1,1,87,0,0.439907," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/4),x, algorithm=""giac"")","-\frac{\frac{3 \, a^{3} \arctan\left(\frac{\sqrt{-\frac{b x^{2} + a}{x^{2}}}}{\sqrt{b}}\right)}{\sqrt{b}} + \frac{{\left(5 \, a^{3} {\left(b + \frac{a}{x^{2}}\right)} \sqrt{-\frac{b x^{2} + a}{x^{2}}} - 3 \, a^{3} b \sqrt{-\frac{b x^{2} + a}{x^{2}}}\right)} x^{4}}{a^{2}}}{8 \, a}"," ",0,"-1/8*(3*a^3*arctan(sqrt(-(b*x^2 + a)/x^2)/sqrt(b))/sqrt(b) + (5*a^3*(b + a/x^2)*sqrt(-(b*x^2 + a)/x^2) - 3*a^3*b*sqrt(-(b*x^2 + a)/x^2))*x^4/a^2)/a","A",0
2,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(1/4),x, algorithm=""giac"")","\int {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{4}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(1/4), x)","F",0
3,1,24,0,0.215974," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/4),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{-\frac{b x^{2} + a}{x^{2}}}}{\sqrt{b}}\right)}{\sqrt{b}}"," ",0,"-arctan(sqrt(-(b*x^2 + a)/x^2)/sqrt(b))/sqrt(b)","A",0
4,1,19,0,0.259558," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/4),x, algorithm=""giac"")","-\frac{1}{a \sqrt{-\frac{b x^{2} + a}{x^{2}}}}"," ",0,"-1/(a*sqrt(-(b*x^2 + a)/x^2))","A",0
5,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(-5/4), x)","F",0
6,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(7/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(-7/4), x)","F",0
7,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(9/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(-9/4), x)","F",0
8,1,75,0,0.161867," ","integrate(1/(x^4+2*a*x^2+a^2+b),x, algorithm=""giac"")","-\frac{\sqrt{a + \sqrt{-b}} \arctan\left(\frac{x}{\sqrt{a + \sqrt{-b}}}\right)}{2 \, {\left(a \sqrt{-b} - b\right)}} + \frac{\sqrt{a - \sqrt{-b}} \arctan\left(\frac{x}{\sqrt{a - \sqrt{-b}}}\right)}{2 \, {\left(a \sqrt{-b} + b\right)}}"," ",0,"-1/2*sqrt(a + sqrt(-b))*arctan(x/sqrt(a + sqrt(-b)))/(a*sqrt(-b) - b) + 1/2*sqrt(a - sqrt(-b))*arctan(x/sqrt(a - sqrt(-b)))/(a*sqrt(-b) + b)","A",0
9,1,31,0,0.148773," ","integrate(1/(x^4+2*a*x^2+a^2-1),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{x}{\sqrt{a + 1}}\right)}{2 \, \sqrt{a + 1}} + \frac{\arctan\left(\frac{x}{\sqrt{a - 1}}\right)}{2 \, \sqrt{a - 1}}"," ",0,"-1/2*arctan(x/sqrt(a + 1))/sqrt(a + 1) + 1/2*arctan(x/sqrt(a - 1))/sqrt(a - 1)","A",0
10,-1,0,0,0.000000," ","integrate(1/(x^4+2*a*x^2+a^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,1,29,0,0.203177," ","integrate(1/(x^4-5*x^2+4),x, algorithm=""giac"")","-\frac{1}{12} \, \log\left({\left| x + 2 \right|}\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right) + \frac{1}{12} \, \log\left({\left| x - 2 \right|}\right)"," ",0,"-1/12*log(abs(x + 2)) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1)) + 1/12*log(abs(x - 2))","B",0
12,1,17,0,0.169032," ","integrate(1/(x^4+4*x^2+3),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) + \frac{1}{2} \, \arctan\left(x\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*x) + 1/2*arctan(x)","A",0
13,1,53,0,0.195305," ","integrate(1/(x^4+5*x^2+9),x, algorithm=""giac"")","\frac{1}{66} \, \sqrt{11} \arctan\left(\frac{1}{11} \, \sqrt{11} {\left(2 \, x + 1\right)}\right) + \frac{1}{66} \, \sqrt{11} \arctan\left(\frac{1}{11} \, \sqrt{11} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{2} + x + 3\right) - \frac{1}{12} \, \log\left(x^{2} - x + 3\right)"," ",0,"1/66*sqrt(11)*arctan(1/11*sqrt(11)*(2*x + 1)) + 1/66*sqrt(11)*arctan(1/11*sqrt(11)*(2*x - 1)) + 1/12*log(x^2 + x + 3) - 1/12*log(x^2 - x + 3)","A",0
14,1,56,0,0.188626," ","integrate(1/(x^4-x^2+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{2} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{2} \, \arctan\left(2 \, x - \sqrt{3}\right)"," ",0,"1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/2*arctan(2*x + sqrt(3)) + 1/2*arctan(2*x - sqrt(3))","A",0
15,1,143,0,0.533645," ","integrate(1/(x^4+2*x^2+2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{\sqrt{2} - 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x + 2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2}\right)}}{2 \, \sqrt{\sqrt{2} + 2}}\right) + \frac{1}{4} \, \sqrt{\sqrt{2} - 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x - 2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2}\right)}}{2 \, \sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 1} \log\left(x^{2} + 2^{\frac{1}{4}} x \sqrt{-\sqrt{2} + 2} + \sqrt{2}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 1} \log\left(x^{2} - 2^{\frac{1}{4}} x \sqrt{-\sqrt{2} + 2} + \sqrt{2}\right)"," ",0,"1/4*sqrt(sqrt(2) - 1)*arctan(1/2*2^(3/4)*(2*x + 2^(1/4)*sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/4*sqrt(sqrt(2) - 1)*arctan(1/2*2^(3/4)*(2*x - 2^(1/4)*sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 1)*log(x^2 + 2^(1/4)*x*sqrt(-sqrt(2) + 2) + sqrt(2)) - 1/8*sqrt(sqrt(2) + 1)*log(x^2 - 2^(1/4)*x*sqrt(-sqrt(2) + 2) + sqrt(2))","A",0
16,0,0,0,0.000000," ","integrate(1/(-3*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 5*x^2 + 2), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(-3*x^4+4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 4*x^2 + 2), x)","F",0
18,0,0,0,0.000000," ","integrate(1/(-3*x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 3*x^2 + 2), x)","F",0
19,0,0,0,0.000000," ","integrate(1/(-3*x^4+2*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 2*x^2 + 2), x)","F",0
20,0,0,0,0.000000," ","integrate(1/(-3*x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + x^2 + 2), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(-3*x^4+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 2), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(-3*x^4-x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - x^2 + 2), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(-3*x^4-2*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 2*x^2 + 2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(-3*x^4-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 3*x^2 + 2), x)","F",0
25,0,0,0,0.000000," ","integrate(1/(-3*x^4-4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 4*x^2 + 2), x)","F",0
26,0,0,0,0.000000," ","integrate(1/(-3*x^4-5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 5*x^2 + 2), x)","F",0
27,0,0,0,0.000000," ","integrate(1/(-2*x^4+7*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 7 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 7*x^2 + 3), x)","F",0
28,0,0,0,0.000000," ","integrate(1/(-2*x^4+6*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 6 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 6*x^2 + 3), x)","F",0
29,0,0,0,0.000000," ","integrate(1/(-2*x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 5 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 5*x^2 + 3), x)","F",0
30,0,0,0,0.000000," ","integrate(1/(-2*x^4+4*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 4 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 4*x^2 + 3), x)","F",0
31,0,0,0,0.000000," ","integrate(1/(-2*x^4+3*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 3 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 3*x^2 + 3), x)","F",0
32,0,0,0,0.000000," ","integrate(1/(-2*x^4+2*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 2 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 2*x^2 + 3), x)","F",0
33,0,0,0,0.000000," ","integrate(1/(-2*x^4+x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + x^2 + 3), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(-2*x^4+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 3), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(-2*x^4-x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - x^2 + 3), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(-2*x^4-2*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 2 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 2*x^2 + 3), x)","F",0
37,0,0,0,0.000000," ","integrate(1/(-2*x^4-3*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 3 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 3*x^2 + 3), x)","F",0
38,0,0,0,0.000000," ","integrate(1/(-2*x^4-4*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 4 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 4*x^2 + 3), x)","F",0
39,0,0,0,0.000000," ","integrate(1/(-2*x^4-5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 5 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 5*x^2 + 3), x)","F",0
40,0,0,0,0.000000," ","integrate(1/(-2*x^4-6*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 6 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 6*x^2 + 3), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(-2*x^4-7*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 7 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 7*x^2 + 3), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(3*x^4+5*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 5 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 5*x^2 - 2), x)","F",0
43,0,0,0,0.000000," ","integrate(1/(3*x^4+4*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 4 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 4*x^2 - 2), x)","F",0
44,0,0,0,0.000000," ","integrate(1/(3*x^4+3*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 3 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 3*x^2 - 2), x)","F",0
45,0,0,0,0.000000," ","integrate(1/(3*x^4+2*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 2 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 2*x^2 - 2), x)","F",0
46,0,0,0,0.000000," ","integrate(1/(3*x^4+x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + x^2 - 2), x)","F",0
47,0,0,0,0.000000," ","integrate(1/(3*x^4-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 2), x)","F",0
48,0,0,0,0.000000," ","integrate(1/(3*x^4-x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - x^2 - 2), x)","F",0
49,0,0,0,0.000000," ","integrate(1/(3*x^4-2*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 2 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 2*x^2 - 2), x)","F",0
50,0,0,0,0.000000," ","integrate(1/(3*x^4-3*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 3 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 3*x^2 - 2), x)","F",0
51,0,0,0,0.000000," ","integrate(1/(3*x^4-4*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 4 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 4*x^2 - 2), x)","F",0
52,0,0,0,0.000000," ","integrate(1/(3*x^4-5*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 5 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 5*x^2 - 2), x)","F",0
53,0,0,0,0.000000," ","integrate(1/(2*x^4+7*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 7 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 7*x^2 - 3), x)","F",0
54,0,0,0,0.000000," ","integrate(1/(2*x^4+6*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 6 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 6*x^2 - 3), x)","F",0
55,0,0,0,0.000000," ","integrate(1/(2*x^4+5*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 5 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 5*x^2 - 3), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(2*x^4+4*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 4 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 4*x^2 - 3), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(2*x^4+3*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 3 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 3*x^2 - 3), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(2*x^4+2*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 2 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 2*x^2 - 3), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(2*x^4+x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + x^2 - 3), x)","F",0
60,0,0,0,0.000000," ","integrate(1/(2*x^4-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 3), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(2*x^4-x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - x^2 - 3), x)","F",0
62,0,0,0,0.000000," ","integrate(1/(2*x^4-2*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 2 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 2*x^2 - 3), x)","F",0
63,0,0,0,0.000000," ","integrate(1/(2*x^4-3*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 3 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 3*x^2 - 3), x)","F",0
64,0,0,0,0.000000," ","integrate(1/(2*x^4-4*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 4 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 4*x^2 - 3), x)","F",0
65,0,0,0,0.000000," ","integrate(1/(2*x^4-5*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 5 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 5*x^2 - 3), x)","F",0
66,0,0,0,0.000000," ","integrate(1/(3*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 5*x^2 + 2), x)","F",0
67,0,0,0,0.000000," ","integrate(1/(3*x^4+4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 4*x^2 + 2), x)","F",0
68,0,0,0,0.000000," ","integrate(1/(3*x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 3*x^2 + 2), x)","F",0
69,0,0,0,0.000000," ","integrate(1/(3*x^4+2*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 2*x^2 + 2), x)","F",0
70,0,0,0,0.000000," ","integrate(1/(3*x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + x^2 + 2), x)","F",0
71,0,0,0,0.000000," ","integrate(1/(3*x^4+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 2), x)","F",0
72,0,0,0,0.000000," ","integrate(1/(3*x^4-x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - x^2 + 2), x)","F",0
73,0,0,0,0.000000," ","integrate(1/(3*x^4-2*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 2*x^2 + 2), x)","F",0
74,0,0,0,0.000000," ","integrate(1/(3*x^4-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 3*x^2 + 2), x)","F",0
75,0,0,0,0.000000," ","integrate(1/(3*x^4-4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 4*x^2 + 2), x)","F",0
76,0,0,0,0.000000," ","integrate(1/(3*x^4-5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 5*x^2 + 2), x)","F",0
77,0,0,0,0.000000," ","integrate(1/(3*x^4-6*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} - 6 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 - 6*x^2 + 2), x)","F",0
78,0,0,0,0.000000," ","integrate(1/(2*x^4+9*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 9 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 9*x^2 + 3), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(2*x^4+8*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 8 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 8*x^2 + 3), x)","F",0
80,0,0,0,0.000000," ","integrate(1/(2*x^4+7*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 7 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 7*x^2 + 3), x)","F",0
81,0,0,0,0.000000," ","integrate(1/(2*x^4+6*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 6 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 6*x^2 + 3), x)","F",0
82,0,0,0,0.000000," ","integrate(1/(2*x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 5 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 5*x^2 + 3), x)","F",0
83,0,0,0,0.000000," ","integrate(1/(2*x^4+4*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 4 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 4*x^2 + 3), x)","F",0
84,0,0,0,0.000000," ","integrate(1/(2*x^4+3*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 3 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 3*x^2 + 3), x)","F",0
85,0,0,0,0.000000," ","integrate(1/(2*x^4+2*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 2 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 2*x^2 + 3), x)","F",0
86,0,0,0,0.000000," ","integrate(1/(2*x^4+x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + x^2 + 3), x)","F",0
87,0,0,0,0.000000," ","integrate(1/(2*x^4+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 3), x)","F",0
88,0,0,0,0.000000," ","integrate(1/(2*x^4-x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - x^2 + 3), x)","F",0
89,0,0,0,0.000000," ","integrate(1/(2*x^4-2*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 2 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 2*x^2 + 3), x)","F",0
90,0,0,0,0.000000," ","integrate(1/(2*x^4-3*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 3 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 3*x^2 + 3), x)","F",0
91,0,0,0,0.000000," ","integrate(1/(2*x^4-4*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 4 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 4*x^2 + 3), x)","F",0
92,0,0,0,0.000000," ","integrate(1/(2*x^4-5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 5 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 5*x^2 + 3), x)","F",0
93,0,0,0,0.000000," ","integrate(1/(2*x^4-6*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 6 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 6*x^2 + 3), x)","F",0
94,0,0,0,0.000000," ","integrate(1/(2*x^4-7*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} - 7 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 - 7*x^2 + 3), x)","F",0
95,0,0,0,0.000000," ","integrate(1/(-2*x^4+7*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 7 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 7*x^2 - 3), x)","F",0
96,0,0,0,0.000000," ","integrate(1/(-2*x^4+6*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 6 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 6*x^2 - 3), x)","F",0
97,0,0,0,0.000000," ","integrate(1/(-2*x^4+5*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 5 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 5*x^2 - 3), x)","F",0
98,0,0,0,0.000000," ","integrate(1/(-2*x^4+4*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 4 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 4*x^2 - 3), x)","F",0
99,0,0,0,0.000000," ","integrate(1/(-2*x^4+3*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 3 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 3*x^2 - 3), x)","F",0
100,0,0,0,0.000000," ","integrate(1/(-2*x^4+2*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 2 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 2*x^2 - 3), x)","F",0
101,0,0,0,0.000000," ","integrate(1/(-2*x^4+x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + x^2 - 3), x)","F",0
102,0,0,0,0.000000," ","integrate(1/(-2*x^4-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 3), x)","F",0
103,0,0,0,0.000000," ","integrate(1/(-2*x^4-x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - x^2 - 3), x)","F",0
104,0,0,0,0.000000," ","integrate(1/(-2*x^4-2*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 2 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 2*x^2 - 3), x)","F",0
105,0,0,0,0.000000," ","integrate(1/(-2*x^4-3*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 3 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 3*x^2 - 3), x)","F",0
106,0,0,0,0.000000," ","integrate(1/(-2*x^4-4*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 4 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 4*x^2 - 3), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(-2*x^4-5*x^2-3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} - 5 \, x^{2} - 3}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 - 5*x^2 - 3), x)","F",0
108,0,0,0,0.000000," ","integrate(1/(-3*x^4+6*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 6 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 6*x^2 - 2), x)","F",0
109,0,0,0,0.000000," ","integrate(1/(-3*x^4+5*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 5 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 5*x^2 - 2), x)","F",0
110,0,0,0,0.000000," ","integrate(1/(-3*x^4+4*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 4 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 4*x^2 - 2), x)","F",0
111,0,0,0,0.000000," ","integrate(1/(-3*x^4+3*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 3 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 3*x^2 - 2), x)","F",0
112,0,0,0,0.000000," ","integrate(1/(-3*x^4+2*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 2 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 2*x^2 - 2), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(-3*x^4+x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + x^2 - 2), x)","F",0
114,0,0,0,0.000000," ","integrate(1/(-3*x^4-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 2), x)","F",0
115,0,0,0,0.000000," ","integrate(1/(-3*x^4-x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - x^2 - 2), x)","F",0
116,0,0,0,0.000000," ","integrate(1/(-3*x^4-2*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 2 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 2*x^2 - 2), x)","F",0
117,0,0,0,0.000000," ","integrate(1/(-3*x^4-3*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 3 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 3*x^2 - 2), x)","F",0
118,0,0,0,0.000000," ","integrate(1/(-3*x^4-4*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 4 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 4*x^2 - 2), x)","F",0
119,0,0,0,0.000000," ","integrate(1/(-3*x^4-5*x^2-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} - 5 \, x^{2} - 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 - 5*x^2 - 2), x)","F",0
120,0,0,0,0.000000," ","integrate(1/(5*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{5 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(5*x^4 + 5*x^2 + 2), x)","F",0
121,0,0,0,0.000000," ","integrate(1/(4*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(4*x^4 + 5*x^2 + 2), x)","F",0
122,0,0,0,0.000000," ","integrate(1/(3*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 5*x^2 + 2), x)","F",0
123,0,0,0,0.000000," ","integrate(1/(2*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(2*x^4 + 5*x^2 + 2), x)","F",0
124,0,0,0,0.000000," ","integrate(1/(x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(x^4 + 5*x^2 + 2), x)","F",0
125,0,0,0,0.000000," ","integrate(1/(-x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 + 5*x^2 + 2), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(-2*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-2*x^4 + 5*x^2 + 2), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(-3*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-3*x^4 + 5*x^2 + 2), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(-4*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-4 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-4*x^4 + 5*x^2 + 2), x)","F",0
129,0,0,0,0.000000," ","integrate(1/(-5*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-5 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-5*x^4 + 5*x^2 + 2), x)","F",0
130,0,0,0,0.000000," ","integrate(1/(-6*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-6 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-6*x^4 + 5*x^2 + 2), x)","F",0
131,0,0,0,0.000000," ","integrate(1/(-7*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-7 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-7*x^4 + 5*x^2 + 2), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(-8*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-8 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-8*x^4 + 5*x^2 + 2), x)","F",0
133,0,0,0,0.000000," ","integrate(1/(-9*x^4+5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-9 \, x^{4} + 5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-9*x^4 + 5*x^2 + 2), x)","F",0
134,1,13,0,0.164385," ","integrate(x^2*(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5}"," ",0,"1/7*c*x^7 + 1/5*b*x^5","A",0
135,1,13,0,0.166204," ","integrate(x*(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{1}{6} \, c x^{6} + \frac{1}{4} \, b x^{4}"," ",0,"1/6*c*x^6 + 1/4*b*x^4","A",0
136,1,13,0,0.152827," ","integrate(c*x^4+b*x^2,x, algorithm=""giac"")","\frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3}"," ",0,"1/5*c*x^5 + 1/3*b*x^3","A",0
137,1,13,0,0.154065," ","integrate((c*x^4+b*x^2)/x,x, algorithm=""giac"")","\frac{1}{4} \, c x^{4} + \frac{1}{2} \, b x^{2}"," ",0,"1/4*c*x^4 + 1/2*b*x^2","A",0
138,1,10,0,0.146952," ","integrate((c*x^4+b*x^2)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} + b x"," ",0,"1/3*c*x^3 + b*x","A",0
139,1,14,0,0.146771," ","integrate((c*x^4+b*x^2)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, c x^{2} + \frac{1}{2} \, b \log\left(x^{2}\right)"," ",0,"1/2*c*x^2 + 1/2*b*log(x^2)","A",0
140,1,10,0,0.162041," ","integrate((c*x^4+b*x^2)/x^4,x, algorithm=""giac"")","c x - \frac{b}{x}"," ",0,"c*x - b/x","A",0
141,1,20,0,0.149082," ","integrate((c*x^4+b*x^2)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, c \log\left(x^{2}\right) - \frac{c x^{2} + b}{2 \, x^{2}}"," ",0,"1/2*c*log(x^2) - 1/2*(c*x^2 + b)/x^2","A",0
142,1,13,0,0.181233," ","integrate((c*x^4+b*x^2)/x^6,x, algorithm=""giac"")","-\frac{3 \, c x^{2} + b}{3 \, x^{3}}"," ",0,"-1/3*(3*c*x^2 + b)/x^3","A",0
143,1,13,0,0.186558," ","integrate((c*x^4+b*x^2)/x^7,x, algorithm=""giac"")","-\frac{2 \, c x^{2} + b}{4 \, x^{4}}"," ",0,"-1/4*(2*c*x^2 + b)/x^4","A",0
144,1,15,0,0.168486," ","integrate((c*x^4+b*x^2)/x^8,x, algorithm=""giac"")","-\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}}"," ",0,"-1/15*(5*c*x^2 + 3*b)/x^5","A",0
145,1,24,0,0.157525," ","integrate((c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5}"," ",0,"1/9*c^2*x^9 + 2/7*b*c*x^7 + 1/5*b^2*x^5","A",0
146,1,24,0,0.194956," ","integrate((c*x^4+b*x^2)^2/x,x, algorithm=""giac"")","\frac{1}{8} \, c^{2} x^{8} + \frac{1}{3} \, b c x^{6} + \frac{1}{4} \, b^{2} x^{4}"," ",0,"1/8*c^2*x^8 + 1/3*b*c*x^6 + 1/4*b^2*x^4","A",0
147,1,24,0,0.167506," ","integrate((c*x^4+b*x^2)^2/x^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{2} x^{7} + \frac{2}{5} \, b c x^{5} + \frac{1}{3} \, b^{2} x^{3}"," ",0,"1/7*c^2*x^7 + 2/5*b*c*x^5 + 1/3*b^2*x^3","A",0
148,1,24,0,0.152467," ","integrate((c*x^4+b*x^2)^2/x^3,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} x^{6} + \frac{1}{2} \, b c x^{4} + \frac{1}{2} \, b^{2} x^{2}"," ",0,"1/6*c^2*x^6 + 1/2*b*c*x^4 + 1/2*b^2*x^2","A",0
149,1,21,0,0.180250," ","integrate((c*x^4+b*x^2)^2/x^4,x, algorithm=""giac"")","\frac{1}{5} \, c^{2} x^{5} + \frac{2}{3} \, b c x^{3} + b^{2} x"," ",0,"1/5*c^2*x^5 + 2/3*b*c*x^3 + b^2*x","A",0
150,1,24,0,0.148799," ","integrate((c*x^4+b*x^2)^2/x^5,x, algorithm=""giac"")","\frac{1}{4} \, c^{2} x^{4} + b c x^{2} + \frac{1}{2} \, b^{2} \log\left(x^{2}\right)"," ",0,"1/4*c^2*x^4 + b*c*x^2 + 1/2*b^2*log(x^2)","A",0
151,1,22,0,0.151069," ","integrate((c*x^4+b*x^2)^2/x^6,x, algorithm=""giac"")","\frac{1}{3} \, c^{2} x^{3} + 2 \, b c x - \frac{b^{2}}{x}"," ",0,"1/3*c^2*x^3 + 2*b*c*x - b^2/x","A",0
152,1,32,0,0.167841," ","integrate((c*x^4+b*x^2)^2/x^7,x, algorithm=""giac"")","\frac{1}{2} \, c^{2} x^{2} + b c \log\left(x^{2}\right) - \frac{2 \, b c x^{2} + b^{2}}{2 \, x^{2}}"," ",0,"1/2*c^2*x^2 + b*c*log(x^2) - 1/2*(2*b*c*x^2 + b^2)/x^2","A",0
153,1,22,0,0.159817," ","integrate((c*x^4+b*x^2)^2/x^8,x, algorithm=""giac"")","c^{2} x - \frac{6 \, b c x^{2} + b^{2}}{3 \, x^{3}}"," ",0,"c^2*x - 1/3*(6*b*c*x^2 + b^2)/x^3","A",0
154,1,34,0,0.180222," ","integrate((c*x^4+b*x^2)^2/x^9,x, algorithm=""giac"")","\frac{1}{2} \, c^{2} \log\left(x^{2}\right) - \frac{3 \, c^{2} x^{4} + 4 \, b c x^{2} + b^{2}}{4 \, x^{4}}"," ",0,"1/2*c^2*log(x^2) - 1/4*(3*c^2*x^4 + 4*b*c*x^2 + b^2)/x^4","A",0
155,1,26,0,0.165071," ","integrate((c*x^4+b*x^2)^2/x^10,x, algorithm=""giac"")","-\frac{15 \, c^{2} x^{4} + 10 \, b c x^{2} + 3 \, b^{2}}{15 \, x^{5}}"," ",0,"-1/15*(15*c^2*x^4 + 10*b*c*x^2 + 3*b^2)/x^5","A",0
156,1,24,0,0.174162," ","integrate((c*x^4+b*x^2)^2/x^11,x, algorithm=""giac"")","-\frac{3 \, c^{2} x^{4} + 3 \, b c x^{2} + b^{2}}{6 \, x^{6}}"," ",0,"-1/6*(3*c^2*x^4 + 3*b*c*x^2 + b^2)/x^6","A",0
157,1,26,0,0.154803," ","integrate((c*x^4+b*x^2)^2/x^12,x, algorithm=""giac"")","-\frac{35 \, c^{2} x^{4} + 42 \, b c x^{2} + 15 \, b^{2}}{105 \, x^{7}}"," ",0,"-1/105*(35*c^2*x^4 + 42*b*c*x^2 + 15*b^2)/x^7","A",0
158,1,35,0,0.147703," ","integrate((c*x^4+b*x^2)^3/x^2,x, algorithm=""giac"")","\frac{1}{11} \, c^{3} x^{11} + \frac{1}{3} \, b c^{2} x^{9} + \frac{3}{7} \, b^{2} c x^{7} + \frac{1}{5} \, b^{3} x^{5}"," ",0,"1/11*c^3*x^11 + 1/3*b*c^2*x^9 + 3/7*b^2*c*x^7 + 1/5*b^3*x^5","A",0
159,1,35,0,0.176723," ","integrate((c*x^4+b*x^2)^3/x^3,x, algorithm=""giac"")","\frac{1}{10} \, c^{3} x^{10} + \frac{3}{8} \, b c^{2} x^{8} + \frac{1}{2} \, b^{2} c x^{6} + \frac{1}{4} \, b^{3} x^{4}"," ",0,"1/10*c^3*x^10 + 3/8*b*c^2*x^8 + 1/2*b^2*c*x^6 + 1/4*b^3*x^4","A",0
160,1,35,0,0.166023," ","integrate((c*x^4+b*x^2)^3/x^4,x, algorithm=""giac"")","\frac{1}{9} \, c^{3} x^{9} + \frac{3}{7} \, b c^{2} x^{7} + \frac{3}{5} \, b^{2} c x^{5} + \frac{1}{3} \, b^{3} x^{3}"," ",0,"1/9*c^3*x^9 + 3/7*b*c^2*x^7 + 3/5*b^2*c*x^5 + 1/3*b^3*x^3","A",0
161,1,35,0,0.149118," ","integrate((c*x^4+b*x^2)^3/x^5,x, algorithm=""giac"")","\frac{1}{8} \, c^{3} x^{8} + \frac{1}{2} \, b c^{2} x^{6} + \frac{3}{4} \, b^{2} c x^{4} + \frac{1}{2} \, b^{3} x^{2}"," ",0,"1/8*c^3*x^8 + 1/2*b*c^2*x^6 + 3/4*b^2*c*x^4 + 1/2*b^3*x^2","B",0
162,1,31,0,0.161694," ","integrate((c*x^4+b*x^2)^3/x^6,x, algorithm=""giac"")","\frac{1}{7} \, c^{3} x^{7} + \frac{3}{5} \, b c^{2} x^{5} + b^{2} c x^{3} + b^{3} x"," ",0,"1/7*c^3*x^7 + 3/5*b*c^2*x^5 + b^2*c*x^3 + b^3*x","A",0
163,1,36,0,0.152897," ","integrate((c*x^4+b*x^2)^3/x^7,x, algorithm=""giac"")","\frac{1}{6} \, c^{3} x^{6} + \frac{3}{4} \, b c^{2} x^{4} + \frac{3}{2} \, b^{2} c x^{2} + \frac{1}{2} \, b^{3} \log\left(x^{2}\right)"," ",0,"1/6*c^3*x^6 + 3/4*b*c^2*x^4 + 3/2*b^2*c*x^2 + 1/2*b^3*log(x^2)","A",0
164,1,32,0,0.150650," ","integrate((c*x^4+b*x^2)^3/x^8,x, algorithm=""giac"")","\frac{1}{5} \, c^{3} x^{5} + b c^{2} x^{3} + 3 \, b^{2} c x - \frac{b^{3}}{x}"," ",0,"1/5*c^3*x^5 + b*c^2*x^3 + 3*b^2*c*x - b^3/x","A",0
165,1,46,0,0.158115," ","integrate((c*x^4+b*x^2)^3/x^9,x, algorithm=""giac"")","\frac{1}{4} \, c^{3} x^{4} + \frac{3}{2} \, b c^{2} x^{2} + \frac{3}{2} \, b^{2} c \log\left(x^{2}\right) - \frac{3 \, b^{2} c x^{2} + b^{3}}{2 \, x^{2}}"," ",0,"1/4*c^3*x^4 + 3/2*b*c^2*x^2 + 3/2*b^2*c*log(x^2) - 1/2*(3*b^2*c*x^2 + b^3)/x^2","A",0
166,1,34,0,0.167095," ","integrate((c*x^4+b*x^2)^3/x^10,x, algorithm=""giac"")","\frac{1}{3} \, c^{3} x^{3} + 3 \, b c^{2} x - \frac{9 \, b^{2} c x^{2} + b^{3}}{3 \, x^{3}}"," ",0,"1/3*c^3*x^3 + 3*b*c^2*x - 1/3*(9*b^2*c*x^2 + b^3)/x^3","A",0
167,1,46,0,0.149827," ","integrate((c*x^4+b*x^2)^3/x^11,x, algorithm=""giac"")","\frac{1}{2} \, c^{3} x^{2} + \frac{3}{2} \, b c^{2} \log\left(x^{2}\right) - \frac{9 \, b c^{2} x^{4} + 6 \, b^{2} c x^{2} + b^{3}}{4 \, x^{4}}"," ",0,"1/2*c^3*x^2 + 3/2*b*c^2*log(x^2) - 1/4*(9*b*c^2*x^4 + 6*b^2*c*x^2 + b^3)/x^4","A",0
168,1,33,0,0.165836," ","integrate((c*x^4+b*x^2)^3/x^12,x, algorithm=""giac"")","c^{3} x - \frac{15 \, b c^{2} x^{4} + 5 \, b^{2} c x^{2} + b^{3}}{5 \, x^{5}}"," ",0,"c^3*x - 1/5*(15*b*c^2*x^4 + 5*b^2*c*x^2 + b^3)/x^5","A",0
169,1,47,0,0.155764," ","integrate((c*x^4+b*x^2)^3/x^13,x, algorithm=""giac"")","\frac{1}{2} \, c^{3} \log\left(x^{2}\right) - \frac{11 \, c^{3} x^{6} + 18 \, b c^{2} x^{4} + 9 \, b^{2} c x^{2} + 2 \, b^{3}}{12 \, x^{6}}"," ",0,"1/2*c^3*log(x^2) - 1/12*(11*c^3*x^6 + 18*b*c^2*x^4 + 9*b^2*c*x^2 + 2*b^3)/x^6","A",0
170,1,37,0,0.163182," ","integrate((c*x^4+b*x^2)^3/x^14,x, algorithm=""giac"")","-\frac{35 \, c^{3} x^{6} + 35 \, b c^{2} x^{4} + 21 \, b^{2} c x^{2} + 5 \, b^{3}}{35 \, x^{7}}"," ",0,"-1/35*(35*c^3*x^6 + 35*b*c^2*x^4 + 21*b^2*c*x^2 + 5*b^3)/x^7","A",0
171,1,35,0,0.151789," ","integrate((c*x^4+b*x^2)^3/x^15,x, algorithm=""giac"")","-\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}}"," ",0,"-1/8*(4*c^3*x^6 + 6*b*c^2*x^4 + 4*b^2*c*x^2 + b^3)/x^8","B",0
172,1,37,0,0.172847," ","integrate((c*x^4+b*x^2)^3/x^16,x, algorithm=""giac"")","-\frac{105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}}"," ",0,"-1/315*(105*c^3*x^6 + 189*b*c^2*x^4 + 135*b^2*c*x^2 + 35*b^3)/x^9","A",0
173,1,37,0,0.149969," ","integrate((c*x^4+b*x^2)^3/x^17,x, algorithm=""giac"")","-\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}}"," ",0,"-1/40*(10*c^3*x^6 + 20*b*c^2*x^4 + 15*b^2*c*x^2 + 4*b^3)/x^10","A",0
174,1,65,0,0.188848," ","integrate(x^10/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{b^{4} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} c^{4}} + \frac{15 \, c^{6} x^{7} - 21 \, b c^{5} x^{5} + 35 \, b^{2} c^{4} x^{3} - 105 \, b^{3} c^{3} x}{105 \, c^{7}}"," ",0,"b^4*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^4) + 1/105*(15*c^6*x^7 - 21*b*c^5*x^5 + 35*b^2*c^4*x^3 - 105*b^3*c^3*x)/c^7","A",0
175,1,47,0,0.159008," ","integrate(x^9/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{b^{3} \log\left({\left| c x^{2} + b \right|}\right)}{2 \, c^{4}} + \frac{2 \, c^{2} x^{6} - 3 \, b c x^{4} + 6 \, b^{2} x^{2}}{12 \, c^{3}}"," ",0,"-1/2*b^3*log(abs(c*x^2 + b))/c^4 + 1/12*(2*c^2*x^6 - 3*b*c*x^4 + 6*b^2*x^2)/c^3","A",0
176,1,55,0,0.183793," ","integrate(x^8/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{b^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} c^{3}} + \frac{3 \, c^{4} x^{5} - 5 \, b c^{3} x^{3} + 15 \, b^{2} c^{2} x}{15 \, c^{5}}"," ",0,"-b^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^3) + 1/15*(3*c^4*x^5 - 5*b*c^3*x^3 + 15*b^2*c^2*x)/c^5","A",0
177,1,35,0,0.154606," ","integrate(x^7/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| c x^{2} + b \right|}\right)}{2 \, c^{3}} + \frac{c x^{4} - 2 \, b x^{2}}{4 \, c^{2}}"," ",0,"1/2*b^2*log(abs(c*x^2 + b))/c^3 + 1/4*(c*x^4 - 2*b*x^2)/c^2","A",0
178,1,40,0,0.174325," ","integrate(x^6/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} c^{2}} + \frac{c^{2} x^{3} - 3 \, b c x}{3 \, c^{3}}"," ",0,"b^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^2) + 1/3*(c^2*x^3 - 3*b*c*x)/c^3","A",0
179,1,24,0,0.157047," ","integrate(x^5/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, c} - \frac{b \log\left({\left| c x^{2} + b \right|}\right)}{2 \, c^{2}}"," ",0,"1/2*x^2/c - 1/2*b*log(abs(c*x^2 + b))/c^2","A",0
180,1,26,0,0.168943," ","integrate(x^4/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} c} + \frac{x}{c}"," ",0,"-b*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c) + x/c","A",0
181,1,14,0,0.148875," ","integrate(x^3/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\log\left({\left| c x^{2} + b \right|}\right)}{2 \, c}"," ",0,"1/2*log(abs(c*x^2 + b))/c","A",0
182,1,15,0,0.150908," ","integrate(x^2/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}}"," ",0,"arctan(c*x/sqrt(b*c))/sqrt(b*c)","A",0
183,1,22,0,0.168171," ","integrate(x/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{\log\left({\left| c x^{2} + b \right|}\right)}{2 \, b} + \frac{\log\left({\left| x \right|}\right)}{b}"," ",0,"-1/2*log(abs(c*x^2 + b))/b + log(abs(x))/b","A",0
184,1,29,0,0.164866," ","integrate(1/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{c \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} b} - \frac{1}{b x}"," ",0,"-c*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b) - 1/(b*x)","A",0
185,1,43,0,0.150062," ","integrate(1/x/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{c \log\left(x^{2}\right)}{2 \, b^{2}} + \frac{c \log\left({\left| c x^{2} + b \right|}\right)}{2 \, b^{2}} + \frac{c x^{2} - b}{2 \, b^{2} x^{2}}"," ",0,"-1/2*c*log(x^2)/b^2 + 1/2*c*log(abs(c*x^2 + b))/b^2 + 1/2*(c*x^2 - b)/(b^2*x^2)","A",0
186,1,40,0,0.167754," ","integrate(1/x^2/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{c^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} b^{2}} + \frac{3 \, c x^{2} - b}{3 \, b^{2} x^{3}}"," ",0,"c^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^2) + 1/3*(3*c*x^2 - b)/(b^2*x^3)","A",0
187,1,57,0,0.171754," ","integrate(1/x^3/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{c^{2} \log\left(x^{2}\right)}{2 \, b^{3}} - \frac{c^{2} \log\left({\left| c x^{2} + b \right|}\right)}{2 \, b^{3}} - \frac{3 \, c^{2} x^{4} - 2 \, b c x^{2} + b^{2}}{4 \, b^{3} x^{4}}"," ",0,"1/2*c^2*log(x^2)/b^3 - 1/2*c^2*log(abs(c*x^2 + b))/b^3 - 1/4*(3*c^2*x^4 - 2*b*c*x^2 + b^2)/(b^3*x^4)","A",0
188,1,52,0,0.165573," ","integrate(1/x^4/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{c^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} b^{3}} - \frac{15 \, c^{2} x^{4} - 5 \, b c x^{2} + 3 \, b^{2}}{15 \, b^{3} x^{5}}"," ",0,"-c^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^3) - 1/15*(15*c^2*x^4 - 5*b*c*x^2 + 3*b^2)/(b^3*x^5)","A",0
189,1,70,0,0.147469," ","integrate(1/x^5/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{c^{3} \log\left(x^{2}\right)}{2 \, b^{4}} + \frac{c^{3} \log\left({\left| c x^{2} + b \right|}\right)}{2 \, b^{4}} + \frac{11 \, c^{3} x^{6} - 6 \, b c^{2} x^{4} + 3 \, b^{2} c x^{2} - 2 \, b^{3}}{12 \, b^{4} x^{6}}"," ",0,"-1/2*c^3*log(x^2)/b^4 + 1/2*c^3*log(abs(c*x^2 + b))/b^4 + 1/12*(11*c^3*x^6 - 6*b*c^2*x^4 + 3*b^2*c*x^2 - 2*b^3)/(b^4*x^6)","A",0
190,1,73,0,0.156715," ","integrate(x^12/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{7 \, b^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c^{4}} + \frac{b^{3} x}{2 \, {\left(c x^{2} + b\right)} c^{4}} + \frac{3 \, c^{8} x^{5} - 10 \, b c^{7} x^{3} + 45 \, b^{2} c^{6} x}{15 \, c^{10}}"," ",0,"-7/2*b^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^4) + 1/2*b^3*x/((c*x^2 + b)*c^4) + 1/15*(3*c^8*x^5 - 10*b*c^7*x^3 + 45*b^2*c^6*x)/c^10","A",0
191,1,67,0,0.180303," ","integrate(x^11/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{3 \, b^{2} \log\left({\left| c x^{2} + b \right|}\right)}{2 \, c^{4}} + \frac{c^{2} x^{4} - 4 \, b c x^{2}}{4 \, c^{4}} - \frac{3 \, b^{2} c x^{2} + 2 \, b^{3}}{2 \, {\left(c x^{2} + b\right)} c^{4}}"," ",0,"3/2*b^2*log(abs(c*x^2 + b))/c^4 + 1/4*(c^2*x^4 - 4*b*c*x^2)/c^4 - 1/2*(3*b^2*c*x^2 + 2*b^3)/((c*x^2 + b)*c^4)","A",0
192,1,61,0,0.168541," ","integrate(x^10/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{5 \, b^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c^{3}} - \frac{b^{2} x}{2 \, {\left(c x^{2} + b\right)} c^{3}} + \frac{c^{4} x^{3} - 6 \, b c^{3} x}{3 \, c^{6}}"," ",0,"5/2*b^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^3) - 1/2*b^2*x/((c*x^2 + b)*c^3) + 1/3*(c^4*x^3 - 6*b*c^3*x)/c^6","A",0
193,1,49,0,0.174381," ","integrate(x^9/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{x^{2}}{2 \, c^{2}} - \frac{b \log\left({\left| c x^{2} + b \right|}\right)}{c^{3}} + \frac{2 \, b c x^{2} + b^{2}}{2 \, {\left(c x^{2} + b\right)} c^{3}}"," ",0,"1/2*x^2/c^2 - b*log(abs(c*x^2 + b))/c^3 + 1/2*(2*b*c*x^2 + b^2)/((c*x^2 + b)*c^3)","A",0
194,1,42,0,0.167099," ","integrate(x^8/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{3 \, b \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c^{2}} + \frac{b x}{2 \, {\left(c x^{2} + b\right)} c^{2}} + \frac{x}{c^{2}}"," ",0,"-3/2*b*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^2) + 1/2*b*x/((c*x^2 + b)*c^2) + x/c^2","A",0
195,1,32,0,0.150134," ","integrate(x^7/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{x^{2}}{2 \, {\left(c x^{2} + b\right)} c} + \frac{\log\left({\left| c x^{2} + b \right|}\right)}{2 \, c^{2}}"," ",0,"-1/2*x^2/((c*x^2 + b)*c) + 1/2*log(abs(c*x^2 + b))/c^2","A",0
196,1,35,0,0.170888," ","integrate(x^6/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c} - \frac{x}{2 \, {\left(c x^{2} + b\right)} c}"," ",0,"1/2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c) - 1/2*x/((c*x^2 + b)*c)","A",0
197,1,14,0,0.168160," ","integrate(x^5/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(c x^{2} + b\right)} c}"," ",0,"-1/2/((c*x^2 + b)*c)","A",0
198,1,35,0,0.153786," ","integrate(x^4/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b} + \frac{x}{2 \, {\left(c x^{2} + b\right)} b}"," ",0,"1/2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b) + 1/2*x/((c*x^2 + b)*b)","A",0
199,1,36,0,0.155036," ","integrate(x^3/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| c x^{2} + b \right|}\right)}{2 \, b^{2}} + \frac{\log\left({\left| x \right|}\right)}{b^{2}} + \frac{1}{2 \, {\left(c x^{2} + b\right)} b}"," ",0,"-1/2*log(abs(c*x^2 + b))/b^2 + log(abs(x))/b^2 + 1/2/((c*x^2 + b)*b)","A",0
200,1,47,0,0.155376," ","integrate(x^2/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{3 \, c \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b^{2}} - \frac{3 \, c x^{2} + 2 \, b}{2 \, {\left(c x^{3} + b x\right)} b^{2}}"," ",0,"-3/2*c*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^2) - 1/2*(3*c*x^2 + 2*b)/((c*x^3 + b*x)*b^2)","A",0
201,1,50,0,0.174766," ","integrate(x/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{c \log\left({\left| c x^{2} + b \right|}\right)}{b^{3}} - \frac{2 \, c \log\left({\left| x \right|}\right)}{b^{3}} - \frac{2 \, c x^{2} + b}{2 \, {\left(c x^{4} + b x^{2}\right)} b^{2}}"," ",0,"c*log(abs(c*x^2 + b))/b^3 - 2*c*log(abs(x))/b^3 - 1/2*(2*c*x^2 + b)/((c*x^4 + b*x^2)*b^2)","A",0
202,1,59,0,0.152246," ","integrate(1/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{5 \, c^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b^{3}} + \frac{c^{2} x}{2 \, {\left(c x^{2} + b\right)} b^{3}} + \frac{6 \, c x^{2} - b}{3 \, b^{3} x^{3}}"," ",0,"5/2*c^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^3) + 1/2*c^2*x/((c*x^2 + b)*b^3) + 1/3*(6*c*x^2 - b)/(b^3*x^3)","A",0
203,1,86,0,0.151674," ","integrate(1/x/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{3 \, c^{2} \log\left(x^{2}\right)}{2 \, b^{4}} - \frac{3 \, c^{2} \log\left({\left| c x^{2} + b \right|}\right)}{2 \, b^{4}} + \frac{3 \, c^{3} x^{2} + 4 \, b c^{2}}{2 \, {\left(c x^{2} + b\right)} b^{4}} - \frac{9 \, c^{2} x^{4} - 4 \, b c x^{2} + b^{2}}{4 \, b^{4} x^{4}}"," ",0,"3/2*c^2*log(x^2)/b^4 - 3/2*c^2*log(abs(c*x^2 + b))/b^4 + 1/2*(3*c^3*x^2 + 4*b*c^2)/((c*x^2 + b)*b^4) - 1/4*(9*c^2*x^4 - 4*b*c*x^2 + b^2)/(b^4*x^4)","A",0
204,1,70,0,0.175846," ","integrate(1/x^2/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{7 \, c^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b^{4}} - \frac{c^{3} x}{2 \, {\left(c x^{2} + b\right)} b^{4}} - \frac{45 \, c^{2} x^{4} - 10 \, b c x^{2} + 3 \, b^{2}}{15 \, b^{4} x^{5}}"," ",0,"-7/2*c^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^4) - 1/2*c^3*x/((c*x^2 + b)*b^4) - 1/15*(45*c^2*x^4 - 10*b*c*x^2 + 3*b^2)/(b^4*x^5)","A",0
205,1,73,0,0.157489," ","integrate(x^14/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{35 \, b^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} c^{4}} - \frac{13 \, b^{2} c x^{3} + 11 \, b^{3} x}{8 \, {\left(c x^{2} + b\right)}^{2} c^{4}} + \frac{c^{6} x^{3} - 9 \, b c^{5} x}{3 \, c^{9}}"," ",0,"35/8*b^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^4) - 1/8*(13*b^2*c*x^3 + 11*b^3*x)/((c*x^2 + b)^2*c^4) + 1/3*(c^6*x^3 - 9*b*c^5*x)/c^9","A",0
206,1,62,0,0.194947," ","integrate(x^13/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{x^{2}}{2 \, c^{3}} - \frac{3 \, b \log\left({\left| c x^{2} + b \right|}\right)}{2 \, c^{4}} + \frac{9 \, b c^{2} x^{4} + 12 \, b^{2} c x^{2} + 4 \, b^{3}}{4 \, {\left(c x^{2} + b\right)}^{2} c^{4}}"," ",0,"1/2*x^2/c^3 - 3/2*b*log(abs(c*x^2 + b))/c^4 + 1/4*(9*b*c^2*x^4 + 12*b^2*c*x^2 + 4*b^3)/((c*x^2 + b)^2*c^4)","A",0
207,1,54,0,0.171929," ","integrate(x^12/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{15 \, b \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} c^{3}} + \frac{x}{c^{3}} + \frac{9 \, b c x^{3} + 7 \, b^{2} x}{8 \, {\left(c x^{2} + b\right)}^{2} c^{3}}"," ",0,"-15/8*b*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^3) + x/c^3 + 1/8*(9*b*c*x^3 + 7*b^2*x)/((c*x^2 + b)^2*c^3)","A",0
208,1,42,0,0.179083," ","integrate(x^11/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{\log\left({\left| c x^{2} + b \right|}\right)}{2 \, c^{3}} - \frac{3 \, c x^{4} + 2 \, b x^{2}}{4 \, {\left(c x^{2} + b\right)}^{2} c^{2}}"," ",0,"1/2*log(abs(c*x^2 + b))/c^3 - 1/4*(3*c*x^4 + 2*b*x^2)/((c*x^2 + b)^2*c^2)","A",0
209,1,45,0,0.160534," ","integrate(x^10/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} c^{2}} - \frac{5 \, c x^{3} + 3 \, b x}{8 \, {\left(c x^{2} + b\right)}^{2} c^{2}}"," ",0,"3/8*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^2) - 1/8*(5*c*x^3 + 3*b*x)/((c*x^2 + b)^2*c^2)","A",0
210,1,22,0,0.159139," ","integrate(x^9/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{2 \, c x^{2} + b}{4 \, {\left(c x^{2} + b\right)}^{2} c^{2}}"," ",0,"-1/4*(2*c*x^2 + b)/((c*x^2 + b)^2*c^2)","A",0
211,1,50,0,0.159145," ","integrate(x^8/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b c} + \frac{c x^{3} - b x}{8 \, {\left(c x^{2} + b\right)}^{2} b c}"," ",0,"1/8*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b*c) + 1/8*(c*x^3 - b*x)/((c*x^2 + b)^2*b*c)","A",0
212,1,14,0,0.153786," ","integrate(x^7/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(c x^{2} + b\right)}^{2} c}"," ",0,"-1/4/((c*x^2 + b)^2*c)","A",0
213,1,45,0,0.202781," ","integrate(x^6/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{2}} + \frac{3 \, c x^{3} + 5 \, b x}{8 \, {\left(c x^{2} + b\right)}^{2} b^{2}}"," ",0,"3/8*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^2) + 1/8*(3*c*x^3 + 5*b*x)/((c*x^2 + b)^2*b^2)","A",0
214,1,59,0,0.155235," ","integrate(x^5/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, b^{3}} - \frac{\log\left({\left| c x^{2} + b \right|}\right)}{2 \, b^{3}} + \frac{3 \, c^{2} x^{4} + 8 \, b c x^{2} + 6 \, b^{2}}{4 \, {\left(c x^{2} + b\right)}^{2} b^{3}}"," ",0,"1/2*log(x^2)/b^3 - 1/2*log(abs(c*x^2 + b))/b^3 + 1/4*(3*c^2*x^4 + 8*b*c*x^2 + 6*b^2)/((c*x^2 + b)^2*b^3)","A",0
215,1,57,0,0.172054," ","integrate(x^4/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{15 \, c \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{3}} - \frac{7 \, c^{2} x^{3} + 9 \, b c x}{8 \, {\left(c x^{2} + b\right)}^{2} b^{3}} - \frac{1}{b^{3} x}"," ",0,"-15/8*c*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^3) - 1/8*(7*c^2*x^3 + 9*b*c*x)/((c*x^2 + b)^2*b^3) - 1/(b^3*x)","A",0
216,1,66,0,0.165200," ","integrate(x^3/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{3 \, c \log\left({\left| c x^{2} + b \right|}\right)}{2 \, b^{4}} - \frac{3 \, c \log\left({\left| x \right|}\right)}{b^{4}} - \frac{6 \, b c^{2} x^{4} + 9 \, b^{2} c x^{2} + 2 \, b^{3}}{4 \, {\left(c x^{2} + b\right)}^{2} b^{4} x^{2}}"," ",0,"3/2*c*log(abs(c*x^2 + b))/b^4 - 3*c*log(abs(x))/b^4 - 1/4*(6*b*c^2*x^4 + 9*b^2*c*x^2 + 2*b^3)/((c*x^2 + b)^2*b^4*x^2)","A",0
217,1,71,0,0.175829," ","integrate(x^2/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{35 \, c^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{4}} + \frac{11 \, c^{3} x^{3} + 13 \, b c^{2} x}{8 \, {\left(c x^{2} + b\right)}^{2} b^{4}} + \frac{9 \, c x^{2} - b}{3 \, b^{4} x^{3}}"," ",0,"35/8*c^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^4) + 1/8*(11*c^3*x^3 + 13*b*c^2*x)/((c*x^2 + b)^2*b^4) + 1/3*(9*c*x^2 - b)/(b^4*x^3)","A",0
218,1,79,0,0.155828," ","integrate(x/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{3 \, c^{2} \log\left({\left| c x^{2} + b \right|}\right)}{b^{5}} + \frac{6 \, c^{2} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{12 \, c^{3} x^{6} + 18 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} - b^{3}}{4 \, {\left(c x^{4} + b x^{2}\right)}^{2} b^{4}}"," ",0,"-3*c^2*log(abs(c*x^2 + b))/b^5 + 6*c^2*log(abs(x))/b^5 + 1/4*(12*c^3*x^6 + 18*b*c^2*x^4 + 4*b^2*c*x^2 - b^3)/((c*x^4 + b*x^2)^2*b^4)","A",0
219,1,80,0,0.178350," ","integrate(1/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{63 \, c^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{5}} - \frac{15 \, c^{4} x^{3} + 17 \, b c^{3} x}{8 \, {\left(c x^{2} + b\right)}^{2} b^{5}} - \frac{30 \, c^{2} x^{4} - 5 \, b c x^{2} + b^{2}}{5 \, b^{5} x^{5}}"," ",0,"-63/8*c^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^5) - 1/8*(15*c^4*x^3 + 17*b*c^3*x)/((c*x^2 + b)^2*b^5) - 1/5*(30*c^2*x^4 - 5*b*c*x^2 + b^2)/(b^5*x^5)","A",0
220,1,110,0,0.154451," ","integrate(1/x/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{5 \, c^{3} \log\left(x^{2}\right)}{b^{6}} + \frac{5 \, c^{3} \log\left({\left| c x^{2} + b \right|}\right)}{b^{6}} - \frac{30 \, c^{5} x^{4} + 68 \, b c^{4} x^{2} + 39 \, b^{2} c^{3}}{4 \, {\left(c x^{2} + b\right)}^{2} b^{6}} + \frac{110 \, c^{3} x^{6} - 36 \, b c^{2} x^{4} + 9 \, b^{2} c x^{2} - 2 \, b^{3}}{12 \, b^{6} x^{6}}"," ",0,"-5*c^3*log(x^2)/b^6 + 5*c^3*log(abs(c*x^2 + b))/b^6 - 1/4*(30*c^5*x^4 + 68*b*c^4*x^2 + 39*b^2*c^3)/((c*x^2 + b)^2*b^6) + 1/12*(110*c^3*x^6 - 36*b*c^2*x^4 + 9*b^2*c*x^2 - 2*b^3)/(b^6*x^6)","A",0
221,1,101,0,0.192671," ","integrate(x^5*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, x^{2} \mathrm{sgn}\left(x\right) + \frac{b \mathrm{sgn}\left(x\right)}{c}\right)} x^{2} - \frac{5 \, b^{2} \mathrm{sgn}\left(x\right)}{c^{2}}\right)} x^{2} + \frac{15 \, b^{3} \mathrm{sgn}\left(x\right)}{c^{3}}\right)} \sqrt{c x^{2} + b} x + \frac{5 \, b^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, c^{\frac{7}{2}}} - \frac{5 \, b^{4} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/384*(2*(4*(6*x^2*sgn(x) + b*sgn(x)/c)*x^2 - 5*b^2*sgn(x)/c^2)*x^2 + 15*b^3*sgn(x)/c^3)*sqrt(c*x^2 + b)*x + 5/128*b^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))*sgn(x)/c^(7/2) - 5/256*b^4*log(abs(b))*sgn(x)/c^(7/2)","A",0
222,1,85,0,0.185466," ","integrate(x^3*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, x^{2} \mathrm{sgn}\left(x\right) + \frac{b \mathrm{sgn}\left(x\right)}{c}\right)} x^{2} - \frac{3 \, b^{2} \mathrm{sgn}\left(x\right)}{c^{2}}\right)} \sqrt{c x^{2} + b} x - \frac{b^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, c^{\frac{5}{2}}} + \frac{b^{3} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{32 \, c^{\frac{5}{2}}}"," ",0,"1/48*(2*(4*x^2*sgn(x) + b*sgn(x)/c)*x^2 - 3*b^2*sgn(x)/c^2)*sqrt(c*x^2 + b)*x - 1/16*b^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))*sgn(x)/c^(5/2) + 1/32*b^3*log(abs(b))*sgn(x)/c^(5/2)","A",0
223,1,69,0,0.189130," ","integrate(x*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{c x^{2} + b} {\left(2 \, x^{2} \mathrm{sgn}\left(x\right) + \frac{b \mathrm{sgn}\left(x\right)}{c}\right)} x + \frac{b^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, c^{\frac{3}{2}}} - \frac{b^{2} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/8*sqrt(c*x^2 + b)*(2*x^2*sgn(x) + b*sgn(x)/c)*x + 1/8*b^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))*sgn(x)/c^(3/2) - 1/16*b^2*log(abs(b))*sgn(x)/c^(3/2)","A",0
224,1,52,0,0.174482," ","integrate((c*x^4+b*x^2)^(1/2)/x,x, algorithm=""giac"")","\frac{b \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{4 \, \sqrt{c}} + \frac{1}{2} \, {\left(\sqrt{c x^{2} + b} x - \frac{b \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right)}{\sqrt{c}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/4*b*log(abs(b))*sgn(x)/sqrt(c) + 1/2*(sqrt(c*x^2 + b)*x - b*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))/sqrt(c))*sgn(x)","A",0
225,1,61,0,0.272500," ","integrate((c*x^4+b*x^2)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{c} \log\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, b \sqrt{c} \mathrm{sgn}\left(x\right)}{{\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b}"," ",0,"-1/2*sqrt(c)*log((sqrt(c)*x - sqrt(c*x^2 + b))^2)*sgn(x) + 2*b*sqrt(c)*sgn(x)/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)","A",0
226,1,63,0,0.225431," ","integrate((c*x^4+b*x^2)^(1/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} c^{\frac{3}{2}} \mathrm{sgn}\left(x\right) + b^{2} c^{\frac{3}{2}} \mathrm{sgn}\left(x\right)\right)}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b))^4*c^(3/2)*sgn(x) + b^2*c^(3/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^3","B",0
227,1,120,0,0.221092," ","integrate((c*x^4+b*x^2)^(1/2)/x^7,x, algorithm=""giac"")","\frac{4 \, {\left(15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} c^{\frac{5}{2}} \mathrm{sgn}\left(x\right) + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b c^{\frac{5}{2}} \mathrm{sgn}\left(x\right) + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{2} c^{\frac{5}{2}} \mathrm{sgn}\left(x\right) - b^{3} c^{\frac{5}{2}} \mathrm{sgn}\left(x\right)\right)}}{15 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{5}}"," ",0,"4/15*(15*(sqrt(c)*x - sqrt(c*x^2 + b))^6*c^(5/2)*sgn(x) + 5*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b*c^(5/2)*sgn(x) + 5*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^2*c^(5/2)*sgn(x) - b^3*c^(5/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^5","B",0
228,1,148,0,0.238274," ","integrate((c*x^4+b*x^2)^(1/2)/x^9,x, algorithm=""giac"")","\frac{16 \, {\left(70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} b c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{2} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{3} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + b^{4} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right)\right)}}{105 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{7}}"," ",0,"16/105*(70*(sqrt(c)*x - sqrt(c*x^2 + b))^8*c^(7/2)*sgn(x) + 35*(sqrt(c)*x - sqrt(c*x^2 + b))^6*b*c^(7/2)*sgn(x) + 21*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^2*c^(7/2)*sgn(x) - 7*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^3*c^(7/2)*sgn(x) + b^4*c^(7/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^7","B",0
229,1,178,0,0.294300," ","integrate((c*x^4+b*x^2)^(1/2)/x^11,x, algorithm=""giac"")","\frac{32 \, {\left(315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{10} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 189 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} b c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} b^{2} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{3} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{4} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) - b^{5} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right)\right)}}{315 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{9}}"," ",0,"32/315*(315*(sqrt(c)*x - sqrt(c*x^2 + b))^10*c^(9/2)*sgn(x) + 189*(sqrt(c)*x - sqrt(c*x^2 + b))^8*b*c^(9/2)*sgn(x) + 84*(sqrt(c)*x - sqrt(c*x^2 + b))^6*b^2*c^(9/2)*sgn(x) - 36*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^3*c^(9/2)*sgn(x) + 9*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^4*c^(9/2)*sgn(x) - b^5*c^(9/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^9","A",0
230,1,206,0,0.252751," ","integrate((c*x^4+b*x^2)^(1/2)/x^13,x, algorithm=""giac"")","\frac{256 \, {\left(1386 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{12} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 924 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{10} b c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} b^{2} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 165 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} b^{3} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 55 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{4} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{5} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + b^{6} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right)\right)}}{3465 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{11}}"," ",0,"256/3465*(1386*(sqrt(c)*x - sqrt(c*x^2 + b))^12*c^(11/2)*sgn(x) + 924*(sqrt(c)*x - sqrt(c*x^2 + b))^10*b*c^(11/2)*sgn(x) + 330*(sqrt(c)*x - sqrt(c*x^2 + b))^8*b^2*c^(11/2)*sgn(x) - 165*(sqrt(c)*x - sqrt(c*x^2 + b))^6*b^3*c^(11/2)*sgn(x) + 55*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^4*c^(11/2)*sgn(x) - 11*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^5*c^(11/2)*sgn(x) + b^6*c^(11/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^11","A",0
231,1,60,0,0.159128," ","integrate(x^4*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{8 \, b^{\frac{7}{2}} \mathrm{sgn}\left(x\right)}{105 \, c^{3}} + \frac{15 \, {\left(c x^{2} + b\right)}^{\frac{7}{2}} \mathrm{sgn}\left(x\right) - 42 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} b \mathrm{sgn}\left(x\right) + 35 \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} b^{2} \mathrm{sgn}\left(x\right)}{105 \, c^{3}}"," ",0,"-8/105*b^(7/2)*sgn(x)/c^3 + 1/105*(15*(c*x^2 + b)^(7/2)*sgn(x) - 42*(c*x^2 + b)^(5/2)*b*sgn(x) + 35*(c*x^2 + b)^(3/2)*b^2*sgn(x))/c^3","A",0
232,1,44,0,0.158924," ","integrate(x^2*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, b^{\frac{5}{2}} \mathrm{sgn}\left(x\right)}{15 \, c^{2}} + \frac{3 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} \mathrm{sgn}\left(x\right) - 5 \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} b \mathrm{sgn}\left(x\right)}{15 \, c^{2}}"," ",0,"2/15*b^(5/2)*sgn(x)/c^2 + 1/15*(3*(c*x^2 + b)^(5/2)*sgn(x) - 5*(c*x^2 + b)^(3/2)*b*sgn(x))/c^2","A",0
233,1,27,0,0.154459," ","integrate((c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(c x^{2} + b\right)}^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{3 \, c} - \frac{b^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{3 \, c}"," ",0,"1/3*(c*x^2 + b)^(3/2)*sgn(x)/c - 1/3*b^(3/2)*sgn(x)/c","A",0
234,1,69,0,0.180214," ","integrate((c*x^4+b*x^2)^(1/2)/x^2,x, algorithm=""giac"")","\frac{b \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + \sqrt{c x^{2} + b} \mathrm{sgn}\left(x\right) - \frac{{\left(b \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + \sqrt{-b} \sqrt{b}\right)} \mathrm{sgn}\left(x\right)}{\sqrt{-b}}"," ",0,"b*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + sqrt(c*x^2 + b)*sgn(x) - (b*arctan(sqrt(b)/sqrt(-b)) + sqrt(-b)*sqrt(b))*sgn(x)/sqrt(-b)","A",0
235,1,50,0,0.200251," ","integrate((c*x^4+b*x^2)^(1/2)/x^4,x, algorithm=""giac"")","\frac{\frac{c^{2} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} - \frac{\sqrt{c x^{2} + b} c \mathrm{sgn}\left(x\right)}{x^{2}}}{2 \, c}"," ",0,"1/2*(c^2*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) - sqrt(c*x^2 + b)*c*sgn(x)/x^2)/c","A",0
236,1,78,0,0.212073," ","integrate((c*x^4+b*x^2)^(1/2)/x^6,x, algorithm=""giac"")","-\frac{\frac{c^{3} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b} + \frac{{\left(c x^{2} + b\right)}^{\frac{3}{2}} c^{3} \mathrm{sgn}\left(x\right) + \sqrt{c x^{2} + b} b c^{3} \mathrm{sgn}\left(x\right)}{b c^{2} x^{4}}}{8 \, c}"," ",0,"-1/8*(c^3*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b) + ((c*x^2 + b)^(3/2)*c^3*sgn(x) + sqrt(c*x^2 + b)*b*c^3*sgn(x))/(b*c^2*x^4))/c","A",0
237,1,100,0,0.266520," ","integrate((c*x^4+b*x^2)^(1/2)/x^8,x, algorithm=""giac"")","\frac{\frac{3 \, c^{4} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b^{2}} + \frac{3 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} c^{4} \mathrm{sgn}\left(x\right) - 8 \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} b c^{4} \mathrm{sgn}\left(x\right) - 3 \, \sqrt{c x^{2} + b} b^{2} c^{4} \mathrm{sgn}\left(x\right)}{b^{2} c^{3} x^{6}}}{48 \, c}"," ",0,"1/48*(3*c^4*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b^2) + (3*(c*x^2 + b)^(5/2)*c^4*sgn(x) - 8*(c*x^2 + b)^(3/2)*b*c^4*sgn(x) - 3*sqrt(c*x^2 + b)*b^2*c^4*sgn(x))/(b^2*c^3*x^6))/c","A",0
238,1,115,0,0.278220," ","integrate(x^3*(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, b^{5} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{256 \, c^{\frac{7}{2}}} - \frac{3 \, b^{5} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{512 \, c^{\frac{7}{2}}} + \frac{1}{1280} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, c x^{2} \mathrm{sgn}\left(x\right) + 11 \, b \mathrm{sgn}\left(x\right)\right)} x^{2} + \frac{b^{2} \mathrm{sgn}\left(x\right)}{c}\right)} x^{2} - \frac{5 \, b^{3} \mathrm{sgn}\left(x\right)}{c^{2}}\right)} x^{2} + \frac{15 \, b^{4} \mathrm{sgn}\left(x\right)}{c^{3}}\right)} \sqrt{c x^{2} + b} x"," ",0,"3/256*b^5*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))*sgn(x)/c^(7/2) - 3/512*b^5*log(abs(b))*sgn(x)/c^(7/2) + 1/1280*(2*(4*(2*(8*c*x^2*sgn(x) + 11*b*sgn(x))*x^2 + b^2*sgn(x)/c)*x^2 - 5*b^3*sgn(x)/c^2)*x^2 + 15*b^4*sgn(x)/c^3)*sqrt(c*x^2 + b)*x","A",0
239,1,99,0,0.194161," ","integrate(x*(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{3 \, b^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, c^{\frac{5}{2}}} + \frac{3 \, b^{4} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{256 \, c^{\frac{5}{2}}} + \frac{1}{128} \, {\left(2 \, {\left(4 \, {\left(2 \, c x^{2} \mathrm{sgn}\left(x\right) + 3 \, b \mathrm{sgn}\left(x\right)\right)} x^{2} + \frac{b^{2} \mathrm{sgn}\left(x\right)}{c}\right)} x^{2} - \frac{3 \, b^{3} \mathrm{sgn}\left(x\right)}{c^{2}}\right)} \sqrt{c x^{2} + b} x"," ",0,"-3/128*b^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))*sgn(x)/c^(5/2) + 3/256*b^4*log(abs(b))*sgn(x)/c^(5/2) + 1/128*(2*(4*(2*c*x^2*sgn(x) + 3*b*sgn(x))*x^2 + b^2*sgn(x)/c)*x^2 - 3*b^3*sgn(x)/c^2)*sqrt(c*x^2 + b)*x","A",0
240,1,84,0,0.206465," ","integrate((c*x^4+b*x^2)^(3/2)/x,x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, c^{\frac{3}{2}}} - \frac{b^{3} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{32 \, c^{\frac{3}{2}}} + \frac{1}{48} \, {\left(2 \, {\left(4 \, c x^{2} \mathrm{sgn}\left(x\right) + 7 \, b \mathrm{sgn}\left(x\right)\right)} x^{2} + \frac{3 \, b^{2} \mathrm{sgn}\left(x\right)}{c}\right)} \sqrt{c x^{2} + b} x"," ",0,"1/16*b^3*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))*sgn(x)/c^(3/2) - 1/32*b^3*log(abs(b))*sgn(x)/c^(3/2) + 1/48*(2*(4*c*x^2*sgn(x) + 7*b*sgn(x))*x^2 + 3*b^2*sgn(x)/c)*sqrt(c*x^2 + b)*x","A",0
241,1,68,0,0.248050," ","integrate((c*x^4+b*x^2)^(3/2)/x^3,x, algorithm=""giac"")","-\frac{3 \, b^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, \sqrt{c}} + \frac{3 \, b^{2} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, \sqrt{c}} + \frac{1}{8} \, {\left(2 \, c x^{2} \mathrm{sgn}\left(x\right) + 5 \, b \mathrm{sgn}\left(x\right)\right)} \sqrt{c x^{2} + b} x"," ",0,"-3/8*b^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + b)))*sgn(x)/sqrt(c) + 3/16*b^2*log(abs(b))*sgn(x)/sqrt(c) + 1/8*(2*c*x^2*sgn(x) + 5*b*sgn(x))*sqrt(c*x^2 + b)*x","A",0
242,1,79,0,0.271869," ","integrate((c*x^4+b*x^2)^(3/2)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} + b} c x \mathrm{sgn}\left(x\right) - \frac{3}{4} \, b \sqrt{c} \log\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, b^{2} \sqrt{c} \mathrm{sgn}\left(x\right)}{{\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b}"," ",0,"1/2*sqrt(c*x^2 + b)*c*x*sgn(x) - 3/4*b*sqrt(c)*log((sqrt(c)*x - sqrt(c*x^2 + b))^2)*sgn(x) + 2*b^2*sqrt(c)*sgn(x)/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)","A",0
243,1,122,0,0.437343," ","integrate((c*x^4+b*x^2)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{1}{2} \, c^{\frac{3}{2}} \log\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{4 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b c^{\frac{3}{2}} \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{2} c^{\frac{3}{2}} \mathrm{sgn}\left(x\right) + 2 \, b^{3} c^{\frac{3}{2}} \mathrm{sgn}\left(x\right)\right)}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"-1/2*c^(3/2)*log((sqrt(c)*x - sqrt(c*x^2 + b))^2)*sgn(x) + 4/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b*c^(3/2)*sgn(x) - 3*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^2*c^(3/2)*sgn(x) + 2*b^3*c^(3/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^3","A",0
244,1,92,0,0.302668," ","integrate((c*x^4+b*x^2)^(3/2)/x^9,x, algorithm=""giac"")","\frac{2 \, {\left(5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} c^{\frac{5}{2}} \mathrm{sgn}\left(x\right) + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{2} c^{\frac{5}{2}} \mathrm{sgn}\left(x\right) + b^{4} c^{\frac{5}{2}} \mathrm{sgn}\left(x\right)\right)}}{5 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{5}}"," ",0,"2/5*(5*(sqrt(c)*x - sqrt(c*x^2 + b))^8*c^(5/2)*sgn(x) + 10*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^2*c^(5/2)*sgn(x) + b^4*c^(5/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^5","B",0
245,1,178,0,0.254981," ","integrate((c*x^4+b*x^2)^(3/2)/x^11,x, algorithm=""giac"")","\frac{4 \, {\left(35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{10} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} b c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} b^{2} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{3} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{4} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) - b^{5} c^{\frac{7}{2}} \mathrm{sgn}\left(x\right)\right)}}{35 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{7}}"," ",0,"4/35*(35*(sqrt(c)*x - sqrt(c*x^2 + b))^10*c^(7/2)*sgn(x) + 35*(sqrt(c)*x - sqrt(c*x^2 + b))^8*b*c^(7/2)*sgn(x) + 70*(sqrt(c)*x - sqrt(c*x^2 + b))^6*b^2*c^(7/2)*sgn(x) + 14*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^3*c^(7/2)*sgn(x) + 7*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^4*c^(7/2)*sgn(x) - b^5*c^(7/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^7","B",0
246,1,206,0,0.267003," ","integrate((c*x^4+b*x^2)^(3/2)/x^13,x, algorithm=""giac"")","\frac{16 \, {\left(210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{12} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{10} b c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 441 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} b^{2} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 126 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} b^{3} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{4} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{5} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + b^{6} c^{\frac{9}{2}} \mathrm{sgn}\left(x\right)\right)}}{315 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{9}}"," ",0,"16/315*(210*(sqrt(c)*x - sqrt(c*x^2 + b))^12*c^(9/2)*sgn(x) + 315*(sqrt(c)*x - sqrt(c*x^2 + b))^10*b*c^(9/2)*sgn(x) + 441*(sqrt(c)*x - sqrt(c*x^2 + b))^8*b^2*c^(9/2)*sgn(x) + 126*(sqrt(c)*x - sqrt(c*x^2 + b))^6*b^3*c^(9/2)*sgn(x) + 36*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^4*c^(9/2)*sgn(x) - 9*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^5*c^(9/2)*sgn(x) + b^6*c^(9/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^9","B",0
247,1,236,0,0.275784," ","integrate((c*x^4+b*x^2)^(3/2)/x^15,x, algorithm=""giac"")","\frac{32 \, {\left(1155 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{14} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 2079 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{12} b c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 2541 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{10} b^{2} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 825 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} b^{3} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 165 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} b^{4} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 55 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{5} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{6} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - b^{7} c^{\frac{11}{2}} \mathrm{sgn}\left(x\right)\right)}}{1155 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{11}}"," ",0,"32/1155*(1155*(sqrt(c)*x - sqrt(c*x^2 + b))^14*c^(11/2)*sgn(x) + 2079*(sqrt(c)*x - sqrt(c*x^2 + b))^12*b*c^(11/2)*sgn(x) + 2541*(sqrt(c)*x - sqrt(c*x^2 + b))^10*b^2*c^(11/2)*sgn(x) + 825*(sqrt(c)*x - sqrt(c*x^2 + b))^8*b^3*c^(11/2)*sgn(x) + 165*(sqrt(c)*x - sqrt(c*x^2 + b))^6*b^4*c^(11/2)*sgn(x) - 55*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^5*c^(11/2)*sgn(x) + 11*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^6*c^(11/2)*sgn(x) - b^7*c^(11/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^11","B",0
248,1,264,0,0.285837," ","integrate((c*x^4+b*x^2)^(3/2)/x^17,x, algorithm=""giac"")","\frac{256 \, {\left(6006 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{16} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 12012 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{14} b c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 13728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{12} b^{2} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 4719 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{10} b^{3} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 715 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{8} b^{4} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) - 286 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{6} b^{5} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{4} b^{6} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) - 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} b^{7} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + b^{8} c^{\frac{13}{2}} \mathrm{sgn}\left(x\right)\right)}}{15015 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b}\right)}^{2} - b\right)}^{13}}"," ",0,"256/15015*(6006*(sqrt(c)*x - sqrt(c*x^2 + b))^16*c^(13/2)*sgn(x) + 12012*(sqrt(c)*x - sqrt(c*x^2 + b))^14*b*c^(13/2)*sgn(x) + 13728*(sqrt(c)*x - sqrt(c*x^2 + b))^12*b^2*c^(13/2)*sgn(x) + 4719*(sqrt(c)*x - sqrt(c*x^2 + b))^10*b^3*c^(13/2)*sgn(x) + 715*(sqrt(c)*x - sqrt(c*x^2 + b))^8*b^4*c^(13/2)*sgn(x) - 286*(sqrt(c)*x - sqrt(c*x^2 + b))^6*b^5*c^(13/2)*sgn(x) + 78*(sqrt(c)*x - sqrt(c*x^2 + b))^4*b^6*c^(13/2)*sgn(x) - 13*(sqrt(c)*x - sqrt(c*x^2 + b))^2*b^7*c^(13/2)*sgn(x) + b^8*c^(13/2)*sgn(x))/((sqrt(c)*x - sqrt(c*x^2 + b))^2 - b)^13","B",0
249,1,92,0,0.187319," ","integrate(x^6*(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{128 \, b^{\frac{13}{2}} \mathrm{sgn}\left(x\right)}{15015 \, c^{5}} + \frac{1155 \, {\left(c x^{2} + b\right)}^{\frac{13}{2}} \mathrm{sgn}\left(x\right) - 5460 \, {\left(c x^{2} + b\right)}^{\frac{11}{2}} b \mathrm{sgn}\left(x\right) + 10010 \, {\left(c x^{2} + b\right)}^{\frac{9}{2}} b^{2} \mathrm{sgn}\left(x\right) - 8580 \, {\left(c x^{2} + b\right)}^{\frac{7}{2}} b^{3} \mathrm{sgn}\left(x\right) + 3003 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} b^{4} \mathrm{sgn}\left(x\right)}{15015 \, c^{5}}"," ",0,"-128/15015*b^(13/2)*sgn(x)/c^5 + 1/15015*(1155*(c*x^2 + b)^(13/2)*sgn(x) - 5460*(c*x^2 + b)^(11/2)*b*sgn(x) + 10010*(c*x^2 + b)^(9/2)*b^2*sgn(x) - 8580*(c*x^2 + b)^(7/2)*b^3*sgn(x) + 3003*(c*x^2 + b)^(5/2)*b^4*sgn(x))/c^5","A",0
250,1,76,0,0.164666," ","integrate(x^4*(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\frac{16 \, b^{\frac{11}{2}} \mathrm{sgn}\left(x\right)}{1155 \, c^{4}} + \frac{105 \, {\left(c x^{2} + b\right)}^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 385 \, {\left(c x^{2} + b\right)}^{\frac{9}{2}} b \mathrm{sgn}\left(x\right) + 495 \, {\left(c x^{2} + b\right)}^{\frac{7}{2}} b^{2} \mathrm{sgn}\left(x\right) - 231 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} b^{3} \mathrm{sgn}\left(x\right)}{1155 \, c^{4}}"," ",0,"16/1155*b^(11/2)*sgn(x)/c^4 + 1/1155*(105*(c*x^2 + b)^(11/2)*sgn(x) - 385*(c*x^2 + b)^(9/2)*b*sgn(x) + 495*(c*x^2 + b)^(7/2)*b^2*sgn(x) - 231*(c*x^2 + b)^(5/2)*b^3*sgn(x))/c^4","A",0
251,1,60,0,0.160524," ","integrate(x^2*(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{8 \, b^{\frac{9}{2}} \mathrm{sgn}\left(x\right)}{315 \, c^{3}} + \frac{35 \, {\left(c x^{2} + b\right)}^{\frac{9}{2}} \mathrm{sgn}\left(x\right) - 90 \, {\left(c x^{2} + b\right)}^{\frac{7}{2}} b \mathrm{sgn}\left(x\right) + 63 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} b^{2} \mathrm{sgn}\left(x\right)}{315 \, c^{3}}"," ",0,"-8/315*b^(9/2)*sgn(x)/c^3 + 1/315*(35*(c*x^2 + b)^(9/2)*sgn(x) - 90*(c*x^2 + b)^(7/2)*b*sgn(x) + 63*(c*x^2 + b)^(5/2)*b^2*sgn(x))/c^3","A",0
252,1,44,0,0.164167," ","integrate((c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, b^{\frac{7}{2}} \mathrm{sgn}\left(x\right)}{35 \, c^{2}} + \frac{5 \, {\left(c x^{2} + b\right)}^{\frac{7}{2}} \mathrm{sgn}\left(x\right) - 7 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} b \mathrm{sgn}\left(x\right)}{35 \, c^{2}}"," ",0,"2/35*b^(7/2)*sgn(x)/c^2 + 1/35*(5*(c*x^2 + b)^(7/2)*sgn(x) - 7*(c*x^2 + b)^(5/2)*b*sgn(x))/c^2","A",0
253,1,27,0,0.155884," ","integrate((c*x^4+b*x^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{{\left(c x^{2} + b\right)}^{\frac{5}{2}} \mathrm{sgn}\left(x\right)}{5 \, c} - \frac{b^{\frac{5}{2}} \mathrm{sgn}\left(x\right)}{5 \, c}"," ",0,"1/5*(c*x^2 + b)^(5/2)*sgn(x)/c - 1/5*b^(5/2)*sgn(x)/c","A",0
254,1,89,0,0.165964," ","integrate((c*x^4+b*x^2)^(3/2)/x^4,x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + \frac{1}{3} \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} \mathrm{sgn}\left(x\right) + \sqrt{c x^{2} + b} b \mathrm{sgn}\left(x\right) - \frac{{\left(3 \, b^{2} \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + 4 \, \sqrt{-b} b^{\frac{3}{2}}\right)} \mathrm{sgn}\left(x\right)}{3 \, \sqrt{-b}}"," ",0,"b^2*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + 1/3*(c*x^2 + b)^(3/2)*sgn(x) + sqrt(c*x^2 + b)*b*sgn(x) - 1/3*(3*b^2*arctan(sqrt(b)/sqrt(-b)) + 4*sqrt(-b)*b^(3/2))*sgn(x)/sqrt(-b)","A",0
255,1,69,0,0.201451," ","integrate((c*x^4+b*x^2)^(3/2)/x^6,x, algorithm=""giac"")","\frac{\frac{3 \, b c^{2} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + 2 \, \sqrt{c x^{2} + b} c^{2} \mathrm{sgn}\left(x\right) - \frac{\sqrt{c x^{2} + b} b c \mathrm{sgn}\left(x\right)}{x^{2}}}{2 \, c}"," ",0,"1/2*(3*b*c^2*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + 2*sqrt(c*x^2 + b)*c^2*sgn(x) - sqrt(c*x^2 + b)*b*c*sgn(x)/x^2)/c","A",0
256,1,76,0,0.240147," ","integrate((c*x^4+b*x^2)^(3/2)/x^8,x, algorithm=""giac"")","\frac{\frac{3 \, c^{3} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} - \frac{5 \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} c^{3} \mathrm{sgn}\left(x\right) - 3 \, \sqrt{c x^{2} + b} b c^{3} \mathrm{sgn}\left(x\right)}{c^{2} x^{4}}}{8 \, c}"," ",0,"1/8*(3*c^3*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) - (5*(c*x^2 + b)^(3/2)*c^3*sgn(x) - 3*sqrt(c*x^2 + b)*b*c^3*sgn(x))/(c^2*x^4))/c","A",0
257,1,100,0,0.235138," ","integrate((c*x^4+b*x^2)^(3/2)/x^10,x, algorithm=""giac"")","-\frac{\frac{3 \, c^{4} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b} + \frac{3 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} c^{4} \mathrm{sgn}\left(x\right) + 8 \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} b c^{4} \mathrm{sgn}\left(x\right) - 3 \, \sqrt{c x^{2} + b} b^{2} c^{4} \mathrm{sgn}\left(x\right)}{b c^{3} x^{6}}}{48 \, c}"," ",0,"-1/48*(3*c^4*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b) + (3*(c*x^2 + b)^(5/2)*c^4*sgn(x) + 8*(c*x^2 + b)^(3/2)*b*c^4*sgn(x) - 3*sqrt(c*x^2 + b)*b^2*c^4*sgn(x))/(b*c^3*x^6))/c","A",0
258,1,119,0,0.232683," ","integrate((c*x^4+b*x^2)^(3/2)/x^12,x, algorithm=""giac"")","\frac{\frac{3 \, c^{5} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b^{2}} + \frac{3 \, {\left(c x^{2} + b\right)}^{\frac{7}{2}} c^{5} \mathrm{sgn}\left(x\right) - 11 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} b c^{5} \mathrm{sgn}\left(x\right) - 11 \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} b^{2} c^{5} \mathrm{sgn}\left(x\right) + 3 \, \sqrt{c x^{2} + b} b^{3} c^{5} \mathrm{sgn}\left(x\right)}{b^{2} c^{4} x^{8}}}{128 \, c}"," ",0,"1/128*(3*c^5*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b^2) + (3*(c*x^2 + b)^(7/2)*c^5*sgn(x) - 11*(c*x^2 + b)^(5/2)*b*c^5*sgn(x) - 11*(c*x^2 + b)^(3/2)*b^2*c^5*sgn(x) + 3*sqrt(c*x^2 + b)*b^3*c^5*sgn(x))/(b^2*c^4*x^8))/c","A",0
259,1,138,0,0.379467," ","integrate((c*x^4+b*x^2)^(3/2)/x^14,x, algorithm=""giac"")","-\frac{\frac{15 \, c^{6} \arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b^{3}} + \frac{15 \, {\left(c x^{2} + b\right)}^{\frac{9}{2}} c^{6} \mathrm{sgn}\left(x\right) - 70 \, {\left(c x^{2} + b\right)}^{\frac{7}{2}} b c^{6} \mathrm{sgn}\left(x\right) + 128 \, {\left(c x^{2} + b\right)}^{\frac{5}{2}} b^{2} c^{6} \mathrm{sgn}\left(x\right) + 70 \, {\left(c x^{2} + b\right)}^{\frac{3}{2}} b^{3} c^{6} \mathrm{sgn}\left(x\right) - 15 \, \sqrt{c x^{2} + b} b^{4} c^{6} \mathrm{sgn}\left(x\right)}{b^{3} c^{5} x^{10}}}{1280 \, c}"," ",0,"-1/1280*(15*c^6*arctan(sqrt(c*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b^3) + (15*(c*x^2 + b)^(9/2)*c^6*sgn(x) - 70*(c*x^2 + b)^(7/2)*b*c^6*sgn(x) + 128*(c*x^2 + b)^(5/2)*b^2*c^6*sgn(x) + 70*(c*x^2 + b)^(3/2)*b^3*c^6*sgn(x) - 15*sqrt(c*x^2 + b)*b^4*c^6*sgn(x))/(b^3*c^5*x^10))/c","A",0
260,1,87,0,0.223004," ","integrate(x^7/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{c x^{4} + b x^{2}} {\left(2 \, x^{2} {\left(\frac{4 \, x^{2}}{c} - \frac{5 \, b}{c^{2}}\right)} + \frac{15 \, b^{2}}{c^{3}}\right)} + \frac{5 \, b^{3} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{32 \, c^{\frac{7}{2}}}"," ",0,"1/48*sqrt(c*x^4 + b*x^2)*(2*x^2*(4*x^2/c - 5*b/c^2) + 15*b^2/c^3) + 5/32*b^3*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/c^(7/2)","A",0
261,1,73,0,0.215066," ","integrate(x^5/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{c x^{4} + b x^{2}} {\left(\frac{2 \, x^{2}}{c} - \frac{3 \, b}{c^{2}}\right)} - \frac{3 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/8*sqrt(c*x^4 + b*x^2)*(2*x^2/c - 3*b/c^2) - 3/16*b^2*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/c^(5/2)","A",0
262,1,59,0,0.198709," ","integrate(x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{4} + b x^{2}}}{2 \, c}"," ",0,"1/4*b*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/c^(3/2) + 1/2*sqrt(c*x^4 + b*x^2)/c","A",0
263,1,39,0,0.187699," ","integrate(x/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}}"," ",0,"-1/2*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/sqrt(c)","A",0
264,1,25,0,0.181486," ","integrate(1/x/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}}"," ",0,"1/(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))","A",0
265,1,57,0,0.185670," ","integrate(1/x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} + b}{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)}^{3}}"," ",0,"1/3*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) + b)/(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))^3","A",0
266,1,90,0,0.208918," ","integrate(1/x^5/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{20 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)}^{2} c + 15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} b \sqrt{c} + 3 \, b^{2}}{15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)}^{5}}"," ",0,"1/15*(20*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))^2*c + 15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*b*sqrt(c) + 3*b^2)/(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))^5","A",0
267,1,123,0,0.199831," ","integrate(1/x^7/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{70 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)}^{3} c^{\frac{3}{2}} + 84 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)}^{2} b c + 35 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} b^{2} \sqrt{c} + 5 \, b^{3}}{35 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)}^{7}}"," ",0,"1/35*(70*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))^3*c^(3/2) + 84*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))^2*b*c + 35*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*b^2*sqrt(c) + 5*b^3)/(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))^7","A",0
268,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^4/sqrt(c*x^4 + b*x^2), x)","F",0
269,1,31,0,0.185312," ","integrate(x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{b}}{{\left(\sqrt{c + \frac{b}{x^{2}}} - \frac{\sqrt{b}}{x}\right)}^{2} - c}"," ",0,"-2*sqrt(b)/((sqrt(c + b/x^2) - sqrt(b)/x)^2 - c)","A",0
270,1,46,0,0.169581," ","integrate(1/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + \frac{\arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right)}{\sqrt{-b} \mathrm{sgn}\left(x\right)}"," ",0,"-arctan(sqrt(b)/sqrt(-b))*sgn(x)/sqrt(-b) + arctan(sqrt(c*x^2 + b)/sqrt(-b))/(sqrt(-b)*sgn(x))","A",0
271,-2,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^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,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [64.3995612673,65,-85]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [66.1769613782,93,91]-1/2/b/x*sqrt(b*(1/x)^2+c)-2*c/4/b/sqrt(b)*ln(abs(sqrt(b*(1/x)^2+c)-sqrt(b)/x))","F(-2)",0
272,-2,0,0,0.000000," ","integrate(1/x^4/(c*x^4+b*x^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,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [64.3995612673,65,-85]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [66.1769613782,93,91]2*(-2*b^2/16/b^3/x/x+3*b*c/16/b^3)/x*sqrt(b*(1/x)^2+c)+6*c^2/16/b^2/sqrt(b)*ln(abs(sqrt(b*(1/x)^2+c)-sqrt(b)/x))","F(-2)",0
273,1,114,0,0.269014," ","integrate(x^9/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{c x^{4} + b x^{2}} {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{7 \, b}{c^{3}}\right)} - \frac{15 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}} - \frac{b^{3}}{{\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} c + b \sqrt{c}\right)} c^{3}}"," ",0,"1/8*sqrt(c*x^4 + b*x^2)*(2*x^2/c^2 - 7*b/c^3) - 15/16*b^2*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/c^(7/2) - b^3/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*c + b*sqrt(c))*c^3)","A",0
274,1,99,0,0.240309," ","integrate(x^7/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, b \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{5}{2}}} + \frac{b^{2}}{{\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} c + b \sqrt{c}\right)} c^{2}} + \frac{\sqrt{c x^{4} + b x^{2}}}{2 \, c^{2}}"," ",0,"3/4*b*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/c^(5/2) + b^2/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*c + b*sqrt(c))*c^2) + 1/2*sqrt(c*x^4 + b*x^2)/c^2","A",0
275,-2,0,0,0.000000," ","integrate(x^5/(c*x^4+b*x^2)^(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:Unable to divide, perhaps due to rounding error%%%{%%%{-2,[1]%%%},[2,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3]%%%}+%%%{-2,[0,4]%%%} / %%%{%%%{1,[2]%%%},[2,0]%%%}+%%%{%%{[%%%{-2,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1]%%%},[0,2]%%%} Error: Bad Argument Value","F(-2)",0
276,1,35,0,0.178789," ","integrate(x^3/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{{\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} + b\right)} \sqrt{c}}"," ",0,"1/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) + b)*sqrt(c))","A",0
277,1,28,0,0.194315," ","integrate(x/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, c x^{2}}{b^{2}} + \frac{1}{b}}{\sqrt{c x^{4} + b x^{2}}}"," ",0,"-(2*c*x^2/b^2 + 1/b)/sqrt(c*x^4 + b*x^2)","A",0
278,0,0,0,0.000000," ","integrate(1/x/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2)^(3/2)*x), x)","F",0
279,0,0,0,0.000000," ","integrate(1/x^3/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2)^(3/2)*x^3), x)","F",0
280,0,0,0,0.000000," ","integrate(1/x^5/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2)^(3/2)*x^5), x)","F",0
281,1,52,0,0.209316," ","integrate(x^6/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{b}}{{\left({\left(\sqrt{c + \frac{b}{x^{2}}} - \frac{\sqrt{b}}{x}\right)}^{2} - c\right)} c} + \frac{b}{\sqrt{c + \frac{b}{x^{2}}} c^{2} x}"," ",0,"-2*sqrt(b)/(((sqrt(c + b/x^2) - sqrt(b)/x)^2 - c)*c) + b/(sqrt(c + b/x^2)*c^2*x)","A",0
282,1,17,0,0.205932," ","integrate(x^4/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{\sqrt{c + \frac{b}{x^{2}}} c x}"," ",0,"-1/(sqrt(c + b/x^2)*c*x)","A",0
283,-2,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [64.3995612673,65,-85]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [66.1769613782,93,91]1/b/x*sqrt(b*(1/x)^2+c)/(b*(1/x)^2+c)+1/b/sqrt(b)*ln(abs(sqrt(b*(1/x)^2+c)-sqrt(b)/x))","F(-2)",0
284,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
285,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2)^(3/2)*x^2), x)","F",0
286,1,26,0,0.176285," ","integrate(x^3/(-4*x^4+3*x^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{-4 \, x^{4} + 3 \, x^{2}} + \frac{3}{32} \, \arcsin\left(\frac{8}{3} \, x^{2} - 1\right)"," ",0,"-1/8*sqrt(-4*x^4 + 3*x^2) + 3/32*arcsin(8/3*x^2 - 1)","A",0
287,1,27,0,0.206680," ","integrate(x^3/(-4*x^4-3*x^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{4 \, x^{4} + 3 \, x^{2}} i - \frac{3}{32} \, \arcsin\left(\frac{8}{3} \, x^{2} + 1\right)"," ",0,"-1/8*sqrt(4*x^4 + 3*x^2)*i - 3/32*arcsin(8/3*x^2 + 1)","A",0
288,1,41,0,0.171455," ","integrate(x^3/(4*x^4+3*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{4 \, x^{4} + 3 \, x^{2}} + \frac{3}{32} \, \log\left(8 \, x^{2} - 4 \, \sqrt{4 \, x^{4} + 3 \, x^{2}} + 3\right)"," ",0,"1/8*sqrt(4*x^4 + 3*x^2) + 3/32*log(8*x^2 - 4*sqrt(4*x^4 + 3*x^2) + 3)","A",0
289,1,42,0,0.172561," ","integrate(x^3/(4*x^4-3*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{4 \, x^{4} - 3 \, x^{2}} - \frac{3}{32} \, \log\left({\left| -8 \, x^{2} + 4 \, \sqrt{4 \, x^{4} - 3 \, x^{2}} + 3 \right|}\right)"," ",0,"1/8*sqrt(4*x^4 - 3*x^2) - 3/32*log(abs(-8*x^2 + 4*sqrt(4*x^4 - 3*x^2) + 3))","A",0
290,1,59,0,0.198760," ","integrate(x^3/(b*x^4+a*x^2)^(1/2),x, algorithm=""giac"")","\frac{a \log\left({\left| -2 \, {\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a x^{2}}\right)} \sqrt{b} - a \right|}\right)}{4 \, b^{\frac{3}{2}}} + \frac{\sqrt{b x^{4} + a x^{2}}}{2 \, b}"," ",0,"1/4*a*log(abs(-2*(sqrt(b)*x^2 - sqrt(b*x^4 + a*x^2))*sqrt(b) - a))/b^(3/2) + 1/2*sqrt(b*x^4 + a*x^2)/b","A",0
291,1,68,0,0.201241," ","integrate(x^3/(-b*x^4+a*x^2)^(1/2),x, algorithm=""giac"")","-\frac{a \log\left({\left| 2 \, {\left(\sqrt{-b} x^{2} - \sqrt{-b x^{4} + a x^{2}}\right)} \sqrt{-b} + a \right|}\right)}{4 \, \sqrt{-b} b} - \frac{\sqrt{-b x^{4} + a x^{2}}}{2 \, b}"," ",0,"-1/4*a*log(abs(2*(sqrt(-b)*x^2 - sqrt(-b*x^4 + a*x^2))*sqrt(-b) + a))/(sqrt(-b)*b) - 1/2*sqrt(-b*x^4 + a*x^2)/b","A",0
292,1,13,0,0.146974," ","integrate(x^(7/2)*(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{2}{17} \, c x^{\frac{17}{2}} + \frac{2}{13} \, b x^{\frac{13}{2}}"," ",0,"2/17*c*x^(17/2) + 2/13*b*x^(13/2)","A",0
293,1,13,0,0.154485," ","integrate(x^(5/2)*(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{2}{15} \, c x^{\frac{15}{2}} + \frac{2}{11} \, b x^{\frac{11}{2}}"," ",0,"2/15*c*x^(15/2) + 2/11*b*x^(11/2)","A",0
294,1,13,0,0.160528," ","integrate(x^(3/2)*(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{2}{13} \, c x^{\frac{13}{2}} + \frac{2}{9} \, b x^{\frac{9}{2}}"," ",0,"2/13*c*x^(13/2) + 2/9*b*x^(9/2)","A",0
295,1,13,0,0.212156," ","integrate(x^(1/2)*(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{7} \, b x^{\frac{7}{2}}"," ",0,"2/11*c*x^(11/2) + 2/7*b*x^(7/2)","A",0
296,1,13,0,0.150328," ","integrate((c*x^4+b*x^2)/x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, c x^{\frac{9}{2}} + \frac{2}{5} \, b x^{\frac{5}{2}}"," ",0,"2/9*c*x^(9/2) + 2/5*b*x^(5/2)","A",0
297,1,13,0,0.199941," ","integrate((c*x^4+b*x^2)/x^(3/2),x, algorithm=""giac"")","\frac{2}{7} \, c x^{\frac{7}{2}} + \frac{2}{3} \, b x^{\frac{3}{2}}"," ",0,"2/7*c*x^(7/2) + 2/3*b*x^(3/2)","A",0
298,1,13,0,0.153031," ","integrate((c*x^4+b*x^2)/x^(5/2),x, algorithm=""giac"")","\frac{2}{5} \, c x^{\frac{5}{2}} + 2 \, b \sqrt{x}"," ",0,"2/5*c*x^(5/2) + 2*b*sqrt(x)","A",0
299,1,13,0,0.162953," ","integrate((c*x^4+b*x^2)/x^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, c x^{\frac{3}{2}} - \frac{2 \, b}{\sqrt{x}}"," ",0,"2/3*c*x^(3/2) - 2*b/sqrt(x)","A",0
300,1,24,0,0.147160," ","integrate(x^(7/2)*(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{2}{25} \, c^{2} x^{\frac{25}{2}} + \frac{4}{21} \, b c x^{\frac{21}{2}} + \frac{2}{17} \, b^{2} x^{\frac{17}{2}}"," ",0,"2/25*c^2*x^(25/2) + 4/21*b*c*x^(21/2) + 2/17*b^2*x^(17/2)","A",0
301,1,24,0,0.150971," ","integrate(x^(5/2)*(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{19} \, b c x^{\frac{19}{2}} + \frac{2}{15} \, b^{2} x^{\frac{15}{2}}"," ",0,"2/23*c^2*x^(23/2) + 4/19*b*c*x^(19/2) + 2/15*b^2*x^(15/2)","A",0
302,1,24,0,0.158741," ","integrate(x^(3/2)*(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{17} \, b c x^{\frac{17}{2}} + \frac{2}{13} \, b^{2} x^{\frac{13}{2}}"," ",0,"2/21*c^2*x^(21/2) + 4/17*b*c*x^(17/2) + 2/13*b^2*x^(13/2)","A",0
303,1,24,0,0.144675," ","integrate(x^(1/2)*(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{2}{19} \, c^{2} x^{\frac{19}{2}} + \frac{4}{15} \, b c x^{\frac{15}{2}} + \frac{2}{11} \, b^{2} x^{\frac{11}{2}}"," ",0,"2/19*c^2*x^(19/2) + 4/15*b*c*x^(15/2) + 2/11*b^2*x^(11/2)","A",0
304,1,24,0,0.150908," ","integrate((c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, c^{2} x^{\frac{17}{2}} + \frac{4}{13} \, b c x^{\frac{13}{2}} + \frac{2}{9} \, b^{2} x^{\frac{9}{2}}"," ",0,"2/17*c^2*x^(17/2) + 4/13*b*c*x^(13/2) + 2/9*b^2*x^(9/2)","A",0
305,1,24,0,0.152138," ","integrate((c*x^4+b*x^2)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b c x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} x^{\frac{7}{2}}"," ",0,"2/15*c^2*x^(15/2) + 4/11*b*c*x^(11/2) + 2/7*b^2*x^(7/2)","A",0
306,1,24,0,0.148742," ","integrate((c*x^4+b*x^2)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{9} \, b c x^{\frac{9}{2}} + \frac{2}{5} \, b^{2} x^{\frac{5}{2}}"," ",0,"2/13*c^2*x^(13/2) + 4/9*b*c*x^(9/2) + 2/5*b^2*x^(5/2)","A",0
307,1,24,0,0.146927," ","integrate((c*x^4+b*x^2)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{11} \, c^{2} x^{\frac{11}{2}} + \frac{4}{7} \, b c x^{\frac{7}{2}} + \frac{2}{3} \, b^{2} x^{\frac{3}{2}}"," ",0,"2/11*c^2*x^(11/2) + 4/7*b*c*x^(7/2) + 2/3*b^2*x^(3/2)","A",0
308,1,35,0,0.181585," ","integrate(x^(7/2)*(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{2}{33} \, c^{3} x^{\frac{33}{2}} + \frac{6}{29} \, b c^{2} x^{\frac{29}{2}} + \frac{6}{25} \, b^{2} c x^{\frac{25}{2}} + \frac{2}{21} \, b^{3} x^{\frac{21}{2}}"," ",0,"2/33*c^3*x^(33/2) + 6/29*b*c^2*x^(29/2) + 6/25*b^2*c*x^(25/2) + 2/21*b^3*x^(21/2)","A",0
309,1,35,0,0.167440," ","integrate(x^(5/2)*(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{2}{31} \, c^{3} x^{\frac{31}{2}} + \frac{2}{9} \, b c^{2} x^{\frac{27}{2}} + \frac{6}{23} \, b^{2} c x^{\frac{23}{2}} + \frac{2}{19} \, b^{3} x^{\frac{19}{2}}"," ",0,"2/31*c^3*x^(31/2) + 2/9*b*c^2*x^(27/2) + 6/23*b^2*c*x^(23/2) + 2/19*b^3*x^(19/2)","A",0
310,1,35,0,0.153835," ","integrate(x^(3/2)*(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{2}{29} \, c^{3} x^{\frac{29}{2}} + \frac{6}{25} \, b c^{2} x^{\frac{25}{2}} + \frac{2}{7} \, b^{2} c x^{\frac{21}{2}} + \frac{2}{17} \, b^{3} x^{\frac{17}{2}}"," ",0,"2/29*c^3*x^(29/2) + 6/25*b*c^2*x^(25/2) + 2/7*b^2*c*x^(21/2) + 2/17*b^3*x^(17/2)","A",0
311,1,35,0,0.151214," ","integrate(x^(1/2)*(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{2}{27} \, c^{3} x^{\frac{27}{2}} + \frac{6}{23} \, b c^{2} x^{\frac{23}{2}} + \frac{6}{19} \, b^{2} c x^{\frac{19}{2}} + \frac{2}{15} \, b^{3} x^{\frac{15}{2}}"," ",0,"2/27*c^3*x^(27/2) + 6/23*b*c^2*x^(23/2) + 6/19*b^2*c*x^(19/2) + 2/15*b^3*x^(15/2)","A",0
312,1,35,0,0.150782," ","integrate((c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{25} \, c^{3} x^{\frac{25}{2}} + \frac{2}{7} \, b c^{2} x^{\frac{21}{2}} + \frac{6}{17} \, b^{2} c x^{\frac{17}{2}} + \frac{2}{13} \, b^{3} x^{\frac{13}{2}}"," ",0,"2/25*c^3*x^(25/2) + 2/7*b*c^2*x^(21/2) + 6/17*b^2*c*x^(17/2) + 2/13*b^3*x^(13/2)","A",0
313,1,35,0,0.152340," ","integrate((c*x^4+b*x^2)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{23} \, c^{3} x^{\frac{23}{2}} + \frac{6}{19} \, b c^{2} x^{\frac{19}{2}} + \frac{2}{5} \, b^{2} c x^{\frac{15}{2}} + \frac{2}{11} \, b^{3} x^{\frac{11}{2}}"," ",0,"2/23*c^3*x^(23/2) + 6/19*b*c^2*x^(19/2) + 2/5*b^2*c*x^(15/2) + 2/11*b^3*x^(11/2)","A",0
314,1,35,0,0.150612," ","integrate((c*x^4+b*x^2)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{21} \, c^{3} x^{\frac{21}{2}} + \frac{6}{17} \, b c^{2} x^{\frac{17}{2}} + \frac{6}{13} \, b^{2} c x^{\frac{13}{2}} + \frac{2}{9} \, b^{3} x^{\frac{9}{2}}"," ",0,"2/21*c^3*x^(21/2) + 6/17*b*c^2*x^(17/2) + 6/13*b^2*c*x^(13/2) + 2/9*b^3*x^(9/2)","A",0
315,1,35,0,0.177930," ","integrate((c*x^4+b*x^2)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{19} \, c^{3} x^{\frac{19}{2}} + \frac{2}{5} \, b c^{2} x^{\frac{15}{2}} + \frac{6}{11} \, b^{2} c x^{\frac{11}{2}} + \frac{2}{7} \, b^{3} x^{\frac{7}{2}}"," ",0,"2/19*c^3*x^(19/2) + 2/5*b*c^2*x^(15/2) + 6/11*b^2*c*x^(11/2) + 2/7*b^3*x^(7/2)","A",0
316,1,197,0,0.174427," ","integrate(x^(13/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{5}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{5}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{5}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{5}} + \frac{2 \, {\left(3 \, c^{6} x^{\frac{7}{2}} - 7 \, b c^{5} x^{\frac{3}{2}}\right)}}{21 \, c^{7}}"," ",0,"1/2*sqrt(2)*(b*c^3)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^5 + 1/2*sqrt(2)*(b*c^3)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^5 - 1/4*sqrt(2)*(b*c^3)^(3/4)*b*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^5 + 1/4*sqrt(2)*(b*c^3)^(3/4)*b*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^5 + 2/21*(3*c^6*x^(7/2) - 7*b*c^5*x^(3/2))/c^7","A",0
317,1,196,0,0.167844," ","integrate(x^(11/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{3}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{3}} + \frac{2 \, {\left(c^{4} x^{\frac{5}{2}} - 5 \, b c^{3} \sqrt{x}\right)}}{5 \, c^{5}}"," ",0,"1/2*sqrt(2)*(b*c^3)^(1/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^3 + 1/2*sqrt(2)*(b*c^3)^(1/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^3 + 1/4*sqrt(2)*(b*c^3)^(1/4)*b*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^3 - 1/4*sqrt(2)*(b*c^3)^(1/4)*b*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^3 + 2/5*(c^4*x^(5/2) - 5*b*c^3*sqrt(x))/c^5","A",0
318,1,178,0,0.176901," ","integrate(x^(9/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{2 \, x^{\frac{3}{2}}}{3 \, c} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{4}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{4}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{4}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{4}}"," ",0,"2/3*x^(3/2)/c - 1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^4 - 1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^4 + 1/4*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^4 - 1/4*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^4","A",0
319,1,178,0,0.164569," ","integrate(x^(7/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{2}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, c^{2}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{2}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, c^{2}} + \frac{2 \, \sqrt{x}}{c}"," ",0,"-1/2*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^2 - 1/2*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^2 - 1/4*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^2 + 1/4*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^2 + 2*sqrt(x)/c","A",0
320,1,182,0,0.194477," ","integrate(x^(5/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b c^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b c^{3}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b c^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b c^{3}}"," ",0,"1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b*c^3) + 1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b*c^3) - 1/4*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^3) + 1/4*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^3)","A",0
321,1,182,0,0.160507," ","integrate(x^(3/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b c} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b c} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b c} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b c}"," ",0,"1/2*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b*c) + 1/2*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b*c) + 1/4*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c) - 1/4*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c)","A",0
322,1,190,0,0.167157," ","integrate(x^(1/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{2}{b \sqrt{x}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{2} c^{2}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{2} c^{2}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{2} c^{2}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{2} c^{2}}"," ",0,"-2/(b*sqrt(x)) - 1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^2) - 1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^2) + 1/4*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^2) - 1/4*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^2)","A",0
323,1,178,0,0.163980," ","integrate(1/(c*x^4+b*x^2)/x^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{2}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{2}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{2}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{2}} - \frac{2}{3 \, b x^{\frac{3}{2}}}"," ",0,"-1/2*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^2 - 1/2*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^2 - 1/4*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^2 + 1/4*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^2 - 2/3/(b*x^(3/2))","A",0
324,1,200,0,0.166662," ","integrate(1/x^(3/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{3} c} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{3} c} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{3} c} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{3} c} + \frac{2 \, {\left(5 \, c x^{2} - b\right)}}{5 \, b^{2} x^{\frac{5}{2}}}"," ",0,"1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^3*c) + 1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^3*c) - 1/4*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c) + 1/4*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c) + 2/5*(5*c*x^2 - b)/(b^2*x^(5/2))","A",0
325,1,192,0,0.197842," ","integrate(1/x^(5/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{3}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{3}} + \frac{2 \, {\left(7 \, c x^{2} - 3 \, b\right)}}{21 \, b^{2} x^{\frac{7}{2}}}"," ",0,"1/2*sqrt(2)*(b*c^3)^(1/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^3 + 1/2*sqrt(2)*(b*c^3)^(1/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^3 + 1/4*sqrt(2)*(b*c^3)^(1/4)*c*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^3 - 1/4*sqrt(2)*(b*c^3)^(1/4)*c*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^3 + 2/21*(7*c*x^2 - 3*b)/(b^2*x^(7/2))","A",0
326,1,199,0,0.178105," ","integrate(1/x^(7/2)/(c*x^4+b*x^2),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{4}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{2 \, b^{4}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{4}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{4 \, b^{4}} - \frac{2 \, {\left(45 \, c^{2} x^{4} - 9 \, b c x^{2} + 5 \, b^{2}\right)}}{45 \, b^{3} x^{\frac{9}{2}}}"," ",0,"-1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^4 - 1/2*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^4 + 1/4*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^4 - 1/4*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^4 - 2/45*(45*c^2*x^4 - 9*b*c*x^2 + 5*b^2)/(b^3*x^(9/2))","A",0
327,1,216,0,0.195494," ","integrate(x^(19/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, c^{4}} + \frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, c^{4}} + \frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, c^{4}} - \frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, c^{4}} - \frac{b^{2} \sqrt{x}}{2 \, {\left(c x^{2} + b\right)} c^{3}} + \frac{2 \, {\left(c^{8} x^{\frac{5}{2}} - 10 \, b c^{7} \sqrt{x}\right)}}{5 \, c^{10}}"," ",0,"9/8*sqrt(2)*(b*c^3)^(1/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^4 + 9/8*sqrt(2)*(b*c^3)^(1/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^4 + 9/16*sqrt(2)*(b*c^3)^(1/4)*b*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^4 - 9/16*sqrt(2)*(b*c^3)^(1/4)*b*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^4 - 1/2*b^2*sqrt(x)/((c*x^2 + b)*c^3) + 2/5*(c^8*x^(5/2) - 10*b*c^7*sqrt(x))/c^10","A",0
328,1,196,0,0.180429," ","integrate(x^(17/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{b x^{\frac{3}{2}}}{2 \, {\left(c x^{2} + b\right)} c^{2}} + \frac{2 \, x^{\frac{3}{2}}}{3 \, c^{2}} - \frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, c^{5}} - \frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, c^{5}} + \frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, c^{5}} - \frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, c^{5}}"," ",0,"1/2*b*x^(3/2)/((c*x^2 + b)*c^2) + 2/3*x^(3/2)/c^2 - 7/8*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^5 - 7/8*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^5 + 7/16*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^5 - 7/16*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^5","A",0
329,1,196,0,0.197913," ","integrate(x^(15/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, c^{3}} - \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, c^{3}} - \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, c^{3}} + \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, c^{3}} + \frac{b \sqrt{x}}{2 \, {\left(c x^{2} + b\right)} c^{2}} + \frac{2 \, \sqrt{x}}{c^{2}}"," ",0,"-5/8*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^3 - 5/8*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^3 - 5/16*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^3 + 5/16*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^3 + 1/2*b*sqrt(x)/((c*x^2 + b)*c^2) + 2*sqrt(x)/c^2","A",0
330,1,199,0,0.182475," ","integrate(x^(13/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{x^{\frac{3}{2}}}{2 \, {\left(c x^{2} + b\right)} c} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b c^{4}} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b c^{4}} - \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b c^{4}} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b c^{4}}"," ",0,"-1/2*x^(3/2)/((c*x^2 + b)*c) + 3/8*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b*c^4) + 3/8*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b*c^4) - 3/16*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^4) + 3/16*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^4)","A",0
331,1,199,0,0.169867," ","integrate(x^(11/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b c^{2}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b c^{2}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b c^{2}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b c^{2}} - \frac{\sqrt{x}}{2 \, {\left(c x^{2} + b\right)} c}"," ",0,"1/8*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b*c^2) + 1/8*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b*c^2) + 1/16*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^2) - 1/16*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^2) - 1/2*sqrt(x)/((c*x^2 + b)*c)","A",0
332,1,199,0,0.180589," ","integrate(x^(9/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{x^{\frac{3}{2}}}{2 \, {\left(c x^{2} + b\right)} b} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{2} c^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{2} c^{3}} - \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{2} c^{3}} + \frac{\sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{2} c^{3}}"," ",0,"1/2*x^(3/2)/((c*x^2 + b)*b) + 1/8*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^3) + 1/8*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^3) - 1/16*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^3) + 1/16*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^3)","A",0
333,1,199,0,0.187109," ","integrate(x^(7/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{2} c} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{2} c} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{2} c} - \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{2} c} + \frac{\sqrt{x}}{2 \, {\left(c x^{2} + b\right)} b}"," ",0,"3/8*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^2*c) + 3/8*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^2*c) + 3/16*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c) - 3/16*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c) + 1/2*sqrt(x)/((c*x^2 + b)*b)","A",0
334,1,210,0,0.171062," ","integrate(x^(5/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{5 \, c x^{2} + 4 \, b}{2 \, {\left(c x^{\frac{5}{2}} + b \sqrt{x}\right)} b^{2}} - \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{3} c^{2}} - \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{3} c^{2}} + \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{3} c^{2}} - \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{3} c^{2}}"," ",0,"-1/2*(5*c*x^2 + 4*b)/((c*x^(5/2) + b*sqrt(x))*b^2) - 5/8*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^3*c^2) - 5/8*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^3*c^2) + 5/16*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c^2) - 5/16*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c^2)","A",0
335,1,196,0,0.183908," ","integrate(x^(3/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{3}} - \frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{3}} - \frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{3}} + \frac{7 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{3}} - \frac{c \sqrt{x}}{2 \, {\left(c x^{2} + b\right)} b^{2}} - \frac{2}{3 \, b^{2} x^{\frac{3}{2}}}"," ",0,"-7/8*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^3 - 7/8*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^3 - 7/16*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^3 + 7/16*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^3 - 1/2*c*sqrt(x)/((c*x^2 + b)*b^2) - 2/3/(b^2*x^(3/2))","A",0
336,1,220,0,0.193593," ","integrate(x^(1/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{c^{2} x^{\frac{3}{2}}}{2 \, {\left(c x^{2} + b\right)} b^{3}} + \frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{4} c} + \frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{4} c} - \frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{4} c} + \frac{9 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{4} c} + \frac{2 \, {\left(10 \, c x^{2} - b\right)}}{5 \, b^{3} x^{\frac{5}{2}}}"," ",0,"1/2*c^2*x^(3/2)/((c*x^2 + b)*b^3) + 9/8*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^4*c) + 9/8*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^4*c) - 9/16*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^4*c) + 9/16*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^4*c) + 2/5*(10*c*x^2 - b)/(b^3*x^(5/2))","A",0
337,1,212,0,0.169025," ","integrate(1/(c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""giac"")","\frac{11 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{4}} + \frac{11 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{4}} + \frac{11 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{4}} - \frac{11 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{4}} + \frac{c^{2} \sqrt{x}}{2 \, {\left(c x^{2} + b\right)} b^{3}} + \frac{2 \, {\left(14 \, c x^{2} - 3 \, b\right)}}{21 \, b^{3} x^{\frac{7}{2}}}"," ",0,"11/8*sqrt(2)*(b*c^3)^(1/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^4 + 11/8*sqrt(2)*(b*c^3)^(1/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^4 + 11/16*sqrt(2)*(b*c^3)^(1/4)*c*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^4 - 11/16*sqrt(2)*(b*c^3)^(1/4)*c*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^4 + 1/2*c^2*sqrt(x)/((c*x^2 + b)*b^3) + 2/21*(14*c*x^2 - 3*b)/(b^3*x^(7/2))","A",0
338,1,219,0,0.173527," ","integrate(1/x^(3/2)/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","-\frac{c^{3} x^{\frac{3}{2}}}{2 \, {\left(c x^{2} + b\right)} b^{4}} - \frac{13 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{5}} - \frac{13 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{8 \, b^{5}} + \frac{13 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{5}} - \frac{13 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{16 \, b^{5}} - \frac{2 \, {\left(135 \, c^{2} x^{4} - 18 \, b c x^{2} + 5 \, b^{2}\right)}}{45 \, b^{4} x^{\frac{9}{2}}}"," ",0,"-1/2*c^3*x^(3/2)/((c*x^2 + b)*b^4) - 13/8*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^5 - 13/8*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^5 + 13/16*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^5 - 13/16*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^5 - 2/45*(135*c^2*x^4 - 18*b*c*x^2 + 5*b^2)/(b^4*x^(9/2))","A",0
339,1,208,0,0.183767," ","integrate(x^(23/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, c^{4}} - \frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, c^{4}} - \frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, c^{4}} + \frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, c^{4}} + \frac{2 \, \sqrt{x}}{c^{3}} + \frac{17 \, b c x^{\frac{5}{2}} + 13 \, b^{2} \sqrt{x}}{16 \, {\left(c x^{2} + b\right)}^{2} c^{3}}"," ",0,"-45/64*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/c^4 - 45/64*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/c^4 - 45/128*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^4 + 45/128*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/c^4 + 2*sqrt(x)/c^3 + 1/16*(17*b*c*x^(5/2) + 13*b^2*sqrt(x))/((c*x^2 + b)^2*c^3)","A",0
340,1,209,0,0.219744," ","integrate(x^(21/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{11 \, c x^{\frac{7}{2}} + 7 \, b x^{\frac{3}{2}}}{16 \, {\left(c x^{2} + b\right)}^{2} c^{2}} + \frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b c^{5}} + \frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b c^{5}} - \frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b c^{5}} + \frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b c^{5}}"," ",0,"-1/16*(11*c*x^(7/2) + 7*b*x^(3/2))/((c*x^2 + b)^2*c^2) + 21/64*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b*c^5) + 21/64*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b*c^5) - 21/128*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^5) + 21/128*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^5)","A",0
341,1,209,0,0.180063," ","integrate(x^(19/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b c^{3}} + \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b c^{3}} + \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b c^{3}} - \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b c^{3}} - \frac{9 \, c x^{\frac{5}{2}} + 5 \, b \sqrt{x}}{16 \, {\left(c x^{2} + b\right)}^{2} c^{2}}"," ",0,"5/64*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b*c^3) + 5/64*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b*c^3) + 5/128*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^3) - 5/128*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b*c^3) - 1/16*(9*c*x^(5/2) + 5*b*sqrt(x))/((c*x^2 + b)^2*c^2)","A",0
342,1,212,0,0.184825," ","integrate(x^(17/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{3 \, c x^{\frac{7}{2}} - b x^{\frac{3}{2}}}{16 \, {\left(c x^{2} + b\right)}^{2} b c} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{2} c^{4}} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{2} c^{4}} - \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{2} c^{4}} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{2} c^{4}}"," ",0,"1/16*(3*c*x^(7/2) - b*x^(3/2))/((c*x^2 + b)^2*b*c) + 3/64*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^4) + 3/64*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^4) - 3/128*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^4) + 3/128*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^4)","A",0
343,1,211,0,0.177003," ","integrate(x^(15/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{2} c^{2}} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{2} c^{2}} + \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{2} c^{2}} - \frac{3 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{2} c^{2}} + \frac{c x^{\frac{5}{2}} - 3 \, b \sqrt{x}}{16 \, {\left(c x^{2} + b\right)}^{2} b c}"," ",0,"3/64*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^2) + 3/64*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^2*c^2) + 3/128*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^2) - 3/128*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^2*c^2) + 1/16*(c*x^(5/2) - 3*b*sqrt(x))/((c*x^2 + b)^2*b*c)","A",0
344,1,209,0,0.197454," ","integrate(x^(13/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{5 \, c x^{\frac{7}{2}} + 9 \, b x^{\frac{3}{2}}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{2}} + \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{3} c^{3}} + \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{3} c^{3}} - \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{3} c^{3}} + \frac{5 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{3} c^{3}}"," ",0,"1/16*(5*c*x^(7/2) + 9*b*x^(3/2))/((c*x^2 + b)^2*b^2) + 5/64*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^3*c^3) + 5/64*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^3*c^3) - 5/128*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c^3) + 5/128*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c^3)","A",0
345,1,209,0,0.207314," ","integrate(x^(11/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{3} c} + \frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{3} c} + \frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{3} c} - \frac{21 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{3} c} + \frac{7 \, c x^{\frac{5}{2}} + 11 \, b \sqrt{x}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{2}}"," ",0,"21/64*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^3*c) + 21/64*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^3*c) + 21/128*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c) - 21/128*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^3*c) + 1/16*(7*c*x^(5/2) + 11*b*sqrt(x))/((c*x^2 + b)^2*b^2)","A",0
346,1,220,0,0.186551," ","integrate(x^(9/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{2}{b^{3} \sqrt{x}} - \frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{4} c^{2}} - \frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{4} c^{2}} + \frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{4} c^{2}} - \frac{45 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{4} c^{2}} - \frac{13 \, c^{2} x^{\frac{7}{2}} + 17 \, b c x^{\frac{3}{2}}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{3}}"," ",0,"-2/(b^3*sqrt(x)) - 45/64*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^4*c^2) - 45/64*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^4*c^2) + 45/128*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^4*c^2) - 45/128*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^4*c^2) - 1/16*(13*c^2*x^(7/2) + 17*b*c*x^(3/2))/((c*x^2 + b)^2*b^3)","A",0
347,1,208,0,0.181792," ","integrate(x^(7/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{77 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{4}} - \frac{77 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{4}} - \frac{77 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{4}} + \frac{77 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{4}} - \frac{15 \, c^{2} x^{\frac{5}{2}} + 19 \, b c \sqrt{x}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{3}} - \frac{2}{3 \, b^{3} x^{\frac{3}{2}}}"," ",0,"-77/64*sqrt(2)*(b*c^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^4 - 77/64*sqrt(2)*(b*c^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^4 - 77/128*sqrt(2)*(b*c^3)^(1/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^4 + 77/128*sqrt(2)*(b*c^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^4 - 1/16*(15*c^2*x^(5/2) + 19*b*c*sqrt(x))/((c*x^2 + b)^2*b^3) - 2/3/(b^3*x^(3/2))","A",0
348,1,232,0,0.269129," ","integrate(x^(5/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{117 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{5} c} + \frac{117 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{5} c} - \frac{117 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{5} c} + \frac{117 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{5} c} + \frac{21 \, c^{3} x^{\frac{7}{2}} + 25 \, b c^{2} x^{\frac{3}{2}}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{4}} + \frac{2 \, {\left(15 \, c x^{2} - b\right)}}{5 \, b^{4} x^{\frac{5}{2}}}"," ",0,"117/64*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/(b^5*c) + 117/64*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/(b^5*c) - 117/128*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^5*c) + 117/128*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/(b^5*c) + 1/16*(21*c^3*x^(7/2) + 25*b*c^2*x^(3/2))/((c*x^2 + b)^2*b^4) + 2/5*(15*c*x^2 - b)/(b^4*x^(5/2))","A",0
349,1,224,0,0.206552," ","integrate(x^(3/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{165 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{5}} + \frac{165 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{5}} + \frac{165 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{5}} - \frac{165 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{5}} + \frac{23 \, c^{3} x^{\frac{5}{2}} + 27 \, b c^{2} \sqrt{x}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{4}} + \frac{2 \, {\left(7 \, c x^{2} - b\right)}}{7 \, b^{4} x^{\frac{7}{2}}}"," ",0,"165/64*sqrt(2)*(b*c^3)^(1/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^5 + 165/64*sqrt(2)*(b*c^3)^(1/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^5 + 165/128*sqrt(2)*(b*c^3)^(1/4)*c*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^5 - 165/128*sqrt(2)*(b*c^3)^(1/4)*c*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^5 + 1/16*(23*c^3*x^(5/2) + 27*b*c^2*sqrt(x))/((c*x^2 + b)^2*b^4) + 2/7*(7*c*x^2 - b)/(b^4*x^(7/2))","A",0
350,1,231,0,0.185912," ","integrate(x^(1/2)/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","-\frac{221 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{6}} - \frac{221 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{6}} + \frac{221 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{6}} - \frac{221 \, \sqrt{2} \left(b c^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{6}} - \frac{29 \, c^{4} x^{\frac{7}{2}} + 33 \, b c^{3} x^{\frac{3}{2}}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{5}} - \frac{2 \, {\left(270 \, c^{2} x^{4} - 27 \, b c x^{2} + 5 \, b^{2}\right)}}{45 \, b^{5} x^{\frac{9}{2}}}"," ",0,"-221/64*sqrt(2)*(b*c^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^6 - 221/64*sqrt(2)*(b*c^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^6 + 221/128*sqrt(2)*(b*c^3)^(3/4)*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^6 - 221/128*sqrt(2)*(b*c^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^6 - 1/16*(29*c^4*x^(7/2) + 33*b*c^3*x^(3/2))/((c*x^2 + b)^2*b^5) - 2/45*(270*c^2*x^4 - 27*b*c*x^2 + 5*b^2)/(b^5*x^(9/2))","A",0
351,1,243,0,0.171219," ","integrate(1/(c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""giac"")","-\frac{285 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{6}} - \frac{285 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{b}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{b}{c}\right)^{\frac{1}{4}}}\right)}{64 \, b^{6}} - \frac{285 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c^{2} \log\left(\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{6}} + \frac{285 \, \sqrt{2} \left(b c^{3}\right)^{\frac{1}{4}} c^{2} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{b}{c}\right)^{\frac{1}{4}} + x + \sqrt{\frac{b}{c}}\right)}{128 \, b^{6}} - \frac{31 \, c^{4} x^{\frac{5}{2}} + 35 \, b c^{3} \sqrt{x}}{16 \, {\left(c x^{2} + b\right)}^{2} b^{5}} - \frac{2 \, {\left(154 \, c^{2} x^{4} - 33 \, b c x^{2} + 7 \, b^{2}\right)}}{77 \, b^{5} x^{\frac{11}{2}}}"," ",0,"-285/64*sqrt(2)*(b*c^3)^(1/4)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) + 2*sqrt(x))/(b/c)^(1/4))/b^6 - 285/64*sqrt(2)*(b*c^3)^(1/4)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(b/c)^(1/4) - 2*sqrt(x))/(b/c)^(1/4))/b^6 - 285/128*sqrt(2)*(b*c^3)^(1/4)*c^2*log(sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^6 + 285/128*sqrt(2)*(b*c^3)^(1/4)*c^2*log(-sqrt(2)*sqrt(x)*(b/c)^(1/4) + x + sqrt(b/c))/b^6 - 1/16*(31*c^4*x^(5/2) + 35*b*c^3*sqrt(x))/((c*x^2 + b)^2*b^5) - 2/77*(154*c^2*x^4 - 33*b*c*x^2 + 7*b^2)/(b^5*x^(11/2))","A",0
352,0,0,0,0.000000," ","integrate(x^(7/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2}} x^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)*x^(7/2), x)","F",0
353,0,0,0,0.000000," ","integrate(x^(5/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2}} x^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)*x^(5/2), x)","F",0
354,0,0,0,0.000000," ","integrate(x^(3/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2}} x^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)*x^(3/2), x)","F",0
355,0,0,0,0.000000," ","integrate(x^(1/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2}} \sqrt{x}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)*sqrt(x), x)","F",0
356,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{\sqrt{x}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/sqrt(x), x)","F",0
357,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^(3/2), x)","F",0
358,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^(5/2), x)","F",0
359,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^(7/2), x)","F",0
360,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(9/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^(9/2), x)","F",0
361,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(11/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^(11/2), x)","F",0
362,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(13/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{13}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^(13/2), x)","F",0
363,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^(15/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{\frac{15}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^(15/2), x)","F",0
364,0,0,0,0.000000," ","integrate(x^(3/2)*(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)*x^(3/2), x)","F",0
365,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)*x^(1/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} \sqrt{x}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)*sqrt(x), x)","F",0
366,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{\sqrt{x}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/sqrt(x), x)","F",0
367,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(3/2), x)","F",0
368,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(5/2), x)","F",0
369,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(7/2), x)","F",0
370,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(9/2), x)","F",0
371,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(11/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(11/2), x)","F",0
372,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(13/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(13/2), x)","F",0
373,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(15/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(15/2), x)","F",0
374,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(17/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{17}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(17/2), x)","F",0
375,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(19/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{19}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(19/2), x)","F",0
376,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(21/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{21}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(21/2), x)","F",0
377,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^(23/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{\frac{23}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^(23/2), x)","F",0
378,0,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{13}{2}}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^(13/2)/sqrt(c*x^4 + b*x^2), x)","F",0
379,0,0,0,0.000000," ","integrate(x^(11/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{11}{2}}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^(11/2)/sqrt(c*x^4 + b*x^2), x)","F",0
380,0,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{9}{2}}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^(9/2)/sqrt(c*x^4 + b*x^2), x)","F",0
381,0,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{7}{2}}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^(7/2)/sqrt(c*x^4 + b*x^2), x)","F",0
382,0,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{5}{2}}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^(5/2)/sqrt(c*x^4 + b*x^2), x)","F",0
383,0,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{3}{2}}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^(3/2)/sqrt(c*x^4 + b*x^2), x)","F",0
384,0,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(sqrt(x)/sqrt(c*x^4 + b*x^2), x)","F",0
385,0,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} \sqrt{x}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*sqrt(x)), x)","F",0
386,0,0,0,0.000000," ","integrate(1/x^(3/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^(3/2)), x)","F",0
387,0,0,0,0.000000," ","integrate(1/x^(5/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^(5/2)), x)","F",0
388,0,0,0,0.000000," ","integrate(1/x^(7/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^(7/2)), x)","F",0
389,0,0,0,0.000000," ","integrate(1/x^(9/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^(9/2)), x)","F",0
390,0,0,0,0.000000," ","integrate(1/x^(11/2)/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^(11/2)), x)","F",0
391,0,0,0,0.000000," ","integrate(x^(17/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{17}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(17/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
392,0,0,0,0.000000," ","integrate(x^(15/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{15}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(15/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
393,0,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{13}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(13/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
394,0,0,0,0.000000," ","integrate(x^(11/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{11}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(11/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
395,0,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{9}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(9/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{7}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(7/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
397,0,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{5}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(5/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
398,0,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{3}{2}}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(3/2)/(c*x^4 + b*x^2)^(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{x}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(x)/(c*x^4 + b*x^2)^(3/2), x)","F",0
400,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2)^(3/2)/x^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} \sqrt{x}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2)^(3/2)*sqrt(x)), x)","F",0
401,0,0,0,0.000000," ","integrate(1/x^(3/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2)^(3/2)*x^(3/2)), x)","F",0
402,0,0,0,0.000000," ","integrate(1/x^(5/2)/(c*x^4+b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2)^(3/2)*x^(5/2)), x)","F",0
403,1,264,0,0.181499," ","integrate((c*x)^m*(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\frac{\left(c x\right)^{m} c^{3} m^{3} x^{13} + 27 \, \left(c x\right)^{m} c^{3} m^{2} x^{13} + 3 \, \left(c x\right)^{m} b c^{2} m^{3} x^{11} + 239 \, \left(c x\right)^{m} c^{3} m x^{13} + 87 \, \left(c x\right)^{m} b c^{2} m^{2} x^{11} + 693 \, \left(c x\right)^{m} c^{3} x^{13} + 3 \, \left(c x\right)^{m} b^{2} c m^{3} x^{9} + 813 \, \left(c x\right)^{m} b c^{2} m x^{11} + 93 \, \left(c x\right)^{m} b^{2} c m^{2} x^{9} + 2457 \, \left(c x\right)^{m} b c^{2} x^{11} + \left(c x\right)^{m} b^{3} m^{3} x^{7} + 933 \, \left(c x\right)^{m} b^{2} c m x^{9} + 33 \, \left(c x\right)^{m} b^{3} m^{2} x^{7} + 3003 \, \left(c x\right)^{m} b^{2} c x^{9} + 359 \, \left(c x\right)^{m} b^{3} m x^{7} + 1287 \, \left(c x\right)^{m} b^{3} x^{7}}{m^{4} + 40 \, m^{3} + 590 \, m^{2} + 3800 \, m + 9009}"," ",0,"((c*x)^m*c^3*m^3*x^13 + 27*(c*x)^m*c^3*m^2*x^13 + 3*(c*x)^m*b*c^2*m^3*x^11 + 239*(c*x)^m*c^3*m*x^13 + 87*(c*x)^m*b*c^2*m^2*x^11 + 693*(c*x)^m*c^3*x^13 + 3*(c*x)^m*b^2*c*m^3*x^9 + 813*(c*x)^m*b*c^2*m*x^11 + 93*(c*x)^m*b^2*c*m^2*x^9 + 2457*(c*x)^m*b*c^2*x^11 + (c*x)^m*b^3*m^3*x^7 + 933*(c*x)^m*b^2*c*m*x^9 + 33*(c*x)^m*b^3*m^2*x^7 + 3003*(c*x)^m*b^2*c*x^9 + 359*(c*x)^m*b^3*m*x^7 + 1287*(c*x)^m*b^3*x^7)/(m^4 + 40*m^3 + 590*m^2 + 3800*m + 9009)","B",0
404,1,141,0,0.174505," ","integrate((c*x)^m*(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\frac{\left(c x\right)^{m} c^{2} m^{2} x^{9} + 12 \, \left(c x\right)^{m} c^{2} m x^{9} + 2 \, \left(c x\right)^{m} b c m^{2} x^{7} + 35 \, \left(c x\right)^{m} c^{2} x^{9} + 28 \, \left(c x\right)^{m} b c m x^{7} + \left(c x\right)^{m} b^{2} m^{2} x^{5} + 90 \, \left(c x\right)^{m} b c x^{7} + 16 \, \left(c x\right)^{m} b^{2} m x^{5} + 63 \, \left(c x\right)^{m} b^{2} x^{5}}{m^{3} + 21 \, m^{2} + 143 \, m + 315}"," ",0,"((c*x)^m*c^2*m^2*x^9 + 12*(c*x)^m*c^2*m*x^9 + 2*(c*x)^m*b*c*m^2*x^7 + 35*(c*x)^m*c^2*x^9 + 28*(c*x)^m*b*c*m*x^7 + (c*x)^m*b^2*m^2*x^5 + 90*(c*x)^m*b*c*x^7 + 16*(c*x)^m*b^2*m*x^5 + 63*(c*x)^m*b^2*x^5)/(m^3 + 21*m^2 + 143*m + 315)","B",0
405,1,56,0,0.197416," ","integrate((c*x)^m*(c*x^4+b*x^2),x, algorithm=""giac"")","\frac{\left(c x\right)^{m} c m x^{5} + 3 \, \left(c x\right)^{m} c x^{5} + \left(c x\right)^{m} b m x^{3} + 5 \, \left(c x\right)^{m} b x^{3}}{m^{2} + 8 \, m + 15}"," ",0,"((c*x)^m*c*m*x^5 + 3*(c*x)^m*c*x^5 + (c*x)^m*b*m*x^3 + 5*(c*x)^m*b*x^3)/(m^2 + 8*m + 15)","A",0
406,0,0,0,0.000000," ","integrate((c*x)^m/(c*x^4+b*x^2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{c x^{4} + b x^{2}}\,{d x}"," ",0,"integrate((c*x)^m/(c*x^4 + b*x^2), x)","F",0
407,0,0,0,0.000000," ","integrate((c*x)^m/(c*x^4+b*x^2)^2,x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{{\left(c x^{4} + b x^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((c*x)^m/(c*x^4 + b*x^2)^2, x)","F",0
408,0,0,0,0.000000," ","integrate((c*x)^m/(c*x^4+b*x^2)^3,x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{{\left(c x^{4} + b x^{2}\right)}^{3}}\,{d x}"," ",0,"integrate((c*x)^m/(c*x^4 + b*x^2)^3, x)","F",0
409,1,24,0,0.149010," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{1}{8} \, b^{2} x^{8} + \frac{1}{3} \, a b x^{6} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"1/8*b^2*x^8 + 1/3*a*b*x^6 + 1/4*a^2*x^4","A",0
410,1,24,0,0.147619," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{1}{7} \, b^{2} x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"1/7*b^2*x^7 + 2/5*a*b*x^5 + 1/3*a^2*x^3","A",0
411,1,24,0,0.170310," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{1}{6} \, b^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/6*b^2*x^6 + 1/2*a*b*x^4 + 1/2*a^2*x^2","A",0
412,1,21,0,0.149859," ","integrate(b^2*x^4+2*a*b*x^2+a^2,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} x^{5} + \frac{2}{3} \, a b x^{3} + a^{2} x"," ",0,"1/5*b^2*x^5 + 2/3*a*b*x^3 + a^2*x","A",0
413,1,24,0,0.171363," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x,x, algorithm=""giac"")","\frac{1}{4} \, b^{2} x^{4} + a b x^{2} + \frac{1}{2} \, a^{2} \log\left(x^{2}\right)"," ",0,"1/4*b^2*x^4 + a*b*x^2 + 1/2*a^2*log(x^2)","A",0
414,1,22,0,0.146246," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, b^{2} x^{3} + 2 \, a b x - \frac{a^{2}}{x}"," ",0,"1/3*b^2*x^3 + 2*a*b*x - a^2/x","A",0
415,1,32,0,0.186822," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, b^{2} x^{2} + a b \log\left(x^{2}\right) - \frac{2 \, a b x^{2} + a^{2}}{2 \, x^{2}}"," ",0,"1/2*b^2*x^2 + a*b*log(x^2) - 1/2*(2*a*b*x^2 + a^2)/x^2","A",0
416,1,22,0,0.199911," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^4,x, algorithm=""giac"")","b^{2} x - \frac{6 \, a b x^{2} + a^{2}}{3 \, x^{3}}"," ",0,"b^2*x - 1/3*(6*a*b*x^2 + a^2)/x^3","A",0
417,1,34,0,0.150838," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, b^{2} \log\left(x^{2}\right) - \frac{3 \, b^{2} x^{4} + 4 \, a b x^{2} + a^{2}}{4 \, x^{4}}"," ",0,"1/2*b^2*log(x^2) - 1/4*(3*b^2*x^4 + 4*a*b*x^2 + a^2)/x^4","A",0
418,1,26,0,0.170815," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^6,x, algorithm=""giac"")","-\frac{15 \, b^{2} x^{4} + 10 \, a b x^{2} + 3 \, a^{2}}{15 \, x^{5}}"," ",0,"-1/15*(15*b^2*x^4 + 10*a*b*x^2 + 3*a^2)/x^5","A",0
419,1,24,0,0.177432," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^7,x, algorithm=""giac"")","-\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, x^{6}}"," ",0,"-1/6*(3*b^2*x^4 + 3*a*b*x^2 + a^2)/x^6","A",0
420,1,26,0,0.168063," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^8,x, algorithm=""giac"")","-\frac{35 \, b^{2} x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}}"," ",0,"-1/105*(35*b^2*x^4 + 42*a*b*x^2 + 15*a^2)/x^7","A",0
421,1,46,0,0.147187," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{15} \, b^{4} x^{15} + \frac{4}{13} \, a b^{3} x^{13} + \frac{6}{11} \, a^{2} b^{2} x^{11} + \frac{4}{9} \, a^{3} b x^{9} + \frac{1}{7} \, a^{4} x^{7}"," ",0,"1/15*b^4*x^15 + 4/13*a*b^3*x^13 + 6/11*a^2*b^2*x^11 + 4/9*a^3*b*x^9 + 1/7*a^4*x^7","A",0
422,1,46,0,0.149084," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{14} \, b^{4} x^{14} + \frac{1}{3} \, a b^{3} x^{12} + \frac{3}{5} \, a^{2} b^{2} x^{10} + \frac{1}{2} \, a^{3} b x^{8} + \frac{1}{6} \, a^{4} x^{6}"," ",0,"1/14*b^4*x^14 + 1/3*a*b^3*x^12 + 3/5*a^2*b^2*x^10 + 1/2*a^3*b*x^8 + 1/6*a^4*x^6","A",0
423,1,46,0,0.157537," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{13} \, b^{4} x^{13} + \frac{4}{11} \, a b^{3} x^{11} + \frac{2}{3} \, a^{2} b^{2} x^{9} + \frac{4}{7} \, a^{3} b x^{7} + \frac{1}{5} \, a^{4} x^{5}"," ",0,"1/13*b^4*x^13 + 4/11*a*b^3*x^11 + 2/3*a^2*b^2*x^9 + 4/7*a^3*b*x^7 + 1/5*a^4*x^5","A",0
424,1,46,0,0.149957," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{12} \, b^{4} x^{12} + \frac{2}{5} \, a b^{3} x^{10} + \frac{3}{4} \, a^{2} b^{2} x^{8} + \frac{2}{3} \, a^{3} b x^{6} + \frac{1}{4} \, a^{4} x^{4}"," ",0,"1/12*b^4*x^12 + 2/5*a*b^3*x^10 + 3/4*a^2*b^2*x^8 + 2/3*a^3*b*x^6 + 1/4*a^4*x^4","A",0
425,1,46,0,0.148215," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{4} x^{11} + \frac{4}{9} \, a b^{3} x^{9} + \frac{6}{7} \, a^{2} b^{2} x^{7} + \frac{4}{5} \, a^{3} b x^{5} + \frac{1}{3} \, a^{4} x^{3}"," ",0,"1/11*b^4*x^11 + 4/9*a*b^3*x^9 + 6/7*a^2*b^2*x^7 + 4/5*a^3*b*x^5 + 1/3*a^4*x^3","A",0
426,1,44,0,0.146659," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{4} x^{10} + \frac{1}{2} \, a b^{3} x^{8} + a^{2} b^{2} x^{6} + a^{3} b x^{4} + \frac{1}{2} \, a^{4} x^{2}"," ",0,"1/10*b^4*x^10 + 1/2*a*b^3*x^8 + a^2*b^2*x^6 + a^3*b*x^4 + 1/2*a^4*x^2","B",0
427,1,43,0,0.143010," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{4} x^{9} + \frac{4}{7} \, a b^{3} x^{7} + \frac{6}{5} \, a^{2} b^{2} x^{5} + \frac{4}{3} \, a^{3} b x^{3} + a^{4} x"," ",0,"1/9*b^4*x^9 + 4/7*a*b^3*x^7 + 6/5*a^2*b^2*x^5 + 4/3*a^3*b*x^3 + a^4*x","A",0
428,1,47,0,0.147681," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x,x, algorithm=""giac"")","\frac{1}{8} \, b^{4} x^{8} + \frac{2}{3} \, a b^{3} x^{6} + \frac{3}{2} \, a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + \frac{1}{2} \, a^{4} \log\left(x^{2}\right)"," ",0,"1/8*b^4*x^8 + 2/3*a*b^3*x^6 + 3/2*a^2*b^2*x^4 + 2*a^3*b*x^2 + 1/2*a^4*log(x^2)","A",0
429,1,44,0,0.148260," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{4} x^{7} + \frac{4}{5} \, a b^{3} x^{5} + 2 \, a^{2} b^{2} x^{3} + 4 \, a^{3} b x - \frac{a^{4}}{x}"," ",0,"1/7*b^4*x^7 + 4/5*a*b^3*x^5 + 2*a^2*b^2*x^3 + 4*a^3*b*x - a^4/x","A",0
430,1,56,0,0.155778," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^3,x, algorithm=""giac"")","\frac{1}{6} \, b^{4} x^{6} + a b^{3} x^{4} + 3 \, a^{2} b^{2} x^{2} + 2 \, a^{3} b \log\left(x^{2}\right) - \frac{4 \, a^{3} b x^{2} + a^{4}}{2 \, x^{2}}"," ",0,"1/6*b^4*x^6 + a*b^3*x^4 + 3*a^2*b^2*x^2 + 2*a^3*b*log(x^2) - 1/2*(4*a^3*b*x^2 + a^4)/x^2","A",0
431,1,45,0,0.171527," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^4,x, algorithm=""giac"")","\frac{1}{5} \, b^{4} x^{5} + \frac{4}{3} \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x - \frac{12 \, a^{3} b x^{2} + a^{4}}{3 \, x^{3}}"," ",0,"1/5*b^4*x^5 + 4/3*a*b^3*x^3 + 6*a^2*b^2*x - 1/3*(12*a^3*b*x^2 + a^4)/x^3","A",0
432,1,59,0,0.150165," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^5,x, algorithm=""giac"")","\frac{1}{4} \, b^{4} x^{4} + 2 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} \log\left(x^{2}\right) - \frac{18 \, a^{2} b^{2} x^{4} + 8 \, a^{3} b x^{2} + a^{4}}{4 \, x^{4}}"," ",0,"1/4*b^4*x^4 + 2*a*b^3*x^2 + 3*a^2*b^2*log(x^2) - 1/4*(18*a^2*b^2*x^4 + 8*a^3*b*x^2 + a^4)/x^4","A",0
433,1,47,0,0.151559," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^6,x, algorithm=""giac"")","\frac{1}{3} \, b^{4} x^{3} + 4 \, a b^{3} x - \frac{90 \, a^{2} b^{2} x^{4} + 20 \, a^{3} b x^{2} + 3 \, a^{4}}{15 \, x^{5}}"," ",0,"1/3*b^4*x^3 + 4*a*b^3*x - 1/15*(90*a^2*b^2*x^4 + 20*a^3*b*x^2 + 3*a^4)/x^5","A",0
434,1,57,0,0.166647," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^7,x, algorithm=""giac"")","\frac{1}{2} \, b^{4} x^{2} + 2 \, a b^{3} \log\left(x^{2}\right) - \frac{22 \, a b^{3} x^{6} + 18 \, a^{2} b^{2} x^{4} + 6 \, a^{3} b x^{2} + a^{4}}{6 \, x^{6}}"," ",0,"1/2*b^4*x^2 + 2*a*b^3*log(x^2) - 1/6*(22*a*b^3*x^6 + 18*a^2*b^2*x^4 + 6*a^3*b*x^2 + a^4)/x^6","A",0
435,1,46,0,0.155729," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^8,x, algorithm=""giac"")","b^{4} x - \frac{140 \, a b^{3} x^{6} + 70 \, a^{2} b^{2} x^{4} + 28 \, a^{3} b x^{2} + 5 \, a^{4}}{35 \, x^{7}}"," ",0,"b^4*x - 1/35*(140*a*b^3*x^6 + 70*a^2*b^2*x^4 + 28*a^3*b*x^2 + 5*a^4)/x^7","A",0
436,1,58,0,0.151586," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^9,x, algorithm=""giac"")","\frac{1}{2} \, b^{4} \log\left(x^{2}\right) - \frac{25 \, b^{4} x^{8} + 48 \, a b^{3} x^{6} + 36 \, a^{2} b^{2} x^{4} + 16 \, a^{3} b x^{2} + 3 \, a^{4}}{24 \, x^{8}}"," ",0,"1/2*b^4*log(x^2) - 1/24*(25*b^4*x^8 + 48*a*b^3*x^6 + 36*a^2*b^2*x^4 + 16*a^3*b*x^2 + 3*a^4)/x^8","A",0
437,1,48,0,0.172017," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^10,x, algorithm=""giac"")","-\frac{315 \, b^{4} x^{8} + 420 \, a b^{3} x^{6} + 378 \, a^{2} b^{2} x^{4} + 180 \, a^{3} b x^{2} + 35 \, a^{4}}{315 \, x^{9}}"," ",0,"-1/315*(315*b^4*x^8 + 420*a*b^3*x^6 + 378*a^2*b^2*x^4 + 180*a^3*b*x^2 + 35*a^4)/x^9","A",0
438,1,46,0,0.184118," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^11,x, algorithm=""giac"")","-\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}}"," ",0,"-1/10*(5*b^4*x^8 + 10*a*b^3*x^6 + 10*a^2*b^2*x^4 + 5*a^3*b*x^2 + a^4)/x^10","B",0
439,1,48,0,0.156510," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^12,x, algorithm=""giac"")","-\frac{1155 \, b^{4} x^{8} + 2772 \, a b^{3} x^{6} + 2970 \, a^{2} b^{2} x^{4} + 1540 \, a^{3} b x^{2} + 315 \, a^{4}}{3465 \, x^{11}}"," ",0,"-1/3465*(1155*b^4*x^8 + 2772*a*b^3*x^6 + 2970*a^2*b^2*x^4 + 1540*a^3*b*x^2 + 315*a^4)/x^11","A",0
440,1,48,0,0.148013," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^13,x, algorithm=""giac"")","-\frac{15 \, b^{4} x^{8} + 40 \, a b^{3} x^{6} + 45 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x^{2} + 5 \, a^{4}}{60 \, x^{12}}"," ",0,"-1/60*(15*b^4*x^8 + 40*a*b^3*x^6 + 45*a^2*b^2*x^4 + 24*a^3*b*x^2 + 5*a^4)/x^12","A",0
441,1,48,0,0.213824," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^14,x, algorithm=""giac"")","-\frac{3003 \, b^{4} x^{8} + 8580 \, a b^{3} x^{6} + 10010 \, a^{2} b^{2} x^{4} + 5460 \, a^{3} b x^{2} + 1155 \, a^{4}}{15015 \, x^{13}}"," ",0,"-1/15015*(3003*b^4*x^8 + 8580*a*b^3*x^6 + 10010*a^2*b^2*x^4 + 5460*a^3*b*x^2 + 1155*a^4)/x^13","A",0
442,1,48,0,0.153790," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^15,x, algorithm=""giac"")","-\frac{35 \, b^{4} x^{8} + 105 \, a b^{3} x^{6} + 126 \, a^{2} b^{2} x^{4} + 70 \, a^{3} b x^{2} + 15 \, a^{4}}{210 \, x^{14}}"," ",0,"-1/210*(35*b^4*x^8 + 105*a*b^3*x^6 + 126*a^2*b^2*x^4 + 70*a^3*b*x^2 + 15*a^4)/x^14","A",0
443,1,48,0,0.151790," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^16,x, algorithm=""giac"")","-\frac{6435 \, b^{4} x^{8} + 20020 \, a b^{3} x^{6} + 24570 \, a^{2} b^{2} x^{4} + 13860 \, a^{3} b x^{2} + 3003 \, a^{4}}{45045 \, x^{15}}"," ",0,"-1/45045*(6435*b^4*x^8 + 20020*a*b^3*x^6 + 24570*a^2*b^2*x^4 + 13860*a^3*b*x^2 + 3003*a^4)/x^15","A",0
444,1,68,0,0.160187," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{21} \, b^{6} x^{21} + \frac{6}{19} \, a b^{5} x^{19} + \frac{15}{17} \, a^{2} b^{4} x^{17} + \frac{4}{3} \, a^{3} b^{3} x^{15} + \frac{15}{13} \, a^{4} b^{2} x^{13} + \frac{6}{11} \, a^{5} b x^{11} + \frac{1}{9} \, a^{6} x^{9}"," ",0,"1/21*b^6*x^21 + 6/19*a*b^5*x^19 + 15/17*a^2*b^4*x^17 + 4/3*a^3*b^3*x^15 + 15/13*a^4*b^2*x^13 + 6/11*a^5*b*x^11 + 1/9*a^6*x^9","A",0
445,1,68,0,0.151694," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{20} \, b^{6} x^{20} + \frac{1}{3} \, a b^{5} x^{18} + \frac{15}{16} \, a^{2} b^{4} x^{16} + \frac{10}{7} \, a^{3} b^{3} x^{14} + \frac{5}{4} \, a^{4} b^{2} x^{12} + \frac{3}{5} \, a^{5} b x^{10} + \frac{1}{8} \, a^{6} x^{8}"," ",0,"1/20*b^6*x^20 + 1/3*a*b^5*x^18 + 15/16*a^2*b^4*x^16 + 10/7*a^3*b^3*x^14 + 5/4*a^4*b^2*x^12 + 3/5*a^5*b*x^10 + 1/8*a^6*x^8","A",0
446,1,67,0,0.150453," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{19} \, b^{6} x^{19} + \frac{6}{17} \, a b^{5} x^{17} + a^{2} b^{4} x^{15} + \frac{20}{13} \, a^{3} b^{3} x^{13} + \frac{15}{11} \, a^{4} b^{2} x^{11} + \frac{2}{3} \, a^{5} b x^{9} + \frac{1}{7} \, a^{6} x^{7}"," ",0,"1/19*b^6*x^19 + 6/17*a*b^5*x^17 + a^2*b^4*x^15 + 20/13*a^3*b^3*x^13 + 15/11*a^4*b^2*x^11 + 2/3*a^5*b*x^9 + 1/7*a^6*x^7","A",0
447,1,68,0,0.152530," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{18} \, b^{6} x^{18} + \frac{3}{8} \, a b^{5} x^{16} + \frac{15}{14} \, a^{2} b^{4} x^{14} + \frac{5}{3} \, a^{3} b^{3} x^{12} + \frac{3}{2} \, a^{4} b^{2} x^{10} + \frac{3}{4} \, a^{5} b x^{8} + \frac{1}{6} \, a^{6} x^{6}"," ",0,"1/18*b^6*x^18 + 3/8*a*b^5*x^16 + 15/14*a^2*b^4*x^14 + 5/3*a^3*b^3*x^12 + 3/2*a^4*b^2*x^10 + 3/4*a^5*b*x^8 + 1/6*a^6*x^6","A",0
448,1,68,0,0.165256," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{17} \, b^{6} x^{17} + \frac{2}{5} \, a b^{5} x^{15} + \frac{15}{13} \, a^{2} b^{4} x^{13} + \frac{20}{11} \, a^{3} b^{3} x^{11} + \frac{5}{3} \, a^{4} b^{2} x^{9} + \frac{6}{7} \, a^{5} b x^{7} + \frac{1}{5} \, a^{6} x^{5}"," ",0,"1/17*b^6*x^17 + 2/5*a*b^5*x^15 + 15/13*a^2*b^4*x^13 + 20/11*a^3*b^3*x^11 + 5/3*a^4*b^2*x^9 + 6/7*a^5*b*x^7 + 1/5*a^6*x^5","A",0
449,1,67,0,0.169873," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{16} \, b^{6} x^{16} + \frac{3}{7} \, a b^{5} x^{14} + \frac{5}{4} \, a^{2} b^{4} x^{12} + 2 \, a^{3} b^{3} x^{10} + \frac{15}{8} \, a^{4} b^{2} x^{8} + a^{5} b x^{6} + \frac{1}{4} \, a^{6} x^{4}"," ",0,"1/16*b^6*x^16 + 3/7*a*b^5*x^14 + 5/4*a^2*b^4*x^12 + 2*a^3*b^3*x^10 + 15/8*a^4*b^2*x^8 + a^5*b*x^6 + 1/4*a^6*x^4","B",0
450,1,68,0,0.151086," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{15} \, b^{6} x^{15} + \frac{6}{13} \, a b^{5} x^{13} + \frac{15}{11} \, a^{2} b^{4} x^{11} + \frac{20}{9} \, a^{3} b^{3} x^{9} + \frac{15}{7} \, a^{4} b^{2} x^{7} + \frac{6}{5} \, a^{5} b x^{5} + \frac{1}{3} \, a^{6} x^{3}"," ",0,"1/15*b^6*x^15 + 6/13*a*b^5*x^13 + 15/11*a^2*b^4*x^11 + 20/9*a^3*b^3*x^9 + 15/7*a^4*b^2*x^7 + 6/5*a^5*b*x^5 + 1/3*a^6*x^3","A",0
451,1,68,0,0.154707," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{14} \, b^{6} x^{14} + \frac{1}{2} \, a b^{5} x^{12} + \frac{3}{2} \, a^{2} b^{4} x^{10} + \frac{5}{2} \, a^{3} b^{3} x^{8} + \frac{5}{2} \, a^{4} b^{2} x^{6} + \frac{3}{2} \, a^{5} b x^{4} + \frac{1}{2} \, a^{6} x^{2}"," ",0,"1/14*b^6*x^14 + 1/2*a*b^5*x^12 + 3/2*a^2*b^4*x^10 + 5/2*a^3*b^3*x^8 + 5/2*a^4*b^2*x^6 + 3/2*a^5*b*x^4 + 1/2*a^6*x^2","B",0
452,1,65,0,0.156033," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{6} x^{13} + \frac{6}{11} \, a b^{5} x^{11} + \frac{5}{3} \, a^{2} b^{4} x^{9} + \frac{20}{7} \, a^{3} b^{3} x^{7} + 3 \, a^{4} b^{2} x^{5} + 2 \, a^{5} b x^{3} + a^{6} x"," ",0,"1/13*b^6*x^13 + 6/11*a*b^5*x^11 + 5/3*a^2*b^4*x^9 + 20/7*a^3*b^3*x^7 + 3*a^4*b^2*x^5 + 2*a^5*b*x^3 + a^6*x","A",0
453,1,69,0,0.150663," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x,x, algorithm=""giac"")","\frac{1}{12} \, b^{6} x^{12} + \frac{3}{5} \, a b^{5} x^{10} + \frac{15}{8} \, a^{2} b^{4} x^{8} + \frac{10}{3} \, a^{3} b^{3} x^{6} + \frac{15}{4} \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + \frac{1}{2} \, a^{6} \log\left(x^{2}\right)"," ",0,"1/12*b^6*x^12 + 3/5*a*b^5*x^10 + 15/8*a^2*b^4*x^8 + 10/3*a^3*b^3*x^6 + 15/4*a^4*b^2*x^4 + 3*a^5*b*x^2 + 1/2*a^6*log(x^2)","A",0
454,1,66,0,0.156296," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{6} x^{11} + \frac{2}{3} \, a b^{5} x^{9} + \frac{15}{7} \, a^{2} b^{4} x^{7} + 4 \, a^{3} b^{3} x^{5} + 5 \, a^{4} b^{2} x^{3} + 6 \, a^{5} b x - \frac{a^{6}}{x}"," ",0,"1/11*b^6*x^11 + 2/3*a*b^5*x^9 + 15/7*a^2*b^4*x^7 + 4*a^3*b^3*x^5 + 5*a^4*b^2*x^3 + 6*a^5*b*x - a^6/x","A",0
455,1,79,0,0.152960," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{6} x^{10} + \frac{3}{4} \, a b^{5} x^{8} + \frac{5}{2} \, a^{2} b^{4} x^{6} + 5 \, a^{3} b^{3} x^{4} + \frac{15}{2} \, a^{4} b^{2} x^{2} + 3 \, a^{5} b \log\left(x^{2}\right) - \frac{6 \, a^{5} b x^{2} + a^{6}}{2 \, x^{2}}"," ",0,"1/10*b^6*x^10 + 3/4*a*b^5*x^8 + 5/2*a^2*b^4*x^6 + 5*a^3*b^3*x^4 + 15/2*a^4*b^2*x^2 + 3*a^5*b*log(x^2) - 1/2*(6*a^5*b*x^2 + a^6)/x^2","A",0
456,1,67,0,0.184427," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^4,x, algorithm=""giac"")","\frac{1}{9} \, b^{6} x^{9} + \frac{6}{7} \, a b^{5} x^{7} + 3 \, a^{2} b^{4} x^{5} + \frac{20}{3} \, a^{3} b^{3} x^{3} + 15 \, a^{4} b^{2} x - \frac{18 \, a^{5} b x^{2} + a^{6}}{3 \, x^{3}}"," ",0,"1/9*b^6*x^9 + 6/7*a*b^5*x^7 + 3*a^2*b^4*x^5 + 20/3*a^3*b^3*x^3 + 15*a^4*b^2*x - 1/3*(18*a^5*b*x^2 + a^6)/x^3","A",0
457,1,80,0,0.158941," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^5,x, algorithm=""giac"")","\frac{1}{8} \, b^{6} x^{8} + a b^{5} x^{6} + \frac{15}{4} \, a^{2} b^{4} x^{4} + 10 \, a^{3} b^{3} x^{2} + \frac{15}{2} \, a^{4} b^{2} \log\left(x^{2}\right) - \frac{45 \, a^{4} b^{2} x^{4} + 12 \, a^{5} b x^{2} + a^{6}}{4 \, x^{4}}"," ",0,"1/8*b^6*x^8 + a*b^5*x^6 + 15/4*a^2*b^4*x^4 + 10*a^3*b^3*x^2 + 15/2*a^4*b^2*log(x^2) - 1/4*(45*a^4*b^2*x^4 + 12*a^5*b*x^2 + a^6)/x^4","A",0
458,1,67,0,0.156038," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^6,x, algorithm=""giac"")","\frac{1}{7} \, b^{6} x^{7} + \frac{6}{5} \, a b^{5} x^{5} + 5 \, a^{2} b^{4} x^{3} + 20 \, a^{3} b^{3} x - \frac{75 \, a^{4} b^{2} x^{4} + 10 \, a^{5} b x^{2} + a^{6}}{5 \, x^{5}}"," ",0,"1/7*b^6*x^7 + 6/5*a*b^5*x^5 + 5*a^2*b^4*x^3 + 20*a^3*b^3*x - 1/5*(75*a^4*b^2*x^4 + 10*a^5*b*x^2 + a^6)/x^5","A",0
459,1,81,0,0.152776," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^7,x, algorithm=""giac"")","\frac{1}{6} \, b^{6} x^{6} + \frac{3}{2} \, a b^{5} x^{4} + \frac{15}{2} \, a^{2} b^{4} x^{2} + 10 \, a^{3} b^{3} \log\left(x^{2}\right) - \frac{110 \, a^{3} b^{3} x^{6} + 45 \, a^{4} b^{2} x^{4} + 9 \, a^{5} b x^{2} + a^{6}}{6 \, x^{6}}"," ",0,"1/6*b^6*x^6 + 3/2*a*b^5*x^4 + 15/2*a^2*b^4*x^2 + 10*a^3*b^3*log(x^2) - 1/6*(110*a^3*b^3*x^6 + 45*a^4*b^2*x^4 + 9*a^5*b*x^2 + a^6)/x^6","A",0
460,1,69,0,0.151067," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^8,x, algorithm=""giac"")","\frac{1}{5} \, b^{6} x^{5} + 2 \, a b^{5} x^{3} + 15 \, a^{2} b^{4} x - \frac{700 \, a^{3} b^{3} x^{6} + 175 \, a^{4} b^{2} x^{4} + 42 \, a^{5} b x^{2} + 5 \, a^{6}}{35 \, x^{7}}"," ",0,"1/5*b^6*x^5 + 2*a*b^5*x^3 + 15*a^2*b^4*x - 1/35*(700*a^3*b^3*x^6 + 175*a^4*b^2*x^4 + 42*a^5*b*x^2 + 5*a^6)/x^7","A",0
461,1,81,0,0.156169," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^9,x, algorithm=""giac"")","\frac{1}{4} \, b^{6} x^{4} + 3 \, a b^{5} x^{2} + \frac{15}{2} \, a^{2} b^{4} \log\left(x^{2}\right) - \frac{125 \, a^{2} b^{4} x^{8} + 80 \, a^{3} b^{3} x^{6} + 30 \, a^{4} b^{2} x^{4} + 8 \, a^{5} b x^{2} + a^{6}}{8 \, x^{8}}"," ",0,"1/4*b^6*x^4 + 3*a*b^5*x^2 + 15/2*a^2*b^4*log(x^2) - 1/8*(125*a^2*b^4*x^8 + 80*a^3*b^3*x^6 + 30*a^4*b^2*x^4 + 8*a^5*b*x^2 + a^6)/x^8","A",0
462,1,69,0,0.240116," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^10,x, algorithm=""giac"")","\frac{1}{3} \, b^{6} x^{3} + 6 \, a b^{5} x - \frac{945 \, a^{2} b^{4} x^{8} + 420 \, a^{3} b^{3} x^{6} + 189 \, a^{4} b^{2} x^{4} + 54 \, a^{5} b x^{2} + 7 \, a^{6}}{63 \, x^{9}}"," ",0,"1/3*b^6*x^3 + 6*a*b^5*x - 1/63*(945*a^2*b^4*x^8 + 420*a^3*b^3*x^6 + 189*a^4*b^2*x^4 + 54*a^5*b*x^2 + 7*a^6)/x^9","A",0
463,1,81,0,0.151498," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^11,x, algorithm=""giac"")","\frac{1}{2} \, b^{6} x^{2} + 3 \, a b^{5} \log\left(x^{2}\right) - \frac{137 \, a b^{5} x^{10} + 150 \, a^{2} b^{4} x^{8} + 100 \, a^{3} b^{3} x^{6} + 50 \, a^{4} b^{2} x^{4} + 15 \, a^{5} b x^{2} + 2 \, a^{6}}{20 \, x^{10}}"," ",0,"1/2*b^6*x^2 + 3*a*b^5*log(x^2) - 1/20*(137*a*b^5*x^10 + 150*a^2*b^4*x^8 + 100*a^3*b^3*x^6 + 50*a^4*b^2*x^4 + 15*a^5*b*x^2 + 2*a^6)/x^10","A",0
464,1,68,0,0.152560," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^12,x, algorithm=""giac"")","b^{6} x - \frac{1386 \, a b^{5} x^{10} + 1155 \, a^{2} b^{4} x^{8} + 924 \, a^{3} b^{3} x^{6} + 495 \, a^{4} b^{2} x^{4} + 154 \, a^{5} b x^{2} + 21 \, a^{6}}{231 \, x^{11}}"," ",0,"b^6*x - 1/231*(1386*a*b^5*x^10 + 1155*a^2*b^4*x^8 + 924*a^3*b^3*x^6 + 495*a^4*b^2*x^4 + 154*a^5*b*x^2 + 21*a^6)/x^11","A",0
465,1,80,0,0.152411," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^13,x, algorithm=""giac"")","\frac{1}{2} \, b^{6} \log\left(x^{2}\right) - \frac{147 \, b^{6} x^{12} + 360 \, a b^{5} x^{10} + 450 \, a^{2} b^{4} x^{8} + 400 \, a^{3} b^{3} x^{6} + 225 \, a^{4} b^{2} x^{4} + 72 \, a^{5} b x^{2} + 10 \, a^{6}}{120 \, x^{12}}"," ",0,"1/2*b^6*log(x^2) - 1/120*(147*b^6*x^12 + 360*a*b^5*x^10 + 450*a^2*b^4*x^8 + 400*a^3*b^3*x^6 + 225*a^4*b^2*x^4 + 72*a^5*b*x^2 + 10*a^6)/x^12","A",0
466,1,70,0,0.176959," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^14,x, algorithm=""giac"")","-\frac{3003 \, b^{6} x^{12} + 6006 \, a b^{5} x^{10} + 9009 \, a^{2} b^{4} x^{8} + 8580 \, a^{3} b^{3} x^{6} + 5005 \, a^{4} b^{2} x^{4} + 1638 \, a^{5} b x^{2} + 231 \, a^{6}}{3003 \, x^{13}}"," ",0,"-1/3003*(3003*b^6*x^12 + 6006*a*b^5*x^10 + 9009*a^2*b^4*x^8 + 8580*a^3*b^3*x^6 + 5005*a^4*b^2*x^4 + 1638*a^5*b*x^2 + 231*a^6)/x^13","A",0
467,1,68,0,0.158672," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^15,x, algorithm=""giac"")","-\frac{7 \, b^{6} x^{12} + 21 \, a b^{5} x^{10} + 35 \, a^{2} b^{4} x^{8} + 35 \, a^{3} b^{3} x^{6} + 21 \, a^{4} b^{2} x^{4} + 7 \, a^{5} b x^{2} + a^{6}}{14 \, x^{14}}"," ",0,"-1/14*(7*b^6*x^12 + 21*a*b^5*x^10 + 35*a^2*b^4*x^8 + 35*a^3*b^3*x^6 + 21*a^4*b^2*x^4 + 7*a^5*b*x^2 + a^6)/x^14","B",0
468,1,70,0,0.152633," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^16,x, algorithm=""giac"")","-\frac{15015 \, b^{6} x^{12} + 54054 \, a b^{5} x^{10} + 96525 \, a^{2} b^{4} x^{8} + 100100 \, a^{3} b^{3} x^{6} + 61425 \, a^{4} b^{2} x^{4} + 20790 \, a^{5} b x^{2} + 3003 \, a^{6}}{45045 \, x^{15}}"," ",0,"-1/45045*(15015*b^6*x^12 + 54054*a*b^5*x^10 + 96525*a^2*b^4*x^8 + 100100*a^3*b^3*x^6 + 61425*a^4*b^2*x^4 + 20790*a^5*b*x^2 + 3003*a^6)/x^15","A",0
469,1,70,0,0.168989," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^17,x, algorithm=""giac"")","-\frac{28 \, b^{6} x^{12} + 112 \, a b^{5} x^{10} + 210 \, a^{2} b^{4} x^{8} + 224 \, a^{3} b^{3} x^{6} + 140 \, a^{4} b^{2} x^{4} + 48 \, a^{5} b x^{2} + 7 \, a^{6}}{112 \, x^{16}}"," ",0,"-1/112*(28*b^6*x^12 + 112*a*b^5*x^10 + 210*a^2*b^4*x^8 + 224*a^3*b^3*x^6 + 140*a^4*b^2*x^4 + 48*a^5*b*x^2 + 7*a^6)/x^16","A",0
470,1,70,0,0.168271," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^18,x, algorithm=""giac"")","-\frac{51051 \, b^{6} x^{12} + 218790 \, a b^{5} x^{10} + 425425 \, a^{2} b^{4} x^{8} + 464100 \, a^{3} b^{3} x^{6} + 294525 \, a^{4} b^{2} x^{4} + 102102 \, a^{5} b x^{2} + 15015 \, a^{6}}{255255 \, x^{17}}"," ",0,"-1/255255*(51051*b^6*x^12 + 218790*a*b^5*x^10 + 425425*a^2*b^4*x^8 + 464100*a^3*b^3*x^6 + 294525*a^4*b^2*x^4 + 102102*a^5*b*x^2 + 15015*a^6)/x^17","A",0
471,1,70,0,0.165695," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^19,x, algorithm=""giac"")","-\frac{84 \, b^{6} x^{12} + 378 \, a b^{5} x^{10} + 756 \, a^{2} b^{4} x^{8} + 840 \, a^{3} b^{3} x^{6} + 540 \, a^{4} b^{2} x^{4} + 189 \, a^{5} b x^{2} + 28 \, a^{6}}{504 \, x^{18}}"," ",0,"-1/504*(84*b^6*x^12 + 378*a*b^5*x^10 + 756*a^2*b^4*x^8 + 840*a^3*b^3*x^6 + 540*a^4*b^2*x^4 + 189*a^5*b*x^2 + 28*a^6)/x^18","A",0
472,1,70,0,0.176743," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^20,x, algorithm=""giac"")","-\frac{138567 \, b^{6} x^{12} + 646646 \, a b^{5} x^{10} + 1322685 \, a^{2} b^{4} x^{8} + 1492260 \, a^{3} b^{3} x^{6} + 969969 \, a^{4} b^{2} x^{4} + 342342 \, a^{5} b x^{2} + 51051 \, a^{6}}{969969 \, x^{19}}"," ",0,"-1/969969*(138567*b^6*x^12 + 646646*a*b^5*x^10 + 1322685*a^2*b^4*x^8 + 1492260*a^3*b^3*x^6 + 969969*a^4*b^2*x^4 + 342342*a^5*b*x^2 + 51051*a^6)/x^19","A",0
473,1,70,0,0.154467," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^21,x, algorithm=""giac"")","-\frac{210 \, b^{6} x^{12} + 1008 \, a b^{5} x^{10} + 2100 \, a^{2} b^{4} x^{8} + 2400 \, a^{3} b^{3} x^{6} + 1575 \, a^{4} b^{2} x^{4} + 560 \, a^{5} b x^{2} + 84 \, a^{6}}{1680 \, x^{20}}"," ",0,"-1/1680*(210*b^6*x^12 + 1008*a*b^5*x^10 + 2100*a^2*b^4*x^8 + 2400*a^3*b^3*x^6 + 1575*a^4*b^2*x^4 + 560*a^5*b*x^2 + 84*a^6)/x^20","A",0
474,1,70,0,0.171869," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^22,x, algorithm=""giac"")","-\frac{323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}}"," ",0,"-1/2909907*(323323*b^6*x^12 + 1587222*a*b^5*x^10 + 3357585*a^2*b^4*x^8 + 3879876*a^3*b^3*x^6 + 2567565*a^4*b^2*x^4 + 918918*a^5*b*x^2 + 138567*a^6)/x^21","A",0
475,1,92,0,0.161153," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{5 \, a^{4} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{6}} - \frac{5 \, a^{4} b x^{2} + 4 \, a^{5}}{2 \, {\left(b x^{2} + a\right)} b^{6}} + \frac{3 \, b^{6} x^{8} - 8 \, a b^{5} x^{6} + 18 \, a^{2} b^{4} x^{4} - 48 \, a^{3} b^{3} x^{2}}{24 \, b^{8}}"," ",0,"5/2*a^4*log(abs(b*x^2 + a))/b^6 - 1/2*(5*a^4*b*x^2 + 4*a^5)/((b*x^2 + a)*b^6) + 1/24*(3*b^6*x^8 - 8*a*b^5*x^6 + 18*a^2*b^4*x^4 - 48*a^3*b^3*x^2)/b^8","A",0
476,1,80,0,0.172668," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{2 \, a^{3} \log\left({\left| b x^{2} + a \right|}\right)}{b^{5}} + \frac{b^{4} x^{6} - 3 \, a b^{3} x^{4} + 9 \, a^{2} b^{2} x^{2}}{6 \, b^{6}} + \frac{4 \, a^{3} b x^{2} + 3 \, a^{4}}{2 \, {\left(b x^{2} + a\right)} b^{5}}"," ",0,"-2*a^3*log(abs(b*x^2 + a))/b^5 + 1/6*(b^4*x^6 - 3*a*b^3*x^4 + 9*a^2*b^2*x^2)/b^6 + 1/2*(4*a^3*b*x^2 + 3*a^4)/((b*x^2 + a)*b^5)","A",0
477,1,67,0,0.159763," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}} + \frac{b^{2} x^{4} - 4 \, a b x^{2}}{4 \, b^{4}} - \frac{3 \, a^{2} b x^{2} + 2 \, a^{3}}{2 \, {\left(b x^{2} + a\right)} b^{4}}"," ",0,"3/2*a^2*log(abs(b*x^2 + a))/b^4 + 1/4*(b^2*x^4 - 4*a*b*x^2)/b^4 - 1/2*(3*a^2*b*x^2 + 2*a^3)/((b*x^2 + a)*b^4)","A",0
478,1,49,0,0.169406," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, b^{2}} - \frac{a \log\left({\left| b x^{2} + a \right|}\right)}{b^{3}} + \frac{2 \, a b x^{2} + a^{2}}{2 \, {\left(b x^{2} + a\right)} b^{3}}"," ",0,"1/2*x^2/b^2 - a*log(abs(b*x^2 + a))/b^3 + 1/2*(2*a*b*x^2 + a^2)/((b*x^2 + a)*b^3)","A",0
479,1,30,0,0.161629," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{2}} + \frac{a}{2 \, {\left(b x^{2} + a\right)} b^{2}}"," ",0,"1/2*log(abs(b*x^2 + a))/b^2 + 1/2*a/((b*x^2 + a)*b^2)","A",0
480,1,14,0,0.170070," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{1}{2 \, {\left(b x^{2} + a\right)} b}"," ",0,"-1/2/((b*x^2 + a)*b)","A",0
481,1,47,0,0.151694," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, a^{2}} - \frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2}} + \frac{b x^{2} + 2 \, a}{2 \, {\left(b x^{2} + a\right)} a^{2}}"," ",0,"1/2*log(x^2)/a^2 - 1/2*log(abs(b*x^2 + a))/a^2 + 1/2*(b*x^2 + 2*a)/((b*x^2 + a)*a^2)","A",0
482,1,51,0,0.163109," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{b \log\left(x^{2}\right)}{a^{3}} + \frac{b \log\left({\left| b x^{2} + a \right|}\right)}{a^{3}} - \frac{2 \, b x^{2} + a}{2 \, {\left(b x^{4} + a x^{2}\right)} a^{2}}"," ",0,"-b*log(x^2)/a^3 + b*log(abs(b*x^2 + a))/a^3 - 1/2*(2*b*x^2 + a)/((b*x^4 + a*x^2)*a^2)","A",0
483,1,86,0,0.173458," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{3 \, b^{2} \log\left(x^{2}\right)}{2 \, a^{4}} - \frac{3 \, b^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{4}} + \frac{3 \, b^{3} x^{2} + 4 \, a b^{2}}{2 \, {\left(b x^{2} + a\right)} a^{4}} - \frac{9 \, b^{2} x^{4} - 4 \, a b x^{2} + a^{2}}{4 \, a^{4} x^{4}}"," ",0,"3/2*b^2*log(x^2)/a^4 - 3/2*b^2*log(abs(b*x^2 + a))/a^4 + 1/2*(3*b^3*x^2 + 4*a*b^2)/((b*x^2 + a)*a^4) - 1/4*(9*b^2*x^4 - 4*a*b*x^2 + a^2)/(a^4*x^4)","A",0
484,1,84,0,0.153249," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{9 \, a^{4} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{5}} - \frac{a^{4} x}{2 \, {\left(b x^{2} + a\right)} b^{5}} + \frac{5 \, b^{12} x^{7} - 14 \, a b^{11} x^{5} + 35 \, a^{2} b^{10} x^{3} - 140 \, a^{3} b^{9} x}{35 \, b^{14}}"," ",0,"9/2*a^4*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) - 1/2*a^4*x/((b*x^2 + a)*b^5) + 1/35*(5*b^12*x^7 - 14*a*b^11*x^5 + 35*a^2*b^10*x^3 - 140*a^3*b^9*x)/b^14","A",0
485,1,73,0,0.151045," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{7 \, a^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{4}} + \frac{a^{3} x}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{3 \, b^{8} x^{5} - 10 \, a b^{7} x^{3} + 45 \, a^{2} b^{6} x}{15 \, b^{10}}"," ",0,"-7/2*a^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/2*a^3*x/((b*x^2 + a)*b^4) + 1/15*(3*b^8*x^5 - 10*a*b^7*x^3 + 45*a^2*b^6*x)/b^10","A",0
486,1,61,0,0.155523," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{5 \, a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} - \frac{a^{2} x}{2 \, {\left(b x^{2} + a\right)} b^{3}} + \frac{b^{4} x^{3} - 6 \, a b^{3} x}{3 \, b^{6}}"," ",0,"5/2*a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/2*a^2*x/((b*x^2 + a)*b^3) + 1/3*(b^4*x^3 - 6*a*b^3*x)/b^6","A",0
487,1,42,0,0.153118," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{3 \, a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}} + \frac{a x}{2 \, {\left(b x^{2} + a\right)} b^{2}} + \frac{x}{b^{2}}"," ",0,"-3/2*a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/2*a*x/((b*x^2 + a)*b^2) + x/b^2","A",0
488,1,35,0,0.196897," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b} - \frac{x}{2 \, {\left(b x^{2} + a\right)} b}"," ",0,"1/2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) - 1/2*x/((b*x^2 + a)*b)","A",0
489,1,35,0,0.153084," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a} + \frac{x}{2 \, {\left(b x^{2} + a\right)} a}"," ",0,"1/2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) + 1/2*x/((b*x^2 + a)*a)","A",0
490,1,47,0,0.179211," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{3 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}} - \frac{3 \, b x^{2} + 2 \, a}{2 \, {\left(b x^{3} + a x\right)} a^{2}}"," ",0,"-3/2*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/2*(3*b*x^2 + 2*a)/((b*x^3 + a*x)*a^2)","A",0
491,1,59,0,0.151679," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{5 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3}} + \frac{b^{2} x}{2 \, {\left(b x^{2} + a\right)} a^{3}} + \frac{6 \, b x^{2} - a}{3 \, a^{3} x^{3}}"," ",0,"5/2*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) + 1/2*b^2*x/((b*x^2 + a)*a^3) + 1/3*(6*b*x^2 - a)/(a^3*x^3)","A",0
492,1,70,0,0.153735," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{7 \, b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{4}} - \frac{b^{3} x}{2 \, {\left(b x^{2} + a\right)} a^{4}} - \frac{45 \, b^{2} x^{4} - 10 \, a b x^{2} + 3 \, a^{2}}{15 \, a^{4} x^{5}}"," ",0,"-7/2*b^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) - 1/2*b^3*x/((b*x^2 + a)*a^4) - 1/15*(45*b^2*x^4 - 10*a*b*x^2 + 3*a^2)/(a^4*x^5)","A",0
493,1,91,0,0.174928," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \log\left({\left| b x^{2} + a \right|}\right)}{b^{6}} + \frac{b^{4} x^{4} - 8 \, a b^{3} x^{2}}{4 \, b^{8}} - \frac{110 \, a^{2} b^{3} x^{6} + 270 \, a^{3} b^{2} x^{4} + 225 \, a^{4} b x^{2} + 63 \, a^{5}}{12 \, {\left(b x^{2} + a\right)}^{3} b^{6}}"," ",0,"5*a^2*log(abs(b*x^2 + a))/b^6 + 1/4*(b^4*x^4 - 8*a*b^3*x^2)/b^8 - 1/12*(110*a^2*b^3*x^6 + 270*a^3*b^2*x^4 + 225*a^4*b*x^2 + 63*a^5)/((b*x^2 + a)^3*b^6)","A",0
494,1,73,0,0.156477," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{x^{2}}{2 \, b^{4}} - \frac{2 \, a \log\left({\left| b x^{2} + a \right|}\right)}{b^{5}} + \frac{22 \, a b^{3} x^{6} + 48 \, a^{2} b^{2} x^{4} + 36 \, a^{3} b x^{2} + 9 \, a^{4}}{6 \, {\left(b x^{2} + a\right)}^{3} b^{5}}"," ",0,"1/2*x^2/b^4 - 2*a*log(abs(b*x^2 + a))/b^5 + 1/6*(22*a*b^3*x^6 + 48*a^2*b^2*x^4 + 36*a^3*b*x^2 + 9*a^4)/((b*x^2 + a)^3*b^5)","A",0
495,1,53,0,0.168096," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}} - \frac{11 \, b^{2} x^{6} + 15 \, a b x^{4} + 6 \, a^{2} x^{2}}{12 \, {\left(b x^{2} + a\right)}^{3} b^{3}}"," ",0,"1/2*log(abs(b*x^2 + a))/b^4 - 1/12*(11*b^2*x^6 + 15*a*b*x^4 + 6*a^2*x^2)/((b*x^2 + a)^3*b^3)","A",0
496,1,33,0,0.191428," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, {\left(b x^{2} + a\right)}^{3} b^{3}}"," ",0,"-1/6*(3*b^2*x^4 + 3*a*b*x^2 + a^2)/((b*x^2 + a)^3*b^3)","A",0
497,1,22,0,0.155140," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{3 \, b x^{2} + a}{12 \, {\left(b x^{2} + a\right)}^{3} b^{2}}"," ",0,"-1/12*(3*b*x^2 + a)/((b*x^2 + a)^3*b^2)","A",0
498,1,14,0,0.153240," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{1}{6 \, {\left(b x^{2} + a\right)}^{3} b}"," ",0,"-1/6/((b*x^2 + a)^3*b)","A",0
499,1,70,0,0.152697," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, a^{4}} - \frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{4}} + \frac{11 \, b^{3} x^{6} + 39 \, a b^{2} x^{4} + 48 \, a^{2} b x^{2} + 22 \, a^{3}}{12 \, {\left(b x^{2} + a\right)}^{3} a^{4}}"," ",0,"1/2*log(x^2)/a^4 - 1/2*log(abs(b*x^2 + a))/a^4 + 1/12*(11*b^3*x^6 + 39*a*b^2*x^4 + 48*a^2*b*x^2 + 22*a^3)/((b*x^2 + a)^3*a^4)","A",0
500,1,93,0,0.160324," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{2 \, b \log\left(x^{2}\right)}{a^{5}} + \frac{2 \, b \log\left({\left| b x^{2} + a \right|}\right)}{a^{5}} + \frac{4 \, b x^{2} - a}{2 \, a^{5} x^{2}} - \frac{22 \, b^{4} x^{6} + 75 \, a b^{3} x^{4} + 87 \, a^{2} b^{2} x^{2} + 35 \, a^{3} b}{6 \, {\left(b x^{2} + a\right)}^{3} a^{5}}"," ",0,"-2*b*log(x^2)/a^5 + 2*b*log(abs(b*x^2 + a))/a^5 + 1/2*(4*b*x^2 - a)/(a^5*x^2) - 1/6*(22*b^4*x^6 + 75*a*b^3*x^4 + 87*a^2*b^2*x^2 + 35*a^3*b)/((b*x^2 + a)^3*a^5)","A",0
501,1,108,0,0.156492," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{5 \, b^{2} \log\left(x^{2}\right)}{a^{6}} - \frac{5 \, b^{2} \log\left({\left| b x^{2} + a \right|}\right)}{a^{6}} + \frac{110 \, b^{5} x^{6} + 366 \, a b^{4} x^{4} + 411 \, a^{2} b^{3} x^{2} + 157 \, a^{3} b^{2}}{12 \, {\left(b x^{2} + a\right)}^{3} a^{6}} - \frac{30 \, b^{2} x^{4} - 8 \, a b x^{2} + a^{2}}{4 \, a^{6} x^{4}}"," ",0,"5*b^2*log(x^2)/a^6 - 5*b^2*log(abs(b*x^2 + a))/a^6 + 1/12*(110*b^5*x^6 + 366*a*b^4*x^4 + 411*a^2*b^3*x^2 + 157*a^3*b^2)/((b*x^2 + a)^3*a^6) - 1/4*(30*b^2*x^4 - 8*a*b*x^2 + a^2)/(a^6*x^4)","A",0
502,1,96,0,0.152753," ","integrate(x^12/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{231 \, a^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{6}} + \frac{267 \, a^{3} b^{2} x^{5} + 472 \, a^{4} b x^{3} + 213 \, a^{5} x}{48 \, {\left(b x^{2} + a\right)}^{3} b^{6}} + \frac{3 \, b^{16} x^{5} - 20 \, a b^{15} x^{3} + 150 \, a^{2} b^{14} x}{15 \, b^{20}}"," ",0,"-231/16*a^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/48*(267*a^3*b^2*x^5 + 472*a^4*b*x^3 + 213*a^5*x)/((b*x^2 + a)^3*b^6) + 1/15*(3*b^16*x^5 - 20*a*b^15*x^3 + 150*a^2*b^14*x)/b^20","A",0
503,1,84,0,0.163461," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{105 \, a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{5}} - \frac{165 \, a^{2} b^{2} x^{5} + 280 \, a^{3} b x^{3} + 123 \, a^{4} x}{48 \, {\left(b x^{2} + a\right)}^{3} b^{5}} + \frac{b^{8} x^{3} - 12 \, a b^{7} x}{3 \, b^{12}}"," ",0,"105/16*a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) - 1/48*(165*a^2*b^2*x^5 + 280*a^3*b*x^3 + 123*a^4*x)/((b*x^2 + a)^3*b^5) + 1/3*(b^8*x^3 - 12*a*b^7*x)/b^12","A",0
504,1,65,0,0.158681," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{35 \, a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{4}} + \frac{x}{b^{4}} + \frac{87 \, a b^{2} x^{5} + 136 \, a^{2} b x^{3} + 57 \, a^{3} x}{48 \, {\left(b x^{2} + a\right)}^{3} b^{4}}"," ",0,"-35/16*a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + x/b^4 + 1/48*(87*a*b^2*x^5 + 136*a^2*b*x^3 + 57*a^3*x)/((b*x^2 + a)^3*b^4)","A",0
505,1,56,0,0.167984," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{5 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{3}} - \frac{33 \, b^{2} x^{5} + 40 \, a b x^{3} + 15 \, a^{2} x}{48 \, {\left(b x^{2} + a\right)}^{3} b^{3}}"," ",0,"5/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/48*(33*b^2*x^5 + 40*a*b*x^3 + 15*a^2*x)/((b*x^2 + a)^3*b^3)","A",0
506,1,62,0,0.156228," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a b^{2}} + \frac{3 \, b^{2} x^{5} - 8 \, a b x^{3} - 3 \, a^{2} x}{48 \, {\left(b x^{2} + a\right)}^{3} a b^{2}}"," ",0,"1/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2) + 1/48*(3*b^2*x^5 - 8*a*b*x^3 - 3*a^2*x)/((b*x^2 + a)^3*a*b^2)","A",0
507,1,62,0,0.184700," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{2} b} + \frac{3 \, b^{2} x^{5} + 8 \, a b x^{3} - 3 \, a^{2} x}{48 \, {\left(b x^{2} + a\right)}^{3} a^{2} b}"," ",0,"1/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/48*(3*b^2*x^5 + 8*a*b*x^3 - 3*a^2*x)/((b*x^2 + a)^3*a^2*b)","A",0
508,1,56,0,0.154299," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{5 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{3}} + \frac{15 \, b^{2} x^{5} + 40 \, a b x^{3} + 33 \, a^{2} x}{48 \, {\left(b x^{2} + a\right)}^{3} a^{3}}"," ",0,"5/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) + 1/48*(15*b^2*x^5 + 40*a*b*x^3 + 33*a^2*x)/((b*x^2 + a)^3*a^3)","A",0
509,1,68,0,0.160251," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{35 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{4}} - \frac{1}{a^{4} x} - \frac{57 \, b^{3} x^{5} + 136 \, a b^{2} x^{3} + 87 \, a^{2} b x}{48 \, {\left(b x^{2} + a\right)}^{3} a^{4}}"," ",0,"-35/16*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) - 1/(a^4*x) - 1/48*(57*b^3*x^5 + 136*a*b^2*x^3 + 87*a^2*b*x)/((b*x^2 + a)^3*a^4)","A",0
510,1,82,0,0.167751," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{105 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{5}} + \frac{315 \, b^{4} x^{8} + 840 \, a b^{3} x^{6} + 693 \, a^{2} b^{2} x^{4} + 144 \, a^{3} b x^{2} - 16 \, a^{4}}{48 \, {\left(b x^{3} + a x\right)}^{3} a^{5}}"," ",0,"105/16*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5) + 1/48*(315*b^4*x^8 + 840*a*b^3*x^6 + 693*a^2*b^2*x^4 + 144*a^3*b*x^2 - 16*a^4)/((b*x^3 + a*x)^3*a^5)","A",0
511,1,93,0,0.158645," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{231 \, b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{6}} - \frac{213 \, b^{5} x^{5} + 472 \, a b^{4} x^{3} + 267 \, a^{2} b^{3} x}{48 \, {\left(b x^{2} + a\right)}^{3} a^{6}} - \frac{150 \, b^{2} x^{4} - 20 \, a b x^{2} + 3 \, a^{2}}{15 \, a^{6} x^{5}}"," ",0,"-231/16*b^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6) - 1/48*(213*b^5*x^5 + 472*a*b^4*x^3 + 267*a^2*b^3*x)/((b*x^2 + a)^3*a^6) - 1/15*(150*b^2*x^4 - 20*a*b*x^2 + 3*a^2)/(a^6*x^5)","A",0
512,1,113,0,0.156625," ","integrate(x^15/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{21 \, a^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{8}} + \frac{b^{6} x^{4} - 12 \, a b^{5} x^{2}}{4 \, b^{12}} - \frac{959 \, a^{2} b^{5} x^{10} + 4095 \, a^{3} b^{4} x^{8} + 7140 \, a^{4} b^{3} x^{6} + 6300 \, a^{5} b^{2} x^{4} + 2800 \, a^{6} b x^{2} + 500 \, a^{7}}{40 \, {\left(b x^{2} + a\right)}^{5} b^{8}}"," ",0,"21/2*a^2*log(abs(b*x^2 + a))/b^8 + 1/4*(b^6*x^4 - 12*a*b^5*x^2)/b^12 - 1/40*(959*a^2*b^5*x^10 + 4095*a^3*b^4*x^8 + 7140*a^4*b^3*x^6 + 6300*a^5*b^2*x^4 + 2800*a^6*b*x^2 + 500*a^7)/((b*x^2 + a)^5*b^8)","A",0
513,1,95,0,0.231826," ","integrate(x^13/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{x^{2}}{2 \, b^{6}} - \frac{3 \, a \log\left({\left| b x^{2} + a \right|}\right)}{b^{7}} + \frac{137 \, a b^{5} x^{10} + 535 \, a^{2} b^{4} x^{8} + 870 \, a^{3} b^{3} x^{6} + 720 \, a^{4} b^{2} x^{4} + 300 \, a^{5} b x^{2} + 50 \, a^{6}}{20 \, {\left(b x^{2} + a\right)}^{5} b^{7}}"," ",0,"1/2*x^2/b^6 - 3*a*log(abs(b*x^2 + a))/b^7 + 1/20*(137*a*b^5*x^10 + 535*a^2*b^4*x^8 + 870*a^3*b^3*x^6 + 720*a^4*b^2*x^4 + 300*a^5*b*x^2 + 50*a^6)/((b*x^2 + a)^5*b^7)","A",0
514,1,75,0,0.157396," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{6}} - \frac{137 \, b^{4} x^{10} + 385 \, a b^{3} x^{8} + 470 \, a^{2} b^{2} x^{6} + 270 \, a^{3} b x^{4} + 60 \, a^{4} x^{2}}{120 \, {\left(b x^{2} + a\right)}^{5} b^{5}}"," ",0,"1/2*log(abs(b*x^2 + a))/b^6 - 1/120*(137*b^4*x^10 + 385*a*b^3*x^8 + 470*a^2*b^2*x^6 + 270*a^3*b*x^4 + 60*a^4*x^2)/((b*x^2 + a)^5*b^5)","A",0
515,1,55,0,0.197234," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, {\left(b x^{2} + a\right)}^{5} b^{5}}"," ",0,"-1/10*(5*b^4*x^8 + 10*a*b^3*x^6 + 10*a^2*b^2*x^4 + 5*a^3*b*x^2 + a^4)/((b*x^2 + a)^5*b^5)","B",0
516,1,44,0,0.159166," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{10 \, b^{3} x^{6} + 10 \, a b^{2} x^{4} + 5 \, a^{2} b x^{2} + a^{3}}{40 \, {\left(b x^{2} + a\right)}^{5} b^{4}}"," ",0,"-1/40*(10*b^3*x^6 + 10*a*b^2*x^4 + 5*a^2*b*x^2 + a^3)/((b*x^2 + a)^5*b^4)","A",0
517,1,33,0,0.191858," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{10 \, b^{2} x^{4} + 5 \, a b x^{2} + a^{2}}{60 \, {\left(b x^{2} + a\right)}^{5} b^{3}}"," ",0,"-1/60*(10*b^2*x^4 + 5*a*b*x^2 + a^2)/((b*x^2 + a)^5*b^3)","A",0
518,1,22,0,0.159059," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{5 \, b x^{2} + a}{40 \, {\left(b x^{2} + a\right)}^{5} b^{2}}"," ",0,"-1/40*(5*b*x^2 + a)/((b*x^2 + a)^5*b^2)","A",0
519,1,14,0,0.194393," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{1}{10 \, {\left(b x^{2} + a\right)}^{5} b}"," ",0,"-1/10/((b*x^2 + a)^5*b)","A",0
520,1,92,0,0.152470," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, a^{6}} - \frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{6}} + \frac{137 \, b^{5} x^{10} + 745 \, a b^{4} x^{8} + 1640 \, a^{2} b^{3} x^{6} + 1840 \, a^{3} b^{2} x^{4} + 1070 \, a^{4} b x^{2} + 274 \, a^{5}}{120 \, {\left(b x^{2} + a\right)}^{5} a^{6}}"," ",0,"1/2*log(x^2)/a^6 - 1/2*log(abs(b*x^2 + a))/a^6 + 1/120*(137*b^5*x^10 + 745*a*b^4*x^8 + 1640*a^2*b^3*x^6 + 1840*a^3*b^2*x^4 + 1070*a^4*b*x^2 + 274*a^5)/((b*x^2 + a)^5*a^6)","A",0
521,1,115,0,0.158931," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{3 \, b \log\left(x^{2}\right)}{a^{7}} + \frac{3 \, b \log\left({\left| b x^{2} + a \right|}\right)}{a^{7}} + \frac{6 \, b x^{2} - a}{2 \, a^{7} x^{2}} - \frac{137 \, b^{6} x^{10} + 735 \, a b^{5} x^{8} + 1590 \, a^{2} b^{4} x^{6} + 1740 \, a^{3} b^{3} x^{4} + 970 \, a^{4} b^{2} x^{2} + 224 \, a^{5} b}{20 \, {\left(b x^{2} + a\right)}^{5} a^{7}}"," ",0,"-3*b*log(x^2)/a^7 + 3*b*log(abs(b*x^2 + a))/a^7 + 1/2*(6*b*x^2 - a)/(a^7*x^2) - 1/20*(137*b^6*x^10 + 735*a*b^5*x^8 + 1590*a^2*b^4*x^6 + 1740*a^3*b^3*x^4 + 970*a^4*b^2*x^2 + 224*a^5*b)/((b*x^2 + a)^5*a^7)","A",0
522,1,130,0,0.159183," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{21 \, b^{2} \log\left(x^{2}\right)}{2 \, a^{8}} - \frac{21 \, b^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{8}} - \frac{63 \, b^{2} x^{4} - 12 \, a b x^{2} + a^{2}}{4 \, a^{8} x^{4}} + \frac{959 \, b^{7} x^{10} + 5095 \, a b^{6} x^{8} + 10890 \, a^{2} b^{5} x^{6} + 11730 \, a^{3} b^{4} x^{4} + 6390 \, a^{4} b^{3} x^{2} + 1418 \, a^{5} b^{2}}{40 \, {\left(b x^{2} + a\right)}^{5} a^{8}}"," ",0,"21/2*b^2*log(x^2)/a^8 - 21/2*b^2*log(abs(b*x^2 + a))/a^8 - 1/4*(63*b^2*x^4 - 12*a*b*x^2 + a^2)/(a^8*x^4) + 1/40*(959*b^7*x^10 + 5095*a*b^6*x^8 + 10890*a^2*b^5*x^6 + 11730*a^3*b^4*x^4 + 6390*a^4*b^3*x^2 + 1418*a^5*b^2)/((b*x^2 + a)^5*a^8)","A",0
523,1,117,0,0.168936," ","integrate(x^16/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{9009 \, a^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{8}} + \frac{26635 \, a^{3} b^{4} x^{9} + 94430 \, a^{4} b^{3} x^{7} + 128128 \, a^{5} b^{2} x^{5} + 78370 \, a^{6} b x^{3} + 18165 \, a^{7} x}{1280 \, {\left(b x^{2} + a\right)}^{5} b^{8}} + \frac{b^{24} x^{5} - 10 \, a b^{23} x^{3} + 105 \, a^{2} b^{22} x}{5 \, b^{30}}"," ",0,"-9009/256*a^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^8) + 1/1280*(26635*a^3*b^4*x^9 + 94430*a^4*b^3*x^7 + 128128*a^5*b^2*x^5 + 78370*a^6*b*x^3 + 18165*a^7*x)/((b*x^2 + a)^5*b^8) + 1/5*(b^24*x^5 - 10*a*b^23*x^3 + 105*a^2*b^22*x)/b^30","A",0
524,1,106,0,0.160016," ","integrate(x^14/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{3003 \, a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{7}} - \frac{35595 \, a^{2} b^{4} x^{9} + 121310 \, a^{3} b^{3} x^{7} + 160384 \, a^{4} b^{2} x^{5} + 96290 \, a^{5} b x^{3} + 22005 \, a^{6} x}{3840 \, {\left(b x^{2} + a\right)}^{5} b^{7}} + \frac{b^{12} x^{3} - 18 \, a b^{11} x}{3 \, b^{18}}"," ",0,"3003/256*a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^7) - 1/3840*(35595*a^2*b^4*x^9 + 121310*a^3*b^3*x^7 + 160384*a^4*b^2*x^5 + 96290*a^5*b*x^3 + 22005*a^6*x)/((b*x^2 + a)^5*b^7) + 1/3*(b^12*x^3 - 18*a*b^11*x)/b^18","A",0
525,1,87,0,0.170952," ","integrate(x^12/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{693 \, a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{6}} + \frac{x}{b^{6}} + \frac{4215 \, a b^{4} x^{9} + 13270 \, a^{2} b^{3} x^{7} + 16768 \, a^{3} b^{2} x^{5} + 9770 \, a^{4} b x^{3} + 2185 \, a^{5} x}{1280 \, {\left(b x^{2} + a\right)}^{5} b^{6}}"," ",0,"-693/256*a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + x/b^6 + 1/1280*(4215*a*b^4*x^9 + 13270*a^2*b^3*x^7 + 16768*a^3*b^2*x^5 + 9770*a^4*b*x^3 + 2185*a^5*x)/((b*x^2 + a)^5*b^6)","A",0
526,1,78,0,0.185244," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{63 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{5}} - \frac{965 \, b^{4} x^{9} + 2370 \, a b^{3} x^{7} + 2688 \, a^{2} b^{2} x^{5} + 1470 \, a^{3} b x^{3} + 315 \, a^{4} x}{1280 \, {\left(b x^{2} + a\right)}^{5} b^{5}}"," ",0,"63/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) - 1/1280*(965*b^4*x^9 + 2370*a*b^3*x^7 + 2688*a^2*b^2*x^5 + 1470*a^3*b*x^3 + 315*a^4*x)/((b*x^2 + a)^5*b^5)","A",0
527,1,84,0,0.160083," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{7 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a b^{4}} + \frac{105 \, b^{4} x^{9} - 790 \, a b^{3} x^{7} - 896 \, a^{2} b^{2} x^{5} - 490 \, a^{3} b x^{3} - 105 \, a^{4} x}{3840 \, {\left(b x^{2} + a\right)}^{5} a b^{4}}"," ",0,"7/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^4) + 1/3840*(105*b^4*x^9 - 790*a*b^3*x^7 - 896*a^2*b^2*x^5 - 490*a^3*b*x^3 - 105*a^4*x)/((b*x^2 + a)^5*a*b^4)","A",0
528,1,84,0,0.156959," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{2} b^{3}} + \frac{15 \, b^{4} x^{9} + 70 \, a b^{3} x^{7} - 128 \, a^{2} b^{2} x^{5} - 70 \, a^{3} b x^{3} - 15 \, a^{4} x}{1280 \, {\left(b x^{2} + a\right)}^{5} a^{2} b^{3}}"," ",0,"3/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^3) + 1/1280*(15*b^4*x^9 + 70*a*b^3*x^7 - 128*a^2*b^2*x^5 - 70*a^3*b*x^3 - 15*a^4*x)/((b*x^2 + a)^5*a^2*b^3)","A",0
529,1,84,0,0.164457," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{3} b^{2}} + \frac{15 \, b^{4} x^{9} + 70 \, a b^{3} x^{7} + 128 \, a^{2} b^{2} x^{5} - 70 \, a^{3} b x^{3} - 15 \, a^{4} x}{1280 \, {\left(b x^{2} + a\right)}^{5} a^{3} b^{2}}"," ",0,"3/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b^2) + 1/1280*(15*b^4*x^9 + 70*a*b^3*x^7 + 128*a^2*b^2*x^5 - 70*a^3*b*x^3 - 15*a^4*x)/((b*x^2 + a)^5*a^3*b^2)","A",0
530,1,84,0,0.169890," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{7 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{4} b} + \frac{105 \, b^{4} x^{9} + 490 \, a b^{3} x^{7} + 896 \, a^{2} b^{2} x^{5} + 790 \, a^{3} b x^{3} - 105 \, a^{4} x}{3840 \, {\left(b x^{2} + a\right)}^{5} a^{4} b}"," ",0,"7/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4*b) + 1/3840*(105*b^4*x^9 + 490*a*b^3*x^7 + 896*a^2*b^2*x^5 + 790*a^3*b*x^3 - 105*a^4*x)/((b*x^2 + a)^5*a^4*b)","A",0
531,1,78,0,0.168201," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{63 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{5}} + \frac{315 \, b^{4} x^{9} + 1470 \, a b^{3} x^{7} + 2688 \, a^{2} b^{2} x^{5} + 2370 \, a^{3} b x^{3} + 965 \, a^{4} x}{1280 \, {\left(b x^{2} + a\right)}^{5} a^{5}}"," ",0,"63/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5) + 1/1280*(315*b^4*x^9 + 1470*a*b^3*x^7 + 2688*a^2*b^2*x^5 + 2370*a^3*b*x^3 + 965*a^4*x)/((b*x^2 + a)^5*a^5)","A",0
532,1,90,0,0.158400," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{693 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{6}} - \frac{1}{a^{6} x} - \frac{2185 \, b^{5} x^{9} + 9770 \, a b^{4} x^{7} + 16768 \, a^{2} b^{3} x^{5} + 13270 \, a^{3} b^{2} x^{3} + 4215 \, a^{4} b x}{1280 \, {\left(b x^{2} + a\right)}^{5} a^{6}}"," ",0,"-693/256*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6) - 1/(a^6*x) - 1/1280*(2185*b^5*x^9 + 9770*a*b^4*x^7 + 16768*a^2*b^3*x^5 + 13270*a^3*b^2*x^3 + 4215*a^4*b*x)/((b*x^2 + a)^5*a^6)","A",0
533,1,104,0,0.158820," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{3003 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{7}} + \frac{18 \, b x^{2} - a}{3 \, a^{7} x^{3}} + \frac{22005 \, b^{6} x^{9} + 96290 \, a b^{5} x^{7} + 160384 \, a^{2} b^{4} x^{5} + 121310 \, a^{3} b^{3} x^{3} + 35595 \, a^{4} b^{2} x}{3840 \, {\left(b x^{2} + a\right)}^{5} a^{7}}"," ",0,"3003/256*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^7) + 1/3*(18*b*x^2 - a)/(a^7*x^3) + 1/3840*(22005*b^6*x^9 + 96290*a*b^5*x^7 + 160384*a^2*b^4*x^5 + 121310*a^3*b^3*x^3 + 35595*a^4*b^2*x)/((b*x^2 + a)^5*a^7)","A",0
534,1,115,0,0.164325," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{9009 \, b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{8}} - \frac{45045 \, b^{7} x^{14} + 210210 \, a b^{6} x^{12} + 384384 \, a^{2} b^{5} x^{10} + 338910 \, a^{3} b^{4} x^{8} + 137995 \, a^{4} b^{3} x^{6} + 16640 \, a^{5} b^{2} x^{4} - 1280 \, a^{6} b x^{2} + 256 \, a^{7}}{1280 \, {\left(b x^{3} + a x\right)}^{5} a^{8}}"," ",0,"-9009/256*b^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^8) - 1/1280*(45045*b^7*x^14 + 210210*a*b^6*x^12 + 384384*a^2*b^5*x^10 + 338910*a^3*b^4*x^8 + 137995*a^4*b^3*x^6 + 16640*a^5*b^2*x^4 - 1280*a^6*b*x^2 + 256*a^7)/((b*x^3 + a*x)^5*a^8)","A",0
535,1,15,0,0.149035," ","integrate(1/(x^4+2*x^2+1),x, algorithm=""giac"")","\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right)"," ",0,"1/2*x/(x^2 + 1) + 1/2*arctan(x)","A",0
536,1,9,0,0.149072," ","integrate(x/(x^4+2*x^2+1),x, algorithm=""giac"")","-\frac{1}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"-1/2/(x^2 + 1)","A",0
537,1,15,0,0.157372," ","integrate(x^2/(x^4+2*x^2+1),x, algorithm=""giac"")","-\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right)"," ",0,"-1/2*x/(x^2 + 1) + 1/2*arctan(x)","A",0
538,1,18,0,0.195697," ","integrate(x^3/(x^4+2*x^2+1),x, algorithm=""giac"")","\frac{1}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"1/2/(x^2 + 1) + 1/2*log(x^2 + 1)","A",0
539,1,9,0,0.162435," ","integrate(x/(x^4-18*x^2+81),x, algorithm=""giac"")","-\frac{1}{2 \, {\left(x^{2} - 9\right)}}"," ",0,"-1/2/(x^2 - 9)","A",0
540,1,19,0,0.150696," ","integrate(x^3/(x^4-8*x^2+16),x, algorithm=""giac"")","-\frac{2}{x^{2} - 4} + \frac{1}{2} \, \log\left({\left| x^{2} - 4 \right|}\right)"," ",0,"-2/(x^2 - 4) + 1/2*log(abs(x^2 - 4))","A",0
541,1,29,0,0.156797," ","integrate(x^5*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, b x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{6} \, a x^{6} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/8*b*x^8*sgn(b*x^2 + a) + 1/6*a*x^6*sgn(b*x^2 + a)","A",0
542,1,23,0,0.183535," ","integrate(x^3*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, b x^{6} + 3 \, a x^{4}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/12*(2*b*x^6 + 3*a*x^4)*sgn(b*x^2 + a)","A",0
543,1,22,0,0.156706," ","integrate(x*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(b x^{4} + 2 \, a x^{2}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/4*(b*x^4 + 2*a*x^2)*sgn(b*x^2 + a)","A",0
544,1,30,0,0.158145," ","integrate(((b*x^2+a)^2)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{2} \, a \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/2*b*x^2*sgn(b*x^2 + a) + 1/2*a*log(x^2)*sgn(b*x^2 + a)","A",0
545,1,45,0,0.234804," ","integrate(((b*x^2+a)^2)^(1/2)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, b \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a \mathrm{sgn}\left(b x^{2} + a\right)}{2 \, x^{2}}"," ",0,"1/2*b*log(x^2)*sgn(b*x^2 + a) - 1/2*(b*x^2*sgn(b*x^2 + a) + a*sgn(b*x^2 + a))/x^2","A",0
546,1,30,0,0.157482," ","integrate(((b*x^2+a)^2)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{2 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a \mathrm{sgn}\left(b x^{2} + a\right)}{4 \, x^{4}}"," ",0,"-1/4*(2*b*x^2*sgn(b*x^2 + a) + a*sgn(b*x^2 + a))/x^4","A",0
547,1,31,0,0.155465," ","integrate(((b*x^2+a)^2)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{3 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, a \mathrm{sgn}\left(b x^{2} + a\right)}{12 \, x^{6}}"," ",0,"-1/12*(3*b*x^2*sgn(b*x^2 + a) + 2*a*sgn(b*x^2 + a))/x^6","A",0
548,1,31,0,0.157617," ","integrate(((b*x^2+a)^2)^(1/2)/x^9,x, algorithm=""giac"")","-\frac{4 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a \mathrm{sgn}\left(b x^{2} + a\right)}{24 \, x^{8}}"," ",0,"-1/24*(4*b*x^2*sgn(b*x^2 + a) + 3*a*sgn(b*x^2 + a))/x^8","A",0
549,1,31,0,0.163910," ","integrate(((b*x^2+a)^2)^(1/2)/x^11,x, algorithm=""giac"")","-\frac{5 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, a \mathrm{sgn}\left(b x^{2} + a\right)}{40 \, x^{10}}"," ",0,"-1/40*(5*b*x^2*sgn(b*x^2 + a) + 4*a*sgn(b*x^2 + a))/x^10","A",0
550,1,29,0,0.166374," ","integrate(x^4*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{7} \, b x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{5} \, a x^{5} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/7*b*x^7*sgn(b*x^2 + a) + 1/5*a*x^5*sgn(b*x^2 + a)","A",0
551,1,29,0,0.153687," ","integrate(x^2*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{3} \, a x^{3} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/5*b*x^5*sgn(b*x^2 + a) + 1/3*a*x^3*sgn(b*x^2 + a)","A",0
552,1,20,0,0.184751," ","integrate(((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(b x^{3} + 3 \, a x\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/3*(b*x^3 + 3*a*x)*sgn(b*x^2 + a)","A",0
553,1,26,0,0.156270," ","integrate(((b*x^2+a)^2)^(1/2)/x^2,x, algorithm=""giac"")","b x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{a \mathrm{sgn}\left(b x^{2} + a\right)}{x}"," ",0,"b*x*sgn(b*x^2 + a) - a*sgn(b*x^2 + a)/x","A",0
554,1,30,0,0.173178," ","integrate(((b*x^2+a)^2)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{3 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a \mathrm{sgn}\left(b x^{2} + a\right)}{3 \, x^{3}}"," ",0,"-1/3*(3*b*x^2*sgn(b*x^2 + a) + a*sgn(b*x^2 + a))/x^3","A",0
555,1,31,0,0.151597," ","integrate(((b*x^2+a)^2)^(1/2)/x^6,x, algorithm=""giac"")","-\frac{5 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a \mathrm{sgn}\left(b x^{2} + a\right)}{15 \, x^{5}}"," ",0,"-1/15*(5*b*x^2*sgn(b*x^2 + a) + 3*a*sgn(b*x^2 + a))/x^5","A",0
556,1,31,0,0.156187," ","integrate(((b*x^2+a)^2)^(1/2)/x^8,x, algorithm=""giac"")","-\frac{7 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a \mathrm{sgn}\left(b x^{2} + a\right)}{35 \, x^{7}}"," ",0,"-1/35*(7*b*x^2*sgn(b*x^2 + a) + 5*a*sgn(b*x^2 + a))/x^7","A",0
557,1,31,0,0.161153," ","integrate(((b*x^2+a)^2)^(1/2)/x^10,x, algorithm=""giac"")","-\frac{9 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 7 \, a \mathrm{sgn}\left(b x^{2} + a\right)}{63 \, x^{9}}"," ",0,"-1/63*(9*b*x^2*sgn(b*x^2 + a) + 7*a*sgn(b*x^2 + a))/x^9","A",0
558,1,67,0,0.155613," ","integrate(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{16} \, b^{3} x^{16} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{14} \, a b^{2} x^{14} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{4} \, a^{2} b x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{10} \, a^{3} x^{10} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/16*b^3*x^16*sgn(b*x^2 + a) + 3/14*a*b^2*x^14*sgn(b*x^2 + a) + 1/4*a^2*b*x^12*sgn(b*x^2 + a) + 1/10*a^3*x^10*sgn(b*x^2 + a)","A",0
559,1,67,0,0.158492," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{14} \, b^{3} x^{14} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{4} \, a b^{2} x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{10} \, a^{2} b x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{8} \, a^{3} x^{8} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/14*b^3*x^14*sgn(b*x^2 + a) + 1/4*a*b^2*x^12*sgn(b*x^2 + a) + 3/10*a^2*b*x^10*sgn(b*x^2 + a) + 1/8*a^3*x^8*sgn(b*x^2 + a)","A",0
560,1,67,0,0.219390," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{12} \, b^{3} x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{10} \, a b^{2} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{8} \, a^{2} b x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{6} \, a^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/12*b^3*x^12*sgn(b*x^2 + a) + 3/10*a*b^2*x^10*sgn(b*x^2 + a) + 3/8*a^2*b*x^8*sgn(b*x^2 + a) + 1/6*a^3*x^6*sgn(b*x^2 + a)","A",0
561,1,45,0,0.154018," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{40} \, {\left(4 \, b^{3} x^{10} + 15 \, a b^{2} x^{8} + 20 \, a^{2} b x^{6} + 10 \, a^{3} x^{4}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/40*(4*b^3*x^10 + 15*a*b^2*x^8 + 20*a^2*b*x^6 + 10*a^3*x^4)*sgn(b*x^2 + a)","A",0
562,1,44,0,0.150927," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, {\left(b x^{4} + 2 \, a x^{2}\right)} a^{2} + {\left(b x^{4} + 2 \, a x^{2}\right)}^{2} b\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/8*(2*(b*x^4 + 2*a*x^2)*a^2 + (b*x^4 + 2*a*x^2)^2*b)*sgn(b*x^2 + a)","A",0
563,1,68,0,0.191136," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{6} \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{4} \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{2} \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{2} \, a^{3} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/6*b^3*x^6*sgn(b*x^2 + a) + 3/4*a*b^2*x^4*sgn(b*x^2 + a) + 3/2*a^2*b*x^2*sgn(b*x^2 + a) + 1/2*a^3*log(x^2)*sgn(b*x^2 + a)","A",0
564,1,87,0,0.160665," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, b^{3} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{2} \, a b^{2} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{2} \, a^{2} b \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{3 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{2 \, x^{2}}"," ",0,"1/4*b^3*x^4*sgn(b*x^2 + a) + 3/2*a*b^2*x^2*sgn(b*x^2 + a) + 3/2*a^2*b*log(x^2)*sgn(b*x^2 + a) - 1/2*(3*a^2*b*x^2*sgn(b*x^2 + a) + a^3*sgn(b*x^2 + a))/x^2","A",0
565,1,87,0,0.173221," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, b^{3} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{2} \, a b^{2} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{9 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{4 \, x^{4}}"," ",0,"1/2*b^3*x^2*sgn(b*x^2 + a) + 3/2*a*b^2*log(x^2)*sgn(b*x^2 + a) - 1/4*(9*a*b^2*x^4*sgn(b*x^2 + a) + 6*a^2*b*x^2*sgn(b*x^2 + a) + a^3*sgn(b*x^2 + a))/x^4","A",0
566,1,87,0,0.187839," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^7,x, algorithm=""giac"")","\frac{1}{2} \, b^{3} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{11 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 18 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 9 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{12 \, x^{6}}"," ",0,"1/2*b^3*log(x^2)*sgn(b*x^2 + a) - 1/12*(11*b^3*x^6*sgn(b*x^2 + a) + 18*a*b^2*x^4*sgn(b*x^2 + a) + 9*a^2*b*x^2*sgn(b*x^2 + a) + 2*a^3*sgn(b*x^2 + a))/x^6","A",0
567,1,68,0,0.173554," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^9,x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{8 \, x^{8}}"," ",0,"-1/8*(4*b^3*x^6*sgn(b*x^2 + a) + 6*a*b^2*x^4*sgn(b*x^2 + a) + 4*a^2*b*x^2*sgn(b*x^2 + a) + a^3*sgn(b*x^2 + a))/x^8","B",0
568,1,69,0,0.207217," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^11,x, algorithm=""giac"")","-\frac{10 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 20 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{40 \, x^{10}}"," ",0,"-1/40*(10*b^3*x^6*sgn(b*x^2 + a) + 20*a*b^2*x^4*sgn(b*x^2 + a) + 15*a^2*b*x^2*sgn(b*x^2 + a) + 4*a^3*sgn(b*x^2 + a))/x^10","A",0
569,1,69,0,0.161762," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^13,x, algorithm=""giac"")","-\frac{20 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 45 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 36 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{120 \, x^{12}}"," ",0,"-1/120*(20*b^3*x^6*sgn(b*x^2 + a) + 45*a*b^2*x^4*sgn(b*x^2 + a) + 36*a^2*b*x^2*sgn(b*x^2 + a) + 10*a^3*sgn(b*x^2 + a))/x^12","A",0
570,1,69,0,0.155650," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^15,x, algorithm=""giac"")","-\frac{35 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 84 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 70 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 20 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{280 \, x^{14}}"," ",0,"-1/280*(35*b^3*x^6*sgn(b*x^2 + a) + 84*a*b^2*x^4*sgn(b*x^2 + a) + 70*a^2*b*x^2*sgn(b*x^2 + a) + 20*a^3*sgn(b*x^2 + a))/x^14","A",0
571,1,69,0,0.182596," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^17,x, algorithm=""giac"")","-\frac{56 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 140 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 120 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 35 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{560 \, x^{16}}"," ",0,"-1/560*(56*b^3*x^6*sgn(b*x^2 + a) + 140*a*b^2*x^4*sgn(b*x^2 + a) + 120*a^2*b*x^2*sgn(b*x^2 + a) + 35*a^3*sgn(b*x^2 + a))/x^16","A",0
572,1,67,0,0.159105," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{15} \, b^{3} x^{15} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{13} \, a b^{2} x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{11} \, a^{2} b x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{9} \, a^{3} x^{9} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/15*b^3*x^15*sgn(b*x^2 + a) + 3/13*a*b^2*x^13*sgn(b*x^2 + a) + 3/11*a^2*b*x^11*sgn(b*x^2 + a) + 1/9*a^3*x^9*sgn(b*x^2 + a)","A",0
573,1,67,0,0.158203," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{13} \, b^{3} x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{11} \, a b^{2} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{3} \, a^{2} b x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{7} \, a^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/13*b^3*x^13*sgn(b*x^2 + a) + 3/11*a*b^2*x^11*sgn(b*x^2 + a) + 1/3*a^2*b*x^9*sgn(b*x^2 + a) + 1/7*a^3*x^7*sgn(b*x^2 + a)","A",0
574,1,67,0,0.180657," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{11} \, b^{3} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{3} \, a b^{2} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{7} \, a^{2} b x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{5} \, a^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/11*b^3*x^11*sgn(b*x^2 + a) + 1/3*a*b^2*x^9*sgn(b*x^2 + a) + 3/7*a^2*b*x^7*sgn(b*x^2 + a) + 1/5*a^3*x^5*sgn(b*x^2 + a)","A",0
575,1,67,0,0.155211," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{7} \, a b^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{5} \, a^{2} b x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{3} \, a^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/9*b^3*x^9*sgn(b*x^2 + a) + 3/7*a*b^2*x^7*sgn(b*x^2 + a) + 3/5*a^2*b*x^5*sgn(b*x^2 + a) + 1/3*a^3*x^3*sgn(b*x^2 + a)","A",0
576,1,63,0,0.183684," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{3}{5} \, a b^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + a^{2} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} x \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/7*b^3*x^7*sgn(b*x^2 + a) + 3/5*a*b^2*x^5*sgn(b*x^2 + a) + a^2*b*x^3*sgn(b*x^2 + a) + a^3*x*sgn(b*x^2 + a)","A",0
577,1,64,0,0.163313," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{5} \, b^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + a b^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a^{2} b x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{x}"," ",0,"1/5*b^3*x^5*sgn(b*x^2 + a) + a*b^2*x^3*sgn(b*x^2 + a) + 3*a^2*b*x*sgn(b*x^2 + a) - a^3*sgn(b*x^2 + a)/x","A",0
578,1,67,0,0.157837," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, b^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a b^{2} x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{9 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{3 \, x^{3}}"," ",0,"1/3*b^3*x^3*sgn(b*x^2 + a) + 3*a*b^2*x*sgn(b*x^2 + a) - 1/3*(9*a^2*b*x^2*sgn(b*x^2 + a) + a^3*sgn(b*x^2 + a))/x^3","A",0
579,1,66,0,0.189873," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^6,x, algorithm=""giac"")","b^{3} x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{15 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{5 \, x^{5}}"," ",0,"b^3*x*sgn(b*x^2 + a) - 1/5*(15*a*b^2*x^4*sgn(b*x^2 + a) + 5*a^2*b*x^2*sgn(b*x^2 + a) + a^3*sgn(b*x^2 + a))/x^5","A",0
580,1,69,0,0.218724," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^8,x, algorithm=""giac"")","-\frac{35 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 35 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 21 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{35 \, x^{7}}"," ",0,"-1/35*(35*b^3*x^6*sgn(b*x^2 + a) + 35*a*b^2*x^4*sgn(b*x^2 + a) + 21*a^2*b*x^2*sgn(b*x^2 + a) + 5*a^3*sgn(b*x^2 + a))/x^7","A",0
581,1,69,0,0.190022," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^10,x, algorithm=""giac"")","-\frac{105 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 189 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 135 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 35 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{315 \, x^{9}}"," ",0,"-1/315*(105*b^3*x^6*sgn(b*x^2 + a) + 189*a*b^2*x^4*sgn(b*x^2 + a) + 135*a^2*b*x^2*sgn(b*x^2 + a) + 35*a^3*sgn(b*x^2 + a))/x^9","A",0
582,1,69,0,0.157208," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^12,x, algorithm=""giac"")","-\frac{231 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 495 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 385 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{1155 \, x^{11}}"," ",0,"-1/1155*(231*b^3*x^6*sgn(b*x^2 + a) + 495*a*b^2*x^4*sgn(b*x^2 + a) + 385*a^2*b*x^2*sgn(b*x^2 + a) + 105*a^3*sgn(b*x^2 + a))/x^11","A",0
583,1,69,0,0.157370," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^14,x, algorithm=""giac"")","-\frac{429 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 1001 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 819 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 231 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{3003 \, x^{13}}"," ",0,"-1/3003*(429*b^3*x^6*sgn(b*x^2 + a) + 1001*a*b^2*x^4*sgn(b*x^2 + a) + 819*a^2*b*x^2*sgn(b*x^2 + a) + 231*a^3*sgn(b*x^2 + a))/x^13","A",0
584,1,69,0,0.205618," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^16,x, algorithm=""giac"")","-\frac{715 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 1755 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 1485 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 429 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{6435 \, x^{15}}"," ",0,"-1/6435*(715*b^3*x^6*sgn(b*x^2 + a) + 1755*a*b^2*x^4*sgn(b*x^2 + a) + 1485*a^2*b*x^2*sgn(b*x^2 + a) + 429*a^3*sgn(b*x^2 + a))/x^15","A",0
585,1,105,0,0.156559," ","integrate(x^13*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24} \, b^{5} x^{24} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{22} \, a b^{4} x^{22} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{2} \, a^{2} b^{3} x^{20} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{9} \, a^{3} b^{2} x^{18} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{16} \, a^{4} b x^{16} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{14} \, a^{5} x^{14} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/24*b^5*x^24*sgn(b*x^2 + a) + 5/22*a*b^4*x^22*sgn(b*x^2 + a) + 1/2*a^2*b^3*x^20*sgn(b*x^2 + a) + 5/9*a^3*b^2*x^18*sgn(b*x^2 + a) + 5/16*a^4*b*x^16*sgn(b*x^2 + a) + 1/14*a^5*x^14*sgn(b*x^2 + a)","A",0
586,1,105,0,0.153840," ","integrate(x^11*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{22} \, b^{5} x^{22} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{4} \, a b^{4} x^{20} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{9} \, a^{2} b^{3} x^{18} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{8} \, a^{3} b^{2} x^{16} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{14} \, a^{4} b x^{14} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{12} \, a^{5} x^{12} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/22*b^5*x^22*sgn(b*x^2 + a) + 1/4*a*b^4*x^20*sgn(b*x^2 + a) + 5/9*a^2*b^3*x^18*sgn(b*x^2 + a) + 5/8*a^3*b^2*x^16*sgn(b*x^2 + a) + 5/14*a^4*b*x^14*sgn(b*x^2 + a) + 1/12*a^5*x^12*sgn(b*x^2 + a)","A",0
587,1,105,0,0.160409," ","integrate(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{20} \, b^{5} x^{20} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{18} \, a b^{4} x^{18} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{8} \, a^{2} b^{3} x^{16} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{7} \, a^{3} b^{2} x^{14} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{12} \, a^{4} b x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{10} \, a^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/20*b^5*x^20*sgn(b*x^2 + a) + 5/18*a*b^4*x^18*sgn(b*x^2 + a) + 5/8*a^2*b^3*x^16*sgn(b*x^2 + a) + 5/7*a^3*b^2*x^14*sgn(b*x^2 + a) + 5/12*a^4*b*x^12*sgn(b*x^2 + a) + 1/10*a^5*x^10*sgn(b*x^2 + a)","A",0
588,1,105,0,0.156267," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{18} \, b^{5} x^{18} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{16} \, a b^{4} x^{16} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{7} \, a^{2} b^{3} x^{14} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{6} \, a^{3} b^{2} x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{2} \, a^{4} b x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{8} \, a^{5} x^{8} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/18*b^5*x^18*sgn(b*x^2 + a) + 5/16*a*b^4*x^16*sgn(b*x^2 + a) + 5/7*a^2*b^3*x^14*sgn(b*x^2 + a) + 5/6*a^3*b^2*x^12*sgn(b*x^2 + a) + 1/2*a^4*b*x^10*sgn(b*x^2 + a) + 1/8*a^5*x^8*sgn(b*x^2 + a)","A",0
589,1,104,0,0.192781," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{16} \, b^{5} x^{16} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{14} \, a b^{4} x^{14} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{6} \, a^{2} b^{3} x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} b^{2} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{8} \, a^{4} b x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{6} \, a^{5} x^{6} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/16*b^5*x^16*sgn(b*x^2 + a) + 5/14*a*b^4*x^14*sgn(b*x^2 + a) + 5/6*a^2*b^3*x^12*sgn(b*x^2 + a) + a^3*b^2*x^10*sgn(b*x^2 + a) + 5/8*a^4*b*x^8*sgn(b*x^2 + a) + 1/6*a^5*x^6*sgn(b*x^2 + a)","A",0
590,1,67,0,0.202127," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{84} \, {\left(6 \, b^{5} x^{14} + 35 \, a b^{4} x^{12} + 84 \, a^{2} b^{3} x^{10} + 105 \, a^{3} b^{2} x^{8} + 70 \, a^{4} b x^{6} + 21 \, a^{5} x^{4}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/84*(6*b^5*x^14 + 35*a*b^4*x^12 + 84*a^2*b^3*x^10 + 105*a^3*b^2*x^8 + 70*a^4*b*x^6 + 21*a^5*x^4)*sgn(b*x^2 + a)","A",0
591,1,66,0,0.157612," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, {\left(b x^{4} + 2 \, a x^{2}\right)} a^{4} + 3 \, {\left(b x^{4} + 2 \, a x^{2}\right)}^{2} a^{2} b + {\left(b x^{4} + 2 \, a x^{2}\right)}^{3} b^{2}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/12*(3*(b*x^4 + 2*a*x^2)*a^4 + 3*(b*x^4 + 2*a*x^2)^2*a^2*b + (b*x^4 + 2*a*x^2)^3*b^2)*sgn(b*x^2 + a)","B",0
592,1,106,0,0.192775," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x,x, algorithm=""giac"")","\frac{1}{10} \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{8} \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{3} \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{2} \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{2} \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{2} \, a^{5} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/10*b^5*x^10*sgn(b*x^2 + a) + 5/8*a*b^4*x^8*sgn(b*x^2 + a) + 5/3*a^2*b^3*x^6*sgn(b*x^2 + a) + 5/2*a^3*b^2*x^4*sgn(b*x^2 + a) + 5/2*a^4*b*x^2*sgn(b*x^2 + a) + 1/2*a^5*log(x^2)*sgn(b*x^2 + a)","A",0
593,1,125,0,0.161587," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^3,x, algorithm=""giac"")","\frac{1}{8} \, b^{5} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{6} \, a b^{4} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{2} \, a^{2} b^{3} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{2} \, a^{4} b \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{5 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{2 \, x^{2}}"," ",0,"1/8*b^5*x^8*sgn(b*x^2 + a) + 5/6*a*b^4*x^6*sgn(b*x^2 + a) + 5/2*a^2*b^3*x^4*sgn(b*x^2 + a) + 5*a^3*b^2*x^2*sgn(b*x^2 + a) + 5/2*a^4*b*log(x^2)*sgn(b*x^2 + a) - 1/2*(5*a^4*b*x^2*sgn(b*x^2 + a) + a^5*sgn(b*x^2 + a))/x^2","A",0
594,1,127,0,0.159038," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^5,x, algorithm=""giac"")","\frac{1}{6} \, b^{5} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{4} \, a b^{4} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a^{2} b^{3} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a^{3} b^{2} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{30 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{4 \, x^{4}}"," ",0,"1/6*b^5*x^6*sgn(b*x^2 + a) + 5/4*a*b^4*x^4*sgn(b*x^2 + a) + 5*a^2*b^3*x^2*sgn(b*x^2 + a) + 5*a^3*b^2*log(x^2)*sgn(b*x^2 + a) - 1/4*(30*a^3*b^2*x^4*sgn(b*x^2 + a) + 10*a^4*b*x^2*sgn(b*x^2 + a) + a^5*sgn(b*x^2 + a))/x^4","A",0
595,1,128,0,0.158366," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^7,x, algorithm=""giac"")","\frac{1}{4} \, b^{5} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{2} \, a b^{4} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a^{2} b^{3} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{110 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 60 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{12 \, x^{6}}"," ",0,"1/4*b^5*x^4*sgn(b*x^2 + a) + 5/2*a*b^4*x^2*sgn(b*x^2 + a) + 5*a^2*b^3*log(x^2)*sgn(b*x^2 + a) - 1/12*(110*a^2*b^3*x^6*sgn(b*x^2 + a) + 60*a^3*b^2*x^4*sgn(b*x^2 + a) + 15*a^4*b*x^2*sgn(b*x^2 + a) + 2*a^5*sgn(b*x^2 + a))/x^6","A",0
596,1,126,0,0.192455," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^9,x, algorithm=""giac"")","\frac{1}{2} \, b^{5} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{2} \, a b^{4} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{125 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 120 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 60 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 20 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{24 \, x^{8}}"," ",0,"1/2*b^5*x^2*sgn(b*x^2 + a) + 5/2*a*b^4*log(x^2)*sgn(b*x^2 + a) - 1/24*(125*a*b^4*x^8*sgn(b*x^2 + a) + 120*a^2*b^3*x^6*sgn(b*x^2 + a) + 60*a^3*b^2*x^4*sgn(b*x^2 + a) + 20*a^4*b*x^2*sgn(b*x^2 + a) + 3*a^5*sgn(b*x^2 + a))/x^8","A",0
597,1,125,0,0.163808," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^11,x, algorithm=""giac"")","\frac{1}{2} \, b^{5} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{137 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 300 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 300 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 200 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 75 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 12 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{120 \, x^{10}}"," ",0,"1/2*b^5*log(x^2)*sgn(b*x^2 + a) - 1/120*(137*b^5*x^10*sgn(b*x^2 + a) + 300*a*b^4*x^8*sgn(b*x^2 + a) + 300*a^2*b^3*x^6*sgn(b*x^2 + a) + 200*a^3*b^2*x^4*sgn(b*x^2 + a) + 75*a^4*b*x^2*sgn(b*x^2 + a) + 12*a^5*sgn(b*x^2 + a))/x^10","A",0
598,1,106,0,0.158406," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^13,x, algorithm=""giac"")","-\frac{6 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 20 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{12 \, x^{12}}"," ",0,"-1/12*(6*b^5*x^10*sgn(b*x^2 + a) + 15*a*b^4*x^8*sgn(b*x^2 + a) + 20*a^2*b^3*x^6*sgn(b*x^2 + a) + 15*a^3*b^2*x^4*sgn(b*x^2 + a) + 6*a^4*b*x^2*sgn(b*x^2 + a) + a^5*sgn(b*x^2 + a))/x^12","B",0
599,1,107,0,0.161491," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^15,x, algorithm=""giac"")","-\frac{21 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 70 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 84 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 35 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{84 \, x^{14}}"," ",0,"-1/84*(21*b^5*x^10*sgn(b*x^2 + a) + 70*a*b^4*x^8*sgn(b*x^2 + a) + 105*a^2*b^3*x^6*sgn(b*x^2 + a) + 84*a^3*b^2*x^4*sgn(b*x^2 + a) + 35*a^4*b*x^2*sgn(b*x^2 + a) + 6*a^5*sgn(b*x^2 + a))/x^14","A",0
600,1,107,0,0.212919," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^17,x, algorithm=""giac"")","-\frac{56 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 210 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 336 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 280 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 120 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 21 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{336 \, x^{16}}"," ",0,"-1/336*(56*b^5*x^10*sgn(b*x^2 + a) + 210*a*b^4*x^8*sgn(b*x^2 + a) + 336*a^2*b^3*x^6*sgn(b*x^2 + a) + 280*a^3*b^2*x^4*sgn(b*x^2 + a) + 120*a^4*b*x^2*sgn(b*x^2 + a) + 21*a^5*sgn(b*x^2 + a))/x^16","A",0
601,1,107,0,0.170073," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^19,x, algorithm=""giac"")","-\frac{126 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 504 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 840 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 720 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 315 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 56 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{1008 \, x^{18}}"," ",0,"-1/1008*(126*b^5*x^10*sgn(b*x^2 + a) + 504*a*b^4*x^8*sgn(b*x^2 + a) + 840*a^2*b^3*x^6*sgn(b*x^2 + a) + 720*a^3*b^2*x^4*sgn(b*x^2 + a) + 315*a^4*b*x^2*sgn(b*x^2 + a) + 56*a^5*sgn(b*x^2 + a))/x^18","A",0
602,1,107,0,0.163119," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^21,x, algorithm=""giac"")","-\frac{252 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 1050 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 1800 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 1575 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 700 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 126 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{2520 \, x^{20}}"," ",0,"-1/2520*(252*b^5*x^10*sgn(b*x^2 + a) + 1050*a*b^4*x^8*sgn(b*x^2 + a) + 1800*a^2*b^3*x^6*sgn(b*x^2 + a) + 1575*a^3*b^2*x^4*sgn(b*x^2 + a) + 700*a^4*b*x^2*sgn(b*x^2 + a) + 126*a^5*sgn(b*x^2 + a))/x^20","A",0
603,1,107,0,0.185831," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^23,x, algorithm=""giac"")","-\frac{462 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 1980 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 3465 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 3080 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 1386 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 252 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{5544 \, x^{22}}"," ",0,"-1/5544*(462*b^5*x^10*sgn(b*x^2 + a) + 1980*a*b^4*x^8*sgn(b*x^2 + a) + 3465*a^2*b^3*x^6*sgn(b*x^2 + a) + 3080*a^3*b^2*x^4*sgn(b*x^2 + a) + 1386*a^4*b*x^2*sgn(b*x^2 + a) + 252*a^5*sgn(b*x^2 + a))/x^22","A",0
604,1,107,0,0.166454," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^25,x, algorithm=""giac"")","-\frac{792 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 3465 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 6160 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 5544 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 2520 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 462 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{11088 \, x^{24}}"," ",0,"-1/11088*(792*b^5*x^10*sgn(b*x^2 + a) + 3465*a*b^4*x^8*sgn(b*x^2 + a) + 6160*a^2*b^3*x^6*sgn(b*x^2 + a) + 5544*a^3*b^2*x^4*sgn(b*x^2 + a) + 2520*a^4*b*x^2*sgn(b*x^2 + a) + 462*a^5*sgn(b*x^2 + a))/x^24","A",0
605,1,105,0,0.157100," ","integrate(x^12*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{23} \, b^{5} x^{23} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{21} \, a b^{4} x^{21} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{19} \, a^{2} b^{3} x^{19} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{17} \, a^{3} b^{2} x^{17} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{3} \, a^{4} b x^{15} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{13} \, a^{5} x^{13} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/23*b^5*x^23*sgn(b*x^2 + a) + 5/21*a*b^4*x^21*sgn(b*x^2 + a) + 10/19*a^2*b^3*x^19*sgn(b*x^2 + a) + 10/17*a^3*b^2*x^17*sgn(b*x^2 + a) + 1/3*a^4*b*x^15*sgn(b*x^2 + a) + 1/13*a^5*x^13*sgn(b*x^2 + a)","A",0
606,1,105,0,0.159778," ","integrate(x^10*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{21} \, b^{5} x^{21} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{19} \, a b^{4} x^{19} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{17} \, a^{2} b^{3} x^{17} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{3} \, a^{3} b^{2} x^{15} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{13} \, a^{4} b x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{11} \, a^{5} x^{11} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/21*b^5*x^21*sgn(b*x^2 + a) + 5/19*a*b^4*x^19*sgn(b*x^2 + a) + 10/17*a^2*b^3*x^17*sgn(b*x^2 + a) + 2/3*a^3*b^2*x^15*sgn(b*x^2 + a) + 5/13*a^4*b*x^13*sgn(b*x^2 + a) + 1/11*a^5*x^11*sgn(b*x^2 + a)","A",0
607,1,105,0,0.164476," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{19} \, b^{5} x^{19} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{17} \, a b^{4} x^{17} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{3} \, a^{2} b^{3} x^{15} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{13} \, a^{3} b^{2} x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{11} \, a^{4} b x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{9} \, a^{5} x^{9} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/19*b^5*x^19*sgn(b*x^2 + a) + 5/17*a*b^4*x^17*sgn(b*x^2 + a) + 2/3*a^2*b^3*x^15*sgn(b*x^2 + a) + 10/13*a^3*b^2*x^13*sgn(b*x^2 + a) + 5/11*a^4*b*x^11*sgn(b*x^2 + a) + 1/9*a^5*x^9*sgn(b*x^2 + a)","A",0
608,1,105,0,0.172407," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{17} \, b^{5} x^{17} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{3} \, a b^{4} x^{15} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{13} \, a^{2} b^{3} x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{11} \, a^{3} b^{2} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{9} \, a^{4} b x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{7} \, a^{5} x^{7} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/17*b^5*x^17*sgn(b*x^2 + a) + 1/3*a*b^4*x^15*sgn(b*x^2 + a) + 10/13*a^2*b^3*x^13*sgn(b*x^2 + a) + 10/11*a^3*b^2*x^11*sgn(b*x^2 + a) + 5/9*a^4*b*x^9*sgn(b*x^2 + a) + 1/7*a^5*x^7*sgn(b*x^2 + a)","A",0
609,1,105,0,0.157890," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{15} \, b^{5} x^{15} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{13} \, a b^{4} x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{11} \, a^{2} b^{3} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{9} \, a^{3} b^{2} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{7} \, a^{4} b x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{5} \, a^{5} x^{5} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/15*b^5*x^15*sgn(b*x^2 + a) + 5/13*a*b^4*x^13*sgn(b*x^2 + a) + 10/11*a^2*b^3*x^11*sgn(b*x^2 + a) + 10/9*a^3*b^2*x^9*sgn(b*x^2 + a) + 5/7*a^4*b*x^7*sgn(b*x^2 + a) + 1/5*a^5*x^5*sgn(b*x^2 + a)","A",0
610,1,104,0,0.179581," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{13} \, b^{5} x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{11} \, a b^{4} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{9} \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{7} \, a^{3} b^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + a^{4} b x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{1}{3} \, a^{5} x^{3} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/13*b^5*x^13*sgn(b*x^2 + a) + 5/11*a*b^4*x^11*sgn(b*x^2 + a) + 10/9*a^2*b^3*x^9*sgn(b*x^2 + a) + 10/7*a^3*b^2*x^7*sgn(b*x^2 + a) + a^4*b*x^5*sgn(b*x^2 + a) + 1/3*a^5*x^3*sgn(b*x^2 + a)","A",0
611,1,102,0,0.161708," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{11} \, b^{5} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{9} \, a b^{4} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{7} \, a^{2} b^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, a^{3} b^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{3} \, a^{4} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + a^{5} x \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/11*b^5*x^11*sgn(b*x^2 + a) + 5/9*a*b^4*x^9*sgn(b*x^2 + a) + 10/7*a^2*b^3*x^7*sgn(b*x^2 + a) + 2*a^3*b^2*x^5*sgn(b*x^2 + a) + 5/3*a^4*b*x^3*sgn(b*x^2 + a) + a^5*x*sgn(b*x^2 + a)","A",0
612,1,103,0,0.162413," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{5} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{7} \, a b^{4} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, a^{2} b^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{3} \, a^{3} b^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a^{4} b x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{x}"," ",0,"1/9*b^5*x^9*sgn(b*x^2 + a) + 5/7*a*b^4*x^7*sgn(b*x^2 + a) + 2*a^2*b^3*x^5*sgn(b*x^2 + a) + 10/3*a^3*b^2*x^3*sgn(b*x^2 + a) + 5*a^4*b*x*sgn(b*x^2 + a) - a^5*sgn(b*x^2 + a)/x","A",0
613,1,104,0,0.159757," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^4,x, algorithm=""giac"")","\frac{1}{7} \, b^{5} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + a b^{4} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{3} \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, a^{3} b^{2} x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{15 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{3 \, x^{3}}"," ",0,"1/7*b^5*x^7*sgn(b*x^2 + a) + a*b^4*x^5*sgn(b*x^2 + a) + 10/3*a^2*b^3*x^3*sgn(b*x^2 + a) + 10*a^3*b^2*x*sgn(b*x^2 + a) - 1/3*(15*a^4*b*x^2*sgn(b*x^2 + a) + a^5*sgn(b*x^2 + a))/x^3","A",0
614,1,106,0,0.174254," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^6,x, algorithm=""giac"")","\frac{1}{5} \, b^{5} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{5}{3} \, a b^{4} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, a^{2} b^{3} x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{150 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 25 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{15 \, x^{5}}"," ",0,"1/5*b^5*x^5*sgn(b*x^2 + a) + 5/3*a*b^4*x^3*sgn(b*x^2 + a) + 10*a^2*b^3*x*sgn(b*x^2 + a) - 1/15*(150*a^3*b^2*x^4*sgn(b*x^2 + a) + 25*a^4*b*x^2*sgn(b*x^2 + a) + 3*a^5*sgn(b*x^2 + a))/x^5","A",0
615,1,106,0,0.159413," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^8,x, algorithm=""giac"")","\frac{1}{3} \, b^{5} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a b^{4} x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{210 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 70 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 21 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{21 \, x^{7}}"," ",0,"1/3*b^5*x^3*sgn(b*x^2 + a) + 5*a*b^4*x*sgn(b*x^2 + a) - 1/21*(210*a^2*b^3*x^6*sgn(b*x^2 + a) + 70*a^3*b^2*x^4*sgn(b*x^2 + a) + 21*a^4*b*x^2*sgn(b*x^2 + a) + 3*a^5*sgn(b*x^2 + a))/x^7","A",0
616,1,105,0,0.167934," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^10,x, algorithm=""giac"")","b^{5} x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{315 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 210 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 126 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 45 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 7 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{63 \, x^{9}}"," ",0,"b^5*x*sgn(b*x^2 + a) - 1/63*(315*a*b^4*x^8*sgn(b*x^2 + a) + 210*a^2*b^3*x^6*sgn(b*x^2 + a) + 126*a^3*b^2*x^4*sgn(b*x^2 + a) + 45*a^4*b*x^2*sgn(b*x^2 + a) + 7*a^5*sgn(b*x^2 + a))/x^9","A",0
617,1,107,0,0.158941," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^12,x, algorithm=""giac"")","-\frac{693 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 1155 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 1386 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 990 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 385 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 63 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{693 \, x^{11}}"," ",0,"-1/693*(693*b^5*x^10*sgn(b*x^2 + a) + 1155*a*b^4*x^8*sgn(b*x^2 + a) + 1386*a^2*b^3*x^6*sgn(b*x^2 + a) + 990*a^3*b^2*x^4*sgn(b*x^2 + a) + 385*a^4*b*x^2*sgn(b*x^2 + a) + 63*a^5*sgn(b*x^2 + a))/x^11","A",0
618,1,107,0,0.177552," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^14,x, algorithm=""giac"")","-\frac{3003 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 9009 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 12870 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 10010 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 4095 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 693 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{9009 \, x^{13}}"," ",0,"-1/9009*(3003*b^5*x^10*sgn(b*x^2 + a) + 9009*a*b^4*x^8*sgn(b*x^2 + a) + 12870*a^2*b^3*x^6*sgn(b*x^2 + a) + 10010*a^3*b^2*x^4*sgn(b*x^2 + a) + 4095*a^4*b*x^2*sgn(b*x^2 + a) + 693*a^5*sgn(b*x^2 + a))/x^13","A",0
619,1,107,0,0.160110," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^16,x, algorithm=""giac"")","-\frac{9009 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 32175 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 50050 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 40950 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 17325 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 3003 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{45045 \, x^{15}}"," ",0,"-1/45045*(9009*b^5*x^10*sgn(b*x^2 + a) + 32175*a*b^4*x^8*sgn(b*x^2 + a) + 50050*a^2*b^3*x^6*sgn(b*x^2 + a) + 40950*a^3*b^2*x^4*sgn(b*x^2 + a) + 17325*a^4*b*x^2*sgn(b*x^2 + a) + 3003*a^5*sgn(b*x^2 + a))/x^15","A",0
620,1,107,0,0.167991," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^18,x, algorithm=""giac"")","-\frac{21879 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 85085 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 139230 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 117810 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 51051 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 9009 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{153153 \, x^{17}}"," ",0,"-1/153153*(21879*b^5*x^10*sgn(b*x^2 + a) + 85085*a*b^4*x^8*sgn(b*x^2 + a) + 139230*a^2*b^3*x^6*sgn(b*x^2 + a) + 117810*a^3*b^2*x^4*sgn(b*x^2 + a) + 51051*a^4*b*x^2*sgn(b*x^2 + a) + 9009*a^5*sgn(b*x^2 + a))/x^17","A",0
621,1,107,0,0.199333," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^20,x, algorithm=""giac"")","-\frac{46189 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 188955 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 319770 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 277134 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 122265 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 21879 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{415701 \, x^{19}}"," ",0,"-1/415701*(46189*b^5*x^10*sgn(b*x^2 + a) + 188955*a*b^4*x^8*sgn(b*x^2 + a) + 319770*a^2*b^3*x^6*sgn(b*x^2 + a) + 277134*a^3*b^2*x^4*sgn(b*x^2 + a) + 122265*a^4*b*x^2*sgn(b*x^2 + a) + 21879*a^5*sgn(b*x^2 + a))/x^19","A",0
622,1,107,0,0.160777," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^22,x, algorithm=""giac"")","-\frac{88179 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 373065 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 646646 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 570570 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 255255 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 46189 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{969969 \, x^{21}}"," ",0,"-1/969969*(88179*b^5*x^10*sgn(b*x^2 + a) + 373065*a*b^4*x^8*sgn(b*x^2 + a) + 646646*a^2*b^3*x^6*sgn(b*x^2 + a) + 570570*a^3*b^2*x^4*sgn(b*x^2 + a) + 255255*a^4*b*x^2*sgn(b*x^2 + a) + 46189*a^5*sgn(b*x^2 + a))/x^21","A",0
623,1,107,0,0.159970," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^24,x, algorithm=""giac"")","-\frac{156009 \, b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 676039 \, a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 1193010 \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 1067430 \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 482885 \, a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 88179 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{2028117 \, x^{23}}"," ",0,"-1/2028117*(156009*b^5*x^10*sgn(b*x^2 + a) + 676039*a*b^4*x^8*sgn(b*x^2 + a) + 1193010*a^2*b^3*x^6*sgn(b*x^2 + a) + 1067430*a^3*b^2*x^4*sgn(b*x^2 + a) + 482885*a^4*b*x^2*sgn(b*x^2 + a) + 88179*a^5*sgn(b*x^2 + a))/x^23","A",0
624,1,59,0,0.180768," ","integrate(x^5/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| b x^{2} + a \right|}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{2 \, b^{3}} + \frac{b x^{4} \mathrm{sgn}\left(b x^{2} + a\right) - 2 \, a x^{2} \mathrm{sgn}\left(b x^{2} + a\right)}{4 \, b^{2}}"," ",0,"1/2*a^2*log(abs(b*x^2 + a))*sgn(b*x^2 + a)/b^3 + 1/4*(b*x^4*sgn(b*x^2 + a) - 2*a*x^2*sgn(b*x^2 + a))/b^2","A",0
625,1,33,0,0.170622," ","integrate(x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{x^{2}}{b} - \frac{a \log\left({\left| b x^{2} + a \right|}\right)}{b^{2}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/2*(x^2/b - a*log(abs(b*x^2 + a))/b^2)*sgn(b*x^2 + a)","A",0
626,1,22,0,0.152598," ","integrate(x/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{2} + a \right|}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{2 \, b}"," ",0,"1/2*log(abs(b*x^2 + a))*sgn(b*x^2 + a)/b","A",0
627,1,33,0,0.152247," ","integrate(1/x/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{\log\left(x^{2}\right)}{a} - \frac{\log\left({\left| b x^{2} + a \right|}\right)}{a}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/2*(log(x^2)/a - log(abs(b*x^2 + a))/a)*sgn(b*x^2 + a)","A",0
628,1,52,0,0.155568," ","integrate(1/x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{b \log\left(x^{2}\right)}{a^{2}} - \frac{b \log\left({\left| b x^{2} + a \right|}\right)}{a^{2}} - \frac{b x^{2} - a}{a^{2} x^{2}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"-1/2*(b*log(x^2)/a^2 - b*log(abs(b*x^2 + a))/a^2 - (b*x^2 - a)/(a^2*x^2))*sgn(b*x^2 + a)","A",0
629,1,64,0,0.159720," ","integrate(x^4/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{a b} b^{2}} + \frac{b^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) - 3 \, a b x \mathrm{sgn}\left(b x^{2} + a\right)}{3 \, b^{3}}"," ",0,"a^2*arctan(b*x/sqrt(a*b))*sgn(b*x^2 + a)/(sqrt(a*b)*b^2) + 1/3*(b^2*x^3*sgn(b*x^2 + a) - 3*a*b*x*sgn(b*x^2 + a))/b^3","A",0
630,1,42,0,0.230636," ","integrate(x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{b x}{\sqrt{a b}}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{a b} b} + \frac{x \mathrm{sgn}\left(b x^{2} + a\right)}{b}"," ",0,"-a*arctan(b*x/sqrt(a*b))*sgn(b*x^2 + a)/(sqrt(a*b)*b) + x*sgn(b*x^2 + a)/b","A",0
631,1,23,0,0.177271," ","integrate(1/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{a b}}"," ",0,"arctan(b*x/sqrt(a*b))*sgn(b*x^2 + a)/sqrt(a*b)","A",0
632,1,37,0,0.153393," ","integrate(1/x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-{\left(\frac{b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} + \frac{1}{a x}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"-(b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) + 1/(a*x))*sgn(b*x^2 + a)","A",0
633,1,50,0,0.158645," ","integrate(1/x^4/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\frac{3 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{3 \, b x^{2} - a}{a^{2} x^{3}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/3*(3*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) + (3*b*x^2 - a)/(a^2*x^3))*sgn(b*x^2 + a)","A",0
634,1,83,0,0.248205," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, b^{3} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{3 \, a \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{6 \, a^{2} b x^{2} + 5 \, a^{3}}{4 \, {\left(b x^{2} + a\right)}^{2} b^{4} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"1/2*x^2/(b^3*sgn(b*x^2 + a)) - 3/2*a*log(abs(b*x^2 + a))/(b^4*sgn(b*x^2 + a)) - 1/4*(6*a^2*b*x^2 + 5*a^3)/((b*x^2 + a)^2*b^4*sgn(b*x^2 + a))","A",0
635,1,64,0,0.226795," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{3} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{4 \, a x^{2} + \frac{3 \, a^{2}}{b}}{4 \, {\left(b x^{2} + a\right)}^{2} b^{2} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"1/2*log(abs(b*x^2 + a))/(b^3*sgn(b*x^2 + a)) + 1/4*(4*a*x^2 + 3*a^2/b)/((b*x^2 + a)^2*b^2*sgn(b*x^2 + a))","A",0
636,1,32,0,0.226777," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, b x^{2} + a}{4 \, {\left(b x^{2} + a\right)}^{2} b^{2} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/4*(2*b*x^2 + a)/((b*x^2 + a)^2*b^2*sgn(b*x^2 + a))","A",0
637,1,24,0,0.203838," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{4 \, {\left(b x^{2} + a\right)}^{2} b \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/4/((b*x^2 + a)^2*b*sgn(b*x^2 + a))","A",0
638,1,79,0,0.272958," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{\log\left({\left| x \right|}\right)}{a^{3} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{2 \, a b x^{2} + 3 \, a^{2}}{4 \, {\left(b x^{2} + a\right)}^{2} a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/2*log(abs(b*x^2 + a))/(a^3*sgn(b*x^2 + a)) + log(abs(x))/(a^3*sgn(b*x^2 + a)) + 1/4*(2*a*b*x^2 + 3*a^2)/((b*x^2 + a)^2*a^3*sgn(b*x^2 + a))","A",0
639,1,96,0,0.235894," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, b \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{4} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{3 \, b \log\left({\left| x \right|}\right)}{a^{4} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{6 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3}}{4 \, {\left(b x^{2} + a\right)}^{2} a^{4} x^{2} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"3/2*b*log(abs(b*x^2 + a))/(a^4*sgn(b*x^2 + a)) - 3*b*log(abs(x))/(a^4*sgn(b*x^2 + a)) - 1/4*(6*a*b^2*x^4 + 9*a^2*b*x^2 + 2*a^3)/((b*x^2 + a)^2*a^4*x^2*sgn(b*x^2 + a))","A",0
640,0,0,0,0.000000," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
641,0,0,0,0.000000," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
642,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
643,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
644,0,0,0,0.000000," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
645,1,105,0,0.249585," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, b^{5} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{5 \, a \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{6} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{120 \, a^{2} b^{3} x^{6} + 300 \, a^{3} b^{2} x^{4} + 260 \, a^{4} b x^{2} + 77 \, a^{5}}{24 \, {\left(b x^{2} + a\right)}^{4} b^{6} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"1/2*x^2/(b^5*sgn(b*x^2 + a)) - 5/2*a*log(abs(b*x^2 + a))/(b^6*sgn(b*x^2 + a)) - 1/24*(120*a^2*b^3*x^6 + 300*a^3*b^2*x^4 + 260*a^4*b*x^2 + 77*a^5)/((b*x^2 + a)^4*b^6*sgn(b*x^2 + a))","A",0
646,1,84,0,0.210971," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{5} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{48 \, a b^{2} x^{6} + 108 \, a^{2} b x^{4} + 88 \, a^{3} x^{2} + \frac{25 \, a^{4}}{b}}{24 \, {\left(b x^{2} + a\right)}^{4} b^{4} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"1/2*log(abs(b*x^2 + a))/(b^5*sgn(b*x^2 + a)) + 1/24*(48*a*b^2*x^6 + 108*a^2*b*x^4 + 88*a^3*x^2 + 25*a^4/b)/((b*x^2 + a)^4*b^4*sgn(b*x^2 + a))","A",0
647,1,54,0,0.217124," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, {\left(b x^{2} + a\right)}^{4} b^{4} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/8*(4*b^3*x^6 + 6*a*b^2*x^4 + 4*a^2*b*x^2 + a^3)/((b*x^2 + a)^4*b^4*sgn(b*x^2 + a))","A",0
648,1,43,0,0.213095," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{6 \, b^{2} x^{4} + 4 \, a b x^{2} + a^{2}}{24 \, {\left(b x^{2} + a\right)}^{4} b^{3} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/24*(6*b^2*x^4 + 4*a*b*x^2 + a^2)/((b*x^2 + a)^4*b^3*sgn(b*x^2 + a))","A",0
649,1,32,0,0.214486," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{4 \, b x^{2} + a}{24 \, {\left(b x^{2} + a\right)}^{4} b^{2} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/24*(4*b*x^2 + a)/((b*x^2 + a)^4*b^2*sgn(b*x^2 + a))","A",0
650,1,24,0,0.208339," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{1}{8 \, {\left(b x^{2} + a\right)}^{4} b \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/8/((b*x^2 + a)^4*b*sgn(b*x^2 + a))","A",0
651,1,101,0,0.265960," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{\log\left({\left| x \right|}\right)}{a^{5} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{12 \, a b^{3} x^{6} + 42 \, a^{2} b^{2} x^{4} + 52 \, a^{3} b x^{2} + 25 \, a^{4}}{24 \, {\left(b x^{2} + a\right)}^{4} a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/2*log(abs(b*x^2 + a))/(a^5*sgn(b*x^2 + a)) + log(abs(x))/(a^5*sgn(b*x^2 + a)) + 1/24*(12*a*b^3*x^6 + 42*a^2*b^2*x^4 + 52*a^3*b*x^2 + 25*a^4)/((b*x^2 + a)^4*a^5*sgn(b*x^2 + a))","A",0
652,1,118,0,0.221605," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{5 \, b \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{6} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{5 \, b \log\left({\left| x \right|}\right)}{a^{6} \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{60 \, a b^{4} x^{8} + 210 \, a^{2} b^{3} x^{6} + 260 \, a^{3} b^{2} x^{4} + 125 \, a^{4} b x^{2} + 12 \, a^{5}}{24 \, {\left(b x^{2} + a\right)}^{4} a^{6} x^{2} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"5/2*b*log(abs(b*x^2 + a))/(a^6*sgn(b*x^2 + a)) - 5*b*log(abs(x))/(a^6*sgn(b*x^2 + a)) - 1/24*(60*a*b^4*x^8 + 210*a^2*b^3*x^6 + 260*a^3*b^2*x^4 + 125*a^4*b*x^2 + 12*a^5)/((b*x^2 + a)^4*a^6*x^2*sgn(b*x^2 + a))","A",0
653,0,0,0,0.000000," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
654,0,0,0,0.000000," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
655,0,0,0,0.000000," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
656,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
657,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
658,0,0,0,0.000000," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
659,0,0,0,0.000000," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^2/(b^2*x^4 + 2*a*b*x^2 + a^2)^(1/3), x)","F",0
660,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(-1/3), x)","F",0
661,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{1}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((b^2*x^4 + 2*a*b*x^2 + a^2)^(1/3)*x^2), x)","F",0
662,0,0,0,0.000000," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^2/(b^2*x^4 + 2*a*b*x^2 + a^2)^(2/3), x)","F",0
663,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(-2/3), x)","F",0
664,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{2}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((b^2*x^4 + 2*a*b*x^2 + a^2)^(2/3)*x^2), x)","F",0
665,1,48,0,0.167463," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{2}{15} \, \sqrt{d x} b^{2} d^{2} x^{7} + \frac{4}{11} \, \sqrt{d x} a b d^{2} x^{5} + \frac{2}{7} \, \sqrt{d x} a^{2} d^{2} x^{3}"," ",0,"2/15*sqrt(d*x)*b^2*d^2*x^7 + 4/11*sqrt(d*x)*a*b*d^2*x^5 + 2/7*sqrt(d*x)*a^2*d^2*x^3","A",0
666,1,42,0,0.149144," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{2}{585} \, {\left(45 \, \sqrt{d x} b^{2} x^{6} + 130 \, \sqrt{d x} a b x^{4} + 117 \, \sqrt{d x} a^{2} x^{2}\right)} d"," ",0,"2/585*(45*sqrt(d*x)*b^2*x^6 + 130*sqrt(d*x)*a*b*x^4 + 117*sqrt(d*x)*a^2*x^2)*d","A",0
667,1,37,0,0.150367," ","integrate((b^2*x^4+2*a*b*x^2+a^2)*(d*x)^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, \sqrt{d x} b^{2} x^{5} + \frac{4}{7} \, \sqrt{d x} a b x^{3} + \frac{2}{3} \, \sqrt{d x} a^{2} x"," ",0,"2/11*sqrt(d*x)*b^2*x^5 + 4/7*sqrt(d*x)*a*b*x^3 + 2/3*sqrt(d*x)*a^2*x","A",0
668,1,41,0,0.151066," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(5 \, \sqrt{d x} b^{2} x^{4} + 18 \, \sqrt{d x} a b x^{2} + 45 \, \sqrt{d x} a^{2}\right)}}{45 \, d}"," ",0,"2/45*(5*sqrt(d*x)*b^2*x^4 + 18*sqrt(d*x)*a*b*x^2 + 45*sqrt(d*x)*a^2)/d","A",0
669,1,51,0,0.221166," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{21 \, a^{2}}{\sqrt{d x}} - \frac{3 \, \sqrt{d x} b^{2} d^{27} x^{3} + 14 \, \sqrt{d x} a b d^{27} x}{d^{28}}\right)}}{21 \, d}"," ",0,"-2/21*(21*a^2/sqrt(d*x) - (3*sqrt(d*x)*b^2*d^27*x^3 + 14*sqrt(d*x)*a*b*d^27*x)/d^28)/d","A",0
670,1,53,0,0.153606," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, a^{2} d}{\sqrt{d x} x} - \frac{3 \, {\left(\sqrt{d x} b^{2} d^{10} x^{2} + 10 \, \sqrt{d x} a b d^{10}\right)}}{d^{10}}\right)}}{15 \, d^{3}}"," ",0,"-2/15*(5*a^2*d/(sqrt(d*x)*x) - 3*(sqrt(d*x)*b^2*d^10*x^2 + 10*sqrt(d*x)*a*b*d^10)/d^10)/d^3","A",0
671,1,48,0,0.154614," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left(5 \, \sqrt{d x} b^{2} x - \frac{3 \, {\left(10 \, a b d^{3} x^{2} + a^{2} d^{3}\right)}}{\sqrt{d x} d^{2} x^{2}}\right)}}{15 \, d^{4}}"," ",0,"2/15*(5*sqrt(d*x)*b^2*x - 3*(10*a*b*d^3*x^2 + a^2*d^3)/(sqrt(d*x)*d^2*x^2))/d^4","A",0
672,1,86,0,0.154748," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{2}{23} \, \sqrt{d x} b^{4} d^{2} x^{11} + \frac{8}{19} \, \sqrt{d x} a b^{3} d^{2} x^{9} + \frac{4}{5} \, \sqrt{d x} a^{2} b^{2} d^{2} x^{7} + \frac{8}{11} \, \sqrt{d x} a^{3} b d^{2} x^{5} + \frac{2}{7} \, \sqrt{d x} a^{4} d^{2} x^{3}"," ",0,"2/23*sqrt(d*x)*b^4*d^2*x^11 + 8/19*sqrt(d*x)*a*b^3*d^2*x^9 + 4/5*sqrt(d*x)*a^2*b^2*d^2*x^7 + 8/11*sqrt(d*x)*a^3*b*d^2*x^5 + 2/7*sqrt(d*x)*a^4*d^2*x^3","A",0
673,1,74,0,0.171299," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{2}{69615} \, {\left(3315 \, \sqrt{d x} b^{4} x^{10} + 16380 \, \sqrt{d x} a b^{3} x^{8} + 32130 \, \sqrt{d x} a^{2} b^{2} x^{6} + 30940 \, \sqrt{d x} a^{3} b x^{4} + 13923 \, \sqrt{d x} a^{4} x^{2}\right)} d"," ",0,"2/69615*(3315*sqrt(d*x)*b^4*x^10 + 16380*sqrt(d*x)*a*b^3*x^8 + 32130*sqrt(d*x)*a^2*b^2*x^6 + 30940*sqrt(d*x)*a^3*b*x^4 + 13923*sqrt(d*x)*a^4*x^2)*d","A",0
674,1,69,0,0.158324," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2*(d*x)^(1/2),x, algorithm=""giac"")","\frac{2}{19} \, \sqrt{d x} b^{4} x^{9} + \frac{8}{15} \, \sqrt{d x} a b^{3} x^{7} + \frac{12}{11} \, \sqrt{d x} a^{2} b^{2} x^{5} + \frac{8}{7} \, \sqrt{d x} a^{3} b x^{3} + \frac{2}{3} \, \sqrt{d x} a^{4} x"," ",0,"2/19*sqrt(d*x)*b^4*x^9 + 8/15*sqrt(d*x)*a*b^3*x^7 + 12/11*sqrt(d*x)*a^2*b^2*x^5 + 8/7*sqrt(d*x)*a^3*b*x^3 + 2/3*sqrt(d*x)*a^4*x","A",0
675,1,73,0,0.259947," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(195 \, \sqrt{d x} b^{4} x^{8} + 1020 \, \sqrt{d x} a b^{3} x^{6} + 2210 \, \sqrt{d x} a^{2} b^{2} x^{4} + 2652 \, \sqrt{d x} a^{3} b x^{2} + 3315 \, \sqrt{d x} a^{4}\right)}}{3315 \, d}"," ",0,"2/3315*(195*sqrt(d*x)*b^4*x^8 + 1020*sqrt(d*x)*a*b^3*x^6 + 2210*sqrt(d*x)*a^2*b^2*x^4 + 2652*sqrt(d*x)*a^3*b*x^2 + 3315*sqrt(d*x)*a^4)/d","A",0
676,1,89,0,0.176740," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{1155 \, a^{4}}{\sqrt{d x}} - \frac{77 \, \sqrt{d x} b^{4} d^{119} x^{7} + 420 \, \sqrt{d x} a b^{3} d^{119} x^{5} + 990 \, \sqrt{d x} a^{2} b^{2} d^{119} x^{3} + 1540 \, \sqrt{d x} a^{3} b d^{119} x}{d^{120}}\right)}}{1155 \, d}"," ",0,"-2/1155*(1155*a^4/sqrt(d*x) - (77*sqrt(d*x)*b^4*d^119*x^7 + 420*sqrt(d*x)*a*b^3*d^119*x^5 + 990*sqrt(d*x)*a^2*b^2*d^119*x^3 + 1540*sqrt(d*x)*a^3*b*d^119*x)/d^120)/d","A",0
677,1,92,0,0.158388," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{195 \, a^{4} d}{\sqrt{d x} x} - \frac{45 \, \sqrt{d x} b^{4} d^{78} x^{6} + 260 \, \sqrt{d x} a b^{3} d^{78} x^{4} + 702 \, \sqrt{d x} a^{2} b^{2} d^{78} x^{2} + 2340 \, \sqrt{d x} a^{3} b d^{78}}{d^{78}}\right)}}{585 \, d^{3}}"," ",0,"-2/585*(195*a^4*d/(sqrt(d*x)*x) - (45*sqrt(d*x)*b^4*d^78*x^6 + 260*sqrt(d*x)*a*b^3*d^78*x^4 + 702*sqrt(d*x)*a^2*b^2*d^78*x^2 + 2340*sqrt(d*x)*a^3*b*d^78)/d^78)/d^3","A",0
678,1,95,0,0.175468," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{77 \, {\left(20 \, a^{3} b d^{3} x^{2} + a^{4} d^{3}\right)}}{\sqrt{d x} d^{2} x^{2}} - \frac{5 \, {\left(7 \, \sqrt{d x} b^{4} d^{55} x^{5} + 44 \, \sqrt{d x} a b^{3} d^{55} x^{3} + 154 \, \sqrt{d x} a^{2} b^{2} d^{55} x\right)}}{d^{55}}\right)}}{385 \, d^{4}}"," ",0,"-2/385*(77*(20*a^3*b*d^3*x^2 + a^4*d^3)/(sqrt(d*x)*d^2*x^2) - 5*(7*sqrt(d*x)*b^4*d^55*x^5 + 44*sqrt(d*x)*a*b^3*d^55*x^3 + 154*sqrt(d*x)*a^2*b^2*d^55*x)/d^55)/d^4","A",0
679,1,124,0,0.160535," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{2}{31} \, \sqrt{d x} b^{6} d^{2} x^{15} + \frac{4}{9} \, \sqrt{d x} a b^{5} d^{2} x^{13} + \frac{30}{23} \, \sqrt{d x} a^{2} b^{4} d^{2} x^{11} + \frac{40}{19} \, \sqrt{d x} a^{3} b^{3} d^{2} x^{9} + 2 \, \sqrt{d x} a^{4} b^{2} d^{2} x^{7} + \frac{12}{11} \, \sqrt{d x} a^{5} b d^{2} x^{5} + \frac{2}{7} \, \sqrt{d x} a^{6} d^{2} x^{3}"," ",0,"2/31*sqrt(d*x)*b^6*d^2*x^15 + 4/9*sqrt(d*x)*a*b^5*d^2*x^13 + 30/23*sqrt(d*x)*a^2*b^4*d^2*x^11 + 40/19*sqrt(d*x)*a^3*b^3*d^2*x^9 + 2*sqrt(d*x)*a^4*b^2*d^2*x^7 + 12/11*sqrt(d*x)*a^5*b*d^2*x^5 + 2/7*sqrt(d*x)*a^6*d^2*x^3","A",0
680,1,106,0,0.191232," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{2}{3364725} \, {\left(116025 \, \sqrt{d x} b^{6} x^{14} + 807534 \, \sqrt{d x} a b^{5} x^{12} + 2403375 \, \sqrt{d x} a^{2} b^{4} x^{10} + 3958500 \, \sqrt{d x} a^{3} b^{3} x^{8} + 3882375 \, \sqrt{d x} a^{4} b^{2} x^{6} + 2243150 \, \sqrt{d x} a^{5} b x^{4} + 672945 \, \sqrt{d x} a^{6} x^{2}\right)} d"," ",0,"2/3364725*(116025*sqrt(d*x)*b^6*x^14 + 807534*sqrt(d*x)*a*b^5*x^12 + 2403375*sqrt(d*x)*a^2*b^4*x^10 + 3958500*sqrt(d*x)*a^3*b^3*x^8 + 3882375*sqrt(d*x)*a^4*b^2*x^6 + 2243150*sqrt(d*x)*a^5*b*x^4 + 672945*sqrt(d*x)*a^6*x^2)*d","A",0
681,1,101,0,0.175237," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3*(d*x)^(1/2),x, algorithm=""giac"")","\frac{2}{27} \, \sqrt{d x} b^{6} x^{13} + \frac{12}{23} \, \sqrt{d x} a b^{5} x^{11} + \frac{30}{19} \, \sqrt{d x} a^{2} b^{4} x^{9} + \frac{8}{3} \, \sqrt{d x} a^{3} b^{3} x^{7} + \frac{30}{11} \, \sqrt{d x} a^{4} b^{2} x^{5} + \frac{12}{7} \, \sqrt{d x} a^{5} b x^{3} + \frac{2}{3} \, \sqrt{d x} a^{6} x"," ",0,"2/27*sqrt(d*x)*b^6*x^13 + 12/23*sqrt(d*x)*a*b^5*x^11 + 30/19*sqrt(d*x)*a^2*b^4*x^9 + 8/3*sqrt(d*x)*a^3*b^3*x^7 + 30/11*sqrt(d*x)*a^4*b^2*x^5 + 12/7*sqrt(d*x)*a^5*b*x^3 + 2/3*sqrt(d*x)*a^6*x","A",0
682,1,105,0,0.179881," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(4641 \, \sqrt{d x} b^{6} x^{12} + 33150 \, \sqrt{d x} a b^{5} x^{10} + 102375 \, \sqrt{d x} a^{2} b^{4} x^{8} + 178500 \, \sqrt{d x} a^{3} b^{3} x^{6} + 193375 \, \sqrt{d x} a^{4} b^{2} x^{4} + 139230 \, \sqrt{d x} a^{5} b x^{2} + 116025 \, \sqrt{d x} a^{6}\right)}}{116025 \, d}"," ",0,"2/116025*(4641*sqrt(d*x)*b^6*x^12 + 33150*sqrt(d*x)*a*b^5*x^10 + 102375*sqrt(d*x)*a^2*b^4*x^8 + 178500*sqrt(d*x)*a^3*b^3*x^6 + 193375*sqrt(d*x)*a^4*b^2*x^4 + 139230*sqrt(d*x)*a^5*b*x^2 + 116025*sqrt(d*x)*a^6)/d","A",0
683,1,127,0,0.198556," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{33649 \, a^{6}}{\sqrt{d x}} - \frac{1463 \, \sqrt{d x} b^{6} d^{275} x^{11} + 10626 \, \sqrt{d x} a b^{5} d^{275} x^{9} + 33649 \, \sqrt{d x} a^{2} b^{4} d^{275} x^{7} + 61180 \, \sqrt{d x} a^{3} b^{3} d^{275} x^{5} + 72105 \, \sqrt{d x} a^{4} b^{2} d^{275} x^{3} + 67298 \, \sqrt{d x} a^{5} b d^{275} x}{d^{276}}\right)}}{33649 \, d}"," ",0,"-2/33649*(33649*a^6/sqrt(d*x) - (1463*sqrt(d*x)*b^6*d^275*x^11 + 10626*sqrt(d*x)*a*b^5*d^275*x^9 + 33649*sqrt(d*x)*a^2*b^4*d^275*x^7 + 61180*sqrt(d*x)*a^3*b^3*d^275*x^5 + 72105*sqrt(d*x)*a^4*b^2*d^275*x^3 + 67298*sqrt(d*x)*a^5*b*d^275*x)/d^276)/d","A",0
684,1,130,0,0.169384," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{4641 \, a^{6} d}{\sqrt{d x} x} - \frac{663 \, \sqrt{d x} b^{6} d^{210} x^{10} + 4914 \, \sqrt{d x} a b^{5} d^{210} x^{8} + 16065 \, \sqrt{d x} a^{2} b^{4} d^{210} x^{6} + 30940 \, \sqrt{d x} a^{3} b^{3} d^{210} x^{4} + 41769 \, \sqrt{d x} a^{4} b^{2} d^{210} x^{2} + 83538 \, \sqrt{d x} a^{5} b d^{210}}{d^{210}}\right)}}{13923 \, d^{3}}"," ",0,"-2/13923*(4641*a^6*d/(sqrt(d*x)*x) - (663*sqrt(d*x)*b^6*d^210*x^10 + 4914*sqrt(d*x)*a*b^5*d^210*x^8 + 16065*sqrt(d*x)*a^2*b^4*d^210*x^6 + 30940*sqrt(d*x)*a^3*b^3*d^210*x^4 + 41769*sqrt(d*x)*a^4*b^2*d^210*x^2 + 83538*sqrt(d*x)*a^5*b*d^210)/d^210)/d^3","A",0
685,1,133,0,0.174155," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{1463 \, {\left(30 \, a^{5} b d^{3} x^{2} + a^{6} d^{3}\right)}}{\sqrt{d x} d^{2} x^{2}} - \frac{385 \, \sqrt{d x} b^{6} d^{171} x^{9} + 2926 \, \sqrt{d x} a b^{5} d^{171} x^{7} + 9975 \, \sqrt{d x} a^{2} b^{4} d^{171} x^{5} + 20900 \, \sqrt{d x} a^{3} b^{3} d^{171} x^{3} + 36575 \, \sqrt{d x} a^{4} b^{2} d^{171} x}{d^{171}}\right)}}{7315 \, d^{4}}"," ",0,"-2/7315*(1463*(30*a^5*b*d^3*x^2 + a^6*d^3)/(sqrt(d*x)*d^2*x^2) - (385*sqrt(d*x)*b^6*d^171*x^9 + 2926*sqrt(d*x)*a*b^5*d^171*x^7 + 9975*sqrt(d*x)*a^2*b^4*d^171*x^5 + 20900*sqrt(d*x)*a^3*b^3*d^171*x^3 + 36575*sqrt(d*x)*a^4*b^2*d^171*x)/d^171)/d^4","A",0
686,1,297,0,0.213484," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{1}{80} \, d^{5} {\left(\frac{40 \, \sqrt{d x} a^{2} d^{2}}{{\left(b d^{2} x^{2} + a d^{2}\right)} b^{3}} - \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} - \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{4}} - \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{4}} + \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{4}} - \frac{32 \, {\left(\sqrt{d x} b^{8} d^{10} x^{2} - 10 \, \sqrt{d x} a b^{7} d^{10}\right)}}{b^{10} d^{10}}\right)}"," ",0,"-1/80*d^5*(40*sqrt(d*x)*a^2*d^2/((b*d^2*x^2 + a*d^2)*b^3) - 90*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^4 - 90*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^4 - 45*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^4 + 45*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^4 - 32*(sqrt(d*x)*b^8*d^10*x^2 - 10*sqrt(d*x)*a*b^7*d^10)/(b^10*d^10))","A",0
687,1,277,0,0.192122," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(\frac{24 \, \sqrt{d x} a d^{2} x}{{\left(b d^{2} x^{2} + a d^{2}\right)} b^{2}} + \frac{32 \, \sqrt{d x} x}{b^{2}} - \frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{5} d} - \frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{5} d} + \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{5} d} - \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{5} d}\right)} d^{4}"," ",0,"1/48*(24*sqrt(d*x)*a*d^2*x/((b*d^2*x^2 + a*d^2)*b^2) + 32*sqrt(d*x)*x/b^2 - 42*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^5*d) - 42*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^5*d) + 21*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^5*d) - 21*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^5*d))*d^4","A",0
688,1,263,0,0.188926," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{1}{16} \, d^{3} {\left(\frac{8 \, \sqrt{d x} a d^{2}}{{\left(b d^{2} x^{2} + a d^{2}\right)} b^{2}} - \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{3}} - \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{3}} - \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{3}} + \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{3}} + \frac{32 \, \sqrt{d x}}{b^{2}}\right)}"," ",0,"1/16*d^3*(8*sqrt(d*x)*a*d^2/((b*d^2*x^2 + a*d^2)*b^2) - 10*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^3 - 10*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^3 - 5*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^3 + 5*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^3 + 32*sqrt(d*x)/b^2)","A",0
689,1,277,0,0.231615," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{1}{16} \, {\left(\frac{8 \, \sqrt{d x} d^{2} x}{{\left(b d^{2} x^{2} + a d^{2}\right)} b} - \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4} d} - \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4} d} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{4} d} - \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{4} d}\right)} d^{2}"," ",0,"-1/16*(8*sqrt(d*x)*d^2*x/((b*d^2*x^2 + a*d^2)*b) - 6*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^4*d) - 6*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^4*d) + 3*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^4*d) - 3*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^4*d))*d^2","A",0
690,1,261,0,0.233538," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{1}{16} \, d {\left(\frac{8 \, \sqrt{d x} d^{2}}{{\left(b d^{2} x^{2} + a d^{2}\right)} b} - \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{2}} - \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{2}} - \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{2}} + \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{2}}\right)}"," ",0,"-1/16*d*(8*sqrt(d*x)*d^2/((b*d^2*x^2 + a*d^2)*b) - 2*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^2) - 2*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^2) - sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^2) + sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^2))","A",0
691,1,264,0,0.190250," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\frac{8 \, \sqrt{d x} d^{3} x}{{\left(b d^{2} x^{2} + a d^{2}\right)} a} + \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{3}} + \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{3}} - \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{3}} + \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{3}}}{16 \, d}"," ",0,"1/16*(8*sqrt(d*x)*d^3*x/((b*d^2*x^2 + a*d^2)*a) + 2*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^3) + 2*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^3) - sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^3) + sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^3))/d","A",0
692,1,269,0,0.192273," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{d x} d}{2 \, {\left(b d^{2} x^{2} + a d^{2}\right)} a} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b d} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b d} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{16 \, a^{2} b d} - \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{16 \, a^{2} b d}"," ",0,"1/2*sqrt(d*x)*d/((b*d^2*x^2 + a*d^2)*a) + 3/8*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b*d) + 3/8*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b*d) + 3/16*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b*d) - 3/16*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b*d)","A",0
693,1,294,0,0.180610," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{\frac{8 \, {\left(5 \, b d^{2} x^{2} + 4 \, a d^{2}\right)}}{{\left(\sqrt{d x} b d^{2} x^{2} + \sqrt{d x} a d^{2}\right)} a^{2}} + \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{2} d^{2}} + \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{2} d^{2}} - \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{2} d^{2}} + \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{2} d^{2}}}{16 \, d}"," ",0,"-1/16*(8*(5*b*d^2*x^2 + 4*a*d^2)/((sqrt(d*x)*b*d^2*x^2 + sqrt(d*x)*a*d^2)*a^2) + 10*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^2*d^2) + 10*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^2*d^2) - 5*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^2*d^2) + 5*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^2*d^2))/d","A",0
694,1,276,0,0.194611," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","-\frac{\sqrt{d x} b}{2 \, {\left(b d^{2} x^{2} + a d^{2}\right)} a^{2} d} - \frac{7 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} d^{3}} - \frac{7 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} d^{3}} - \frac{7 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{16 \, a^{3} d^{3}} + \frac{7 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{16 \, a^{3} d^{3}} - \frac{2}{3 \, \sqrt{d x} a^{2} d^{2} x}"," ",0,"-1/2*sqrt(d*x)*b/((b*d^2*x^2 + a*d^2)*a^2*d) - 7/8*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*d^3) - 7/8*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*d^3) - 7/16*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*d^3) + 7/16*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*d^3) - 2/3/(sqrt(d*x)*a^2*d^2*x)","A",0
695,1,307,0,0.184899," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\sqrt{d x} b^{2} x}{2 \, {\left(b d^{2} x^{2} + a d^{2}\right)} a^{3} d^{2}} + \frac{9 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b d^{5}} + \frac{9 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b d^{5}} - \frac{9 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{16 \, a^{4} b d^{5}} + \frac{9 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{16 \, a^{4} b d^{5}} + \frac{2 \, {\left(10 \, b d^{2} x^{2} - a d^{2}\right)}}{5 \, \sqrt{d x} a^{3} d^{5} x^{2}}"," ",0,"1/2*sqrt(d*x)*b^2*x/((b*d^2*x^2 + a*d^2)*a^3*d^2) + 9/8*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b*d^5) + 9/8*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b*d^5) - 9/16*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b*d^5) + 9/16*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b*d^5) + 2/5*(10*b*d^2*x^2 - a*d^2)/(sqrt(d*x)*a^3*d^5*x^2)","A",0
696,1,336,0,0.216174," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{7680} \, d^{9} {\left(\frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{6}} + \frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{6}} + \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{6}} - \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{6}} - \frac{40 \, {\left(617 \, \sqrt{d x} a^{2} b^{2} d^{6} x^{4} + 1038 \, \sqrt{d x} a^{3} b d^{6} x^{2} + 453 \, \sqrt{d x} a^{4} d^{6}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} b^{5}} + \frac{3072 \, {\left(\sqrt{d x} b^{16} d^{10} x^{2} - 20 \, \sqrt{d x} a b^{15} d^{10}\right)}}{b^{20} d^{10}}\right)}"," ",0,"1/7680*d^9*(19890*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^6 + 19890*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^6 + 9945*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^6 - 9945*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^6 - 40*(617*sqrt(d*x)*a^2*b^2*d^6*x^4 + 1038*sqrt(d*x)*a^3*b*d^6*x^2 + 453*sqrt(d*x)*a^4*d^6)/((b*d^2*x^2 + a*d^2)^3*b^5) + 3072*(sqrt(d*x)*b^16*d^10*x^2 - 20*sqrt(d*x)*a*b^15*d^10)/(b^20*d^10))","A",0
697,1,316,0,0.235274," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{1536} \, d^{8} {\left(\frac{1024 \, \sqrt{d x} x}{b^{4}} - \frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{7} d} - \frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{7} d} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{7} d} - \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{7} d} + \frac{8 \, {\left(381 \, \sqrt{d x} a b^{2} d^{6} x^{5} + 606 \, \sqrt{d x} a^{2} b d^{6} x^{3} + 257 \, \sqrt{d x} a^{3} d^{6} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} b^{4}}\right)}"," ",0,"1/1536*d^8*(1024*sqrt(d*x)*x/b^4 - 2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^7*d) - 2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^7*d) + 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^7*d) - 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^7*d) + 8*(381*sqrt(d*x)*a*b^2*d^6*x^5 + 606*sqrt(d*x)*a^2*b*d^6*x^3 + 257*sqrt(d*x)*a^3*d^6*x)/((b*d^2*x^2 + a*d^2)^3*b^4))","A",0
698,1,302,0,0.198601," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{1}{1536} \, d^{7} {\left(\frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{5}} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{5}} + \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{5}} - \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{5}} - \frac{3072 \, \sqrt{d x}}{b^{4}} - \frac{8 \, {\left(317 \, \sqrt{d x} a b^{2} d^{6} x^{4} + 486 \, \sqrt{d x} a^{2} b d^{6} x^{2} + 201 \, \sqrt{d x} a^{3} d^{6}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} b^{4}}\right)}"," ",0,"-1/1536*d^7*(1170*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^5 + 1170*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^5 + 585*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^5 - 585*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^5 - 3072*sqrt(d*x)/b^4 - 8*(317*sqrt(d*x)*a*b^2*d^6*x^4 + 486*sqrt(d*x)*a^2*b*d^6*x^2 + 201*sqrt(d*x)*a^3*d^6)/((b*d^2*x^2 + a*d^2)^3*b^4))","A",0
699,1,314,0,0.202461," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{1}{1536} \, d^{6} {\left(\frac{8 \, {\left(153 \, \sqrt{d x} b^{2} d^{6} x^{5} + 198 \, \sqrt{d x} a b d^{6} x^{3} + 77 \, \sqrt{d x} a^{2} d^{6} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} b^{3}} - \frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{6} d} - \frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{6} d} + \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{6} d} - \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{6} d}\right)}"," ",0,"-1/1536*d^6*(8*(153*sqrt(d*x)*b^2*d^6*x^5 + 198*sqrt(d*x)*a*b*d^6*x^3 + 77*sqrt(d*x)*a^2*d^6*x)/((b*d^2*x^2 + a*d^2)^3*b^3) - 462*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^6*d) - 462*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^6*d) + 231*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^6*d) - 231*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^6*d))","A",0
700,1,301,0,0.213329," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{1536} \, d^{5} {\left(\frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} + \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{4}} + \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{4}} - \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{4}} - \frac{8 \, {\left(113 \, \sqrt{d x} b^{2} d^{6} x^{4} + 126 \, \sqrt{d x} a b d^{6} x^{2} + 45 \, \sqrt{d x} a^{2} d^{6}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} b^{3}}\right)}"," ",0,"1/1536*d^5*(90*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^4) + 90*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^4) + 45*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^4) - 45*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^4) - 8*(113*sqrt(d*x)*b^2*d^6*x^4 + 126*sqrt(d*x)*a*b*d^6*x^2 + 45*sqrt(d*x)*a^2*d^6)/((b*d^2*x^2 + a*d^2)^3*b^3))","A",0
701,1,317,0,0.214584," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{1536} \, d^{4} {\left(\frac{8 \, {\left(21 \, \sqrt{d x} b^{2} d^{6} x^{5} - 18 \, \sqrt{d x} a b d^{6} x^{3} - 7 \, \sqrt{d x} a^{2} d^{6} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a b^{2}} + \frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{5} d} + \frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{5} d} - \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{5} d} + \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{5} d}\right)}"," ",0,"1/1536*d^4*(8*(21*sqrt(d*x)*b^2*d^6*x^5 - 18*sqrt(d*x)*a*b*d^6*x^3 - 7*sqrt(d*x)*a^2*d^6*x)/((b*d^2*x^2 + a*d^2)^3*a*b^2) + 42*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^5*d) + 42*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^5*d) - 21*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^5*d) + 21*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^5*d))","A",0
702,1,304,0,0.236248," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{1536} \, d^{3} {\left(\frac{30 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{3}} + \frac{30 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{3}} + \frac{15 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{3}} - \frac{15 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{3}} + \frac{8 \, {\left(5 \, \sqrt{d x} b^{2} d^{6} x^{4} - 42 \, \sqrt{d x} a b d^{6} x^{2} - 15 \, \sqrt{d x} a^{2} d^{6}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a b^{2}}\right)}"," ",0,"1/1536*d^3*(30*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^3) + 30*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^3) + 15*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^3) - 15*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^3) + 8*(5*sqrt(d*x)*b^2*d^6*x^4 - 42*sqrt(d*x)*a*b*d^6*x^2 - 15*sqrt(d*x)*a^2*d^6)/((b*d^2*x^2 + a*d^2)^3*a*b^2))","A",0
703,1,317,0,0.217744," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{1536} \, d^{2} {\left(\frac{8 \, {\left(15 \, \sqrt{d x} b^{2} d^{6} x^{5} + 42 \, \sqrt{d x} a b d^{6} x^{3} - 5 \, \sqrt{d x} a^{2} d^{6} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a^{2} b} + \frac{30 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4} d} + \frac{30 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4} d} - \frac{15 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{4} d} + \frac{15 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{4} d}\right)}"," ",0,"1/1536*d^2*(8*(15*sqrt(d*x)*b^2*d^6*x^5 + 42*sqrt(d*x)*a*b*d^6*x^3 - 5*sqrt(d*x)*a^2*d^6*x)/((b*d^2*x^2 + a*d^2)^3*a^2*b) + 30*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^4*d) + 30*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^4*d) - 15*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^4*d) + 15*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^4*d))","A",0
704,1,302,0,0.196766," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{1}{1536} \, d {\left(\frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{2}} + \frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{2}} + \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{2}} - \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{2}} + \frac{8 \, {\left(7 \, \sqrt{d x} b^{2} d^{6} x^{4} + 18 \, \sqrt{d x} a b d^{6} x^{2} - 21 \, \sqrt{d x} a^{2} d^{6}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a^{2} b}\right)}"," ",0,"1/1536*d*(42*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^2) + 42*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^2) + 21*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^2) - 21*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^2) + 8*(7*sqrt(d*x)*b^2*d^6*x^4 + 18*sqrt(d*x)*a*b*d^6*x^2 - 21*sqrt(d*x)*a^2*d^6)/((b*d^2*x^2 + a*d^2)^3*a^2*b))","A",0
705,1,302,0,0.220983," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{3}} + \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{3}} - \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{3}} + \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{3}} + \frac{8 \, {\left(45 \, \sqrt{d x} b^{2} d^{7} x^{5} + 126 \, \sqrt{d x} a b d^{7} x^{3} + 113 \, \sqrt{d x} a^{2} d^{7} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a^{3}}}{1536 \, d}"," ",0,"1/1536*(90*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^3) + 90*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^3) - 45*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^3) + 45*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^3) + 8*(45*sqrt(d*x)*b^2*d^7*x^5 + 126*sqrt(d*x)*a*b*d^7*x^3 + 113*sqrt(d*x)*a^2*d^7*x)/((b*d^2*x^2 + a*d^2)^3*a^3))/d","A",0
706,1,308,0,0.268049," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x, algorithm=""giac"")","\frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{256 \, a^{4} b d} + \frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{256 \, a^{4} b d} + \frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{512 \, a^{4} b d} - \frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{512 \, a^{4} b d} + \frac{77 \, \sqrt{d x} b^{2} d^{5} x^{4} + 198 \, \sqrt{d x} a b d^{5} x^{2} + 153 \, \sqrt{d x} a^{2} d^{5}}{192 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a^{3}}"," ",0,"77/256*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b*d) + 77/256*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b*d) + 77/512*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b*d) - 77/512*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b*d) + 1/192*(77*sqrt(d*x)*b^2*d^5*x^4 + 198*sqrt(d*x)*a*b*d^5*x^2 + 153*sqrt(d*x)*a^2*d^5)/((b*d^2*x^2 + a*d^2)^3*a^3)","A",0
707,1,327,0,0.195362," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{\frac{3072}{\sqrt{d x} a^{4}} + \frac{8 \, {\left(201 \, \sqrt{d x} b^{3} d^{5} x^{5} + 486 \, \sqrt{d x} a b^{2} d^{5} x^{3} + 317 \, \sqrt{d x} a^{2} b d^{5} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a^{4}} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{2} d^{2}} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{2} d^{2}} - \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{2} d^{2}} + \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{2} d^{2}}}{1536 \, d}"," ",0,"-1/1536*(3072/(sqrt(d*x)*a^4) + 8*(201*sqrt(d*x)*b^3*d^5*x^5 + 486*sqrt(d*x)*a*b^2*d^5*x^3 + 317*sqrt(d*x)*a^2*b*d^5*x)/((b*d^2*x^2 + a*d^2)^3*a^4) + 1170*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^2*d^2) + 1170*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^2*d^2) - 585*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^2*d^2) + 585*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^2*d^2))/d","A",0
708,1,308,0,0.216468," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{385 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{256 \, a^{5} d^{3}} - \frac{385 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{256 \, a^{5} d^{3}} - \frac{385 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{512 \, a^{5} d^{3}} + \frac{385 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{512 \, a^{5} d^{3}} - \frac{385 \, b^{3} d^{6} x^{6} + 990 \, a b^{2} d^{6} x^{4} + 765 \, a^{2} b d^{6} x^{2} + 128 \, a^{3} d^{6}}{192 \, {\left(\sqrt{d x} b d^{2} x^{2} + \sqrt{d x} a d^{2}\right)}^{3} a^{4} d}"," ",0,"-385/256*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*d^3) - 385/256*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*d^3) - 385/512*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*d^3) + 385/512*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*d^3) - 1/192*(385*b^3*d^6*x^6 + 990*a*b^2*d^6*x^4 + 765*a^2*b*d^6*x^2 + 128*a^3*d^6)/((sqrt(d*x)*b*d^2*x^2 + sqrt(d*x)*a*d^2)^3*a^4*d)","A",0
709,1,349,0,0.218436," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{663 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{256 \, a^{6} b d^{5}} + \frac{663 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{256 \, a^{6} b d^{5}} - \frac{663 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{512 \, a^{6} b d^{5}} + \frac{663 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{512 \, a^{6} b d^{5}} + \frac{453 \, \sqrt{d x} b^{4} d^{5} x^{5} + 1038 \, \sqrt{d x} a b^{3} d^{5} x^{3} + 617 \, \sqrt{d x} a^{2} b^{2} d^{5} x}{192 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{3} a^{5} d^{3}} + \frac{2 \, {\left(20 \, b d^{2} x^{2} - a d^{2}\right)}}{5 \, \sqrt{d x} a^{5} d^{5} x^{2}}"," ",0,"663/256*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b*d^5) + 663/256*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b*d^5) - 663/512*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b*d^5) + 663/512*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b*d^5) + 1/192*(453*sqrt(d*x)*b^4*d^5*x^5 + 1038*sqrt(d*x)*a*b^3*d^5*x^3 + 617*sqrt(d*x)*a^2*b^2*d^5*x)/((b*d^2*x^2 + a*d^2)^3*a^5*d^3) + 2/5*(20*b*d^2*x^2 - a*d^2)/(sqrt(d*x)*a^5*d^5*x^2)","A",0
710,1,374,0,0.242370," ","integrate((d*x)^(27/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d^{13} {\left(\frac{696150 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{8}} + \frac{696150 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{8}} + \frac{348075 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{8}} - \frac{348075 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{8}} - \frac{8 \, {\left(170695 \, \sqrt{d x} a^{2} b^{4} d^{10} x^{8} + 575520 \, \sqrt{d x} a^{3} b^{3} d^{10} x^{6} + 754710 \, \sqrt{d x} a^{4} b^{2} d^{10} x^{4} + 450152 \, \sqrt{d x} a^{5} b d^{10} x^{2} + 102315 \, \sqrt{d x} a^{6} d^{10}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} b^{7}} + \frac{65536 \, {\left(\sqrt{d x} b^{24} d^{10} x^{2} - 30 \, \sqrt{d x} a b^{23} d^{10}\right)}}{b^{30} d^{10}}\right)}"," ",0,"1/163840*d^13*(696150*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^8 + 696150*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^8 + 348075*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^8 - 348075*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^8 - 8*(170695*sqrt(d*x)*a^2*b^4*d^10*x^8 + 575520*sqrt(d*x)*a^3*b^3*d^10*x^6 + 754710*sqrt(d*x)*a^4*b^2*d^10*x^4 + 450152*sqrt(d*x)*a^5*b*d^10*x^2 + 102315*sqrt(d*x)*a^6*d^10)/((b*d^2*x^2 + a*d^2)^5*b^7) + 65536*(sqrt(d*x)*b^24*d^10*x^2 - 30*sqrt(d*x)*a*b^23*d^10)/(b^30*d^10))","A",0
711,1,354,0,0.224011," ","integrate((d*x)^(25/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{491520} \, d^{12} {\left(\frac{327680 \, \sqrt{d x} x}{b^{6}} - \frac{1009470 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{9} d} - \frac{1009470 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{9} d} + \frac{504735 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{9} d} - \frac{504735 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{9} d} + \frac{8 \, {\left(232545 \, \sqrt{d x} a b^{4} d^{10} x^{9} + 747576 \, \sqrt{d x} a^{2} b^{3} d^{10} x^{7} + 958210 \, \sqrt{d x} a^{3} b^{2} d^{10} x^{5} + 564320 \, \sqrt{d x} a^{4} b d^{10} x^{3} + 127285 \, \sqrt{d x} a^{5} d^{10} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} b^{6}}\right)}"," ",0,"1/491520*d^12*(327680*sqrt(d*x)*x/b^6 - 1009470*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^9*d) - 1009470*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^9*d) + 504735*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^9*d) - 504735*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^9*d) + 8*(232545*sqrt(d*x)*a*b^4*d^10*x^9 + 747576*sqrt(d*x)*a^2*b^3*d^10*x^7 + 958210*sqrt(d*x)*a^3*b^2*d^10*x^5 + 564320*sqrt(d*x)*a^4*b*d^10*x^3 + 127285*sqrt(d*x)*a^5*d^10*x)/((b*d^2*x^2 + a*d^2)^5*b^6))","A",0
712,1,340,0,0.248340," ","integrate((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{1}{163840} \, d^{11} {\left(\frac{139230 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{7}} + \frac{139230 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{7}} + \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{7}} - \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{7}} - \frac{327680 \, \sqrt{d x}}{b^{6}} - \frac{8 \, {\left(58715 \, \sqrt{d x} a b^{4} d^{10} x^{8} + 180640 \, \sqrt{d x} a^{2} b^{3} d^{10} x^{6} + 224670 \, \sqrt{d x} a^{3} b^{2} d^{10} x^{4} + 129352 \, \sqrt{d x} a^{4} b d^{10} x^{2} + 28655 \, \sqrt{d x} a^{5} d^{10}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} b^{6}}\right)}"," ",0,"-1/163840*d^11*(139230*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^7 + 139230*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^7 + 69615*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^7 - 69615*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^7 - 327680*sqrt(d*x)/b^6 - 8*(58715*sqrt(d*x)*a*b^4*d^10*x^8 + 180640*sqrt(d*x)*a^2*b^3*d^10*x^6 + 224670*sqrt(d*x)*a^3*b^2*d^10*x^4 + 129352*sqrt(d*x)*a^4*b*d^10*x^2 + 28655*sqrt(d*x)*a^5*d^10)/((b*d^2*x^2 + a*d^2)^5*b^6))","A",0
713,1,352,0,0.208580," ","integrate((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d^{10} {\left(\frac{43890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{8} d} + \frac{43890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{8} d} - \frac{21945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{8} d} + \frac{21945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{8} d} - \frac{8 \, {\left(19015 \, \sqrt{d x} b^{4} d^{10} x^{9} + 50312 \, \sqrt{d x} a b^{3} d^{10} x^{7} + 59470 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{5} + 33440 \, \sqrt{d x} a^{3} b d^{10} x^{3} + 7315 \, \sqrt{d x} a^{4} d^{10} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} b^{5}}\right)}"," ",0,"1/163840*d^10*(43890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^8*d) + 43890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^8*d) - 21945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^8*d) + 21945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^8*d) - 8*(19015*sqrt(d*x)*b^4*d^10*x^9 + 50312*sqrt(d*x)*a*b^3*d^10*x^7 + 59470*sqrt(d*x)*a^2*b^2*d^10*x^5 + 33440*sqrt(d*x)*a^3*b*d^10*x^3 + 7315*sqrt(d*x)*a^4*d^10*x)/((b*d^2*x^2 + a*d^2)^5*b^5))","A",0
714,1,339,0,0.244202," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{491520} \, d^{9} {\left(\frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{6}} + \frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{6}} + \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{6}} - \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{6}} - \frac{8 \, {\left(37645 \, \sqrt{d x} b^{4} d^{10} x^{8} + 84320 \, \sqrt{d x} a b^{3} d^{10} x^{6} + 90610 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{4} + 47736 \, \sqrt{d x} a^{3} b d^{10} x^{2} + 9945 \, \sqrt{d x} a^{4} d^{10}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} b^{5}}\right)}"," ",0,"1/491520*d^9*(19890*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^6) + 19890*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^6) + 9945*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^6) - 9945*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^6) - 8*(37645*sqrt(d*x)*b^4*d^10*x^8 + 84320*sqrt(d*x)*a*b^3*d^10*x^6 + 90610*sqrt(d*x)*a^2*b^2*d^10*x^4 + 47736*sqrt(d*x)*a^3*b*d^10*x^2 + 9945*sqrt(d*x)*a^4*d^10)/((b*d^2*x^2 + a*d^2)^5*b^5))","A",0
715,1,355,0,0.209540," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d^{8} {\left(\frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{7} d} + \frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{7} d} - \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{7} d} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{7} d} + \frac{8 \, {\left(1155 \, \sqrt{d x} b^{4} d^{10} x^{9} - 2648 \, \sqrt{d x} a b^{3} d^{10} x^{7} - 3130 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{5} - 1760 \, \sqrt{d x} a^{3} b d^{10} x^{3} - 385 \, \sqrt{d x} a^{4} d^{10} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a b^{4}}\right)}"," ",0,"1/163840*d^8*(2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^7*d) + 2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^7*d) - 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^7*d) + 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^7*d) + 8*(1155*sqrt(d*x)*b^4*d^10*x^9 - 2648*sqrt(d*x)*a*b^3*d^10*x^7 - 3130*sqrt(d*x)*a^2*b^2*d^10*x^5 - 1760*sqrt(d*x)*a^3*b*d^10*x^3 - 385*sqrt(d*x)*a^4*d^10*x)/((b*d^2*x^2 + a*d^2)^5*a*b^4))","A",0
716,1,342,0,0.223176," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d^{7} {\left(\frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{5}} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{5}} + \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{5}} - \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{5}} + \frac{8 \, {\left(195 \, \sqrt{d x} b^{4} d^{10} x^{8} - 4960 \, \sqrt{d x} a b^{3} d^{10} x^{6} - 5330 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{4} - 2808 \, \sqrt{d x} a^{3} b d^{10} x^{2} - 585 \, \sqrt{d x} a^{4} d^{10}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a b^{4}}\right)}"," ",0,"1/163840*d^7*(1170*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^5) + 1170*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^5) + 585*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^5) - 585*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^5) + 8*(195*sqrt(d*x)*b^4*d^10*x^8 - 4960*sqrt(d*x)*a*b^3*d^10*x^6 - 5330*sqrt(d*x)*a^2*b^2*d^10*x^4 - 2808*sqrt(d*x)*a^3*b*d^10*x^2 - 585*sqrt(d*x)*a^4*d^10)/((b*d^2*x^2 + a*d^2)^5*a*b^4))","A",0
717,1,355,0,0.226274," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{491520} \, d^{6} {\left(\frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{6} d} + \frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{6} d} - \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{6} d} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{6} d} + \frac{8 \, {\left(1155 \, \sqrt{d x} b^{4} d^{10} x^{9} + 5544 \, \sqrt{d x} a b^{3} d^{10} x^{7} - 3130 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{5} - 1760 \, \sqrt{d x} a^{3} b d^{10} x^{3} - 385 \, \sqrt{d x} a^{4} d^{10} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{2} b^{3}}\right)}"," ",0,"1/491520*d^6*(2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^6*d) + 2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^6*d) - 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^6*d) + 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^6*d) + 8*(1155*sqrt(d*x)*b^4*d^10*x^9 + 5544*sqrt(d*x)*a*b^3*d^10*x^7 - 3130*sqrt(d*x)*a^2*b^2*d^10*x^5 - 1760*sqrt(d*x)*a^3*b*d^10*x^3 - 385*sqrt(d*x)*a^4*d^10*x)/((b*d^2*x^2 + a*d^2)^5*a^2*b^3))","A",0
718,1,342,0,0.213491," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d^{5} {\left(\frac{630 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} + \frac{630 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{4}} + \frac{315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{4}} - \frac{315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{4}} + \frac{8 \, {\left(105 \, \sqrt{d x} b^{4} d^{10} x^{8} + 480 \, \sqrt{d x} a b^{3} d^{10} x^{6} - 2870 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{4} - 1512 \, \sqrt{d x} a^{3} b d^{10} x^{2} - 315 \, \sqrt{d x} a^{4} d^{10}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{2} b^{3}}\right)}"," ",0,"1/163840*d^5*(630*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^4) + 630*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^4) + 315*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^4) - 315*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^4) + 8*(105*sqrt(d*x)*b^4*d^10*x^8 + 480*sqrt(d*x)*a*b^3*d^10*x^6 - 2870*sqrt(d*x)*a^2*b^2*d^10*x^4 - 1512*sqrt(d*x)*a^3*b*d^10*x^2 - 315*sqrt(d*x)*a^4*d^10)/((b*d^2*x^2 + a*d^2)^5*a^2*b^3))","A",0
719,1,355,0,0.258655," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d^{4} {\left(\frac{630 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{5} d} + \frac{630 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{5} d} - \frac{315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{5} d} + \frac{315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{5} d} + \frac{8 \, {\left(315 \, \sqrt{d x} b^{4} d^{10} x^{9} + 1512 \, \sqrt{d x} a b^{3} d^{10} x^{7} + 2870 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{5} - 480 \, \sqrt{d x} a^{3} b d^{10} x^{3} - 105 \, \sqrt{d x} a^{4} d^{10} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{3} b^{2}}\right)}"," ",0,"1/163840*d^4*(630*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^5*d) + 630*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^5*d) - 315*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^5*d) + 315*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^5*d) + 8*(315*sqrt(d*x)*b^4*d^10*x^9 + 1512*sqrt(d*x)*a*b^3*d^10*x^7 + 2870*sqrt(d*x)*a^2*b^2*d^10*x^5 - 480*sqrt(d*x)*a^3*b*d^10*x^3 - 105*sqrt(d*x)*a^4*d^10*x)/((b*d^2*x^2 + a*d^2)^5*a^3*b^2))","A",0
720,1,342,0,0.220566," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{491520} \, d^{3} {\left(\frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{3}} + \frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{3}} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{3}} - \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{3}} + \frac{8 \, {\left(385 \, \sqrt{d x} b^{4} d^{10} x^{8} + 1760 \, \sqrt{d x} a b^{3} d^{10} x^{6} + 3130 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{4} - 5544 \, \sqrt{d x} a^{3} b d^{10} x^{2} - 1155 \, \sqrt{d x} a^{4} d^{10}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{3} b^{2}}\right)}"," ",0,"1/491520*d^3*(2310*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^3) + 2310*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^3) + 1155*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^3) - 1155*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^3) + 8*(385*sqrt(d*x)*b^4*d^10*x^8 + 1760*sqrt(d*x)*a*b^3*d^10*x^6 + 3130*sqrt(d*x)*a^2*b^2*d^10*x^4 - 5544*sqrt(d*x)*a^3*b*d^10*x^2 - 1155*sqrt(d*x)*a^4*d^10)/((b*d^2*x^2 + a*d^2)^5*a^3*b^2))","A",0
721,1,355,0,0.216733," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d^{2} {\left(\frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{4} d} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{4} d} - \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{4} d} + \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{4} d} + \frac{8 \, {\left(585 \, \sqrt{d x} b^{4} d^{10} x^{9} + 2808 \, \sqrt{d x} a b^{3} d^{10} x^{7} + 5330 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{5} + 4960 \, \sqrt{d x} a^{3} b d^{10} x^{3} - 195 \, \sqrt{d x} a^{4} d^{10} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{4} b}\right)}"," ",0,"1/163840*d^2*(1170*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^4*d) + 1170*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^4*d) - 585*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^4*d) + 585*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^4*d) + 8*(585*sqrt(d*x)*b^4*d^10*x^9 + 2808*sqrt(d*x)*a*b^3*d^10*x^7 + 5330*sqrt(d*x)*a^2*b^2*d^10*x^5 + 4960*sqrt(d*x)*a^3*b*d^10*x^3 - 195*sqrt(d*x)*a^4*d^10*x)/((b*d^2*x^2 + a*d^2)^5*a^4*b))","A",0
722,1,340,0,0.208744," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{163840} \, d {\left(\frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{2}} + \frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{2}} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{2}} - \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{2}} + \frac{8 \, {\left(385 \, \sqrt{d x} b^{4} d^{10} x^{8} + 1760 \, \sqrt{d x} a b^{3} d^{10} x^{6} + 3130 \, \sqrt{d x} a^{2} b^{2} d^{10} x^{4} + 2648 \, \sqrt{d x} a^{3} b d^{10} x^{2} - 1155 \, \sqrt{d x} a^{4} d^{10}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{4} b}\right)}"," ",0,"1/163840*d*(2310*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^2) + 2310*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^2) + 1155*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^2) - 1155*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^2) + 8*(385*sqrt(d*x)*b^4*d^10*x^8 + 1760*sqrt(d*x)*a*b^3*d^10*x^6 + 3130*sqrt(d*x)*a^2*b^2*d^10*x^4 + 2648*sqrt(d*x)*a^3*b*d^10*x^2 - 1155*sqrt(d*x)*a^4*d^10)/((b*d^2*x^2 + a*d^2)^5*a^4*b))","A",0
723,1,340,0,0.220915," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{\frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{6} b^{3}} + \frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{6} b^{3}} - \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{6} b^{3}} + \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{6} b^{3}} + \frac{8 \, {\left(9945 \, \sqrt{d x} b^{4} d^{11} x^{9} + 47736 \, \sqrt{d x} a b^{3} d^{11} x^{7} + 90610 \, \sqrt{d x} a^{2} b^{2} d^{11} x^{5} + 84320 \, \sqrt{d x} a^{3} b d^{11} x^{3} + 37645 \, \sqrt{d x} a^{4} d^{11} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{5}}}{491520 \, d}"," ",0,"1/491520*(19890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b^3) + 19890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b^3) - 9945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b^3) + 9945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b^3) + 8*(9945*sqrt(d*x)*b^4*d^11*x^9 + 47736*sqrt(d*x)*a*b^3*d^11*x^7 + 90610*sqrt(d*x)*a^2*b^2*d^11*x^5 + 84320*sqrt(d*x)*a^3*b*d^11*x^3 + 37645*sqrt(d*x)*a^4*d^11*x)/((b*d^2*x^2 + a*d^2)^5*a^5))/d","A",0
724,1,346,0,0.192408," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x, algorithm=""giac"")","\frac{4389 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{16384 \, a^{6} b d} + \frac{4389 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{16384 \, a^{6} b d} + \frac{4389 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{32768 \, a^{6} b d} - \frac{4389 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{32768 \, a^{6} b d} + \frac{7315 \, \sqrt{d x} b^{4} d^{9} x^{8} + 33440 \, \sqrt{d x} a b^{3} d^{9} x^{6} + 59470 \, \sqrt{d x} a^{2} b^{2} d^{9} x^{4} + 50312 \, \sqrt{d x} a^{3} b d^{9} x^{2} + 19015 \, \sqrt{d x} a^{4} d^{9}}{20480 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{5}}"," ",0,"4389/16384*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b*d) + 4389/16384*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b*d) + 4389/32768*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b*d) - 4389/32768*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b*d) + 1/20480*(7315*sqrt(d*x)*b^4*d^9*x^8 + 33440*sqrt(d*x)*a*b^3*d^9*x^6 + 59470*sqrt(d*x)*a^2*b^2*d^9*x^4 + 50312*sqrt(d*x)*a^3*b*d^9*x^2 + 19015*sqrt(d*x)*a^4*d^9)/((b*d^2*x^2 + a*d^2)^5*a^5)","A",0
725,1,365,0,0.202762," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{\frac{327680}{\sqrt{d x} a^{6}} + \frac{139230 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{7} b^{2} d^{2}} + \frac{139230 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{7} b^{2} d^{2}} - \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{7} b^{2} d^{2}} + \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{7} b^{2} d^{2}} + \frac{8 \, {\left(28655 \, \sqrt{d x} b^{5} d^{9} x^{9} + 129352 \, \sqrt{d x} a b^{4} d^{9} x^{7} + 224670 \, \sqrt{d x} a^{2} b^{3} d^{9} x^{5} + 180640 \, \sqrt{d x} a^{3} b^{2} d^{9} x^{3} + 58715 \, \sqrt{d x} a^{4} b d^{9} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{6}}}{163840 \, d}"," ",0,"-1/163840*(327680/(sqrt(d*x)*a^6) + 139230*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^7*b^2*d^2) + 139230*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^7*b^2*d^2) - 69615*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^7*b^2*d^2) + 69615*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^7*b^2*d^2) + 8*(28655*sqrt(d*x)*b^5*d^9*x^9 + 129352*sqrt(d*x)*a*b^4*d^9*x^7 + 224670*sqrt(d*x)*a^2*b^3*d^9*x^5 + 180640*sqrt(d*x)*a^3*b^2*d^9*x^3 + 58715*sqrt(d*x)*a^4*b*d^9*x)/((b*d^2*x^2 + a*d^2)^5*a^6))/d","A",0
726,1,356,0,0.200926," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{33649 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{16384 \, a^{7} d^{3}} - \frac{33649 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{16384 \, a^{7} d^{3}} - \frac{33649 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{32768 \, a^{7} d^{3}} + \frac{33649 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{32768 \, a^{7} d^{3}} - \frac{2}{3 \, \sqrt{d x} a^{6} d^{2} x} - \frac{127285 \, \sqrt{d x} b^{5} d^{8} x^{8} + 564320 \, \sqrt{d x} a b^{4} d^{8} x^{6} + 958210 \, \sqrt{d x} a^{2} b^{3} d^{8} x^{4} + 747576 \, \sqrt{d x} a^{3} b^{2} d^{8} x^{2} + 232545 \, \sqrt{d x} a^{4} b d^{8}}{61440 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{5} a^{6} d}"," ",0,"-33649/16384*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^7*d^3) - 33649/16384*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^7*d^3) - 33649/32768*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^7*d^3) + 33649/32768*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^7*d^3) - 2/3/(sqrt(d*x)*a^6*d^2*x) - 1/61440*(127285*sqrt(d*x)*b^5*d^8*x^8 + 564320*sqrt(d*x)*a*b^4*d^8*x^6 + 958210*sqrt(d*x)*a^2*b^3*d^8*x^4 + 747576*sqrt(d*x)*a^3*b^2*d^8*x^2 + 232545*sqrt(d*x)*a^4*b*d^8)/((b*d^2*x^2 + a*d^2)^5*a^6*d)","A",0
727,1,362,0,0.202567," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{16384 \, a^{8} b d^{5}} + \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{16384 \, a^{8} b d^{5}} - \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{32768 \, a^{8} b d^{5}} + \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{32768 \, a^{8} b d^{5}} + \frac{348075 \, b^{6} d^{12} x^{12} + 1670760 \, a b^{5} d^{12} x^{10} + 3171350 \, a^{2} b^{4} d^{12} x^{8} + 2951200 \, a^{3} b^{3} d^{12} x^{6} + 1317575 \, a^{4} b^{2} d^{12} x^{4} + 204800 \, a^{5} b d^{12} x^{2} - 8192 \, a^{6} d^{12}}{20480 \, {\left(\sqrt{d x} b d^{2} x^{2} + \sqrt{d x} a d^{2}\right)}^{5} a^{7} d^{3}}"," ",0,"69615/16384*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^8*b*d^5) + 69615/16384*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^8*b*d^5) - 69615/32768*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^8*b*d^5) + 69615/32768*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^8*b*d^5) + 1/20480*(348075*b^6*d^12*x^12 + 1670760*a*b^5*d^12*x^10 + 3171350*a^2*b^4*d^12*x^8 + 2951200*a^3*b^3*d^12*x^6 + 1317575*a^4*b^2*d^12*x^4 + 204800*a^5*b*d^12*x^2 - 8192*a^6*d^12)/((sqrt(d*x)*b*d^2*x^2 + sqrt(d*x)*a*d^2)^5*a^7*d^3)","A",0
728,1,45,0,0.177304," ","integrate((d*x)^(5/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, \sqrt{d x} b d^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{7} \, \sqrt{d x} a d^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"2/11*sqrt(d*x)*b*d^2*x^5*sgn(b*x^2 + a) + 2/7*sqrt(d*x)*a*d^2*x^3*sgn(b*x^2 + a)","A",0
729,1,42,0,0.156603," ","integrate((d*x)^(3/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{45} \, {\left(5 \, \sqrt{d x} b x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 9 \, \sqrt{d x} a x^{2} \mathrm{sgn}\left(b x^{2} + a\right)\right)} d"," ",0,"2/45*(5*sqrt(d*x)*b*x^4*sgn(b*x^2 + a) + 9*sqrt(d*x)*a*x^2*sgn(b*x^2 + a))*d","A",0
730,1,37,0,0.169184," ","integrate((d*x)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{7} \, \sqrt{d x} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{3} \, \sqrt{d x} a x \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"2/7*sqrt(d*x)*b*x^3*sgn(b*x^2 + a) + 2/3*sqrt(d*x)*a*x*sgn(b*x^2 + a)","A",0
731,1,40,0,0.171235," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\sqrt{d x} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \sqrt{d x} a \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{5 \, d}"," ",0,"2/5*(sqrt(d*x)*b*x^2*sgn(b*x^2 + a) + 5*sqrt(d*x)*a*sgn(b*x^2 + a))/d","A",0
732,1,41,0,0.157890," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{d x} b x \mathrm{sgn}\left(b x^{2} + a\right)}{d} - \frac{3 \, a \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{d x}}\right)}}{3 \, d}"," ",0,"2/3*(sqrt(d*x)*b*x*sgn(b*x^2 + a)/d - 3*a*sgn(b*x^2 + a)/sqrt(d*x))/d","A",0
733,1,42,0,0.161731," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \sqrt{d x} b \mathrm{sgn}\left(b x^{2} + a\right) - \frac{a d \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{d x} x}\right)}}{3 \, d^{3}}"," ",0,"2/3*(3*sqrt(d*x)*b*sgn(b*x^2 + a) - a*d*sgn(b*x^2 + a)/(sqrt(d*x)*x))/d^3","A",0
734,1,44,0,0.181199," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, b d^{3} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a d^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{5 \, \sqrt{d x} d^{6} x^{2}}"," ",0,"-2/5*(5*b*d^3*x^2*sgn(b*x^2 + a) + a*d^3*sgn(b*x^2 + a))/(sqrt(d*x)*d^6*x^2)","A",0
735,1,99,0,0.162879," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{19} \, \sqrt{d x} b^{3} d^{2} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{5} \, \sqrt{d x} a b^{2} d^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{6}{11} \, \sqrt{d x} a^{2} b d^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{7} \, \sqrt{d x} a^{3} d^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"2/19*sqrt(d*x)*b^3*d^2*x^9*sgn(b*x^2 + a) + 2/5*sqrt(d*x)*a*b^2*d^2*x^7*sgn(b*x^2 + a) + 6/11*sqrt(d*x)*a^2*b*d^2*x^5*sgn(b*x^2 + a) + 2/7*sqrt(d*x)*a^3*d^2*x^3*sgn(b*x^2 + a)","A",0
736,1,90,0,0.214422," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{3315} \, {\left(195 \, \sqrt{d x} b^{3} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 765 \, \sqrt{d x} a b^{2} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 1105 \, \sqrt{d x} a^{2} b x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 663 \, \sqrt{d x} a^{3} x^{2} \mathrm{sgn}\left(b x^{2} + a\right)\right)} d"," ",0,"2/3315*(195*sqrt(d*x)*b^3*x^8*sgn(b*x^2 + a) + 765*sqrt(d*x)*a*b^2*x^6*sgn(b*x^2 + a) + 1105*sqrt(d*x)*a^2*b*x^4*sgn(b*x^2 + a) + 663*sqrt(d*x)*a^3*x^2*sgn(b*x^2 + a))*d","A",0
737,1,85,0,0.161405," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)*(d*x)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, \sqrt{d x} b^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{6}{11} \, \sqrt{d x} a b^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{6}{7} \, \sqrt{d x} a^{2} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{3} \, \sqrt{d x} a^{3} x \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"2/15*sqrt(d*x)*b^3*x^7*sgn(b*x^2 + a) + 6/11*sqrt(d*x)*a*b^2*x^5*sgn(b*x^2 + a) + 6/7*sqrt(d*x)*a^2*b*x^3*sgn(b*x^2 + a) + 2/3*sqrt(d*x)*a^3*x*sgn(b*x^2 + a)","A",0
738,1,89,0,0.167293," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{d x} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 65 \, \sqrt{d x} a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 117 \, \sqrt{d x} a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 195 \, \sqrt{d x} a^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{195 \, d}"," ",0,"2/195*(15*sqrt(d*x)*b^3*x^6*sgn(b*x^2 + a) + 65*sqrt(d*x)*a*b^2*x^4*sgn(b*x^2 + a) + 117*sqrt(d*x)*a^2*b*x^2*sgn(b*x^2 + a) + 195*sqrt(d*x)*a^3*sgn(b*x^2 + a))/d","A",0
739,1,102,0,0.168364," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{77 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{d x}} - \frac{7 \, \sqrt{d x} b^{3} d^{65} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 33 \, \sqrt{d x} a b^{2} d^{65} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 77 \, \sqrt{d x} a^{2} b d^{65} x \mathrm{sgn}\left(b x^{2} + a\right)}{d^{66}}\right)}}{77 \, d}"," ",0,"-2/77*(77*a^3*sgn(b*x^2 + a)/sqrt(d*x) - (7*sqrt(d*x)*b^3*d^65*x^5*sgn(b*x^2 + a) + 33*sqrt(d*x)*a*b^2*d^65*x^3*sgn(b*x^2 + a) + 77*sqrt(d*x)*a^2*b*d^65*x*sgn(b*x^2 + a))/d^66)/d","A",0
740,1,105,0,0.174345," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{15 \, a^{3} d \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{d x} x} - \frac{5 \, \sqrt{d x} b^{3} d^{36} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 27 \, \sqrt{d x} a b^{2} d^{36} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 135 \, \sqrt{d x} a^{2} b d^{36} \mathrm{sgn}\left(b x^{2} + a\right)}{d^{36}}\right)}}{45 \, d^{3}}"," ",0,"-2/45*(15*a^3*d*sgn(b*x^2 + a)/(sqrt(d*x)*x) - (5*sqrt(d*x)*b^3*d^36*x^4*sgn(b*x^2 + a) + 27*sqrt(d*x)*a*b^2*d^36*x^2*sgn(b*x^2 + a) + 135*sqrt(d*x)*a^2*b*d^36*sgn(b*x^2 + a))/d^36)/d^3","A",0
741,1,107,0,0.220300," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{7 \, {\left(15 \, a^{2} b d^{3} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} d^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{\sqrt{d x} d^{2} x^{2}} - \frac{5 \, {\left(\sqrt{d x} b^{3} d^{21} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 7 \, \sqrt{d x} a b^{2} d^{21} x \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{d^{21}}\right)}}{35 \, d^{4}}"," ",0,"-2/35*(7*(15*a^2*b*d^3*x^2*sgn(b*x^2 + a) + a^3*d^3*sgn(b*x^2 + a))/(sqrt(d*x)*d^2*x^2) - 5*(sqrt(d*x)*b^3*d^21*x^3*sgn(b*x^2 + a) + 7*sqrt(d*x)*a*b^2*d^21*x*sgn(b*x^2 + a))/d^21)/d^4","A",0
742,1,153,0,0.170823," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{27} \, \sqrt{d x} b^{5} d^{2} x^{13} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{23} \, \sqrt{d x} a b^{4} d^{2} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{20}{19} \, \sqrt{d x} a^{2} b^{3} d^{2} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{4}{3} \, \sqrt{d x} a^{3} b^{2} d^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{11} \, \sqrt{d x} a^{4} b d^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{7} \, \sqrt{d x} a^{5} d^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"2/27*sqrt(d*x)*b^5*d^2*x^13*sgn(b*x^2 + a) + 10/23*sqrt(d*x)*a*b^4*d^2*x^11*sgn(b*x^2 + a) + 20/19*sqrt(d*x)*a^2*b^3*d^2*x^9*sgn(b*x^2 + a) + 4/3*sqrt(d*x)*a^3*b^2*d^2*x^7*sgn(b*x^2 + a) + 10/11*sqrt(d*x)*a^4*b*d^2*x^5*sgn(b*x^2 + a) + 2/7*sqrt(d*x)*a^5*d^2*x^3*sgn(b*x^2 + a)","A",0
743,1,138,0,0.202443," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{348075} \, {\left(13923 \, \sqrt{d x} b^{5} x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + 82875 \, \sqrt{d x} a b^{4} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 204750 \, \sqrt{d x} a^{2} b^{3} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 267750 \, \sqrt{d x} a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 193375 \, \sqrt{d x} a^{4} b x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 69615 \, \sqrt{d x} a^{5} x^{2} \mathrm{sgn}\left(b x^{2} + a\right)\right)} d"," ",0,"2/348075*(13923*sqrt(d*x)*b^5*x^12*sgn(b*x^2 + a) + 82875*sqrt(d*x)*a*b^4*x^10*sgn(b*x^2 + a) + 204750*sqrt(d*x)*a^2*b^3*x^8*sgn(b*x^2 + a) + 267750*sqrt(d*x)*a^3*b^2*x^6*sgn(b*x^2 + a) + 193375*sqrt(d*x)*a^4*b*x^4*sgn(b*x^2 + a) + 69615*sqrt(d*x)*a^5*x^2*sgn(b*x^2 + a))*d","A",0
744,1,133,0,0.201736," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)*(d*x)^(1/2),x, algorithm=""giac"")","\frac{2}{23} \, \sqrt{d x} b^{5} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{19} \, \sqrt{d x} a b^{4} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{4}{3} \, \sqrt{d x} a^{2} b^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{20}{11} \, \sqrt{d x} a^{3} b^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{10}{7} \, \sqrt{d x} a^{4} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2}{3} \, \sqrt{d x} a^{5} x \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"2/23*sqrt(d*x)*b^5*x^11*sgn(b*x^2 + a) + 10/19*sqrt(d*x)*a*b^4*x^9*sgn(b*x^2 + a) + 4/3*sqrt(d*x)*a^2*b^3*x^7*sgn(b*x^2 + a) + 20/11*sqrt(d*x)*a^3*b^2*x^5*sgn(b*x^2 + a) + 10/7*sqrt(d*x)*a^4*b*x^3*sgn(b*x^2 + a) + 2/3*sqrt(d*x)*a^5*x*sgn(b*x^2 + a)","A",0
745,1,137,0,0.174169," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(663 \, \sqrt{d x} b^{5} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 4095 \, \sqrt{d x} a b^{4} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 10710 \, \sqrt{d x} a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 15470 \, \sqrt{d x} a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 13923 \, \sqrt{d x} a^{4} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 13923 \, \sqrt{d x} a^{5} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{13923 \, d}"," ",0,"2/13923*(663*sqrt(d*x)*b^5*x^10*sgn(b*x^2 + a) + 4095*sqrt(d*x)*a*b^4*x^8*sgn(b*x^2 + a) + 10710*sqrt(d*x)*a^2*b^3*x^6*sgn(b*x^2 + a) + 15470*sqrt(d*x)*a^3*b^2*x^4*sgn(b*x^2 + a) + 13923*sqrt(d*x)*a^4*b*x^2*sgn(b*x^2 + a) + 13923*sqrt(d*x)*a^5*sgn(b*x^2 + a))/d","A",0
746,1,156,0,0.187736," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{4389 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{d x}} - \frac{231 \, \sqrt{d x} b^{5} d^{189} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 1463 \, \sqrt{d x} a b^{4} d^{189} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 3990 \, \sqrt{d x} a^{2} b^{3} d^{189} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 6270 \, \sqrt{d x} a^{3} b^{2} d^{189} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 7315 \, \sqrt{d x} a^{4} b d^{189} x \mathrm{sgn}\left(b x^{2} + a\right)}{d^{190}}\right)}}{4389 \, d}"," ",0,"-2/4389*(4389*a^5*sgn(b*x^2 + a)/sqrt(d*x) - (231*sqrt(d*x)*b^5*d^189*x^9*sgn(b*x^2 + a) + 1463*sqrt(d*x)*a*b^4*d^189*x^7*sgn(b*x^2 + a) + 3990*sqrt(d*x)*a^2*b^3*d^189*x^5*sgn(b*x^2 + a) + 6270*sqrt(d*x)*a^3*b^2*d^189*x^3*sgn(b*x^2 + a) + 7315*sqrt(d*x)*a^4*b*d^189*x*sgn(b*x^2 + a))/d^190)/d","A",0
747,1,159,0,0.186707," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{663 \, a^{5} d \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{d x} x} - \frac{117 \, \sqrt{d x} b^{5} d^{136} x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 765 \, \sqrt{d x} a b^{4} d^{136} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 2210 \, \sqrt{d x} a^{2} b^{3} d^{136} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 3978 \, \sqrt{d x} a^{3} b^{2} d^{136} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 9945 \, \sqrt{d x} a^{4} b d^{136} \mathrm{sgn}\left(b x^{2} + a\right)}{d^{136}}\right)}}{1989 \, d^{3}}"," ",0,"-2/1989*(663*a^5*d*sgn(b*x^2 + a)/(sqrt(d*x)*x) - (117*sqrt(d*x)*b^5*d^136*x^8*sgn(b*x^2 + a) + 765*sqrt(d*x)*a*b^4*d^136*x^6*sgn(b*x^2 + a) + 2210*sqrt(d*x)*a^2*b^3*d^136*x^4*sgn(b*x^2 + a) + 3978*sqrt(d*x)*a^3*b^2*d^136*x^2*sgn(b*x^2 + a) + 9945*sqrt(d*x)*a^4*b*d^136*sgn(b*x^2 + a))/d^136)/d^3","A",0
748,1,162,0,0.203733," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{231 \, {\left(25 \, a^{4} b d^{3} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{5} d^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{\sqrt{d x} d^{2} x^{2}} - \frac{77 \, \sqrt{d x} b^{5} d^{105} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 525 \, \sqrt{d x} a b^{4} d^{105} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 1650 \, \sqrt{d x} a^{2} b^{3} d^{105} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 3850 \, \sqrt{d x} a^{3} b^{2} d^{105} x \mathrm{sgn}\left(b x^{2} + a\right)}{d^{105}}\right)}}{1155 \, d^{4}}"," ",0,"-2/1155*(231*(25*a^4*b*d^3*x^2*sgn(b*x^2 + a) + a^5*d^3*sgn(b*x^2 + a))/(sqrt(d*x)*d^2*x^2) - (77*sqrt(d*x)*b^5*d^105*x^7*sgn(b*x^2 + a) + 525*sqrt(d*x)*a*b^4*d^105*x^5*sgn(b*x^2 + a) + 1650*sqrt(d*x)*a^2*b^3*d^105*x^3*sgn(b*x^2 + a) + 3850*sqrt(d*x)*a^3*b^2*d^105*x*sgn(b*x^2 + a))/d^105)/d^4","A",0
749,1,273,0,0.195789," ","integrate((d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{20} \, d^{3} {\left(\frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{3}} + \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{3}} + \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{3}} - \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{3}} + \frac{8 \, {\left(\sqrt{d x} b^{4} d^{10} x^{2} - 5 \, \sqrt{d x} a b^{3} d^{10}\right)}}{b^{5} d^{10}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/20*d^3*(10*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^3 + 10*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^3 + 5*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^3 - 5*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^3 + 8*(sqrt(d*x)*b^4*d^10*x^2 - 5*sqrt(d*x)*a*b^3*d^10)/(b^5*d^10))*sgn(b*x^2 + a)","A",0
750,1,254,0,0.197380," ","integrate((d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, d^{2} {\left(\frac{8 \, \sqrt{d x} x}{b} - \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{4} d} - \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{4} d} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{4} d} - \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{4} d}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/12*d^2*(8*sqrt(d*x)*x/b - 6*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^4*d) - 6*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^4*d) + 3*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^4*d) - 3*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^4*d))*sgn(b*x^2 + a)","A",0
751,1,238,0,0.243259," ","integrate((d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, d {\left(\frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{2}} + \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{2}} - \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{2}} - \frac{8 \, \sqrt{d x}}{b}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"-1/4*d*(2*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^2 + 2*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/b^2 + sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^2 - sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/b^2 - 8*sqrt(d*x)/b)*sgn(b*x^2 + a)","A",0
752,1,242,0,0.192831," ","integrate((d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(\frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{3}} + \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{3}} - \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{3}} + \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{3}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^3) + 2*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^3) - sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^3) + sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^3))*sgn(b*x^2 + a)/d","A",0
753,1,251,0,0.255598," ","integrate(1/(d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b d} + \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b d} + \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b d} - \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b d}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/4*(2*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b*d) + 2*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b*d) + sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b*d) - sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b*d))*sgn(b*x^2 + a)","A",0
754,1,264,0,0.234095," ","integrate(1/(d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(\frac{8}{\sqrt{d x} a} + \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{2} d^{2}} + \frac{2 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{2} d^{2}} - \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{2} d^{2}} + \frac{\sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{2} d^{2}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)}{4 \, d}"," ",0,"-1/4*(8/(sqrt(d*x)*a) + 2*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^2*d^2) + 2*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^2*d^2) - sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^2*d^2) + sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^2*d^2))*sgn(b*x^2 + a)/d","A",0
755,1,256,0,0.244744," ","integrate(1/(d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} d^{3}} + \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} d^{3}} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} d^{3}} - \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} d^{3}} + \frac{8}{\sqrt{d x} a d^{2} x}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"-1/12*(6*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*d^3) + 6*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*d^3) + 3*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*d^3) - 3*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*d^3) + 8/(sqrt(d*x)*a*d^2*x))*sgn(b*x^2 + a)","A",0
756,1,284,0,0.316500," ","integrate(1/(d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{20} \, {\left(\frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b d^{5}} + \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b d^{5}} - \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b d^{5}} + \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b d^{5}} + \frac{8 \, {\left(5 \, b d^{2} x^{2} - a d^{2}\right)}}{\sqrt{d x} a^{2} d^{5} x^{2}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/20*(10*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b*d^5) + 10*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b*d^5) - 5*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b*d^5) + 5*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b*d^5) + 8*(5*b*d^2*x^2 - a*d^2)/(sqrt(d*x)*a^2*d^5*x^2))*sgn(b*x^2 + a)","A",0
757,1,419,0,0.348890," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{640} \, d^{7} {\left(\frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{40 \, {\left(25 \, \sqrt{d x} a^{2} b d^{4} x^{2} + 21 \, \sqrt{d x} a^{3} d^{4}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{256 \, {\left(\sqrt{d x} b^{12} d^{10} x^{2} - 15 \, \sqrt{d x} a b^{11} d^{10}\right)}}{b^{15} d^{10} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/640*d^7*(1170*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^5*sgn(b*d^4*x^2 + a*d^4)) + 1170*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^5*sgn(b*d^4*x^2 + a*d^4)) + 585*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^5*sgn(b*d^4*x^2 + a*d^4)) - 585*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^5*sgn(b*d^4*x^2 + a*d^4)) - 40*(25*sqrt(d*x)*a^2*b*d^4*x^2 + 21*sqrt(d*x)*a^3*d^4)/((b*d^2*x^2 + a*d^2)^2*b^4*sgn(b*d^4*x^2 + a*d^4)) + 256*(sqrt(d*x)*b^12*d^10*x^2 - 15*sqrt(d*x)*a*b^11*d^10)/(b^15*d^10*sgn(b*d^4*x^2 + a*d^4)))","A",0
758,1,399,0,0.409600," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{384} \, d^{6} {\left(\frac{256 \, \sqrt{d x} x}{b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{24 \, {\left(19 \, \sqrt{d x} a b d^{4} x^{3} + 15 \, \sqrt{d x} a^{2} d^{4} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/384*d^6*(256*sqrt(d*x)*x/(b^3*sgn(b*d^4*x^2 + a*d^4)) + 24*(19*sqrt(d*x)*a*b*d^4*x^3 + 15*sqrt(d*x)*a^2*d^4*x)/((b*d^2*x^2 + a*d^2)^2*b^3*sgn(b*d^4*x^2 + a*d^4)) - 462*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^6*d*sgn(b*d^4*x^2 + a*d^4)) - 462*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^6*d*sgn(b*d^4*x^2 + a*d^4)) + 231*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^6*d*sgn(b*d^4*x^2 + a*d^4)) - 231*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^6*d*sgn(b*d^4*x^2 + a*d^4)))","A",0
759,1,385,0,0.313805," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{128} \, d^{5} {\left(\frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{256 \, \sqrt{d x}}{b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{8 \, {\left(17 \, \sqrt{d x} a b d^{4} x^{2} + 13 \, \sqrt{d x} a^{2} d^{4}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"-1/128*d^5*(90*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^4*sgn(b*d^4*x^2 + a*d^4)) + 90*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^4*sgn(b*d^4*x^2 + a*d^4)) + 45*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^4*sgn(b*d^4*x^2 + a*d^4)) - 45*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^4*sgn(b*d^4*x^2 + a*d^4)) - 256*sqrt(d*x)/(b^3*sgn(b*d^4*x^2 + a*d^4)) - 8*(17*sqrt(d*x)*a*b*d^4*x^2 + 13*sqrt(d*x)*a^2*d^4)/((b*d^2*x^2 + a*d^2)^2*b^3*sgn(b*d^4*x^2 + a*d^4)))","A",0
760,1,380,0,0.318025," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{128} \, d^{4} {\left(\frac{8 \, {\left(11 \, \sqrt{d x} b d^{4} x^{3} + 7 \, \sqrt{d x} a d^{4} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{42 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"-1/128*d^4*(8*(11*sqrt(d*x)*b*d^4*x^3 + 7*sqrt(d*x)*a*d^4*x)/((b*d^2*x^2 + a*d^2)^2*b^2*sgn(b*d^4*x^2 + a*d^4)) - 42*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^5*d*sgn(b*d^4*x^2 + a*d^4)) - 42*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^5*d*sgn(b*d^4*x^2 + a*d^4)) + 21*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^5*d*sgn(b*d^4*x^2 + a*d^4)) - 21*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^5*d*sgn(b*d^4*x^2 + a*d^4)))","A",0
761,1,367,0,0.307082," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{128} \, d^{3} {\left(\frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{8 \, {\left(9 \, \sqrt{d x} b d^{4} x^{2} + 5 \, \sqrt{d x} a d^{4}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/128*d^3*(10*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^3*sgn(b*d^4*x^2 + a*d^4)) + 10*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^3*sgn(b*d^4*x^2 + a*d^4)) + 5*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^3*sgn(b*d^4*x^2 + a*d^4)) - 5*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^3*sgn(b*d^4*x^2 + a*d^4)) - 8*(9*sqrt(d*x)*b*d^4*x^2 + 5*sqrt(d*x)*a*d^4)/((b*d^2*x^2 + a*d^2)^2*b^2*sgn(b*d^4*x^2 + a*d^4)))","A",0
762,1,383,0,0.319411," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{128} \, d^{2} {\left(\frac{8 \, {\left(3 \, \sqrt{d x} b d^{4} x^{3} - \sqrt{d x} a d^{4} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} a b \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/128*d^2*(8*(3*sqrt(d*x)*b*d^4*x^3 - sqrt(d*x)*a*d^4*x)/((b*d^2*x^2 + a*d^2)^2*a*b*sgn(b*d^4*x^2 + a*d^4)) + 6*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^4*d*sgn(b*d^4*x^2 + a*d^4)) + 6*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^4*d*sgn(b*d^4*x^2 + a*d^4)) - 3*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^4*d*sgn(b*d^4*x^2 + a*d^4)) + 3*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^4*d*sgn(b*d^4*x^2 + a*d^4)))","A",0
763,1,367,0,0.336965," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{128} \, d {\left(\frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{6 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{3 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(\sqrt{d x} b d^{4} x^{2} - 3 \, \sqrt{d x} a d^{4}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} a b \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/128*d*(6*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^2*sgn(b*d^4*x^2 + a*d^4)) + 6*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^2*sgn(b*d^4*x^2 + a*d^4)) + 3*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^2*sgn(b*d^4*x^2 + a*d^4)) - 3*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^2*sgn(b*d^4*x^2 + a*d^4)) + 8*(sqrt(d*x)*b*d^4*x^2 - 3*sqrt(d*x)*a*d^4)/((b*d^2*x^2 + a*d^2)^2*a*b*sgn(b*d^4*x^2 + a*d^4)))","A",0
764,1,368,0,0.336029," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{\frac{8 \, {\left(5 \, \sqrt{d x} b d^{5} x^{3} + 9 \, \sqrt{d x} a d^{5} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} a^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{10 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{5 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}}{128 \, d}"," ",0,"1/128*(8*(5*sqrt(d*x)*b*d^5*x^3 + 9*sqrt(d*x)*a*d^5*x)/((b*d^2*x^2 + a*d^2)^2*a^2*sgn(b*d^4*x^2 + a*d^4)) + 10*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)) + 10*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)) - 5*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)) + 5*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)))/d","A",0
765,1,374,0,0.290759," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x, algorithm=""giac"")","\frac{7 \, \sqrt{d x} b d^{3} x^{2} + 11 \, \sqrt{d x} a d^{3}}{16 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{2} a^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{128 \, a^{3} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{21 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{128 \, a^{3} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}"," ",0,"1/16*(7*sqrt(d*x)*b*d^3*x^2 + 11*sqrt(d*x)*a*d^3)/((b*d^2*x^2 + a*d^2)^2*a^2*sgn(b*d^4*x^2 + a*d^4)) + 21/64*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b*d*sgn(b*d^4*x^2 + a*d^4)) + 21/64*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b*d*sgn(b*d^4*x^2 + a*d^4)) + 21/128*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b*d*sgn(b*d^4*x^2 + a*d^4)) - 21/128*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b*d*sgn(b*d^4*x^2 + a*d^4))","A",0
766,1,410,0,0.314229," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{\frac{256}{\sqrt{d x} a^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(13 \, \sqrt{d x} b^{2} d^{3} x^{3} + 17 \, \sqrt{d x} a b d^{3} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{2} a^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}}{128 \, d}"," ",0,"-1/128*(256/(sqrt(d*x)*a^3*sgn(b*d^4*x^2 + a*d^4)) + 8*(13*sqrt(d*x)*b^2*d^3*x^3 + 17*sqrt(d*x)*a*b*d^3*x)/((b*d^2*x^2 + a*d^2)^2*a^3*sgn(b*d^4*x^2 + a*d^4)) + 90*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)) + 90*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)) - 45*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)) + 45*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)))/d","A",0
767,1,401,0,0.351393," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{15 \, \sqrt{d x} b^{2} d^{2} x^{2} + 19 \, \sqrt{d x} a b d^{2}}{16 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{2} a^{3} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{128 \, a^{4} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{77 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{128 \, a^{4} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{2}{3 \, \sqrt{d x} a^{3} d^{2} x \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}"," ",0,"-1/16*(15*sqrt(d*x)*b^2*d^2*x^2 + 19*sqrt(d*x)*a*b*d^2)/((b*d^2*x^2 + a*d^2)^2*a^3*d*sgn(b*d^4*x^2 + a*d^4)) - 77/64*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*d^3*sgn(b*d^4*x^2 + a*d^4)) - 77/64*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*d^3*sgn(b*d^4*x^2 + a*d^4)) - 77/128*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*d^3*sgn(b*d^4*x^2 + a*d^4)) + 77/128*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*d^3*sgn(b*d^4*x^2 + a*d^4)) - 2/3/(sqrt(d*x)*a^3*d^2*x*sgn(b*d^4*x^2 + a*d^4))","A",0
768,1,432,0,0.339285," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{21 \, \sqrt{d x} b^{3} d^{3} x^{3} + 25 \, \sqrt{d x} a b^{2} d^{3} x}{16 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{2} a^{4} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{117 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{5} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{117 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{5} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{117 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{128 \, a^{5} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{117 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{128 \, a^{5} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{2 \, {\left(15 \, b d^{2} x^{2} - a d^{2}\right)}}{5 \, \sqrt{d x} a^{4} d^{5} x^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}"," ",0,"1/16*(21*sqrt(d*x)*b^3*d^3*x^3 + 25*sqrt(d*x)*a*b^2*d^3*x)/((b*d^2*x^2 + a*d^2)^2*a^4*d^3*sgn(b*d^4*x^2 + a*d^4)) + 117/64*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b*d^5*sgn(b*d^4*x^2 + a*d^4)) + 117/64*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b*d^5*sgn(b*d^4*x^2 + a*d^4)) - 117/128*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b*d^5*sgn(b*d^4*x^2 + a*d^4)) + 117/128*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b*d^5*sgn(b*d^4*x^2 + a*d^4)) + 2/5*(15*b*d^2*x^2 - a*d^2)/(sqrt(d*x)*a^4*d^5*x^2*sgn(b*d^4*x^2 + a*d^4))","A",0
769,1,457,0,0.445458," ","integrate((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{40960} \, d^{11} {\left(\frac{139230 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{7} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{139230 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{7} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{7} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{69615 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} a \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{7} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{40 \, {\left(5599 \, \sqrt{d x} a^{2} b^{3} d^{8} x^{6} + 14145 \, \sqrt{d x} a^{3} b^{2} d^{8} x^{4} + 12357 \, \sqrt{d x} a^{4} b d^{8} x^{2} + 3683 \, \sqrt{d x} a^{5} d^{8}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} b^{6} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{16384 \, {\left(\sqrt{d x} b^{20} d^{10} x^{2} - 25 \, \sqrt{d x} a b^{19} d^{10}\right)}}{b^{25} d^{10} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/40960*d^11*(139230*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^7*sgn(b*d^4*x^2 + a*d^4)) + 139230*sqrt(2)*(a*b^3*d^2)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^7*sgn(b*d^4*x^2 + a*d^4)) + 69615*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^7*sgn(b*d^4*x^2 + a*d^4)) - 69615*sqrt(2)*(a*b^3*d^2)^(1/4)*a*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^7*sgn(b*d^4*x^2 + a*d^4)) - 40*(5599*sqrt(d*x)*a^2*b^3*d^8*x^6 + 14145*sqrt(d*x)*a^3*b^2*d^8*x^4 + 12357*sqrt(d*x)*a^4*b*d^8*x^2 + 3683*sqrt(d*x)*a^5*d^8)/((b*d^2*x^2 + a*d^2)^4*b^6*sgn(b*d^4*x^2 + a*d^4)) + 16384*(sqrt(d*x)*b^20*d^10*x^2 - 25*sqrt(d*x)*a*b^19*d^10)/(b^25*d^10*sgn(b*d^4*x^2 + a*d^4)))","A",0
770,1,437,0,0.419310," ","integrate((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24576} \, d^{10} {\left(\frac{16384 \, \sqrt{d x} x}{b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{43890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{8} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{43890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{8} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{21945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{8} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{21945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{8} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(8775 \, \sqrt{d x} a b^{3} d^{8} x^{7} + 21057 \, \sqrt{d x} a^{2} b^{2} d^{8} x^{5} + 17933 \, \sqrt{d x} a^{3} b d^{8} x^{3} + 5267 \, \sqrt{d x} a^{4} d^{8} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/24576*d^10*(16384*sqrt(d*x)*x/(b^5*sgn(b*d^4*x^2 + a*d^4)) - 43890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^8*d*sgn(b*d^4*x^2 + a*d^4)) - 43890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^8*d*sgn(b*d^4*x^2 + a*d^4)) + 21945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^8*d*sgn(b*d^4*x^2 + a*d^4)) - 21945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^8*d*sgn(b*d^4*x^2 + a*d^4)) + 8*(8775*sqrt(d*x)*a*b^3*d^8*x^7 + 21057*sqrt(d*x)*a^2*b^2*d^8*x^5 + 17933*sqrt(d*x)*a^3*b*d^8*x^3 + 5267*sqrt(d*x)*a^4*d^8*x)/((b*d^2*x^2 + a*d^2)^4*b^5*sgn(b*d^4*x^2 + a*d^4)))","A",0
771,1,423,0,0.420146," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{1}{24576} \, d^{9} {\left(\frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{6} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{b^{6} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{6} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{b^{6} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{49152 \, \sqrt{d x}}{b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{8 \, {\left(6925 \, \sqrt{d x} a b^{3} d^{8} x^{6} + 15955 \, \sqrt{d x} a^{2} b^{2} d^{8} x^{4} + 13215 \, \sqrt{d x} a^{3} b d^{8} x^{2} + 3801 \, \sqrt{d x} a^{4} d^{8}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"-1/24576*d^9*(19890*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^6*sgn(b*d^4*x^2 + a*d^4)) + 19890*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(b^6*sgn(b*d^4*x^2 + a*d^4)) + 9945*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^6*sgn(b*d^4*x^2 + a*d^4)) - 9945*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(b^6*sgn(b*d^4*x^2 + a*d^4)) - 49152*sqrt(d*x)/(b^5*sgn(b*d^4*x^2 + a*d^4)) - 8*(6925*sqrt(d*x)*a*b^3*d^8*x^6 + 15955*sqrt(d*x)*a^2*b^2*d^8*x^4 + 13215*sqrt(d*x)*a^3*b*d^8*x^2 + 3801*sqrt(d*x)*a^4*d^8)/((b*d^2*x^2 + a*d^2)^4*b^5*sgn(b*d^4*x^2 + a*d^4)))","A",0
772,1,418,0,0.366300," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8192} \, d^{8} {\left(\frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{7} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{2310 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{7} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{7} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{7} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{8 \, {\left(893 \, \sqrt{d x} b^{3} d^{8} x^{7} + 1755 \, \sqrt{d x} a b^{2} d^{8} x^{5} + 1375 \, \sqrt{d x} a^{2} b d^{8} x^{3} + 385 \, \sqrt{d x} a^{3} d^{8} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/8192*d^8*(2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^7*d*sgn(b*d^4*x^2 + a*d^4)) + 2310*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^7*d*sgn(b*d^4*x^2 + a*d^4)) - 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^7*d*sgn(b*d^4*x^2 + a*d^4)) + 1155*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^7*d*sgn(b*d^4*x^2 + a*d^4)) - 8*(893*sqrt(d*x)*b^3*d^8*x^7 + 1755*sqrt(d*x)*a*b^2*d^8*x^5 + 1375*sqrt(d*x)*a^2*b*d^8*x^3 + 385*sqrt(d*x)*a^3*d^8*x)/((b*d^2*x^2 + a*d^2)^4*b^4*sgn(b*d^4*x^2 + a*d^4)))","A",0
773,1,405,0,0.347939," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24576} \, d^{7} {\left(\frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a b^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{8 \, {\left(1853 \, \sqrt{d x} b^{3} d^{8} x^{6} + 3107 \, \sqrt{d x} a b^{2} d^{8} x^{4} + 2223 \, \sqrt{d x} a^{2} b d^{8} x^{2} + 585 \, \sqrt{d x} a^{3} d^{8}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/24576*d^7*(1170*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^5*sgn(b*d^4*x^2 + a*d^4)) + 1170*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a*b^5*sgn(b*d^4*x^2 + a*d^4)) + 585*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^5*sgn(b*d^4*x^2 + a*d^4)) - 585*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a*b^5*sgn(b*d^4*x^2 + a*d^4)) - 8*(1853*sqrt(d*x)*b^3*d^8*x^6 + 3107*sqrt(d*x)*a*b^2*d^8*x^4 + 2223*sqrt(d*x)*a^2*b*d^8*x^2 + 585*sqrt(d*x)*a^3*d^8)/((b*d^2*x^2 + a*d^2)^4*b^4*sgn(b*d^4*x^2 + a*d^4)))","A",0
774,1,421,0,0.363431," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24576} \, d^{6} {\left(\frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{6} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(231 \, \sqrt{d x} b^{3} d^{8} x^{7} - 351 \, \sqrt{d x} a b^{2} d^{8} x^{5} - 275 \, \sqrt{d x} a^{2} b d^{8} x^{3} - 77 \, \sqrt{d x} a^{3} d^{8} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/24576*d^6*(462*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^6*d*sgn(b*d^4*x^2 + a*d^4)) + 462*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^6*d*sgn(b*d^4*x^2 + a*d^4)) - 231*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^6*d*sgn(b*d^4*x^2 + a*d^4)) + 231*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^6*d*sgn(b*d^4*x^2 + a*d^4)) + 8*(231*sqrt(d*x)*b^3*d^8*x^7 - 351*sqrt(d*x)*a*b^2*d^8*x^5 - 275*sqrt(d*x)*a^2*b*d^8*x^3 - 77*sqrt(d*x)*a^3*d^8*x)/((b*d^2*x^2 + a*d^2)^4*a*b^3*sgn(b*d^4*x^2 + a*d^4)))","A",0
775,1,408,0,0.345450," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8192} \, d^{5} {\left(\frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{2} b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{2} b^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(15 \, \sqrt{d x} b^{3} d^{8} x^{6} - 239 \, \sqrt{d x} a b^{2} d^{8} x^{4} - 171 \, \sqrt{d x} a^{2} b d^{8} x^{2} - 45 \, \sqrt{d x} a^{3} d^{8}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/8192*d^5*(90*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^4*sgn(b*d^4*x^2 + a*d^4)) + 90*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^2*b^4*sgn(b*d^4*x^2 + a*d^4)) + 45*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^4*sgn(b*d^4*x^2 + a*d^4)) - 45*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^2*b^4*sgn(b*d^4*x^2 + a*d^4)) + 8*(15*sqrt(d*x)*b^3*d^8*x^6 - 239*sqrt(d*x)*a*b^2*d^8*x^4 - 171*sqrt(d*x)*a^2*b*d^8*x^2 - 45*sqrt(d*x)*a^3*d^8)/((b*d^2*x^2 + a*d^2)^4*a*b^3*sgn(b*d^4*x^2 + a*d^4)))","A",0
776,1,421,0,0.364627," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24576} \, d^{4} {\left(\frac{210 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{210 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{105 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{105 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(105 \, \sqrt{d x} b^{3} d^{8} x^{7} + 399 \, \sqrt{d x} a b^{2} d^{8} x^{5} - 125 \, \sqrt{d x} a^{2} b d^{8} x^{3} - 35 \, \sqrt{d x} a^{3} d^{8} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/24576*d^4*(210*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^5*d*sgn(b*d^4*x^2 + a*d^4)) + 210*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^5*d*sgn(b*d^4*x^2 + a*d^4)) - 105*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^5*d*sgn(b*d^4*x^2 + a*d^4)) + 105*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^5*d*sgn(b*d^4*x^2 + a*d^4)) + 8*(105*sqrt(d*x)*b^3*d^8*x^7 + 399*sqrt(d*x)*a*b^2*d^8*x^5 - 125*sqrt(d*x)*a^2*b*d^8*x^3 - 35*sqrt(d*x)*a^3*d^8*x)/((b*d^2*x^2 + a*d^2)^4*a^2*b^2*sgn(b*d^4*x^2 + a*d^4)))","A",0
777,1,408,0,0.352330," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24576} \, d^{3} {\left(\frac{210 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{210 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{105 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{105 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{3} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(35 \, \sqrt{d x} b^{3} d^{8} x^{6} + 125 \, \sqrt{d x} a b^{2} d^{8} x^{4} - 399 \, \sqrt{d x} a^{2} b d^{8} x^{2} - 105 \, \sqrt{d x} a^{3} d^{8}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{2} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/24576*d^3*(210*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)) + 210*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)) + 105*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)) - 105*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^3*b^3*sgn(b*d^4*x^2 + a*d^4)) + 8*(35*sqrt(d*x)*b^3*d^8*x^6 + 125*sqrt(d*x)*a*b^2*d^8*x^4 - 399*sqrt(d*x)*a^2*b*d^8*x^2 - 105*sqrt(d*x)*a^3*d^8)/((b*d^2*x^2 + a*d^2)^4*a^2*b^2*sgn(b*d^4*x^2 + a*d^4)))","A",0
778,1,421,0,0.369714," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8192} \, d^{2} {\left(\frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{90 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{45 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{4} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(45 \, \sqrt{d x} b^{3} d^{8} x^{7} + 171 \, \sqrt{d x} a b^{2} d^{8} x^{5} + 239 \, \sqrt{d x} a^{2} b d^{8} x^{3} - 15 \, \sqrt{d x} a^{3} d^{8} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{3} b \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/8192*d^2*(90*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^4*d*sgn(b*d^4*x^2 + a*d^4)) + 90*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^4*d*sgn(b*d^4*x^2 + a*d^4)) - 45*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^4*d*sgn(b*d^4*x^2 + a*d^4)) + 45*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^4*d*sgn(b*d^4*x^2 + a*d^4)) + 8*(45*sqrt(d*x)*b^3*d^8*x^7 + 171*sqrt(d*x)*a*b^2*d^8*x^5 + 239*sqrt(d*x)*a^2*b*d^8*x^3 - 15*sqrt(d*x)*a^3*d^8*x)/((b*d^2*x^2 + a*d^2)^4*a^3*b*sgn(b*d^4*x^2 + a*d^4)))","A",0
779,1,406,0,0.347880," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{24576} \, d {\left(\frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{462 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{4} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{231 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{4} b^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(77 \, \sqrt{d x} b^{3} d^{8} x^{6} + 275 \, \sqrt{d x} a b^{2} d^{8} x^{4} + 351 \, \sqrt{d x} a^{2} b d^{8} x^{2} - 231 \, \sqrt{d x} a^{3} d^{8}\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{3} b \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}\right)}"," ",0,"1/24576*d*(462*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^2*sgn(b*d^4*x^2 + a*d^4)) + 462*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^4*b^2*sgn(b*d^4*x^2 + a*d^4)) + 231*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^2*sgn(b*d^4*x^2 + a*d^4)) - 231*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^4*b^2*sgn(b*d^4*x^2 + a*d^4)) + 8*(77*sqrt(d*x)*b^3*d^8*x^6 + 275*sqrt(d*x)*a*b^2*d^8*x^4 + 351*sqrt(d*x)*a^2*b*d^8*x^2 - 231*sqrt(d*x)*a^3*d^8)/((b*d^2*x^2 + a*d^2)^4*a^3*b*sgn(b*d^4*x^2 + a*d^4)))","A",0
780,1,406,0,0.378118," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{\frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{1170 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{5} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{585 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{5} b^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(585 \, \sqrt{d x} b^{3} d^{9} x^{7} + 2223 \, \sqrt{d x} a b^{2} d^{9} x^{5} + 3107 \, \sqrt{d x} a^{2} b d^{9} x^{3} + 1853 \, \sqrt{d x} a^{3} d^{9} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}}{24576 \, d}"," ",0,"1/24576*(1170*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^3*sgn(b*d^4*x^2 + a*d^4)) + 1170*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b^3*sgn(b*d^4*x^2 + a*d^4)) - 585*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^3*sgn(b*d^4*x^2 + a*d^4)) + 585*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b^3*sgn(b*d^4*x^2 + a*d^4)) + 8*(585*sqrt(d*x)*b^3*d^9*x^7 + 2223*sqrt(d*x)*a*b^2*d^9*x^5 + 3107*sqrt(d*x)*a^2*b*d^9*x^3 + 1853*sqrt(d*x)*a^3*d^9*x)/((b*d^2*x^2 + a*d^2)^4*a^4*sgn(b*d^4*x^2 + a*d^4)))/d","A",0
781,1,412,0,0.333678," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x, algorithm=""giac"")","\frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{4096 \, a^{5} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{4096 \, a^{5} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{8192 \, a^{5} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{1155 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{8192 \, a^{5} b d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{385 \, \sqrt{d x} b^{3} d^{7} x^{6} + 1375 \, \sqrt{d x} a b^{2} d^{7} x^{4} + 1755 \, \sqrt{d x} a^{2} b d^{7} x^{2} + 893 \, \sqrt{d x} a^{3} d^{7}}{1024 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{4} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}"," ",0,"1155/4096*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b*d*sgn(b*d^4*x^2 + a*d^4)) + 1155/4096*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^5*b*d*sgn(b*d^4*x^2 + a*d^4)) + 1155/8192*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b*d*sgn(b*d^4*x^2 + a*d^4)) - 1155/8192*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^5*b*d*sgn(b*d^4*x^2 + a*d^4)) + 1/1024*(385*sqrt(d*x)*b^3*d^7*x^6 + 1375*sqrt(d*x)*a*b^2*d^7*x^4 + 1755*sqrt(d*x)*a^2*b*d^7*x^2 + 893*sqrt(d*x)*a^3*d^7)/((b*d^2*x^2 + a*d^2)^4*a^4*sgn(b*d^4*x^2 + a*d^4))","A",0
782,1,448,0,0.371725," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{\frac{49152}{\sqrt{d x} a^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{6} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{19890 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{a^{6} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{6} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{9945 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{a^{6} b^{2} d^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{8 \, {\left(3801 \, \sqrt{d x} b^{4} d^{7} x^{7} + 13215 \, \sqrt{d x} a b^{3} d^{7} x^{5} + 15955 \, \sqrt{d x} a^{2} b^{2} d^{7} x^{3} + 6925 \, \sqrt{d x} a^{3} b d^{7} x\right)}}{{\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}}{24576 \, d}"," ",0,"-1/24576*(49152/(sqrt(d*x)*a^5*sgn(b*d^4*x^2 + a*d^4)) + 19890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)) + 19890*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)) - 9945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)) + 9945*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*b^2*d^2*sgn(b*d^4*x^2 + a*d^4)) + 8*(3801*sqrt(d*x)*b^4*d^7*x^7 + 13215*sqrt(d*x)*a*b^3*d^7*x^5 + 15955*sqrt(d*x)*a^2*b^2*d^7*x^3 + 6925*sqrt(d*x)*a^3*b*d^7*x)/((b*d^2*x^2 + a*d^2)^4*a^5*sgn(b*d^4*x^2 + a*d^4)))/d","A",0
783,1,439,0,0.738664," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","-\frac{7315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{4096 \, a^{6} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{7315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{4096 \, a^{6} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{7315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{8192 \, a^{6} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{7315 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{8192 \, a^{6} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{2}{3 \, \sqrt{d x} a^{5} d^{2} x \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{5267 \, \sqrt{d x} b^{4} d^{6} x^{6} + 17933 \, \sqrt{d x} a b^{3} d^{6} x^{4} + 21057 \, \sqrt{d x} a^{2} b^{2} d^{6} x^{2} + 8775 \, \sqrt{d x} a^{3} b d^{6}}{3072 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{5} d \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}"," ",0,"-7315/4096*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*d^3*sgn(b*d^4*x^2 + a*d^4)) - 7315/4096*sqrt(2)*(a*b^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^6*d^3*sgn(b*d^4*x^2 + a*d^4)) - 7315/8192*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*d^3*sgn(b*d^4*x^2 + a*d^4)) + 7315/8192*sqrt(2)*(a*b^3*d^2)^(1/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^6*d^3*sgn(b*d^4*x^2 + a*d^4)) - 2/3/(sqrt(d*x)*a^5*d^2*x*sgn(b*d^4*x^2 + a*d^4)) - 1/3072*(5267*sqrt(d*x)*b^4*d^6*x^6 + 17933*sqrt(d*x)*a*b^3*d^6*x^4 + 21057*sqrt(d*x)*a^2*b^2*d^6*x^2 + 8775*sqrt(d*x)*a^3*b*d^6)/((b*d^2*x^2 + a*d^2)^4*a^5*d*sgn(b*d^4*x^2 + a*d^4))","A",0
784,1,470,0,0.364904," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{13923 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{4096 \, a^{7} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{13923 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}}}\right)}{4096 \, a^{7} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} - \frac{13923 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x + \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{8192 \, a^{7} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{13923 \, \sqrt{2} \left(a b^{3} d^{2}\right)^{\frac{3}{4}} \log\left(d x - \sqrt{2} \left(\frac{a d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x} + \sqrt{\frac{a d^{2}}{b}}\right)}{8192 \, a^{7} b d^{5} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{3683 \, \sqrt{d x} b^{5} d^{7} x^{7} + 12357 \, \sqrt{d x} a b^{4} d^{7} x^{5} + 14145 \, \sqrt{d x} a^{2} b^{3} d^{7} x^{3} + 5599 \, \sqrt{d x} a^{3} b^{2} d^{7} x}{1024 \, {\left(b d^{2} x^{2} + a d^{2}\right)}^{4} a^{6} d^{3} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)} + \frac{2 \, {\left(25 \, b d^{2} x^{2} - a d^{2}\right)}}{5 \, \sqrt{d x} a^{6} d^{5} x^{2} \mathrm{sgn}\left(b d^{4} x^{2} + a d^{4}\right)}"," ",0,"13923/4096*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) + 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^7*b*d^5*sgn(b*d^4*x^2 + a*d^4)) + 13923/4096*sqrt(2)*(a*b^3*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2/b)^(1/4) - 2*sqrt(d*x))/(a*d^2/b)^(1/4))/(a^7*b*d^5*sgn(b*d^4*x^2 + a*d^4)) - 13923/8192*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x + sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^7*b*d^5*sgn(b*d^4*x^2 + a*d^4)) + 13923/8192*sqrt(2)*(a*b^3*d^2)^(3/4)*log(d*x - sqrt(2)*(a*d^2/b)^(1/4)*sqrt(d*x) + sqrt(a*d^2/b))/(a^7*b*d^5*sgn(b*d^4*x^2 + a*d^4)) + 1/1024*(3683*sqrt(d*x)*b^5*d^7*x^7 + 12357*sqrt(d*x)*a*b^4*d^7*x^5 + 14145*sqrt(d*x)*a^2*b^3*d^7*x^3 + 5599*sqrt(d*x)*a^3*b^2*d^7*x)/((b*d^2*x^2 + a*d^2)^4*a^6*d^3*sgn(b*d^4*x^2 + a*d^4)) + 2/5*(25*b*d^2*x^2 - a*d^2)/(sqrt(d*x)*a^6*d^5*x^2*sgn(b*d^4*x^2 + a*d^4))","A",0
785,1,847,0,0.251241," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b^{6} m^{6} x^{13} + 36 \, \left(d x\right)^{m} b^{6} m^{5} x^{13} + 6 \, \left(d x\right)^{m} a b^{5} m^{6} x^{11} + 505 \, \left(d x\right)^{m} b^{6} m^{4} x^{13} + 228 \, \left(d x\right)^{m} a b^{5} m^{5} x^{11} + 3480 \, \left(d x\right)^{m} b^{6} m^{3} x^{13} + 15 \, \left(d x\right)^{m} a^{2} b^{4} m^{6} x^{9} + 3330 \, \left(d x\right)^{m} a b^{5} m^{4} x^{11} + 12139 \, \left(d x\right)^{m} b^{6} m^{2} x^{13} + 600 \, \left(d x\right)^{m} a^{2} b^{4} m^{5} x^{9} + 23640 \, \left(d x\right)^{m} a b^{5} m^{3} x^{11} + 19524 \, \left(d x\right)^{m} b^{6} m x^{13} + 20 \, \left(d x\right)^{m} a^{3} b^{3} m^{6} x^{7} + 9195 \, \left(d x\right)^{m} a^{2} b^{4} m^{4} x^{9} + 84234 \, \left(d x\right)^{m} a b^{5} m^{2} x^{11} + 10395 \, \left(d x\right)^{m} b^{6} x^{13} + 840 \, \left(d x\right)^{m} a^{3} b^{3} m^{5} x^{7} + 67920 \, \left(d x\right)^{m} a^{2} b^{4} m^{3} x^{9} + 137412 \, \left(d x\right)^{m} a b^{5} m x^{11} + 15 \, \left(d x\right)^{m} a^{4} b^{2} m^{6} x^{5} + 13580 \, \left(d x\right)^{m} a^{3} b^{3} m^{4} x^{7} + 249405 \, \left(d x\right)^{m} a^{2} b^{4} m^{2} x^{9} + 73710 \, \left(d x\right)^{m} a b^{5} x^{11} + 660 \, \left(d x\right)^{m} a^{4} b^{2} m^{5} x^{5} + 105840 \, \left(d x\right)^{m} a^{3} b^{3} m^{3} x^{7} + 415320 \, \left(d x\right)^{m} a^{2} b^{4} m x^{9} + 6 \, \left(d x\right)^{m} a^{5} b m^{6} x^{3} + 11295 \, \left(d x\right)^{m} a^{4} b^{2} m^{4} x^{5} + 406700 \, \left(d x\right)^{m} a^{3} b^{3} m^{2} x^{7} + 225225 \, \left(d x\right)^{m} a^{2} b^{4} x^{9} + 276 \, \left(d x\right)^{m} a^{5} b m^{5} x^{3} + 94200 \, \left(d x\right)^{m} a^{4} b^{2} m^{3} x^{5} + 699720 \, \left(d x\right)^{m} a^{3} b^{3} m x^{7} + \left(d x\right)^{m} a^{6} m^{6} x + 5010 \, \left(d x\right)^{m} a^{5} b m^{4} x^{3} + 389685 \, \left(d x\right)^{m} a^{4} b^{2} m^{2} x^{5} + 386100 \, \left(d x\right)^{m} a^{3} b^{3} x^{7} + 48 \, \left(d x\right)^{m} a^{6} m^{5} x + 45240 \, \left(d x\right)^{m} a^{5} b m^{3} x^{3} + 711540 \, \left(d x\right)^{m} a^{4} b^{2} m x^{5} + 925 \, \left(d x\right)^{m} a^{6} m^{4} x + 208554 \, \left(d x\right)^{m} a^{5} b m^{2} x^{3} + 405405 \, \left(d x\right)^{m} a^{4} b^{2} x^{5} + 9120 \, \left(d x\right)^{m} a^{6} m^{3} x + 438324 \, \left(d x\right)^{m} a^{5} b m x^{3} + 48259 \, \left(d x\right)^{m} a^{6} m^{2} x + 270270 \, \left(d x\right)^{m} a^{5} b x^{3} + 129072 \, \left(d x\right)^{m} a^{6} m x + 135135 \, \left(d x\right)^{m} a^{6} x}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((d*x)^m*b^6*m^6*x^13 + 36*(d*x)^m*b^6*m^5*x^13 + 6*(d*x)^m*a*b^5*m^6*x^11 + 505*(d*x)^m*b^6*m^4*x^13 + 228*(d*x)^m*a*b^5*m^5*x^11 + 3480*(d*x)^m*b^6*m^3*x^13 + 15*(d*x)^m*a^2*b^4*m^6*x^9 + 3330*(d*x)^m*a*b^5*m^4*x^11 + 12139*(d*x)^m*b^6*m^2*x^13 + 600*(d*x)^m*a^2*b^4*m^5*x^9 + 23640*(d*x)^m*a*b^5*m^3*x^11 + 19524*(d*x)^m*b^6*m*x^13 + 20*(d*x)^m*a^3*b^3*m^6*x^7 + 9195*(d*x)^m*a^2*b^4*m^4*x^9 + 84234*(d*x)^m*a*b^5*m^2*x^11 + 10395*(d*x)^m*b^6*x^13 + 840*(d*x)^m*a^3*b^3*m^5*x^7 + 67920*(d*x)^m*a^2*b^4*m^3*x^9 + 137412*(d*x)^m*a*b^5*m*x^11 + 15*(d*x)^m*a^4*b^2*m^6*x^5 + 13580*(d*x)^m*a^3*b^3*m^4*x^7 + 249405*(d*x)^m*a^2*b^4*m^2*x^9 + 73710*(d*x)^m*a*b^5*x^11 + 660*(d*x)^m*a^4*b^2*m^5*x^5 + 105840*(d*x)^m*a^3*b^3*m^3*x^7 + 415320*(d*x)^m*a^2*b^4*m*x^9 + 6*(d*x)^m*a^5*b*m^6*x^3 + 11295*(d*x)^m*a^4*b^2*m^4*x^5 + 406700*(d*x)^m*a^3*b^3*m^2*x^7 + 225225*(d*x)^m*a^2*b^4*x^9 + 276*(d*x)^m*a^5*b*m^5*x^3 + 94200*(d*x)^m*a^4*b^2*m^3*x^5 + 699720*(d*x)^m*a^3*b^3*m*x^7 + (d*x)^m*a^6*m^6*x + 5010*(d*x)^m*a^5*b*m^4*x^3 + 389685*(d*x)^m*a^4*b^2*m^2*x^5 + 386100*(d*x)^m*a^3*b^3*x^7 + 48*(d*x)^m*a^6*m^5*x + 45240*(d*x)^m*a^5*b*m^3*x^3 + 711540*(d*x)^m*a^4*b^2*m*x^5 + 925*(d*x)^m*a^6*m^4*x + 208554*(d*x)^m*a^5*b*m^2*x^3 + 405405*(d*x)^m*a^4*b^2*x^5 + 9120*(d*x)^m*a^6*m^3*x + 438324*(d*x)^m*a^5*b*m*x^3 + 48259*(d*x)^m*a^6*m^2*x + 270270*(d*x)^m*a^5*b*x^3 + 129072*(d*x)^m*a^6*m*x + 135135*(d*x)^m*a^6*x)/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
786,1,415,0,0.180757," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b^{4} m^{4} x^{9} + 16 \, \left(d x\right)^{m} b^{4} m^{3} x^{9} + 4 \, \left(d x\right)^{m} a b^{3} m^{4} x^{7} + 86 \, \left(d x\right)^{m} b^{4} m^{2} x^{9} + 72 \, \left(d x\right)^{m} a b^{3} m^{3} x^{7} + 176 \, \left(d x\right)^{m} b^{4} m x^{9} + 6 \, \left(d x\right)^{m} a^{2} b^{2} m^{4} x^{5} + 416 \, \left(d x\right)^{m} a b^{3} m^{2} x^{7} + 105 \, \left(d x\right)^{m} b^{4} x^{9} + 120 \, \left(d x\right)^{m} a^{2} b^{2} m^{3} x^{5} + 888 \, \left(d x\right)^{m} a b^{3} m x^{7} + 4 \, \left(d x\right)^{m} a^{3} b m^{4} x^{3} + 780 \, \left(d x\right)^{m} a^{2} b^{2} m^{2} x^{5} + 540 \, \left(d x\right)^{m} a b^{3} x^{7} + 88 \, \left(d x\right)^{m} a^{3} b m^{3} x^{3} + 1800 \, \left(d x\right)^{m} a^{2} b^{2} m x^{5} + \left(d x\right)^{m} a^{4} m^{4} x + 656 \, \left(d x\right)^{m} a^{3} b m^{2} x^{3} + 1134 \, \left(d x\right)^{m} a^{2} b^{2} x^{5} + 24 \, \left(d x\right)^{m} a^{4} m^{3} x + 1832 \, \left(d x\right)^{m} a^{3} b m x^{3} + 206 \, \left(d x\right)^{m} a^{4} m^{2} x + 1260 \, \left(d x\right)^{m} a^{3} b x^{3} + 744 \, \left(d x\right)^{m} a^{4} m x + 945 \, \left(d x\right)^{m} a^{4} x}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((d*x)^m*b^4*m^4*x^9 + 16*(d*x)^m*b^4*m^3*x^9 + 4*(d*x)^m*a*b^3*m^4*x^7 + 86*(d*x)^m*b^4*m^2*x^9 + 72*(d*x)^m*a*b^3*m^3*x^7 + 176*(d*x)^m*b^4*m*x^9 + 6*(d*x)^m*a^2*b^2*m^4*x^5 + 416*(d*x)^m*a*b^3*m^2*x^7 + 105*(d*x)^m*b^4*x^9 + 120*(d*x)^m*a^2*b^2*m^3*x^5 + 888*(d*x)^m*a*b^3*m*x^7 + 4*(d*x)^m*a^3*b*m^4*x^3 + 780*(d*x)^m*a^2*b^2*m^2*x^5 + 540*(d*x)^m*a*b^3*x^7 + 88*(d*x)^m*a^3*b*m^3*x^3 + 1800*(d*x)^m*a^2*b^2*m*x^5 + (d*x)^m*a^4*m^4*x + 656*(d*x)^m*a^3*b*m^2*x^3 + 1134*(d*x)^m*a^2*b^2*x^5 + 24*(d*x)^m*a^4*m^3*x + 1832*(d*x)^m*a^3*b*m*x^3 + 206*(d*x)^m*a^4*m^2*x + 1260*(d*x)^m*a^3*b*x^3 + 744*(d*x)^m*a^4*m*x + 945*(d*x)^m*a^4*x)/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
787,1,135,0,0.159612," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b^{2} m^{2} x^{5} + 4 \, \left(d x\right)^{m} b^{2} m x^{5} + 2 \, \left(d x\right)^{m} a b m^{2} x^{3} + 3 \, \left(d x\right)^{m} b^{2} x^{5} + 12 \, \left(d x\right)^{m} a b m x^{3} + \left(d x\right)^{m} a^{2} m^{2} x + 10 \, \left(d x\right)^{m} a b x^{3} + 8 \, \left(d x\right)^{m} a^{2} m x + 15 \, \left(d x\right)^{m} a^{2} x}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((d*x)^m*b^2*m^2*x^5 + 4*(d*x)^m*b^2*m*x^5 + 2*(d*x)^m*a*b*m^2*x^3 + 3*(d*x)^m*b^2*x^5 + 12*(d*x)^m*a*b*m*x^3 + (d*x)^m*a^2*m^2*x + 10*(d*x)^m*a*b*x^3 + 8*(d*x)^m*a^2*m*x + 15*(d*x)^m*a^2*x)/(m^3 + 9*m^2 + 23*m + 15)","B",0
788,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
789,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2)^2, x)","F",0
790,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{3}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2)^3, x)","F",0
791,1,900,0,0.278363," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b^{5} m^{5} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 25 \, \left(d x\right)^{m} b^{5} m^{4} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(d x\right)^{m} a b^{4} m^{5} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 230 \, \left(d x\right)^{m} b^{5} m^{3} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 135 \, \left(d x\right)^{m} a b^{4} m^{4} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 950 \, \left(d x\right)^{m} b^{5} m^{2} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, \left(d x\right)^{m} a^{2} b^{3} m^{5} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 1310 \, \left(d x\right)^{m} a b^{4} m^{3} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 1689 \, \left(d x\right)^{m} b^{5} m x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 290 \, \left(d x\right)^{m} a^{2} b^{3} m^{4} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 5610 \, \left(d x\right)^{m} a b^{4} m^{2} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 945 \, \left(d x\right)^{m} b^{5} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, \left(d x\right)^{m} a^{3} b^{2} m^{5} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 3020 \, \left(d x\right)^{m} a^{2} b^{3} m^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 10205 \, \left(d x\right)^{m} a b^{4} m x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 310 \, \left(d x\right)^{m} a^{3} b^{2} m^{4} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 13660 \, \left(d x\right)^{m} a^{2} b^{3} m^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 5775 \, \left(d x\right)^{m} a b^{4} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(d x\right)^{m} a^{4} b m^{5} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 3500 \, \left(d x\right)^{m} a^{3} b^{2} m^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 25770 \, \left(d x\right)^{m} a^{2} b^{3} m x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 165 \, \left(d x\right)^{m} a^{4} b m^{4} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 17300 \, \left(d x\right)^{m} a^{3} b^{2} m^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 14850 \, \left(d x\right)^{m} a^{2} b^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \left(d x\right)^{m} a^{5} m^{5} x \mathrm{sgn}\left(b x^{2} + a\right) + 2030 \, \left(d x\right)^{m} a^{4} b m^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 34890 \, \left(d x\right)^{m} a^{3} b^{2} m x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 35 \, \left(d x\right)^{m} a^{5} m^{4} x \mathrm{sgn}\left(b x^{2} + a\right) + 11310 \, \left(d x\right)^{m} a^{4} b m^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 20790 \, \left(d x\right)^{m} a^{3} b^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 470 \, \left(d x\right)^{m} a^{5} m^{3} x \mathrm{sgn}\left(b x^{2} + a\right) + 26765 \, \left(d x\right)^{m} a^{4} b m x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 3010 \, \left(d x\right)^{m} a^{5} m^{2} x \mathrm{sgn}\left(b x^{2} + a\right) + 17325 \, \left(d x\right)^{m} a^{4} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 9129 \, \left(d x\right)^{m} a^{5} m x \mathrm{sgn}\left(b x^{2} + a\right) + 10395 \, \left(d x\right)^{m} a^{5} x \mathrm{sgn}\left(b x^{2} + a\right)}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((d*x)^m*b^5*m^5*x^11*sgn(b*x^2 + a) + 25*(d*x)^m*b^5*m^4*x^11*sgn(b*x^2 + a) + 5*(d*x)^m*a*b^4*m^5*x^9*sgn(b*x^2 + a) + 230*(d*x)^m*b^5*m^3*x^11*sgn(b*x^2 + a) + 135*(d*x)^m*a*b^4*m^4*x^9*sgn(b*x^2 + a) + 950*(d*x)^m*b^5*m^2*x^11*sgn(b*x^2 + a) + 10*(d*x)^m*a^2*b^3*m^5*x^7*sgn(b*x^2 + a) + 1310*(d*x)^m*a*b^4*m^3*x^9*sgn(b*x^2 + a) + 1689*(d*x)^m*b^5*m*x^11*sgn(b*x^2 + a) + 290*(d*x)^m*a^2*b^3*m^4*x^7*sgn(b*x^2 + a) + 5610*(d*x)^m*a*b^4*m^2*x^9*sgn(b*x^2 + a) + 945*(d*x)^m*b^5*x^11*sgn(b*x^2 + a) + 10*(d*x)^m*a^3*b^2*m^5*x^5*sgn(b*x^2 + a) + 3020*(d*x)^m*a^2*b^3*m^3*x^7*sgn(b*x^2 + a) + 10205*(d*x)^m*a*b^4*m*x^9*sgn(b*x^2 + a) + 310*(d*x)^m*a^3*b^2*m^4*x^5*sgn(b*x^2 + a) + 13660*(d*x)^m*a^2*b^3*m^2*x^7*sgn(b*x^2 + a) + 5775*(d*x)^m*a*b^4*x^9*sgn(b*x^2 + a) + 5*(d*x)^m*a^4*b*m^5*x^3*sgn(b*x^2 + a) + 3500*(d*x)^m*a^3*b^2*m^3*x^5*sgn(b*x^2 + a) + 25770*(d*x)^m*a^2*b^3*m*x^7*sgn(b*x^2 + a) + 165*(d*x)^m*a^4*b*m^4*x^3*sgn(b*x^2 + a) + 17300*(d*x)^m*a^3*b^2*m^2*x^5*sgn(b*x^2 + a) + 14850*(d*x)^m*a^2*b^3*x^7*sgn(b*x^2 + a) + (d*x)^m*a^5*m^5*x*sgn(b*x^2 + a) + 2030*(d*x)^m*a^4*b*m^3*x^3*sgn(b*x^2 + a) + 34890*(d*x)^m*a^3*b^2*m*x^5*sgn(b*x^2 + a) + 35*(d*x)^m*a^5*m^4*x*sgn(b*x^2 + a) + 11310*(d*x)^m*a^4*b*m^2*x^3*sgn(b*x^2 + a) + 20790*(d*x)^m*a^3*b^2*x^5*sgn(b*x^2 + a) + 470*(d*x)^m*a^5*m^3*x*sgn(b*x^2 + a) + 26765*(d*x)^m*a^4*b*m*x^3*sgn(b*x^2 + a) + 3010*(d*x)^m*a^5*m^2*x*sgn(b*x^2 + a) + 17325*(d*x)^m*a^4*b*x^3*sgn(b*x^2 + a) + 9129*(d*x)^m*a^5*m*x*sgn(b*x^2 + a) + 10395*(d*x)^m*a^5*x*sgn(b*x^2 + a))/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","B",0
792,1,384,0,0.209682," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b^{3} m^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 9 \, \left(d x\right)^{m} b^{3} m^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(d x\right)^{m} a b^{2} m^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 23 \, \left(d x\right)^{m} b^{3} m x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 33 \, \left(d x\right)^{m} a b^{2} m^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, \left(d x\right)^{m} b^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(d x\right)^{m} a^{2} b m^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 93 \, \left(d x\right)^{m} a b^{2} m x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 39 \, \left(d x\right)^{m} a^{2} b m^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 63 \, \left(d x\right)^{m} a b^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + \left(d x\right)^{m} a^{3} m^{3} x \mathrm{sgn}\left(b x^{2} + a\right) + 141 \, \left(d x\right)^{m} a^{2} b m x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, \left(d x\right)^{m} a^{3} m^{2} x \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, \left(d x\right)^{m} a^{2} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 71 \, \left(d x\right)^{m} a^{3} m x \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, \left(d x\right)^{m} a^{3} x \mathrm{sgn}\left(b x^{2} + a\right)}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((d*x)^m*b^3*m^3*x^7*sgn(b*x^2 + a) + 9*(d*x)^m*b^3*m^2*x^7*sgn(b*x^2 + a) + 3*(d*x)^m*a*b^2*m^3*x^5*sgn(b*x^2 + a) + 23*(d*x)^m*b^3*m*x^7*sgn(b*x^2 + a) + 33*(d*x)^m*a*b^2*m^2*x^5*sgn(b*x^2 + a) + 15*(d*x)^m*b^3*x^7*sgn(b*x^2 + a) + 3*(d*x)^m*a^2*b*m^3*x^3*sgn(b*x^2 + a) + 93*(d*x)^m*a*b^2*m*x^5*sgn(b*x^2 + a) + 39*(d*x)^m*a^2*b*m^2*x^3*sgn(b*x^2 + a) + 63*(d*x)^m*a*b^2*x^5*sgn(b*x^2 + a) + (d*x)^m*a^3*m^3*x*sgn(b*x^2 + a) + 141*(d*x)^m*a^2*b*m*x^3*sgn(b*x^2 + a) + 15*(d*x)^m*a^3*m^2*x*sgn(b*x^2 + a) + 105*(d*x)^m*a^2*b*x^3*sgn(b*x^2 + a) + 71*(d*x)^m*a^3*m*x*sgn(b*x^2 + a) + 105*(d*x)^m*a^3*x*sgn(b*x^2 + a))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
793,1,83,0,0.162584," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} b m x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + \left(d x\right)^{m} b x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + \left(d x\right)^{m} a m x \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(d x\right)^{m} a x \mathrm{sgn}\left(b x^{2} + a\right)}{m^{2} + 4 \, m + 3}"," ",0,"((d*x)^m*b*m*x^3*sgn(b*x^2 + a) + (d*x)^m*b*x^3*sgn(b*x^2 + a) + (d*x)^m*a*m*x*sgn(b*x^2 + a) + 3*(d*x)^m*a*x*sgn(b*x^2 + a))/(m^2 + 4*m + 3)","A",0
794,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
795,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2)^(3/2), x)","F",0
796,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2)^(5/2), x)","F",0
797,0,0,0,0.000000," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p*(d*x)^m, x)","F",0
798,1,375,0,0.192838," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\frac{4 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{4} p^{3} x^{8} + 12 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{4} p^{2} x^{8} + 4 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{3} p^{3} x^{6} + 11 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{4} p x^{8} + 6 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{3} p^{2} x^{6} + 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{4} x^{8} + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{3} p x^{6} - 6 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{2} b^{2} p^{2} x^{4} - 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{2} b^{2} p x^{4} + 6 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{3} b p x^{2} - 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{4}}{4 \, {\left(4 \, b^{4} p^{4} + 20 \, b^{4} p^{3} + 35 \, b^{4} p^{2} + 25 \, b^{4} p + 6 \, b^{4}\right)}}"," ",0,"1/4*(4*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^4*p^3*x^8 + 12*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^4*p^2*x^8 + 4*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^3*p^3*x^6 + 11*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^4*p*x^8 + 6*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^3*p^2*x^6 + 3*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^4*x^8 + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^3*p*x^6 - 6*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^2*b^2*p^2*x^4 - 3*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^2*b^2*p*x^4 + 6*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^3*b*p*x^2 - 3*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^4)/(4*b^4*p^4 + 20*b^4*p^3 + 35*b^4*p^2 + 25*b^4*p + 6*b^4)","B",0
799,1,235,0,0.186065," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{3} p^{2} x^{6} + 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{3} p x^{6} + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{2} p^{2} x^{4} + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{3} x^{6} + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{2} p x^{4} - 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{2} b p x^{2} + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{3}}{2 \, {\left(4 \, b^{3} p^{3} + 12 \, b^{3} p^{2} + 11 \, b^{3} p + 3 \, b^{3}\right)}}"," ",0,"1/2*(2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^3*p^2*x^6 + 3*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^3*p*x^6 + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^2*p^2*x^4 + (b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^3*x^6 + (b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^2*p*x^4 - 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^2*b*p*x^2 + (b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^3)/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","A",0
800,1,132,0,0.216679," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{2} p x^{4} + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{2} x^{4} + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b p x^{2} - {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{2}}{4 \, {\left(2 \, b^{2} p^{2} + 3 \, b^{2} p + b^{2}\right)}}"," ",0,"1/4*(2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^2*p*x^4 + (b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^2*x^4 + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b*p*x^2 - (b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^2)/(2*b^2*p^2 + 3*b^2*p + b^2)","A",0
801,1,58,0,0.261624," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b x^{2} + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a}{2 \, {\left(2 \, b p + b\right)}}"," ",0,"1/2*((b^2*x^4 + 2*a*b*x^2 + a^2)^p*b*x^2 + (b^2*x^4 + 2*a*b*x^2 + a^2)^p*a)/(2*b*p + b)","A",0
802,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x, x)","F",0
803,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x^3, x)","F",0
804,0,0,0,0.000000," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} x^{4}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p*x^4, x)","F",0
805,0,0,0,0.000000," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p*x^2, x)","F",0
806,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p, x)","F",0
807,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x^2, x)","F",0
808,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x^4,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{x^{4}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p/x^4, x)","F",0
809,0,0,0,0.000000," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\int \left(d x\right)^{\frac{3}{2}} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((d*x)^(3/2)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p, x)","F",0
810,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\int \sqrt{d x} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate(sqrt(d*x)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p, x)","F",0
811,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{\sqrt{d x}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p/sqrt(d*x), x)","F",0
812,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{\left(d x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p/(d*x)^(3/2), x)","F",0
813,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{\left(d x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^p/(d*x)^(5/2), x)","F",0
814,1,19,0,0.148290," ","integrate(x^2*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5} + \frac{1}{3} \, a x^{3}"," ",0,"1/7*c*x^7 + 1/5*b*x^5 + 1/3*a*x^3","A",0
815,1,19,0,0.151367," ","integrate(x*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{6} \, c x^{6} + \frac{1}{4} \, b x^{4} + \frac{1}{2} \, a x^{2}"," ",0,"1/6*c*x^6 + 1/4*b*x^4 + 1/2*a*x^2","A",0
816,1,16,0,0.148459," ","integrate(c*x^4+b*x^2+a,x, algorithm=""giac"")","\frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x"," ",0,"1/5*c*x^5 + 1/3*b*x^3 + a*x","A",0
817,1,20,0,0.149432," ","integrate((c*x^4+b*x^2+a)/x,x, algorithm=""giac"")","\frac{1}{4} \, c x^{4} + \frac{1}{2} \, b x^{2} + \frac{1}{2} \, a \log\left(x^{2}\right)"," ",0,"1/4*c*x^4 + 1/2*b*x^2 + 1/2*a*log(x^2)","A",0
818,1,16,0,0.147157," ","integrate((c*x^4+b*x^2+a)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} + b x - \frac{a}{x}"," ",0,"1/3*c*x^3 + b*x - a/x","A",0
819,1,26,0,0.152145," ","integrate((c*x^4+b*x^2+a)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, c x^{2} + \frac{1}{2} \, b \log\left(x^{2}\right) - \frac{b x^{2} + a}{2 \, x^{2}}"," ",0,"1/2*c*x^2 + 1/2*b*log(x^2) - 1/2*(b*x^2 + a)/x^2","A",0
820,1,17,0,0.152939," ","integrate((c*x^4+b*x^2+a)/x^4,x, algorithm=""giac"")","c x - \frac{3 \, b x^{2} + a}{3 \, x^{3}}"," ",0,"c*x - 1/3*(3*b*x^2 + a)/x^3","A",0
821,1,27,0,0.163440," ","integrate((c*x^4+b*x^2+a)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, c \log\left(x^{2}\right) - \frac{3 \, c x^{4} + 2 \, b x^{2} + a}{4 \, x^{4}}"," ",0,"1/2*c*log(x^2) - 1/4*(3*c*x^4 + 2*b*x^2 + a)/x^4","A",0
822,1,21,0,0.152009," ","integrate((c*x^4+b*x^2+a)/x^6,x, algorithm=""giac"")","-\frac{15 \, c x^{4} + 5 \, b x^{2} + 3 \, a}{15 \, x^{5}}"," ",0,"-1/15*(15*c*x^4 + 5*b*x^2 + 3*a)/x^5","A",0
823,1,21,0,0.147734," ","integrate((c*x^4+b*x^2+a)/x^7,x, algorithm=""giac"")","-\frac{6 \, c x^{4} + 3 \, b x^{2} + 2 \, a}{12 \, x^{6}}"," ",0,"-1/12*(6*c*x^4 + 3*b*x^2 + 2*a)/x^6","A",0
824,1,21,0,0.167232," ","integrate((c*x^4+b*x^2+a)/x^8,x, algorithm=""giac"")","-\frac{35 \, c x^{4} + 21 \, b x^{2} + 15 \, a}{105 \, x^{7}}"," ",0,"-1/105*(35*c*x^4 + 21*b*x^2 + 15*a)/x^7","A",0
825,1,46,0,0.148211," ","integrate(x^2*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, c^{2} x^{11} + \frac{2}{9} \, b c x^{9} + \frac{1}{7} \, b^{2} x^{7} + \frac{2}{7} \, a c x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"1/11*c^2*x^11 + 2/9*b*c*x^9 + 1/7*b^2*x^7 + 2/7*a*c*x^7 + 2/5*a*b*x^5 + 1/3*a^2*x^3","A",0
826,1,46,0,0.163127," ","integrate(x*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{10} \, c^{2} x^{10} + \frac{1}{4} \, b c x^{8} + \frac{1}{6} \, b^{2} x^{6} + \frac{1}{3} \, a c x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/10*c^2*x^10 + 1/4*b*c*x^8 + 1/6*b^2*x^6 + 1/3*a*c*x^6 + 1/2*a*b*x^4 + 1/2*a^2*x^2","A",0
827,1,43,0,0.148938," ","integrate((c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} + \frac{2}{5} \, a c x^{5} + \frac{2}{3} \, a b x^{3} + a^{2} x"," ",0,"1/9*c^2*x^9 + 2/7*b*c*x^7 + 1/5*b^2*x^5 + 2/5*a*c*x^5 + 2/3*a*b*x^3 + a^2*x","A",0
828,1,46,0,0.151937," ","integrate((c*x^4+b*x^2+a)^2/x,x, algorithm=""giac"")","\frac{1}{8} \, c^{2} x^{8} + \frac{1}{3} \, b c x^{6} + \frac{1}{4} \, b^{2} x^{4} + \frac{1}{2} \, a c x^{4} + a b x^{2} + \frac{1}{2} \, a^{2} \log\left(x^{2}\right)"," ",0,"1/8*c^2*x^8 + 1/3*b*c*x^6 + 1/4*b^2*x^4 + 1/2*a*c*x^4 + a*b*x^2 + 1/2*a^2*log(x^2)","A",0
829,1,44,0,0.183945," ","integrate((c*x^4+b*x^2+a)^2/x^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{2} x^{7} + \frac{2}{5} \, b c x^{5} + \frac{1}{3} \, b^{2} x^{3} + \frac{2}{3} \, a c x^{3} + 2 \, a b x - \frac{a^{2}}{x}"," ",0,"1/7*c^2*x^7 + 2/5*b*c*x^5 + 1/3*b^2*x^3 + 2/3*a*c*x^3 + 2*a*b*x - a^2/x","A",0
830,1,53,0,0.151672," ","integrate((c*x^4+b*x^2+a)^2/x^3,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} x^{6} + \frac{1}{2} \, b c x^{4} + \frac{1}{2} \, b^{2} x^{2} + a c x^{2} + a b \log\left(x^{2}\right) - \frac{2 \, a b x^{2} + a^{2}}{2 \, x^{2}}"," ",0,"1/6*c^2*x^6 + 1/2*b*c*x^4 + 1/2*b^2*x^2 + a*c*x^2 + a*b*log(x^2) - 1/2*(2*a*b*x^2 + a^2)/x^2","A",0
831,1,42,0,0.150163," ","integrate((c*x^4+b*x^2+a)^2/x^4,x, algorithm=""giac"")","\frac{1}{5} \, c^{2} x^{5} + \frac{2}{3} \, b c x^{3} + b^{2} x + 2 \, a c x - \frac{6 \, a b x^{2} + a^{2}}{3 \, x^{3}}"," ",0,"1/5*c^2*x^5 + 2/3*b*c*x^3 + b^2*x + 2*a*c*x - 1/3*(6*a*b*x^2 + a^2)/x^3","A",0
832,1,60,0,0.176920," ","integrate((c*x^4+b*x^2+a)^2/x^5,x, algorithm=""giac"")","\frac{1}{4} \, c^{2} x^{4} + b c x^{2} + \frac{1}{2} \, {\left(b^{2} + 2 \, a c\right)} \log\left(x^{2}\right) - \frac{3 \, b^{2} x^{4} + 6 \, a c x^{4} + 4 \, a b x^{2} + a^{2}}{4 \, x^{4}}"," ",0,"1/4*c^2*x^4 + b*c*x^2 + 1/2*(b^2 + 2*a*c)*log(x^2) - 1/4*(3*b^2*x^4 + 6*a*c*x^4 + 4*a*b*x^2 + a^2)/x^4","A",0
833,1,47,0,0.147871," ","integrate((c*x^4+b*x^2+a)^2/x^6,x, algorithm=""giac"")","\frac{1}{3} \, c^{2} x^{3} + 2 \, b c x - \frac{15 \, b^{2} x^{4} + 30 \, a c x^{4} + 10 \, a b x^{2} + 3 \, a^{2}}{15 \, x^{5}}"," ",0,"1/3*c^2*x^3 + 2*b*c*x - 1/15*(15*b^2*x^4 + 30*a*c*x^4 + 10*a*b*x^2 + 3*a^2)/x^5","A",0
834,1,54,0,0.156233," ","integrate((c*x^4+b*x^2+a)^2/x^7,x, algorithm=""giac"")","\frac{1}{2} \, c^{2} x^{2} + b c \log\left(x^{2}\right) - \frac{11 \, b c x^{6} + 3 \, b^{2} x^{4} + 6 \, a c x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, x^{6}}"," ",0,"1/2*c^2*x^2 + b*c*log(x^2) - 1/6*(11*b*c*x^6 + 3*b^2*x^4 + 6*a*c*x^4 + 3*a*b*x^2 + a^2)/x^6","A",0
835,1,46,0,0.167144," ","integrate((c*x^4+b*x^2+a)^2/x^8,x, algorithm=""giac"")","c^{2} x - \frac{210 \, b c x^{6} + 35 \, b^{2} x^{4} + 70 \, a c x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}}"," ",0,"c^2*x - 1/105*(210*b*c*x^6 + 35*b^2*x^4 + 70*a*c*x^4 + 42*a*b*x^2 + 15*a^2)/x^7","A",0
836,1,58,0,0.150856," ","integrate((c*x^4+b*x^2+a)^2/x^9,x, algorithm=""giac"")","\frac{1}{2} \, c^{2} \log\left(x^{2}\right) - \frac{25 \, c^{2} x^{8} + 24 \, b c x^{6} + 6 \, b^{2} x^{4} + 12 \, a c x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}}"," ",0,"1/2*c^2*log(x^2) - 1/24*(25*c^2*x^8 + 24*b*c*x^6 + 6*b^2*x^4 + 12*a*c*x^4 + 8*a*b*x^2 + 3*a^2)/x^8","A",0
837,1,48,0,0.148854," ","integrate((c*x^4+b*x^2+a)^2/x^10,x, algorithm=""giac"")","-\frac{315 \, c^{2} x^{8} + 210 \, b c x^{6} + 63 \, b^{2} x^{4} + 126 \, a c x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}}"," ",0,"-1/315*(315*c^2*x^8 + 210*b*c*x^6 + 63*b^2*x^4 + 126*a*c*x^4 + 90*a*b*x^2 + 35*a^2)/x^9","A",0
838,1,48,0,0.216251," ","integrate((c*x^4+b*x^2+a)^2/x^11,x, algorithm=""giac"")","-\frac{30 \, c^{2} x^{8} + 30 \, b c x^{6} + 10 \, b^{2} x^{4} + 20 \, a c x^{4} + 15 \, a b x^{2} + 6 \, a^{2}}{60 \, x^{10}}"," ",0,"-1/60*(30*c^2*x^8 + 30*b*c*x^6 + 10*b^2*x^4 + 20*a*c*x^4 + 15*a*b*x^2 + 6*a^2)/x^10","A",0
839,1,48,0,0.194674," ","integrate((c*x^4+b*x^2+a)^2/x^12,x, algorithm=""giac"")","-\frac{1155 \, c^{2} x^{8} + 1386 \, b c x^{6} + 495 \, b^{2} x^{4} + 990 \, a c x^{4} + 770 \, a b x^{2} + 315 \, a^{2}}{3465 \, x^{11}}"," ",0,"-1/3465*(1155*c^2*x^8 + 1386*b*c*x^6 + 495*b^2*x^4 + 990*a*c*x^4 + 770*a*b*x^2 + 315*a^2)/x^11","A",0
840,1,48,0,0.145969," ","integrate((c*x^4+b*x^2+a)^2/x^13,x, algorithm=""giac"")","-\frac{30 \, c^{2} x^{8} + 40 \, b c x^{6} + 15 \, b^{2} x^{4} + 30 \, a c x^{4} + 24 \, a b x^{2} + 10 \, a^{2}}{120 \, x^{12}}"," ",0,"-1/120*(30*c^2*x^8 + 40*b*c*x^6 + 15*b^2*x^4 + 30*a*c*x^4 + 24*a*b*x^2 + 10*a^2)/x^12","A",0
841,1,87,0,0.192704," ","integrate(x^2*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{15} \, c^{3} x^{15} + \frac{3}{13} \, b c^{2} x^{13} + \frac{3}{11} \, b^{2} c x^{11} + \frac{3}{11} \, a c^{2} x^{11} + \frac{1}{9} \, b^{3} x^{9} + \frac{2}{3} \, a b c x^{9} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{7} \, a^{2} c x^{7} + \frac{3}{5} \, a^{2} b x^{5} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/15*c^3*x^15 + 3/13*b*c^2*x^13 + 3/11*b^2*c*x^11 + 3/11*a*c^2*x^11 + 1/9*b^3*x^9 + 2/3*a*b*c*x^9 + 3/7*a*b^2*x^7 + 3/7*a^2*c*x^7 + 3/5*a^2*b*x^5 + 1/3*a^3*x^3","A",0
842,1,87,0,0.168528," ","integrate(x*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{14} \, c^{3} x^{14} + \frac{1}{4} \, b c^{2} x^{12} + \frac{3}{10} \, b^{2} c x^{10} + \frac{3}{10} \, a c^{2} x^{10} + \frac{1}{8} \, b^{3} x^{8} + \frac{3}{4} \, a b c x^{8} + \frac{1}{2} \, a b^{2} x^{6} + \frac{1}{2} \, a^{2} c x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/14*c^3*x^14 + 1/4*b*c^2*x^12 + 3/10*b^2*c*x^10 + 3/10*a*c^2*x^10 + 1/8*b^3*x^8 + 3/4*a*b*c*x^8 + 1/2*a*b^2*x^6 + 1/2*a^2*c*x^6 + 3/4*a^2*b*x^4 + 1/2*a^3*x^2","A",0
843,1,83,0,0.149917," ","integrate((c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{13} \, c^{3} x^{13} + \frac{3}{11} \, b c^{2} x^{11} + \frac{1}{3} \, b^{2} c x^{9} + \frac{1}{3} \, a c^{2} x^{9} + \frac{1}{7} \, b^{3} x^{7} + \frac{6}{7} \, a b c x^{7} + \frac{3}{5} \, a b^{2} x^{5} + \frac{3}{5} \, a^{2} c x^{5} + a^{2} b x^{3} + a^{3} x"," ",0,"1/13*c^3*x^13 + 3/11*b*c^2*x^11 + 1/3*b^2*c*x^9 + 1/3*a*c^2*x^9 + 1/7*b^3*x^7 + 6/7*a*b*c*x^7 + 3/5*a*b^2*x^5 + 3/5*a^2*c*x^5 + a^2*b*x^3 + a^3*x","A",0
844,1,87,0,0.159657," ","integrate((c*x^4+b*x^2+a)^3/x,x, algorithm=""giac"")","\frac{1}{12} \, c^{3} x^{12} + \frac{3}{10} \, b c^{2} x^{10} + \frac{3}{8} \, b^{2} c x^{8} + \frac{3}{8} \, a c^{2} x^{8} + \frac{1}{6} \, b^{3} x^{6} + a b c x^{6} + \frac{3}{4} \, a b^{2} x^{4} + \frac{3}{4} \, a^{2} c x^{4} + \frac{3}{2} \, a^{2} b x^{2} + \frac{1}{2} \, a^{3} \log\left(x^{2}\right)"," ",0,"1/12*c^3*x^12 + 3/10*b*c^2*x^10 + 3/8*b^2*c*x^8 + 3/8*a*c^2*x^8 + 1/6*b^3*x^6 + a*b*c*x^6 + 3/4*a*b^2*x^4 + 3/4*a^2*c*x^4 + 3/2*a^2*b*x^2 + 1/2*a^3*log(x^2)","A",0
845,1,83,0,0.148620," ","integrate((c*x^4+b*x^2+a)^3/x^2,x, algorithm=""giac"")","\frac{1}{11} \, c^{3} x^{11} + \frac{1}{3} \, b c^{2} x^{9} + \frac{3}{7} \, b^{2} c x^{7} + \frac{3}{7} \, a c^{2} x^{7} + \frac{1}{5} \, b^{3} x^{5} + \frac{6}{5} \, a b c x^{5} + a b^{2} x^{3} + a^{2} c x^{3} + 3 \, a^{2} b x - \frac{a^{3}}{x}"," ",0,"1/11*c^3*x^11 + 1/3*b*c^2*x^9 + 3/7*b^2*c*x^7 + 3/7*a*c^2*x^7 + 1/5*b^3*x^5 + 6/5*a*b*c*x^5 + a*b^2*x^3 + a^2*c*x^3 + 3*a^2*b*x - a^3/x","A",0
846,1,98,0,0.164255," ","integrate((c*x^4+b*x^2+a)^3/x^3,x, algorithm=""giac"")","\frac{1}{10} \, c^{3} x^{10} + \frac{3}{8} \, b c^{2} x^{8} + \frac{1}{2} \, b^{2} c x^{6} + \frac{1}{2} \, a c^{2} x^{6} + \frac{1}{4} \, b^{3} x^{4} + \frac{3}{2} \, a b c x^{4} + \frac{3}{2} \, a b^{2} x^{2} + \frac{3}{2} \, a^{2} c x^{2} + \frac{3}{2} \, a^{2} b \log\left(x^{2}\right) - \frac{3 \, a^{2} b x^{2} + a^{3}}{2 \, x^{2}}"," ",0,"1/10*c^3*x^10 + 3/8*b*c^2*x^8 + 1/2*b^2*c*x^6 + 1/2*a*c^2*x^6 + 1/4*b^3*x^4 + 3/2*a*b*c*x^4 + 3/2*a*b^2*x^2 + 3/2*a^2*c*x^2 + 3/2*a^2*b*log(x^2) - 1/2*(3*a^2*b*x^2 + a^3)/x^2","A",0
847,1,84,0,0.177160," ","integrate((c*x^4+b*x^2+a)^3/x^4,x, algorithm=""giac"")","\frac{1}{9} \, c^{3} x^{9} + \frac{3}{7} \, b c^{2} x^{7} + \frac{3}{5} \, b^{2} c x^{5} + \frac{3}{5} \, a c^{2} x^{5} + \frac{1}{3} \, b^{3} x^{3} + 2 \, a b c x^{3} + 3 \, a b^{2} x + 3 \, a^{2} c x - \frac{9 \, a^{2} b x^{2} + a^{3}}{3 \, x^{3}}"," ",0,"1/9*c^3*x^9 + 3/7*b*c^2*x^7 + 3/5*b^2*c*x^5 + 3/5*a*c^2*x^5 + 1/3*b^3*x^3 + 2*a*b*c*x^3 + 3*a*b^2*x + 3*a^2*c*x - 1/3*(9*a^2*b*x^2 + a^3)/x^3","A",0
848,1,92,0,0.564205," ","integrate(x^7/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{c x^{4} - 2 \, b x^{2}}{4 \, c^{2}} + \frac{{\left(b^{2} - a c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}} - \frac{{\left(b^{3} - 3 \, a b c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/4*(c*x^4 - 2*b*x^2)/c^2 + 1/4*(b^2 - a*c)*log(c*x^4 + b*x^2 + a)/c^3 - 1/2*(b^3 - 3*a*b*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
849,1,75,0,0.619520," ","integrate(x^5/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{x^{2}}{2 \, c} - \frac{b \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"1/2*x^2/c - 1/4*b*log(c*x^4 + b*x^2 + a)/c^2 + 1/2*(b^2 - 2*a*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
850,1,59,0,0.572754," ","integrate(x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c} + \frac{\log\left(c x^{4} + b x^{2} + a\right)}{4 \, c}"," ",0,"-1/2*b*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c) + 1/4*log(c*x^4 + b*x^2 + a)/c","A",0
851,1,35,0,0.569612," ","integrate(x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
852,1,68,0,0.574908," ","integrate(1/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a} - \frac{\log\left(c x^{4} + b x^{2} + a\right)}{4 \, a} + \frac{\log\left(x^{2}\right)}{2 \, a}"," ",0,"-1/2*b*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a) - 1/4*log(c*x^4 + b*x^2 + a)/a + 1/2*log(x^2)/a","A",0
853,1,94,0,0.579945," ","integrate(1/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{b \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{2}} - \frac{b \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a^{2}} + \frac{b x^{2} - a}{2 \, a^{2} x^{2}}"," ",0,"1/4*b*log(c*x^4 + b*x^2 + a)/a^2 - 1/2*b*log(x^2)/a^2 + 1/2*(b^2 - 2*a*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) + 1/2*(b*x^2 - a)/(a^2*x^2)","A",0
854,1,126,0,0.553405," ","integrate(1/x^5/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} - a c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{3}} + \frac{{\left(b^{2} - a c\right)} \log\left(x^{2}\right)}{2 \, a^{3}} - \frac{{\left(b^{3} - 3 \, a b c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a^{3}} - \frac{3 \, b^{2} x^{4} - 3 \, a c x^{4} - 2 \, a b x^{2} + a^{2}}{4 \, a^{3} x^{4}}"," ",0,"-1/4*(b^2 - a*c)*log(c*x^4 + b*x^2 + a)/a^3 + 1/2*(b^2 - a*c)*log(x^2)/a^3 - 1/2*(b^3 - 3*a*b*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^3) - 1/4*(3*b^2*x^4 - 3*a*c*x^4 - 2*a*b*x^2 + a^2)/(a^3*x^4)","A",0
855,1,2457,0,1.012843," ","integrate(x^6/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 32 \, a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} + \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} + \frac{{\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 32 \, a^{3} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} - \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} + \frac{c^{2} x^{3} - 3 \, b c x}{3 \, c^{3}}"," ",0,"-1/8*(2*b^6*c^4 - 14*a*b^4*c^5 + 24*a^2*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5 - (2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*c^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 32*a^3*b*c^5 - 2*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 + sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 1/8*(2*b^6*c^4 - 14*a*b^4*c^5 + 24*a^2*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5 - (2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*c^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 32*a^3*b*c^5 + 2*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 - sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 1/3*(c^2*x^3 - 3*b*c*x)/c^3","B",0
856,1,2109,0,0.974108," ","integrate(x^4/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{x}{c} + \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}} - \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}}"," ",0,"x/c + 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 32*a^3*c^5 - 2*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 32*a^3*c^5 + 2*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2)","B",0
857,1,503,0,1.049808," ","integrate(x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} {\left| c \right|}} + \frac{{\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} {\left| c \right|}}"," ",0,"-1/2*(2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((b^4 - 8*a*b^2*c - 2*b^3*c + 16*a^2*c^2 + 8*a*b*c^2 + b^2*c^2 - 4*a*c^3)*abs(c)) + 1/2*(2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((b^4 - 8*a*b^2*c - 2*b^3*c + 16*a^2*c^2 + 8*a*b*c^2 + b^2*c^2 - 4*a*c^3)*abs(c))","B",0
858,1,1024,0,0.575234," ","integrate(1/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"1/4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
859,1,1839,0,0.967209," ","integrate(1/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + {\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} a^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b + \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + {\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} a^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b - \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| a \right|} {\left| c \right|}} - \frac{1}{a x}"," ",0,"-1/8*(2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 + (2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*a^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(a))*arctan(2*sqrt(1/2)*x/sqrt((a*b + sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(a)*abs(c)) + 1/8*(2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 + (2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*a^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(a))*arctan(2*sqrt(1/2)*x/sqrt((a*b - sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(a)*abs(c)) - 1/(a*x)","B",0
860,1,1640,0,1.157697," ","integrate(1/x^4/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 18 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 48 \, a^{2} b^{2} c^{3} - 14 \, a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 32 \, a^{3} c^{4} + 24 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b + \sqrt{a^{4} b^{2} - 4 \, a^{5} c}}{a^{2} c}}}\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c \right|}} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 18 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 48 \, a^{2} b^{2} c^{3} + 14 \, a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 32 \, a^{3} c^{4} - 24 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b - \sqrt{a^{4} b^{2} - 4 \, a^{5} c}}{a^{2} c}}}\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c \right|}} + \frac{3 \, b x^{2} - a}{3 \, a^{2} x^{3}}"," ",0,"1/4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 2*b^6*c + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 18*a*b^4*c^2 + 2*b^5*c^2 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 48*a^2*b^2*c^3 - 14*a*b^3*c^3 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 32*a^3*c^4 + 24*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*(b^2 - 4*a*c)*b^4*c - 10*(b^2 - 4*a*c)*a*b^2*c^2 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3 + 6*(b^2 - 4*a*c)*a*b*c^3)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b + sqrt(a^4*b^2 - 4*a^5*c))/(a^2*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c)) + 1/4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 2*b^6*c + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 18*a*b^4*c^2 - 2*b^5*c^2 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 48*a^2*b^2*c^3 + 14*a*b^3*c^3 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 32*a^3*c^4 - 24*a^2*b*c^4 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 - 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^4*c + 10*(b^2 - 4*a*c)*a*b^2*c^2 + 2*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b*c^3)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b - sqrt(a^4*b^2 - 4*a^5*c))/(a^2*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c)) + 1/3*(3*b*x^2 - a)/(a^2*x^3)","B",0
861,1,152,0,0.600228," ","integrate(x^7/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(b^{3} - 6 \, a b c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b^{2} c x^{4} - 4 \, a c^{2} x^{4} - b^{3} x^{2} + 2 \, a b c x^{2} - a b^{2}}{4 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}} + \frac{\log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{2}}"," ",0,"-1/2*(b^3 - 6*a*b*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2 - 4*a*c^3)*sqrt(-b^2 + 4*a*c)) - 1/4*(b^2*c*x^4 - 4*a*c^2*x^4 - b^3*x^2 + 2*a*b*c*x^2 - a*b^2)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) + 1/4*log(c*x^4 + b*x^2 + a)/c^2","A",0
862,1,96,0,0.913425," ","integrate(x^5/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, a \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b^{2} x^{2} - 2 \, a c x^{2} + a b}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}"," ",0,"-2*a*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(b^2*x^2 - 2*a*c*x^2 + a*b)/((c*x^4 + b*x^2 + a)*(b^2*c - 4*a*c^2))","A",0
863,1,82,0,0.618886," ","integrate(x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{b x^{2} + 2 \, a}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"b*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) + 1/2*(b*x^2 + 2*a)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c))","A",0
864,1,82,0,0.576550," ","integrate(x/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, c \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c x^{2} + b}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-2*c*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*c*x^2 + b)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c))","A",0
865,1,166,0,0.556177," ","integrate(1/x/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(b^{3} - 6 \, a b c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{b^{2} c x^{4} - 4 \, a c^{2} x^{4} + b^{3} x^{2} - 2 \, a b c x^{2} + 3 \, a b^{2} - 8 \, a^{2} c}{4 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} - \frac{\log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{2}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2}}"," ",0,"-1/2*(b^3 - 6*a*b*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^2*b^2 - 4*a^3*c)*sqrt(-b^2 + 4*a*c)) + 1/4*(b^2*c*x^4 - 4*a*c^2*x^4 + b^3*x^2 - 2*a*b*c*x^2 + 3*a*b^2 - 8*a^2*c)/((c*x^4 + b*x^2 + a)*(a^2*b^2 - 4*a^3*c)) - 1/4*log(c*x^4 + b*x^2 + a)/a^2 + 1/2*log(x^2)/a^2","A",0
866,1,182,0,0.589134," ","integrate(1/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{4} - 6 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{2} c x^{4} - 6 \, a c^{2} x^{4} + 2 \, b^{3} x^{2} - 7 \, a b c x^{2} + a b^{2} - 4 \, a^{2} c}{2 \, {\left(c x^{6} + b x^{4} + a x^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} + \frac{b \log\left(c x^{4} + b x^{2} + a\right)}{2 \, a^{3}} - \frac{b \log\left(x^{2}\right)}{a^{3}}"," ",0,"(b^4 - 6*a*b^2*c + 6*a^2*c^2)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^3*b^2 - 4*a^4*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*b^2*c*x^4 - 6*a*c^2*x^4 + 2*b^3*x^2 - 7*a*b*c*x^2 + a*b^2 - 4*a^2*c)/((c*x^6 + b*x^4 + a*x^2)*(a^2*b^2 - 4*a^3*c)) + 1/2*b*log(c*x^4 + b*x^2 + a)/a^3 - b*log(x^2)/a^3","A",0
867,1,3339,0,1.168081," ","integrate(x^8/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b^{3} x^{3} - 3 \, a b c x^{3} + a b^{2} x - 2 \, a^{2} c x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}} + \frac{x}{c^{2}} + \frac{{\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9} - {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} - 320 \, a^{4} c^{7} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} + \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{16 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}} - \frac{{\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9} - {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 320 \, a^{4} c^{7} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} - \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{16 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}}"," ",0,"1/2*(b^3*x^3 - 3*a*b*c*x^3 + a*b^2*x - 2*a^2*c*x)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) + x/c^2 + 1/16*(6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9 - (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2 - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 - 320*a^4*c^7 - 6*(b^2 - 4*a*c)*a*b^4*c^4 + 44*(b^2 - 4*a*c)*a^2*b^2*c^5 - 80*(b^2 - 4*a*c)*a^3*c^6)*abs(-b^2*c^2 + 4*a*c^3))*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 + sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c)) - 1/16*(6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9 - (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2 + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 320*a^4*c^7 + 6*(b^2 - 4*a*c)*a*b^4*c^4 - 44*(b^2 - 4*a*c)*a^2*b^2*c^5 + 80*(b^2 - 4*a*c)*a^3*c^6)*abs(-b^2*c^2 + 4*a*c^3))*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 - sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c))","B",0
868,1,2736,0,1.059703," ","integrate(x^6/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{b^{2} x^{3} - 2 \, a c x^{3} + a b x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}} - \frac{{\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6} - {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 32 \, a^{3} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} + \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{16 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}} + \frac{{\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6} - {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 32 \, a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} - \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{16 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}}"," ",0,"-1/2*(b^2*x^3 - 2*a*c*x^3 + a*b*x)/((c*x^4 + b*x^2 + a)*(b^2*c - 4*a*c^2)) - 1/16*(2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6 - (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 32*a^3*b*c^5 + 2*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*abs(b^2*c - 4*a*c^2))*arctan(2*sqrt(1/2)*x/sqrt((b^3*c - 4*a*b*c^2 + sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c)) + 1/16*(2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6 - (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 32*a^3*b*c^5 - 2*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*abs(b^2*c - 4*a*c^2))*arctan(2*sqrt(1/2)*x/sqrt((b^3*c - 4*a*b*c^2 - sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c))","B",0
869,1,2132,0,1.055311," ","integrate(x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b x^{3} + 2 \, a x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4} - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} + 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 32 \, a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left| b^{2} - 4 \, a c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4} - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} - 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 32 \, a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left| b^{2} - 4 \, a c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}}"," ",0,"1/2*(b*x^3 + 2*a*x)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/16*(2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4 - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2 + 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*a*b^4*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 16*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 32*a^3*c^4 + 2*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*abs(b^2 - 4*a*c))*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/16*(2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4 - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2 - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*a*b^4*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 16*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 32*a^3*c^4 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*abs(b^2 - 4*a*c))*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c))","B",0
870,1,1970,0,0.984118," ","integrate(x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, c x^{3} + b x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} + \frac{{\left(4 \, b^{6} c^{2} - 32 \, a b^{4} c^{3} + 64 \, a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - {\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, a b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 32 \, a^{2} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left| b^{2} - 4 \, a c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left(a b^{6} - 12 \, a^{2} b^{4} c - 2 \, a b^{5} c + 48 \, a^{3} b^{2} c^{2} + 16 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} - 64 \, a^{4} c^{3} - 32 \, a^{3} b c^{3} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} - \frac{{\left(4 \, b^{6} c^{2} - 32 \, a b^{4} c^{3} + 64 \, a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - {\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, a b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 32 \, a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left| b^{2} - 4 \, a c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left(a b^{6} - 12 \, a^{2} b^{4} c - 2 \, a b^{5} c + 48 \, a^{3} b^{2} c^{2} + 16 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} - 64 \, a^{4} c^{3} - 32 \, a^{3} b c^{3} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}}"," ",0,"-1/2*(2*c*x^3 + b*x)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) + 1/8*(4*b^6*c^2 - 32*a*b^4*c^3 + 64*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*(b^2 - 4*a*c)*b^4*c^2 + 16*(b^2 - 4*a*c)*a*b^2*c^3 - (2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*(b^2 - 4*a*c)^2 + (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 2*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*a*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 32*a^2*b*c^3 + 2*(b^2 - 4*a*c)*b^3*c - 8*(b^2 - 4*a*c)*a*b*c^2)*abs(b^2 - 4*a*c))*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6 - 12*a^2*b^4*c - 2*a*b^5*c + 48*a^3*b^2*c^2 + 16*a^2*b^3*c^2 + a*b^4*c^2 - 64*a^4*c^3 - 32*a^3*b*c^3 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*abs(b^2 - 4*a*c)*abs(c)) - 1/8*(4*b^6*c^2 - 32*a*b^4*c^3 + 64*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*(b^2 - 4*a*c)*b^4*c^2 + 16*(b^2 - 4*a*c)*a*b^2*c^3 - (2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*(b^2 - 4*a*c)^2 - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 2*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*a*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 32*a^2*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c + 8*(b^2 - 4*a*c)*a*b*c^2)*abs(b^2 - 4*a*c))*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6 - 12*a^2*b^4*c - 2*a*b^5*c + 48*a^3*b^2*c^2 + 16*a^2*b^3*c^2 + a*b^4*c^2 - 64*a^4*c^3 - 32*a^3*b*c^3 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*abs(b^2 - 4*a*c)*abs(c))","B",0
871,1,2682,0,0.863668," ","integrate(1/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c x^{3} + b^{2} x - 2 \, a c x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}} + \frac{{\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4} + {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 192 \, a^{4} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4} + {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 192 \, a^{4} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}}"," ",0,"1/2*(b*c*x^3 + b^2*x - 2*a*c*x)/((c*x^4 + b*x^2 + a)*(a*b^2 - 4*a^2*c)) + 1/16*(2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4 + (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 192*a^4*c^4 + 2*(b^2 - 4*a*c)*a*b^4*c - 20*(b^2 - 4*a*c)*a^2*b^2*c^2 + 48*(b^2 - 4*a*c)*a^3*c^3)*abs(a*b^2 - 4*a^2*c))*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/16*(2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4 + (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 192*a^4*c^4 - 2*(b^2 - 4*a*c)*a*b^4*c + 20*(b^2 - 4*a*c)*a^2*b^2*c^2 - 48*(b^2 - 4*a*c)*a^3*c^3)*abs(a*b^2 - 4*a^2*c))*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c))","B",0
872,1,3087,0,1.338724," ","integrate(1/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} c x^{4} - 10 \, a c^{2} x^{4} + 3 \, b^{3} x^{2} - 11 \, a b c x^{2} + 2 \, a b^{2} - 8 \, a^{2} c}{2 \, {\left(c x^{5} + b x^{3} + a x\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} - \frac{{\left(6 \, a^{4} b^{8} c^{2} - 80 \, a^{5} b^{6} c^{3} + 352 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4} + {\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 6 \, a^{2} b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 74 \, a^{3} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 304 \, a^{4} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 416 \, a^{5} b c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c + \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{16 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 48 \, a^{7} b^{2} c^{2} + 16 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} - 64 \, a^{8} c^{3} - 32 \, a^{7} b c^{3} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}} + \frac{{\left(6 \, a^{4} b^{8} c^{2} - 80 \, a^{5} b^{6} c^{3} + 352 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4} + {\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + 6 \, a^{2} b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 74 \, a^{3} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 304 \, a^{4} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 416 \, a^{5} b c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c - \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{16 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 48 \, a^{7} b^{2} c^{2} + 16 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} - 64 \, a^{8} c^{3} - 32 \, a^{7} b c^{3} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}}"," ",0,"-1/2*(3*b^2*c*x^4 - 10*a*c^2*x^4 + 3*b^3*x^2 - 11*a*b*c*x^2 + 2*a*b^2 - 8*a^2*c)/((c*x^5 + b*x^3 + a*x)*(a^2*b^2 - 4*a^3*c)) - 1/16*(6*a^4*b^8*c^2 - 80*a^5*b^6*c^3 + 352*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 6*(b^2 - 4*a*c)*a^4*b^6*c^2 + 56*(b^2 - 4*a*c)*a^5*b^4*c^3 - 128*(b^2 - 4*a*c)*a^6*b^2*c^4 + (6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*(a^2*b^2 - 4*a^3*c)^2 + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 6*a^2*b^7*c + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 74*a^3*b^5*c^2 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 304*a^4*b^3*c^3 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + 416*a^5*b*c^4 + 6*(b^2 - 4*a*c)*a^2*b^5*c - 50*(b^2 - 4*a*c)*a^3*b^3*c^2 + 104*(b^2 - 4*a*c)*a^4*b*c^3)*abs(a^2*b^2 - 4*a^3*c))*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^3 - 4*a^3*b*c + sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6 - 12*a^6*b^4*c - 2*a^5*b^5*c + 48*a^7*b^2*c^2 + 16*a^6*b^3*c^2 + a^5*b^4*c^2 - 64*a^8*c^3 - 32*a^7*b*c^3 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*abs(a^2*b^2 - 4*a^3*c)*abs(c)) + 1/16*(6*a^4*b^8*c^2 - 80*a^5*b^6*c^3 + 352*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 6*(b^2 - 4*a*c)*a^4*b^6*c^2 + 56*(b^2 - 4*a*c)*a^5*b^4*c^3 - 128*(b^2 - 4*a*c)*a^6*b^2*c^4 + (6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*(a^2*b^2 - 4*a^3*c)^2 - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + 6*a^2*b^7*c + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 50*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - 74*a^3*b^5*c^2 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 25*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 304*a^4*b^3*c^3 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 416*a^5*b*c^4 - 6*(b^2 - 4*a*c)*a^2*b^5*c + 50*(b^2 - 4*a*c)*a^3*b^3*c^2 - 104*(b^2 - 4*a*c)*a^4*b*c^3)*abs(a^2*b^2 - 4*a^3*c))*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^3 - 4*a^3*b*c - sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6 - 12*a^6*b^4*c - 2*a^5*b^5*c + 48*a^7*b^2*c^2 + 16*a^6*b^3*c^2 + a^5*b^4*c^2 - 64*a^8*c^3 - 32*a^7*b*c^3 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*abs(a^2*b^2 - 4*a^3*c)*abs(c))","B",0
873,1,306,0,1.841133," ","integrate(x^11/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(b^{5} - 10 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{3 \, b^{4} c^{2} x^{8} - 24 \, a b^{2} c^{3} x^{8} + 48 \, a^{2} c^{4} x^{8} - 2 \, b^{5} c x^{6} + 12 \, a b^{3} c^{2} x^{6} - 4 \, a^{2} b c^{3} x^{6} - 3 \, b^{6} x^{4} + 20 \, a b^{4} c x^{4} - 22 \, a^{2} b^{2} c^{2} x^{4} + 32 \, a^{3} c^{3} x^{4} - 6 \, a b^{5} x^{2} + 40 \, a^{2} b^{3} c x^{2} - 28 \, a^{3} b c^{2} x^{2} - 3 \, a^{2} b^{4} + 18 \, a^{3} b^{2} c}{8 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}} + \frac{\log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}}"," ",0,"-1/2*(b^5 - 10*a*b^3*c + 30*a^2*b*c^2)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(-b^2 + 4*a*c)) - 1/8*(3*b^4*c^2*x^8 - 24*a*b^2*c^3*x^8 + 48*a^2*c^4*x^8 - 2*b^5*c*x^6 + 12*a*b^3*c^2*x^6 - 4*a^2*b*c^3*x^6 - 3*b^6*x^4 + 20*a*b^4*c*x^4 - 22*a^2*b^2*c^2*x^4 + 32*a^3*c^3*x^4 - 6*a*b^5*x^2 + 40*a^2*b^3*c*x^2 - 28*a^3*b*c^2*x^2 - 3*a^2*b^4 + 18*a^3*b^2*c)/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*(c*x^4 + b*x^2 + a)^2) + 1/4*log(c*x^4 + b*x^2 + a)/c^3","A",0
874,1,212,0,1.871654," ","integrate(x^9/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{6 \, a^{2} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{4} c x^{6} - 16 \, a b^{2} c^{2} x^{6} + 20 \, a^{2} c^{3} x^{6} + b^{5} x^{4} - 8 \, a b^{3} c x^{4} - 2 \, a^{2} b c^{2} x^{4} + 2 \, a b^{4} x^{2} - 20 \, a^{2} b^{2} c x^{2} + 12 \, a^{3} c^{2} x^{2} + a^{2} b^{3} - 10 \, a^{3} b c}{4 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"6*a^2*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(2*b^4*c*x^6 - 16*a*b^2*c^2*x^6 + 20*a^2*c^3*x^6 + b^5*x^4 - 8*a*b^3*c*x^4 - 2*a^2*b*c^2*x^4 + 2*a*b^4*x^2 - 20*a^2*b^2*c*x^2 + 12*a^3*c^2*x^2 + a^2*b^3 - 10*a^3*b*c)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^4 + b*x^2 + a)^2)","A",0
875,1,171,0,1.772067," ","integrate(x^7/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, a b \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, a b c^{2} x^{6} + b^{4} x^{4} + a b^{2} c x^{4} + 16 \, a^{2} c^{2} x^{4} + 2 \, a b^{3} x^{2} + 10 \, a^{2} b c x^{2} + a^{2} b^{2} + 8 \, a^{3} c}{4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"-3*a*b*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(6*a*b*c^2*x^6 + b^4*x^4 + a*b^2*c*x^4 + 16*a^2*c^2*x^4 + 2*a*b^3*x^2 + 10*a^2*b*c*x^2 + a^2*b^2 + 8*a^3*c)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^4 + b*x^2 + a)^2)","A",0
876,1,161,0,1.812753," ","integrate(x^5/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(b^{2} + 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, b^{2} c x^{6} + 4 \, a c^{2} x^{6} + 3 \, b^{3} x^{4} + 6 \, a b c x^{4} + 10 \, a b^{2} x^{2} - 4 \, a^{2} c x^{2} + 6 \, a^{2} b}{4 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"(b^2 + 2*a*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/4*(2*b^2*c*x^6 + 4*a*c^2*x^6 + 3*b^3*x^4 + 6*a*b*c*x^4 + 10*a*b^2*x^2 - 4*a^2*c*x^2 + 6*a^2*b)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","A",0
877,1,143,0,1.786389," ","integrate(x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, b c \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, b c^{2} x^{6} + 9 \, b^{2} c x^{4} + 2 \, b^{3} x^{2} + 10 \, a b c x^{2} + a b^{2} + 8 \, a^{2} c}{4 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"-3*b*c*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(6*b*c^2*x^6 + 9*b^2*c*x^4 + 2*b^3*x^2 + 10*a*b*c*x^2 + a*b^2 + 8*a^2*c)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","A",0
878,1,144,0,1.773891," ","integrate(x/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{6 \, c^{2} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} x^{6} + 18 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + 20 \, a c^{2} x^{2} - b^{3} + 10 \, a b c}{4 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"6*c^2*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/4*(12*c^3*x^6 + 18*b*c^2*x^4 + 4*b^2*c*x^2 + 20*a*c^2*x^2 - b^3 + 10*a*b*c)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","A",0
879,1,323,0,1.878981," ","integrate(1/x/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(b^{5} - 10 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, b^{4} c^{2} x^{8} - 24 \, a b^{2} c^{3} x^{8} + 48 \, a^{2} c^{4} x^{8} + 6 \, b^{5} c x^{6} - 44 \, a b^{3} c^{2} x^{6} + 68 \, a^{2} b c^{3} x^{6} + 3 \, b^{6} x^{4} - 10 \, a b^{4} c x^{4} - 58 \, a^{2} b^{2} c^{2} x^{4} + 128 \, a^{3} c^{3} x^{4} + 10 \, a b^{5} x^{2} - 72 \, a^{2} b^{3} c x^{2} + 92 \, a^{3} b c^{2} x^{2} + 9 \, a^{2} b^{4} - 66 \, a^{3} b^{2} c + 96 \, a^{4} c^{2}}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}} - \frac{\log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{3}} + \frac{\log\left(x^{2}\right)}{2 \, a^{3}}"," ",0,"-1/2*(b^5 - 10*a*b^3*c + 30*a^2*b*c^2)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt(-b^2 + 4*a*c)) + 1/8*(3*b^4*c^2*x^8 - 24*a*b^2*c^3*x^8 + 48*a^2*c^4*x^8 + 6*b^5*c*x^6 - 44*a*b^3*c^2*x^6 + 68*a^2*b*c^3*x^6 + 3*b^6*x^4 - 10*a*b^4*c*x^4 - 58*a^2*b^2*c^2*x^4 + 128*a^3*c^3*x^4 + 10*a*b^5*x^2 - 72*a^2*b^3*c*x^2 + 92*a^3*b*c^2*x^2 + 9*a^2*b^4 - 66*a^3*b^2*c + 96*a^4*c^2)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(c*x^4 + b*x^2 + a)^2) - 1/4*log(c*x^4 + b*x^2 + a)/a^3 + 1/2*log(x^2)/a^3","A",0
880,1,382,0,1.801249," ","integrate(1/x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b^{6} - 10 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{9 \, b^{5} c^{2} x^{8} - 72 \, a b^{3} c^{3} x^{8} + 144 \, a^{2} b c^{4} x^{8} + 18 \, b^{6} c x^{6} - 136 \, a b^{4} c^{2} x^{6} + 236 \, a^{2} b^{2} c^{3} x^{6} + 56 \, a^{3} c^{4} x^{6} + 9 \, b^{7} x^{4} - 38 \, a b^{5} c x^{4} - 110 \, a^{2} b^{3} c^{2} x^{4} + 436 \, a^{3} b c^{3} x^{4} + 26 \, a b^{6} x^{2} - 192 \, a^{2} b^{4} c x^{2} + 316 \, a^{3} b^{2} c^{2} x^{2} + 72 \, a^{4} c^{3} x^{2} + 19 \, a^{2} b^{5} - 144 \, a^{3} b^{3} c + 260 \, a^{4} b c^{2}}{8 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}} + \frac{3 \, b \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{4}} - \frac{3 \, b \log\left(x^{2}\right)}{2 \, a^{4}} + \frac{3 \, b x^{2} - a}{2 \, a^{4} x^{2}}"," ",0,"3/2*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*sqrt(-b^2 + 4*a*c)) - 1/8*(9*b^5*c^2*x^8 - 72*a*b^3*c^3*x^8 + 144*a^2*b*c^4*x^8 + 18*b^6*c*x^6 - 136*a*b^4*c^2*x^6 + 236*a^2*b^2*c^3*x^6 + 56*a^3*c^4*x^6 + 9*b^7*x^4 - 38*a*b^5*c*x^4 - 110*a^2*b^3*c^2*x^4 + 436*a^3*b*c^3*x^4 + 26*a*b^6*x^2 - 192*a^2*b^4*c*x^2 + 316*a^3*b^2*c^2*x^2 + 72*a^4*c^3*x^2 + 19*a^2*b^5 - 144*a^3*b^3*c + 260*a^4*b*c^2)/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(c*x^4 + b*x^2 + a)^2) + 3/4*b*log(c*x^4 + b*x^2 + a)/a^4 - 3/2*b*log(x^2)/a^4 + 1/2*(3*b*x^2 - a)/(a^4*x^2)","A",0
881,1,2430,0,3.625650," ","integrate(x^10/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 160 \, a^{2} b^{3} c^{3} + 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 256 \, a^{3} b c^{4} - 192 \, a^{2} b^{2} c^{4} + 448 \, a^{3} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} + \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{32 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} + \frac{3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 32 \, a b^{5} c^{2} + 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 160 \, a^{2} b^{3} c^{3} - 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 256 \, a^{3} b c^{4} + 192 \, a^{2} b^{2} c^{4} - 448 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} - \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{32 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} - \frac{5 \, b^{4} c x^{7} - 37 \, a b^{2} c^{2} x^{7} + 44 \, a^{2} c^{3} x^{7} + 3 \, b^{5} x^{5} - 20 \, a b^{3} c x^{5} - 4 \, a^{2} b c^{2} x^{5} + 6 \, a b^{4} x^{3} - 49 \, a^{2} b^{2} c x^{3} + 28 \, a^{3} c^{2} x^{3} + 3 \, a^{2} b^{3} x - 24 \, a^{3} b c x}{8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"3/32*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 2*b^7*c + 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*a*b^5*c^2 - 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 160*a^2*b^3*c^3 + 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 256*a^3*b*c^4 - 192*a^2*b^2*c^4 + 448*a^3*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 2*(b^2 - 4*a*c)*b^5*c - 24*(b^2 - 4*a*c)*a*b^3*c^2 + 2*(b^2 - 4*a*c)*b^4*c^2 + 64*(b^2 - 4*a*c)*a^2*b*c^3 - 20*(b^2 - 4*a*c)*a*b^2*c^3 + 112*(b^2 - 4*a*c)*a^2*c^4)*arctan(2*sqrt(1/2)*x/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 + sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) + 3/32*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 2*b^7*c + 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 32*a*b^5*c^2 + 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 160*a^2*b^3*c^3 - 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 256*a^3*b*c^4 + 192*a^2*b^2*c^4 - 448*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^5*c + 24*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*b^4*c^2 - 64*(b^2 - 4*a*c)*a^2*b*c^3 + 20*(b^2 - 4*a*c)*a*b^2*c^3 - 112*(b^2 - 4*a*c)*a^2*c^4)*arctan(2*sqrt(1/2)*x/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 - sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) - 1/8*(5*b^4*c*x^7 - 37*a*b^2*c^2*x^7 + 44*a^2*c^3*x^7 + 3*b^5*x^5 - 20*a*b^3*c*x^5 - 4*a^2*b*c^2*x^5 + 6*a*b^4*x^3 - 49*a^2*b^2*c*x^3 + 28*a^3*c^2*x^3 + 3*a^2*b^3*x - 24*a^3*b*c*x)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^4 + b*x^2 + a)^2)","B",0
882,1,4558,0,2.456888," ","integrate(x^8/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(2 \, b^{13} c^{4} - 68 \, a b^{11} c^{5} + 688 \, a^{2} b^{9} c^{6} - 2688 \, a^{3} b^{7} c^{7} + 2048 \, a^{4} b^{5} c^{8} + 11264 \, a^{5} b^{3} c^{9} - 20480 \, a^{6} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{13} c^{2} + 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{11} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} - 344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{9} c^{4} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{5} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} + 30 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{9} c^{5} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{6} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} - 5632 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{7} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 10240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{8} + 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{11} c^{4} + 60 \, {\left(b^{2} - 4 \, a c\right)} a b^{9} c^{5} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{7} c^{6} + 896 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{7} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{8} - 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{9} - {\left(2 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 128 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 2 \, a b^{8} c^{3} - 192 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 16 \, a^{2} b^{6} c^{4} + 896 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 288 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 384 \, a^{3} b^{4} c^{5} - 1280 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 640 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 1792 \, a^{4} b^{2} c^{6} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} + 2560 \, a^{5} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} + 640 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + \sqrt{{\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)}^{2} - 4 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{64 \, {\left(a b^{10} c^{3} - 20 \, a^{2} b^{8} c^{4} - 2 \, a b^{9} c^{4} + 160 \, a^{3} b^{6} c^{5} + 32 \, a^{2} b^{7} c^{5} + a b^{8} c^{5} - 640 \, a^{4} b^{4} c^{6} - 192 \, a^{3} b^{5} c^{6} - 16 \, a^{2} b^{6} c^{6} + 1280 \, a^{5} b^{2} c^{7} + 512 \, a^{4} b^{3} c^{7} + 96 \, a^{3} b^{4} c^{7} - 1024 \, a^{6} c^{8} - 512 \, a^{5} b c^{8} - 256 \, a^{4} b^{2} c^{8} + 256 \, a^{5} c^{9}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} {\left| c \right|}} + \frac{{\left(2 \, b^{13} c^{4} - 68 \, a b^{11} c^{5} + 688 \, a^{2} b^{9} c^{6} - 2688 \, a^{3} b^{7} c^{7} + 2048 \, a^{4} b^{5} c^{8} + 11264 \, a^{5} b^{3} c^{9} - 20480 \, a^{6} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{13} c^{2} + 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{11} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} - 344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{9} c^{4} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{5} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} + 30 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{9} c^{5} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{6} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} - 5632 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{7} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 10240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{8} + 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{11} c^{4} + 60 \, {\left(b^{2} - 4 \, a c\right)} a b^{9} c^{5} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{7} c^{6} + 896 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{7} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{8} - 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{9} - {\left(2 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 128 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} + 2 \, a b^{8} c^{3} - 192 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 16 \, a^{2} b^{6} c^{4} + 896 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 288 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} - 384 \, a^{3} b^{4} c^{5} - 1280 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 640 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} + 1792 \, a^{4} b^{2} c^{6} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} - 2560 \, a^{5} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} + 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} - 640 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} - \sqrt{{\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)}^{2} - 4 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{64 \, {\left(a b^{10} c^{3} - 20 \, a^{2} b^{8} c^{4} - 2 \, a b^{9} c^{4} + 160 \, a^{3} b^{6} c^{5} + 32 \, a^{2} b^{7} c^{5} + a b^{8} c^{5} - 640 \, a^{4} b^{4} c^{6} - 192 \, a^{3} b^{5} c^{6} - 16 \, a^{2} b^{6} c^{6} + 1280 \, a^{5} b^{2} c^{7} + 512 \, a^{4} b^{3} c^{7} + 96 \, a^{3} b^{4} c^{7} - 1024 \, a^{6} c^{8} - 512 \, a^{5} b c^{8} - 256 \, a^{4} b^{2} c^{8} + 256 \, a^{5} c^{9}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} {\left| c \right|}} + \frac{b^{3} c x^{7} - 16 \, a b c^{2} x^{7} - b^{4} x^{5} - 5 \, a b^{2} c x^{5} - 36 \, a^{2} c^{2} x^{5} - 2 \, a b^{3} x^{3} - 28 \, a^{2} b c x^{3} - a^{2} b^{2} x - 20 \, a^{3} c x}{8 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"-1/64*(2*b^13*c^4 - 68*a*b^11*c^5 + 688*a^2*b^9*c^6 - 2688*a^3*b^7*c^7 + 2048*a^4*b^5*c^8 + 11264*a^5*b^3*c^9 - 20480*a^6*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^13*c^2 + 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^11*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^12*c^3 - 344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^9*c^4 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^5 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 + 30*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^9*c^5 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^6 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 - 5632*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^7 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 10240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^8 + 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^9 - 2*(b^2 - 4*a*c)*b^11*c^4 + 60*(b^2 - 4*a*c)*a*b^9*c^5 - 448*(b^2 - 4*a*c)*a^2*b^7*c^6 + 896*(b^2 - 4*a*c)*a^3*b^5*c^7 + 1536*(b^2 - 4*a*c)*a^4*b^3*c^8 - 5120*(b^2 - 4*a*c)*a^5*b*c^9 - (2*b^5*c^2 - 40*a*b^3*c^3 + 128*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 32*(b^2 - 4*a*c)*a*b*c^3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 2*a*b^8*c^3 - 192*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 16*a^2*b^6*c^4 + 896*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 288*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + 384*a^3*b^4*c^5 - 1280*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 640*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 1792*a^4*b^2*c^6 + 320*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^7 + 2560*a^5*c^7 + 2*(b^2 - 4*a*c)*a*b^6*c^3 + 24*(b^2 - 4*a*c)*a^2*b^4*c^4 - 288*(b^2 - 4*a*c)*a^3*b^2*c^5 + 640*(b^2 - 4*a*c)*a^4*c^6)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3))*arctan(2*sqrt(1/2)*x/sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)^2 - 4*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/((a*b^10*c^3 - 20*a^2*b^8*c^4 - 2*a*b^9*c^4 + 160*a^3*b^6*c^5 + 32*a^2*b^7*c^5 + a*b^8*c^5 - 640*a^4*b^4*c^6 - 192*a^3*b^5*c^6 - 16*a^2*b^6*c^6 + 1280*a^5*b^2*c^7 + 512*a^4*b^3*c^7 + 96*a^3*b^4*c^7 - 1024*a^6*c^8 - 512*a^5*b*c^8 - 256*a^4*b^2*c^8 + 256*a^5*c^9)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*abs(c)) + 1/64*(2*b^13*c^4 - 68*a*b^11*c^5 + 688*a^2*b^9*c^6 - 2688*a^3*b^7*c^7 + 2048*a^4*b^5*c^8 + 11264*a^5*b^3*c^9 - 20480*a^6*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^13*c^2 + 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^11*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^12*c^3 - 344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^9*c^4 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^5 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 + 30*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^9*c^5 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^6 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 - 5632*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^7 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 10240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^8 + 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^9 - 2*(b^2 - 4*a*c)*b^11*c^4 + 60*(b^2 - 4*a*c)*a*b^9*c^5 - 448*(b^2 - 4*a*c)*a^2*b^7*c^6 + 896*(b^2 - 4*a*c)*a^3*b^5*c^7 + 1536*(b^2 - 4*a*c)*a^4*b^3*c^8 - 5120*(b^2 - 4*a*c)*a^5*b*c^9 - (2*b^5*c^2 - 40*a*b^3*c^3 + 128*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 32*(b^2 - 4*a*c)*a*b*c^3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 + 2*a*b^8*c^3 - 192*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 + 16*a^2*b^6*c^4 + 896*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 288*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 - 384*a^3*b^4*c^5 - 1280*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 640*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 + 1792*a^4*b^2*c^6 + 320*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^7 - 2560*a^5*c^7 - 2*(b^2 - 4*a*c)*a*b^6*c^3 - 24*(b^2 - 4*a*c)*a^2*b^4*c^4 + 288*(b^2 - 4*a*c)*a^3*b^2*c^5 - 640*(b^2 - 4*a*c)*a^4*c^6)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3))*arctan(2*sqrt(1/2)*x/sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 - sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)^2 - 4*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/((a*b^10*c^3 - 20*a^2*b^8*c^4 - 2*a*b^9*c^4 + 160*a^3*b^6*c^5 + 32*a^2*b^7*c^5 + a*b^8*c^5 - 640*a^4*b^4*c^6 - 192*a^3*b^5*c^6 - 16*a^2*b^6*c^6 + 1280*a^5*b^2*c^7 + 512*a^4*b^3*c^7 + 96*a^3*b^4*c^7 - 1024*a^6*c^8 - 512*a^5*b*c^8 - 256*a^4*b^2*c^8 + 256*a^5*c^9)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*abs(c)) + 1/8*(b^3*c*x^7 - 16*a*b*c^2*x^7 - b^4*x^5 - 5*a*b^2*c*x^5 - 36*a^2*c^2*x^5 - 2*a*b^3*x^3 - 28*a^2*b*c*x^3 - a^2*b^2*x - 20*a^3*c*x)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^4 + b*x^2 + a)^2)","B",0
883,1,1750,0,2.816918," ","integrate(x^6/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 4 \, b^{5} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 32 \, a b^{3} c^{2} + 6 \, b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 64 \, a^{2} b c^{3} - 16 \, a b^{2} c^{3} - 32 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{16 \, {\left(b^{8} - 16 \, a b^{6} c - 2 \, b^{7} c + 96 \, a^{2} b^{4} c^{2} + 24 \, a b^{5} c^{2} + b^{6} c^{2} - 256 \, a^{3} b^{2} c^{3} - 96 \, a^{2} b^{3} c^{3} - 12 \, a b^{4} c^{3} + 256 \, a^{4} c^{4} + 128 \, a^{3} b c^{4} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} {\left| c \right|}} - \frac{3 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 4 \, b^{5} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 32 \, a b^{3} c^{2} - 6 \, b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 64 \, a^{2} b c^{3} + 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} - \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{16 \, {\left(b^{8} - 16 \, a b^{6} c - 2 \, b^{7} c + 96 \, a^{2} b^{4} c^{2} + 24 \, a b^{5} c^{2} + b^{6} c^{2} - 256 \, a^{3} b^{2} c^{3} - 96 \, a^{2} b^{3} c^{3} - 12 \, a b^{4} c^{3} + 256 \, a^{4} c^{4} + 128 \, a^{3} b c^{4} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} {\left| c \right|}} + \frac{3 \, b^{2} c x^{7} + 12 \, a c^{2} x^{7} + 5 \, b^{3} x^{5} + 16 \, a b c x^{5} + 19 \, a b^{2} x^{3} - 4 \, a^{2} c x^{3} + 12 \, a^{2} b x}{8 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"-3/16*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 4*b^5*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 32*a*b^3*c^2 + 6*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 64*a^2*b*c^3 - 16*a*b^2*c^3 - 32*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 + 4*(b^2 - 4*a*c)*b^3*c - 16*(b^2 - 4*a*c)*a*b*c^2 - 6*(b^2 - 4*a*c)*b^2*c^2 - 8*(b^2 - 4*a*c)*a*c^3)*arctan(2*sqrt(1/2)*x/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((b^8 - 16*a*b^6*c - 2*b^7*c + 96*a^2*b^4*c^2 + 24*a*b^5*c^2 + b^6*c^2 - 256*a^3*b^2*c^3 - 96*a^2*b^3*c^3 - 12*a*b^4*c^3 + 256*a^4*c^4 + 128*a^3*b*c^4 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*abs(c)) - 3/16*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 4*b^5*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 32*a*b^3*c^2 - 6*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 64*a^2*b*c^3 + 16*a*b^2*c^3 + 32*a^2*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 4*(b^2 - 4*a*c)*b^3*c + 16*(b^2 - 4*a*c)*a*b*c^2 + 6*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*arctan(2*sqrt(1/2)*x/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 - sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((b^8 - 16*a*b^6*c - 2*b^7*c + 96*a^2*b^4*c^2 + 24*a*b^5*c^2 + b^6*c^2 - 256*a^3*b^2*c^3 - 96*a^2*b^3*c^3 - 12*a*b^4*c^3 + 256*a^4*c^4 + 128*a^3*b*c^4 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*abs(c)) + 1/8*(3*b^2*c*x^7 + 12*a*c^2*x^7 + 5*b^3*x^5 + 16*a*b*c*x^5 + 19*a*b^2*x^3 - 4*a^2*c*x^3 + 12*a^2*b*x)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","B",0
884,1,1861,0,2.642051," ","integrate(x^4/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 8 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{2} b^{2} c^{3} + 16 \, a b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 128 \, a^{3} c^{4} - 96 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{32 \, {\left(a b^{8} - 16 \, a^{2} b^{6} c - 2 \, a b^{7} c + 96 \, a^{3} b^{4} c^{2} + 24 \, a^{2} b^{5} c^{2} + a b^{6} c^{2} - 256 \, a^{4} b^{2} c^{3} - 96 \, a^{3} b^{3} c^{3} - 12 \, a^{2} b^{4} c^{3} + 256 \, a^{5} c^{4} + 128 \, a^{4} b c^{4} + 48 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} {\left| c \right|}} + \frac{3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 8 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{2} b^{2} c^{3} - 16 \, a b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 128 \, a^{3} c^{4} + 96 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} - \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{32 \, {\left(a b^{8} - 16 \, a^{2} b^{6} c - 2 \, a b^{7} c + 96 \, a^{3} b^{4} c^{2} + 24 \, a^{2} b^{5} c^{2} + a b^{6} c^{2} - 256 \, a^{4} b^{2} c^{3} - 96 \, a^{3} b^{3} c^{3} - 12 \, a^{2} b^{4} c^{3} + 256 \, a^{5} c^{4} + 128 \, a^{4} b c^{4} + 48 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} {\left| c \right|}} - \frac{12 \, b c^{2} x^{7} + 19 \, b^{2} c x^{5} - 4 \, a c^{2} x^{5} + 5 \, b^{3} x^{3} + 16 \, a b c x^{3} + 3 \, a b^{2} x + 12 \, a^{2} c x}{8 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"3/32*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 2*b^6*c - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 8*a*b^4*c^2 + 2*b^5*c^2 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^2*b^2*c^3 + 16*a*b^3*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 128*a^3*c^4 - 96*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*(b^2 - 4*a*c)*b^4*c - 2*(b^2 - 4*a*c)*b^3*c^2 - 32*(b^2 - 4*a*c)*a^2*c^3 - 24*(b^2 - 4*a*c)*a*b*c^3)*arctan(2*sqrt(1/2)*x/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((a*b^8 - 16*a^2*b^6*c - 2*a*b^7*c + 96*a^3*b^4*c^2 + 24*a^2*b^5*c^2 + a*b^6*c^2 - 256*a^4*b^2*c^3 - 96*a^3*b^3*c^3 - 12*a^2*b^4*c^3 + 256*a^5*c^4 + 128*a^4*b*c^4 + 48*a^3*b^2*c^4 - 64*a^4*c^5)*abs(c)) + 3/32*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 2*b^6*c - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 8*a*b^4*c^2 - 2*b^5*c^2 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^2*b^2*c^3 - 16*a*b^3*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 128*a^3*c^4 + 96*a^2*b*c^4 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^4*c + 2*(b^2 - 4*a*c)*b^3*c^2 + 32*(b^2 - 4*a*c)*a^2*c^3 + 24*(b^2 - 4*a*c)*a*b*c^3)*arctan(2*sqrt(1/2)*x/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 - sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((a*b^8 - 16*a^2*b^6*c - 2*a*b^7*c + 96*a^3*b^4*c^2 + 24*a^2*b^5*c^2 + a*b^6*c^2 - 256*a^4*b^2*c^3 - 96*a^3*b^3*c^3 - 12*a^2*b^4*c^3 + 256*a^5*c^4 + 128*a^4*b*c^4 + 48*a^3*b^2*c^4 - 64*a^4*c^5)*abs(c)) - 1/8*(12*b*c^2*x^7 + 19*b^2*c*x^5 - 4*a*c^2*x^5 + 5*b^3*x^3 + 16*a*b*c*x^3 + 3*a*b^2*x + 12*a^2*c*x)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","B",0
885,1,4270,0,2.453899," ","integrate(x^2/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(2 \, a^{2} b^{12} c^{2} - 136 \, a^{3} b^{10} c^{3} + 1856 \, a^{4} b^{8} c^{4} - 10496 \, a^{5} b^{6} c^{5} + 27136 \, a^{6} b^{4} c^{6} - 26624 \, a^{7} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{12} + 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{11} c - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{10} c^{2} + 5248 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{3} - 13568 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{4} + 13312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{10} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{8} c^{3} - 1344 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{4} + 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{6} + {\left(2 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} - 160 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 40 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{9} - 28 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c - 2 \, a b^{9} c + 240 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} + 56 \, a^{2} b^{7} c^{2} - 832 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 288 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 480 \, a^{3} b^{5} c^{3} + 1024 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 512 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 1664 \, a^{4} b^{3} c^{4} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 2048 \, a^{5} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{7} c - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 512 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + \sqrt{{\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)}}}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}}}}\right)}{64 \, {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c - 2 \, a^{3} b^{9} c + 160 \, a^{5} b^{6} c^{2} + 32 \, a^{4} b^{7} c^{2} + a^{3} b^{8} c^{2} - 640 \, a^{6} b^{4} c^{3} - 192 \, a^{5} b^{5} c^{3} - 16 \, a^{4} b^{6} c^{3} + 1280 \, a^{7} b^{2} c^{4} + 512 \, a^{6} b^{3} c^{4} + 96 \, a^{5} b^{4} c^{4} - 1024 \, a^{8} c^{5} - 512 \, a^{7} b c^{5} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} {\left| c \right|}} - \frac{{\left(2 \, a^{2} b^{12} c^{2} - 136 \, a^{3} b^{10} c^{3} + 1856 \, a^{4} b^{8} c^{4} - 10496 \, a^{5} b^{6} c^{5} + 27136 \, a^{6} b^{4} c^{6} - 26624 \, a^{7} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{12} + 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{11} c - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{10} c^{2} + 5248 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{3} - 13568 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{4} + 13312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{10} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{8} c^{3} - 1344 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{4} + 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{6} + {\left(2 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} - 160 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 40 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{9} - 28 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c + 2 \, a b^{9} c + 240 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} - 56 \, a^{2} b^{7} c^{2} - 832 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 288 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 480 \, a^{3} b^{5} c^{3} + 1024 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 512 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 1664 \, a^{4} b^{3} c^{4} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 2048 \, a^{5} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{7} c + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} + 512 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} - \sqrt{{\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)}}}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}}}}\right)}{64 \, {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c - 2 \, a^{3} b^{9} c + 160 \, a^{5} b^{6} c^{2} + 32 \, a^{4} b^{7} c^{2} + a^{3} b^{8} c^{2} - 640 \, a^{6} b^{4} c^{3} - 192 \, a^{5} b^{5} c^{3} - 16 \, a^{4} b^{6} c^{3} + 1280 \, a^{7} b^{2} c^{4} + 512 \, a^{6} b^{3} c^{4} + 96 \, a^{5} b^{4} c^{4} - 1024 \, a^{8} c^{5} - 512 \, a^{7} b c^{5} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} {\left| c \right|}} + \frac{b^{2} c^{2} x^{7} + 20 \, a c^{3} x^{7} + 2 \, b^{3} c x^{5} + 28 \, a b c^{2} x^{5} + b^{4} x^{3} + 5 \, a b^{2} c x^{3} + 36 \, a^{2} c^{2} x^{3} - a b^{3} x + 16 \, a^{2} b c x}{8 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"1/64*(2*a^2*b^12*c^2 - 136*a^3*b^10*c^3 + 1856*a^4*b^8*c^4 - 10496*a^5*b^6*c^5 + 27136*a^6*b^4*c^6 - 26624*a^7*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^12 + 68*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^11*c - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^10*c^2 + 5248*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^3 - 13568*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^4 + 13312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^6 - 2*(b^2 - 4*a*c)*a^2*b^10*c^2 + 128*(b^2 - 4*a*c)*a^3*b^8*c^3 - 1344*(b^2 - 4*a*c)*a^4*b^6*c^4 + 5120*(b^2 - 4*a*c)*a^5*b^4*c^5 - 6656*(b^2 - 4*a*c)*a^6*b^2*c^6 + (2*b^4*c^2 + 32*a*b^2*c^3 - 160*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 - 40*(b^2 - 4*a*c)*a*c^3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^9 - 28*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c - 2*a*b^9*c + 240*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 + 56*a^2*b^7*c^2 - 832*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 288*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 480*a^3*b^5*c^3 + 1024*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 512*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 1664*a^4*b^3*c^4 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 2048*a^5*b*c^5 + 2*(b^2 - 4*a*c)*a*b^7*c - 48*(b^2 - 4*a*c)*a^2*b^5*c^2 + 288*(b^2 - 4*a*c)*a^3*b^3*c^3 - 512*(b^2 - 4*a*c)*a^4*b*c^4)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2))*arctan(2*sqrt(1/2)*x/sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)^2 - 4*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/((a^3*b^10 - 20*a^4*b^8*c - 2*a^3*b^9*c + 160*a^5*b^6*c^2 + 32*a^4*b^7*c^2 + a^3*b^8*c^2 - 640*a^6*b^4*c^3 - 192*a^5*b^5*c^3 - 16*a^4*b^6*c^3 + 1280*a^7*b^2*c^4 + 512*a^6*b^3*c^4 + 96*a^5*b^4*c^4 - 1024*a^8*c^5 - 512*a^7*b*c^5 - 256*a^6*b^2*c^5 + 256*a^7*c^6)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*abs(c)) - 1/64*(2*a^2*b^12*c^2 - 136*a^3*b^10*c^3 + 1856*a^4*b^8*c^4 - 10496*a^5*b^6*c^5 + 27136*a^6*b^4*c^6 - 26624*a^7*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^12 + 68*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^11*c - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^10*c^2 + 5248*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^3 - 13568*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^4 + 13312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^6 - 2*(b^2 - 4*a*c)*a^2*b^10*c^2 + 128*(b^2 - 4*a*c)*a^3*b^8*c^3 - 1344*(b^2 - 4*a*c)*a^4*b^6*c^4 + 5120*(b^2 - 4*a*c)*a^5*b^4*c^5 - 6656*(b^2 - 4*a*c)*a^6*b^2*c^6 + (2*b^4*c^2 + 32*a*b^2*c^3 - 160*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 - 40*(b^2 - 4*a*c)*a*c^3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^9 - 28*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c + 2*a*b^9*c + 240*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 - 56*a^2*b^7*c^2 - 832*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 288*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 480*a^3*b^5*c^3 + 1024*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 512*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 1664*a^4*b^3*c^4 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 2048*a^5*b*c^5 - 2*(b^2 - 4*a*c)*a*b^7*c + 48*(b^2 - 4*a*c)*a^2*b^5*c^2 - 288*(b^2 - 4*a*c)*a^3*b^3*c^3 + 512*(b^2 - 4*a*c)*a^4*b*c^4)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2))*arctan(2*sqrt(1/2)*x/sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 - sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)^2 - 4*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/((a^3*b^10 - 20*a^4*b^8*c - 2*a^3*b^9*c + 160*a^5*b^6*c^2 + 32*a^4*b^7*c^2 + a^3*b^8*c^2 - 640*a^6*b^4*c^3 - 192*a^5*b^5*c^3 - 16*a^4*b^6*c^3 + 1280*a^7*b^2*c^4 + 512*a^6*b^3*c^4 + 96*a^5*b^4*c^4 - 1024*a^8*c^5 - 512*a^7*b*c^5 - 256*a^6*b^2*c^5 + 256*a^7*c^6)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*abs(c)) + 1/8*(b^2*c^2*x^7 + 20*a*c^3*x^7 + 2*b^3*c*x^5 + 28*a*b*c^2*x^5 + b^4*x^3 + 5*a*b^2*c*x^3 + 36*a^2*c^2*x^3 - a*b^3*x + 16*a^2*b*c*x)/((a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(c*x^4 + b*x^2 + a)^2)","B",0
886,1,2705,0,1.432525," ","integrate(1/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} - 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} + 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} - 352 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + \sqrt{{\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)}}}{a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}}}}\right)}{32 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c - 2 \, a^{3} b^{7} c + 96 \, a^{5} b^{4} c^{2} + 24 \, a^{4} b^{5} c^{2} + a^{3} b^{6} c^{2} - 256 \, a^{6} b^{2} c^{3} - 96 \, a^{5} b^{3} c^{3} - 12 \, a^{4} b^{4} c^{3} + 256 \, a^{7} c^{4} + 128 \, a^{6} b c^{4} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} {\left| c \right|}} + \frac{3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} - \sqrt{{\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)}}}{a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}}}}\right)}{32 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c - 2 \, a^{3} b^{7} c + 96 \, a^{5} b^{4} c^{2} + 24 \, a^{4} b^{5} c^{2} + a^{3} b^{6} c^{2} - 256 \, a^{6} b^{2} c^{3} - 96 \, a^{5} b^{3} c^{3} - 12 \, a^{4} b^{4} c^{3} + 256 \, a^{7} c^{4} + 128 \, a^{6} b c^{4} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} {\left| c \right|}} + \frac{3 \, b^{3} c^{2} x^{7} - 24 \, a b c^{3} x^{7} + 6 \, b^{4} c x^{5} - 49 \, a b^{2} c^{2} x^{5} + 28 \, a^{2} c^{3} x^{5} + 3 \, b^{5} x^{3} - 20 \, a b^{3} c x^{3} - 4 \, a^{2} b c^{2} x^{3} + 5 \, a b^{4} x - 37 \, a^{2} b^{2} c x + 44 \, a^{3} c^{2} x}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"3/32*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8 - 17*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c - 2*b^8*c + 116*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 26*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 34*a*b^6*c^2 + 2*b^7*c^2 - 368*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 13*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 232*a^2*b^4*c^3 - 30*a*b^5*c^3 + 448*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 736*a^3*b^2*c^4 + 176*a^2*b^3*c^4 - 112*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 896*a^4*c^5 - 352*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 2*(b^2 - 4*a*c)*b^6*c - 26*(b^2 - 4*a*c)*a*b^4*c^2 - 2*(b^2 - 4*a*c)*b^5*c^2 + 128*(b^2 - 4*a*c)*a^2*b^2*c^3 + 22*(b^2 - 4*a*c)*a*b^3*c^3 - 224*(b^2 - 4*a*c)*a^3*c^4 - 88*(b^2 - 4*a*c)*a^2*b*c^4)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)^2 - 4*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/((a^3*b^8 - 16*a^4*b^6*c - 2*a^3*b^7*c + 96*a^5*b^4*c^2 + 24*a^4*b^5*c^2 + a^3*b^6*c^2 - 256*a^6*b^2*c^3 - 96*a^5*b^3*c^3 - 12*a^4*b^4*c^3 + 256*a^7*c^4 + 128*a^6*b*c^4 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*abs(c)) + 3/32*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8 - 17*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c + 2*b^8*c + 116*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 26*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 - 34*a*b^6*c^2 - 2*b^7*c^2 - 368*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 13*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 232*a^2*b^4*c^3 + 30*a*b^5*c^3 + 448*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 224*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 736*a^3*b^2*c^4 - 176*a^2*b^3*c^4 - 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 896*a^4*c^5 + 352*a^3*b*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^6*c + 26*(b^2 - 4*a*c)*a*b^4*c^2 + 2*(b^2 - 4*a*c)*b^5*c^2 - 128*(b^2 - 4*a*c)*a^2*b^2*c^3 - 22*(b^2 - 4*a*c)*a*b^3*c^3 + 224*(b^2 - 4*a*c)*a^3*c^4 + 88*(b^2 - 4*a*c)*a^2*b*c^4)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 - sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)^2 - 4*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/((a^3*b^8 - 16*a^4*b^6*c - 2*a^3*b^7*c + 96*a^5*b^4*c^2 + 24*a^4*b^5*c^2 + a^3*b^6*c^2 - 256*a^6*b^2*c^3 - 96*a^5*b^3*c^3 - 12*a^4*b^4*c^3 + 256*a^7*c^4 + 128*a^6*b*c^4 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*abs(c)) + 1/8*(3*b^3*c^2*x^7 - 24*a*b*c^3*x^7 + 6*b^4*c*x^5 - 49*a*b^2*c^2*x^5 + 28*a^2*c^3*x^5 + 3*b^5*x^3 - 20*a*b^3*c*x^3 - 4*a^2*b*c^2*x^3 + 5*a*b^4*x - 37*a^2*b^2*c*x + 44*a^3*c^2*x)/((a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(c*x^4 + b*x^2 + a)^2)","B",0
887,1,5273,0,2.615876," ","integrate(1/x^2/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(10 \, a^{6} b^{14} c^{2} - 254 \, a^{7} b^{12} c^{3} + 2712 \, a^{8} b^{10} c^{4} - 15552 \, a^{9} b^{8} c^{5} + 50432 \, a^{10} b^{6} c^{6} - 87552 \, a^{11} b^{4} c^{7} + 63488 \, a^{12} b^{2} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{14} + 127 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{13} c - 1356 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - 214 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{12} c^{2} + 7776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 1856 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} + 107 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{10} c^{3} - 25216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 8128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{8} c^{4} + 43776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 17920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} + 4064 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} c^{5} - 31744 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 15872 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} - 8960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c^{6} + 7936 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{7} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{12} c^{2} + 214 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{10} c^{3} - 1856 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{8} c^{4} + 8128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{6} c^{5} - 17920 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{4} c^{6} + 15872 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{2} c^{7} + {\left(10 \, b^{6} c^{2} - 114 \, a b^{4} c^{3} + 416 \, a^{2} b^{2} c^{4} - 480 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 57 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 37 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 120 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} - 102 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c - 10 \, a^{3} b^{11} c + 836 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + 164 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} + 204 \, a^{4} b^{9} c^{2} - 3440 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 1016 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 82 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} - 1672 \, a^{5} b^{7} c^{3} + 7104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 2816 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 508 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} + 6880 \, a^{6} b^{5} c^{4} - 5888 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 2944 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 1408 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} - 14208 \, a^{7} b^{3} c^{5} + 1472 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} + 11776 \, a^{8} b c^{6} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c - 164 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} + 1016 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} - 2816 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} + 2944 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + \sqrt{{\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right)}{64 \, {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c - 2 \, a^{7} b^{9} c + 160 \, a^{9} b^{6} c^{2} + 32 \, a^{8} b^{7} c^{2} + a^{7} b^{8} c^{2} - 640 \, a^{10} b^{4} c^{3} - 192 \, a^{9} b^{5} c^{3} - 16 \, a^{8} b^{6} c^{3} + 1280 \, a^{11} b^{2} c^{4} + 512 \, a^{10} b^{3} c^{4} + 96 \, a^{9} b^{4} c^{4} - 1024 \, a^{12} c^{5} - 512 \, a^{11} b c^{5} - 256 \, a^{10} b^{2} c^{5} + 256 \, a^{11} c^{6}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} {\left| c \right|}} + \frac{3 \, {\left(10 \, a^{6} b^{14} c^{2} - 254 \, a^{7} b^{12} c^{3} + 2712 \, a^{8} b^{10} c^{4} - 15552 \, a^{9} b^{8} c^{5} + 50432 \, a^{10} b^{6} c^{6} - 87552 \, a^{11} b^{4} c^{7} + 63488 \, a^{12} b^{2} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{14} + 127 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{13} c - 1356 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - 214 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{12} c^{2} + 7776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 1856 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} + 107 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{10} c^{3} - 25216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 8128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{8} c^{4} + 43776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 17920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} + 4064 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} c^{5} - 31744 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 15872 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} - 8960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c^{6} + 7936 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{7} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{12} c^{2} + 214 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{10} c^{3} - 1856 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{8} c^{4} + 8128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{6} c^{5} - 17920 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{4} c^{6} + 15872 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{2} c^{7} + {\left(10 \, b^{6} c^{2} - 114 \, a b^{4} c^{3} + 416 \, a^{2} b^{2} c^{4} - 480 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 57 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 37 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 120 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} - 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} - 102 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 10 \, a^{3} b^{11} c + 836 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + 164 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - 204 \, a^{4} b^{9} c^{2} - 3440 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 1016 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 82 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 1672 \, a^{5} b^{7} c^{3} + 7104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 2816 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 508 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 6880 \, a^{6} b^{5} c^{4} - 5888 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 2944 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 1408 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 14208 \, a^{7} b^{3} c^{5} + 1472 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 11776 \, a^{8} b c^{6} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c + 164 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} - 1016 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} + 2816 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} - 2944 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} - \sqrt{{\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right)}{64 \, {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c - 2 \, a^{7} b^{9} c + 160 \, a^{9} b^{6} c^{2} + 32 \, a^{8} b^{7} c^{2} + a^{7} b^{8} c^{2} - 640 \, a^{10} b^{4} c^{3} - 192 \, a^{9} b^{5} c^{3} - 16 \, a^{8} b^{6} c^{3} + 1280 \, a^{11} b^{2} c^{4} + 512 \, a^{10} b^{3} c^{4} + 96 \, a^{9} b^{4} c^{4} - 1024 \, a^{12} c^{5} - 512 \, a^{11} b c^{5} - 256 \, a^{10} b^{2} c^{5} + 256 \, a^{11} c^{6}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} {\left| c \right|}} - \frac{7 \, b^{4} c^{2} x^{7} - 47 \, a b^{2} c^{3} x^{7} + 52 \, a^{2} c^{4} x^{7} + 14 \, b^{5} c x^{5} - 99 \, a b^{3} c^{2} x^{5} + 136 \, a^{2} b c^{3} x^{5} + 7 \, b^{6} x^{3} - 43 \, a b^{4} c x^{3} + 25 \, a^{2} b^{2} c^{2} x^{3} + 68 \, a^{3} c^{3} x^{3} + 9 \, a b^{5} x - 66 \, a^{2} b^{3} c x + 108 \, a^{3} b c^{2} x}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}} - \frac{1}{a^{3} x}"," ",0,"-3/64*(10*a^6*b^14*c^2 - 254*a^7*b^12*c^3 + 2712*a^8*b^10*c^4 - 15552*a^9*b^8*c^5 + 50432*a^10*b^6*c^6 - 87552*a^11*b^4*c^7 + 63488*a^12*b^2*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^14 + 127*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^13*c - 1356*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - 214*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^12*c^2 + 7776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 1856*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 + 107*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^10*c^3 - 25216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 8128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^8*c^4 + 43776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 17920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 + 4064*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^6*c^5 - 31744*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 15872*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 - 8960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c^6 + 7936*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^7 - 10*(b^2 - 4*a*c)*a^6*b^12*c^2 + 214*(b^2 - 4*a*c)*a^7*b^10*c^3 - 1856*(b^2 - 4*a*c)*a^8*b^8*c^4 + 8128*(b^2 - 4*a*c)*a^9*b^6*c^5 - 17920*(b^2 - 4*a*c)*a^10*b^4*c^6 + 15872*(b^2 - 4*a*c)*a^11*b^2*c^7 + (10*b^6*c^2 - 114*a*b^4*c^3 + 416*a^2*b^2*c^4 - 480*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 57*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 37*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 74*(b^2 - 4*a*c)*a*b^2*c^3 - 120*(b^2 - 4*a*c)*a^2*c^4)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2 + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^11 - 102*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c - 10*a^3*b^11*c + 836*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + 164*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 + 204*a^4*b^9*c^2 - 3440*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 1016*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 82*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 - 1672*a^5*b^7*c^3 + 7104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 2816*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 508*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 + 6880*a^6*b^5*c^4 - 5888*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 2944*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 1408*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 - 14208*a^7*b^3*c^5 + 1472*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 + 11776*a^8*b*c^6 + 10*(b^2 - 4*a*c)*a^3*b^9*c - 164*(b^2 - 4*a*c)*a^4*b^7*c^2 + 1016*(b^2 - 4*a*c)*a^5*b^5*c^3 - 2816*(b^2 - 4*a*c)*a^6*b^3*c^4 + 2944*(b^2 - 4*a*c)*a^7*b*c^5)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2))*arctan(2*sqrt(1/2)*x/sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)^2 - 4*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/((a^7*b^10 - 20*a^8*b^8*c - 2*a^7*b^9*c + 160*a^9*b^6*c^2 + 32*a^8*b^7*c^2 + a^7*b^8*c^2 - 640*a^10*b^4*c^3 - 192*a^9*b^5*c^3 - 16*a^8*b^6*c^3 + 1280*a^11*b^2*c^4 + 512*a^10*b^3*c^4 + 96*a^9*b^4*c^4 - 1024*a^12*c^5 - 512*a^11*b*c^5 - 256*a^10*b^2*c^5 + 256*a^11*c^6)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*abs(c)) + 3/64*(10*a^6*b^14*c^2 - 254*a^7*b^12*c^3 + 2712*a^8*b^10*c^4 - 15552*a^9*b^8*c^5 + 50432*a^10*b^6*c^6 - 87552*a^11*b^4*c^7 + 63488*a^12*b^2*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^14 + 127*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^13*c - 1356*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - 214*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^12*c^2 + 7776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 1856*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 + 107*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^10*c^3 - 25216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 8128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^8*c^4 + 43776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 17920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 + 4064*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^6*c^5 - 31744*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 15872*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 - 8960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c^6 + 7936*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^7 - 10*(b^2 - 4*a*c)*a^6*b^12*c^2 + 214*(b^2 - 4*a*c)*a^7*b^10*c^3 - 1856*(b^2 - 4*a*c)*a^8*b^8*c^4 + 8128*(b^2 - 4*a*c)*a^9*b^6*c^5 - 17920*(b^2 - 4*a*c)*a^10*b^4*c^6 + 15872*(b^2 - 4*a*c)*a^11*b^2*c^7 + (10*b^6*c^2 - 114*a*b^4*c^3 + 416*a^2*b^2*c^4 - 480*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 57*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 37*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 74*(b^2 - 4*a*c)*a*b^2*c^3 - 120*(b^2 - 4*a*c)*a^2*c^4)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2 - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^11 - 102*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 10*a^3*b^11*c + 836*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + 164*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - 204*a^4*b^9*c^2 - 3440*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 1016*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 82*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 1672*a^5*b^7*c^3 + 7104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 2816*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 508*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 6880*a^6*b^5*c^4 - 5888*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 2944*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 1408*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 14208*a^7*b^3*c^5 + 1472*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 11776*a^8*b*c^6 - 10*(b^2 - 4*a*c)*a^3*b^9*c + 164*(b^2 - 4*a*c)*a^4*b^7*c^2 - 1016*(b^2 - 4*a*c)*a^5*b^5*c^3 + 2816*(b^2 - 4*a*c)*a^6*b^3*c^4 - 2944*(b^2 - 4*a*c)*a^7*b*c^5)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2))*arctan(2*sqrt(1/2)*x/sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 - sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)^2 - 4*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/((a^7*b^10 - 20*a^8*b^8*c - 2*a^7*b^9*c + 160*a^9*b^6*c^2 + 32*a^8*b^7*c^2 + a^7*b^8*c^2 - 640*a^10*b^4*c^3 - 192*a^9*b^5*c^3 - 16*a^8*b^6*c^3 + 1280*a^11*b^2*c^4 + 512*a^10*b^3*c^4 + 96*a^9*b^4*c^4 - 1024*a^12*c^5 - 512*a^11*b*c^5 - 256*a^10*b^2*c^5 + 256*a^11*c^6)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*abs(c)) - 1/8*(7*b^4*c^2*x^7 - 47*a*b^2*c^3*x^7 + 52*a^2*c^4*x^7 + 14*b^5*c*x^5 - 99*a*b^3*c^2*x^5 + 136*a^2*b*c^3*x^5 + 7*b^6*x^3 - 43*a*b^4*c*x^3 + 25*a^2*b^2*c^2*x^3 + 68*a^3*c^3*x^3 + 9*a*b^5*x - 66*a^2*b^3*c*x + 108*a^3*b*c^2*x)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(c*x^4 + b*x^2 + a)^2) - 1/(a^3*x)","B",0
888,1,78,0,0.532815," ","integrate(x^5/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{x^{2}}{2 \, c} + \frac{b \log\left(c x^{4} - b x^{2} + a\right)}{4 \, c^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{2} - b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"1/2*x^2/c + 1/4*b*log(c*x^4 - b*x^2 + a)/c^2 + 1/2*(b^2 - 2*a*c)*arctan((2*c*x^2 - b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
889,1,62,0,0.566497," ","integrate(x^3/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{2 \, c x^{2} - b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c} + \frac{\log\left(c x^{4} - b x^{2} + a\right)}{4 \, c}"," ",0,"1/2*b*arctan((2*c*x^2 - b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c) + 1/4*log(c*x^4 - b*x^2 + a)/c","A",0
890,1,37,0,0.572767," ","integrate(x/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{2 \, c x^{2} - b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"arctan((2*c*x^2 - b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
891,1,71,0,0.569192," ","integrate(1/x/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{2 \, c x^{2} - b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a} - \frac{\log\left(c x^{4} - b x^{2} + a\right)}{4 \, a} + \frac{\log\left(x^{2}\right)}{2 \, a}"," ",0,"1/2*b*arctan((2*c*x^2 - b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a) - 1/4*log(c*x^4 - b*x^2 + a)/a + 1/2*log(x^2)/a","A",0
892,1,95,0,0.588303," ","integrate(1/x^3/(c*x^4-b*x^2+a),x, algorithm=""giac"")","-\frac{b \log\left(c x^{4} - b x^{2} + a\right)}{4 \, a^{2}} + \frac{b \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{{\left(b^{2} - 2 \, a c\right)} \arctan\left(\frac{2 \, c x^{2} - b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a^{2}} - \frac{b x^{2} + a}{2 \, a^{2} x^{2}}"," ",0,"-1/4*b*log(c*x^4 - b*x^2 + a)/a^2 + 1/2*b*log(x^2)/a^2 + 1/2*(b^2 - 2*a*c)*arctan((2*c*x^2 - b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) - 1/2*(b*x^2 + a)/(a^2*x^2)","A",0
893,1,2153,0,0.984362," ","integrate(x^4/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{x}{c} + \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} - 2 \, {\left(\sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 8 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} - 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}} - \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} + 2 \, {\left(\sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 8 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} - 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}}"," ",0,"x/c + 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2 - 2*(sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 2*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 8*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 32*a^3*c^5 + 2*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt(-(b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 + 2*a*b^3*c^4 + 16*a^3*c^5 - 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2 + 2*(sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 2*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 8*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 32*a^3*c^5 - 2*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c))*arctan(2*sqrt(1/2)*x/sqrt(-(b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 + 2*a*b^3*c^4 + 16*a^3*c^5 - 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2)","B",0
894,1,513,0,1.063223," ","integrate(x^2/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{{\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 2 \, b^{3} c + 16 \, a^{2} c^{2} - 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} {\left| c \right|}} - \frac{{\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 2 \, b^{3} c + 16 \, a^{2} c^{2} - 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} {\left| c \right|}}"," ",0,"1/2*(2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*arctan(2*sqrt(1/2)*x/sqrt(-(b + sqrt(b^2 - 4*a*c))/c))/((b^4 - 8*a*b^2*c + 2*b^3*c + 16*a^2*c^2 - 8*a*b*c^2 + b^2*c^2 - 4*a*c^3)*abs(c)) - 1/2*(2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*arctan(2*sqrt(1/2)*x/sqrt(-(b - sqrt(b^2 - 4*a*c))/c))/((b^4 - 8*a*b^2*c + 2*b^3*c + 16*a^2*c^2 - 8*a*b*c^2 + b^2*c^2 - 4*a*c^3)*abs(c))","B",0
895,1,1050,0,0.566681," ","integrate(1/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 2 \, a b^{3} c + 16 \, a^{3} c^{2} - 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left(\sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 2 \, a b^{3} c + 16 \, a^{3} c^{2} - 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"1/4*(sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 + 2*b^3*c^2 - 4*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x/sqrt(-(b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c + 2*a*b^3*c + 16*a^3*c^2 - 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/4*(sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x/sqrt(-(b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c + 2*a*b^3*c + 16*a^3*c^2 - 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
896,1,1877,0,1.014028," ","integrate(1/x^2/(c*x^4-b*x^2+a),x, algorithm=""giac"")","\frac{{\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + {\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} a^{2} + 2 \, {\left(\sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{a b + \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} - 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| a \right|} {\left| c \right|}} - \frac{{\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + {\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} a^{2} - 2 \, {\left(\sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-\frac{a b - \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} - 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| a \right|} {\left| c \right|}} - \frac{1}{a x}"," ",0,"1/8*(2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 + (2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*a^2 + 2*(sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*a*b^5*c + 16*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 8*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(-b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(a))*arctan(2*sqrt(1/2)*x/sqrt(-(a*b + sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4 - 8*a^4*b^2*c + 2*a^3*b^3*c + 16*a^5*c^2 - 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(a)*abs(c)) - 1/8*(2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 + (2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*a^2 - 2*(sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*a*b^5*c + 16*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 8*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(-b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(a))*arctan(2*sqrt(1/2)*x/sqrt(-(a*b - sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4 - 8*a^4*b^2*c + 2*a^3*b^3*c + 16*a^5*c^2 - 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(a)*abs(c)) - 1/(a*x)","B",0
897,1,60,0,0.260492," ","integrate(x^5/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","\frac{x^{2}}{2 \, a} + \frac{{\left(a + b\right)} \arctan\left(\frac{a x^{2} + a}{\sqrt{-a b}}\right)}{2 \, \sqrt{-a b} a} - \frac{\log\left(a x^{4} + 2 \, a x^{2} + a - b\right)}{2 \, a}"," ",0,"1/2*x^2/a + 1/2*(a + b)*arctan((a*x^2 + a)/sqrt(-a*b))/(sqrt(-a*b)*a) - 1/2*log(a*x^4 + 2*a*x^2 + a - b)/a","A",0
898,1,46,0,0.259800," ","integrate(x^3/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{a x^{2} + a}{\sqrt{-a b}}\right)}{2 \, \sqrt{-a b}} + \frac{\log\left(a x^{4} + 2 \, a x^{2} + a - b\right)}{4 \, a}"," ",0,"-1/2*arctan((a*x^2 + a)/sqrt(-a*b))/sqrt(-a*b) + 1/4*log(a*x^4 + 2*a*x^2 + a - b)/a","A",0
899,1,23,0,0.262335," ","integrate(x/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","\frac{\arctan\left(\frac{a x^{2} + a}{\sqrt{-a b}}\right)}{2 \, \sqrt{-a b}}"," ",0,"1/2*arctan((a*x^2 + a)/sqrt(-a*b))/sqrt(-a*b)","A",0
900,1,71,0,0.328476," ","integrate(1/x/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{a x^{2} + a}{\sqrt{-a b}}\right)}{2 \, \sqrt{-a b} {\left(a - b\right)}} - \frac{\log\left(a x^{4} + 2 \, a x^{2} + a - b\right)}{4 \, {\left(a - b\right)}} + \frac{\log\left(x^{2}\right)}{2 \, {\left(a - b\right)}}"," ",0,"-1/2*a*arctan((a*x^2 + a)/sqrt(-a*b))/(sqrt(-a*b)*(a - b)) - 1/4*log(a*x^4 + 2*a*x^2 + a - b)/(a - b) + 1/2*log(x^2)/(a - b)","A",0
901,1,126,0,0.281925," ","integrate(1/x^3/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","\frac{a \log\left(a x^{4} + 2 \, a x^{2} + a - b\right)}{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)}} - \frac{a \log\left(x^{2}\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(a^{2} + a b\right)} \arctan\left(\frac{a x^{2} + a}{\sqrt{-a b}}\right)}{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{-a b}} + \frac{2 \, a x^{2} - a + b}{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} x^{2}}"," ",0,"1/2*a*log(a*x^4 + 2*a*x^2 + a - b)/(a^2 - 2*a*b + b^2) - a*log(x^2)/(a^2 - 2*a*b + b^2) + 1/2*(a^2 + a*b)*arctan((a*x^2 + a)/sqrt(-a*b))/((a^2 - 2*a*b + b^2)*sqrt(-a*b)) + 1/2*(2*a*x^2 - a + b)/((a^2 - 2*a*b + b^2)*x^2)","A",0
902,1,511,0,0.356817," ","integrate(x^4/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","-\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{4} - \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{3} b - 4 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{2} b^{2} - 2 \, {\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a b - 4 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} b^{2}\right)} a^{2} + {\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} a^{3} b - 7 \, \sqrt{a^{2} + \sqrt{a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} + \sqrt{a b} a} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{x}{\sqrt{\frac{a^{2} + \sqrt{a^{4} - {\left(a^{2} - a b\right)} a^{2}}}{a^{2}}}}\right)}{2 \, {\left(3 \, a^{6} b - 7 \, a^{5} b^{2} + 4 \, a^{4} b^{3}\right)}} + \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{4} - \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{3} b - 4 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{2} b^{2} - 2 \, {\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a b - 4 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} b^{2}\right)} a^{2} - {\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} a^{3} b - 7 \, \sqrt{a^{2} - \sqrt{a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} - \sqrt{a b} a} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{x}{\sqrt{\frac{a^{2} - \sqrt{a^{4} - {\left(a^{2} - a b\right)} a^{2}}}{a^{2}}}}\right)}{2 \, {\left(3 \, a^{6} b - 7 \, a^{5} b^{2} + 4 \, a^{4} b^{3}\right)}} + \frac{x}{a}"," ",0,"-1/2*(3*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a^4 - sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a^3*b - 4*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a^2*b^2 - 2*(3*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a*b - 4*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*b^2)*a^2 + (3*sqrt(a^2 + sqrt(a*b)*a)*a^3*b - 7*sqrt(a^2 + sqrt(a*b)*a)*a^2*b^2 + 4*sqrt(a^2 + sqrt(a*b)*a)*a*b^3)*abs(a))*arctan(x/sqrt((a^2 + sqrt(a^4 - (a^2 - a*b)*a^2))/a^2))/(3*a^6*b - 7*a^5*b^2 + 4*a^4*b^3) + 1/2*(3*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a^4 - sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a^3*b - 4*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a^2*b^2 - 2*(3*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a*b - 4*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*b^2)*a^2 - (3*sqrt(a^2 - sqrt(a*b)*a)*a^3*b - 7*sqrt(a^2 - sqrt(a*b)*a)*a^2*b^2 + 4*sqrt(a^2 - sqrt(a*b)*a)*a*b^3)*abs(a))*arctan(x/sqrt((a^2 - sqrt(a^4 - (a^2 - a*b)*a^2))/a^2))/(3*a^6*b - 7*a^5*b^2 + 4*a^4*b^3) + x/a","B",0
903,1,199,0,0.359962," ","integrate(x^2/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a - 4 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a - b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{4} b - 4 \, a^{3} b^{2}\right)}} - \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a - 4 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a - b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{4} b - 4 \, a^{3} b^{2}\right)}}"," ",0,"1/2*(3*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a - 4*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a + sqrt(-4*(a - b)*a + 4*a^2))/a))/(3*a^4*b - 4*a^3*b^2) - 1/2*(3*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a - 4*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a - sqrt(-4*(a - b)*a + 4*a^2))/a))/(3*a^4*b - 4*a^3*b^2)","B",0
904,1,299,0,0.246622," ","integrate(1/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} a^{2} b - 4 \, \sqrt{a^{2} + \sqrt{a b} a} a b^{2} - 3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{2} + 4 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a - b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{5} b - 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}\right)}} + \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} a^{2} b - 4 \, \sqrt{a^{2} - \sqrt{a b} a} a b^{2} + 3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{2} - 4 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a - b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{5} b - 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}\right)}}"," ",0,"1/2*(3*sqrt(a^2 + sqrt(a*b)*a)*a^2*b - 4*sqrt(a^2 + sqrt(a*b)*a)*a*b^2 - 3*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a^2 + 4*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a + sqrt(-4*(a - b)*a + 4*a^2))/a))/(3*a^5*b - 7*a^4*b^2 + 4*a^3*b^3) + 1/2*(3*sqrt(a^2 - sqrt(a*b)*a)*a^2*b - 4*sqrt(a^2 - sqrt(a*b)*a)*a*b^2 + 3*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a^2 - 4*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a - sqrt(-4*(a - b)*a + 4*a^2))/a))/(3*a^5*b - 7*a^4*b^2 + 4*a^3*b^3)","B",0
905,1,698,0,0.383740," ","integrate(1/x^2/(a*x^4+2*a*x^2+a-b),x, algorithm=""giac"")","\frac{{\left({\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a b - 4 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} b^{2}\right)} {\left(a - b\right)}^{2} {\left| a \right|} - 2 \, {\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} a^{3} b - 7 \, \sqrt{a^{2} + \sqrt{a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} + \sqrt{a b} a} a b^{3}\right)} {\left| a - b \right|} {\left| a \right|} + {\left(3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{4} - 10 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{3} b + 11 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{2} b^{2} - 4 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{x}{\sqrt{\frac{a^{2} - a b + \sqrt{{\left(a^{2} - a b\right)}^{2} - {\left(a^{2} - a b\right)} {\left(a^{2} - 2 \, a b + b^{2}\right)}}}{a^{2} - a b}}}\right)}{2 \, {\left(3 \, a^{6} b - 13 \, a^{5} b^{2} + 21 \, a^{4} b^{3} - 15 \, a^{3} b^{4} + 4 \, a^{2} b^{5}\right)} {\left| a - b \right|}} - \frac{{\left({\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a b - 4 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} b^{2}\right)} {\left(a - b\right)}^{2} {\left| a \right|} + 2 \, {\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} a^{3} b - 7 \, \sqrt{a^{2} - \sqrt{a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} - \sqrt{a b} a} a b^{3}\right)} {\left| a - b \right|} {\left| a \right|} + {\left(3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{4} - 10 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{3} b + 11 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{2} b^{2} - 4 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{x}{\sqrt{\frac{a^{2} - a b - \sqrt{{\left(a^{2} - a b\right)}^{2} - {\left(a^{2} - a b\right)} {\left(a^{2} - 2 \, a b + b^{2}\right)}}}{a^{2} - a b}}}\right)}{2 \, {\left(3 \, a^{6} b - 13 \, a^{5} b^{2} + 21 \, a^{4} b^{3} - 15 \, a^{3} b^{4} + 4 \, a^{2} b^{5}\right)} {\left| a - b \right|}} - \frac{1}{{\left(a - b\right)} x}"," ",0,"1/2*((3*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a*b - 4*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*b^2)*(a - b)^2*abs(a) - 2*(3*sqrt(a^2 + sqrt(a*b)*a)*a^3*b - 7*sqrt(a^2 + sqrt(a*b)*a)*a^2*b^2 + 4*sqrt(a^2 + sqrt(a*b)*a)*a*b^3)*abs(a - b)*abs(a) + (3*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a^4 - 10*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a^3*b + 11*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a^2*b^2 - 4*sqrt(a^2 + sqrt(a*b)*a)*sqrt(a*b)*a*b^3)*abs(a))*arctan(x/sqrt((a^2 - a*b + sqrt((a^2 - a*b)^2 - (a^2 - a*b)*(a^2 - 2*a*b + b^2)))/(a^2 - a*b)))/((3*a^6*b - 13*a^5*b^2 + 21*a^4*b^3 - 15*a^3*b^4 + 4*a^2*b^5)*abs(a - b)) - 1/2*((3*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a*b - 4*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*b^2)*(a - b)^2*abs(a) + 2*(3*sqrt(a^2 - sqrt(a*b)*a)*a^3*b - 7*sqrt(a^2 - sqrt(a*b)*a)*a^2*b^2 + 4*sqrt(a^2 - sqrt(a*b)*a)*a*b^3)*abs(a - b)*abs(a) + (3*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a^4 - 10*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a^3*b + 11*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a^2*b^2 - 4*sqrt(a^2 - sqrt(a*b)*a)*sqrt(a*b)*a*b^3)*abs(a))*arctan(x/sqrt((a^2 - a*b - sqrt((a^2 - a*b)^2 - (a^2 - a*b)*(a^2 - 2*a*b + b^2)))/(a^2 - a*b)))/((3*a^6*b - 13*a^5*b^2 + 21*a^4*b^3 - 15*a^3*b^4 + 4*a^2*b^5)*abs(a - b)) - 1/((a - b)*x)","B",0
906,1,58,0,0.247922," ","integrate(x^5/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","\frac{x^{2}}{2 \, a} + \frac{{\left(a - b\right)} \arctan\left(\frac{a x^{2} + a}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a} - \frac{\log\left(a x^{4} + 2 \, a x^{2} + a + b\right)}{2 \, a}"," ",0,"1/2*x^2/a + 1/2*(a - b)*arctan((a*x^2 + a)/sqrt(a*b))/(sqrt(a*b)*a) - 1/2*log(a*x^4 + 2*a*x^2 + a + b)/a","A",0
907,1,42,0,0.229833," ","integrate(x^3/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{a x^{2} + a}{\sqrt{a b}}\right)}{2 \, \sqrt{a b}} + \frac{\log\left(a x^{4} + 2 \, a x^{2} + a + b\right)}{4 \, a}"," ",0,"-1/2*arctan((a*x^2 + a)/sqrt(a*b))/sqrt(a*b) + 1/4*log(a*x^4 + 2*a*x^2 + a + b)/a","A",0
908,1,21,0,0.240582," ","integrate(x/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","\frac{\arctan\left(\frac{a x^{2} + a}{\sqrt{a b}}\right)}{2 \, \sqrt{a b}}"," ",0,"1/2*arctan((a*x^2 + a)/sqrt(a*b))/sqrt(a*b)","A",0
909,1,61,0,0.234043," ","integrate(1/x/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{a x^{2} + a}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} {\left(a + b\right)}} - \frac{\log\left(a x^{4} + 2 \, a x^{2} + a + b\right)}{4 \, {\left(a + b\right)}} + \frac{\log\left(x^{2}\right)}{2 \, {\left(a + b\right)}}"," ",0,"-1/2*a*arctan((a*x^2 + a)/sqrt(a*b))/(sqrt(a*b)*(a + b)) - 1/4*log(a*x^4 + 2*a*x^2 + a + b)/(a + b) + 1/2*log(x^2)/(a + b)","A",0
910,1,125,0,0.276952," ","integrate(1/x^3/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","\frac{a \log\left(a x^{4} + 2 \, a x^{2} + a + b\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{a \log\left(x^{2}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{{\left(a^{2} - a b\right)} \arctan\left(\frac{a x^{2} + a}{\sqrt{a b}}\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b}} + \frac{2 \, a x^{2} - a - b}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} x^{2}}"," ",0,"1/2*a*log(a*x^4 + 2*a*x^2 + a + b)/(a^2 + 2*a*b + b^2) - a*log(x^2)/(a^2 + 2*a*b + b^2) + 1/2*(a^2 - a*b)*arctan((a*x^2 + a)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)) + 1/2*(2*a*x^2 - a - b)/((a^2 + 2*a*b + b^2)*x^2)","A",0
911,1,533,0,0.345719," ","integrate(x^4/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{4} + \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{3} b - 4 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{2} b^{2} + 2 \, {\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a b + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} b^{2}\right)} a^{2} - {\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} a^{3} b + 7 \, \sqrt{a^{2} + \sqrt{-a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{x}{\sqrt{\frac{a^{2} + \sqrt{a^{4} - {\left(a^{2} + a b\right)} a^{2}}}{a^{2}}}}\right)}{2 \, {\left(3 \, a^{6} b + 7 \, a^{5} b^{2} + 4 \, a^{4} b^{3}\right)}} - \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{4} + \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{3} b - 4 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{2} b^{2} + 2 \, {\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a b + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} b^{2}\right)} a^{2} + {\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} a^{3} b + 7 \, \sqrt{a^{2} - \sqrt{-a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{x}{\sqrt{\frac{a^{2} - \sqrt{a^{4} - {\left(a^{2} + a b\right)} a^{2}}}{a^{2}}}}\right)}{2 \, {\left(3 \, a^{6} b + 7 \, a^{5} b^{2} + 4 \, a^{4} b^{3}\right)}} + \frac{x}{a}"," ",0,"1/2*(3*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a^4 + sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a^3*b - 4*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a^2*b^2 + 2*(3*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a*b + 4*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*b^2)*a^2 - (3*sqrt(a^2 + sqrt(-a*b)*a)*a^3*b + 7*sqrt(a^2 + sqrt(-a*b)*a)*a^2*b^2 + 4*sqrt(a^2 + sqrt(-a*b)*a)*a*b^3)*abs(a))*arctan(x/sqrt((a^2 + sqrt(a^4 - (a^2 + a*b)*a^2))/a^2))/(3*a^6*b + 7*a^5*b^2 + 4*a^4*b^3) - 1/2*(3*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a^4 + sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a^3*b - 4*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a^2*b^2 + 2*(3*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a*b + 4*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*b^2)*a^2 + (3*sqrt(a^2 - sqrt(-a*b)*a)*a^3*b + 7*sqrt(a^2 - sqrt(-a*b)*a)*a^2*b^2 + 4*sqrt(a^2 - sqrt(-a*b)*a)*a*b^3)*abs(a))*arctan(x/sqrt((a^2 - sqrt(a^4 - (a^2 + a*b)*a^2))/a^2))/(3*a^6*b + 7*a^5*b^2 + 4*a^4*b^3) + x/a","A",0
912,1,203,0,0.343094," ","integrate(x^2/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","-\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{4} b + 4 \, a^{3} b^{2}\right)}} + \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{4} b + 4 \, a^{3} b^{2}\right)}}"," ",0,"-1/2*(3*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a + 4*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a + sqrt(-4*(a + b)*a + 4*a^2))/a))/(3*a^4*b + 4*a^3*b^2) + 1/2*(3*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a + 4*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a - sqrt(-4*(a + b)*a + 4*a^2))/a))/(3*a^4*b + 4*a^3*b^2)","A",0
913,1,307,0,0.248738," ","integrate(1/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} a^{2} b + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} a b^{2} + 3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{2} + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}\right)}} + \frac{{\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} a^{2} b + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} a b^{2} - 3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{2} - 4 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a b\right)} {\left| a \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} a + 4 \, a^{2}}}{a}}}\right)}{2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}\right)}}"," ",0,"1/2*(3*sqrt(a^2 + sqrt(-a*b)*a)*a^2*b + 4*sqrt(a^2 + sqrt(-a*b)*a)*a*b^2 + 3*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a^2 + 4*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a + sqrt(-4*(a + b)*a + 4*a^2))/a))/(3*a^5*b + 7*a^4*b^2 + 4*a^3*b^3) + 1/2*(3*sqrt(a^2 - sqrt(-a*b)*a)*a^2*b + 4*sqrt(a^2 - sqrt(-a*b)*a)*a*b^2 - 3*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a^2 - 4*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a*b)*abs(a)*arctan(2*sqrt(1/2)*x/sqrt((2*a - sqrt(-4*(a + b)*a + 4*a^2))/a))/(3*a^5*b + 7*a^4*b^2 + 4*a^3*b^3)","A",0
914,1,742,0,0.375388," ","integrate(1/x^2/(a*x^4+2*a*x^2+a+b),x, algorithm=""giac"")","\frac{{\left({\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a b + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} b^{2}\right)} {\left(a + b\right)}^{2} {\left| a \right|} - 2 \, {\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} a^{3} b + 7 \, \sqrt{a^{2} - \sqrt{-a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} a b^{3}\right)} {\left| a \right|} {\left| -a - b \right|} - {\left(3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{4} + 10 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{3} b + 11 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{2} b^{2} + 4 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a^{2} + 2 \, a b + \sqrt{-4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(a^{2} + a b\right)} + 4 \, {\left(a^{2} + a b\right)}^{2}}}{a^{2} + a b}}}\right)}{2 \, {\left(3 \, a^{6} b + 13 \, a^{5} b^{2} + 21 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 4 \, a^{2} b^{5}\right)} {\left| -a - b \right|}} - \frac{{\left({\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a b + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} b^{2}\right)} {\left(a + b\right)}^{2} {\left| a \right|} + 2 \, {\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} a^{3} b + 7 \, \sqrt{a^{2} + \sqrt{-a b} a} a^{2} b^{2} + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} a b^{3}\right)} {\left| a \right|} {\left| -a - b \right|} - {\left(3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{4} + 10 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{3} b + 11 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{2} b^{2} + 4 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a b^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{2 \, a^{2} + 2 \, a b - \sqrt{-4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} {\left(a^{2} + a b\right)} + 4 \, {\left(a^{2} + a b\right)}^{2}}}{a^{2} + a b}}}\right)}{2 \, {\left(3 \, a^{6} b + 13 \, a^{5} b^{2} + 21 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 4 \, a^{2} b^{5}\right)} {\left| -a - b \right|}} - \frac{1}{{\left(a + b\right)} x}"," ",0,"1/2*((3*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a*b + 4*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*b^2)*(a + b)^2*abs(a) - 2*(3*sqrt(a^2 - sqrt(-a*b)*a)*a^3*b + 7*sqrt(a^2 - sqrt(-a*b)*a)*a^2*b^2 + 4*sqrt(a^2 - sqrt(-a*b)*a)*a*b^3)*abs(a)*abs(-a - b) - (3*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a^4 + 10*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a^3*b + 11*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a^2*b^2 + 4*sqrt(a^2 - sqrt(-a*b)*a)*sqrt(-a*b)*a*b^3)*abs(a))*arctan(2*sqrt(1/2)*x/sqrt((2*a^2 + 2*a*b + sqrt(-4*(a^2 + 2*a*b + b^2)*(a^2 + a*b) + 4*(a^2 + a*b)^2))/(a^2 + a*b)))/((3*a^6*b + 13*a^5*b^2 + 21*a^4*b^3 + 15*a^3*b^4 + 4*a^2*b^5)*abs(-a - b)) - 1/2*((3*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a*b + 4*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*b^2)*(a + b)^2*abs(a) + 2*(3*sqrt(a^2 + sqrt(-a*b)*a)*a^3*b + 7*sqrt(a^2 + sqrt(-a*b)*a)*a^2*b^2 + 4*sqrt(a^2 + sqrt(-a*b)*a)*a*b^3)*abs(a)*abs(-a - b) - (3*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a^4 + 10*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a^3*b + 11*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a^2*b^2 + 4*sqrt(a^2 + sqrt(-a*b)*a)*sqrt(-a*b)*a*b^3)*abs(a))*arctan(2*sqrt(1/2)*x/sqrt((2*a^2 + 2*a*b - sqrt(-4*(a^2 + 2*a*b + b^2)*(a^2 + a*b) + 4*(a^2 + a*b)^2))/(a^2 + a*b)))/((3*a^6*b + 13*a^5*b^2 + 21*a^4*b^3 + 15*a^3*b^4 + 4*a^2*b^5)*abs(-a - b)) - 1/((a + b)*x)","B",0
915,1,18,0,0.150787," ","integrate(x/(x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1))","A",0
916,1,10,0,0.586442," ","integrate(x/(x^4+2*x^2+10),x, algorithm=""giac"")","\frac{1}{6} \, \arctan\left(\frac{1}{3} \, x^{2} + \frac{1}{3}\right)"," ",0,"1/6*arctan(1/3*x^2 + 1/3)","A",0
917,1,18,0,0.191650," ","integrate(x^2/(x^4+9*x^2+20),x, algorithm=""giac"")","\sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} x\right) - 2 \, \arctan\left(\frac{1}{2} \, x\right)"," ",0,"sqrt(5)*arctan(1/5*sqrt(5)*x) - 2*arctan(1/2*x)","A",0
918,1,56,0,0.171546," ","integrate(x^2/(x^4-x^2+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{2} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{2} \, \arctan\left(2 \, x - \sqrt{3}\right)"," ",0,"-1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/2*arctan(2*x + sqrt(3)) + 1/2*arctan(2*x - sqrt(3))","A",0
919,1,147,0,0.848986," ","integrate(x^2/(x^4-2*x^2+2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x + 2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2 \, x - 2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2 \, \sqrt{2} - 2} \log\left(x^{2} + 2^{\frac{1}{4}} x \sqrt{\sqrt{2} + 2} + \sqrt{2}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{2} - 2} \log\left(x^{2} - 2^{\frac{1}{4}} x \sqrt{\sqrt{2} + 2} + \sqrt{2}\right)"," ",0,"1/4*sqrt(2*sqrt(2) + 2)*arctan(1/2*2^(3/4)*(2*x + 2^(1/4)*sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/4*sqrt(2*sqrt(2) + 2)*arctan(1/2*2^(3/4)*(2*x - 2^(1/4)*sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(2*sqrt(2) - 2)*log(x^2 + 2^(1/4)*x*sqrt(sqrt(2) + 2) + sqrt(2)) + 1/8*sqrt(2*sqrt(2) - 2)*log(x^2 - 2^(1/4)*x*sqrt(sqrt(2) + 2) + sqrt(2))","A",0
920,1,172,0,0.250283," ","integrate(x^7*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{3840} \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{7 \, b^{2} c^{2} - 16 \, a c^{3}}{c^{4}}\right)} x^{2} + \frac{35 \, b^{3} c - 116 \, a b c^{2}}{c^{4}}\right)} x^{2} - \frac{105 \, b^{4} - 460 \, a b^{2} c + 256 \, a^{2} c^{2}}{c^{4}}\right)} - \frac{{\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{512 \, c^{\frac{9}{2}}}"," ",0,"1/3840*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*(8*x^2 + b/c)*x^2 - (7*b^2*c^2 - 16*a*c^3)/c^4)*x^2 + (35*b^3*c - 116*a*b*c^2)/c^4)*x^2 - (105*b^4 - 460*a*b^2*c + 256*a^2*c^2)/c^4) - 1/512*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(9/2)","A",0
921,1,134,0,0.231625," ","integrate(x^5*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{5 \, b^{2} c - 12 \, a c^{2}}{c^{3}}\right)} x^{2} + \frac{15 \, b^{3} - 52 \, a b c}{c^{3}}\right)} + \frac{{\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/384*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*x^2 + b/c)*x^2 - (5*b^2*c - 12*a*c^2)/c^3)*x^2 + (15*b^3 - 52*a*b*c)/c^3) + 1/256*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(7/2)","A",0
922,1,98,0,0.215113," ","integrate(x^3*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{3 \, b^{2} - 8 \, a c}{c^{2}}\right)} - \frac{{\left(b^{3} - 4 \, a b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{32 \, c^{\frac{5}{2}}}"," ",0,"1/48*sqrt(c*x^4 + b*x^2 + a)*(2*(4*x^2 + b/c)*x^2 - (3*b^2 - 8*a*c)/c^2) - 1/32*(b^3 - 4*a*b*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(5/2)","A",0
923,1,76,0,0.204140," ","integrate(x*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, x^{2} + \frac{b}{c}\right)} + \frac{{\left(b^{2} - 4 \, a c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/8*sqrt(c*x^4 + b*x^2 + a)*(2*x^2 + b/c) + 1/16*(b^2 - 4*a*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(3/2)","A",0
924,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(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:index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
925,1,148,0,0.291667," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^3,x, algorithm=""giac"")","\frac{b \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}} - \frac{1}{2} \, \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right) + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} b + 2 \, a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}}"," ",0,"1/2*b*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/sqrt(-a) - 1/2*sqrt(c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b)) + 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*b + 2*a*sqrt(c))/((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)","A",0
926,1,241,0,0.224222," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{{\left(b^{2} - 4 \, a c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a} + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} b^{2} + 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a c + 8 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a b \sqrt{c} + {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a b^{2} + 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{2} c}{8 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{2} a}"," ",0,"-1/8*(b^2 - 4*a*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/8*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*b^2 + 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a*c + 8*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a*b*sqrt(c) + (sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a*b^2 + 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^2*c)/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^2*a)","B",0
927,1,359,0,0.301348," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^7,x, algorithm=""giac"")","\frac{{\left(b^{3} - 4 \, a b c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{16 \, \sqrt{-a} a^{2}} - \frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} b^{3} - 12 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a b c - 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} - 8 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a b^{3} - 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{2} b c - 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{2} b^{2} \sqrt{c} - 3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{2} b^{3} - 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{3} b c - 16 \, a^{4} c^{\frac{3}{2}}}{48 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{3} a^{2}}"," ",0,"1/16*(b^3 - 4*a*b*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) - 1/48*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*b^3 - 12*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a*b*c - 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^2*c^(3/2) - 8*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a*b^3 - 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^2*b*c - 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^2*b^2*sqrt(c) - 3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^2*b^3 - 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^3*b*c - 16*a^4*c^(3/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^3*a^2)","B",0
928,1,617,0,0.280791," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^9,x, algorithm=""giac"")","-\frac{{\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{128 \, \sqrt{-a} a^{3}} + \frac{15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} b^{4} - 72 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a b^{2} c + 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{2} c^{2} - 55 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a b^{4} + 264 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{2} b^{2} c + 336 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{3} c^{2} + 1152 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{3} b c^{\frac{3}{2}} + 73 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{2} b^{4} + 648 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{3} b^{2} c + 336 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{4} c^{2} + 384 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{3} b^{3} \sqrt{c} + 256 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{4} b c^{\frac{3}{2}} + 15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{3} b^{4} + 312 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{4} b^{2} c + 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{5} c^{2} + 128 \, a^{5} b c^{\frac{3}{2}}}{384 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{4} a^{3}}"," ",0,"-1/128*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^3) + 1/384*(15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*b^4 - 72*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a*b^2*c + 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^2*c^2 - 55*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a*b^4 + 264*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^2*b^2*c + 336*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^3*c^2 + 1152*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^3*b*c^(3/2) + 73*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^2*b^4 + 648*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^3*b^2*c + 336*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^4*c^2 + 384*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^3*b^3*sqrt(c) + 256*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^4*b*c^(3/2) + 15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^3*b^4 + 312*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^4*b^2*c + 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^5*c^2 + 128*a^5*b*c^(3/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^4*a^3)","B",0
929,1,842,0,0.356578," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^11,x, algorithm=""giac"")","\frac{{\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{256 \, \sqrt{-a} a^{4}} - \frac{105 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} b^{5} - 600 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a b^{3} c + 720 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a^{2} b c^{2} - 490 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a b^{5} + 2800 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{2} b^{3} c - 3360 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{3} b c^{2} - 7680 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{6} a^{4} c^{\frac{5}{2}} + 896 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{2} b^{5} - 5120 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{3} b^{3} c - 15360 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{4} b c^{2} - 24320 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{4} b^{2} c^{\frac{3}{2}} - 2560 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} - 790 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{3} b^{5} - 9200 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{4} b^{3} c - 12000 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{5} b c^{2} - 3840 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{4} b^{4} \sqrt{c} - 5120 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{5} b^{2} c^{\frac{3}{2}} - 2560 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{6} c^{\frac{5}{2}} - 105 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{4} b^{5} - 3240 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{5} b^{3} c - 720 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{6} b c^{2} - 1280 \, a^{6} b^{2} c^{\frac{3}{2}} + 512 \, a^{7} c^{\frac{5}{2}}}{3840 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{5} a^{4}}"," ",0,"1/256*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^4) - 1/3840*(105*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*b^5 - 600*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a*b^3*c + 720*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a^2*b*c^2 - 490*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a*b^5 + 2800*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^2*b^3*c - 3360*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^3*b*c^2 - 7680*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^6*a^4*c^(5/2) + 896*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^2*b^5 - 5120*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^3*b^3*c - 15360*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^4*b*c^2 - 24320*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^4*b^2*c^(3/2) - 2560*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^5*c^(5/2) - 790*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^3*b^5 - 9200*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^4*b^3*c - 12000*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^5*b*c^2 - 3840*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^4*b^4*sqrt(c) - 5120*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^5*b^2*c^(3/2) - 2560*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^6*c^(5/2) - 105*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^4*b^5 - 3240*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^5*b^3*c - 720*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^6*b*c^2 - 1280*a^6*b^2*c^(3/2) + 512*a^7*c^(5/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^5*a^4)","B",0
930,0,0,0,0.000000," ","integrate(x^4*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} x^{4}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*x^4, x)","F",0
931,0,0,0,0.000000," ","integrate(x^2*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} x^{2}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*x^2, x)","F",0
932,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a), x)","F",0
933,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2} + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)/x^2, x)","F",0
934,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2} + a}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)/x^4, x)","F",0
935,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2} + a}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)/x^6, x)","F",0
936,1,669,0,0.404681," ","integrate(x^7*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{7680} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{7 \, b^{2} c^{2} - 16 \, a c^{3}}{c^{4}}\right)} x^{2} + \frac{35 \, b^{3} c - 116 \, a b c^{2}}{c^{4}}\right)} x^{2} - \frac{105 \, b^{4} - 460 \, a b^{2} c + 256 \, a^{2} c^{2}}{c^{4}}\right)} - \frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{9}{2}}}\right)} a + \frac{1}{30720} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{9 \, b^{2} c^{3} - 20 \, a c^{4}}{c^{5}}\right)} x^{2} + \frac{21 \, b^{3} c^{2} - 68 \, a b c^{3}}{c^{5}}\right)} x^{2} - \frac{105 \, b^{4} c - 448 \, a b^{2} c^{2} + 240 \, a^{2} c^{3}}{c^{5}}\right)} x^{2} + \frac{315 \, b^{5} - 1680 \, a b^{3} c + 1808 \, a^{2} b c^{2}}{c^{5}}\right)} + \frac{15 \, {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{11}{2}}}\right)} b + \frac{1}{430080} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{11 \, b^{2} c^{4} - 24 \, a c^{5}}{c^{6}}\right)} x^{2} + \frac{99 \, b^{3} c^{3} - 316 \, a b c^{4}}{c^{6}}\right)} x^{2} - \frac{231 \, b^{4} c^{2} - 972 \, a b^{2} c^{3} + 512 \, a^{2} c^{4}}{c^{6}}\right)} x^{2} + \frac{1155 \, b^{5} c - 6048 \, a b^{3} c^{2} + 6352 \, a^{2} b c^{3}}{c^{6}}\right)} x^{2} - \frac{3465 \, b^{6} - 21840 \, a b^{4} c + 34608 \, a^{2} b^{2} c^{2} - 8192 \, a^{3} c^{3}}{c^{6}}\right)} - \frac{105 \, {\left(33 \, b^{7} - 252 \, a b^{5} c + 560 \, a^{2} b^{3} c^{2} - 320 \, a^{3} b c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{13}{2}}}\right)} c"," ",0,"1/7680*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*(8*x^2 + b/c)*x^2 - (7*b^2*c^2 - 16*a*c^3)/c^4)*x^2 + (35*b^3*c - 116*a*b*c^2)/c^4)*x^2 - (105*b^4 - 460*a*b^2*c + 256*a^2*c^2)/c^4) - 15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(9/2))*a + 1/30720*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(2*(8*(10*x^2 + b/c)*x^2 - (9*b^2*c^3 - 20*a*c^4)/c^5)*x^2 + (21*b^3*c^2 - 68*a*b*c^3)/c^5)*x^2 - (105*b^4*c - 448*a*b^2*c^2 + 240*a^2*c^3)/c^5)*x^2 + (315*b^5 - 1680*a*b^3*c + 1808*a^2*b*c^2)/c^5) + 15*(21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(11/2))*b + 1/430080*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(2*(8*(10*(12*x^2 + b/c)*x^2 - (11*b^2*c^4 - 24*a*c^5)/c^6)*x^2 + (99*b^3*c^3 - 316*a*b*c^4)/c^6)*x^2 - (231*b^4*c^2 - 972*a*b^2*c^3 + 512*a^2*c^4)/c^6)*x^2 + (1155*b^5*c - 6048*a*b^3*c^2 + 6352*a^2*b*c^3)/c^6)*x^2 - (3465*b^6 - 21840*a*b^4*c + 34608*a^2*b^2*c^2 - 8192*a^3*c^3)/c^6) - 105*(33*b^7 - 252*a*b^5*c + 560*a^2*b^3*c^2 - 320*a^3*b*c^3)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(13/2))*c","B",0
937,1,535,0,0.397309," ","integrate(x^5*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{768} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{5 \, b^{2} c - 12 \, a c^{2}}{c^{3}}\right)} x^{2} + \frac{15 \, b^{3} - 52 \, a b c}{c^{3}}\right)} + \frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{7}{2}}}\right)} a + \frac{1}{7680} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{7 \, b^{2} c^{2} - 16 \, a c^{3}}{c^{4}}\right)} x^{2} + \frac{35 \, b^{3} c - 116 \, a b c^{2}}{c^{4}}\right)} x^{2} - \frac{105 \, b^{4} - 460 \, a b^{2} c + 256 \, a^{2} c^{2}}{c^{4}}\right)} - \frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{9}{2}}}\right)} b + \frac{1}{30720} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{9 \, b^{2} c^{3} - 20 \, a c^{4}}{c^{5}}\right)} x^{2} + \frac{21 \, b^{3} c^{2} - 68 \, a b c^{3}}{c^{5}}\right)} x^{2} - \frac{105 \, b^{4} c - 448 \, a b^{2} c^{2} + 240 \, a^{2} c^{3}}{c^{5}}\right)} x^{2} + \frac{315 \, b^{5} - 1680 \, a b^{3} c + 1808 \, a^{2} b c^{2}}{c^{5}}\right)} + \frac{15 \, {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{11}{2}}}\right)} c"," ",0,"1/768*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*x^2 + b/c)*x^2 - (5*b^2*c - 12*a*c^2)/c^3)*x^2 + (15*b^3 - 52*a*b*c)/c^3) + 3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(7/2))*a + 1/7680*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*(8*x^2 + b/c)*x^2 - (7*b^2*c^2 - 16*a*c^3)/c^4)*x^2 + (35*b^3*c - 116*a*b*c^2)/c^4)*x^2 - (105*b^4 - 460*a*b^2*c + 256*a^2*c^2)/c^4) - 15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(9/2))*b + 1/30720*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(2*(8*(10*x^2 + b/c)*x^2 - (9*b^2*c^3 - 20*a*c^4)/c^5)*x^2 + (21*b^3*c^2 - 68*a*b*c^3)/c^5)*x^2 - (105*b^4*c - 448*a*b^2*c^2 + 240*a^2*c^3)/c^5)*x^2 + (315*b^5 - 1680*a*b^3*c + 1808*a^2*b*c^2)/c^5) + 15*(21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(11/2))*c","B",0
938,1,414,0,0.394361," ","integrate(x^3*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{3 \, b^{2} - 8 \, a c}{c^{2}}\right)} - \frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}}\right)} a + \frac{1}{768} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{5 \, b^{2} c - 12 \, a c^{2}}{c^{3}}\right)} x^{2} + \frac{15 \, b^{3} - 52 \, a b c}{c^{3}}\right)} + \frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{7}{2}}}\right)} b + \frac{1}{7680} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{7 \, b^{2} c^{2} - 16 \, a c^{3}}{c^{4}}\right)} x^{2} + \frac{35 \, b^{3} c - 116 \, a b c^{2}}{c^{4}}\right)} x^{2} - \frac{105 \, b^{4} - 460 \, a b^{2} c + 256 \, a^{2} c^{2}}{c^{4}}\right)} - \frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{9}{2}}}\right)} c"," ",0,"1/96*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*x^2 + b/c)*x^2 - (3*b^2 - 8*a*c)/c^2) - 3*(b^3 - 4*a*b*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(5/2))*a + 1/768*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*x^2 + b/c)*x^2 - (5*b^2*c - 12*a*c^2)/c^3)*x^2 + (15*b^3 - 52*a*b*c)/c^3) + 3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(7/2))*b + 1/7680*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*(8*x^2 + b/c)*x^2 - (7*b^2*c^2 - 16*a*c^3)/c^4)*x^2 + (35*b^3*c - 116*a*b*c^2)/c^4)*x^2 - (105*b^4 - 460*a*b^2*c + 256*a^2*c^2)/c^4) - 15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(9/2))*c","B",0
939,1,317,0,0.388942," ","integrate(x*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{16} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, x^{2} + \frac{b}{c}\right)} + \frac{{\left(b^{2} - 4 \, a c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}}\right)} a + \frac{1}{96} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{3 \, b^{2} - 8 \, a c}{c^{2}}\right)} - \frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}}\right)} b + \frac{1}{768} \, {\left(2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + \frac{b}{c}\right)} x^{2} - \frac{5 \, b^{2} c - 12 \, a c^{2}}{c^{3}}\right)} x^{2} + \frac{15 \, b^{3} - 52 \, a b c}{c^{3}}\right)} + \frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{7}{2}}}\right)} c"," ",0,"1/16*(2*sqrt(c*x^4 + b*x^2 + a)*(2*x^2 + b/c) + (b^2 - 4*a*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(3/2))*a + 1/96*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*x^2 + b/c)*x^2 - (3*b^2 - 8*a*c)/c^2) - 3*(b^3 - 4*a*b*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(5/2))*b + 1/768*(2*sqrt(c*x^4 + b*x^2 + a)*(2*(4*(6*x^2 + b/c)*x^2 - (5*b^2*c - 12*a*c^2)/c^3)*x^2 + (15*b^3 - 52*a*b*c)/c^3) + 3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(7/2))*c","B",0
940,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/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, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
941,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(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:Unable to divide, perhaps due to rounding error%%%{%%{[1,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0]%%%}+%%%{%%{[1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,0]%%%} / %%%{%%%{1,[1]%%%},[4,0,0]%%%}+%%%{%%%{-2,[1]%%%},[2,1,0]%%%}+%%%{%%%{1,[1]%%%},[0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
942,1,302,0,0.446358," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^5,x, algorithm=""giac"")","-\frac{3}{4} \, b \sqrt{c} \log\left({\left| 2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} + b \right|}\right) + \frac{1}{2} \, \sqrt{c x^{4} + b x^{2} + a} c + \frac{3 \, {\left(b^{2} + 4 \, a c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a}} + \frac{5 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} b^{2} + 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a c + 16 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a b \sqrt{c} - 3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a b^{2} + 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{2} c - 8 \, a^{2} b \sqrt{c}}{8 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{2}}"," ",0,"-3/4*b*sqrt(c)*log(abs(2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) + b)) + 1/2*sqrt(c*x^4 + b*x^2 + a)*c + 3/8*(b^2 + 4*a*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/sqrt(-a) + 1/8*(5*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*b^2 + 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a*c + 16*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a*b*sqrt(c) - 3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a*b^2 + 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^2*c - 8*a^2*b*sqrt(c))/((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^2","B",0
943,1,412,0,0.677331," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{1}{2} \, c^{\frac{3}{2}} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right) - \frac{{\left(b^{3} - 12 \, a b c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{16 \, \sqrt{-a} a} + \frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} b^{3} \sqrt{c} + 60 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a b c^{\frac{3}{2}} + 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a b^{2} c + 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{2} c^{2} + 8 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a b^{3} \sqrt{c} - 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{3} c^{2} - 3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{2} b^{3} \sqrt{c} + 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{3} b c^{\frac{3}{2}} + 64 \, a^{4} c^{2}}{48 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{3} a \sqrt{c}}"," ",0,"-1/2*c^(3/2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b)) - 1/16*(b^3 - 12*a*b*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/48*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*b^3*sqrt(c) + 60*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a*b*c^(3/2) + 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a*b^2*c + 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^2*c^2 + 8*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a*b^3*sqrt(c) - 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^3*c^2 - 3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^2*b^3*sqrt(c) + 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^3*b*c^(3/2) + 64*a^4*c^2)/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^3*a*sqrt(c))","B",0
944,1,606,0,0.494957," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^9,x, algorithm=""giac"")","\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{128 \, \sqrt{-a} a^{2}} - \frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} b^{4} - 24 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a b^{2} c - 80 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{2} c^{2} - 256 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{6} a^{2} b c^{\frac{3}{2}} - 11 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a b^{4} - 168 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{2} b^{2} c - 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{3} c^{2} - 128 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{2} b^{3} \sqrt{c} - 11 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{2} b^{4} - 168 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{3} b^{2} c - 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{4} c^{2} - 256 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{4} b c^{\frac{3}{2}} + 3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{3} b^{4} - 24 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{4} b^{2} c - 80 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{5} c^{2}}{128 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{4} a^{2}}"," ",0,"3/128*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) - 1/128*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*b^4 - 24*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a*b^2*c - 80*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^2*c^2 - 256*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^6*a^2*b*c^(3/2) - 11*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a*b^4 - 168*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^2*b^2*c - 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^3*c^2 - 128*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^2*b^3*sqrt(c) - 11*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^2*b^4 - 168*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^3*b^2*c - 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^4*c^2 - 256*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^4*b*c^(3/2) + 3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^3*b^4 - 24*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^4*b^2*c - 80*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^5*c^2)/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^4*a^2)","B",0
945,1,832,0,0.529728," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^11,x, algorithm=""giac"")","-\frac{3 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{256 \, \sqrt{-a} a^{3}} + \frac{15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} b^{5} - 120 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a b^{3} c + 240 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a^{2} b c^{2} + 1280 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} - 70 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a b^{5} + 560 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{2} b^{3} c + 2720 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{3} b c^{2} + 5120 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{6} a^{3} b^{2} c^{\frac{3}{2}} + 128 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{2} b^{5} + 2560 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{3} b^{3} c + 3840 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{4} b c^{2} + 1280 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{3} b^{4} \sqrt{c} + 2560 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{4} b^{2} c^{\frac{3}{2}} + 2560 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} + 70 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{3} b^{5} + 2000 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{4} b^{3} c + 2400 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{5} b c^{2} + 2560 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{5} b^{2} c^{\frac{3}{2}} - 15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{4} b^{5} + 120 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{5} b^{3} c + 1040 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{6} b c^{2} + 256 \, a^{7} c^{\frac{5}{2}}}{1280 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{5} a^{3}}"," ",0,"-3/256*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^3) + 1/1280*(15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*b^5 - 120*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a*b^3*c + 240*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a^2*b*c^2 + 1280*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^8*a^3*c^(5/2) - 70*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a*b^5 + 560*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^2*b^3*c + 2720*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^3*b*c^2 + 5120*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^6*a^3*b^2*c^(3/2) + 128*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^2*b^5 + 2560*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^3*b^3*c + 3840*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^4*b*c^2 + 1280*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^3*b^4*sqrt(c) + 2560*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^4*b^2*c^(3/2) + 2560*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^5*c^(5/2) + 70*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^3*b^5 + 2000*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^4*b^3*c + 2400*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^5*b*c^2 + 2560*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^5*b^2*c^(3/2) - 15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^4*b^5 + 120*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^5*b^3*c + 1040*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^6*b*c^2 + 256*a^7*c^(5/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^5*a^3)","B",0
946,1,1235,0,0.701213," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^13,x, algorithm=""giac"")","\frac{{\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{1024 \, \sqrt{-a} a^{4}} - \frac{105 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{11} b^{6} - 900 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{11} a b^{4} c + 2160 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{11} a^{2} b^{2} c^{2} - 960 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{11} a^{3} c^{3} - 595 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a b^{6} + 5100 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a^{2} b^{4} c - 12240 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a^{3} b^{2} c^{2} - 15040 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{9} a^{4} c^{3} - 76800 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{8} a^{4} b c^{\frac{5}{2}} + 1386 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{2} b^{6} - 11880 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{3} b^{4} c - 97440 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{4} b^{2} c^{2} - 24960 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{7} a^{5} c^{3} - 112640 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{6} a^{4} b^{3} c^{\frac{3}{2}} - 61440 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{6} a^{5} b c^{\frac{5}{2}} - 1686 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{3} b^{6} - 42600 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{4} b^{4} c - 128160 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{5} b^{2} c^{2} - 24960 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a^{6} c^{3} - 15360 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{4} b^{5} \sqrt{c} - 61440 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{5} b^{3} c^{\frac{3}{2}} - 92160 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{4} a^{6} b c^{\frac{5}{2}} - 595 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{4} b^{6} - 25620 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{5} b^{4} c - 58320 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{6} b^{2} c^{2} - 15040 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{7} c^{3} - 30720 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{6} b^{3} c^{\frac{3}{2}} - 12288 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{7} b c^{\frac{5}{2}} + 105 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{5} b^{6} - 900 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{6} b^{4} c - 13200 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{7} b^{2} c^{2} - 960 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{8} c^{3} - 3072 \, a^{8} b c^{\frac{5}{2}}}{15360 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{6} a^{4}}"," ",0,"1/1024*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^4) - 1/15360*(105*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^11*b^6 - 900*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^11*a*b^4*c + 2160*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^11*a^2*b^2*c^2 - 960*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^11*a^3*c^3 - 595*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a*b^6 + 5100*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a^2*b^4*c - 12240*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a^3*b^2*c^2 - 15040*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^9*a^4*c^3 - 76800*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^8*a^4*b*c^(5/2) + 1386*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^2*b^6 - 11880*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^3*b^4*c - 97440*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^4*b^2*c^2 - 24960*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^7*a^5*c^3 - 112640*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^6*a^4*b^3*c^(3/2) - 61440*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^6*a^5*b*c^(5/2) - 1686*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^3*b^6 - 42600*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^4*b^4*c - 128160*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^5*b^2*c^2 - 24960*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a^6*c^3 - 15360*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^4*b^5*sqrt(c) - 61440*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^5*b^3*c^(3/2) - 92160*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^4*a^6*b*c^(5/2) - 595*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^4*b^6 - 25620*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^5*b^4*c - 58320*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^6*b^2*c^2 - 15040*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^7*c^3 - 30720*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^6*b^3*c^(3/2) - 12288*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^7*b*c^(5/2) + 105*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^5*b^6 - 900*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^6*b^4*c - 13200*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^7*b^2*c^2 - 960*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^8*c^3 - 3072*a^8*b*c^(5/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^6*a^4)","B",0
947,0,0,0,0.000000," ","integrate(x^4*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} x^{4}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*x^4, x)","F",0
948,0,0,0,0.000000," ","integrate(x^2*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*x^2, x)","F",0
949,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2), x)","F",0
950,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)/x^2, x)","F",0
951,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)/x^4, x)","F",0
952,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{6}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)/x^6, x)","F",0
953,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^8,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{x^{8}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)/x^8, x)","F",0
954,0,0,0,0.000000," ","integrate((-x^4-2*x^2+3)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} - 2 \, x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(-x^4 - 2*x^2 + 3), x)","F",0
955,1,103,0,0.210875," ","integrate(x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, x^{2} {\left(\frac{4 \, x^{2}}{c} - \frac{5 \, b}{c^{2}}\right)} + \frac{15 \, b^{2} - 16 \, a c}{c^{3}}\right)} + \frac{{\left(5 \, b^{3} - 12 \, a b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{32 \, c^{\frac{7}{2}}}"," ",0,"1/48*sqrt(c*x^4 + b*x^2 + a)*(2*x^2*(4*x^2/c - 5*b/c^2) + (15*b^2 - 16*a*c)/c^3) + 1/32*(5*b^3 - 12*a*b*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(7/2)","A",0
956,1,82,0,0.240324," ","integrate(x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{c x^{4} + b x^{2} + a} {\left(\frac{2 \, x^{2}}{c} - \frac{3 \, b}{c^{2}}\right)} - \frac{{\left(3 \, b^{2} - 4 \, a c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/8*sqrt(c*x^4 + b*x^2 + a)*(2*x^2/c - 3*b/c^2) - 1/16*(3*b^2 - 4*a*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(5/2)","A",0
957,1,61,0,0.213122," ","integrate(x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{4} + b x^{2} + a}}{2 \, c}"," ",0,"1/4*b*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(3/2) + 1/2*sqrt(c*x^4 + b*x^2 + a)/c","A",0
958,1,40,0,0.211372," ","integrate(x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}}"," ",0,"-1/2*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/sqrt(c)","A",0
959,1,38,0,0.249540," ","integrate(1/x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}"," ",0,"arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/sqrt(-a)","A",0
960,1,114,0,0.433512," ","integrate(1/x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{b \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a} + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} b + 2 \, a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)} a}"," ",0,"-1/2*b*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*b + 2*a*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)*a)","A",0
961,1,221,0,0.298353," ","integrate(1/x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{2}} - \frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} b^{2} - 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a c - 5 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a b^{2} - 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{2} c - 8 \, a^{2} b \sqrt{c}}{8 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{2} a^{2}}"," ",0,"1/8*(3*b^2 - 4*a*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) - 1/8*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*b^2 - 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a*c - 5*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a*b^2 - 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^2*c - 8*a^2*b*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^2*a^2)","B",0
962,1,335,0,0.264729," ","integrate(1/x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(5 \, b^{3} - 12 \, a b c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{16 \, \sqrt{-a} a^{3}} + \frac{15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} b^{3} - 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} a b c - 40 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a b^{3} + 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a^{2} b c + 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} + 33 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{2} b^{3} + 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{3} b c + 48 \, a^{3} b^{2} \sqrt{c} - 32 \, a^{4} c^{\frac{3}{2}}}{48 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{3} a^{3}}"," ",0,"-1/16*(5*b^3 - 12*a*b*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^3) + 1/48*(15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*b^3 - 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*a*b*c - 40*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a*b^3 + 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a^2*b*c + 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a^3*c^(3/2) + 33*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^2*b^3 + 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^3*b*c + 48*a^3*b^2*sqrt(c) - 32*a^4*c^(3/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^3*a^3)","B",0
963,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(x^4/sqrt(c*x^4 + b*x^2 + a), x)","F",0
964,0,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(c*x^4 + b*x^2 + a), x)","F",0
965,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^4 + b*x^2 + a), x)","F",0
966,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2 + a)*x^2), x)","F",0
967,0,0,0,0.000000," ","integrate(1/x^4/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} + a} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2 + a)*x^4), x)","F",0
968,1,112,0,0.259243," ","integrate(x^7/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{1}{48} \, \sqrt{-c x^{4} + b x^{2} + a} {\left(2 \, x^{2} {\left(\frac{4 \, x^{2}}{c} + \frac{5 \, b}{c^{2}}\right)} + \frac{15 \, b^{2} + 16 \, a c}{c^{3}}\right)} - \frac{{\left(5 \, b^{3} + 12 \, a b c\right)} \log\left({\left| 2 \, {\left(\sqrt{-c} x^{2} - \sqrt{-c x^{4} + b x^{2} + a}\right)} \sqrt{-c} + b \right|}\right)}{32 \, \sqrt{-c} c^{3}}"," ",0,"-1/48*sqrt(-c*x^4 + b*x^2 + a)*(2*x^2*(4*x^2/c + 5*b/c^2) + (15*b^2 + 16*a*c)/c^3) - 1/32*(5*b^3 + 12*a*b*c)*log(abs(2*(sqrt(-c)*x^2 - sqrt(-c*x^4 + b*x^2 + a))*sqrt(-c) + b))/(sqrt(-c)*c^3)","A",0
969,1,91,0,0.211843," ","integrate(x^5/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{-c x^{4} + b x^{2} + a} {\left(\frac{2 \, x^{2}}{c} + \frac{3 \, b}{c^{2}}\right)} - \frac{{\left(3 \, b^{2} + 4 \, a c\right)} \log\left({\left| 2 \, {\left(\sqrt{-c} x^{2} - \sqrt{-c x^{4} + b x^{2} + a}\right)} \sqrt{-c} + b \right|}\right)}{16 \, \sqrt{-c} c^{2}}"," ",0,"-1/8*sqrt(-c*x^4 + b*x^2 + a)*(2*x^2/c + 3*b/c^2) - 1/16*(3*b^2 + 4*a*c)*log(abs(2*(sqrt(-c)*x^2 - sqrt(-c*x^4 + b*x^2 + a))*sqrt(-c) + b))/(sqrt(-c)*c^2)","A",0
970,1,70,0,0.265200," ","integrate(x^3/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{b \log\left({\left| 2 \, {\left(\sqrt{-c} x^{2} - \sqrt{-c x^{4} + b x^{2} + a}\right)} \sqrt{-c} + b \right|}\right)}{4 \, \sqrt{-c} c} - \frac{\sqrt{-c x^{4} + b x^{2} + a}}{2 \, c}"," ",0,"-1/4*b*log(abs(2*(sqrt(-c)*x^2 - sqrt(-c*x^4 + b*x^2 + a))*sqrt(-c) + b))/(sqrt(-c)*c) - 1/2*sqrt(-c*x^4 + b*x^2 + a)/c","A",0
971,1,45,0,0.205113," ","integrate(x/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| 2 \, {\left(\sqrt{-c} x^{2} - \sqrt{-c x^{4} + b x^{2} + a}\right)} \sqrt{-c} + b \right|}\right)}{2 \, \sqrt{-c}}"," ",0,"-1/2*log(abs(2*(sqrt(-c)*x^2 - sqrt(-c*x^4 + b*x^2 + a))*sqrt(-c) + b))/sqrt(-c)","A",0
972,1,36,0,0.207234," ","integrate(1/x/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}}{\sqrt{a}}\right)}{\sqrt{a}}"," ",0,"arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))/sqrt(a))/sqrt(a)","A",0
973,1,111,0,0.216544," ","integrate(1/x^3/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\frac{b \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}}{\sqrt{a}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)} b - 2 \, a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{2} + a\right)} a}"," ",0,"1/2*b*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))/sqrt(a))/a^(3/2) - 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))*b - 2*a*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^2 + a)*a)","A",0
974,1,224,0,0.225033," ","integrate(1/x^5/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} + 4 \, a c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}}{\sqrt{a}}\right)}{8 \, a^{\frac{5}{2}}} - \frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{3} b^{2} + 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{3} a c + 5 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)} a b^{2} - 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)} a^{2} c - 8 \, a^{2} b \sqrt{c}}{8 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{2} + a\right)}^{2} a^{2}}"," ",0,"1/8*(3*b^2 + 4*a*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))/sqrt(a))/a^(5/2) - 1/8*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^3*b^2 + 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^3*a*c + 5*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))*a*b^2 - 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))*a^2*c - 8*a^2*b*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^2 + a)^2*a^2)","B",0
975,1,344,0,0.266727," ","integrate(1/x^7/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\frac{{\left(5 \, b^{3} + 12 \, a b c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}}{\sqrt{a}}\right)}{16 \, a^{\frac{7}{2}}} - \frac{15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{5} b^{3} + 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{5} a b c + 40 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{3} a b^{3} + 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{3} a^{2} b c - 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{2} a^{3} c^{\frac{3}{2}} + 33 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)} a^{2} b^{3} - 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)} a^{3} b c - 48 \, a^{3} b^{2} \sqrt{c} - 32 \, a^{4} c^{\frac{3}{2}}}{48 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} - a}\right)}^{2} + a\right)}^{3} a^{3}}"," ",0,"1/16*(5*b^3 + 12*a*b*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))/sqrt(a))/a^(7/2) - 1/48*(15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^5*b^3 + 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^5*a*b*c + 40*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^3*a*b^3 + 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^3*a^2*b*c - 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^2*a^3*c^(3/2) + 33*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))*a^2*b^3 - 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))*a^3*b*c - 48*a^3*b^2*sqrt(c) - 32*a^4*c^(3/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 - a))^2 + a)^3*a^3)","B",0
976,0,0,0,0.000000," ","integrate(x^4/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{-c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(x^4/sqrt(-c*x^4 + b*x^2 + a), x)","F",0
977,0,0,0,0.000000," ","integrate(x^2/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(-c*x^4 + b*x^2 + a), x)","F",0
978,0,0,0,0.000000," ","integrate(1/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(-c*x^4 + b*x^2 + a), x)","F",0
979,0,0,0,0.000000," ","integrate(1/x^2/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + b x^{2} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + b*x^2 + a)*x^2), x)","F",0
980,0,0,0,0.000000," ","integrate(1/x^4/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + b x^{2} + a} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + b*x^2 + a)*x^4), x)","F",0
981,1,215,0,0.274231," ","integrate(x^9/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2}}{b^{2} c^{3} - 4 \, a c^{4}} - \frac{5 \, {\left(b^{3} c - 4 \, a b c^{2}\right)}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x^{2} - \frac{15 \, b^{4} - 62 \, a b^{2} c + 24 \, a^{2} c^{2}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x^{2} - \frac{15 \, a b^{3} - 52 \, a^{2} b c}{b^{2} c^{3} - 4 \, a c^{4}}}{8 \, \sqrt{c x^{4} + b x^{2} + a}} - \frac{3 \, {\left(5 \, b^{2} - 4 \, a c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/8*(((2*(b^2*c^2 - 4*a*c^3)*x^2/(b^2*c^3 - 4*a*c^4) - 5*(b^3*c - 4*a*b*c^2)/(b^2*c^3 - 4*a*c^4))*x^2 - (15*b^4 - 62*a*b^2*c + 24*a^2*c^2)/(b^2*c^3 - 4*a*c^4))*x^2 - (15*a*b^3 - 52*a^2*b*c)/(b^2*c^3 - 4*a*c^4))/sqrt(c*x^4 + b*x^2 + a) - 3/16*(5*b^2 - 4*a*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(7/2)","A",0
982,1,154,0,0.273265," ","integrate(x^7/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{2}}{b^{2} c^{2} - 4 \, a c^{3}} + \frac{3 \, b^{3} - 10 \, a b c}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x^{2} + \frac{3 \, a b^{2} - 8 \, a^{2} c}{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, \sqrt{c x^{4} + b x^{2} + a}} + \frac{3 \, b \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{5}{2}}}"," ",0,"1/2*(((b^2*c - 4*a*c^2)*x^2/(b^2*c^2 - 4*a*c^3) + (3*b^3 - 10*a*b*c)/(b^2*c^2 - 4*a*c^3))*x^2 + (3*a*b^2 - 8*a^2*c)/(b^2*c^2 - 4*a*c^3))/sqrt(c*x^4 + b*x^2 + a) + 3/4*b*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(5/2)","A",0
983,1,101,0,0.258815," ","integrate(x^5/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(b^{2} - 2 \, a c\right)} x^{2}}{b^{2} c - 4 \, a c^{2}} + \frac{a b}{b^{2} c - 4 \, a c^{2}}}{\sqrt{c x^{4} + b x^{2} + a}} - \frac{\log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"-((b^2 - 2*a*c)*x^2/(b^2*c - 4*a*c^2) + a*b/(b^2*c - 4*a*c^2))/sqrt(c*x^4 + b*x^2 + a) - 1/2*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(3/2)","A",0
984,1,44,0,0.283941," ","integrate(x^3/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{b x^{2}}{b^{2} - 4 \, a c} + \frac{2 \, a}{b^{2} - 4 \, a c}}{\sqrt{c x^{4} + b x^{2} + a}}"," ",0,"(b*x^2/(b^2 - 4*a*c) + 2*a/(b^2 - 4*a*c))/sqrt(c*x^4 + b*x^2 + a)","A",0
985,1,45,0,0.195251," ","integrate(x/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, c x^{2}}{b^{2} - 4 \, a c} + \frac{b}{b^{2} - 4 \, a c}}{\sqrt{c x^{4} + b x^{2} + a}}"," ",0,"-(2*c*x^2/(b^2 - 4*a*c) + b/(b^2 - 4*a*c))/sqrt(c*x^4 + b*x^2 + a)","A",0
986,1,110,0,0.202701," ","integrate(1/x/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{a b c x^{2}}{a^{2} b^{2} - 4 \, a^{3} c} + \frac{a b^{2} - 2 \, a^{2} c}{a^{2} b^{2} - 4 \, a^{3} c}}{\sqrt{c x^{4} + b x^{2} + a}} + \frac{\arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a}"," ",0,"(a*b*c*x^2/(a^2*b^2 - 4*a^3*c) + (a*b^2 - 2*a^2*c)/(a^2*b^2 - 4*a^3*c))/sqrt(c*x^4 + b*x^2 + a) + arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a)","A",0
987,1,200,0,0.275681," ","integrate(1/x^3/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} x^{2}}{a^{4} b^{2} - 4 \, a^{5} c} + \frac{a^{2} b^{3} - 3 \, a^{3} b c}{a^{4} b^{2} - 4 \, a^{5} c}}{\sqrt{c x^{4} + b x^{2} + a}} - \frac{3 \, b \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a^{2}} + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} b + 2 \, a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)} a^{2}}"," ",0,"-((a^2*b^2*c - 2*a^3*c^2)*x^2/(a^4*b^2 - 4*a^5*c) + (a^2*b^3 - 3*a^3*b*c)/(a^4*b^2 - 4*a^5*c))/sqrt(c*x^4 + b*x^2 + a) - 3/2*b*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) + 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*b + 2*a*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)*a^2)","A",0
988,1,350,0,0.376649," ","integrate(1/x^5/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(a^{3} b^{3} c - 3 \, a^{4} b c^{2}\right)} x^{2}}{a^{6} b^{2} - 4 \, a^{7} c} + \frac{a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}{\sqrt{c x^{4} + b x^{2} + a}} + \frac{3 \, {\left(5 \, b^{2} - 4 \, a c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{3}} - \frac{7 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} b^{2} - 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} a c + 8 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} a b \sqrt{c} - 9 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a b^{2} - 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} a^{2} c - 16 \, a^{2} b \sqrt{c}}{8 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{2} a^{3}}"," ",0,"((a^3*b^3*c - 3*a^4*b*c^2)*x^2/(a^6*b^2 - 4*a^7*c) + (a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2)/(a^6*b^2 - 4*a^7*c))/sqrt(c*x^4 + b*x^2 + a) + 3/8*(5*b^2 - 4*a*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^3) - 1/8*(7*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*b^2 - 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*a*c + 8*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*a*b*sqrt(c) - 9*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a*b^2 - 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*a^2*c - 16*a^2*b*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^2*a^3)","A",0
989,0,0,0,0.000000," ","integrate(x^6/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^6/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
990,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
991,0,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
992,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(-3/2), x)","F",0
993,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2 + a)^(3/2)*x^2), x)","F",0
994,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(x^4/sqrt(c*x^4 + b*x^2), x)","F",0
995,1,59,0,0.198183," ","integrate(x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{4} + b x^{2}}}{2 \, c}"," ",0,"1/4*b*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/c^(3/2) + 1/2*sqrt(c*x^4 + b*x^2)/c","A",0
996,1,31,0,0.182583," ","integrate(x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{b}}{{\left(\sqrt{c + \frac{b}{x^{2}}} - \frac{\sqrt{b}}{x}\right)}^{2} - c}"," ",0,"-2*sqrt(b)/((sqrt(c + b/x^2) - sqrt(b)/x)^2 - c)","A",0
997,1,39,0,0.185333," ","integrate(x/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}}"," ",0,"-1/2*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) - b))/sqrt(c)","A",0
998,1,46,0,0.188555," ","integrate(1/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + \frac{\arctan\left(\frac{\sqrt{c x^{2} + b}}{\sqrt{-b}}\right)}{\sqrt{-b} \mathrm{sgn}\left(x\right)}"," ",0,"-arctan(sqrt(b)/sqrt(-b))*sgn(x)/sqrt(-b) + arctan(sqrt(c*x^2 + b)/sqrt(-b))/(sqrt(-b)*sgn(x))","A",0
999,1,25,0,0.180375," ","integrate(1/x/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}}"," ",0,"1/(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))","A",0
1000,-2,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^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,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [64.3995612673,65,-85]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [66.1769613782,93,91]-1/2/b/x*sqrt(b*(1/x)^2+c)-2*c/4/b/sqrt(b)*ln(abs(sqrt(b*(1/x)^2+c)-sqrt(b)/x))","F(-2)",0
1001,1,57,0,0.185184," ","integrate(1/x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)} \sqrt{c} + b}{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2}}\right)}^{3}}"," ",0,"1/3*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))*sqrt(c) + b)/(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2))^3","A",0
1002,-2,0,0,0.000000," ","integrate(1/x^4/(c*x^4+b*x^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,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [64.3995612673,65,-85]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%},0,%%%{1,[0,2,4]%%%}] at parameters values [66.1769613782,93,91]2*(-2*b^2/16/b^3/x/x+3*b*c/16/b^3)/x*sqrt(b*(1/x)^2+c)+6*c^2/16/b^2/sqrt(b)*ln(abs(sqrt(b*(1/x)^2+c)-sqrt(b)/x))","F(-2)",0
1003,0,0,0,0.000000," ","integrate(x^4/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate(x^4/sqrt(c*x^4 + a), x)","F",0
1004,1,14,0,0.186610," ","integrate(x^3/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{4} + a}}{2 \, c}"," ",0,"1/2*sqrt(c*x^4 + a)/c","A",0
1005,0,0,0,0.000000," ","integrate(x^2/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(c*x^4 + a), x)","F",0
1006,1,25,0,0.164356," ","integrate(x/(c*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{c} x^{2} + \sqrt{c x^{4} + a} \right|}\right)}{2 \, \sqrt{c}}"," ",0,"-1/2*log(abs(-sqrt(c)*x^2 + sqrt(c*x^4 + a)))/sqrt(c)","A",0
1007,0,0,0,0.000000," ","integrate(1/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^4 + a), x)","F",0
1008,1,23,0,0.152081," ","integrate(1/x/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{c x^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}}"," ",0,"1/2*arctan(sqrt(c*x^4 + a)/sqrt(-a))/sqrt(-a)","A",0
1009,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*x^2), x)","F",0
1010,1,31,0,0.169122," ","integrate(1/x^3/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c}}{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a}"," ",0,"sqrt(c)/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)","A",0
1011,0,0,0,0.000000," ","integrate(1/x^4/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*x^4), x)","F",0
1012,1,54,0,0.293457," ","integrate(x^4/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{b x^{2} + a} x {\left(\frac{2 \, x^{2}}{b} - \frac{3 \, a}{b^{2}}\right)} - \frac{3 \, a^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{5}{2}}}"," ",0,"1/8*sqrt(b*x^2 + a)*x*(2*x^2/b - 3*a/b^2) - 3/8*a^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
1013,1,30,0,0.149839," ","integrate(x^3/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{3 \, b^{2}} - \frac{\sqrt{b x^{2} + a} a}{b^{2}}"," ",0,"1/3*(b*x^2 + a)^(3/2)/b^2 - sqrt(b*x^2 + a)*a/b^2","A",0
1014,1,40,0,0.184523," ","integrate(x^2/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a} x}{2 \, b} + \frac{a \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/2*sqrt(b*x^2 + a)*x/b + 1/2*a*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
1015,1,13,0,0.154615," ","integrate(x/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a}}{b}"," ",0,"sqrt(b*x^2 + a)/b","A",0
1016,1,23,0,0.182851," ","integrate(1/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b)","A",0
1017,1,22,0,0.158035," ","integrate(1/x/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}"," ",0,"arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a)","A",0
1018,1,30,0,0.181180," ","integrate(1/x^2/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a}"," ",0,"2*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)","A",0
1019,1,51,0,0.167892," ","integrate(1/x^3/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\frac{b^{2} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{\sqrt{b x^{2} + a} b}{a x^{2}}}{2 \, b}"," ",0,"-1/2*(b^2*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) + sqrt(b*x^2 + a)*b/(a*x^2))/b","A",0
1020,1,55,0,0.282881," ","integrate(1/x^4/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} b^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"4/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*b^(3/2)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3","A",0
1021,1,8,0,0.151307," ","integrate(x^4/(c*x^4)^(1/2),x, algorithm=""giac"")","\frac{x^{3}}{3 \, \sqrt{c}}"," ",0,"1/3*x^3/sqrt(c)","A",0
1022,1,8,0,0.148231," ","integrate(x^3/(c*x^4)^(1/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, \sqrt{c}}"," ",0,"1/2*x^2/sqrt(c)","A",0
1023,1,5,0,0.169549," ","integrate(x^2/(c*x^4)^(1/2),x, algorithm=""giac"")","\frac{x}{\sqrt{c}}"," ",0,"x/sqrt(c)","A",0
1024,1,7,0,0.150319," ","integrate(x/(c*x^4)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| x \right|}\right)}{\sqrt{c}}"," ",0,"log(abs(x))/sqrt(c)","A",0
1025,1,8,0,0.149892," ","integrate(1/(c*x^4)^(1/2),x, algorithm=""giac"")","-\frac{1}{\sqrt{c} x}"," ",0,"-1/(sqrt(c)*x)","A",0
1026,1,8,0,0.158671," ","integrate(1/x/(c*x^4)^(1/2),x, algorithm=""giac"")","-\frac{1}{2 \, \sqrt{c} x^{2}}"," ",0,"-1/2/(sqrt(c)*x^2)","A",0
1027,1,8,0,0.155094," ","integrate(1/x^2/(c*x^4)^(1/2),x, algorithm=""giac"")","-\frac{1}{3 \, \sqrt{c} x^{3}}"," ",0,"-1/3/(sqrt(c)*x^3)","A",0
1028,1,8,0,0.161534," ","integrate(1/x^3/(c*x^4)^(1/2),x, algorithm=""giac"")","-\frac{1}{4 \, \sqrt{c} x^{4}}"," ",0,"-1/4/(sqrt(c)*x^4)","A",0
1029,1,8,0,0.153250," ","integrate(1/x^4/(c*x^4)^(1/2),x, algorithm=""giac"")","-\frac{1}{5 \, \sqrt{c} x^{5}}"," ",0,"-1/5/(sqrt(c)*x^5)","A",0
1030,1,8,0,0.148743," ","integrate(x^4/a^(1/2),x, algorithm=""giac"")","\frac{x^{5}}{5 \, \sqrt{a}}"," ",0,"1/5*x^5/sqrt(a)","A",0
1031,1,8,0,0.175273," ","integrate(x^3/a^(1/2),x, algorithm=""giac"")","\frac{x^{4}}{4 \, \sqrt{a}}"," ",0,"1/4*x^4/sqrt(a)","A",0
1032,1,8,0,0.149795," ","integrate(x^2/a^(1/2),x, algorithm=""giac"")","\frac{x^{3}}{3 \, \sqrt{a}}"," ",0,"1/3*x^3/sqrt(a)","A",0
1033,1,8,0,0.150313," ","integrate(x/a^(1/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, \sqrt{a}}"," ",0,"1/2*x^2/sqrt(a)","A",0
1034,1,5,0,0.150015," ","integrate(1/a^(1/2),x, algorithm=""giac"")","\frac{x}{\sqrt{a}}"," ",0,"x/sqrt(a)","A",0
1035,1,7,0,0.148427," ","integrate(1/x/a^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| x \right|}\right)}{\sqrt{a}}"," ",0,"log(abs(x))/sqrt(a)","A",0
1036,1,8,0,0.181654," ","integrate(1/x^2/a^(1/2),x, algorithm=""giac"")","-\frac{1}{\sqrt{a} x}"," ",0,"-1/(sqrt(a)*x)","A",0
1037,1,8,0,0.148453," ","integrate(1/x^3/a^(1/2),x, algorithm=""giac"")","-\frac{1}{2 \, \sqrt{a} x^{2}}"," ",0,"-1/2/(sqrt(a)*x^2)","A",0
1038,1,8,0,0.178129," ","integrate(1/x^4/a^(1/2),x, algorithm=""giac"")","-\frac{1}{3 \, \sqrt{a} x^{3}}"," ",0,"-1/3/(sqrt(a)*x^3)","A",0
1039,0,0,0,0.000000," ","integrate(1/(-x^4-2*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} - 2 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 - 2*x^2 + 3), x)","F",0
1040,0,0,0,0.000000," ","integrate(1/(-x^4+5*x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 5 \, x^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 + 5*x^2 - 1), x)","F",0
1041,1,19,0,0.163648," ","integrate(x^(5/2)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{2}{15} \, c x^{\frac{15}{2}} + \frac{2}{11} \, b x^{\frac{11}{2}} + \frac{2}{7} \, a x^{\frac{7}{2}}"," ",0,"2/15*c*x^(15/2) + 2/11*b*x^(11/2) + 2/7*a*x^(7/2)","A",0
1042,1,19,0,0.209420," ","integrate(x^(3/2)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{2}{13} \, c x^{\frac{13}{2}} + \frac{2}{9} \, b x^{\frac{9}{2}} + \frac{2}{5} \, a x^{\frac{5}{2}}"," ",0,"2/13*c*x^(13/2) + 2/9*b*x^(9/2) + 2/5*a*x^(5/2)","A",0
1043,1,19,0,0.169379," ","integrate(x^(1/2)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{7} \, b x^{\frac{7}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}}"," ",0,"2/11*c*x^(11/2) + 2/7*b*x^(7/2) + 2/3*a*x^(3/2)","A",0
1044,1,19,0,0.152359," ","integrate((c*x^4+b*x^2+a)/x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, c x^{\frac{9}{2}} + \frac{2}{5} \, b x^{\frac{5}{2}} + 2 \, a \sqrt{x}"," ",0,"2/9*c*x^(9/2) + 2/5*b*x^(5/2) + 2*a*sqrt(x)","A",0
1045,1,19,0,0.148980," ","integrate((c*x^4+b*x^2+a)/x^(3/2),x, algorithm=""giac"")","\frac{2}{7} \, c x^{\frac{7}{2}} + \frac{2}{3} \, b x^{\frac{3}{2}} - \frac{2 \, a}{\sqrt{x}}"," ",0,"2/7*c*x^(7/2) + 2/3*b*x^(3/2) - 2*a/sqrt(x)","A",0
1046,1,19,0,0.325531," ","integrate((c*x^4+b*x^2+a)/x^(5/2),x, algorithm=""giac"")","\frac{2}{5} \, c x^{\frac{5}{2}} + 2 \, b \sqrt{x} - \frac{2 \, a}{3 \, x^{\frac{3}{2}}}"," ",0,"2/5*c*x^(5/2) + 2*b*sqrt(x) - 2/3*a/x^(3/2)","A",0
1047,1,20,0,0.209064," ","integrate((c*x^4+b*x^2+a)/x^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, c x^{\frac{3}{2}} - \frac{2 \, {\left(5 \, b x^{2} + a\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/3*c*x^(3/2) - 2/5*(5*b*x^2 + a)/x^(5/2)","A",0
1048,1,46,0,0.206140," ","integrate(x^(5/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{19} \, b c x^{\frac{19}{2}} + \frac{2}{15} \, b^{2} x^{\frac{15}{2}} + \frac{4}{15} \, a c x^{\frac{15}{2}} + \frac{4}{11} \, a b x^{\frac{11}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}}"," ",0,"2/23*c^2*x^(23/2) + 4/19*b*c*x^(19/2) + 2/15*b^2*x^(15/2) + 4/15*a*c*x^(15/2) + 4/11*a*b*x^(11/2) + 2/7*a^2*x^(7/2)","A",0
1049,1,46,0,0.171750," ","integrate(x^(3/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{17} \, b c x^{\frac{17}{2}} + \frac{2}{13} \, b^{2} x^{\frac{13}{2}} + \frac{4}{13} \, a c x^{\frac{13}{2}} + \frac{4}{9} \, a b x^{\frac{9}{2}} + \frac{2}{5} \, a^{2} x^{\frac{5}{2}}"," ",0,"2/21*c^2*x^(21/2) + 4/17*b*c*x^(17/2) + 2/13*b^2*x^(13/2) + 4/13*a*c*x^(13/2) + 4/9*a*b*x^(9/2) + 2/5*a^2*x^(5/2)","A",0
1050,1,46,0,0.149879," ","integrate(x^(1/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{19} \, c^{2} x^{\frac{19}{2}} + \frac{4}{15} \, b c x^{\frac{15}{2}} + \frac{2}{11} \, b^{2} x^{\frac{11}{2}} + \frac{4}{11} \, a c x^{\frac{11}{2}} + \frac{4}{7} \, a b x^{\frac{7}{2}} + \frac{2}{3} \, a^{2} x^{\frac{3}{2}}"," ",0,"2/19*c^2*x^(19/2) + 4/15*b*c*x^(15/2) + 2/11*b^2*x^(11/2) + 4/11*a*c*x^(11/2) + 4/7*a*b*x^(7/2) + 2/3*a^2*x^(3/2)","A",0
1051,1,46,0,0.151184," ","integrate((c*x^4+b*x^2+a)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, c^{2} x^{\frac{17}{2}} + \frac{4}{13} \, b c x^{\frac{13}{2}} + \frac{2}{9} \, b^{2} x^{\frac{9}{2}} + \frac{4}{9} \, a c x^{\frac{9}{2}} + \frac{4}{5} \, a b x^{\frac{5}{2}} + 2 \, a^{2} \sqrt{x}"," ",0,"2/17*c^2*x^(17/2) + 4/13*b*c*x^(13/2) + 2/9*b^2*x^(9/2) + 4/9*a*c*x^(9/2) + 4/5*a*b*x^(5/2) + 2*a^2*sqrt(x)","A",0
1052,1,46,0,0.153790," ","integrate((c*x^4+b*x^2+a)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b c x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} x^{\frac{7}{2}} + \frac{4}{7} \, a c x^{\frac{7}{2}} + \frac{4}{3} \, a b x^{\frac{3}{2}} - \frac{2 \, a^{2}}{\sqrt{x}}"," ",0,"2/15*c^2*x^(15/2) + 4/11*b*c*x^(11/2) + 2/7*b^2*x^(7/2) + 4/7*a*c*x^(7/2) + 4/3*a*b*x^(3/2) - 2*a^2/sqrt(x)","A",0
1053,1,46,0,0.150736," ","integrate((c*x^4+b*x^2+a)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{9} \, b c x^{\frac{9}{2}} + \frac{2}{5} \, b^{2} x^{\frac{5}{2}} + \frac{4}{5} \, a c x^{\frac{5}{2}} + 4 \, a b \sqrt{x} - \frac{2 \, a^{2}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/13*c^2*x^(13/2) + 4/9*b*c*x^(9/2) + 2/5*b^2*x^(5/2) + 4/5*a*c*x^(5/2) + 4*a*b*sqrt(x) - 2/3*a^2/x^(3/2)","A",0
1054,1,47,0,0.160321," ","integrate((c*x^4+b*x^2+a)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{11} \, c^{2} x^{\frac{11}{2}} + \frac{4}{7} \, b c x^{\frac{7}{2}} + \frac{2}{3} \, b^{2} x^{\frac{3}{2}} + \frac{4}{3} \, a c x^{\frac{3}{2}} - \frac{2 \, {\left(10 \, a b x^{2} + a^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/11*c^2*x^(11/2) + 4/7*b*c*x^(7/2) + 2/3*b^2*x^(3/2) + 4/3*a*c*x^(3/2) - 2/5*(10*a*b*x^2 + a^2)/x^(5/2)","A",0
1055,1,87,0,0.157016," ","integrate(x^(5/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{31} \, c^{3} x^{\frac{31}{2}} + \frac{2}{9} \, b c^{2} x^{\frac{27}{2}} + \frac{6}{23} \, b^{2} c x^{\frac{23}{2}} + \frac{6}{23} \, a c^{2} x^{\frac{23}{2}} + \frac{2}{19} \, b^{3} x^{\frac{19}{2}} + \frac{12}{19} \, a b c x^{\frac{19}{2}} + \frac{2}{5} \, a b^{2} x^{\frac{15}{2}} + \frac{2}{5} \, a^{2} c x^{\frac{15}{2}} + \frac{6}{11} \, a^{2} b x^{\frac{11}{2}} + \frac{2}{7} \, a^{3} x^{\frac{7}{2}}"," ",0,"2/31*c^3*x^(31/2) + 2/9*b*c^2*x^(27/2) + 6/23*b^2*c*x^(23/2) + 6/23*a*c^2*x^(23/2) + 2/19*b^3*x^(19/2) + 12/19*a*b*c*x^(19/2) + 2/5*a*b^2*x^(15/2) + 2/5*a^2*c*x^(15/2) + 6/11*a^2*b*x^(11/2) + 2/7*a^3*x^(7/2)","A",0
1056,1,87,0,0.165779," ","integrate(x^(3/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{29} \, c^{3} x^{\frac{29}{2}} + \frac{6}{25} \, b c^{2} x^{\frac{25}{2}} + \frac{2}{7} \, b^{2} c x^{\frac{21}{2}} + \frac{2}{7} \, a c^{2} x^{\frac{21}{2}} + \frac{2}{17} \, b^{3} x^{\frac{17}{2}} + \frac{12}{17} \, a b c x^{\frac{17}{2}} + \frac{6}{13} \, a b^{2} x^{\frac{13}{2}} + \frac{6}{13} \, a^{2} c x^{\frac{13}{2}} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{2}{5} \, a^{3} x^{\frac{5}{2}}"," ",0,"2/29*c^3*x^(29/2) + 6/25*b*c^2*x^(25/2) + 2/7*b^2*c*x^(21/2) + 2/7*a*c^2*x^(21/2) + 2/17*b^3*x^(17/2) + 12/17*a*b*c*x^(17/2) + 6/13*a*b^2*x^(13/2) + 6/13*a^2*c*x^(13/2) + 2/3*a^2*b*x^(9/2) + 2/5*a^3*x^(5/2)","A",0
1057,1,87,0,0.159503," ","integrate(x^(1/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{27} \, c^{3} x^{\frac{27}{2}} + \frac{6}{23} \, b c^{2} x^{\frac{23}{2}} + \frac{6}{19} \, b^{2} c x^{\frac{19}{2}} + \frac{6}{19} \, a c^{2} x^{\frac{19}{2}} + \frac{2}{15} \, b^{3} x^{\frac{15}{2}} + \frac{4}{5} \, a b c x^{\frac{15}{2}} + \frac{6}{11} \, a b^{2} x^{\frac{11}{2}} + \frac{6}{11} \, a^{2} c x^{\frac{11}{2}} + \frac{6}{7} \, a^{2} b x^{\frac{7}{2}} + \frac{2}{3} \, a^{3} x^{\frac{3}{2}}"," ",0,"2/27*c^3*x^(27/2) + 6/23*b*c^2*x^(23/2) + 6/19*b^2*c*x^(19/2) + 6/19*a*c^2*x^(19/2) + 2/15*b^3*x^(15/2) + 4/5*a*b*c*x^(15/2) + 6/11*a*b^2*x^(11/2) + 6/11*a^2*c*x^(11/2) + 6/7*a^2*b*x^(7/2) + 2/3*a^3*x^(3/2)","A",0
1058,1,87,0,0.170776," ","integrate((c*x^4+b*x^2+a)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{25} \, c^{3} x^{\frac{25}{2}} + \frac{2}{7} \, b c^{2} x^{\frac{21}{2}} + \frac{6}{17} \, b^{2} c x^{\frac{17}{2}} + \frac{6}{17} \, a c^{2} x^{\frac{17}{2}} + \frac{2}{13} \, b^{3} x^{\frac{13}{2}} + \frac{12}{13} \, a b c x^{\frac{13}{2}} + \frac{2}{3} \, a b^{2} x^{\frac{9}{2}} + \frac{2}{3} \, a^{2} c x^{\frac{9}{2}} + \frac{6}{5} \, a^{2} b x^{\frac{5}{2}} + 2 \, a^{3} \sqrt{x}"," ",0,"2/25*c^3*x^(25/2) + 2/7*b*c^2*x^(21/2) + 6/17*b^2*c*x^(17/2) + 6/17*a*c^2*x^(17/2) + 2/13*b^3*x^(13/2) + 12/13*a*b*c*x^(13/2) + 2/3*a*b^2*x^(9/2) + 2/3*a^2*c*x^(9/2) + 6/5*a^2*b*x^(5/2) + 2*a^3*sqrt(x)","A",0
1059,1,87,0,0.156311," ","integrate((c*x^4+b*x^2+a)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{23} \, c^{3} x^{\frac{23}{2}} + \frac{6}{19} \, b c^{2} x^{\frac{19}{2}} + \frac{2}{5} \, b^{2} c x^{\frac{15}{2}} + \frac{2}{5} \, a c^{2} x^{\frac{15}{2}} + \frac{2}{11} \, b^{3} x^{\frac{11}{2}} + \frac{12}{11} \, a b c x^{\frac{11}{2}} + \frac{6}{7} \, a b^{2} x^{\frac{7}{2}} + \frac{6}{7} \, a^{2} c x^{\frac{7}{2}} + 2 \, a^{2} b x^{\frac{3}{2}} - \frac{2 \, a^{3}}{\sqrt{x}}"," ",0,"2/23*c^3*x^(23/2) + 6/19*b*c^2*x^(19/2) + 2/5*b^2*c*x^(15/2) + 2/5*a*c^2*x^(15/2) + 2/11*b^3*x^(11/2) + 12/11*a*b*c*x^(11/2) + 6/7*a*b^2*x^(7/2) + 6/7*a^2*c*x^(7/2) + 2*a^2*b*x^(3/2) - 2*a^3/sqrt(x)","A",0
1060,1,87,0,0.197943," ","integrate((c*x^4+b*x^2+a)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{21} \, c^{3} x^{\frac{21}{2}} + \frac{6}{17} \, b c^{2} x^{\frac{17}{2}} + \frac{6}{13} \, b^{2} c x^{\frac{13}{2}} + \frac{6}{13} \, a c^{2} x^{\frac{13}{2}} + \frac{2}{9} \, b^{3} x^{\frac{9}{2}} + \frac{4}{3} \, a b c x^{\frac{9}{2}} + \frac{6}{5} \, a b^{2} x^{\frac{5}{2}} + \frac{6}{5} \, a^{2} c x^{\frac{5}{2}} + 6 \, a^{2} b \sqrt{x} - \frac{2 \, a^{3}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/21*c^3*x^(21/2) + 6/17*b*c^2*x^(17/2) + 6/13*b^2*c*x^(13/2) + 6/13*a*c^2*x^(13/2) + 2/9*b^3*x^(9/2) + 4/3*a*b*c*x^(9/2) + 6/5*a*b^2*x^(5/2) + 6/5*a^2*c*x^(5/2) + 6*a^2*b*sqrt(x) - 2/3*a^3/x^(3/2)","A",0
1061,1,88,0,0.174074," ","integrate((c*x^4+b*x^2+a)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{19} \, c^{3} x^{\frac{19}{2}} + \frac{2}{5} \, b c^{2} x^{\frac{15}{2}} + \frac{6}{11} \, b^{2} c x^{\frac{11}{2}} + \frac{6}{11} \, a c^{2} x^{\frac{11}{2}} + \frac{2}{7} \, b^{3} x^{\frac{7}{2}} + \frac{12}{7} \, a b c x^{\frac{7}{2}} + 2 \, a b^{2} x^{\frac{3}{2}} + 2 \, a^{2} c x^{\frac{3}{2}} - \frac{2 \, {\left(15 \, a^{2} b x^{2} + a^{3}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/19*c^3*x^(19/2) + 2/5*b*c^2*x^(15/2) + 6/11*b^2*c*x^(11/2) + 6/11*a*c^2*x^(11/2) + 2/7*b^3*x^(7/2) + 12/7*a*b*c*x^(7/2) + 2*a*b^2*x^(3/2) + 2*a^2*c*x^(3/2) - 2/5*(15*a^2*b*x^2 + a^3)/x^(5/2)","A",0
1062,-2,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2+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:Evaluation time: 19.14Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1063,-2,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2+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:Evaluation time: 14.51Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1064,0,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{x^{\frac{5}{2}}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate(x^(5/2)/(c*x^4 + b*x^2 + a), x)","F",0
1065,0,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{x^{\frac{3}{2}}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate(x^(3/2)/(c*x^4 + b*x^2 + a), x)","F",0
1066,0,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{\sqrt{x}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate(sqrt(x)/(c*x^4 + b*x^2 + a), x)","F",0
1067,0,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2} + a\right)} \sqrt{x}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2 + a)*sqrt(x)), x)","F",0
1068,-2,0,0,0.000000," ","integrate(1/x^(3/2)/(c*x^4+b*x^2+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:Evaluation time: 7.01Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1069,-2,0,0,0.000000," ","integrate(1/x^(5/2)/(c*x^4+b*x^2+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:Evaluation time: 13.91Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1070,-2,0,0,0.000000," ","integrate(1/x^(7/2)/(c*x^4+b*x^2+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:Evaluation time: 14.71Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1071,-2,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2+a)^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: 46.99Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1072,-2,0,0,0.000000," ","integrate(x^(11/2)/(c*x^4+b*x^2+a)^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: 47.04Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1073,-2,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2+a)^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: 47.21Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1074,-2,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2+a)^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: 47.2Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1075,-2,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2+a)^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: 47.37Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1076,-2,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2+a)^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: 47.03Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1077,-2,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2+a)^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: 47.23Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1078,-2,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a)^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: 47.36Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1079,-2,0,0,0.000000," ","integrate(1/x^(3/2)/(c*x^4+b*x^2+a)^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: 50.43Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1080,-2,0,0,0.000000," ","integrate(x^(15/2)/(c*x^4+b*x^2+a)^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: 192.56Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1081,-2,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2+a)^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: 191.18Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1082,-2,0,0,0.000000," ","integrate(x^(11/2)/(c*x^4+b*x^2+a)^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: 191.55Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1083,-2,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2+a)^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: 191.51Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1084,-2,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2+a)^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: 191.21Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1085,-2,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2+a)^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: 191.33Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1086,-2,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2+a)^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: 191.63Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1087,-2,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2+a)^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: 191.53Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1088,-2,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a)^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: 191.11Unable to convert to real 1/4 Error: Bad Argument Value","F(-2)",0
1089,0,0,0,0.000000," ","integrate((d*x)^(3/2)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} \left(d x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(d*x)^(3/2), x)","F",0
1090,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x), x)","F",0
1091,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/(d*x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2} + a}}{\sqrt{d x}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)/sqrt(d*x), x)","F",0
1092,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/(d*x)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2} + a}}{\left(d x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)/(d*x)^(3/2), x)","F",0
1093,0,0,0,0.000000," ","integrate((d*x)^(3/2)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \left(d x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(d*x)^(3/2), x)","F",0
1094,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*sqrt(d*x), x)","F",0
1095,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/(d*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{d x}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)/sqrt(d*x), x)","F",0
1096,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/(d*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}{\left(d x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)/(d*x)^(3/2), x)","F",0
1097,0,0,0,0.000000," ","integrate((d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((d*x)^(3/2)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
1098,0,0,0,0.000000," ","integrate((d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
1099,0,0,0,0.000000," ","integrate(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} + a} \sqrt{d x}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2 + a)*sqrt(d*x)), x)","F",0
1100,0,0,0,0.000000," ","integrate(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} + a} \left(d x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2 + a)*(d*x)^(3/2)), x)","F",0
1101,0,0,0,0.000000," ","integrate((d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{\frac{3}{2}}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^(3/2)/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
1102,0,0,0,0.000000," ","integrate((d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*x)/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
1103,0,0,0,0.000000," ","integrate(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2 + a)^(3/2)*sqrt(d*x)), x)","F",0
1104,0,0,0,0.000000," ","integrate(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \left(d x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c*x^4 + b*x^2 + a)^(3/2)*(d*x)^(3/2)), x)","F",0
1105,1,1132,0,0.225768," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c^{3} m^{6} x^{13} + 36 \, \left(d x\right)^{m} c^{3} m^{5} x^{13} + 3 \, \left(d x\right)^{m} b c^{2} m^{6} x^{11} + 505 \, \left(d x\right)^{m} c^{3} m^{4} x^{13} + 114 \, \left(d x\right)^{m} b c^{2} m^{5} x^{11} + 3480 \, \left(d x\right)^{m} c^{3} m^{3} x^{13} + 3 \, \left(d x\right)^{m} b^{2} c m^{6} x^{9} + 3 \, \left(d x\right)^{m} a c^{2} m^{6} x^{9} + 1665 \, \left(d x\right)^{m} b c^{2} m^{4} x^{11} + 12139 \, \left(d x\right)^{m} c^{3} m^{2} x^{13} + 120 \, \left(d x\right)^{m} b^{2} c m^{5} x^{9} + 120 \, \left(d x\right)^{m} a c^{2} m^{5} x^{9} + 11820 \, \left(d x\right)^{m} b c^{2} m^{3} x^{11} + 19524 \, \left(d x\right)^{m} c^{3} m x^{13} + \left(d x\right)^{m} b^{3} m^{6} x^{7} + 6 \, \left(d x\right)^{m} a b c m^{6} x^{7} + 1839 \, \left(d x\right)^{m} b^{2} c m^{4} x^{9} + 1839 \, \left(d x\right)^{m} a c^{2} m^{4} x^{9} + 42117 \, \left(d x\right)^{m} b c^{2} m^{2} x^{11} + 10395 \, \left(d x\right)^{m} c^{3} x^{13} + 42 \, \left(d x\right)^{m} b^{3} m^{5} x^{7} + 252 \, \left(d x\right)^{m} a b c m^{5} x^{7} + 13584 \, \left(d x\right)^{m} b^{2} c m^{3} x^{9} + 13584 \, \left(d x\right)^{m} a c^{2} m^{3} x^{9} + 68706 \, \left(d x\right)^{m} b c^{2} m x^{11} + 3 \, \left(d x\right)^{m} a b^{2} m^{6} x^{5} + 3 \, \left(d x\right)^{m} a^{2} c m^{6} x^{5} + 679 \, \left(d x\right)^{m} b^{3} m^{4} x^{7} + 4074 \, \left(d x\right)^{m} a b c m^{4} x^{7} + 49881 \, \left(d x\right)^{m} b^{2} c m^{2} x^{9} + 49881 \, \left(d x\right)^{m} a c^{2} m^{2} x^{9} + 36855 \, \left(d x\right)^{m} b c^{2} x^{11} + 132 \, \left(d x\right)^{m} a b^{2} m^{5} x^{5} + 132 \, \left(d x\right)^{m} a^{2} c m^{5} x^{5} + 5292 \, \left(d x\right)^{m} b^{3} m^{3} x^{7} + 31752 \, \left(d x\right)^{m} a b c m^{3} x^{7} + 83064 \, \left(d x\right)^{m} b^{2} c m x^{9} + 83064 \, \left(d x\right)^{m} a c^{2} m x^{9} + 3 \, \left(d x\right)^{m} a^{2} b m^{6} x^{3} + 2259 \, \left(d x\right)^{m} a b^{2} m^{4} x^{5} + 2259 \, \left(d x\right)^{m} a^{2} c m^{4} x^{5} + 20335 \, \left(d x\right)^{m} b^{3} m^{2} x^{7} + 122010 \, \left(d x\right)^{m} a b c m^{2} x^{7} + 45045 \, \left(d x\right)^{m} b^{2} c x^{9} + 45045 \, \left(d x\right)^{m} a c^{2} x^{9} + 138 \, \left(d x\right)^{m} a^{2} b m^{5} x^{3} + 18840 \, \left(d x\right)^{m} a b^{2} m^{3} x^{5} + 18840 \, \left(d x\right)^{m} a^{2} c m^{3} x^{5} + 34986 \, \left(d x\right)^{m} b^{3} m x^{7} + 209916 \, \left(d x\right)^{m} a b c m x^{7} + \left(d x\right)^{m} a^{3} m^{6} x + 2505 \, \left(d x\right)^{m} a^{2} b m^{4} x^{3} + 77937 \, \left(d x\right)^{m} a b^{2} m^{2} x^{5} + 77937 \, \left(d x\right)^{m} a^{2} c m^{2} x^{5} + 19305 \, \left(d x\right)^{m} b^{3} x^{7} + 115830 \, \left(d x\right)^{m} a b c x^{7} + 48 \, \left(d x\right)^{m} a^{3} m^{5} x + 22620 \, \left(d x\right)^{m} a^{2} b m^{3} x^{3} + 142308 \, \left(d x\right)^{m} a b^{2} m x^{5} + 142308 \, \left(d x\right)^{m} a^{2} c m x^{5} + 925 \, \left(d x\right)^{m} a^{3} m^{4} x + 104277 \, \left(d x\right)^{m} a^{2} b m^{2} x^{3} + 81081 \, \left(d x\right)^{m} a b^{2} x^{5} + 81081 \, \left(d x\right)^{m} a^{2} c x^{5} + 9120 \, \left(d x\right)^{m} a^{3} m^{3} x + 219162 \, \left(d x\right)^{m} a^{2} b m x^{3} + 48259 \, \left(d x\right)^{m} a^{3} m^{2} x + 135135 \, \left(d x\right)^{m} a^{2} b x^{3} + 129072 \, \left(d x\right)^{m} a^{3} m x + 135135 \, \left(d x\right)^{m} a^{3} x}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((d*x)^m*c^3*m^6*x^13 + 36*(d*x)^m*c^3*m^5*x^13 + 3*(d*x)^m*b*c^2*m^6*x^11 + 505*(d*x)^m*c^3*m^4*x^13 + 114*(d*x)^m*b*c^2*m^5*x^11 + 3480*(d*x)^m*c^3*m^3*x^13 + 3*(d*x)^m*b^2*c*m^6*x^9 + 3*(d*x)^m*a*c^2*m^6*x^9 + 1665*(d*x)^m*b*c^2*m^4*x^11 + 12139*(d*x)^m*c^3*m^2*x^13 + 120*(d*x)^m*b^2*c*m^5*x^9 + 120*(d*x)^m*a*c^2*m^5*x^9 + 11820*(d*x)^m*b*c^2*m^3*x^11 + 19524*(d*x)^m*c^3*m*x^13 + (d*x)^m*b^3*m^6*x^7 + 6*(d*x)^m*a*b*c*m^6*x^7 + 1839*(d*x)^m*b^2*c*m^4*x^9 + 1839*(d*x)^m*a*c^2*m^4*x^9 + 42117*(d*x)^m*b*c^2*m^2*x^11 + 10395*(d*x)^m*c^3*x^13 + 42*(d*x)^m*b^3*m^5*x^7 + 252*(d*x)^m*a*b*c*m^5*x^7 + 13584*(d*x)^m*b^2*c*m^3*x^9 + 13584*(d*x)^m*a*c^2*m^3*x^9 + 68706*(d*x)^m*b*c^2*m*x^11 + 3*(d*x)^m*a*b^2*m^6*x^5 + 3*(d*x)^m*a^2*c*m^6*x^5 + 679*(d*x)^m*b^3*m^4*x^7 + 4074*(d*x)^m*a*b*c*m^4*x^7 + 49881*(d*x)^m*b^2*c*m^2*x^9 + 49881*(d*x)^m*a*c^2*m^2*x^9 + 36855*(d*x)^m*b*c^2*x^11 + 132*(d*x)^m*a*b^2*m^5*x^5 + 132*(d*x)^m*a^2*c*m^5*x^5 + 5292*(d*x)^m*b^3*m^3*x^7 + 31752*(d*x)^m*a*b*c*m^3*x^7 + 83064*(d*x)^m*b^2*c*m*x^9 + 83064*(d*x)^m*a*c^2*m*x^9 + 3*(d*x)^m*a^2*b*m^6*x^3 + 2259*(d*x)^m*a*b^2*m^4*x^5 + 2259*(d*x)^m*a^2*c*m^4*x^5 + 20335*(d*x)^m*b^3*m^2*x^7 + 122010*(d*x)^m*a*b*c*m^2*x^7 + 45045*(d*x)^m*b^2*c*x^9 + 45045*(d*x)^m*a*c^2*x^9 + 138*(d*x)^m*a^2*b*m^5*x^3 + 18840*(d*x)^m*a*b^2*m^3*x^5 + 18840*(d*x)^m*a^2*c*m^3*x^5 + 34986*(d*x)^m*b^3*m*x^7 + 209916*(d*x)^m*a*b*c*m*x^7 + (d*x)^m*a^3*m^6*x + 2505*(d*x)^m*a^2*b*m^4*x^3 + 77937*(d*x)^m*a*b^2*m^2*x^5 + 77937*(d*x)^m*a^2*c*m^2*x^5 + 19305*(d*x)^m*b^3*x^7 + 115830*(d*x)^m*a*b*c*x^7 + 48*(d*x)^m*a^3*m^5*x + 22620*(d*x)^m*a^2*b*m^3*x^3 + 142308*(d*x)^m*a*b^2*m*x^5 + 142308*(d*x)^m*a^2*c*m*x^5 + 925*(d*x)^m*a^3*m^4*x + 104277*(d*x)^m*a^2*b*m^2*x^3 + 81081*(d*x)^m*a*b^2*x^5 + 81081*(d*x)^m*a^2*c*x^5 + 9120*(d*x)^m*a^3*m^3*x + 219162*(d*x)^m*a^2*b*m*x^3 + 48259*(d*x)^m*a^3*m^2*x + 135135*(d*x)^m*a^2*b*x^3 + 129072*(d*x)^m*a^3*m*x + 135135*(d*x)^m*a^3*x)/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
1106,1,449,0,0.181169," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c^{2} m^{4} x^{9} + 16 \, \left(d x\right)^{m} c^{2} m^{3} x^{9} + 2 \, \left(d x\right)^{m} b c m^{4} x^{7} + 86 \, \left(d x\right)^{m} c^{2} m^{2} x^{9} + 36 \, \left(d x\right)^{m} b c m^{3} x^{7} + 176 \, \left(d x\right)^{m} c^{2} m x^{9} + \left(d x\right)^{m} b^{2} m^{4} x^{5} + 2 \, \left(d x\right)^{m} a c m^{4} x^{5} + 208 \, \left(d x\right)^{m} b c m^{2} x^{7} + 105 \, \left(d x\right)^{m} c^{2} x^{9} + 20 \, \left(d x\right)^{m} b^{2} m^{3} x^{5} + 40 \, \left(d x\right)^{m} a c m^{3} x^{5} + 444 \, \left(d x\right)^{m} b c m x^{7} + 2 \, \left(d x\right)^{m} a b m^{4} x^{3} + 130 \, \left(d x\right)^{m} b^{2} m^{2} x^{5} + 260 \, \left(d x\right)^{m} a c m^{2} x^{5} + 270 \, \left(d x\right)^{m} b c x^{7} + 44 \, \left(d x\right)^{m} a b m^{3} x^{3} + 300 \, \left(d x\right)^{m} b^{2} m x^{5} + 600 \, \left(d x\right)^{m} a c m x^{5} + \left(d x\right)^{m} a^{2} m^{4} x + 328 \, \left(d x\right)^{m} a b m^{2} x^{3} + 189 \, \left(d x\right)^{m} b^{2} x^{5} + 378 \, \left(d x\right)^{m} a c x^{5} + 24 \, \left(d x\right)^{m} a^{2} m^{3} x + 916 \, \left(d x\right)^{m} a b m x^{3} + 206 \, \left(d x\right)^{m} a^{2} m^{2} x + 630 \, \left(d x\right)^{m} a b x^{3} + 744 \, \left(d x\right)^{m} a^{2} m x + 945 \, \left(d x\right)^{m} a^{2} x}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((d*x)^m*c^2*m^4*x^9 + 16*(d*x)^m*c^2*m^3*x^9 + 2*(d*x)^m*b*c*m^4*x^7 + 86*(d*x)^m*c^2*m^2*x^9 + 36*(d*x)^m*b*c*m^3*x^7 + 176*(d*x)^m*c^2*m*x^9 + (d*x)^m*b^2*m^4*x^5 + 2*(d*x)^m*a*c*m^4*x^5 + 208*(d*x)^m*b*c*m^2*x^7 + 105*(d*x)^m*c^2*x^9 + 20*(d*x)^m*b^2*m^3*x^5 + 40*(d*x)^m*a*c*m^3*x^5 + 444*(d*x)^m*b*c*m*x^7 + 2*(d*x)^m*a*b*m^4*x^3 + 130*(d*x)^m*b^2*m^2*x^5 + 260*(d*x)^m*a*c*m^2*x^5 + 270*(d*x)^m*b*c*x^7 + 44*(d*x)^m*a*b*m^3*x^3 + 300*(d*x)^m*b^2*m*x^5 + 600*(d*x)^m*a*c*m*x^5 + (d*x)^m*a^2*m^4*x + 328*(d*x)^m*a*b*m^2*x^3 + 189*(d*x)^m*b^2*x^5 + 378*(d*x)^m*a*c*x^5 + 24*(d*x)^m*a^2*m^3*x + 916*(d*x)^m*a*b*m*x^3 + 206*(d*x)^m*a^2*m^2*x + 630*(d*x)^m*a*b*x^3 + 744*(d*x)^m*a^2*m*x + 945*(d*x)^m*a^2*x)/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
1107,1,119,0,0.160415," ","integrate((d*x)^m*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c m^{2} x^{5} + 4 \, \left(d x\right)^{m} c m x^{5} + \left(d x\right)^{m} b m^{2} x^{3} + 3 \, \left(d x\right)^{m} c x^{5} + 6 \, \left(d x\right)^{m} b m x^{3} + \left(d x\right)^{m} a m^{2} x + 5 \, \left(d x\right)^{m} b x^{3} + 8 \, \left(d x\right)^{m} a m x + 15 \, \left(d x\right)^{m} a x}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((d*x)^m*c*m^2*x^5 + 4*(d*x)^m*c*m*x^5 + (d*x)^m*b*m^2*x^3 + 3*(d*x)^m*c*x^5 + 6*(d*x)^m*b*m*x^3 + (d*x)^m*a*m^2*x + 5*(d*x)^m*b*x^3 + 8*(d*x)^m*a*m*x + 15*(d*x)^m*a*x)/(m^3 + 9*m^2 + 23*m + 15)","B",0
1108,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^4 + b*x^2 + a), x)","F",0
1109,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{4} + b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^4 + b*x^2 + a)^2, x)","F",0
1110,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(d*x)^m, x)","F",0
1111,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(d*x)^m, x)","F",0
1112,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(c*x^4 + b*x^2 + a), x)","F",0
1113,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
1114,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p*(d*x)^m, x)","F",0
1115,0,0,0,0.000000," ","integrate(x^7*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p} x^{7}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p*x^7, x)","F",0
1116,0,0,0,0.000000," ","integrate(x^5*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p} x^{5}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p*x^5, x)","F",0
1117,0,0,0,0.000000," ","integrate(x^3*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p*x^3, x)","F",0
1118,0,0,0,0.000000," ","integrate(x*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p} x\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p*x, x)","F",0
1119,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^p/x,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p/x, x)","F",0
1120,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p/x^3, x)","F",0
1121,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^p/x^5,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{5}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p/x^5, x)","F",0
1122,0,0,0,0.000000," ","integrate(x^4*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p} x^{4}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p*x^4, x)","F",0
1123,0,0,0,0.000000," ","integrate(x^2*(c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p*x^2, x)","F",0
1124,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p, x)","F",0
1125,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p/x^2, x)","F",0
1126,0,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^p/x^4,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{p}}{x^{4}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^p/x^4, x)","F",0
