 3*a^2*d*x - (d - 1)*x^3 + (3*a*d - b)*x^2)*((a - x)*(b - x)*x^2)^(3/4)*(a - x)), x)","F",0
1910,0,0,0,0.000000," ","integrate(x^2/(x^3-x^2-x)^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{4} - 1\right)} \sqrt{x^{3} - x^{2} - x}}\,{d x}"," ",0,"integrate(x^2/((x^4 - 1)*sqrt(x^3 - x^2 - x)), x)","F",0
1911,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+x^2+1)^(1/2)/(x^2+1)/(x^4+x^3+x^2+x+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} - 1\right)}}{{\left(x^{4} + x^{3} + x^{2} + x + 1\right)} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)*(x^2 - 1)/((x^4 + x^3 + x^2 + x + 1)*(x^2 + 1)), x)","F",0
1912,0,0,0,0.000000," ","integrate(x^6/(a*x^4-b)/(a*x^4+b)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(a x^{4} + b\right)}^{\frac{3}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate(x^6/((a*x^4 + b)^(3/4)*(a*x^4 - b)), x)","F",0
1913,1,215,0,0.227804," ","integrate((a*x^3-b)/x^3/(a*x^3+b)/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b} + \frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{3 \, b} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{3 \, b} - \frac{4 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}}}{9 \, b}"," ",0,"2/3*2^(1/4)*(-a)^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/b + 2/3*2^(1/4)*(-a)^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/b - 1/3*2^(1/4)*(-a)^(3/4)*log(2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/b + 1/3*2^(1/4)*(-a)^(3/4)*log(-2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/b - 4/9*(a - b/x^3)^(3/4)/b","B",0
1914,0,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4+b)^(1/4)/(3*a*x^4-b),x, algorithm=""giac"")","\int \frac{a x^{4} - b}{{\left(3 \, a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 - b)/((3*a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
1915,0,0,0,0.000000," ","integrate((a*x^2-2*b)/(a*x^2-b)^(1/4)/(c*x^4+a*x^2-b),x, algorithm=""giac"")","\int \frac{a x^{2} - 2 \, b}{{\left(c x^{4} + a x^{2} - b\right)} {\left(a x^{2} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^2 - 2*b)/((c*x^4 + a*x^2 - b)*(a*x^2 - b)^(1/4)), x)","F",0
1916,0,0,0,0.000000," ","integrate((p*x^2-q)*(p^2*x^4+q^2)^(1/2)/x^2/(a*p*x^2+a*q+b*x),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{4} + q^{2}} {\left(p x^{2} - q\right)}}{{\left(a p x^{2} + a q + b x\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^4 + q^2)*(p*x^2 - q)/((a*p*x^2 + a*q + b*x)*x^2), x)","F",0
1917,0,0,0,0.000000," ","integrate((x^5+1)^(1/3)*(2*x^5-3)/x^2/(2*x^5-x^3+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 3\right)} {\left(x^{5} + 1\right)}^{\frac{1}{3}}}{{\left(2 \, x^{5} - x^{3} + 2\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^5 - 3)*(x^5 + 1)^(1/3)/((2*x^5 - x^3 + 2)*x^2), x)","F",0
1918,0,0,0,0.000000," ","integrate(x^2*(a*x^5+4*b)/(a*x^5-b)^(3/4)/(a*x^5+c*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} + 4 \, b\right)} x^{2}}{{\left(a x^{5} + c x^{4} - b\right)} {\left(a x^{5} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^5 + 4*b)*x^2/((a*x^5 + c*x^4 - b)*(a*x^5 - b)^(3/4)), x)","F",0
1919,0,0,0,0.000000," ","integrate((x^6-1)*(x^6+1)^(2/3)/x^3/(2*x^6-x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 1\right)}^{\frac{2}{3}} {\left(x^{6} - 1\right)}}{{\left(2 \, x^{6} - x^{3} + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^6 + 1)^(2/3)*(x^6 - 1)/((2*x^6 - x^3 + 2)*x^3), x)","F",0
1920,0,0,0,0.000000," ","integrate(x^2*(a*x^6+2*b)/(a*x^6-b)^(3/4)/(a*x^6+c*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} + 2 \, b\right)} x^{2}}{{\left(a x^{6} + c x^{4} - b\right)} {\left(a x^{6} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^6 + 2*b)*x^2/((a*x^6 + c*x^4 - b)*(a*x^6 - b)^(3/4)), x)","F",0
1921,0,0,0,0.000000," ","integrate(x^2*(x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 1} \sqrt{x^{2} + \sqrt{x^{4} + 1}} x^{2}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*sqrt(x^2 + sqrt(x^4 + 1))*x^2, x)","F",0
1922,1,312,0,1.755355," ","integrate((1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8}{315} \, {\left({\left(35 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{9}{2}} - 180 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{7}{2}} + 378 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{5}{2}} - 420 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{3}{2}} + 315 \, \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x + 1} + 1\right)}^{2} - 8 \, \sqrt{x + 1} - 7\right) + 9 \, {\left(5 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{7}{2}} - 21 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{5}{2}} + 35 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{3}{2}} - 35 \, \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x + 1} + 1\right)}^{2} - 8 \, \sqrt{x + 1} - 7\right) - 21 \, {\left(3 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{5}{2}} - 10 \, {\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{3}{2}} + 15 \, \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x + 1} + 1\right)}^{2} - 8 \, \sqrt{x + 1} - 7\right) - 105 \, {\left({\left(\sqrt{\sqrt{x + 1} + 1} + 1\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x + 1} + 1\right)}^{2} - 8 \, \sqrt{x + 1} - 7\right)\right)} \mathrm{sgn}\left(4 \, x + 1\right)"," ",0,"8/315*((35*(sqrt(sqrt(x + 1) + 1) + 1)^(9/2) - 180*(sqrt(sqrt(x + 1) + 1) + 1)^(7/2) + 378*(sqrt(sqrt(x + 1) + 1) + 1)^(5/2) - 420*(sqrt(sqrt(x + 1) + 1) + 1)^(3/2) + 315*sqrt(sqrt(sqrt(x + 1) + 1) + 1))*sgn(4*(sqrt(x + 1) + 1)^2 - 8*sqrt(x + 1) - 7) + 9*(5*(sqrt(sqrt(x + 1) + 1) + 1)^(7/2) - 21*(sqrt(sqrt(x + 1) + 1) + 1)^(5/2) + 35*(sqrt(sqrt(x + 1) + 1) + 1)^(3/2) - 35*sqrt(sqrt(sqrt(x + 1) + 1) + 1))*sgn(4*(sqrt(x + 1) + 1)^2 - 8*sqrt(x + 1) - 7) - 21*(3*(sqrt(sqrt(x + 1) + 1) + 1)^(5/2) - 10*(sqrt(sqrt(x + 1) + 1) + 1)^(3/2) + 15*sqrt(sqrt(sqrt(x + 1) + 1) + 1))*sgn(4*(sqrt(x + 1) + 1)^2 - 8*sqrt(x + 1) - 7) - 105*((sqrt(sqrt(x + 1) + 1) + 1)^(3/2) - 3*sqrt(sqrt(sqrt(x + 1) + 1) + 1))*sgn(4*(sqrt(x + 1) + 1)^2 - 8*sqrt(x + 1) - 7))*sgn(4*x + 1)","C",0
1923,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1924,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1925,0,0,0,0.000000," ","integrate((x^3-2)*(x^3+1)^(2/3)/x^6/(2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)}}{{\left(2 \, x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 1)^(2/3)*(x^3 - 2)/((2*x^3 - 1)*x^6), x)","F",0
1926,0,0,0,0.000000," ","integrate(1/x^3/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{3} + b\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^3 + b)*x^3), x)","F",0
1927,0,0,0,0.000000," ","integrate(1/x^3/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(a x^{3} + b\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^2*x^2)^(1/3)*(a*x^3 + b)*x^3), x)","F",0
1928,1,184,0,0.222108," ","integrate((x^4+x-1)*(x^4-x^3)^(1/4)/(1+x),x, algorithm=""giac"")","\frac{1}{30720} \, {\left(32575 \, {\left(\frac{1}{x} - 1\right)}^{4} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 131360 \, {\left(\frac{1}{x} - 1\right)}^{3} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 188230 \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 120744 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 25155 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{5} + 2 \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{9869}{4096} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{9869}{8192} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{9869}{8192} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/30720*(32575*(1/x - 1)^4*(-1/x + 1)^(1/4) + 131360*(1/x - 1)^3*(-1/x + 1)^(1/4) + 188230*(1/x - 1)^2*(-1/x + 1)^(1/4) - 120744*(-1/x + 1)^(5/4) + 25155*(-1/x + 1)^(1/4))*x^5 + 2*2^(1/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) - 2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4))) - 9869/4096*arctan((-1/x + 1)^(1/4)) - 9869/8192*log((-1/x + 1)^(1/4) + 1) + 9869/8192*log(abs((-1/x + 1)^(1/4) - 1))","A",0
1929,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(2/3)/x^3/(2*x^4+x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{{\left(2 \, x^{4} + x^{3} + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^4 + 1)^(2/3)*(x^4 - 3)/((2*x^4 + x^3 + 2)*x^3), x)","F",0
1930,0,0,0,0.000000," ","integrate((a*x^4-4*b)*(a*x^4+b)^(3/4)/x^8/(a*x^4+4*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b\right)}^{\frac{3}{4}} {\left(a x^{4} - 4 \, b\right)}}{{\left(a x^{4} + 4 \, b\right)} x^{8}}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)*(a*x^4 - 4*b)/((a*x^4 + 4*b)*x^8), x)","F",0
1931,0,0,0,0.000000," ","integrate((a*x^4+b)^(3/4)*(a*x^4+2*b)/x^8/(a*x^4+4*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{3}{4}}}{{\left(a x^{4} + 4 \, b\right)} x^{8}}\,{d x}"," ",0,"integrate((a*x^4 + 2*b)*(a*x^4 + b)^(3/4)/((a*x^4 + 4*b)*x^8), x)","F",0
1932,1,295,0,0.736549," ","integrate(x^4*(a*x^4+b*x^3)^(1/4)/(a*x+b),x, algorithm=""giac"")","-\frac{\frac{43890 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{6} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{6}} + \frac{43890 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{6} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{6}} + \frac{21945 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{6} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a^{6}} + \frac{21945 \, \sqrt{2} b^{6} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{5}} - \frac{8 \, {\left(7315 \, {\left(a + \frac{b}{x}\right)}^{\frac{17}{4}} b^{6} - 33440 \, {\left(a + \frac{b}{x}\right)}^{\frac{13}{4}} a b^{6} + 59470 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} a^{2} b^{6} - 50312 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a^{3} b^{6} + 19015 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{4} b^{6}\right)} x^{5}}{a^{5} b^{5}}}{81920 \, b}"," ",0,"-1/81920*(43890*sqrt(2)*(-a)^(1/4)*b^6*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^6 + 43890*sqrt(2)*(-a)^(1/4)*b^6*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^6 + 21945*sqrt(2)*(-a)^(1/4)*b^6*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^6 + 21945*sqrt(2)*b^6*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^5) - 8*(7315*(a + b/x)^(17/4)*b^6 - 33440*(a + b/x)^(13/4)*a*b^6 + 59470*(a + b/x)^(9/4)*a^2*b^6 - 50312*(a + b/x)^(5/4)*a^3*b^6 + 19015*(a + b/x)^(1/4)*a^4*b^6)*x^5/(a^5*b^5))/b","B",0
1933,0,0,0,0.000000," ","integrate((a*x^2+b)/(a*x^2-b)/(a^2*x^4+b^2)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{\sqrt{a^{2} x^{4} + b^{2}} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/(sqrt(a^2*x^4 + b^2)*(a*x^2 - b)), x)","F",0
1934,0,0,0,0.000000," ","integrate((x^2+1)*(1+(x^2+1)^(1/2))^(1/2)/(x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)} \sqrt{\sqrt{x^{2} + 1} + 1}}{x^{2} - 1}\,{d x}"," ",0,"integrate((x^2 + 1)*sqrt(sqrt(x^2 + 1) + 1)/(x^2 - 1), x)","F",0
1935,0,0,0,0.000000," ","integrate(1/(a*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{3} - b\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x^3 - b)^(-1/3), x)","F",0
1936,0,0,0,0.000000," ","integrate((a^2-2*a*x+x^2)*(-a*b-a*c+3*b*c+2*(a-b-c)*x+x^2)/((-a+x)*(-b+x)*(-c+x))^(3/4)/(-b*c-a^3*d+(3*a^2*d+b+c)*x-(3*a*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{{\left(a^{2} - 2 \, a x + x^{2}\right)} {\left(a b + a c - 3 \, b c - 2 \, {\left(a - b - c\right)} x - x^{2}\right)}}{{\left(a^{3} d - d x^{3} + {\left(3 \, a d + 1\right)} x^{2} + b c - {\left(3 \, a^{2} d + b + c\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a^2 - 2*a*x + x^2)*(a*b + a*c - 3*b*c - 2*(a - b - c)*x - x^2)/((a^3*d - d*x^3 + (3*a*d + 1)*x^2 + b*c - (3*a^2*d + b + c)*x)*(-(a - x)*(b - x)*(c - x))^(3/4)), x)","F",0
1937,0,0,0,0.000000," ","integrate((x^5-4)*(x^5-2*x^4+1)^(1/4)/x^2/(x^5+1),x, algorithm=""giac"")","\int \frac{{\left(x^{5} - 2 \, x^{4} + 1\right)}^{\frac{1}{4}} {\left(x^{5} - 4\right)}}{{\left(x^{5} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^5 - 2*x^4 + 1)^(1/4)*(x^5 - 4)/((x^5 + 1)*x^2), x)","F",0
1938,1,88,0,0.215660," ","integrate((a*x^6+b)/x^6/(x^3+x)^(1/3),x, algorithm=""giac"")","-\frac{3}{16} \, b {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{8}{3}} + \frac{3}{5} \, b {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{5}{3}} - \frac{1}{2} \, \sqrt{3} a \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{4} \, a \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{2} \, a \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right) - \frac{3}{4} \, b {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/16*b*(1/x^2 + 1)^(8/3) + 3/5*b*(1/x^2 + 1)^(5/3) - 1/2*sqrt(3)*a*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) + 1/4*a*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - 1/2*a*log(abs((1/x^2 + 1)^(1/3) - 1)) - 3/4*b*(1/x^2 + 1)^(2/3)","A",0
1939,0,0,0,0.000000," ","integrate((a^2*x^2+b^2)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{a^{2} x^{2} + b^{2}}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a^2*x^2 + b^2)/sqrt(a*x + sqrt(a^2*x^2 + b^2)), x)","F",0
1940,0,0,0,0.000000," ","integrate(x^2/(a*x^2+b)^(3/4)/(a*x^2+2*b),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a x^{2} + 2 \, b\right)} {\left(a x^{2} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((a*x^2 + 2*b)*(a*x^2 + b)^(3/4)), x)","F",0
1941,0,0,0,0.000000," ","integrate(x/(a*x^3-b)^(2/3),x, algorithm=""giac"")","\int \frac{x}{{\left(a x^{3} - b\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x/(a*x^3 - b)^(2/3), x)","F",0
1942,0,0,0,0.000000," ","integrate(x*(x^4+x^2)^(1/3)/(2*x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} x}{2 \, x^{2} + 1}\,{d x}"," ",0,"integrate((x^4 + x^2)^(1/3)*x/(2*x^2 + 1), x)","F",0
1943,1,233,0,0.204569," ","integrate((a*x^3+b)/x^6/(a*x^3-b)/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","-\frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b^{2}} - \frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b^{2}} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{3 \, b^{2}} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{3 \, b^{2}} + \frac{4 \, {\left(3 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{12} + 7 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{12}\right)}}{63 \, b^{14}}"," ",0,"-2/3*2^(1/4)*(-a)^(3/4)*a*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/b^2 - 2/3*2^(1/4)*(-a)^(3/4)*a*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/b^2 + 1/3*2^(1/4)*(-a)^(3/4)*a*log(2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/b^2 - 1/3*2^(1/4)*(-a)^(3/4)*a*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/b^2 + 4/63*(3*(a + b/x^3)^(7/4)*b^12 + 7*(a + b/x^3)^(3/4)*a*b^12)/b^14","B",0
1944,0,0,0,0.000000," ","integrate((x^4-1)*(x^6+x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{8} + x^{4} + 1}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^4 - 1)/(x^8 + x^4 + 1), x)","F",0
1945,0,0,0,0.000000," ","integrate((x^4-1)*(x^6+x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{8} + x^{4} + 1}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^4 - 1)/(x^8 + x^4 + 1), x)","F",0
1946,1,112,0,0.752467," ","integrate(x*(a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(48 \, b^{2} + 8 \, b - 5\right)} \log\left({\left| -2 \, \sqrt{a x - b} + 2 \, \sqrt{a x + \sqrt{a x - b}} - 1 \right|}\right) - 2 \, \sqrt{a x + \sqrt{a x - b}} {\left(2 \, \sqrt{a x - b} {\left(4 \, \sqrt{a x - b} {\left(6 \, \sqrt{a x - b} + 1\right)} + 60 \, b - 5\right)} - 4 \, b + 15\right)}}{192 \, a^{2}}"," ",0,"-1/192*(3*(48*b^2 + 8*b - 5)*log(abs(-2*sqrt(a*x - b) + 2*sqrt(a*x + sqrt(a*x - b)) - 1)) - 2*sqrt(a*x + sqrt(a*x - b))*(2*sqrt(a*x - b)*(4*sqrt(a*x - b)*(6*sqrt(a*x - b) + 1) + 60*b - 5) - 4*b + 15))/a^2","A",0
1947,1,181,0,1.281791," ","integrate((a*x-1)*(a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(48 \, b^{2} + 8 \, b - 5\right)} \log\left({\left| -2 \, \sqrt{a x - b} + 2 \, \sqrt{a x + \sqrt{a x - b}} - 1 \right|}\right) - 48 \, {\left(4 \, b - 1\right)} \log\left({\left| -2 \, \sqrt{a x - b} + 2 \, \sqrt{a x + \sqrt{a x - b}} - 1 \right|}\right) - 2 \, \sqrt{a x + \sqrt{a x - b}} {\left(2 \, \sqrt{a x - b} {\left(4 \, \sqrt{a x - b} {\left(6 \, \sqrt{a x - b} + 1\right)} + 60 \, b - 5\right)} - 4 \, b + 15\right)} + 96 \, \sqrt{a x + \sqrt{a x - b}} {\left(2 \, \sqrt{a x - b} + 1\right)}}{192 \, a}"," ",0,"-1/192*(3*(48*b^2 + 8*b - 5)*log(abs(-2*sqrt(a*x - b) + 2*sqrt(a*x + sqrt(a*x - b)) - 1)) - 48*(4*b - 1)*log(abs(-2*sqrt(a*x - b) + 2*sqrt(a*x + sqrt(a*x - b)) - 1)) - 2*sqrt(a*x + sqrt(a*x - b))*(2*sqrt(a*x - b)*(4*sqrt(a*x - b)*(6*sqrt(a*x - b) + 1) + 60*b - 5) - 4*b + 15) + 96*sqrt(a*x + sqrt(a*x - b))*(2*sqrt(a*x - b) + 1))/a","A",0
1948,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{4} + 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^4 + 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
1949,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{4} + 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^4 + 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
1950,1,244,0,0.254976," ","integrate(1/(x^4-x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","-\frac{1}{8} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{16} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{16} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - 8 i \, \left(-\frac{1}{33554432} i + \frac{1}{33554432}\right)^{\frac{1}{4}} \log\left(i \, \left(-37778931862957161709568 i + 37778931862957161709568\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 524288\right) + 8 i \, \left(-\frac{1}{33554432} i + \frac{1}{33554432}\right)^{\frac{1}{4}} \log\left(-i \, \left(-37778931862957161709568 i + 37778931862957161709568\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 524288\right) - i \, \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(\left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) + \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(i \, \left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) - \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(-i \, \left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) + i \, \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(-\left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) - \left(-\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(\left(-549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1024\right) + \left(-\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(-\left(-549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1024\right) + \frac{1}{2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"-1/8*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) + 1/16*2^(3/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) - 1/16*2^(3/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4)) - 8*I*(-1/33554432*I + 1/33554432)^(1/4)*log(I*(-37778931862957161709568*I + 37778931862957161709568)^(1/4)*(-1/x^2 + 1)^(1/4) - 524288) + 8*I*(-1/33554432*I + 1/33554432)^(1/4)*log(-I*(-37778931862957161709568*I + 37778931862957161709568)^(1/4)*(-1/x^2 + 1)^(1/4) - 524288) - I*(1/8192*I + 1/8192)^(1/4)*log((549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) + (1/8192*I + 1/8192)^(1/4)*log(I*(549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) - (1/8192*I + 1/8192)^(1/4)*log(-I*(549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) + I*(1/8192*I + 1/8192)^(1/4)*log(-(549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) - (-1/8192*I + 1/8192)^(1/4)*log((-549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) - 1024) + (-1/8192*I + 1/8192)^(1/4)*log(-(-549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) - 1024) + 1/2/(-1/x^2 + 1)^(1/4)","B",0
1951,1,244,0,0.278538," ","integrate(1/(x^4-x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","-\frac{1}{8} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{16} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{16} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - 8 i \, \left(-\frac{1}{33554432} i + \frac{1}{33554432}\right)^{\frac{1}{4}} \log\left(i \, \left(-37778931862957161709568 i + 37778931862957161709568\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 524288\right) + 8 i \, \left(-\frac{1}{33554432} i + \frac{1}{33554432}\right)^{\frac{1}{4}} \log\left(-i \, \left(-37778931862957161709568 i + 37778931862957161709568\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 524288\right) - i \, \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(\left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) + \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(i \, \left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) - \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(-i \, \left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) + i \, \left(\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(-\left(549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1024 i\right) - \left(-\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(\left(-549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1024\right) + \left(-\frac{1}{8192} i + \frac{1}{8192}\right)^{\frac{1}{4}} \log\left(-\left(-549755813888 i + 549755813888\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 1024\right) + \frac{1}{2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"-1/8*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) + 1/16*2^(3/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) - 1/16*2^(3/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4)) - 8*I*(-1/33554432*I + 1/33554432)^(1/4)*log(I*(-37778931862957161709568*I + 37778931862957161709568)^(1/4)*(-1/x^2 + 1)^(1/4) - 524288) + 8*I*(-1/33554432*I + 1/33554432)^(1/4)*log(-I*(-37778931862957161709568*I + 37778931862957161709568)^(1/4)*(-1/x^2 + 1)^(1/4) - 524288) - I*(1/8192*I + 1/8192)^(1/4)*log((549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) + (1/8192*I + 1/8192)^(1/4)*log(I*(549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) - (1/8192*I + 1/8192)^(1/4)*log(-I*(549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) + I*(1/8192*I + 1/8192)^(1/4)*log(-(549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) + 1024*I) - (-1/8192*I + 1/8192)^(1/4)*log((-549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) - 1024) + (-1/8192*I + 1/8192)^(1/4)*log(-(-549755813888*I + 549755813888)^(1/4)*(-1/x^2 + 1)^(1/4) - 1024) + 1/2/(-1/x^2 + 1)^(1/4)","B",0
1952,0,0,0,0.000000," ","integrate((x^4-2)/(x^4+1)^(1/4)/(2*x^8-x^4-1),x, algorithm=""giac"")","\int \frac{x^{4} - 2}{{\left(2 \, x^{8} - x^{4} - 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 - 2)/((2*x^8 - x^4 - 1)*(x^4 + 1)^(1/4)), x)","F",0
1953,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{{\left(a x^{2} + b^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2)^(5/2), x)","F",0
1954,1,175,0,0.271634," ","integrate((a*x^2-b)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} b^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{2} \, \sqrt{2} b^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} b^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right) + \frac{1}{4} \, \sqrt{2} b^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right) + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}"," ",0,"-1/2*sqrt(2)*b^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^2 - b)^(1/4))/b^(1/4)) - 1/2*sqrt(2)*b^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^2 - b)^(1/4))/b^(1/4)) - 1/4*sqrt(2)*b^(1/4)*log(sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b)) + 1/4*sqrt(2)*b^(1/4)*log(-sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b)) + 2*(a*x^2 - b)^(1/4)","A",0
1955,1,105,0,0.864612," ","integrate((a*x^2+b)*(x^3-x)^(1/3)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - \frac{1}{6} \, \sqrt{3} {\left(a - 3 \, b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{12} \, {\left(a - 3 \, b\right)} \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, {\left(a - 3 \, b\right)} \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right) - \frac{3}{2} \, b {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}"," ",0,"1/2*a*x^2*(-1/x^2 + 1)^(1/3) - 1/6*sqrt(3)*(a - 3*b)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) - 1/12*(a - 3*b)*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) + 1/6*(a - 3*b)*log(abs((-1/x^2 + 1)^(1/3) - 1)) - 3/2*b*(-1/x^2 + 1)^(1/3)","A",0
1956,0,0,0,0.000000," ","integrate((a*x-b)/x/(a^3*x^3+b^3)^(1/3),x, algorithm=""giac"")","\int \frac{a x - b}{{\left(a^{3} x^{3} + b^{3}\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((a*x - b)/((a^3*x^3 + b^3)^(1/3)*x), x)","F",0
1957,1,149,0,0.631668," ","integrate(x^2*(x^4-x^3)^(1/4)/(2+x),x, algorithm=""giac"")","-\frac{1}{96} \, {\left(401 \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 702 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 333 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{3} - 8 \cdot 24^{\frac{1}{4}} \arctan\left(\frac{2}{3} \, \left(\frac{3}{2}\right)^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 4 \cdot 24^{\frac{1}{4}} \log\left(\left(\frac{3}{2}\right)^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 4 \cdot 24^{\frac{1}{4}} \log\left({\left| -\left(\frac{3}{2}\right)^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + \frac{1135}{64} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1135}{128} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1135}{128} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/96*(401*(1/x - 1)^2*(-1/x + 1)^(1/4) - 702*(-1/x + 1)^(5/4) + 333*(-1/x + 1)^(1/4))*x^3 - 8*24^(1/4)*arctan(2/3*(3/2)^(3/4)*(-1/x + 1)^(1/4)) - 4*24^(1/4)*log((3/2)^(1/4) + (-1/x + 1)^(1/4)) + 4*24^(1/4)*log(abs(-(3/2)^(1/4) + (-1/x + 1)^(1/4))) + 1135/64*arctan((-1/x + 1)^(1/4)) + 1135/128*log((-1/x + 1)^(1/4) + 1) - 1135/128*log(abs((-1/x + 1)^(1/4) - 1))","A",0
1958,0,0,0,0.000000," ","integrate((-1+x)*(12*x^4-8*x^2+8*x-3)/x/((-2*x^2+1)/(2*x^2+1))^(2/3)/(2*x^2+1)/(2*x^4-6*x^3+7*x^2-7*x+3),x, algorithm=""giac"")","\int \frac{{\left(12 \, x^{4} - 8 \, x^{2} + 8 \, x - 3\right)} {\left(x - 1\right)}}{{\left(2 \, x^{4} - 6 \, x^{3} + 7 \, x^{2} - 7 \, x + 3\right)} {\left(2 \, x^{2} + 1\right)} x \left(-\frac{2 \, x^{2} - 1}{2 \, x^{2} + 1}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((12*x^4 - 8*x^2 + 8*x - 3)*(x - 1)/((2*x^4 - 6*x^3 + 7*x^2 - 7*x + 3)*(2*x^2 + 1)*x*(-(2*x^2 - 1)/(2*x^2 + 1))^(2/3)), x)","F",0
1959,-2,0,0,0.000000," ","integrate((-a*x^5+b)/(b*x+a)^(1/2)/(x^5+a*b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[-15360,46080]:[1,0,-5]%%},[0,6]%%%}+%%%{%%{[-1280,14080]:[1,0,-5]%%},[0,5]%%%}+%%%{%%{[11904,640]:[1,0,-5]%%},[0,4]%%%}+%%%{%%{[3168,23520]:[1,0,-5]%%},[0,3]%%%}+%%%{%%{[660,9220]:[1,0,-5]%%},[0,2]%%%}+%%%{%%{[495,635]:[1,0,-5]%%},[0,1]%%%}+%%%{150,[0,0]%%%} / %%%{30720,[0,6]%%%}+%%%{%%{[5120,17920]:[1,0,-5]%%},[0,5]%%%}+%%%{%%{[18176,30720]:[1,0,-5]%%},[0,4]%%%}+%%%{%%{[16512,43200]:[1,0,-5]%%},[0,3]%%%}+%%%{%%{[5600,15480]:[1,0,-5]%%},[0,2]%%%}+%%%{%%{[1060,2190]:[1,0,-5]%%},[0,1]%%%}+%%%{%%{[75,225]:[1,0,-5]%%},[0,0]%%%} Error: Bad Argument Value","F(-2)",0
1960,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+x^3+1)/x^6/(x^6-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 + x^3 + 1)*(x^3 - 1)^(2/3)/((x^6 - 1)*x^6), x)","F",0
1961,0,0,0,0.000000," ","integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1962,0,0,0,0.000000," ","integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1963,1,107,0,0.224024," ","integrate(x/(x^2*(-a+x))^(2/3)/(-a*d+(-1+d)*x),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left| d \right|}^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} d^{\frac{1}{3}} {\left(2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} + \frac{1}{d^{\frac{1}{3}}}\right)}\right)}{a d} - \frac{{\left| d \right|}^{\frac{2}{3}} \log\left({\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{d^{\frac{1}{3}}} + \frac{1}{d^{\frac{2}{3}}}\right)}{2 \, a d} + \frac{\log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} - \frac{1}{d^{\frac{1}{3}}} \right|}\right)}{a d^{\frac{1}{3}}}"," ",0,"-sqrt(3)*abs(d)^(2/3)*arctan(1/3*sqrt(3)*d^(1/3)*(2*(-a/x + 1)^(1/3) + 1/d^(1/3)))/(a*d) - 1/2*abs(d)^(2/3)*log((-a/x + 1)^(2/3) + (-a/x + 1)^(1/3)/d^(1/3) + 1/d^(2/3))/(a*d) + log(abs((-a/x + 1)^(1/3) - 1/d^(1/3)))/(a*d^(1/3))","A",0
1964,1,175,0,0.129075," ","integrate((a*x^2-b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{2} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) + \frac{1}{4} \, \sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right) - \frac{1}{4} \, \sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right) + \frac{2}{3} \, {\left(a x^{2} - b\right)}^{\frac{3}{4}}"," ",0,"-1/2*sqrt(2)*b^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^2 - b)^(1/4))/b^(1/4)) - 1/2*sqrt(2)*b^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^2 - b)^(1/4))/b^(1/4)) + 1/4*sqrt(2)*b^(3/4)*log(sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b)) - 1/4*sqrt(2)*b^(3/4)*log(-sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b)) + 2/3*(a*x^2 - b)^(3/4)","A",0
1965,0,0,0,0.000000," ","integrate((x^2-2*x)/(x^2-x+1)/(x^4+1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2} - 2 \, x}{{\left(x^{4} + 1\right)}^{\frac{1}{4}} {\left(x^{2} - x + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 2*x)/((x^4 + 1)^(1/4)*(x^2 - x + 1)), x)","F",0
1966,0,0,0,0.000000," ","integrate((k^4*x^4+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^4*x^4-1),x, algorithm=""giac"")","\int \frac{k^{4} x^{4} + 1}{{\left(k^{4} x^{4} - 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^4*x^4 + 1)/((k^4*x^4 - 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
1967,-2,0,0,0.000000," ","integrate((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1968,-2,0,0,0.000000," ","integrate((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1969,-2,0,0,0.000000," ","integrate((x^8-1)*(x^8+1)/(x^8-x^4-1)^(1/4)/(x^16-3*x^8+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1970,1,103,0,0.444645," ","integrate(1/(x^2*(-a+x))^(1/3)/(-a*d+(-1+d)*x),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} d^{\frac{1}{3}} {\left(2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} + \frac{1}{d^{\frac{1}{3}}}\right)}\right)}{a {\left| d \right|}^{\frac{2}{3}}} - \frac{{\left| d \right|}^{\frac{4}{3}} \log\left({\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{d^{\frac{1}{3}}} + \frac{1}{d^{\frac{2}{3}}}\right)}{2 \, a d^{2}} + \frac{\log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} - \frac{1}{d^{\frac{1}{3}}} \right|}\right)}{a d^{\frac{2}{3}}}"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*d^(1/3)*(2*(-a/x + 1)^(1/3) + 1/d^(1/3)))/(a*abs(d)^(2/3)) - 1/2*abs(d)^(4/3)*log((-a/x + 1)^(2/3) + (-a/x + 1)^(1/3)/d^(1/3) + 1/d^(2/3))/(a*d^2) + log(abs((-a/x + 1)^(1/3) - 1/d^(1/3)))/(a*d^(2/3))","A",0
1971,0,0,0,0.000000," ","integrate((x^2+2*x+6)^(1/3)/(1+x),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 2 \, x + 6\right)}^{\frac{1}{3}}}{x + 1}\,{d x}"," ",0,"integrate((x^2 + 2*x + 6)^(1/3)/(x + 1), x)","F",0
1972,0,0,0,0.000000," ","integrate((-1+x)/x/(x^3-1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} - 1\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((x - 1)/((x^3 - 1)^(1/3)*x), x)","F",0
1973,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+1)/x^6/(x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 1)*(x^3 - 1)^(2/3)/((x^3 - 2)*x^6), x)","F",0
1974,1,97,0,0.178598," ","integrate((x^2-4)*(x^3+x)^(1/3)/x^4/(x^2+2),x, algorithm=""giac"")","\frac{3}{4} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{3}{4} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} + \frac{3}{16} \cdot 4^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) - \frac{3}{4} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \log\left({\left| -\left(\frac{1}{2}\right)^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right) - \frac{9}{4} \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}"," ",0,"3/4*sqrt(3)*(1/2)^(1/3)*arctan(2/3*sqrt(3)*(1/2)^(2/3)*((1/2)^(1/3) + 2*(1/x^2 + 1)^(1/3))) + 3/4*(1/x^2 + 1)^(4/3) + 3/16*4^(1/3)*log((1/2)^(2/3) + (1/2)^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3)) - 3/4*(1/2)^(1/3)*log(abs(-(1/2)^(1/3) + (1/x^2 + 1)^(1/3))) - 9/4*(1/x^2 + 1)^(1/3)","A",0
1975,0,0,0,0.000000," ","integrate((x^2+2)/(x^2+1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 2}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 2)/((x^3 - x^2)^(1/3)*(x^2 + 1)), x)","F",0
1976,0,0,0,0.000000," ","integrate(x/(a*x^2+b)/(a*x^3-b*x)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{a x^{3} - b x} {\left(a x^{2} + b\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(a*x^3 - b*x)*(a*x^2 + b)), x)","F",0
1977,0,0,0,0.000000," ","integrate((a*x^2-b)/(a*x^2+b)/(a*x^3-b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{\sqrt{a x^{3} - b x} {\left(a x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/(sqrt(a*x^3 - b*x)*(a*x^2 + b)), x)","F",0
1978,0,0,0,0.000000," ","integrate((a*x^3-b*x)^(1/2)/(a^2*x^4-b^2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3} - b x}}{a^{2} x^{4} - b^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^3 - b*x)/(a^2*x^4 - b^2), x)","F",0
1979,0,0,0,0.000000," ","integrate((x^5+1)^(2/3)*(2*x^5-3)*(2*x^5+x^3+2)/x^6/(2*x^5-x^3+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} + x^{3} + 2\right)} {\left(2 \, x^{5} - 3\right)} {\left(x^{5} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{5} - x^{3} + 2\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^5 + x^3 + 2)*(2*x^5 - 3)*(x^5 + 1)^(2/3)/((2*x^5 - x^3 + 2)*x^6), x)","F",0
1980,0,0,0,0.000000," ","integrate((a*x^6+b)/(a*x^6-b)/(a*x^6+a^3*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{6} + b}{{\left(a x^{6} + a^{3} x^{3} - b\right)}^{\frac{1}{3}} {\left(a x^{6} - b\right)}}\,{d x}"," ",0,"integrate((a*x^6 + b)/((a*x^6 + a^3*x^3 - b)^(1/3)*(a*x^6 - b)), x)","F",0
1981,0,0,0,0.000000," ","integrate((x^2+1)*(x^8+1)*(x^8+x^6+x^4+x^2+1)^(1/2)/x^7/(x^2-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{8} + x^{6} + x^{4} + x^{2} + 1} {\left(x^{8} + 1\right)} {\left(x^{2} + 1\right)}}{{\left(x^{2} - 1\right)} x^{7}}\,{d x}"," ",0,"integrate(sqrt(x^8 + x^6 + x^4 + x^2 + 1)*(x^8 + 1)*(x^2 + 1)/((x^2 - 1)*x^7), x)","F",0
1982,-2,0,0,0.000000," ","integrate((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1983,-2,0,0,0.000000," ","integrate((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Not invertible Error: Bad Argument Value","F(-2)",0
1984,0,0,0,0.000000," ","integrate((x^4-1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}{x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - 1)*sqrt(x + sqrt(x^2 + 1))/(x^4 + 1), x)","F",0
1985,0,0,0,0.000000," ","integrate((x^4-1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}{x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - 1)*sqrt(x + sqrt(x^2 + 1))/(x^4 + 1), x)","F",0
1986,0,0,0,0.000000," ","integrate(x^2*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + x} x^{2}}{\sqrt{x^{2} + \sqrt{x^{2} + x} x}}\,{d x}"," ",0,"integrate(sqrt(x^2 + x)*x^2/sqrt(x^2 + sqrt(x^2 + x)*x), x)","F",0
1987,0,0,0,0.000000," ","integrate(1/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(1/((c*x^2 + d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
1988,0,0,0,0.000000," ","integrate(1/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(1/((c*x^2 + d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
1989,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x^2+1)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1990,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x^2+1)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1991,0,0,0,0.000000," ","integrate((a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/3)),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} + b}}{x^{2} - {\left(a x - \sqrt{a^{2} x^{2} + b}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + b)/(x^2 - (a*x - sqrt(a^2*x^2 + b))^(1/3)), x)","F",0
1992,0,0,0,0.000000," ","integrate((a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} + b}}{x^{2} - \sqrt{a x - \sqrt{a^{2} x^{2} + b}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + b)/(x^2 - sqrt(a*x - sqrt(a^2*x^2 + b))), x)","F",0
1993,0,0,0,0.000000," ","integrate((x^2-2*x-6)^(1/3)/(-1+x),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - 2 \, x - 6\right)}^{\frac{1}{3}}}{x - 1}\,{d x}"," ",0,"integrate((x^2 - 2*x - 6)^(1/3)/(x - 1), x)","F",0
1994,0,0,0,0.000000," ","integrate((-1+x)/(x^3-x^2-x+1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} - x^{2} - x + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x - 1)/(x^3 - x^2 - x + 1)^(1/3), x)","F",0
1995,0,0,0,0.000000," ","integrate(x/(x^3+x^2-x-1)^(1/3),x, algorithm=""giac"")","\int \frac{x}{{\left(x^{3} + x^{2} - x - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x/(x^3 + x^2 - x - 1)^(1/3), x)","F",0
1996,0,0,0,0.000000," ","integrate((3+2*x)*(3*x^3+x+1)^(2/3)/x^3/(x^3+x+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} + x + 1\right)}^{\frac{2}{3}} {\left(2 \, x + 3\right)}}{{\left(x^{3} + x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((3*x^3 + x + 1)^(2/3)*(2*x + 3)/((x^3 + x + 1)*x^3), x)","F",0
1997,0,0,0,0.000000," ","integrate(x^2*(-3*a*b^3+2*b^2*(3*a+b)*x-3*b*(a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^3)^(3/4)/(a*b^3-b^2*(3*a+b)*x+3*b*(a+b)*x^2-(a+3*b+d)*x^3+x^4),x, algorithm=""giac"")","\int -\frac{{\left(3 \, a b^{3} - 2 \, {\left(3 \, a + b\right)} b^{2} x + 3 \, {\left(a + b\right)} b x^{2} - x^{4}\right)} x^{2}}{\left({\left(a - x\right)} {\left(b - x\right)}^{3} x\right)^{\frac{3}{4}} {\left(a b^{3} - {\left(3 \, a + b\right)} b^{2} x + 3 \, {\left(a + b\right)} b x^{2} - {\left(a + 3 \, b + d\right)} x^{3} + x^{4}\right)}}\,{d x}"," ",0,"integrate(-(3*a*b^3 - 2*(3*a + b)*b^2*x + 3*(a + b)*b*x^2 - x^4)*x^2/(((a - x)*(b - x)^3*x)^(3/4)*(a*b^3 - (3*a + b)*b^2*x + 3*(a + b)*b*x^2 - (a + 3*b + d)*x^3 + x^4)), x)","F",0
1998,0,0,0,0.000000," ","integrate(x^6/(a*x^4-b)^(3/4)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(a x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^6/((a*x^4 + b)*(a*x^4 - b)^(3/4)), x)","F",0
1999,1,377,0,0.233257," ","integrate((2*a*x^2-b)/(a*x^2-b)/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{2 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{2 \, a} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{2 \, a} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{2 \, a} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{4 \, a} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{4 \, a}"," ",0,"sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a + sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a - 1/2*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/a + 1/2*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/a - 1/2*2^(1/4)*(-a)^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a - 1/2*2^(1/4)*(-a)^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a + 1/4*2^(1/4)*(-a)^(3/4)*log(2^(3/4)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^2))/a - 1/4*2^(1/4)*(-a)^(3/4)*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^2))/a","B",0
2000,0,0,0,0.000000," ","integrate((2*a*x^4-3*b)/(a*x^4-2*b)/(a*x^4+b)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x^{4} - 3 \, b}{{\left(a x^{4} + b\right)}^{\frac{1}{4}} {\left(a x^{4} - 2 \, b\right)}}\,{d x}"," ",0,"integrate((2*a*x^4 - 3*b)/((a*x^4 + b)^(1/4)*(a*x^4 - 2*b)), x)","F",0
2001,0,0,0,0.000000," ","integrate((a*x^4+b)/(a*x^4-b)^(1/4)/(3*a*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(3 \, a x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((3*a*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
2002,0,0,0,0.000000," ","integrate((x^6+2)*(x^6-x^4-1)/(-x^6-x^4+1)^(1/4)/(x^6-1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} - 1\right)} {\left(x^{6} + 2\right)}}{{\left(x^{6} - 1\right)}^{2} {\left(-x^{6} - x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^6 - x^4 - 1)*(x^6 + 2)/((x^6 - 1)^2*(-x^6 - x^4 + 1)^(1/4)), x)","F",0
2003,0,0,0,0.000000," ","integrate((a*x^6-2*b)*(a*x^6-c*x^4+b)/x^2/(a*x^6+b)^(3/4)/(a*x^6+c*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} - c x^{4} + b\right)} {\left(a x^{6} - 2 \, b\right)}}{{\left(a x^{6} + c x^{4} + b\right)} {\left(a x^{6} + b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a*x^6 - c*x^4 + b)*(a*x^6 - 2*b)/((a*x^6 + c*x^4 + b)*(a*x^6 + b)^(3/4)*x^2), x)","F",0
2004,1,177,0,0.196386," ","integrate((2*x^4+1)^(1/4)*(2*x^8-x^4-1)/x^6/(x^4+2),x, algorithm=""giac"")","-\frac{1}{16} \cdot 54^{\frac{3}{4}} \arctan\left(\frac{24^{\frac{3}{4}} {\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}}}{12 \, x}\right) - \frac{1}{32} \cdot 54^{\frac{3}{4}} \log\left(\frac{1}{2} \cdot 24^{\frac{1}{4}} + \frac{{\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{32} \cdot 54^{\frac{3}{4}} \log\left(-\frac{1}{2} \cdot 24^{\frac{1}{4}} + \frac{{\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) + 2^{\frac{1}{4}} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}}}{2 \, x}\right) + \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + \frac{{\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left(-2^{\frac{1}{4}} + \frac{{\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}}}{x}\right) + \frac{{\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}} {\left(\frac{1}{x^{4}} + 2\right)}}{10 \, x} + \frac{{\left(2 \, x^{4} + 1\right)}^{\frac{1}{4}}}{4 \, x}"," ",0,"-1/16*54^(3/4)*arctan(1/12*24^(3/4)*(2*x^4 + 1)^(1/4)/x) - 1/32*54^(3/4)*log(1/2*24^(1/4) + (2*x^4 + 1)^(1/4)/x) + 1/32*54^(3/4)*log(-1/2*24^(1/4) + (2*x^4 + 1)^(1/4)/x) + 2^(1/4)*arctan(1/2*2^(3/4)*(2*x^4 + 1)^(1/4)/x) + 1/2*2^(1/4)*log(2^(1/4) + (2*x^4 + 1)^(1/4)/x) - 1/2*2^(1/4)*log(-2^(1/4) + (2*x^4 + 1)^(1/4)/x) + 1/10*(2*x^4 + 1)^(1/4)*(1/x^4 + 2)/x + 1/4*(2*x^4 + 1)^(1/4)/x","A",0
2005,0,0,0,0.000000," ","integrate((2*a^4*x^4-b^8)/(a^4*x^4-b^8)^(1/4)/(a^8*x^8-b^8-c*x^4),x, algorithm=""giac"")","\int -\frac{b^{8} - 2 \, a^{4} x^{4}}{{\left(a^{8} x^{8} - b^{8} - c x^{4}\right)} {\left(-b^{8} + a^{4} x^{4}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(b^8 - 2*a^4*x^4)/((a^8*x^8 - b^8 - c*x^4)*(-b^8 + a^4*x^4)^(1/4)), x)","F",0
2006,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{2} + 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^2 + 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
2007,1,90,0,0.226886," ","integrate((x^2+1)*(2*x^3+x)^(1/3)/x^4/(x^2-1),x, algorithm=""giac"")","-3^{\frac{5}{6}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(3^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 2\right)}^{\frac{1}{3}}\right)}\right) + \frac{3}{8} \, {\left(\frac{1}{x^{2}} + 2\right)}^{\frac{4}{3}} - \frac{1}{2} \cdot 3^{\frac{1}{3}} \log\left(3^{\frac{2}{3}} + 3^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 2\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 2\right)}^{\frac{2}{3}}\right) + 3^{\frac{1}{3}} \log\left({\left| -3^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 2\right)}^{\frac{1}{3}} \right|}\right) + 3 \, {\left(\frac{1}{x^{2}} + 2\right)}^{\frac{1}{3}}"," ",0,"-3^(5/6)*arctan(1/3*3^(1/6)*(3^(1/3) + 2*(1/x^2 + 2)^(1/3))) + 3/8*(1/x^2 + 2)^(4/3) - 1/2*3^(1/3)*log(3^(2/3) + 3^(1/3)*(1/x^2 + 2)^(1/3) + (1/x^2 + 2)^(2/3)) + 3^(1/3)*log(abs(-3^(1/3) + (1/x^2 + 2)^(1/3))) + 3*(1/x^2 + 2)^(1/3)","A",0
2008,0,0,0,0.000000," ","integrate((a^3*x^3-b)*(a^3*x^3+b)^(1/3)/x^5,x, algorithm=""giac"")","\int \frac{{\left(a^{3} x^{3} + b\right)}^{\frac{1}{3}} {\left(a^{3} x^{3} - b\right)}}{x^{5}}\,{d x}"," ",0,"integrate((a^3*x^3 + b)^(1/3)*(a^3*x^3 - b)/x^5, x)","F",0
2009,0,0,0,0.000000," ","integrate((a*x^2-3*b)/(-2*a*x^2+3*b)^(1/4)/(3*x^4-2*a*x^2+3*b),x, algorithm=""giac"")","\int \frac{a x^{2} - 3 \, b}{{\left(3 \, x^{4} - 2 \, a x^{2} + 3 \, b\right)} {\left(-2 \, a x^{2} + 3 \, b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^2 - 3*b)/((3*x^4 - 2*a*x^2 + 3*b)*(-2*a*x^2 + 3*b)^(1/4)), x)","F",0
2010,0,0,0,0.000000," ","integrate((a*x^5-4*b)*(a*x^5-c*x^4+b)/x^2/(a*x^5+b)^(3/4)/(a*x^5+c*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} - c x^{4} + b\right)} {\left(a x^{5} - 4 \, b\right)}}{{\left(a x^{5} + c x^{4} + b\right)} {\left(a x^{5} + b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a*x^5 - c*x^4 + b)*(a*x^5 - 4*b)/((a*x^5 + c*x^4 + b)*(a*x^5 + b)^(3/4)*x^2), x)","F",0
2011,0,0,0,0.000000," ","integrate((x^3-1)*(x^6+1)^(2/3)*(x^6-x^3+1)/x^6/(x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{3} + 1\right)} {\left(x^{6} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 1\right)}}{{\left(x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - x^3 + 1)*(x^6 + 1)^(2/3)*(x^3 - 1)/((x^3 + 1)*x^6), x)","F",0
2012,0,0,0,0.000000," ","integrate((a*x^2-b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^2,x, algorithm=""giac"")","\int \frac{{\left(a x^{2} - b^{2}\right)}^{2} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}{{\left(a x^{2} + b^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((a*x^2 - b^2)^2*sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2)^2, x)","F",0
2013,0,0,0,0.000000," ","integrate((x^3+2)*(2*x^3+1)^(2/3)/x^6/(x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} + 2\right)}}{{\left(x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^3 + 1)^(2/3)*(x^3 + 2)/((x^3 - 1)*x^6), x)","F",0
2014,0,0,0,0.000000," ","integrate((x^2-4)*(-2*x^4-x^2+2)^(1/4)/x^2/(x^2-2),x, algorithm=""giac"")","\int \frac{{\left(-2 \, x^{4} - x^{2} + 2\right)}^{\frac{1}{4}} {\left(x^{2} - 4\right)}}{{\left(x^{2} - 2\right)} x^{2}}\,{d x}"," ",0,"integrate((-2*x^4 - x^2 + 2)^(1/4)*(x^2 - 4)/((x^2 - 2)*x^2), x)","F",0
2015,0,0,0,0.000000," ","integrate(1/(1+x)/(-x^4+x^2+2*x-2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2016,0,0,0,0.000000," ","integrate((2*x^4-3)*(2*x^4+1)^(2/3)/x^3/(4*x^4-x^3+2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + 1\right)}^{\frac{2}{3}} {\left(2 \, x^{4} - 3\right)}}{{\left(4 \, x^{4} - x^{3} + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((2*x^4 + 1)^(2/3)*(2*x^4 - 3)/((4*x^4 - x^3 + 2)*x^3), x)","F",0
2017,1,241,0,0.215224," ","integrate((a*x^3-b)/x^6/(a*x^3+b)/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","-\frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b^{2}} - \frac{2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, b^{2}} + \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{3 \, b^{2}} - \frac{2^{\frac{1}{4}} \left(-a\right)^{\frac{3}{4}} a \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{3 \, b^{2}} + \frac{4 \, {\left(3 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{7}{4}} b^{12} + 7 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{3}{4}} a b^{12}\right)}}{63 \, b^{14}}"," ",0,"-2/3*2^(1/4)*(-a)^(3/4)*a*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/b^2 - 2/3*2^(1/4)*(-a)^(3/4)*a*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/b^2 + 1/3*2^(1/4)*(-a)^(3/4)*a*log(2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/b^2 - 1/3*2^(1/4)*(-a)^(3/4)*a*log(-2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/b^2 + 4/63*(3*(a - b/x^3)^(7/4)*b^12 + 7*(a - b/x^3)^(3/4)*a*b^12)/b^14","B",0
2018,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+4*x^3+4)/x^9/(x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 4 \, x^{3} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{3} + 1\right)} x^{9}}\,{d x}"," ",0,"integrate((x^6 + 4*x^3 + 4)*(x^3 - 1)^(2/3)/((x^3 + 1)*x^9), x)","F",0
2019,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6-2*x^3-1)/x^9/(x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 2 \, x^{3} - 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{3} - 1\right)} x^{9}}\,{d x}"," ",0,"integrate((2*x^6 - 2*x^3 - 1)*(x^3 + 1)^(2/3)/((x^3 - 1)*x^9), x)","F",0
2020,0,0,0,0.000000," ","integrate(1/(a^4*x^4-b^4)^(1/4)/(a^8*x^8-b^8-c*x^4),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{8} x^{8} - b^{8} - c x^{4}\right)} {\left(a^{4} x^{4} - b^{4}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((a^8*x^8 - b^8 - c*x^4)*(a^4*x^4 - b^4)^(1/4)), x)","F",0
2021,0,0,0,0.000000," ","integrate(1/(a^4*x^4-b^4)^(1/4)/(a^8*x^8-b^8-c*x^4),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{8} x^{8} - b^{8} - c x^{4}\right)} {\left(a^{4} x^{4} - b^{4}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((a^8*x^8 - b^8 - c*x^4)*(a^4*x^4 - b^4)^(1/4)), x)","F",0
2022,0,0,0,0.000000," ","integrate((x-(x^2+1)^(1/2))/(1+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{x^{2} + 1}}{\sqrt{\sqrt{x^{2} + 1} + 1}}\,{d x}"," ",0,"integrate((x - sqrt(x^2 + 1))/sqrt(sqrt(x^2 + 1) + 1), x)","F",0
2023,0,0,0,0.000000," ","integrate((x^3-4)*(x^3-2)*(x^3-1)^(2/3)/x^9/(3*x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)} {\left(x^{3} - 4\right)}}{{\left(3 \, x^{3} - 2\right)} x^{9}}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)*(x^3 - 2)*(x^3 - 4)/((3*x^3 - 2)*x^9), x)","F",0
2024,0,0,0,0.000000," ","integrate(1/(-1+x)/(x^4-3*x^3-2*x^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2025,1,162,0,0.206952," ","integrate(1/(2*a*x^3+b)/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, a^{\frac{1}{4}}}\right)}{3 \, a^{\frac{1}{4}} b} - \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, a^{\frac{1}{4}}}\right)}{3 \, a^{\frac{1}{4}} b} + \frac{\sqrt{2} \log\left(\sqrt{2} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} a^{\frac{1}{4}} + \sqrt{a + \frac{b}{x^{3}}} + \sqrt{a}\right)}{6 \, a^{\frac{1}{4}} b} - \frac{\sqrt{2} \log\left(-\sqrt{2} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} a^{\frac{1}{4}} + \sqrt{a + \frac{b}{x^{3}}} + \sqrt{a}\right)}{6 \, a^{\frac{1}{4}} b}"," ",0,"-1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4) + 2*(a + b/x^3)^(1/4))/a^(1/4))/(a^(1/4)*b) - 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4) - 2*(a + b/x^3)^(1/4))/a^(1/4))/(a^(1/4)*b) + 1/6*sqrt(2)*log(sqrt(2)*(a + b/x^3)^(1/4)*a^(1/4) + sqrt(a + b/x^3) + sqrt(a))/(a^(1/4)*b) - 1/6*sqrt(2)*log(-sqrt(2)*(a + b/x^3)^(1/4)*a^(1/4) + sqrt(a + b/x^3) + sqrt(a))/(a^(1/4)*b)","A",0
2026,0,0,0,0.000000," ","integrate((-x^7+1)^(1/3)*(2*x^7+x^3-2)*(4*x^7+3)/x^2/(x^7-1)/(4*x^7+x^3-4),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{7} + 3\right)} {\left(2 \, x^{7} + x^{3} - 2\right)} {\left(-x^{7} + 1\right)}^{\frac{1}{3}}}{{\left(4 \, x^{7} + x^{3} - 4\right)} {\left(x^{7} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((4*x^7 + 3)*(2*x^7 + x^3 - 2)*(-x^7 + 1)^(1/3)/((4*x^7 + x^3 - 4)*(x^7 - 1)*x^2), x)","F",0
2027,1,152,0,0.246643," ","integrate((x^2-1)*(x^2+1)^3*((x^2+1)^2)^(1/2)/(x^4+1)/(x^8-x^6+x^4-x^2+1),x, algorithm=""giac"")","-\sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} + \frac{2}{x} \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} + \frac{2}{x} \right|}}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{5}{2}} + \frac{1}{x} \right|}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{5}{2}} + \frac{1}{x} \right|}\right) - \frac{1}{4} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| x + \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{5}{2}} + \frac{1}{x} \right|}\right) + \frac{1}{4} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| x - \sqrt{-\frac{1}{2} \, \sqrt{5} + \frac{5}{2}} + \frac{1}{x} \right|}\right)"," ",0,"-sqrt(2)*log(abs(2*x - 2*sqrt(2) + 2/x)/abs(2*x + 2*sqrt(2) + 2/x)) - 1/4*sqrt(2*sqrt(5) + 10)*log(abs(x + sqrt(1/2*sqrt(5) + 5/2) + 1/x)) + 1/4*sqrt(2*sqrt(5) + 10)*log(abs(x - sqrt(1/2*sqrt(5) + 5/2) + 1/x)) - 1/4*sqrt(-2*sqrt(5) + 10)*log(abs(x + sqrt(-1/2*sqrt(5) + 5/2) + 1/x)) + 1/4*sqrt(-2*sqrt(5) + 10)*log(abs(x - sqrt(-1/2*sqrt(5) + 5/2) + 1/x))","B",0
2028,0,0,0,0.000000," ","integrate(1/x^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b + \sqrt{a x^{2} + b^{2}}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b + sqrt(a*x^2 + b^2))*x^2), x)","F",0
2029,1,175,0,0.475173," ","integrate((a*x^3-b)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{2} b^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{3} \, \sqrt{2} b^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} b^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right) + \frac{1}{6} \, \sqrt{2} b^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right) + \frac{4}{3} \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}"," ",0,"-1/3*sqrt(2)*b^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4)) - 1/3*sqrt(2)*b^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4)) - 1/6*sqrt(2)*b^(1/4)*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b)) + 1/6*sqrt(2)*b^(1/4)*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b)) + 4/3*(a*x^3 - b)^(1/4)","A",0
2030,1,175,0,0.308757," ","integrate((a*x^3-b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{3} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) + \frac{1}{6} \, \sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right) - \frac{1}{6} \, \sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right) + \frac{4}{9} \, {\left(a x^{3} - b\right)}^{\frac{3}{4}}"," ",0,"-1/3*sqrt(2)*b^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4)) - 1/3*sqrt(2)*b^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4)) + 1/6*sqrt(2)*b^(3/4)*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b)) - 1/6*sqrt(2)*b^(3/4)*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b)) + 4/9*(a*x^3 - b)^(3/4)","A",0
2031,0,0,0,0.000000," ","integrate((x^4-1)^(2/3)*(x^4+3)*(x^4-x^3-1)/x^6/(2*x^4-x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} - 1\right)} {\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{4} - x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 - x^3 - 1)*(x^4 + 3)*(x^4 - 1)^(2/3)/((2*x^4 - x^3 - 2)*x^6), x)","F",0
2032,1,175,0,0.296035," ","integrate((a*x^4-b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) + \frac{1}{8} \, \sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right) - \frac{1}{8} \, \sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right) + \frac{1}{3} \, {\left(a x^{4} - b\right)}^{\frac{3}{4}}"," ",0,"-1/4*sqrt(2)*b^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^4 - b)^(1/4))/b^(1/4)) - 1/4*sqrt(2)*b^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^4 - b)^(1/4))/b^(1/4)) + 1/8*sqrt(2)*b^(3/4)*log(sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b)) - 1/8*sqrt(2)*b^(3/4)*log(-sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b)) + 1/3*(a*x^4 - b)^(3/4)","A",0
2033,0,0,0,0.000000," ","integrate((-3*a*b^3+2*b^2*(3*a+b)*x-3*b*(a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^3)^(1/4)/(a*b^3*d-b^2*(3*a+b)*d*x+3*b*(a+b)*d*x^2-(a*d+3*b*d+1)*x^3+d*x^4),x, algorithm=""giac"")","\int -\frac{3 \, a b^{3} - 2 \, {\left(3 \, a + b\right)} b^{2} x + 3 \, {\left(a + b\right)} b x^{2} - x^{4}}{{\left(a b^{3} d - {\left(3 \, a + b\right)} b^{2} d x + 3 \, {\left(a + b\right)} b d x^{2} + d x^{4} - {\left(a d + 3 \, b d + 1\right)} x^{3}\right)} \left({\left(a - x\right)} {\left(b - x\right)}^{3} x\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(3*a*b^3 - 2*(3*a + b)*b^2*x + 3*(a + b)*b*x^2 - x^4)/((a*b^3*d - (3*a + b)*b^2*d*x + 3*(a + b)*b*d*x^2 + d*x^4 - (a*d + 3*b*d + 1)*x^3)*((a - x)*(b - x)^3*x)^(1/4)), x)","F",0
2034,1,175,0,0.143687," ","integrate((a*x^5-b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{5} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{5} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) + \frac{1}{10} \, \sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right) - \frac{1}{10} \, \sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right) + \frac{4}{15} \, {\left(a x^{5} - b\right)}^{\frac{3}{4}}"," ",0,"-1/5*sqrt(2)*b^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^5 - b)^(1/4))/b^(1/4)) - 1/5*sqrt(2)*b^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^5 - b)^(1/4))/b^(1/4)) + 1/10*sqrt(2)*b^(3/4)*log(sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b)) - 1/10*sqrt(2)*b^(3/4)*log(-sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b)) + 4/15*(a*x^5 - b)^(3/4)","A",0
2035,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+x^3+4)/x^9/(x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{3} - 2\right)} x^{9}}\,{d x}"," ",0,"integrate((x^6 + x^3 + 4)*(x^3 - 1)^(2/3)/((x^3 - 2)*x^9), x)","F",0
2036,0,0,0,0.000000," ","integrate((3*x^6-4*x-3)/(x^6+2*x+1)/(x^6+2*x^3+2*x+1)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x^{6} - 4 \, x - 3}{{\left(x^{6} + 2 \, x^{3} + 2 \, x + 1\right)}^{\frac{1}{3}} {\left(x^{6} + 2 \, x + 1\right)}}\,{d x}"," ",0,"integrate((3*x^6 - 4*x - 3)/((x^6 + 2*x^3 + 2*x + 1)^(1/3)*(x^6 + 2*x + 1)), x)","F",0
2037,1,175,0,0.253414," ","integrate((a*x^6-b)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{1}{6} \, \sqrt{2} b^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) + \frac{1}{12} \, \sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right) - \frac{1}{12} \, \sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right) + \frac{2}{9} \, {\left(a x^{6} - b\right)}^{\frac{3}{4}}"," ",0,"-1/6*sqrt(2)*b^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^6 - b)^(1/4))/b^(1/4)) - 1/6*sqrt(2)*b^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^6 - b)^(1/4))/b^(1/4)) + 1/12*sqrt(2)*b^(3/4)*log(sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b)) - 1/12*sqrt(2)*b^(3/4)*log(-sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b)) + 2/9*(a*x^6 - b)^(3/4)","A",0
2038,1,133,0,0.245545," ","integrate((a*x^6+b)/(x^3-x)^(1/3),x, algorithm=""giac"")","\frac{1}{108} \, {\left(28 \, a {\left(\frac{1}{x^{2}} - 1\right)}^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} - 77 \, a {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{5}{3}} + 67 \, a {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)} x^{6} - \frac{1}{162} \, \sqrt{3} {\left(14 \, a + 81 \, b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{324} \, {\left(14 \, a + 81 \, b\right)} \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{162} \, {\left(14 \, a + 81 \, b\right)} \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/108*(28*a*(1/x^2 - 1)^2*(-1/x^2 + 1)^(2/3) - 77*a*(-1/x^2 + 1)^(5/3) + 67*a*(-1/x^2 + 1)^(2/3))*x^6 - 1/162*sqrt(3)*(14*a + 81*b)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) + 1/324*(14*a + 81*b)*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) - 1/162*(14*a + 81*b)*log(abs((-1/x^2 + 1)^(1/3) - 1))","A",0
2039,0,0,0,0.000000," ","integrate((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/4)/(-a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x\right)}^{\frac{1}{4}}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)^(1/4)/sqrt(a^2*x^2/b^2 - a/b^2), x)","F",0
2040,1,100,0,0.224904," ","integrate(1/(x^2*(-a+x))^(1/3)/(a+(-1+d)*x),x, algorithm=""giac"")","-\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(d^{\frac{1}{3}} + 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, d^{\frac{1}{3}}}\right)}{a d^{\frac{1}{3}}} + \frac{\log\left(d^{\frac{2}{3}} + d^{\frac{1}{3}} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}\right)}{2 \, a d^{\frac{1}{3}}} - \frac{\log\left({\left| -d^{\frac{1}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} \right|}\right)}{a d^{\frac{1}{3}}}"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(d^(1/3) + 2*(-a/x + 1)^(1/3))/d^(1/3))/(a*d^(1/3)) + 1/2*log(d^(2/3) + d^(1/3)*(-a/x + 1)^(1/3) + (-a/x + 1)^(2/3))/(a*d^(1/3)) - log(abs(-d^(1/3) + (-a/x + 1)^(1/3)))/(a*d^(1/3))","A",0
2041,0,0,0,0.000000," ","integrate((-x^4-x^3+x+2)^(2/3)*(x^4+2*x+6)*(x^4+x^3-x-2)/x^6/(x^4+2*x^3-x-2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} - x - 2\right)} {\left(x^{4} + 2 \, x + 6\right)} {\left(-x^{4} - x^{3} + x + 2\right)}^{\frac{2}{3}}}{{\left(x^{4} + 2 \, x^{3} - x - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^4 + x^3 - x - 2)*(x^4 + 2*x + 6)*(-x^4 - x^3 + x + 2)^(2/3)/((x^4 + 2*x^3 - x - 2)*x^6), x)","F",0
2042,0,0,0,0.000000," ","integrate((x^4-3)*(x^4+1)^(2/3)*(2*x^4+x^3+2)/x^6/(4*x^4-x^3+4),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + x^{3} + 2\right)} {\left(x^{4} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{{\left(4 \, x^{4} - x^{3} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^4 + x^3 + 2)*(x^4 + 1)^(2/3)*(x^4 - 3)/((4*x^4 - x^3 + 4)*x^6), x)","F",0
2043,0,0,0,0.000000," ","integrate((2*x^6-x^4-1)*(x^7-x^5+x)^(1/3)/(x^6-x^4+x^2+1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{7} - x^{5} + x\right)}^{\frac{1}{3}} {\left(2 \, x^{6} - x^{4} - 1\right)}}{{\left(x^{6} - x^{4} + x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^7 - x^5 + x)^(1/3)*(2*x^6 - x^4 - 1)/(x^6 - x^4 + x^2 + 1)^2, x)","F",0
2044,0,0,0,0.000000," ","integrate(x^4*(a*x^3-4*b)/(a*x^3-b)^(1/4)/(-a^2*x^6+x^8+2*a*b*x^3-b^2),x, algorithm=""giac"")","\int -\frac{{\left(a x^{3} - 4 \, b\right)} x^{4}}{{\left(a^{2} x^{6} - x^{8} - 2 \, a b x^{3} + b^{2}\right)} {\left(a x^{3} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(a*x^3 - 4*b)*x^4/((a^2*x^6 - x^8 - 2*a*b*x^3 + b^2)*(a*x^3 - b)^(1/4)), x)","F",0
2045,0,0,0,0.000000," ","integrate((x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{2} - 1} x} \sqrt{x^{2} - 1}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^2 - 1)*x)*sqrt(x^2 - 1)/(x^2 + 1), x)","F",0
2046,1,99,0,0.223178," ","integrate(x/(x^2*(-a+x))^(2/3)/(a+(-1+d)*x),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(d^{\frac{1}{3}} + 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, d^{\frac{1}{3}}}\right)}{a d^{\frac{2}{3}}} + \frac{\log\left(d^{\frac{2}{3}} + d^{\frac{1}{3}} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}\right)}{2 \, a d^{\frac{2}{3}}} - \frac{\log\left({\left| -d^{\frac{1}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} \right|}\right)}{a d^{\frac{2}{3}}}"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*(d^(1/3) + 2*(-a/x + 1)^(1/3))/d^(1/3))/(a*d^(2/3)) + 1/2*log(d^(2/3) + d^(1/3)*(-a/x + 1)^(1/3) + (-a/x + 1)^(2/3))/(a*d^(2/3)) - log(abs(-d^(1/3) + (-a/x + 1)^(1/3)))/(a*d^(2/3))","A",0
2047,0,0,0,0.000000," ","integrate((x^2+x+2)/(x^2+2*x+3)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + x + 2}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + 2 \, x + 3\right)}}\,{d x}"," ",0,"integrate((x^2 + x + 2)/((x^3 + x^2)^(1/3)*(x^2 + 2*x + 3)), x)","F",0
2048,0,0,0,0.000000," ","integrate((x^2+x+2)/(x^2+2*x+3)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + x + 2}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + 2 \, x + 3\right)}}\,{d x}"," ",0,"integrate((x^2 + x + 2)/((x^3 + x^2)^(1/3)*(x^2 + 2*x + 3)), x)","F",0
2049,0,0,0,0.000000," ","integrate((a*x^2-c*x+b)/(a*x^2-b)/(a*x^3+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} - c x + b}{\sqrt{a x^{3} + b x} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - c*x + b)/(sqrt(a*x^3 + b*x)*(a*x^2 - b)), x)","F",0
2050,0,0,0,0.000000," ","integrate((a*x^2+c*x+b)/(a*x^2-b)/(a*x^3+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + c x + b}{\sqrt{a x^{3} + b x} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + c*x + b)/(sqrt(a*x^3 + b*x)*(a*x^2 - b)), x)","F",0
2051,1,384,0,0.590425," ","integrate((1+x)*(x^4-x^3)^(1/4)/(x^2-x+1),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{4} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{4} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{4} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{4} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - x {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \frac{7}{2} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{7}{4} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{7}{4} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/2*(sqrt(6) + sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/2*(sqrt(6) + sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/2*(sqrt(6) - sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/2*(sqrt(6) - sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/4*(sqrt(6) + sqrt(2))*log(1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/4*(sqrt(6) + sqrt(2))*log(-1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/4*(sqrt(6) - sqrt(2))*log(1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/4*(sqrt(6) - sqrt(2))*log(-1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - x*(-1/x + 1)^(1/4) - 7/2*arctan((-1/x + 1)^(1/4)) - 7/4*log((-1/x + 1)^(1/4) + 1) + 7/4*log(abs((-1/x + 1)^(1/4) - 1))","B",0
2052,1,384,0,0.258961," ","integrate((1+x)*(x^4-x^3)^(1/4)/(x^2-x+1),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{4} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{4} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{4} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{4} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - x {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \frac{7}{2} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{7}{4} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{7}{4} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/2*(sqrt(6) + sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/2*(sqrt(6) + sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/2*(sqrt(6) - sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/2*(sqrt(6) - sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/4*(sqrt(6) + sqrt(2))*log(1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/4*(sqrt(6) + sqrt(2))*log(-1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/4*(sqrt(6) - sqrt(2))*log(1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/4*(sqrt(6) - sqrt(2))*log(-1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - x*(-1/x + 1)^(1/4) - 7/2*arctan((-1/x + 1)^(1/4)) - 7/4*log((-1/x + 1)^(1/4) + 1) + 7/4*log(abs((-1/x + 1)^(1/4) - 1))","B",0
2053,0,0,0,0.000000," ","integrate((-a*x^6+b)^(1/3)*(a*x^6+b)/x^2/(a*x^6+c*x^3-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} + b\right)} {\left(-a x^{6} + b\right)}^{\frac{1}{3}}}{{\left(a x^{6} + c x^{3} - b\right)} x^{2}}\,{d x}"," ",0,"integrate((a*x^6 + b)*(-a*x^6 + b)^(1/3)/((a*x^6 + c*x^3 - b)*x^2), x)","F",0
2054,0,0,0,0.000000," ","integrate(x^2*(7*x^3+4)/(x^4+x)^(1/3)/(x^7+x^4-1),x, algorithm=""giac"")","\int \frac{{\left(7 \, x^{3} + 4\right)} x^{2}}{{\left(x^{7} + x^{4} - 1\right)} {\left(x^{4} + x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((7*x^3 + 4)*x^2/((x^7 + x^4 - 1)*(x^4 + x)^(1/3)), x)","F",0
2055,0,0,0,0.000000," ","integrate((c*x^4+2*d)/(a*x^4-b)^(1/4)/(e*x^8-2*f),x, algorithm=""giac"")","\int \frac{c x^{4} + 2 \, d}{{\left(e x^{8} - 2 \, f\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((c*x^4 + 2*d)/((e*x^8 - 2*f)*(a*x^4 - b)^(1/4)), x)","F",0
2056,1,208,0,0.938597," ","integrate((1+x)^(1/2)*(x^2+1)/(x^2-1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} - 3\right)} + 4 \, \sqrt{\frac{1}{2} \, \sqrt{2} + \frac{1}{2}} \arctan\left(\frac{\sqrt{2} - \sqrt{x + \sqrt{x + 1}} + \sqrt{x + 1}}{\sqrt{\sqrt{2} - 1}}\right) - 2 \, \sqrt{\frac{1}{2} \, \sqrt{2} - \frac{1}{2}} \log\left({\left| 10 \, \sqrt{2} \sqrt{2 \, \sqrt{2} - 2} + 20 \, \sqrt{2} + 20 \, \sqrt{x + \sqrt{x + 1}} - 20 \, \sqrt{x + 1} + 20 \, \sqrt{2 \, \sqrt{2} - 2} \right|}\right) + 2 \, \sqrt{\frac{1}{2} \, \sqrt{2} - \frac{1}{2}} \log\left({\left| -2 \, \sqrt{2} \sqrt{2 \, \sqrt{2} - 2} + 4 \, \sqrt{2} + 4 \, \sqrt{x + \sqrt{x + 1}} - 4 \, \sqrt{x + 1} - 4 \, \sqrt{2 \, \sqrt{2} - 2} \right|}\right) - \frac{7}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) - 3) + 4*sqrt(1/2*sqrt(2) + 1/2)*arctan((sqrt(2) - sqrt(x + sqrt(x + 1)) + sqrt(x + 1))/sqrt(sqrt(2) - 1)) - 2*sqrt(1/2*sqrt(2) - 1/2)*log(abs(10*sqrt(2)*sqrt(2*sqrt(2) - 2) + 20*sqrt(2) + 20*sqrt(x + sqrt(x + 1)) - 20*sqrt(x + 1) + 20*sqrt(2*sqrt(2) - 2))) + 2*sqrt(1/2*sqrt(2) - 1/2)*log(abs(-2*sqrt(2)*sqrt(2*sqrt(2) - 2) + 4*sqrt(2) + 4*sqrt(x + sqrt(x + 1)) - 4*sqrt(x + 1) - 4*sqrt(2*sqrt(2) - 2))) - 7/4*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","B",0
2057,1,208,0,0.772735," ","integrate((1+x)^(1/2)*(x^2+1)/(x^2-1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x + 1}} {\left(2 \, \sqrt{x + 1} - 3\right)} + 4 \, \sqrt{\frac{1}{2} \, \sqrt{2} + \frac{1}{2}} \arctan\left(\frac{\sqrt{2} - \sqrt{x + \sqrt{x + 1}} + \sqrt{x + 1}}{\sqrt{\sqrt{2} - 1}}\right) - 2 \, \sqrt{\frac{1}{2} \, \sqrt{2} - \frac{1}{2}} \log\left({\left| 10 \, \sqrt{2} \sqrt{2 \, \sqrt{2} - 2} + 20 \, \sqrt{2} + 20 \, \sqrt{x + \sqrt{x + 1}} - 20 \, \sqrt{x + 1} + 20 \, \sqrt{2 \, \sqrt{2} - 2} \right|}\right) + 2 \, \sqrt{\frac{1}{2} \, \sqrt{2} - \frac{1}{2}} \log\left({\left| -2 \, \sqrt{2} \sqrt{2 \, \sqrt{2} - 2} + 4 \, \sqrt{2} + 4 \, \sqrt{x + \sqrt{x + 1}} - 4 \, \sqrt{x + 1} - 4 \, \sqrt{2 \, \sqrt{2} - 2} \right|}\right) - \frac{7}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/2*sqrt(x + sqrt(x + 1))*(2*sqrt(x + 1) - 3) + 4*sqrt(1/2*sqrt(2) + 1/2)*arctan((sqrt(2) - sqrt(x + sqrt(x + 1)) + sqrt(x + 1))/sqrt(sqrt(2) - 1)) - 2*sqrt(1/2*sqrt(2) - 1/2)*log(abs(10*sqrt(2)*sqrt(2*sqrt(2) - 2) + 20*sqrt(2) + 20*sqrt(x + sqrt(x + 1)) - 20*sqrt(x + 1) + 20*sqrt(2*sqrt(2) - 2))) + 2*sqrt(1/2*sqrt(2) - 1/2)*log(abs(-2*sqrt(2)*sqrt(2*sqrt(2) - 2) + 4*sqrt(2) + 4*sqrt(x + sqrt(x + 1)) - 4*sqrt(x + 1) - 4*sqrt(2*sqrt(2) - 2))) - 7/4*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","B",0
2058,0,0,0,0.000000," ","integrate((x-(x^2-1)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{x - \sqrt{x^{2} - 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(x - sqrt(x^2 - 1))/x^2, x)","F",0
2059,-1,0,0,0.000000," ","integrate((a*x+(a^2*x^2-b*x)^(1/2))^(3/4)/(a^2*x^2-b*x)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2060,1,362,0,0.689504," ","integrate((1+x)*(x^4+x^3)^(1/4)/x/(x^3-1),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + 4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - 4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + 4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - 4 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{1}{x} + 1} + 1\right) + \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{1}{x} + 1} + 1\right) - \frac{1}{3} \cdot 8^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"1/6*(sqrt(6) + sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/6*(sqrt(6) + sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/6*(sqrt(6) - sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/6*(sqrt(6) - sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/12*(sqrt(6) + sqrt(2))*log(1/2*(sqrt(6) + sqrt(2))*(1/x + 1)^(1/4) + sqrt(1/x + 1) + 1) - 1/12*(sqrt(6) + sqrt(2))*log(-1/2*(sqrt(6) + sqrt(2))*(1/x + 1)^(1/4) + sqrt(1/x + 1) + 1) + 1/12*(sqrt(6) - sqrt(2))*log(1/2*(sqrt(6) - sqrt(2))*(1/x + 1)^(1/4) + sqrt(1/x + 1) + 1) - 1/12*(sqrt(6) - sqrt(2))*log(-1/2*(sqrt(6) - sqrt(2))*(1/x + 1)^(1/4) + sqrt(1/x + 1) + 1) - 1/3*8^(3/4)*arctan(1/2*2^(3/4)*(1/x + 1)^(1/4)) - 2/3*2^(1/4)*log(2^(1/4) + (1/x + 1)^(1/4)) + 2/3*2^(1/4)*log(abs(-2^(1/4) + (1/x + 1)^(1/4)))","B",0
2061,1,296,0,1.256136," ","integrate((a*x^4-b*x^3)^(1/4)*(c*x^4-d)/x^4,x, algorithm=""giac"")","\frac{\frac{270 \, \sqrt{2} b^{3} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{270 \, \sqrt{2} b^{3} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{135 \, \sqrt{2} b^{3} c \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{135 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} c \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{a^{2}} + \frac{360 \, {\left({\left(a - \frac{b}{x}\right)}^{\frac{5}{4}} b^{3} c + 3 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} a b^{3} c\right)} x^{2}}{a b^{2}} + \frac{256 \, {\left(5 \, {\left(a - \frac{b}{x}\right)}^{\frac{9}{4}} b^{8} d - 9 \, {\left(a - \frac{b}{x}\right)}^{\frac{5}{4}} a b^{8} d\right)}}{b^{9}}}{2880 \, b}"," ",0,"1/2880*(270*sqrt(2)*b^3*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + 270*sqrt(2)*b^3*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + 135*sqrt(2)*b^3*c*log(sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/((-a)^(3/4)*a) + 135*sqrt(2)*(-a)^(1/4)*b^3*c*log(-sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/a^2 + 360*((a - b/x)^(5/4)*b^3*c + 3*(a - b/x)^(1/4)*a*b^3*c)*x^2/(a*b^2) + 256*(5*(a - b/x)^(9/4)*b^8*d - 9*(a - b/x)^(5/4)*a*b^8*d)/b^9)/b","B",0
2062,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+2)/x^6/(x^3+4),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{3} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 + 1)^(2/3)/((x^3 + 4)*x^6), x)","F",0
2063,0,0,0,0.000000," ","integrate((x^3-1)*(3*x^3+1)^(2/3)/x^6/(x^3+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{3} - 1\right)}}{{\left(x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((3*x^3 + 1)^(2/3)*(x^3 - 1)/((x^3 + 1)*x^6), x)","F",0
2064,0,0,0,0.000000," ","integrate((-12*x^4+8*x^2-8*x+3)/x/((-2*x^2+1)/(2*x^2+1))^(1/3)/(2*x^2+1)/(2*x^4-6*x^3+7*x^2-7*x+3),x, algorithm=""giac"")","\int -\frac{12 \, x^{4} - 8 \, x^{2} + 8 \, x - 3}{{\left(2 \, x^{4} - 6 \, x^{3} + 7 \, x^{2} - 7 \, x + 3\right)} {\left(2 \, x^{2} + 1\right)} x \left(-\frac{2 \, x^{2} - 1}{2 \, x^{2} + 1}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(12*x^4 - 8*x^2 + 8*x - 3)/((2*x^4 - 6*x^3 + 7*x^2 - 7*x + 3)*(2*x^2 + 1)*x*(-(2*x^2 - 1)/(2*x^2 + 1))^(1/3)), x)","F",0
2065,0,0,0,0.000000," ","integrate(x^2/(a*x^3+b*x)^(1/2)/(a^2*x^4-b^2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a^{2} x^{4} - b^{2}\right)} \sqrt{a x^{3} + b x}}\,{d x}"," ",0,"integrate(x^2/((a^2*x^4 - b^2)*sqrt(a*x^3 + b*x)), x)","F",0
2066,1,272,0,0.300082," ","integrate((a*x^6+b)/x^6/(a*x^3-b)/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{6 \, b^{2}} - \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{6 \, b^{2}} + \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{12 \, b^{2}} - \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{12 \, b^{2}} + \frac{4 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{4}}}{21 \, b^{2}}"," ",0,"-1/6*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/b^2 - 1/6*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/b^2 + 1/12*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*log(2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/b^2 - 1/12*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/b^2 + 4/21*(a + b/x^3)^(7/4)/b^2","B",0
2067,0,0,0,0.000000," ","integrate((x^8+2*x^3-1)^(1/3)*(5*x^8+3)/x^2/(x^8-1),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{8} + 3\right)} {\left(x^{8} + 2 \, x^{3} - 1\right)}^{\frac{1}{3}}}{{\left(x^{8} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((5*x^8 + 3)*(x^8 + 2*x^3 - 1)^(1/3)/((x^8 - 1)*x^2), x)","F",0
2068,0,0,0,0.000000," ","integrate((a*x^2+b^2)^(1/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + b^{2}}}{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + b^2)/sqrt(b + sqrt(a*x^2 + b^2)), x)","F",0
2069,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^3,x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{{\left(a x^{2} + b^{2}\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2)^3, x)","F",0
2070,1,196,0,0.172241," ","integrate((a*x^2-b)^(3/4)/x^3,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{2} - b\right)}^{\frac{3}{4}} a}{x^{2}}}{16 \, a}"," ",0,"1/16*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(1/4) - 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(1/4) + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(1/4) - 8*(a*x^2 - b)^(3/4)*a/x^2)/a","A",0
2071,0,0,0,0.000000," ","integrate((x^3+1)*(2*x^3-1)^(2/3)/x^6/(2*x^3+1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{3} + 1\right)}}{{\left(2 \, x^{3} + 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^3 - 1)^(2/3)*(x^3 + 1)/((2*x^3 + 1)*x^6), x)","F",0
2072,0,0,0,0.000000," ","integrate((-x^3+1)^(2/3)*(4*x^3-1)/x^6/(3*x^3-2),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{3} - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(3 \, x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((4*x^3 - 1)*(-x^3 + 1)^(2/3)/((3*x^3 - 2)*x^6), x)","F",0
2073,1,195,0,0.182960," ","integrate((a*x^3-b)^(1/4)/x^4,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{3}{4}}} + \frac{\sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{8 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}} a}{x^{3}}}{24 \, a}"," ",0,"1/24*(2*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(3/4) + 2*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(3/4) + sqrt(2)*a^2*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(3/4) - sqrt(2)*a^2*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(3/4) - 8*(a*x^3 - b)^(1/4)*a/x^3)/a","A",0
2074,1,196,0,0.318781," ","integrate((a*x^3-b)^(3/4)/x^4,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{3} - b\right)}^{\frac{3}{4}} a}{x^{3}}}{24 \, a}"," ",0,"1/24*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(1/4) - 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(1/4) + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(1/4) - 8*(a*x^3 - b)^(3/4)*a/x^3)/a","A",0
2075,0,0,0,0.000000," ","integrate((-a+x)*(-3*a*b+(a+2*b)*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/x/(x*(-a+x)*(-b+x)^2)^(3/4)/(a*b^2-b*(2*a+b)*x+(a+2*b)*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int -\frac{{\left(b^{3} - 3 \, b^{2} x + 3 \, b x^{2} - x^{3}\right)} {\left(3 \, a b - {\left(a + 2 \, b\right)} x\right)} {\left(a - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{3}{4}} {\left({\left(d - 1\right)} x^{3} + a b^{2} - {\left(2 \, a + b\right)} b x + {\left(a + 2 \, b\right)} x^{2}\right)} x}\,{d x}"," ",0,"integrate(-(b^3 - 3*b^2*x + 3*b*x^2 - x^3)*(3*a*b - (a + 2*b)*x)*(a - x)/((-(a - x)*(b - x)^2*x)^(3/4)*((d - 1)*x^3 + a*b^2 - (2*a + b)*b*x + (a + 2*b)*x^2)*x), x)","F",0
2076,1,196,0,0.167367," ","integrate((a*x^5-b)^(3/4)/x^6,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{5} - b\right)}^{\frac{3}{4}} a}{x^{5}}}{40 \, a}"," ",0,"1/40*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(1/4) - 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(1/4) + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(1/4) - 8*(a*x^5 - b)^(3/4)*a/x^5)/a","A",0
2077,1,196,0,0.293980," ","integrate((a*x^6-b)^(3/4)/x^7,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{1}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right)}{b^{\frac{1}{4}}} - \frac{8 \, {\left(a x^{6} - b\right)}^{\frac{3}{4}} a}{x^{6}}}{48 \, a}"," ",0,"1/48*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^6 - b)^(1/4))/b^(1/4))/b^(1/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^6 - b)^(1/4))/b^(1/4))/b^(1/4) - 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b))/b^(1/4) + 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b))/b^(1/4) - 8*(a*x^6 - b)^(3/4)*a/x^6)/a","A",0
2078,0,0,0,0.000000," ","integrate((5*x^7-4)*(-x^8+2*x^3-2*x)^(1/3)/(x^7+2)/(x^7-2*x^2+2),x, algorithm=""giac"")","\int \frac{{\left(-x^{8} + 2 \, x^{3} - 2 \, x\right)}^{\frac{1}{3}} {\left(5 \, x^{7} - 4\right)}}{{\left(x^{7} - 2 \, x^{2} + 2\right)} {\left(x^{7} + 2\right)}}\,{d x}"," ",0,"integrate((-x^8 + 2*x^3 - 2*x)^(1/3)*(5*x^7 - 4)/((x^7 - 2*x^2 + 2)*(x^7 + 2)), x)","F",0
2079,0,0,0,0.000000," ","integrate((2*x^8-2*a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - 2 \, a x^{4} + b}{{\left(x^{8} - a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - 2*a*x^4 + b)/((x^8 - a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
2080,0,0,0,0.000000," ","integrate((2*x^8+2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} + 2 \, a x^{4} - b}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 + 2*a*x^4 - b)/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
2081,0,0,0,0.000000," ","integrate((2*x^8+2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} + 2 \, a x^{4} - b}{{\left(x^{8} + a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 + 2*a*x^4 - b)/((x^8 + a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
2082,0,0,0,0.000000," ","integrate((a^4*x^4-b^4)^(1/2)*(a^4*x^4+b^4)/(a^8*x^8+b^8),x, algorithm=""giac"")","\int \frac{{\left(a^{4} x^{4} + b^{4}\right)} \sqrt{a^{4} x^{4} - b^{4}}}{a^{8} x^{8} + b^{8}}\,{d x}"," ",0,"integrate((a^4*x^4 + b^4)*sqrt(a^4*x^4 - b^4)/(a^8*x^8 + b^8), x)","F",0
2083,0,0,0,0.000000," ","integrate((a^8*x^8-b^8)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8+b^8),x, algorithm=""giac"")","\int \frac{a^{8} x^{8} - b^{8}}{{\left(a^{8} x^{8} + b^{8}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^8*x^8 - b^8)/((a^8*x^8 + b^8)*sqrt(a^4*x^4 - b^4)), x)","F",0
2084,0,0,0,0.000000," ","integrate(x^3*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + x} x^{3}}{\sqrt{x^{2} + \sqrt{x^{2} + x} x}}\,{d x}"," ",0,"integrate(sqrt(x^2 + x)*x^3/sqrt(x^2 + sqrt(x^2 + x)*x), x)","F",0
2085,1,189,0,0.255640," ","integrate((a*x^2-b)^(3/4)*(2*a*x^2+3*b)/x,x, algorithm=""giac"")","-\frac{3}{2} \, \sqrt{2} b^{\frac{7}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) - \frac{3}{2} \, \sqrt{2} b^{\frac{7}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right) + \frac{3}{4} \, \sqrt{2} b^{\frac{7}{4}} \log\left(\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right) - \frac{3}{4} \, \sqrt{2} b^{\frac{7}{4}} \log\left(-\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right) + \frac{4}{7} \, {\left(a x^{2} - b\right)}^{\frac{7}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{3}{4}} b"," ",0,"-3/2*sqrt(2)*b^(7/4)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^2 - b)^(1/4))/b^(1/4)) - 3/2*sqrt(2)*b^(7/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^2 - b)^(1/4))/b^(1/4)) + 3/4*sqrt(2)*b^(7/4)*log(sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b)) - 3/4*sqrt(2)*b^(7/4)*log(-sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b)) + 4/7*(a*x^2 - b)^(7/4) + 2*(a*x^2 - b)^(3/4)*b","A",0
2086,0,0,0,0.000000," ","integrate((x^2-6)*(x^3-x^2+2)^(2/3)/x^3/(x^3+x^2-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2} + 2\right)}^{\frac{2}{3}} {\left(x^{2} - 6\right)}}{{\left(x^{3} + x^{2} - 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 - x^2 + 2)^(2/3)*(x^2 - 6)/((x^3 + x^2 - 2)*x^3), x)","F",0
2087,1,235,0,0.273345," ","integrate(x^3*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(x^4+a*d-d*x),x, algorithm=""giac"")","-\sqrt{3} \left(-\frac{1}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} d {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \sqrt{3} a {\left| d \right|}^{\frac{2}{3}} - \sqrt{3} d {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{d {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + a {\left| d \right|}^{\frac{2}{3}} - d {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}\right) - \frac{1}{2} \, \left(-\frac{1}{d}\right)^{\frac{1}{3}} \log\left(\frac{3}{4} \, a^{2} d^{\frac{4}{3}} + \frac{1}{4} \, {\left(2 \, d {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} - a d^{\frac{2}{3}} - 2 \, d {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}^{2}\right) + \frac{1}{2} \, \left(-\frac{1}{d}\right)^{\frac{1}{3}} \log\left({\left(\sqrt{3} d {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \sqrt{3} a {\left| d \right|}^{\frac{2}{3}} - \sqrt{3} d {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}^{2} + {\left(d {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + a {\left| d \right|}^{\frac{2}{3}} - d {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}^{2}\right)"," ",0,"-sqrt(3)*(-1/d)^(1/3)*arctan(-(sqrt(3)*d*(-a/x + 1)^(4/3) + sqrt(3)*a*abs(d)^(2/3) - sqrt(3)*d*(-a/x + 1)^(1/3))/(d*(-a/x + 1)^(4/3) + a*abs(d)^(2/3) - d*(-a/x + 1)^(1/3))) - 1/2*(-1/d)^(1/3)*log(3/4*a^2*d^(4/3) + 1/4*(2*d*(-a/x + 1)^(4/3) - a*d^(2/3) - 2*d*(-a/x + 1)^(1/3))^2) + 1/2*(-1/d)^(1/3)*log((sqrt(3)*d*(-a/x + 1)^(4/3) + sqrt(3)*a*abs(d)^(2/3) - sqrt(3)*d*(-a/x + 1)^(1/3))^2 + (d*(-a/x + 1)^(4/3) + a*abs(d)^(2/3) - d*(-a/x + 1)^(1/3))^2)","A",0
2088,0,0,0,0.000000," ","integrate((k^4*x^4-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^4*x^4+1),x, algorithm=""giac"")","\int \frac{k^{4} x^{4} - 1}{{\left(k^{4} x^{4} + 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^4*x^4 - 1)/((k^4*x^4 + 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
2089,0,0,0,0.000000," ","integrate((-x^4+1)/(x^4+1)/(x^5+x^3)^(1/4),x, algorithm=""giac"")","\int -\frac{x^{4} - 1}{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(-(x^4 - 1)/((x^5 + x^3)^(1/4)*(x^4 + 1)), x)","F",0
2090,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^6+2)/x^6/(x^3-1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{3} - 1\right)}^{2} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 2)*(x^3 + 1)^(2/3)/((x^3 - 1)^2*x^6), x)","F",0
2091,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+2*x^3-2)/x^6/(x^3+1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2 \, x^{3} - 2\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{3} + 1\right)}^{2} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 2*x^3 - 2)*(x^3 - 1)^(2/3)/((x^3 + 1)^2*x^6), x)","F",0
2092,0,0,0,0.000000," ","integrate((a*x^6+2*b)*(a*x^6-c*x^4-b)/x^2/(a*x^6-b)^(3/4)/(a*x^6+c*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} - c x^{4} - b\right)} {\left(a x^{6} + 2 \, b\right)}}{{\left(a x^{6} + c x^{4} - b\right)} {\left(a x^{6} - b\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate((a*x^6 - c*x^4 - b)*(a*x^6 + 2*b)/((a*x^6 + c*x^4 - b)*(a*x^6 - b)^(3/4)*x^2), x)","F",0
2093,1,288,0,0.198195," ","integrate((c+d*(a*x^2+b)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, \sqrt{\sqrt{a x^{2} + b} d + c} d + \frac{{\left(\sqrt{b} c d^{3} \mathrm{sgn}\left({\left(\sqrt{a x^{2} + b} d + c\right)} d - c d\right) - b d^{3} {\left| d \right|} + c^{2} d {\left| d \right|} \mathrm{sgn}\left({\left(\sqrt{a x^{2} + b} d + c\right)} d - c d\right) - \sqrt{b} c d^{3}\right)} \arctan\left(\frac{\sqrt{\sqrt{a x^{2} + b} d + c}}{\sqrt{-c + \sqrt{b d^{2}}}}\right)}{{\left(\sqrt{b} d + c\right)} \sqrt{\sqrt{b} d - c} {\left| d \right|}} + \frac{{\left(\sqrt{b} c d^{3} \mathrm{sgn}\left({\left(\sqrt{a x^{2} + b} d + c\right)} d - c d\right) + b d^{3} {\left| d \right|} - c^{2} d {\left| d \right|} \mathrm{sgn}\left({\left(\sqrt{a x^{2} + b} d + c\right)} d - c d\right) - \sqrt{b} c d^{3}\right)} \arctan\left(\frac{\sqrt{\sqrt{a x^{2} + b} d + c}}{\sqrt{-c - \sqrt{b d^{2}}}}\right)}{{\left(\sqrt{b} d - c\right)} \sqrt{-\sqrt{b} d - c} {\left| d \right|}}}{d}"," ",0,"(2*sqrt(sqrt(a*x^2 + b)*d + c)*d + (sqrt(b)*c*d^3*sgn((sqrt(a*x^2 + b)*d + c)*d - c*d) - b*d^3*abs(d) + c^2*d*abs(d)*sgn((sqrt(a*x^2 + b)*d + c)*d - c*d) - sqrt(b)*c*d^3)*arctan(sqrt(sqrt(a*x^2 + b)*d + c)/sqrt(-c + sqrt(b*d^2)))/((sqrt(b)*d + c)*sqrt(sqrt(b)*d - c)*abs(d)) + (sqrt(b)*c*d^3*sgn((sqrt(a*x^2 + b)*d + c)*d - c*d) + b*d^3*abs(d) - c^2*d*abs(d)*sgn((sqrt(a*x^2 + b)*d + c)*d - c*d) - sqrt(b)*c*d^3)*arctan(sqrt(sqrt(a*x^2 + b)*d + c)/sqrt(-c - sqrt(b*d^2)))/((sqrt(b)*d - c)*sqrt(-sqrt(b)*d - c)*abs(d)))/d","B",0
2094,0,0,0,0.000000," ","integrate((a^2*x^4-b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{4} - b\right)} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b}}\,{d x}"," ",0,"integrate((a^2*x^4 - b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/sqrt(a^2*x^4 + b), x)","F",0
2095,-2,0,0,0.000000," ","integrate((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,x]=[-53,73,-58]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,x]=[-62,-47,-7]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-60,56,-86]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-35,-31,25]schur row 3 6.14083e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[37,16,-50]schur row 3 6.81038e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-89,-87,-6]schur row 3 -3.32574e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-15,-47,-99]schur row 3 6.63154e-12Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[4,51,52]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[95,47,-75]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-81,99,6]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[60,98,14]schur row 3 -1.41002e-07Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-61,-5,-81]schur row 3 -3.62988e-11Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[69,4,92]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-86,29,62]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[97,39,62]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[12,-89,27]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[75,-77,-41]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[37,-64,-25]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-84,-28,-58]schur row 3 1.98116e-10Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[92,64,-69]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-71,-97,65]schur row 3 -8.62952e-11Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[38,22,35]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[5,-43,43]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[51,28,-73]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-20,28,31]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[23,-43,-65]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[29,-31,-73]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-47,29,-38]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-61,93,-37]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-32,44,87]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[85,86,-73]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-76,72,56]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-88,76,-73]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-35,-51,70]schur row 3 -2.55512e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-28,-18,-32]schur row 3 -1.27129e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-8,45,5]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-94,53,-97]schur row 3 -2.84124e-11Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-90,15,-80]schur row 3 -4.4424e-11Unable to divide, perhaps due to rounding error%%%{%%%{%%{[-2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueUnable to divide, perhaps due to rounding error%%%{%%%{%%{[2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueEvaluation time: 10.56integrate((4*a^2*x^4*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)-2*a^2*x^4-4*a*x^2*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)+4*b*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)-2*b+sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)+2*(a^2*x^4+b))/(4*a^2*x^4-4*a*x^2+4*b+1),x)","F(-2)",0
2096,0,0,0,0.000000," ","integrate(1/(a*x+2*b)/(a*x^3+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{3} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x + 2 \, b\right)}}\,{d x}"," ",0,"integrate(1/((a*x^3 + b*x^2)^(1/4)*(a*x + 2*b)), x)","F",0
2097,1,1,0,0.258640," ","integrate(x*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(x^4+a*d-d*x),x, algorithm=""giac"")","0"," ",0,"0","A",0
2098,0,0,0,0.000000," ","integrate((a*x^5-b)^(3/4)*(a*x^5+4*b)/x^4/(a*x^5+c*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} + 4 \, b\right)} {\left(a x^{5} - b\right)}^{\frac{3}{4}}}{{\left(a x^{5} + c x^{4} - b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^5 + 4*b)*(a*x^5 - b)^(3/4)/((a*x^5 + c*x^4 - b)*x^4), x)","F",0
2099,0,0,0,0.000000," ","integrate((x^8+1)^(3/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + 1\right)}^{\frac{3}{4}}}{x^{8} - 1}\,{d x}"," ",0,"integrate((x^8 + 1)^(3/4)/(x^8 - 1), x)","F",0
2100,-2,0,0,0.000000," ","integrate(x^4/(x^4-1)^(1/4)/(x^8+2*x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2101,-2,0,0,0.000000," ","integrate((x^4-1)^(3/4)/(x^8+2*x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2102,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(1+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{4} - 1\right)} \sqrt{\sqrt{x^{2} + 1} + 1}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^4 - 1)*sqrt(sqrt(x^2 + 1) + 1)), x)","F",0
2103,1,199,0,0.340705," ","integrate(1/x^3/(a*x^2-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{2} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{2} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} + \frac{8 \, {\left(a x^{2} - b\right)}^{\frac{1}{4}} a}{b x^{2}}}{16 \, a}"," ",0,"1/16*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(7/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^2 - b)^(1/4))/b^(1/4))/b^(7/4) + 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(7/4) - 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^2 - b)^(1/4)*b^(1/4) + sqrt(a*x^2 - b) + sqrt(b))/b^(7/4) + 8*(a*x^2 - b)^(1/4)*a/(b*x^2))/a","A",0
2104,0,0,0,0.000000," ","integrate((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^3)^(1/4)/(b-(a*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a b - 2 \, b x + x^{2}}{\left({\left(a - x\right)} {\left(b - x\right)}^{3} x\right)^{\frac{1}{4}} {\left(d x^{2} - {\left(a d + 1\right)} x + b\right)}}\,{d x}"," ",0,"integrate((a*b - 2*b*x + x^2)/(((a - x)*(b - x)^3*x)^(1/4)*(d*x^2 - (a*d + 1)*x + b)), x)","F",0
2105,1,199,0,0.177222," ","integrate(1/x^4/(a*x^3-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} + \frac{8 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}} a}{b x^{3}}}{24 \, a}"," ",0,"1/24*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(7/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(7/4) + 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(7/4) - 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(7/4) + 8*(a*x^3 - b)^(1/4)*a/(b*x^3))/a","A",0
2106,1,198,0,0.299519," ","integrate(1/x^4/(a*x^3-b)^(1/4),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{5}{4}}} + \frac{2 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{5}{4}}} - \frac{\sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{5}{4}}} + \frac{\sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{5}{4}}} + \frac{8 \, {\left(a x^{3} - b\right)}^{\frac{3}{4}} a}{b x^{3}}}{24 \, a}"," ",0,"1/24*(2*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(5/4) + 2*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(5/4) - sqrt(2)*a^2*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(5/4) + sqrt(2)*a^2*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(5/4) + 8*(a*x^3 - b)^(3/4)*a/(b*x^3))/a","A",0
2107,0,0,0,0.000000," ","integrate(1/2*(2+x)*(x^2-x-1)*((-2*x^2+x+1)/(4*x^2+x+1))^(1/4)/x/(x^4+x^2+2*x+1),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - x - 1\right)} {\left(x + 2\right)} \left(-\frac{2 \, x^{2} - x - 1}{4 \, x^{2} + x + 1}\right)^{\frac{1}{4}}}{2 \, {\left(x^{4} + x^{2} + 2 \, x + 1\right)} x}\,{d x}"," ",0,"integrate(1/2*(x^2 - x - 1)*(x + 2)*(-(2*x^2 - x - 1)/(4*x^2 + x + 1))^(1/4)/((x^4 + x^2 + 2*x + 1)*x), x)","F",0
2108,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(x^4+x^3-x^2-x+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^4 - 1)), x)","F",0
2109,1,199,0,0.175718," ","integrate(1/x^5/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} + \frac{8 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}} a}{b x^{4}}}{32 \, a}"," ",0,"1/32*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(7/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(7/4) + 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(7/4) - 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(7/4) + 8*(a*x^4 - b)^(1/4)*a/(b*x^4))/a","A",0
2110,0,0,0,0.000000," ","integrate((a*b^3-2*(3*a-b)*b^2*x+3*(3*a-b)*b*x^2-4*a*x^3+x^4)/(x*(-a+x)*(-b+x)^3)^(1/4)/(a^3-(b^3*d+3*a^2)*x+3*(b^2*d+a)*x^2-(3*b*d+1)*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{a b^{3} - 2 \, {\left(3 \, a - b\right)} b^{2} x + 3 \, {\left(3 \, a - b\right)} b x^{2} - 4 \, a x^{3} + x^{4}}{\left({\left(a - x\right)} {\left(b - x\right)}^{3} x\right)^{\frac{1}{4}} {\left(d x^{4} - {\left(3 \, b d + 1\right)} x^{3} + a^{3} + 3 \, {\left(b^{2} d + a\right)} x^{2} - {\left(b^{3} d + 3 \, a^{2}\right)} x\right)}}\,{d x}"," ",0,"integrate((a*b^3 - 2*(3*a - b)*b^2*x + 3*(3*a - b)*b*x^2 - 4*a*x^3 + x^4)/(((a - x)*(b - x)^3*x)^(1/4)*(d*x^4 - (3*b*d + 1)*x^3 + a^3 + 3*(b^2*d + a)*x^2 - (b^3*d + 3*a^2)*x)), x)","F",0
2111,1,199,0,0.323072," ","integrate(1/x^6/(a*x^5-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} + \frac{8 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}} a}{b x^{5}}}{40 \, a}"," ",0,"1/40*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(7/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(7/4) + 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(7/4) - 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(7/4) + 8*(a*x^5 - b)^(1/4)*a/(b*x^5))/a","A",0
2112,1,199,0,0.178037," ","integrate(1/x^7/(a*x^6-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{6 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{3 \, \sqrt{2} a^{2} \log\left(\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} - \frac{3 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} {\left(a x^{6} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{6} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} + \frac{8 \, {\left(a x^{6} - b\right)}^{\frac{1}{4}} a}{b x^{6}}}{48 \, a}"," ",0,"1/48*(6*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^6 - b)^(1/4))/b^(1/4))/b^(7/4) + 6*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^6 - b)^(1/4))/b^(1/4))/b^(7/4) + 3*sqrt(2)*a^2*log(sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b))/b^(7/4) - 3*sqrt(2)*a^2*log(-sqrt(2)*(a*x^6 - b)^(1/4)*b^(1/4) + sqrt(a*x^6 - b) + sqrt(b))/b^(7/4) + 8*(a*x^6 - b)^(1/4)*a/(b*x^6))/a","A",0
2113,0,0,0,0.000000," ","integrate((a^6*x^6+b^6)/(a^4*x^4+b^4)^(1/2)/(a^6*x^6-b^6),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} + b^{6}}{{\left(a^{6} x^{6} - b^{6}\right)} \sqrt{a^{4} x^{4} + b^{4}}}\,{d x}"," ",0,"integrate((a^6*x^6 + b^6)/((a^6*x^6 - b^6)*sqrt(a^4*x^4 + b^4)), x)","F",0
2114,0,0,0,0.000000," ","integrate((x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2)/(1+x),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{2} - 1} x} \sqrt{x^{2} - 1}}{x + 1}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^2 - 1)*x)*sqrt(x^2 - 1)/(x + 1), x)","F",0
2115,0,0,0,0.000000," ","integrate((x^4+1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)} \sqrt{\sqrt{x^{2} + 1} + 1}}{x^{4} - 1}\,{d x}"," ",0,"integrate((x^4 + 1)*sqrt(sqrt(x^2 + 1) + 1)/(x^4 - 1), x)","F",0
2116,0,0,0,0.000000," ","integrate((a*x^2-b^2)/(a*x^2+b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} - b^{2}}{{\left(a x^{2} + b^{2}\right)} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 - b^2)/((a*x^2 + b^2)*sqrt(b + sqrt(a*x^2 + b^2))), x)","F",0
2117,0,0,0,0.000000," ","integrate(x/(1+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x + \sqrt{x^{2} + 1}} + 1}\,{d x}"," ",0,"integrate(x/(sqrt(x + sqrt(x^2 + 1)) + 1), x)","F",0
2118,1,130,0,0.578744," ","integrate((-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-b*(1+k)*x+(b*k-1)*x^2),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left| b \right|}^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} b^{\frac{1}{3}} {\left(2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} + \frac{1}{b^{\frac{1}{3}}}\right)}\right)}{b} - \frac{{\left| b \right|}^{\frac{2}{3}} \log\left({\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \frac{{\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{b^{\frac{1}{3}}} + \frac{1}{b^{\frac{2}{3}}}\right)}{2 \, b} + \frac{\log\left({\left| {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} - \frac{1}{b^{\frac{1}{3}}} \right|}\right)}{b^{\frac{1}{3}}}"," ",0,"-sqrt(3)*abs(b)^(2/3)*arctan(1/3*sqrt(3)*b^(1/3)*(2*(k - k/x - 1/x + 1/x^2)^(1/3) + 1/b^(1/3)))/b - 1/2*abs(b)^(2/3)*log((k - k/x - 1/x + 1/x^2)^(2/3) + (k - k/x - 1/x + 1/x^2)^(1/3)/b^(1/3) + 1/b^(2/3))/b + log(abs((k - k/x - 1/x + 1/x^2)^(1/3) - 1/b^(1/3)))/b^(1/3)","A",0
2119,0,0,0,0.000000," ","integrate((a*x^2-b)*(a*x^3-b*x)^(1/2)/x^2/(a*x^2+b),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3} - b x} {\left(a x^{2} - b\right)}}{{\left(a x^{2} + b\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^3 - b*x)*(a*x^2 - b)/((a*x^2 + b)*x^2), x)","F",0
2120,1,392,0,0.293875," ","integrate((x^4-x^3)^(1/4)/x/(x^3+1),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{2}{3} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{3} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{3} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"-1/6*(sqrt(6) - sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) - 1/6*(sqrt(6) - sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) - 1/6*(sqrt(6) + sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) - 1/6*(sqrt(6) + sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) - 1/12*(sqrt(6) - sqrt(2))*log(1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/12*(sqrt(6) - sqrt(2))*log(-1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/12*(sqrt(6) + sqrt(2))*log(1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/12*(sqrt(6) + sqrt(2))*log(-1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 2/3*2^(1/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 1/3*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) - 1/3*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4)))","B",0
2121,1,392,0,0.275351," ","integrate((x^4-x^3)^(1/4)/x/(x^3+1),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) - \frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) - \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{2}{3} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{3} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{3} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"-1/6*(sqrt(6) - sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) - 1/6*(sqrt(6) - sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) - 1/6*(sqrt(6) + sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) - 1/6*(sqrt(6) + sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) - 1/12*(sqrt(6) - sqrt(2))*log(1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/12*(sqrt(6) - sqrt(2))*log(-1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/12*(sqrt(6) + sqrt(2))*log(1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/12*(sqrt(6) + sqrt(2))*log(-1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 2/3*2^(1/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 1/3*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) - 1/3*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4)))","B",0
2122,0,0,0,0.000000," ","integrate((x^4-3)*(x^4-x^3+1)^(2/3)/x^3/(x^4+x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{4} - 3\right)}}{{\left(x^{4} + x^{3} + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^4 - x^3 + 1)^(2/3)*(x^4 - 3)/((x^4 + x^3 + 1)*x^3), x)","F",0
2123,0,0,0,0.000000," ","integrate((a*x^5-4*b)*(a*x^5+b)^(3/4)/x^4/(2*a*x^5+c*x^4+2*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} + b\right)}^{\frac{3}{4}} {\left(a x^{5} - 4 \, b\right)}}{{\left(2 \, a x^{5} + c x^{4} + 2 \, b\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x^5 + b)^(3/4)*(a*x^5 - 4*b)/((2*a*x^5 + c*x^4 + 2*b)*x^4), x)","F",0
2124,0,0,0,0.000000," ","integrate((x^6-1)/(x^4+x^2)^(1/3)/(x^6+1),x, algorithm=""giac"")","\int \frac{x^{6} - 1}{{\left(x^{6} + 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 - 1)/((x^6 + 1)*(x^4 + x^2)^(1/3)), x)","F",0
2125,1,221,0,0.172705," ","integrate((3*x^4+2)^(1/4)*(x^8+6*x^4+4)/x^6/(x^4+1)/(2*x^4+1),x, algorithm=""giac"")","-\frac{5}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2 \, {\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x}\right)}\right) - \frac{5}{4} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2 \, {\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x}\right)}\right) - \frac{5}{8} \, \sqrt{2} \log\left(\frac{\sqrt{2} {\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x} + \frac{\sqrt{3 \, x^{4} + 2}}{x^{2}} + 1\right) + \frac{5}{8} \, \sqrt{2} \log\left(-\frac{\sqrt{2} {\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x} + \frac{\sqrt{3 \, x^{4} + 2}}{x^{2}} + 1\right) - \frac{2 \, {\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}} {\left(\frac{2}{x^{4}} + 3\right)}}{5 \, x} + \frac{6 \, {\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x} - \frac{1}{2} \, \arctan\left(\frac{{\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x}\right) - \frac{1}{4} \, \log\left(\frac{{\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x} + 1\right) + \frac{1}{4} \, \log\left(\frac{{\left(3 \, x^{4} + 2\right)}^{\frac{1}{4}}}{x} - 1\right)"," ",0,"-5/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(3*x^4 + 2)^(1/4)/x)) - 5/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(3*x^4 + 2)^(1/4)/x)) - 5/8*sqrt(2)*log(sqrt(2)*(3*x^4 + 2)^(1/4)/x + sqrt(3*x^4 + 2)/x^2 + 1) + 5/8*sqrt(2)*log(-sqrt(2)*(3*x^4 + 2)^(1/4)/x + sqrt(3*x^4 + 2)/x^2 + 1) - 2/5*(3*x^4 + 2)^(1/4)*(2/x^4 + 3)/x + 6*(3*x^4 + 2)^(1/4)/x - 1/2*arctan((3*x^4 + 2)^(1/4)/x) - 1/4*log((3*x^4 + 2)^(1/4)/x + 1) + 1/4*log((3*x^4 + 2)^(1/4)/x - 1)","A",0
2126,0,0,0,0.000000," ","integrate((x^8-16*x^6+96*x^4-256*x^2+256)^(1/8)/(x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256\right)}^{\frac{1}{8}}}{x^{3} - 1}\,{d x}"," ",0,"integrate((x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)^(1/8)/(x^3 - 1), x)","F",0
2127,0,0,0,0.000000," ","integrate((x^6+6*x^3-6*x^2-36)/x/(x^3-6)/((x^3+6)/(x^3-6))^(1/6)/(x^8-6*x^7+15*x^6-26*x^5+51*x^4-96*x^3+122*x^2-90*x+36),x, algorithm=""giac"")","\int \frac{x^{6} + 6 \, x^{3} - 6 \, x^{2} - 36}{{\left(x^{8} - 6 \, x^{7} + 15 \, x^{6} - 26 \, x^{5} + 51 \, x^{4} - 96 \, x^{3} + 122 \, x^{2} - 90 \, x + 36\right)} {\left(x^{3} - 6\right)} x \left(\frac{x^{3} + 6}{x^{3} - 6}\right)^{\frac{1}{6}}}\,{d x}"," ",0,"integrate((x^6 + 6*x^3 - 6*x^2 - 36)/((x^8 - 6*x^7 + 15*x^6 - 26*x^5 + 51*x^4 - 96*x^3 + 122*x^2 - 90*x + 36)*(x^3 - 6)*x*((x^3 + 6)/(x^3 - 6))^(1/6)), x)","F",0
2128,0,0,0,0.000000," ","integrate((2*x^8-a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} + 2 \, b}{{\left(x^{8} + a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 + 2*b)/((x^8 + a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
2129,0,0,0,0.000000," ","integrate((2*x^8-a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} + 2 \, b}{{\left(x^{8} + a x^{4} - 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 + 2*b)/((x^8 + a*x^4 - 2*b)*(a*x^4 + b)^(1/4)), x)","F",0
2130,0,0,0,0.000000," ","integrate((a*x^8-b)/(a*x^8+b)/(a*x^8-c*x^4+b)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{8} - b}{{\left(a x^{8} - c x^{4} + b\right)}^{\frac{1}{4}} {\left(a x^{8} + b\right)}}\,{d x}"," ",0,"integrate((a*x^8 - b)/((a*x^8 - c*x^4 + b)^(1/4)*(a*x^8 + b)), x)","F",0
2131,0,0,0,0.000000," ","integrate(1/x^2/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a^{2} x^{2} - b x} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*x^2 - b*x)*(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2)*x^2), x)","F",0
2132,0,0,0,0.000000," ","integrate((1+(x^2+1)^(1/2))/(1+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1} + 1}{\sqrt{x + \sqrt{x^{2} + 1}} + 1}\,{d x}"," ",0,"integrate((sqrt(x^2 + 1) + 1)/(sqrt(x + sqrt(x^2 + 1)) + 1), x)","F",0
2133,1,129,0,0.591938," ","integrate((-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-b*(1+k)*x+(b*k-1)*x^2),x, algorithm=""giac"")","\frac{\sqrt{3} {\left| b \right|}^{\frac{4}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} b^{\frac{1}{3}} {\left(2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} + \frac{1}{b^{\frac{1}{3}}}\right)}\right)}{b^{2}} - \frac{{\left| b \right|}^{\frac{4}{3}} \log\left({\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \frac{{\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{b^{\frac{1}{3}}} + \frac{1}{b^{\frac{2}{3}}}\right)}{2 \, b^{2}} + \frac{\log\left({\left| {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} - \frac{1}{b^{\frac{1}{3}}} \right|}\right)}{b^{\frac{2}{3}}}"," ",0,"sqrt(3)*abs(b)^(4/3)*arctan(1/3*sqrt(3)*b^(1/3)*(2*(k - k/x - 1/x + 1/x^2)^(1/3) + 1/b^(1/3)))/b^2 - 1/2*abs(b)^(4/3)*log((k - k/x - 1/x + 1/x^2)^(2/3) + (k - k/x - 1/x + 1/x^2)^(1/3)/b^(1/3) + 1/b^(2/3))/b^2 + log(abs((k - k/x - 1/x + 1/x^2)^(1/3) - 1/b^(1/3)))/b^(2/3)","A",0
2134,0,0,0,0.000000," ","integrate((a*x^4-b)^(1/4)*(a*x^8-8*b)/x^10/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{8} - 8 \, b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}{{\left(a x^{4} + b\right)} x^{10}}\,{d x}"," ",0,"integrate((a*x^8 - 8*b)*(a*x^4 - b)^(1/4)/((a*x^4 + b)*x^10), x)","F",0
2135,0,0,0,0.000000," ","integrate(x/(x+(x+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x + \sqrt{x + \sqrt{x + 1}}}\,{d x}"," ",0,"integrate(x/(x + sqrt(x + sqrt(x + 1))), x)","F",0
2136,0,0,0,0.000000," ","integrate(x/(x+(x+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x + \sqrt{x + \sqrt{x + 1}}}\,{d x}"," ",0,"integrate(x/(x + sqrt(x + sqrt(x + 1))), x)","F",0
2137,0,0,0,0.000000," ","integrate((x^2-6)*(x^2-2)*(x^3-x^2+2)*(2*x^3+x^2-2)^(1/3)/x^5/(x^3+x^2-2)^2,x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + x^{2} - 2\right)}^{\frac{1}{3}} {\left(x^{3} - x^{2} + 2\right)} {\left(x^{2} - 2\right)} {\left(x^{2} - 6\right)}}{{\left(x^{3} + x^{2} - 2\right)}^{2} x^{5}}\,{d x}"," ",0,"integrate((2*x^3 + x^2 - 2)^(1/3)*(x^3 - x^2 + 2)*(x^2 - 2)*(x^2 - 6)/((x^3 + x^2 - 2)^2*x^5), x)","F",0
2138,1,392,0,1.069354," ","integrate((-1+x)*(x^4-x^3)^(1/4)/x/(x^3+1),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{3} \cdot 8^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"1/6*(sqrt(6) + sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/6*(sqrt(6) + sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/6*(sqrt(6) - sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/6*(sqrt(6) - sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/12*(sqrt(6) + sqrt(2))*log(1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/12*(sqrt(6) + sqrt(2))*log(-1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/12*(sqrt(6) - sqrt(2))*log(1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/12*(sqrt(6) - sqrt(2))*log(-1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/3*8^(3/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) - 2/3*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) + 2/3*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4)))","B",0
2139,1,392,0,0.308281," ","integrate((-1+x)*(x^4-x^3)^(1/4)/x/(x^3+1),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} - \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} - \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} + \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(\frac{\sqrt{6} + \sqrt{2} + 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{6} \, {\left(\sqrt{6} - \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{6} + \sqrt{2} - 4 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{6} - \sqrt{2}}\right) + \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} + \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{12} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left(-\frac{1}{2} \, {\left(\sqrt{6} - \sqrt{2}\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{1}{3} \cdot 8^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"1/6*(sqrt(6) + sqrt(2))*arctan((sqrt(6) - sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/6*(sqrt(6) + sqrt(2))*arctan(-(sqrt(6) - sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) + sqrt(2))) + 1/6*(sqrt(6) - sqrt(2))*arctan((sqrt(6) + sqrt(2) + 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/6*(sqrt(6) - sqrt(2))*arctan(-(sqrt(6) + sqrt(2) - 4*(-1/x + 1)^(1/4))/(sqrt(6) - sqrt(2))) + 1/12*(sqrt(6) + sqrt(2))*log(1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/12*(sqrt(6) + sqrt(2))*log(-1/2*(sqrt(6) + sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 1/12*(sqrt(6) - sqrt(2))*log(1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/12*(sqrt(6) - sqrt(2))*log(-1/2*(sqrt(6) - sqrt(2))*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 1/3*8^(3/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) - 2/3*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) + 2/3*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4)))","B",0
2140,0,0,0,0.000000," ","integrate((1+x)*(x^5+x^3)^(1/4)/x/(x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x + 1\right)}}{{\left(x^{3} - 1\right)} x}\,{d x}"," ",0,"integrate((x^5 + x^3)^(1/4)*(x + 1)/((x^3 - 1)*x), x)","F",0
2141,0,0,0,0.000000," ","integrate(x^3/(a*x^3-b*x^2)^(1/3)/(a^2*x^6-b^2),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(a^{2} x^{6} - b^{2}\right)} {\left(a x^{3} - b x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^3/((a^2*x^6 - b^2)*(a*x^3 - b*x^2)^(1/3)), x)","F",0
2142,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{2} - 1\right)} \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^2 - 1)*sqrt(sqrt(sqrt(x + 1) + 1) + 1)), x)","F",0
2143,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{2} - 1\right)} \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^2 - 1)*sqrt(sqrt(sqrt(x + 1) + 1) + 1)), x)","F",0
2144,0,0,0,0.000000," ","integrate((x^3+x-1)/(x^3-x+1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} + x - 1}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - x + 1\right)}}\,{d x}"," ",0,"integrate((x^3 + x - 1)/((x^3 - x^2)^(1/3)*(x^3 - x + 1)), x)","F",0
2145,0,0,0,0.000000," ","integrate((x^3+x-1)/(x^3-x+1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} + x - 1}{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - x + 1\right)}}\,{d x}"," ",0,"integrate((x^3 + x - 1)/((x^3 - x^2)^(1/3)*(x^3 - x + 1)), x)","F",0
2146,0,0,0,0.000000," ","integrate((2*x^3+1)^(4/3)*(3*x^3+1)/x^8/(4*x^3+1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} + 1\right)} {\left(2 \, x^{3} + 1\right)}^{\frac{4}{3}}}{{\left(4 \, x^{3} + 1\right)} x^{8}}\,{d x}"," ",0,"integrate((3*x^3 + 1)*(2*x^3 + 1)^(4/3)/((4*x^3 + 1)*x^8), x)","F",0
2147,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^4-x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{{\left(x^{4} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/((x^4 - x^2)^(1/3)*(x^2 + 1)), x)","F",0
2148,0,0,0,0.000000," ","integrate((a*x^4-b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(2 \, a x^{4} - b\right)} {\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}}}{a x^{4} + b}\,{d x}"," ",0,"integrate((2*a*x^4 - b)*(a*x^4 - b*x^2)^(1/4)/(a*x^4 + b), x)","F",0
2149,0,0,0,0.000000," ","integrate((a*x^4-b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(2 \, a x^{4} - b\right)} {\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}}}{a x^{4} + b}\,{d x}"," ",0,"integrate((2*a*x^4 - b)*(a*x^4 - b*x^2)^(1/4)/(a*x^4 + b), x)","F",0
2150,1,1,0,0.497692," ","integrate(x^3*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(d*x^4+a-x),x, algorithm=""giac"")","0"," ",0,"0","A",0
2151,1,279,0,0.320667," ","integrate((a*x^6+b)/x^6/(a*x^3+b)/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{6 \, b^{2}} + \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{6 \, b^{2}} - \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{12 \, b^{2}} + \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{3}}}\right)}{12 \, b^{2}} - \frac{4 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{7}{4}}}{21 \, b^{2}}"," ",0,"1/6*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/b^2 + 1/6*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a - b/x^3)^(1/4))/(-a)^(1/4))/b^2 - 1/12*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*log(2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/b^2 + 1/12*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*log(-2^(3/4)*(-a)^(1/4)*(a - b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^3))/b^2 - 4/21*(a - b/x^3)^(7/4)/b^2","B",0
2152,0,0,0,0.000000," ","integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2153,0,0,0,0.000000," ","integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2154,-2,0,0,0.000000," ","integrate(x^2*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{%%{[-2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueUnable to divide, perhaps due to rounding error%%%{%%%{%%{[2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueEvaluation time: 1integrate((4*a^2*x^6*sqrt(sqrt(a^2*x^4+b)+a*x^2)-4*a^2*x^6-4*a*x^4*sqrt(sqrt(a^2*x^4+b)+a*x^2)+4*b*x^2*sqrt(sqrt(a^2*x^4+b)+a*x^2)-4*b*x^2+x^2*sqrt(sqrt(a^2*x^4+b)+a*x^2)+4*x^2*(a^2*x^4+b))/(4*a^2*x^4-4*a*x^2+4*b+1),x)","F(-2)",0
2155,-1,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2156,0,0,0,0.000000," ","integrate((2*a-3*b+x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/(-b+x)/((-a+x)*(-b+x)^2)^(1/4)/(-a^3-b^2*d+(3*a^2+2*b*d)*x-(3*a+d)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{{\left(a^{3} - 3 \, a^{2} x + 3 \, a x^{2} - x^{3}\right)} {\left(2 \, a - 3 \, b + x\right)}}{{\left(a^{3} + b^{2} d + {\left(3 \, a + d\right)} x^{2} - x^{3} - {\left(3 \, a^{2} + 2 \, b d\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{4}} {\left(b - x\right)}}\,{d x}"," ",0,"integrate(-(a^3 - 3*a^2*x + 3*a*x^2 - x^3)*(2*a - 3*b + x)/((a^3 + b^2*d + (3*a + d)*x^2 - x^3 - (3*a^2 + 2*b*d)*x)*(-(a - x)*(b - x)^2)^(1/4)*(b - x)), x)","F",0
2157,-2,0,0,0.000000," ","integrate((2*x^2-x+2)*(x^4-x^3)^(1/4)/(x^2-2*x-2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2158,-2,0,0,0.000000," ","integrate((2*x^2-x+2)*(x^4-x^3)^(1/4)/(x^2-2*x-2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2159,0,0,0,0.000000," ","integrate((-2*x^4-3*x^2+1)^(1/2)*(2*x^4+1)/(2*x^4+x^2-1)/(2*x^4+2*x^2-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} + 1\right)} \sqrt{-2 \, x^{4} - 3 \, x^{2} + 1}}{{\left(2 \, x^{4} + 2 \, x^{2} - 1\right)} {\left(2 \, x^{4} + x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((2*x^4 + 1)*sqrt(-2*x^4 - 3*x^2 + 1)/((2*x^4 + 2*x^2 - 1)*(2*x^4 + x^2 - 1)), x)","F",0
2160,0,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4-2*b),x, algorithm=""giac"")","\int \frac{{\left(2 \, a x^{4} - b\right)} {\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}{a x^{4} - 2 \, b}\,{d x}"," ",0,"integrate((2*a*x^4 - b)*(a*x^4 + b*x^2)^(1/4)/(a*x^4 - 2*b), x)","F",0
2161,0,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4-2*b),x, algorithm=""giac"")","\int \frac{{\left(2 \, a x^{4} - b\right)} {\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}}}{a x^{4} - 2 \, b}\,{d x}"," ",0,"integrate((2*a*x^4 - b)*(a*x^4 + b*x^2)^(1/4)/(a*x^4 - 2*b), x)","F",0
2162,-2,0,0,0.000000," ","integrate(x*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(d*x^4+a-x),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 1/2*(-1/d)^(1/3)*ln((sqrt(3)*(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)*(-a/x+1)-sqrt(3)*(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)+(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)*(-a/x+1)-(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)+2*d*a)*(sqrt(3)*(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)*(-a/x+1)-sqrt(3)*(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)+(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)*(-a/x+1)-(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)+2*d*a)+(-sqrt(3)*(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)*(-a/x+1)+sqrt(3)*(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)+(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)*(-a/x+1)-(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3))*(-sqrt(3)*(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)*(-a/x+1)+sqrt(3)*(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)+(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)*(-a/x+1)-(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)))-sqrt(3)*(-1/d)^(1/3)*atan((sqrt(3)*(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)*(-a/x+1)-sqrt(3)*(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)+(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)*(-a/x+1)-(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)+2*d*a)/(-sqrt(3)*(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)*(-a/x+1)+sqrt(3)*(abs(d)^(1/3))^2/2*(-a/x+1)^(1/3)+(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)*(-a/x+1)-(abs(d)^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)))-(-1/d)^(1/3)/2*ln((-(d^(1/3))^2/2*(-a/x+1)^(1/3)*(-a/x+1)+(d^(1/3))^2/2*(-a/x+1)^(1/3)+d*a)^2+(-(d^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3)*(-a/x+1)+(d^(1/3))^2*sqrt(3)/2*(-a/x+1)^(1/3))^2)","F(-2)",0
2163,0,0,0,0.000000," ","integrate((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - 2 \, a x^{4} - b}{{\left(x^{8} - a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - 2*a*x^4 - b)/((x^8 - a*x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
2164,0,0,0,0.000000," ","integrate((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - 2 \, a x^{4} - b}{{\left(x^{8} - a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - 2*a*x^4 - b)/((x^8 - a*x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
2165,1,98,0,0.204826," ","integrate(1/(x^2-1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{8} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{4} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) - \frac{3}{2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}"," ",0,"1/4*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) - 1/8*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) + 1/4*2^(2/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3))) - 3/2/(-1/x + 1)^(1/3)","A",0
2166,0,0,0,0.000000," ","integrate((a^2*x^4-b^2)/(a*x^3-b*x)^(1/2)/(a^2*x^4+c*x^2+b^2),x, algorithm=""giac"")","\int \frac{a^{2} x^{4} - b^{2}}{{\left(a^{2} x^{4} + c x^{2} + b^{2}\right)} \sqrt{a x^{3} - b x}}\,{d x}"," ",0,"integrate((a^2*x^4 - b^2)/((a^2*x^4 + c*x^2 + b^2)*sqrt(a*x^3 - b*x)), x)","F",0
2167,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x/(b*x^2+a*(p*x^3+q)^2),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left(2 \, p x^{3} - q\right)}}{{\left({\left(p x^{3} + q\right)}^{2} a + b x^{2}\right)} x}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 + 2*p*q*x^3 - 2*p*q*x^2 + q^2)*(2*p*x^3 - q)/(((p*x^3 + q)^2*a + b*x^2)*x), x)","F",0
2168,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x/(b*x^4+a*(p*x^3+q)^2),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(p x^{3} - 2 \, q\right)}}{{\left(b x^{4} + {\left(p x^{3} + q\right)}^{2} a\right)} x}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(p*x^3 - 2*q)/((b*x^4 + (p*x^3 + q)^2*a)*x), x)","F",0
2169,0,0,0,0.000000," ","integrate((x^2-(x^2+1)^(1/2))/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x^{2} - \sqrt{x^{2} + 1}}{x^{2} + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^2 - sqrt(x^2 + 1))/(x^2 + sqrt(x + sqrt(x^2 + 1))), x)","F",0
2170,0,0,0,0.000000," ","integrate((x^2-(x^2+1)^(1/2))/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x^{2} - \sqrt{x^{2} + 1}}{x^{2} + \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^2 - sqrt(x^2 + 1))/(x^2 + sqrt(x + sqrt(x^2 + 1))), x)","F",0
2171,-2,0,0,0.000000," ","integrate((1+(1-(1+1/x^2)^(1/2))^(1/2))^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueEvaluation time: 1.7Done","F(-2)",0
2172,1,122,0,0.525743," ","integrate((-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x, algorithm=""giac"")","-\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{2}{3}}} - \frac{\log\left(b^{\frac{2}{3}} + b^{\frac{1}{3}} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}}\right)}{2 \, b^{\frac{2}{3}}} + \frac{\log\left({\left| -b^{\frac{1}{3}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} \right|}\right)}{b^{\frac{2}{3}}}"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(k - k/x - 1/x + 1/x^2)^(1/3))/b^(1/3))/b^(2/3) - 1/2*log(b^(2/3) + b^(1/3)*(k - k/x - 1/x + 1/x^2)^(1/3) + (k - k/x - 1/x + 1/x^2)^(2/3))/b^(2/3) + log(abs(-b^(1/3) + (k - k/x - 1/x + 1/x^2)^(1/3)))/b^(2/3)","A",0
2173,0,0,0,0.000000," ","integrate((2-(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x),x, algorithm=""giac"")","\int \frac{{\left(k + 1\right)} x - 2}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left({\left(k + 1\right)} x - 1\right)}}\,{d x}"," ",0,"integrate(((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(1/3)*((k + 1)*x - 1)), x)","F",0
2174,1,121,0,0.295177," ","integrate((-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(b^{\frac{1}{3}} + 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{b^{\frac{1}{3}}} - \frac{\log\left(b^{\frac{2}{3}} + b^{\frac{1}{3}} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}}\right)}{2 \, b^{\frac{1}{3}}} + \frac{\log\left({\left| -b^{\frac{1}{3}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} \right|}\right)}{b^{\frac{1}{3}}}"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*(b^(1/3) + 2*(k - k/x - 1/x + 1/x^2)^(1/3))/b^(1/3))/b^(1/3) - 1/2*log(b^(2/3) + b^(1/3)*(k - k/x - 1/x + 1/x^2)^(1/3) + (k - k/x - 1/x + 1/x^2)^(2/3))/b^(1/3) + log(abs(-b^(1/3) + (k - k/x - 1/x + 1/x^2)^(1/3)))/b^(1/3)","A",0
2175,0,0,0,0.000000," ","integrate((2*x^2+3)*(2*x^3+2*x^2+1)^(2/3)/x^3/(x^3-2*x^2-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} + 2 \, x^{2} + 1\right)}^{\frac{2}{3}} {\left(2 \, x^{2} + 3\right)}}{{\left(x^{3} - 2 \, x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((2*x^3 + 2*x^2 + 1)^(2/3)*(2*x^2 + 3)/((x^3 - 2*x^2 - 1)*x^3), x)","F",0
2176,0,0,0,0.000000," ","integrate((a*x^2+c*x-b)/(a*x^2+b)/(a*x^3-b*x)^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + c x - b}{\sqrt{a x^{3} - b x} {\left(a x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + c*x - b)/(sqrt(a*x^3 - b*x)*(a*x^2 + b)), x)","F",0
2177,0,0,0,0.000000," ","integrate((x^4+2*x^2-2*x-4)/x/(x^2-2)/((x^2+2)/(x^2-2))^(1/4)/(x^5-4*x^4+4*x^3+4*x^2-10*x+8),x, algorithm=""giac"")","\int \frac{x^{4} + 2 \, x^{2} - 2 \, x - 4}{{\left(x^{5} - 4 \, x^{4} + 4 \, x^{3} + 4 \, x^{2} - 10 \, x + 8\right)} {\left(x^{2} - 2\right)} x \left(\frac{x^{2} + 2}{x^{2} - 2}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 + 2*x^2 - 2*x - 4)/((x^5 - 4*x^4 + 4*x^3 + 4*x^2 - 10*x + 8)*(x^2 - 2)*x*((x^2 + 2)/(x^2 - 2))^(1/4)), x)","F",0
2178,0,0,0,0.000000," ","integrate((1+x)^(1/2)*(x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2179,0,0,0,0.000000," ","integrate((1+x)^(1/2)*(x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2180,0,0,0,0.000000," ","integrate((c*x-d)/x^4/(a*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{c x - d}{{\left(a x^{3} - b\right)}^{\frac{1}{3}} x^{4}}\,{d x}"," ",0,"integrate((c*x - d)/((a*x^3 - b)^(1/3)*x^4), x)","F",0
2181,1,350,0,0.500828," ","integrate((a*x^4-b*x^3)^(1/4)*(c*x^4-d)/x^2,x, algorithm=""giac"")","\frac{49152 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} b d + \frac{6 \, \sqrt{2} {\left(77 \, b^{5} c + 2048 \, a^{4} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{3}} + \frac{6 \, \sqrt{2} {\left(77 \, b^{5} c + 2048 \, a^{4} b d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{3}} + \frac{3 \, \sqrt{2} {\left(77 \, b^{5} c + 2048 \, a^{4} b d\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{3}} - \frac{3 \, \sqrt{2} {\left(77 \, b^{5} c + 2048 \, a^{4} b d\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{3}} + \frac{8 \, {\left(77 \, {\left(a - \frac{b}{x}\right)}^{\frac{13}{4}} b^{5} c - 275 \, {\left(a - \frac{b}{x}\right)}^{\frac{9}{4}} a b^{5} c + 351 \, {\left(a - \frac{b}{x}\right)}^{\frac{5}{4}} a^{2} b^{5} c + 231 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} a^{3} b^{5} c\right)} x^{4}}{a^{3} b^{4}}}{12288 \, b}"," ",0,"1/12288*(49152*(a - b/x)^(1/4)*b*d + 6*sqrt(2)*(77*b^5*c + 2048*a^4*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^3) + 6*sqrt(2)*(77*b^5*c + 2048*a^4*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^3) + 3*sqrt(2)*(77*b^5*c + 2048*a^4*b*d)*log(sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/((-a)^(3/4)*a^3) - 3*sqrt(2)*(77*b^5*c + 2048*a^4*b*d)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/((-a)^(3/4)*a^3) + 8*(77*(a - b/x)^(13/4)*b^5*c - 275*(a - b/x)^(9/4)*a*b^5*c + 351*(a - b/x)^(5/4)*a^2*b^5*c + 231*(a - b/x)^(1/4)*a^3*b^5*c)*x^4/(a^3*b^4))/b","B",0
2182,0,0,0,0.000000," ","integrate(x^3*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-b+b*(1+k)*x-b*k*x^2+x^5),x, algorithm=""giac"")","\int \frac{{\left(3 \, k x^{2} - 4 \, {\left(k + 1\right)} x + 5\right)} x^{3}}{{\left(x^{5} - b k x^{2} + b {\left(k + 1\right)} x - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((3*k*x^2 - 4*(k + 1)*x + 5)*x^3/((x^5 - b*k*x^2 + b*(k + 1)*x - b)*((k*x - 1)*(x - 1)*x)^(2/3)), x)","F",0
2183,0,0,0,0.000000," ","integrate((x^5-8)*(x^5+2)*(x^5-3*x^4+2)^(1/4)/x^6/(2*x^5-3*x^4+4),x, algorithm=""giac"")","\int \frac{{\left(x^{5} - 3 \, x^{4} + 2\right)}^{\frac{1}{4}} {\left(x^{5} + 2\right)} {\left(x^{5} - 8\right)}}{{\left(2 \, x^{5} - 3 \, x^{4} + 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^5 - 3*x^4 + 2)^(1/4)*(x^5 + 2)*(x^5 - 8)/((2*x^5 - 3*x^4 + 4)*x^6), x)","F",0
2184,0,0,0,0.000000," ","integrate(x^2/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(x^2/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2185,0,0,0,0.000000," ","integrate(x^2/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(x^2/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2186,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2187,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2188,0,0,0,0.000000," ","integrate((x^4-x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - x^{2} + 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 - x^2 + 1)/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2189,0,0,0,0.000000," ","integrate((x^4-x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - x^{2} + 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 - x^2 + 1)/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2190,0,0,0,0.000000," ","integrate((x^4+x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} + x^{2} + 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2191,0,0,0,0.000000," ","integrate((x^4+x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} + x^{2} + 1}{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)/((x^6 + x^2)^(1/4)*(x^4 - 1)), x)","F",0
2192,0,0,0,0.000000," ","integrate((x^3-4)*(x^3-2)*(x^3-1)^(2/3)/x^6/(x^6+x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)} {\left(x^{3} - 4\right)}}{{\left(x^{6} + x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)*(x^3 - 2)*(x^3 - 4)/((x^6 + x^3 - 2)*x^6), x)","F",0
2193,0,0,0,0.000000," ","integrate((x^4-1)*(x^6+x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{8} + 1}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^4 - 1)/(x^8 + 1), x)","F",0
2194,0,0,0,0.000000," ","integrate((x^4-1)*(x^6+x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{8} + 1}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^4 - 1)/(x^8 + 1), x)","F",0
2195,0,0,0,0.000000," ","integrate((x^8-1)/(x^6+x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + 1)*(x^6 + x^2)^(1/4)), x)","F",0
2196,0,0,0,0.000000," ","integrate((x^8-1)/(x^6+x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + 1)*(x^6 + x^2)^(1/4)), x)","F",0
2197,0,0,0,0.000000," ","integrate(x^5*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-b+b*(1+k)*x-b*k*x^2+x^8),x, algorithm=""giac"")","\int \frac{{\left(6 \, k x^{2} - 7 \, {\left(k + 1\right)} x + 8\right)} x^{5}}{{\left(x^{8} - b k x^{2} + b {\left(k + 1\right)} x - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((6*k*x^2 - 7*(k + 1)*x + 8)*x^5/((x^8 - b*k*x^2 + b*(k + 1)*x - b)*((k*x - 1)*(x - 1)*x)^(2/3)), x)","F",0
2198,0,0,0,0.000000," ","integrate((2*x^8-a*x^4-2*b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} - 2 \, b}{{\left(x^{8} - a x^{4} - 2 \, b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 - 2*b)/((x^8 - a*x^4 - 2*b)*(a*x^4 - b)^(1/4)), x)","F",0
2199,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/x^4, x)","F",0
2200,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/x^4/(a*x^2+b^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{\sqrt{a x^{2} + b^{2}} x^{4}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(sqrt(a*x^2 + b^2)*x^4), x)","F",0
2201,1,941,0,0.316987," ","integrate(1/(x^3+x)^(1/3)/(x^6-1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{24} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"1/12*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x^2 + 1)^(1/3))) - 1/6*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/6*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/6*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/12*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/12*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/12*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/24*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3)) + 1/12*2^(2/3)*log(abs(-2^(1/3) + (1/x^2 + 1)^(1/3)))","B",0
2202,1,941,0,0.319339," ","integrate(1/(x^3+x)^(1/3)/(x^6-1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{24} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"1/12*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x^2 + 1)^(1/3))) - 1/6*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/6*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/6*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/12*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/12*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/12*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/24*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3)) + 1/12*2^(2/3)*log(abs(-2^(1/3) + (1/x^2 + 1)^(1/3)))","B",0
2203,-2,0,0,0.000000," ","integrate((x^3+1)*(x^6-x^3-2)^(1/2)/x^4/(x^6-2*x^3-1),x, algorithm=""giac"")","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError >> type","F(-2)",0
2204,0,0,0,0.000000," ","integrate(x^2*(7*x^3-4)/(x^4-x)^(1/3)/(x^7-x^4-1),x, algorithm=""giac"")","\int \frac{{\left(7 \, x^{3} - 4\right)} x^{2}}{{\left(x^{7} - x^{4} - 1\right)} {\left(x^{4} - x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((7*x^3 - 4)*x^2/((x^7 - x^4 - 1)*(x^4 - x)^(1/3)), x)","F",0
2205,-2,0,0,0.000000," ","integrate((x^8+a*x^4)/(a*x^4-b*x^2)^(1/4)/(x^8+2*a*x^4-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.86Unable to divide, perhaps due to rounding 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/ %%%{134217728,[0,17,10,9]%%%}+%%%{-402653184,[0,16,11,9]%%%}+%%%{-65536,[0,16,10,5]%%%}+%%%{536870912,[0,15,12,9]%%%}+%%%{402653184,[0,15,11,9]%%%}+%%%{163840,[0,15,11,5]%%%}+%%%{8,[0,15,10,1]%%%}+%%%{-536870912,[0,14,13,9]%%%}+%%%{-1207959552,[0,14,12,9]%%%}+%%%{-65536,[0,14,12,5]%%%}+%%%{-196608,[0,14,11,5]%%%}+%%%{-24,[0,14,11,1]%%%}+%%%{1610612736,[0,13,13,9]%%%}+%%%{402653184,[0,13,12,9]%%%}+%%%{524288,[0,13,12,5]%%%}+%%%{16,[0,13,12,1]%%%}+%%%{24,[0,13,11,1]%%%}+%%%{-2147483648,[0,12,14,9]%%%}+%%%{-1207959552,[0,12,13,9]%%%}+%%%{-163840,[0,12,13,5]%%%}+%%%{-196608,[0,12,12,5]%%%}+%%%{-80,[0,12,12,1]%%%}+%%%{1476395008,[0,11,14,9]%%%}+%%%{134217728,[0,11,13,9]%%%}+%%%{589824,[0,11,13,5]%%%}+%%%{56,[0,11,13,1]%%%}+%%%{24,[0,11,12,1]%%%}+%%%{-3355443200,[0,10,15,9]%%%}+%%%{-402653184,[0,10,14,9]%%%}+%%%{-65536,[0,10,14,5]%%%}+%%%{-65536,[0,10,13,5]%%%}+%%%{-96,[0,10,13,1]%%%}+%%%{134217728,[0,9,15,9]%%%}+%%%{262144,[0,9,14,5]%%%}+%%%{72,[0,9,14,1]%%%}+%%%{8,[0,9,13,1]%%%}+%%%{-2550136832,[0,8,16,9]%%%}+%%%{131072,[0,8,15,5]%%%}+%%%{-48,[0,8,14,1]%%%}+%%%{-402653184,[0,7,16,9]%%%}+%%%{32768,[0,7,15,5]%%%}+%%%{40,[0,7,15,1]%%%}+%%%{-939524096,[0,6,17,9]%%%}+%%%{131072,[0,6,16,5]%%%}+%%%{-8,[0,6,15,1]%%%}+%%%{-134217728,[0,5,17,9]%%%}+%%%{8,[0,5,16,1]%%%}+%%%{-134217728,[0,4,18,9]%%%}+%%%{32768,[0,4,17,5]%%%} Error: Bad Argument Value","F(-2)",0
2206,-2,0,0,0.000000," ","integrate((x^8+a*x^4)/(a*x^4-b*x^2)^(1/4)/(x^8+2*a*x^4-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.8Unable to divide, perhaps due to rounding 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/ %%%{134217728,[0,17,10,9]%%%}+%%%{-402653184,[0,16,11,9]%%%}+%%%{-65536,[0,16,10,5]%%%}+%%%{536870912,[0,15,12,9]%%%}+%%%{402653184,[0,15,11,9]%%%}+%%%{163840,[0,15,11,5]%%%}+%%%{8,[0,15,10,1]%%%}+%%%{-536870912,[0,14,13,9]%%%}+%%%{-1207959552,[0,14,12,9]%%%}+%%%{-65536,[0,14,12,5]%%%}+%%%{-196608,[0,14,11,5]%%%}+%%%{-24,[0,14,11,1]%%%}+%%%{1610612736,[0,13,13,9]%%%}+%%%{402653184,[0,13,12,9]%%%}+%%%{524288,[0,13,12,5]%%%}+%%%{16,[0,13,12,1]%%%}+%%%{24,[0,13,11,1]%%%}+%%%{-2147483648,[0,12,14,9]%%%}+%%%{-1207959552,[0,12,13,9]%%%}+%%%{-163840,[0,12,13,5]%%%}+%%%{-196608,[0,12,12,5]%%%}+%%%{-80,[0,12,12,1]%%%}+%%%{1476395008,[0,11,14,9]%%%}+%%%{134217728,[0,11,13,9]%%%}+%%%{589824,[0,11,13,5]%%%}+%%%{56,[0,11,13,1]%%%}+%%%{24,[0,11,12,1]%%%}+%%%{-3355443200,[0,10,15,9]%%%}+%%%{-402653184,[0,10,14,9]%%%}+%%%{-65536,[0,10,14,5]%%%}+%%%{-65536,[0,10,13,5]%%%}+%%%{-96,[0,10,13,1]%%%}+%%%{134217728,[0,9,15,9]%%%}+%%%{262144,[0,9,14,5]%%%}+%%%{72,[0,9,14,1]%%%}+%%%{8,[0,9,13,1]%%%}+%%%{-2550136832,[0,8,16,9]%%%}+%%%{131072,[0,8,15,5]%%%}+%%%{-48,[0,8,14,1]%%%}+%%%{-402653184,[0,7,16,9]%%%}+%%%{32768,[0,7,15,5]%%%}+%%%{40,[0,7,15,1]%%%}+%%%{-939524096,[0,6,17,9]%%%}+%%%{131072,[0,6,16,5]%%%}+%%%{-8,[0,6,15,1]%%%}+%%%{-134217728,[0,5,17,9]%%%}+%%%{8,[0,5,16,1]%%%}+%%%{-134217728,[0,4,18,9]%%%}+%%%{32768,[0,4,17,5]%%%} Error: Bad Argument Value","F(-2)",0
2207,0,0,0,0.000000," ","integrate((-x^4+2*x^2+1)^(1/2)*(x^4-1)*(x^4+1)/(x^4-x^2-1)/(x^8-3*x^6-x^4+3*x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)} {\left(x^{4} - 1\right)} \sqrt{-x^{4} + 2 \, x^{2} + 1}}{{\left(x^{8} - 3 \, x^{6} - x^{4} + 3 \, x^{2} + 1\right)} {\left(x^{4} - x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)*(x^4 - 1)*sqrt(-x^4 + 2*x^2 + 1)/((x^8 - 3*x^6 - x^4 + 3*x^2 + 1)*(x^4 - x^2 - 1)), x)","F",0
2208,0,0,0,0.000000," ","integrate(1/(x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(1/((x^2 - 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
2209,0,0,0,0.000000," ","integrate((-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}}}{\sqrt{a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2/b^2 - a/b^2)/sqrt(a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x), x)","F",0
2210,-2,0,0,0.000000," ","integrate((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
2211,0,0,0,0.000000," ","integrate((-3+x)*(-2+x)*(2*x^3-x+2)^(2/3)/x^6/(2*x^3+x-2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{3} - x + 2\right)}^{\frac{2}{3}} {\left(x - 2\right)} {\left(x - 3\right)}}{{\left(2 \, x^{3} + x - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^3 - x + 2)^(2/3)*(x - 2)*(x - 3)/((2*x^3 + x - 2)*x^6), x)","F",0
2212,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^3+2)/x^6/(x^6-x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 2)*(x^3 + 1)^(2/3)/((x^6 - x^3 - 2)*x^6), x)","F",0
2213,0,0,0,0.000000," ","integrate((a*x^6+b)/(x^3+x)^(1/3)/(c*x^6+d),x, algorithm=""giac"")","\int \frac{a x^{6} + b}{{\left(c x^{6} + d\right)} {\left(x^{3} + x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x^6 + b)/((c*x^6 + d)*(x^3 + x)^(1/3)), x)","F",0
2214,0,0,0,0.000000," ","integrate((a*x^6+b)/(x^3+x)^(1/3)/(c*x^6+d),x, algorithm=""giac"")","\int \frac{a x^{6} + b}{{\left(c x^{6} + d\right)} {\left(x^{3} + x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x^6 + b)/((c*x^6 + d)*(x^3 + x)^(1/3)), x)","F",0
2215,0,0,0,0.000000," ","integrate(1/(2+x)/(x^2+x+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + x + 1\right)}^{\frac{1}{3}} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + x + 1)^(1/3)*(x + 2)), x)","F",0
2216,0,0,0,0.000000," ","integrate((-3+2*x)*(x^3+x-1)^(1/3)/x^2/(x^3-2*x+2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + x - 1\right)}^{\frac{1}{3}} {\left(2 \, x - 3\right)}}{{\left(x^{3} - 2 \, x + 2\right)} x^{2}}\,{d x}"," ",0,"integrate((x^3 + x - 1)^(1/3)*(2*x - 3)/((x^3 - 2*x + 2)*x^2), x)","F",0
2217,0,0,0,0.000000," ","integrate((-(2*a-b)*b^2+(4*a-b)*b*x-(2*a+b)*x^2+x^3)/(-a+x)/((-a+x)*(-b+x)^2)^(1/4)/(b^2+a*d-(2*b+d)*x+x^2),x, algorithm=""giac"")","\int \frac{{\left(2 \, a - b\right)} b^{2} - {\left(4 \, a - b\right)} b x + {\left(2 \, a + b\right)} x^{2} - x^{3}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{4}} {\left(b^{2} + a d - {\left(2 \, b + d\right)} x + x^{2}\right)} {\left(a - x\right)}}\,{d x}"," ",0,"integrate(((2*a - b)*b^2 - (4*a - b)*b*x + (2*a + b)*x^2 - x^3)/((-(a - x)*(b - x)^2)^(1/4)*(b^2 + a*d - (2*b + d)*x + x^2)*(a - x)), x)","F",0
2218,0,0,0,0.000000," ","integrate(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}^{2}}\,{d x}"," ",0,"integrate(x^4/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)^2), x)","F",0
2219,0,0,0,0.000000," ","integrate(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}^{2}}\,{d x}"," ",0,"integrate(x^4/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)^2), x)","F",0
2220,0,0,0,0.000000," ","integrate(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}^{2}}\,{d x}"," ",0,"integrate(x^4/((a*x^4 + b*x^2)^(1/4)*(a*x^4 + b)^2), x)","F",0
2221,0,0,0,0.000000," ","integrate((a*x^4-b)*(a*x^4+b)^(3/4)/x^8/(2*a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b\right)}^{\frac{3}{4}} {\left(a x^{4} - b\right)}}{{\left(2 \, a x^{4} + b\right)} x^{8}}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)*(a*x^4 - b)/((2*a*x^4 + b)*x^8), x)","F",0
2222,0,0,0,0.000000," ","integrate(x*(a*x+b)^(1/2)/(x+(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a x + b} x}{x + \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(sqrt(a*x + b)*x/(x + sqrt(c + sqrt(a*x + b))), x)","F",0
2223,0,0,0,0.000000," ","integrate(x*(a*x+b)^(1/2)/(x+(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a x + b} x}{x + \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(sqrt(a*x + b)*x/(x + sqrt(c + sqrt(a*x + b))), x)","F",0
2224,0,0,0,0.000000," ","integrate((1-(1-(1-1/x)^(1/2))^(1/2))^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-\sqrt{-\sqrt{-\frac{1}{x} + 1} + 1} + 1}}{x}\,{d x}"," ",0,"integrate(sqrt(-sqrt(-sqrt(-1/x + 1) + 1) + 1)/x, x)","F",0
2225,0,0,0,0.000000," ","integrate((-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{2 \, a b x - {\left(a + b\right)} x^{2}}{{\left(a b d - {\left(a + b\right)} d x + {\left(d - 1\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-(2*a*b*x - (a + b)*x^2)/((a*b*d - (a + b)*d*x + (d - 1)*x^2)*((a - x)*(b - x)*x)^(2/3)), x)","F",0
2226,1,223,0,0.353194," ","integrate((a*x^3-b)^(1/4)/x^7,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{6 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{7}{4}}} + \frac{3 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} - \frac{3 \, \sqrt{2} a^{3} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{7}{4}}} + \frac{8 \, {\left({\left(a x^{3} - b\right)}^{\frac{5}{4}} a^{3} - 3 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}} a^{3} b\right)}}{a^{2} b x^{6}}}{192 \, a}"," ",0,"1/192*(6*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(7/4) + 6*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(7/4) + 3*sqrt(2)*a^3*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(7/4) - 3*sqrt(2)*a^3*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(7/4) + 8*((a*x^3 - b)^(5/4)*a^3 - 3*(a*x^3 - b)^(1/4)*a^3*b)/(a^2*b*x^6))/a","A",0
2227,1,394,0,0.279378," ","integrate((2*a*x^2+b)*(a*x^4+b*x^2)^(1/4)/(a*x^2-b),x, algorithm=""giac"")","{\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} x^{2} - \frac{3 \cdot 2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{2 \, a} - \frac{3 \cdot 2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{2 \, a} + \frac{3 \cdot 2^{\frac{3}{4}} b \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{4 \, \left(-a\right)^{\frac{3}{4}}} + \frac{3 \cdot 2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{4 \, a} + \frac{7 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} + \frac{7 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} + \frac{7 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{8 \, a} + \frac{7 \, \sqrt{2} b \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{2}}}\right)}{8 \, \left(-a\right)^{\frac{3}{4}}}"," ",0,"(a + b/x^2)^(1/4)*x^2 - 3/2*2^(3/4)*(-a)^(1/4)*b*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a - 3/2*2^(3/4)*(-a)^(1/4)*b*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a + 3/4*2^(3/4)*b*log(2^(3/4)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^2))/(-a)^(3/4) + 3/4*2^(3/4)*(-a)^(1/4)*b*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^2))/a + 7/4*sqrt(2)*(-a)^(1/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a + 7/4*sqrt(2)*(-a)^(1/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^2)^(1/4))/(-a)^(1/4))/a + 7/8*sqrt(2)*(-a)^(1/4)*b*log(sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/a + 7/8*sqrt(2)*b*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^2)^(1/4) + sqrt(-a) + sqrt(a + b/x^2))/(-a)^(3/4)","B",0
2228,0,0,0,0.000000," ","integrate((a^4*x^4-b^4)/(a^2*x^3-b^2*x)^(1/2)/(a^4*x^4+b^4),x, algorithm=""giac"")","\int \frac{a^{4} x^{4} - b^{4}}{{\left(a^{4} x^{4} + b^{4}\right)} \sqrt{a^{2} x^{3} - b^{2} x}}\,{d x}"," ",0,"integrate((a^4*x^4 - b^4)/((a^4*x^4 + b^4)*sqrt(a^2*x^3 - b^2*x)), x)","F",0
2229,0,0,0,0.000000," ","integrate((x^5-1)/(x^4+1)^(1/2)/(x^5+1),x, algorithm=""giac"")","\int \frac{x^{5} - 1}{{\left(x^{5} + 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^5 - 1)/((x^5 + 1)*sqrt(x^4 + 1)), x)","F",0
2230,0,0,0,0.000000," ","integrate((x^5-1)/(x^4+1)^(1/2)/(x^5+1),x, algorithm=""giac"")","\int \frac{x^{5} - 1}{{\left(x^{5} + 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^5 - 1)/((x^5 + 1)*sqrt(x^4 + 1)), x)","F",0
2231,0,0,0,0.000000," ","integrate((x^5+1)/(x^4+1)^(1/2)/(x^5-1),x, algorithm=""giac"")","\int \frac{x^{5} + 1}{{\left(x^{5} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^5 + 1)/((x^5 - 1)*sqrt(x^4 + 1)), x)","F",0
2232,0,0,0,0.000000," ","integrate((x^5+1)/(x^4+1)^(1/2)/(x^5-1),x, algorithm=""giac"")","\int \frac{x^{5} + 1}{{\left(x^{5} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^5 + 1)/((x^5 - 1)*sqrt(x^4 + 1)), x)","F",0
2233,0,0,0,0.000000," ","integrate((a^6*x^6-b^6)/(a^4*x^4+b^4)^(1/2)/(a^6*x^6+b^6),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} - b^{6}}{{\left(a^{6} x^{6} + b^{6}\right)} \sqrt{a^{4} x^{4} + b^{4}}}\,{d x}"," ",0,"integrate((a^6*x^6 - b^6)/((a^6*x^6 + b^6)*sqrt(a^4*x^4 + b^4)), x)","F",0
2234,0,0,0,0.000000," ","integrate((-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{2 \, a b - {\left(a + b\right)} x}{{\left(a b d - {\left(a + b\right)} d x + {\left(d - 1\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(2*a*b - (a + b)*x)/((a*b*d - (a + b)*d*x + (d - 1)*x^2)*((a - x)*(b - x)*x)^(1/3)), x)","F",0
2235,1,224,0,0.189112," ","integrate(1/x^7/(a*x^3-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{11}{4}}} + \frac{42 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{11}{4}}} + \frac{21 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{11}{4}}} - \frac{21 \, \sqrt{2} a^{3} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{11}{4}}} + \frac{8 \, {\left(7 \, {\left(a x^{3} - b\right)}^{\frac{5}{4}} a^{3} + 11 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}} a^{3} b\right)}}{a^{2} b^{2} x^{6}}}{192 \, a}"," ",0,"1/192*(42*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(11/4) + 42*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(11/4) + 21*sqrt(2)*a^3*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(11/4) - 21*sqrt(2)*a^3*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(11/4) + 8*(7*(a*x^3 - b)^(5/4)*a^3 + 11*(a*x^3 - b)^(1/4)*a^3*b)/(a^2*b^2*x^6))/a","A",0
2236,1,224,0,0.329334," ","integrate(1/x^7/(a*x^3-b)^(1/4),x, algorithm=""giac"")","\frac{\frac{10 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{9}{4}}} + \frac{10 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{3} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{9}{4}}} - \frac{5 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{9}{4}}} + \frac{5 \, \sqrt{2} a^{3} \log\left(-\sqrt{2} {\left(a x^{3} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{3} - b} + \sqrt{b}\right)}{b^{\frac{9}{4}}} + \frac{8 \, {\left(5 \, {\left(a x^{3} - b\right)}^{\frac{7}{4}} a^{3} + 9 \, {\left(a x^{3} - b\right)}^{\frac{3}{4}} a^{3} b\right)}}{a^{2} b^{2} x^{6}}}{192 \, a}"," ",0,"1/192*(10*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(9/4) + 10*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^3 - b)^(1/4))/b^(1/4))/b^(9/4) - 5*sqrt(2)*a^3*log(sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(9/4) + 5*sqrt(2)*a^3*log(-sqrt(2)*(a*x^3 - b)^(1/4)*b^(1/4) + sqrt(a*x^3 - b) + sqrt(b))/b^(9/4) + 8*(5*(a*x^3 - b)^(7/4)*a^3 + 9*(a*x^3 - b)^(3/4)*a^3*b)/(a^2*b^2*x^6))/a","A",0
2237,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^4 + x^2)^(1/3)*(x^2 - 1)), x)","F",0
2238,0,0,0,0.000000," ","integrate((x^4-1)^(2/3)*(x^4+3)*(2*x^4-x^3-2)/x^6/(2*x^4+3*x^3-2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{4} - x^{3} - 2\right)} {\left(x^{4} + 3\right)} {\left(x^{4} - 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{4} + 3 \, x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^4 - x^3 - 2)*(x^4 + 3)*(x^4 - 1)^(2/3)/((2*x^4 + 3*x^3 - 2)*x^6), x)","F",0
2239,1,224,0,0.270587," ","integrate(1/x^9/(a*x^4-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{11}{4}}} + \frac{42 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{11}{4}}} + \frac{21 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{b^{\frac{11}{4}}} - \frac{21 \, \sqrt{2} a^{3} \log\left(-\sqrt{2} {\left(a x^{4} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{4} - b} + \sqrt{b}\right)}{b^{\frac{11}{4}}} + \frac{8 \, {\left(7 \, {\left(a x^{4} - b\right)}^{\frac{5}{4}} a^{3} + 11 \, {\left(a x^{4} - b\right)}^{\frac{1}{4}} a^{3} b\right)}}{a^{2} b^{2} x^{8}}}{256 \, a}"," ",0,"1/256*(42*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(11/4) + 42*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^4 - b)^(1/4))/b^(1/4))/b^(11/4) + 21*sqrt(2)*a^3*log(sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(11/4) - 21*sqrt(2)*a^3*log(-sqrt(2)*(a*x^4 - b)^(1/4)*b^(1/4) + sqrt(a*x^4 - b) + sqrt(b))/b^(11/4) + 8*(7*(a*x^4 - b)^(5/4)*a^3 + 11*(a*x^4 - b)^(1/4)*a^3*b)/(a^2*b^2*x^8))/a","A",0
2240,0,0,0,0.000000," ","integrate((a^2*x^4+c*x^2+b^2)/(a*x^3+b*x)^(1/2)/(a^2*x^4-b^2),x, algorithm=""giac"")","\int \frac{a^{2} x^{4} + c x^{2} + b^{2}}{{\left(a^{2} x^{4} - b^{2}\right)} \sqrt{a x^{3} + b x}}\,{d x}"," ",0,"integrate((a^2*x^4 + c*x^2 + b^2)/((a^2*x^4 - b^2)*sqrt(a*x^3 + b*x)), x)","F",0
2241,1,224,0,0.256043," ","integrate(1/x^11/(a*x^5-b)^(3/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} a^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{11}{4}}} + \frac{42 \, \sqrt{2} a^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{b^{\frac{11}{4}}} + \frac{21 \, \sqrt{2} a^{3} \log\left(\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{b^{\frac{11}{4}}} - \frac{21 \, \sqrt{2} a^{3} \log\left(-\sqrt{2} {\left(a x^{5} - b\right)}^{\frac{1}{4}} b^{\frac{1}{4}} + \sqrt{a x^{5} - b} + \sqrt{b}\right)}{b^{\frac{11}{4}}} + \frac{8 \, {\left(7 \, {\left(a x^{5} - b\right)}^{\frac{5}{4}} a^{3} + 11 \, {\left(a x^{5} - b\right)}^{\frac{1}{4}} a^{3} b\right)}}{a^{2} b^{2} x^{10}}}{320 \, a}"," ",0,"1/320*(42*sqrt(2)*a^3*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(11/4) + 42*sqrt(2)*a^3*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(a*x^5 - b)^(1/4))/b^(1/4))/b^(11/4) + 21*sqrt(2)*a^3*log(sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(11/4) - 21*sqrt(2)*a^3*log(-sqrt(2)*(a*x^5 - b)^(1/4)*b^(1/4) + sqrt(a*x^5 - b) + sqrt(b))/b^(11/4) + 8*(7*(a*x^5 - b)^(5/4)*a^3 + 11*(a*x^5 - b)^(1/4)*a^3*b)/(a^2*b^2*x^10))/a","A",0
2242,0,0,0,0.000000," ","integrate((x^6+1)/(x^4-x^2)^(1/3)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{6} + 1}{{\left(x^{6} - 1\right)} {\left(x^{4} - x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 + 1)/((x^6 - 1)*(x^4 - x^2)^(1/3)), x)","F",0
2243,0,0,0,0.000000," ","integrate((a^6*x^6-b^6)/(a^2*x^3+b^2*x)^(1/2)/(a^6*x^6+b^6),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} - b^{6}}{{\left(a^{6} x^{6} + b^{6}\right)} \sqrt{a^{2} x^{3} + b^{2} x}}\,{d x}"," ",0,"integrate((a^6*x^6 - b^6)/((a^6*x^6 + b^6)*sqrt(a^2*x^3 + b^2*x)), x)","F",0
2244,0,0,0,0.000000," ","integrate((a*x^2+1)/(a*x^2-1)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + 1}{{\left(a x^{2} - 1\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b}}}\,{d x}"," ",0,"integrate((a*x^2 + 1)/((a*x^2 - 1)*sqrt(a*x + sqrt(a^2*x^2 + b))), x)","F",0
2245,0,0,0,0.000000," ","integrate((-a/b^2+a^2*x^2/b^2)^(1/2)/x^2/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}}}{\sqrt{a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x} x^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2/b^2 - a/b^2)/(sqrt(a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)*x^2), x)","F",0
2246,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p*x^3+q)^(1/2)/(b*x^4+a*(p*x^3+q)^2),x, algorithm=""giac"")","\int \frac{\sqrt{p x^{3} + q} {\left(p x^{3} - 2 \, q\right)}}{b x^{4} + {\left(p x^{3} + q\right)}^{2} a}\,{d x}"," ",0,"integrate(sqrt(p*x^3 + q)*(p*x^3 - 2*q)/(b*x^4 + (p*x^3 + q)^2*a), x)","F",0
2247,0,0,0,0.000000," ","integrate(x^4*(x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 1} \sqrt{x^{2} + \sqrt{x^{4} + 1}} x^{4}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*sqrt(x^2 + sqrt(x^4 + 1))*x^4, x)","F",0
2248,-1,0,0,0.000000," ","integrate((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(b*x^4+a*(p*x^5+q)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2249,0,0,0,0.000000," ","integrate((-3+x)/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{x - 3}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x - 3)/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
2250,0,0,0,0.000000," ","integrate(x^3*(-3*a*b+(a+2*b)*x)/(-a+x)/(-b+x)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-a*b^2*d+b*(2*a+b)*d*x-(a+2*b)*d*x^2+(-1+d)*x^3),x, algorithm=""giac"")","\int \frac{{\left(3 \, a b - {\left(a + 2 \, b\right)} x\right)} x^{3}}{{\left(a b^{2} d - {\left(2 \, a + b\right)} b d x + {\left(a + 2 \, b\right)} d x^{2} - {\left(d - 1\right)} x^{3}\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{4}} {\left(a - x\right)} {\left(b - x\right)}}\,{d x}"," ",0,"integrate((3*a*b - (a + 2*b)*x)*x^3/((a*b^2*d - (2*a + b)*b*d*x + (a + 2*b)*d*x^2 - (d - 1)*x^3)*(-(a - x)*(b - x)^2*x)^(1/4)*(a - x)*(b - x)), x)","F",0
2251,0,0,0,0.000000," ","integrate((a*x+(a^2*x^2+b^2)^(1/2))/(b+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{a x + \sqrt{a^{2} x^{2} + b^{2}}}{b + \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a*x + sqrt(a^2*x^2 + b^2))/(b + sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2252,0,0,0,0.000000," ","integrate(1/(x^2+3)/(3*x^2+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} + 1\right)}^{\frac{1}{3}} {\left(x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(1/((3*x^2 + 1)^(1/3)*(x^2 + 3)), x)","F",0
2253,0,0,0,0.000000," ","integrate((x^2+1)*(x^5+x^3)^(1/4)/x^2/(x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{2} + 1\right)}}{{\left(x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((x^5 + x^3)^(1/4)*(x^2 + 1)/((x^2 - 1)*x^2), x)","F",0
2254,0,0,0,0.000000," ","integrate((x^5+x^2+4)*(2*x^5-2*x^4-x^2-2)^(1/4)/x^2/(2*x^5-x^2-2),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{5} - 2 \, x^{4} - x^{2} - 2\right)}^{\frac{1}{4}} {\left(x^{5} + x^{2} + 4\right)}}{{\left(2 \, x^{5} - x^{2} - 2\right)} x^{2}}\,{d x}"," ",0,"integrate((2*x^5 - 2*x^4 - x^2 - 2)^(1/4)*(x^5 + x^2 + 4)/((2*x^5 - x^2 - 2)*x^2), x)","F",0
2255,0,0,0,0.000000," ","integrate((x^4-1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)}^{2} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{{\left(x^{4} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^4 - 1)^2*sqrt(x^2 + sqrt(x^4 + 1))/(x^4 + 1)^2, x)","F",0
2256,0,0,0,0.000000," ","integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2257,0,0,0,0.000000," ","integrate((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2258,1,66,0,0.193037," ","integrate(1/(1-x^(1/2))^(1/2)-(1-x^(1/2)-x)^(1/2),x, algorithm=""giac"")","-\frac{1}{12} \, {\left(2 \, \sqrt{x} {\left(4 \, \sqrt{x} + 1\right)} - 11\right)} \sqrt{-x - \sqrt{x} + 1} + \frac{4}{3} \, {\left(-\sqrt{x} + 1\right)}^{\frac{3}{2}} - 4 \, \sqrt{-\sqrt{x} + 1} + \frac{5}{8} \, \arcsin\left(\frac{1}{5} \, \sqrt{5} {\left(2 \, \sqrt{x} + 1\right)}\right)"," ",0,"-1/12*(2*sqrt(x)*(4*sqrt(x) + 1) - 11)*sqrt(-x - sqrt(x) + 1) + 4/3*(-sqrt(x) + 1)^(3/2) - 4*sqrt(-sqrt(x) + 1) + 5/8*arcsin(1/5*sqrt(5)*(2*sqrt(x) + 1))","A",0
2259,0,0,0,0.000000," ","integrate((-5+x)/(x^2-x-2)^(1/3)/(x^2+4*x-3),x, algorithm=""giac"")","\int \frac{x - 5}{{\left(x^{2} + 4 \, x - 3\right)} {\left(x^{2} - x - 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x - 5)/((x^2 + 4*x - 3)*(x^2 - x - 2)^(1/3)), x)","F",0
2260,0,0,0,0.000000," ","integrate((-a+x)*(-2*a+b+x)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^2*d-(2*b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{{\left(2 \, a - b - x\right)} {\left(a - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{3}{4}} {\left(b^{2} d + d x^{2} - {\left(2 \, b d + 1\right)} x + a\right)}}\,{d x}"," ",0,"integrate((2*a - b - x)*(a - x)/((-(a - x)*(b - x)^2)^(3/4)*(b^2*d + d*x^2 - (2*b*d + 1)*x + a)), x)","F",0
2261,0,0,0,0.000000," ","integrate((1+x)/(x^2+4*x+1)/(-x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(-x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{2} + 4 \, x + 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((-x^3 + 1)^(1/3)*(x^2 + 4*x + 1)), x)","F",0
2262,0,0,0,0.000000," ","integrate(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}^{2}}\,{d x}"," ",0,"integrate(x^4/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - b)^2), x)","F",0
2263,0,0,0,0.000000," ","integrate(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}^{2}}\,{d x}"," ",0,"integrate(x^4/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - b)^2), x)","F",0
2264,0,0,0,0.000000," ","integrate(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}^{2}}\,{d x}"," ",0,"integrate(x^4/((a*x^4 + b*x^2)^(1/4)*(a*x^4 - b)^2), x)","F",0
2265,0,0,0,0.000000," ","integrate(x^8/(x^4-1)^(1/2)/(x^16-1),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(x^{16} - 1\right)} \sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(x^8/((x^16 - 1)*sqrt(x^4 - 1)), x)","F",0
2266,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^4,x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{{\left(a x^{2} + b^{2}\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 + b^2)^4, x)","F",0
2267,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(x^2 + 1), x)","F",0
2268,-2,0,0,0.000000," ","integrate((1-(1-(1-1/x^2)^(1/2))^(1/2))^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^8-4*x^6+4*x^4-4*x^2)]Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument ValueDiscontinuities at zeroes of x^8-4*x^6+4*x^4-4*x^2 were not checkedEvaluation time: 2.24Done","F(-2)",0
2269,0,0,0,0.000000," ","integrate(1/(1+x)/(-x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{3} + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((-x^3 + 1)^(1/3)*(x + 1)), x)","F",0
2270,0,0,0,0.000000," ","integrate((a*b-2*b*x+x^2)*(b^2-2*b*x+x^2)/(x*(-a+x)*(-b+x)^3)^(3/4)/(b*d-(a+d)*x+x^2),x, algorithm=""giac"")","\int \frac{{\left(a b - 2 \, b x + x^{2}\right)} {\left(b^{2} - 2 \, b x + x^{2}\right)}}{\left({\left(a - x\right)} {\left(b - x\right)}^{3} x\right)^{\frac{3}{4}} {\left(b d - {\left(a + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate((a*b - 2*b*x + x^2)*(b^2 - 2*b*x + x^2)/(((a - x)*(b - x)^3*x)^(3/4)*(b*d - (a + d)*x + x^2)), x)","F",0
2271,0,0,0,0.000000," ","integrate((-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a*b+(a+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{2 \, a b - {\left(a + b\right)} x}{\left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{3}} {\left({\left(d - 1\right)} x^{2} - a b + {\left(a + b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(2*a*b - (a + b)*x)/(((a - x)*(b - x)*x)^(1/3)*((d - 1)*x^2 - a*b + (a + b)*x)), x)","F",0
2272,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+1)/x^6/(x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{3} + 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 1)*(x^3 - 1)^(2/3)/((x^3 + 2)*x^6), x)","F",0
2273,0,0,0,0.000000," ","integrate(1/(1+x)/(-2*x^4+3*x^3-2*x^2+3*x-2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2274,1,257,0,0.291867," ","integrate(x^2*(x^4+x^3)^(1/4)/(x^4-1),x, algorithm=""giac"")","-\frac{1}{2} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 \, \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} - \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 \, \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} + \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} - \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} + \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} + \left(70368744177664 i + 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} - \left(70368744177664 i + 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 16 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(-i \, \left(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464 i - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464\right)^{\frac{1}{4}} + \left(2475880078570760549798248448 i + 2475880078570760549798248448\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 16 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(-i \, \left(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464 i - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464\right)^{\frac{1}{4}} - \left(2475880078570760549798248448 i + 2475880078570760549798248448\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + 2 \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/2*2^(1/4)*arctan(1/2*2^(3/4)*(1/x + 1)^(1/4)) - 1/4*2^(1/4)*log(2^(1/4) + (1/x + 1)^(1/4)) + 2*(-1/4096*I + 1/4096)^(1/4)*log(I*(98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) - (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) - 2*(-1/4096*I + 1/4096)^(1/4)*log(I*(98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) + (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) - 2*I*(1/4096*I + 1/4096)^(1/4)*log(I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) - (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) + 2*I*(1/4096*I + 1/4096)^(1/4)*log(I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) + (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) + 2*(1/4096*I + 1/4096)^(1/4)*log(-I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) + (70368744177664*I + 70368744177664)*(1/x + 1)^(1/4)) - 2*(1/4096*I + 1/4096)^(1/4)*log(-I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) - (70368744177664*I + 70368744177664)*(1/x + 1)^(1/4)) + 16*I*(-1/16777216*I + 1/16777216)^(1/4)*log(-I*(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464*I - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464)^(1/4) + (2475880078570760549798248448*I + 2475880078570760549798248448)*(1/x + 1)^(1/4)) - 16*I*(-1/16777216*I + 1/16777216)^(1/4)*log(-I*(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464*I - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464)^(1/4) - (2475880078570760549798248448*I + 2475880078570760549798248448)*(1/x + 1)^(1/4)) + 1/4*2^(1/4)*log(abs(-2^(1/4) + (1/x + 1)^(1/4))) + 2*arctan((1/x + 1)^(1/4)) + log((1/x + 1)^(1/4) + 1) - log(abs((1/x + 1)^(1/4) - 1))","B",0
2275,1,257,0,0.285555," ","integrate(x^2*(x^4+x^3)^(1/4)/(x^4-1),x, algorithm=""giac"")","-\frac{1}{2} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 \, \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} - \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 \, \left(-\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} + \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} - \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 i \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} + \left(70368744177664 i - 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} + \left(70368744177664 i + 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 \, \left(\frac{1}{4096} i + \frac{1}{4096}\right)^{\frac{1}{4}} \log\left(-i \, \left(-98079714615416886934934209737619787751599303819750539264 i - 98079714615416886934934209737619787751599303819750539264\right)^{\frac{1}{4}} - \left(70368744177664 i + 70368744177664\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 16 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(-i \, \left(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464 i - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464\right)^{\frac{1}{4}} + \left(2475880078570760549798248448 i + 2475880078570760549798248448\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 16 i \, \left(-\frac{1}{16777216} i + \frac{1}{16777216}\right)^{\frac{1}{4}} \log\left(-i \, \left(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464 i - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464\right)^{\frac{1}{4}} - \left(2475880078570760549798248448 i + 2475880078570760549798248448\right) \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + 2 \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/2*2^(1/4)*arctan(1/2*2^(3/4)*(1/x + 1)^(1/4)) - 1/4*2^(1/4)*log(2^(1/4) + (1/x + 1)^(1/4)) + 2*(-1/4096*I + 1/4096)^(1/4)*log(I*(98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) - (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) - 2*(-1/4096*I + 1/4096)^(1/4)*log(I*(98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) + (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) - 2*I*(1/4096*I + 1/4096)^(1/4)*log(I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) - (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) + 2*I*(1/4096*I + 1/4096)^(1/4)*log(I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) + (70368744177664*I - 70368744177664)*(1/x + 1)^(1/4)) + 2*(1/4096*I + 1/4096)^(1/4)*log(-I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) + (70368744177664*I + 70368744177664)*(1/x + 1)^(1/4)) - 2*(1/4096*I + 1/4096)^(1/4)*log(-I*(-98079714615416886934934209737619787751599303819750539264*I - 98079714615416886934934209737619787751599303819750539264)^(1/4) - (70368744177664*I + 70368744177664)*(1/x + 1)^(1/4)) + 16*I*(-1/16777216*I + 1/16777216)^(1/4)*log(-I*(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464*I - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464)^(1/4) + (2475880078570760549798248448*I + 2475880078570760549798248448)*(1/x + 1)^(1/4)) - 16*I*(-1/16777216*I + 1/16777216)^(1/4)*log(-I*(150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464*I - 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625196994043838464)^(1/4) - (2475880078570760549798248448*I + 2475880078570760549798248448)*(1/x + 1)^(1/4)) + 1/4*2^(1/4)*log(abs(-2^(1/4) + (1/x + 1)^(1/4))) + 2*arctan((1/x + 1)^(1/4)) + log((1/x + 1)^(1/4) + 1) - log(abs((1/x + 1)^(1/4) - 1))","B",0
2276,1,967,0,0.532397," ","integrate(1/(x^3-x)^(1/3)/(x^6+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) + \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) + \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{24} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"-1/12*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x^2 + 1)^(1/3))) + 1/6*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(-1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) + 1/6*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(-1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) - 1/6*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(-1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) + 1/12*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3) + 1) + 1/12*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3) + 1) + 1/12*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3) + 1) + 1/24*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3)) - 1/12*2^(2/3)*log(abs(-2^(1/3) + (-1/x^2 + 1)^(1/3)))","B",0
2277,1,967,0,0.431833," ","integrate(1/(x^3-x)^(1/3)/(x^6+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) + \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) + \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{12} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{24} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"-1/12*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x^2 + 1)^(1/3))) + 1/6*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(-1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) + 1/6*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(-1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) - 1/6*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(-1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) + 1/12*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3) + 1) + 1/12*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3) + 1) + 1/12*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3) + 1) + 1/24*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3)) - 1/12*2^(2/3)*log(abs(-2^(1/3) + (-1/x^2 + 1)^(1/3)))","B",0
2278,1,207,0,1.097340," ","integrate((x^4-x)^(1/2)/(a*x^6-b),x, algorithm=""giac"")","\frac{{\left(4 \, \sqrt{a b} \sqrt{-b^{2} - \sqrt{a b} b} a + 5 \, \sqrt{a b} \sqrt{-b^{2} - \sqrt{a b} b} b\right)} {\left| b \right|} \arctan\left(\frac{\sqrt{-\frac{1}{x^{3}} + 1}}{\sqrt{-\frac{b + \sqrt{{\left(a - b\right)} b + b^{2}}}{b}}}\right)}{3 \, {\left(4 \, a^{2} b^{3} + 5 \, a b^{4}\right)}} - \frac{{\left(4 \, \sqrt{a b} \sqrt{-b^{2} + \sqrt{a b} b} a + 5 \, \sqrt{a b} \sqrt{-b^{2} + \sqrt{a b} b} b\right)} {\left| b \right|} \arctan\left(\frac{\sqrt{-\frac{1}{x^{3}} + 1}}{\sqrt{-\frac{b - \sqrt{{\left(a - b\right)} b + b^{2}}}{b}}}\right)}{3 \, {\left(4 \, a^{2} b^{3} + 5 \, a b^{4}\right)}}"," ",0,"1/3*(4*sqrt(a*b)*sqrt(-b^2 - sqrt(a*b)*b)*a + 5*sqrt(a*b)*sqrt(-b^2 - sqrt(a*b)*b)*b)*abs(b)*arctan(sqrt(-1/x^3 + 1)/sqrt(-(b + sqrt((a - b)*b + b^2))/b))/(4*a^2*b^3 + 5*a*b^4) - 1/3*(4*sqrt(a*b)*sqrt(-b^2 + sqrt(a*b)*b)*a + 5*sqrt(a*b)*sqrt(-b^2 + sqrt(a*b)*b)*b)*abs(b)*arctan(sqrt(-1/x^3 + 1)/sqrt(-(b - sqrt((a - b)*b + b^2))/b))/(4*a^2*b^3 + 5*a*b^4)","A",0
2279,0,0,0,0.000000," ","integrate((2*x^8+1)*(2*x^8-2*x^4-1)^(1/4)*(4*x^16-3*x^8+1)/x^10/(2*x^8-1),x, algorithm=""giac"")","\int \frac{{\left(4 \, x^{16} - 3 \, x^{8} + 1\right)} {\left(2 \, x^{8} - 2 \, x^{4} - 1\right)}^{\frac{1}{4}} {\left(2 \, x^{8} + 1\right)}}{{\left(2 \, x^{8} - 1\right)} x^{10}}\,{d x}"," ",0,"integrate((4*x^16 - 3*x^8 + 1)*(2*x^8 - 2*x^4 - 1)^(1/4)*(2*x^8 + 1)/((2*x^8 - 1)*x^10), x)","F",0
2280,0,0,0,0.000000," ","integrate((a*x^2+b^2)^(3/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} + b^{2}\right)}^{\frac{3}{2}}}{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)^(3/2)/sqrt(b + sqrt(a*x^2 + b^2)), x)","F",0
2281,0,0,0,0.000000," ","integrate(x*(p*x^6-2*q)*(p*x^6+q)^(1/2)/(b*x^8+a*(p*x^6+q)^2),x, algorithm=""giac"")","\int \frac{\sqrt{p x^{6} + q} {\left(p x^{6} - 2 \, q\right)} x}{b x^{8} + {\left(p x^{6} + q\right)}^{2} a}\,{d x}"," ",0,"integrate(sqrt(p*x^6 + q)*(p*x^6 - 2*q)*x/(b*x^8 + (p*x^6 + q)^2*a), x)","F",0
2282,0,0,0,0.000000," ","integrate((6*x^2-2*x-1)^(1/3)/(-1+6*x),x, algorithm=""giac"")","\int \frac{{\left(6 \, x^{2} - 2 \, x - 1\right)}^{\frac{1}{3}}}{6 \, x - 1}\,{d x}"," ",0,"integrate((6*x^2 - 2*x - 1)^(1/3)/(6*x - 1), x)","F",0
2283,0,0,0,0.000000," ","integrate((-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(-a*b+(a+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{2 \, a b x - {\left(a + b\right)} x^{2}}{\left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{2}{3}} {\left({\left(d - 1\right)} x^{2} - a b + {\left(a + b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(2*a*b*x - (a + b)*x^2)/(((a - x)*(b - x)*x)^(2/3)*((d - 1)*x^2 - a*b + (a + b)*x)), x)","F",0
2284,0,0,0,0.000000," ","integrate(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int -\frac{{\left(a b - x^{2}\right)} x}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{2}{3}} {\left(a b d + d x^{2} - {\left(a d + b d + 1\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b - x^2)*x/(((a - x)*(b - x)*x^2)^(2/3)*(a*b*d + d*x^2 - (a*d + b*d + 1)*x)), x)","F",0
2285,0,0,0,0.000000," ","integrate((x^3-2)*(x^3-1)^(2/3)/x^3/(2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 1\right)}^{\frac{2}{3}} {\left(x^{3} - 2\right)}}{{\left(2 \, x^{3} - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 - 1)^(2/3)*(x^3 - 2)/((2*x^3 - 1)*x^3), x)","F",0
2286,1,403,0,0.383080," ","integrate((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^2+b),x, algorithm=""giac"")","\frac{1}{2} \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} x^{2} + \frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{2 \, a} - \frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{2 \, a} + \frac{9 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{8 \, \left(-a\right)^{\frac{3}{4}}} + \frac{9 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{8 \, \left(-a\right)^{\frac{3}{4}}} + \frac{9 \, \sqrt{2} b \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{16 \, \left(-a\right)^{\frac{3}{4}}} + \frac{9 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x^{2}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x^{2}}}\right)}{16 \, a}"," ",0,"1/2*(a - b/x^2)^(1/4)*x^2 + 2^(3/4)*(-a)^(1/4)*b*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/a + 2^(3/4)*(-a)^(1/4)*b*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/a + 1/2*2^(3/4)*(-a)^(1/4)*b*log(2^(3/4)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^2))/a - 1/2*2^(3/4)*(-a)^(1/4)*b*log(-2^(3/4)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a - b/x^2))/a + 9/8*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 9/8*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x^2)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 9/16*sqrt(2)*b*log(sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2))/(-a)^(3/4) + 9/16*sqrt(2)*(-a)^(1/4)*b*log(-sqrt(2)*(-a)^(1/4)*(a - b/x^2)^(1/4) + sqrt(-a) + sqrt(a - b/x^2))/a","B",0
2287,-1,0,0,0.000000," ","integrate((x^3+1)/(x^3-1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2288,0,0,0,0.000000," ","integrate((a*x^6-b)/(x^3-x)^(1/3)/(c*x^6-d),x, algorithm=""giac"")","\int \frac{a x^{6} - b}{{\left(c x^{6} - d\right)} {\left(x^{3} - x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x^6 - b)/((c*x^6 - d)*(x^3 - x)^(1/3)), x)","F",0
2289,0,0,0,0.000000," ","integrate((a*x^6-b)/(x^3-x)^(1/3)/(c*x^6-d),x, algorithm=""giac"")","\int \frac{a x^{6} - b}{{\left(c x^{6} - d\right)} {\left(x^{3} - x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x^6 - b)/((c*x^6 - d)*(x^3 - x)^(1/3)), x)","F",0
2290,1,190,0,4.499862," ","integrate(1/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(15 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{7}{2}} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) - 63 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{5}{2}} d \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) + 105 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} d^{2} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) - 105 \, \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d^{3} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) - 35 \, c {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) + 105 \, c \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right)\right)}}{105 \, a}"," ",0,"8/105*(15*(d + sqrt(c + sqrt(a*x + b)))^(7/2)*sgn(sqrt(c + sqrt(a*x + b))) - 63*(d + sqrt(c + sqrt(a*x + b)))^(5/2)*d*sgn(sqrt(c + sqrt(a*x + b))) + 105*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*d^2*sgn(sqrt(c + sqrt(a*x + b))) - 105*sqrt(d + sqrt(c + sqrt(a*x + b)))*d^3*sgn(sqrt(c + sqrt(a*x + b))) - 35*c*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*sgn(sqrt(c + sqrt(a*x + b))) + 105*c*sqrt(d + sqrt(c + sqrt(a*x + b)))*d*sgn(sqrt(c + sqrt(a*x + b))))/a","A",0
2291,0,0,0,0.000000," ","integrate(1/x/(x^2+3*x+3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3 \, x + 3\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate(1/((x^2 + 3*x + 3)^(1/3)*x), x)","F",0
2292,0,0,0,0.000000," ","integrate((-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x, algorithm=""giac"")","\int -\frac{a b - x^{2}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{3}} {\left(a b d + d x^{2} - {\left(a d + b d + 1\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b - x^2)/(((a - x)*(b - x)*x^2)^(1/3)*(a*b*d + d*x^2 - (a*d + b*d + 1)*x)), x)","F",0
2293,0,0,0,0.000000," ","integrate((-3+2*x)*(x^3-x+1)^(2/3)/x^3/(x^3+2*x-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x + 1\right)}^{\frac{2}{3}} {\left(2 \, x - 3\right)}}{{\left(x^{3} + 2 \, x - 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 - x + 1)^(2/3)*(2*x - 3)/((x^3 + 2*x - 2)*x^3), x)","F",0
2294,0,0,0,0.000000," ","integrate((-3+4*x)*(x^3+2*x-1)^(2/3)/x^3/(x^3-4*x+2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 2 \, x - 1\right)}^{\frac{2}{3}} {\left(4 \, x - 3\right)}}{{\left(x^{3} - 4 \, x + 2\right)} x^{3}}\,{d x}"," ",0,"integrate((x^3 + 2*x - 1)^(2/3)*(4*x - 3)/((x^3 - 4*x + 2)*x^3), x)","F",0
2295,1,62,0,0.376786," ","integrate((x^6-13*x^5+65*x^4-150*x^3+135*x^2+27*x-81)^(1/2)/(-1+x),x, algorithm=""giac"")","\frac{1}{24} \, {\left(2 \, {\left(4 \, x - 31\right)} x + 115\right)} \sqrt{x^{2} - x - 1} - 8 \, \arctan\left(-x + \sqrt{x^{2} - x - 1} + 1\right) - \frac{77}{16} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1 \right|}\right)"," ",0,"1/24*(2*(4*x - 31)*x + 115)*sqrt(x^2 - x - 1) - 8*arctan(-x + sqrt(x^2 - x - 1) + 1) - 77/16*log(abs(-2*x + 2*sqrt(x^2 - x - 1) + 1))","A",0
2296,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^2/(a*p*x^3+a*q+b*x),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left(2 \, p x^{3} - q\right)}}{{\left(a p x^{3} + a q + b x\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 + 2*p*q*x^3 - 2*p*q*x^2 + q^2)*(2*p*x^3 - q)/((a*p*x^3 + a*q + b*x)*x^2), x)","F",0
2297,0,0,0,0.000000," ","integrate(1/x^2/(x^8+x^7-5*x^6-2*x^5+10*x^4-2*x^3-7*x^2+5*x-1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} + x^{7} - 5 \, x^{6} - 2 \, x^{5} + 10 \, x^{4} - 2 \, x^{3} - 7 \, x^{2} + 5 \, x - 1\right)}^{\frac{1}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^8 + x^7 - 5*x^6 - 2*x^5 + 10*x^4 - 2*x^3 - 7*x^2 + 5*x - 1)^(1/3)*x^2), x)","F",0
2298,0,0,0,0.000000," ","integrate((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2-1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}}{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)/(sqrt(x^4 + 1)*(x^2 - 1)), x)","F",0
2299,0,0,0,0.000000," ","integrate((2+x)/(-3+x)/(-x^2+1)^(1/4)/(x^2+1),x, algorithm=""giac"")","\int \frac{x + 2}{{\left(x^{2} + 1\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{4}} {\left(x - 3\right)}}\,{d x}"," ",0,"integrate((x + 2)/((x^2 + 1)*(-x^2 + 1)^(1/4)*(x - 3)), x)","F",0
2300,1,183,0,0.298844," ","integrate((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x/(a^2*x^6-b^2),x, algorithm=""giac"")","\frac{2}{3} \, b \log\left({\left| b + \sqrt{a^{2} x^{3} + b^{2}} \right|}\right) - \frac{2}{3} \, b \log\left({\left| -b + \sqrt{a^{2} x^{3} + b^{2}} \right|}\right) + \frac{2}{3} \, \sqrt{a^{2} x^{3} + b^{2}} - \frac{{\left(3 \, a^{2} b - 3 \, a b^{2} - a c + b c\right)} \arctan\left(\frac{\sqrt{a^{2} x^{3} + b^{2}}}{\sqrt{a b - b^{2}}}\right)}{3 \, \sqrt{a b - b^{2}} a} + \frac{{\left(3 \, a^{2} b + 3 \, a b^{2} + a c + b c\right)} \arctan\left(\frac{\sqrt{a^{2} x^{3} + b^{2}}}{\sqrt{-a b - b^{2}}}\right)}{3 \, \sqrt{-a b - b^{2}} a}"," ",0,"2/3*b*log(abs(b + sqrt(a^2*x^3 + b^2))) - 2/3*b*log(abs(-b + sqrt(a^2*x^3 + b^2))) + 2/3*sqrt(a^2*x^3 + b^2) - 1/3*(3*a^2*b - 3*a*b^2 - a*c + b*c)*arctan(sqrt(a^2*x^3 + b^2)/sqrt(a*b - b^2))/(sqrt(a*b - b^2)*a) + 1/3*(3*a^2*b + 3*a*b^2 + a*c + b*c)*arctan(sqrt(a^2*x^3 + b^2)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*a)","A",0
2301,-2,0,0,0.000000," ","integrate((2*x^8-x^4+1)/(x^4+1)^(1/4)/(x^8-2*x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2302,0,0,0,0.000000," ","integrate((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} - 1\right)}}{\sqrt{x^{4} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 - 1)/(sqrt(x^4 + 1)*(x^2 + 1)), x)","F",0
2303,0,0,0,0.000000," ","integrate(x/(x+(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x + \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(x/(x + sqrt(c + sqrt(a*x + b))), x)","F",0
2304,0,0,0,0.000000," ","integrate(x/(x+(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x + \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(x/(x + sqrt(c + sqrt(a*x + b))), x)","F",0
2305,0,0,0,0.000000," ","integrate(1/(1+x)/(x^2-x+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - x + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 - x + 1)^(1/3)*(x + 1)), x)","F",0
2306,1,272,0,0.489747," ","integrate((x^4+1)*(x^4-x^3)^(1/4)/x^4/(x^4-1),x, algorithm=""giac"")","-\frac{4}{9} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \frac{4}{5} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \left(-\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} - \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \left(-\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} + \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - i \, \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} - \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + i \, \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} + \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(-i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} + \left(65536 i + 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(-i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} - \left(65536 i + 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 i \, \left(-\frac{1}{256} i + \frac{1}{256}\right)^{\frac{1}{4}} \log\left(-i \, \left(85070591730234615865843651857942052864 i - 85070591730234615865843651857942052864\right)^{\frac{1}{4}} + \left(2147483648 i + 2147483648\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 i \, \left(-\frac{1}{256} i + \frac{1}{256}\right)^{\frac{1}{4}} \log\left(-i \, \left(85070591730234615865843651857942052864 i - 85070591730234615865843651857942052864\right)^{\frac{1}{4}} - \left(2147483648 i + 2147483648\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"-4/9*(1/x - 1)^2*(-1/x + 1)^(1/4) + 4/5*(-1/x + 1)^(5/4) + 2^(1/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 1/2*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) + (-1/16*I + 1/16)^(1/4)*log(I*(73786976294838206464*I - 73786976294838206464)^(1/4) - (65536*I - 65536)*(-1/x + 1)^(1/4)) - (-1/16*I + 1/16)^(1/4)*log(I*(73786976294838206464*I - 73786976294838206464)^(1/4) + (65536*I - 65536)*(-1/x + 1)^(1/4)) - I*(1/16*I + 1/16)^(1/4)*log(I*(-73786976294838206464*I - 73786976294838206464)^(1/4) - (65536*I - 65536)*(-1/x + 1)^(1/4)) + I*(1/16*I + 1/16)^(1/4)*log(I*(-73786976294838206464*I - 73786976294838206464)^(1/4) + (65536*I - 65536)*(-1/x + 1)^(1/4)) + (1/16*I + 1/16)^(1/4)*log(-I*(-73786976294838206464*I - 73786976294838206464)^(1/4) + (65536*I + 65536)*(-1/x + 1)^(1/4)) - (1/16*I + 1/16)^(1/4)*log(-I*(-73786976294838206464*I - 73786976294838206464)^(1/4) - (65536*I + 65536)*(-1/x + 1)^(1/4)) + 2*I*(-1/256*I + 1/256)^(1/4)*log(-I*(85070591730234615865843651857942052864*I - 85070591730234615865843651857942052864)^(1/4) + (2147483648*I + 2147483648)*(-1/x + 1)^(1/4)) - 2*I*(-1/256*I + 1/256)^(1/4)*log(-I*(85070591730234615865843651857942052864*I - 85070591730234615865843651857942052864)^(1/4) - (2147483648*I + 2147483648)*(-1/x + 1)^(1/4)) - 1/2*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4)))","B",0
2307,1,272,0,0.588707," ","integrate((x^4+1)*(x^4-x^3)^(1/4)/x^4/(x^4-1),x, algorithm=""giac"")","-\frac{4}{9} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \frac{4}{5} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \left(-\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} - \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \left(-\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} + \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - i \, \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} - \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + i \, \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} + \left(65536 i - 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(-i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} + \left(65536 i + 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \left(\frac{1}{16} i + \frac{1}{16}\right)^{\frac{1}{4}} \log\left(-i \, \left(-73786976294838206464 i - 73786976294838206464\right)^{\frac{1}{4}} - \left(65536 i + 65536\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + 2 i \, \left(-\frac{1}{256} i + \frac{1}{256}\right)^{\frac{1}{4}} \log\left(-i \, \left(85070591730234615865843651857942052864 i - 85070591730234615865843651857942052864\right)^{\frac{1}{4}} + \left(2147483648 i + 2147483648\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - 2 i \, \left(-\frac{1}{256} i + \frac{1}{256}\right)^{\frac{1}{4}} \log\left(-i \, \left(85070591730234615865843651857942052864 i - 85070591730234615865843651857942052864\right)^{\frac{1}{4}} - \left(2147483648 i + 2147483648\right) \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right)"," ",0,"-4/9*(1/x - 1)^2*(-1/x + 1)^(1/4) + 4/5*(-1/x + 1)^(5/4) + 2^(1/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 1/2*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) + (-1/16*I + 1/16)^(1/4)*log(I*(73786976294838206464*I - 73786976294838206464)^(1/4) - (65536*I - 65536)*(-1/x + 1)^(1/4)) - (-1/16*I + 1/16)^(1/4)*log(I*(73786976294838206464*I - 73786976294838206464)^(1/4) + (65536*I - 65536)*(-1/x + 1)^(1/4)) - I*(1/16*I + 1/16)^(1/4)*log(I*(-73786976294838206464*I - 73786976294838206464)^(1/4) - (65536*I - 65536)*(-1/x + 1)^(1/4)) + I*(1/16*I + 1/16)^(1/4)*log(I*(-73786976294838206464*I - 73786976294838206464)^(1/4) + (65536*I - 65536)*(-1/x + 1)^(1/4)) + (1/16*I + 1/16)^(1/4)*log(-I*(-73786976294838206464*I - 73786976294838206464)^(1/4) + (65536*I + 65536)*(-1/x + 1)^(1/4)) - (1/16*I + 1/16)^(1/4)*log(-I*(-73786976294838206464*I - 73786976294838206464)^(1/4) - (65536*I + 65536)*(-1/x + 1)^(1/4)) + 2*I*(-1/256*I + 1/256)^(1/4)*log(-I*(85070591730234615865843651857942052864*I - 85070591730234615865843651857942052864)^(1/4) + (2147483648*I + 2147483648)*(-1/x + 1)^(1/4)) - 2*I*(-1/256*I + 1/256)^(1/4)*log(-I*(85070591730234615865843651857942052864*I - 85070591730234615865843651857942052864)^(1/4) - (2147483648*I + 2147483648)*(-1/x + 1)^(1/4)) - 1/2*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4)))","B",0
2308,-1,0,0,0.000000," ","integrate((a*x^3+b*x)^(1/3)*(a*x^4+b)/x^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2309,0,0,0,0.000000," ","integrate((a^4*x^4+b^4)/(a^2*x^3-b^2*x)^(1/2)/(a^4*x^4-b^4),x, algorithm=""giac"")","\int \frac{a^{4} x^{4} + b^{4}}{{\left(a^{4} x^{4} - b^{4}\right)} \sqrt{a^{2} x^{3} - b^{2} x}}\,{d x}"," ",0,"integrate((a^4*x^4 + b^4)/((a^4*x^4 - b^4)*sqrt(a^2*x^3 - b^2*x)), x)","F",0
2310,0,0,0,0.000000," ","integrate((1+x)/(x^3-1)/(x^8-16*x^6+96*x^4-256*x^2+256)^(1/8),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256\right)}^{\frac{1}{8}} {\left(x^{3} - 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)^(1/8)*(x^3 - 1)), x)","F",0
2311,0,0,0,0.000000," ","integrate(1/x^2/(x^8-5*x^7+7*x^6+2*x^5-10*x^4+2*x^3+5*x^2-x-1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - 5 \, x^{7} + 7 \, x^{6} + 2 \, x^{5} - 10 \, x^{4} + 2 \, x^{3} + 5 \, x^{2} - x - 1\right)}^{\frac{1}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^8 - 5*x^7 + 7*x^6 + 2*x^5 - 10*x^4 + 2*x^3 + 5*x^2 - x - 1)^(1/3)*x^2), x)","F",0
2312,0,0,0,0.000000," ","integrate(c*x^6*(a*x^5-4*b)/(a*x^5+b)^(3/4)/(a^2*x^10-c^2*x^8+2*a*b*x^5+b^2),x, algorithm=""giac"")","\int \frac{{\left(a x^{5} - 4 \, b\right)} c x^{6}}{{\left(a^{2} x^{10} - c^{2} x^{8} + 2 \, a b x^{5} + b^{2}\right)} {\left(a x^{5} + b\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((a*x^5 - 4*b)*c*x^6/((a^2*x^10 - c^2*x^8 + 2*a*b*x^5 + b^2)*(a*x^5 + b)^(3/4)), x)","F",0
2313,1,224,0,2.086682," ","integrate(x^2*(a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a x + \sqrt{a x - b}} {\left(2 \, \sqrt{a x - b} {\left(4 \, \sqrt{a x - b} {\left(2 \, \sqrt{a x - b} {\left(8 \, \sqrt{a x - b} {\left(\frac{10 \, \sqrt{a x - b}}{a^{2}} + \frac{1}{a^{2}}\right)} + \frac{260 \, a^{12} b - 9 \, a^{12}}{a^{14}}\right)} + \frac{3 \, {\left(4 \, a^{12} b + 7 \, a^{12}\right)}}{a^{14}}\right)} + \frac{3 \, {\left(880 \, a^{12} b^{2} + 16 \, a^{12} b - 35 \, a^{12}\right)}}{a^{14}}\right)} - \frac{3 \, {\left(144 \, a^{12} b^{2} + 160 \, a^{12} b - 105 \, a^{12}\right)}}{a^{14}}\right)} - \frac{15 \, {\left(320 \, b^{3} + 16 \, b^{2} + 60 \, b - 21\right)} \log\left({\left| -2 \, \sqrt{a x - b} + 2 \, \sqrt{a x + \sqrt{a x - b}} - 1 \right|}\right)}{a^{2}}}{7680 \, a}"," ",0,"1/7680*(2*sqrt(a*x + sqrt(a*x - b))*(2*sqrt(a*x - b)*(4*sqrt(a*x - b)*(2*sqrt(a*x - b)*(8*sqrt(a*x - b)*(10*sqrt(a*x - b)/a^2 + 1/a^2) + (260*a^12*b - 9*a^12)/a^14) + 3*(4*a^12*b + 7*a^12)/a^14) + 3*(880*a^12*b^2 + 16*a^12*b - 35*a^12)/a^14) - 3*(144*a^12*b^2 + 160*a^12*b - 105*a^12)/a^14) - 15*(320*b^3 + 16*b^2 + 60*b - 21)*log(abs(-2*sqrt(a*x - b) + 2*sqrt(a*x + sqrt(a*x - b)) - 1))/a^2)/a","A",0
2314,0,0,0,0.000000," ","integrate((a*k^4*x^4+b*x^2+a)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^4*x^4-1),x, algorithm=""giac"")","\int \frac{a k^{4} x^{4} + b x^{2} + a}{{\left(k^{4} x^{4} - 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((a*k^4*x^4 + b*x^2 + a)/((k^4*x^4 - 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
2315,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(a*p^2*x^6+2*a*p*q*x^3+b*x^4+a*q^2)/x^9,x, algorithm=""giac"")","\int \frac{{\left(a p^{2} x^{6} + 2 \, a p q x^{3} + b x^{4} + a q^{2}\right)} \sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(p x^{3} - 2 \, q\right)}}{x^{9}}\,{d x}"," ",0,"integrate((a*p^2*x^6 + 2*a*p*q*x^3 + b*x^4 + a*q^2)*sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(p*x^3 - 2*q)/x^9, x)","F",0
2316,-1,0,0,0.000000," ","integrate((x^3-1)/(x^3+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2317,0,0,0,0.000000," ","integrate((5*x-4*(1+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(1+k)*x-k*x^2+b*x^5),x, algorithm=""giac"")","\int \frac{3 \, k x^{3} - 4 \, {\left(k + 1\right)} x^{2} + 5 \, x}{{\left(b x^{5} - k x^{2} + {\left(k + 1\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*k*x^3 - 4*(k + 1)*x^2 + 5*x)/((b*x^5 - k*x^2 + (k + 1)*x - 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2318,0,0,0,0.000000," ","integrate(x^2*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(1+k)*x-k*x^2+b*x^8),x, algorithm=""giac"")","\int \frac{{\left(6 \, k x^{2} - 7 \, {\left(k + 1\right)} x + 8\right)} x^{2}}{{\left(b x^{8} - k x^{2} + {\left(k + 1\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((6*k*x^2 - 7*(k + 1)*x + 8)*x^2/((b*x^8 - k*x^2 + (k + 1)*x - 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2319,0,0,0,0.000000," ","integrate(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(a*b-(a+b+d)*x+x^2),x, algorithm=""giac"")","\int -\frac{{\left(a b - x^{2}\right)} x}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{2}{3}} {\left(a b - {\left(a + b + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate(-(a*b - x^2)*x/(((a - x)*(b - x)*x^2)^(2/3)*(a*b - (a + b + d)*x + x^2)), x)","F",0
2320,0,0,0,0.000000," ","integrate((x^3+b)*(x^3+c)/(x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + b\right)} {\left(x^{3} + c\right)}}{{\left(x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 + b)*(x^3 + c)/(x^3 + a)^(1/3), x)","F",0
2321,1,967,0,67.340689," ","integrate(1/(x^3+1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) + \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) - \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"-1/6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) + 1/3*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) + 1/3*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) - 1/3*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) + 1/6*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) + 1/6*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) + 1/6*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) + 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) - 1/6*2^(2/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3)))","B",0
2322,1,967,0,66.767578," ","integrate(1/(x^3+1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) + \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) - \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"-1/6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) + 1/3*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) + 1/3*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) - 1/3*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) + 1/6*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) + 1/6*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) + 1/6*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) + 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) - 1/6*2^(2/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3)))","B",0
2323,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^3/(a*p*x^3+b*x^2+a*q),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(p x^{3} - 2 \, q\right)}}{{\left(a p x^{3} + b x^{2} + a q\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(p*x^3 - 2*q)/((a*p*x^3 + b*x^2 + a*q)*x^3), x)","F",0
2324,0,0,0,0.000000," ","integrate((x^6+x^2)^(1/4)*(x^8+1)/x^4/(x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}{{\left(x^{4} - 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^8 + 1)*(x^6 + x^2)^(1/4)/((x^4 - 1)*x^4), x)","F",0
2325,0,0,0,0.000000," ","integrate((x^6+x^2)^(1/4)*(x^8+1)/x^4/(x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}{{\left(x^{4} - 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^8 + 1)*(x^6 + x^2)^(1/4)/((x^4 - 1)*x^4), x)","F",0
2326,0,0,0,0.000000," ","integrate(1/x/(x^2-3*x+2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 3 \, x + 2\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate(1/((x^2 - 3*x + 2)^(1/3)*x), x)","F",0
2327,0,0,0,0.000000," ","integrate((a*b-x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a*b-(a+b+d)*x+x^2),x, algorithm=""giac"")","\int \frac{a b - x^{2}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{3}} {\left(a b - {\left(a + b + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate((a*b - x^2)/(((a - x)*(b - x)*x^2)^(1/3)*(a*b - (a + b + d)*x + x^2)), x)","F",0
2328,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^2+a*(p*x^3+q)^2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left(2 \, p x^{3} - q\right)} {\left({\left(p x^{3} + q\right)}^{2} a + b x^{2}\right)}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 + 2*p*q*x^3 - 2*p*q*x^2 + q^2)*(2*p*x^3 - q)*((p*x^3 + q)^2*a + b*x^2)/x^5, x)","F",0
2329,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x - 1\right)} \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}}\,{d x}"," ",0,"integrate((x + 1)/((x - 1)*sqrt(sqrt(sqrt(x + 1) + 1) + 1)), x)","F",0
2330,0,0,0,0.000000," ","integrate((1+x)/(-1+x)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x - 1\right)} \sqrt{\sqrt{\sqrt{x + 1} + 1} + 1}}\,{d x}"," ",0,"integrate((x + 1)/((x - 1)*sqrt(sqrt(sqrt(x + 1) + 1) + 1)), x)","F",0
2331,0,0,0,0.000000," ","integrate(1/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{c x + d + \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(1/(c*x + d + sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2332,0,0,0,0.000000," ","integrate(1/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{c x + d + \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(1/(c*x + d + sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2333,0,0,0,0.000000," ","integrate((c*x-d)/x^7/(a*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{c x - d}{{\left(a x^{3} - b\right)}^{\frac{1}{3}} x^{7}}\,{d x}"," ",0,"integrate((c*x - d)/((a*x^3 - b)^(1/3)*x^7), x)","F",0
2334,0,0,0,0.000000," ","integrate((x^4+x^2+1)/(-x^4+1)/(x^5+x^3)^(1/4),x, algorithm=""giac"")","\int -\frac{x^{4} + x^{2} + 1}{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^4 + x^2 + 1)/((x^5 + x^3)^(1/4)*(x^4 - 1)), x)","F",0
2335,1,55,0,0.474936," ","integrate((2*x^4-1)^(1/2)*(2*x^8-1)/x^7/(x^8+2*x^4-1),x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} {\left(3 \, {\left(\sqrt{2} x^{2} - \sqrt{2 \, x^{4} - 1}\right)}^{2} + 1\right)}}{3 \, {\left({\left(\sqrt{2} x^{2} - \sqrt{2 \, x^{4} - 1}\right)}^{2} + 1\right)}^{3}}"," ",0,"-4/3*sqrt(2)*(3*(sqrt(2)*x^2 - sqrt(2*x^4 - 1))^2 + 1)/((sqrt(2)*x^2 - sqrt(2*x^4 - 1))^2 + 1)^3","B",0
2336,-2,0,0,0.000000," ","integrate((1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)/x/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1]%%%}+%%%{-4,[0]%%%},%%%{-4,[1]%%%}+%%%{-4,[0]%%%},%%%{1,[2]%%%}+%%%{-1,[1]%%%}+%%%{-1,[0]%%%}] at parameters values [-72]Warning, choosing root of [1,0,%%%{-2,[1]%%%}+%%%{-4,[0]%%%},%%%{-4,[1]%%%}+%%%{-4,[0]%%%},%%%{1,[2]%%%}+%%%{-1,[1]%%%}+%%%{-1,[0]%%%}] at parameters values [11]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [x]=[91]4*(2/5*sqrt(sqrt(sqrt(x+1)+1)+1)*(sqrt(sqrt(x+1)+1)+1)^2-4/3*sqrt(sqrt(sqrt(x+1)+1)+1)*(sqrt(sqrt(x+1)+1)+1)+2*sqrt(sqrt(sqrt(x+1)+1)+1)+sqrt(2*(sqrt(2)-1))/4*ln(abs(sqrt(sqrt(sqrt(x+1)+1)+1)-sqrt((2+2*sqrt(2))/2)))-sqrt(2*(sqrt(2)-1))/4*ln(sqrt(sqrt(sqrt(x+1)+1)+1)+sqrt((2+2*sqrt(2))/2))-sqrt(2*(sqrt(2)+1))/2*atan(sqrt(sqrt(sqrt(x+1)+1)+1)/sqrt(-(2-2*sqrt(2))/2)))","F(-2)",0
2337,0,0,0,0.000000," ","integrate((1+x)/(3+x)/(1+2*x)/(x^2+1)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(2 \, x + 1\right)} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate((x + 1)/((x^2 + 1)^(1/3)*(2*x + 1)*(x + 3)), x)","F",0
2338,0,0,0,0.000000," ","integrate((x^3-x^2)^(1/3)/(x^2+x+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}}}{x^{2} + x + 1}\,{d x}"," ",0,"integrate((x^3 - x^2)^(1/3)/(x^2 + x + 1), x)","F",0
2339,0,0,0,0.000000," ","integrate((x^3-x^2)^(1/3)/(x^2+x+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}}}{x^{2} + x + 1}\,{d x}"," ",0,"integrate((x^3 - x^2)^(1/3)/(x^2 + x + 1), x)","F",0
2340,0,0,0,0.000000," ","integrate(x*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(b*k+b)*x-b*k*x^2+x^5),x, algorithm=""giac"")","\int \frac{{\left(3 \, k x^{2} - 4 \, {\left(k + 1\right)} x + 5\right)} x}{{\left(x^{5} - b k x^{2} + {\left(b k + b\right)} x - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*k*x^2 - 4*(k + 1)*x + 5)*x/((x^5 - b*k*x^2 + (b*k + b)*x - b)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2341,0,0,0,0.000000," ","integrate((x^4+1)/(-x^4+1)/(x^5+x^3)^(1/4),x, algorithm=""giac"")","\int -\frac{x^{4} + 1}{{\left(x^{5} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^4 + 1)/((x^5 + x^3)^(1/4)*(x^4 - 1)), x)","F",0
2342,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^6+x^3+2)/x^6/(x^3-2)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{3} + 2\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{3} - 2\right)}^{2} x^{6}}\,{d x}"," ",0,"integrate((x^6 + x^3 + 2)*(x^3 + 1)^(2/3)/((x^3 - 2)^2*x^6), x)","F",0
2343,0,0,0,0.000000," ","integrate((x^8+1)/(x^6+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{8} + 1}{{\left(x^{8} - 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 + 1)/((x^8 - 1)*(x^6 + x^2)^(1/4)), x)","F",0
2344,0,0,0,0.000000," ","integrate((x^8+1)/(x^6+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{8} + 1}{{\left(x^{8} - 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 + 1)/((x^8 - 1)*(x^6 + x^2)^(1/4)), x)","F",0
2345,0,0,0,0.000000," ","integrate(x^2*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-b+b*(1+k)*x-b*k*x^2+x^8),x, algorithm=""giac"")","\int \frac{{\left(6 \, k x^{2} - 7 \, {\left(k + 1\right)} x + 8\right)} x^{2}}{{\left(x^{8} - b k x^{2} + b {\left(k + 1\right)} x - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((6*k*x^2 - 7*(k + 1)*x + 8)*x^2/((x^8 - b*k*x^2 + b*(k + 1)*x - b)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2346,0,0,0,0.000000," ","integrate(1/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 1\right)}^{2} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(1/((x^2 + 1)^2*sqrt(x + sqrt(x^2 + 1))), x)","F",0
2347,0,0,0,0.000000," ","integrate(x*(-a+x)*(a*b+(a-2*b)*x)/(x*(-a+x)*(-b+x)^2)^(3/4)/(b^2*d+(-2*b*d+a)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(a b + {\left(a - 2 \, b\right)} x\right)} {\left(a - x\right)} x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{3}{4}} {\left(b^{2} d + {\left(d - 1\right)} x^{2} - {\left(2 \, b d - a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b + (a - 2*b)*x)*(a - x)*x/((-(a - x)*(b - x)^2*x)^(3/4)*(b^2*d + (d - 1)*x^2 - (2*b*d - a)*x)), x)","F",0
2348,0,0,0,0.000000," ","integrate((x^2+1)*(x^4-3*x^2+1)/x^2/((2*x^2+x-2)/(x^2+x-1))^(1/2)/(x^4+x^3-3*x^2-x+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 3 \, x^{2} + 1\right)} {\left(x^{2} + 1\right)}}{{\left(x^{4} + x^{3} - 3 \, x^{2} - x + 1\right)} x^{2} \sqrt{\frac{2 \, x^{2} + x - 2}{x^{2} + x - 1}}}\,{d x}"," ",0,"integrate((x^4 - 3*x^2 + 1)*(x^2 + 1)/((x^4 + x^3 - 3*x^2 - x + 1)*x^2*sqrt((2*x^2 + x - 2)/(x^2 + x - 1))), x)","F",0
2349,0,0,0,0.000000," ","integrate(x^3*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-1+(1+k)*x-k*x^2+b*x^5),x, algorithm=""giac"")","\int \frac{{\left(3 \, k x^{2} - 4 \, {\left(k + 1\right)} x + 5\right)} x^{3}}{{\left(b x^{5} - k x^{2} + {\left(k + 1\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((3*k*x^2 - 4*(k + 1)*x + 5)*x^3/((b*x^5 - k*x^2 + (k + 1)*x - 1)*((k*x - 1)*(x - 1)*x)^(2/3)), x)","F",0
2350,0,0,0,0.000000," ","integrate((x^4-2)*(x^4+2)^(1/2)/(x^8+3*x^4+4),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 2} {\left(x^{4} - 2\right)}}{x^{8} + 3 \, x^{4} + 4}\,{d x}"," ",0,"integrate(sqrt(x^4 + 2)*(x^4 - 2)/(x^8 + 3*x^4 + 4), x)","F",0
2351,0,0,0,0.000000," ","integrate((x^8-5*x^7+7*x^6+2*x^5-10*x^4+2*x^3+5*x^2-x-1)^(1/3)/x^2,x, algorithm=""giac"")","\int \frac{{\left(x^{8} - 5 \, x^{7} + 7 \, x^{6} + 2 \, x^{5} - 10 \, x^{4} + 2 \, x^{3} + 5 \, x^{2} - x - 1\right)}^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate((x^8 - 5*x^7 + 7*x^6 + 2*x^5 - 10*x^4 + 2*x^3 + 5*x^2 - x - 1)^(1/3)/x^2, x)","F",0
2352,0,0,0,0.000000," ","integrate((a^2*x^2-b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - b\right)} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b}}\,{d x}"," ",0,"integrate((a^2*x^2 - b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/sqrt(a^2*x^4 + b), x)","F",0
2353,0,0,0,0.000000," ","integrate((1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + 1}}{x + \sqrt{x + \sqrt{x + 1}}}\,{d x}"," ",0,"integrate(sqrt(x + 1)/(x + sqrt(x + sqrt(x + 1))), x)","F",0
2354,0,0,0,0.000000," ","integrate((1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + 1}}{x + \sqrt{x + \sqrt{x + 1}}}\,{d x}"," ",0,"integrate(sqrt(x + 1)/(x + sqrt(x + sqrt(x + 1))), x)","F",0
2355,0,0,0,0.000000," ","integrate((-I+k^(1/2)*x)/(I+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{k} x - i}{\sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}} {\left(\sqrt{k} x + i\right)}}\,{d x}"," ",0,"integrate((sqrt(k)*x - I)/(sqrt((k^2*x^2 - 1)*(x^2 - 1))*(sqrt(k)*x + I)), x)","F",0
2356,0,0,0,0.000000," ","integrate((I+k^(1/2)*x)/(-I+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{k} x + i}{\sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}} {\left(\sqrt{k} x - i\right)}}\,{d x}"," ",0,"integrate((sqrt(k)*x + I)/(sqrt((k^2*x^2 - 1)*(x^2 - 1))*(sqrt(k)*x - I)), x)","F",0
2357,0,0,0,0.000000," ","integrate(1/(x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1)^4,x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{3} + x^{2} - 2 \, x - 1\right)}^{4} {\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((3*x^3 + x^2 - 2*x - 1)^4*(x^3 - 3*x^2 + 3*x - 1)^(1/4)), x)","F",0
2358,0,0,0,0.000000," ","integrate((a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2359,0,0,0,0.000000," ","integrate((a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2360,0,0,0,0.000000," ","integrate(x^4/(x^6+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{8} - 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((x^8 - 1)*(x^6 + x^2)^(1/4)), x)","F",0
2361,0,0,0,0.000000," ","integrate(x^4/(x^6+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{8} - 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((x^8 - 1)*(x^6 + x^2)^(1/4)), x)","F",0
2362,0,0,0,0.000000," ","integrate((x^4-1)*(x^6+x^2)^(1/4)/(x^8-x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^4 - 1)/(x^8 - x^4 + 1), x)","F",0
2363,0,0,0,0.000000," ","integrate((x^4-1)*(x^6+x^2)^(1/4)/(x^8-x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate((x^6 + x^2)^(1/4)*(x^4 - 1)/(x^8 - x^4 + 1), x)","F",0
2364,0,0,0,0.000000," ","integrate((x^8-x^4+1)/(x^6+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{8} - x^{4} + 1}{{\left(x^{8} - 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - x^4 + 1)/((x^8 - 1)*(x^6 + x^2)^(1/4)), x)","F",0
2365,0,0,0,0.000000," ","integrate((x^8-x^4+1)/(x^6+x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","\int \frac{x^{8} - x^{4} + 1}{{\left(x^{8} - 1\right)} {\left(x^{6} + x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - x^4 + 1)/((x^8 - 1)*(x^6 + x^2)^(1/4)), x)","F",0
2366,1,317,0,0.223629," ","integrate(1/(a*x-b)/(x^4-x^3)^(1/4),x, algorithm=""giac"")","-\frac{2 \, {\left(a b^{3} - b^{4}\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a - b}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} - \sqrt{2} b^{4}} - \frac{2 \, {\left(a b^{3} - b^{4}\right)}^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} - 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a - b}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} - \sqrt{2} b^{4}} + \frac{{\left(a b^{3} - b^{4}\right)}^{\frac{3}{4}} \log\left(\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{a - b}{b}} + \sqrt{-\frac{1}{x} + 1}\right)}{\sqrt{2} a b^{3} - \sqrt{2} b^{4}} - \frac{{\left(a b^{3} - b^{4}\right)}^{\frac{3}{4}} \log\left(-\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{a - b}{b}} + \sqrt{-\frac{1}{x} + 1}\right)}{\sqrt{2} a b^{3} - \sqrt{2} b^{4}}"," ",0,"-2*(a*b^3 - b^4)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*((a - b)/b)^(1/4) + 2*(-1/x + 1)^(1/4))/((a - b)/b)^(1/4))/(sqrt(2)*a*b^3 - sqrt(2)*b^4) - 2*(a*b^3 - b^4)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*((a - b)/b)^(1/4) - 2*(-1/x + 1)^(1/4))/((a - b)/b)^(1/4))/(sqrt(2)*a*b^3 - sqrt(2)*b^4) + (a*b^3 - b^4)^(3/4)*log(sqrt(2)*((a - b)/b)^(1/4)*(-1/x + 1)^(1/4) + sqrt((a - b)/b) + sqrt(-1/x + 1))/(sqrt(2)*a*b^3 - sqrt(2)*b^4) - (a*b^3 - b^4)^(3/4)*log(-sqrt(2)*((a - b)/b)^(1/4)*(-1/x + 1)^(1/4) + sqrt((a - b)/b) + sqrt(-1/x + 1))/(sqrt(2)*a*b^3 - sqrt(2)*b^4)","B",0
2367,0,0,0,0.000000," ","integrate((x^2-x)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-2*x+1),x, algorithm=""giac"")","\int \frac{x^{2} - x}{{\left(k^{2} x^{2} - 2 \, x + 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((x^2 - x)/((k^2*x^2 - 2*x + 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
2368,0,0,0,0.000000," ","integrate((a^3*x^2-b)/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a^{3} x^{2} - b}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a^3*x^2 - b)/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 + b)), x)","F",0
2369,0,0,0,0.000000," ","integrate((a^3*x^2-b)/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a^{3} x^{2} - b}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a^3*x^2 - b)/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 + b)), x)","F",0
2370,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*(x^2 - 1)), x)","F",0
2371,0,0,0,0.000000," ","integrate(x^4*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{2}\right)}^{\frac{1}{4}} x^{4}}{x^{8} + x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - x^2)^(1/4)*x^4/(x^8 + x^4 + 1), x)","F",0
2372,0,0,0,0.000000," ","integrate(x^4*(x^4-x^2)^(1/4)/(x^8+x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{2}\right)}^{\frac{1}{4}} x^{4}}{x^{8} + x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - x^2)^(1/4)*x^4/(x^8 + x^4 + 1), x)","F",0
2373,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p*x^3+q)^(1/2)/(c*x^4+b*x^2*(p*x^3+q)+a*(p*x^3+q)^2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2374,0,0,0,0.000000," ","integrate((x^4-1)^2/(x^4+1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)}^{2}}{{\left(x^{4} + 1\right)}^{2} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}\,{d x}"," ",0,"integrate((x^4 - 1)^2/((x^4 + 1)^2*sqrt(x^2 + sqrt(x^4 + 1))), x)","F",0
2375,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)^2/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\sqrt{x^{4} + 1} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(sqrt(x^4 + 1)*(x^2 + 1)^2), x)","F",0
2376,-1,0,0,0.000000," ","integrate((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(c*x^4+b*x^2*(p*x^5+q)+a*(p*x^5+q)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2377,-1,0,0,0.000000," ","integrate(1/x/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2378,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/3)/(x^2+9),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 9\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 9)*(x^2 + 1)^(1/3)), x)","F",0
2379,0,0,0,0.000000," ","integrate((a^3*x^2+b)/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a^{3} x^{2} + b}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a^3*x^2 + b)/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 - b)), x)","F",0
2380,0,0,0,0.000000," ","integrate((a^3*x^2+b)/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a^{3} x^{2} + b}{{\left(a^{3} x^{3} - b x^{2}\right)}^{\frac{1}{3}} {\left(a^{3} x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a^3*x^2 + b)/((a^3*x^3 - b*x^2)^(1/3)*(a^3*x^2 - b)), x)","F",0
2381,0,0,0,0.000000," ","integrate((-3-2*(k^2+1)*x+(k^2+1)*x^2+4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(2+d)*x-(d*k^2+1)*x^2+d*k^2*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{4} + 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} x^{2} - 2 \, {\left(k^{2} + 1\right)} x - 3}{{\left(d k^{2} x^{3} - {\left(d k^{2} + 1\right)} x^{2} - {\left(d + 2\right)} x + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^2*x^4 + 4*k^2*x^3 + (k^2 + 1)*x^2 - 2*(k^2 + 1)*x - 3)/((d*k^2*x^3 - (d*k^2 + 1)*x^2 - (d + 2)*x + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2382,0,0,0,0.000000," ","integrate((x^5+x^3)^(1/4)*(x^8+x^4+1)/x^4/(x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{4} + 1\right)} {\left(x^{5} + x^{3}\right)}^{\frac{1}{4}}}{{\left(x^{4} - 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^8 + x^4 + 1)*(x^5 + x^3)^(1/4)/((x^4 - 1)*x^4), x)","F",0
2383,1,187,0,0.381276," ","integrate(1/(a*x^2+b)/(x^3+x)^(1/3),x, algorithm=""giac"")","\frac{3 \, {\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a - b}{b}\right)^{\frac{1}{3}}}\right)}{2 \, {\left(\sqrt{3} a b^{2} - \sqrt{3} b^{3}\right)}} - \frac{{\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \log\left(\left(-\frac{a - b}{b}\right)^{\frac{2}{3}} + \left(-\frac{a - b}{b}\right)^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, {\left(a b^{2} - b^{3}\right)}} + \frac{\left(-\frac{a - b}{b}\right)^{\frac{2}{3}} \log\left({\left| -\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(a - b\right)}}"," ",0,"3/2*(-a*b^2 + b^3)^(2/3)*arctan(1/3*sqrt(3)*((-(a - b)/b)^(1/3) + 2*(1/x^2 + 1)^(1/3))/(-(a - b)/b)^(1/3))/(sqrt(3)*a*b^2 - sqrt(3)*b^3) - 1/4*(-a*b^2 + b^3)^(2/3)*log((-(a - b)/b)^(2/3) + (-(a - b)/b)^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3))/(a*b^2 - b^3) + 1/2*(-(a - b)/b)^(2/3)*log(abs(-(-(a - b)/b)^(1/3) + (1/x^2 + 1)^(1/3)))/(a - b)","A",0
2384,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/x^2/(c*x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2385,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/x^2/(c*x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2386,0,0,0,0.000000," ","integrate((x^3+x)^(1/3)*(a*x^6+b)/(c*x^6+d),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} + b\right)} {\left(x^{3} + x\right)}^{\frac{1}{3}}}{c x^{6} + d}\,{d x}"," ",0,"integrate((a*x^6 + b)*(x^3 + x)^(1/3)/(c*x^6 + d), x)","F",0
2387,0,0,0,0.000000," ","integrate((x^3+x)^(1/3)*(a*x^6+b)/(c*x^6+d),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} + b\right)} {\left(x^{3} + x\right)}^{\frac{1}{3}}}{c x^{6} + d}\,{d x}"," ",0,"integrate((a*x^6 + b)*(x^3 + x)^(1/3)/(c*x^6 + d), x)","F",0
2388,0,0,0,0.000000," ","integrate((2*x^6-1)*(x^7+x)^(1/3)/(x^6-2*x^2+1)/(x^6-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{7} + x\right)}^{\frac{1}{3}} {\left(2 \, x^{6} - 1\right)}}{{\left(x^{6} - x^{2} + 1\right)} {\left(x^{6} - 2 \, x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^7 + x)^(1/3)*(2*x^6 - 1)/((x^6 - x^2 + 1)*(x^6 - 2*x^2 + 1)), x)","F",0
2389,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^3+a*(p*x^3+q)^3)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left({\left(p x^{3} + q\right)}^{3} a + b x^{3}\right)} {\left(2 \, p x^{3} - q\right)}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 + 2*p*q*x^3 - 2*p*q*x^2 + q^2)*((p*x^3 + q)^3*a + b*x^3)*(2*p*x^3 - q)/x^6, x)","F",0
2390,0,0,0,0.000000," ","integrate((-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+b)*x+(b*k+1)*x^2),x, algorithm=""giac"")","\int \frac{{\left(2 \, k - 1\right)} x - 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left({\left(b k + 1\right)} x^{2} - {\left(b + 2\right)} x + 1\right)}}\,{d x}"," ",0,"integrate(((2*k - 1)*x - 1)/(((k*x - 1)*(x - 1)*x)^(1/3)*((b*k + 1)*x^2 - (b + 2)*x + 1)), x)","F",0
2391,0,0,0,0.000000," ","integrate((-3+2*(k^2+1)*x+(k^2+1)*x^2-4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(2+d)*x+(d*k^2+1)*x^2+d*k^2*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{4} - 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} x^{2} + 2 \, {\left(k^{2} + 1\right)} x - 3}{{\left(d k^{2} x^{3} + {\left(d k^{2} + 1\right)} x^{2} - {\left(d + 2\right)} x - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^2*x^4 - 4*k^2*x^3 + (k^2 + 1)*x^2 + 2*(k^2 + 1)*x - 3)/((d*k^2*x^3 + (d*k^2 + 1)*x^2 - (d + 2)*x - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2392,1,237,0,0.513857," ","integrate((3*x^6-3*a*x^3+b)/x^6/(2*a*x^3-b)/(a*x^4-b*x)^(1/4),x, algorithm=""giac"")","\frac{4 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{7}{4}}}{21 \, b^{2}} + \frac{\sqrt{2} {\left(2 \, a^{\frac{11}{4}} - 3 \, a^{\frac{3}{4}} b\right)} \log\left(\sqrt{2} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} a^{\frac{1}{4}} + \sqrt{a - \frac{b}{x^{3}}} + \sqrt{a}\right)}{6 \, a b^{2}} - \frac{\sqrt{2} {\left(2 \, a^{\frac{11}{4}} - 3 \, a^{\frac{3}{4}} b\right)} \log\left(-\sqrt{2} {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}} a^{\frac{1}{4}} + \sqrt{a - \frac{b}{x^{3}}} + \sqrt{a}\right)}{6 \, a b^{2}} - \frac{{\left(2 \, \sqrt{2} a^{\frac{11}{4}} - 3 \, \sqrt{2} a^{\frac{3}{4}} b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, a^{\frac{1}{4}}}\right)}{3 \, a b^{2}} - \frac{{\left(2 \, \sqrt{2} a^{\frac{11}{4}} - 3 \, \sqrt{2} a^{\frac{3}{4}} b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, a^{\frac{1}{4}}}\right)}{3 \, a b^{2}}"," ",0,"4/21*(a - b/x^3)^(7/4)/b^2 + 1/6*sqrt(2)*(2*a^(11/4) - 3*a^(3/4)*b)*log(sqrt(2)*(a - b/x^3)^(1/4)*a^(1/4) + sqrt(a - b/x^3) + sqrt(a))/(a*b^2) - 1/6*sqrt(2)*(2*a^(11/4) - 3*a^(3/4)*b)*log(-sqrt(2)*(a - b/x^3)^(1/4)*a^(1/4) + sqrt(a - b/x^3) + sqrt(a))/(a*b^2) - 1/3*(2*sqrt(2)*a^(11/4) - 3*sqrt(2)*a^(3/4)*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4) + 2*(a - b/x^3)^(1/4))/a^(1/4))/(a*b^2) - 1/3*(2*sqrt(2)*a^(11/4) - 3*sqrt(2)*a^(3/4)*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4) - 2*(a - b/x^3)^(1/4))/a^(1/4))/(a*b^2)","A",0
2393,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^6+a*(p*x^3+q)^3)/x^11,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(b x^{6} + {\left(p x^{3} + q\right)}^{3} a\right)} {\left(p x^{3} - 2 \, q\right)}}{x^{11}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(b*x^6 + (p*x^3 + q)^3*a)*(p*x^3 - 2*q)/x^11, x)","F",0
2394,0,0,0,0.000000," ","integrate(x*(1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + 1} x}{x + \sqrt{x + \sqrt{x + 1}}}\,{d x}"," ",0,"integrate(sqrt(x + 1)*x/(x + sqrt(x + sqrt(x + 1))), x)","F",0
2395,0,0,0,0.000000," ","integrate(x*(1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + 1} x}{x + \sqrt{x + \sqrt{x + 1}}}\,{d x}"," ",0,"integrate(sqrt(x + 1)*x/(x + sqrt(x + sqrt(x + 1))), x)","F",0
2396,1,551,0,0.363274," ","integrate(x^2/((a*x+b)/(c*x+d))^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)} {\left(\frac{3 \, {\left(5 \, b^{4} c^{4} - 8 \, a b^{3} c^{3} d + 2 \, a^{2} b^{2} c^{2} d^{2} + a^{4} d^{4}\right)} \arctan\left(\frac{c \sqrt{\frac{a x + b}{c x + d}}}{\sqrt{-a c}}\right)}{\sqrt{-a c} a^{3} c^{2}} - \frac{33 \, a^{2} b^{4} c^{4} \sqrt{\frac{a x + b}{c x + d}} - \frac{40 \, {\left(a x + b\right)} a b^{4} c^{5} \sqrt{\frac{a x + b}{c x + d}}}{c x + d} + \frac{15 \, {\left(a x + b\right)}^{2} b^{4} c^{6} \sqrt{\frac{a x + b}{c x + d}}}{{\left(c x + d\right)}^{2}} - 72 \, a^{3} b^{3} c^{3} d \sqrt{\frac{a x + b}{c x + d}} + \frac{64 \, {\left(a x + b\right)} a^{2} b^{3} c^{4} d \sqrt{\frac{a x + b}{c x + d}}}{c x + d} - \frac{24 \, {\left(a x + b\right)}^{2} a b^{3} c^{5} d \sqrt{\frac{a x + b}{c x + d}}}{{\left(c x + d\right)}^{2}} + 42 \, a^{4} b^{2} c^{2} d^{2} \sqrt{\frac{a x + b}{c x + d}} + \frac{6 \, {\left(a x + b\right)}^{2} a^{2} b^{2} c^{4} d^{2} \sqrt{\frac{a x + b}{c x + d}}}{{\left(c x + d\right)}^{2}} - \frac{32 \, {\left(a x + b\right)} a^{4} b c^{2} d^{3} \sqrt{\frac{a x + b}{c x + d}}}{c x + d} - 3 \, a^{6} d^{4} \sqrt{\frac{a x + b}{c x + d}} + \frac{8 \, {\left(a x + b\right)} a^{5} c d^{4} \sqrt{\frac{a x + b}{c x + d}}}{c x + d} + \frac{3 \, {\left(a x + b\right)}^{2} a^{4} c^{2} d^{4} \sqrt{\frac{a x + b}{c x + d}}}{{\left(c x + d\right)}^{2}}}{{\left(a - \frac{{\left(a x + b\right)} c}{c x + d}\right)}^{3} a^{3} c^{2}}\right)}"," ",0,"1/24*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)*(3*(5*b^4*c^4 - 8*a*b^3*c^3*d + 2*a^2*b^2*c^2*d^2 + a^4*d^4)*arctan(c*sqrt((a*x + b)/(c*x + d))/sqrt(-a*c))/(sqrt(-a*c)*a^3*c^2) - (33*a^2*b^4*c^4*sqrt((a*x + b)/(c*x + d)) - 40*(a*x + b)*a*b^4*c^5*sqrt((a*x + b)/(c*x + d))/(c*x + d) + 15*(a*x + b)^2*b^4*c^6*sqrt((a*x + b)/(c*x + d))/(c*x + d)^2 - 72*a^3*b^3*c^3*d*sqrt((a*x + b)/(c*x + d)) + 64*(a*x + b)*a^2*b^3*c^4*d*sqrt((a*x + b)/(c*x + d))/(c*x + d) - 24*(a*x + b)^2*a*b^3*c^5*d*sqrt((a*x + b)/(c*x + d))/(c*x + d)^2 + 42*a^4*b^2*c^2*d^2*sqrt((a*x + b)/(c*x + d)) + 6*(a*x + b)^2*a^2*b^2*c^4*d^2*sqrt((a*x + b)/(c*x + d))/(c*x + d)^2 - 32*(a*x + b)*a^4*b*c^2*d^3*sqrt((a*x + b)/(c*x + d))/(c*x + d) - 3*a^6*d^4*sqrt((a*x + b)/(c*x + d)) + 8*(a*x + b)*a^5*c*d^4*sqrt((a*x + b)/(c*x + d))/(c*x + d) + 3*(a*x + b)^2*a^4*c^2*d^4*sqrt((a*x + b)/(c*x + d))/(c*x + d)^2)/((a - (a*x + b)*c/(c*x + d))^3*a^3*c^2))","B",0
2397,0,0,0,0.000000," ","integrate((2*a*x+b)/(a*x-b)/(a*x+2*b)/(a*x^2+b*x-1)^(1/4),x, algorithm=""giac"")","\int \frac{2 \, a x + b}{{\left(a x^{2} + b x - 1\right)}^{\frac{1}{4}} {\left(a x + 2 \, b\right)} {\left(a x - b\right)}}\,{d x}"," ",0,"integrate((2*a*x + b)/((a*x^2 + b*x - 1)^(1/4)*(a*x + 2*b)*(a*x - b)), x)","F",0
2398,0,0,0,0.000000," ","integrate((a*k*x+k*x^2-1)/(k*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{a k x + k x^{2} - 1}{{\left(k x^{2} + 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((a*k*x + k*x^2 - 1)/((k*x^2 + 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
2399,1,197,0,0.611646," ","integrate((x^3-b)*(x^3+b)/(a*x^2+x^3)^(1/3),x, algorithm=""giac"")","-\frac{10 \, \sqrt{3} {\left(728 \, a^{7} - 6561 \, a b^{2}\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{a}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - 5 \, {\left(728 \, a^{7} - 6561 \, a b^{2}\right)} \log\left({\left(\frac{a}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{a}{x} + 1\right)}^{\frac{1}{3}} + 1\right) + 10 \, {\left(728 \, a^{7} - 6561 \, a b^{2}\right)} \log\left({\left| {\left(\frac{a}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right) + \frac{3 \, {\left(7280 \, a^{7} {\left(\frac{a}{x} + 1\right)}^{\frac{17}{3}} - 41860 \, a^{7} {\left(\frac{a}{x} + 1\right)}^{\frac{14}{3}} + 99320 \, a^{7} {\left(\frac{a}{x} + 1\right)}^{\frac{11}{3}} - 123812 \, a^{7} {\left(\frac{a}{x} + 1\right)}^{\frac{8}{3}} + 84592 \, a^{7} {\left(\frac{a}{x} + 1\right)}^{\frac{5}{3}} - 29165 \, a^{7} {\left(\frac{a}{x} + 1\right)}^{\frac{2}{3}}\right)} x^{6}}{a^{6}}}{65610 \, a}"," ",0,"-1/65610*(10*sqrt(3)*(728*a^7 - 6561*a*b^2)*arctan(1/3*sqrt(3)*(2*(a/x + 1)^(1/3) + 1)) - 5*(728*a^7 - 6561*a*b^2)*log((a/x + 1)^(2/3) + (a/x + 1)^(1/3) + 1) + 10*(728*a^7 - 6561*a*b^2)*log(abs((a/x + 1)^(1/3) - 1)) + 3*(7280*a^7*(a/x + 1)^(17/3) - 41860*a^7*(a/x + 1)^(14/3) + 99320*a^7*(a/x + 1)^(11/3) - 123812*a^7*(a/x + 1)^(8/3) + 84592*a^7*(a/x + 1)^(5/3) - 29165*a^7*(a/x + 1)^(2/3))*x^6/a^6)/a","A",0
2400,0,0,0,0.000000," ","integrate(x/(-x^2+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int -\frac{x}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-x/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*(x^2 - 1)), x)","F",0
2401,-2,0,0,0.000000," ","integrate(1/(x^4-1)^(1/4)/(x^8-x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2402,-2,0,0,0.000000," ","integrate((2*x^4-1)/(x^4-1)^(1/4)/(x^8-x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2403,-2,0,0,0.000000," ","integrate(1/(x^4+1)^(1/4)/(x^8+x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2404,-2,0,0,0.000000," ","integrate((x^4-2)/(x^4+1)^(1/4)/(x^8+x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2405,1,358,0,0.665504," ","integrate((a*x^4+b*x^3)^(1/4)*(c*x^8-d)/x^8,x, algorithm=""giac"")","\frac{\frac{2088450 \, \sqrt{2} b^{3} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{2088450 \, \sqrt{2} b^{3} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{1044225 \, \sqrt{2} b^{3} c \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{1044225 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} c \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a^{2}} + \frac{2784600 \, {\left({\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} b^{3} c + 3 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a b^{3} c\right)} x^{2}}{a b^{2}} + \frac{256 \, {\left(13923 \, {\left(a + \frac{b}{x}\right)}^{\frac{25}{4}} b^{120} d - 82875 \, {\left(a + \frac{b}{x}\right)}^{\frac{21}{4}} a b^{120} d + 204750 \, {\left(a + \frac{b}{x}\right)}^{\frac{17}{4}} a^{2} b^{120} d - 267750 \, {\left(a + \frac{b}{x}\right)}^{\frac{13}{4}} a^{3} b^{120} d + 193375 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} a^{4} b^{120} d - 69615 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a^{5} b^{120} d\right)}}{b^{125}}}{22276800 \, b}"," ",0,"1/22276800*(2088450*sqrt(2)*b^3*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + 2088450*sqrt(2)*b^3*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a) + 1044225*sqrt(2)*b^3*c*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a) + 1044225*sqrt(2)*(-a)^(1/4)*b^3*c*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^2 + 2784600*((a + b/x)^(5/4)*b^3*c + 3*(a + b/x)^(1/4)*a*b^3*c)*x^2/(a*b^2) + 256*(13923*(a + b/x)^(25/4)*b^120*d - 82875*(a + b/x)^(21/4)*a*b^120*d + 204750*(a + b/x)^(17/4)*a^2*b^120*d - 267750*(a + b/x)^(13/4)*a^3*b^120*d + 193375*(a + b/x)^(9/4)*a^4*b^120*d - 69615*(a + b/x)^(5/4)*a^5*b^120*d)/b^125)/b","B",0
2406,-2,0,0,0.000000," ","integrate(x^4*(x^5+2)/(x^5+1)^(1/2)/(a*x^10-x^5-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[6]a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-31]Done","F(-2)",0
2407,-2,0,0,0.000000," ","integrate(x^4*(x^5-2)/(x^5-1)^(1/2)/(a*x^10-x^5+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[6]a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-31]Done","F(-2)",0
2408,-2,0,0,0.000000," ","integrate(x^4*(x^5+3)/(x^5+1)^(1/2)/(-1+a-(1+2*a)*x^5+a*x^10),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[6]a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-31]a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-5]Warning, choosing root of [1,0,%%%{16,[2]%%%}+%%%{-12,[1]%%%}+%%%{-2,[0]%%%},%%%{64,[2]%%%}+%%%{8,[1]%%%},%%%{64,[4]%%%}+%%%{128,[3]%%%}+%%%{112,[2]%%%}+%%%{20,[1]%%%}+%%%{1,[0]%%%}] at parameters values [-86]a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-96]Done","F(-2)",0
2409,0,0,0,0.000000," ","integrate(1/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(1/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
2410,0,0,0,0.000000," ","integrate(1/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(1/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
2411,-1,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2412,-1,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2413,0,0,0,0.000000," ","integrate(1/(-3*x^2+1)^(1/3)/(x^2-3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 3\right)} {\left(-3 \, x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 - 3)*(-3*x^2 + 1)^(1/3)), x)","F",0
2414,1,234,0,5.283599," ","integrate((-a+x)/(x^2*(-a+x))^(1/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x, algorithm=""giac"")","-\frac{\left(-\frac{1}{d}\right)^{\frac{5}{6}} \arctan\left(\frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{a} - \frac{\sqrt{3} \log\left(\sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \left(-\frac{1}{d}\right)^{\frac{1}{3}}\right)}{4 \, \left(-d^{5}\right)^{\frac{1}{6}} a} + \frac{\sqrt{3} \log\left(-\sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \left(-\frac{1}{d}\right)^{\frac{1}{3}}\right)}{4 \, \left(-d^{5}\right)^{\frac{1}{6}} a} + \frac{\arctan\left(\frac{\sqrt{3} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{2 \, \left(-d^{5}\right)^{\frac{1}{6}} a} + \frac{\arctan\left(-\frac{\sqrt{3} \left(-\frac{1}{d}\right)^{\frac{1}{6}} - 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{2 \, \left(-d^{5}\right)^{\frac{1}{6}} a}"," ",0,"-(-1/d)^(5/6)*arctan((-a/x + 1)^(1/3)/(-1/d)^(1/6))/a - 1/4*sqrt(3)*log(sqrt(3)*(-a/x + 1)^(1/3)*(-1/d)^(1/6) + (-a/x + 1)^(2/3) + (-1/d)^(1/3))/((-d^5)^(1/6)*a) + 1/4*sqrt(3)*log(-sqrt(3)*(-a/x + 1)^(1/3)*(-1/d)^(1/6) + (-a/x + 1)^(2/3) + (-1/d)^(1/3))/((-d^5)^(1/6)*a) + 1/2*arctan((sqrt(3)*(-1/d)^(1/6) + 2*(-a/x + 1)^(1/3))/(-1/d)^(1/6))/((-d^5)^(1/6)*a) + 1/2*arctan(-(sqrt(3)*(-1/d)^(1/6) - 2*(-a/x + 1)^(1/3))/(-1/d)^(1/6))/((-d^5)^(1/6)*a)","A",0
2415,0,0,0,0.000000," ","integrate((2*x^8-a*x^4+b)/(a*x^4-b)^(1/4)/(3*a*x^4+b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} + b}{{\left(3 \, a x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 + b)/((3*a*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
2416,0,0,0,0.000000," ","integrate((c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{2} + d}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((c*x^2 + d)/sqrt(a*x + sqrt(a^2*x^2 + b^2)), x)","F",0
2417,1,359,0,0.857203," ","integrate((a*x^4+b*x^3)^(1/4)*(d*x^8-c)/x^4,x, algorithm=""giac"")","\frac{\frac{131670 \, \sqrt{2} b^{7} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{131670 \, \sqrt{2} b^{7} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{65835 \, \sqrt{2} b^{7} d \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{65835 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{7} d \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{a^{6}} + \frac{24 \, {\left(7315 \, {\left(a + \frac{b}{x}\right)}^{\frac{21}{4}} b^{7} d - 40755 \, {\left(a + \frac{b}{x}\right)}^{\frac{17}{4}} a b^{7} d + 92910 \, {\left(a + \frac{b}{x}\right)}^{\frac{13}{4}} a^{2} b^{7} d - 109782 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} a^{3} b^{7} d + 69327 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a^{4} b^{7} d + 21945 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{5} b^{7} d\right)} x^{6}}{a^{5} b^{6}} + \frac{524288 \, {\left(5 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} b^{8} c - 9 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a b^{8} c\right)}}{b^{9}}}{5898240 \, b}"," ",0,"1/5898240*(131670*sqrt(2)*b^7*d*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^5) + 131670*sqrt(2)*b^7*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^5) + 65835*sqrt(2)*b^7*d*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^5) + 65835*sqrt(2)*(-a)^(1/4)*b^7*d*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^6 + 24*(7315*(a + b/x)^(21/4)*b^7*d - 40755*(a + b/x)^(17/4)*a*b^7*d + 92910*(a + b/x)^(13/4)*a^2*b^7*d - 109782*(a + b/x)^(9/4)*a^3*b^7*d + 69327*(a + b/x)^(5/4)*a^4*b^7*d + 21945*(a + b/x)^(1/4)*a^5*b^7*d)*x^6/(a^5*b^6) + 524288*(5*(a + b/x)^(9/4)*b^8*c - 9*(a + b/x)^(5/4)*a*b^8*c)/b^9)/b","B",0
2418,0,0,0,0.000000," ","integrate((a*x^2+b^2)^(5/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} + b^{2}\right)}^{\frac{5}{2}}}{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)^(5/2)/sqrt(b + sqrt(a*x^2 + b^2)), x)","F",0
2419,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2420,-1,0,0,0.000000," ","integrate((_C3*x^2-_C4)*(3*_C3*x^2+3*_C4+x)/x/((_C3*x^2+_C0*x+_C4)/(_C3*x^2+_C1*x+_C4))^(1/2)/(_C3^2*x^4+2*_C3*_C4*x^2+_C4^2-x^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2421,0,0,0,0.000000," ","integrate((x^6+1)/(x^5+x)^(1/3)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{6} + 1}{{\left(x^{6} - 1\right)} {\left(x^{5} + x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 + 1)/((x^6 - 1)*(x^5 + x)^(1/3)), x)","F",0
2422,0,0,0,0.000000," ","integrate(1/x^2/(x^8-7*x^7+16*x^6-7*x^5-20*x^4+17*x^3+11*x^2-8*x-4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{8} - 7 \, x^{7} + 16 \, x^{6} - 7 \, x^{5} - 20 \, x^{4} + 17 \, x^{3} + 11 \, x^{2} - 8 \, x - 4\right)}^{\frac{1}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^8 - 7*x^7 + 16*x^6 - 7*x^5 - 20*x^4 + 17*x^3 + 11*x^2 - 8*x - 4)^(1/3)*x^2), x)","F",0
2423,0,0,0,0.000000," ","integrate((a^8*x^8+b^8)/(a^4*x^4+b^4)^(1/2)/(a^8*x^8-b^8),x, algorithm=""giac"")","\int \frac{a^{8} x^{8} + b^{8}}{{\left(a^{8} x^{8} - b^{8}\right)} \sqrt{a^{4} x^{4} + b^{4}}}\,{d x}"," ",0,"integrate((a^8*x^8 + b^8)/((a^8*x^8 - b^8)*sqrt(a^4*x^4 + b^4)), x)","F",0
2424,1,212,0,2.179606," ","integrate((x+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x, algorithm=""giac"")","-8 \, \sqrt{\frac{1}{10} \, \sqrt{5} - \frac{1}{5}} {\left(\arctan\left(2\right) + \arctan\left(\frac{1}{2} \, \sqrt{\sqrt{5} + 1} {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)} - \frac{1}{2} \, \sqrt{\sqrt{5} - 1}\right)\right)} + 4 \, \sqrt{\frac{1}{10} \, \sqrt{5} + \frac{1}{5}} \log\left({\left| 4 \, \sqrt{5} \sqrt{10 \, \sqrt{5} + 20} + 20 \, \sqrt{5} + 40 \, \sqrt{x + \sqrt{x + 1}} - 40 \, \sqrt{x + 1} - 20 \, \sqrt{10 \, \sqrt{5} + 20} + 20 \right|}\right) - 4 \, \sqrt{\frac{1}{10} \, \sqrt{5} + \frac{1}{5}} \log\left({\left| -4 \, \sqrt{5} \sqrt{10 \, \sqrt{5} + 20} + 20 \, \sqrt{5} + 40 \, \sqrt{x + \sqrt{x + 1}} - 40 \, \sqrt{x + 1} + 20 \, \sqrt{10 \, \sqrt{5} + 20} + 20 \right|}\right) + 2 \, \sqrt{x + \sqrt{x + 1}} - 3 \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"-8*sqrt(1/10*sqrt(5) - 1/5)*(arctan(2) + arctan(1/2*sqrt(sqrt(5) + 1)*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)) - 1/2*sqrt(sqrt(5) - 1))) + 4*sqrt(1/10*sqrt(5) + 1/5)*log(abs(4*sqrt(5)*sqrt(10*sqrt(5) + 20) + 20*sqrt(5) + 40*sqrt(x + sqrt(x + 1)) - 40*sqrt(x + 1) - 20*sqrt(10*sqrt(5) + 20) + 20)) - 4*sqrt(1/10*sqrt(5) + 1/5)*log(abs(-4*sqrt(5)*sqrt(10*sqrt(5) + 20) + 20*sqrt(5) + 40*sqrt(x + sqrt(x + 1)) - 40*sqrt(x + 1) + 20*sqrt(10*sqrt(5) + 20) + 20)) + 2*sqrt(x + sqrt(x + 1)) - 3*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","B",0
2425,1,212,0,0.601253," ","integrate((x+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x, algorithm=""giac"")","-8 \, \sqrt{\frac{1}{10} \, \sqrt{5} - \frac{1}{5}} {\left(\arctan\left(2\right) + \arctan\left(\frac{1}{2} \, \sqrt{\sqrt{5} + 1} {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)} - \frac{1}{2} \, \sqrt{\sqrt{5} - 1}\right)\right)} + 4 \, \sqrt{\frac{1}{10} \, \sqrt{5} + \frac{1}{5}} \log\left({\left| 4 \, \sqrt{5} \sqrt{10 \, \sqrt{5} + 20} + 20 \, \sqrt{5} + 40 \, \sqrt{x + \sqrt{x + 1}} - 40 \, \sqrt{x + 1} - 20 \, \sqrt{10 \, \sqrt{5} + 20} + 20 \right|}\right) - 4 \, \sqrt{\frac{1}{10} \, \sqrt{5} + \frac{1}{5}} \log\left({\left| -4 \, \sqrt{5} \sqrt{10 \, \sqrt{5} + 20} + 20 \, \sqrt{5} + 40 \, \sqrt{x + \sqrt{x + 1}} - 40 \, \sqrt{x + 1} + 20 \, \sqrt{10 \, \sqrt{5} + 20} + 20 \right|}\right) + 2 \, \sqrt{x + \sqrt{x + 1}} - 3 \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"-8*sqrt(1/10*sqrt(5) - 1/5)*(arctan(2) + arctan(1/2*sqrt(sqrt(5) + 1)*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)) - 1/2*sqrt(sqrt(5) - 1))) + 4*sqrt(1/10*sqrt(5) + 1/5)*log(abs(4*sqrt(5)*sqrt(10*sqrt(5) + 20) + 20*sqrt(5) + 40*sqrt(x + sqrt(x + 1)) - 40*sqrt(x + 1) - 20*sqrt(10*sqrt(5) + 20) + 20)) - 4*sqrt(1/10*sqrt(5) + 1/5)*log(abs(-4*sqrt(5)*sqrt(10*sqrt(5) + 20) + 20*sqrt(5) + 40*sqrt(x + sqrt(x + 1)) - 40*sqrt(x + 1) + 20*sqrt(10*sqrt(5) + 20) + 20)) + 2*sqrt(x + sqrt(x + 1)) - 3*log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","B",0
2426,0,0,0,0.000000," ","integrate((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2-d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}{c x^{2} - d}\,{d x}"," ",0,"integrate((c*x^2 + d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))/(c*x^2 - d), x)","F",0
2427,0,0,0,0.000000," ","integrate((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2-d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}{c x^{2} - d}\,{d x}"," ",0,"integrate((c*x^2 + d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))/(c*x^2 - d), x)","F",0
2428,0,0,0,0.000000," ","integrate((-a/b^2+a^2*x^2/b^2)^(1/2)/x/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}}}{\sqrt{a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x} x}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2/b^2 - a/b^2)/(sqrt(a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)*x), x)","F",0
2429,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2430,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2431,0,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{x + \sqrt{x^{2} + 1}} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1), x)","F",0
2432,0,0,0,0.000000," ","integrate((2+3*x)/(3*x^2+4)^(1/3)/(9*x^2+52*x-12),x, algorithm=""giac"")","\int \frac{3 \, x + 2}{{\left(9 \, x^{2} + 52 \, x - 12\right)} {\left(3 \, x^{2} + 4\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)/((9*x^2 + 52*x - 12)*(3*x^2 + 4)^(1/3)), x)","F",0
2433,1,208,0,0.487239," ","integrate((a*x^2+b*x+c)^(5/2),x, algorithm=""giac"")","\frac{1}{1536} \, \sqrt{a x^{2} + b x + c} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, a^{2} x + 5 \, a b\right)} x + \frac{27 \, a^{5} b^{2} + 52 \, a^{6} c}{a^{5}}\right)} x + \frac{a^{4} b^{3} + 156 \, a^{5} b c}{a^{5}}\right)} x - \frac{5 \, a^{3} b^{4} - 48 \, a^{4} b^{2} c - 528 \, a^{5} c^{2}}{a^{5}}\right)} x + \frac{15 \, a^{2} b^{5} - 160 \, a^{3} b^{3} c + 528 \, a^{4} b c^{2}}{a^{5}}\right)} + \frac{5 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x + c}\right)} \sqrt{a} - b \right|}\right)}{1024 \, a^{\frac{7}{2}}}"," ",0,"1/1536*sqrt(a*x^2 + b*x + c)*(2*(4*(2*(8*(2*a^2*x + 5*a*b)*x + (27*a^5*b^2 + 52*a^6*c)/a^5)*x + (a^4*b^3 + 156*a^5*b*c)/a^5)*x - (5*a^3*b^4 - 48*a^4*b^2*c - 528*a^5*c^2)/a^5)*x + (15*a^2*b^5 - 160*a^3*b^3*c + 528*a^4*b*c^2)/a^5) + 5/1024*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x + c))*sqrt(a) - b))/a^(7/2)","A",0
2434,-2,0,0,0.000000," ","integrate((x^8-x^4+1)/x^2/(x^4-1)^(3/4)/(x^8-x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2435,0,0,0,0.000000," ","integrate((c*x^2-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} - d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}{c x^{2} + d}\,{d x}"," ",0,"integrate((c*x^2 - d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))/(c*x^2 + d), x)","F",0
2436,0,0,0,0.000000," ","integrate((c*x^2-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} - d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}{c x^{2} + d}\,{d x}"," ",0,"integrate((c*x^2 - d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))/(c*x^2 + d), x)","F",0
2437,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2438,0,0,0,0.000000," ","integrate(1/x/(3*x^2-6*x+4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 6 \, x + 4\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate(1/((3*x^2 - 6*x + 4)^(1/3)*x), x)","F",0
2439,1,461,0,2.864776," ","integrate(x^2*(a*x^4+b*x^3)^(1/4)/(a*x-b),x, algorithm=""giac"")","-\frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{4}} - \frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{4}} - \frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{2 \, a^{4}} + \frac{2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{2 \, a^{4}} + \frac{155 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{128 \, a^{4}} + \frac{155 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{128 \, a^{4}} + \frac{155 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{256 \, a^{4}} + \frac{155 \, \sqrt{2} b^{3} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{256 \, \left(-a\right)^{\frac{3}{4}} a^{3}} + \frac{{\left(101 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} b^{3} - 150 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a b^{3} + 81 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{2} b^{3}\right)} x^{3}}{96 \, a^{3} b^{3}}"," ",0,"-2^(3/4)*(-a)^(1/4)*b^3*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^4 - 2^(3/4)*(-a)^(1/4)*b^3*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^4 - 1/2*2^(3/4)*(-a)^(1/4)*b^3*log(2^(3/4)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x))/a^4 + 1/2*2^(3/4)*(-a)^(1/4)*b^3*log(-2^(3/4)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x))/a^4 + 155/128*sqrt(2)*(-a)^(1/4)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^4 + 155/128*sqrt(2)*(-a)^(1/4)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^4 + 155/256*sqrt(2)*(-a)^(1/4)*b^3*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/a^4 + 155/256*sqrt(2)*b^3*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^3) + 1/96*(101*(a + b/x)^(9/4)*b^3 - 150*(a + b/x)^(5/4)*a*b^3 + 81*(a + b/x)^(1/4)*a^2*b^3)*x^3/(a^3*b^3)","B",0
2440,0,0,0,0.000000," ","integrate((x^6-1)/(x^5+x)^(1/3)/(x^6+1),x, algorithm=""giac"")","\int \frac{x^{6} - 1}{{\left(x^{6} + 1\right)} {\left(x^{5} + x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 - 1)/((x^6 + 1)*(x^5 + x)^(1/3)), x)","F",0
2441,0,0,0,0.000000," ","integrate((a*x^8-2*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-2*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{8} - 2 \, x^{4} + b}{{\left(2 \, a x^{8} - 2 \, x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^8 - 2*x^4 + b)/((2*a*x^8 - 2*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
2442,0,0,0,0.000000," ","integrate((a*x^8-2*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-2*x^4+b),x, algorithm=""giac"")","\int \frac{a x^{8} - 2 \, x^{4} + b}{{\left(2 \, a x^{8} - 2 \, x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((a*x^8 - 2*x^4 + b)/((2*a*x^8 - 2*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
2443,0,0,0,0.000000," ","integrate((2*a*x^8+c*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-c*x^4+b),x, algorithm=""giac"")","\int \frac{2 \, a x^{8} + c x^{4} - b}{{\left(a x^{8} - c x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^8 + c*x^4 - b)/((a*x^8 - c*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
2444,0,0,0,0.000000," ","integrate((2*a*x^8+c*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-c*x^4+b),x, algorithm=""giac"")","\int \frac{2 \, a x^{8} + c x^{4} - b}{{\left(a x^{8} - c x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^8 + c*x^4 - b)/((a*x^8 - c*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
2445,1,373,0,0.670834," ","integrate((a*x^4-b*x^3)^(1/4)*(c*x^8-d)/x^4,x, algorithm=""giac"")","\frac{\frac{131670 \, \sqrt{2} b^{7} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{131670 \, \sqrt{2} b^{7} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{65835 \, \sqrt{2} b^{7} c \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{65835 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{7} c \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{a^{6}} + \frac{24 \, {\left(7315 \, {\left(a - \frac{b}{x}\right)}^{\frac{21}{4}} b^{7} c - 40755 \, {\left(a - \frac{b}{x}\right)}^{\frac{17}{4}} a b^{7} c + 92910 \, {\left(a - \frac{b}{x}\right)}^{\frac{13}{4}} a^{2} b^{7} c - 109782 \, {\left(a - \frac{b}{x}\right)}^{\frac{9}{4}} a^{3} b^{7} c + 69327 \, {\left(a - \frac{b}{x}\right)}^{\frac{5}{4}} a^{4} b^{7} c + 21945 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} a^{5} b^{7} c\right)} x^{6}}{a^{5} b^{6}} + \frac{524288 \, {\left(5 \, {\left(a - \frac{b}{x}\right)}^{\frac{9}{4}} b^{8} d - 9 \, {\left(a - \frac{b}{x}\right)}^{\frac{5}{4}} a b^{8} d\right)}}{b^{9}}}{5898240 \, b}"," ",0,"1/5898240*(131670*sqrt(2)*b^7*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^5) + 131670*sqrt(2)*b^7*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^5) + 65835*sqrt(2)*b^7*c*log(sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/((-a)^(3/4)*a^5) + 65835*sqrt(2)*(-a)^(1/4)*b^7*c*log(-sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/a^6 + 24*(7315*(a - b/x)^(21/4)*b^7*c - 40755*(a - b/x)^(17/4)*a*b^7*c + 92910*(a - b/x)^(13/4)*a^2*b^7*c - 109782*(a - b/x)^(9/4)*a^3*b^7*c + 69327*(a - b/x)^(5/4)*a^4*b^7*c + 21945*(a - b/x)^(1/4)*a^5*b^7*c)*x^6/(a^5*b^6) + 524288*(5*(a - b/x)^(9/4)*b^8*d - 9*(a - b/x)^(5/4)*a*b^8*d)/b^9)/b","B",0
2446,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/x^6, x)","F",0
2447,0,0,0,0.000000," ","integrate((b+(a*x^2+b^2)^(1/2))^(1/2)/x^6/(a*x^2+b^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b + \sqrt{a x^{2} + b^{2}}}}{\sqrt{a x^{2} + b^{2}} x^{6}}\,{d x}"," ",0,"integrate(sqrt(b + sqrt(a*x^2 + b^2))/(sqrt(a*x^2 + b^2)*x^6), x)","F",0
2448,1,444,0,2.656811," ","integrate((d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(35 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{9}{2}} - 180 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{7}{2}} d + 378 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d^{4} - 126 \, c {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{5}{2}} + 420 \, c {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} d - 630 \, c \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d^{2} + 315 \, c^{2} \sqrt{d + \sqrt{c + \sqrt{a x + b}}} + 21 \, {\left(3 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{5}{2}} - 10 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} d + 15 \, \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d^{2} - 15 \, c \sqrt{d + \sqrt{c + \sqrt{a x + b}}}\right)} c + 3 \, {\left(15 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{7}{2}} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) - 63 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{5}{2}} d \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) + 105 \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} d^{2} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) - 105 \, \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d^{3} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) - 35 \, c {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right) + 105 \, c \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d \mathrm{sgn}\left(\sqrt{c + \sqrt{a x + b}}\right)\right)} d\right)}}{315 \, a}"," ",0,"8/315*(35*(d + sqrt(c + sqrt(a*x + b)))^(9/2) - 180*(d + sqrt(c + sqrt(a*x + b)))^(7/2)*d + 378*(d + sqrt(c + sqrt(a*x + b)))^(5/2)*d^2 - 420*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*d^3 + 315*sqrt(d + sqrt(c + sqrt(a*x + b)))*d^4 - 126*c*(d + sqrt(c + sqrt(a*x + b)))^(5/2) + 420*c*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*d - 630*c*sqrt(d + sqrt(c + sqrt(a*x + b)))*d^2 + 315*c^2*sqrt(d + sqrt(c + sqrt(a*x + b))) + 21*(3*(d + sqrt(c + sqrt(a*x + b)))^(5/2) - 10*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*d + 15*sqrt(d + sqrt(c + sqrt(a*x + b)))*d^2 - 15*c*sqrt(d + sqrt(c + sqrt(a*x + b))))*c + 3*(15*(d + sqrt(c + sqrt(a*x + b)))^(7/2)*sgn(sqrt(c + sqrt(a*x + b))) - 63*(d + sqrt(c + sqrt(a*x + b)))^(5/2)*d*sgn(sqrt(c + sqrt(a*x + b))) + 105*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*d^2*sgn(sqrt(c + sqrt(a*x + b))) - 105*sqrt(d + sqrt(c + sqrt(a*x + b)))*d^3*sgn(sqrt(c + sqrt(a*x + b))) - 35*c*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*sgn(sqrt(c + sqrt(a*x + b))) + 105*c*sqrt(d + sqrt(c + sqrt(a*x + b)))*d*sgn(sqrt(c + sqrt(a*x + b))))*d)/a","B",0
2449,1,195,0,0.516540," ","integrate(1/(a*x^2-b)/(x^3-x)^(1/3),x, algorithm=""giac"")","-\frac{3 \, {\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a - b}{b}\right)^{\frac{1}{3}}}\right)}{2 \, {\left(\sqrt{3} a b^{2} - \sqrt{3} b^{3}\right)}} + \frac{{\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \log\left(\left(-\frac{a - b}{b}\right)^{\frac{2}{3}} + \left(-\frac{a - b}{b}\right)^{\frac{1}{3}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, {\left(a b^{2} - b^{3}\right)}} - \frac{\left(-\frac{a - b}{b}\right)^{\frac{2}{3}} \log\left({\left| -\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(a - b\right)}}"," ",0,"-3/2*(-a*b^2 + b^3)^(2/3)*arctan(1/3*sqrt(3)*((-(a - b)/b)^(1/3) + 2*(-1/x^2 + 1)^(1/3))/(-(a - b)/b)^(1/3))/(sqrt(3)*a*b^2 - sqrt(3)*b^3) + 1/4*(-a*b^2 + b^3)^(2/3)*log((-(a - b)/b)^(2/3) + (-(a - b)/b)^(1/3)*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3))/(a*b^2 - b^3) - 1/2*(-(a - b)/b)^(2/3)*log(abs(-(-(a - b)/b)^(1/3) + (-1/x^2 + 1)^(1/3)))/(a - b)","A",0
2450,1,968,0,61.421366," ","integrate(1/x^3/(x^3-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(\frac{1}{x} + 1\right)}^{\frac{8}{3}} + \frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{6}{5} \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{3}} - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) + \frac{3}{2} \, {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(1/x + 1)^(8/3) + 1/6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x + 1)^(1/3))) - 1/3*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/3*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/3*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/6*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 6/5*(1/x + 1)^(5/3) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x + 1)^(1/3) + (1/x + 1)^(2/3)) + 1/6*2^(2/3)*log(abs(-2^(1/3) + (1/x + 1)^(1/3))) + 3/2*(1/x + 1)^(2/3)","B",0
2451,1,968,0,60.722027," ","integrate(1/x^3/(x^3-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(\frac{1}{x} + 1\right)}^{\frac{8}{3}} + \frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{6}{5} \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{3}} - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) + \frac{3}{2} \, {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(1/x + 1)^(8/3) + 1/6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x + 1)^(1/3))) - 1/3*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/3*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/3*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/6*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 6/5*(1/x + 1)^(5/3) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x + 1)^(1/3) + (1/x + 1)^(2/3)) + 1/6*2^(2/3)*log(abs(-2^(1/3) + (1/x + 1)^(1/3))) + 3/2*(1/x + 1)^(2/3)","B",0
2452,-1,0,0,0.000000," ","integrate(1/x^6/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2453,-1,0,0,0.000000," ","integrate(1/x^6/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2454,0,0,0,0.000000," ","integrate((x^2-1)*(x^2+x+1)*(x^4+3*x^2+1)^(1/2)/(x^4+x^3+x^2+x+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 1} {\left(x^{2} + x + 1\right)} {\left(x^{2} - 1\right)}}{{\left(x^{4} + x^{3} + x^{2} + x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 1)*(x^2 + x + 1)*(x^2 - 1)/(x^4 + x^3 + x^2 + x + 1)^2, x)","F",0
2455,0,0,0,0.000000," ","integrate((a*x^4+b)/(a*x^4-b)/(a^2*x^8+c*x^4+b^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a^{2} x^{8} + c x^{4} + b^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a^2*x^8 + c*x^4 + b^2)^(1/4)*(a*x^4 - b)), x)","F",0
2456,-2,0,0,0.000000," ","integrate((-x^9+2*x^4)/(x^5-1)^(1/2)/(x^10-a*x^5+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[88]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-46]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
2457,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{2} - 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^2 - 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
2458,0,0,0,0.000000," ","integrate((c*x^2+d)/(c*x^2-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{2} + d}{{\left(c x^{2} - d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((c*x^2 + d)/((c*x^2 - d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2459,0,0,0,0.000000," ","integrate((c*x^2+d)/(c*x^2-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{2} + d}{{\left(c x^{2} - d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((c*x^2 + d)/((c*x^2 - d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2460,-1,0,0,0.000000," ","integrate(1/x^6/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2461,-1,0,0,0.000000," ","integrate(1/x^6/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2462,0,0,0,0.000000," ","integrate((p*x^2-q)*(a*p*x^2+a*q+b*x)*(p^2*x^4+q^2)^(1/2)/x^3/(c*p*x^2+c*q+d*x),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{4} + q^{2}} {\left(a p x^{2} + a q + b x\right)} {\left(p x^{2} - q\right)}}{{\left(c p x^{2} + c q + d x\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^4 + q^2)*(a*p*x^2 + a*q + b*x)*(p*x^2 - q)/((c*p*x^2 + c*q + d*x)*x^3), x)","F",0
2463,0,0,0,0.000000," ","integrate(x*(7*x^4+3)/(x^4+1)^(1/3)/(x^7+x^3-4),x, algorithm=""giac"")","\int \frac{{\left(7 \, x^{4} + 3\right)} x}{{\left(x^{7} + x^{3} - 4\right)} {\left(x^{4} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((7*x^4 + 3)*x/((x^7 + x^3 - 4)*(x^4 + 1)^(1/3)), x)","F",0
2464,0,0,0,0.000000," ","integrate((c*x^2-d)/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{2} - d}{{\left(c x^{2} + d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((c*x^2 - d)/((c*x^2 + d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2465,0,0,0,0.000000," ","integrate((c*x^2-d)/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{2} - d}{{\left(c x^{2} + d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((c*x^2 - d)/((c*x^2 + d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2466,0,0,0,0.000000," ","integrate((a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} - b x}}{\sqrt{a x^{2} + \sqrt{a^{2} x^{2} - b x} x}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 - b*x)/sqrt(a*x^2 + sqrt(a^2*x^2 - b*x)*x), x)","F",0
2467,0,0,0,0.000000," ","integrate((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(a^2+b*d-(2*a+d)*x+x^2),x, algorithm=""giac"")","\int \frac{a - 2 \, b + x}{{\left(a^{2} + b d - {\left(2 \, a + d\right)} x + x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a - 2*b + x)/((a^2 + b*d - (2*a + d)*x + x^2)*((a - x)*(b - x))^(1/3)), x)","F",0
2468,0,0,0,0.000000," ","integrate((-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(b+a^2*d-(2*a*d+1)*x+d*x^2),x, algorithm=""giac"")","\int -\frac{{\left(a - 2 \, b\right)} a + 2 \, b x - x^{2}}{{\left(a^{2} d + d x^{2} - {\left(2 \, a d + 1\right)} x + b\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-((a - 2*b)*a + 2*b*x - x^2)/((a^2*d + d*x^2 - (2*a*d + 1)*x + b)*((a - x)*(b - x))^(2/3)), x)","F",0
2469,0,0,0,0.000000," ","integrate((-1+(2-k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(b+2*k)*x+(k^2+b)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(k - 2\right)} x + 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left({\left(k^{2} + b\right)} x^{2} - {\left(b + 2 \, k\right)} x + 1\right)}}\,{d x}"," ",0,"integrate(-((k - 2)*x + 1)/(((k*x - 1)*(x - 1)*x)^(1/3)*((k^2 + b)*x^2 - (b + 2*k)*x + 1)), x)","F",0
2470,0,0,0,0.000000," ","integrate((-3*k-2*(k^2+1)*x+k*(k^2+1)*x^2+4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(2+d)*k*x-(k^2+d)*x^2+d*k*x^3),x, algorithm=""giac"")","\int \frac{k^{3} x^{4} + 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} k x^{2} - 2 \, {\left(k^{2} + 1\right)} x - 3 \, k}{{\left(d k x^{3} - {\left(d + 2\right)} k x - {\left(k^{2} + d\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^3*x^4 + 4*k^2*x^3 + (k^2 + 1)*k*x^2 - 2*(k^2 + 1)*x - 3*k)/((d*k*x^3 - (d + 2)*k*x - (k^2 + d)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2471,-2,0,0,0.000000," ","integrate((2*x^4-1)/(x^4+1)^(1/4)/(x^8+x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2472,0,0,0,0.000000," ","integrate((-2*x+(1+k)*x^2)*(a-a*(1+k)*x+(a*k+1)*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(2/3)/(k*x-1)/(b-b*(1+k)*x+(b*k-1)*x^2),x, algorithm=""giac"")","\int \frac{{\left(a {\left(k + 1\right)} x - {\left(a k + 1\right)} x^{2} - a\right)} {\left({\left(k + 1\right)} x^{2} - 2 \, x\right)}}{{\left(b {\left(k + 1\right)} x - {\left(b k - 1\right)} x^{2} - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left(k x - 1\right)} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((a*(k + 1)*x - (a*k + 1)*x^2 - a)*((k + 1)*x^2 - 2*x)/((b*(k + 1)*x - (b*k - 1)*x^2 - b)*((k*x - 1)*(x - 1)*x)^(2/3)*(k*x - 1)*(x - 1)), x)","F",0
2473,0,0,0,0.000000," ","integrate((-3*k+2*(k^2+1)*x+k*(k^2+1)*x^2-4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(2+d)*k*x+(k^2+d)*x^2+d*k*x^3),x, algorithm=""giac"")","\int \frac{k^{3} x^{4} - 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} k x^{2} + 2 \, {\left(k^{2} + 1\right)} x - 3 \, k}{{\left(d k x^{3} - {\left(d + 2\right)} k x + {\left(k^{2} + d\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^3*x^4 - 4*k^2*x^3 + (k^2 + 1)*k*x^2 + 2*(k^2 + 1)*x - 3*k)/((d*k*x^3 - (d + 2)*k*x + (k^2 + d)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2474,0,0,0,0.000000," ","integrate((x^3-x)^(1/3)*(a*x^6-b)/(c*x^6-d),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} - b\right)} {\left(x^{3} - x\right)}^{\frac{1}{3}}}{c x^{6} - d}\,{d x}"," ",0,"integrate((a*x^6 - b)*(x^3 - x)^(1/3)/(c*x^6 - d), x)","F",0
2475,0,0,0,0.000000," ","integrate((x^3-x)^(1/3)*(a*x^6-b)/(c*x^6-d),x, algorithm=""giac"")","\int \frac{{\left(a x^{6} - b\right)} {\left(x^{3} - x\right)}^{\frac{1}{3}}}{c x^{6} - d}\,{d x}"," ",0,"integrate((a*x^6 - b)*(x^3 - x)^(1/3)/(c*x^6 - d), x)","F",0
2476,-2,0,0,0.000000," ","integrate(1/(1-x*(a*x^2+b*x+c)^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
2477,0,0,0,0.000000," ","integrate((a*x^2-b)/(2*a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(2 \, a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a^3*x^3 + b^2*x^2)^(1/3)*(2*a*x^2 - b)), x)","F",0
2478,0,0,0,0.000000," ","integrate((a*x^2-b)/(2*a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(2 \, a x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a^3*x^3 + b^2*x^2)^(1/3)*(2*a*x^2 - b)), x)","F",0
2479,0,0,0,0.000000," ","integrate((a*x^2+b)/(2*a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(2 \, a x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/((a^3*x^3 + b^2*x^2)^(1/3)*(2*a*x^2 + b)), x)","F",0
2480,0,0,0,0.000000," ","integrate((a*x^2+b)/(2*a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{2} + b}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(2 \, a x^{2} + b\right)}}\,{d x}"," ",0,"integrate((a*x^2 + b)/((a^3*x^3 + b^2*x^2)^(1/3)*(2*a*x^2 + b)), x)","F",0
2481,0,0,0,0.000000," ","integrate(x*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a*b+(a+b)*x-x^2+d*x^4),x, algorithm=""giac"")","\int \frac{{\left(4 \, a b - 3 \, {\left(a + b\right)} x + 2 \, x^{2}\right)} x}{{\left(d x^{4} - a b + {\left(a + b\right)} x - x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((4*a*b - 3*(a + b)*x + 2*x^2)*x/((d*x^4 - a*b + (a + b)*x - x^2)*((a - x)*(b - x)*x^2)^(1/3)), x)","F",0
2482,0,0,0,0.000000," ","integrate((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x, algorithm=""giac"")","\int \frac{{\left(3 \, a x^{4} + 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}{{\left(a x^{8} + b\right)} x^{6}}\,{d x}"," ",0,"integrate((3*a*x^4 + 2*b)*(a*x^4 + b)^(1/4)/((a*x^8 + b)*x^6), x)","F",0
2483,0,0,0,0.000000," ","integrate((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x, algorithm=""giac"")","\int \frac{{\left(3 \, a x^{4} + 2 \, b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}{{\left(a x^{8} + b\right)} x^{6}}\,{d x}"," ",0,"integrate((3*a*x^4 + 2*b)*(a*x^4 + b)^(1/4)/((a*x^8 + b)*x^6), x)","F",0
2484,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2485,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2486,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(x^2-(1+x)^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + \sqrt{x + 1}}}{x^{2} - \sqrt{x + 1}}\,{d x}"," ",0,"integrate(sqrt(x + sqrt(x + 1))/(x^2 - sqrt(x + 1)), x)","F",0
2487,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(x^2-(1+x)^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + \sqrt{x + 1}}}{x^{2} - \sqrt{x + 1}}\,{d x}"," ",0,"integrate(sqrt(x + sqrt(x + 1))/(x^2 - sqrt(x + 1)), x)","F",0
2488,1,209,0,0.220843," ","integrate(x^2/(x^2*(-a+x))^(2/3)/(-a^2+2*a*x+(-1+d)*x^2),x, algorithm=""giac"")","-\frac{\sqrt{3} \log\left(\sqrt{3} \left(-d\right)^{\frac{1}{6}} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \left(-d\right)^{\frac{1}{3}}\right)}{4 \, a \left(-d\right)^{\frac{5}{6}}} - \frac{\sqrt{3} \left(-d\right)^{\frac{1}{6}} \log\left(-\sqrt{3} \left(-d\right)^{\frac{1}{6}} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \left(-d\right)^{\frac{1}{3}}\right)}{4 \, a d} - \frac{\arctan\left(\frac{\sqrt{3} \left(-d\right)^{\frac{1}{6}} + 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{\left(-d\right)^{\frac{1}{6}}}\right)}{2 \, a \left(-d\right)^{\frac{5}{6}}} - \frac{\arctan\left(-\frac{\sqrt{3} \left(-d\right)^{\frac{1}{6}} - 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{\left(-d\right)^{\frac{1}{6}}}\right)}{2 \, a \left(-d\right)^{\frac{5}{6}}} - \frac{\arctan\left(\frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{\left(-d\right)^{\frac{1}{6}}}\right)}{a \left(-d\right)^{\frac{5}{6}}}"," ",0,"-1/4*sqrt(3)*log(sqrt(3)*(-d)^(1/6)*(-a/x + 1)^(1/3) + (-a/x + 1)^(2/3) + (-d)^(1/3))/(a*(-d)^(5/6)) - 1/4*sqrt(3)*(-d)^(1/6)*log(-sqrt(3)*(-d)^(1/6)*(-a/x + 1)^(1/3) + (-a/x + 1)^(2/3) + (-d)^(1/3))/(a*d) - 1/2*arctan((sqrt(3)*(-d)^(1/6) + 2*(-a/x + 1)^(1/3))/(-d)^(1/6))/(a*(-d)^(5/6)) - 1/2*arctan(-(sqrt(3)*(-d)^(1/6) - 2*(-a/x + 1)^(1/3))/(-d)^(1/6))/(a*(-d)^(5/6)) - arctan((-a/x + 1)^(1/3)/(-d)^(1/6))/(a*(-d)^(5/6))","A",0
2489,0,0,0,0.000000," ","integrate((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/x/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x, algorithm=""giac"")","\int -\frac{{\left({\left(a + k\right)} x^{2} - {\left(k + 1\right)} x + 1\right)} {\left({\left(k + 1\right)} x - 2\right)}}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left({\left(b - k\right)} x^{2} + {\left(k + 1\right)} x - 1\right)} x}\,{d x}"," ",0,"integrate(-((a + k)*x^2 - (k + 1)*x + 1)*((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(2/3)*((b - k)*x^2 + (k + 1)*x - 1)*x), x)","F",0
2490,0,0,0,0.000000," ","integrate((-2*a^2*b*x+a*(3*a+2*b)*x^2-4*a*x^3+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a^2+2*a*x-(b*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int -\frac{2 \, a^{2} b x - {\left(3 \, a + 2 \, b\right)} a x^{2} + 4 \, a x^{3} - x^{4}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{2}{3}} {\left(d x^{3} - {\left(b d + 1\right)} x^{2} - a^{2} + 2 \, a x\right)}}\,{d x}"," ",0,"integrate(-(2*a^2*b*x - (3*a + 2*b)*a*x^2 + 4*a*x^3 - x^4)/(((a - x)*(b - x)*x^2)^(2/3)*(d*x^3 - (b*d + 1)*x^2 - a^2 + 2*a*x)), x)","F",0
2491,0,0,0,0.000000," ","integrate(1/(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(81 \, x^{4} - 135 \, x^{3} + 54 \, x^{2} + 12 \, x - 8\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((81*x^4 - 135*x^3 + 54*x^2 + 12*x - 8)^(-1/3), x)","F",0
2492,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-x-1)/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{6} - 1\right)}^{\frac{1}{3}} {\left(x^{2} - x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^6 - 1)^(1/3)*(x^2 - x - 1)), x)","F",0
2493,0,0,0,0.000000," ","integrate((x^2+1)/(x^2-x-1)/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{6} - 1\right)}^{\frac{1}{3}} {\left(x^{2} - x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^6 - 1)^(1/3)*(x^2 - x - 1)), x)","F",0
2494,0,0,0,0.000000," ","integrate((4*x^6+3*x^5-2*x^4+2)*(x^7+x^6-x^5+2*x^3-x)^(1/3)/(x^6+x^5-x^4+x^2-1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{7} + x^{6} - x^{5} + 2 \, x^{3} - x\right)}^{\frac{1}{3}} {\left(4 \, x^{6} + 3 \, x^{5} - 2 \, x^{4} + 2\right)}}{{\left(x^{6} + x^{5} - x^{4} + x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^7 + x^6 - x^5 + 2*x^3 - x)^(1/3)*(4*x^6 + 3*x^5 - 2*x^4 + 2)/(x^6 + x^5 - x^4 + x^2 - 1)^2, x)","F",0
2495,0,0,0,0.000000," ","integrate((-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-(1+2*b)*x+(b+k)*x^2),x, algorithm=""giac"")","\int \frac{{\left(2 \, k - 1\right)} x - 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left({\left(b + k\right)} x^{2} - {\left(2 \, b + 1\right)} x + b\right)}}\,{d x}"," ",0,"integrate(((2*k - 1)*x - 1)/(((k*x - 1)*(x - 1)*x)^(1/3)*((b + k)*x^2 - (2*b + 1)*x + b)), x)","F",0
2496,1,308,0,0.191233," ","integrate((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x^7/(a^2*x^6-b^2),x, algorithm=""giac"")","-\frac{{\left(3 \, a^{3} b - 3 \, a^{2} b^{2} - a^{2} c + a b c\right)} \arctan\left(\frac{\sqrt{a^{2} x^{3} + b^{2}}}{\sqrt{a b - b^{2}}}\right)}{3 \, \sqrt{a b - b^{2}} b^{2}} + \frac{{\left(3 \, a^{3} b + 3 \, a^{2} b^{2} + a^{2} c + a b c\right)} \arctan\left(\frac{\sqrt{a^{2} x^{3} + b^{2}}}{\sqrt{-a b - b^{2}}}\right)}{3 \, \sqrt{-a b - b^{2}} b^{2}} - \frac{{\left(a^{4} - 12 \, a^{2} b^{2} - 2 \, a^{2} c\right)} \log\left({\left| b + \sqrt{a^{2} x^{3} + b^{2}} \right|}\right)}{12 \, b^{3}} + \frac{{\left(a^{4} - 12 \, a^{2} b^{2} - 2 \, a^{2} c\right)} \log\left({\left| -b + \sqrt{a^{2} x^{3} + b^{2}} \right|}\right)}{12 \, b^{3}} + \frac{\sqrt{a^{2} x^{3} + b^{2}} a^{4} b^{2} + {\left(a^{2} x^{3} + b^{2}\right)}^{\frac{3}{2}} a^{4} - 2 \, \sqrt{a^{2} x^{3} + b^{2}} a^{2} b^{2} c + 2 \, {\left(a^{2} x^{3} + b^{2}\right)}^{\frac{3}{2}} a^{2} c}{6 \, a^{4} b^{2} x^{6}}"," ",0,"-1/3*(3*a^3*b - 3*a^2*b^2 - a^2*c + a*b*c)*arctan(sqrt(a^2*x^3 + b^2)/sqrt(a*b - b^2))/(sqrt(a*b - b^2)*b^2) + 1/3*(3*a^3*b + 3*a^2*b^2 + a^2*c + a*b*c)*arctan(sqrt(a^2*x^3 + b^2)/sqrt(-a*b - b^2))/(sqrt(-a*b - b^2)*b^2) - 1/12*(a^4 - 12*a^2*b^2 - 2*a^2*c)*log(abs(b + sqrt(a^2*x^3 + b^2)))/b^3 + 1/12*(a^4 - 12*a^2*b^2 - 2*a^2*c)*log(abs(-b + sqrt(a^2*x^3 + b^2)))/b^3 + 1/6*(sqrt(a^2*x^3 + b^2)*a^4*b^2 + (a^2*x^3 + b^2)^(3/2)*a^4 - 2*sqrt(a^2*x^3 + b^2)*a^2*b^2*c + 2*(a^2*x^3 + b^2)^(3/2)*a^2*c)/(a^4*b^2*x^6)","A",0
2497,1,399,0,0.960634," ","integrate(x^7*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(d*x^8-a^2+2*a*x-x^2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} \frac{1}{d^{5}}^{\frac{1}{6}} \arctan\left(\frac{\sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} - \sqrt{3} a d^{\frac{1}{6}} - \sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{{\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + a d^{\frac{1}{6}} - {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}\right) + \frac{1}{2} \, \sqrt{3} \frac{1}{d^{5}}^{\frac{1}{6}} \arctan\left(-\frac{\sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \sqrt{3} a d^{\frac{1}{6}} - \sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}{{\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} - a d^{\frac{1}{6}} - {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}}\right) + \frac{1}{4} \, \frac{1}{d^{5}}^{\frac{1}{6}} \log\left({\left(\sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \sqrt{3} a d^{\frac{1}{6}} - \sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}^{2} + {\left({\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} - a d^{\frac{1}{6}} - {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}^{2}\right) - \frac{1}{4} \, \frac{1}{d^{5}}^{\frac{1}{6}} \log\left({\left(\sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} - \sqrt{3} a d^{\frac{1}{6}} - \sqrt{3} {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}^{2} + {\left({\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + a d^{\frac{1}{6}} - {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}}\right)}^{2}\right) + \frac{1}{2} \, \frac{1}{d^{5}}^{\frac{1}{6}} \log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + a d^{\frac{1}{6}} - {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) - \frac{1}{2} \, \frac{1}{d^{5}}^{\frac{1}{6}} \log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} - a d^{\frac{1}{6}} - {\left(-\frac{a}{x} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"1/2*sqrt(3)*(d^(-5))^(1/6)*arctan((sqrt(3)*(-a/x + 1)^(4/3) - sqrt(3)*a*d^(1/6) - sqrt(3)*(-a/x + 1)^(1/3))/((-a/x + 1)^(4/3) + a*d^(1/6) - (-a/x + 1)^(1/3))) + 1/2*sqrt(3)*(d^(-5))^(1/6)*arctan(-(sqrt(3)*(-a/x + 1)^(4/3) + sqrt(3)*a*d^(1/6) - sqrt(3)*(-a/x + 1)^(1/3))/((-a/x + 1)^(4/3) - a*d^(1/6) - (-a/x + 1)^(1/3))) + 1/4*(d^(-5))^(1/6)*log((sqrt(3)*(-a/x + 1)^(4/3) + sqrt(3)*a*d^(1/6) - sqrt(3)*(-a/x + 1)^(1/3))^2 + ((-a/x + 1)^(4/3) - a*d^(1/6) - (-a/x + 1)^(1/3))^2) - 1/4*(d^(-5))^(1/6)*log((sqrt(3)*(-a/x + 1)^(4/3) - sqrt(3)*a*d^(1/6) - sqrt(3)*(-a/x + 1)^(1/3))^2 + ((-a/x + 1)^(4/3) + a*d^(1/6) - (-a/x + 1)^(1/3))^2) + 1/2*(d^(-5))^(1/6)*log(abs((-a/x + 1)^(4/3) + a*d^(1/6) - (-a/x + 1)^(1/3))) - 1/2*(d^(-5))^(1/6)*log(abs((-a/x + 1)^(4/3) - a*d^(1/6) - (-a/x + 1)^(1/3)))","B",0
2498,0,0,0,0.000000," ","integrate((-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-(2*b*k+1)*x+(b*k^2+1)*x^2),x, algorithm=""giac"")","\int \frac{{\left(k^{2} - 2 \, k\right)} x^{2} + 2 \, x - 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left({\left(b k^{2} + 1\right)} x^{2} - {\left(2 \, b k + 1\right)} x + b\right)}}\,{d x}"," ",0,"integrate(((k^2 - 2*k)*x^2 + 2*x - 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((b*k^2 + 1)*x^2 - (2*b*k + 1)*x + b)), x)","F",0
2499,0,0,0,0.000000," ","integrate(1/(x^3-x^2)^(1/3)/(x^4-1),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} - 1\right)} {\left(x^{3} - x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^4 - 1)*(x^3 - x^2)^(1/3)), x)","F",0
2500,0,0,0,0.000000," ","integrate(1/(x^3-x^2)^(1/3)/(x^4-1),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} - 1\right)} {\left(x^{3} - x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^4 - 1)*(x^3 - x^2)^(1/3)), x)","F",0
2501,0,0,0,0.000000," ","integrate((x^4-x^2)^(1/3)/x/(x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{2}\right)}^{\frac{1}{3}}}{{\left(x^{2} + 1\right)} x}\,{d x}"," ",0,"integrate((x^4 - x^2)^(1/3)/((x^2 + 1)*x), x)","F",0
2502,1,437,0,0.213894," ","integrate((a*x^6+b)/x^3/(a*x^3-b)/(a*x^4+b*x)^(1/4),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{3 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, a} - \frac{2^{\frac{1}{4}} {\left(a + b\right)} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, \left(-a\right)^{\frac{1}{4}} b} + \frac{2^{\frac{1}{4}} {\left(a + b\right)} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x^{3}}}\right)}{6 \, \left(-a\right)^{\frac{1}{4}} b} - \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{6 \, a b} - \frac{\sqrt{2} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} a + 2^{\frac{3}{4}} \left(-a\right)^{\frac{3}{4}} b\right)} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{6 \, a b} + \frac{4 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{4}}}{9 \, b}"," ",0,"1/3*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a + 1/3*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/a - 1/6*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a + 1/6*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(-a) + sqrt(a + b/x^3))/a - 1/6*2^(1/4)*(a + b)*log(2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/((-a)^(1/4)*b) + 1/6*2^(1/4)*(a + b)*log(-2^(3/4)*(-a)^(1/4)*(a + b/x^3)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x^3))/((-a)^(1/4)*b) - 1/6*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(a*b) - 1/6*sqrt(2)*(2^(3/4)*(-a)^(3/4)*a + 2^(3/4)*(-a)^(3/4)*b)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x^3)^(1/4))/(-a)^(1/4))/(a*b) + 4/9*(a + b/x^3)^(3/4)/b","B",0
2503,1,221,0,0.283900," ","integrate((a*x+(a*x-b)^(1/2))^(1/2)/x^2/(a*x-b)^(1/2),x, algorithm=""giac"")","\frac{2 \, a^{2} b {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{2} - a^{2} {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{3} + 2 \, a^{2} b^{2} + 5 \, a^{2} b {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)} + a^{2} b}{{\left({\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{4} + 2 \, b {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{2} + b^{2} + 4 \, b {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)} + b\right)} a b}"," ",0,"(2*a^2*b*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^2 - a^2*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^3 + 2*a^2*b^2 + 5*a^2*b*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b))) + a^2*b)/(((sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^4 + 2*b*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^2 + b^2 + 4*b*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b))) + b)*a*b)","B",0
2504,0,0,0,0.000000," ","integrate((3+x)/(x^2-1)^(1/3)/(2*x^2-x+5),x, algorithm=""giac"")","\int \frac{x + 3}{{\left(2 \, x^{2} - x + 5\right)} {\left(x^{2} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x + 3)/((2*x^2 - x + 5)*(x^2 - 1)^(1/3)), x)","F",0
2505,0,0,0,0.000000," ","integrate((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/x^2/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x, algorithm=""giac"")","\int -\frac{{\left({\left(a + k\right)} x^{2} - {\left(k + 1\right)} x + 1\right)} {\left({\left(k + 1\right)} x - 2\right)}}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left({\left(b - k\right)} x^{2} + {\left(k + 1\right)} x - 1\right)} x^{2}}\,{d x}"," ",0,"integrate(-((a + k)*x^2 - (k + 1)*x + 1)*((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(1/3)*((b - k)*x^2 + (k + 1)*x - 1)*x^2), x)","F",0
2506,0,0,0,0.000000," ","integrate((x^3-2)*(x^4+x^3+x)^(1/3)/(x^3+1)/(x^3-x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{3} - 2\right)}}{{\left(x^{3} - x^{2} + 1\right)} {\left(x^{3} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 + x^3 + x)^(1/3)*(x^3 - 2)/((x^3 - x^2 + 1)*(x^3 + 1)), x)","F",0
2507,1,174,0,2.962649," ","integrate((a*x^4+b*x^3)^(1/4)/(a*x+2*x^2-2*b),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)"," ",0,"1/2*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4)) + 1/2*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4)) + 1/4*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) - 1/4*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))","B",0
2508,1,174,0,2.942847," ","integrate((a*x^4+b*x^3)^(1/4)/(a*x+2*x^2-2*b),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)"," ",0,"1/2*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4)) + 1/2*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4)) + 1/4*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) - 1/4*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))","B",0
2509,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6-1)/x^6/(2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 - 1)*(x^3 + 1)^(2/3)/((2*x^3 - 1)*x^6), x)","F",0
2510,0,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4+b)/(a^2*x^8+c*x^4+b^2)^(1/4),x, algorithm=""giac"")","\int \frac{a x^{4} - b}{{\left(a^{2} x^{8} + c x^{4} + b^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} + b\right)}}\,{d x}"," ",0,"integrate((a*x^4 - b)/((a^2*x^8 + c*x^4 + b^2)^(1/4)*(a*x^4 + b)), x)","F",0
2511,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^2+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2512,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^2+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2513,0,0,0,0.000000," ","integrate((2+x)^2*(9*x^3-30*x^2+66*x-19)^(1/3)/(-3+2*x)^2/(x^3-6*x^2+6*x-5),x, algorithm=""giac"")","\int \frac{{\left(9 \, x^{3} - 30 \, x^{2} + 66 \, x - 19\right)}^{\frac{1}{3}} {\left(x + 2\right)}^{2}}{{\left(x^{3} - 6 \, x^{2} + 6 \, x - 5\right)} {\left(2 \, x - 3\right)}^{2}}\,{d x}"," ",0,"integrate((9*x^3 - 30*x^2 + 66*x - 19)^(1/3)*(x + 2)^2/((x^3 - 6*x^2 + 6*x - 5)*(2*x - 3)^2), x)","F",0
2514,0,0,0,0.000000," ","integrate((x^3+1)/(x^3-1)/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} + 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}\,{d x}"," ",0,"integrate((x^3 + 1)/((x^4 + x^2)^(1/3)*(x^3 - 1)), x)","F",0
2515,0,0,0,0.000000," ","integrate(x*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a*b*d+(a+b)*d*x-d*x^2+x^4),x, algorithm=""giac"")","\int \frac{{\left(4 \, a b - 3 \, {\left(a + b\right)} x + 2 \, x^{2}\right)} x}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{3}} {\left(x^{4} - a b d + {\left(a + b\right)} d x - d x^{2}\right)}}\,{d x}"," ",0,"integrate((4*a*b - 3*(a + b)*x + 2*x^2)*x/(((a - x)*(b - x)*x^2)^(1/3)*(x^4 - a*b*d + (a + b)*d*x - d*x^2)), x)","F",0
2516,0,0,0,0.000000," ","integrate((a*x^4+b)^(1/2)/(a*x^4-b),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{4} + b}}{a x^{4} - b}\,{d x}"," ",0,"integrate(sqrt(a*x^4 + b)/(a*x^4 - b), x)","F",0
2517,0,0,0,0.000000," ","integrate((x^2+1)/(x^2+x-1)/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{6} - 1\right)}^{\frac{1}{3}} {\left(x^{2} + x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^6 - 1)^(1/3)*(x^2 + x - 1)), x)","F",0
2518,0,0,0,0.000000," ","integrate((x^2+1)/(x^2+x-1)/(x^6-1)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{6} - 1\right)}^{\frac{1}{3}} {\left(x^{2} + x - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 1)/((x^6 - 1)^(1/3)*(x^2 + x - 1)), x)","F",0
2519,0,0,0,0.000000," ","integrate(x^3*(x^3-x^2)^(1/3)/(x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} x^{3}}{x^{6} + 1}\,{d x}"," ",0,"integrate((x^3 - x^2)^(1/3)*x^3/(x^6 + 1), x)","F",0
2520,0,0,0,0.000000," ","integrate((2*a*x^8-2*c*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, a x^{8} - 2 \, c x^{4} + b}{{\left(2 \, a x^{8} - c x^{4} - 2 \, b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^8 - 2*c*x^4 + b)/((2*a*x^8 - c*x^4 - 2*b)*(a*x^4 - b)^(1/4)), x)","F",0
2521,0,0,0,0.000000," ","integrate((2*a*x^8-2*c*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x, algorithm=""giac"")","\int \frac{2 \, a x^{8} - 2 \, c x^{4} + b}{{\left(2 \, a x^{8} - c x^{4} - 2 \, b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*a*x^8 - 2*c*x^4 + b)/((2*a*x^8 - c*x^4 - 2*b)*(a*x^4 - b)^(1/4)), x)","F",0
2522,1,1007,0,67.892312," ","integrate(1/x^3/(x^3+1)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(\frac{1}{x} - 1\right)}^{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + \frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{6}{5} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{3}} - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) + \frac{3}{2} \, {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(1/x - 1)^2*(-1/x + 1)^(2/3) + 1/6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) - 1/3*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/3*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/3*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(-1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/6*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3) + 1) - 6/5*(-1/x + 1)^(5/3) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) + 1/6*2^(2/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3))) + 3/2*(-1/x + 1)^(2/3)","B",0
2523,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+x^3)^(1/4)/(x^4+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}{x^{4} + x^{2} + 1}\,{d x}"," ",0,"integrate((x^4 + x^3)^(1/4)*(x^2 - 1)/(x^4 + x^2 + 1), x)","F",0
2524,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+x^3)^(1/4)/(x^4+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3}\right)}^{\frac{1}{4}} {\left(x^{2} - 1\right)}}{x^{4} + x^{2} + 1}\,{d x}"," ",0,"integrate((x^4 + x^3)^(1/4)*(x^2 - 1)/(x^4 + x^2 + 1), x)","F",0
2525,-2,0,0,0.000000," ","integrate((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[8,-70]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[24,84]Evaluation time: 2.42Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2526,-2,0,0,0.000000," ","integrate((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[8,-70]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[24,84]Evaluation time: 2.42Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2527,0,0,0,0.000000," ","integrate((a*x^2-b^2)^2/(a*x^2+b^2)^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} - b^{2}\right)}^{2}}{{\left(a x^{2} + b^{2}\right)}^{2} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 - b^2)^2/((a*x^2 + b^2)^2*sqrt(b + sqrt(a*x^2 + b^2))), x)","F",0
2528,0,0,0,0.000000," ","integrate((-2+(1+k)*x)*(a-a*(1+k)*x+(a*k+1)*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(1/3)/(k*x-1)/(b-b*(1+k)*x+(b*k-1)*x^2),x, algorithm=""giac"")","\int \frac{{\left(a {\left(k + 1\right)} x - {\left(a k + 1\right)} x^{2} - a\right)} {\left({\left(k + 1\right)} x - 2\right)}}{{\left(b {\left(k + 1\right)} x - {\left(b k - 1\right)} x^{2} - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left(k x - 1\right)} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((a*(k + 1)*x - (a*k + 1)*x^2 - a)*((k + 1)*x - 2)/((b*(k + 1)*x - (b*k - 1)*x^2 - b)*((k*x - 1)*(x - 1)*x)^(1/3)*(k*x - 1)*(x - 1)), x)","F",0
2529,0,0,0,0.000000," ","integrate((x^3+b)^3/(x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + b\right)}^{3}}{{\left(x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 + b)^3/(x^3 + a)^(1/3), x)","F",0
2530,0,0,0,0.000000," ","integrate((x^3-x^2+1)/(x^3-x^2-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} - x^{2} + 1}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^3 - x^2 + 1)/((x^3 + x^2)^(1/3)*(x^3 - x^2 - 1)), x)","F",0
2531,0,0,0,0.000000," ","integrate((x^3-x^2+1)/(x^3-x^2-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} - x^{2} + 1}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} - x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^3 - x^2 + 1)/((x^3 + x^2)^(1/3)*(x^3 - x^2 - 1)), x)","F",0
2532,0,0,0,0.000000," ","integrate((-3+(-2*k^2+1)*x+3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(2+d)*x-(d*k^2+1)*x^2+d*k^2*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} + 3 \, k^{2} x^{2} - {\left(2 \, k^{2} - 1\right)} x - 3}{{\left(d k^{2} x^{3} - {\left(d k^{2} + 1\right)} x^{2} - {\left(d + 2\right)} x + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 + 3*k^2*x^2 - (2*k^2 - 1)*x - 3)/((d*k^2*x^3 - (d*k^2 + 1)*x^2 - (d + 2)*x + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2533,0,0,0,0.000000," ","integrate(x^2/(a*x^4-b)/(a*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{a x^{4} + b} {\left(a x^{4} - b\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(a*x^4 + b)*(a*x^4 - b)), x)","F",0
2534,1,290,0,0.476065," ","integrate((-1+x)*(k*x-1)*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-2*(b*k+b)*x+(b*k^2+4*b*k+b)*x^2-2*b*k*(1+k)*x^3+(b*k^2-1)*x^4),x, algorithm=""giac"")","\frac{\sqrt{3} \left(-b^{5}\right)^{\frac{5}{6}} \log\left(\sqrt{3} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{6}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \left(-\frac{1}{b}\right)^{\frac{1}{3}}\right)}{4 \, b^{5}} - \frac{\sqrt{3} \left(-b^{5}\right)^{\frac{5}{6}} \log\left(-\sqrt{3} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{6}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \left(-\frac{1}{b}\right)^{\frac{1}{3}}\right)}{4 \, b^{5}} - \frac{\left(-b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{\sqrt{3} \left(-\frac{1}{b}\right)^{\frac{1}{6}} + 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-\frac{1}{b}\right)^{\frac{1}{6}}}\right)}{2 \, b^{5}} - \frac{\left(-b^{5}\right)^{\frac{5}{6}} \arctan\left(-\frac{\sqrt{3} \left(-\frac{1}{b}\right)^{\frac{1}{6}} - 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-\frac{1}{b}\right)^{\frac{1}{6}}}\right)}{2 \, b^{5}} - \frac{\left(-b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{{\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-\frac{1}{b}\right)^{\frac{1}{6}}}\right)}{b^{5}}"," ",0,"1/4*sqrt(3)*(-b^5)^(5/6)*log(sqrt(3)*(k - k/x - 1/x + 1/x^2)^(1/3)*(-1/b)^(1/6) + (k - k/x - 1/x + 1/x^2)^(2/3) + (-1/b)^(1/3))/b^5 - 1/4*sqrt(3)*(-b^5)^(5/6)*log(-sqrt(3)*(k - k/x - 1/x + 1/x^2)^(1/3)*(-1/b)^(1/6) + (k - k/x - 1/x + 1/x^2)^(2/3) + (-1/b)^(1/3))/b^5 - 1/2*(-b^5)^(5/6)*arctan((sqrt(3)*(-1/b)^(1/6) + 2*(k - k/x - 1/x + 1/x^2)^(1/3))/(-1/b)^(1/6))/b^5 - 1/2*(-b^5)^(5/6)*arctan(-(sqrt(3)*(-1/b)^(1/6) - 2*(k - k/x - 1/x + 1/x^2)^(1/3))/(-1/b)^(1/6))/b^5 - (-b^5)^(5/6)*arctan((k - k/x - 1/x + 1/x^2)^(1/3)/(-1/b)^(1/6))/b^5","A",0
2535,1,2516,0,1.136363," ","integrate((f*x^2-g)*(c+(a*x+b)^(1/2))^(1/2)/(d*x^2+e),x, algorithm=""giac"")","\frac{4 \, {\left(3 \, a^{4} {\left(c + \sqrt{a x + b}\right)}^{\frac{5}{2}} d^{4} f - 5 \, a^{4} {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}} c d^{4} f\right)}}{15 \, a^{5} d^{5}} + \frac{\frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} + \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} + \frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}} + \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}}}{2 \, a^{6} d^{5}}"," ",0,"4/15*(3*a^4*(c + sqrt(a*x + b))^(5/2)*d^4*f - 5*a^4*(c + sqrt(a*x + b))^(3/2)*c*d^4*f)/(a^5*d^5) + 1/2*((a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d)))/((c + sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d))) - (a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d)))/((c + sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d))) + (a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d)))/((c - sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d))) - (a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d)))/((c - sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d))) + (a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d)))/((c + sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d))) - (a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d)))/((c + sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d))) + (a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d)))/((c - sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d))) - (a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d)))/((c - sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d))))/(a^6*d^5)","B",0
2536,0,0,0,0.000000," ","integrate((a^2*x^2+b^2)^(1/2)/(d+c*x^2+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} + b^{2}}}{c x^{2} + d + \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + b^2)/(c*x^2 + d + sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2537,0,0,0,0.000000," ","integrate((a^2*x^2+b^2)^(1/2)/(d+c*x^2+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} + b^{2}}}{c x^{2} + d + \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + b^2)/(c*x^2 + d + sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2538,0,0,0,0.000000," ","integrate((1-(1-(1-1/x)^(1/2))^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-\sqrt{-\sqrt{-\frac{1}{x} + 1} + 1} + 1}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-sqrt(-sqrt(-1/x + 1) + 1) + 1)/x^2, x)","F",0
2539,0,0,0,0.000000," ","integrate((x^4+x^2)^(1/3)/x/(x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}}}{{\left(x^{2} - 1\right)} x}\,{d x}"," ",0,"integrate((x^4 + x^2)^(1/3)/((x^2 - 1)*x), x)","F",0
2540,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a^2*x^2+b)^(1/2)/(a*x-(a^2*x^2+b)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a^{2} x^{2} + b} \sqrt{a x - \sqrt{a^{2} x^{2} + b}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*x^2 + b)*sqrt(a*x - sqrt(a^2*x^2 + b))*(d*x + c)), x)","F",0
2541,-2,0,0,0.000000," ","integrate((1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)/x^2/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1]%%%}+%%%{-4,[0]%%%},%%%{-4,[1]%%%}+%%%{-4,[0]%%%},%%%{1,[2]%%%}+%%%{-1,[1]%%%}+%%%{-1,[0]%%%}] at parameters values [60]Warning, choosing root of [1,0,%%%{-2,[1]%%%}+%%%{-4,[0]%%%},%%%{-4,[1]%%%}+%%%{-4,[0]%%%},%%%{1,[2]%%%}+%%%{-1,[1]%%%}+%%%{-1,[0]%%%}] at parameters values [-9]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [x]=[44]4*(-1/8*ln(sqrt(sqrt(sqrt(x+1)+1)+1)-1)+1/8*ln(sqrt(sqrt(sqrt(x+1)+1)+1)+1)+sqrt(25*sqrt(2)-17)/32*ln(abs(sqrt(sqrt(sqrt(x+1)+1)+1)-sqrt((16+16*sqrt(2))/2/8)))-sqrt(25*sqrt(2)-17)/32*ln(sqrt(sqrt(sqrt(x+1)+1)+1)+sqrt((16+16*sqrt(2))/2/8))-sqrt(25*sqrt(2)+17)/16*atan(sqrt(sqrt(sqrt(x+1)+1)+1)/sqrt(-(16-16*sqrt(2))/2/8))+(-sqrt(sqrt(sqrt(x+1)+1)+1)*(sqrt(sqrt(x+1)+1)+1)^2+5*sqrt(sqrt(sqrt(x+1)+1)+1))/8/((sqrt(sqrt(x+1)+1)+1)^3-3*(sqrt(sqrt(x+1)+1)+1)^2+sqrt(sqrt(x+1)+1)+2))","F(-2)",0
2542,0,0,0,0.000000," ","integrate((-1+(2-k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-(2*b*k+1)*x+(b*k^2+1)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(k - 2\right)} x + 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left({\left(b k^{2} + 1\right)} x^{2} - {\left(2 \, b k + 1\right)} x + b\right)}}\,{d x}"," ",0,"integrate(-((k - 2)*x + 1)/(((k*x - 1)*(x - 1)*x)^(1/3)*((b*k^2 + 1)*x^2 - (2*b*k + 1)*x + b)), x)","F",0
2543,1,986,0,68.494185," ","integrate(1/x^6/(x^3-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{17} \, {\left(\frac{1}{x} + 1\right)}^{\frac{17}{3}} - \frac{15}{14} \, {\left(\frac{1}{x} + 1\right)}^{\frac{14}{3}} + \frac{30}{11} \, {\left(\frac{1}{x} + 1\right)}^{\frac{11}{3}} - \frac{27}{8} \, {\left(\frac{1}{x} + 1\right)}^{\frac{8}{3}} + \frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{9}{5} \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{3}} - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"3/17*(1/x + 1)^(17/3) - 15/14*(1/x + 1)^(14/3) + 30/11*(1/x + 1)^(11/3) - 27/8*(1/x + 1)^(8/3) + 1/6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x + 1)^(1/3))) - 1/3*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/3*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/3*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/6*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) + 9/5*(1/x + 1)^(5/3) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x + 1)^(1/3) + (1/x + 1)^(2/3)) + 1/6*2^(2/3)*log(abs(-2^(1/3) + (1/x + 1)^(1/3)))","B",0
2544,1,986,0,69.053905," ","integrate(1/x^6/(x^3-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{17} \, {\left(\frac{1}{x} + 1\right)}^{\frac{17}{3}} - \frac{15}{14} \, {\left(\frac{1}{x} + 1\right)}^{\frac{14}{3}} + \frac{30}{11} \, {\left(\frac{1}{x} + 1\right)}^{\frac{11}{3}} - \frac{27}{8} \, {\left(\frac{1}{x} + 1\right)}^{\frac{8}{3}} + \frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{3} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + 1\right) + \frac{9}{5} \, {\left(\frac{1}{x} + 1\right)}^{\frac{5}{3}} - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right)"," ",0,"3/17*(1/x + 1)^(17/3) - 15/14*(1/x + 1)^(14/3) + 30/11*(1/x + 1)^(11/3) - 27/8*(1/x + 1)^(8/3) + 1/6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x + 1)^(1/3))) - 1/3*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/3*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/3*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/6*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) - 1/6*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x + 1)^(1/3) + (1/x + 1)^(2/3) + 1) + 9/5*(1/x + 1)^(5/3) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x + 1)^(1/3) + (1/x + 1)^(2/3)) + 1/6*2^(2/3)*log(abs(-2^(1/3) + (1/x + 1)^(1/3)))","B",0
2545,0,0,0,0.000000," ","integrate((3+(-2*k^2+1)*x-3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(2+d)*x+(d*k^2+1)*x^2+d*k^2*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} - 3 \, k^{2} x^{2} - {\left(2 \, k^{2} - 1\right)} x + 3}{{\left(d k^{2} x^{3} + {\left(d k^{2} + 1\right)} x^{2} - {\left(d + 2\right)} x - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 - 3*k^2*x^2 - (2*k^2 - 1)*x + 3)/((d*k^2*x^3 + (d*k^2 + 1)*x^2 - (d + 2)*x - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2546,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^6-4*x^3+8)/x^6/(x^3+2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 4 \, x^{3} + 8\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(x^{3} + 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 4*x^3 + 8)*(x^3 + 1)^(2/3)/((x^3 + 2)*x^6), x)","F",0
2547,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+2*x^3+8)/x^6/(x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 2 \, x^{3} + 8\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 2*x^3 + 8)*(x^3 - 1)^(2/3)/((x^3 - 2)*x^6), x)","F",0
2548,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(c*x^4+b*x^2*(p*x^3+q)+a*(p*x^3+q)^2)/x^9,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(c x^{4} + {\left(p x^{3} + q\right)} b x^{2} + {\left(p x^{3} + q\right)}^{2} a\right)} {\left(p x^{3} - 2 \, q\right)}}{x^{9}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(c*x^4 + (p*x^3 + q)*b*x^2 + (p*x^3 + q)^2*a)*(p*x^3 - 2*q)/x^9, x)","F",0
2549,1,195,0,0.310642," ","integrate((a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{3} {\left(9 \, a^{5} b^{3} - 2 \, b^{6}\right)} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, a}\right)}{a^{6}} - \frac{{\left(9 \, a^{5} b^{3} - 2 \, b^{6}\right)} \log\left(a^{2} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{a^{6}} + \frac{2 \, {\left(9 \, a^{5} b^{3} - 2 \, b^{6}\right)} \log\left({\left| -a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{a^{6}} + \frac{3 \, {\left(7 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}} a^{3} b^{6} - 4 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{5}{3}} b^{6}\right)} x^{2}}{a^{5} b^{4}}}{18 \, b^{2}}"," ",0,"1/18*(2*sqrt(3)*(9*a^5*b^3 - 2*b^6)*arctan(1/3*sqrt(3)*(a + 2*(a^3 + b^2/x)^(1/3))/a)/a^6 - (9*a^5*b^3 - 2*b^6)*log(a^2 + (a^3 + b^2/x)^(1/3)*a + (a^3 + b^2/x)^(2/3))/a^6 + 2*(9*a^5*b^3 - 2*b^6)*log(abs(-a + (a^3 + b^2/x)^(1/3)))/a^6 + 3*(7*(a^3 + b^2/x)^(2/3)*a^3*b^6 - 4*(a^3 + b^2/x)^(5/3)*b^6)*x^2/(a^5*b^4))/b^2","A",0
2550,1,195,0,0.286759," ","integrate((a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{3} {\left(9 \, a^{5} b^{3} + 2 \, b^{6}\right)} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, a}\right)}{a^{6}} - \frac{{\left(9 \, a^{5} b^{3} + 2 \, b^{6}\right)} \log\left(a^{2} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{a^{6}} + \frac{2 \, {\left(9 \, a^{5} b^{3} + 2 \, b^{6}\right)} \log\left({\left| -a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{a^{6}} - \frac{3 \, {\left(7 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}} a^{3} b^{6} - 4 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{5}{3}} b^{6}\right)} x^{2}}{a^{5} b^{4}}}{18 \, b^{2}}"," ",0,"-1/18*(2*sqrt(3)*(9*a^5*b^3 + 2*b^6)*arctan(1/3*sqrt(3)*(a + 2*(a^3 + b^2/x)^(1/3))/a)/a^6 - (9*a^5*b^3 + 2*b^6)*log(a^2 + (a^3 + b^2/x)^(1/3)*a + (a^3 + b^2/x)^(2/3))/a^6 + 2*(9*a^5*b^3 + 2*b^6)*log(abs(-a + (a^3 + b^2/x)^(1/3)))/a^6 - 3*(7*(a^3 + b^2/x)^(2/3)*a^3*b^6 - 4*(a^3 + b^2/x)^(5/3)*b^6)*x^2/(a^5*b^4))/b^2","A",0
2551,0,0,0,0.000000," ","integrate((-a^2*b+4*a*b*x-(2*a+3*b)*x^2+2*x^3)/(x*(-a+x)^2*(-b+x)^3)^(1/4)/(b+(a^2*d-1)*x-2*a*d*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{a^{2} b - 4 \, a b x + {\left(2 \, a + 3 \, b\right)} x^{2} - 2 \, x^{3}}{\left(-{\left(a - x\right)}^{2} {\left(b - x\right)}^{3} x\right)^{\frac{1}{4}} {\left(2 \, a d x^{2} - d x^{3} - {\left(a^{2} d - 1\right)} x - b\right)}}\,{d x}"," ",0,"integrate((a^2*b - 4*a*b*x + (2*a + 3*b)*x^2 - 2*x^3)/((-(a - x)^2*(b - x)^3*x)^(1/4)*(2*a*d*x^2 - d*x^3 - (a^2*d - 1)*x - b)), x)","F",0
2552,0,0,0,0.000000," ","integrate((a*x^2+b)*(a*x^4+b*x^3)^(1/4)/x^2/(a*x^2-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{3}\right)}^{\frac{1}{4}} {\left(a x^{2} + b\right)}}{{\left(a x^{2} - b\right)} x^{2}}\,{d x}"," ",0,"integrate((a*x^4 + b*x^3)^(1/4)*(a*x^2 + b)/((a*x^2 - b)*x^2), x)","F",0
2553,0,0,0,0.000000," ","integrate((a*b^3-(6*a-b)*b^2*x+9*a*b*x^2-(4*a+3*b)*x^3+2*x^4)/(x*(-a+x)^2*(-b+x)^3)^(1/4)/(-a^2+(-b^3*d+2*a)*x+(3*b^2*d-1)*x^2-3*b*d*x^3+d*x^4),x, algorithm=""giac"")","\int -\frac{a b^{3} - {\left(6 \, a - b\right)} b^{2} x + 9 \, a b x^{2} - {\left(4 \, a + 3 \, b\right)} x^{3} + 2 \, x^{4}}{\left(-{\left(a - x\right)}^{2} {\left(b - x\right)}^{3} x\right)^{\frac{1}{4}} {\left(3 \, b d x^{3} - d x^{4} - {\left(3 \, b^{2} d - 1\right)} x^{2} + a^{2} + {\left(b^{3} d - 2 \, a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b^3 - (6*a - b)*b^2*x + 9*a*b*x^2 - (4*a + 3*b)*x^3 + 2*x^4)/((-(a - x)^2*(b - x)^3*x)^(1/4)*(3*b*d*x^3 - d*x^4 - (3*b^2*d - 1)*x^2 + a^2 + (b^3*d - 2*a)*x)), x)","F",0
2554,0,0,0,0.000000," ","integrate((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{8} + c x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}{{\left(2 \, a x^{8} + b\right)} x^{6}}\,{d x}"," ",0,"integrate((a*x^8 + c*x^4 + b)*(a*x^4 - b)^(1/4)/((2*a*x^8 + b)*x^6), x)","F",0
2555,0,0,0,0.000000," ","integrate((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{8} + c x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}{{\left(2 \, a x^{8} + b\right)} x^{6}}\,{d x}"," ",0,"integrate((a*x^8 + c*x^4 + b)*(a*x^4 - b)^(1/4)/((2*a*x^8 + b)*x^6), x)","F",0
2556,0,0,0,0.000000," ","integrate(1/(c*x+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}} {\left(c x + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*x + sqrt(a^2*x^2 + b^2))*(c*x + d)), x)","F",0
2557,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*q*x+c*x^2+b*p*x^4+a*(p*x^3+q)^2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left(b p x^{4} + {\left(p x^{3} + q\right)}^{2} a + b q x + c x^{2}\right)} {\left(2 \, p x^{3} - q\right)}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 + 2*p*q*x^3 - 2*p*q*x^2 + q^2)*(b*p*x^4 + (p*x^3 + q)^2*a + b*q*x + c*x^2)*(2*p*x^3 - q)/x^5, x)","F",0
2558,0,0,0,0.000000," ","integrate((-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(a^2+b*d-(2*a+d)*x+x^2),x, algorithm=""giac"")","\int -\frac{{\left(a - 2 \, b\right)} a + 2 \, b x - x^{2}}{{\left(a^{2} + b d - {\left(2 \, a + d\right)} x + x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-((a - 2*b)*a + 2*b*x - x^2)/((a^2 + b*d - (2*a + d)*x + x^2)*((a - x)*(b - x))^(2/3)), x)","F",0
2559,0,0,0,0.000000," ","integrate((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(b+a^2*d+(-2*a*d-1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a - 2 \, b + x}{{\left(a^{2} d + d x^{2} - {\left(2 \, a d + 1\right)} x + b\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a - 2*b + x)/((a^2*d + d*x^2 - (2*a*d + 1)*x + b)*((a - x)*(b - x))^(1/3)), x)","F",0
2560,0,0,0,0.000000," ","integrate((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(b+a^2*d-(2*a*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a - 2 \, b + x}{{\left(a^{2} d + d x^{2} - {\left(2 \, a d + 1\right)} x + b\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a - 2*b + x)/((a^2*d + d*x^2 - (2*a*d + 1)*x + b)*((a - x)*(b - x))^(1/3)), x)","F",0
2561,0,0,0,0.000000," ","integrate((-1+2*k*x+(1-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-(1+2*b)*x+(b+k)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, k - 1\right)} x^{2} - 2 \, k x + 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left({\left(b + k\right)} x^{2} - {\left(2 \, b + 1\right)} x + b\right)}}\,{d x}"," ",0,"integrate(-((2*k - 1)*x^2 - 2*k*x + 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((b + k)*x^2 - (2*b + 1)*x + b)), x)","F",0
2562,1,147,0,0.246943," ","integrate((-1+x)/(1+x)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{2} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) - \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) - 1/2*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) + 2^(2/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3))) - sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
2563,0,0,0,0.000000," ","integrate((x^6+x^3+x-1)^(2/3)*(3*x^6-2*x+3)/(x^6+x-1)/(x^6-x^3+x-1),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{6} - 2 \, x + 3\right)} {\left(x^{6} + x^{3} + x - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - x^{3} + x - 1\right)} {\left(x^{6} + x - 1\right)}}\,{d x}"," ",0,"integrate((3*x^6 - 2*x + 3)*(x^6 + x^3 + x - 1)^(2/3)/((x^6 - x^3 + x - 1)*(x^6 + x - 1)), x)","F",0
2564,-2,0,0,0.000000," ","integrate((2*x^8-2*x^4-1)/(x^4-1)^(1/4)/(x^8-x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2565,-2,0,0,0.000000," ","integrate((2*x^8+2*x^4-1)/(x^4+1)^(1/4)/(x^8+x^4-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to convert to real 1/4 Error: Bad Argument ValueUnable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2566,0,0,0,0.000000," ","integrate((-a*b+(2*a-b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^2+(-b*d+2*a)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{a b - {\left(2 \, a - b\right)} x}{\left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{3}} {\left({\left(d - 1\right)} x^{2} - a^{2} - {\left(b d - 2 \, a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b - (2*a - b)*x)/(((a - x)*(b - x)*x)^(1/3)*((d - 1)*x^2 - a^2 - (b*d - 2*a)*x)), x)","F",0
2567,-2,0,0,0.000000," ","integrate((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{4,[0,1,4,1,0]%%%}+%%%{-1,[0,1,0,0,1]%%%} / %%%{8,[0,0,0,1,0]%%%} Error: Bad Argument Value","F(-2)",0
2568,-2,0,0,0.000000," ","integrate((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{4,[0,1,4,1,0]%%%}+%%%{-1,[0,1,0,0,1]%%%} / %%%{8,[0,0,0,1,0]%%%} Error: Bad Argument Value","F(-2)",0
2569,1,149,0,0.323040," ","integrate(x/(1+x)/(x^3-x^2)^(1/3),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{4} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{2} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) - \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/2*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) - 1/4*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) + 1/2*2^(2/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3))) - sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
2570,1,148,0,0.213851," ","integrate((x^3-x^2)^(1/3)/(x^2-1),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) + \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{4} \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{2} \cdot 2^{\frac{1}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) + \frac{1}{2} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/2*sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) + sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) - 1/4*2^(1/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) + 1/2*2^(1/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3))) + 1/2*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - log(abs((-1/x + 1)^(1/3) - 1))","A",0
2571,-2,0,0,0.000000," ","integrate(x^2*(a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,x]=[0,-68,-97]Precision problem choosing root in common_EXT, current precision 14Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,x]=[-67,8,-61]schur row 3 -1.00112e-08Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[24,49,-35]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[20,8,5]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[3,-23,44]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-92,-93,-41]schur row 3 -1.33253e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[93,-2,-73]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[40,96,-96]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-24,-84,-66]schur row 3 -9.75014e-10Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[66,44,-64]schur row 3 3.13659e-08Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-95,-41,-48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[1,69,4]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[99,-63,-95]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[81,83,-9]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-89,27,4]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[56,75,-77]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[37,-64,-25]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-98,-33,59]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[92,64,-69]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[21,-17,-9]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-4,96,-65]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-85,-1,-30]schur row 3 -5.59763e-10Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-75,7,-7]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-4,-6,-56]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-5,-69,82]schur row 3 1.56409e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-71,32,48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[73,53,-20]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[16,51,70]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-53,-39,82]schur row 3 -6.64448e-11Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-15,91,-72]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[74,86,-86]schur row 1 6.32223e-07Francis algorithm not precise enough for[1.0,0.0,-599084431612,-1.19816667401e+12,8.97248832883e+22]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-28,72,-21]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[64,-73,13]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-74,31,29]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[95,-80,-59]schur row 3 7.64423e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-12,53,99]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[69,-96,-89]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[26,-78,-6]Unable to divide, perhaps due to rounding error%%%{%%%{%%{[-2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueUnable to divide, perhaps due to rounding error%%%{%%%{%%{[2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueEvaluation time: 10.71integrate((4*a^2*x^6*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)-2*a^2*x^6-4*a*x^4*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)+4*b*x^2*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)-2*b*x^2+x^2*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)+2*x^2*(a^2*x^4+b))/(4*a^2*x^4-4*a*x^2+4*b+1),x)","F(-2)",0
2572,0,0,0,0.000000," ","integrate((a^2*x^2-b*x)^(3/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} - b x\right)}^{\frac{3}{2}}}{{\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a^2*x^2 - b*x)^(3/2)/(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2), x)","F",0
2573,0,0,0,0.000000," ","integrate((-3*k+(k^2-2)*x+3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(2+d)*k*x-(k^2+d)*x^2+d*k*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} + 3 \, k x^{2} + {\left(k^{2} - 2\right)} x - 3 \, k}{{\left(d k x^{3} - {\left(d + 2\right)} k x - {\left(k^{2} + d\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 + 3*k*x^2 + (k^2 - 2)*x - 3*k)/((d*k*x^3 - (d + 2)*k*x - (k^2 + d)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2574,1,386,0,0.212724," ","integrate((b*x+a)/x/(c*x-d)/(x^4-x^3)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a c + b d\right)} \log\left(-\sqrt{2} \left(\frac{c - d}{d}\right)^{\frac{1}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{c - d}{d}} + \sqrt{-\frac{1}{x} + 1}\right)}{2 \, {\left(c d^{3} - d^{4}\right)}^{\frac{1}{4}} d} - \frac{{\left(\sqrt{2} {\left(c d^{3} - d^{4}\right)}^{\frac{3}{4}} a c + \sqrt{2} {\left(c d^{3} - d^{4}\right)}^{\frac{3}{4}} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c - d}{d}\right)^{\frac{1}{4}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c - d}{d}\right)^{\frac{1}{4}}}\right)}{c d^{4} - d^{5}} - \frac{{\left(\sqrt{2} {\left(c d^{3} - d^{4}\right)}^{\frac{3}{4}} a c + \sqrt{2} {\left(c d^{3} - d^{4}\right)}^{\frac{3}{4}} b d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c - d}{d}\right)^{\frac{1}{4}} - 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c - d}{d}\right)^{\frac{1}{4}}}\right)}{c d^{4} - d^{5}} + \frac{{\left({\left(c d^{3} - d^{4}\right)}^{\frac{3}{4}} a c + {\left(c d^{3} - d^{4}\right)}^{\frac{3}{4}} b d\right)} \log\left(\sqrt{2} \left(\frac{c - d}{d}\right)^{\frac{1}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{c - d}{d}} + \sqrt{-\frac{1}{x} + 1}\right)}{\sqrt{2} c d^{4} - \sqrt{2} d^{5}} + \frac{4 \, a {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{4}}}{3 \, d}"," ",0,"-1/2*sqrt(2)*(a*c + b*d)*log(-sqrt(2)*((c - d)/d)^(1/4)*(-1/x + 1)^(1/4) + sqrt((c - d)/d) + sqrt(-1/x + 1))/((c*d^3 - d^4)^(1/4)*d) - (sqrt(2)*(c*d^3 - d^4)^(3/4)*a*c + sqrt(2)*(c*d^3 - d^4)^(3/4)*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*((c - d)/d)^(1/4) + 2*(-1/x + 1)^(1/4))/((c - d)/d)^(1/4))/(c*d^4 - d^5) - (sqrt(2)*(c*d^3 - d^4)^(3/4)*a*c + sqrt(2)*(c*d^3 - d^4)^(3/4)*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*((c - d)/d)^(1/4) - 2*(-1/x + 1)^(1/4))/((c - d)/d)^(1/4))/(c*d^4 - d^5) + ((c*d^3 - d^4)^(3/4)*a*c + (c*d^3 - d^4)^(3/4)*b*d)*log(sqrt(2)*((c - d)/d)^(1/4)*(-1/x + 1)^(1/4) + sqrt((c - d)/d) + sqrt(-1/x + 1))/(sqrt(2)*c*d^4 - sqrt(2)*d^5) + 4/3*a*(-1/x + 1)^(3/4)/d","B",0
2575,0,0,0,0.000000," ","integrate((-4+3*x)*((b*x^4+a*x-a)/(d*x^4+c*x-c))^(1/4)/(-1+x)/x,x, algorithm=""giac"")","\int \frac{{\left(3 \, x - 4\right)} \left(\frac{b x^{4} + a x - a}{d x^{4} + c x - c}\right)^{\frac{1}{4}}}{{\left(x - 1\right)} x}\,{d x}"," ",0,"integrate((3*x - 4)*((b*x^4 + a*x - a)/(d*x^4 + c*x - c))^(1/4)/((x - 1)*x), x)","F",0
2576,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(2*x^6-2*x^3+1)/x^6/(2*x^6-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(2 \, x^{6} - 2 \, x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} - x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((2*x^6 - 2*x^3 + 1)*(x^3 + 1)^(2/3)/((2*x^6 - x^3 - 1)*x^6), x)","F",0
2577,0,0,0,0.000000," ","integrate(2/(3+x)/(8*x^2-8*x+2)^(2/3),x, algorithm=""giac"")","\int \frac{2}{{\left(8 \, x^{2} - 8 \, x + 2\right)}^{\frac{2}{3}} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(2/((8*x^2 - 8*x + 2)^(2/3)*(x + 3)), x)","F",0
2578,0,0,0,0.000000," ","integrate((1-(-3+2*k)*x-(4+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(5+b)*x-(b*k+10)*x^2+10*x^3-5*x^4+x^5),x, algorithm=""giac"")","\int \frac{3 \, k x^{3} - {\left(k + 4\right)} x^{2} - {\left(2 \, k - 3\right)} x + 1}{{\left(x^{5} - 5 \, x^{4} - {\left(b k + 10\right)} x^{2} + 10 \, x^{3} + {\left(b + 5\right)} x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*k*x^3 - (k + 4)*x^2 - (2*k - 3)*x + 1)/((x^5 - 5*x^4 - (b*k + 10)*x^2 + 10*x^3 + (b + 5)*x - 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2579,0,0,0,0.000000," ","integrate(1/x/((1+x)*(2*q*x+x^2+q))^(1/3),x, algorithm=""giac"")","\int \frac{1}{\left({\left(2 \, q x + x^{2} + q\right)} {\left(x + 1\right)}\right)^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate(1/(((2*q*x + x^2 + q)*(x + 1))^(1/3)*x), x)","F",0
2580,0,0,0,0.000000," ","integrate((-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(b+2*k)*x+(k^2+b)*x^2),x, algorithm=""giac"")","\int \frac{{\left(k^{2} - 2 \, k\right)} x^{2} + 2 \, x - 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left({\left(k^{2} + b\right)} x^{2} - {\left(b + 2 \, k\right)} x + 1\right)}}\,{d x}"," ",0,"integrate(((k^2 - 2*k)*x^2 + 2*x - 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((k^2 + b)*x^2 - (b + 2*k)*x + 1)), x)","F",0
2581,0,0,0,0.000000," ","integrate((3*k+(k^2-2)*x-3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(2+d)*k*x+(k^2+d)*x^2+d*k*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} - 3 \, k x^{2} + {\left(k^{2} - 2\right)} x + 3 \, k}{{\left(d k x^{3} - {\left(d + 2\right)} k x + {\left(k^{2} + d\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 - 3*k*x^2 + (k^2 - 2)*x + 3*k)/((d*k*x^3 - (d + 2)*k*x + (k^2 + d)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2582,0,0,0,0.000000," ","integrate((3+2*(k^2+1)*x-(k^2+1)*x^2-4*k^2*x^3-k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(1+2*d)*x-(k^2+d)*x^2+k^2*x^3),x, algorithm=""giac"")","\int -\frac{k^{2} x^{4} + 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} x^{2} - 2 \, {\left(k^{2} + 1\right)} x - 3}{{\left(k^{2} x^{3} - {\left(k^{2} + d\right)} x^{2} - {\left(2 \, d + 1\right)} x - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-(k^2*x^4 + 4*k^2*x^3 + (k^2 + 1)*x^2 - 2*(k^2 + 1)*x - 3)/((k^2*x^3 - (k^2 + d)*x^2 - (2*d + 1)*x - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2583,1,250,0,0.649100," ","integrate((((-1+x)/(1+2*x))^(1/4)-3*((-1+x)/(1+2*x))^(3/4))/(-1+x)/(1+x)^2/(-1+2*x),x, algorithm=""giac"")","-\frac{1}{72} \, \sqrt{55819 \, \sqrt{2} + 24420} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}}\right) + \frac{1}{144} \, \sqrt{55819 \, \sqrt{2} - 24420} \log\left(2^{\frac{1}{4}} + \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}}\right) - \frac{1}{144} \, \sqrt{55819 \, \sqrt{2} - 24420} \log\left({\left| -2^{\frac{1}{4}} + \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}} \right|}\right) + \frac{3 \, \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{3}{4}} - \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}}}{2 \, {\left(\frac{x - 1}{2 \, x + 1} - 2\right)}} - \frac{2}{9} \, \arctan\left(2 \, \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}} + 1\right) - \frac{2}{9} \, \arctan\left(2 \, \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}} - 1\right) + \frac{5}{9} \, \log\left(2 \, \sqrt{\frac{x - 1}{2 \, x + 1}} + 2 \, \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}} + 1\right) - \frac{5}{9} \, \log\left(2 \, \sqrt{\frac{x - 1}{2 \, x + 1}} - 2 \, \left(\frac{x - 1}{2 \, x + 1}\right)^{\frac{1}{4}} + 1\right)"," ",0,"-1/72*sqrt(55819*sqrt(2) + 24420)*arctan(1/2*2^(3/4)*((x - 1)/(2*x + 1))^(1/4)) + 1/144*sqrt(55819*sqrt(2) - 24420)*log(2^(1/4) + ((x - 1)/(2*x + 1))^(1/4)) - 1/144*sqrt(55819*sqrt(2) - 24420)*log(abs(-2^(1/4) + ((x - 1)/(2*x + 1))^(1/4))) + 1/2*(3*((x - 1)/(2*x + 1))^(3/4) - ((x - 1)/(2*x + 1))^(1/4))/((x - 1)/(2*x + 1) - 2) - 2/9*arctan(2*((x - 1)/(2*x + 1))^(1/4) + 1) - 2/9*arctan(2*((x - 1)/(2*x + 1))^(1/4) - 1) + 5/9*log(2*sqrt((x - 1)/(2*x + 1)) + 2*((x - 1)/(2*x + 1))^(1/4) + 1) - 5/9*log(2*sqrt((x - 1)/(2*x + 1)) - 2*((x - 1)/(2*x + 1))^(1/4) + 1)","A",0
2584,0,0,0,0.000000," ","integrate((p*x^2-q)*(p^2*x^4+q^2)^(1/2)/(b*x^3+a*(p*x^2+q)^3),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{4} + q^{2}} {\left(p x^{2} - q\right)}}{{\left(p x^{2} + q\right)}^{3} a + b x^{3}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^4 + q^2)*(p*x^2 - q)/((p*x^2 + q)^3*a + b*x^3), x)","F",0
2585,0,0,0,0.000000," ","integrate((p*x^2-q)*(p^2*x^4+q^2)^(1/2)/(b*x^3+a*(p*x^2+q)^3),x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{4} + q^{2}} {\left(p x^{2} - q\right)}}{{\left(p x^{2} + q\right)}^{3} a + b x^{3}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^4 + q^2)*(p*x^2 - q)/((p*x^2 + q)^3*a + b*x^3), x)","F",0
2586,0,0,0,0.000000," ","integrate((x^2-1)^2/(x^2+1)^2/(x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - 1\right)}^{2}}{\sqrt{x^{4} + 1} \sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^2 - 1)^2/(sqrt(x^4 + 1)*sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)^2), x)","F",0
2587,0,0,0,0.000000," ","integrate((-3+2*(k^2+1)*x+(k^2+1)*x^2-4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(-1-2*d)*x+(k^2+d)*x^2+k^2*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{4} - 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} x^{2} + 2 \, {\left(k^{2} + 1\right)} x - 3}{{\left(k^{2} x^{3} + {\left(k^{2} + d\right)} x^{2} - {\left(2 \, d + 1\right)} x + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^2*x^4 - 4*k^2*x^3 + (k^2 + 1)*x^2 + 2*(k^2 + 1)*x - 3)/((k^2*x^3 + (k^2 + d)*x^2 - (2*d + 1)*x + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2588,1,262,0,0.760814," ","integrate(x^3*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(2/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-(2*k^2+2*k)*x^3+(k^2-b)*x^4),x, algorithm=""giac"")","-\frac{\sqrt{3} \left(-b\right)^{\frac{1}{6}} \log\left(\sqrt{3} \left(-b\right)^{\frac{1}{6}} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \left(-b\right)^{\frac{1}{3}}\right)}{4 \, b} + \frac{\sqrt{3} \left(-b\right)^{\frac{1}{6}} \log\left(-\sqrt{3} \left(-b\right)^{\frac{1}{6}} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \left(-b\right)^{\frac{1}{3}}\right)}{4 \, b} - \frac{\left(-b\right)^{\frac{1}{6}} \arctan\left(\frac{\sqrt{3} \left(-b\right)^{\frac{1}{6}} + 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-b\right)^{\frac{1}{6}}}\right)}{2 \, b} - \frac{\left(-b\right)^{\frac{1}{6}} \arctan\left(-\frac{\sqrt{3} \left(-b\right)^{\frac{1}{6}} - 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-b\right)^{\frac{1}{6}}}\right)}{2 \, b} - \frac{\left(-b\right)^{\frac{1}{6}} \arctan\left(\frac{{\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-b\right)^{\frac{1}{6}}}\right)}{b}"," ",0,"-1/4*sqrt(3)*(-b)^(1/6)*log(sqrt(3)*(-b)^(1/6)*(k - k/x - 1/x + 1/x^2)^(1/3) + (k - k/x - 1/x + 1/x^2)^(2/3) + (-b)^(1/3))/b + 1/4*sqrt(3)*(-b)^(1/6)*log(-sqrt(3)*(-b)^(1/6)*(k - k/x - 1/x + 1/x^2)^(1/3) + (k - k/x - 1/x + 1/x^2)^(2/3) + (-b)^(1/3))/b - 1/2*(-b)^(1/6)*arctan((sqrt(3)*(-b)^(1/6) + 2*(k - k/x - 1/x + 1/x^2)^(1/3))/(-b)^(1/6))/b - 1/2*(-b)^(1/6)*arctan(-(sqrt(3)*(-b)^(1/6) - 2*(k - k/x - 1/x + 1/x^2)^(1/3))/(-b)^(1/6))/b - (-b)^(1/6)*arctan((k - k/x - 1/x + 1/x^2)^(1/3)/(-b)^(1/6))/b","A",0
2589,0,0,0,0.000000," ","integrate((x^2+1)^2/(x^2-1)^2/(x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{2}}{\sqrt{x^{4} + 1} \sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^2 + 1)^2/(sqrt(x^4 + 1)*sqrt(x^2 + sqrt(x^4 + 1))*(x^2 - 1)^2), x)","F",0
2590,0,0,0,0.000000," ","integrate((x^2-1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)^2/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} - 1\right)}^{2}}{\sqrt{x^{4} + 1} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 - 1)^2/(sqrt(x^4 + 1)*(x^2 + 1)^2), x)","F",0
2591,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2592,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2593,0,0,0,0.000000," ","integrate((-2+x)*(x^3-x^2+x)^(1/3)/(-1+x)/(x^2+x-1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2} + x\right)}^{\frac{1}{3}} {\left(x - 2\right)}}{{\left(x^{2} + x - 1\right)} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate((x^3 - x^2 + x)^(1/3)*(x - 2)/((x^2 + x - 1)*(x - 1)), x)","F",0
2594,1,154,0,0.315017," ","integrate((x^2+1)*(x^3+x^2)^(1/3)/(x^2-1),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(\frac{1}{x} + 1\right)}^{\frac{4}{3}} + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)} x^{2} - \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{17}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{2} \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + 2^{\frac{1}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) + \frac{17}{18} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{17}{9} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/6*((1/x + 1)^(4/3) + 2*(1/x + 1)^(1/3))*x^2 - sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x + 1)^(1/3))) + 17/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x + 1)^(1/3) + 1)) - 1/2*2^(1/3)*log(2^(2/3) + 2^(1/3)*(1/x + 1)^(1/3) + (1/x + 1)^(2/3)) + 2^(1/3)*log(abs(-2^(1/3) + (1/x + 1)^(1/3))) + 17/18*log((1/x + 1)^(2/3) + (1/x + 1)^(1/3) + 1) - 17/9*log(abs((1/x + 1)^(1/3) - 1))","A",0
2595,0,0,0,0.000000," ","integrate((a*x-b)/x/(a^3*x^3-b^3)^(1/3),x, algorithm=""giac"")","\int \frac{a x - b}{{\left(a^{3} x^{3} - b^{3}\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((a*x - b)/((a^3*x^3 - b^3)^(1/3)*x), x)","F",0
2596,0,0,0,0.000000," ","integrate((x^3-2)*(x^4+2*x^3+x)^(1/3)/(x^3+1)/(x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 2 \, x^{3} + x\right)}^{\frac{1}{3}} {\left(x^{3} - 2\right)}}{{\left(x^{3} + x^{2} + 1\right)} {\left(x^{3} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 2*x^3 + x)^(1/3)*(x^3 - 2)/((x^3 + x^2 + 1)*(x^3 + 1)), x)","F",0
2597,0,0,0,0.000000," ","integrate(x^4/(x^4-1)^(1/4)/(2*x^8-2*x^4+1),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(2 \, x^{8} - 2 \, x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((2*x^8 - 2*x^4 + 1)*(x^4 - 1)^(1/4)), x)","F",0
2598,0,0,0,0.000000," ","integrate((x^4-1)^(3/4)/(2*x^8-2*x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - 1\right)}^{\frac{3}{4}}}{2 \, x^{8} - 2 \, x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 - 1)^(3/4)/(2*x^8 - 2*x^4 + 1), x)","F",0
2599,0,0,0,0.000000," ","integrate(x^4/(x^4+1)^(1/4)/(2*x^8+2*x^4+1),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(2 \, x^{8} + 2 \, x^{4} + 1\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((2*x^8 + 2*x^4 + 1)*(x^4 + 1)^(1/4)), x)","F",0
2600,0,0,0,0.000000," ","integrate((x^4+1)^(3/4)/(2*x^8+2*x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{3}{4}}}{2 \, x^{8} + 2 \, x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)^(3/4)/(2*x^8 + 2*x^4 + 1), x)","F",0
2601,0,0,0,0.000000," ","integrate(x^2*(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} - b x} x^{2}}{{\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 - b*x)*x^2/(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2), x)","F",0
2602,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(1+x)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\sqrt{x^{4} + 1} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(sqrt(x^4 + 1)*(x + 1)), x)","F",0
2603,0,0,0,0.000000," ","integrate((a*x^2-b)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(2 \, a x^{3} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a^3*x^3 + b^2*x^2)^(1/3)*(2*a*x^3 - b)), x)","F",0
2604,0,0,0,0.000000," ","integrate((a*x^2-b)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{a x^{2} - b}{{\left(a^{3} x^{3} + b^{2} x^{2}\right)}^{\frac{1}{3}} {\left(2 \, a x^{3} - b\right)}}\,{d x}"," ",0,"integrate((a*x^2 - b)/((a^3*x^3 + b^2*x^2)^(1/3)*(2*a*x^3 - b)), x)","F",0
2605,0,0,0,0.000000," ","integrate((2*a*b*x-3*a*x^2+x^3)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^2+2*a*x-(b*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int \frac{2 \, a b x - 3 \, a x^{2} + x^{3}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{3}} {\left(d x^{3} - {\left(b d + 1\right)} x^{2} - a^{2} + 2 \, a x\right)}}\,{d x}"," ",0,"integrate((2*a*b*x - 3*a*x^2 + x^3)/(((a - x)*(b - x)*x^2)^(1/3)*(d*x^3 - (b*d + 1)*x^2 - a^2 + 2*a*x)), x)","F",0
2606,0,0,0,0.000000," ","integrate(((k^2-2)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d+(d*k^2-2)*x^2+x^4),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} + {\left(k^{2} - 2\right)} x}{{\left(x^{4} + {\left(d k^{2} - 2\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 + (k^2 - 2)*x)/((x^4 + (d*k^2 - 2)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2607,1,225,0,0.398041," ","integrate((1+2*x)*(x^4+x^3)^(1/4)/(x^2+x-1),x, algorithm=""giac"")","-\sqrt{2 \, \sqrt{5} - 2} \arctan\left(\frac{{\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \sqrt{2 \, \sqrt{5} + 2} \arctan\left(\frac{{\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{2} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \, \sqrt{2 \, \sqrt{5} + 2} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{1}{2} \, \sqrt{2 \, \sqrt{5} + 2} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + 2 \, x {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-sqrt(2*sqrt(5) - 2)*arctan((1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) + 1/2)) + sqrt(2*sqrt(5) + 2)*arctan((1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) - 1/2)) - 1/2*sqrt(2*sqrt(5) - 2)*log(sqrt(1/2*sqrt(5) + 1/2) + (1/x + 1)^(1/4)) + 1/2*sqrt(2*sqrt(5) + 2)*log(sqrt(1/2*sqrt(5) - 1/2) + (1/x + 1)^(1/4)) + 1/2*sqrt(2*sqrt(5) - 2)*log(abs(-sqrt(1/2*sqrt(5) + 1/2) + (1/x + 1)^(1/4))) - 1/2*sqrt(2*sqrt(5) + 2)*log(abs(-sqrt(1/2*sqrt(5) - 1/2) + (1/x + 1)^(1/4))) + 2*x*(1/x + 1)^(1/4) - arctan((1/x + 1)^(1/4)) - 1/2*log((1/x + 1)^(1/4) + 1) + 1/2*log(abs((1/x + 1)^(1/4) - 1))","A",0
2608,0,0,0,0.000000," ","integrate(((2*k^2-1)*x-2*k^4*x^3+k^4*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(-2*d*k^2+1)*x^2+d*k^4*x^4),x, algorithm=""giac"")","\int \frac{k^{4} x^{5} - 2 \, k^{4} x^{3} + {\left(2 \, k^{2} - 1\right)} x}{{\left(d k^{4} x^{4} - {\left(2 \, d k^{2} - 1\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^4*x^5 - 2*k^4*x^3 + (2*k^2 - 1)*x)/((d*k^4*x^4 - (2*d*k^2 - 1)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2609,1,318,0,0.589240," ","integrate((-a+x)*(-b+x)*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2+4*a*b+b^2)*d*x^2-2*(a+b)*d*x^3+(-1+d)*x^4),x, algorithm=""giac"")","\frac{\sqrt{3} \left(-d^{5}\right)^{\frac{5}{6}} \log\left(\sqrt{3} {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{2}{3}} + \left(-\frac{1}{d}\right)^{\frac{1}{3}}\right)}{4 \, d^{5}} - \frac{\sqrt{3} \left(-d^{5}\right)^{\frac{5}{6}} \log\left(-\sqrt{3} {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{2}{3}} + \left(-\frac{1}{d}\right)^{\frac{1}{3}}\right)}{4 \, d^{5}} - \frac{\left(-d^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{\sqrt{3} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + 2 \, {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{2 \, d^{5}} - \frac{\left(-d^{5}\right)^{\frac{5}{6}} \arctan\left(-\frac{\sqrt{3} \left(-\frac{1}{d}\right)^{\frac{1}{6}} - 2 \, {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{2 \, d^{5}} - \frac{\left(-d^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{{\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{d^{5}}"," ",0,"1/4*sqrt(3)*(-d^5)^(5/6)*log(sqrt(3)*(a*b/x^2 - a/x - b/x + 1)^(1/3)*(-1/d)^(1/6) + (a*b/x^2 - a/x - b/x + 1)^(2/3) + (-1/d)^(1/3))/d^5 - 1/4*sqrt(3)*(-d^5)^(5/6)*log(-sqrt(3)*(a*b/x^2 - a/x - b/x + 1)^(1/3)*(-1/d)^(1/6) + (a*b/x^2 - a/x - b/x + 1)^(2/3) + (-1/d)^(1/3))/d^5 - 1/2*(-d^5)^(5/6)*arctan((sqrt(3)*(-1/d)^(1/6) + 2*(a*b/x^2 - a/x - b/x + 1)^(1/3))/(-1/d)^(1/6))/d^5 - 1/2*(-d^5)^(5/6)*arctan(-(sqrt(3)*(-1/d)^(1/6) - 2*(a*b/x^2 - a/x - b/x + 1)^(1/3))/(-1/d)^(1/6))/d^5 - (-d^5)^(5/6)*arctan((a*b/x^2 - a/x - b/x + 1)^(1/3)/(-1/d)^(1/6))/d^5","A",0
2610,-2,0,0,0.000000," ","integrate((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x/(a^2*x^6+b^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-25,89]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[11,12]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-33,-91]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-45,-7]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-14,70]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[84,29]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-27,-21]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-43,4]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-60,90]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-10,65]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-37,53]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 6.42Done","F(-2)",0
2611,-2,0,0,0.000000," ","integrate((x^4+x)^(1/2)*(a*x^6+b)/(c*x^6-d),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[19,-71]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[-57,-3]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[-66,-2]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[22,71]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[-36,13]-a/6/c*ln(abs(sqrt((1/x)^3+1)-1))+a/6/c*ln(sqrt((1/x)^3+1)+1)+((2*c*d^3-4*c*d*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-5*d^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-2*d^2*c*d)*a*c^2*abs(d)+(-2*c^2*d^4+4*c^2*d^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+5*c*d^3*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+2*c*d^3*c*d)*a*abs(d)+(2*c^2*d^2-4*c^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-5*c*d*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-2*c*d*c*d)*b*c^2*abs(d)+(-2*c^3*d^3+4*c^3*d*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+5*c^2*d^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+2*c^2*d^2*c*d)*b*abs(d))/(12*c^4*d^3+3*c^3*d^4-15*c^2*d^5)/abs(c)*atan(sqrt((1/x)^3+1)/sqrt(-(6*c*d+sqrt(6*c*d*6*c*d-12*c*d*(-3*c^2+3*c*d)))/2/3/c/d))-((2*c*d^3-4*c*d*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-5*d^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-2*d^2*c*d)*a*c^2*abs(d)+(-2*c^2*d^4+4*c^2*d^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+5*c*d^3*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+2*c*d^3*c*d)*a*abs(d)+(2*c^2*d^2-4*c^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-5*c*d*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-2*c*d*c*d)*b*c^2*abs(d)+(-2*c^3*d^3+4*c^3*d*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+5*c^2*d^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+2*c^2*d^2*c*d)*b*abs(d))/(12*c^4*d^3+3*c^3*d^4-15*c^2*d^5)/abs(c)*atan(sqrt((1/x)^3+1)/sqrt(-(6*c*d-sqrt(6*c*d*6*c*d-12*c*d*(-3*c^2+3*c*d)))/2/3/c/d))+8*a*c*1/24/c^2*x*sqrt(x^4+x)","F(-2)",0
2612,0,0,0,0.000000," ","integrate(x*(k*x-1)*(1-2*k*x+(-1+2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-1+4*x+(-6+b)*x^2+(-2*b*k+4)*x^3+(b*k^2-1)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(2 \, k - 1\right)} x^{2} - 2 \, k x + 1\right)} {\left(k x - 1\right)} x}{{\left({\left(b k^{2} - 1\right)} x^{4} - 2 \, {\left(b k - 2\right)} x^{3} + {\left(b - 6\right)} x^{2} + 4 \, x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(((2*k - 1)*x^2 - 2*k*x + 1)*(k*x - 1)*x/(((b*k^2 - 1)*x^4 - 2*(b*k - 2)*x^3 + (b - 6)*x^2 + 4*x - 1)*((k*x - 1)*(x - 1)*x)^(2/3)), x)","F",0
2613,-1,0,0,0.000000," ","integrate((a*p*x^4+4*b*p*x^3-3*a*q)/(p*x^4+q)^(1/3)/(a^3*d*x^3+3*a^2*b*d*x^2+c*p*x^4+3*a*b^2*d*x+b^3*d+c*q),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2614,0,0,0,0.000000," ","integrate(x^2/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x^{2}}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(x^2/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
2615,0,0,0,0.000000," ","integrate(x^2/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x^{2}}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(x^2/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
2616,0,0,0,0.000000," ","integrate((3+(2*k^2-1)*x-3*k^2*x^2-k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(1+2*d)*x-(k^2+d)*x^2+k^2*x^3),x, algorithm=""giac"")","\int -\frac{k^{2} x^{3} + 3 \, k^{2} x^{2} - {\left(2 \, k^{2} - 1\right)} x - 3}{{\left(k^{2} x^{3} - {\left(k^{2} + d\right)} x^{2} - {\left(2 \, d + 1\right)} x - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(k^2*x^3 + 3*k^2*x^2 - (2*k^2 - 1)*x - 3)/((k^2*x^3 - (k^2 + d)*x^2 - (2*d + 1)*x - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2617,0,0,0,0.000000," ","integrate((3+(-2*k^2+1)*x-3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(1+2*d)*x+(k^2+d)*x^2+k^2*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} - 3 \, k^{2} x^{2} - {\left(2 \, k^{2} - 1\right)} x + 3}{{\left(k^{2} x^{3} + {\left(k^{2} + d\right)} x^{2} - {\left(2 \, d + 1\right)} x + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 - 3*k^2*x^2 - (2*k^2 - 1)*x + 3)/((k^2*x^3 + (k^2 + d)*x^2 - (2*d + 1)*x + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2618,0,0,0,0.000000," ","integrate((a^4*x^4-b^4)^(1/2)*(a^4*x^4+b^4)/(a^8*x^8+b^8-c*x^4),x, algorithm=""giac"")","\int \frac{{\left(a^{4} x^{4} + b^{4}\right)} \sqrt{a^{4} x^{4} - b^{4}}}{a^{8} x^{8} + b^{8} - c x^{4}}\,{d x}"," ",0,"integrate((a^4*x^4 + b^4)*sqrt(a^4*x^4 - b^4)/(a^8*x^8 + b^8 - c*x^4), x)","F",0
2619,0,0,0,0.000000," ","integrate((a^8*x^8-b^8)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8+b^8-c*x^4),x, algorithm=""giac"")","\int \frac{a^{8} x^{8} - b^{8}}{{\left(a^{8} x^{8} + b^{8} - c x^{4}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^8*x^8 - b^8)/((a^8*x^8 + b^8 - c*x^4)*sqrt(a^4*x^4 - b^4)), x)","F",0
2620,1,240,0,0.987290," ","integrate((a*x+(a*x-b)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\frac{2 \, a^{2} {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{3} + 2 \, a^{2} b {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)} + 3 \, a^{2} {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{2} + a^{2} b + a^{2} {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}}{{\left({\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{4} + 2 \, b {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{2} + b^{2} + 4 \, b {\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)} + b\right)} a}"," ",0,"(2*a^2*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^3 + 2*a^2*b*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b))) + 3*a^2*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^2 + a^2*b + a^2*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b))))/(((sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^4 + 2*b*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^2 + b^2 + 4*b*(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b))) + b)*a)","B",0
2621,0,0,0,0.000000," ","integrate((-1+2*k*x+(1-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(2+b)*x+(b*k+1)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, k - 1\right)} x^{2} - 2 \, k x + 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left({\left(b k + 1\right)} x^{2} - {\left(b + 2\right)} x + 1\right)}}\,{d x}"," ",0,"integrate(-((2*k - 1)*x^2 - 2*k*x + 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((b*k + 1)*x^2 - (b + 2)*x + 1)), x)","F",0
2622,0,0,0,0.000000," ","integrate(x^3*(x^2+3)/(x^2+1)/(-x^3+x^2+1)^(1/3)/(x^3+x^2+1),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 3\right)} x^{3}}{{\left(x^{3} + x^{2} + 1\right)} {\left(-x^{3} + x^{2} + 1\right)}^{\frac{1}{3}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 + 3)*x^3/((x^3 + x^2 + 1)*(-x^3 + x^2 + 1)^(1/3)*(x^2 + 1)), x)","F",0
2623,1,244,0,0.483047," ","integrate((x^2+1)*(x^4-x^3)^(1/4)/(2*x^2+x-1),x, algorithm=""giac"")","-\frac{1}{16} \, {\left(5 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} - {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{2} + \frac{1}{3} \cdot 8^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{5}{24} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{5}{24} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{5}{48} \, \sqrt{2} \log\left(\sqrt{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) - \frac{5}{48} \, \sqrt{2} \log\left(-\sqrt{2} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{-\frac{1}{x} + 1} + 1\right) + \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{2}{3} \cdot 2^{\frac{1}{4}} \log\left({\left| -2^{\frac{1}{4}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{57}{32} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{57}{64} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{57}{64} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/16*(5*(-1/x + 1)^(5/4) - (-1/x + 1)^(1/4))*x^2 + 1/3*8^(3/4)*arctan(1/2*2^(3/4)*(-1/x + 1)^(1/4)) + 5/24*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(-1/x + 1)^(1/4))) + 5/24*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(-1/x + 1)^(1/4))) + 5/48*sqrt(2)*log(sqrt(2)*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) - 5/48*sqrt(2)*log(-sqrt(2)*(-1/x + 1)^(1/4) + sqrt(-1/x + 1) + 1) + 2/3*2^(1/4)*log(2^(1/4) + (-1/x + 1)^(1/4)) - 2/3*2^(1/4)*log(abs(-2^(1/4) + (-1/x + 1)^(1/4))) - 57/32*arctan((-1/x + 1)^(1/4)) - 57/64*log((-1/x + 1)^(1/4) + 1) + 57/64*log(abs((-1/x + 1)^(1/4) - 1))","A",0
2624,-1,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)*(x^8+a*x^4+b)/(a*x^4+b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2625,-1,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)*(x^8+a*x^4+b)/(a*x^4+b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2626,0,0,0,0.000000," ","integrate(1/(x^2-1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(x^{2} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(x^2 - 1)^(1/3)), x)","F",0
2627,0,0,0,0.000000," ","integrate((1+x)/(x^2+3*x+1)/(-x^3+1)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(-x^{3} + 1\right)}^{\frac{1}{3}} {\left(x^{2} + 3 \, x + 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((-x^3 + 1)^(1/3)*(x^2 + 3*x + 1)), x)","F",0
2628,0,0,0,0.000000," ","integrate((3*k+2*(k^2+1)*x-k*(k^2+1)*x^2-4*k^2*x^3-k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(1+2*d)*k*x-(d*k^2+1)*x^2+k*x^3),x, algorithm=""giac"")","\int -\frac{k^{3} x^{4} + 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} k x^{2} - 2 \, {\left(k^{2} + 1\right)} x - 3 \, k}{{\left(k x^{3} - {\left(2 \, d + 1\right)} k x - {\left(d k^{2} + 1\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-(k^3*x^4 + 4*k^2*x^3 + (k^2 + 1)*k*x^2 - 2*(k^2 + 1)*x - 3*k)/((k*x^3 - (2*d + 1)*k*x - (d*k^2 + 1)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2629,-2,0,0,0.000000," ","integrate((x^4-x)^(1/2)*(a*x^6+b)/(c*x^6-d),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[35,45]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[-45,5]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[-13,69]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[-66,-2]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c,d]=[-9,-88]a/6/c*ln(abs(sqrt(-(1/x)^3+1)-1))-a/6/c*ln(sqrt(-(1/x)^3+1)+1)+((-2*c*d^3+4*c*d*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+5*d^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+2*d^2*c*d)*a*c^2*abs(d)+(2*c^2*d^4-4*c^2*d^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-5*c*d^3*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-2*c*d^3*c*d)*a*abs(d)+(-2*c^2*d^2+4*c^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+5*c*d*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)+2*c*d*c*d)*b*c^2*abs(d)+(2*c^3*d^3-4*c^3*d*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-5*c^2*d^2*sqrt(-d^2-d*sqrt(c*d))*sqrt(c*d)-2*c^2*d^2*c*d)*b*abs(d))/(12*c^4*d^3+3*c^3*d^4-15*c^2*d^5)/abs(c)*atan(sqrt(-(1/x)^3+1)/sqrt(-(6*c*d+sqrt(6*c*d*6*c*d-12*c*d*(-3*c^2+3*c*d)))/2/3/c/d))-((-2*c*d^3+4*c*d*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+5*d^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+2*d^2*c*d)*a*c^2*abs(d)+(2*c^2*d^4-4*c^2*d^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-5*c*d^3*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-2*c*d^3*c*d)*a*abs(d)+(-2*c^2*d^2+4*c^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+5*c*d*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)+2*c*d*c*d)*b*c^2*abs(d)+(2*c^3*d^3-4*c^3*d*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-5*c^2*d^2*sqrt(-d^2+d*sqrt(c*d))*sqrt(c*d)-2*c^2*d^2*c*d)*b*abs(d))/(12*c^4*d^3+3*c^3*d^4-15*c^2*d^5)/abs(c)*atan(sqrt(-(1/x)^3+1)/sqrt(-(6*c*d-sqrt(6*c*d*6*c*d-12*c*d*(-3*c^2+3*c*d)))/2/3/c/d))+8*a*c*1/24/c^2*x*sqrt(x^4-x)","F(-2)",0
2630,0,0,0,0.000000," ","integrate((a^2*b-2*a^2*x+(2*a-b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2*d+(-2*a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int \frac{a^{2} b - 2 \, a^{2} x + {\left(2 \, a - b\right)} x^{2}}{{\left(a^{2} d + {\left(d - 1\right)} x^{2} - {\left(2 \, a d - b\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((a^2*b - 2*a^2*x + (2*a - b)*x^2)/((a^2*d + (d - 1)*x^2 - (2*a*d - b)*x)*((a - x)*(b - x)*x)^(2/3)), x)","F",0
2631,0,0,0,0.000000," ","integrate((2*a*b^2*x-b*(2*a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^2)^(2/3)/(-a*b^2+b*(2*a+b)*x-(a+2*b+d)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{2 \, a b^{2} x - {\left(2 \, a + b\right)} b x^{2} + x^{4}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{2}{3}} {\left(a b^{2} - {\left(2 \, a + b\right)} b x + {\left(a + 2 \, b + d\right)} x^{2} - x^{3}\right)}}\,{d x}"," ",0,"integrate(-(2*a*b^2*x - (2*a + b)*b*x^2 + x^4)/((-(a - x)*(b - x)^2*x)^(2/3)*(a*b^2 - (2*a + b)*b*x + (a + 2*b + d)*x^2 - x^3)), x)","F",0
2632,0,0,0,0.000000," ","integrate((-3*k+2*(k^2+1)*x+k*(k^2+1)*x^2-4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(1+2*d)*k*x+(d*k^2+1)*x^2+k*x^3),x, algorithm=""giac"")","\int \frac{k^{3} x^{4} - 4 \, k^{2} x^{3} + {\left(k^{2} + 1\right)} k x^{2} + 2 \, {\left(k^{2} + 1\right)} x - 3 \, k}{{\left(k x^{3} - {\left(2 \, d + 1\right)} k x + {\left(d k^{2} + 1\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^3*x^4 - 4*k^2*x^3 + (k^2 + 1)*k*x^2 + 2*(k^2 + 1)*x - 3*k)/((k*x^3 - (2*d + 1)*k*x + (d*k^2 + 1)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2633,-2,0,0,0.000000," ","integrate((1-((-1+3*x)*(3+4*x))^(3/2))/(1+((-1+3*x)*(3+4*x))^(3/2)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -2*1/3/sqrt(217)*ln(abs(24*x+5-sqrt(217))/abs(24*x+5+sqrt(217)))-(1/22753*sqrt(22753*(2*sqrt(22753)-217))*ln((9453972458735129516744113708531264794407905484097024*x*sqrt(22753)+1370826006516593779927896487737033395189146295194068480*x+196957759556981864932169035594401349883498030918688*sqrt(2*(sqrt(22753)+145))*sqrt(22753)+28558875135762370415164510161188195733107214483209760*sqrt(2*(sqrt(22753)+145))+1969577595569818649321690355944013498834980309186880*sqrt(22753)+285588751357623704151645101611881957331072144832097600)*(9453972458735129516744113708531264794407905484097024*x*sqrt(22753)+1370826006516593779927896487737033395189146295194068480*x+196957759556981864932169035594401349883498030918688*sqrt(2*(sqrt(22753)+145))*sqrt(22753)+28558875135762370415164510161188195733107214483209760*sqrt(2*(sqrt(22753)+145))+1969577595569818649321690355944013498834980309186880*sqrt(22753)+285588751357623704151645101611881957331072144832097600)+4726986229367564758372056854265632397203952742048512*sqrt(2*(sqrt(22753)+145))*sqrt(3)*4726986229367564758372056854265632397203952742048512*sqrt(2*(sqrt(22753)+145))*sqrt(3))-2/22753*sqrt(22753*(2*sqrt(22753)-217))*242/22753*sqrt(3)/(4/22753*sqrt(22753)-434/22753)*atan((822831873418741599297009319826345466799848262527058008105795284587008*sqrt(2*(sqrt(22753)+145))*sqrt(22753)+119310621645717531898066351374820092685977998066423411175340316265116160*sqrt(2*(sqrt(22753)+145))+226689595064275405519716881708084225714849079625162795294394388798817152+8228318734187415992970093198263454667998482625270580081057952845870080*sqrt(22753)+966416621392899913460946632040116701144930901039071316459008773852344448+(39495929924099596766256447351664582406392716601298784389078173660176384*sqrt(22753)+5726909838994441531107184865991364448926943907188323736416335180725575680)*x)*1/19747964962049798383128223675832291203196358300649392194539086830088192/sqrt(6*(sqrt(22753)+145)))-1/22753*sqrt(22753*(2*sqrt(22753)-217))*ln((9453972458735129516744113708531264794407905484097024*x*sqrt(22753)+1370826006516593779927896487737033395189146295194068480*x-196957759556981864932169035594401349883498030918688*sqrt(2*(sqrt(22753)+145))*sqrt(22753)-28558875135762370415164510161188195733107214483209760*sqrt(2*(sqrt(22753)+145))+1969577595569818649321690355944013498834980309186880*sqrt(22753)+285588751357623704151645101611881957331072144832097600)*(9453972458735129516744113708531264794407905484097024*x*sqrt(22753)+1370826006516593779927896487737033395189146295194068480*x-196957759556981864932169035594401349883498030918688*sqrt(2*(sqrt(22753)+145))*sqrt(22753)-28558875135762370415164510161188195733107214483209760*sqrt(2*(sqrt(22753)+145))+1969577595569818649321690355944013498834980309186880*sqrt(22753)+285588751357623704151645101611881957331072144832097600)+4726986229367564758372056854265632397203952742048512*sqrt(2*(sqrt(22753)+145))*sqrt(3)*4726986229367564758372056854265632397203952742048512*sqrt(2*(sqrt(22753)+145))*sqrt(3))-2/22753*sqrt(22753*(2*sqrt(22753)-217))*242/22753*sqrt(3)/(4/22753*sqrt(22753)-434/22753)*atan((-822831873418741599297009319826345466799848262527058008105795284587008*sqrt(2*(sqrt(22753)+145))*sqrt(22753)-119310621645717531898066351374820092685977998066423411175340316265116160*sqrt(2*(sqrt(22753)+145))-260026300220786494566734070194567200084679826628863206367099445975113792+8228318734187415992970093198263454667998482625270580081057952845870080*sqrt(22753)+1453132516677961813547397583942768126944459807293097318120502608626275392+(39495929924099596766256447351664582406392716601298784389078173660176384*sqrt(22753)+5726909838994441531107184865991364448926943907188323736416335180725575680)*x)*1/19747964962049798383128223675832291203196358300649392194539086830088192/sqrt(6*(sqrt(22753)+145))))/3-1728*x/1728-2*(sqrt(3)/3/sqrt(651)*ln(abs(-5*sqrt(3)-12+12*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)-sqrt(651))/abs(-5*sqrt(3)-12+12*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)+sqrt(651)))-sqrt(3)/3/sqrt(651)*ln(abs(-5*sqrt(3)+12+12*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)-sqrt(651))/(-5*sqrt(3)+12+12*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)+sqrt(651)))+(4877896607655611412062659525613868719683257653962336870247744752140297073073401374828026243445558427859549434988611031267869339771334211907262284122307027711813484544/22753*sqrt(22753*(2*sqrt(22753)-217))*ln((sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)++infinity*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x))-4877896607655611412062659525613868719683257653962336870247744752140297073073401374828026243445558427859549434988611031267869339771334211907262284122307027711813484544/22753*sqrt(22753*(2*sqrt(22753)-217))*ln((sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)++infinity*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x))+undef)/29267379645933668472375957153683212318099545923774021221486468512841782438440408248968157460673350567157296609931666187607216038628005271443573704733842166270880907264+(4877896607655611412062659525613868719683257653962336870247744752140297073073401374828026243445558427859549434988611031267869339771334211907262284122307027711813484544/22753*sqrt(22753*(2*sqrt(22753)-217))*ln((sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)++infinity*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x))-4877896607655611412062659525613868719683257653962336870247744752140297073073401374828026243445558427859549434988611031267869339771334211907262284122307027711813484544/22753*sqrt(22753*(2*sqrt(22753)-217))*ln((sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)++infinity*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x)*(sqrt(12*x^2+5*x-3)-2*sqrt(3)*x))+undef)/29267379645933668472375957153683212318099545923774021221486468512841782438440408248968157460673350567157296609931666187607216038628005271443573704733842166270880907264)","F(-2)",0
2634,0,0,0,0.000000," ","integrate(1/(a^2*x^2-b*x)^(3/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - b x\right)}^{\frac{3}{2}} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - b*x)^(3/2)*(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2)), x)","F",0
2635,0,0,0,0.000000," ","integrate(1/x/((-1+x)*(-2*q*x+x^2+q))^(1/3),x, algorithm=""giac"")","\int \frac{1}{\left(-{\left(2 \, q x - x^{2} - q\right)} {\left(x - 1\right)}\right)^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate(1/((-(2*q*x - x^2 - q)*(x - 1))^(1/3)*x), x)","F",0
2636,0,0,0,0.000000," ","integrate((a*b+(-2*a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a^2*d+(-2*a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int \frac{a b - {\left(2 \, a - b\right)} x}{{\left(a^{2} d + {\left(d - 1\right)} x^{2} - {\left(2 \, a d - b\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*b - (2*a - b)*x)/((a^2*d + (d - 1)*x^2 - (2*a*d - b)*x)*((a - x)*(b - x)*x)^(1/3)), x)","F",0
2637,1,232,0,0.476492," ","integrate((x^4+1)/(x^4-x^2-1)/(x^4-x^2)^(1/4),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2 \, \sqrt{5} - 2} \arctan\left(\frac{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) - \frac{1}{2} \, \sqrt{2 \, \sqrt{5} + 2} \arctan\left(\frac{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 2} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 2} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right) + \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"-1/2*sqrt(2*sqrt(5) - 2)*arctan((-1/x^2 + 1)^(1/4)/sqrt(1/2*sqrt(5) + 1/2)) - 1/2*sqrt(2*sqrt(5) + 2)*arctan((-1/x^2 + 1)^(1/4)/sqrt(1/2*sqrt(5) - 1/2)) + 1/4*sqrt(2*sqrt(5) - 2)*log(sqrt(1/2*sqrt(5) + 1/2) + (-1/x^2 + 1)^(1/4)) - 1/4*sqrt(2*sqrt(5) - 2)*log(sqrt(1/2*sqrt(5) + 1/2) - (-1/x^2 + 1)^(1/4)) + 1/4*sqrt(2*sqrt(5) + 2)*log(sqrt(1/2*sqrt(5) - 1/2) + (-1/x^2 + 1)^(1/4)) - 1/4*sqrt(2*sqrt(5) + 2)*log(abs(-sqrt(1/2*sqrt(5) - 1/2) + (-1/x^2 + 1)^(1/4))) + arctan((-1/x^2 + 1)^(1/4)) - 1/2*log((-1/x^2 + 1)^(1/4) + 1) + 1/2*log(-(-1/x^2 + 1)^(1/4) + 1)","A",0
2638,-2,0,0,0.000000," ","integrate(x^3*(-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
2639,1,171,0,0.497890," ","integrate((x^3-x)^(1/3)*(x^4-2)/x^4/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{3}{4} \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{4}{3}} + \frac{1}{4} \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) - \frac{1}{2} \cdot 2^{\frac{1}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right) - 3 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + \frac{1}{4} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{2} \, \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/2*sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x^2 + 1)^(1/3))) + 1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1)) - 3/4*(-1/x^2 + 1)^(4/3) + 1/4*2^(1/3)*log(2^(2/3) + 2^(1/3)*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3)) - 1/2*2^(1/3)*log(abs(-2^(1/3) + (-1/x^2 + 1)^(1/3))) - 3*(-1/x^2 + 1)^(1/3) + 1/4*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1) - 1/2*log(abs((-1/x^2 + 1)^(1/3) - 1))","A",0
2640,0,0,0,0.000000," ","integrate(2*(a*p*x^5-2*b*p*x^3+3*a*q*x)/(p*x^4+q)^(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, algorithm=""giac"")","\int \frac{2 \, {\left(a p x^{5} - 2 \, b p x^{3} + 3 \, a q x\right)}}{{\left(a^{3} d x^{6} + 3 \, a b^{2} d x^{2} + {\left(3 \, a^{2} b d + c p\right)} x^{4} + b^{3} d + c q\right)} {\left(p x^{4} + q\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(2*(a*p*x^5 - 2*b*p*x^3 + 3*a*q*x)/((a^3*d*x^6 + 3*a*b^2*d*x^2 + (3*a^2*b*d + c*p)*x^4 + b^3*d + c*q)*(p*x^4 + q)^(1/3)), x)","F",0
2641,0,0,0,0.000000," ","integrate((b^2-2*b*x+x^2)*(-a^2*b+4*a*b*x-(2*a+3*b)*x^2+2*x^3)/(x*(-a+x)^2*(-b+x)^3)^(3/4)/(b*d+(a^2-d)*x-2*a*x^2+x^3),x, algorithm=""giac"")","\int \frac{{\left(a^{2} b - 4 \, a b x + {\left(2 \, a + 3 \, b\right)} x^{2} - 2 \, x^{3}\right)} {\left(b^{2} - 2 \, b x + x^{2}\right)}}{\left(-{\left(a - x\right)}^{2} {\left(b - x\right)}^{3} x\right)^{\frac{3}{4}} {\left(2 \, a x^{2} - x^{3} - b d - {\left(a^{2} - d\right)} x\right)}}\,{d x}"," ",0,"integrate((a^2*b - 4*a*b*x + (2*a + 3*b)*x^2 - 2*x^3)*(b^2 - 2*b*x + x^2)/((-(a - x)^2*(b - x)^3*x)^(3/4)*(2*a*x^2 - x^3 - b*d - (a^2 - d)*x)), x)","F",0
2642,0,0,0,0.000000," ","integrate((-2+(1+k)*x)*(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2+a)*x^4)/x^3/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x, algorithm=""giac"")","\int -\frac{{\left({\left(k^{2} + a\right)} x^{4} - 2 \, {\left(k^{2} + k\right)} x^{3} + {\left(k^{2} + 4 \, k + 1\right)} x^{2} - 2 \, {\left(k + 1\right)} x + 1\right)} {\left({\left(k + 1\right)} x - 2\right)}}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left({\left(b - k\right)} x^{2} + {\left(k + 1\right)} x - 1\right)} x^{3}}\,{d x}"," ",0,"integrate(-((k^2 + a)*x^4 - 2*(k^2 + k)*x^3 + (k^2 + 4*k + 1)*x^2 - 2*(k + 1)*x + 1)*((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(2/3)*((b - k)*x^2 + (k + 1)*x - 1)*x^3), x)","F",0
2643,0,0,0,0.000000," ","integrate((x^3+1)*(x^3-x^2)^(1/3)/(x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} + 1\right)}}{x^{6} + 1}\,{d x}"," ",0,"integrate((x^3 - x^2)^(1/3)*(x^3 + 1)/(x^6 + 1), x)","F",0
2644,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(c x^{2} + d\right)}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(c*x^2 + d)), x)","F",0
2645,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(c x^{2} + d\right)}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(c*x^2 + d)), x)","F",0
2646,-2,0,0,0.000000," ","integrate((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(4*a^2*x^2-4*a*x+4*b+1)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[14,-38,-55]schur row 3 5.50999e-08sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[3,57,80]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [-43,4,18]schur row 3 2.66498e-08Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [-82,-64,-74]Warning, choosing root of [1,0,%%%{-10,[2,0,2]%%%}+%%%{8,[1,0,1]%%%}+%%%{-10,[0,1,0]%%%}+%%%{-2,[0,0,0]%%%},0,%%%{9,[4,0,4]%%%}+%%%{-24,[3,0,3]%%%}+%%%{18,[2,1,2]%%%}+%%%{22,[2,0,2]%%%}+%%%{-24,[1,1,1]%%%}+%%%{-8,[1,0,1]%%%}+%%%{9,[0,2,0]%%%}+%%%{6,[0,1,0]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-19,90,91]Warning, choosing root of [1,0,%%%{-10,[2,0,2]%%%}+%%%{-8,[1,0,1]%%%}+%%%{-10,[0,1,0]%%%}+%%%{-2,[0,0,0]%%%},0,%%%{9,[4,0,4]%%%}+%%%{24,[3,0,3]%%%}+%%%{18,[2,1,2]%%%}+%%%{22,[2,0,2]%%%}+%%%{24,[1,1,1]%%%}+%%%{8,[1,0,1]%%%}+%%%{9,[0,2,0]%%%}+%%%{6,[0,1,0]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [81,95,-98]Discontinuities at zeroes of 4*a^2*x^2-4*a*x+4*b+1 were not checkedEvaluation time: 16.46Done","F(-2)",0
2647,-2,0,0,0.000000," ","integrate((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(4*a^2*x^2-4*a*x+4*b+1)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[14,-38,-55]schur row 3 5.50999e-08sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[3,57,80]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [-43,4,18]schur row 3 2.66498e-08Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [-82,-64,-74]Warning, choosing root of [1,0,%%%{-10,[2,0,2]%%%}+%%%{8,[1,0,1]%%%}+%%%{-10,[0,1,0]%%%}+%%%{-2,[0,0,0]%%%},0,%%%{9,[4,0,4]%%%}+%%%{-24,[3,0,3]%%%}+%%%{18,[2,1,2]%%%}+%%%{22,[2,0,2]%%%}+%%%{-24,[1,1,1]%%%}+%%%{-8,[1,0,1]%%%}+%%%{9,[0,2,0]%%%}+%%%{6,[0,1,0]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-19,90,91]Warning, choosing root of [1,0,%%%{-10,[2,0,2]%%%}+%%%{-8,[1,0,1]%%%}+%%%{-10,[0,1,0]%%%}+%%%{-2,[0,0,0]%%%},0,%%%{9,[4,0,4]%%%}+%%%{24,[3,0,3]%%%}+%%%{18,[2,1,2]%%%}+%%%{22,[2,0,2]%%%}+%%%{24,[1,1,1]%%%}+%%%{8,[1,0,1]%%%}+%%%{9,[0,2,0]%%%}+%%%{6,[0,1,0]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [81,95,-98]Discontinuities at zeroes of 4*a^2*x^2-4*a*x+4*b+1 were not checkedEvaluation time: 16.03Done","F(-2)",0
2648,0,0,0,0.000000," ","integrate((a*k*x+k*x^2+1)/(k*x^2-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{a k x + k x^{2} + 1}{{\left(k x^{2} - 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((a*k*x + k*x^2 + 1)/((k*x^2 - 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
2649,0,0,0,0.000000," ","integrate((3*k+(-k^2+2)*x-3*k*x^2-k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(1+2*d)*k*x+(-d*k^2-1)*x^2+k*x^3),x, algorithm=""giac"")","\int -\frac{k^{2} x^{3} + 3 \, k x^{2} + {\left(k^{2} - 2\right)} x - 3 \, k}{{\left(k x^{3} - {\left(2 \, d + 1\right)} k x - {\left(d k^{2} + 1\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(k^2*x^3 + 3*k*x^2 + (k^2 - 2)*x - 3*k)/((k*x^3 - (2*d + 1)*k*x - (d*k^2 + 1)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2650,0,0,0,0.000000," ","integrate((3*k+(k^2-2)*x-3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(1+2*d)*k*x+(d*k^2+1)*x^2+k*x^3),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} - 3 \, k x^{2} + {\left(k^{2} - 2\right)} x + 3 \, k}{{\left(k x^{3} - {\left(2 \, d + 1\right)} k x + {\left(d k^{2} + 1\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 - 3*k*x^2 + (k^2 - 2)*x + 3*k)/((k*x^3 - (2*d + 1)*k*x + (d*k^2 + 1)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2651,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/(c*x^2+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2652,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/(c*x^2+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2653,0,0,0,0.000000," ","integrate((c*x^4+d)/x/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{4} + d}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}} x}\,{d x}"," ",0,"integrate((c*x^4 + d)/(sqrt(a*x + sqrt(a^2*x^2 + b^2))*x), x)","F",0
2654,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2655,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2656,1,325,0,3.004583," ","integrate((x^4-x^3)^(1/4)/x/(a*x-b),x, algorithm=""giac"")","-\frac{2 \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}{a} - \frac{\log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right)}{a} + \frac{\log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)}{a} + \frac{\sqrt{2} {\left(a b^{3} - b^{4}\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a - b}{b}\right)^{\frac{1}{4}}}\right)}{a b} + \frac{\sqrt{2} {\left(a b^{3} - b^{4}\right)}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} - 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a - b}{b}\right)^{\frac{1}{4}}}\right)}{a b} + \frac{\sqrt{2} {\left(a b^{3} - b^{4}\right)}^{\frac{1}{4}} \log\left(\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{a - b}{b}} + \sqrt{-\frac{1}{x} + 1}\right)}{2 \, a b} - \frac{\sqrt{2} {\left(a b^{3} - b^{4}\right)}^{\frac{1}{4}} \log\left(-\sqrt{2} \left(\frac{a - b}{b}\right)^{\frac{1}{4}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + \sqrt{\frac{a - b}{b}} + \sqrt{-\frac{1}{x} + 1}\right)}{2 \, a b}"," ",0,"-2*arctan((-1/x + 1)^(1/4))/a - log((-1/x + 1)^(1/4) + 1)/a + log(abs((-1/x + 1)^(1/4) - 1))/a + sqrt(2)*(a*b^3 - b^4)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*((a - b)/b)^(1/4) + 2*(-1/x + 1)^(1/4))/((a - b)/b)^(1/4))/(a*b) + sqrt(2)*(a*b^3 - b^4)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*((a - b)/b)^(1/4) - 2*(-1/x + 1)^(1/4))/((a - b)/b)^(1/4))/(a*b) + 1/2*sqrt(2)*(a*b^3 - b^4)^(1/4)*log(sqrt(2)*((a - b)/b)^(1/4)*(-1/x + 1)^(1/4) + sqrt((a - b)/b) + sqrt(-1/x + 1))/(a*b) - 1/2*sqrt(2)*(a*b^3 - b^4)^(1/4)*log(-sqrt(2)*((a - b)/b)^(1/4)*(-1/x + 1)^(1/4) + sqrt((a - b)/b) + sqrt(-1/x + 1))/(a*b)","A",0
2657,0,0,0,0.000000," ","integrate(x^3*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(2/3)/(-a^2*b^2+2*a*b*(a+b)*x-(a^2+4*a*b+b^2)*x^2+2*(a+b)*x^3+(-1+d)*x^4),x, algorithm=""giac"")","\int -\frac{{\left(2 \, a b - {\left(a + b\right)} x\right)} x^{3}}{{\left({\left(d - 1\right)} x^{4} - a^{2} b^{2} + 2 \, {\left(a + b\right)} a b x + 2 \, {\left(a + b\right)} x^{3} - {\left(a^{2} + 4 \, a b + b^{2}\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-(2*a*b - (a + b)*x)*x^3/(((d - 1)*x^4 - a^2*b^2 + 2*(a + b)*a*b*x + 2*(a + b)*x^3 - (a^2 + 4*a*b + b^2)*x^2)*((a - x)*(b - x)*x)^(2/3)), x)","F",0
2658,1,995,0,0.793935," ","integrate((2*x^6+1)/(x^3+x)^(1/3)/(x^6-1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{2} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{2} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{2} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{4} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{4} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{4} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{8} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{4} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right) - \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{2} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/4*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x^2 + 1)^(1/3))) - 1/2*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/2*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/2*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/4*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/4*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/4*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/8*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3)) + 1/4*2^(2/3)*log(abs(-2^(1/3) + (1/x^2 + 1)^(1/3))) - sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) + 1/2*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - log(abs((1/x^2 + 1)^(1/3) - 1))","B",0
2659,1,995,0,0.548085," ","integrate((2*x^6+1)/(x^3+x)^(1/3)/(x^6-1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{2} \, {\left(\sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) + 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} - \sin\left(\frac{4}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{4}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{4}{9} \, \pi\right)}\right) - \frac{1}{2} \, {\left(\sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} - 5 \, \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) + 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} - \sin\left(\frac{2}{9} \, \pi\right)^{5} + \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)\right)} \arctan\left(\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{2}{9} \, \pi\right) + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{2}{9} \, \pi\right)}\right) + \frac{1}{2} \, {\left(\sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{5} - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} + 5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} + 5 \, \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sin\left(\frac{1}{9} \, \pi\right)^{5} - \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 2 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)\right)} \arctan\left(-\frac{{\left(-i \, \sqrt{3} - 1\right)} \cos\left(\frac{1}{9} \, \pi\right) - 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{-{\left(-i \, \sqrt{3} - 1\right)} \sin\left(\frac{1}{9} \, \pi\right)}\right) - \frac{1}{4} \, {\left(5 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{4} \sin\left(\frac{4}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right)^{2} \sin\left(\frac{4}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{4}{9} \, \pi\right)^{5} + \cos\left(\frac{4}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{4}{9} \, \pi\right)^{3} \sin\left(\frac{4}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{4}{9} \, \pi\right) - \cos\left(\frac{4}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{4} \, {\left(5 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{4} \sin\left(\frac{2}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right)^{2} \sin\left(\frac{2}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{2}{9} \, \pi\right)^{5} + \cos\left(\frac{2}{9} \, \pi\right)^{5} - 10 \, \cos\left(\frac{2}{9} \, \pi\right)^{3} \sin\left(\frac{2}{9} \, \pi\right)^{2} + 5 \, \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right)^{4} + 2 \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) + \cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left({\left(-i \, \sqrt{3} \cos\left(\frac{2}{9} \, \pi\right) - \cos\left(\frac{2}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{4} \, {\left(5 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{4} \sin\left(\frac{1}{9} \, \pi\right) - 10 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right)^{2} \sin\left(\frac{1}{9} \, \pi\right)^{3} + \sqrt{3} \sin\left(\frac{1}{9} \, \pi\right)^{5} - \cos\left(\frac{1}{9} \, \pi\right)^{5} + 10 \, \cos\left(\frac{1}{9} \, \pi\right)^{3} \sin\left(\frac{1}{9} \, \pi\right)^{2} - 5 \, \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right)^{4} - 2 \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left({\left(i \, \sqrt{3} \cos\left(\frac{1}{9} \, \pi\right) + \cos\left(\frac{1}{9} \, \pi\right)\right)} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + 1\right) - \frac{1}{8} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{4} \cdot 2^{\frac{2}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right) - \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{1}{2} \, \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right) - \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/4*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(1/x^2 + 1)^(1/3))) - 1/2*(sqrt(3)*cos(4/9*pi)^5 - 10*sqrt(3)*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*sqrt(3)*cos(4/9*pi)*sin(4/9*pi)^4 - 5*cos(4/9*pi)^4*sin(4/9*pi) + 10*cos(4/9*pi)^2*sin(4/9*pi)^3 - sin(4/9*pi)^5 + sqrt(3)*cos(4/9*pi)^2 - sqrt(3)*sin(4/9*pi)^2 - 2*cos(4/9*pi)*sin(4/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(4/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(4/9*pi))) - 1/2*(sqrt(3)*cos(2/9*pi)^5 - 10*sqrt(3)*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*sqrt(3)*cos(2/9*pi)*sin(2/9*pi)^4 - 5*cos(2/9*pi)^4*sin(2/9*pi) + 10*cos(2/9*pi)^2*sin(2/9*pi)^3 - sin(2/9*pi)^5 + sqrt(3)*cos(2/9*pi)^2 - sqrt(3)*sin(2/9*pi)^2 - 2*cos(2/9*pi)*sin(2/9*pi))*arctan(1/2*((-I*sqrt(3) - 1)*cos(2/9*pi) + 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(2/9*pi))) + 1/2*(sqrt(3)*cos(1/9*pi)^5 - 10*sqrt(3)*cos(1/9*pi)^3*sin(1/9*pi)^2 + 5*sqrt(3)*cos(1/9*pi)*sin(1/9*pi)^4 + 5*cos(1/9*pi)^4*sin(1/9*pi) - 10*cos(1/9*pi)^2*sin(1/9*pi)^3 + sin(1/9*pi)^5 - sqrt(3)*cos(1/9*pi)^2 + sqrt(3)*sin(1/9*pi)^2 - 2*cos(1/9*pi)*sin(1/9*pi))*arctan(-1/2*((-I*sqrt(3) - 1)*cos(1/9*pi) - 2*(1/x^2 + 1)^(1/3))/((1/2*I*sqrt(3) + 1/2)*sin(1/9*pi))) - 1/4*(5*sqrt(3)*cos(4/9*pi)^4*sin(4/9*pi) - 10*sqrt(3)*cos(4/9*pi)^2*sin(4/9*pi)^3 + sqrt(3)*sin(4/9*pi)^5 + cos(4/9*pi)^5 - 10*cos(4/9*pi)^3*sin(4/9*pi)^2 + 5*cos(4/9*pi)*sin(4/9*pi)^4 + 2*sqrt(3)*cos(4/9*pi)*sin(4/9*pi) + cos(4/9*pi)^2 - sin(4/9*pi)^2)*log((-I*sqrt(3)*cos(4/9*pi) - cos(4/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/4*(5*sqrt(3)*cos(2/9*pi)^4*sin(2/9*pi) - 10*sqrt(3)*cos(2/9*pi)^2*sin(2/9*pi)^3 + sqrt(3)*sin(2/9*pi)^5 + cos(2/9*pi)^5 - 10*cos(2/9*pi)^3*sin(2/9*pi)^2 + 5*cos(2/9*pi)*sin(2/9*pi)^4 + 2*sqrt(3)*cos(2/9*pi)*sin(2/9*pi) + cos(2/9*pi)^2 - sin(2/9*pi)^2)*log((-I*sqrt(3)*cos(2/9*pi) - cos(2/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/4*(5*sqrt(3)*cos(1/9*pi)^4*sin(1/9*pi) - 10*sqrt(3)*cos(1/9*pi)^2*sin(1/9*pi)^3 + sqrt(3)*sin(1/9*pi)^5 - cos(1/9*pi)^5 + 10*cos(1/9*pi)^3*sin(1/9*pi)^2 - 5*cos(1/9*pi)*sin(1/9*pi)^4 - 2*sqrt(3)*cos(1/9*pi)*sin(1/9*pi) + cos(1/9*pi)^2 - sin(1/9*pi)^2)*log((I*sqrt(3)*cos(1/9*pi) + cos(1/9*pi))*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3) + 1) - 1/8*2^(2/3)*log(2^(2/3) + 2^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3)) + 1/4*2^(2/3)*log(abs(-2^(1/3) + (1/x^2 + 1)^(1/3))) - sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1)) + 1/2*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1) - log(abs((1/x^2 + 1)^(1/3) - 1))","B",0
2660,0,0,0,0.000000," ","integrate((a*x^3-4*b)*(a*x^3+b)^(1/3)/x^5/(a*x^3-2*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{3} + b\right)}^{\frac{1}{3}} {\left(a x^{3} - 4 \, b\right)}}{{\left(a x^{3} - 2 \, b\right)} x^{5}}\,{d x}"," ",0,"integrate((a*x^3 + b)^(1/3)*(a*x^3 - 4*b)/((a*x^3 - 2*b)*x^5), x)","F",0
2661,0,0,0,0.000000," ","integrate((-2*a^2*b*x+a*(3*a+2*b)*x^2-4*a*x^3+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a^2*d+2*a*d*x-(b+d)*x^2+x^3),x, algorithm=""giac"")","\int \frac{2 \, a^{2} b x - {\left(3 \, a + 2 \, b\right)} a x^{2} + 4 \, a x^{3} - x^{4}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{2}{3}} {\left(a^{2} d - 2 \, a d x + {\left(b + d\right)} x^{2} - x^{3}\right)}}\,{d x}"," ",0,"integrate((2*a^2*b*x - (3*a + 2*b)*a*x^2 + 4*a*x^3 - x^4)/(((a - x)*(b - x)*x^2)^(2/3)*(a^2*d - 2*a*d*x + (b + d)*x^2 - x^3)), x)","F",0
2662,0,0,0,0.000000," ","integrate((-2+(1+k)*x)*(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2+a)*x^4)/x^4/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x, algorithm=""giac"")","\int -\frac{{\left({\left(k^{2} + a\right)} x^{4} - 2 \, {\left(k^{2} + k\right)} x^{3} + {\left(k^{2} + 4 \, k + 1\right)} x^{2} - 2 \, {\left(k + 1\right)} x + 1\right)} {\left({\left(k + 1\right)} x - 2\right)}}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}} {\left({\left(b - k\right)} x^{2} + {\left(k + 1\right)} x - 1\right)} x^{4}}\,{d x}"," ",0,"integrate(-((k^2 + a)*x^4 - 2*(k^2 + k)*x^3 + (k^2 + 4*k + 1)*x^2 - 2*(k + 1)*x + 1)*((k + 1)*x - 2)/(((k*x - 1)*(x - 1)*x)^(1/3)*((b - k)*x^2 + (k + 1)*x - 1)*x^4), x)","F",0
2663,-2,0,0,0.000000," ","integrate(x^6*(x^4+x)^(1/2)/(a*x^6+b),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-34,84]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-24,-10]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[80,82]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[57,-56]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[45,-8]-1/6/a*ln(abs(sqrt((1/x)^3+1)-1))+1/6/a*ln(sqrt((1/x)^3+1)+1)+((-2*a*b^2+4*a*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b))+2*b*a*b-5*b*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b)))*a^2*abs(b)+(-2*a^2*b^3+4*a^2*b*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b))+2*a*b^2*a*b-5*a*b^2*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b)))*abs(b))/(12*a^4*b^2-3*a^3*b^3-15*a^2*b^4)/abs(a)*atan(sqrt((1/x)^3+1)/sqrt(-(6*a*b+sqrt(6*a*b*6*a*b-12*a*b*(3*a^2+3*a*b)))/2/3/a/b))-((-2*a*b^2+4*a*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b))+2*b*a*b-5*b*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b)))*a^2*abs(b)+(-2*a^2*b^3+4*a^2*b*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b))+2*a*b^2*a*b-5*a*b^2*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b)))*abs(b))/(12*a^4*b^2-3*a^3*b^3-15*a^2*b^4)/abs(a)*atan(sqrt((1/x)^3+1)/sqrt(-(6*a*b-sqrt(6*a*b*6*a*b-12*a*b*(3*a^2+3*a*b)))/2/3/a/b))+8*a*1/24/a^2*x*sqrt(x^4+x)","F(-2)",0
2664,-1,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)*(x^8-a*x^4-b)/(a*x^4-b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2665,-1,0,0,0.000000," ","integrate((a*x^4+b*x^2)^(1/4)*(x^8-a*x^4-b)/(a*x^4-b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2666,0,0,0,0.000000," ","integrate((5*x^7+2*x^4-2)*(x^8+x^5-x^3+x)^(1/3)/(2*x^7+2*x^4+x^2+2)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{5} - x^{3} + x\right)}^{\frac{1}{3}} {\left(5 \, x^{7} + 2 \, x^{4} - 2\right)}}{{\left(2 \, x^{7} + 2 \, x^{4} + x^{2} + 2\right)}^{2}}\,{d x}"," ",0,"integrate((x^8 + x^5 - x^3 + x)^(1/3)*(5*x^7 + 2*x^4 - 2)/(2*x^7 + 2*x^4 + x^2 + 2)^2, x)","F",0
2667,0,0,0,0.000000," ","integrate((a^5*x^5-b^5)/(a^2*x^3+b^2*x)^(1/2)/(a^5*x^5+b^5),x, algorithm=""giac"")","\int \frac{a^{5} x^{5} - b^{5}}{{\left(a^{5} x^{5} + b^{5}\right)} \sqrt{a^{2} x^{3} + b^{2} x}}\,{d x}"," ",0,"integrate((a^5*x^5 - b^5)/((a^5*x^5 + b^5)*sqrt(a^2*x^3 + b^2*x)), x)","F",0
2668,0,0,0,0.000000," ","integrate((a^5*x^5+b^5)/(a^2*x^3+b^2*x)^(1/2)/(a^5*x^5-b^5),x, algorithm=""giac"")","\int \frac{a^{5} x^{5} + b^{5}}{{\left(a^{5} x^{5} - b^{5}\right)} \sqrt{a^{2} x^{3} + b^{2} x}}\,{d x}"," ",0,"integrate((a^5*x^5 + b^5)/((a^5*x^5 - b^5)*sqrt(a^2*x^3 + b^2*x)), x)","F",0
2669,0,0,0,0.000000," ","integrate((2*x^8-a*x^4-2*b)/x^4/(a*x^4-b)^(1/4)/(2*a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} - 2 \, b}{{\left(2 \, a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 - 2*b)/((2*a*x^4 - b)*(a*x^4 - b)^(1/4)*x^4), x)","F",0
2670,0,0,0,0.000000," ","integrate((x^16-1)/(x^4-1)^(1/2)/(x^16+x^8+1),x, algorithm=""giac"")","\int \frac{x^{16} - 1}{{\left(x^{16} + x^{8} + 1\right)} \sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate((x^16 - 1)/((x^16 + x^8 + 1)*sqrt(x^4 - 1)), x)","F",0
2671,0,0,0,0.000000," ","integrate((2*a*b*x-3*a*x^2+x^3)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^2*d+2*a*d*x-(b+d)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{2 \, a b x - 3 \, a x^{2} + x^{3}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{3}} {\left(a^{2} d - 2 \, a d x + {\left(b + d\right)} x^{2} - x^{3}\right)}}\,{d x}"," ",0,"integrate(-(2*a*b*x - 3*a*x^2 + x^3)/(((a - x)*(b - x)*x^2)^(1/3)*(a^2*d - 2*a*d*x + (b + d)*x^2 - x^3)), x)","F",0
2672,0,0,0,0.000000," ","integrate((c*x^2+d)*(a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2673,0,0,0,0.000000," ","integrate((c*x^2+d)*(a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2674,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*(x^4 + 1)), x)","F",0
2675,0,0,0,0.000000," ","integrate(((k^2-2)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d+(k^2-2*d)*x^2+d*x^4),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} + {\left(k^{2} - 2\right)} x}{{\left(d x^{4} + {\left(k^{2} - 2 \, d\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 + (k^2 - 2)*x)/((d*x^4 + (k^2 - 2*d)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2676,0,0,0,0.000000," ","integrate(((2*k^2-1)*x-2*k^4*x^3+k^4*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d+(-2*k^2+d)*x^2+k^4*x^4),x, algorithm=""giac"")","\int \frac{k^{4} x^{5} - 2 \, k^{4} x^{3} + {\left(2 \, k^{2} - 1\right)} x}{{\left(k^{4} x^{4} - {\left(2 \, k^{2} - d\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^4*x^5 - 2*k^4*x^3 + (2*k^2 - 1)*x)/((k^4*x^4 - (2*k^2 - d)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2677,0,0,0,0.000000," ","integrate((x^6-2)*(x^6-x^4+1)/(x^6+1)^(1/4)/(x^12+x^8+2*x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} + 1\right)} {\left(x^{6} - 2\right)}}{{\left(x^{12} + x^{8} + 2 \, x^{6} + 1\right)} {\left(x^{6} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^6 - x^4 + 1)*(x^6 - 2)/((x^12 + x^8 + 2*x^6 + 1)*(x^6 + 1)^(1/4)), x)","F",0
2678,-2,0,0,0.000000," ","integrate((2*p*x^3-q)*(a*p*x^3+a*q+b*x)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^3/(c*p*x^3+c*q+d*x),x, algorithm=""giac"")","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError >> type","F(-2)",0
2679,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)), x)","F",0
2680,0,0,0,0.000000," ","integrate((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} - 1\right)}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 - 1)/(x^2 + 1), x)","F",0
2681,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2682,1,108,0,2.639787," ","integrate(x*(-a+x)/(x^2*(-a+x))^(2/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x, algorithm=""giac"")","\frac{\sqrt{3} {\left| d \right|}^{\frac{4}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} d^{\frac{1}{3}} {\left(2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \frac{1}{d^{\frac{1}{3}}}\right)}\right)}{2 \, a d^{2}} - \frac{{\left| d \right|}^{\frac{4}{3}} \log\left({\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}}{d^{\frac{1}{3}}} + \frac{1}{d^{\frac{2}{3}}}\right)}{4 \, a d^{2}} + \frac{\log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} - \frac{1}{d^{\frac{1}{3}}} \right|}\right)}{2 \, a d^{\frac{2}{3}}}"," ",0,"1/2*sqrt(3)*abs(d)^(4/3)*arctan(1/3*sqrt(3)*d^(1/3)*(2*(-a/x + 1)^(2/3) + 1/d^(1/3)))/(a*d^2) - 1/4*abs(d)^(4/3)*log((-a/x + 1)^(4/3) + (-a/x + 1)^(2/3)/d^(1/3) + 1/d^(2/3))/(a*d^2) + 1/2*log(abs((-a/x + 1)^(2/3) - 1/d^(1/3)))/(a*d^(2/3))","A",0
2683,1,108,0,0.498625," ","integrate(x/(x^2*(-a+x))^(1/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left| d \right|}^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} d^{\frac{1}{3}} {\left(2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \frac{1}{d^{\frac{1}{3}}}\right)}\right)}{2 \, a d} - \frac{{\left| d \right|}^{\frac{2}{3}} \log\left({\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}}{d^{\frac{1}{3}}} + \frac{1}{d^{\frac{2}{3}}}\right)}{4 \, a d} + \frac{\log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} - \frac{1}{d^{\frac{1}{3}}} \right|}\right)}{2 \, a d^{\frac{1}{3}}}"," ",0,"-1/2*sqrt(3)*abs(d)^(2/3)*arctan(1/3*sqrt(3)*d^(1/3)*(2*(-a/x + 1)^(2/3) + 1/d^(1/3)))/(a*d) - 1/4*abs(d)^(2/3)*log((-a/x + 1)^(4/3) + (-a/x + 1)^(2/3)/d^(1/3) + 1/d^(2/3))/(a*d) + 1/2*log(abs((-a/x + 1)^(2/3) - 1/d^(1/3)))/(a*d^(1/3))","A",0
2684,1,108,0,0.493032," ","integrate((-a*x+x^2)/(x^2*(-a+x))^(2/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x, algorithm=""giac"")","\frac{\sqrt{3} {\left| d \right|}^{\frac{4}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} d^{\frac{1}{3}} {\left(2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + \frac{1}{d^{\frac{1}{3}}}\right)}\right)}{2 \, a d^{2}} - \frac{{\left| d \right|}^{\frac{4}{3}} \log\left({\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}}{d^{\frac{1}{3}}} + \frac{1}{d^{\frac{2}{3}}}\right)}{4 \, a d^{2}} + \frac{\log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} - \frac{1}{d^{\frac{1}{3}}} \right|}\right)}{2 \, a d^{\frac{2}{3}}}"," ",0,"1/2*sqrt(3)*abs(d)^(4/3)*arctan(1/3*sqrt(3)*d^(1/3)*(2*(-a/x + 1)^(2/3) + 1/d^(1/3)))/(a*d^2) - 1/4*abs(d)^(4/3)*log((-a/x + 1)^(4/3) + (-a/x + 1)^(2/3)/d^(1/3) + 1/d^(2/3))/(a*d^2) + 1/2*log(abs((-a/x + 1)^(2/3) - 1/d^(1/3)))/(a*d^(2/3))","A",0
2685,0,0,0,0.000000," ","integrate((-1+x)/(1+x)/(x^3-1)^(1/3),x, algorithm=""giac"")","\int \frac{x - 1}{{\left(x^{3} - 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x - 1)/((x^3 - 1)^(1/3)*(x + 1)), x)","F",0
2686,1,174,0,0.855782," ","integrate((x^2+1)*(x^3-x^2)^(1/3)/(x^2-1),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(-\frac{1}{x} + 1\right)}^{\frac{4}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)} x^{2} - \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{17}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{1}{2} \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}}\right) + 2^{\frac{1}{3}} \log\left({\left| -2^{\frac{1}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} \right|}\right) + \frac{17}{18} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{17}{9} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"1/6*((-1/x + 1)^(4/3) + 2*(-1/x + 1)^(1/3))*x^2 - sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3) + 2*(-1/x + 1)^(1/3))) + 17/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x + 1)^(1/3) + 1)) - 1/2*2^(1/3)*log(2^(2/3) + 2^(1/3)*(-1/x + 1)^(1/3) + (-1/x + 1)^(2/3)) + 2^(1/3)*log(abs(-2^(1/3) + (-1/x + 1)^(1/3))) + 17/18*log((-1/x + 1)^(2/3) + (-1/x + 1)^(1/3) + 1) - 17/9*log(abs((-1/x + 1)^(1/3) - 1))","A",0
2687,-2,0,0,0.000000," ","integrate((a*x^4+b)/(x^4-a*x^2-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-86,67]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[89,-63]Evaluation time: 5.96Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2688,-2,0,0,0.000000," ","integrate((a*x^4+b)/(x^4-a*x^2-b)/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-86,67]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[89,-63]Evaluation time: 6Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2689,0,0,0,0.000000," ","integrate(((-2*k^2+1)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d+(-2*k^2+d)*x^2+k^4*x^4),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} - {\left(2 \, k^{2} - 1\right)} x}{{\left(k^{4} x^{4} - {\left(2 \, k^{2} - d\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 - (2*k^2 - 1)*x)/((k^4*x^4 - (2*k^2 - d)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2690,0,0,0,0.000000," ","integrate(((-k^2+2)*x-2*x^3+k^2*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(k^2-2*d)*x^2+d*x^4),x, algorithm=""giac"")","\int \frac{k^{2} x^{5} - 2 \, x^{3} - {\left(k^{2} - 2\right)} x}{{\left(d x^{4} + {\left(k^{2} - 2 \, d\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^2*x^5 - 2*x^3 - (k^2 - 2)*x)/((d*x^4 + (k^2 - 2*d)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2691,0,0,0,0.000000," ","integrate(1/x^4/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b + \sqrt{a x^{2} + b^{2}}} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(b + sqrt(a*x^2 + b^2))*x^4), x)","F",0
2692,0,0,0,0.000000," ","integrate((-a*(a-5*b)-(3*a+5*b)*x+4*x^2)/((-a+x)*(-b+x))^(1/3)/(-a^5+b*d-(-5*a^4+d)*x-10*a^3*x^2+10*a^2*x^3-5*a*x^4+x^5),x, algorithm=""giac"")","\int \frac{{\left(a - 5 \, b\right)} a + {\left(3 \, a + 5 \, b\right)} x - 4 \, x^{2}}{{\left(a^{5} + 10 \, a^{3} x^{2} - 10 \, a^{2} x^{3} + 5 \, a x^{4} - x^{5} - b d - {\left(5 \, a^{4} - d\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((a - 5*b)*a + (3*a + 5*b)*x - 4*x^2)/((a^5 + 10*a^3*x^2 - 10*a^2*x^3 + 5*a*x^4 - x^5 - b*d - (5*a^4 - d)*x)*((a - x)*(b - x))^(1/3)), x)","F",0
2693,-2,0,0,0.000000," ","integrate(x^6*(x^4-x)^(1/2)/(a*x^6+b),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-11,-20]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-92,-22]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[23,98]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-99,-57]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-53,-45]1/6/a*ln(abs(sqrt(-(1/x)^3+1)-1))-1/6/a*ln(sqrt(-(1/x)^3+1)+1)+((2*a*b^2-4*a*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b))-2*b*a*b+5*b*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b)))*a^2*abs(b)+(2*a^2*b^3-4*a^2*b*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b))-2*a*b^2*a*b+5*a*b^2*sqrt(-a*b)*sqrt(-b^2-b*sqrt(-a*b)))*abs(b))/(12*a^4*b^2-3*a^3*b^3-15*a^2*b^4)/abs(a)*atan(sqrt(-(1/x)^3+1)/sqrt(-(6*a*b+sqrt(6*a*b*6*a*b-12*a*b*(3*a^2+3*a*b)))/2/3/a/b))-((-2*a*b^2+4*a*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b))+2*b*a*b-5*b*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b)))*a^2*abs(b)+(-2*a^2*b^3+4*a^2*b*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b))+2*a*b^2*a*b-5*a*b^2*sqrt(-a*b)*sqrt(-b^2+b*sqrt(-a*b)))*abs(b))/(12*a^4*b^2-3*a^3*b^3-15*a^2*b^4)/abs(a)*atan(sqrt(-(1/x)^3+1)/sqrt(-(6*a*b-sqrt(6*a*b*6*a*b-12*a*b*(3*a^2+3*a*b)))/2/3/a/b))+8*a*1/24/a^2*x*sqrt(x^4-x)","F(-2)",0
2694,0,0,0,0.000000," ","integrate((a^6*x^6+b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6-b^6),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} + b^{6}}{{\left(a^{6} x^{6} - b^{6}\right)} \sqrt{a^{2} x^{3} - b^{2} x}}\,{d x}"," ",0,"integrate((a^6*x^6 + b^6)/((a^6*x^6 - b^6)*sqrt(a^2*x^3 - b^2*x)), x)","F",0
2695,0,0,0,0.000000," ","integrate((a^2*b-2*a^2*x+(2*a-b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2+(b*d-2*a)*x+(1-d)*x^2),x, algorithm=""giac"")","\int -\frac{a^{2} b - 2 \, a^{2} x + {\left(2 \, a - b\right)} x^{2}}{\left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{2}{3}} {\left({\left(d - 1\right)} x^{2} - a^{2} - {\left(b d - 2 \, a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a^2*b - 2*a^2*x + (2*a - b)*x^2)/(((a - x)*(b - x)*x)^(2/3)*((d - 1)*x^2 - a^2 - (b*d - 2*a)*x)), x)","F",0
2696,0,0,0,0.000000," ","integrate((a^6*x^6+b^6)/(a^2*x^3+b^2*x)^(1/2)/(a^6*x^6-b^6),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} + b^{6}}{{\left(a^{6} x^{6} - b^{6}\right)} \sqrt{a^{2} x^{3} + b^{2} x}}\,{d x}"," ",0,"integrate((a^6*x^6 + b^6)/((a^6*x^6 - b^6)*sqrt(a^2*x^3 + b^2*x)), x)","F",0
2697,0,0,0,0.000000," ","integrate((5*x^7+2)*(x^8-x^3-x)^(1/3)/(x^7-1)/(x^7+x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - x^{3} - x\right)}^{\frac{1}{3}} {\left(5 \, x^{7} + 2\right)}}{{\left(x^{7} + x^{2} - 1\right)} {\left(x^{7} - 1\right)}}\,{d x}"," ",0,"integrate((x^8 - x^3 - x)^(1/3)*(5*x^7 + 2)/((x^7 + x^2 - 1)*(x^7 - 1)), x)","F",0
2698,0,0,0,0.000000," ","integrate(x^6*(x^3-4)/(x^3-1)^(3/4)/(x^8+x^6-2*x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{3} - 4\right)} x^{6}}{{\left(x^{8} + x^{6} - 2 \, x^{3} + 1\right)} {\left(x^{3} - 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((x^3 - 4)*x^6/((x^8 + x^6 - 2*x^3 + 1)*(x^3 - 1)^(3/4)), x)","F",0
2699,0,0,0,0.000000," ","integrate(x^6*(x^5+4)/(x^5-1)^(3/4)/(x^10+x^8-2*x^5+1),x, algorithm=""giac"")","\int \frac{{\left(x^{5} + 4\right)} x^{6}}{{\left(x^{10} + x^{8} - 2 \, x^{5} + 1\right)} {\left(x^{5} - 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((x^5 + 4)*x^6/((x^10 + x^8 - 2*x^5 + 1)*(x^5 - 1)^(3/4)), x)","F",0
2700,1,2731,0,146.733826," ","integrate((a*x+b)^(1/2)*(f*x^2-g)/(d*x^2+e)/(c+(a*x+b)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(3 \, a^{4} {\left(c + \sqrt{a x + b}\right)}^{\frac{5}{2}} d^{4} f - 10 \, a^{4} {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}} c d^{4} f + 15 \, a^{4} \sqrt{c + \sqrt{a x + b}} c^{2} d^{4} f\right)}}{15 \, a^{5} d^{5}} + \frac{\frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} + \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d + \sqrt{-d e} a}{d}}}} + \frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c + \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}} + \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} + \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}} - \frac{{\left(a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{5} g - 2 \, a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{5} g + a^{7} c^{2} d^{5} g + a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{2} d^{4} f e - 2 \, a^{7} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)} c d^{4} f e + a^{7} c^{2} d^{4} f e\right)} \log\left(\sqrt{c + \sqrt{a x + b}} - \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}\right)}{{\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{7}{2}} d - 3 \, {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{5}{2}} c d + {\left(3 \, c^{2} d - b d\right)} {\left(c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}\right)}^{\frac{3}{2}} - {\left(c^{3} d - b c d\right)} \sqrt{c - \sqrt{\frac{b d - \sqrt{-d e} a}{d}}}}}{2 \, a^{6} d^{5}}"," ",0,"4/15*(3*a^4*(c + sqrt(a*x + b))^(5/2)*d^4*f - 10*a^4*(c + sqrt(a*x + b))^(3/2)*c*d^4*f + 15*a^4*sqrt(c + sqrt(a*x + b))*c^2*d^4*f)/(a^5*d^5) + 1/2*((a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d)))/((c + sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d))) - (a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c + sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d)))/((c + sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d + sqrt(-d*e)*a)/d))) + (a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d)))/((c - sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d))) - (a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c - sqrt((b*d + sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d)))/((c - sqrt((b*d + sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d + sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d + sqrt(-d*e)*a)/d))) + (a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d)))/((c + sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d))) - (a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c + sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d)))/((c + sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c + sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c + sqrt((b*d - sqrt(-d*e)*a)/d))) + (a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) + sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d)))/((c - sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d))) - (a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^5*g - 2*a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^5*g + a^7*c^2*d^5*g + a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^2*d^4*f*e - 2*a^7*(c - sqrt((b*d - sqrt(-d*e)*a)/d))*c*d^4*f*e + a^7*c^2*d^4*f*e)*log(sqrt(c + sqrt(a*x + b)) - sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d)))/((c - sqrt((b*d - sqrt(-d*e)*a)/d))^(7/2)*d - 3*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(5/2)*c*d + (3*c^2*d - b*d)*(c - sqrt((b*d - sqrt(-d*e)*a)/d))^(3/2) - (c^3*d - b*c*d)*sqrt(c - sqrt((b*d - sqrt(-d*e)*a)/d))))/(a^6*d^5)","B",0
2701,0,0,0,0.000000," ","integrate((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*sqrt(x^2 + sqrt(x^4 + 1))/(x^2 + 1), x)","F",0
2702,0,0,0,0.000000," ","integrate(x/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(x/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2703,0,0,0,0.000000," ","integrate(x/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(x/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2704,-1,0,0,0.000000," ","integrate((a*x+b)^(1/2)*(1+(a*x+b)^(1/2))^(1/2)/x^2/(1+(1+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2705,-1,0,0,0.000000," ","integrate((a*x+b)^(1/2)*(1+(a*x+b)^(1/2))^(1/2)/x^2/(1+(1+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2706,-1,0,0,0.000000," ","integrate(x^4*(a*x^4+b*x^2)^(1/4)/(x^4+a*x^2+b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2707,-2,0,0,0.000000," ","integrate(x^4*(a*x^4+b*x^2)^(1/4)/(x^4+a*x^2+b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[79,41]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[84,-86]Evaluation time: 2.77Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2708,-1,0,0,0.000000," ","integrate((a*x+b)*(a*p*x^4+4*b*p*x^3-3*a*q)/(p*x^4+q)^(2/3)/(a^3*c*x^3+3*a^2*b*c*x^2+d*p*x^4+3*a*b^2*c*x+b^3*c+d*q),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2709,-2,0,0,0.000000," ","integrate((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x^7/(a^2*x^6+b^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-4,-35]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[12,21]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[24,16]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-71,69]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-22,57]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[84,29]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-27,-21]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-43,4]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-60,90]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-10,65]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [abs(b)]=[-4,-25]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 7.12Done","F(-2)",0
2710,0,0,0,0.000000," ","integrate((x^4-2)*(x^4+2)^(1/2)/(x^4+x^2+2)/(x^4+2*x^2+2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 2} {\left(x^{4} - 2\right)}}{{\left(x^{4} + 2 \, x^{2} + 2\right)} {\left(x^{4} + x^{2} + 2\right)}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 2)*(x^4 - 2)/((x^4 + 2*x^2 + 2)*(x^4 + x^2 + 2)), x)","F",0
2711,0,0,0,0.000000," ","integrate(x^2*(x^8-2)*(x^8-2*x^4+2)^(1/4)/(x^8+2)/(2*x^8-x^4+4),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - 2 \, x^{4} + 2\right)}^{\frac{1}{4}} {\left(x^{8} - 2\right)} x^{2}}{{\left(2 \, x^{8} - x^{4} + 4\right)} {\left(x^{8} + 2\right)}}\,{d x}"," ",0,"integrate((x^8 - 2*x^4 + 2)^(1/4)*(x^8 - 2)*x^2/((2*x^8 - x^4 + 4)*(x^8 + 2)), x)","F",0
2712,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2713,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2714,0,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/3),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a^{2} x^{2} - b} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b} x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*x^2 - b)*(a*x^2 + sqrt(a^2*x^2 - b)*x)^(1/3)), x)","F",0
2715,1,395,0,1.067926," ","integrate((a*x-b)^(1/2)/(1+(a*x+(a*x-b)^(1/2))^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{a x + \sqrt{a x - b}} {\left(\frac{2 \, \sqrt{a x - b}}{a} - \frac{3}{a}\right)} + \frac{{\left(4 \, b - 11\right)} \log\left({\left| -2 \, \sqrt{a x - b} + 2 \, \sqrt{a x + \sqrt{a x - b}} - 1 \right|}\right)}{4 \, a} + \frac{2 \, {\left(2 \, b - 3\right)} \arctan\left(-\frac{2 \, \sqrt{a x - b} - 2 \, \sqrt{a x + \sqrt{a x - b}} + 3}{\sqrt{4 \, b - 5}}\right)}{a \sqrt{4 \, b - 5}} - \frac{2 \, {\left(2 \, b - 3\right)} \arctan\left(-\frac{2 \, \sqrt{a x - b} - 2 \, \sqrt{a x + \sqrt{a x - b}} - 1}{\sqrt{4 \, b - 5}}\right)}{a \sqrt{4 \, b - 5}} + \frac{2 \, {\left(2 \, b - 3\right)} \arctan\left(\frac{2 \, \sqrt{a x - b} + 1}{\sqrt{4 \, b - 5}}\right)}{a \sqrt{4 \, b - 5}} + \frac{\log\left(a x + \sqrt{a x - b} - 1\right)}{a} - \frac{\log\left({\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{2} + b + 3 \, \sqrt{a x - b} - 3 \, \sqrt{a x + \sqrt{a x - b}} + 1\right)}{a} + \frac{\log\left({\left(\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}}\right)}^{2} + b - \sqrt{a x - b} + \sqrt{a x + \sqrt{a x - b}} - 1\right)}{a} - \frac{2 \, \sqrt{a x - b}}{a}"," ",0,"1/2*sqrt(a*x + sqrt(a*x - b))*(2*sqrt(a*x - b)/a - 3/a) + 1/4*(4*b - 11)*log(abs(-2*sqrt(a*x - b) + 2*sqrt(a*x + sqrt(a*x - b)) - 1))/a + 2*(2*b - 3)*arctan(-(2*sqrt(a*x - b) - 2*sqrt(a*x + sqrt(a*x - b)) + 3)/sqrt(4*b - 5))/(a*sqrt(4*b - 5)) - 2*(2*b - 3)*arctan(-(2*sqrt(a*x - b) - 2*sqrt(a*x + sqrt(a*x - b)) - 1)/sqrt(4*b - 5))/(a*sqrt(4*b - 5)) + 2*(2*b - 3)*arctan((2*sqrt(a*x - b) + 1)/sqrt(4*b - 5))/(a*sqrt(4*b - 5)) + log(a*x + sqrt(a*x - b) - 1)/a - log((sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^2 + b + 3*sqrt(a*x - b) - 3*sqrt(a*x + sqrt(a*x - b)) + 1)/a + log((sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)))^2 + b - sqrt(a*x - b) + sqrt(a*x + sqrt(a*x - b)) - 1)/a - 2*sqrt(a*x - b)/a","A",0
2716,1,77,0,0.155372," ","integrate(x*(1+2^(1/2)+2^(1/2)*x+x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} {\left(2 \, \sqrt{2} + 1\right)} \log\left(-\sqrt{2} {\left(x - \sqrt{x^{2} + \sqrt{2} x + \sqrt{2} + 1}\right)} - 1\right) + \frac{1}{24} \, {\left(2 \, {\left(4 \, x + \sqrt{2}\right)} x + \sqrt{2} {\left(\sqrt{2} + 8\right)}\right)} \sqrt{x^{2} + \sqrt{2} x + \sqrt{2} + 1}"," ",0,"1/8*sqrt(2)*(2*sqrt(2) + 1)*log(-sqrt(2)*(x - sqrt(x^2 + sqrt(2)*x + sqrt(2) + 1)) - 1) + 1/24*(2*(4*x + sqrt(2))*x + sqrt(2)*(sqrt(2) + 8))*sqrt(x^2 + sqrt(2)*x + sqrt(2) + 1)","A",0
2717,1,100,0,0.254125," ","integrate((-a*x+x^2)/(x^2*(-a+x))^(2/3)/(a^2-2*a*x+(1-d)*x^2),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + d^{\frac{1}{3}}\right)}}{3 \, d^{\frac{1}{3}}}\right)}{2 \, a d^{\frac{1}{3}}} - \frac{\log\left({\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + d^{\frac{1}{3}} {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + d^{\frac{2}{3}}\right)}{4 \, a d^{\frac{1}{3}}} + \frac{\log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} - d^{\frac{1}{3}} \right|}\right)}{2 \, a d^{\frac{1}{3}}}"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-a/x + 1)^(2/3) + d^(1/3))/d^(1/3))/(a*d^(1/3)) - 1/4*log((-a/x + 1)^(4/3) + d^(1/3)*(-a/x + 1)^(2/3) + d^(2/3))/(a*d^(1/3)) + 1/2*log(abs((-a/x + 1)^(2/3) - d^(1/3)))/(a*d^(1/3))","A",0
2718,1,100,0,0.249339," ","integrate(x/(x^2*(-a+x))^(1/3)/(-a^2+2*a*x+(-1+d)*x^2),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + d^{\frac{1}{3}}\right)}}{3 \, d^{\frac{1}{3}}}\right)}{2 \, a d^{\frac{2}{3}}} + \frac{\log\left({\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + d^{\frac{1}{3}} {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + d^{\frac{2}{3}}\right)}{4 \, a d^{\frac{2}{3}}} - \frac{\log\left({\left| {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} - d^{\frac{1}{3}} \right|}\right)}{2 \, a d^{\frac{2}{3}}}"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-a/x + 1)^(2/3) + d^(1/3))/d^(1/3))/(a*d^(2/3)) + 1/4*log((-a/x + 1)^(4/3) + d^(1/3)*(-a/x + 1)^(2/3) + d^(2/3))/(a*d^(2/3)) - 1/2*log(abs((-a/x + 1)^(2/3) - d^(1/3)))/(a*d^(2/3))","A",0
2719,0,0,0,0.000000," ","integrate((-a*b*x^2+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x, algorithm=""giac"")","\int -\frac{a b x^{2} - x^{4}}{{\left(a^{2} b^{2} - 2 \, {\left(a + b\right)} a b x - 2 \, {\left(a + b\right)} x^{3} + x^{4} + {\left(a^{2} + 4 \, a b + b^{2} - d\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-(a*b*x^2 - x^4)/((a^2*b^2 - 2*(a + b)*a*b*x - 2*(a + b)*x^3 + x^4 + (a^2 + 4*a*b + b^2 - d)*x^2)*((a - x)*(b - x)*x^2)^(2/3)), x)","F",0
2720,0,0,0,0.000000," ","integrate(((a*x^10+4*a*x^8+x^8+6*a*x^6+4*x^6+4*a*x^4+6*x^4+a*x^2+4*x^2+1)/x^2)^(1/4)/x,x, algorithm=""giac"")","\int \frac{\left(\frac{a x^{10} + 4 \, a x^{8} + x^{8} + 6 \, a x^{6} + 4 \, x^{6} + 4 \, a x^{4} + 6 \, x^{4} + a x^{2} + 4 \, x^{2} + 1}{x^{2}}\right)^{\frac{1}{4}}}{x}\,{d x}"," ",0,"integrate(((a*x^10 + 4*a*x^8 + x^8 + 6*a*x^6 + 4*x^6 + 4*a*x^4 + 6*x^4 + a*x^2 + 4*x^2 + 1)/x^2)^(1/4)/x, x)","F",0
2721,0,0,0,0.000000," ","integrate((8*x^2-8*x+2)^(1/3)/(3+x),x, algorithm=""giac"")","\int \frac{{\left(8 \, x^{2} - 8 \, x + 2\right)}^{\frac{1}{3}}}{x + 3}\,{d x}"," ",0,"integrate((8*x^2 - 8*x + 2)^(1/3)/(x + 3), x)","F",0
2722,0,0,0,0.000000," ","integrate((a*x+b)*(b*p*x^2-a*q)/(p*x^3+q)^(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, algorithm=""giac"")","\int \frac{{\left(b p x^{2} - a q\right)} {\left(a x + b\right)}}{{\left(3 \, a^{2} b c x^{2} + 3 \, a b^{2} c x + b^{3} c + {\left(a^{3} c + d p\right)} x^{3} + d q\right)} {\left(p x^{3} + q\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*p*x^2 - a*q)*(a*x + b)/((3*a^2*b*c*x^2 + 3*a*b^2*c*x + b^3*c + (a^3*c + d*p)*x^3 + d*q)*(p*x^3 + q)^(2/3)), x)","F",0
2723,0,0,0,0.000000," ","integrate((-b+x)*(-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(a^4-b^2*d-2*(2*a^3-b*d)*x+(6*a^2-d)*x^2-4*a*x^3+x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(a - 2 \, b\right)} a + 2 \, b x - x^{2}\right)} {\left(b - x\right)}}{{\left(a^{4} - 4 \, a x^{3} + x^{4} - b^{2} d + {\left(6 \, a^{2} - d\right)} x^{2} - 2 \, {\left(2 \, a^{3} - b d\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(((a - 2*b)*a + 2*b*x - x^2)*(b - x)/((a^4 - 4*a*x^3 + x^4 - b^2*d + (6*a^2 - d)*x^2 - 2*(2*a^3 - b*d)*x)*((a - x)*(b - x))^(2/3)), x)","F",0
2724,-2,0,0,0.000000," ","integrate((x^5+1)^(1/2)*(x^5+2)/x^6/(a*x^10-x^5-1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-16]a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[-4]Done","F(-2)",0
2725,-2,0,0,0.000000," ","integrate((x^5-2)*(x^5-1)^(1/2)/x^6/(a*x^10-x^5+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[6]a: recursive definition (in sto)  Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a]=[39]Precision problem choosing root in common_EXT, current precision 14Done","F(-2)",0
2726,0,0,0,0.000000," ","integrate(1/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(1/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2727,0,0,0,0.000000," ","integrate(1/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(1/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2728,-1,0,0,0.000000," ","integrate(x*(_C3*x^2-_C4)/((_C3*x^2+_C0*x+_C4)/(_C3*x^2+_C1*x+_C4))^(1/2)/(3*_C3*x^2+3*_C4+x)/(_C3^2*x^4+2*_C3*_C4*x^2+_C4^2-x^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2729,0,0,0,0.000000," ","integrate(1/(a*x^4-b)^2/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}^{2}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)^2), x)","F",0
2730,0,0,0,0.000000," ","integrate(1/(a*x^4-b)^2/(a*x^4-b*x^2)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(a x^{4} - b\right)}^{2}}\,{d x}"," ",0,"integrate(1/((a*x^4 - b*x^2)^(1/4)*(a*x^4 - b)^2), x)","F",0
2731,-1,0,0,0.000000," ","integrate((p*x^3-2*q)*(a*p*x^3+b*x^2+a*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^5/(c*p*x^3+d*x^2+c*q),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2732,0,0,0,0.000000," ","integrate(-(-1+x)*x*(-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-4*k*x+(6*k^2-b)*x^2+(-4*k^3+2*b)*x^3+(k^4-b)*x^4),x, algorithm=""giac"")","\int -\frac{{\left({\left(k^{2} - 2 \, k\right)} x^{2} + 2 \, x - 1\right)} {\left(x - 1\right)} x}{{\left({\left(k^{4} - b\right)} x^{4} - 2 \, {\left(2 \, k^{3} - b\right)} x^{3} + {\left(6 \, k^{2} - b\right)} x^{2} - 4 \, k x + 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-((k^2 - 2*k)*x^2 + 2*x - 1)*(x - 1)*x/(((k^4 - b)*x^4 - 2*(2*k^3 - b)*x^3 + (6*k^2 - b)*x^2 - 4*k*x + 1)*((k*x - 1)*(x - 1)*x)^(2/3)), x)","F",0
2733,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^8+a*(p*x^3+q)^4)/x^13,x, algorithm=""giac"")","\int \frac{{\left(b x^{8} + {\left(p x^{3} + q\right)}^{4} a\right)} \sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(p x^{3} - 2 \, q\right)}}{x^{13}}\,{d x}"," ",0,"integrate((b*x^8 + (p*x^3 + q)^4*a)*sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(p*x^3 - 2*q)/x^13, x)","F",0
2734,0,0,0,0.000000," ","integrate(x^2/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x^{2}}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(x^2/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2735,0,0,0,0.000000," ","integrate(x^2/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x^{2}}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(x^2/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2736,0,0,0,0.000000," ","integrate(1/x/(x^4-4*x^3+6*x^2-4*x+1)^(1/5),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right)}^{\frac{1}{5}} x}\,{d x}"," ",0,"integrate(1/((x^4 - 4*x^3 + 6*x^2 - 4*x + 1)^(1/5)*x), x)","F",0
2737,0,0,0,0.000000," ","integrate((x^2-x+1)/(x^2-1)/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} - x + 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 - x + 1)/((x^4 + x^2)^(1/3)*(x^2 - 1)), x)","F",0
2738,0,0,0,0.000000," ","integrate((x^2+x+1)/(x^2-1)/(x^4+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2} + x + 1}{{\left(x^{4} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^2 + x + 1)/((x^4 + x^2)^(1/3)*(x^2 - 1)), x)","F",0
2739,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+x^3-x^2-x+1)^(1/2)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^2 - 1)/((x^2 + 1)*x^2), x)","F",0
2740,0,0,0,0.000000," ","integrate((x^2-1)*(x^4+x^3-x^2-x+1)^(1/2)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{3} - x^{2} - x + 1} {\left(x^{2} - 1\right)}}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^3 - x^2 - x + 1)*(x^2 - 1)/((x^2 + 1)*x^2), x)","F",0
2741,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^3+4)/x^6/(x^6-x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{3} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - x^{3} - 2\right)} x^{6}}\,{d x}"," ",0,"integrate((x^3 + 4)*(x^3 - 1)^(2/3)/((x^6 - x^3 - 2)*x^6), x)","F",0
2742,-1,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3)/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2743,1,238,0,1.120758," ","integrate((x^2+x)*(x^4+x^3)^(1/4)/(x^2+x-1),x, algorithm=""giac"")","\frac{1}{8} \, {\left({\left(\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{2} - \frac{1}{5} \, \sqrt{10 \, \sqrt{5} - 10} \arctan\left(\frac{{\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) - \frac{1}{5} \, \sqrt{10 \, \sqrt{5} + 10} \arctan\left(\frac{{\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{10} \, \sqrt{10 \, \sqrt{5} - 10} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{10} \, \sqrt{10 \, \sqrt{5} + 10} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{10} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + \frac{1}{10} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) + \frac{29}{16} \, \arctan\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{29}{32} \, \log\left({\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) - \frac{29}{32} \, \log\left({\left| {\left(\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/8*((1/x + 1)^(5/4) + 3*(1/x + 1)^(1/4))*x^2 - 1/5*sqrt(10*sqrt(5) - 10)*arctan((1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) + 1/2)) - 1/5*sqrt(10*sqrt(5) + 10)*arctan((1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) - 1/2)) - 1/10*sqrt(10*sqrt(5) - 10)*log(sqrt(1/2*sqrt(5) + 1/2) + (1/x + 1)^(1/4)) - 1/10*sqrt(10*sqrt(5) + 10)*log(sqrt(1/2*sqrt(5) - 1/2) + (1/x + 1)^(1/4)) + 1/10*sqrt(10*sqrt(5) - 10)*log(abs(-sqrt(1/2*sqrt(5) + 1/2) + (1/x + 1)^(1/4))) + 1/10*sqrt(10*sqrt(5) + 10)*log(abs(-sqrt(1/2*sqrt(5) - 1/2) + (1/x + 1)^(1/4))) + 29/16*arctan((1/x + 1)^(1/4)) + 29/32*log((1/x + 1)^(1/4) + 1) - 29/32*log(abs((1/x + 1)^(1/4) - 1))","A",0
2744,0,0,0,0.000000," ","integrate((x^4+b)^2/(x^20+a*x^16+4*b*x^16+4*a*b*x^12+6*b^2*x^12+6*a*b^2*x^8+4*b^3*x^8+4*a*b^3*x^4+b^4*x^4+a*b^4)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + b\right)}^{2}}{{\left(x^{20} + a x^{16} + 4 \, b x^{16} + 4 \, a b x^{12} + 6 \, b^{2} x^{12} + 6 \, a b^{2} x^{8} + 4 \, b^{3} x^{8} + 4 \, a b^{3} x^{4} + b^{4} x^{4} + a b^{4}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 + b)^2/(x^20 + a*x^16 + 4*b*x^16 + 4*a*b*x^12 + 6*b^2*x^12 + 6*a*b^2*x^8 + 4*b^3*x^8 + 4*a*b^3*x^4 + b^4*x^4 + a*b^4)^(1/4), x)","F",0
2745,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^4+a*(p*x^3+q)^4)/x^7,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left({\left(p x^{3} + q\right)}^{4} a + b x^{4}\right)} {\left(2 \, p x^{3} - q\right)}}{x^{7}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 + 2*p*q*x^3 - 2*p*q*x^2 + q^2)*((p*x^3 + q)^4*a + b*x^4)*(2*p*x^3 - q)/x^7, x)","F",0
2746,0,0,0,0.000000," ","integrate((1-(x-(x^2+1)^(1/2))^(1/2))/(x^4-2*x^2*(x^2+1)^(1/2)),x, algorithm=""giac"")","\int -\frac{\sqrt{x - \sqrt{x^{2} + 1}} - 1}{x^{4} - 2 \, \sqrt{x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(-(sqrt(x - sqrt(x^2 + 1)) - 1)/(x^4 - 2*sqrt(x^2 + 1)*x^2), x)","F",0
2747,-1,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2748,0,0,0,0.000000," ","integrate(((-2*k^2+1)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d+(-2*d*k^2+1)*x^2+d*k^4*x^4),x, algorithm=""giac"")","\int \frac{k^{2} x^{3} - {\left(2 \, k^{2} - 1\right)} x}{{\left(d k^{4} x^{4} - {\left(2 \, d k^{2} - 1\right)} x^{2} + d - 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^3 - (2*k^2 - 1)*x)/((d*k^4*x^4 - (2*d*k^2 - 1)*x^2 + d - 1)*((k^2*x^2 - 1)*(x^2 - 1))^(1/3)), x)","F",0
2749,0,0,0,0.000000," ","integrate(((-k^2+2)*x-2*x^3+k^2*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d+(d*k^2-2)*x^2+x^4),x, algorithm=""giac"")","\int \frac{k^{2} x^{5} - 2 \, x^{3} - {\left(k^{2} - 2\right)} x}{{\left(x^{4} + {\left(d k^{2} - 2\right)} x^{2} - d + 1\right)} \left({\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((k^2*x^5 - 2*x^3 - (k^2 - 2)*x)/((x^4 + (d*k^2 - 2)*x^2 - d + 1)*((k^2*x^2 - 1)*(x^2 - 1))^(2/3)), x)","F",0
2750,1,248,0,1.917672," ","integrate((x^4-1)*(x^4-x^2)^(1/4)/(x^4-x^2-1),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + \frac{1}{10} \, \sqrt{10 \, \sqrt{5} - 10} \arctan\left(\frac{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{10} \, \sqrt{10 \, \sqrt{5} + 10} \arctan\left(\frac{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) + \frac{1}{20} \, \sqrt{10 \, \sqrt{5} - 10} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{20} \, \sqrt{10 \, \sqrt{5} - 10} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{20} \, \sqrt{10 \, \sqrt{5} + 10} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{20} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{3}{4} \, \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{3}{8} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{3}{8} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"-1/2*x^2*(-1/x^2 + 1)^(1/4) + 1/10*sqrt(10*sqrt(5) - 10)*arctan((-1/x^2 + 1)^(1/4)/sqrt(1/2*sqrt(5) + 1/2)) + 1/10*sqrt(10*sqrt(5) + 10)*arctan((-1/x^2 + 1)^(1/4)/sqrt(1/2*sqrt(5) - 1/2)) + 1/20*sqrt(10*sqrt(5) - 10)*log(sqrt(1/2*sqrt(5) + 1/2) + (-1/x^2 + 1)^(1/4)) - 1/20*sqrt(10*sqrt(5) - 10)*log(sqrt(1/2*sqrt(5) + 1/2) - (-1/x^2 + 1)^(1/4)) + 1/20*sqrt(10*sqrt(5) + 10)*log(sqrt(1/2*sqrt(5) - 1/2) + (-1/x^2 + 1)^(1/4)) - 1/20*sqrt(10*sqrt(5) + 10)*log(abs(-sqrt(1/2*sqrt(5) - 1/2) + (-1/x^2 + 1)^(1/4))) - 3/4*arctan((-1/x^2 + 1)^(1/4)) - 3/8*log((-1/x^2 + 1)^(1/4) + 1) + 3/8*log(-(-1/x^2 + 1)^(1/4) + 1)","A",0
2751,0,0,0,0.000000," ","integrate((1+(3-2*k)*x-(4+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(1+5*b)*x-(10*b+k)*x^2+10*b*x^3-5*b*x^4+b*x^5),x, algorithm=""giac"")","\int \frac{3 \, k x^{3} - {\left(k + 4\right)} x^{2} - {\left(2 \, k - 3\right)} x + 1}{{\left(b x^{5} - 5 \, b x^{4} + 10 \, b x^{3} - {\left(10 \, b + k\right)} x^{2} + {\left(5 \, b + 1\right)} x - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*k*x^3 - (k + 4)*x^2 - (2*k - 3)*x + 1)/((b*x^5 - 5*b*x^4 + 10*b*x^3 - (10*b + k)*x^2 + (5*b + 1)*x - b)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2752,0,0,0,0.000000," ","integrate(x^3/(x^3-x^2)^(1/3)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(x^{6} - 1\right)} {\left(x^{3} - x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^3/((x^6 - 1)*(x^3 - x^2)^(1/3)), x)","F",0
2753,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2754,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2755,-1,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2756,0,0,0,0.000000," ","integrate((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(b-(a*d+1)*x+d*x^2),x, algorithm=""giac"")","\int -\frac{{\left(a b - 2 \, b x + x^{2}\right)} {\left(b - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{2}{3}} {\left(d x^{2} - {\left(a d + 1\right)} x + b\right)}}\,{d x}"," ",0,"integrate(-(a*b - 2*b*x + x^2)*(b - x)/((-(a - x)*(b - x)^2*x)^(2/3)*(d*x^2 - (a*d + 1)*x + b)), x)","F",0
2757,0,0,0,0.000000," ","integrate((a-5*b+4*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/((-a+x)*(-b+x))^(2/3)/(-a^5+b*d-(-5*a^4+d)*x-10*a^3*x^2+10*a^2*x^3-5*a*x^4+x^5),x, algorithm=""giac"")","\int \frac{{\left(a^{3} - 3 \, a^{2} x + 3 \, a x^{2} - x^{3}\right)} {\left(a - 5 \, b + 4 \, x\right)}}{{\left(a^{5} + 10 \, a^{3} x^{2} - 10 \, a^{2} x^{3} + 5 \, a x^{4} - x^{5} - b d - {\left(5 \, a^{4} - d\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((a^3 - 3*a^2*x + 3*a*x^2 - x^3)*(a - 5*b + 4*x)/((a^5 + 10*a^3*x^2 - 10*a^2*x^3 + 5*a*x^4 - x^5 - b*d - (5*a^4 - d)*x)*((a - x)*(b - x))^(2/3)), x)","F",0
2758,0,0,0,0.000000," ","integrate((1-x^3*(5+4*x)^(1/3)-x^3*(5+4*x)^(2/3))/(1-x*(5+4*x)^(1/2)),x, algorithm=""giac"")","\int \frac{{\left(4 \, x + 5\right)}^{\frac{2}{3}} x^{3} + {\left(4 \, x + 5\right)}^{\frac{1}{3}} x^{3} - 1}{\sqrt{4 \, x + 5} x - 1}\,{d x}"," ",0,"integrate(((4*x + 5)^(2/3)*x^3 + (4*x + 5)^(1/3)*x^3 - 1)/(sqrt(4*x + 5)*x - 1), x)","F",0
2759,-1,0,0,0.000000," ","integrate(x^3*(_C3*x^3-2*_C4)*((_C3*x^3+_C0*x^2+_C4)/(_C3*x^3+_C1*x^2+_C4))^(1/2)/(2*_C3*x^3+x^2+2*_C4)/(_C3^2*x^6+2*_C3*_C4*x^3-x^4+_C4^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2760,-1,0,0,0.000000," ","integrate(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3^2*x^10+2*_C3*_C4*x^5-x^6+_C4^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2761,-1,0,0,0.000000," ","integrate((x^2-1)^2*(x^3+x)/(x^4+1)^(1/2)/(x^8-2*x^6+4*x^4-2*x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2762,1,261,0,1.097611," ","integrate((2*x^2+x-1)*(x^4-x^3)^(1/4)/(x^2-x-1),x, algorithm=""giac"")","\frac{1}{4} \, {\left(11 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} - 15 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{2} - \sqrt{10 \, \sqrt{5} - 22} \arctan\left(\frac{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \sqrt{10 \, \sqrt{5} + 22} \arctan\left(\frac{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{2} \, \sqrt{10 \, \sqrt{5} - 22} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \, \sqrt{10 \, \sqrt{5} + 22} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{2} \, \sqrt{10 \, \sqrt{5} - 22} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{1}{2} \, \sqrt{10 \, \sqrt{5} + 22} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{49}{8} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{49}{16} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{49}{16} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/4*(11*(-1/x + 1)^(5/4) - 15*(-1/x + 1)^(1/4))*x^2 - sqrt(10*sqrt(5) - 22)*arctan((-1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) + 1/2)) + sqrt(10*sqrt(5) + 22)*arctan((-1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) - 1/2)) - 1/2*sqrt(10*sqrt(5) - 22)*log(sqrt(1/2*sqrt(5) + 1/2) + (-1/x + 1)^(1/4)) + 1/2*sqrt(10*sqrt(5) + 22)*log(sqrt(1/2*sqrt(5) - 1/2) + (-1/x + 1)^(1/4)) + 1/2*sqrt(10*sqrt(5) - 22)*log(abs(-sqrt(1/2*sqrt(5) + 1/2) + (-1/x + 1)^(1/4))) - 1/2*sqrt(10*sqrt(5) + 22)*log(abs(-sqrt(1/2*sqrt(5) - 1/2) + (-1/x + 1)^(1/4))) - 49/8*arctan((-1/x + 1)^(1/4)) - 49/16*log((-1/x + 1)^(1/4) + 1) + 49/16*log(abs((-1/x + 1)^(1/4) - 1))","A",0
2763,0,0,0,0.000000," ","integrate((x^6+2)*(x^6+x^4-1)/(x^6-1)^(1/4)/(x^12+x^8-2*x^6+1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{4} - 1\right)} {\left(x^{6} + 2\right)}}{{\left(x^{12} + x^{8} - 2 \, x^{6} + 1\right)} {\left(x^{6} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^6 + x^4 - 1)*(x^6 + 2)/((x^12 + x^8 - 2*x^6 + 1)*(x^6 - 1)^(1/4)), x)","F",0
2764,0,0,0,0.000000," ","integrate(1/(c*x+d)^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}} {\left(c x + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a*x + sqrt(a^2*x^2 + b^2))*(c*x + d)^2), x)","F",0
2765,0,0,0,0.000000," ","integrate((x^2+1)^2/(x^2-1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{2}}{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^2 + 1)^2/(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 - 1)^2), x)","F",0
2766,0,0,0,0.000000," ","integrate((a*(a*b+a*c-2*b*c)-2*(a^2-b*c)*x+(2*a-b-c)*x^2)/((-a+x)*(-b+x)*(-c+x))^(2/3)/(a^2-b*c*d+(b*d+c*d-2*a)*x+(1-d)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, a - b - c\right)} x^{2} + {\left(a b + a c - 2 \, b c\right)} a - 2 \, {\left(a^{2} - b c\right)} x}{\left(-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}\right)^{\frac{2}{3}} {\left(b c d + {\left(d - 1\right)} x^{2} - a^{2} - {\left(b d + c d - 2 \, a\right)} x\right)}}\,{d x}"," ",0,"integrate(-((2*a - b - c)*x^2 + (a*b + a*c - 2*b*c)*a - 2*(a^2 - b*c)*x)/((-(a - x)*(b - x)*(c - x))^(2/3)*(b*c*d + (d - 1)*x^2 - a^2 - (b*d + c*d - 2*a)*x)), x)","F",0
2767,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*(x^4 - 1)), x)","F",0
2768,0,0,0,0.000000," ","integrate((x^2-1)^2/(x^2+1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - 1\right)}^{2}}{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((x^2 - 1)^2/(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)^2), x)","F",0
2769,0,0,0,0.000000," ","integrate((2*a*b^2-b*(2*a+b)*x+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a*b^2+b*(2*a+b)*x-(a+2*b+d)*x^2+x^3),x, algorithm=""giac"")","\int -\frac{2 \, a b^{2} - {\left(2 \, a + b\right)} b x + x^{3}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}} {\left(a b^{2} - {\left(2 \, a + b\right)} b x + {\left(a + 2 \, b + d\right)} x^{2} - x^{3}\right)}}\,{d x}"," ",0,"integrate(-(2*a*b^2 - (2*a + b)*b*x + x^3)/((-(a - x)*(b - x)^2*x)^(1/3)*(a*b^2 - (2*a + b)*b*x + (a + 2*b + d)*x^2 - x^3)), x)","F",0
2770,0,0,0,0.000000," ","integrate((c*x-d)/x/(a*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{c x - d}{{\left(a x^{3} - b\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((c*x - d)/((a*x^3 - b)^(1/3)*x), x)","F",0
2771,0,0,0,0.000000," ","integrate((a^4*x^4-b^4+c^2*x^2)/(a^4*x^4-b^4)^(1/2)/(a^4*x^4+b^4),x, algorithm=""giac"")","\int \frac{a^{4} x^{4} - b^{4} + c^{2} x^{2}}{{\left(a^{4} x^{4} + b^{4}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^4*x^4 - b^4 + c^2*x^2)/((a^4*x^4 + b^4)*sqrt(a^4*x^4 - b^4)), x)","F",0
2772,0,0,0,0.000000," ","integrate(x^2/(-x^4+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2}}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(-x^2/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*(x^4 - 1)), x)","F",0
2773,0,0,0,0.000000," ","integrate(x*(-b+x)*(-a^2*b+2*a^2*x+(-2*a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(-a^4+4*a^3*x+(b^2*d-6*a^2)*x^2+2*(-b*d+2*a)*x^3+(-1+d)*x^4),x, algorithm=""giac"")","\int \frac{{\left(a^{2} b - 2 \, a^{2} x + {\left(2 \, a - b\right)} x^{2}\right)} {\left(b - x\right)} x}{{\left({\left(d - 1\right)} x^{4} - a^{4} + 4 \, a^{3} x - 2 \, {\left(b d - 2 \, a\right)} x^{3} + {\left(b^{2} d - 6 \, a^{2}\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((a^2*b - 2*a^2*x + (2*a - b)*x^2)*(b - x)*x/(((d - 1)*x^4 - a^4 + 4*a^3*x - 2*(b*d - 2*a)*x^3 + (b^2*d - 6*a^2)*x^2)*((a - x)*(b - x)*x)^(2/3)), x)","F",0
2774,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 8 \, x^{3} + 8\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{3} - 2\right)} {\left(x^{3} - 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 8*x^3 + 8)*(x^3 - 1)^(2/3)/((x^3 - 2)*(x^3 - 4)*x^6), x)","F",0
2775,-1,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2-b)^(1/2))^(3/4))^(4/3)/(a^2*x^2-b)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2776,0,0,0,0.000000," ","integrate(1/(a*x-b)/(a^3*x^3+b^3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} + b^{3}\right)}^{\frac{1}{3}} {\left(a x - b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 + b^3)^(1/3)*(a*x - b)), x)","F",0
2777,0,0,0,0.000000," ","integrate((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/3)/(-a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x\right)}^{\frac{1}{3}}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)^(1/3)/sqrt(a^2*x^2/b^2 - a/b^2), x)","F",0
2778,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2779,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2780,0,0,0,0.000000," ","integrate((-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(b-a*d+(-1+d)*x),x, algorithm=""giac"")","\int \frac{b - x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(a d - {\left(d - 1\right)} x - b\right)}}\,{d x}"," ",0,"integrate((b - x)/((-(a - x)*(b - x)^2)^(2/3)*(a*d - (d - 1)*x - b)), x)","F",0
2781,-1,0,0,0.000000," ","integrate((b*p*x^3-a*q*x)/(p*x^4+q)^(1/2)/(b^2*c+d*q+2*a*b*c*x^2+(a^2*c+d*p)*x^4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2782,-1,0,0,0.000000," ","integrate((a*x+b)^2*(a*p*x^3+3*b*p*x^2-2*a*q)/(p*x^3+q)^(1/2)/(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, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2783,-1,0,0,0.000000," ","integrate((x^2+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2784,-1,0,0,0.000000," ","integrate((x^2+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2785,0,0,0,0.000000," ","integrate((k^4*x^4-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(a*k^4*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{k^{4} x^{4} - 1}{{\left(a k^{4} x^{4} + b x^{2} + a\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate((k^4*x^4 - 1)/((a*k^4*x^4 + b*x^2 + a)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
2786,1,1,0,1.135525," ","integrate(x^5*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(d*x^8-a^2+2*a*x-x^2),x, algorithm=""giac"")","0"," ",0,"0","A",0
2787,1,133,0,0.190581," ","integrate(1/8*(1-x)^(1/2)/(1+x)^(7/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{5}}{2560 \, {\left(x + 1\right)}^{\frac{5}{2}}} + \frac{{\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{3}}{1536 \, {\left(x + 1\right)}^{\frac{3}{2}}} - \frac{\sqrt{2} - \sqrt{-x + 1}}{256 \, \sqrt{x + 1}} + \frac{{\left(\frac{30 \, {\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{4}}{{\left(x + 1\right)}^{2}} - \frac{5 \, {\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{2}}{x + 1} - 3\right)} {\left(x + 1\right)}^{\frac{5}{2}}}{7680 \, {\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{5}}"," ",0,"1/2560*(sqrt(2) - sqrt(-x + 1))^5/(x + 1)^(5/2) + 1/1536*(sqrt(2) - sqrt(-x + 1))^3/(x + 1)^(3/2) - 1/256*(sqrt(2) - sqrt(-x + 1))/sqrt(x + 1) + 1/7680*(30*(sqrt(2) - sqrt(-x + 1))^4/(x + 1)^2 - 5*(sqrt(2) - sqrt(-x + 1))^2/(x + 1) - 3)*(x + 1)^(5/2)/(sqrt(2) - sqrt(-x + 1))^5","A",0
2788,0,0,0,0.000000," ","integrate((2*a*b^2-b*(2*a+b)*x+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a*b^2*d+b*(2*a+b)*d*x-(a*d+2*b*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int -\frac{2 \, a b^{2} - {\left(2 \, a + b\right)} b x + x^{3}}{{\left(a b^{2} d - {\left(2 \, a + b\right)} b d x - d x^{3} + {\left(a d + 2 \, b d + 1\right)} x^{2}\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(2*a*b^2 - (2*a + b)*b*x + x^3)/((a*b^2*d - (2*a + b)*b*d*x - d*x^3 + (a*d + 2*b*d + 1)*x^2)*(-(a - x)*(b - x)^2*x)^(1/3)), x)","F",0
2789,1,260,0,0.696301," ","integrate((x^2-x)*(x^4-x^3)^(1/4)/(x^2-x-1),x, algorithm=""giac"")","-\frac{1}{8} \, {\left({\left(-\frac{1}{x} + 1\right)}^{\frac{5}{4}} + 3 \, {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right)} x^{2} + \frac{1}{5} \, \sqrt{10 \, \sqrt{5} - 10} \arctan\left(\frac{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{5} \, \sqrt{10 \, \sqrt{5} + 10} \arctan\left(\frac{{\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) + \frac{1}{10} \, \sqrt{10 \, \sqrt{5} - 10} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{10} \, \sqrt{10 \, \sqrt{5} + 10} \log\left(\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{10} \, \sqrt{10 \, \sqrt{5} - 10} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{1}{10} \, \sqrt{10 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} + {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} \right|}\right) - \frac{29}{16} \, \arctan\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}}\right) - \frac{29}{32} \, \log\left({\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{29}{32} \, \log\left({\left| {\left(-\frac{1}{x} + 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/8*((-1/x + 1)^(5/4) + 3*(-1/x + 1)^(1/4))*x^2 + 1/5*sqrt(10*sqrt(5) - 10)*arctan((-1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) + 1/2)) + 1/5*sqrt(10*sqrt(5) + 10)*arctan((-1/x + 1)^(1/4)/sqrt(1/2*sqrt(5) - 1/2)) + 1/10*sqrt(10*sqrt(5) - 10)*log(sqrt(1/2*sqrt(5) + 1/2) + (-1/x + 1)^(1/4)) + 1/10*sqrt(10*sqrt(5) + 10)*log(sqrt(1/2*sqrt(5) - 1/2) + (-1/x + 1)^(1/4)) - 1/10*sqrt(10*sqrt(5) - 10)*log(abs(-sqrt(1/2*sqrt(5) + 1/2) + (-1/x + 1)^(1/4))) - 1/10*sqrt(10*sqrt(5) + 10)*log(abs(-sqrt(1/2*sqrt(5) - 1/2) + (-1/x + 1)^(1/4))) - 29/16*arctan((-1/x + 1)^(1/4)) - 29/32*log((-1/x + 1)^(1/4) + 1) + 29/32*log(abs((-1/x + 1)^(1/4) - 1))","A",0
2790,1,1404,0,57.852664," ","integrate((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/x/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8}{5} \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{5}{2}} - \frac{16}{3} \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} d + 8 \, \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d^{2} - \frac{{\left(b {\left(d + \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d + \sqrt{c + \sqrt{b}}}\right)}{{\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c + \sqrt{b}}} d} + \frac{{\left(b {\left(d + \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d + \sqrt{c + \sqrt{b}}}\right)}{{\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c + \sqrt{b}}} d} - \frac{{\left(b {\left(d - \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d - \sqrt{c + \sqrt{b}}}\right)}{{\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c + \sqrt{b}}} d} + \frac{{\left(b {\left(d - \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d - \sqrt{c + \sqrt{b}}}\right)}{{\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c + \sqrt{b}}} d} - \frac{{\left(b {\left(d + \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d + \sqrt{c - \sqrt{b}}}\right)}{{\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c - \sqrt{b}}} d} + \frac{{\left(b {\left(d + \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d + \sqrt{c - \sqrt{b}}}\right)}{{\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c - \sqrt{b}}} d} - \frac{{\left(b {\left(d - \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d - \sqrt{c - \sqrt{b}}}\right)}{{\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c - \sqrt{b}}} d} + \frac{{\left(b {\left(d - \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d - \sqrt{c - \sqrt{b}}}\right)}{{\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c - \sqrt{b}}} d}"," ",0,"8/5*(d + sqrt(c + sqrt(a*x + b)))^(5/2) - 16/3*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*d + 8*sqrt(d + sqrt(c + sqrt(a*x + b)))*d^2 - (b*(d + sqrt(c + sqrt(b)))^2 - 2*b*(d + sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d + sqrt(c + sqrt(b))))/((d + sqrt(c + sqrt(b)))^(7/2) - 3*(d + sqrt(c + sqrt(b)))^(5/2)*d + 3*(d + sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c + sqrt(b)))*d^3 - c*(d + sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c + sqrt(b)))*d) + (b*(d + sqrt(c + sqrt(b)))^2 - 2*b*(d + sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d + sqrt(c + sqrt(b))))/((d + sqrt(c + sqrt(b)))^(7/2) - 3*(d + sqrt(c + sqrt(b)))^(5/2)*d + 3*(d + sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c + sqrt(b)))*d^3 - c*(d + sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c + sqrt(b)))*d) - (b*(d - sqrt(c + sqrt(b)))^2 - 2*b*(d - sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d - sqrt(c + sqrt(b))))/((d - sqrt(c + sqrt(b)))^(7/2) - 3*(d - sqrt(c + sqrt(b)))^(5/2)*d + 3*(d - sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c + sqrt(b)))*d^3 - c*(d - sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c + sqrt(b)))*d) + (b*(d - sqrt(c + sqrt(b)))^2 - 2*b*(d - sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d - sqrt(c + sqrt(b))))/((d - sqrt(c + sqrt(b)))^(7/2) - 3*(d - sqrt(c + sqrt(b)))^(5/2)*d + 3*(d - sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c + sqrt(b)))*d^3 - c*(d - sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c + sqrt(b)))*d) - (b*(d + sqrt(c - sqrt(b)))^2 - 2*b*(d + sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d + sqrt(c - sqrt(b))))/((d + sqrt(c - sqrt(b)))^(7/2) - 3*(d + sqrt(c - sqrt(b)))^(5/2)*d + 3*(d + sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c - sqrt(b)))*d^3 - c*(d + sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c - sqrt(b)))*d) + (b*(d + sqrt(c - sqrt(b)))^2 - 2*b*(d + sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d + sqrt(c - sqrt(b))))/((d + sqrt(c - sqrt(b)))^(7/2) - 3*(d + sqrt(c - sqrt(b)))^(5/2)*d + 3*(d + sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c - sqrt(b)))*d^3 - c*(d + sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c - sqrt(b)))*d) - (b*(d - sqrt(c - sqrt(b)))^2 - 2*b*(d - sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d - sqrt(c - sqrt(b))))/((d - sqrt(c - sqrt(b)))^(7/2) - 3*(d - sqrt(c - sqrt(b)))^(5/2)*d + 3*(d - sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c - sqrt(b)))*d^3 - c*(d - sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c - sqrt(b)))*d) + (b*(d - sqrt(c - sqrt(b)))^2 - 2*b*(d - sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d - sqrt(c - sqrt(b))))/((d - sqrt(c - sqrt(b)))^(7/2) - 3*(d - sqrt(c - sqrt(b)))^(5/2)*d + 3*(d - sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c - sqrt(b)))*d^3 - c*(d - sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c - sqrt(b)))*d)","B",0
2791,1,1404,0,57.912019," ","integrate((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/x/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8}{5} \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{5}{2}} - \frac{16}{3} \, {\left(d + \sqrt{c + \sqrt{a x + b}}\right)}^{\frac{3}{2}} d + 8 \, \sqrt{d + \sqrt{c + \sqrt{a x + b}}} d^{2} - \frac{{\left(b {\left(d + \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d + \sqrt{c + \sqrt{b}}}\right)}{{\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c + \sqrt{b}}} d} + \frac{{\left(b {\left(d + \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d + \sqrt{c + \sqrt{b}}}\right)}{{\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c + \sqrt{b}}} d} - \frac{{\left(b {\left(d - \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d - \sqrt{c + \sqrt{b}}}\right)}{{\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c + \sqrt{b}}} d} + \frac{{\left(b {\left(d - \sqrt{c + \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c + \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d - \sqrt{c + \sqrt{b}}}\right)}{{\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c + \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c + \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c + \sqrt{b}}} d} - \frac{{\left(b {\left(d + \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d + \sqrt{c - \sqrt{b}}}\right)}{{\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c - \sqrt{b}}} d} + \frac{{\left(b {\left(d + \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d + \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d + \sqrt{c - \sqrt{b}}}\right)}{{\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d + \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d + \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d + \sqrt{c - \sqrt{b}}} d} - \frac{{\left(b {\left(d - \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} + \sqrt{d - \sqrt{c - \sqrt{b}}}\right)}{{\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c - \sqrt{b}}} d} + \frac{{\left(b {\left(d - \sqrt{c - \sqrt{b}}\right)}^{2} - 2 \, b {\left(d - \sqrt{c - \sqrt{b}}\right)} d + b d^{2}\right)} \log\left(\sqrt{d + \sqrt{c + \sqrt{a x + b}}} - \sqrt{d - \sqrt{c - \sqrt{b}}}\right)}{{\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{7}{2}} - 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{5}{2}} d + 3 \, {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} d^{2} - \sqrt{d - \sqrt{c - \sqrt{b}}} d^{3} - c {\left(d - \sqrt{c - \sqrt{b}}\right)}^{\frac{3}{2}} + c \sqrt{d - \sqrt{c - \sqrt{b}}} d}"," ",0,"8/5*(d + sqrt(c + sqrt(a*x + b)))^(5/2) - 16/3*(d + sqrt(c + sqrt(a*x + b)))^(3/2)*d + 8*sqrt(d + sqrt(c + sqrt(a*x + b)))*d^2 - (b*(d + sqrt(c + sqrt(b)))^2 - 2*b*(d + sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d + sqrt(c + sqrt(b))))/((d + sqrt(c + sqrt(b)))^(7/2) - 3*(d + sqrt(c + sqrt(b)))^(5/2)*d + 3*(d + sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c + sqrt(b)))*d^3 - c*(d + sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c + sqrt(b)))*d) + (b*(d + sqrt(c + sqrt(b)))^2 - 2*b*(d + sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d + sqrt(c + sqrt(b))))/((d + sqrt(c + sqrt(b)))^(7/2) - 3*(d + sqrt(c + sqrt(b)))^(5/2)*d + 3*(d + sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c + sqrt(b)))*d^3 - c*(d + sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c + sqrt(b)))*d) - (b*(d - sqrt(c + sqrt(b)))^2 - 2*b*(d - sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d - sqrt(c + sqrt(b))))/((d - sqrt(c + sqrt(b)))^(7/2) - 3*(d - sqrt(c + sqrt(b)))^(5/2)*d + 3*(d - sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c + sqrt(b)))*d^3 - c*(d - sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c + sqrt(b)))*d) + (b*(d - sqrt(c + sqrt(b)))^2 - 2*b*(d - sqrt(c + sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d - sqrt(c + sqrt(b))))/((d - sqrt(c + sqrt(b)))^(7/2) - 3*(d - sqrt(c + sqrt(b)))^(5/2)*d + 3*(d - sqrt(c + sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c + sqrt(b)))*d^3 - c*(d - sqrt(c + sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c + sqrt(b)))*d) - (b*(d + sqrt(c - sqrt(b)))^2 - 2*b*(d + sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d + sqrt(c - sqrt(b))))/((d + sqrt(c - sqrt(b)))^(7/2) - 3*(d + sqrt(c - sqrt(b)))^(5/2)*d + 3*(d + sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c - sqrt(b)))*d^3 - c*(d + sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c - sqrt(b)))*d) + (b*(d + sqrt(c - sqrt(b)))^2 - 2*b*(d + sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d + sqrt(c - sqrt(b))))/((d + sqrt(c - sqrt(b)))^(7/2) - 3*(d + sqrt(c - sqrt(b)))^(5/2)*d + 3*(d + sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d + sqrt(c - sqrt(b)))*d^3 - c*(d + sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d + sqrt(c - sqrt(b)))*d) - (b*(d - sqrt(c - sqrt(b)))^2 - 2*b*(d - sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) + sqrt(d - sqrt(c - sqrt(b))))/((d - sqrt(c - sqrt(b)))^(7/2) - 3*(d - sqrt(c - sqrt(b)))^(5/2)*d + 3*(d - sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c - sqrt(b)))*d^3 - c*(d - sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c - sqrt(b)))*d) + (b*(d - sqrt(c - sqrt(b)))^2 - 2*b*(d - sqrt(c - sqrt(b)))*d + b*d^2)*log(sqrt(d + sqrt(c + sqrt(a*x + b))) - sqrt(d - sqrt(c - sqrt(b))))/((d - sqrt(c - sqrt(b)))^(7/2) - 3*(d - sqrt(c - sqrt(b)))^(5/2)*d + 3*(d - sqrt(c - sqrt(b)))^(3/2)*d^2 - sqrt(d - sqrt(c - sqrt(b)))*d^3 - c*(d - sqrt(c - sqrt(b)))^(3/2) + c*sqrt(d - sqrt(c - sqrt(b)))*d)","B",0
2792,-1,0,0,0.000000," ","integrate(1/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2793,1,289,0,2.631710," ","integrate((-1+x)*(k*x-1)*(-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-2*b*(1+k)*x+(b*k^2+4*b*k+b)*x^2-2*b*k*(1+k)*x^3+(b*k^2-1)*x^4),x, algorithm=""giac"")","-\frac{{\left| b \right|} \log\left({\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \left(-\frac{1}{b}\right)^{\frac{1}{3}}\right)}{2 \, \left(-b^{5}\right)^{\frac{1}{3}}} + \frac{\sqrt{3} \left(-b^{5}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} \left(-\frac{1}{b}\right)^{\frac{1}{6}} + 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-\frac{1}{b}\right)^{\frac{1}{6}}}\right)}{2 \, b^{4}} - \frac{\sqrt{3} \left(-b^{5}\right)^{\frac{2}{3}} \arctan\left(-\frac{\sqrt{3} \left(-\frac{1}{b}\right)^{\frac{1}{6}} - 2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}}}{\left(-\frac{1}{b}\right)^{\frac{1}{6}}}\right)}{2 \, b^{4}} - \frac{\left(-b^{5}\right)^{\frac{2}{3}} \log\left(\sqrt{3} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{6}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \left(-\frac{1}{b}\right)^{\frac{1}{3}}\right)}{4 \, b^{4}} - \frac{\left(-b^{5}\right)^{\frac{2}{3}} \log\left(-\sqrt{3} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{6}} + {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + \left(-\frac{1}{b}\right)^{\frac{1}{3}}\right)}{4 \, b^{4}}"," ",0,"-1/2*abs(b)*log((k - k/x - 1/x + 1/x^2)^(2/3) + (-1/b)^(1/3))/(-b^5)^(1/3) + 1/2*sqrt(3)*(-b^5)^(2/3)*arctan((sqrt(3)*(-1/b)^(1/6) + 2*(k - k/x - 1/x + 1/x^2)^(1/3))/(-1/b)^(1/6))/b^4 - 1/2*sqrt(3)*(-b^5)^(2/3)*arctan(-(sqrt(3)*(-1/b)^(1/6) - 2*(k - k/x - 1/x + 1/x^2)^(1/3))/(-1/b)^(1/6))/b^4 - 1/4*(-b^5)^(2/3)*log(sqrt(3)*(k - k/x - 1/x + 1/x^2)^(1/3)*(-1/b)^(1/6) + (k - k/x - 1/x + 1/x^2)^(2/3) + (-1/b)^(1/3))/b^4 - 1/4*(-b^5)^(2/3)*log(-sqrt(3)*(k - k/x - 1/x + 1/x^2)^(1/3)*(-1/b)^(1/6) + (k - k/x - 1/x + 1/x^2)^(2/3) + (-1/b)^(1/3))/b^4","A",0
2794,0,0,0,0.000000," ","integrate((-1+2*(-2+k)*x+3*k*x^2)*(x^3-3*x^2+3*x-1)/((1-x)*x*(-k*x+1))^(2/3)/(-b+(1+5*b)*x-(10*b+k)*x^2+10*b*x^3-5*b*x^4+b*x^5),x, algorithm=""giac"")","\int \frac{{\left(3 \, k x^{2} + 2 \, {\left(k - 2\right)} x - 1\right)} {\left(x^{3} - 3 \, x^{2} + 3 \, x - 1\right)}}{{\left(b x^{5} - 5 \, b x^{4} + 10 \, b x^{3} - {\left(10 \, b + k\right)} x^{2} + {\left(5 \, b + 1\right)} x - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((3*k*x^2 + 2*(k - 2)*x - 1)*(x^3 - 3*x^2 + 3*x - 1)/((b*x^5 - 5*b*x^4 + 10*b*x^3 - (10*b + k)*x^2 + (5*b + 1)*x - b)*((k*x - 1)*(x - 1)*x)^(2/3)), x)","F",0
2795,0,0,0,0.000000," ","integrate((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{8} - 4 \, b\right)} {\left(a x^{4} + 2 \, b\right)}^{\frac{1}{4}}}{{\left(a x^{8} + c x^{4} - 4 \, b\right)} x^{6}}\,{d x}"," ",0,"integrate((a*x^8 - 4*b)*(a*x^4 + 2*b)^(1/4)/((a*x^8 + c*x^4 - 4*b)*x^6), x)","F",0
2796,0,0,0,0.000000," ","integrate((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x, algorithm=""giac"")","\int \frac{{\left(a x^{8} - 4 \, b\right)} {\left(a x^{4} + 2 \, b\right)}^{\frac{1}{4}}}{{\left(a x^{8} + c x^{4} - 4 \, b\right)} x^{6}}\,{d x}"," ",0,"integrate((a*x^8 - 4*b)*(a*x^4 + 2*b)^(1/4)/((a*x^8 + c*x^4 - 4*b)*x^6), x)","F",0
2797,0,0,0,0.000000," ","integrate((a^12*x^12-b^12)/(a^4*x^4-b^4)^(1/2)/(a^12*x^12+b^12),x, algorithm=""giac"")","\int \frac{a^{12} x^{12} - b^{12}}{{\left(a^{12} x^{12} + b^{12}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^12*x^12 - b^12)/((a^12*x^12 + b^12)*sqrt(a^4*x^4 - b^4)), x)","F",0
2798,-2,0,0,0.000000," ","integrate(1/(1-(1+x)*(a*x^2+b*x+c)^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
2799,0,0,0,0.000000," ","integrate((-x^4+1)*(-x^9+x^8+4*x^7-4*x^6-6*x^5+6*x^4+4*x^3-4*x^2-x+1)^(1/4)/(x^4+1),x, algorithm=""giac"")","\int -\frac{{\left(-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)}^{\frac{1}{4}} {\left(x^{4} - 1\right)}}{x^{4} + 1}\,{d x}"," ",0,"integrate(-(-x^9 + x^8 + 4*x^7 - 4*x^6 - 6*x^5 + 6*x^4 + 4*x^3 - 4*x^2 - x + 1)^(1/4)*(x^4 - 1)/(x^4 + 1), x)","F",0
2800,0,0,0,0.000000," ","integrate((-a*(a-5*b)-(3*a+5*b)*x+4*x^2)/((-a+x)*(-b+x))^(1/3)/(b-a^5*d-(-5*a^4*d+1)*x-10*a^3*d*x^2+10*a^2*d*x^3-5*a*d*x^4+d*x^5),x, algorithm=""giac"")","\int \frac{{\left(a - 5 \, b\right)} a + {\left(3 \, a + 5 \, b\right)} x - 4 \, x^{2}}{{\left(a^{5} d + 10 \, a^{3} d x^{2} - 10 \, a^{2} d x^{3} + 5 \, a d x^{4} - d x^{5} - {\left(5 \, a^{4} d - 1\right)} x - b\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((a - 5*b)*a + (3*a + 5*b)*x - 4*x^2)/((a^5*d + 10*a^3*d*x^2 - 10*a^2*d*x^3 + 5*a*d*x^4 - d*x^5 - (5*a^4*d - 1)*x - b)*((a - x)*(b - x))^(1/3)), x)","F",0
2801,1,282,0,0.277999," ","integrate((x^8+1)/(x^4-x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","-\frac{1}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + 4 i \, \left(-\frac{1}{131072} i + \frac{1}{131072}\right)^{\frac{1}{4}} \log\left(i \, \left(-2251799813685248 i + 2251799813685248\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 8192\right) - 4 i \, \left(-\frac{1}{131072} i + \frac{1}{131072}\right)^{\frac{1}{4}} \log\left(-i \, \left(-2251799813685248 i + 2251799813685248\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 8192\right) + i \, \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(\left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) - \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(i \, \left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) + \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(-i \, \left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) - i \, \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(-\left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) + \left(-\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(\left(-134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 128\right) - \left(-\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(-\left(-134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 128\right) + \frac{1}{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}} + \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"-1/4*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) + 1/8*2^(3/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) - 1/8*2^(3/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4)) + 4*I*(-1/131072*I + 1/131072)^(1/4)*log(I*(-2251799813685248*I + 2251799813685248)^(1/4)*(-1/x^2 + 1)^(1/4) + 8192) - 4*I*(-1/131072*I + 1/131072)^(1/4)*log(-I*(-2251799813685248*I + 2251799813685248)^(1/4)*(-1/x^2 + 1)^(1/4) + 8192) + I*(1/512*I + 1/512)^(1/4)*log((134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) - (1/512*I + 1/512)^(1/4)*log(I*(134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) + (1/512*I + 1/512)^(1/4)*log(-I*(134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) - I*(1/512*I + 1/512)^(1/4)*log(-(134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) + (-1/512*I + 1/512)^(1/4)*log((-134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) + 128) - (-1/512*I + 1/512)^(1/4)*log(-(-134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) + 128) + 1/(-1/x^2 + 1)^(1/4) + arctan((-1/x^2 + 1)^(1/4)) - 1/2*log((-1/x^2 + 1)^(1/4) + 1) + 1/2*log(-(-1/x^2 + 1)^(1/4) + 1)","B",0
2802,1,282,0,0.401659," ","integrate((x^8+1)/(x^4-x^2)^(1/4)/(x^8-1),x, algorithm=""giac"")","-\frac{1}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) + 4 i \, \left(-\frac{1}{131072} i + \frac{1}{131072}\right)^{\frac{1}{4}} \log\left(i \, \left(-2251799813685248 i + 2251799813685248\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 8192\right) - 4 i \, \left(-\frac{1}{131072} i + \frac{1}{131072}\right)^{\frac{1}{4}} \log\left(-i \, \left(-2251799813685248 i + 2251799813685248\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 8192\right) + i \, \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(\left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) - \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(i \, \left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) + \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(-i \, \left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) - i \, \left(\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(-\left(134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} - 128 i\right) + \left(-\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(\left(-134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 128\right) - \left(-\frac{1}{512} i + \frac{1}{512}\right)^{\frac{1}{4}} \log\left(-\left(-134217728 i + 134217728\right)^{\frac{1}{4}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 128\right) + \frac{1}{{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}} + \arctan\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}}\right) - \frac{1}{2} \, \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \log\left(-{\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"-1/4*2^(3/4)*arctan(1/2*2^(3/4)*(-1/x^2 + 1)^(1/4)) + 1/8*2^(3/4)*log(2^(1/4) + (-1/x^2 + 1)^(1/4)) - 1/8*2^(3/4)*log(2^(1/4) - (-1/x^2 + 1)^(1/4)) + 4*I*(-1/131072*I + 1/131072)^(1/4)*log(I*(-2251799813685248*I + 2251799813685248)^(1/4)*(-1/x^2 + 1)^(1/4) + 8192) - 4*I*(-1/131072*I + 1/131072)^(1/4)*log(-I*(-2251799813685248*I + 2251799813685248)^(1/4)*(-1/x^2 + 1)^(1/4) + 8192) + I*(1/512*I + 1/512)^(1/4)*log((134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) - (1/512*I + 1/512)^(1/4)*log(I*(134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) + (1/512*I + 1/512)^(1/4)*log(-I*(134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) - I*(1/512*I + 1/512)^(1/4)*log(-(134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) - 128*I) + (-1/512*I + 1/512)^(1/4)*log((-134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) + 128) - (-1/512*I + 1/512)^(1/4)*log(-(-134217728*I + 134217728)^(1/4)*(-1/x^2 + 1)^(1/4) + 128) + 1/(-1/x^2 + 1)^(1/4) + arctan((-1/x^2 + 1)^(1/4)) - 1/2*log((-1/x^2 + 1)^(1/4) + 1) + 1/2*log(-(-1/x^2 + 1)^(1/4) + 1)","B",0
2803,0,0,0,0.000000," ","integrate((a*b-(a+b)*x+x^2)/((-a+x)*(-b+x)^2)^(2/3)/(a^2-b^2*d-2*(-b*d+a)*x+(1-d)*x^2),x, algorithm=""giac"")","\int -\frac{a b - {\left(a + b\right)} x + x^{2}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(b^{2} d + {\left(d - 1\right)} x^{2} - a^{2} - 2 \, {\left(b d - a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b - (a + b)*x + x^2)/((-(a - x)*(b - x)^2)^(2/3)*(b^2*d + (d - 1)*x^2 - a^2 - 2*(b*d - a)*x)), x)","F",0
2804,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(x^4-1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\sqrt{x^{4} + 1} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(sqrt(x^4 + 1)*(x^4 - 1)), x)","F",0
2805,0,0,0,0.000000," ","integrate((x^6-1)/(x^4-x^2)^(1/3)/(x^6+1),x, algorithm=""giac"")","\int \frac{x^{6} - 1}{{\left(x^{6} + 1\right)} {\left(x^{4} - x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 - 1)/((x^6 + 1)*(x^4 - x^2)^(1/3)), x)","F",0
2806,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(1+x),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{x + 1}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(x + 1), x)","F",0
2807,0,0,0,0.000000," ","integrate((a*x^2+b)/(-a*x^2+b)/(a*x^5+b*x^3)^(1/4),x, algorithm=""giac"")","\int -\frac{a x^{2} + b}{{\left(a x^{5} + b x^{3}\right)}^{\frac{1}{4}} {\left(a x^{2} - b\right)}}\,{d x}"," ",0,"integrate(-(a*x^2 + b)/((a*x^5 + b*x^3)^(1/4)*(a*x^2 - b)), x)","F",0
2808,0,0,0,0.000000," ","integrate((x^3+4)*(x^4+x^3+1)/(x^3+1)^(1/4)/(x^8+x^6+2*x^3+1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{3} + 1\right)} {\left(x^{3} + 4\right)}}{{\left(x^{8} + x^{6} + 2 \, x^{3} + 1\right)} {\left(x^{3} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^4 + x^3 + 1)*(x^3 + 4)/((x^8 + x^6 + 2*x^3 + 1)*(x^3 + 1)^(1/4)), x)","F",0
2809,0,0,0,0.000000," ","integrate(x^2*(1+x)^(1/2)/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + 1} x^{2}}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(sqrt(x + 1)*x^2/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2810,0,0,0,0.000000," ","integrate(x^2*(1+x)^(1/2)/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{x + 1} x^{2}}{x^{2} - \sqrt{x + 1} \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(sqrt(x + 1)*x^2/(x^2 - sqrt(x + 1)*sqrt(sqrt(x + 1) + 1)), x)","F",0
2811,1,704,0,0.331286," ","integrate((x^4-a*x-b)*(a*x^4+b*x^3)^(1/4)/(a*x-b),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(19712 \, a^{4} b^{2} - 9843 \, b^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{8192 \, \left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{\sqrt{2} {\left(19712 \, a^{4} b^{2} - 9843 \, b^{5}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{8192 \, \left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{\sqrt{2} {\left(19712 \, a^{4} b^{2} - 9843 \, b^{5}\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{16384 \, \left(-a\right)^{\frac{3}{4}} a^{5}} - \frac{\sqrt{2} {\left(19712 \, a^{4} b^{2} - 9843 \, b^{5}\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{16384 \, \left(-a\right)^{\frac{3}{4}} a^{5}} + \frac{\sqrt{2} {\left(2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} a^{4} b^{2} - 2^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} b^{5}\right)} \log\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{2 \, a^{6}} - \frac{\sqrt{2} {\left(2 \cdot 2^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} a^{4} b^{2} - 2^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} b^{5}\right)} \log\left(-2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{2} \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right)}{2 \, a^{6}} - \frac{{\left(65280 \, {\left(a + \frac{b}{x}\right)}^{\frac{17}{4}} a^{4} b^{2} - 245760 \, {\left(a + \frac{b}{x}\right)}^{\frac{13}{4}} a^{5} b^{2} + 345600 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} a^{6} b^{2} - 215040 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a^{7} b^{2} + 49920 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{8} b^{2} - 32705 \, {\left(a + \frac{b}{x}\right)}^{\frac{17}{4}} b^{5} + 114400 \, {\left(a + \frac{b}{x}\right)}^{\frac{13}{4}} a b^{5} - 157370 \, {\left(a + \frac{b}{x}\right)}^{\frac{9}{4}} a^{2} b^{5} + 94296 \, {\left(a + \frac{b}{x}\right)}^{\frac{5}{4}} a^{3} b^{5} - 24765 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a^{4} b^{5}\right)} x^{5}}{30720 \, a^{5} b^{5}} + \frac{{\left(2 \cdot 2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} a^{4} b^{2} - 2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b^{5}\right)} \arctan\left(\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{6}} + \frac{{\left(2 \cdot 2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} a^{4} b^{2} - 2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} b^{5}\right)} \arctan\left(-\frac{2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{6}}"," ",0,"1/8192*sqrt(2)*(19712*a^4*b^2 - 9843*b^5)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^5) + 1/8192*sqrt(2)*(19712*a^4*b^2 - 9843*b^5)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^5) + 1/16384*sqrt(2)*(19712*a^4*b^2 - 9843*b^5)*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^5) - 1/16384*sqrt(2)*(19712*a^4*b^2 - 9843*b^5)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x))/((-a)^(3/4)*a^5) + 1/2*sqrt(2)*(2*2^(1/4)*(-a)^(1/4)*a^4*b^2 - 2^(1/4)*(-a)^(1/4)*b^5)*log(2^(3/4)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x))/a^6 - 1/2*sqrt(2)*(2*2^(1/4)*(-a)^(1/4)*a^4*b^2 - 2^(1/4)*(-a)^(1/4)*b^5)*log(-2^(3/4)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(2)*sqrt(-a) + sqrt(a + b/x))/a^6 - 1/30720*(65280*(a + b/x)^(17/4)*a^4*b^2 - 245760*(a + b/x)^(13/4)*a^5*b^2 + 345600*(a + b/x)^(9/4)*a^6*b^2 - 215040*(a + b/x)^(5/4)*a^7*b^2 + 49920*(a + b/x)^(1/4)*a^8*b^2 - 32705*(a + b/x)^(17/4)*b^5 + 114400*(a + b/x)^(13/4)*a*b^5 - 157370*(a + b/x)^(9/4)*a^2*b^5 + 94296*(a + b/x)^(5/4)*a^3*b^5 - 24765*(a + b/x)^(1/4)*a^4*b^5)*x^5/(a^5*b^5) + (2*2^(3/4)*(-a)^(1/4)*a^4*b^2 - 2^(3/4)*(-a)^(1/4)*b^5)*arctan(1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^6 + (2*2^(3/4)*(-a)^(1/4)*a^4*b^2 - 2^(3/4)*(-a)^(1/4)*b^5)*arctan(-1/2*2^(1/4)*(2^(3/4)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4))/a^6","B",0
2812,0,0,0,0.000000," ","integrate((-4*a+b+3*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/((-a+x)*(-b+x)^2)^(2/3)/(a+b^4*d-(4*b^3*d+1)*x+6*b^2*d*x^2-4*b*d*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{{\left(b^{3} - 3 \, b^{2} x + 3 \, b x^{2} - x^{3}\right)} {\left(4 \, a - b - 3 \, x\right)}}{{\left(b^{4} d + 6 \, b^{2} d x^{2} - 4 \, b d x^{3} + d x^{4} - {\left(4 \, b^{3} d + 1\right)} x + a\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b^3 - 3*b^2*x + 3*b*x^2 - x^3)*(4*a - b - 3*x)/((b^4*d + 6*b^2*d*x^2 - 4*b*d*x^3 + d*x^4 - (4*b^3*d + 1)*x + a)*(-(a - x)*(b - x)^2)^(2/3)), x)","F",0
2813,1,123,0,0.368689," ","integrate(x^2*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-(2*k^2+2*k)*x^3+(k^2-b)*x^4),x, algorithm=""giac"")","-\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + b^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right)}{2 \, b^{\frac{2}{3}}} - \frac{\log\left({\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{4}{3}} + b^{\frac{1}{3}} {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} + b^{\frac{2}{3}}\right)}{4 \, b^{\frac{2}{3}}} + \frac{\log\left({\left| {\left(k - \frac{k}{x} - \frac{1}{x} + \frac{1}{x^{2}}\right)}^{\frac{2}{3}} - b^{\frac{1}{3}} \right|}\right)}{2 \, b^{\frac{2}{3}}}"," ",0,"-1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(k - k/x - 1/x + 1/x^2)^(2/3) + b^(1/3))/b^(1/3))/b^(2/3) - 1/4*log((k - k/x - 1/x + 1/x^2)^(4/3) + b^(1/3)*(k - k/x - 1/x + 1/x^2)^(2/3) + b^(2/3))/b^(2/3) + 1/2*log(abs((k - k/x - 1/x + 1/x^2)^(2/3) - b^(1/3)))/b^(2/3)","A",0
2814,0,0,0,0.000000," ","integrate(1/(c+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{c + \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(1/(c + sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2815,0,0,0,0.000000," ","integrate((-7+x)*(3*x^3-5*x^2+x+1)^(1/3)/(-5+x)/(-1+x)^3,x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{3} - 5 \, x^{2} + x + 1\right)}^{\frac{1}{3}} {\left(x - 7\right)}}{{\left(x - 1\right)}^{3} {\left(x - 5\right)}}\,{d x}"," ",0,"integrate((3*x^3 - 5*x^2 + x + 1)^(1/3)*(x - 7)/((x - 1)^3*(x - 5)), x)","F",0
2816,-2,0,0,0.000000," ","integrate((a^2*x^2+b^2)/(a^2*x^2-b^2)^3/(a*x^3-b*x^2)^(1/3),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Algebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootof-(13*((a-b/x)^(1/3))^2*(a-b/x)-23*((a-b/x)^(1/3))^2*a)/48/b^4/(a-b/x-2*a)^2+(-336*(a-b/x)^2+105*(a-b/x)*a-24*a^2)/224/b^4/(a-b/x)^(1/3)/(a-b/x)^2-59/288/(2*a)^(1/3)/b^4*ln(((a-b/x)^(1/3))^2+(2*a)^(1/3)*(a-b/x)^(1/3)+(2*a)^(1/3)*(2*a)^(1/3))+59*((2*a)^(1/3))^2/96/sqrt(3)/a/b^4*atan(((a-b/x)^(1/3)+1/2*(2*a)^(1/3))/sqrt(3)*2/(2*a)^(1/3))+59*(2*a)^(1/3)*(2*a)^(1/3)/288/b^4/a*ln(abs((a-b/x)^(1/3)-(2*a)^(1/3)))","F(-2)",0
2817,0,0,0,0.000000," ","integrate((c*x+d)/(c*x-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x + d}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}} {\left(c x - d\right)}}\,{d x}"," ",0,"integrate((c*x + d)/(sqrt(a*x + sqrt(a^2*x^2 + b^2))*(c*x - d)), x)","F",0
2818,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/(-2*c*x+x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2819,0,0,0,0.000000," ","integrate((a*x^4-b*x^3)^(1/4)/(-2*c*x+x^2-d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
2820,0,0,0,0.000000," ","integrate(x*(k*x-1)*(-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(-1+4*x+(-6+b)*x^2+(-2*b*k+4)*x^3+(b*k^2-1)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(2 \, k - 1\right)} x - 1\right)} {\left(k x - 1\right)} x}{{\left({\left(b k^{2} - 1\right)} x^{4} - 2 \, {\left(b k - 2\right)} x^{3} + {\left(b - 6\right)} x^{2} + 4 \, x - 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((2*k - 1)*x - 1)*(k*x - 1)*x/(((b*k^2 - 1)*x^4 - 2*(b*k - 2)*x^3 + (b - 6)*x^2 + 4*x - 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2821,-1,0,0,0.000000," ","integrate((1+(-2+3*k)*x-(4*k^2+k)*x^2+3*k^2*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(5*b*k+1)*x-(10*b*k^2+1)*x^2+10*b*k^3*x^3-5*b*k^4*x^4+b*k^5*x^5),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2822,0,0,0,0.000000," ","integrate((c*x+d)^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x + d\right)}^{2}}{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((c*x + d)^2/sqrt(a*x + sqrt(a^2*x^2 + b^2)), x)","F",0
2823,0,0,0,0.000000," ","integrate((1-(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3))/(x^2+(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3)),x, algorithm=""giac"")","\int -\frac{{\left(-3 \, x^{10} + x^{9} - 9 \, x^{7} + 3 \, x^{6} - 9 \, x^{4} + 3 \, x^{3} - 3 \, x + 1\right)}^{\frac{1}{3}} - 1}{x^{2} + {\left(-3 \, x^{10} + x^{9} - 9 \, x^{7} + 3 \, x^{6} - 9 \, x^{4} + 3 \, x^{3} - 3 \, x + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-((-3*x^10 + x^9 - 9*x^7 + 3*x^6 - 9*x^4 + 3*x^3 - 3*x + 1)^(1/3) - 1)/(x^2 + (-3*x^10 + x^9 - 9*x^7 + 3*x^6 - 9*x^4 + 3*x^3 - 3*x + 1)^(1/3)), x)","F",0
2824,0,0,0,0.000000," ","integrate((-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(2/3),x, algorithm=""giac"")","\int -\frac{k x - 1}{\left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}} {\left({\left(k - 2\right)} x + 1\right)}}\,{d x}"," ",0,"integrate(-(k*x - 1)/(((k*x - 1)*(x - 1)*x)^(2/3)*((k - 2)*x + 1)), x)","F",0
2825,0,0,0,0.000000," ","integrate((x^3+x^2+1)/(x^3+x^2-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} + x^{2} + 1}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} + x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^3 + x^2 + 1)/((x^3 + x^2)^(1/3)*(x^3 + x^2 - 1)), x)","F",0
2826,0,0,0,0.000000," ","integrate((x^3+x^2+1)/(x^3+x^2-1)/(x^3+x^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} + x^{2} + 1}{{\left(x^{3} + x^{2}\right)}^{\frac{1}{3}} {\left(x^{3} + x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((x^3 + x^2 + 1)/((x^3 + x^2)^(1/3)*(x^3 + x^2 - 1)), x)","F",0
2827,-1,0,0,0.000000," ","integrate((a*x+(a*x-b)^(1/2))^(1/2)/x/(a*x-b)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2828,-1,0,0,0.000000," ","integrate((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2829,-2,0,0,0.000000," ","integrate(x^4*(a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,x]=[0,-68,-97]Precision problem choosing root in common_EXT, current precision 14Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,x]=[-67,8,-61]schur row 3 -1.00112e-08Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[24,49,-35]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[20,8,5]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[3,-23,44]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-92,-93,-41]schur row 3 -1.33253e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[93,-2,-73]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[40,96,-96]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-24,-84,-66]schur row 3 -9.75014e-10Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[66,44,-64]schur row 3 3.13659e-08Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-95,-41,-48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[1,69,4]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[99,-63,-95]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[81,83,-9]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-89,27,4]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[56,75,-77]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[37,-64,-25]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-98,-33,59]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[92,64,-69]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[21,-17,-9]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-4,96,-65]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-85,-1,-30]schur row 3 -5.59763e-10Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-75,7,-7]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-4,-6,-56]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-5,-69,82]schur row 3 1.56409e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-71,32,48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[73,53,-20]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[16,51,70]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-53,-39,82]schur row 3 -6.64448e-11Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-15,91,-72]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[74,86,-86]schur row 1 6.32223e-07Francis algorithm not precise enough for[1.0,0.0,-599084431612,-1.19816667401e+12,8.97248832883e+22]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-28,72,-21]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[64,-73,13]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-74,31,29]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[95,-80,-59]schur row 3 7.64423e-09Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-12,53,99]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[69,-96,-89]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[26,-78,-6]Unable to divide, perhaps due to rounding error%%%{%%%{%%{[-2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueUnable to divide, perhaps due to rounding error%%%{%%%{%%{[2,%%%{4,[1]%%%}]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%}/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[1]%%%}+%%%{%%%{1,[1]%%%},[0]%%%} / %%%{%%%{1/%%%{%%{[-2,1]:[1,0,%%%{1,[1]%%%}]%%},[0]%%%},[0]%%%},[0]%%%} Error: Bad Argument ValueEvaluation time: 10.42integrate((4*a^2*x^8*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)-2*a^2*x^8-4*a*x^6*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)+4*b*x^4*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)-2*b*x^4+x^4*sqrt(sqrt(a^2*x^4+b)+a*x^2)*sqrt(a^2*x^4+b)+2*x^4*(a^2*x^4+b))/(4*a^2*x^4-4*a*x^2+4*b+1),x)","F(-2)",0
2830,-2,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(4*a^2*x^2-4*a*x+4*b+1)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[51,-96,32]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[-32,-18,-85]schur row 3 -9.50039e-09sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [23,15,-30]Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [26,40,-54]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[89,80,72]schur row 3 -1.62329e-07Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-43,-85,11]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[62,-15,-10]schur row 3 4.84558e-08Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[92,90,-98]schur row 3 -1.16593e-07Discontinuities at zeroes of 4*a^2*x^2-4*a*x+4*b+1 were not checkedEvaluation time: 40.41Done","F(-2)",0
2831,-2,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(4*a^2*x^2-4*a*x+4*b+1)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[51,-96,32]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [c]=[-32,-18,-85]schur row 3 -9.50039e-09sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [23,15,-30]Warning, choosing root of [1,0,%%%{-2,[2,0,2]%%%}+%%%{2,[1,0,1]%%%}+%%%{-2,[0,1,0]%%%},%%%{4,[2,0,2]%%%}+%%%{4,[0,1,0]%%%},%%%{1,[4,0,4]%%%}+%%%{2,[3,0,3]%%%}+%%%{2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,2,0]%%%}+%%%{-1,[0,1,0]%%%}] at parameters values [26,40,-54]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[89,80,72]schur row 3 -1.62329e-07Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[-43,-85,11]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[62,-15,-10]schur row 3 4.84558e-08Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,t_nostep]=[92,90,-98]schur row 3 -1.16593e-07Discontinuities at zeroes of 4*a^2*x^2-4*a*x+4*b+1 were not checkedEvaluation time: 40.63Done","F(-2)",0
2832,1,256,0,0.412134," ","integrate(x^2/(a*x^2+b)/(x^3+x)^(1/3),x, algorithm=""giac"")","-\frac{b \left(-\frac{a - b}{b}\right)^{\frac{2}{3}} \log\left({\left| -\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(a^{2} - a b\right)}} - \frac{3 \, {\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a - b}{b}\right)^{\frac{1}{3}}}\right)}{2 \, {\left(\sqrt{3} a^{2} b - \sqrt{3} a b^{2}\right)}} + \frac{{\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \log\left(\left(-\frac{a - b}{b}\right)^{\frac{2}{3}} + \left(-\frac{a - b}{b}\right)^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, {\left(a^{2} b - a b^{2}\right)}} - \frac{\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right)}{2 \, a} + \frac{\log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}{4 \, a} - \frac{\log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)}{2 \, a}"," ",0,"-1/2*b*(-(a - b)/b)^(2/3)*log(abs(-(-(a - b)/b)^(1/3) + (1/x^2 + 1)^(1/3)))/(a^2 - a*b) - 3/2*(-a*b^2 + b^3)^(2/3)*arctan(1/3*sqrt(3)*((-(a - b)/b)^(1/3) + 2*(1/x^2 + 1)^(1/3))/(-(a - b)/b)^(1/3))/(sqrt(3)*a^2*b - sqrt(3)*a*b^2) + 1/4*(-a*b^2 + b^3)^(2/3)*log((-(a - b)/b)^(2/3) + (-(a - b)/b)^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3))/(a^2*b - a*b^2) - 1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1))/a + 1/4*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1)/a - 1/2*log(abs((1/x^2 + 1)^(1/3) - 1))/a","A",0
2833,0,0,0,0.000000," ","integrate((x^6+1)/(x^4+x^2)^(1/3)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{6} + 1}{{\left(x^{6} - 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 + 1)/((x^6 - 1)*(x^4 + x^2)^(1/3)), x)","F",0
2834,1,178,0,1.660716," ","integrate((3*x^4-2)^(1/2)*(3*x^4-1)/x^3/(3*x^8-3*x^4+1),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{3} {\left({\left(\sqrt{3} x^{2} - \sqrt{3 \, x^{4} - 2}\right)}^{4} - 8 \, {\left(\sqrt{3} x^{2} - \sqrt{3 \, x^{4} - 2}\right)}^{2} + 4\right)} \log\left({\left| -{\left(\sqrt{3} x^{2} - \sqrt{3 \, x^{4} - 2}\right)}^{8} + 4 \, {\left(\sqrt{3} x^{2} - \sqrt{3 \, x^{4} - 2}\right)}^{6} - 24 \, {\left(\sqrt{3} x^{2} - \sqrt{3 \, x^{4} - 2}\right)}^{4} + 16 \, {\left(\sqrt{3} x^{2} - \sqrt{3 \, x^{4} - 2}\right)}^{2} - 16 \right|}\right) + \frac{2 \, \sqrt{3}}{{\left(\sqrt{3} x^{2} - \sqrt{3 \, x^{4} - 2}\right)}^{2} + 2}"," ",0,"1/16*sqrt(3)*((sqrt(3)*x^2 - sqrt(3*x^4 - 2))^4 - 8*(sqrt(3)*x^2 - sqrt(3*x^4 - 2))^2 + 4)*log(abs(-(sqrt(3)*x^2 - sqrt(3*x^4 - 2))^8 + 4*(sqrt(3)*x^2 - sqrt(3*x^4 - 2))^6 - 24*(sqrt(3)*x^2 - sqrt(3*x^4 - 2))^4 + 16*(sqrt(3)*x^2 - sqrt(3*x^4 - 2))^2 - 16)) + 2*sqrt(3)/((sqrt(3)*x^2 - sqrt(3*x^4 - 2))^2 + 2)","B",0
2835,0,0,0,0.000000," ","integrate(1/(a^2*x^2-b*x)^(5/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{2} - b x\right)}^{\frac{5}{2}} {\left(a x^{2} + \sqrt{a^{2} x^{2} - b x} x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a^2*x^2 - b*x)^(5/2)*(a*x^2 + sqrt(a^2*x^2 - b*x)*x)^(3/2)), x)","F",0
2836,0,0,0,0.000000," ","integrate((a-2*b+x)*(-b+x)/((-a+x)*(-b+x))^(1/3)/(a^4-b^2*d-2*(2*a^3-b*d)*x+(6*a^2-d)*x^2-4*a*x^3+x^4),x, algorithm=""giac"")","\int -\frac{{\left(a - 2 \, b + x\right)} {\left(b - x\right)}}{{\left(a^{4} - 4 \, a x^{3} + x^{4} - b^{2} d + {\left(6 \, a^{2} - d\right)} x^{2} - 2 \, {\left(2 \, a^{3} - b d\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(a - 2*b + x)*(b - x)/((a^4 - 4*a*x^3 + x^4 - b^2*d + (6*a^2 - d)*x^2 - 2*(2*a^3 - b*d)*x)*((a - x)*(b - x))^(1/3)), x)","F",0
2837,0,0,0,0.000000," ","integrate((-1+x)*x*(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-4*k*x+(6*k^2-b)*x^2+(-4*k^3+2*b)*x^3+(k^4-b)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(k - 2\right)} x + 1\right)} {\left(x - 1\right)} x}{{\left({\left(k^{4} - b\right)} x^{4} - 2 \, {\left(2 \, k^{3} - b\right)} x^{3} + {\left(6 \, k^{2} - b\right)} x^{2} - 4 \, k x + 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((k - 2)*x + 1)*(x - 1)*x/(((k^4 - b)*x^4 - 2*(2*k^3 - b)*x^3 + (6*k^2 - b)*x^2 - 4*k*x + 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2838,0,0,0,0.000000," ","integrate((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6-4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + 4\right)} {\left(x^{3} - 1\right)}^{\frac{2}{3}}}{{\left(x^{6} - 4\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 + 4)*(x^3 - 1)^(2/3)/((x^6 - 4)*x^6), x)","F",0
2839,-1,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6)/(a^2*x^2-b)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2840,0,0,0,0.000000," ","integrate((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(b*d-(a+d)*x+x^2),x, algorithm=""giac"")","\int -\frac{{\left(a b - 2 \, b x + x^{2}\right)} {\left(b - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{2}{3}} {\left(b d - {\left(a + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate(-(a*b - 2*b*x + x^2)*(b - x)/((-(a - x)*(b - x)^2*x)^(2/3)*(b*d - (a + d)*x + x^2)), x)","F",0
2841,0,0,0,0.000000," ","integrate((c*x^4-d)/x/(a*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{c x^{4} - d}{{\left(a x^{3} - b\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((c*x^4 - d)/((a*x^3 - b)^(1/3)*x), x)","F",0
2842,0,0,0,0.000000," ","integrate((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(b-(a*d+1)*x+d*x^2),x, algorithm=""giac"")","\int \frac{a b - 2 \, b x + x^{2}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}} {\left(d x^{2} - {\left(a d + 1\right)} x + b\right)}}\,{d x}"," ",0,"integrate((a*b - 2*b*x + x^2)/((-(a - x)*(b - x)^2*x)^(1/3)*(d*x^2 - (a*d + 1)*x + b)), x)","F",0
2843,0,0,0,0.000000," ","integrate((-a*b^2+(4*a-b)*b*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a^2+(b^2*d+2*a)*x-(2*b*d+1)*x^2+d*x^3),x, algorithm=""giac"")","\int -\frac{a b^{2} - {\left(4 \, a - b\right)} b x + 3 \, a x^{2} - x^{3}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}} {\left(d x^{3} - {\left(2 \, b d + 1\right)} x^{2} - a^{2} + {\left(b^{2} d + 2 \, a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b^2 - (4*a - b)*b*x + 3*a*x^2 - x^3)/((-(a - x)*(b - x)^2*x)^(1/3)*(d*x^3 - (2*b*d + 1)*x^2 - a^2 + (b^2*d + 2*a)*x)), x)","F",0
2844,0,0,0,0.000000," ","integrate((-4*a+b+3*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/((-a+x)*(-b+x)^2)^(2/3)/(b^4+a*d-(4*b^3+d)*x+6*b^2*x^2-4*b*x^3+x^4),x, algorithm=""giac"")","\int \frac{{\left(b^{3} - 3 \, b^{2} x + 3 \, b x^{2} - x^{3}\right)} {\left(4 \, a - b - 3 \, x\right)}}{{\left(b^{4} + 6 \, b^{2} x^{2} - 4 \, b x^{3} + x^{4} + a d - {\left(4 \, b^{3} + d\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b^3 - 3*b^2*x + 3*b*x^2 - x^3)*(4*a - b - 3*x)/((b^4 + 6*b^2*x^2 - 4*b*x^3 + x^4 + a*d - (4*b^3 + d)*x)*(-(a - x)*(b - x)^2)^(2/3)), x)","F",0
2845,1,505,0,0.513063," ","integrate((a*x^4-b*x^3)^(1/4)/x/(c*x-d),x, algorithm=""giac"")","\frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{c} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{c} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{2 \, c} - \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a - \frac{b}{x}}\right)}{2 \, c} - \frac{\sqrt{2} {\left(b c d^{3} - a d^{4}\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b c - a d}{d}\right)^{\frac{1}{4}} + 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{b c - a d}{d}\right)^{\frac{1}{4}}}\right)}{c d} - \frac{\sqrt{2} {\left(b c d^{3} - a d^{4}\right)}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b c - a d}{d}\right)^{\frac{1}{4}} - 2 \, {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(\frac{b c - a d}{d}\right)^{\frac{1}{4}}}\right)}{c d} - \frac{\sqrt{2} {\left(b c d^{3} - a d^{4}\right)}^{\frac{1}{4}} \log\left(\sqrt{2} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} \left(\frac{b c - a d}{d}\right)^{\frac{1}{4}} + \sqrt{a - \frac{b}{x}} + \sqrt{\frac{b c - a d}{d}}\right)}{2 \, c d} + \frac{\sqrt{2} {\left(b c d^{3} - a d^{4}\right)}^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(a - \frac{b}{x}\right)}^{\frac{1}{4}} \left(\frac{b c - a d}{d}\right)^{\frac{1}{4}} + \sqrt{a - \frac{b}{x}} + \sqrt{\frac{b c - a d}{d}}\right)}{2 \, c d}"," ",0,"sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a - b/x)^(1/4))/(-a)^(1/4))/c + sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a - b/x)^(1/4))/(-a)^(1/4))/c + 1/2*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/c - 1/2*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-a)^(1/4)*(a - b/x)^(1/4) + sqrt(-a) + sqrt(a - b/x))/c - sqrt(2)*(b*c*d^3 - a*d^4)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*((b*c - a*d)/d)^(1/4) + 2*(a - b/x)^(1/4))/((b*c - a*d)/d)^(1/4))/(c*d) - sqrt(2)*(b*c*d^3 - a*d^4)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*((b*c - a*d)/d)^(1/4) - 2*(a - b/x)^(1/4))/((b*c - a*d)/d)^(1/4))/(c*d) - 1/2*sqrt(2)*(b*c*d^3 - a*d^4)^(1/4)*log(sqrt(2)*(a - b/x)^(1/4)*((b*c - a*d)/d)^(1/4) + sqrt(a - b/x) + sqrt((b*c - a*d)/d))/(c*d) + 1/2*sqrt(2)*(b*c*d^3 - a*d^4)^(1/4)*log(-sqrt(2)*(a - b/x)^(1/4)*((b*c - a*d)/d)^(1/4) + sqrt(a - b/x) + sqrt((b*c - a*d)/d))/(c*d)","B",0
2846,1,317,0,1.253792," ","integrate((-a+x)*(-b+x)*(-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2+4*a*b+b^2)*d*x^2-2*(a+b)*d*x^3+(-1+d)*x^4),x, algorithm=""giac"")","-\frac{{\left| d \right|} \log\left({\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{2}{3}} + \left(-\frac{1}{d}\right)^{\frac{1}{3}}\right)}{2 \, \left(-d^{5}\right)^{\frac{1}{3}}} + \frac{\sqrt{3} \left(-d^{5}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + 2 \, {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{2 \, d^{4}} - \frac{\sqrt{3} \left(-d^{5}\right)^{\frac{2}{3}} \arctan\left(-\frac{\sqrt{3} \left(-\frac{1}{d}\right)^{\frac{1}{6}} - 2 \, {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}}}{\left(-\frac{1}{d}\right)^{\frac{1}{6}}}\right)}{2 \, d^{4}} - \frac{\left(-d^{5}\right)^{\frac{2}{3}} \log\left(\sqrt{3} {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{2}{3}} + \left(-\frac{1}{d}\right)^{\frac{1}{3}}\right)}{4 \, d^{4}} - \frac{\left(-d^{5}\right)^{\frac{2}{3}} \log\left(-\sqrt{3} {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{1}{3}} \left(-\frac{1}{d}\right)^{\frac{1}{6}} + {\left(\frac{a b}{x^{2}} - \frac{a}{x} - \frac{b}{x} + 1\right)}^{\frac{2}{3}} + \left(-\frac{1}{d}\right)^{\frac{1}{3}}\right)}{4 \, d^{4}}"," ",0,"-1/2*abs(d)*log((a*b/x^2 - a/x - b/x + 1)^(2/3) + (-1/d)^(1/3))/(-d^5)^(1/3) + 1/2*sqrt(3)*(-d^5)^(2/3)*arctan((sqrt(3)*(-1/d)^(1/6) + 2*(a*b/x^2 - a/x - b/x + 1)^(1/3))/(-1/d)^(1/6))/d^4 - 1/2*sqrt(3)*(-d^5)^(2/3)*arctan(-(sqrt(3)*(-1/d)^(1/6) - 2*(a*b/x^2 - a/x - b/x + 1)^(1/3))/(-1/d)^(1/6))/d^4 - 1/4*(-d^5)^(2/3)*log(sqrt(3)*(a*b/x^2 - a/x - b/x + 1)^(1/3)*(-1/d)^(1/6) + (a*b/x^2 - a/x - b/x + 1)^(2/3) + (-1/d)^(1/3))/d^4 - 1/4*(-d^5)^(2/3)*log(-sqrt(3)*(a*b/x^2 - a/x - b/x + 1)^(1/3)*(-1/d)^(1/6) + (a*b/x^2 - a/x - b/x + 1)^(2/3) + (-1/d)^(1/3))/d^4","A",0
2847,0,0,0,0.000000," ","integrate((x^6+x^3+1)/(x^5+x^3)^(1/4)/(-x^6+1),x, algorithm=""giac"")","\int -\frac{x^{6} + x^{3} + 1}{{\left(x^{6} - 1\right)} {\left(x^{5} + x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(x^6 + x^3 + 1)/((x^6 - 1)*(x^5 + x^3)^(1/4)), x)","F",0
2848,0,0,0,0.000000," ","integrate((-a-b*x+(a*k^2+b)*x^2)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-2*x+1),x, algorithm=""giac"")","\int \frac{{\left(a k^{2} + b\right)} x^{2} - b x - a}{{\left(k^{2} x^{2} - 2 \, x + 1\right)} \sqrt{{\left(k^{2} x - 1\right)} {\left(x - 1\right)} x}}\,{d x}"," ",0,"integrate(((a*k^2 + b)*x^2 - b*x - a)/((k^2*x^2 - 2*x + 1)*sqrt((k^2*x - 1)*(x - 1)*x)), x)","F",0
2849,0,0,0,0.000000," ","integrate((x^8-2*x^4+1)/(x^4-1)^(1/4)/(2*x^8-2*x^4+1),x, algorithm=""giac"")","\int \frac{x^{8} - 2 \, x^{4} + 1}{{\left(2 \, x^{8} - 2 \, x^{4} + 1\right)} {\left(x^{4} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - 2*x^4 + 1)/((2*x^8 - 2*x^4 + 1)*(x^4 - 1)^(1/4)), x)","F",0
2850,0,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{c + \sqrt{a x + \sqrt{a^{2} x^{2} + b}}}\,{d x}"," ",0,"integrate(sqrt(c + sqrt(a*x + sqrt(a^2*x^2 + b))), x)","F",0
2851,1,209,0,0.288172," ","integrate(x^3/(x^2*(-a+x))^(1/3)/(-a^4+4*a^3*x-6*a^2*x^2+4*a*x^3+(-1+d)*x^4),x, algorithm=""giac"")","-\frac{\sqrt{3} \log\left(\sqrt{3} \left(-d\right)^{\frac{1}{6}} {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \left(-d\right)^{\frac{1}{3}}\right)}{8 \, a \left(-d\right)^{\frac{5}{6}}} - \frac{\sqrt{3} \left(-d\right)^{\frac{1}{6}} \log\left(-\sqrt{3} \left(-d\right)^{\frac{1}{6}} {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{a}{x} + 1\right)}^{\frac{4}{3}} + \left(-d\right)^{\frac{1}{3}}\right)}{8 \, a d} - \frac{\arctan\left(\frac{\sqrt{3} \left(-d\right)^{\frac{1}{6}} + 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}}{\left(-d\right)^{\frac{1}{6}}}\right)}{4 \, a \left(-d\right)^{\frac{5}{6}}} - \frac{\arctan\left(-\frac{\sqrt{3} \left(-d\right)^{\frac{1}{6}} - 2 \, {\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}}{\left(-d\right)^{\frac{1}{6}}}\right)}{4 \, a \left(-d\right)^{\frac{5}{6}}} - \frac{\arctan\left(\frac{{\left(-\frac{a}{x} + 1\right)}^{\frac{2}{3}}}{\left(-d\right)^{\frac{1}{6}}}\right)}{2 \, a \left(-d\right)^{\frac{5}{6}}}"," ",0,"-1/8*sqrt(3)*log(sqrt(3)*(-d)^(1/6)*(-a/x + 1)^(2/3) + (-a/x + 1)^(4/3) + (-d)^(1/3))/(a*(-d)^(5/6)) - 1/8*sqrt(3)*(-d)^(1/6)*log(-sqrt(3)*(-d)^(1/6)*(-a/x + 1)^(2/3) + (-a/x + 1)^(4/3) + (-d)^(1/3))/(a*d) - 1/4*arctan((sqrt(3)*(-d)^(1/6) + 2*(-a/x + 1)^(2/3))/(-d)^(1/6))/(a*(-d)^(5/6)) - 1/4*arctan(-(sqrt(3)*(-d)^(1/6) - 2*(-a/x + 1)^(2/3))/(-d)^(1/6))/(a*(-d)^(5/6)) - 1/2*arctan((-a/x + 1)^(2/3)/(-d)^(1/6))/(a*(-d)^(5/6))","A",0
2852,-2,0,0,0.000000," ","integrate((c+(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/2))^(1/2)/(a^2*x^2-b)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(4*a^2*x^2-4*a*x^2+x^2-4*b)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 1.4gen.cc:simplify/tmp.type!=_EXT Error: Bad Argument Value","F(-2)",0
2853,0,0,0,0.000000," ","integrate((-a*(a*b+a*c-2*b*c)+2*(a^2-b*c)*x+(-2*a+b+c)*x^2)/((-a+x)*(-b+x)*(-c+x))^(2/3)/(-b*c+a^2*d+(-2*a*d+b+c)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, a - b - c\right)} x^{2} + {\left(a b + a c - 2 \, b c\right)} a - 2 \, {\left(a^{2} - b c\right)} x}{\left(-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}\right)^{\frac{2}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b c - {\left(2 \, a d - b - c\right)} x\right)}}\,{d x}"," ",0,"integrate(-((2*a - b - c)*x^2 + (a*b + a*c - 2*b*c)*a - 2*(a^2 - b*c)*x)/((-(a - x)*(b - x)*(c - x))^(2/3)*(a^2*d + (d - 1)*x^2 - b*c - (2*a*d - b - c)*x)), x)","F",0
2854,0,0,0,0.000000," ","integrate(x^2*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^2*b^2+2*a*b*(a+b)*x-(a^2+4*a*b+b^2)*x^2+2*(a+b)*x^3+(-1+d)*x^4),x, algorithm=""giac"")","\int -\frac{{\left(2 \, a b - {\left(a + b\right)} x\right)} x^{2}}{{\left({\left(d - 1\right)} x^{4} - a^{2} b^{2} + 2 \, {\left(a + b\right)} a b x + 2 \, {\left(a + b\right)} x^{3} - {\left(a^{2} + 4 \, a b + b^{2}\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(2*a*b - (a + b)*x)*x^2/(((d - 1)*x^4 - a^2*b^2 + 2*(a + b)*a*b*x + 2*(a + b)*x^3 - (a^2 + 4*a*b + b^2)*x^2)*((a - x)*(b - x)*x)^(1/3)), x)","F",0
2855,0,0,0,0.000000," ","integrate((x^6+1)/(x^5+x^3)^(1/4)/(-x^6+1),x, algorithm=""giac"")","\int -\frac{x^{6} + 1}{{\left(x^{6} - 1\right)} {\left(x^{5} + x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(x^6 + 1)/((x^6 - 1)*(x^5 + x^3)^(1/4)), x)","F",0
2856,0,0,0,0.000000," ","integrate((a^16*x^16+b^16)/(a^4*x^4-b^4)^(1/2)/(a^16*x^16-b^16),x, algorithm=""giac"")","\int \frac{a^{16} x^{16} + b^{16}}{{\left(a^{16} x^{16} - b^{16}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^16*x^16 + b^16)/((a^16*x^16 - b^16)*sqrt(a^4*x^4 - b^4)), x)","F",0
2857,0,0,0,0.000000," ","integrate((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2+b),x, algorithm=""giac"")","\int \frac{{\left(a^{3} x^{3} - b^{2} x^{2}\right)}^{\frac{1}{3}}}{a x^{2} + b}\,{d x}"," ",0,"integrate((a^3*x^3 - b^2*x^2)^(1/3)/(a*x^2 + b), x)","F",0
2858,0,0,0,0.000000," ","integrate((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2+b),x, algorithm=""giac"")","\int \frac{{\left(a^{3} x^{3} - b^{2} x^{2}\right)}^{\frac{1}{3}}}{a x^{2} + b}\,{d x}"," ",0,"integrate((a^3*x^3 - b^2*x^2)^(1/3)/(a*x^2 + b), x)","F",0
2859,0,0,0,0.000000," ","integrate((a^8*x^8+b^8+x^4)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8-b^8),x, algorithm=""giac"")","\int \frac{a^{8} x^{8} + b^{8} + x^{4}}{{\left(a^{8} x^{8} - b^{8}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^8*x^8 + b^8 + x^4)/((a^8*x^8 - b^8)*sqrt(a^4*x^4 - b^4)), x)","F",0
2860,0,0,0,0.000000," ","integrate((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2-b),x, algorithm=""giac"")","\int \frac{{\left(a^{3} x^{3} - b^{2} x^{2}\right)}^{\frac{1}{3}}}{a x^{2} - b}\,{d x}"," ",0,"integrate((a^3*x^3 - b^2*x^2)^(1/3)/(a*x^2 - b), x)","F",0
2861,0,0,0,0.000000," ","integrate((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2-b),x, algorithm=""giac"")","\int \frac{{\left(a^{3} x^{3} - b^{2} x^{2}\right)}^{\frac{1}{3}}}{a x^{2} - b}\,{d x}"," ",0,"integrate((a^3*x^3 - b^2*x^2)^(1/3)/(a*x^2 - b), x)","F",0
2862,0,0,0,0.000000," ","integrate((-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(a-b*d+(-1+d)*x),x, algorithm=""giac"")","\int \frac{b - x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(b d - {\left(d - 1\right)} x - a\right)}}\,{d x}"," ",0,"integrate((b - x)/((-(a - x)*(b - x)^2)^(2/3)*(b*d - (d - 1)*x - a)), x)","F",0
2863,0,0,0,0.000000," ","integrate((x^2-b)^(1/2)*(x^4+c)*(x+(x^2-b)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + c\right)} \sqrt{x^{2} - b} \sqrt{x + \sqrt{x^{2} - b}}}{x}\,{d x}"," ",0,"integrate((x^4 + c)*sqrt(x^2 - b)*sqrt(x + sqrt(x^2 - b))/x, x)","F",0
2864,0,0,0,0.000000," ","integrate(x^8/(a^4*x^4-b^4)^(1/2)/(a^16*x^16-b^16),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(a^{16} x^{16} - b^{16}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate(x^8/((a^16*x^16 - b^16)*sqrt(a^4*x^4 - b^4)), x)","F",0
2865,1,272,0,0.246664," ","integrate(x^2/(a*x^2-b)/(x^3-x)^(1/3),x, algorithm=""giac"")","-\frac{b \left(-\frac{a - b}{b}\right)^{\frac{2}{3}} \log\left({\left| -\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(a^{2} - a b\right)}} - \frac{3 \, {\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{a - b}{b}\right)^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a - b}{b}\right)^{\frac{1}{3}}}\right)}{2 \, {\left(\sqrt{3} a^{2} b - \sqrt{3} a b^{2}\right)}} + \frac{{\left(-a b^{2} + b^{3}\right)}^{\frac{2}{3}} \log\left(\left(-\frac{a - b}{b}\right)^{\frac{2}{3}} + \left(-\frac{a - b}{b}\right)^{\frac{1}{3}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, {\left(a^{2} b - a b^{2}\right)}} - \frac{\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right)}{2 \, a} + \frac{\log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}{4 \, a} - \frac{\log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)}{2 \, a}"," ",0,"-1/2*b*(-(a - b)/b)^(2/3)*log(abs(-(-(a - b)/b)^(1/3) + (-1/x^2 + 1)^(1/3)))/(a^2 - a*b) - 3/2*(-a*b^2 + b^3)^(2/3)*arctan(1/3*sqrt(3)*((-(a - b)/b)^(1/3) + 2*(-1/x^2 + 1)^(1/3))/(-(a - b)/b)^(1/3))/(sqrt(3)*a^2*b - sqrt(3)*a*b^2) + 1/4*(-a*b^2 + b^3)^(2/3)*log((-(a - b)/b)^(2/3) + (-(a - b)/b)^(1/3)*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3))/(a^2*b - a*b^2) - 1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1))/a + 1/4*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1)/a - 1/2*log(abs((-1/x^2 + 1)^(1/3) - 1))/a","A",0
2866,0,0,0,0.000000," ","integrate((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}{x^{4} - 1}\,{d x}"," ",0,"integrate((x^4 + 1)*sqrt(x + sqrt(x^2 + 1))/(x^4 - 1), x)","F",0
2867,0,0,0,0.000000," ","integrate((-a+x)*(-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int \frac{{\left(a - x\right)} {\left(b - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b^{2} - 2 \, {\left(a d - b\right)} x\right)}}\,{d x}"," ",0,"integrate((a - x)*(b - x)/((-(a - x)*(b - x)^2)^(2/3)*(a^2*d + (d - 1)*x^2 - b^2 - 2*(a*d - b)*x)), x)","F",0
2868,0,0,0,0.000000," ","integrate((a*b-(a+b)*x+x^2)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int \frac{a b - {\left(a + b\right)} x + x^{2}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b^{2} - 2 \, {\left(a d - b\right)} x\right)}}\,{d x}"," ",0,"integrate((a*b - (a + b)*x + x^2)/((-(a - x)*(b - x)^2)^(2/3)*(a^2*d + (d - 1)*x^2 - b^2 - 2*(a*d - b)*x)), x)","F",0
2869,0,0,0,0.000000," ","integrate(x/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(x/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
2870,0,0,0,0.000000," ","integrate(x/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{x}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(x/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
2871,0,0,0,0.000000," ","integrate((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(b*d-(a+d)*x+x^2),x, algorithm=""giac"")","\int \frac{a b - 2 \, b x + x^{2}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}} {\left(b d - {\left(a + d\right)} x + x^{2}\right)}}\,{d x}"," ",0,"integrate((a*b - 2*b*x + x^2)/((-(a - x)*(b - x)^2*x)^(1/3)*(b*d - (a + d)*x + x^2)), x)","F",0
2872,0,0,0,0.000000," ","integrate((-a*b^2+(4*a-b)*b*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a^2*d+(2*a*d+b^2)*x-(2*b+d)*x^2+x^3),x, algorithm=""giac"")","\int \frac{a b^{2} - {\left(4 \, a - b\right)} b x + 3 \, a x^{2} - x^{3}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}} {\left(a^{2} d + {\left(2 \, b + d\right)} x^{2} - x^{3} - {\left(b^{2} + 2 \, a d\right)} x\right)}}\,{d x}"," ",0,"integrate((a*b^2 - (4*a - b)*b*x + 3*a*x^2 - x^3)/((-(a - x)*(b - x)^2*x)^(1/3)*(a^2*d + (2*b + d)*x^2 - x^3 - (b^2 + 2*a*d)*x)), x)","F",0
2873,0,0,0,0.000000," ","integrate((c*x^7-d)/x/(a*x^3-b)^(1/3),x, algorithm=""giac"")","\int \frac{c x^{7} - d}{{\left(a x^{3} - b\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate((c*x^7 - d)/((a*x^3 - b)^(1/3)*x), x)","F",0
2874,1,210,0,0.195434," ","integrate((c+(a*x+b)^(1/2))^(1/2)/(x-(a*x+b)^(1/2)),x, algorithm=""giac"")","-\frac{4 \, \sqrt{a^{2} + 4 \, b} \sqrt{-2 \, a - 4 \, c + 2 \, \sqrt{a^{2} + 4 \, b}} b \arctan\left(\frac{\sqrt{c + \sqrt{a x + b}}}{\sqrt{-\frac{1}{2} \, a - c + \frac{1}{2} \, \sqrt{{\left(a + 2 \, c\right)}^{2} - 4 \, a c - 4 \, c^{2} + 4 \, b}}}\right)}{a^{3} + 4 \, a b + {\left(a^{2} + 4 \, b\right)}^{\frac{3}{2}}} + \frac{4 \, \sqrt{a^{2} + 4 \, b} \sqrt{-2 \, a - 4 \, c - 2 \, \sqrt{a^{2} + 4 \, b}} b \arctan\left(\frac{\sqrt{c + \sqrt{a x + b}}}{\sqrt{-\frac{1}{2} \, a - c - \frac{1}{2} \, \sqrt{{\left(a + 2 \, c\right)}^{2} - 4 \, a c - 4 \, c^{2} + 4 \, b}}}\right)}{a^{3} + 4 \, a b - {\left(a^{2} + 4 \, b\right)}^{\frac{3}{2}}} + 4 \, \sqrt{c + \sqrt{a x + b}}"," ",0,"-4*sqrt(a^2 + 4*b)*sqrt(-2*a - 4*c + 2*sqrt(a^2 + 4*b))*b*arctan(sqrt(c + sqrt(a*x + b))/sqrt(-1/2*a - c + 1/2*sqrt((a + 2*c)^2 - 4*a*c - 4*c^2 + 4*b)))/(a^3 + 4*a*b + (a^2 + 4*b)^(3/2)) + 4*sqrt(a^2 + 4*b)*sqrt(-2*a - 4*c - 2*sqrt(a^2 + 4*b))*b*arctan(sqrt(c + sqrt(a*x + b))/sqrt(-1/2*a - c - 1/2*sqrt((a + 2*c)^2 - 4*a*c - 4*c^2 + 4*b)))/(a^3 + 4*a*b - (a^2 + 4*b)^(3/2)) + 4*sqrt(c + sqrt(a*x + b))","A",0
2875,0,0,0,0.000000," ","integrate((1+x)/(1+2*x)/(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x^{5} + 9 \, x^{4} + 28 \, x^{3} + 36 \, x^{2} + 27 \, x + 27\right)}^{\frac{1}{3}} {\left(2 \, x + 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/((x^5 + 9*x^4 + 28*x^3 + 36*x^2 + 27*x + 27)^(1/3)*(2*x + 1)), x)","F",0
2876,-1,0,0,0.000000," ","integrate((a*x^3-b*x)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2877,-1,0,0,0.000000," ","integrate((a*x^3-b*x)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2878,-1,0,0,0.000000," ","integrate((a*x^3+b*x)/(2*a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2879,0,0,0,0.000000," ","integrate(x*(-b+x)*(a*b+(-2*a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^4+4*a^3*x+(b^2*d-6*a^2)*x^2+2*(-b*d+2*a)*x^3+(-1+d)*x^4),x, algorithm=""giac"")","\int -\frac{{\left(a b - {\left(2 \, a - b\right)} x\right)} {\left(b - x\right)} x}{{\left({\left(d - 1\right)} x^{4} - a^{4} + 4 \, a^{3} x - 2 \, {\left(b d - 2 \, a\right)} x^{3} + {\left(b^{2} d - 6 \, a^{2}\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(a*b - (2*a - b)*x)*(b - x)*x/(((d - 1)*x^4 - a^4 + 4*a^3*x - 2*(b*d - 2*a)*x^3 + (b^2*d - 6*a^2)*x^2)*((a - x)*(b - x)*x)^(1/3)), x)","F",0
2880,0,0,0,0.000000," ","integrate((-a*b-a*c+2*b*c+(2*a-b-c)*x)/((-a+x)*(-b+x)*(-c+x))^(1/3)/(-b*c+a^2*d+(-2*a*d+b+c)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{a b + a c - 2 \, b c - {\left(2 \, a - b - c\right)} x}{\left(-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}\right)^{\frac{1}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b c - {\left(2 \, a d - b - c\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b + a*c - 2*b*c - (2*a - b - c)*x)/((-(a - x)*(b - x)*(c - x))^(1/3)*(a^2*d + (d - 1)*x^2 - b*c - (2*a*d - b - c)*x)), x)","F",0
2881,0,0,0,0.000000," ","integrate(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x, algorithm=""giac"")","\int -\frac{{\left(a b - x^{2}\right)} x}{{\left(a^{2} b^{2} - 2 \, {\left(a + b\right)} a b x - 2 \, {\left(a + b\right)} x^{3} + x^{4} + {\left(a^{2} + 4 \, a b + b^{2} - d\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(a*b - x^2)*x/((a^2*b^2 - 2*(a + b)*a*b*x - 2*(a + b)*x^3 + x^4 + (a^2 + 4*a*b + b^2 - d)*x^2)*((a - x)*(b - x)*x^2)^(1/3)), x)","F",0
2882,0,0,0,0.000000," ","integrate((a^6*x^6-b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6+b^6),x, algorithm=""giac"")","\int \frac{a^{6} x^{6} - b^{6}}{{\left(a^{6} x^{6} + b^{6}\right)} \sqrt{a^{2} x^{3} - b^{2} x}}\,{d x}"," ",0,"integrate((a^6*x^6 - b^6)/((a^6*x^6 + b^6)*sqrt(a^2*x^3 - b^2*x)), x)","F",0
2883,0,0,0,0.000000," ","integrate((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{x^{4} - 1}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)*sqrt(x^2 + sqrt(x^4 + 1))/(x^4 - 1), x)","F",0
2884,0,0,0,0.000000," ","integrate(x^4/(1-x*(x^2+1)^(1/2)*(x-(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int -\frac{x^{4}}{\sqrt{x^{2} + 1} \sqrt{x - \sqrt{x^{2} + 1}} x - 1}\,{d x}"," ",0,"integrate(-x^4/(sqrt(x^2 + 1)*sqrt(x - sqrt(x^2 + 1))*x - 1), x)","F",0
2885,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(1+x)^2/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{\sqrt{x^{4} + 1} {\left(x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(sqrt(x^4 + 1)*(x + 1)^2), x)","F",0
2886,0,0,0,0.000000," ","integrate((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-b^2*d+2*b*d*x-(-a^2+d)*x^2-2*a*x^3+x^4),x, algorithm=""giac"")","\int \frac{{\left(a b - 2 \, b x + x^{2}\right)} {\left(b - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}} {\left(2 \, a x^{3} - x^{4} + b^{2} d - 2 \, b d x - {\left(a^{2} - d\right)} x^{2}\right)}}\,{d x}"," ",0,"integrate((a*b - 2*b*x + x^2)*(b - x)/((-(a - x)*(b - x)^2*x)^(1/3)*(2*a*x^3 - x^4 + b^2*d - 2*b*d*x - (a^2 - d)*x^2)), x)","F",0
2887,0,0,0,0.000000," ","integrate((a^8*x^8+b^8)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8-b^8),x, algorithm=""giac"")","\int \frac{a^{8} x^{8} + b^{8}}{{\left(a^{8} x^{8} - b^{8}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^8*x^8 + b^8)/((a^8*x^8 - b^8)*sqrt(a^4*x^4 - b^4)), x)","F",0
2888,1,367,0,6.007700," ","integrate(1/(x^2-1)^(1/2)/(x^(1/2)+(x^2-1)^(1/2))^2,x, algorithm=""giac"")","\frac{2}{5} \, \sqrt{\frac{1}{10}} \sqrt{5 \, \sqrt{5} - 11} \arctan\left(\frac{2 \, x + \sqrt{5} - 2 \, \sqrt{x^{2} - 1} - 1}{\sqrt{2 \, \sqrt{5} - 2}}\right) + \frac{1}{5} \, \sqrt{\frac{1}{10}} \sqrt{5 \, \sqrt{5} + 11} \log\left({\left| -153040 \, x + 22956 \, \sqrt{5} \sqrt{50 \, \sqrt{5} + 110} + 76520 \, \sqrt{5} + 153040 \, \sqrt{x^{2} - 1} - 38260 \, \sqrt{50 \, \sqrt{5} + 110} + 76520 \right|}\right) - \frac{1}{5} \, \sqrt{\frac{1}{10}} \sqrt{5 \, \sqrt{5} + 11} \log\left({\left| -153040 \, x - 22956 \, \sqrt{5} \sqrt{50 \, \sqrt{5} + 110} + 76520 \, \sqrt{5} + 153040 \, \sqrt{x^{2} - 1} + 38260 \, \sqrt{50 \, \sqrt{5} + 110} + 76520 \right|}\right) + \frac{1}{25} \, \sqrt{50 \, \sqrt{5} - 110} \arctan\left(\frac{\sqrt{x}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) - \frac{1}{50} \, \sqrt{50 \, \sqrt{5} + 110} \log\left(\sqrt{x} + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}\right) + \frac{1}{50} \, \sqrt{50 \, \sqrt{5} + 110} \log\left({\left| \sqrt{x} - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right) + \frac{4 \, {\left({\left(x - \sqrt{x^{2} - 1}\right)}^{3} + 2 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 3 \, x - 3 \, \sqrt{x^{2} - 1} - 2\right)}}{5 \, {\left({\left(x - \sqrt{x^{2} - 1}\right)}^{4} - 2 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{3} - 2 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{2} - 2 \, x + 2 \, \sqrt{x^{2} - 1} + 1\right)}} + \frac{2 \, {\left(2 \, x^{\frac{3}{2}} - \sqrt{x}\right)}}{5 \, {\left(x^{2} - x - 1\right)}}"," ",0,"2/5*sqrt(1/10)*sqrt(5*sqrt(5) - 11)*arctan((2*x + sqrt(5) - 2*sqrt(x^2 - 1) - 1)/sqrt(2*sqrt(5) - 2)) + 1/5*sqrt(1/10)*sqrt(5*sqrt(5) + 11)*log(abs(-153040*x + 22956*sqrt(5)*sqrt(50*sqrt(5) + 110) + 76520*sqrt(5) + 153040*sqrt(x^2 - 1) - 38260*sqrt(50*sqrt(5) + 110) + 76520)) - 1/5*sqrt(1/10)*sqrt(5*sqrt(5) + 11)*log(abs(-153040*x - 22956*sqrt(5)*sqrt(50*sqrt(5) + 110) + 76520*sqrt(5) + 153040*sqrt(x^2 - 1) + 38260*sqrt(50*sqrt(5) + 110) + 76520)) + 1/25*sqrt(50*sqrt(5) - 110)*arctan(sqrt(x)/sqrt(1/2*sqrt(5) - 1/2)) - 1/50*sqrt(50*sqrt(5) + 110)*log(sqrt(x) + sqrt(1/2*sqrt(5) + 1/2)) + 1/50*sqrt(50*sqrt(5) + 110)*log(abs(sqrt(x) - sqrt(1/2*sqrt(5) + 1/2))) + 4/5*((x - sqrt(x^2 - 1))^3 + 2*(x - sqrt(x^2 - 1))^2 + 3*x - 3*sqrt(x^2 - 1) - 2)/((x - sqrt(x^2 - 1))^4 - 2*(x - sqrt(x^2 - 1))^3 - 2*(x - sqrt(x^2 - 1))^2 - 2*x + 2*sqrt(x^2 - 1) + 1) + 2/5*(2*x^(3/2) - sqrt(x))/(x^2 - x - 1)","A",0
2889,1,284,0,0.372860," ","integrate((a*x^2+b)/(c*x^2+d)/(x^3+x)^(1/3),x, algorithm=""giac"")","-\frac{\sqrt{3} a \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right)}{2 \, c} + \frac{{\left(b c \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} - a d \left(-\frac{c - d}{d}\right)^{\frac{1}{3}}\right)} \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} \log\left({\left| -\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(c^{2} - c d\right)}} + \frac{a \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}{4 \, c} - \frac{a \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)}{2 \, c} - \frac{{\left(\sqrt{3} b c - \sqrt{3} a d\right)} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c - d}{d}\right)^{\frac{1}{3}}}\right)}{2 \, {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} c} + \frac{{\left(b c - a d\right)} \log\left(\left(-\frac{c - d}{d}\right)^{\frac{2}{3}} + \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} c}"," ",0,"-1/2*sqrt(3)*a*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1))/c + 1/2*(b*c*(-(c - d)/d)^(1/3) - a*d*(-(c - d)/d)^(1/3))*(-(c - d)/d)^(1/3)*log(abs(-(-(c - d)/d)^(1/3) + (1/x^2 + 1)^(1/3)))/(c^2 - c*d) + 1/4*a*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1)/c - 1/2*a*log(abs((1/x^2 + 1)^(1/3) - 1))/c - 1/2*(sqrt(3)*b*c - sqrt(3)*a*d)*arctan(1/3*sqrt(3)*((-(c - d)/d)^(1/3) + 2*(1/x^2 + 1)^(1/3))/(-(c - d)/d)^(1/3))/((-c*d^2 + d^3)^(1/3)*c) + 1/4*(b*c - a*d)*log((-(c - d)/d)^(2/3) + (-(c - d)/d)^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3))/((-c*d^2 + d^3)^(1/3)*c)","A",0
2890,0,0,0,0.000000," ","integrate(x^3*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a*b+(a+b)*x-x^2+d*x^4),x, algorithm=""giac"")","\int \frac{{\left(4 \, a b - 3 \, {\left(a + b\right)} x + 2 \, x^{2}\right)} x^{3}}{{\left(d x^{4} - a b + {\left(a + b\right)} x - x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((4*a*b - 3*(a + b)*x + 2*x^2)*x^3/((d*x^4 - a*b + (a + b)*x - x^2)*((a - x)*(b - x)*x^2)^(2/3)), x)","F",0
2891,-1,0,0,0.000000," ","integrate((a*x^3+b*x)/(2*a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2892,0,0,0,0.000000," ","integrate(1/((-1+2*x)^(1/2)*(4+3*x)+(1+x)*(-3+4*x)^(1/2)),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x + 4\right)} \sqrt{2 \, x - 1} + \sqrt{4 \, x - 3} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((3*x + 4)*sqrt(2*x - 1) + sqrt(4*x - 3)*(x + 1)), x)","F",0
2893,-2,0,0,0.000000," ","integrate((e*x+f)/(g*x+h)/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-d)]Unable to divide, perhaps due to rounding error%%%{-1073741824,[2,10,18,5,4,2,0,0]%%%}+%%%{2147483648,[2,10,18,3,5,2,0,0]%%%}+%%%{1073741824,[2,10,18,3,3,3,0,0]%%%}+%%%{-1073741824,[2,10,18,1,6,2,0,0]%%%}+%%%{-1073741824,[2,10,18,1,4,3,0,0]%%%}+%%%{2147483648,[2,10,17,5,4,1,1,1]%%%}+%%%{-4294967296,[2,10,17,3,5,1,1,1]%%%}+%%%{-3221225472,[2,10,17,3,3,2,1,1]%%%}+%%%{2147483648,[2,10,17,1,6,1,1,1]%%%}+%%%{3221225472,[2,10,17,1,4,2,1,1]%%%}+%%%{-1073741824,[2,10,16,5,4,0,2,2]%%%}+%%%{2147483648,[2,10,16,3,5,0,2,2]%%%}+%%%{3221225472,[2,10,16,3,3,1,2,2]%%%}+%%%{-1073741824,[2,10,16,1,6,0,2,2]%%%}+%%%{-3221225472,[2,10,16,1,4,1,2,2]%%%}+%%%{-1073741824,[2,10,15,3,3,0,3,3]%%%}+%%%{1073741824,[2,10,15,1,4,0,3,3]%%%}+%%%{33554432,[2,8,16,4,3,1,0,0]%%%}+%%%{-50331648,[2,8,16,2,4,1,0,0]%%%}+%%%{16777216,[2,8,16,0,5,1,0,0]%%%}+%%%{-33554432,[2,8,15,4,3,0,1,1]%%%}+%%%{50331648,[2,8,15,2,4,0,1,1]%%%}+%%%{-16777216,[2,8,15,0,5,0,1,1]%%%}+%%%{-262144,[2,6,14,3,2,0,0,0]%%%}+%%%{262144,[2,6,14,1,3,0,0,0]%%%}+%%%{-134217728,[1,9,17,4,3,2,0,0]%%%}+%%%{402653184,[1,9,17,2,4,2,0,0]%%%}+%%%{-268435456,[1,9,17,0,5,2,0,0]%%%}+%%%{268435456,[1,9,16,4,3,1,1,1]%%%}+%%%{-805306368,[1,9,16,2,4,1,1,1]%%%}+%%%{536870912,[1,9,16,0,5,1,1,1]%%%}+%%%{-134217728,[1,9,15,4,3,0,2,2]%%%}+%%%{402653184,[1,9,15,2,4,0,2,2]%%%}+%%%{-268435456,[1,9,15,0,5,0,2,2]%%%}+%%%{2097152,[1,7,15,3,2,1,0,0]%%%}+%%%{-2097152,[1,7,15,1,3,1,0,0]%%%}+%%%{-2097152,[1,7,14,3,2,0,1,1]%%%}+%%%{2097152,[1,7,14,1,3,0,1,1]%%%}+%%%{1073741824,[0,10,18,6,4,2,0,0]%%%}+%%%{-3221225472,[0,10,18,4,5,2,0,0]%%%}+%%%{3221225472,[0,10,18,2,6,2,0,0]%%%}+%%%{-1073741824,[0,10,18,2,4,3,0,0]%%%}+%%%{-1073741824,[0,10,18,0,7,2,0,0]%%%}+%%%{1073741824,[0,10,18,0,5,3,0,0]%%%}+%%%{-2147483648,[0,10,17,6,4,1,1,1]%%%}+%%%{6442450944,[0,10,17,4,5,1,1,1]%%%}+%%%{-6442450944,[0,10,17,2,6,1,1,1]%%%}+%%%{3221225472,[0,10,17,2,4,2,1,1]%%%}+%%%{2147483648,[0,10,17,0,7,1,1,1]%%%}+%%%{-3221225472,[0,10,17,0,5,2,1,1]%%%}+%%%{1073741824,[0,10,16,6,4,0,2,2]%%%}+%%%{-3221225472,[0,10,16,4,5,0,2,2]%%%}+%%%{3221225472,[0,10,16,2,6,0,2,2]%%%}+%%%{-3221225472,[0,10,16,2,4,1,2,2]%%%}+%%%{-1073741824,[0,10,16,0,7,0,2,2]%%%}+%%%{3221225472,[0,10,16,0,5,1,2,2]%%%}+%%%{1073741824,[0,10,15,2,4,0,3,3]%%%}+%%%{-1073741824,[0,10,15,0,5,0,3,3]%%%}+%%%{-33554432,[0,8,16,5,3,1,0,0]%%%}+%%%{67108864,[0,8,16,3,4,1,0,0]%%%}+%%%{-33554432,[0,8,16,1,5,1,0,0]%%%}+%%%{33554432,[0,8,15,5,3,0,1,1]%%%}+%%%{-67108864,[0,8,15,3,4,0,1,1]%%%}+%%%{33554432,[0,8,15,1,5,0,1,1]%%%}+%%%{262144,[0,6,14,4,2,0,0,0]%%%}+%%%{-262144,[0,6,14,2,3,0,0,0]%%%} / %%%{4096,[0,4,7,2,2,0,0,0]%%%}+%%%{-4096,[0,4,7,0,3,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
2894,-1,0,0,0.000000," ","integrate((x^2+1)^(3/2)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2895,0,0,0,0.000000," ","integrate((a-5*b+4*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/((-a+x)*(-b+x))^(2/3)/(b-a^5*d-(-5*a^4*d+1)*x-10*a^3*d*x^2+10*a^2*d*x^3-5*a*d*x^4+d*x^5),x, algorithm=""giac"")","\int \frac{{\left(a^{3} - 3 \, a^{2} x + 3 \, a x^{2} - x^{3}\right)} {\left(a - 5 \, b + 4 \, x\right)}}{{\left(a^{5} d + 10 \, a^{3} d x^{2} - 10 \, a^{2} d x^{3} + 5 \, a d x^{4} - d x^{5} - {\left(5 \, a^{4} d - 1\right)} x - b\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((a^3 - 3*a^2*x + 3*a*x^2 - x^3)*(a - 5*b + 4*x)/((a^5*d + 10*a^3*d*x^2 - 10*a^2*d*x^3 + 5*a*d*x^4 - d*x^5 - (5*a^4*d - 1)*x - b)*((a - x)*(b - x))^(2/3)), x)","F",0
2896,0,0,0,0.000000," ","integrate((3*x^4-3*x^3+2*x^2-2*x+2)*(x^6-x^4-x^3-x)^(1/3)/(1+x)/(x^3-2*x^2+2*x-1)/(x^5-x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - x^{4} - x^{3} - x\right)}^{\frac{1}{3}} {\left(3 \, x^{4} - 3 \, x^{3} + 2 \, x^{2} - 2 \, x + 2\right)}}{{\left(x^{5} - x^{3} - 1\right)} {\left(x^{3} - 2 \, x^{2} + 2 \, x - 1\right)} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate((x^6 - x^4 - x^3 - x)^(1/3)*(3*x^4 - 3*x^3 + 2*x^2 - 2*x + 2)/((x^5 - x^3 - 1)*(x^3 - 2*x^2 + 2*x - 1)*(x + 1)), x)","F",0
2897,-1,0,0,0.000000," ","integrate(1/(a*x-b)/(a^3*x^3-b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2898,0,0,0,0.000000," ","integrate((-b+x)*(-4*a+b+3*x)/((-a+x)*(-b+x)^2)^(1/3)/(b^4+a*d-(4*b^3+d)*x+6*b^2*x^2-4*b*x^3+x^4),x, algorithm=""giac"")","\int \frac{{\left(4 \, a - b - 3 \, x\right)} {\left(b - x\right)}}{{\left(b^{4} + 6 \, b^{2} x^{2} - 4 \, b x^{3} + x^{4} + a d - {\left(4 \, b^{3} + d\right)} x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((4*a - b - 3*x)*(b - x)/((b^4 + 6*b^2*x^2 - 4*b*x^3 + x^4 + a*d - (4*b^3 + d)*x)*(-(a - x)*(b - x)^2)^(1/3)), x)","F",0
2899,0,0,0,0.000000," ","integrate(x^4/(a^4*x^4-b^4)^(1/2)/(a^8*x^8-b^8),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a^{8} x^{8} - b^{8}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate(x^4/((a^8*x^8 - b^8)*sqrt(a^4*x^4 - b^4)), x)","F",0
2900,-1,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2901,0,0,0,0.000000," ","integrate((x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}^{2}}{{\left(x^{4} + x^{2} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)^2/((x^4 + x^2 - 1)*sqrt(x^4 + 1)), x)","F",0
2902,0,0,0,0.000000," ","integrate((x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}^{2}}{{\left(x^{4} + x^{2} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)^2/((x^4 + x^2 - 1)*sqrt(x^4 + 1)), x)","F",0
2903,-1,0,0,0.000000," ","integrate(x^2*(a*x^4+b*x^3)^(1/4)/(a*x^4-b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2904,-1,0,0,0.000000," ","integrate(x^2*(a*x^4+b*x^3)^(1/4)/(a*x^4-b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2905,-1,0,0,0.000000," ","integrate((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2906,-1,0,0,0.000000," ","integrate((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2907,-1,0,0,0.000000," ","integrate(x^3*(-b+x)*(2*a*b-3*a*x+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^4+4*a^3*x-6*a^2*x^2+4*a*x^3+(b^2*d-1)*x^4-2*b*d*x^5+d*x^6),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2908,0,0,0,0.000000," ","integrate((x^3+1)^(2/3)*(x^6-1)/x^6/(2*x^6-2*x^3-1),x, algorithm=""giac"")","\int \frac{{\left(x^{6} - 1\right)} {\left(x^{3} + 1\right)}^{\frac{2}{3}}}{{\left(2 \, x^{6} - 2 \, x^{3} - 1\right)} x^{6}}\,{d x}"," ",0,"integrate((x^6 - 1)*(x^3 + 1)^(2/3)/((2*x^6 - 2*x^3 - 1)*x^6), x)","F",0
2909,0,0,0,0.000000," ","integrate((x^4+1)/(x^4-1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} + 1}{{\left(x^{4} - 1\right)} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate((x^4 + 1)/((x^4 - 1)*sqrt(x + sqrt(x^2 + 1))), x)","F",0
2910,1,243,0,4.273851," ","integrate((2*a*x+b)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{2} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) + \frac{1}{4} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a x"," ",0,"-1/2*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4)) - 1/2*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) + 1/4*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) + 2*(a + b/x)^(1/4)*a*x","B",0
2911,1,243,0,5.238213," ","integrate((2*a*x+b)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{2} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \log\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) + \frac{1}{4} \, \sqrt{2} {\left(4 \, \left(-a\right)^{\frac{1}{4}} a^{2} - 3 \, \left(-a\right)^{\frac{1}{4}} b\right)} \log\left(-\sqrt{2} \left(-a\right)^{\frac{1}{4}} {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} + \sqrt{-a} + \sqrt{a + \frac{b}{x}}\right) + 2 \, {\left(a + \frac{b}{x}\right)}^{\frac{1}{4}} a x"," ",0,"-1/2*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(a + b/x)^(1/4))/(-a)^(1/4)) - 1/2*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(a + b/x)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*log(sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) + 1/4*sqrt(2)*(4*(-a)^(1/4)*a^2 - 3*(-a)^(1/4)*b)*log(-sqrt(2)*(-a)^(1/4)*(a + b/x)^(1/4) + sqrt(-a) + sqrt(a + b/x)) + 2*(a + b/x)^(1/4)*a*x","B",0
2912,0,0,0,0.000000," ","integrate(x^3/(x^4-x^2)^(1/3)/(x^6+1),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(x^{6} + 1\right)} {\left(x^{4} - x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^3/((x^6 + 1)*(x^4 - x^2)^(1/3)), x)","F",0
2913,0,0,0,0.000000," ","integrate(x^4*(a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} + b} x^{4}}{x^{2} - \sqrt{a x - \sqrt{a^{2} x^{2} + b}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + b)*x^4/(x^2 - sqrt(a*x - sqrt(a^2*x^2 + b))), x)","F",0
2914,1,1490,0,7.672866," ","integrate((x^2-1)/((a*x+b)/(c*x+d))^(1/4),x, algorithm=""giac"")","-\frac{1}{768} \, {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)} {\left(\frac{6 \, \sqrt{2} {\left(32 \, a^{2} b^{2} c^{4} - 15 \, b^{4} c^{4} - 64 \, a^{3} b c^{3} d + 20 \, a b^{3} c^{3} d + 32 \, a^{4} c^{2} d^{2} - 2 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{a}{c}\right)^{\frac{1}{4}} + 2 \, \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{\left(-a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2}} + \frac{6 \, \sqrt{2} {\left(32 \, a^{2} b^{2} c^{4} - 15 \, b^{4} c^{4} - 64 \, a^{3} b c^{3} d + 20 \, a b^{3} c^{3} d + 32 \, a^{4} c^{2} d^{2} - 2 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{a}{c}\right)^{\frac{1}{4}} - 2 \, \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{\left(-a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2}} - \frac{3 \, \sqrt{2} {\left(32 \, a^{2} b^{2} c^{4} - 15 \, b^{4} c^{4} - 64 \, a^{3} b c^{3} d + 20 \, a b^{3} c^{3} d + 32 \, a^{4} c^{2} d^{2} - 2 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \log\left(\sqrt{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}} \left(-\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a x + b}{c x + d}} + \sqrt{-\frac{a}{c}}\right)}{\left(-a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2}} + \frac{3 \, \sqrt{2} {\left(32 \, a^{2} b^{2} c^{4} - 15 \, b^{4} c^{4} - 64 \, a^{3} b c^{3} d + 20 \, a b^{3} c^{3} d + 32 \, a^{4} c^{2} d^{2} - 2 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \log\left(-\sqrt{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}} \left(-\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a x + b}{c x + d}} + \sqrt{-\frac{a}{c}}\right)}{\left(-a c^{3}\right)^{\frac{1}{4}} a^{3} c^{2}} - \frac{8 \, {\left(96 \, a^{4} b^{2} c^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - 113 \, a^{2} b^{4} c^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{192 \, {\left(a x + b\right)} a^{3} b^{2} c^{5} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} + \frac{126 \, {\left(a x + b\right)} a b^{4} c^{5} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} + \frac{96 \, {\left(a x + b\right)}^{2} a^{2} b^{2} c^{6} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - \frac{45 \, {\left(a x + b\right)}^{2} b^{4} c^{6} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - 192 \, a^{5} b c^{3} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} + 236 \, a^{3} b^{3} c^{3} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} + \frac{384 \, {\left(a x + b\right)} a^{4} b c^{4} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - \frac{168 \, {\left(a x + b\right)} a^{2} b^{3} c^{4} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - \frac{192 \, {\left(a x + b\right)}^{2} a^{3} b c^{5} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} + \frac{60 \, {\left(a x + b\right)}^{2} a b^{3} c^{5} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} + 96 \, a^{6} c^{2} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - 126 \, a^{4} b^{2} c^{2} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{192 \, {\left(a x + b\right)} a^{5} c^{3} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - \frac{60 \, {\left(a x + b\right)} a^{3} b^{2} c^{3} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} + \frac{96 \, {\left(a x + b\right)}^{2} a^{4} c^{4} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - \frac{6 \, {\left(a x + b\right)}^{2} a^{2} b^{2} c^{4} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - 4 \, a^{5} b c d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} + \frac{120 \, {\left(a x + b\right)} a^{4} b c^{2} d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} + \frac{12 \, {\left(a x + b\right)}^{2} a^{3} b c^{3} d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} + 7 \, a^{6} d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{18 \, {\left(a x + b\right)} a^{5} c d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - \frac{21 \, {\left(a x + b\right)}^{2} a^{4} c^{2} d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}}\right)}}{{\left(a - \frac{{\left(a x + b\right)} c}{c x + d}\right)}^{3} a^{3} c^{2}}\right)}"," ",0,"-1/768*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)*(6*sqrt(2)*(32*a^2*b^2*c^4 - 15*b^4*c^4 - 64*a^3*b*c^3*d + 20*a*b^3*c^3*d + 32*a^4*c^2*d^2 - 2*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 7*a^4*d^4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a/c)^(1/4) + 2*((a*x + b)/(c*x + d))^(1/4))/(-a/c)^(1/4))/((-a*c^3)^(1/4)*a^3*c^2) + 6*sqrt(2)*(32*a^2*b^2*c^4 - 15*b^4*c^4 - 64*a^3*b*c^3*d + 20*a*b^3*c^3*d + 32*a^4*c^2*d^2 - 2*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 7*a^4*d^4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a/c)^(1/4) - 2*((a*x + b)/(c*x + d))^(1/4))/(-a/c)^(1/4))/((-a*c^3)^(1/4)*a^3*c^2) - 3*sqrt(2)*(32*a^2*b^2*c^4 - 15*b^4*c^4 - 64*a^3*b*c^3*d + 20*a*b^3*c^3*d + 32*a^4*c^2*d^2 - 2*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 7*a^4*d^4)*log(sqrt(2)*((a*x + b)/(c*x + d))^(1/4)*(-a/c)^(1/4) + sqrt((a*x + b)/(c*x + d)) + sqrt(-a/c))/((-a*c^3)^(1/4)*a^3*c^2) + 3*sqrt(2)*(32*a^2*b^2*c^4 - 15*b^4*c^4 - 64*a^3*b*c^3*d + 20*a*b^3*c^3*d + 32*a^4*c^2*d^2 - 2*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 7*a^4*d^4)*log(-sqrt(2)*((a*x + b)/(c*x + d))^(1/4)*(-a/c)^(1/4) + sqrt((a*x + b)/(c*x + d)) + sqrt(-a/c))/((-a*c^3)^(1/4)*a^3*c^2) - 8*(96*a^4*b^2*c^4*((a*x + b)/(c*x + d))^(3/4) - 113*a^2*b^4*c^4*((a*x + b)/(c*x + d))^(3/4) - 192*(a*x + b)*a^3*b^2*c^5*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) + 126*(a*x + b)*a*b^4*c^5*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) + 96*(a*x + b)^2*a^2*b^2*c^6*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 45*(a*x + b)^2*b^4*c^6*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 192*a^5*b*c^3*d*((a*x + b)/(c*x + d))^(3/4) + 236*a^3*b^3*c^3*d*((a*x + b)/(c*x + d))^(3/4) + 384*(a*x + b)*a^4*b*c^4*d*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 168*(a*x + b)*a^2*b^3*c^4*d*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 192*(a*x + b)^2*a^3*b*c^5*d*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 + 60*(a*x + b)^2*a*b^3*c^5*d*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 + 96*a^6*c^2*d^2*((a*x + b)/(c*x + d))^(3/4) - 126*a^4*b^2*c^2*d^2*((a*x + b)/(c*x + d))^(3/4) - 192*(a*x + b)*a^5*c^3*d^2*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 60*(a*x + b)*a^3*b^2*c^3*d^2*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) + 96*(a*x + b)^2*a^4*c^4*d^2*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 6*(a*x + b)^2*a^2*b^2*c^4*d^2*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 4*a^5*b*c*d^3*((a*x + b)/(c*x + d))^(3/4) + 120*(a*x + b)*a^4*b*c^2*d^3*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) + 12*(a*x + b)^2*a^3*b*c^3*d^3*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 + 7*a^6*d^4*((a*x + b)/(c*x + d))^(3/4) - 18*(a*x + b)*a^5*c*d^4*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 21*(a*x + b)^2*a^4*c^2*d^4*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2)/((a - (a*x + b)*c/(c*x + d))^3*a^3*c^2))","B",0
2915,0,0,0,0.000000," ","integrate((a*x^4-b)/(a*x^4+b)^(1/2)/(a*x^4-c^2*x^2+b),x, algorithm=""giac"")","\int \frac{a x^{4} - b}{{\left(a x^{4} - c^{2} x^{2} + b\right)} \sqrt{a x^{4} + b}}\,{d x}"," ",0,"integrate((a*x^4 - b)/((a*x^4 - c^2*x^2 + b)*sqrt(a*x^4 + b)), x)","F",0
2916,0,0,0,0.000000," ","integrate((x^2+1)*(x^6+x^4-x^2-1)^(1/3)/x,x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{4} - x^{2} - 1\right)}^{\frac{1}{3}} {\left(x^{2} + 1\right)}}{x}\,{d x}"," ",0,"integrate((x^6 + x^4 - x^2 - 1)^(1/3)*(x^2 + 1)/x, x)","F",0
2917,-2,0,0,0.000000," ","integrate((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
2918,1,300,0,0.274902," ","integrate((a*x^2-b)/(c*x^2-d)/(x^3-x)^(1/3),x, algorithm=""giac"")","-\frac{\sqrt{3} a \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right)}{2 \, c} + \frac{{\left(b c \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} - a d \left(-\frac{c - d}{d}\right)^{\frac{1}{3}}\right)} \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} \log\left({\left| -\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(c^{2} - c d\right)}} + \frac{a \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}{4 \, c} - \frac{a \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)}{2 \, c} - \frac{{\left(\sqrt{3} b c - \sqrt{3} a d\right)} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c - d}{d}\right)^{\frac{1}{3}}}\right)}{2 \, {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} c} + \frac{{\left(b c - a d\right)} \log\left(\left(-\frac{c - d}{d}\right)^{\frac{2}{3}} + \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} c}"," ",0,"-1/2*sqrt(3)*a*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1))/c + 1/2*(b*c*(-(c - d)/d)^(1/3) - a*d*(-(c - d)/d)^(1/3))*(-(c - d)/d)^(1/3)*log(abs(-(-(c - d)/d)^(1/3) + (-1/x^2 + 1)^(1/3)))/(c^2 - c*d) + 1/4*a*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1)/c - 1/2*a*log(abs((-1/x^2 + 1)^(1/3) - 1))/c - 1/2*(sqrt(3)*b*c - sqrt(3)*a*d)*arctan(1/3*sqrt(3)*((-(c - d)/d)^(1/3) + 2*(-1/x^2 + 1)^(1/3))/(-(c - d)/d)^(1/3))/((-c*d^2 + d^3)^(1/3)*c) + 1/4*(b*c - a*d)*log((-(c - d)/d)^(2/3) + (-(c - d)/d)^(1/3)*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3))/((-c*d^2 + d^3)^(1/3)*c)","A",0
2919,0,0,0,0.000000," ","integrate(1/(a*x+b)/(a^3*x^3-b^3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{3} x^{3} - b^{3}\right)}^{\frac{1}{3}} {\left(a x + b\right)}}\,{d x}"," ",0,"integrate(1/((a^3*x^3 - b^3)^(1/3)*(a*x + b)), x)","F",0
2920,0,0,0,0.000000," ","integrate((a^12*x^12-b^12)/(a^4*x^4+b^4)^(1/2)/(a^12*x^12+b^12),x, algorithm=""giac"")","\int \frac{a^{12} x^{12} - b^{12}}{{\left(a^{12} x^{12} + b^{12}\right)} \sqrt{a^{4} x^{4} + b^{4}}}\,{d x}"," ",0,"integrate((a^12*x^12 - b^12)/((a^12*x^12 + b^12)*sqrt(a^4*x^4 + b^4)), x)","F",0
2921,-2,0,0,0.000000," ","integrate((a*x^2+b*x+c)^(5/2)/(b*x+c),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2922,0,0,0,0.000000," ","integrate((x^4-a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - a x^{2} - b\right)}}{a x^{4} + b}\,{d x}"," ",0,"integrate((a*x^4 + b*x^2)^(1/4)*(x^4 - a*x^2 - b)/(a*x^4 + b), x)","F",0
2923,0,0,0,0.000000," ","integrate((x^4-a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - a x^{2} - b\right)}}{a x^{4} + b}\,{d x}"," ",0,"integrate((a*x^4 + b*x^2)^(1/4)*(x^4 - a*x^2 - b)/(a*x^4 + b), x)","F",0
2924,0,0,0,0.000000," ","integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2925,0,0,0,0.000000," ","integrate((1+x)^(1/2)*(x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2926,1,929,0,1.023302," ","integrate((-x^2+(2*x^2+1)^(1/2)+(2*x^2+1)^(5/2))/(x^2-x*(2*x^2+1)^(3/2)),x, algorithm=""giac"")","-x^{2} + \frac{1}{20} \, {\left(\sqrt{5 \, \sqrt{2} - 1} + 8\right)} \arctan\left(-\frac{\sqrt{2} {\left(2 \, \sqrt{2} x + \sqrt{2} {\left(2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, x^{2} + 1}\right)}}{2 \, {\left(2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}}}\right) + \frac{1}{20} \, {\left(\sqrt{5 \, \sqrt{2} - 1} - 8\right)} \arctan\left(-\frac{\sqrt{2} {\left(2 \, \sqrt{2} x - \sqrt{2} {\left(2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, x^{2} + 1}\right)}}{2 \, {\left(2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}}}\right) + \frac{1}{20} \, {\left(\sqrt{5 \, \sqrt{2} - 1} + 8\right)} \arctan\left(\frac{8 \, \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(2 \, x + \left(\frac{1}{8}\right)^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2}\right)}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{20} \, {\left(\sqrt{5 \, \sqrt{2} - 1} - 8\right)} \arctan\left(\frac{8 \, \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(2 \, x - \left(\frac{1}{8}\right)^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2}\right)}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{20} \, {\left(\sqrt{5 \, \sqrt{2} - 1} - 8\right)} \arctan\left(-\frac{\sqrt{2} {\left(2 \, \sqrt{2} x + \sqrt{2} {\left(-2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, x^{2} + 1}\right)}}{2 \, {\left(-2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}}}\right) - \frac{1}{20} \, {\left(\sqrt{5 \, \sqrt{2} - 1} + 8\right)} \arctan\left(-\frac{\sqrt{2} {\left(2 \, \sqrt{2} x - \sqrt{2} {\left(-2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, x^{2} + 1}\right)}}{2 \, {\left(-2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}}}\right) + \frac{1}{40} \, \sqrt{5 \, \sqrt{2} + 1} \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} + \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)} {\left(2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} + \sqrt{2 \, \sqrt{2} + 3}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{2} + 1} \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} - \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)} {\left(2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} + \sqrt{2 \, \sqrt{2} + 3}\right) + \frac{1}{40} \, \sqrt{5 \, \sqrt{2} + 1} \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} + \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)} {\left(-2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} + \sqrt{-2 \, \sqrt{2} + 3}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{2} + 1} \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} - \sqrt{2} {\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)} {\left(-2 \, \sqrt{2} + 3\right)}^{\frac{1}{4}} + \sqrt{-2 \, \sqrt{2} + 3}\right) - \frac{1}{40} \, \sqrt{5 \, \sqrt{2} + 1} \log\left(x^{2} + \left(\frac{1}{8}\right)^{\frac{1}{4}} x \sqrt{-\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{\frac{1}{2}}\right) + \frac{1}{40} \, \sqrt{5 \, \sqrt{2} + 1} \log\left(x^{2} - \left(\frac{1}{8}\right)^{\frac{1}{4}} x \sqrt{-\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{\frac{1}{2}}\right) - \frac{{\left(50305164660422142002238655969020 \, \sqrt{2} - 71142246120180725728612927680401\right)} \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 1}\right)}{71142246120180725728612927680401 \, \sqrt{2} - 100610329320844284004477311938040} - \frac{1}{5} \, \arctan\left(x\right) + \frac{1}{5} \, \arctan\left(-\frac{\sqrt{2} x - \sqrt{2 \, x^{2} + 1}}{\sqrt{2} + 1}\right) - \frac{1}{5} \, \arctan\left(-\frac{\sqrt{2} x - \sqrt{2 \, x^{2} + 1}}{\sqrt{2} - 1}\right) - \frac{3}{20} \, \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{4} + 2 \, \sqrt{2} + 3\right) + \frac{3}{20} \, \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{4} - 2 \, \sqrt{2} + 3\right) + \frac{3}{20} \, \log\left(8 \, x^{4} + 4 \, x^{2} + 1\right) + \frac{1}{5} \, \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} + 2 \, \sqrt{2} + 3\right) - \frac{1}{5} \, \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} - 2 \, \sqrt{2} + 3\right) + \frac{1}{5} \, \log\left(x^{2} + 1\right) - 2 \, \log\left({\left| x \right|}\right)"," ",0,"-x^2 + 1/20*(sqrt(5*sqrt(2) - 1) + 8)*arctan(-1/2*sqrt(2)*(2*sqrt(2)*x + sqrt(2)*(2*sqrt(2) + 3)^(1/4) - 2*sqrt(2*x^2 + 1))/(2*sqrt(2) + 3)^(1/4)) + 1/20*(sqrt(5*sqrt(2) - 1) - 8)*arctan(-1/2*sqrt(2)*(2*sqrt(2)*x - sqrt(2)*(2*sqrt(2) + 3)^(1/4) - 2*sqrt(2*x^2 + 1))/(2*sqrt(2) + 3)^(1/4)) + 1/20*(sqrt(5*sqrt(2) - 1) + 8)*arctan(8*(1/8)^(3/4)*(2*x + (1/8)^(1/4)*sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/20*(sqrt(5*sqrt(2) - 1) - 8)*arctan(8*(1/8)^(3/4)*(2*x - (1/8)^(1/4)*sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/20*(sqrt(5*sqrt(2) - 1) - 8)*arctan(-1/2*sqrt(2)*(2*sqrt(2)*x + sqrt(2)*(-2*sqrt(2) + 3)^(1/4) - 2*sqrt(2*x^2 + 1))/(-2*sqrt(2) + 3)^(1/4)) - 1/20*(sqrt(5*sqrt(2) - 1) + 8)*arctan(-1/2*sqrt(2)*(2*sqrt(2)*x - sqrt(2)*(-2*sqrt(2) + 3)^(1/4) - 2*sqrt(2*x^2 + 1))/(-2*sqrt(2) + 3)^(1/4)) + 1/40*sqrt(5*sqrt(2) + 1)*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 + sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 + 1))*(2*sqrt(2) + 3)^(1/4) + sqrt(2*sqrt(2) + 3)) - 1/40*sqrt(5*sqrt(2) + 1)*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 - sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 + 1))*(2*sqrt(2) + 3)^(1/4) + sqrt(2*sqrt(2) + 3)) + 1/40*sqrt(5*sqrt(2) + 1)*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 + sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 + 1))*(-2*sqrt(2) + 3)^(1/4) + sqrt(-2*sqrt(2) + 3)) - 1/40*sqrt(5*sqrt(2) + 1)*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 - sqrt(2)*(sqrt(2)*x - sqrt(2*x^2 + 1))*(-2*sqrt(2) + 3)^(1/4) + sqrt(-2*sqrt(2) + 3)) - 1/40*sqrt(5*sqrt(2) + 1)*log(x^2 + (1/8)^(1/4)*x*sqrt(-sqrt(2) + 2) + 1/2*sqrt(1/2)) + 1/40*sqrt(5*sqrt(2) + 1)*log(x^2 - (1/8)^(1/4)*x*sqrt(-sqrt(2) + 2) + 1/2*sqrt(1/2)) - (50305164660422142002238655969020*sqrt(2) - 71142246120180725728612927680401)*log(-sqrt(2)*x + sqrt(2*x^2 + 1))/(71142246120180725728612927680401*sqrt(2) - 100610329320844284004477311938040) - 1/5*arctan(x) + 1/5*arctan(-(sqrt(2)*x - sqrt(2*x^2 + 1))/(sqrt(2) + 1)) - 1/5*arctan(-(sqrt(2)*x - sqrt(2*x^2 + 1))/(sqrt(2) - 1)) - 3/20*log((sqrt(2)*x - sqrt(2*x^2 + 1))^4 + 2*sqrt(2) + 3) + 3/20*log((sqrt(2)*x - sqrt(2*x^2 + 1))^4 - 2*sqrt(2) + 3) + 3/20*log(8*x^4 + 4*x^2 + 1) + 1/5*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 + 2*sqrt(2) + 3) - 1/5*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 - 2*sqrt(2) + 3) + 1/5*log(x^2 + 1) - 2*log(abs(x))","B",0
2927,1,572,0,0.485739," ","integrate((x^3-b)*(x^3+b)*(x^3-c)/(a*x^2+x^3)^(1/3),x, algorithm=""giac"")","\frac{280 \, \sqrt{3} {\left(135850 \, a^{10} + 176904 \, a^{7} c - 275562 \, a^{4} b^{2} - 1594323 \, a b^{2} c\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{a}{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - 140 \, {\left(135850 \, a^{10} + 176904 \, a^{7} c - 275562 \, a^{4} b^{2} - 1594323 \, a b^{2} c\right)} \log\left({\left(\frac{a}{x} + 1\right)}^{\frac{2}{3}} + {\left(\frac{a}{x} + 1\right)}^{\frac{1}{3}} + 1\right) + 280 \, {\left(135850 \, a^{10} + 176904 \, a^{7} c - 275562 \, a^{4} b^{2} - 1594323 \, a b^{2} c\right)} \log\left({\left| {\left(\frac{a}{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right) + \frac{3 \, {\left(38038000 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{26}{3}} - 332832500 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{23}{3}} + 1289216500 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{20}{3}} + 49533120 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{26}{3}} - 2897952200 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{17}{3}} - 433414800 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{23}{3}} + 4158305800 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{14}{3}} + 1678818960 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{20}{3}} - 77157360 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{26}{3}} - 3938066825 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{11}{3}} - 3773716128 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{17}{3}} + 675126900 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{23}{3}} + 2448101425 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{8}{3}} + 5414949792 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{14}{3}} - 2615083380 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{20}{3}} - 952462700 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{5}{3}} - 5128154388 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{11}{3}} + 5833647540 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{17}{3}} + 204186220 \, a^{10} {\left(\frac{a}{x} + 1\right)}^{\frac{2}{3}} + 3164424732 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{8}{3}} - 8170413300 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{14}{3}} - 1170879948 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{5}{3}} + 7338216060 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{11}{3}} + 198438660 \, a^{7} c {\left(\frac{a}{x} + 1\right)}^{\frac{2}{3}} - 4119651900 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{8}{3}} + 1319941980 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{5}{3}} - 184626540 \, a^{4} b^{2} {\left(\frac{a}{x} + 1\right)}^{\frac{2}{3}}\right)} x^{9}}{a^{9}}}{446410440 \, a}"," ",0,"1/446410440*(280*sqrt(3)*(135850*a^10 + 176904*a^7*c - 275562*a^4*b^2 - 1594323*a*b^2*c)*arctan(1/3*sqrt(3)*(2*(a/x + 1)^(1/3) + 1)) - 140*(135850*a^10 + 176904*a^7*c - 275562*a^4*b^2 - 1594323*a*b^2*c)*log((a/x + 1)^(2/3) + (a/x + 1)^(1/3) + 1) + 280*(135850*a^10 + 176904*a^7*c - 275562*a^4*b^2 - 1594323*a*b^2*c)*log(abs((a/x + 1)^(1/3) - 1)) + 3*(38038000*a^10*(a/x + 1)^(26/3) - 332832500*a^10*(a/x + 1)^(23/3) + 1289216500*a^10*(a/x + 1)^(20/3) + 49533120*a^7*c*(a/x + 1)^(26/3) - 2897952200*a^10*(a/x + 1)^(17/3) - 433414800*a^7*c*(a/x + 1)^(23/3) + 4158305800*a^10*(a/x + 1)^(14/3) + 1678818960*a^7*c*(a/x + 1)^(20/3) - 77157360*a^4*b^2*(a/x + 1)^(26/3) - 3938066825*a^10*(a/x + 1)^(11/3) - 3773716128*a^7*c*(a/x + 1)^(17/3) + 675126900*a^4*b^2*(a/x + 1)^(23/3) + 2448101425*a^10*(a/x + 1)^(8/3) + 5414949792*a^7*c*(a/x + 1)^(14/3) - 2615083380*a^4*b^2*(a/x + 1)^(20/3) - 952462700*a^10*(a/x + 1)^(5/3) - 5128154388*a^7*c*(a/x + 1)^(11/3) + 5833647540*a^4*b^2*(a/x + 1)^(17/3) + 204186220*a^10*(a/x + 1)^(2/3) + 3164424732*a^7*c*(a/x + 1)^(8/3) - 8170413300*a^4*b^2*(a/x + 1)^(14/3) - 1170879948*a^7*c*(a/x + 1)^(5/3) + 7338216060*a^4*b^2*(a/x + 1)^(11/3) + 198438660*a^7*c*(a/x + 1)^(2/3) - 4119651900*a^4*b^2*(a/x + 1)^(8/3) + 1319941980*a^4*b^2*(a/x + 1)^(5/3) - 184626540*a^4*b^2*(a/x + 1)^(2/3))*x^9/a^9)/a","A",0
2928,0,0,0,0.000000," ","integrate(x*(-a+x)*(-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(-b^2+2*b*x-(-a^2*d+1)*x^2-2*a*d*x^3+d*x^4),x, algorithm=""giac"")","\int -\frac{{\left(a b - 2 \, b x + x^{2}\right)} {\left(a - x\right)} {\left(b - x\right)} x}{{\left(2 \, a d x^{3} - d x^{4} - {\left(a^{2} d - 1\right)} x^{2} + b^{2} - 2 \, b x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(-(a*b - 2*b*x + x^2)*(a - x)*(b - x)*x/((2*a*d*x^3 - d*x^4 - (a^2*d - 1)*x^2 + b^2 - 2*b*x)*(-(a - x)*(b - x)^2*x)^(2/3)), x)","F",0
2929,0,0,0,0.000000," ","integrate((x^4-a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - a x^{2} - b\right)}}{a x^{4} + b}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)*(x^4 - a*x^2 - b)/(a*x^4 + b), x)","F",0
2930,0,0,0,0.000000," ","integrate((x^4-a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} - a x^{2} - b\right)}}{a x^{4} + b}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)*(x^4 - a*x^2 - b)/(a*x^4 + b), x)","F",0
2931,-2,0,0,0.000000," ","integrate((a^2*x^2+a*b*c-b^2*x)/(a*x^2+b*x+c)^(1/2)/(b*x^2+c),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2932,0,0,0,0.000000," ","integrate((x^4+a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + a x^{2} + b\right)}}{a x^{4} - b}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)*(x^4 + a*x^2 + b)/(a*x^4 - b), x)","F",0
2933,0,0,0,0.000000," ","integrate((x^4+a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + a x^{2} + b\right)}}{a x^{4} - b}\,{d x}"," ",0,"integrate((a*x^4 - b*x^2)^(1/4)*(x^4 + a*x^2 + b)/(a*x^4 - b), x)","F",0
2934,0,0,0,0.000000," ","integrate((-1+(-1+2*k)*x)*(x^2-2*x+1)/((1-x)*x*(-k*x+1))^(1/3)/(-b+4*b*x+(1-6*b)*x^2+(4*b-2*k)*x^3+(k^2-b)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(2 \, k - 1\right)} x - 1\right)} {\left(x^{2} - 2 \, x + 1\right)}}{{\left({\left(k^{2} - b\right)} x^{4} + 2 \, {\left(2 \, b - k\right)} x^{3} - {\left(6 \, b - 1\right)} x^{2} + 4 \, b x - b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((2*k - 1)*x - 1)*(x^2 - 2*x + 1)/(((k^2 - b)*x^4 + 2*(2*b - k)*x^3 - (6*b - 1)*x^2 + 4*b*x - b)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2935,0,0,0,0.000000," ","integrate(1/(a*x+b)/(a^2*x^3+b^2*x)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(a^{2} x^{3} + b^{2} x\right)}^{\frac{1}{4}} {\left(a x + b\right)}}\,{d x}"," ",0,"integrate(1/((a^2*x^3 + b^2*x)^(1/4)*(a*x + b)), x)","F",0
2936,-2,0,0,0.000000," ","integrate((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-96,-29]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[22,61]Evaluation time: 8.9Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2937,-2,0,0,0.000000," ","integrate((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-96,-29]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[22,61]Evaluation time: 8.79Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2938,0,0,0,0.000000," ","integrate((-b+x)*(-4*a+b+3*x)/((-a+x)*(-b+x)^2)^(1/3)/(a+b^4*d-(4*b^3*d+1)*x+6*b^2*d*x^2-4*b*d*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{{\left(4 \, a - b - 3 \, x\right)} {\left(b - x\right)}}{{\left(b^{4} d + 6 \, b^{2} d x^{2} - 4 \, b d x^{3} + d x^{4} - {\left(4 \, b^{3} d + 1\right)} x + a\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((4*a - b - 3*x)*(b - x)/((b^4*d + 6*b^2*d*x^2 - 4*b*d*x^3 + d*x^4 - (4*b^3*d + 1)*x + a)*(-(a - x)*(b - x)^2)^(1/3)), x)","F",0
2939,0,0,0,0.000000," ","integrate((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(e*x^2+f),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + d\right)} \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}{e x^{2} + f}\,{d x}"," ",0,"integrate((c*x^2 + d)*sqrt(a*x + sqrt(a^2*x^2 + b^2))/(e*x^2 + f), x)","F",0
2940,0,0,0,0.000000," ","integrate((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}}{{\left(x^{4} + x^{2} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)/((x^4 + x^2 - 1)*sqrt(x^4 + 1)), x)","F",0
2941,0,0,0,0.000000," ","integrate((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x^{2} + 1\right)}}{{\left(x^{4} + x^{2} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))*(x^2 + 1)/((x^4 + x^2 - 1)*sqrt(x^4 + 1)), x)","F",0
2942,0,0,0,0.000000," ","integrate((-x^4+1)/(x^4+x^2+1)/(x^5-x^3)^(1/4),x, algorithm=""giac"")","\int -\frac{x^{4} - 1}{{\left(x^{5} - x^{3}\right)}^{\frac{1}{4}} {\left(x^{4} + x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(-(x^4 - 1)/((x^5 - x^3)^(1/4)*(x^4 + x^2 + 1)), x)","F",0
2943,0,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)/(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/3),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{2} - b}}{{\left(a x^{2} + \sqrt{a^{2} x^{2} - b} x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 - b)/(a*x^2 + sqrt(a^2*x^2 - b)*x)^(1/3), x)","F",0
2944,0,0,0,0.000000," ","integrate((a^2*x^2+b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^2-b)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} + b\right)} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(a^{2} x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a^2*x^2 + b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(a^2*x^2 - b)), x)","F",0
2945,0,0,0,0.000000," ","integrate((a^2*x^2+b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^2-b)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a^{2} x^{2} + b\right)} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(a^{2} x^{2} - b\right)}}\,{d x}"," ",0,"integrate((a^2*x^2 + b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(a^2*x^2 - b)), x)","F",0
2946,-1,0,0,0.000000," ","integrate(x^3/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(-x^6+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2947,0,0,0,0.000000," ","integrate((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^6+a*(p*x^3+q)^6)/x^9,x, algorithm=""giac"")","\int \frac{\sqrt{p^{2} x^{6} + 2 \, p q x^{3} - 2 \, p q x^{2} + q^{2}} {\left({\left(p x^{3} + q\right)}^{6} a + b x^{6}\right)} {\left(2 \, p x^{3} - q\right)}}{x^{9}}\,{d x}"," ",0,"integrate(sqrt(p^2*x^6 + 2*p*q*x^3 - 2*p*q*x^2 + q^2)*((p*x^3 + q)^6*a + b*x^6)*(2*p*x^3 - q)/x^9, x)","F",0
2948,0,0,0,0.000000," ","integrate((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^12+a*(p*x^3+q)^6)/x^17,x, algorithm=""giac"")","\int \frac{{\left(b x^{12} + {\left(p x^{3} + q\right)}^{6} a\right)} \sqrt{p^{2} x^{6} - 2 \, p q x^{4} + 2 \, p q x^{3} + q^{2}} {\left(p x^{3} - 2 \, q\right)}}{x^{17}}\,{d x}"," ",0,"integrate((b*x^12 + (p*x^3 + q)^6*a)*sqrt(p^2*x^6 - 2*p*q*x^4 + 2*p*q*x^3 + q^2)*(p*x^3 - 2*q)/x^17, x)","F",0
2949,-1,0,0,0.000000," ","integrate((p*x^4-q)*(p*x^4+q)^(1/2)/(b*x^4+a*(p*x^4+q)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2950,0,0,0,0.000000," ","integrate((a*x-3*b)/(-a^2*x^2+b^2)^(1/3)/(a^2*x^2+3*b^2),x, algorithm=""giac"")","\int \frac{a x - 3 \, b}{{\left(a^{2} x^{2} + 3 \, b^{2}\right)} {\left(-a^{2} x^{2} + b^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x - 3*b)/((a^2*x^2 + 3*b^2)*(-a^2*x^2 + b^2)^(1/3)), x)","F",0
2951,0,0,0,0.000000," ","integrate((x+(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2))/(1-(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)),x, algorithm=""giac"")","\int -\frac{x + \sqrt{2 \, x^{5} + 5 \, x^{4} + 8 \, x^{3} + 7 \, x^{2} + 4 \, x + 1}}{\sqrt{2 \, x^{5} + 5 \, x^{4} + 8 \, x^{3} + 7 \, x^{2} + 4 \, x + 1} - 1}\,{d x}"," ",0,"integrate(-(x + sqrt(2*x^5 + 5*x^4 + 8*x^3 + 7*x^2 + 4*x + 1))/(sqrt(2*x^5 + 5*x^4 + 8*x^3 + 7*x^2 + 4*x + 1) - 1), x)","F",0
2952,0,0,0,0.000000," ","integrate(x^3*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a*b*d+(a+b)*d*x-d*x^2+x^4),x, algorithm=""giac"")","\int \frac{{\left(4 \, a b - 3 \, {\left(a + b\right)} x + 2 \, x^{2}\right)} x^{3}}{\left({\left(a - x\right)} {\left(b - x\right)} x^{2}\right)^{\frac{2}{3}} {\left(x^{4} - a b d + {\left(a + b\right)} d x - d x^{2}\right)}}\,{d x}"," ",0,"integrate((4*a*b - 3*(a + b)*x + 2*x^2)*x^3/(((a - x)*(b - x)*x^2)^(2/3)*(x^4 - a*b*d + (a + b)*d*x - d*x^2)), x)","F",0
2953,0,0,0,0.000000," ","integrate(x^3/(x^4+x^2)^(1/3)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(x^{6} - 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^3/((x^6 - 1)*(x^4 + x^2)^(1/3)), x)","F",0
2954,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2955,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2956,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2957,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2958,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2959,-1,0,0,0.000000," ","integrate((a*x^2+b*x+c)^(5/2)/(b*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2960,0,0,0,0.000000," ","integrate((x^4+1)^2/(x^4-1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 1\right)}^{2}}{{\left(x^{4} - 1\right)}^{2} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}\,{d x}"," ",0,"integrate((x^4 + 1)^2/((x^4 - 1)^2*sqrt(x^2 + sqrt(x^4 + 1))), x)","F",0
2961,1,127,0,6.044249," ","integrate((a*x+(a*x-b)^(1/2))^(1/2)/(1+(a*x-b)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{a x + \sqrt{a x - b}} {\left(\frac{2 \, \sqrt{a x - b}}{a} - \frac{3}{a}\right)} - \frac{{\left(4 \, b + 3\right)} \log\left({\left| -2 \, \sqrt{a x - b} + 2 \, \sqrt{a x + \sqrt{a x - b}} - 1 \right|}\right)}{4 \, a} - \frac{4 \, b \arctan\left(-\frac{\sqrt{a x - b} - \sqrt{a x + \sqrt{a x - b}} + 1}{\sqrt{-b}}\right)}{a \sqrt{-b}}"," ",0,"1/2*sqrt(a*x + sqrt(a*x - b))*(2*sqrt(a*x - b)/a - 3/a) - 1/4*(4*b + 3)*log(abs(-2*sqrt(a*x - b) + 2*sqrt(a*x + sqrt(a*x - b)) - 1))/a - 4*b*arctan(-(sqrt(a*x - b) - sqrt(a*x + sqrt(a*x - b)) + 1)/sqrt(-b))/(a*sqrt(-b))","A",0
2962,-2,0,0,0.000000," ","integrate((a*x^2+b*x)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 5.74Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2963,-2,0,0,0.000000," ","integrate((a*x^2+b*x)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 5.82Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
2964,0,0,0,0.000000," ","integrate((a^10*x^10-b^10)/(a^4*x^4+b^4)^(1/2)/(a^10*x^10+b^10),x, algorithm=""giac"")","\int \frac{a^{10} x^{10} - b^{10}}{{\left(a^{10} x^{10} + b^{10}\right)} \sqrt{a^{4} x^{4} + b^{4}}}\,{d x}"," ",0,"integrate((a^10*x^10 - b^10)/((a^10*x^10 + b^10)*sqrt(a^4*x^4 + b^4)), x)","F",0
2965,0,0,0,0.000000," ","integrate((a^10*x^10-b^10)/(a^4*x^4+b^4)^(1/2)/(a^10*x^10+b^10),x, algorithm=""giac"")","\int \frac{a^{10} x^{10} - b^{10}}{{\left(a^{10} x^{10} + b^{10}\right)} \sqrt{a^{4} x^{4} + b^{4}}}\,{d x}"," ",0,"integrate((a^10*x^10 - b^10)/((a^10*x^10 + b^10)*sqrt(a^4*x^4 + b^4)), x)","F",0
2966,1,354,0,0.893255," ","integrate((a*x^2+b)*(x^3+x)^(1/3)/(c*x^2+d),x, algorithm=""giac"")","\frac{a x^{2} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{2 \, c} + \frac{{\left(b c^{2} - a c d - b c d + a d^{2}\right)} \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} \log\left({\left| -\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(c^{3} - c^{2} d\right)}} + \frac{\sqrt{3} {\left(a c + 3 \, b c - 3 \, a d\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right)}{6 \, c^{2}} + \frac{{\left(a c + 3 \, b c - 3 \, a d\right)} \log\left({\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}{12 \, c^{2}} - \frac{{\left(a c + 3 \, b c - 3 \, a d\right)} \log\left({\left| {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)}{6 \, c^{2}} - \frac{{\left(\sqrt{3} {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} b c - \sqrt{3} {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} a d\right)} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + 2 \, {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c - d}{d}\right)^{\frac{1}{3}}}\right)}{2 \, c^{2} d} - \frac{{\left({\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} b c - {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} a d\right)} \log\left(\left(-\frac{c - d}{d}\right)^{\frac{2}{3}} + \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, c^{2} d}"," ",0,"1/2*a*x^2*(1/x^2 + 1)^(1/3)/c + 1/2*(b*c^2 - a*c*d - b*c*d + a*d^2)*(-(c - d)/d)^(1/3)*log(abs(-(-(c - d)/d)^(1/3) + (1/x^2 + 1)^(1/3)))/(c^3 - c^2*d) + 1/6*sqrt(3)*(a*c + 3*b*c - 3*a*d)*arctan(1/3*sqrt(3)*(2*(1/x^2 + 1)^(1/3) + 1))/c^2 + 1/12*(a*c + 3*b*c - 3*a*d)*log((1/x^2 + 1)^(2/3) + (1/x^2 + 1)^(1/3) + 1)/c^2 - 1/6*(a*c + 3*b*c - 3*a*d)*log(abs((1/x^2 + 1)^(1/3) - 1))/c^2 - 1/2*(sqrt(3)*(-c*d^2 + d^3)^(1/3)*b*c - sqrt(3)*(-c*d^2 + d^3)^(1/3)*a*d)*arctan(1/3*sqrt(3)*((-(c - d)/d)^(1/3) + 2*(1/x^2 + 1)^(1/3))/(-(c - d)/d)^(1/3))/(c^2*d) - 1/4*((-c*d^2 + d^3)^(1/3)*b*c - (-c*d^2 + d^3)^(1/3)*a*d)*log((-(c - d)/d)^(2/3) + (-(c - d)/d)^(1/3)*(1/x^2 + 1)^(1/3) + (1/x^2 + 1)^(2/3))/(c^2*d)","A",0
2967,-1,0,0,0.000000," ","integrate(x^2*(a*x^3+b)*(2*a*p*x^3+3*a*q-b*p)/(p*x^3+q)^(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, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2968,0,0,0,0.000000," ","integrate((a*b+a*c-2*b*c+(-2*a+b+c)*x)/((-a+x)*(-b+x)*(-c+x))^(1/3)/(a^2-b*c*d+(b*d+c*d-2*a)*x+(1-d)*x^2),x, algorithm=""giac"")","\int -\frac{a b + a c - 2 \, b c - {\left(2 \, a - b - c\right)} x}{\left(-{\left(a - x\right)} {\left(b - x\right)} {\left(c - x\right)}\right)^{\frac{1}{3}} {\left(b c d + {\left(d - 1\right)} x^{2} - a^{2} - {\left(b d + c d - 2 \, a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*b + a*c - 2*b*c - (2*a - b - c)*x)/((-(a - x)*(b - x)*(c - x))^(1/3)*(b*c*d + (d - 1)*x^2 - a^2 - (b*d + c*d - 2*a)*x)), x)","F",0
2969,0,0,0,0.000000," ","integrate((-2+x)*(x^2-x+1)/x^3/(x^2+x-1)/((2*x^2-x+1)/(3*x^2-x+1))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(x^{2} - x + 1\right)} {\left(x - 2\right)}}{{\left(x^{2} + x - 1\right)} x^{3} \left(\frac{2 \, x^{2} - x + 1}{3 \, x^{2} - x + 1}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^2 - x + 1)*(x - 2)/((x^2 + x - 1)*x^3*((2*x^2 - x + 1)/(3*x^2 - x + 1))^(1/3)), x)","F",0
2970,0,0,0,0.000000," ","integrate(x^3*(9*a*x^4+5*b)/(a*x^5+b*x)^(1/4)/(a*x^9+b*x^5+1),x, algorithm=""giac"")","\int \frac{{\left(9 \, a x^{4} + 5 \, b\right)} x^{3}}{{\left(a x^{9} + b x^{5} + 1\right)} {\left(a x^{5} + b x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((9*a*x^4 + 5*b)*x^3/((a*x^9 + b*x^5 + 1)*(a*x^5 + b*x)^(1/4)), x)","F",0
2971,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2972,-1,0,0,0.000000," ","integrate((x^2+1)^(1/2)*(x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2973,0,0,0,0.000000," ","integrate((a^12*x^12+b^12)/(a^4*x^4-b^4)^(1/2)/(a^12*x^12-b^12),x, algorithm=""giac"")","\int \frac{a^{12} x^{12} + b^{12}}{{\left(a^{12} x^{12} - b^{12}\right)} \sqrt{a^{4} x^{4} - b^{4}}}\,{d x}"," ",0,"integrate((a^12*x^12 + b^12)/((a^12*x^12 - b^12)*sqrt(a^4*x^4 - b^4)), x)","F",0
2974,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2)/(c*x^4+d),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(c x^{4} + d\right)}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(c*x^4 + d)), x)","F",0
2975,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2)/(c*x^4+d),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(c x^{4} + d\right)}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(c*x^4 + d)), x)","F",0
2976,0,0,0,0.000000," ","integrate(x/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int -\frac{x}{\sqrt{a x + b} \sqrt{c + \sqrt{a x + b}} - x}\,{d x}"," ",0,"integrate(-x/(sqrt(a*x + b)*sqrt(c + sqrt(a*x + b)) - x), x)","F",0
2977,0,0,0,0.000000," ","integrate(x/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int -\frac{x}{\sqrt{a x + b} \sqrt{c + \sqrt{a x + b}} - x}\,{d x}"," ",0,"integrate(-x/(sqrt(a*x + b)*sqrt(c + sqrt(a*x + b)) - x), x)","F",0
2978,0,0,0,0.000000," ","integrate((-2*x+(1+k)*x^2)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2-b)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(a + k\right)} x^{2} - {\left(k + 1\right)} x + 1\right)} {\left({\left(k + 1\right)} x^{2} - 2 \, x\right)}}{{\left({\left(k^{2} - b\right)} x^{4} - 2 \, {\left(k^{2} + k\right)} x^{3} + {\left(k^{2} + 4 \, k + 1\right)} x^{2} - 2 \, {\left(k + 1\right)} x + 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(((a + k)*x^2 - (k + 1)*x + 1)*((k + 1)*x^2 - 2*x)/(((k^2 - b)*x^4 - 2*(k^2 + k)*x^3 + (k^2 + 4*k + 1)*x^2 - 2*(k + 1)*x + 1)*((k*x - 1)*(x - 1)*x)^(2/3)), x)","F",0
2979,0,0,0,0.000000," ","integrate((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2-b)*x^4),x, algorithm=""giac"")","\int \frac{{\left({\left(a + k\right)} x^{2} - {\left(k + 1\right)} x + 1\right)} {\left({\left(k + 1\right)} x - 2\right)}}{{\left({\left(k^{2} - b\right)} x^{4} - 2 \, {\left(k^{2} + k\right)} x^{3} + {\left(k^{2} + 4 \, k + 1\right)} x^{2} - 2 \, {\left(k + 1\right)} x + 1\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((a + k)*x^2 - (k + 1)*x + 1)*((k + 1)*x - 2)/(((k^2 - b)*x^4 - 2*(k^2 + k)*x^3 + (k^2 + 4*k + 1)*x^2 - 2*(k + 1)*x + 1)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
2980,-1,0,0,0.000000," ","integrate(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2981,-1,0,0,0.000000," ","integrate(x/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2982,-1,0,0,0.000000," ","integrate((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(5/4)/(a^2*x^2-b)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2983,1,372,0,3.067723," ","integrate((a*x^2-b)*(x^3-x)^(1/3)/(c*x^2-d),x, algorithm=""giac"")","\frac{a x^{2} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}}{2 \, c} - \frac{{\left(b c^{2} - a c d - b c d + a d^{2}\right)} \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} \log\left({\left| -\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(c^{3} - c^{2} d\right)}} - \frac{\sqrt{3} {\left(a c + 3 \, b c - 3 \, a d\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}\right)}{6 \, c^{2}} - \frac{{\left(a c + 3 \, b c - 3 \, a d\right)} \log\left({\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + 1\right)}{12 \, c^{2}} + \frac{{\left(a c + 3 \, b c - 3 \, a d\right)} \log\left({\left| {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)}{6 \, c^{2}} + \frac{{\left(\sqrt{3} {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} b c - \sqrt{3} {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} a d\right)} \arctan\left(\frac{\sqrt{3} {\left(\left(-\frac{c - d}{d}\right)^{\frac{1}{3}} + 2 \, {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c - d}{d}\right)^{\frac{1}{3}}}\right)}{2 \, c^{2} d} + \frac{{\left({\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} b c - {\left(-c d^{2} + d^{3}\right)}^{\frac{1}{3}} a d\right)} \log\left(\left(-\frac{c - d}{d}\right)^{\frac{2}{3}} + \left(-\frac{c - d}{d}\right)^{\frac{1}{3}} {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{1}{3}} + {\left(-\frac{1}{x^{2}} + 1\right)}^{\frac{2}{3}}\right)}{4 \, c^{2} d}"," ",0,"1/2*a*x^2*(-1/x^2 + 1)^(1/3)/c - 1/2*(b*c^2 - a*c*d - b*c*d + a*d^2)*(-(c - d)/d)^(1/3)*log(abs(-(-(c - d)/d)^(1/3) + (-1/x^2 + 1)^(1/3)))/(c^3 - c^2*d) - 1/6*sqrt(3)*(a*c + 3*b*c - 3*a*d)*arctan(1/3*sqrt(3)*(2*(-1/x^2 + 1)^(1/3) + 1))/c^2 - 1/12*(a*c + 3*b*c - 3*a*d)*log((-1/x^2 + 1)^(2/3) + (-1/x^2 + 1)^(1/3) + 1)/c^2 + 1/6*(a*c + 3*b*c - 3*a*d)*log(abs((-1/x^2 + 1)^(1/3) - 1))/c^2 + 1/2*(sqrt(3)*(-c*d^2 + d^3)^(1/3)*b*c - sqrt(3)*(-c*d^2 + d^3)^(1/3)*a*d)*arctan(1/3*sqrt(3)*((-(c - d)/d)^(1/3) + 2*(-1/x^2 + 1)^(1/3))/(-(c - d)/d)^(1/3))/(c^2*d) + 1/4*((-c*d^2 + d^3)^(1/3)*b*c - (-c*d^2 + d^3)^(1/3)*a*d)*log((-(c - d)/d)^(2/3) + (-(c - d)/d)^(1/3)*(-1/x^2 + 1)^(1/3) + (-1/x^2 + 1)^(2/3))/(c^2*d)","A",0
2984,0,0,0,0.000000," ","integrate((-a*b+(2*a-b)*x)*(a^2-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/3)/(a^4*d-4*a^3*d*x+(6*a^2*d-b^2)*x^2+2*(-2*a*d+b)*x^3+(-1+d)*x^4),x, algorithm=""giac"")","\int -\frac{{\left(a^{2} - 2 \, a x + x^{2}\right)} {\left(a b - {\left(2 \, a - b\right)} x\right)}}{{\left(a^{4} d - 4 \, a^{3} d x + {\left(d - 1\right)} x^{4} - 2 \, {\left(2 \, a d - b\right)} x^{3} + {\left(6 \, a^{2} d - b^{2}\right)} x^{2}\right)} \left({\left(a - x\right)} {\left(b - x\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(a^2 - 2*a*x + x^2)*(a*b - (2*a - b)*x)/((a^4*d - 4*a^3*d*x + (d - 1)*x^4 - 2*(2*a*d - b)*x^3 + (6*a^2*d - b^2)*x^2)*((a - x)*(b - x)*x)^(1/3)), x)","F",0
2985,1,1632,0,6.051728," ","integrate((d*x+b)/x^4/((a*x+b)/(c*x+d))^(1/4),x, algorithm=""giac"")","\frac{1}{768} \, {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)} {\left(\frac{6 \, \sqrt{2} {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 2 \, a^{2} b^{2} c^{2} d^{2} - 12 \, b^{3} c^{3} d^{2} - 20 \, a^{3} b c d^{3} + 4 \, a b^{2} c^{2} d^{3} + 15 \, a^{4} d^{4} + 28 \, a^{2} b c d^{4} - 20 \, a^{3} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{b}{d}\right)^{\frac{1}{4}} + 2 \, \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{b}{d}\right)^{\frac{1}{4}}}\right)}{\left(-b d^{3}\right)^{\frac{1}{4}} b^{2} d^{2}} + \frac{6 \, \sqrt{2} {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 2 \, a^{2} b^{2} c^{2} d^{2} - 12 \, b^{3} c^{3} d^{2} - 20 \, a^{3} b c d^{3} + 4 \, a b^{2} c^{2} d^{3} + 15 \, a^{4} d^{4} + 28 \, a^{2} b c d^{4} - 20 \, a^{3} d^{5}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{b}{d}\right)^{\frac{1}{4}} - 2 \, \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{b}{d}\right)^{\frac{1}{4}}}\right)}{\left(-b d^{3}\right)^{\frac{1}{4}} b^{2} d^{2}} - \frac{3 \, \sqrt{2} {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 2 \, a^{2} b^{2} c^{2} d^{2} - 12 \, b^{3} c^{3} d^{2} - 20 \, a^{3} b c d^{3} + 4 \, a b^{2} c^{2} d^{3} + 15 \, a^{4} d^{4} + 28 \, a^{2} b c d^{4} - 20 \, a^{3} d^{5}\right)} \log\left(\sqrt{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}} \left(-\frac{b}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{a x + b}{c x + d}} + \sqrt{-\frac{b}{d}}\right)}{\left(-b d^{3}\right)^{\frac{1}{4}} b^{2} d^{2}} + \frac{3 \, \sqrt{2} {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 2 \, a^{2} b^{2} c^{2} d^{2} - 12 \, b^{3} c^{3} d^{2} - 20 \, a^{3} b c d^{3} + 4 \, a b^{2} c^{2} d^{3} + 15 \, a^{4} d^{4} + 28 \, a^{2} b c d^{4} - 20 \, a^{3} d^{5}\right)} \log\left(-\sqrt{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{1}{4}} \left(-\frac{b}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{a x + b}{c x + d}} + \sqrt{-\frac{b}{d}}\right)}{\left(-b d^{3}\right)^{\frac{1}{4}} b^{2} d^{2}} + \frac{8 \, {\left(7 \, b^{6} c^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - 4 \, a b^{5} c^{3} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{18 \, {\left(a x + b\right)} b^{5} c^{4} d \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - 126 \, a^{2} b^{4} c^{2} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} + \frac{120 \, {\left(a x + b\right)} a b^{4} c^{3} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - 12 \, b^{5} c^{3} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{21 \, {\left(a x + b\right)}^{2} b^{4} c^{4} d^{2} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} + 236 \, a^{3} b^{3} c d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{60 \, {\left(a x + b\right)} a^{2} b^{3} c^{2} d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} + 132 \, a b^{4} c^{2} d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} + \frac{12 \, {\left(a x + b\right)}^{2} a b^{3} c^{3} d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - \frac{24 \, {\left(a x + b\right)} b^{4} c^{3} d^{3} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - 113 \, a^{4} b^{2} d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{168 \, {\left(a x + b\right)} a^{3} b^{2} c d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - 228 \, a^{2} b^{3} c d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} - \frac{6 \, {\left(a x + b\right)}^{2} a^{2} b^{2} c^{2} d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - \frac{120 \, {\left(a x + b\right)} a b^{3} c^{2} d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} + \frac{36 \, {\left(a x + b\right)}^{2} b^{3} c^{3} d^{4} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} + \frac{126 \, {\left(a x + b\right)} a^{4} b d^{5} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} + 108 \, a^{3} b^{2} d^{5} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}} + \frac{60 \, {\left(a x + b\right)}^{2} a^{3} b c d^{5} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} + \frac{312 \, {\left(a x + b\right)} a^{2} b^{2} c d^{5} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - \frac{12 \, {\left(a x + b\right)}^{2} a b^{2} c^{2} d^{5} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - \frac{45 \, {\left(a x + b\right)}^{2} a^{4} d^{6} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} - \frac{168 \, {\left(a x + b\right)} a^{3} b d^{6} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{c x + d} - \frac{84 \, {\left(a x + b\right)}^{2} a^{2} b c d^{6} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}} + \frac{60 \, {\left(a x + b\right)}^{2} a^{3} d^{7} \left(\frac{a x + b}{c x + d}\right)^{\frac{3}{4}}}{{\left(c x + d\right)}^{2}}\right)}}{{\left(b - \frac{{\left(a x + b\right)} d}{c x + d}\right)}^{3} b^{2} d^{2}}\right)}"," ",0,"1/768*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)*(6*sqrt(2)*(7*b^4*c^4 - 4*a*b^3*c^3*d + 2*a^2*b^2*c^2*d^2 - 12*b^3*c^3*d^2 - 20*a^3*b*c*d^3 + 4*a*b^2*c^2*d^3 + 15*a^4*d^4 + 28*a^2*b*c*d^4 - 20*a^3*d^5)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b/d)^(1/4) + 2*((a*x + b)/(c*x + d))^(1/4))/(-b/d)^(1/4))/((-b*d^3)^(1/4)*b^2*d^2) + 6*sqrt(2)*(7*b^4*c^4 - 4*a*b^3*c^3*d + 2*a^2*b^2*c^2*d^2 - 12*b^3*c^3*d^2 - 20*a^3*b*c*d^3 + 4*a*b^2*c^2*d^3 + 15*a^4*d^4 + 28*a^2*b*c*d^4 - 20*a^3*d^5)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b/d)^(1/4) - 2*((a*x + b)/(c*x + d))^(1/4))/(-b/d)^(1/4))/((-b*d^3)^(1/4)*b^2*d^2) - 3*sqrt(2)*(7*b^4*c^4 - 4*a*b^3*c^3*d + 2*a^2*b^2*c^2*d^2 - 12*b^3*c^3*d^2 - 20*a^3*b*c*d^3 + 4*a*b^2*c^2*d^3 + 15*a^4*d^4 + 28*a^2*b*c*d^4 - 20*a^3*d^5)*log(sqrt(2)*((a*x + b)/(c*x + d))^(1/4)*(-b/d)^(1/4) + sqrt((a*x + b)/(c*x + d)) + sqrt(-b/d))/((-b*d^3)^(1/4)*b^2*d^2) + 3*sqrt(2)*(7*b^4*c^4 - 4*a*b^3*c^3*d + 2*a^2*b^2*c^2*d^2 - 12*b^3*c^3*d^2 - 20*a^3*b*c*d^3 + 4*a*b^2*c^2*d^3 + 15*a^4*d^4 + 28*a^2*b*c*d^4 - 20*a^3*d^5)*log(-sqrt(2)*((a*x + b)/(c*x + d))^(1/4)*(-b/d)^(1/4) + sqrt((a*x + b)/(c*x + d)) + sqrt(-b/d))/((-b*d^3)^(1/4)*b^2*d^2) + 8*(7*b^6*c^4*((a*x + b)/(c*x + d))^(3/4) - 4*a*b^5*c^3*d*((a*x + b)/(c*x + d))^(3/4) - 18*(a*x + b)*b^5*c^4*d*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 126*a^2*b^4*c^2*d^2*((a*x + b)/(c*x + d))^(3/4) + 120*(a*x + b)*a*b^4*c^3*d^2*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 12*b^5*c^3*d^2*((a*x + b)/(c*x + d))^(3/4) - 21*(a*x + b)^2*b^4*c^4*d^2*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 + 236*a^3*b^3*c*d^3*((a*x + b)/(c*x + d))^(3/4) - 60*(a*x + b)*a^2*b^3*c^2*d^3*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) + 132*a*b^4*c^2*d^3*((a*x + b)/(c*x + d))^(3/4) + 12*(a*x + b)^2*a*b^3*c^3*d^3*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 24*(a*x + b)*b^4*c^3*d^3*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 113*a^4*b^2*d^4*((a*x + b)/(c*x + d))^(3/4) - 168*(a*x + b)*a^3*b^2*c*d^4*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 228*a^2*b^3*c*d^4*((a*x + b)/(c*x + d))^(3/4) - 6*(a*x + b)^2*a^2*b^2*c^2*d^4*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 120*(a*x + b)*a*b^3*c^2*d^4*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) + 36*(a*x + b)^2*b^3*c^3*d^4*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 + 126*(a*x + b)*a^4*b*d^5*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) + 108*a^3*b^2*d^5*((a*x + b)/(c*x + d))^(3/4) + 60*(a*x + b)^2*a^3*b*c*d^5*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 + 312*(a*x + b)*a^2*b^2*c*d^5*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 12*(a*x + b)^2*a*b^2*c^2*d^5*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 45*(a*x + b)^2*a^4*d^6*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 - 168*(a*x + b)*a^3*b*d^6*((a*x + b)/(c*x + d))^(3/4)/(c*x + d) - 84*(a*x + b)^2*a^2*b*c*d^6*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2 + 60*(a*x + b)^2*a^3*d^7*((a*x + b)/(c*x + d))^(3/4)/(c*x + d)^2)/((b - (a*x + b)*d/(c*x + d))^3*b^2*d^2))","B",0
2986,0,0,0,0.000000," ","integrate((e*x+f)/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{e x + f}{c x + d + \sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((e*x + f)/(c*x + d + sqrt(a*x + sqrt(a^2*x^2 + b^2))), x)","F",0
2987,0,0,0,0.000000," ","integrate((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+1),x, algorithm=""giac"")","\int -\frac{x^{6} + 1}{{\left(x^{6} - 1\right)} {\left(x^{5} - x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-(x^6 + 1)/((x^6 - 1)*(x^5 - x^3)^(1/4)), x)","F",0
2988,0,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)*(c*x^4+d)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + d\right)} \sqrt{a^{2} x^{2} - b} \sqrt{a x + \sqrt{a^{2} x^{2} - b}}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^4 + d)*sqrt(a^2*x^2 - b)*sqrt(a*x + sqrt(a^2*x^2 - b))/x^2, x)","F",0
2989,-1,0,0,0.000000," ","integrate((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2990,-1,0,0,0.000000," ","integrate((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2991,-1,0,0,0.000000," ","integrate((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2992,0,0,0,0.000000," ","integrate((x^4+x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} + 1\right)} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{{\left(x^{4} + x^{2} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)*sqrt(x^2 + sqrt(x^4 + 1))/((x^4 + x^2 - 1)*sqrt(x^4 + 1)), x)","F",0
2993,0,0,0,0.000000," ","integrate((x^4+x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} + 1\right)} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{{\left(x^{4} + x^{2} - 1\right)} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)*sqrt(x^2 + sqrt(x^4 + 1))/((x^4 + x^2 - 1)*sqrt(x^4 + 1)), x)","F",0
2994,0,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)*(c*x^4+d)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + d\right)} \sqrt{a^{2} x^{2} - b} \sqrt{a x + \sqrt{a^{2} x^{2} - b}}}{x}\,{d x}"," ",0,"integrate((c*x^4 + d)*sqrt(a^2*x^2 - b)*sqrt(a*x + sqrt(a^2*x^2 - b))/x, x)","F",0
2995,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{c x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(c*x^2 + d), x)","F",0
2996,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{c x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(c*x^2 + d), x)","F",0
2997,0,0,0,0.000000," ","integrate(x^5*(10*a*x^3+7*b)/(a*x^6+b*x^3)^(1/4)/(a*x^10+b*x^7+1),x, algorithm=""giac"")","\int \frac{{\left(10 \, a x^{3} + 7 \, b\right)} x^{5}}{{\left(a x^{10} + b x^{7} + 1\right)} {\left(a x^{6} + b x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((10*a*x^3 + 7*b)*x^5/((a*x^10 + b*x^7 + 1)*(a*x^6 + b*x^3)^(1/4)), x)","F",0
2998,-1,0,0,0.000000," ","integrate(x^4*(p*x^3-2*q)*(p*x^3+q)^(1/2)/(b*x^8+a*(p*x^3+q)^4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2999,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3000,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3001,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3002,-1,0,0,0.000000," ","integrate((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3003,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3004,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3005,0,0,0,0.000000," ","integrate((1+(-2+k)*x)*(k^2*x^2-2*k*x+1)/((1-x)*x*(-k*x+1))^(1/3)/(b-4*b*k*x+(6*b*k^2-1)*x^2+(-4*b*k^3+2)*x^3+(b*k^4-1)*x^4),x, algorithm=""giac"")","\int \frac{{\left(k^{2} x^{2} - 2 \, k x + 1\right)} {\left({\left(k - 2\right)} x + 1\right)}}{{\left({\left(b k^{4} - 1\right)} x^{4} - 2 \, {\left(2 \, b k^{3} - 1\right)} x^{3} - 4 \, b k x + {\left(6 \, b k^{2} - 1\right)} x^{2} + b\right)} \left({\left(k x - 1\right)} {\left(x - 1\right)} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((k^2*x^2 - 2*k*x + 1)*((k - 2)*x + 1)/(((b*k^4 - 1)*x^4 - 2*(2*b*k^3 - 1)*x^3 - 4*b*k*x + (6*b*k^2 - 1)*x^2 + b)*((k*x - 1)*(x - 1)*x)^(1/3)), x)","F",0
3006,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3007,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3008,0,0,0,0.000000," ","integrate((a-2*b+x)*(a^2-2*a*x+x^2)/((-a+x)*(-b+x))^(1/3)/(-b^2+a^4*d+2*(-2*a^3*d+b)*x+(6*a^2*d-1)*x^2-4*a*d*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{{\left(a^{2} - 2 \, a x + x^{2}\right)} {\left(a - 2 \, b + x\right)}}{{\left(a^{4} d - 4 \, a d x^{3} + d x^{4} + {\left(6 \, a^{2} d - 1\right)} x^{2} - b^{2} - 2 \, {\left(2 \, a^{3} d - b\right)} x\right)} \left({\left(a - x\right)} {\left(b - x\right)}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a^2 - 2*a*x + x^2)*(a - 2*b + x)/((a^4*d - 4*a*d*x^3 + d*x^4 + (6*a^2*d - 1)*x^2 - b^2 - 2*(2*a^3*d - b)*x)*((a - x)*(b - x))^(1/3)), x)","F",0
3009,-1,0,0,0.000000," ","integrate((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3010,-1,0,0,0.000000," ","integrate((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3011,1,259,0,1.045839," ","integrate((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/(x-(a*x+b)^(1/2)),x, algorithm=""giac"")","\frac{4 \, \sqrt{a^{2} + 4 \, b} \sqrt{-2 \, a - 4 \, c + 2 \, \sqrt{a^{2} + 4 \, b}} b^{2} \arctan\left(\frac{\sqrt{c + \sqrt{a x + b}}}{\sqrt{-\frac{1}{2} \, a - c + \frac{1}{2} \, \sqrt{{\left(a + 2 \, c\right)}^{2} - 4 \, a c - 4 \, c^{2} + 4 \, b}}}\right)}{a^{4} + 6 \, a^{2} b + 8 \, b^{2} + {\left(a^{3} + 4 \, a b\right)} \sqrt{a^{2} + 4 \, b}} - \frac{4 \, \sqrt{a^{2} + 4 \, b} \sqrt{-2 \, a - 4 \, c - 2 \, \sqrt{a^{2} + 4 \, b}} b^{2} \arctan\left(\frac{\sqrt{c + \sqrt{a x + b}}}{\sqrt{-\frac{1}{2} \, a - c - \frac{1}{2} \, \sqrt{{\left(a + 2 \, c\right)}^{2} - 4 \, a c - 4 \, c^{2} + 4 \, b}}}\right)}{a^{4} + 6 \, a^{2} b + 8 \, b^{2} - {\left(a^{3} + 4 \, a b\right)} \sqrt{a^{2} + 4 \, b}} + 4 \, a \sqrt{c + \sqrt{a x + b}} + \frac{4}{3} \, {\left(c + \sqrt{a x + b}\right)}^{\frac{3}{2}}"," ",0,"4*sqrt(a^2 + 4*b)*sqrt(-2*a - 4*c + 2*sqrt(a^2 + 4*b))*b^2*arctan(sqrt(c + sqrt(a*x + b))/sqrt(-1/2*a - c + 1/2*sqrt((a + 2*c)^2 - 4*a*c - 4*c^2 + 4*b)))/(a^4 + 6*a^2*b + 8*b^2 + (a^3 + 4*a*b)*sqrt(a^2 + 4*b)) - 4*sqrt(a^2 + 4*b)*sqrt(-2*a - 4*c - 2*sqrt(a^2 + 4*b))*b^2*arctan(sqrt(c + sqrt(a*x + b))/sqrt(-1/2*a - c - 1/2*sqrt((a + 2*c)^2 - 4*a*c - 4*c^2 + 4*b)))/(a^4 + 6*a^2*b + 8*b^2 - (a^3 + 4*a*b)*sqrt(a^2 + 4*b)) + 4*a*sqrt(c + sqrt(a*x + b)) + 4/3*(c + sqrt(a*x + b))^(3/2)","A",0
3012,1,1194,0,8.006705," ","integrate((1+x)/(-a*x+1)/((-b*x+1)/(c+x))^(1/4),x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{8 \, {\left(-a^{4} c^{3} + a^{3} b c^{3} - 3 \, a^{3} c^{2} + 3 \, a^{2} b c^{2} - 3 \, a^{2} c + 3 \, a b c - a + b\right)}^{\frac{3}{4}} {\left(\sqrt{2} a b c + \sqrt{2} b c + \sqrt{2} a + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{a - b}{a c + 1}\right)^{\frac{1}{4}} + 2 \, \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a - b}{a c + 1}\right)^{\frac{1}{4}}}\right)}{a^{5} c^{2} - a^{4} b c^{2} + 2 \, a^{4} c - 2 \, a^{3} b c + a^{3} - a^{2} b} + \frac{8 \, {\left(-a^{4} c^{3} + a^{3} b c^{3} - 3 \, a^{3} c^{2} + 3 \, a^{2} b c^{2} - 3 \, a^{2} c + 3 \, a b c - a + b\right)}^{\frac{3}{4}} {\left(\sqrt{2} a b c + \sqrt{2} b c + \sqrt{2} a + \sqrt{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{a - b}{a c + 1}\right)^{\frac{1}{4}} - 2 \, \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a - b}{a c + 1}\right)^{\frac{1}{4}}}\right)}{a^{5} c^{2} - a^{4} b c^{2} + 2 \, a^{4} c - 2 \, a^{3} b c + a^{3} - a^{2} b} - \frac{8 \, {\left(-a^{4} c^{3} + a^{3} b c^{3} - 3 \, a^{3} c^{2} + 3 \, a^{2} b c^{2} - 3 \, a^{2} c + 3 \, a b c - a + b\right)}^{\frac{3}{4}} {\left(a b c + b c + a + 1\right)} \log\left(\sqrt{2} \left(-\frac{a - b}{a c + 1}\right)^{\frac{1}{4}} \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}} + \sqrt{-\frac{a - b}{a c + 1}} + \sqrt{-\frac{b x - 1}{c + x}}\right)}{\sqrt{2} a^{5} c^{2} - \sqrt{2} a^{4} b c^{2} + 2 \, \sqrt{2} a^{4} c - 2 \, \sqrt{2} a^{3} b c + \sqrt{2} a^{3} - \sqrt{2} a^{2} b} + \frac{8 \, {\left(-a^{4} c^{3} + a^{3} b c^{3} - 3 \, a^{3} c^{2} + 3 \, a^{2} b c^{2} - 3 \, a^{2} c + 3 \, a b c - a + b\right)}^{\frac{3}{4}} {\left(a b c + b c + a + 1\right)} \log\left(-\sqrt{2} \left(-\frac{a - b}{a c + 1}\right)^{\frac{1}{4}} \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}} + \sqrt{-\frac{a - b}{a c + 1}} + \sqrt{-\frac{b x - 1}{c + x}}\right)}{\sqrt{2} a^{5} c^{2} - \sqrt{2} a^{4} b c^{2} + 2 \, \sqrt{2} a^{4} c - 2 \, \sqrt{2} a^{3} b c + \sqrt{2} a^{3} - \sqrt{2} a^{2} b} + \frac{2 \, \sqrt{2} {\left(a b^{\frac{11}{4}} c^{2} + 2 \, {\left(2 \, b^{2} + b\right)} a b^{\frac{3}{4}} c + 4 \, b^{\frac{11}{4}} c + a {\left(4 \, b + 1\right)} b^{\frac{3}{4}} + 4 \, b^{\frac{7}{4}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} + 2 \, \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{a^{2} b^{2}} + \frac{2 \, \sqrt{2} {\left(a b^{\frac{11}{4}} c^{2} + 2 \, {\left(2 \, b^{2} + b\right)} a b^{\frac{3}{4}} c + 4 \, b^{\frac{11}{4}} c + a {\left(4 \, b + 1\right)} b^{\frac{3}{4}} + 4 \, b^{\frac{7}{4}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} - 2 \, \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}}\right)}}{2 \, b^{\frac{1}{4}}}\right)}{a^{2} b^{2}} - \frac{\sqrt{2} {\left(a b^{\frac{11}{4}} c^{2} + 2 \, {\left(2 \, b^{2} + b\right)} a b^{\frac{3}{4}} c + 4 \, b^{\frac{11}{4}} c + a {\left(4 \, b + 1\right)} b^{\frac{3}{4}} + 4 \, b^{\frac{7}{4}}\right)} \log\left(\sqrt{2} b^{\frac{1}{4}} \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}} + \sqrt{b} + \sqrt{-\frac{b x - 1}{c + x}}\right)}{a^{2} b^{2}} + \frac{\sqrt{2} {\left(a b^{\frac{11}{4}} c^{2} + 2 \, {\left(2 \, b^{2} + b\right)} a b^{\frac{3}{4}} c + 4 \, b^{\frac{11}{4}} c + a {\left(4 \, b + 1\right)} b^{\frac{3}{4}} + 4 \, b^{\frac{7}{4}}\right)} \log\left(-\sqrt{2} b^{\frac{1}{4}} \left(-\frac{b x - 1}{c + x}\right)^{\frac{1}{4}} + \sqrt{b} + \sqrt{-\frac{b x - 1}{c + x}}\right)}{a^{2} b^{2}} + \frac{8 \, {\left(b^{2} c^{2} \left(-\frac{b x - 1}{c + x}\right)^{\frac{3}{4}} + 2 \, b c \left(-\frac{b x - 1}{c + x}\right)^{\frac{3}{4}} + \left(-\frac{b x - 1}{c + x}\right)^{\frac{3}{4}}\right)}}{a {\left(b - \frac{b x - 1}{c + x}\right)} b}\right)} {\left(\frac{b c}{{\left(b c + 1\right)}^{2}} + \frac{1}{{\left(b c + 1\right)}^{2}}\right)}"," ",0,"1/8*(8*(-a^4*c^3 + a^3*b*c^3 - 3*a^3*c^2 + 3*a^2*b*c^2 - 3*a^2*c + 3*a*b*c - a + b)^(3/4)*(sqrt(2)*a*b*c + sqrt(2)*b*c + sqrt(2)*a + sqrt(2))*arctan(1/2*sqrt(2)*(sqrt(2)*(-(a - b)/(a*c + 1))^(1/4) + 2*(-(b*x - 1)/(c + x))^(1/4))/(-(a - b)/(a*c + 1))^(1/4))/(a^5*c^2 - a^4*b*c^2 + 2*a^4*c - 2*a^3*b*c + a^3 - a^2*b) + 8*(-a^4*c^3 + a^3*b*c^3 - 3*a^3*c^2 + 3*a^2*b*c^2 - 3*a^2*c + 3*a*b*c - a + b)^(3/4)*(sqrt(2)*a*b*c + sqrt(2)*b*c + sqrt(2)*a + sqrt(2))*arctan(-1/2*sqrt(2)*(sqrt(2)*(-(a - b)/(a*c + 1))^(1/4) - 2*(-(b*x - 1)/(c + x))^(1/4))/(-(a - b)/(a*c + 1))^(1/4))/(a^5*c^2 - a^4*b*c^2 + 2*a^4*c - 2*a^3*b*c + a^3 - a^2*b) - 8*(-a^4*c^3 + a^3*b*c^3 - 3*a^3*c^2 + 3*a^2*b*c^2 - 3*a^2*c + 3*a*b*c - a + b)^(3/4)*(a*b*c + b*c + a + 1)*log(sqrt(2)*(-(a - b)/(a*c + 1))^(1/4)*(-(b*x - 1)/(c + x))^(1/4) + sqrt(-(a - b)/(a*c + 1)) + sqrt(-(b*x - 1)/(c + x)))/(sqrt(2)*a^5*c^2 - sqrt(2)*a^4*b*c^2 + 2*sqrt(2)*a^4*c - 2*sqrt(2)*a^3*b*c + sqrt(2)*a^3 - sqrt(2)*a^2*b) + 8*(-a^4*c^3 + a^3*b*c^3 - 3*a^3*c^2 + 3*a^2*b*c^2 - 3*a^2*c + 3*a*b*c - a + b)^(3/4)*(a*b*c + b*c + a + 1)*log(-sqrt(2)*(-(a - b)/(a*c + 1))^(1/4)*(-(b*x - 1)/(c + x))^(1/4) + sqrt(-(a - b)/(a*c + 1)) + sqrt(-(b*x - 1)/(c + x)))/(sqrt(2)*a^5*c^2 - sqrt(2)*a^4*b*c^2 + 2*sqrt(2)*a^4*c - 2*sqrt(2)*a^3*b*c + sqrt(2)*a^3 - sqrt(2)*a^2*b) + 2*sqrt(2)*(a*b^(11/4)*c^2 + 2*(2*b^2 + b)*a*b^(3/4)*c + 4*b^(11/4)*c + a*(4*b + 1)*b^(3/4) + 4*b^(7/4))*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4) + 2*(-(b*x - 1)/(c + x))^(1/4))/b^(1/4))/(a^2*b^2) + 2*sqrt(2)*(a*b^(11/4)*c^2 + 2*(2*b^2 + b)*a*b^(3/4)*c + 4*b^(11/4)*c + a*(4*b + 1)*b^(3/4) + 4*b^(7/4))*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4) - 2*(-(b*x - 1)/(c + x))^(1/4))/b^(1/4))/(a^2*b^2) - sqrt(2)*(a*b^(11/4)*c^2 + 2*(2*b^2 + b)*a*b^(3/4)*c + 4*b^(11/4)*c + a*(4*b + 1)*b^(3/4) + 4*b^(7/4))*log(sqrt(2)*b^(1/4)*(-(b*x - 1)/(c + x))^(1/4) + sqrt(b) + sqrt(-(b*x - 1)/(c + x)))/(a^2*b^2) + sqrt(2)*(a*b^(11/4)*c^2 + 2*(2*b^2 + b)*a*b^(3/4)*c + 4*b^(11/4)*c + a*(4*b + 1)*b^(3/4) + 4*b^(7/4))*log(-sqrt(2)*b^(1/4)*(-(b*x - 1)/(c + x))^(1/4) + sqrt(b) + sqrt(-(b*x - 1)/(c + x)))/(a^2*b^2) + 8*(b^2*c^2*(-(b*x - 1)/(c + x))^(3/4) + 2*b*c*(-(b*x - 1)/(c + x))^(3/4) + (-(b*x - 1)/(c + x))^(3/4))/(a*(b - (b*x - 1)/(c + x))*b))*(b*c/(b*c + 1)^2 + 1/(b*c + 1)^2)","B",0
3013,0,0,0,0.000000," ","integrate(x^5*(9*a*x^2-7*b)/(a*x^5-b*x^3)^(1/4)/(a*x^9-b*x^7+1),x, algorithm=""giac"")","\int \frac{{\left(9 \, a x^{2} - 7 \, b\right)} x^{5}}{{\left(a x^{9} - b x^{7} + 1\right)} {\left(a x^{5} - b x^{3}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((9*a*x^2 - 7*b)*x^5/((a*x^9 - b*x^7 + 1)*(a*x^5 - b*x^3)^(1/4)), x)","F",0
3014,0,0,0,0.000000," ","integrate((a*x^4+b)/(a*x^4-b)^(1/2)/(a*x^4+c^2*x^2-b),x, algorithm=""giac"")","\int \frac{a x^{4} + b}{{\left(a x^{4} + c^{2} x^{2} - b\right)} \sqrt{a x^{4} - b}}\,{d x}"," ",0,"integrate((a*x^4 + b)/((a*x^4 + c^2*x^2 - b)*sqrt(a*x^4 - b)), x)","F",0
3015,0,0,0,0.000000," ","integrate(x*(-a+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-b^2+2*b*x+(a^2*d-1)*x^2-2*a*d*x^3+d*x^4),x, algorithm=""giac"")","\int \frac{{\left(a b - 2 \, b x + x^{2}\right)} {\left(a - x\right)} x}{{\left(2 \, a d x^{3} - d x^{4} - {\left(a^{2} d - 1\right)} x^{2} + b^{2} - 2 \, b x\right)} \left(-{\left(a - x\right)} {\left(b - x\right)}^{2} x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*b - 2*b*x + x^2)*(a - x)*x/((2*a*d*x^3 - d*x^4 - (a^2*d - 1)*x^2 + b^2 - 2*b*x)*(-(a - x)*(b - x)^2*x)^(1/3)), x)","F",0
3016,-1,0,0,0.000000," ","integrate((a*x+b)/(a*x-b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3017,0,0,0,0.000000," ","integrate((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4-b),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{4} + b} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{a^{2} x^{4} - b}\,{d x}"," ",0,"integrate(sqrt(a^2*x^4 + b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(a^2*x^4 - b), x)","F",0
3018,0,0,0,0.000000," ","integrate((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4-b),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{4} + b} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{a^{2} x^{4} - b}\,{d x}"," ",0,"integrate(sqrt(a^2*x^4 + b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(a^2*x^4 - b), x)","F",0
3019,0,0,0,0.000000," ","integrate(1/((-a+x)*(-b+x)^2)^(1/3)/(b-a*d+(-1+d)*x),x, algorithm=""giac"")","\int -\frac{1}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(a d - {\left(d - 1\right)} x - b\right)}}\,{d x}"," ",0,"integrate(-1/((-(a - x)*(b - x)^2)^(1/3)*(a*d - (d - 1)*x - b)), x)","F",0
3020,0,0,0,0.000000," ","integrate((2*x^2-3*x-4)*(x^4-x^2+x+1)*((2*x^4-x^2+x+1)/(3*x^4-x^2+x+1))^(1/3)/x^5/(x^4+x^2-x-1),x, algorithm=""giac"")","\int \frac{{\left(x^{4} - x^{2} + x + 1\right)} {\left(2 \, x^{2} - 3 \, x - 4\right)} \left(\frac{2 \, x^{4} - x^{2} + x + 1}{3 \, x^{4} - x^{2} + x + 1}\right)^{\frac{1}{3}}}{{\left(x^{4} + x^{2} - x - 1\right)} x^{5}}\,{d x}"," ",0,"integrate((x^4 - x^2 + x + 1)*(2*x^2 - 3*x - 4)*((2*x^4 - x^2 + x + 1)/(3*x^4 - x^2 + x + 1))^(1/3)/((x^4 + x^2 - x - 1)*x^5), x)","F",0
3021,1,255,0,143.517109," ","integrate((a*x-b)/(a*x+b)/(a^3*x^3-b^2*x^2)^(1/3),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left({\left(a^{3} + a b\right)}^{\frac{1}{3}} + 2 \, {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, {\left(a^{3} + a b\right)}^{\frac{1}{3}}}\right)}{{\left(a^{3} + a b\right)}^{\frac{1}{3}}} - \frac{\log\left({\left(a^{3} + a b\right)}^{\frac{2}{3}} + {\left(a^{3} + a b\right)}^{\frac{1}{3}} {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{1}{3}} + {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{{\left(a^{3} + a b\right)}^{\frac{1}{3}}} + \frac{2 \, \log\left({\left| -{\left(a^{3} + a b\right)}^{\frac{1}{3}} + {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{{\left(a^{3} + a b\right)}^{\frac{1}{3}}} - \frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, a}\right)}{a} + \frac{\log\left(a^{2} + {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{1}{3}} a + {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{2 \, a} - \frac{\log\left({\left| -a + {\left(a^{3} - \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{a}"," ",0,"2*sqrt(3)*arctan(1/3*sqrt(3)*((a^3 + a*b)^(1/3) + 2*(a^3 - b^2/x)^(1/3))/(a^3 + a*b)^(1/3))/(a^3 + a*b)^(1/3) - log((a^3 + a*b)^(2/3) + (a^3 + a*b)^(1/3)*(a^3 - b^2/x)^(1/3) + (a^3 - b^2/x)^(2/3))/(a^3 + a*b)^(1/3) + 2*log(abs(-(a^3 + a*b)^(1/3) + (a^3 - b^2/x)^(1/3)))/(a^3 + a*b)^(1/3) - sqrt(3)*arctan(1/3*sqrt(3)*(a + 2*(a^3 - b^2/x)^(1/3))/a)/a + 1/2*log(a^2 + (a^3 - b^2/x)^(1/3)*a + (a^3 - b^2/x)^(2/3))/a - log(abs(-a + (a^3 - b^2/x)^(1/3)))/a","A",0
3022,-1,0,0,0.000000," ","integrate((p*x^4-q)*(p*x^4+q)^(1/2)/(c*x^4+b*x^2*(p*x^4+q)+a*(p*x^4+q)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3023,-1,0,0,0.000000," ","integrate((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(-x^4+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3024,-1,0,0,0.000000," ","integrate((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(-x^4+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3025,0,0,0,0.000000," ","integrate((x^6-x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{6} - x^{3} + 1}{{\left(x^{6} - 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 - x^3 + 1)/((x^6 - 1)*(x^4 + x^2)^(1/3)), x)","F",0
3026,0,0,0,0.000000," ","integrate((x^6+x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x, algorithm=""giac"")","\int \frac{x^{6} + x^{3} + 1}{{\left(x^{6} - 1\right)} {\left(x^{4} + x^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^6 + x^3 + 1)/((x^6 - 1)*(x^4 + x^2)^(1/3)), x)","F",0
3027,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3028,0,0,0,0.000000," ","integrate((a*x^8-1)*(a*x^8+1)^(3/4)/(a^2*x^16+x^8+1),x, algorithm=""giac"")","\int \frac{{\left(a x^{8} + 1\right)}^{\frac{3}{4}} {\left(a x^{8} - 1\right)}}{a^{2} x^{16} + x^{8} + 1}\,{d x}"," ",0,"integrate((a*x^8 + 1)^(3/4)*(a*x^8 - 1)/(a^2*x^16 + x^8 + 1), x)","F",0
3029,1,255,0,141.945597," ","integrate((a*x-b)/(a*x+b)/(a^3*x^3+b^2*x^2)^(1/3),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left({\left(a^{3} - a b\right)}^{\frac{1}{3}} + 2 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, {\left(a^{3} - a b\right)}^{\frac{1}{3}}}\right)}{{\left(a^{3} - a b\right)}^{\frac{1}{3}}} - \frac{\log\left({\left(a^{3} - a b\right)}^{\frac{2}{3}} + {\left(a^{3} - a b\right)}^{\frac{1}{3}} {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{{\left(a^{3} - a b\right)}^{\frac{1}{3}}} + \frac{2 \, \log\left({\left| -{\left(a^{3} - a b\right)}^{\frac{1}{3}} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{{\left(a^{3} - a b\right)}^{\frac{1}{3}}} - \frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, a}\right)}{a} + \frac{\log\left(a^{2} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{2 \, a} - \frac{\log\left({\left| -a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{a}"," ",0,"2*sqrt(3)*arctan(1/3*sqrt(3)*((a^3 - a*b)^(1/3) + 2*(a^3 + b^2/x)^(1/3))/(a^3 - a*b)^(1/3))/(a^3 - a*b)^(1/3) - log((a^3 - a*b)^(2/3) + (a^3 - a*b)^(1/3)*(a^3 + b^2/x)^(1/3) + (a^3 + b^2/x)^(2/3))/(a^3 - a*b)^(1/3) + 2*log(abs(-(a^3 - a*b)^(1/3) + (a^3 + b^2/x)^(1/3)))/(a^3 - a*b)^(1/3) - sqrt(3)*arctan(1/3*sqrt(3)*(a + 2*(a^3 + b^2/x)^(1/3))/a)/a + 1/2*log(a^2 + (a^3 + b^2/x)^(1/3)*a + (a^3 + b^2/x)^(2/3))/a - log(abs(-a + (a^3 + b^2/x)^(1/3)))/a","A",0
3030,0,0,0,0.000000," ","integrate(1/(x^2-1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - 1\right)}^{2} \sqrt{x + \sqrt{x^{2} + 1}}}\,{d x}"," ",0,"integrate(1/((x^2 - 1)^2*sqrt(x + sqrt(x^2 + 1))), x)","F",0
3031,-2,0,0,0.000000," ","integrate((a*x^2+b*x+c)^(3/2)/(1-x*(a*x^2+b*x+c)^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
3032,0,0,0,0.000000," ","integrate((-b+x)^2/((-a+x)*(-b+x)^2)^(2/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int \frac{{\left(b - x\right)}^{2}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(b^{2} d + {\left(d - 1\right)} x^{2} - a^{2} - 2 \, {\left(b d - a\right)} x\right)}}\,{d x}"," ",0,"integrate((b - x)^2/((-(a - x)*(b - x)^2)^(2/3)*(b^2*d + (d - 1)*x^2 - a^2 - 2*(b*d - a)*x)), x)","F",0
3033,-1,0,0,0.000000," ","integrate((a*x+b)/(a*x-b)/(a^3*x^3-b^2*x^2)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3034,-1,0,0,0.000000," ","integrate(1/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3035,0,0,0,0.000000," ","integrate(x^4/(a*x^4-b)^(1/4)/(x^8+2*a*x^4-b),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{8} + 2 \, a x^{4} - b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((x^8 + 2*a*x^4 - b)*(a*x^4 - b)^(1/4)), x)","F",0
3036,-1,0,0,0.000000," ","integrate((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(3/4)/(a^2*x^2-b)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3037,0,0,0,0.000000," ","integrate(x^2/(x^4+1)/(x^6-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/((x^6 - x^2)^(1/4)*(x^4 + 1)), x)","F",0
3038,0,0,0,0.000000," ","integrate(x^2/(x^4+1)/(x^6-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/((x^6 - x^2)^(1/4)*(x^4 + 1)), x)","F",0
3039,0,0,0,0.000000," ","integrate((x^4-1)/(x^4+1)/(x^6-x^2)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{{\left(x^{6} - x^{2}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate((x^4 - 1)/((x^6 - x^2)^(1/4)*(x^4 + 1)), x)","F",0
3040,0,0,0,0.000000," ","integrate((a*x^4-b)^(3/4)/(x^8+2*a*x^4-b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b\right)}^{\frac{3}{4}}}{x^{8} + 2 \, a x^{4} - b}\,{d x}"," ",0,"integrate((a*x^4 - b)^(3/4)/(x^8 + 2*a*x^4 - b), x)","F",0
3041,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3042,-1,0,0,0.000000," ","integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3043,0,0,0,0.000000," ","integrate(x^2*(a*x+b)^(1/2)/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a x + b} x^{2}}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(sqrt(a*x + b)*x^2/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
3044,0,0,0,0.000000," ","integrate(x^2*(a*x+b)^(1/2)/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{\sqrt{a x + b} x^{2}}{x^{2} - \sqrt{a x + b} \sqrt{c + \sqrt{a x + b}}}\,{d x}"," ",0,"integrate(sqrt(a*x + b)*x^2/(x^2 - sqrt(a*x + b)*sqrt(c + sqrt(a*x + b))), x)","F",0
3045,-1,0,0,0.000000," ","integrate((a^2*x^2+b)^(1/2)*(a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3046,0,0,0,0.000000," ","integrate(x^4/(a*x^4+b)^(1/4)/(2*x^8+2*a*x^4+b),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(2 \, x^{8} + 2 \, a x^{4} + b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((2*x^8 + 2*a*x^4 + b)*(a*x^4 + b)^(1/4)), x)","F",0
3047,-1,0,0,0.000000," ","integrate(x^4*(p*x^4-q)*(p*x^4+q)^(1/2)/(b*x^8+a*(p*x^4+q)^4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3048,0,0,0,0.000000," ","integrate(1/(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-3 \, x^{10} + x^{9} - 9 \, x^{7} + 3 \, x^{6} - 9 \, x^{4} + 3 \, x^{3} - 3 \, x + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((-3*x^10 + x^9 - 9*x^7 + 3*x^6 - 9*x^4 + 3*x^3 - 3*x + 1)^(-1/3), x)","F",0
3049,0,0,0,0.000000," ","integrate((a*x^4+b)^(3/4)/(2*x^8+2*a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} + b\right)}^{\frac{3}{4}}}{2 \, x^{8} + 2 \, a x^{4} + b}\,{d x}"," ",0,"integrate((a*x^4 + b)^(3/4)/(2*x^8 + 2*a*x^4 + b), x)","F",0
3050,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(c x + d\right)}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(c*x + d)), x)","F",0
3051,0,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{\sqrt{a^{2} x^{4} + b} {\left(c x + d\right)}}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(sqrt(a^2*x^4 + b)*(c*x + d)), x)","F",0
3052,-2,0,0,0.000000," ","integrate(1/(a*x^2+b*x+c)^(1/2)/(a^3*b^3*x^3+c^3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
3053,0,0,0,0.000000," ","integrate((c*x^2-d)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}} {\left(c x^{2} - d\right)}}{c x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))*(c*x^2 - d)/(c*x^2 + d), x)","F",0
3054,0,0,0,0.000000," ","integrate((c*x^2-d)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}} {\left(c x^{2} - d\right)}}{c x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^4 + b))*(c*x^2 - d)/(c*x^2 + d), x)","F",0
3055,-2,0,0,0.000000," ","integrate(((a*x^5+2*a*x^3-x^4+a*x-2*x^2-1)/(a*x^5-2*a*x^3+x^4+a*x-2*x^2+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^4-1),abs(a*x^5-2*a*x^3+a*x+x^4-2*x^2+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
3056,0,0,0,0.000000," ","integrate((1+x)/(x^2-3)/(x^2+1)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(x^{2} - 3\right)}}\,{d x}"," ",0,"integrate((x + 1)/((x^2 + 1)^(1/3)*(x^2 - 3)), x)","F",0
3057,0,0,0,0.000000," ","integrate((-x^4+1)/(x^4+1)/(x^5-x^3)^(1/4),x, algorithm=""giac"")","\int -\frac{x^{4} - 1}{{\left(x^{5} - x^{3}\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(-(x^4 - 1)/((x^5 - x^3)^(1/4)*(x^4 + 1)), x)","F",0
3058,0,0,0,0.000000," ","integrate((x^8-1)/(x^6-x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + 1\right)} {\left(x^{6} - x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + 1)*(x^6 - x^2)^(1/4)), x)","F",0
3059,0,0,0,0.000000," ","integrate((x^8-1)/(x^6-x^2)^(1/4)/(x^8+1),x, algorithm=""giac"")","\int \frac{x^{8} - 1}{{\left(x^{8} + 1\right)} {\left(x^{6} - x^{2}\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^8 - 1)/((x^8 + 1)*(x^6 - x^2)^(1/4)), x)","F",0
3060,-1,0,0,0.000000," ","integrate((a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3061,0,0,0,0.000000," ","integrate((a*x+b^2)/(a*x-b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int -\frac{b^{2} + a x}{{\left(b^{2} - a x\right)} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate(-(b^2 + a*x)/((b^2 - a*x)*sqrt(b + sqrt(a*x^2 + b^2))), x)","F",0
3062,0,0,0,0.000000," ","integrate((a*x^4-b)^(3/4)/(2*x^8-2*a*x^4+b),x, algorithm=""giac"")","\int \frac{{\left(a x^{4} - b\right)}^{\frac{3}{4}}}{2 \, x^{8} - 2 \, a x^{4} + b}\,{d x}"," ",0,"integrate((a*x^4 - b)^(3/4)/(2*x^8 - 2*a*x^4 + b), x)","F",0
3063,0,0,0,0.000000," ","integrate((c*x^2-d)/(c*x^2+d)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{2} - d}{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}} {\left(c x^{2} + d\right)}}\,{d x}"," ",0,"integrate((c*x^2 - d)/(sqrt(a*x^2 + sqrt(a^2*x^4 + b))*(c*x^2 + d)), x)","F",0
3064,0,0,0,0.000000," ","integrate((c*x^2-d)/(c*x^2+d)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{c x^{2} - d}{\sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}} {\left(c x^{2} + d\right)}}\,{d x}"," ",0,"integrate((c*x^2 - d)/(sqrt(a*x^2 + sqrt(a^2*x^4 + b))*(c*x^2 + d)), x)","F",0
3065,0,0,0,0.000000," ","integrate(x^4/(a*x^4-b)^(1/4)/(2*x^8-2*a*x^4+b),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(2 \, x^{8} - 2 \, a x^{4} + b\right)} {\left(a x^{4} - b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/((2*x^8 - 2*a*x^4 + b)*(a*x^4 - b)^(1/4)), x)","F",0
3066,0,0,0,0.000000," ","integrate(x^3*(6*a*x-5*b)/(a*x^2-b*x)^(1/4)/(a*x^6-b*x^5+c),x, algorithm=""giac"")","\int \frac{{\left(6 \, a x - 5 \, b\right)} x^{3}}{{\left(a x^{6} - b x^{5} + c\right)} {\left(a x^{2} - b x\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((6*a*x - 5*b)*x^3/((a*x^6 - b*x^5 + c)*(a*x^2 - b*x)^(1/4)), x)","F",0
3067,0,0,0,0.000000," ","integrate((-a+x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{a - x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b^{2} - 2 \, {\left(a d - b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a - x)/((-(a - x)*(b - x)^2)^(1/3)*(a^2*d + (d - 1)*x^2 - b^2 - 2*(a*d - b)*x)), x)","F",0
3068,0,0,0,0.000000," ","integrate((2*x^8-a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-b),x, algorithm=""giac"")","\int \frac{2 \, x^{8} - a x^{4} + b}{{\left(x^{8} - 2 \, a x^{4} - b\right)} {\left(a x^{4} + b\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((2*x^8 - a*x^4 + b)/((x^8 - 2*a*x^4 - b)*(a*x^4 + b)^(1/4)), x)","F",0
3069,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3070,0,0,0,0.000000," ","integrate((1+x)/(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3),x, algorithm=""giac"")","\int \frac{x + 1}{{\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)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x + 1)/(8*x^8 + 84*x^7 + 338*x^6 + 679*x^5 + 825*x^4 + 784*x^3 + 522*x^2 + 189*x + 27)^(1/3), x)","F",0
3071,0,0,0,0.000000," ","integrate((k^2*x^4-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4+1),x, algorithm=""giac"")","\int \frac{k^{2} x^{4} - 1}{{\left(k^{2} x^{4} + 1\right)} \sqrt{{\left(k^{2} x^{2} - 1\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate((k^2*x^4 - 1)/((k^2*x^4 + 1)*sqrt((k^2*x^2 - 1)*(x^2 - 1))), x)","F",0
3072,0,0,0,0.000000," ","integrate((1+2*x)/(x^2-1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{2 \, x + 1}{{\left(x^{2} + 3\right)} {\left(x^{2} - 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((2*x + 1)/((x^2 + 3)*(x^2 - 1)^(1/3)), x)","F",0
3073,-1,0,0,0.000000," ","integrate(x/(1-(1-(1-1/x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3074,0,0,0,0.000000," ","integrate((x^6-x^2)^(1/4)*(x^8-x^4+1)/x^4/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - x^{4} + 1\right)} {\left(x^{6} - x^{2}\right)}^{\frac{1}{4}}}{{\left(x^{4} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^8 - x^4 + 1)*(x^6 - x^2)^(1/4)/((x^4 + 1)*x^4), x)","F",0
3075,0,0,0,0.000000," ","integrate((x^6-x^2)^(1/4)*(x^8-x^4+1)/x^4/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} - x^{4} + 1\right)} {\left(x^{6} - x^{2}\right)}^{\frac{1}{4}}}{{\left(x^{4} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^8 - x^4 + 1)*(x^6 - x^2)^(1/4)/((x^4 + 1)*x^4), x)","F",0
3076,0,0,0,0.000000," ","integrate((x^6-x^2)^(1/4)*(x^8+x^4+1)/x^4/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{4} + 1\right)} {\left(x^{6} - x^{2}\right)}^{\frac{1}{4}}}{{\left(x^{4} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^8 + x^4 + 1)*(x^6 - x^2)^(1/4)/((x^4 + 1)*x^4), x)","F",0
3077,0,0,0,0.000000," ","integrate((x^6-x^2)^(1/4)*(x^8+x^4+1)/x^4/(x^4+1),x, algorithm=""giac"")","\int \frac{{\left(x^{8} + x^{4} + 1\right)} {\left(x^{6} - x^{2}\right)}^{\frac{1}{4}}}{{\left(x^{4} + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((x^8 + x^4 + 1)*(x^6 - x^2)^(1/4)/((x^4 + 1)*x^4), x)","F",0
3078,-1,0,0,0.000000," ","integrate((a^3*x^3+b^2*x^2)^(1/3)/(a*x-b),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3079,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3080,0,0,0,0.000000," ","integrate((x^2-3)*(x^6+x^4-2*x^2+1)/x^10/((b*x^3+a*x^2-a)/(d*x^3+c*x^2-c))^(1/4),x, algorithm=""giac"")","\int \frac{{\left(x^{6} + x^{4} - 2 \, x^{2} + 1\right)} {\left(x^{2} - 3\right)}}{x^{10} \left(\frac{b x^{3} + a x^{2} - a}{d x^{3} + c x^{2} - c}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((x^6 + x^4 - 2*x^2 + 1)*(x^2 - 3)/(x^10*((b*x^3 + a*x^2 - a)/(d*x^3 + c*x^2 - c))^(1/4)), x)","F",0
3081,-1,0,0,0.000000," ","integrate((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3082,-1,0,0,0.000000," ","integrate((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3083,-1,0,0,0.000000," ","integrate((a^2*x^2+b)^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3084,1,92,0,0.334933," ","integrate(((x^6-13*x^5+65*x^4-150*x^3+135*x^2+27*x-81)^3)^(1/2)/(-1+x),x, algorithm=""giac"")","\frac{1}{10321920} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, {\left(16 \, x - 325\right)} x + 38869\right)} x - 711617\right)} x + 18004133\right)} x - 168785303\right)} x - 63504203\right)} x + 2211602549\right)} x - 1245336401\right)} \sqrt{x^{2} - x - 1} + 128 \, \arctan\left(-x + \sqrt{x^{2} - x - 1} + 1\right) + \frac{19451047}{65536} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1 \right|}\right)"," ",0,"1/10321920*(2*(4*(2*(8*(10*(4*(14*(16*x - 325)*x + 38869)*x - 711617)*x + 18004133)*x - 168785303)*x - 63504203)*x + 2211602549)*x - 1245336401)*sqrt(x^2 - x - 1) + 128*arctan(-x + sqrt(x^2 - x - 1) + 1) + 19451047/65536*log(abs(-2*x + 2*sqrt(x^2 - x - 1) + 1))","A",0
3085,0,0,0,0.000000," ","integrate((x^4+x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} + 1\right)}^{2} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{{\left(x^{4} + x^{2} - 1\right)}^{2} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)^2*sqrt(x^2 + sqrt(x^4 + 1))/((x^4 + x^2 - 1)^2*sqrt(x^4 + 1)), x)","F",0
3086,0,0,0,0.000000," ","integrate((x^4+x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + x^{2} + 1\right)}^{2} \sqrt{x^{2} + \sqrt{x^{4} + 1}}}{{\left(x^{4} + x^{2} - 1\right)}^{2} \sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate((x^4 + x^2 + 1)^2*sqrt(x^2 + sqrt(x^4 + 1))/((x^4 + x^2 - 1)^2*sqrt(x^4 + 1)), x)","F",0
3087,0,0,0,0.000000," ","integrate((p*x^4-q)*(p*x^4+q)^(1/2)/x^2/(a*p*x^4+b*x^2+a*q),x, algorithm=""giac"")","\int \frac{\sqrt{p x^{4} + q} {\left(p x^{4} - q\right)}}{{\left(a p x^{4} + b x^{2} + a q\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(p*x^4 + q)*(p*x^4 - q)/((a*p*x^4 + b*x^2 + a*q)*x^2), x)","F",0
3088,1,339,0,126.673831," ","integrate((a^3*x^3+b^2*x^2)^(1/3)/(a*x+b),x, algorithm=""giac"")","-\frac{{\left(a^{3} - a b\right)}^{\frac{1}{3}} {\left(a^{2} b - b^{2}\right)} \log\left({\left| -{\left(a^{3} - a b\right)}^{\frac{1}{3}} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{a^{4} - a^{2} b} + \frac{\sqrt{3} {\left(a^{3} - a b\right)}^{\frac{1}{3}} b \arctan\left(\frac{\sqrt{3} {\left({\left(a^{3} - a b\right)}^{\frac{1}{3}} + 2 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, {\left(a^{3} - a b\right)}^{\frac{1}{3}}}\right)}{a^{2}} + \frac{{\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} x}{a} + \frac{{\left(a^{3} - a b\right)}^{\frac{1}{3}} b \log\left({\left(a^{3} - a b\right)}^{\frac{2}{3}} + {\left(a^{3} - a b\right)}^{\frac{1}{3}} {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{2 \, a^{2}} - \frac{\sqrt{3} {\left(3 \, a^{2} b - b^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}}\right)}}{3 \, a}\right)}{3 \, a^{3}} - \frac{{\left(3 \, a^{2} b - b^{2}\right)} \log\left(a^{2} + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{2}{3}}\right)}{6 \, a^{3}} + \frac{{\left(3 \, a^{2} b - b^{2}\right)} \log\left({\left| -a + {\left(a^{3} + \frac{b^{2}}{x}\right)}^{\frac{1}{3}} \right|}\right)}{3 \, a^{3}}"," ",0,"-(a^3 - a*b)^(1/3)*(a^2*b - b^2)*log(abs(-(a^3 - a*b)^(1/3) + (a^3 + b^2/x)^(1/3)))/(a^4 - a^2*b) + sqrt(3)*(a^3 - a*b)^(1/3)*b*arctan(1/3*sqrt(3)*((a^3 - a*b)^(1/3) + 2*(a^3 + b^2/x)^(1/3))/(a^3 - a*b)^(1/3))/a^2 + (a^3 + b^2/x)^(1/3)*x/a + 1/2*(a^3 - a*b)^(1/3)*b*log((a^3 - a*b)^(2/3) + (a^3 - a*b)^(1/3)*(a^3 + b^2/x)^(1/3) + (a^3 + b^2/x)^(2/3))/a^2 - 1/3*sqrt(3)*(3*a^2*b - b^2)*arctan(1/3*sqrt(3)*(a + 2*(a^3 + b^2/x)^(1/3))/a)/a^3 - 1/6*(3*a^2*b - b^2)*log(a^2 + (a^3 + b^2/x)^(1/3)*a + (a^3 + b^2/x)^(2/3))/a^3 + 1/3*(3*a^2*b - b^2)*log(abs(-a + (a^3 + b^2/x)^(1/3)))/a^3","A",0
3089,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(3/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/4)/x,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3090,0,0,0,0.000000," ","integrate((a*x^2+b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2-b^2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} + b^{2}\right)} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}{a x^{2} - b^{2}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)*sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 - b^2), x)","F",0
3091,-1,0,0,0.000000," ","integrate((c*x^4+d)/x/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3092,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(3/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/4)/x^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3093,0,0,0,0.000000," ","integrate((b-x)/((-a+x)*(-b+x)^2)^(1/3)/(a^2-b^2*d-2*(-b*d+a)*x+(1-d)*x^2),x, algorithm=""giac"")","\int -\frac{b - x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(b^{2} d + {\left(d - 1\right)} x^{2} - a^{2} - 2 \, {\left(b d - a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(b - x)/((-(a - x)*(b - x)^2)^(1/3)*(b^2*d + (d - 1)*x^2 - a^2 - 2*(b*d - a)*x)), x)","F",0
3094,0,0,0,0.000000," ","integrate((-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{b - x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(b^{2} d + {\left(d - 1\right)} x^{2} - a^{2} - 2 \, {\left(b d - a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(b - x)/((-(a - x)*(b - x)^2)^(1/3)*(b^2*d + (d - 1)*x^2 - a^2 - 2*(b*d - a)*x)), x)","F",0
3095,0,0,0,0.000000," ","integrate((a*x^2+b^2)/(a*x^2-b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{a x^{2} + b^{2}}{{\left(a x^{2} - b^{2}\right)} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)/((a*x^2 - b^2)*sqrt(b + sqrt(a*x^2 + b^2))), x)","F",0
3096,0,0,0,0.000000," ","integrate(1/((-a+x)*(-b+x)^2)^(1/3)/(a-b*d+(-1+d)*x),x, algorithm=""giac"")","\int -\frac{1}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(b d - {\left(d - 1\right)} x - a\right)}}\,{d x}"," ",0,"integrate(-1/((-(a - x)*(b - x)^2)^(1/3)*(b*d - (d - 1)*x - a)), x)","F",0
3097,0,0,0,0.000000," ","integrate((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{4} + b} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{c x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(a^2*x^4 + b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(c*x^2 + d), x)","F",0
3098,0,0,0,0.000000," ","integrate((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x, algorithm=""giac"")","\int \frac{\sqrt{a^{2} x^{4} + b} \sqrt{a x^{2} + \sqrt{a^{2} x^{4} + b}}}{c x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(a^2*x^4 + b)*sqrt(a*x^2 + sqrt(a^2*x^4 + b))/(c*x^2 + d), x)","F",0
3099,0,0,0,0.000000," ","integrate((x^2+(x^4+1)^(1/2))^(1/2)/(a*x+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + \sqrt{x^{4} + 1}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(x^2 + sqrt(x^4 + 1))/(a*x + 1), x)","F",0
3100,-2,0,0,0.000000," ","integrate(1/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*1_C3+1_C2)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[33,-4,-70,15,2,72]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[86,-68,-66,-39,-82,10]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[48,-16,13,80,82,-92]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-17,63,68,98,0,-13]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-29,45,75,-8,42,-53]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-16,-32,-64,-40,-89,-64]Evaluation time: 7.18Done","F(-2)",0
3101,0,0,0,0.000000," ","integrate((-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{b - x}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b^{2} - 2 \, {\left(a d - b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(b - x)/((-(a - x)*(b - x)^2)^(1/3)*(a^2*d + (d - 1)*x^2 - b^2 - 2*(a*d - b)*x)), x)","F",0
3102,0,0,0,0.000000," ","integrate((a*x^2+b^2)^2/(a*x^2-b^2)^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} + b^{2}\right)}^{2}}{{\left(a x^{2} - b^{2}\right)}^{2} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)^2/((a*x^2 - b^2)^2*sqrt(b + sqrt(a*x^2 + b^2))), x)","F",0
3103,-1,0,0,0.000000," ","integrate((a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2)/(a^2*x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3104,0,0,0,0.000000," ","integrate((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x, algorithm=""giac"")","\int -\frac{{\left(x^{4} + 1\right)} \sqrt{\sqrt{x + \sqrt{x^{2} + 1}} + 1}}{x^{4} - 1}\,{d x}"," ",0,"integrate(-(x^4 + 1)*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^4 - 1), x)","F",0
3105,0,0,0,0.000000," ","integrate((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x, algorithm=""giac"")","\int -\frac{{\left(x^{4} + 1\right)} \sqrt{\sqrt{x + \sqrt{x^{2} + 1}} + 1}}{x^{4} - 1}\,{d x}"," ",0,"integrate(-(x^4 + 1)*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^4 - 1), x)","F",0
3106,-1,0,0,0.000000," ","integrate((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3107,-1,0,0,0.000000," ","integrate((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3108,0,0,0,0.000000," ","integrate((x^4+1)^(1/2)/(1+x)^3/(x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 1}}{\sqrt{x^{2} + \sqrt{x^{4} + 1}} {\left(x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1)/(sqrt(x^2 + sqrt(x^4 + 1))*(x + 1)^3), x)","F",0
3109,-1,0,0,0.000000," ","integrate(x^2/(1-(1-(1-1/x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3110,0,0,0,0.000000," ","integrate((x^2+1)*(a*x^2-b*x-a)/x^2/(c*x^2+d*x-c)/((-_C0*x+x^2-1)/(-_C1*x+x^2-1))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(a x^{2} - b x - a\right)} {\left(x^{2} + 1\right)}}{{\left(c x^{2} + d x - c\right)} x^{2} \left(\frac{_{C_{0}} x - x^{2} + 1}{_{C_{1}} x - x^{2} + 1}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*x^2 - b*x - a)*(x^2 + 1)/((c*x^2 + d*x - c)*x^2*((_C0*x - x^2 + 1)/(_C1*x - x^2 + 1))^(1/3)), x)","F",0
3111,-1,0,0,0.000000," ","integrate((x^2+1)^2*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3112,-1,0,0,0.000000," ","integrate((x^2+1)^2*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3113,-1,0,0,0.000000," ","integrate((x^2+1)^2*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3114,-1,0,0,0.000000," ","integrate((x^2+1)^2*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3115,-1,0,0,0.000000," ","integrate(x^2/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3116,0,0,0,0.000000," ","integrate((x/(a*x^7-3*a*x^5+x^6+3*a*x^3-3*x^4-a*x+3*x^2-1))^(1/3),x, algorithm=""giac"")","\int \left(\frac{x}{a x^{7} - 3 \, a x^{5} + x^{6} + 3 \, a x^{3} - 3 \, x^{4} - a x + 3 \, x^{2} - 1}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((x/(a*x^7 - 3*a*x^5 + x^6 + 3*a*x^3 - 3*x^4 - a*x + 3*x^2 - 1))^(1/3), x)","F",0
3117,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3118,-1,0,0,0.000000," ","integrate((a*x+(a^2*x^2-b)^(1/2))^(1/6)/x^3/(a^2*x^2-b)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3119,0,0,0,0.000000," ","integrate(x^2*(_C3*x^2-_C4)*((_C3*x^2+_C0*x+_C4)/(_C3*x^2+_C1*x+_C4))^(1/4)/(_C3*x^2+_C4-x)/(_C3*x^2+_C4+x)/(_C3^2*x^4+2*_C3*_C4*x^2+_C4^2+x^2),x, algorithm=""giac"")","\int \frac{{\left(_{C_{3}} x^{2} - _{C_{4}}\right)} x^{2} \left(\frac{_{C_{3}} x^{2} + _{C_{0}} x + _{C_{4}}}{_{C_{3}} x^{2} + _{C_{1}} x + _{C_{4}}}\right)^{\frac{1}{4}}}{{\left(_{C_{3}}^{2} x^{4} + 2 \, _{C_{3}} _{C_{4}} x^{2} + _{C_{4}}^{2} + x^{2}\right)} {\left(_{C_{3}} x^{2} + _{C_{4}} + x\right)} {\left(_{C_{3}} x^{2} + _{C_{4}} - x\right)}}\,{d x}"," ",0,"integrate((_C3*x^2 - _C4)*x^2*((_C3*x^2 + _C0*x + _C4)/(_C3*x^2 + _C1*x + _C4))^(1/4)/((_C3^2*x^4 + 2*_C3*_C4*x^2 + _C4^2 + x^2)*(_C3*x^2 + _C4 + x)*(_C3*x^2 + _C4 - x)), x)","F",0
3120,-1,0,0,0.000000," ","integrate(1/(a*x+(a^2*x^2-b)^(1/2))^(1/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3121,-1,0,0,0.000000," ","integrate(1/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3122,0,0,0,0.000000," ","integrate(((a*x^9-4*a*x^7+x^8+6*a*x^5-4*x^6-4*a*x^3+6*x^4+a*x-4*x^2+1)/(b*x-c))^(1/4),x, algorithm=""giac"")","\int \left(\frac{a x^{9} - 4 \, a x^{7} + x^{8} + 6 \, a x^{5} - 4 \, x^{6} - 4 \, a x^{3} + 6 \, x^{4} + a x - 4 \, x^{2} + 1}{b x - c}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(((a*x^9 - 4*a*x^7 + x^8 + 6*a*x^5 - 4*x^6 - 4*a*x^3 + 6*x^4 + a*x - 4*x^2 + 1)/(b*x - c))^(1/4), x)","F",0
3123,-1,0,0,0.000000," ","integrate((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3124,-1,0,0,0.000000," ","integrate((a*x+(a^2*x^2-b)^(1/2))^(1/4)/x/(a^2*x^2-b)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3125,0,0,0,0.000000," ","integrate(x*(2*_C3*x^3-_C4)/(_C3*x^3+_C4-x)/((_C3*x^3+_C0*x+_C4)/(_C3*x^3+_C1*x+_C4))^(1/3)/(_C3^2*x^6+2*_C3*_C4*x^3+_C3*x^4+_C4^2+_C4*x+x^2),x, algorithm=""giac"")","\int \frac{{\left(2 \, _{C_{3}} x^{3} - _{C_{4}}\right)} x}{{\left(_{C_{3}}^{2} x^{6} + 2 \, _{C_{3}} _{C_{4}} x^{3} + _{C_{3}} x^{4} + _{C_{4}}^{2} + _{C_{4}} x + x^{2}\right)} {\left(_{C_{3}} x^{3} + _{C_{4}} - x\right)} \left(\frac{_{C_{3}} x^{3} + _{C_{0}} x + _{C_{4}}}{_{C_{3}} x^{3} + _{C_{1}} x + _{C_{4}}}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((2*_C3*x^3 - _C4)*x/((_C3^2*x^6 + 2*_C3*_C4*x^3 + _C3*x^4 + _C4^2 + _C4*x + x^2)*(_C3*x^3 + _C4 - x)*((_C3*x^3 + _C0*x + _C4)/(_C3*x^3 + _C1*x + _C4))^(1/3)), x)","F",0
3126,0,0,0,0.000000," ","integrate((c*x-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x+d),x, algorithm=""giac"")","\int \frac{\sqrt{a x + \sqrt{a^{2} x^{2} + b^{2}}} {\left(c x - d\right)}}{c x + d}\,{d x}"," ",0,"integrate(sqrt(a*x + sqrt(a^2*x^2 + b^2))*(c*x - d)/(c*x + d), x)","F",0
3127,0,0,0,0.000000," ","integrate((x/(a*x^7-3*a*x^5+x^6+3*a*x^3-3*x^4-a*x+3*x^2-1))^(1/3)/x^3,x, algorithm=""giac"")","\int \frac{\left(\frac{x}{a x^{7} - 3 \, a x^{5} + x^{6} + 3 \, a x^{3} - 3 \, x^{4} - a x + 3 \, x^{2} - 1}\right)^{\frac{1}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((x/(a*x^7 - 3*a*x^5 + x^6 + 3*a*x^3 - 3*x^4 - a*x + 3*x^2 - 1))^(1/3)/x^3, x)","F",0
3128,-2,0,0,0.000000," ","integrate(1/(a*b*c-(a*b*x+c)^2*(a*x^2+b*x+c)^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 5.57sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
3129,-1,0,0,0.000000," ","integrate((a*x+(a^2*x^2-b)^(1/2))^(1/4)/x^2/(a^2*x^2-b)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3130,-1,0,0,0.000000," ","integrate((x^2-1)*(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3131,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3132,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3133,0,0,0,0.000000," ","integrate((a*x^4+b)*(a*x^4-c*x^2-b)^(1/2)/(a*x^4-b)^2,x, algorithm=""giac"")","\int \frac{\sqrt{a x^{4} - c x^{2} - b} {\left(a x^{4} + b\right)}}{{\left(a x^{4} - b\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(a*x^4 - c*x^2 - b)*(a*x^4 + b)/(a*x^4 - b)^2, x)","F",0
3134,0,0,0,0.000000," ","integrate((-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(a-b*d+(-1+d)*x),x, algorithm=""giac"")","\int \frac{b c - {\left(c + 1\right)} x + a}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(b d - {\left(d - 1\right)} x - a\right)}}\,{d x}"," ",0,"integrate((b*c - (c + 1)*x + a)/((-(a - x)*(b - x)^2)^(2/3)*(b*d - (d - 1)*x - a)), x)","F",0
3135,0,0,0,0.000000," ","integrate((-a-b*c+(1+c)*x)/(-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(a-b*d+(-1+d)*x),x, algorithm=""giac"")","\int -\frac{b c - {\left(c + 1\right)} x + a}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(b d - {\left(d - 1\right)} x - a\right)} {\left(b - x\right)}}\,{d x}"," ",0,"integrate(-(b*c - (c + 1)*x + a)/((-(a - x)*(b - x)^2)^(1/3)*(b*d - (d - 1)*x - a)*(b - x)), x)","F",0
3136,-1,0,0,0.000000," ","integrate((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(5/4)/x/(a^2*x^2-b)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3137,-1,0,0,0.000000," ","integrate(1/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3138,-1,0,0,0.000000," ","integrate(((-b*x+1)/(c+x))^(1/6)*(d*x^2+1)/(b*x+1)/(c*x+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3139,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(3/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3140,-2,0,0,0.000000," ","integrate((_C7*x+_C6)/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*1_C3+1_C2)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-39,85,33,-4,-70,15]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-82,36,86,-68,-66,-39]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-86,21,48,-16,13,80]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-3,-76,-17,63,68,98]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[66,23,-29,45,75,-8]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[80,-46,-16,-32,-64,-40]Evaluation time: 11.29Done","F(-2)",0
3141,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3142,-1,0,0,0.000000," ","integrate((a^2*x^2+b)^(3/2)*(a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3143,-1,0,0,0.000000," ","integrate((a^2*x^2-b)^(1/2)*(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3144,-1,0,0,0.000000," ","integrate((a^2*x^2+a*b*c-b^2*x)/(a*x^2+b*x+c)^(1/2)/(b*x^2+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3145,0,0,0,0.000000," ","integrate((a*x^2+b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2-b^2)^2,x, algorithm=""giac"")","\int \frac{{\left(a x^{2} + b^{2}\right)}^{2} \sqrt{b + \sqrt{a x^{2} + b^{2}}}}{{\left(a x^{2} - b^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((a*x^2 + b^2)^2*sqrt(b + sqrt(a*x^2 + b^2))/(a*x^2 - b^2)^2, x)","F",0
3146,-1,0,0,0.000000," ","integrate((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)^2/(a^2*x^4+b)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3147,0,0,0,0.000000," ","integrate((-b-a*c+(1+c)*x)/(-a+x)/((-a+x)*(-b+x)^2)^(1/3)/(b-a*d+(-1+d)*x),x, algorithm=""giac"")","\int -\frac{a c - {\left(c + 1\right)} x + b}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(a d - {\left(d - 1\right)} x - b\right)} {\left(a - x\right)}}\,{d x}"," ",0,"integrate(-(a*c - (c + 1)*x + b)/((-(a - x)*(b - x)^2)^(1/3)*(a*d - (d - 1)*x - b)*(a - x)), x)","F",0
3148,0,0,0,0.000000," ","integrate((-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(1/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{b c - {\left(c + 1\right)} x + a}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(b^{2} d + {\left(d - 1\right)} x^{2} - a^{2} - 2 \, {\left(b d - a\right)} x\right)}}\,{d x}"," ",0,"integrate(-(b*c - (c + 1)*x + a)/((-(a - x)*(b - x)^2)^(1/3)*(b^2*d + (d - 1)*x^2 - a^2 - 2*(b*d - a)*x)), x)","F",0
3149,0,0,0,0.000000," ","integrate((-b-a*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int -\frac{a c - {\left(c + 1\right)} x + b}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{1}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b^{2} - 2 \, {\left(a d - b\right)} x\right)}}\,{d x}"," ",0,"integrate(-(a*c - (c + 1)*x + b)/((-(a - x)*(b - x)^2)^(1/3)*(a^2*d + (d - 1)*x^2 - b^2 - 2*(a*d - b)*x)), x)","F",0
3150,-2,0,0,0.000000," ","integrate((_C9*x+_C8)/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*1_C3+1_C2)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-70,15,2,72,-32,97]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-66,-39,-82,10,16,91]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[13,80,82,-92,-95,41]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[51,55,80,34,31,-65]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-46,-16,-32,-64,-40,-89]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[68,-24,87,84,-84,46]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[69,-62,15,83,-10,18]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-3,-5,78,-5,-95,-95]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*1_C3+1_C2)]Evaluation time: 13.68Done","F(-2)",0
3151,0,0,0,0.000000," ","integrate((-b+x)*(-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int \frac{{\left(b c - {\left(c + 1\right)} x + a\right)} {\left(b - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(b^{2} d + {\left(d - 1\right)} x^{2} - a^{2} - 2 \, {\left(b d - a\right)} x\right)}}\,{d x}"," ",0,"integrate((b*c - (c + 1)*x + a)*(b - x)/((-(a - x)*(b - x)^2)^(2/3)*(b^2*d + (d - 1)*x^2 - a^2 - 2*(b*d - a)*x)), x)","F",0
3152,0,0,0,0.000000," ","integrate((-b+x)*(-b-a*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x, algorithm=""giac"")","\int \frac{{\left(a c - {\left(c + 1\right)} x + b\right)} {\left(b - x\right)}}{\left(-{\left(a - x\right)} {\left(b - x\right)}^{2}\right)^{\frac{2}{3}} {\left(a^{2} d + {\left(d - 1\right)} x^{2} - b^{2} - 2 \, {\left(a d - b\right)} x\right)}}\,{d x}"," ",0,"integrate((a*c - (c + 1)*x + b)*(b - x)/((-(a - x)*(b - x)^2)^(2/3)*(a^2*d + (d - 1)*x^2 - b^2 - 2*(a*d - b)*x)), x)","F",0
3153,-2,0,0,0.000000," ","integrate((x^2-c*x^2*((a*x+b)/(c*x+d))^(3/2))/(a-b*((a*x+b)/(c*x+d))^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x*c+d)]Evaluation time: 0.42Error: Bad Argument Type","F(-2)",0
3154,-2,0,0,0.000000," ","integrate((_C7*x+_C6)^2/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*1_C3+1_C2)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-39,85,33,-4,-70,15]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-82,36,86,-68,-66,-39]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-86,21,48,-16,13,80]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[-3,-76,-17,63,68,98]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[66,23,-29,45,75,-8]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0,0] was discarded and replaced randomly by 0=[80,-46,-16,-32,-64,-40]Evaluation time: 11.4Done","F(-2)",0
