1,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/4),x, algorithm=""maxima"")","\int {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{3}{4}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(3/4), x)","F",0
2,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(1/4),x, algorithm=""maxima"")","\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
3,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\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
4,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^(-3/4), x)","F",0
5,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/4),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
8,0,0,0,0.000000," ","integrate(1/(x^4+2*a*x^2+a^2+b),x, algorithm=""maxima"")","\int \frac{1}{x^{4} + 2 \, a x^{2} + a^{2} + b}\,{d x}"," ",0,"integrate(1/(x^4 + 2*a*x^2 + a^2 + b), x)","F",0
9,-2,0,0,0.000000," ","integrate(1/(x^4+2*a*x^2+a^2-1),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1.0>0)', see `assume?` for more details)Is a-1.0 positive or negative?","F(-2)",0
10,0,0,0,0.000000," ","integrate(1/(x^4+2*a*x^2+a^2+1),x, algorithm=""maxima"")","\int \frac{1}{x^{4} + 2 \, a x^{2} + a^{2} + 1}\,{d x}"," ",0,"integrate(1/(x^4 + 2*a*x^2 + a^2 + 1), x)","F",0
11,1,25,0,1.369566," ","integrate(1/(x^4-5*x^2+4),x, algorithm=""maxima"")","-\frac{1}{12} \, \log\left(x + 2\right) + \frac{1}{6} \, \log\left(x + 1\right) - \frac{1}{6} \, \log\left(x - 1\right) + \frac{1}{12} \, \log\left(x - 2\right)"," ",0,"-1/12*log(x + 2) + 1/6*log(x + 1) - 1/6*log(x - 1) + 1/12*log(x - 2)","B",0
12,1,17,0,2.997314," ","integrate(1/(x^4+4*x^2+3),x, algorithm=""maxima"")","-\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
13,1,53,0,3.035679," ","integrate(1/(x^4+5*x^2+9),x, algorithm=""maxima"")","\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
14,0,0,0,0.000000," ","integrate(1/(x^4-x^2+1),x, algorithm=""maxima"")","\int \frac{1}{x^{4} - x^{2} + 1}\,{d x}"," ",0,"integrate(1/(x^4 - x^2 + 1), x)","F",0
15,0,0,0,0.000000," ","integrate(1/(x^4+2*x^2+2),x, algorithm=""maxima"")","\int \frac{1}{x^{4} + 2 \, x^{2} + 2}\,{d x}"," ",0,"integrate(1/(x^4 + 2*x^2 + 2), x)","F",0
16,0,0,0,0.000000," ","integrate(1/(-3*x^4+5*x^2+2)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
134,1,13,0,1.330395," ","integrate(x^2*(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
135,1,13,0,1.300213," ","integrate(x*(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
136,1,13,0,1.363075," ","integrate(c*x^4+b*x^2,x, algorithm=""maxima"")","\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
137,1,13,0,1.305920," ","integrate((c*x^4+b*x^2)/x,x, algorithm=""maxima"")","\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
138,1,10,0,1.263076," ","integrate((c*x^4+b*x^2)/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, c x^{3} + b x"," ",0,"1/3*c*x^3 + b*x","A",0
139,1,14,0,1.347224," ","integrate((c*x^4+b*x^2)/x^3,x, algorithm=""maxima"")","\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
140,1,10,0,1.333607," ","integrate((c*x^4+b*x^2)/x^4,x, algorithm=""maxima"")","c x - \frac{b}{x}"," ",0,"c*x - b/x","A",0
141,1,14,0,1.351417," ","integrate((c*x^4+b*x^2)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, c \log\left(x^{2}\right) - \frac{b}{2 \, x^{2}}"," ",0,"1/2*c*log(x^2) - 1/2*b/x^2","A",0
142,1,13,0,1.295617," ","integrate((c*x^4+b*x^2)/x^6,x, algorithm=""maxima"")","-\frac{3 \, c x^{2} + b}{3 \, x^{3}}"," ",0,"-1/3*(3*c*x^2 + b)/x^3","A",0
143,1,13,0,1.314845," ","integrate((c*x^4+b*x^2)/x^7,x, algorithm=""maxima"")","-\frac{2 \, c x^{2} + b}{4 \, x^{4}}"," ",0,"-1/4*(2*c*x^2 + b)/x^4","A",0
144,1,15,0,1.246365," ","integrate((c*x^4+b*x^2)/x^8,x, algorithm=""maxima"")","-\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}}"," ",0,"-1/15*(5*c*x^2 + 3*b)/x^5","A",0
145,1,24,0,1.378378," ","integrate((c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\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
146,1,24,0,1.350372," ","integrate((c*x^4+b*x^2)^2/x,x, algorithm=""maxima"")","\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
147,1,24,0,1.316499," ","integrate((c*x^4+b*x^2)^2/x^2,x, algorithm=""maxima"")","\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
148,1,24,0,1.311084," ","integrate((c*x^4+b*x^2)^2/x^3,x, algorithm=""maxima"")","\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
149,1,21,0,1.352841," ","integrate((c*x^4+b*x^2)^2/x^4,x, algorithm=""maxima"")","\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
150,1,24,0,1.346460," ","integrate((c*x^4+b*x^2)^2/x^5,x, algorithm=""maxima"")","\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
151,1,22,0,1.313875," ","integrate((c*x^4+b*x^2)^2/x^6,x, algorithm=""maxima"")","\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
152,1,24,0,1.327879," ","integrate((c*x^4+b*x^2)^2/x^7,x, algorithm=""maxima"")","\frac{1}{2} \, c^{2} x^{2} + b c \log\left(x^{2}\right) - \frac{b^{2}}{2 \, x^{2}}"," ",0,"1/2*c^2*x^2 + b*c*log(x^2) - 1/2*b^2/x^2","A",0
153,1,22,0,1.285613," ","integrate((c*x^4+b*x^2)^2/x^8,x, algorithm=""maxima"")","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
154,1,26,0,1.315262," ","integrate((c*x^4+b*x^2)^2/x^9,x, algorithm=""maxima"")","\frac{1}{2} \, c^{2} \log\left(x^{2}\right) - \frac{4 \, b c x^{2} + b^{2}}{4 \, x^{4}}"," ",0,"1/2*c^2*log(x^2) - 1/4*(4*b*c*x^2 + b^2)/x^4","A",0
155,1,26,0,1.303871," ","integrate((c*x^4+b*x^2)^2/x^10,x, algorithm=""maxima"")","-\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
156,1,24,0,1.227407," ","integrate((c*x^4+b*x^2)^2/x^11,x, algorithm=""maxima"")","-\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
157,1,26,0,1.366731," ","integrate((c*x^4+b*x^2)^2/x^12,x, algorithm=""maxima"")","-\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
158,1,35,0,1.304190," ","integrate((c*x^4+b*x^2)^3/x^2,x, algorithm=""maxima"")","\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
159,1,35,0,1.321597," ","integrate((c*x^4+b*x^2)^3/x^3,x, algorithm=""maxima"")","\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
160,1,35,0,1.344134," ","integrate((c*x^4+b*x^2)^3/x^4,x, algorithm=""maxima"")","\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
161,1,35,0,1.278088," ","integrate((c*x^4+b*x^2)^3/x^5,x, algorithm=""maxima"")","\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
162,1,31,0,1.318314," ","integrate((c*x^4+b*x^2)^3/x^6,x, algorithm=""maxima"")","\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
163,1,36,0,1.326721," ","integrate((c*x^4+b*x^2)^3/x^7,x, algorithm=""maxima"")","\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
164,1,32,0,1.377603," ","integrate((c*x^4+b*x^2)^3/x^8,x, algorithm=""maxima"")","\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
165,1,36,0,1.265620," ","integrate((c*x^4+b*x^2)^3/x^9,x, algorithm=""maxima"")","\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{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*b^3/x^2","A",0
166,1,34,0,1.286239," ","integrate((c*x^4+b*x^2)^3/x^10,x, algorithm=""maxima"")","\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
167,1,37,0,1.342787," ","integrate((c*x^4+b*x^2)^3/x^11,x, algorithm=""maxima"")","\frac{1}{2} \, c^{3} x^{2} + \frac{3}{2} \, b c^{2} \log\left(x^{2}\right) - \frac{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*(6*b^2*c*x^2 + b^3)/x^4","A",0
168,1,33,0,1.303024," ","integrate((c*x^4+b*x^2)^3/x^12,x, algorithm=""maxima"")","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
169,1,39,0,1.318685," ","integrate((c*x^4+b*x^2)^3/x^13,x, algorithm=""maxima"")","\frac{1}{2} \, c^{3} \log\left(x^{2}\right) - \frac{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*(18*b*c^2*x^4 + 9*b^2*c*x^2 + 2*b^3)/x^6","A",0
170,1,37,0,1.347061," ","integrate((c*x^4+b*x^2)^3/x^14,x, algorithm=""maxima"")","-\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
171,1,35,0,1.337697," ","integrate((c*x^4+b*x^2)^3/x^15,x, algorithm=""maxima"")","-\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
172,1,37,0,1.325089," ","integrate((c*x^4+b*x^2)^3/x^16,x, algorithm=""maxima"")","-\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
173,1,37,0,1.313055," ","integrate((c*x^4+b*x^2)^3/x^17,x, algorithm=""maxima"")","-\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
174,1,60,0,3.012013," ","integrate(x^10/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{b^{4} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} c^{4}} + \frac{15 \, c^{3} x^{7} - 21 \, b c^{2} x^{5} + 35 \, b^{2} c x^{3} - 105 \, b^{3} x}{105 \, c^{4}}"," ",0,"b^4*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^4) + 1/105*(15*c^3*x^7 - 21*b*c^2*x^5 + 35*b^2*c*x^3 - 105*b^3*x)/c^4","A",0
175,1,46,0,1.328671," ","integrate(x^9/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{b^{3} \log\left(c x^{2} + b\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(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
176,1,50,0,2.880953," ","integrate(x^8/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{b^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} c^{3}} + \frac{3 \, c^{2} x^{5} - 5 \, b c x^{3} + 15 \, b^{2} x}{15 \, c^{3}}"," ",0,"-b^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^3) + 1/15*(3*c^2*x^5 - 5*b*c*x^3 + 15*b^2*x)/c^3","A",0
177,1,34,0,1.333504," ","integrate(x^7/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{b^{2} \log\left(c x^{2} + b\right)}{2 \, c^{3}} + \frac{c x^{4} - 2 \, b x^{2}}{4 \, c^{2}}"," ",0,"1/2*b^2*log(c*x^2 + b)/c^3 + 1/4*(c*x^4 - 2*b*x^2)/c^2","A",0
178,1,37,0,2.949638," ","integrate(x^6/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c} c^{2}} + \frac{c x^{3} - 3 \, b x}{3 \, c^{2}}"," ",0,"b^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^2) + 1/3*(c*x^3 - 3*b*x)/c^2","A",0
179,1,23,0,1.312783," ","integrate(x^5/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{x^{2}}{2 \, c} - \frac{b \log\left(c x^{2} + b\right)}{2 \, c^{2}}"," ",0,"1/2*x^2/c - 1/2*b*log(c*x^2 + b)/c^2","A",0
180,1,26,0,2.967808," ","integrate(x^4/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\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
181,1,13,0,1.352253," ","integrate(x^3/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{\log\left(c x^{2} + b\right)}{2 \, c}"," ",0,"1/2*log(c*x^2 + b)/c","A",0
182,1,15,0,2.967851," ","integrate(x^2/(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
183,1,23,0,1.364791," ","integrate(x/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{\log\left(c x^{2} + b\right)}{2 \, b} + \frac{\log\left(x^{2}\right)}{2 \, b}"," ",0,"-1/2*log(c*x^2 + b)/b + 1/2*log(x^2)/b","A",0
184,1,29,0,2.883873," ","integrate(1/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\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
185,1,33,0,1.365120," ","integrate(1/x/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{c \log\left(c x^{2} + b\right)}{2 \, b^{2}} - \frac{c \log\left(x^{2}\right)}{2 \, b^{2}} - \frac{1}{2 \, b x^{2}}"," ",0,"1/2*c*log(c*x^2 + b)/b^2 - 1/2*c*log(x^2)/b^2 - 1/2/(b*x^2)","A",0
186,1,40,0,2.961337," ","integrate(1/x^2/(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
187,1,47,0,1.316781," ","integrate(1/x^3/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{c^{2} \log\left(c x^{2} + b\right)}{2 \, b^{3}} + \frac{c^{2} \log\left(x^{2}\right)}{2 \, b^{3}} + \frac{2 \, c x^{2} - b}{4 \, b^{2} x^{4}}"," ",0,"-1/2*c^2*log(c*x^2 + b)/b^3 + 1/2*c^2*log(x^2)/b^3 + 1/4*(2*c*x^2 - b)/(b^2*x^4)","A",0
188,1,52,0,2.888015," ","integrate(1/x^4/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\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
189,1,58,0,1.319370," ","integrate(1/x^5/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{c^{3} \log\left(c x^{2} + b\right)}{2 \, b^{4}} - \frac{c^{3} \log\left(x^{2}\right)}{2 \, b^{4}} - \frac{6 \, c^{2} x^{4} - 3 \, b c x^{2} + 2 \, b^{2}}{12 \, b^{3} x^{6}}"," ",0,"1/2*c^3*log(c*x^2 + b)/b^4 - 1/2*c^3*log(x^2)/b^4 - 1/12*(6*c^2*x^4 - 3*b*c*x^2 + 2*b^2)/(b^3*x^6)","A",0
190,1,71,0,2.909079," ","integrate(x^12/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{b^{3} x}{2 \, {\left(c^{5} x^{2} + b c^{4}\right)}} - \frac{7 \, b^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c^{4}} + \frac{3 \, c^{2} x^{5} - 10 \, b c x^{3} + 45 \, b^{2} x}{15 \, c^{4}}"," ",0,"1/2*b^3*x/(c^5*x^2 + b*c^4) - 7/2*b^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^4) + 1/15*(3*c^2*x^5 - 10*b*c*x^3 + 45*b^2*x)/c^4","A",0
191,1,54,0,1.318627," ","integrate(x^11/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{b^{3}}{2 \, {\left(c^{5} x^{2} + b c^{4}\right)}} + \frac{3 \, b^{2} \log\left(c x^{2} + b\right)}{2 \, c^{4}} + \frac{c x^{4} - 4 \, b x^{2}}{4 \, c^{3}}"," ",0,"1/2*b^3/(c^5*x^2 + b*c^4) + 3/2*b^2*log(c*x^2 + b)/c^4 + 1/4*(c*x^4 - 4*b*x^2)/c^3","A",0
192,1,59,0,2.934523," ","integrate(x^10/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{b^{2} x}{2 \, {\left(c^{4} x^{2} + b c^{3}\right)}} + \frac{5 \, b^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c^{3}} + \frac{c x^{3} - 6 \, b x}{3 \, c^{3}}"," ",0,"-1/2*b^2*x/(c^4*x^2 + b*c^3) + 5/2*b^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^3) + 1/3*(c*x^3 - 6*b*x)/c^3","A",0
193,1,43,0,1.323884," ","integrate(x^9/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{b^{2}}{2 \, {\left(c^{4} x^{2} + b c^{3}\right)}} + \frac{x^{2}}{2 \, c^{2}} - \frac{b \log\left(c x^{2} + b\right)}{c^{3}}"," ",0,"-1/2*b^2/(c^4*x^2 + b*c^3) + 1/2*x^2/c^2 - b*log(c*x^2 + b)/c^3","A",0
194,1,45,0,2.936621," ","integrate(x^8/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{b x}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}} - \frac{3 \, b \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c^{2}} + \frac{x}{c^{2}}"," ",0,"1/2*b*x/(c^3*x^2 + b*c^2) - 3/2*b*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^2) + x/c^2","A",0
195,1,32,0,1.288550," ","integrate(x^7/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{b}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}} + \frac{\log\left(c x^{2} + b\right)}{2 \, c^{2}}"," ",0,"1/2*b/(c^3*x^2 + b*c^2) + 1/2*log(c*x^2 + b)/c^2","A",0
196,1,36,0,3.021803," ","integrate(x^6/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{x}{2 \, {\left(c^{2} x^{2} + b c\right)}} + \frac{\arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} c}"," ",0,"-1/2*x/(c^2*x^2 + b*c) + 1/2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c)","A",0
197,1,15,0,1.321178," ","integrate(x^5/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(c^{2} x^{2} + b c\right)}}"," ",0,"-1/2/(c^2*x^2 + b*c)","A",0
198,1,35,0,2.998499," ","integrate(x^4/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{x}{2 \, {\left(b c x^{2} + b^{2}\right)}} + \frac{\arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b}"," ",0,"1/2*x/(b*c*x^2 + b^2) + 1/2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b)","A",0
199,1,37,0,1.296429," ","integrate(x^3/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{1}{2 \, {\left(b c x^{2} + b^{2}\right)}} - \frac{\log\left(c x^{2} + b\right)}{2 \, b^{2}} + \frac{\log\left(x^{2}\right)}{2 \, b^{2}}"," ",0,"1/2/(b*c*x^2 + b^2) - 1/2*log(c*x^2 + b)/b^2 + 1/2*log(x^2)/b^2","A",0
200,1,49,0,2.963940," ","integrate(x^2/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{3 \, c x^{2} + 2 \, b}{2 \, {\left(b^{2} c x^{3} + b^{3} x\right)}} - \frac{3 \, c \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b^{2}}"," ",0,"-1/2*(3*c*x^2 + 2*b)/(b^2*c*x^3 + b^3*x) - 3/2*c*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^2)","A",0
201,1,52,0,1.342281," ","integrate(x/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{2 \, c x^{2} + b}{2 \, {\left(b^{2} c x^{4} + b^{3} x^{2}\right)}} + \frac{c \log\left(c x^{2} + b\right)}{b^{3}} - \frac{c \log\left(x^{2}\right)}{b^{3}}"," ",0,"-1/2*(2*c*x^2 + b)/(b^2*c*x^4 + b^3*x^2) + c*log(c*x^2 + b)/b^3 - c*log(x^2)/b^3","A",0
202,1,64,0,2.957639," ","integrate(1/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{15 \, c^{2} x^{4} + 10 \, b c x^{2} - 2 \, b^{2}}{6 \, {\left(b^{3} c x^{5} + b^{4} x^{3}\right)}} + \frac{5 \, c^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b^{3}}"," ",0,"1/6*(15*c^2*x^4 + 10*b*c*x^2 - 2*b^2)/(b^3*c*x^5 + b^4*x^3) + 5/2*c^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^3)","A",0
203,1,70,0,1.345106," ","integrate(1/x/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{6 \, c^{2} x^{4} + 3 \, b c x^{2} - b^{2}}{4 \, {\left(b^{3} c x^{6} + b^{4} x^{4}\right)}} - \frac{3 \, c^{2} \log\left(c x^{2} + b\right)}{2 \, b^{4}} + \frac{3 \, c^{2} \log\left(x^{2}\right)}{2 \, b^{4}}"," ",0,"1/4*(6*c^2*x^4 + 3*b*c*x^2 - b^2)/(b^3*c*x^6 + b^4*x^4) - 3/2*c^2*log(c*x^2 + b)/b^4 + 3/2*c^2*log(x^2)/b^4","A",0
204,1,75,0,3.027171," ","integrate(1/x^2/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{105 \, c^{3} x^{6} + 70 \, b c^{2} x^{4} - 14 \, b^{2} c x^{2} + 6 \, b^{3}}{30 \, {\left(b^{4} c x^{7} + b^{5} x^{5}\right)}} - \frac{7 \, c^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{2 \, \sqrt{b c} b^{4}}"," ",0,"-1/30*(105*c^3*x^6 + 70*b*c^2*x^4 - 14*b^2*c*x^2 + 6*b^3)/(b^4*c*x^7 + b^5*x^5) - 7/2*c^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^4)","A",0
205,1,82,0,2.937991," ","integrate(x^14/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{13 \, b^{2} c x^{3} + 11 \, b^{3} x}{8 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}} + \frac{35 \, b^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} c^{4}} + \frac{c x^{3} - 9 \, b x}{3 \, c^{4}}"," ",0,"-1/8*(13*b^2*c*x^3 + 11*b^3*x)/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4) + 35/8*b^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^4) + 1/3*(c*x^3 - 9*b*x)/c^4","A",0
206,1,66,0,1.358237," ","integrate(x^13/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{6 \, b^{2} c x^{2} + 5 \, b^{3}}{4 \, {\left(c^{6} x^{4} + 2 \, b c^{5} x^{2} + b^{2} c^{4}\right)}} + \frac{x^{2}}{2 \, c^{3}} - \frac{3 \, b \log\left(c x^{2} + b\right)}{2 \, c^{4}}"," ",0,"-1/4*(6*b^2*c*x^2 + 5*b^3)/(c^6*x^4 + 2*b*c^5*x^2 + b^2*c^4) + 1/2*x^2/c^3 - 3/2*b*log(c*x^2 + b)/c^4","A",0
207,1,68,0,2.816926," ","integrate(x^12/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{9 \, b c x^{3} + 7 \, b^{2} x}{8 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}} - \frac{15 \, b \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} c^{3}} + \frac{x}{c^{3}}"," ",0,"1/8*(9*b*c*x^3 + 7*b^2*x)/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3) - 15/8*b*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^3) + x/c^3","A",0
208,1,55,0,1.350943," ","integrate(x^11/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{4 \, b c x^{2} + 3 \, b^{2}}{4 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}} + \frac{\log\left(c x^{2} + b\right)}{2 \, c^{3}}"," ",0,"1/4*(4*b*c*x^2 + 3*b^2)/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3) + 1/2*log(c*x^2 + b)/c^3","A",0
209,1,59,0,2.911743," ","integrate(x^10/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{5 \, c x^{3} + 3 \, b x}{8 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}} + \frac{3 \, \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} c^{2}}"," ",0,"-1/8*(5*c*x^3 + 3*b*x)/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2) + 3/8*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*c^2)","A",0
210,1,36,0,1.331138," ","integrate(x^9/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{2 \, c x^{2} + b}{4 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}}"," ",0,"-1/4*(2*c*x^2 + b)/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2)","B",0
211,1,62,0,2.858889," ","integrate(x^8/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{c x^{3} - b x}{8 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)}} + \frac{\arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b c}"," ",0,"1/8*(c*x^3 - b*x)/(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c) + 1/8*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b*c)","A",0
212,1,26,0,1.271570," ","integrate(x^7/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{1}{4 \, {\left(c^{3} x^{4} + 2 \, b c^{2} x^{2} + b^{2} c\right)}}"," ",0,"-1/4/(c^3*x^4 + 2*b*c^2*x^2 + b^2*c)","A",0
213,1,58,0,2.986259," ","integrate(x^6/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{3 \, c x^{3} + 5 \, b x}{8 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)}} + \frac{3 \, \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{2}}"," ",0,"1/8*(3*c*x^3 + 5*b*x)/(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4) + 3/8*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^2)","A",0
214,1,60,0,1.377861," ","integrate(x^5/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{2 \, c x^{2} + 3 \, b}{4 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)}} - \frac{\log\left(c x^{2} + b\right)}{2 \, b^{3}} + \frac{\log\left(x^{2}\right)}{2 \, b^{3}}"," ",0,"1/4*(2*c*x^2 + 3*b)/(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4) - 1/2*log(c*x^2 + b)/b^3 + 1/2*log(x^2)/b^3","A",0
215,1,71,0,3.002212," ","integrate(x^4/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{15 \, c^{2} x^{4} + 25 \, b c x^{2} + 8 \, b^{2}}{8 \, {\left(b^{3} c^{2} x^{5} + 2 \, b^{4} c x^{3} + b^{5} x\right)}} - \frac{15 \, c \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{3}}"," ",0,"-1/8*(15*c^2*x^4 + 25*b*c*x^2 + 8*b^2)/(b^3*c^2*x^5 + 2*b^4*c*x^3 + b^5*x) - 15/8*c*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^3)","A",0
216,1,77,0,1.384429," ","integrate(x^3/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{6 \, c^{2} x^{4} + 9 \, b c x^{2} + 2 \, b^{2}}{4 \, {\left(b^{3} c^{2} x^{6} + 2 \, b^{4} c x^{4} + b^{5} x^{2}\right)}} + \frac{3 \, c \log\left(c x^{2} + b\right)}{2 \, b^{4}} - \frac{3 \, c \log\left(x^{2}\right)}{2 \, b^{4}}"," ",0,"-1/4*(6*c^2*x^4 + 9*b*c*x^2 + 2*b^2)/(b^3*c^2*x^6 + 2*b^4*c*x^4 + b^5*x^2) + 3/2*c*log(c*x^2 + b)/b^4 - 3/2*c*log(x^2)/b^4","A",0
217,1,86,0,2.933982," ","integrate(x^2/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{105 \, c^{3} x^{6} + 175 \, b c^{2} x^{4} + 56 \, b^{2} c x^{2} - 8 \, b^{3}}{24 \, {\left(b^{4} c^{2} x^{7} + 2 \, b^{5} c x^{5} + b^{6} x^{3}\right)}} + \frac{35 \, c^{2} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{4}}"," ",0,"1/24*(105*c^3*x^6 + 175*b*c^2*x^4 + 56*b^2*c*x^2 - 8*b^3)/(b^4*c^2*x^7 + 2*b^5*c*x^5 + b^6*x^3) + 35/8*c^2*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^4)","A",0
218,1,92,0,1.350963," ","integrate(x/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{12 \, c^{3} x^{6} + 18 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} - b^{3}}{4 \, {\left(b^{4} c^{2} x^{8} + 2 \, b^{5} c x^{6} + b^{6} x^{4}\right)}} - \frac{3 \, c^{2} \log\left(c x^{2} + b\right)}{b^{5}} + \frac{3 \, c^{2} \log\left(x^{2}\right)}{b^{5}}"," ",0,"1/4*(12*c^3*x^6 + 18*b*c^2*x^4 + 4*b^2*c*x^2 - b^3)/(b^4*c^2*x^8 + 2*b^5*c*x^6 + b^6*x^4) - 3*c^2*log(c*x^2 + b)/b^5 + 3*c^2*log(x^2)/b^5","A",0
219,1,97,0,2.974893," ","integrate(1/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{315 \, c^{4} x^{8} + 525 \, b c^{3} x^{6} + 168 \, b^{2} c^{2} x^{4} - 24 \, b^{3} c x^{2} + 8 \, b^{4}}{40 \, {\left(b^{5} c^{2} x^{9} + 2 \, b^{6} c x^{7} + b^{7} x^{5}\right)}} - \frac{63 \, c^{3} \arctan\left(\frac{c x}{\sqrt{b c}}\right)}{8 \, \sqrt{b c} b^{5}}"," ",0,"-1/40*(315*c^4*x^8 + 525*b*c^3*x^6 + 168*b^2*c^2*x^4 - 24*b^3*c*x^2 + 8*b^4)/(b^5*c^2*x^9 + 2*b^6*c*x^7 + b^7*x^5) - 63/8*c^3*arctan(c*x/sqrt(b*c))/(sqrt(b*c)*b^5)","A",0
220,1,103,0,1.362815," ","integrate(1/x/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{60 \, c^{4} x^{8} + 90 \, b c^{3} x^{6} + 20 \, b^{2} c^{2} x^{4} - 5 \, b^{3} c x^{2} + 2 \, b^{4}}{12 \, {\left(b^{5} c^{2} x^{10} + 2 \, b^{6} c x^{8} + b^{7} x^{6}\right)}} + \frac{5 \, c^{3} \log\left(c x^{2} + b\right)}{b^{6}} - \frac{5 \, c^{3} \log\left(x^{2}\right)}{b^{6}}"," ",0,"-1/12*(60*c^4*x^8 + 90*b*c^3*x^6 + 20*b^2*c^2*x^4 - 5*b^3*c*x^2 + 2*b^4)/(b^5*c^2*x^10 + 2*b^6*c*x^8 + b^7*x^6) + 5*c^3*log(c*x^2 + b)/b^6 - 5*c^3*log(x^2)/b^6","A",0
221,1,121,0,1.455094," ","integrate(x^5*(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{5 \, \sqrt{c x^{4} + b x^{2}} b^{2} x^{2}}{64 \, c^{2}} + \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{2}}{8 \, c} - \frac{5 \, b^{4} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{256 \, c^{\frac{7}{2}}} + \frac{5 \, \sqrt{c x^{4} + b x^{2}} b^{3}}{128 \, c^{3}} - \frac{5 \, {\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} b}{48 \, c^{2}}"," ",0,"5/64*sqrt(c*x^4 + b*x^2)*b^2*x^2/c^2 + 1/8*(c*x^4 + b*x^2)^(3/2)*x^2/c - 5/256*b^4*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(7/2) + 5/128*sqrt(c*x^4 + b*x^2)*b^3/c^3 - 5/48*(c*x^4 + b*x^2)^(3/2)*b/c^2","A",0
222,1,97,0,1.446627," ","integrate(x^3*(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{4} + b x^{2}} b x^{2}}{8 \, c} + \frac{b^{3} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{32 \, c^{\frac{5}{2}}} - \frac{\sqrt{c x^{4} + b x^{2}} b^{2}}{16 \, c^{2}} + \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{6 \, c}"," ",0,"-1/8*sqrt(c*x^4 + b*x^2)*b*x^2/c + 1/32*b^3*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(5/2) - 1/16*sqrt(c*x^4 + b*x^2)*b^2/c^2 + 1/6*(c*x^4 + b*x^2)^(3/2)/c","A",0
223,1,73,0,1.428026," ","integrate(x*(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{c x^{4} + b x^{2}} x^{2} - \frac{b^{2} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{16 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{4} + b x^{2}} b}{8 \, c}"," ",0,"1/4*sqrt(c*x^4 + b*x^2)*x^2 - 1/16*b^2*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(3/2) + 1/8*sqrt(c*x^4 + b*x^2)*b/c","A",0
224,1,49,0,1.426705," ","integrate((c*x^4+b*x^2)^(1/2)/x,x, algorithm=""maxima"")","\frac{b \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{4 \, \sqrt{c}} + \frac{1}{2} \, \sqrt{c x^{4} + b x^{2}}"," ",0,"1/4*b*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/sqrt(c) + 1/2*sqrt(c*x^4 + b*x^2)","A",0
225,1,51,0,1.390228," ","integrate((c*x^4+b*x^2)^(1/2)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{c} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - \frac{\sqrt{c x^{4} + b x^{2}}}{x^{2}}"," ",0,"1/2*sqrt(c)*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - sqrt(c*x^4 + b*x^2)/x^2","A",0
226,1,41,0,1.438439," ","integrate((c*x^4+b*x^2)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{\sqrt{c x^{4} + b x^{2}} c}{3 \, b x^{2}} - \frac{\sqrt{c x^{4} + b x^{2}}}{3 \, x^{4}}"," ",0,"-1/3*sqrt(c*x^4 + b*x^2)*c/(b*x^2) - 1/3*sqrt(c*x^4 + b*x^2)/x^4","A",0
227,1,65,0,1.422005," ","integrate((c*x^4+b*x^2)^(1/2)/x^7,x, algorithm=""maxima"")","\frac{2 \, \sqrt{c x^{4} + b x^{2}} c^{2}}{15 \, b^{2} x^{2}} - \frac{\sqrt{c x^{4} + b x^{2}} c}{15 \, b x^{4}} - \frac{\sqrt{c x^{4} + b x^{2}}}{5 \, x^{6}}"," ",0,"2/15*sqrt(c*x^4 + b*x^2)*c^2/(b^2*x^2) - 1/15*sqrt(c*x^4 + b*x^2)*c/(b*x^4) - 1/5*sqrt(c*x^4 + b*x^2)/x^6","A",0
228,1,89,0,1.426131," ","integrate((c*x^4+b*x^2)^(1/2)/x^9,x, algorithm=""maxima"")","-\frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{105 \, b^{3} x^{2}} + \frac{4 \, \sqrt{c x^{4} + b x^{2}} c^{2}}{105 \, b^{2} x^{4}} - \frac{\sqrt{c x^{4} + b x^{2}} c}{35 \, b x^{6}} - \frac{\sqrt{c x^{4} + b x^{2}}}{7 \, x^{8}}"," ",0,"-8/105*sqrt(c*x^4 + b*x^2)*c^3/(b^3*x^2) + 4/105*sqrt(c*x^4 + b*x^2)*c^2/(b^2*x^4) - 1/35*sqrt(c*x^4 + b*x^2)*c/(b*x^6) - 1/7*sqrt(c*x^4 + b*x^2)/x^8","A",0
229,1,113,0,1.419816," ","integrate((c*x^4+b*x^2)^(1/2)/x^11,x, algorithm=""maxima"")","\frac{16 \, \sqrt{c x^{4} + b x^{2}} c^{4}}{315 \, b^{4} x^{2}} - \frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{315 \, b^{3} x^{4}} + \frac{2 \, \sqrt{c x^{4} + b x^{2}} c^{2}}{105 \, b^{2} x^{6}} - \frac{\sqrt{c x^{4} + b x^{2}} c}{63 \, b x^{8}} - \frac{\sqrt{c x^{4} + b x^{2}}}{9 \, x^{10}}"," ",0,"16/315*sqrt(c*x^4 + b*x^2)*c^4/(b^4*x^2) - 8/315*sqrt(c*x^4 + b*x^2)*c^3/(b^3*x^4) + 2/105*sqrt(c*x^4 + b*x^2)*c^2/(b^2*x^6) - 1/63*sqrt(c*x^4 + b*x^2)*c/(b*x^8) - 1/9*sqrt(c*x^4 + b*x^2)/x^10","A",0
230,1,137,0,1.531487," ","integrate((c*x^4+b*x^2)^(1/2)/x^13,x, algorithm=""maxima"")","-\frac{128 \, \sqrt{c x^{4} + b x^{2}} c^{5}}{3465 \, b^{5} x^{2}} + \frac{64 \, \sqrt{c x^{4} + b x^{2}} c^{4}}{3465 \, b^{4} x^{4}} - \frac{16 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{1155 \, b^{3} x^{6}} + \frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{2}}{693 \, b^{2} x^{8}} - \frac{\sqrt{c x^{4} + b x^{2}} c}{99 \, b x^{10}} - \frac{\sqrt{c x^{4} + b x^{2}}}{11 \, x^{12}}"," ",0,"-128/3465*sqrt(c*x^4 + b*x^2)*c^5/(b^5*x^2) + 64/3465*sqrt(c*x^4 + b*x^2)*c^4/(b^4*x^4) - 16/1155*sqrt(c*x^4 + b*x^2)*c^3/(b^3*x^6) + 8/693*sqrt(c*x^4 + b*x^2)*c^2/(b^2*x^8) - 1/99*sqrt(c*x^4 + b*x^2)*c/(b*x^10) - 1/11*sqrt(c*x^4 + b*x^2)/x^12","A",0
231,1,46,0,1.406130," ","integrate(x^4*(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(15 \, c^{3} x^{6} + 3 \, b c^{2} x^{4} - 4 \, b^{2} c x^{2} + 8 \, b^{3}\right)} \sqrt{c x^{2} + b}}{105 \, c^{3}}"," ",0,"1/105*(15*c^3*x^6 + 3*b*c^2*x^4 - 4*b^2*c*x^2 + 8*b^3)*sqrt(c*x^2 + b)/c^3","A",0
232,1,34,0,1.393777," ","integrate(x^2*(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(3 \, c^{2} x^{4} + b c x^{2} - 2 \, b^{2}\right)} \sqrt{c x^{2} + b}}{15 \, c^{2}}"," ",0,"1/15*(3*c^2*x^4 + b*c*x^2 - 2*b^2)*sqrt(c*x^2 + b)/c^2","A",0
233,1,14,0,1.429029," ","integrate((c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(c x^{2} + b\right)}^{\frac{3}{2}}}{3 \, c}"," ",0,"1/3*(c*x^2 + b)^(3/2)/c","A",0
234,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^2, x)","F",0
235,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^4, x)","F",0
236,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^6,x, algorithm=""maxima"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^6, x)","F",0
237,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(1/2)/x^8,x, algorithm=""maxima"")","\int \frac{\sqrt{c x^{4} + b x^{2}}}{x^{8}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2)/x^8, x)","F",0
238,1,142,0,1.389506," ","integrate(x^3*(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{c x^{4} + b x^{2}} b^{3} x^{2}}{128 \, c^{2}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} b x^{2}}{16 \, c} - \frac{3 \, b^{5} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{512 \, c^{\frac{7}{2}}} + \frac{3 \, \sqrt{c x^{4} + b x^{2}} b^{4}}{256 \, c^{3}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} b^{2}}{32 \, c^{2}} + \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{5}{2}}}{10 \, c}"," ",0,"3/128*sqrt(c*x^4 + b*x^2)*b^3*x^2/c^2 - 1/16*(c*x^4 + b*x^2)^(3/2)*b*x^2/c - 3/512*b^5*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(7/2) + 3/256*sqrt(c*x^4 + b*x^2)*b^4/c^3 - 1/32*(c*x^4 + b*x^2)^(3/2)*b^2/c^2 + 1/10*(c*x^4 + b*x^2)^(5/2)/c","A",0
239,1,118,0,1.470510," ","integrate(x*(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} x^{2} - \frac{3 \, \sqrt{c x^{4} + b x^{2}} b^{2} x^{2}}{64 \, c} + \frac{3 \, b^{4} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{256 \, c^{\frac{5}{2}}} - \frac{3 \, \sqrt{c x^{4} + b x^{2}} b^{3}}{128 \, c^{2}} + \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} b}{16 \, c}"," ",0,"1/8*(c*x^4 + b*x^2)^(3/2)*x^2 - 3/64*sqrt(c*x^4 + b*x^2)*b^2*x^2/c + 3/256*b^4*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(5/2) - 3/128*sqrt(c*x^4 + b*x^2)*b^3/c^2 + 1/16*(c*x^4 + b*x^2)^(3/2)*b/c","A",0
240,1,91,0,1.415519," ","integrate((c*x^4+b*x^2)^(3/2)/x,x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{c x^{4} + b x^{2}} b x^{2} - \frac{b^{3} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{32 \, c^{\frac{3}{2}}} + \frac{1}{6} \, {\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}} + \frac{\sqrt{c x^{4} + b x^{2}} b^{2}}{16 \, c}"," ",0,"1/8*sqrt(c*x^4 + b*x^2)*b*x^2 - 1/32*b^3*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(3/2) + 1/6*(c*x^4 + b*x^2)^(3/2) + 1/16*sqrt(c*x^4 + b*x^2)*b^2/c","A",0
241,1,70,0,1.444519," ","integrate((c*x^4+b*x^2)^(3/2)/x^3,x, algorithm=""maxima"")","\frac{3 \, b^{2} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{16 \, \sqrt{c}} + \frac{3}{8} \, \sqrt{c x^{4} + b x^{2}} b + \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{4 \, x^{2}}"," ",0,"3/16*b^2*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/sqrt(c) + 3/8*sqrt(c*x^4 + b*x^2)*b + 1/4*(c*x^4 + b*x^2)^(3/2)/x^2","A",0
242,1,71,0,1.444235," ","integrate((c*x^4+b*x^2)^(3/2)/x^5,x, algorithm=""maxima"")","\frac{3}{4} \, b \sqrt{c} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - \frac{3 \, \sqrt{c x^{4} + b x^{2}} b}{2 \, x^{2}} + \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{2 \, x^{4}}"," ",0,"3/4*b*sqrt(c)*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 3/2*sqrt(c*x^4 + b*x^2)*b/x^2 + 1/2*(c*x^4 + b*x^2)^(3/2)/x^4","A",0
243,1,89,0,1.505112," ","integrate((c*x^4+b*x^2)^(3/2)/x^7,x, algorithm=""maxima"")","\frac{1}{2} \, c^{\frac{3}{2}} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right) - \frac{7 \, \sqrt{c x^{4} + b x^{2}} c}{6 \, x^{2}} - \frac{\sqrt{c x^{4} + b x^{2}} b}{6 \, x^{4}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{6 \, x^{6}}"," ",0,"1/2*c^(3/2)*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c)) - 7/6*sqrt(c*x^4 + b*x^2)*c/x^2 - 1/6*sqrt(c*x^4 + b*x^2)*b/x^4 - 1/6*(c*x^4 + b*x^2)^(3/2)/x^6","A",0
244,1,81,0,1.408772," ","integrate((c*x^4+b*x^2)^(3/2)/x^9,x, algorithm=""maxima"")","-\frac{\sqrt{c x^{4} + b x^{2}} c^{2}}{5 \, b x^{2}} + \frac{\sqrt{c x^{4} + b x^{2}} c}{10 \, x^{4}} + \frac{3 \, \sqrt{c x^{4} + b x^{2}} b}{10 \, x^{6}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{2 \, x^{8}}"," ",0,"-1/5*sqrt(c*x^4 + b*x^2)*c^2/(b*x^2) + 1/10*sqrt(c*x^4 + b*x^2)*c/x^4 + 3/10*sqrt(c*x^4 + b*x^2)*b/x^6 - 1/2*(c*x^4 + b*x^2)^(3/2)/x^8","B",0
245,1,105,0,1.463259," ","integrate((c*x^4+b*x^2)^(3/2)/x^11,x, algorithm=""maxima"")","\frac{2 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{35 \, b^{2} x^{2}} - \frac{\sqrt{c x^{4} + b x^{2}} c^{2}}{35 \, b x^{4}} + \frac{3 \, \sqrt{c x^{4} + b x^{2}} c}{140 \, x^{6}} + \frac{3 \, \sqrt{c x^{4} + b x^{2}} b}{28 \, x^{8}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{4 \, x^{10}}"," ",0,"2/35*sqrt(c*x^4 + b*x^2)*c^3/(b^2*x^2) - 1/35*sqrt(c*x^4 + b*x^2)*c^2/(b*x^4) + 3/140*sqrt(c*x^4 + b*x^2)*c/x^6 + 3/28*sqrt(c*x^4 + b*x^2)*b/x^8 - 1/4*(c*x^4 + b*x^2)^(3/2)/x^10","B",0
246,1,129,0,1.519870," ","integrate((c*x^4+b*x^2)^(3/2)/x^13,x, algorithm=""maxima"")","-\frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{4}}{315 \, b^{3} x^{2}} + \frac{4 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{315 \, b^{2} x^{4}} - \frac{\sqrt{c x^{4} + b x^{2}} c^{2}}{105 \, b x^{6}} + \frac{\sqrt{c x^{4} + b x^{2}} c}{126 \, x^{8}} + \frac{\sqrt{c x^{4} + b x^{2}} b}{18 \, x^{10}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{6 \, x^{12}}"," ",0,"-8/315*sqrt(c*x^4 + b*x^2)*c^4/(b^3*x^2) + 4/315*sqrt(c*x^4 + b*x^2)*c^3/(b^2*x^4) - 1/105*sqrt(c*x^4 + b*x^2)*c^2/(b*x^6) + 1/126*sqrt(c*x^4 + b*x^2)*c/x^8 + 1/18*sqrt(c*x^4 + b*x^2)*b/x^10 - 1/6*(c*x^4 + b*x^2)^(3/2)/x^12","A",0
247,1,153,0,1.492463," ","integrate((c*x^4+b*x^2)^(3/2)/x^15,x, algorithm=""maxima"")","\frac{16 \, \sqrt{c x^{4} + b x^{2}} c^{5}}{1155 \, b^{4} x^{2}} - \frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{4}}{1155 \, b^{3} x^{4}} + \frac{2 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{385 \, b^{2} x^{6}} - \frac{\sqrt{c x^{4} + b x^{2}} c^{2}}{231 \, b x^{8}} + \frac{\sqrt{c x^{4} + b x^{2}} c}{264 \, x^{10}} + \frac{3 \, \sqrt{c x^{4} + b x^{2}} b}{88 \, x^{12}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{8 \, x^{14}}"," ",0,"16/1155*sqrt(c*x^4 + b*x^2)*c^5/(b^4*x^2) - 8/1155*sqrt(c*x^4 + b*x^2)*c^4/(b^3*x^4) + 2/385*sqrt(c*x^4 + b*x^2)*c^3/(b^2*x^6) - 1/231*sqrt(c*x^4 + b*x^2)*c^2/(b*x^8) + 1/264*sqrt(c*x^4 + b*x^2)*c/x^10 + 3/88*sqrt(c*x^4 + b*x^2)*b/x^12 - 1/8*(c*x^4 + b*x^2)^(3/2)/x^14","A",0
248,1,177,0,1.468103," ","integrate((c*x^4+b*x^2)^(3/2)/x^17,x, algorithm=""maxima"")","-\frac{128 \, \sqrt{c x^{4} + b x^{2}} c^{6}}{15015 \, b^{5} x^{2}} + \frac{64 \, \sqrt{c x^{4} + b x^{2}} c^{5}}{15015 \, b^{4} x^{4}} - \frac{16 \, \sqrt{c x^{4} + b x^{2}} c^{4}}{5005 \, b^{3} x^{6}} + \frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{3003 \, b^{2} x^{8}} - \frac{\sqrt{c x^{4} + b x^{2}} c^{2}}{429 \, b x^{10}} + \frac{3 \, \sqrt{c x^{4} + b x^{2}} c}{1430 \, x^{12}} + \frac{3 \, \sqrt{c x^{4} + b x^{2}} b}{130 \, x^{14}} - \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{10 \, x^{16}}"," ",0,"-128/15015*sqrt(c*x^4 + b*x^2)*c^6/(b^5*x^2) + 64/15015*sqrt(c*x^4 + b*x^2)*c^5/(b^4*x^4) - 16/5005*sqrt(c*x^4 + b*x^2)*c^4/(b^3*x^6) + 8/3003*sqrt(c*x^4 + b*x^2)*c^3/(b^2*x^8) - 1/429*sqrt(c*x^4 + b*x^2)*c^2/(b*x^10) + 3/1430*sqrt(c*x^4 + b*x^2)*c/x^12 + 3/130*sqrt(c*x^4 + b*x^2)*b/x^14 - 1/10*(c*x^4 + b*x^2)^(3/2)/x^16","A",0
249,1,79,0,1.534409," ","integrate(x^6*(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(1155 \, c^{6} x^{12} + 1470 \, b c^{5} x^{10} + 35 \, b^{2} c^{4} x^{8} - 40 \, b^{3} c^{3} x^{6} + 48 \, b^{4} c^{2} x^{4} - 64 \, b^{5} c x^{2} + 128 \, b^{6}\right)} \sqrt{c x^{2} + b}}{15015 \, c^{5}}"," ",0,"1/15015*(1155*c^6*x^12 + 1470*b*c^5*x^10 + 35*b^2*c^4*x^8 - 40*b^3*c^3*x^6 + 48*b^4*c^2*x^4 - 64*b^5*c*x^2 + 128*b^6)*sqrt(c*x^2 + b)/c^5","A",0
250,1,68,0,1.502540," ","integrate(x^4*(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(105 \, c^{5} x^{10} + 140 \, b c^{4} x^{8} + 5 \, b^{2} c^{3} x^{6} - 6 \, b^{3} c^{2} x^{4} + 8 \, b^{4} c x^{2} - 16 \, b^{5}\right)} \sqrt{c x^{2} + b}}{1155 \, c^{4}}"," ",0,"1/1155*(105*c^5*x^10 + 140*b*c^4*x^8 + 5*b^2*c^3*x^6 - 6*b^3*c^2*x^4 + 8*b^4*c*x^2 - 16*b^5)*sqrt(c*x^2 + b)/c^4","A",0
251,1,57,0,1.445222," ","integrate(x^2*(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(35 \, c^{4} x^{8} + 50 \, b c^{3} x^{6} + 3 \, b^{2} c^{2} x^{4} - 4 \, b^{3} c x^{2} + 8 \, b^{4}\right)} \sqrt{c x^{2} + b}}{315 \, c^{3}}"," ",0,"1/315*(35*c^4*x^8 + 50*b*c^3*x^6 + 3*b^2*c^2*x^4 - 4*b^3*c*x^2 + 8*b^4)*sqrt(c*x^2 + b)/c^3","A",0
252,1,45,0,1.503975," ","integrate((c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(5 \, c^{3} x^{6} + 8 \, b c^{2} x^{4} + b^{2} c x^{2} - 2 \, b^{3}\right)} \sqrt{c x^{2} + b}}{35 \, c^{2}}"," ",0,"1/35*(5*c^3*x^6 + 8*b*c^2*x^4 + b^2*c*x^2 - 2*b^3)*sqrt(c*x^2 + b)/c^2","A",0
253,1,32,0,1.482985," ","integrate((c*x^4+b*x^2)^(3/2)/x^2,x, algorithm=""maxima"")","\frac{{\left(c^{2} x^{4} + 2 \, b c x^{2} + b^{2}\right)} \sqrt{c x^{2} + b}}{5 \, c}"," ",0,"1/5*(c^2*x^4 + 2*b*c*x^2 + b^2)*sqrt(c*x^2 + b)/c","A",0
254,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^4, x)","F",0
255,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^6,x, algorithm=""maxima"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{6}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^6, x)","F",0
256,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^8,x, algorithm=""maxima"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{8}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^8, x)","F",0
257,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^10,x, algorithm=""maxima"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{10}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^10, x)","F",0
258,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^12,x, algorithm=""maxima"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{12}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^12, x)","F",0
259,0,0,0,0.000000," ","integrate((c*x^4+b*x^2)^(3/2)/x^14,x, algorithm=""maxima"")","\int \frac{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}{x^{14}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(3/2)/x^14, x)","F",0
260,1,100,0,1.473832," ","integrate(x^7/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{4} + b x^{2}} x^{4}}{6 \, c} - \frac{5 \, \sqrt{c x^{4} + b x^{2}} b x^{2}}{24 \, c^{2}} - \frac{5 \, b^{3} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{32 \, c^{\frac{7}{2}}} + \frac{5 \, \sqrt{c x^{4} + b x^{2}} b^{2}}{16 \, c^{3}}"," ",0,"1/6*sqrt(c*x^4 + b*x^2)*x^4/c - 5/24*sqrt(c*x^4 + b*x^2)*b*x^2/c^2 - 5/32*b^3*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(7/2) + 5/16*sqrt(c*x^4 + b*x^2)*b^2/c^3","A",0
261,1,76,0,1.453260," ","integrate(x^5/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{4} + b x^{2}} x^{2}}{4 \, c} + \frac{3 \, b^{2} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{16 \, c^{\frac{5}{2}}} - \frac{3 \, \sqrt{c x^{4} + b x^{2}} b}{8 \, c^{2}}"," ",0,"1/4*sqrt(c*x^4 + b*x^2)*x^2/c + 3/16*b^2*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(5/2) - 3/8*sqrt(c*x^4 + b*x^2)*b/c^2","A",0
262,1,52,0,1.447633," ","integrate(x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{b \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{4 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{4} + b x^{2}}}{2 \, c}"," ",0,"-1/4*b*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(3/2) + 1/2*sqrt(c*x^4 + b*x^2)/c","A",0
263,1,32,0,1.460790," ","integrate(x/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{2 \, \sqrt{c}}"," ",0,"1/2*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/sqrt(c)","A",0
264,1,21,0,1.472216," ","integrate(1/x/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{4} + b x^{2}}}{b x^{2}}"," ",0,"-sqrt(c*x^4 + b*x^2)/(b*x^2)","A",0
265,1,44,0,1.429273," ","integrate(1/x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{c x^{4} + b x^{2}} c}{3 \, b^{2} x^{2}} - \frac{\sqrt{c x^{4} + b x^{2}}}{3 \, b x^{4}}"," ",0,"2/3*sqrt(c*x^4 + b*x^2)*c/(b^2*x^2) - 1/3*sqrt(c*x^4 + b*x^2)/(b*x^4)","A",0
266,1,68,0,1.434706," ","integrate(1/x^5/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{2}}{15 \, b^{3} x^{2}} + \frac{4 \, \sqrt{c x^{4} + b x^{2}} c}{15 \, b^{2} x^{4}} - \frac{\sqrt{c x^{4} + b x^{2}}}{5 \, b x^{6}}"," ",0,"-8/15*sqrt(c*x^4 + b*x^2)*c^2/(b^3*x^2) + 4/15*sqrt(c*x^4 + b*x^2)*c/(b^2*x^4) - 1/5*sqrt(c*x^4 + b*x^2)/(b*x^6)","A",0
267,1,92,0,1.408055," ","integrate(1/x^7/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{16 \, \sqrt{c x^{4} + b x^{2}} c^{3}}{35 \, b^{4} x^{2}} - \frac{8 \, \sqrt{c x^{4} + b x^{2}} c^{2}}{35 \, b^{3} x^{4}} + \frac{6 \, \sqrt{c x^{4} + b x^{2}} c}{35 \, b^{2} x^{6}} - \frac{\sqrt{c x^{4} + b x^{2}}}{7 \, b x^{8}}"," ",0,"16/35*sqrt(c*x^4 + b*x^2)*c^3/(b^4*x^2) - 8/35*sqrt(c*x^4 + b*x^2)*c^2/(b^3*x^4) + 6/35*sqrt(c*x^4 + b*x^2)*c/(b^2*x^6) - 1/7*sqrt(c*x^4 + b*x^2)/(b*x^8)","A",0
268,1,34,0,1.504689," ","integrate(x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{c^{2} x^{4} - b c x^{2} - 2 \, b^{2}}{3 \, \sqrt{c x^{2} + b} c^{2}}"," ",0,"1/3*(c^2*x^4 - b*c*x^2 - 2*b^2)/(sqrt(c*x^2 + b)*c^2)","A",0
269,1,13,0,1.419480," ","integrate(x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{2} + b}}{c}"," ",0,"sqrt(c*x^2 + b)/c","A",0
270,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^4 + b*x^2), x)","F",0
271,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^2), x)","F",0
272,0,0,0,0.000000," ","integrate(1/x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^4), x)","F",0
273,1,103,0,1.476677," ","integrate(x^9/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{x^{6}}{4 \, \sqrt{c x^{4} + b x^{2}} c} - \frac{5 \, b x^{4}}{8 \, \sqrt{c x^{4} + b x^{2}} c^{2}} - \frac{15 \, b^{2} x^{2}}{8 \, \sqrt{c x^{4} + b x^{2}} c^{3}} + \frac{15 \, b^{2} \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/4*x^6/(sqrt(c*x^4 + b*x^2)*c) - 5/8*b*x^4/(sqrt(c*x^4 + b*x^2)*c^2) - 15/8*b^2*x^2/(sqrt(c*x^4 + b*x^2)*c^3) + 15/16*b^2*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(7/2)","A",0
274,1,77,0,1.506124," ","integrate(x^7/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{x^{4}}{2 \, \sqrt{c x^{4} + b x^{2}} c} + \frac{3 \, b x^{2}}{2 \, \sqrt{c x^{4} + b x^{2}} c^{2}} - \frac{3 \, b \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{4 \, c^{\frac{5}{2}}}"," ",0,"1/2*x^4/(sqrt(c*x^4 + b*x^2)*c) + 3/2*b*x^2/(sqrt(c*x^4 + b*x^2)*c^2) - 3/4*b*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(5/2)","A",0
275,1,54,0,1.469013," ","integrate(x^5/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","-\frac{x^{2}}{\sqrt{c x^{4} + b x^{2}} c} + \frac{\log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"-x^2/(sqrt(c*x^4 + b*x^2)*c) + 1/2*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(3/2)","A",0
276,1,20,0,1.452808," ","integrate(x^3/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{x^{2}}{\sqrt{c x^{4} + b x^{2}} b}"," ",0,"x^2/(sqrt(c*x^4 + b*x^2)*b)","A",0
277,1,41,0,1.466596," ","integrate(x/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, c x^{2}}{\sqrt{c x^{4} + b x^{2}} b^{2}} - \frac{1}{\sqrt{c x^{4} + b x^{2}} b}"," ",0,"-2*c*x^2/(sqrt(c*x^4 + b*x^2)*b^2) - 1/(sqrt(c*x^4 + b*x^2)*b)","A",0
278,1,65,0,1.485277," ","integrate(1/x/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{8 \, c^{2} x^{2}}{3 \, \sqrt{c x^{4} + b x^{2}} b^{3}} + \frac{4 \, c}{3 \, \sqrt{c x^{4} + b x^{2}} b^{2}} - \frac{1}{3 \, \sqrt{c x^{4} + b x^{2}} b x^{2}}"," ",0,"8/3*c^2*x^2/(sqrt(c*x^4 + b*x^2)*b^3) + 4/3*c/(sqrt(c*x^4 + b*x^2)*b^2) - 1/3/(sqrt(c*x^4 + b*x^2)*b*x^2)","A",0
279,1,89,0,1.510627," ","integrate(1/x^3/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","-\frac{16 \, c^{3} x^{2}}{5 \, \sqrt{c x^{4} + b x^{2}} b^{4}} - \frac{8 \, c^{2}}{5 \, \sqrt{c x^{4} + b x^{2}} b^{3}} + \frac{2 \, c}{5 \, \sqrt{c x^{4} + b x^{2}} b^{2} x^{2}} - \frac{1}{5 \, \sqrt{c x^{4} + b x^{2}} b x^{4}}"," ",0,"-16/5*c^3*x^2/(sqrt(c*x^4 + b*x^2)*b^4) - 8/5*c^2/(sqrt(c*x^4 + b*x^2)*b^3) + 2/5*c/(sqrt(c*x^4 + b*x^2)*b^2*x^2) - 1/5/(sqrt(c*x^4 + b*x^2)*b*x^4)","A",0
280,1,113,0,1.468717," ","integrate(1/x^5/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{128 \, c^{4} x^{2}}{35 \, \sqrt{c x^{4} + b x^{2}} b^{5}} + \frac{64 \, c^{3}}{35 \, \sqrt{c x^{4} + b x^{2}} b^{4}} - \frac{16 \, c^{2}}{35 \, \sqrt{c x^{4} + b x^{2}} b^{3} x^{2}} + \frac{8 \, c}{35 \, \sqrt{c x^{4} + b x^{2}} b^{2} x^{4}} - \frac{1}{7 \, \sqrt{c x^{4} + b x^{2}} b x^{6}}"," ",0,"128/35*c^4*x^2/(sqrt(c*x^4 + b*x^2)*b^5) + 64/35*c^3/(sqrt(c*x^4 + b*x^2)*b^4) - 16/35*c^2/(sqrt(c*x^4 + b*x^2)*b^3*x^2) + 8/35*c/(sqrt(c*x^4 + b*x^2)*b^2*x^4) - 1/7/(sqrt(c*x^4 + b*x^2)*b*x^6)","A",0
281,1,22,0,1.483083," ","integrate(x^6/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\frac{c x^{2} + 2 \, b}{\sqrt{c x^{2} + b} c^{2}}"," ",0,"(c*x^2 + 2*b)/(sqrt(c*x^2 + b)*c^2)","A",0
282,1,14,0,1.442774," ","integrate(x^4/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{c x^{2} + b} c}"," ",0,"-1/(sqrt(c*x^2 + b)*c)","A",0
283,0,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(c*x^4 + b*x^2)^(3/2), x)","F",0
284,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c x^{4} + b x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2)^(-3/2), x)","F",0
285,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2)^(3/2),x, algorithm=""maxima"")","\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
286,1,26,0,3.031975," ","integrate(x^3/(-4*x^4+3*x^2)^(1/2),x, algorithm=""maxima"")","-\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
287,1,26,0,2.979735," ","integrate(x^3/(-4*x^4-3*x^2)^(1/2),x, algorithm=""maxima"")","-\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
288,1,41,0,3.047482," ","integrate(x^3/(4*x^4+3*x^2)^(1/2),x, algorithm=""maxima"")","\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
289,1,41,0,3.043409," ","integrate(x^3/(4*x^4-3*x^2)^(1/2),x, algorithm=""maxima"")","\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
290,1,52,0,1.418554," ","integrate(x^3/(b*x^4+a*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{a \log\left(2 \, b x^{2} + a + 2 \, \sqrt{b x^{4} + a x^{2}} \sqrt{b}\right)}{4 \, b^{\frac{3}{2}}} + \frac{\sqrt{b x^{4} + a x^{2}}}{2 \, b}"," ",0,"-1/4*a*log(2*b*x^2 + a + 2*sqrt(b*x^4 + a*x^2)*sqrt(b))/b^(3/2) + 1/2*sqrt(b*x^4 + a*x^2)/b","A",0
291,1,42,0,3.026394," ","integrate(x^3/(-b*x^4+a*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{a \arcsin\left(-\frac{2 \, b x^{2} - a}{a}\right)}{4 \, b^{\frac{3}{2}}} - \frac{\sqrt{-b x^{4} + a x^{2}}}{2 \, b}"," ",0,"-1/4*a*arcsin(-(2*b*x^2 - a)/a)/b^(3/2) - 1/2*sqrt(-b*x^4 + a*x^2)/b","A",0
292,1,13,0,1.301780," ","integrate(x^(7/2)*(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
293,1,13,0,1.357802," ","integrate(x^(5/2)*(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
294,1,13,0,1.344492," ","integrate(x^(3/2)*(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
295,1,13,0,1.327046," ","integrate(x^(1/2)*(c*x^4+b*x^2),x, algorithm=""maxima"")","\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
296,1,13,0,1.333044," ","integrate((c*x^4+b*x^2)/x^(1/2),x, algorithm=""maxima"")","\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
297,1,13,0,1.303581," ","integrate((c*x^4+b*x^2)/x^(3/2),x, algorithm=""maxima"")","\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
298,1,13,0,1.310076," ","integrate((c*x^4+b*x^2)/x^(5/2),x, algorithm=""maxima"")","\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
299,1,13,0,1.342779," ","integrate((c*x^4+b*x^2)/x^(7/2),x, algorithm=""maxima"")","\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
300,1,24,0,1.278463," ","integrate(x^(7/2)*(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\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
301,1,24,0,1.352662," ","integrate(x^(5/2)*(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\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
302,1,24,0,1.230945," ","integrate(x^(3/2)*(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\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
303,1,24,0,1.358144," ","integrate(x^(1/2)*(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\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
304,1,24,0,1.251189," ","integrate((c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""maxima"")","\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
305,1,24,0,1.329704," ","integrate((c*x^4+b*x^2)^2/x^(3/2),x, algorithm=""maxima"")","\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
306,1,24,0,1.348698," ","integrate((c*x^4+b*x^2)^2/x^(5/2),x, algorithm=""maxima"")","\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
307,1,24,0,1.324764," ","integrate((c*x^4+b*x^2)^2/x^(7/2),x, algorithm=""maxima"")","\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
308,1,35,0,1.344802," ","integrate(x^(7/2)*(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\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
309,1,35,0,1.352301," ","integrate(x^(5/2)*(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\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
310,1,35,0,1.308935," ","integrate(x^(3/2)*(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\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
311,1,35,0,1.327128," ","integrate(x^(1/2)*(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\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
312,1,35,0,1.311082," ","integrate((c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""maxima"")","\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
313,1,35,0,1.306105," ","integrate((c*x^4+b*x^2)^3/x^(3/2),x, algorithm=""maxima"")","\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
314,1,35,0,1.352073," ","integrate((c*x^4+b*x^2)^3/x^(5/2),x, algorithm=""maxima"")","\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
315,1,35,0,1.369631," ","integrate((c*x^4+b*x^2)^3/x^(7/2),x, algorithm=""maxima"")","\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
316,1,198,0,3.005527," ","integrate(x^(13/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{4 \, c^{2}} + \frac{2 \, {\left(3 \, c x^{\frac{7}{2}} - 7 \, b x^{\frac{3}{2}}\right)}}{21 \, c^{2}}"," ",0,"1/4*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/c^2 + 2/21*(3*c*x^(7/2) - 7*b*x^(3/2))/c^2","A",0
317,1,194,0,2.974141," ","integrate(x^(11/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{2 \, {\left(c x^{\frac{5}{2}} - 5 \, b \sqrt{x}\right)}}{5 \, c^{2}} + \frac{\frac{2 \, \sqrt{2} b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} b^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} b^{\frac{5}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} b^{\frac{5}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}}}{4 \, c^{2}}"," ",0,"2/5*(c*x^(5/2) - 5*b*sqrt(x))/c^2 + 1/4*(2*sqrt(2)*b^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + 2*sqrt(2)*b^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + sqrt(2)*b^(5/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4) - sqrt(2)*b^(5/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4))/c^2","A",0
318,1,186,0,3.124412," ","integrate(x^(9/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{4 \, c} + \frac{2 \, x^{\frac{3}{2}}}{3 \, c}"," ",0,"-1/4*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/c + 2/3*x^(3/2)/c","A",0
319,1,185,0,3.046598," ","integrate(x^(7/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} b^{\frac{1}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} b^{\frac{1}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}}}{4 \, c} + \frac{2 \, \sqrt{x}}{c}"," ",0,"-1/4*(2*sqrt(2)*sqrt(b)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + 2*sqrt(2)*sqrt(b)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + sqrt(2)*b^(1/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4) - sqrt(2)*b^(1/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4))/c + 2*sqrt(x)/c","A",0
320,1,172,0,3.002006," ","integrate(x^(5/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{2 \, \sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{2 \, \sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{4 \, b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{4 \, b^{\frac{1}{4}} c^{\frac{3}{4}}}"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - 1/4*sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + 1/4*sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4))","A",0
321,1,172,0,3.023635," ","integrate(x^(3/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{2 \, \sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{2 \, \sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{4 \, b^{\frac{3}{4}} c^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{4 \, b^{\frac{3}{4}} c^{\frac{1}{4}}}"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 1/4*sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)) - 1/4*sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4))","A",0
322,1,186,0,2.916784," ","integrate(x^(1/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{4 \, b} - \frac{2}{b \sqrt{x}}"," ",0,"-1/4*c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b - 2/(b*sqrt(x))","A",0
323,1,187,0,2.988385," ","integrate(1/(c*x^4+b*x^2)/x^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} c^{\frac{3}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} c^{\frac{3}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}}}{4 \, b} - \frac{2}{3 \, b x^{\frac{3}{2}}}"," ",0,"-1/4*(2*sqrt(2)*c*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*c^(3/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4) - sqrt(2)*c^(3/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4))/b - 2/3/(b*x^(3/2))","A",0
324,1,198,0,3.131288," ","integrate(1/x^(3/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{c^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{4 \, b^{2}} + \frac{2 \, {\left(5 \, c x^{2} - b\right)}}{5 \, b^{2} x^{\frac{5}{2}}}"," ",0,"1/4*c^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^2 + 2/5*(5*c*x^2 - b)/(b^2*x^(5/2))","A",0
325,1,201,0,3.119063," ","integrate(1/x^(5/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} c^{\frac{7}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} c^{\frac{7}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}}}{4 \, b^{2}} + \frac{2 \, {\left(7 \, c x^{2} - 3 \, b\right)}}{21 \, b^{2} x^{\frac{7}{2}}}"," ",0,"1/4*(2*sqrt(2)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*c^(7/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4) - sqrt(2)*c^(7/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4))/b^2 + 2/21*(7*c*x^2 - 3*b)/(b^2*x^(7/2))","A",0
326,1,209,0,3.088088," ","integrate(1/x^(7/2)/(c*x^4+b*x^2),x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{4 \, b^{3}} - \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,"-1/4*c^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^3 - 2/45*(45*c^2*x^4 - 9*b*c*x^2 + 5*b^2)/(b^3*x^(9/2))","A",0
327,1,217,0,3.016363," ","integrate(x^(19/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{b^{2} \sqrt{x}}{2 \, {\left(c^{4} x^{2} + b c^{3}\right)}} + \frac{2 \, {\left(c x^{\frac{5}{2}} - 10 \, b \sqrt{x}\right)}}{5 \, c^{3}} + \frac{9 \, {\left(\frac{2 \, \sqrt{2} b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} b^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} b^{\frac{5}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} b^{\frac{5}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}}\right)}}{16 \, c^{3}}"," ",0,"-1/2*b^2*sqrt(x)/(c^4*x^2 + b*c^3) + 2/5*(c*x^(5/2) - 10*b*sqrt(x))/c^3 + 9/16*(2*sqrt(2)*b^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + 2*sqrt(2)*b^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + sqrt(2)*b^(5/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4) - sqrt(2)*b^(5/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4))/c^3","A",0
328,1,207,0,3.045509," ","integrate(x^(17/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{b x^{\frac{3}{2}}}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}} - \frac{7 \, b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{16 \, c^{2}} + \frac{2 \, x^{\frac{3}{2}}}{3 \, c^{2}}"," ",0,"1/2*b*x^(3/2)/(c^3*x^2 + b*c^2) - 7/16*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/c^2 + 2/3*x^(3/2)/c^2","A",0
329,1,206,0,3.063867," ","integrate(x^(15/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{b \sqrt{x}}{2 \, {\left(c^{3} x^{2} + b c^{2}\right)}} - \frac{5 \, {\left(\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} b^{\frac{1}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} b^{\frac{1}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}}\right)}}{16 \, c^{2}} + \frac{2 \, \sqrt{x}}{c^{2}}"," ",0,"1/2*b*sqrt(x)/(c^3*x^2 + b*c^2) - 5/16*(2*sqrt(2)*sqrt(b)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + 2*sqrt(2)*sqrt(b)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + sqrt(2)*b^(1/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4) - sqrt(2)*b^(1/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4))/c^2 + 2*sqrt(x)/c^2","A",0
330,1,195,0,3.004773," ","integrate(x^(13/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{x^{\frac{3}{2}}}{2 \, {\left(c^{2} x^{2} + b c\right)}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{16 \, c}"," ",0,"-1/2*x^(3/2)/(c^2*x^2 + b*c) + 3/16*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/c","A",0
331,1,195,0,3.102088," ","integrate(x^(11/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}}}{16 \, c} - \frac{\sqrt{x}}{2 \, {\left(c^{2} x^{2} + b c\right)}}"," ",0,"1/16*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)) - sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)))/c - 1/2*sqrt(x)/(c^2*x^2 + b*c)","A",0
332,1,194,0,3.040881," ","integrate(x^(9/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{x^{\frac{3}{2}}}{2 \, {\left(b c x^{2} + b^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}}{16 \, b}"," ",0,"1/2*x^(3/2)/(b*c*x^2 + b^2) + 1/16*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b","A",0
333,1,194,0,3.047223," ","integrate(x^(7/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}}\right)}}{16 \, b} + \frac{\sqrt{x}}{2 \, {\left(b c x^{2} + b^{2}\right)}}"," ",0,"3/16*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)) - sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)))/b + 1/2*sqrt(x)/(b*c*x^2 + b^2)","A",0
334,1,208,0,2.930618," ","integrate(x^(5/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{5 \, c x^{2} + 4 \, b}{2 \, {\left(b^{2} c x^{\frac{5}{2}} + b^{3} \sqrt{x}\right)}} - \frac{5 \, c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{16 \, b^{2}}"," ",0,"-1/2*(5*c*x^2 + 4*b)/(b^2*c*x^(5/2) + b^3*sqrt(x)) - 5/16*c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^2","A",0
335,1,209,0,3.029664," ","integrate(x^(3/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{7 \, c x^{2} + 4 \, b}{6 \, {\left(b^{2} c x^{\frac{7}{2}} + b^{3} x^{\frac{3}{2}}\right)}} - \frac{7 \, {\left(\frac{2 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} c^{\frac{3}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} c^{\frac{3}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}}\right)}}{16 \, b^{2}}"," ",0,"-1/6*(7*c*x^2 + 4*b)/(b^2*c*x^(7/2) + b^3*x^(3/2)) - 7/16*(2*sqrt(2)*c*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*c^(3/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4) - sqrt(2)*c^(3/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4))/b^2","A",0
336,1,221,0,2.969368," ","integrate(x^(1/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{45 \, c^{2} x^{4} + 36 \, b c x^{2} - 4 \, b^{2}}{10 \, {\left(b^{3} c x^{\frac{9}{2}} + b^{4} x^{\frac{5}{2}}\right)}} + \frac{9 \, c^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{16 \, b^{3}}"," ",0,"1/10*(45*c^2*x^4 + 36*b*c*x^2 - 4*b^2)/(b^3*c*x^(9/2) + b^4*x^(5/2)) + 9/16*c^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^3","A",0
337,1,224,0,3.155659," ","integrate(1/(c*x^4+b*x^2)^2/x^(1/2),x, algorithm=""maxima"")","\frac{77 \, c^{2} x^{4} + 44 \, b c x^{2} - 12 \, b^{2}}{42 \, {\left(b^{3} c x^{\frac{11}{2}} + b^{4} x^{\frac{7}{2}}\right)}} + \frac{11 \, {\left(\frac{2 \, \sqrt{2} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} c^{\frac{7}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} c^{\frac{7}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}}\right)}}{16 \, b^{3}}"," ",0,"1/42*(77*c^2*x^4 + 44*b*c*x^2 - 12*b^2)/(b^3*c*x^(11/2) + b^4*x^(7/2)) + 11/16*(2*sqrt(2)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*c^(7/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4) - sqrt(2)*c^(7/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4))/b^3","A",0
338,1,232,0,3.006067," ","integrate(1/x^(3/2)/(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","-\frac{585 \, c^{3} x^{6} + 468 \, b c^{2} x^{4} - 52 \, b^{2} c x^{2} + 20 \, b^{3}}{90 \, {\left(b^{4} c x^{\frac{13}{2}} + b^{5} x^{\frac{9}{2}}\right)}} - \frac{13 \, c^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{16 \, b^{4}}"," ",0,"-1/90*(585*c^3*x^6 + 468*b*c^2*x^4 - 52*b^2*c*x^2 + 20*b^3)/(b^4*c*x^(13/2) + b^5*x^(9/2)) - 13/16*c^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^4","A",0
339,1,229,0,2.950033," ","integrate(x^(23/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{17 \, b c x^{\frac{5}{2}} + 13 \, b^{2} \sqrt{x}}{16 \, {\left(c^{5} x^{4} + 2 \, b c^{4} x^{2} + b^{2} c^{3}\right)}} - \frac{45 \, {\left(\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} b^{\frac{1}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} b^{\frac{1}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{c^{\frac{1}{4}}}\right)}}{128 \, c^{3}} + \frac{2 \, \sqrt{x}}{c^{3}}"," ",0,"1/16*(17*b*c*x^(5/2) + 13*b^2*sqrt(x))/(c^5*x^4 + 2*b*c^4*x^2 + b^2*c^3) - 45/128*(2*sqrt(2)*sqrt(b)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + 2*sqrt(2)*sqrt(b)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/sqrt(sqrt(b)*sqrt(c)) + sqrt(2)*b^(1/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4) - sqrt(2)*b^(1/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/c^(1/4))/c^3 + 2*sqrt(x)/c^3","A",0
340,1,218,0,2.954965," ","integrate(x^(21/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{11 \, c x^{\frac{7}{2}} + 7 \, b x^{\frac{3}{2}}}{16 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}} + \frac{21 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{128 \, c^{2}}"," ",0,"-1/16*(11*c*x^(7/2) + 7*b*x^(3/2))/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2) + 21/128*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/c^2","A",0
341,1,218,0,2.980336," ","integrate(x^(19/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{9 \, c x^{\frac{5}{2}} + 5 \, b \sqrt{x}}{16 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right)}} + \frac{5 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}}\right)}}{128 \, c^{2}}"," ",0,"-1/16*(9*c*x^(5/2) + 5*b*sqrt(x))/(c^4*x^4 + 2*b*c^3*x^2 + b^2*c^2) + 5/128*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)) - sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)))/c^2","A",0
342,1,222,0,3.085611," ","integrate(x^(17/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{3 \, c x^{\frac{7}{2}} - b x^{\frac{3}{2}}}{16 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{128 \, b c}"," ",0,"1/16*(3*c*x^(7/2) - b*x^(3/2))/(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c) + 3/128*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/(b*c)","A",0
343,1,221,0,2.962815," ","integrate(x^(15/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{c x^{\frac{5}{2}} - 3 \, b \sqrt{x}}{16 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{2} + b^{3} c\right)}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}}\right)}}{128 \, b c}"," ",0,"1/16*(c*x^(5/2) - 3*b*sqrt(x))/(b*c^3*x^4 + 2*b^2*c^2*x^2 + b^3*c) + 3/128*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)) - sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)))/(b*c)","A",0
344,1,217,0,3.085076," ","integrate(x^(13/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{5 \, c x^{\frac{7}{2}} + 9 \, b x^{\frac{3}{2}}}{16 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)}} + \frac{5 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{128 \, b^{2}}"," ",0,"1/16*(5*c*x^(7/2) + 9*b*x^(3/2))/(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4) + 5/128*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^2","A",0
345,1,217,0,2.965640," ","integrate(x^(11/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{7 \, c x^{\frac{5}{2}} + 11 \, b \sqrt{x}}{16 \, {\left(b^{2} c^{2} x^{4} + 2 \, b^{3} c x^{2} + b^{4}\right)}} + \frac{21 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}} c^{\frac{1}{4}}}\right)}}{128 \, b^{2}}"," ",0,"1/16*(7*c*x^(5/2) + 11*b*sqrt(x))/(b^2*c^2*x^4 + 2*b^3*c*x^2 + b^4) + 21/128*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)) - sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(3/4)*c^(1/4)))/b^2","A",0
346,1,230,0,3.136181," ","integrate(x^(9/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{45 \, c^{2} x^{4} + 81 \, b c x^{2} + 32 \, b^{2}}{16 \, {\left(b^{3} c^{2} x^{\frac{9}{2}} + 2 \, b^{4} c x^{\frac{5}{2}} + b^{5} \sqrt{x}\right)}} - \frac{45 \, c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{128 \, b^{3}}"," ",0,"-1/16*(45*c^2*x^4 + 81*b*c*x^2 + 32*b^2)/(b^3*c^2*x^(9/2) + 2*b^4*c*x^(5/2) + b^5*sqrt(x)) - 45/128*c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^3","A",0
347,1,231,0,3.049087," ","integrate(x^(7/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{77 \, c^{2} x^{4} + 121 \, b c x^{2} + 32 \, b^{2}}{48 \, {\left(b^{3} c^{2} x^{\frac{11}{2}} + 2 \, b^{4} c x^{\frac{7}{2}} + b^{5} x^{\frac{3}{2}}\right)}} - \frac{77 \, {\left(\frac{2 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} c^{\frac{3}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} c^{\frac{3}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}}\right)}}{128 \, b^{3}}"," ",0,"-1/48*(77*c^2*x^4 + 121*b*c*x^2 + 32*b^2)/(b^3*c^2*x^(11/2) + 2*b^4*c*x^(7/2) + b^5*x^(3/2)) - 77/128*(2*sqrt(2)*c*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*c^(3/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4) - sqrt(2)*c^(3/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4))/b^3","A",0
348,1,243,0,3.144204," ","integrate(x^(5/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{585 \, c^{3} x^{6} + 1053 \, b c^{2} x^{4} + 416 \, b^{2} c x^{2} - 32 \, b^{3}}{80 \, {\left(b^{4} c^{2} x^{\frac{13}{2}} + 2 \, b^{5} c x^{\frac{9}{2}} + b^{6} x^{\frac{5}{2}}\right)}} + \frac{117 \, c^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{128 \, b^{4}}"," ",0,"1/80*(585*c^3*x^6 + 1053*b*c^2*x^4 + 416*b^2*c*x^2 - 32*b^3)/(b^4*c^2*x^(13/2) + 2*b^5*c*x^(9/2) + b^6*x^(5/2)) + 117/128*c^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^4","A",0
349,1,246,0,2.928863," ","integrate(x^(3/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{385 \, c^{3} x^{6} + 605 \, b c^{2} x^{4} + 160 \, b^{2} c x^{2} - 32 \, b^{3}}{112 \, {\left(b^{4} c^{2} x^{\frac{15}{2}} + 2 \, b^{5} c x^{\frac{11}{2}} + b^{6} x^{\frac{7}{2}}\right)}} + \frac{165 \, {\left(\frac{2 \, \sqrt{2} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} c^{\frac{7}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} c^{\frac{7}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}}\right)}}{128 \, b^{4}}"," ",0,"1/112*(385*c^3*x^6 + 605*b*c^2*x^4 + 160*b^2*c*x^2 - 32*b^3)/(b^4*c^2*x^(15/2) + 2*b^5*c*x^(11/2) + b^6*x^(7/2)) + 165/128*(2*sqrt(2)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*c^(7/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4) - sqrt(2)*c^(7/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4))/b^4","A",0
350,1,254,0,3.041506," ","integrate(x^(1/2)/(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","-\frac{9945 \, c^{4} x^{8} + 17901 \, b c^{3} x^{6} + 7072 \, b^{2} c^{2} x^{4} - 544 \, b^{3} c x^{2} + 160 \, b^{4}}{720 \, {\left(b^{5} c^{2} x^{\frac{17}{2}} + 2 \, b^{6} c x^{\frac{13}{2}} + b^{7} x^{\frac{9}{2}}\right)}} - \frac{221 \, c^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{\sqrt{b} \sqrt{c}} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{1}{4}} c^{\frac{3}{4}}}\right)}}{128 \, b^{5}}"," ",0,"-1/720*(9945*c^4*x^8 + 17901*b*c^3*x^6 + 7072*b^2*c^2*x^4 - 544*b^3*c*x^2 + 160*b^4)/(b^5*c^2*x^(17/2) + 2*b^6*c*x^(13/2) + b^7*x^(9/2)) - 221/128*c^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(sqrt(b)*sqrt(c))*sqrt(c)) - sqrt(2)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)) + sqrt(2)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/(b^(1/4)*c^(3/4)))/b^5","A",0
351,1,257,0,3.062952," ","integrate(1/(c*x^4+b*x^2)^3/x^(1/2),x, algorithm=""maxima"")","-\frac{7315 \, c^{4} x^{8} + 11495 \, b c^{3} x^{6} + 3040 \, b^{2} c^{2} x^{4} - 608 \, b^{3} c x^{2} + 224 \, b^{4}}{1232 \, {\left(b^{5} c^{2} x^{\frac{19}{2}} + 2 \, b^{6} c x^{\frac{15}{2}} + b^{7} x^{\frac{11}{2}}\right)}} - \frac{285 \, {\left(\frac{2 \, \sqrt{2} c^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} + 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{2 \, \sqrt{2} c^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} - 2 \, \sqrt{c} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{b} \sqrt{c}}}\right)}{\sqrt{b} \sqrt{\sqrt{b} \sqrt{c}}} + \frac{\sqrt{2} c^{\frac{11}{4}} \log\left(\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}} - \frac{\sqrt{2} c^{\frac{11}{4}} \log\left(-\sqrt{2} b^{\frac{1}{4}} c^{\frac{1}{4}} \sqrt{x} + \sqrt{c} x + \sqrt{b}\right)}{b^{\frac{3}{4}}}\right)}}{128 \, b^{5}}"," ",0,"-1/1232*(7315*c^4*x^8 + 11495*b*c^3*x^6 + 3040*b^2*c^2*x^4 - 608*b^3*c*x^2 + 224*b^4)/(b^5*c^2*x^(19/2) + 2*b^6*c*x^(15/2) + b^7*x^(11/2)) - 285/128*(2*sqrt(2)*c^3*arctan(1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) + 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + 2*sqrt(2)*c^3*arctan(-1/2*sqrt(2)*(sqrt(2)*b^(1/4)*c^(1/4) - 2*sqrt(c)*sqrt(x))/sqrt(sqrt(b)*sqrt(c)))/(sqrt(b)*sqrt(sqrt(b)*sqrt(c))) + sqrt(2)*c^(11/4)*log(sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4) - sqrt(2)*c^(11/4)*log(-sqrt(2)*b^(1/4)*c^(1/4)*sqrt(x) + sqrt(c)*x + sqrt(b))/b^(3/4))/b^5","A",0
352,0,0,0,0.000000," ","integrate(x^(7/2)*(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
403,1,76,0,1.508250," ","integrate((c*x)^m*(c*x^4+b*x^2)^3,x, algorithm=""maxima"")","\frac{c^{m + 3} x^{13} x^{m}}{m + 13} + \frac{3 \, b c^{m + 2} x^{11} x^{m}}{m + 11} + \frac{3 \, b^{2} c^{m + 1} x^{9} x^{m}}{m + 9} + \frac{b^{3} c^{m} x^{7} x^{m}}{m + 7}"," ",0,"c^(m + 3)*x^13*x^m/(m + 13) + 3*b*c^(m + 2)*x^11*x^m/(m + 11) + 3*b^2*c^(m + 1)*x^9*x^m/(m + 9) + b^3*c^m*x^7*x^m/(m + 7)","A",0
404,1,55,0,1.448083," ","integrate((c*x)^m*(c*x^4+b*x^2)^2,x, algorithm=""maxima"")","\frac{c^{m + 2} x^{9} x^{m}}{m + 9} + \frac{2 \, b c^{m + 1} x^{7} x^{m}}{m + 7} + \frac{b^{2} c^{m} x^{5} x^{m}}{m + 5}"," ",0,"c^(m + 2)*x^9*x^m/(m + 9) + 2*b*c^(m + 1)*x^7*x^m/(m + 7) + b^2*c^m*x^5*x^m/(m + 5)","A",0
405,1,34,0,1.425629," ","integrate((c*x)^m*(c*x^4+b*x^2),x, algorithm=""maxima"")","\frac{c^{m + 1} x^{5} x^{m}}{m + 5} + \frac{b c^{m} x^{3} x^{m}}{m + 3}"," ",0,"c^(m + 1)*x^5*x^m/(m + 5) + b*c^m*x^3*x^m/(m + 3)","A",0
406,0,0,0,0.000000," ","integrate((c*x)^m/(c*x^4+b*x^2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
409,1,24,0,1.361299," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\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
410,1,24,0,1.328499," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\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
411,1,24,0,1.285477," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\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
412,1,21,0,1.350357," ","integrate(b^2*x^4+2*a*b*x^2+a^2,x, algorithm=""maxima"")","\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
413,1,24,0,1.282813," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x,x, algorithm=""maxima"")","\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
414,1,22,0,1.313692," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^2,x, algorithm=""maxima"")","\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
415,1,24,0,1.316461," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} + a b \log\left(x^{2}\right) - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/2*b^2*x^2 + a*b*log(x^2) - 1/2*a^2/x^2","A",0
416,1,22,0,1.325589," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^4,x, algorithm=""maxima"")","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
417,1,26,0,1.371671," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} \log\left(x^{2}\right) - \frac{4 \, a b x^{2} + a^{2}}{4 \, x^{4}}"," ",0,"1/2*b^2*log(x^2) - 1/4*(4*a*b*x^2 + a^2)/x^4","A",0
418,1,26,0,1.337113," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^6,x, algorithm=""maxima"")","-\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
419,1,24,0,1.327627," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^7,x, algorithm=""maxima"")","-\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
420,1,26,0,1.348397," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/x^8,x, algorithm=""maxima"")","-\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
421,1,46,0,1.328130," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\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
422,1,46,0,1.339187," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\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
423,1,46,0,1.328676," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\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
424,1,46,0,1.279393," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\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
425,1,46,0,1.322870," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\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
426,1,44,0,1.333249," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\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
427,1,55,0,1.282424," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{4} x^{9} + \frac{4}{7} \, a b^{3} x^{7} + \frac{4}{5} \, a^{2} b^{2} x^{5} + a^{4} x + \frac{2}{15} \, {\left(3 \, b^{2} x^{5} + 10 \, a b x^{3}\right)} a^{2}"," ",0,"1/9*b^4*x^9 + 4/7*a*b^3*x^7 + 4/5*a^2*b^2*x^5 + a^4*x + 2/15*(3*b^2*x^5 + 10*a*b*x^3)*a^2","A",0
428,1,47,0,1.340803," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x,x, algorithm=""maxima"")","\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
429,1,44,0,1.337966," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^2,x, algorithm=""maxima"")","\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
430,1,46,0,1.339826," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^3,x, algorithm=""maxima"")","\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{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*a^4/x^2","A",0
431,1,45,0,1.444706," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^4,x, algorithm=""maxima"")","\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
432,1,48,0,1.362173," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, b^{4} x^{4} + 2 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} \log\left(x^{2}\right) - \frac{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*(8*a^3*b*x^2 + a^4)/x^4","A",0
433,1,47,0,1.371357," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^6,x, algorithm=""maxima"")","\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
434,1,48,0,1.308915," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^7,x, algorithm=""maxima"")","\frac{1}{2} \, b^{4} x^{2} + 2 \, a b^{3} \log\left(x^{2}\right) - \frac{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*(18*a^2*b^2*x^4 + 6*a^3*b*x^2 + a^4)/x^6","A",0
435,1,46,0,1.449387," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^8,x, algorithm=""maxima"")","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
436,1,50,0,1.376234," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^9,x, algorithm=""maxima"")","\frac{1}{2} \, b^{4} \log\left(x^{2}\right) - \frac{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*(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
437,1,48,0,1.426314," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^10,x, algorithm=""maxima"")","-\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
438,1,46,0,1.346133," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^11,x, algorithm=""maxima"")","-\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
439,1,48,0,1.300154," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^12,x, algorithm=""maxima"")","-\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
440,1,48,0,1.350764," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^13,x, algorithm=""maxima"")","-\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
441,1,48,0,1.462775," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^14,x, algorithm=""maxima"")","-\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
442,1,48,0,1.434415," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^15,x, algorithm=""maxima"")","-\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
443,1,48,0,1.379614," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/x^16,x, algorithm=""maxima"")","-\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
444,1,68,0,1.348551," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
445,1,68,0,1.430824," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
446,1,67,0,1.389922," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
447,1,68,0,1.362028," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
448,1,68,0,1.293901," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
449,1,67,0,1.360988," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
450,1,68,0,1.356588," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
451,1,68,0,1.379361," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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
452,1,100,0,1.337396," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{1}{13} \, b^{6} x^{13} + \frac{6}{11} \, a b^{5} x^{11} + \frac{4}{3} \, a^{2} b^{4} x^{9} + \frac{8}{7} \, a^{3} b^{3} x^{7} + a^{6} x + \frac{1}{5} \, {\left(3 \, b^{2} x^{5} + 10 \, a b x^{3}\right)} a^{4} + \frac{1}{105} \, {\left(35 \, b^{4} x^{9} + 180 \, a b^{3} x^{7} + 252 \, a^{2} b^{2} x^{5}\right)} a^{2}"," ",0,"1/13*b^6*x^13 + 6/11*a*b^5*x^11 + 4/3*a^2*b^4*x^9 + 8/7*a^3*b^3*x^7 + a^6*x + 1/5*(3*b^2*x^5 + 10*a*b*x^3)*a^4 + 1/105*(35*b^4*x^9 + 180*a*b^3*x^7 + 252*a^2*b^2*x^5)*a^2","A",0
453,1,69,0,1.402806," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x,x, algorithm=""maxima"")","\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
454,1,66,0,1.348828," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^2,x, algorithm=""maxima"")","\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
455,1,69,0,1.434181," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^3,x, algorithm=""maxima"")","\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{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*a^6/x^2","A",0
456,1,67,0,1.290315," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^4,x, algorithm=""maxima"")","\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
457,1,69,0,1.366288," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^5,x, algorithm=""maxima"")","\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{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*(12*a^5*b*x^2 + a^6)/x^4","A",0
458,1,67,0,1.314924," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^6,x, algorithm=""maxima"")","\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
459,1,70,0,1.385787," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^7,x, algorithm=""maxima"")","\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{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*(45*a^4*b^2*x^4 + 9*a^5*b*x^2 + a^6)/x^6","A",0
460,1,69,0,1.380943," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^8,x, algorithm=""maxima"")","\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
461,1,70,0,1.314093," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^9,x, algorithm=""maxima"")","\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{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*(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
462,1,69,0,1.413493," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^10,x, algorithm=""maxima"")","\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
463,1,72,0,1.380655," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^11,x, algorithm=""maxima"")","\frac{1}{2} \, b^{6} x^{2} + 3 \, a b^{5} \log\left(x^{2}\right) - \frac{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*(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
464,1,68,0,1.313620," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^12,x, algorithm=""maxima"")","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
465,1,72,0,1.400139," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^13,x, algorithm=""maxima"")","\frac{1}{2} \, b^{6} \log\left(x^{2}\right) - \frac{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*(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
466,1,70,0,1.340033," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^14,x, algorithm=""maxima"")","-\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
467,1,68,0,1.380188," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^15,x, algorithm=""maxima"")","-\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
468,1,70,0,1.365028," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^16,x, algorithm=""maxima"")","-\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
469,1,70,0,1.390830," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^17,x, algorithm=""maxima"")","-\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
470,1,70,0,1.372559," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^18,x, algorithm=""maxima"")","-\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
471,1,70,0,1.336176," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^19,x, algorithm=""maxima"")","-\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
472,1,70,0,1.353857," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^20,x, algorithm=""maxima"")","-\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
473,1,70,0,1.415623," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^21,x, algorithm=""maxima"")","-\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
474,1,70,0,1.338282," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/x^22,x, algorithm=""maxima"")","-\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
475,1,77,0,1.373472," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{a^{5}}{2 \, {\left(b^{7} x^{2} + a b^{6}\right)}} + \frac{5 \, a^{4} \log\left(b x^{2} + a\right)}{2 \, b^{6}} + \frac{3 \, b^{3} x^{8} - 8 \, a b^{2} x^{6} + 18 \, a^{2} b x^{4} - 48 \, a^{3} x^{2}}{24 \, b^{5}}"," ",0,"1/2*a^5/(b^7*x^2 + a*b^6) + 5/2*a^4*log(b*x^2 + a)/b^6 + 1/24*(3*b^3*x^8 - 8*a*b^2*x^6 + 18*a^2*b*x^4 - 48*a^3*x^2)/b^5","A",0
476,1,65,0,1.353180," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{a^{4}}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} - \frac{2 \, a^{3} \log\left(b x^{2} + a\right)}{b^{5}} + \frac{b^{2} x^{6} - 3 \, a b x^{4} + 9 \, a^{2} x^{2}}{6 \, b^{4}}"," ",0,"-1/2*a^4/(b^6*x^2 + a*b^5) - 2*a^3*log(b*x^2 + a)/b^5 + 1/6*(b^2*x^6 - 3*a*b*x^4 + 9*a^2*x^2)/b^4","A",0
477,1,54,0,1.345556," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{a^{3}}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{3 \, a^{2} \log\left(b x^{2} + a\right)}{2 \, b^{4}} + \frac{b x^{4} - 4 \, a x^{2}}{4 \, b^{3}}"," ",0,"1/2*a^3/(b^5*x^2 + a*b^4) + 3/2*a^2*log(b*x^2 + a)/b^4 + 1/4*(b*x^4 - 4*a*x^2)/b^3","A",0
478,1,43,0,1.295922," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{a^{2}}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} + \frac{x^{2}}{2 \, b^{2}} - \frac{a \log\left(b x^{2} + a\right)}{b^{3}}"," ",0,"-1/2*a^2/(b^4*x^2 + a*b^3) + 1/2*x^2/b^2 - a*log(b*x^2 + a)/b^3","A",0
479,1,32,0,1.413955," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{a}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \frac{\log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*a/(b^3*x^2 + a*b^2) + 1/2*log(b*x^2 + a)/b^2","A",0
480,1,15,0,1.379736," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(b^{2} x^{2} + a b\right)}}"," ",0,"-1/2/(b^2*x^2 + a*b)","A",0
481,1,37,0,1.359363," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{1}{2 \, {\left(a b x^{2} + a^{2}\right)}} - \frac{\log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2}}"," ",0,"1/2/(a*b*x^2 + a^2) - 1/2*log(b*x^2 + a)/a^2 + 1/2*log(x^2)/a^2","A",0
482,1,52,0,1.357291," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{2 \, b x^{2} + a}{2 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)}} + \frac{b \log\left(b x^{2} + a\right)}{a^{3}} - \frac{b \log\left(x^{2}\right)}{a^{3}}"," ",0,"-1/2*(2*b*x^2 + a)/(a^2*b*x^4 + a^3*x^2) + b*log(b*x^2 + a)/a^3 - b*log(x^2)/a^3","A",0
483,1,70,0,1.414684," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{6 \, b^{2} x^{4} + 3 \, a b x^{2} - a^{2}}{4 \, {\left(a^{3} b x^{6} + a^{4} x^{4}\right)}} - \frac{3 \, b^{2} \log\left(b x^{2} + a\right)}{2 \, a^{4}} + \frac{3 \, b^{2} \log\left(x^{2}\right)}{2 \, a^{4}}"," ",0,"1/4*(6*b^2*x^4 + 3*a*b*x^2 - a^2)/(a^3*b*x^6 + a^4*x^4) - 3/2*b^2*log(b*x^2 + a)/a^4 + 3/2*b^2*log(x^2)/a^4","A",0
484,1,82,0,2.992069," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{a^{4} x}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} + \frac{9 \, a^{4} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{5}} + \frac{5 \, b^{3} x^{7} - 14 \, a b^{2} x^{5} + 35 \, a^{2} b x^{3} - 140 \, a^{3} x}{35 \, b^{5}}"," ",0,"-1/2*a^4*x/(b^6*x^2 + a*b^5) + 9/2*a^4*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/35*(5*b^3*x^7 - 14*a*b^2*x^5 + 35*a^2*b*x^3 - 140*a^3*x)/b^5","A",0
485,1,71,0,2.946275," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{a^{3} x}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} - \frac{7 \, a^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{4}} + \frac{3 \, b^{2} x^{5} - 10 \, a b x^{3} + 45 \, a^{2} x}{15 \, b^{4}}"," ",0,"1/2*a^3*x/(b^5*x^2 + a*b^4) - 7/2*a^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/15*(3*b^2*x^5 - 10*a*b*x^3 + 45*a^2*x)/b^4","A",0
486,1,59,0,3.126534," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{a^{2} x}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} + \frac{5 \, a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} + \frac{b x^{3} - 6 \, a x}{3 \, b^{3}}"," ",0,"-1/2*a^2*x/(b^4*x^2 + a*b^3) + 5/2*a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/3*(b*x^3 - 6*a*x)/b^3","A",0
487,1,45,0,3.083310," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{a x}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} - \frac{3 \, a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}} + \frac{x}{b^{2}}"," ",0,"1/2*a*x/(b^3*x^2 + a*b^2) - 3/2*a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + x/b^2","A",0
488,1,36,0,2.995044," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{x}{2 \, {\left(b^{2} x^{2} + a b\right)}} + \frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b}"," ",0,"-1/2*x/(b^2*x^2 + a*b) + 1/2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b)","A",0
489,1,35,0,2.845776," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{x}{2 \, {\left(a b x^{2} + a^{2}\right)}} + \frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a}"," ",0,"1/2*x/(a*b*x^2 + a^2) + 1/2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a)","A",0
490,1,49,0,2.945851," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{3 \, b x^{2} + 2 \, a}{2 \, {\left(a^{2} b x^{3} + a^{3} x\right)}} - \frac{3 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}}"," ",0,"-1/2*(3*b*x^2 + 2*a)/(a^2*b*x^3 + a^3*x) - 3/2*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2)","A",0
491,1,64,0,3.016558," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{15 \, b^{2} x^{4} + 10 \, a b x^{2} - 2 \, a^{2}}{6 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}} + \frac{5 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3}}"," ",0,"1/6*(15*b^2*x^4 + 10*a*b*x^2 - 2*a^2)/(a^3*b*x^5 + a^4*x^3) + 5/2*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3)","A",0
492,1,75,0,3.082994," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{105 \, b^{3} x^{6} + 70 \, a b^{2} x^{4} - 14 \, a^{2} b x^{2} + 6 \, a^{3}}{30 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}} - \frac{7 \, b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{4}}"," ",0,"-1/30*(105*b^3*x^6 + 70*a*b^2*x^4 - 14*a^2*b*x^2 + 6*a^3)/(a^4*b*x^7 + a^5*x^5) - 7/2*b^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4)","A",0
493,1,99,0,1.386454," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{60 \, a^{3} b^{2} x^{4} + 105 \, a^{4} b x^{2} + 47 \, a^{5}}{12 \, {\left(b^{9} x^{6} + 3 \, a b^{8} x^{4} + 3 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}} + \frac{5 \, a^{2} \log\left(b x^{2} + a\right)}{b^{6}} + \frac{b x^{4} - 8 \, a x^{2}}{4 \, b^{5}}"," ",0,"1/12*(60*a^3*b^2*x^4 + 105*a^4*b*x^2 + 47*a^5)/(b^9*x^6 + 3*a*b^8*x^4 + 3*a^2*b^7*x^2 + a^3*b^6) + 5*a^2*log(b*x^2 + a)/b^6 + 1/4*(b*x^4 - 8*a*x^2)/b^5","A",0
494,1,88,0,1.404880," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{18 \, a^{2} b^{2} x^{4} + 30 \, a^{3} b x^{2} + 13 \, a^{4}}{6 \, {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}} + \frac{x^{2}}{2 \, b^{4}} - \frac{2 \, a \log\left(b x^{2} + a\right)}{b^{5}}"," ",0,"-1/6*(18*a^2*b^2*x^4 + 30*a^3*b*x^2 + 13*a^4)/(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5) + 1/2*x^2/b^4 - 2*a*log(b*x^2 + a)/b^5","A",0
495,1,77,0,1.309513," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{18 \, a b^{2} x^{4} + 27 \, a^{2} b x^{2} + 11 \, a^{3}}{12 \, {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}} + \frac{\log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/12*(18*a*b^2*x^4 + 27*a^2*b*x^2 + 11*a^3)/(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4) + 1/2*log(b*x^2 + a)/b^4","A",0
496,1,58,0,1.383664," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{3 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}}{6 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}"," ",0,"-1/6*(3*b^2*x^4 + 3*a*b*x^2 + a^2)/(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3)","B",0
497,1,47,0,1.349269," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{3 \, b x^{2} + a}{12 \, {\left(b^{5} x^{6} + 3 \, a b^{4} x^{4} + 3 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}"," ",0,"-1/12*(3*b*x^2 + a)/(b^5*x^6 + 3*a*b^4*x^4 + 3*a^2*b^3*x^2 + a^3*b^2)","A",0
498,1,37,0,1.339236," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{1}{6 \, {\left(b^{4} x^{6} + 3 \, a b^{3} x^{4} + 3 \, a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"-1/6/(b^4*x^6 + 3*a*b^3*x^4 + 3*a^2*b^2*x^2 + a^3*b)","B",0
499,1,82,0,1.418153," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{6 \, b^{2} x^{4} + 15 \, a b x^{2} + 11 \, a^{2}}{12 \, {\left(a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6}\right)}} - \frac{\log\left(b x^{2} + a\right)}{2 \, a^{4}} + \frac{\log\left(x^{2}\right)}{2 \, a^{4}}"," ",0,"1/12*(6*b^2*x^4 + 15*a*b*x^2 + 11*a^2)/(a^3*b^3*x^6 + 3*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6) - 1/2*log(b*x^2 + a)/a^4 + 1/2*log(x^2)/a^4","A",0
500,1,99,0,1.395933," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{12 \, b^{3} x^{6} + 30 \, a b^{2} x^{4} + 22 \, a^{2} b x^{2} + 3 \, a^{3}}{6 \, {\left(a^{4} b^{3} x^{8} + 3 \, a^{5} b^{2} x^{6} + 3 \, a^{6} b x^{4} + a^{7} x^{2}\right)}} + \frac{2 \, b \log\left(b x^{2} + a\right)}{a^{5}} - \frac{2 \, b \log\left(x^{2}\right)}{a^{5}}"," ",0,"-1/6*(12*b^3*x^6 + 30*a*b^2*x^4 + 22*a^2*b*x^2 + 3*a^3)/(a^4*b^3*x^8 + 3*a^5*b^2*x^6 + 3*a^6*b*x^4 + a^7*x^2) + 2*b*log(b*x^2 + a)/a^5 - 2*b*log(x^2)/a^5","A",0
501,1,114,0,1.420544," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{60 \, b^{4} x^{8} + 150 \, a b^{3} x^{6} + 110 \, a^{2} b^{2} x^{4} + 15 \, a^{3} b x^{2} - 3 \, a^{4}}{12 \, {\left(a^{5} b^{3} x^{10} + 3 \, a^{6} b^{2} x^{8} + 3 \, a^{7} b x^{6} + a^{8} x^{4}\right)}} - \frac{5 \, b^{2} \log\left(b x^{2} + a\right)}{a^{6}} + \frac{5 \, b^{2} \log\left(x^{2}\right)}{a^{6}}"," ",0,"1/12*(60*b^4*x^8 + 150*a*b^3*x^6 + 110*a^2*b^2*x^4 + 15*a^3*b*x^2 - 3*a^4)/(a^5*b^3*x^10 + 3*a^6*b^2*x^8 + 3*a^7*b*x^6 + a^8*x^4) - 5*b^2*log(b*x^2 + a)/a^6 + 5*b^2*log(x^2)/a^6","A",0
502,1,116,0,2.977347," ","integrate(x^12/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{267 \, a^{3} b^{2} x^{5} + 472 \, a^{4} b x^{3} + 213 \, a^{5} x}{48 \, {\left(b^{9} x^{6} + 3 \, a b^{8} x^{4} + 3 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}} - \frac{231 \, a^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{6}} + \frac{3 \, b^{2} x^{5} - 20 \, a b x^{3} + 150 \, a^{2} x}{15 \, b^{6}}"," ",0,"1/48*(267*a^3*b^2*x^5 + 472*a^4*b*x^3 + 213*a^5*x)/(b^9*x^6 + 3*a*b^8*x^4 + 3*a^2*b^7*x^2 + a^3*b^6) - 231/16*a^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/15*(3*b^2*x^5 - 20*a*b*x^3 + 150*a^2*x)/b^6","A",0
503,1,104,0,3.009810," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{165 \, a^{2} b^{2} x^{5} + 280 \, a^{3} b x^{3} + 123 \, a^{4} x}{48 \, {\left(b^{8} x^{6} + 3 \, a b^{7} x^{4} + 3 \, a^{2} b^{6} x^{2} + a^{3} b^{5}\right)}} + \frac{105 \, a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{5}} + \frac{b x^{3} - 12 \, a x}{3 \, b^{5}}"," ",0,"-1/48*(165*a^2*b^2*x^5 + 280*a^3*b*x^3 + 123*a^4*x)/(b^8*x^6 + 3*a*b^7*x^4 + 3*a^2*b^6*x^2 + a^3*b^5) + 105/16*a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/3*(b*x^3 - 12*a*x)/b^5","A",0
504,1,90,0,2.846353," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{87 \, a b^{2} x^{5} + 136 \, a^{2} b x^{3} + 57 \, a^{3} x}{48 \, {\left(b^{7} x^{6} + 3 \, a b^{6} x^{4} + 3 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}} - \frac{35 \, a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{4}} + \frac{x}{b^{4}}"," ",0,"1/48*(87*a*b^2*x^5 + 136*a^2*b*x^3 + 57*a^3*x)/(b^7*x^6 + 3*a*b^6*x^4 + 3*a^2*b^5*x^2 + a^3*b^4) - 35/16*a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + x/b^4","A",0
505,1,81,0,3.068044," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{33 \, b^{2} x^{5} + 40 \, a b x^{3} + 15 \, a^{2} x}{48 \, {\left(b^{6} x^{6} + 3 \, a b^{5} x^{4} + 3 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}} + \frac{5 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} b^{3}}"," ",0,"-1/48*(33*b^2*x^5 + 40*a*b*x^3 + 15*a^2*x)/(b^6*x^6 + 3*a*b^5*x^4 + 3*a^2*b^4*x^2 + a^3*b^3) + 5/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3)","A",0
506,1,87,0,2.927655," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} x^{5} - 8 \, a b x^{3} - 3 \, a^{2} x}{48 \, {\left(a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{4} + 3 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}} + \frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a b^{2}}"," ",0,"1/48*(3*b^2*x^5 - 8*a*b*x^3 - 3*a^2*x)/(a*b^5*x^6 + 3*a^2*b^4*x^4 + 3*a^3*b^3*x^2 + a^4*b^2) + 1/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2)","A",0
507,1,87,0,2.984717," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} x^{5} + 8 \, a b x^{3} - 3 \, a^{2} x}{48 \, {\left(a^{2} b^{4} x^{6} + 3 \, a^{3} b^{3} x^{4} + 3 \, a^{4} b^{2} x^{2} + a^{5} b\right)}} + \frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{2} b}"," ",0,"1/48*(3*b^2*x^5 + 8*a*b*x^3 - 3*a^2*x)/(a^2*b^4*x^6 + 3*a^3*b^3*x^4 + 3*a^4*b^2*x^2 + a^5*b) + 1/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b)","A",0
508,1,80,0,3.008544," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{15 \, b^{2} x^{5} + 40 \, a b x^{3} + 33 \, a^{2} x}{48 \, {\left(a^{3} b^{3} x^{6} + 3 \, a^{4} b^{2} x^{4} + 3 \, a^{5} b x^{2} + a^{6}\right)}} + \frac{5 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{3}}"," ",0,"1/48*(15*b^2*x^5 + 40*a*b*x^3 + 33*a^2*x)/(a^3*b^3*x^6 + 3*a^4*b^2*x^4 + 3*a^5*b*x^2 + a^6) + 5/16*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3)","A",0
509,1,93,0,3.028087," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{105 \, b^{3} x^{6} + 280 \, a b^{2} x^{4} + 231 \, a^{2} b x^{2} + 48 \, a^{3}}{48 \, {\left(a^{4} b^{3} x^{7} + 3 \, a^{5} b^{2} x^{5} + 3 \, a^{6} b x^{3} + a^{7} x\right)}} - \frac{35 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{4}}"," ",0,"-1/48*(105*b^3*x^6 + 280*a*b^2*x^4 + 231*a^2*b*x^2 + 48*a^3)/(a^4*b^3*x^7 + 3*a^5*b^2*x^5 + 3*a^6*b*x^3 + a^7*x) - 35/16*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4)","A",0
510,1,108,0,3.050820," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\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(a^{5} b^{3} x^{9} + 3 \, a^{6} b^{2} x^{7} + 3 \, a^{7} b x^{5} + a^{8} x^{3}\right)}} + \frac{105 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{5}}"," ",0,"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)/(a^5*b^3*x^9 + 3*a^6*b^2*x^7 + 3*a^7*b*x^5 + a^8*x^3) + 105/16*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5)","A",0
511,1,119,0,3.008167," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{3465 \, b^{5} x^{10} + 9240 \, a b^{4} x^{8} + 7623 \, a^{2} b^{3} x^{6} + 1584 \, a^{3} b^{2} x^{4} - 176 \, a^{4} b x^{2} + 48 \, a^{5}}{240 \, {\left(a^{6} b^{3} x^{11} + 3 \, a^{7} b^{2} x^{9} + 3 \, a^{8} b x^{7} + a^{9} x^{5}\right)}} - \frac{231 \, b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{6}}"," ",0,"-1/240*(3465*b^5*x^10 + 9240*a*b^4*x^8 + 7623*a^2*b^3*x^6 + 1584*a^3*b^2*x^4 - 176*a^4*b*x^2 + 48*a^5)/(a^6*b^3*x^11 + 3*a^7*b^2*x^9 + 3*a^8*b*x^7 + a^9*x^5) - 231/16*b^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6)","A",0
512,1,143,0,1.415258," ","integrate(x^15/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{700 \, a^{3} b^{4} x^{8} + 2450 \, a^{4} b^{3} x^{6} + 3290 \, a^{5} b^{2} x^{4} + 1995 \, a^{6} b x^{2} + 459 \, a^{7}}{40 \, {\left(b^{13} x^{10} + 5 \, a b^{12} x^{8} + 10 \, a^{2} b^{11} x^{6} + 10 \, a^{3} b^{10} x^{4} + 5 \, a^{4} b^{9} x^{2} + a^{5} b^{8}\right)}} + \frac{21 \, a^{2} \log\left(b x^{2} + a\right)}{2 \, b^{8}} + \frac{b x^{4} - 12 \, a x^{2}}{4 \, b^{7}}"," ",0,"1/40*(700*a^3*b^4*x^8 + 2450*a^4*b^3*x^6 + 3290*a^5*b^2*x^4 + 1995*a^6*b*x^2 + 459*a^7)/(b^13*x^10 + 5*a*b^12*x^8 + 10*a^2*b^11*x^6 + 10*a^3*b^10*x^4 + 5*a^4*b^9*x^2 + a^5*b^8) + 21/2*a^2*log(b*x^2 + a)/b^8 + 1/4*(b*x^4 - 12*a*x^2)/b^7","A",0
513,1,132,0,1.469223," ","integrate(x^13/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{150 \, a^{2} b^{4} x^{8} + 500 \, a^{3} b^{3} x^{6} + 650 \, a^{4} b^{2} x^{4} + 385 \, a^{5} b x^{2} + 87 \, a^{6}}{20 \, {\left(b^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}} + \frac{x^{2}}{2 \, b^{6}} - \frac{3 \, a \log\left(b x^{2} + a\right)}{b^{7}}"," ",0,"-1/20*(150*a^2*b^4*x^8 + 500*a^3*b^3*x^6 + 650*a^4*b^2*x^4 + 385*a^5*b*x^2 + 87*a^6)/(b^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7) + 1/2*x^2/b^6 - 3*a*log(b*x^2 + a)/b^7","A",0
514,1,121,0,1.422207," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{300 \, a b^{4} x^{8} + 900 \, a^{2} b^{3} x^{6} + 1100 \, a^{3} b^{2} x^{4} + 625 \, a^{4} b x^{2} + 137 \, a^{5}}{120 \, {\left(b^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}} + \frac{\log\left(b x^{2} + a\right)}{2 \, b^{6}}"," ",0,"1/120*(300*a*b^4*x^8 + 900*a^2*b^3*x^6 + 1100*a^3*b^2*x^4 + 625*a^4*b*x^2 + 137*a^5)/(b^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6) + 1/2*log(b*x^2 + a)/b^6","A",0
515,1,102,0,1.369397," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\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^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}"," ",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^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5)","B",0
516,1,91,0,1.393133," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{10 \, b^{3} x^{6} + 10 \, a b^{2} x^{4} + 5 \, a^{2} b x^{2} + a^{3}}{40 \, {\left(b^{9} x^{10} + 5 \, a b^{8} x^{8} + 10 \, a^{2} b^{7} x^{6} + 10 \, a^{3} b^{6} x^{4} + 5 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)}}"," ",0,"-1/40*(10*b^3*x^6 + 10*a*b^2*x^4 + 5*a^2*b*x^2 + a^3)/(b^9*x^10 + 5*a*b^8*x^8 + 10*a^2*b^7*x^6 + 10*a^3*b^6*x^4 + 5*a^4*b^5*x^2 + a^5*b^4)","B",0
517,1,80,0,1.346739," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{10 \, b^{2} x^{4} + 5 \, a b x^{2} + a^{2}}{60 \, {\left(b^{8} x^{10} + 5 \, a b^{7} x^{8} + 10 \, a^{2} b^{6} x^{6} + 10 \, a^{3} b^{5} x^{4} + 5 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}}"," ",0,"-1/60*(10*b^2*x^4 + 5*a*b*x^2 + a^2)/(b^8*x^10 + 5*a*b^7*x^8 + 10*a^2*b^6*x^6 + 10*a^3*b^5*x^4 + 5*a^4*b^4*x^2 + a^5*b^3)","A",0
518,1,69,0,1.354937," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{5 \, b x^{2} + a}{40 \, {\left(b^{7} x^{10} + 5 \, a b^{6} x^{8} + 10 \, a^{2} b^{5} x^{6} + 10 \, a^{3} b^{4} x^{4} + 5 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}"," ",0,"-1/40*(5*b*x^2 + a)/(b^7*x^10 + 5*a*b^6*x^8 + 10*a^2*b^5*x^6 + 10*a^3*b^4*x^4 + 5*a^4*b^3*x^2 + a^5*b^2)","B",0
519,1,59,0,1.314201," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{1}{10 \, {\left(b^{6} x^{10} + 5 \, a b^{5} x^{8} + 10 \, a^{2} b^{4} x^{6} + 10 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}"," ",0,"-1/10/(b^6*x^10 + 5*a*b^5*x^8 + 10*a^2*b^4*x^6 + 10*a^3*b^3*x^4 + 5*a^4*b^2*x^2 + a^5*b)","B",0
520,1,126,0,1.450429," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{60 \, b^{4} x^{8} + 270 \, a b^{3} x^{6} + 470 \, a^{2} b^{2} x^{4} + 385 \, a^{3} b x^{2} + 137 \, a^{4}}{120 \, {\left(a^{5} b^{5} x^{10} + 5 \, a^{6} b^{4} x^{8} + 10 \, a^{7} b^{3} x^{6} + 10 \, a^{8} b^{2} x^{4} + 5 \, a^{9} b x^{2} + a^{10}\right)}} - \frac{\log\left(b x^{2} + a\right)}{2 \, a^{6}} + \frac{\log\left(x^{2}\right)}{2 \, a^{6}}"," ",0,"1/120*(60*b^4*x^8 + 270*a*b^3*x^6 + 470*a^2*b^2*x^4 + 385*a^3*b*x^2 + 137*a^4)/(a^5*b^5*x^10 + 5*a^6*b^4*x^8 + 10*a^7*b^3*x^6 + 10*a^8*b^2*x^4 + 5*a^9*b*x^2 + a^10) - 1/2*log(b*x^2 + a)/a^6 + 1/2*log(x^2)/a^6","A",0
521,1,143,0,1.580662," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{60 \, b^{5} x^{10} + 270 \, a b^{4} x^{8} + 470 \, a^{2} b^{3} x^{6} + 385 \, a^{3} b^{2} x^{4} + 137 \, a^{4} b x^{2} + 10 \, a^{5}}{20 \, {\left(a^{6} b^{5} x^{12} + 5 \, a^{7} b^{4} x^{10} + 10 \, a^{8} b^{3} x^{8} + 10 \, a^{9} b^{2} x^{6} + 5 \, a^{10} b x^{4} + a^{11} x^{2}\right)}} + \frac{3 \, b \log\left(b x^{2} + a\right)}{a^{7}} - \frac{3 \, b \log\left(x^{2}\right)}{a^{7}}"," ",0,"-1/20*(60*b^5*x^10 + 270*a*b^4*x^8 + 470*a^2*b^3*x^6 + 385*a^3*b^2*x^4 + 137*a^4*b*x^2 + 10*a^5)/(a^6*b^5*x^12 + 5*a^7*b^4*x^10 + 10*a^8*b^3*x^8 + 10*a^9*b^2*x^6 + 5*a^10*b*x^4 + a^11*x^2) + 3*b*log(b*x^2 + a)/a^7 - 3*b*log(x^2)/a^7","A",0
522,1,158,0,1.447958," ","integrate(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{420 \, b^{6} x^{12} + 1890 \, a b^{5} x^{10} + 3290 \, a^{2} b^{4} x^{8} + 2695 \, a^{3} b^{3} x^{6} + 959 \, a^{4} b^{2} x^{4} + 70 \, a^{5} b x^{2} - 10 \, a^{6}}{40 \, {\left(a^{7} b^{5} x^{14} + 5 \, a^{8} b^{4} x^{12} + 10 \, a^{9} b^{3} x^{10} + 10 \, a^{10} b^{2} x^{8} + 5 \, a^{11} b x^{6} + a^{12} x^{4}\right)}} - \frac{21 \, b^{2} \log\left(b x^{2} + a\right)}{2 \, a^{8}} + \frac{21 \, b^{2} \log\left(x^{2}\right)}{2 \, a^{8}}"," ",0,"1/40*(420*b^6*x^12 + 1890*a*b^5*x^10 + 3290*a^2*b^4*x^8 + 2695*a^3*b^3*x^6 + 959*a^4*b^2*x^4 + 70*a^5*b*x^2 - 10*a^6)/(a^7*b^5*x^14 + 5*a^8*b^4*x^12 + 10*a^9*b^3*x^10 + 10*a^10*b^2*x^8 + 5*a^11*b*x^6 + a^12*x^4) - 21/2*b^2*log(b*x^2 + a)/a^8 + 21/2*b^2*log(x^2)/a^8","A",0
523,1,159,0,2.885054," ","integrate(x^16/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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^{13} x^{10} + 5 \, a b^{12} x^{8} + 10 \, a^{2} b^{11} x^{6} + 10 \, a^{3} b^{10} x^{4} + 5 \, a^{4} b^{9} x^{2} + a^{5} b^{8}\right)}} - \frac{9009 \, a^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{8}} + \frac{b^{2} x^{5} - 10 \, a b x^{3} + 105 \, a^{2} x}{5 \, b^{8}}"," ",0,"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^13*x^10 + 5*a*b^12*x^8 + 10*a^2*b^11*x^6 + 10*a^3*b^10*x^4 + 5*a^4*b^9*x^2 + a^5*b^8) - 9009/256*a^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^8) + 1/5*(b^2*x^5 - 10*a*b*x^3 + 105*a^2*x)/b^8","A",0
524,1,148,0,2.909368," ","integrate(x^14/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\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^{12} x^{10} + 5 \, a b^{11} x^{8} + 10 \, a^{2} b^{10} x^{6} + 10 \, a^{3} b^{9} x^{4} + 5 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}} + \frac{3003 \, a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{7}} + \frac{b x^{3} - 18 \, a x}{3 \, b^{7}}"," ",0,"-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^12*x^10 + 5*a*b^11*x^8 + 10*a^2*b^10*x^6 + 10*a^3*b^9*x^4 + 5*a^4*b^8*x^2 + a^5*b^7) + 3003/256*a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^7) + 1/3*(b*x^3 - 18*a*x)/b^7","A",0
525,1,134,0,2.989345," ","integrate(x^12/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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^{11} x^{10} + 5 \, a b^{10} x^{8} + 10 \, a^{2} b^{9} x^{6} + 10 \, a^{3} b^{8} x^{4} + 5 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)}} - \frac{693 \, a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{6}} + \frac{x}{b^{6}}"," ",0,"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^11*x^10 + 5*a*b^10*x^8 + 10*a^2*b^9*x^6 + 10*a^3*b^8*x^4 + 5*a^4*b^7*x^2 + a^5*b^6) - 693/256*a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + x/b^6","A",0
526,1,125,0,3.070209," ","integrate(x^10/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\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^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}} + \frac{63 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} b^{5}}"," ",0,"-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^10*x^10 + 5*a*b^9*x^8 + 10*a^2*b^8*x^6 + 10*a^3*b^7*x^4 + 5*a^4*b^6*x^2 + a^5*b^5) + 63/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5)","A",0
527,1,131,0,3.026765," ","integrate(x^8/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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(a b^{9} x^{10} + 5 \, a^{2} b^{8} x^{8} + 10 \, a^{3} b^{7} x^{6} + 10 \, a^{4} b^{6} x^{4} + 5 \, a^{5} b^{5} x^{2} + a^{6} b^{4}\right)}} + \frac{7 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a b^{4}}"," ",0,"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)/(a*b^9*x^10 + 5*a^2*b^8*x^8 + 10*a^3*b^7*x^6 + 10*a^4*b^6*x^4 + 5*a^5*b^5*x^2 + a^6*b^4) + 7/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^4)","A",0
528,1,133,0,2.956618," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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(a^{2} b^{8} x^{10} + 5 \, a^{3} b^{7} x^{8} + 10 \, a^{4} b^{6} x^{6} + 10 \, a^{5} b^{5} x^{4} + 5 \, a^{6} b^{4} x^{2} + a^{7} b^{3}\right)}} + \frac{3 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{2} b^{3}}"," ",0,"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)/(a^2*b^8*x^10 + 5*a^3*b^7*x^8 + 10*a^4*b^6*x^6 + 10*a^5*b^5*x^4 + 5*a^6*b^4*x^2 + a^7*b^3) + 3/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^3)","A",0
529,1,133,0,3.038753," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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(a^{3} b^{7} x^{10} + 5 \, a^{4} b^{6} x^{8} + 10 \, a^{5} b^{5} x^{6} + 10 \, a^{6} b^{4} x^{4} + 5 \, a^{7} b^{3} x^{2} + a^{8} b^{2}\right)}} + \frac{3 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{3} b^{2}}"," ",0,"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)/(a^3*b^7*x^10 + 5*a^4*b^6*x^8 + 10*a^5*b^5*x^6 + 10*a^6*b^4*x^4 + 5*a^7*b^3*x^2 + a^8*b^2) + 3/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b^2)","A",0
530,1,131,0,2.966209," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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(a^{4} b^{6} x^{10} + 5 \, a^{5} b^{5} x^{8} + 10 \, a^{6} b^{4} x^{6} + 10 \, a^{7} b^{3} x^{4} + 5 \, a^{8} b^{2} x^{2} + a^{9} b\right)}} + \frac{7 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{4} b}"," ",0,"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)/(a^4*b^6*x^10 + 5*a^5*b^5*x^8 + 10*a^6*b^4*x^6 + 10*a^7*b^3*x^4 + 5*a^8*b^2*x^2 + a^9*b) + 7/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4*b)","A",0
531,1,124,0,3.041819," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\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(a^{5} b^{5} x^{10} + 5 \, a^{6} b^{4} x^{8} + 10 \, a^{7} b^{3} x^{6} + 10 \, a^{8} b^{2} x^{4} + 5 \, a^{9} b x^{2} + a^{10}\right)}} + \frac{63 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{5}}"," ",0,"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)/(a^5*b^5*x^10 + 5*a^6*b^4*x^8 + 10*a^7*b^3*x^6 + 10*a^8*b^2*x^4 + 5*a^9*b*x^2 + a^10) + 63/256*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5)","A",0
532,1,137,0,3.120920," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{3465 \, b^{5} x^{10} + 16170 \, a b^{4} x^{8} + 29568 \, a^{2} b^{3} x^{6} + 26070 \, a^{3} b^{2} x^{4} + 10615 \, a^{4} b x^{2} + 1280 \, a^{5}}{1280 \, {\left(a^{6} b^{5} x^{11} + 5 \, a^{7} b^{4} x^{9} + 10 \, a^{8} b^{3} x^{7} + 10 \, a^{9} b^{2} x^{5} + 5 \, a^{10} b x^{3} + a^{11} x\right)}} - \frac{693 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{6}}"," ",0,"-1/1280*(3465*b^5*x^10 + 16170*a*b^4*x^8 + 29568*a^2*b^3*x^6 + 26070*a^3*b^2*x^4 + 10615*a^4*b*x^2 + 1280*a^5)/(a^6*b^5*x^11 + 5*a^7*b^4*x^9 + 10*a^8*b^3*x^7 + 10*a^9*b^2*x^5 + 5*a^10*b*x^3 + a^11*x) - 693/256*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6)","A",0
533,1,152,0,3.095543," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{45045 \, b^{6} x^{12} + 210210 \, a b^{5} x^{10} + 384384 \, a^{2} b^{4} x^{8} + 338910 \, a^{3} b^{3} x^{6} + 137995 \, a^{4} b^{2} x^{4} + 16640 \, a^{5} b x^{2} - 1280 \, a^{6}}{3840 \, {\left(a^{7} b^{5} x^{13} + 5 \, a^{8} b^{4} x^{11} + 10 \, a^{9} b^{3} x^{9} + 10 \, a^{10} b^{2} x^{7} + 5 \, a^{11} b x^{5} + a^{12} x^{3}\right)}} + \frac{3003 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{7}}"," ",0,"1/3840*(45045*b^6*x^12 + 210210*a*b^5*x^10 + 384384*a^2*b^4*x^8 + 338910*a^3*b^3*x^6 + 137995*a^4*b^2*x^4 + 16640*a^5*b*x^2 - 1280*a^6)/(a^7*b^5*x^13 + 5*a^8*b^4*x^11 + 10*a^9*b^3*x^9 + 10*a^10*b^2*x^7 + 5*a^11*b*x^5 + a^12*x^3) + 3003/256*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^7)","A",0
534,1,163,0,3.106782," ","integrate(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\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(a^{8} b^{5} x^{15} + 5 \, a^{9} b^{4} x^{13} + 10 \, a^{10} b^{3} x^{11} + 10 \, a^{11} b^{2} x^{9} + 5 \, a^{12} b x^{7} + a^{13} x^{5}\right)}} - \frac{9009 \, b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, \sqrt{a b} a^{8}}"," ",0,"-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)/(a^8*b^5*x^15 + 5*a^9*b^4*x^13 + 10*a^10*b^3*x^11 + 10*a^11*b^2*x^9 + 5*a^12*b*x^7 + a^13*x^5) - 9009/256*b^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^8)","A",0
535,1,15,0,3.055729," ","integrate(1/(x^4+2*x^2+1),x, algorithm=""maxima"")","\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
536,1,9,0,1.346973," ","integrate(x/(x^4+2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"-1/2/(x^2 + 1)","A",0
537,1,15,0,2.969324," ","integrate(x^2/(x^4+2*x^2+1),x, algorithm=""maxima"")","-\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
538,1,18,0,1.276063," ","integrate(x^3/(x^4+2*x^2+1),x, algorithm=""maxima"")","\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
539,1,9,0,1.329672," ","integrate(x/(x^4-18*x^2+81),x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(x^{2} - 9\right)}}"," ",0,"-1/2/(x^2 - 9)","A",0
540,1,18,0,1.318986," ","integrate(x^3/(x^4-8*x^2+16),x, algorithm=""maxima"")","-\frac{2}{x^{2} - 4} + \frac{1}{2} \, \log\left(x^{2} - 4\right)"," ",0,"-2/(x^2 - 4) + 1/2*log(x^2 - 4)","A",0
541,1,13,0,1.353149," ","integrate(x^5*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{8} \, b x^{8} + \frac{1}{6} \, a x^{6}"," ",0,"1/8*b*x^8 + 1/6*a*x^6","A",0
542,1,13,0,1.281244," ","integrate(x^3*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, b x^{6} + \frac{1}{4} \, a x^{4}"," ",0,"1/6*b*x^6 + 1/4*a*x^4","A",0
543,1,14,0,1.320716," ","integrate(x*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{2}}{4 \, b}"," ",0,"1/4*(b*x^2 + a)^2/b","A",0
544,1,14,0,1.385412," ","integrate(((b*x^2+a)^2)^(1/2)/x,x, algorithm=""maxima"")","\frac{1}{2} \, b x^{2} + \frac{1}{2} \, a \log\left(x^{2}\right)"," ",0,"1/2*b*x^2 + 1/2*a*log(x^2)","A",0
545,1,14,0,1.401657," ","integrate(((b*x^2+a)^2)^(1/2)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, b \log\left(x^{2}\right) - \frac{a}{2 \, x^{2}}"," ",0,"1/2*b*log(x^2) - 1/2*a/x^2","A",0
546,1,13,0,1.332886," ","integrate(((b*x^2+a)^2)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{2 \, b x^{2} + a}{4 \, x^{4}}"," ",0,"-1/4*(2*b*x^2 + a)/x^4","A",0
547,1,15,0,1.303146," ","integrate(((b*x^2+a)^2)^(1/2)/x^7,x, algorithm=""maxima"")","-\frac{3 \, b x^{2} + 2 \, a}{12 \, x^{6}}"," ",0,"-1/12*(3*b*x^2 + 2*a)/x^6","A",0
548,1,15,0,1.350776," ","integrate(((b*x^2+a)^2)^(1/2)/x^9,x, algorithm=""maxima"")","-\frac{4 \, b x^{2} + 3 \, a}{24 \, x^{8}}"," ",0,"-1/24*(4*b*x^2 + 3*a)/x^8","A",0
549,1,15,0,1.310352," ","integrate(((b*x^2+a)^2)^(1/2)/x^11,x, algorithm=""maxima"")","-\frac{5 \, b x^{2} + 4 \, a}{40 \, x^{10}}"," ",0,"-1/40*(5*b*x^2 + 4*a)/x^10","A",0
550,1,13,0,1.348294," ","integrate(x^4*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{7} \, b x^{7} + \frac{1}{5} \, a x^{5}"," ",0,"1/7*b*x^7 + 1/5*a*x^5","A",0
551,1,13,0,1.306584," ","integrate(x^2*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{5} \, b x^{5} + \frac{1}{3} \, a x^{3}"," ",0,"1/5*b*x^5 + 1/3*a*x^3","A",0
552,1,10,0,1.319294," ","integrate(((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} + a x"," ",0,"1/3*b*x^3 + a*x","A",0
553,1,10,0,1.344785," ","integrate(((b*x^2+a)^2)^(1/2)/x^2,x, algorithm=""maxima"")","b x - \frac{a}{x}"," ",0,"b*x - a/x","A",0
554,1,13,0,1.383307," ","integrate(((b*x^2+a)^2)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{3 \, b x^{2} + a}{3 \, x^{3}}"," ",0,"-1/3*(3*b*x^2 + a)/x^3","A",0
555,1,15,0,1.306458," ","integrate(((b*x^2+a)^2)^(1/2)/x^6,x, algorithm=""maxima"")","-\frac{5 \, b x^{2} + 3 \, a}{15 \, x^{5}}"," ",0,"-1/15*(5*b*x^2 + 3*a)/x^5","A",0
556,1,15,0,1.270834," ","integrate(((b*x^2+a)^2)^(1/2)/x^8,x, algorithm=""maxima"")","-\frac{7 \, b x^{2} + 5 \, a}{35 \, x^{7}}"," ",0,"-1/35*(7*b*x^2 + 5*a)/x^7","A",0
557,1,15,0,1.293746," ","integrate(((b*x^2+a)^2)^(1/2)/x^10,x, algorithm=""maxima"")","-\frac{9 \, b x^{2} + 7 \, a}{63 \, x^{9}}"," ",0,"-1/63*(9*b*x^2 + 7*a)/x^9","A",0
558,1,35,0,1.314756," ","integrate(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{16} \, b^{3} x^{16} + \frac{3}{14} \, a b^{2} x^{14} + \frac{1}{4} \, a^{2} b x^{12} + \frac{1}{10} \, a^{3} x^{10}"," ",0,"1/16*b^3*x^16 + 3/14*a*b^2*x^14 + 1/4*a^2*b*x^12 + 1/10*a^3*x^10","A",0
559,1,35,0,1.316642," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{14} \, b^{3} x^{14} + \frac{1}{4} \, a b^{2} x^{12} + \frac{3}{10} \, a^{2} b x^{10} + \frac{1}{8} \, a^{3} x^{8}"," ",0,"1/14*b^3*x^14 + 1/4*a*b^2*x^12 + 3/10*a^2*b*x^10 + 1/8*a^3*x^8","A",0
560,1,35,0,1.337132," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{12} \, b^{3} x^{12} + \frac{3}{10} \, a b^{2} x^{10} + \frac{3}{8} \, a^{2} b x^{8} + \frac{1}{6} \, a^{3} x^{6}"," ",0,"1/12*b^3*x^12 + 3/10*a*b^2*x^10 + 3/8*a^2*b*x^8 + 1/6*a^3*x^6","A",0
561,1,35,0,1.325778," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{10} \, b^{3} x^{10} + \frac{3}{8} \, a b^{2} x^{8} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/10*b^3*x^10 + 3/8*a*b^2*x^8 + 1/2*a^2*b*x^6 + 1/4*a^3*x^4","A",0
562,1,35,0,1.355651," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{8} \, b^{3} x^{8} + \frac{1}{2} \, a b^{2} x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/8*b^3*x^8 + 1/2*a*b^2*x^6 + 3/4*a^2*b*x^4 + 1/2*a^3*x^2","A",0
563,1,33,0,1.327849," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x,x, algorithm=""maxima"")","\frac{1}{6} \, b^{3} x^{6} + \frac{3}{4} \, a b^{2} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} \log\left(x\right)"," ",0,"1/6*b^3*x^6 + 3/4*a*b^2*x^4 + 3/2*a^2*b*x^2 + a^3*log(x)","A",0
564,1,34,0,1.292309," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, b^{3} x^{4} + \frac{3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b \log\left(x\right) - \frac{a^{3}}{2 \, x^{2}}"," ",0,"1/4*b^3*x^4 + 3/2*a*b^2*x^2 + 3*a^2*b*log(x) - 1/2*a^3/x^2","A",0
565,1,34,0,1.311752," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, b^{3} x^{2} + 3 \, a b^{2} \log\left(x\right) - \frac{3 \, a^{2} b}{2 \, x^{2}} - \frac{a^{3}}{4 \, x^{4}}"," ",0,"1/2*b^3*x^2 + 3*a*b^2*log(x) - 3/2*a^2*b/x^2 - 1/4*a^3/x^4","A",0
566,1,33,0,1.260994," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^7,x, algorithm=""maxima"")","b^{3} \log\left(x\right) - \frac{3 \, a b^{2}}{2 \, x^{2}} - \frac{3 \, a^{2} b}{4 \, x^{4}} - \frac{a^{3}}{6 \, x^{6}}"," ",0,"b^3*log(x) - 3/2*a*b^2/x^2 - 3/4*a^2*b/x^4 - 1/6*a^3/x^6","A",0
567,1,35,0,1.357989," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^9,x, algorithm=""maxima"")","-\frac{b^{3}}{2 \, x^{2}} - \frac{3 \, a b^{2}}{4 \, x^{4}} - \frac{a^{2} b}{2 \, x^{6}} - \frac{a^{3}}{8 \, x^{8}}"," ",0,"-1/2*b^3/x^2 - 3/4*a*b^2/x^4 - 1/2*a^2*b/x^6 - 1/8*a^3/x^8","A",0
568,1,35,0,1.425938," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^11,x, algorithm=""maxima"")","-\frac{b^{3}}{4 \, x^{4}} - \frac{a b^{2}}{2 \, x^{6}} - \frac{3 \, a^{2} b}{8 \, x^{8}} - \frac{a^{3}}{10 \, x^{10}}"," ",0,"-1/4*b^3/x^4 - 1/2*a*b^2/x^6 - 3/8*a^2*b/x^8 - 1/10*a^3/x^10","A",0
569,1,35,0,1.310038," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^13,x, algorithm=""maxima"")","-\frac{b^{3}}{6 \, x^{6}} - \frac{3 \, a b^{2}}{8 \, x^{8}} - \frac{3 \, a^{2} b}{10 \, x^{10}} - \frac{a^{3}}{12 \, x^{12}}"," ",0,"-1/6*b^3/x^6 - 3/8*a*b^2/x^8 - 3/10*a^2*b/x^10 - 1/12*a^3/x^12","A",0
570,1,35,0,1.132818," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^15,x, algorithm=""maxima"")","-\frac{b^{3}}{8 \, x^{8}} - \frac{3 \, a b^{2}}{10 \, x^{10}} - \frac{a^{2} b}{4 \, x^{12}} - \frac{a^{3}}{14 \, x^{14}}"," ",0,"-1/8*b^3/x^8 - 3/10*a*b^2/x^10 - 1/4*a^2*b/x^12 - 1/14*a^3/x^14","A",0
571,1,35,0,1.322648," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^17,x, algorithm=""maxima"")","-\frac{b^{3}}{10 \, x^{10}} - \frac{a b^{2}}{4 \, x^{12}} - \frac{3 \, a^{2} b}{14 \, x^{14}} - \frac{a^{3}}{16 \, x^{16}}"," ",0,"-1/10*b^3/x^10 - 1/4*a*b^2/x^12 - 3/14*a^2*b/x^14 - 1/16*a^3/x^16","A",0
572,1,35,0,1.297885," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{15} \, b^{3} x^{15} + \frac{3}{13} \, a b^{2} x^{13} + \frac{3}{11} \, a^{2} b x^{11} + \frac{1}{9} \, a^{3} x^{9}"," ",0,"1/15*b^3*x^15 + 3/13*a*b^2*x^13 + 3/11*a^2*b*x^11 + 1/9*a^3*x^9","A",0
573,1,35,0,1.267832," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{13} \, b^{3} x^{13} + \frac{3}{11} \, a b^{2} x^{11} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{7} \, a^{3} x^{7}"," ",0,"1/13*b^3*x^13 + 3/11*a*b^2*x^11 + 1/3*a^2*b*x^9 + 1/7*a^3*x^7","A",0
574,1,35,0,1.393395," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{11} \, b^{3} x^{11} + \frac{1}{3} \, a b^{2} x^{9} + \frac{3}{7} \, a^{2} b x^{7} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/11*b^3*x^11 + 1/3*a*b^2*x^9 + 3/7*a^2*b*x^7 + 1/5*a^3*x^5","A",0
575,1,35,0,1.347281," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{9} \, b^{3} x^{9} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/9*b^3*x^9 + 3/7*a*b^2*x^7 + 3/5*a^2*b*x^5 + 1/3*a^3*x^3","A",0
576,1,31,0,1.364216," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{7} \, b^{3} x^{7} + \frac{3}{5} \, a b^{2} x^{5} + a^{2} b x^{3} + a^{3} x"," ",0,"1/7*b^3*x^7 + 3/5*a*b^2*x^5 + a^2*b*x^3 + a^3*x","A",0
577,1,32,0,1.341918," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{3} x^{5} + a b^{2} x^{3} + 3 \, a^{2} b x - \frac{a^{3}}{x}"," ",0,"1/5*b^3*x^5 + a*b^2*x^3 + 3*a^2*b*x - a^3/x","A",0
578,1,33,0,1.290272," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} x^{3} + 3 \, a b^{2} x - \frac{3 \, a^{2} b}{x} - \frac{a^{3}}{3 \, x^{3}}"," ",0,"1/3*b^3*x^3 + 3*a*b^2*x - 3*a^2*b/x - 1/3*a^3/x^3","A",0
579,1,32,0,1.323347," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^6,x, algorithm=""maxima"")","b^{3} x - \frac{3 \, a b^{2}}{x} - \frac{a^{2} b}{x^{3}} - \frac{a^{3}}{5 \, x^{5}}"," ",0,"b^3*x - 3*a*b^2/x - a^2*b/x^3 - 1/5*a^3/x^5","A",0
580,1,35,0,1.272649," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^8,x, algorithm=""maxima"")","-\frac{b^{3}}{x} - \frac{a b^{2}}{x^{3}} - \frac{3 \, a^{2} b}{5 \, x^{5}} - \frac{a^{3}}{7 \, x^{7}}"," ",0,"-b^3/x - a*b^2/x^3 - 3/5*a^2*b/x^5 - 1/7*a^3/x^7","A",0
581,1,35,0,1.337565," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^10,x, algorithm=""maxima"")","-\frac{b^{3}}{3 \, x^{3}} - \frac{3 \, a b^{2}}{5 \, x^{5}} - \frac{3 \, a^{2} b}{7 \, x^{7}} - \frac{a^{3}}{9 \, x^{9}}"," ",0,"-1/3*b^3/x^3 - 3/5*a*b^2/x^5 - 3/7*a^2*b/x^7 - 1/9*a^3/x^9","A",0
582,1,35,0,1.303030," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^12,x, algorithm=""maxima"")","-\frac{b^{3}}{5 \, x^{5}} - \frac{3 \, a b^{2}}{7 \, x^{7}} - \frac{a^{2} b}{3 \, x^{9}} - \frac{a^{3}}{11 \, x^{11}}"," ",0,"-1/5*b^3/x^5 - 3/7*a*b^2/x^7 - 1/3*a^2*b/x^9 - 1/11*a^3/x^11","A",0
583,1,35,0,1.389811," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^14,x, algorithm=""maxima"")","-\frac{b^{3}}{7 \, x^{7}} - \frac{a b^{2}}{3 \, x^{9}} - \frac{3 \, a^{2} b}{11 \, x^{11}} - \frac{a^{3}}{13 \, x^{13}}"," ",0,"-1/7*b^3/x^7 - 1/3*a*b^2/x^9 - 3/11*a^2*b/x^11 - 1/13*a^3/x^13","A",0
584,1,35,0,1.293975," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^16,x, algorithm=""maxima"")","-\frac{b^{3}}{9 \, x^{9}} - \frac{3 \, a b^{2}}{11 \, x^{11}} - \frac{3 \, a^{2} b}{13 \, x^{13}} - \frac{a^{3}}{15 \, x^{15}}"," ",0,"-1/9*b^3/x^9 - 3/11*a*b^2/x^11 - 3/13*a^2*b/x^13 - 1/15*a^3/x^15","A",0
585,1,57,0,1.318854," ","integrate(x^13*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{24} \, b^{5} x^{24} + \frac{5}{22} \, a b^{4} x^{22} + \frac{1}{2} \, a^{2} b^{3} x^{20} + \frac{5}{9} \, a^{3} b^{2} x^{18} + \frac{5}{16} \, a^{4} b x^{16} + \frac{1}{14} \, a^{5} x^{14}"," ",0,"1/24*b^5*x^24 + 5/22*a*b^4*x^22 + 1/2*a^2*b^3*x^20 + 5/9*a^3*b^2*x^18 + 5/16*a^4*b*x^16 + 1/14*a^5*x^14","A",0
586,1,57,0,1.373716," ","integrate(x^11*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{22} \, b^{5} x^{22} + \frac{1}{4} \, a b^{4} x^{20} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{5}{8} \, a^{3} b^{2} x^{16} + \frac{5}{14} \, a^{4} b x^{14} + \frac{1}{12} \, a^{5} x^{12}"," ",0,"1/22*b^5*x^22 + 1/4*a*b^4*x^20 + 5/9*a^2*b^3*x^18 + 5/8*a^3*b^2*x^16 + 5/14*a^4*b*x^14 + 1/12*a^5*x^12","A",0
587,1,57,0,1.433162," ","integrate(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{20} \, b^{5} x^{20} + \frac{5}{18} \, a b^{4} x^{18} + \frac{5}{8} \, a^{2} b^{3} x^{16} + \frac{5}{7} \, a^{3} b^{2} x^{14} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{10} \, a^{5} x^{10}"," ",0,"1/20*b^5*x^20 + 5/18*a*b^4*x^18 + 5/8*a^2*b^3*x^16 + 5/7*a^3*b^2*x^14 + 5/12*a^4*b*x^12 + 1/10*a^5*x^10","A",0
588,1,57,0,1.399596," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{18} \, b^{5} x^{18} + \frac{5}{16} \, a b^{4} x^{16} + \frac{5}{7} \, a^{2} b^{3} x^{14} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{1}{2} \, a^{4} b x^{10} + \frac{1}{8} \, a^{5} x^{8}"," ",0,"1/18*b^5*x^18 + 5/16*a*b^4*x^16 + 5/7*a^2*b^3*x^14 + 5/6*a^3*b^2*x^12 + 1/2*a^4*b*x^10 + 1/8*a^5*x^8","A",0
589,1,56,0,1.336099," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{16} \, b^{5} x^{16} + \frac{5}{14} \, a b^{4} x^{14} + \frac{5}{6} \, a^{2} b^{3} x^{12} + a^{3} b^{2} x^{10} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{6} \, a^{5} x^{6}"," ",0,"1/16*b^5*x^16 + 5/14*a*b^4*x^14 + 5/6*a^2*b^3*x^12 + a^3*b^2*x^10 + 5/8*a^4*b*x^8 + 1/6*a^5*x^6","A",0
590,1,56,0,1.248797," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{14} \, b^{5} x^{14} + \frac{5}{12} \, a b^{4} x^{12} + a^{2} b^{3} x^{10} + \frac{5}{4} \, a^{3} b^{2} x^{8} + \frac{5}{6} \, a^{4} b x^{6} + \frac{1}{4} \, a^{5} x^{4}"," ",0,"1/14*b^5*x^14 + 5/12*a*b^4*x^12 + a^2*b^3*x^10 + 5/4*a^3*b^2*x^8 + 5/6*a^4*b*x^6 + 1/4*a^5*x^4","A",0
591,1,57,0,1.311324," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{12} \, b^{5} x^{12} + \frac{1}{2} \, a b^{4} x^{10} + \frac{5}{4} \, a^{2} b^{3} x^{8} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{4} \, a^{4} b x^{4} + \frac{1}{2} \, a^{5} x^{2}"," ",0,"1/12*b^5*x^12 + 1/2*a*b^4*x^10 + 5/4*a^2*b^3*x^8 + 5/3*a^3*b^2*x^6 + 5/4*a^4*b*x^4 + 1/2*a^5*x^2","A",0
592,1,55,0,1.361042," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x,x, algorithm=""maxima"")","\frac{1}{10} \, b^{5} x^{10} + \frac{5}{8} \, a b^{4} x^{8} + \frac{5}{3} \, a^{2} b^{3} x^{6} + \frac{5}{2} \, a^{3} b^{2} x^{4} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} \log\left(x\right)"," ",0,"1/10*b^5*x^10 + 5/8*a*b^4*x^8 + 5/3*a^2*b^3*x^6 + 5/2*a^3*b^2*x^4 + 5/2*a^4*b*x^2 + a^5*log(x)","A",0
593,1,56,0,1.338526," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, b^{5} x^{8} + \frac{5}{6} \, a b^{4} x^{6} + \frac{5}{2} \, a^{2} b^{3} x^{4} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b \log\left(x\right) - \frac{a^{5}}{2 \, x^{2}}"," ",0,"1/8*b^5*x^8 + 5/6*a*b^4*x^6 + 5/2*a^2*b^3*x^4 + 5*a^3*b^2*x^2 + 5*a^4*b*log(x) - 1/2*a^5/x^2","A",0
594,1,56,0,1.341001," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^5,x, algorithm=""maxima"")","\frac{1}{6} \, b^{5} x^{6} + \frac{5}{4} \, a b^{4} x^{4} + 5 \, a^{2} b^{3} x^{2} + 10 \, a^{3} b^{2} \log\left(x\right) - \frac{5 \, a^{4} b}{2 \, x^{2}} - \frac{a^{5}}{4 \, x^{4}}"," ",0,"1/6*b^5*x^6 + 5/4*a*b^4*x^4 + 5*a^2*b^3*x^2 + 10*a^3*b^2*log(x) - 5/2*a^4*b/x^2 - 1/4*a^5/x^4","A",0
595,1,56,0,1.383623," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^7,x, algorithm=""maxima"")","\frac{1}{4} \, b^{5} x^{4} + \frac{5}{2} \, a b^{4} x^{2} + 10 \, a^{2} b^{3} \log\left(x\right) - \frac{5 \, a^{3} b^{2}}{x^{2}} - \frac{5 \, a^{4} b}{4 \, x^{4}} - \frac{a^{5}}{6 \, x^{6}}"," ",0,"1/4*b^5*x^4 + 5/2*a*b^4*x^2 + 10*a^2*b^3*log(x) - 5*a^3*b^2/x^2 - 5/4*a^4*b/x^4 - 1/6*a^5/x^6","A",0
596,1,56,0,1.358631," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^9,x, algorithm=""maxima"")","\frac{1}{2} \, b^{5} x^{2} + 5 \, a b^{4} \log\left(x\right) - \frac{5 \, a^{2} b^{3}}{x^{2}} - \frac{5 \, a^{3} b^{2}}{2 \, x^{4}} - \frac{5 \, a^{4} b}{6 \, x^{6}} - \frac{a^{5}}{8 \, x^{8}}"," ",0,"1/2*b^5*x^2 + 5*a*b^4*log(x) - 5*a^2*b^3/x^2 - 5/2*a^3*b^2/x^4 - 5/6*a^4*b/x^6 - 1/8*a^5/x^8","A",0
597,1,55,0,1.324716," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^11,x, algorithm=""maxima"")","b^{5} \log\left(x\right) - \frac{5 \, a b^{4}}{2 \, x^{2}} - \frac{5 \, a^{2} b^{3}}{2 \, x^{4}} - \frac{5 \, a^{3} b^{2}}{3 \, x^{6}} - \frac{5 \, a^{4} b}{8 \, x^{8}} - \frac{a^{5}}{10 \, x^{10}}"," ",0,"b^5*log(x) - 5/2*a*b^4/x^2 - 5/2*a^2*b^3/x^4 - 5/3*a^3*b^2/x^6 - 5/8*a^4*b/x^8 - 1/10*a^5/x^10","A",0
598,1,57,0,1.395998," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^13,x, algorithm=""maxima"")","-\frac{b^{5}}{2 \, x^{2}} - \frac{5 \, a b^{4}}{4 \, x^{4}} - \frac{5 \, a^{2} b^{3}}{3 \, x^{6}} - \frac{5 \, a^{3} b^{2}}{4 \, x^{8}} - \frac{a^{4} b}{2 \, x^{10}} - \frac{a^{5}}{12 \, x^{12}}"," ",0,"-1/2*b^5/x^2 - 5/4*a*b^4/x^4 - 5/3*a^2*b^3/x^6 - 5/4*a^3*b^2/x^8 - 1/2*a^4*b/x^10 - 1/12*a^5/x^12","B",0
599,1,57,0,1.346640," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^15,x, algorithm=""maxima"")","-\frac{b^{5}}{4 \, x^{4}} - \frac{5 \, a b^{4}}{6 \, x^{6}} - \frac{5 \, a^{2} b^{3}}{4 \, x^{8}} - \frac{a^{3} b^{2}}{x^{10}} - \frac{5 \, a^{4} b}{12 \, x^{12}} - \frac{a^{5}}{14 \, x^{14}}"," ",0,"-1/4*b^5/x^4 - 5/6*a*b^4/x^6 - 5/4*a^2*b^3/x^8 - a^3*b^2/x^10 - 5/12*a^4*b/x^12 - 1/14*a^5/x^14","A",0
600,1,57,0,1.351267," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^17,x, algorithm=""maxima"")","-\frac{b^{5}}{6 \, x^{6}} - \frac{5 \, a b^{4}}{8 \, x^{8}} - \frac{a^{2} b^{3}}{x^{10}} - \frac{5 \, a^{3} b^{2}}{6 \, x^{12}} - \frac{5 \, a^{4} b}{14 \, x^{14}} - \frac{a^{5}}{16 \, x^{16}}"," ",0,"-1/6*b^5/x^6 - 5/8*a*b^4/x^8 - a^2*b^3/x^10 - 5/6*a^3*b^2/x^12 - 5/14*a^4*b/x^14 - 1/16*a^5/x^16","A",0
601,1,57,0,1.329802," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^19,x, algorithm=""maxima"")","-\frac{b^{5}}{8 \, x^{8}} - \frac{a b^{4}}{2 \, x^{10}} - \frac{5 \, a^{2} b^{3}}{6 \, x^{12}} - \frac{5 \, a^{3} b^{2}}{7 \, x^{14}} - \frac{5 \, a^{4} b}{16 \, x^{16}} - \frac{a^{5}}{18 \, x^{18}}"," ",0,"-1/8*b^5/x^8 - 1/2*a*b^4/x^10 - 5/6*a^2*b^3/x^12 - 5/7*a^3*b^2/x^14 - 5/16*a^4*b/x^16 - 1/18*a^5/x^18","A",0
602,1,57,0,1.340355," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^21,x, algorithm=""maxima"")","-\frac{b^{5}}{10 \, x^{10}} - \frac{5 \, a b^{4}}{12 \, x^{12}} - \frac{5 \, a^{2} b^{3}}{7 \, x^{14}} - \frac{5 \, a^{3} b^{2}}{8 \, x^{16}} - \frac{5 \, a^{4} b}{18 \, x^{18}} - \frac{a^{5}}{20 \, x^{20}}"," ",0,"-1/10*b^5/x^10 - 5/12*a*b^4/x^12 - 5/7*a^2*b^3/x^14 - 5/8*a^3*b^2/x^16 - 5/18*a^4*b/x^18 - 1/20*a^5/x^20","A",0
603,1,57,0,1.339700," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^23,x, algorithm=""maxima"")","-\frac{b^{5}}{12 \, x^{12}} - \frac{5 \, a b^{4}}{14 \, x^{14}} - \frac{5 \, a^{2} b^{3}}{8 \, x^{16}} - \frac{5 \, a^{3} b^{2}}{9 \, x^{18}} - \frac{a^{4} b}{4 \, x^{20}} - \frac{a^{5}}{22 \, x^{22}}"," ",0,"-1/12*b^5/x^12 - 5/14*a*b^4/x^14 - 5/8*a^2*b^3/x^16 - 5/9*a^3*b^2/x^18 - 1/4*a^4*b/x^20 - 1/22*a^5/x^22","A",0
604,1,57,0,1.376423," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^25,x, algorithm=""maxima"")","-\frac{b^{5}}{14 \, x^{14}} - \frac{5 \, a b^{4}}{16 \, x^{16}} - \frac{5 \, a^{2} b^{3}}{9 \, x^{18}} - \frac{a^{3} b^{2}}{2 \, x^{20}} - \frac{5 \, a^{4} b}{22 \, x^{22}} - \frac{a^{5}}{24 \, x^{24}}"," ",0,"-1/14*b^5/x^14 - 5/16*a*b^4/x^16 - 5/9*a^2*b^3/x^18 - 1/2*a^3*b^2/x^20 - 5/22*a^4*b/x^22 - 1/24*a^5/x^24","A",0
605,1,57,0,1.282901," ","integrate(x^12*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{23} \, b^{5} x^{23} + \frac{5}{21} \, a b^{4} x^{21} + \frac{10}{19} \, a^{2} b^{3} x^{19} + \frac{10}{17} \, a^{3} b^{2} x^{17} + \frac{1}{3} \, a^{4} b x^{15} + \frac{1}{13} \, a^{5} x^{13}"," ",0,"1/23*b^5*x^23 + 5/21*a*b^4*x^21 + 10/19*a^2*b^3*x^19 + 10/17*a^3*b^2*x^17 + 1/3*a^4*b*x^15 + 1/13*a^5*x^13","A",0
606,1,57,0,1.354810," ","integrate(x^10*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{21} \, b^{5} x^{21} + \frac{5}{19} \, a b^{4} x^{19} + \frac{10}{17} \, a^{2} b^{3} x^{17} + \frac{2}{3} \, a^{3} b^{2} x^{15} + \frac{5}{13} \, a^{4} b x^{13} + \frac{1}{11} \, a^{5} x^{11}"," ",0,"1/21*b^5*x^21 + 5/19*a*b^4*x^19 + 10/17*a^2*b^3*x^17 + 2/3*a^3*b^2*x^15 + 5/13*a^4*b*x^13 + 1/11*a^5*x^11","A",0
607,1,57,0,1.327364," ","integrate(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{19} \, b^{5} x^{19} + \frac{5}{17} \, a b^{4} x^{17} + \frac{2}{3} \, a^{2} b^{3} x^{15} + \frac{10}{13} \, a^{3} b^{2} x^{13} + \frac{5}{11} \, a^{4} b x^{11} + \frac{1}{9} \, a^{5} x^{9}"," ",0,"1/19*b^5*x^19 + 5/17*a*b^4*x^17 + 2/3*a^2*b^3*x^15 + 10/13*a^3*b^2*x^13 + 5/11*a^4*b*x^11 + 1/9*a^5*x^9","A",0
608,1,57,0,1.288416," ","integrate(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{17} \, b^{5} x^{17} + \frac{1}{3} \, a b^{4} x^{15} + \frac{10}{13} \, a^{2} b^{3} x^{13} + \frac{10}{11} \, a^{3} b^{2} x^{11} + \frac{5}{9} \, a^{4} b x^{9} + \frac{1}{7} \, a^{5} x^{7}"," ",0,"1/17*b^5*x^17 + 1/3*a*b^4*x^15 + 10/13*a^2*b^3*x^13 + 10/11*a^3*b^2*x^11 + 5/9*a^4*b*x^9 + 1/7*a^5*x^7","A",0
609,1,57,0,1.334201," ","integrate(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{15} \, b^{5} x^{15} + \frac{5}{13} \, a b^{4} x^{13} + \frac{10}{11} \, a^{2} b^{3} x^{11} + \frac{10}{9} \, a^{3} b^{2} x^{9} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{5} \, a^{5} x^{5}"," ",0,"1/15*b^5*x^15 + 5/13*a*b^4*x^13 + 10/11*a^2*b^3*x^11 + 10/9*a^3*b^2*x^9 + 5/7*a^4*b*x^7 + 1/5*a^5*x^5","A",0
610,1,56,0,1.363587," ","integrate(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{13} \, b^{5} x^{13} + \frac{5}{11} \, a b^{4} x^{11} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{10}{7} \, a^{3} b^{2} x^{7} + a^{4} b x^{5} + \frac{1}{3} \, a^{5} x^{3}"," ",0,"1/13*b^5*x^13 + 5/11*a*b^4*x^11 + 10/9*a^2*b^3*x^9 + 10/7*a^3*b^2*x^7 + a^4*b*x^5 + 1/3*a^5*x^3","A",0
611,1,54,0,1.318884," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{11} \, b^{5} x^{11} + \frac{5}{9} \, a b^{4} x^{9} + \frac{10}{7} \, a^{2} b^{3} x^{7} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} x"," ",0,"1/11*b^5*x^11 + 5/9*a*b^4*x^9 + 10/7*a^2*b^3*x^7 + 2*a^3*b^2*x^5 + 5/3*a^4*b*x^3 + a^5*x","A",0
612,1,55,0,1.323744," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{5} x^{9} + \frac{5}{7} \, a b^{4} x^{7} + 2 \, a^{2} b^{3} x^{5} + \frac{10}{3} \, a^{3} b^{2} x^{3} + 5 \, a^{4} b x - \frac{a^{5}}{x}"," ",0,"1/9*b^5*x^9 + 5/7*a*b^4*x^7 + 2*a^2*b^3*x^5 + 10/3*a^3*b^2*x^3 + 5*a^4*b*x - a^5/x","A",0
613,1,54,0,1.328549," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^4,x, algorithm=""maxima"")","\frac{1}{7} \, b^{5} x^{7} + a b^{4} x^{5} + \frac{10}{3} \, a^{2} b^{3} x^{3} + 10 \, a^{3} b^{2} x - \frac{5 \, a^{4} b}{x} - \frac{a^{5}}{3 \, x^{3}}"," ",0,"1/7*b^5*x^7 + a*b^4*x^5 + 10/3*a^2*b^3*x^3 + 10*a^3*b^2*x - 5*a^4*b/x - 1/3*a^5/x^3","A",0
614,1,55,0,1.347338," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^6,x, algorithm=""maxima"")","\frac{1}{5} \, b^{5} x^{5} + \frac{5}{3} \, a b^{4} x^{3} + 10 \, a^{2} b^{3} x - \frac{10 \, a^{3} b^{2}}{x} - \frac{5 \, a^{4} b}{3 \, x^{3}} - \frac{a^{5}}{5 \, x^{5}}"," ",0,"1/5*b^5*x^5 + 5/3*a*b^4*x^3 + 10*a^2*b^3*x - 10*a^3*b^2/x - 5/3*a^4*b/x^3 - 1/5*a^5/x^5","A",0
615,1,55,0,1.287232," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^8,x, algorithm=""maxima"")","\frac{1}{3} \, b^{5} x^{3} + 5 \, a b^{4} x - \frac{10 \, a^{2} b^{3}}{x} - \frac{10 \, a^{3} b^{2}}{3 \, x^{3}} - \frac{a^{4} b}{x^{5}} - \frac{a^{5}}{7 \, x^{7}}"," ",0,"1/3*b^5*x^3 + 5*a*b^4*x - 10*a^2*b^3/x - 10/3*a^3*b^2/x^3 - a^4*b/x^5 - 1/7*a^5/x^7","A",0
616,1,54,0,1.349774," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^10,x, algorithm=""maxima"")","b^{5} x - \frac{5 \, a b^{4}}{x} - \frac{10 \, a^{2} b^{3}}{3 \, x^{3}} - \frac{2 \, a^{3} b^{2}}{x^{5}} - \frac{5 \, a^{4} b}{7 \, x^{7}} - \frac{a^{5}}{9 \, x^{9}}"," ",0,"b^5*x - 5*a*b^4/x - 10/3*a^2*b^3/x^3 - 2*a^3*b^2/x^5 - 5/7*a^4*b/x^7 - 1/9*a^5/x^9","A",0
617,1,57,0,1.334792," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^12,x, algorithm=""maxima"")","-\frac{b^{5}}{x} - \frac{5 \, a b^{4}}{3 \, x^{3}} - \frac{2 \, a^{2} b^{3}}{x^{5}} - \frac{10 \, a^{3} b^{2}}{7 \, x^{7}} - \frac{5 \, a^{4} b}{9 \, x^{9}} - \frac{a^{5}}{11 \, x^{11}}"," ",0,"-b^5/x - 5/3*a*b^4/x^3 - 2*a^2*b^3/x^5 - 10/7*a^3*b^2/x^7 - 5/9*a^4*b/x^9 - 1/11*a^5/x^11","A",0
618,1,57,0,1.335404," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^14,x, algorithm=""maxima"")","-\frac{b^{5}}{3 \, x^{3}} - \frac{a b^{4}}{x^{5}} - \frac{10 \, a^{2} b^{3}}{7 \, x^{7}} - \frac{10 \, a^{3} b^{2}}{9 \, x^{9}} - \frac{5 \, a^{4} b}{11 \, x^{11}} - \frac{a^{5}}{13 \, x^{13}}"," ",0,"-1/3*b^5/x^3 - a*b^4/x^5 - 10/7*a^2*b^3/x^7 - 10/9*a^3*b^2/x^9 - 5/11*a^4*b/x^11 - 1/13*a^5/x^13","A",0
619,1,57,0,1.352497," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^16,x, algorithm=""maxima"")","-\frac{b^{5}}{5 \, x^{5}} - \frac{5 \, a b^{4}}{7 \, x^{7}} - \frac{10 \, a^{2} b^{3}}{9 \, x^{9}} - \frac{10 \, a^{3} b^{2}}{11 \, x^{11}} - \frac{5 \, a^{4} b}{13 \, x^{13}} - \frac{a^{5}}{15 \, x^{15}}"," ",0,"-1/5*b^5/x^5 - 5/7*a*b^4/x^7 - 10/9*a^2*b^3/x^9 - 10/11*a^3*b^2/x^11 - 5/13*a^4*b/x^13 - 1/15*a^5/x^15","A",0
620,1,57,0,1.354676," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^18,x, algorithm=""maxima"")","-\frac{b^{5}}{7 \, x^{7}} - \frac{5 \, a b^{4}}{9 \, x^{9}} - \frac{10 \, a^{2} b^{3}}{11 \, x^{11}} - \frac{10 \, a^{3} b^{2}}{13 \, x^{13}} - \frac{a^{4} b}{3 \, x^{15}} - \frac{a^{5}}{17 \, x^{17}}"," ",0,"-1/7*b^5/x^7 - 5/9*a*b^4/x^9 - 10/11*a^2*b^3/x^11 - 10/13*a^3*b^2/x^13 - 1/3*a^4*b/x^15 - 1/17*a^5/x^17","A",0
621,1,57,0,1.344694," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^20,x, algorithm=""maxima"")","-\frac{b^{5}}{9 \, x^{9}} - \frac{5 \, a b^{4}}{11 \, x^{11}} - \frac{10 \, a^{2} b^{3}}{13 \, x^{13}} - \frac{2 \, a^{3} b^{2}}{3 \, x^{15}} - \frac{5 \, a^{4} b}{17 \, x^{17}} - \frac{a^{5}}{19 \, x^{19}}"," ",0,"-1/9*b^5/x^9 - 5/11*a*b^4/x^11 - 10/13*a^2*b^3/x^13 - 2/3*a^3*b^2/x^15 - 5/17*a^4*b/x^17 - 1/19*a^5/x^19","A",0
622,1,57,0,1.336699," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^22,x, algorithm=""maxima"")","-\frac{b^{5}}{11 \, x^{11}} - \frac{5 \, a b^{4}}{13 \, x^{13}} - \frac{2 \, a^{2} b^{3}}{3 \, x^{15}} - \frac{10 \, a^{3} b^{2}}{17 \, x^{17}} - \frac{5 \, a^{4} b}{19 \, x^{19}} - \frac{a^{5}}{21 \, x^{21}}"," ",0,"-1/11*b^5/x^11 - 5/13*a*b^4/x^13 - 2/3*a^2*b^3/x^15 - 10/17*a^3*b^2/x^17 - 5/19*a^4*b/x^19 - 1/21*a^5/x^21","A",0
623,1,57,0,1.376244," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^24,x, algorithm=""maxima"")","-\frac{b^{5}}{13 \, x^{13}} - \frac{a b^{4}}{3 \, x^{15}} - \frac{10 \, a^{2} b^{3}}{17 \, x^{17}} - \frac{10 \, a^{3} b^{2}}{19 \, x^{19}} - \frac{5 \, a^{4} b}{21 \, x^{21}} - \frac{a^{5}}{23 \, x^{23}}"," ",0,"-1/13*b^5/x^13 - 1/3*a*b^4/x^15 - 10/17*a^2*b^3/x^17 - 10/19*a^3*b^2/x^19 - 5/21*a^4*b/x^21 - 1/23*a^5/x^23","A",0
624,1,34,0,1.389278," ","integrate(x^5/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{a^{2} \log\left(b x^{2} + a\right)}{2 \, b^{3}} + \frac{b x^{4} - 2 \, a x^{2}}{4 \, b^{2}}"," ",0,"1/2*a^2*log(b*x^2 + a)/b^3 + 1/4*(b*x^4 - 2*a*x^2)/b^2","A",0
625,1,23,0,1.311180," ","integrate(x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{x^{2}}{2 \, b} - \frac{a \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*x^2/b - 1/2*a*log(b*x^2 + a)/b^2","A",0
626,1,13,0,1.350637," ","integrate(x/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"1/2*log(b*x^2 + a)/b","A",0
627,1,23,0,1.281498," ","integrate(1/x/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(b x^{2} + a\right)}{2 \, a} + \frac{\log\left(x^{2}\right)}{2 \, a}"," ",0,"-1/2*log(b*x^2 + a)/a + 1/2*log(x^2)/a","A",0
628,1,33,0,1.285454," ","integrate(1/x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{b \log\left(b x^{2} + a\right)}{2 \, a^{2}} - \frac{b \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{1}{2 \, a x^{2}}"," ",0,"1/2*b*log(b*x^2 + a)/a^2 - 1/2*b*log(x^2)/a^2 - 1/2/(a*x^2)","A",0
629,1,37,0,2.930663," ","integrate(x^4/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b x^{3} - 3 \, a x}{3 \, b^{2}}"," ",0,"a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b*x^3 - 3*a*x)/b^2","A",0
630,1,26,0,2.914160," ","integrate(x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{x}{b}"," ",0,"-a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) + x/b","A",0
631,1,15,0,3.030281," ","integrate(1/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"arctan(b*x/sqrt(a*b))/sqrt(a*b)","A",0
632,1,29,0,2.941036," ","integrate(1/x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{1}{a x}"," ",0,"-b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) - 1/(a*x)","A",0
633,1,40,0,3.010259," ","integrate(1/x^4/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{3 \, b x^{2} - a}{3 \, a^{2} x^{3}}"," ",0,"b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) + 1/3*(3*b*x^2 - a)/(a^2*x^3)","A",0
634,1,66,0,1.358790," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{6 \, a^{2} b x^{2} + 5 \, a^{3}}{4 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}} + \frac{x^{2}}{2 \, b^{3}} - \frac{3 \, a \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"-1/4*(6*a^2*b*x^2 + 5*a^3)/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4) + 1/2*x^2/b^3 - 3/2*a*log(b*x^2 + a)/b^4","A",0
635,1,55,0,1.365085," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{4 \, a b x^{2} + 3 \, a^{2}}{4 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{\log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"1/4*(4*a*b*x^2 + 3*a^2)/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3) + 1/2*log(b*x^2 + a)/b^3","A",0
636,1,36,0,1.384810," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, b x^{2} + a}{4 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/4*(2*b*x^2 + a)/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
637,1,26,0,1.321501," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{1}{4 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)}}"," ",0,"-1/4/(b^3*x^4 + 2*a*b^2*x^2 + a^2*b)","A",0
638,1,57,0,1.441156," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{2 \, b x^{2} + 3 \, a}{4 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}} - \frac{\log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{\log\left(x\right)}{a^{3}}"," ",0,"1/4*(2*b*x^2 + 3*a)/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4) - 1/2*log(b*x^2 + a)/a^3 + log(x)/a^3","A",0
639,1,75,0,1.369203," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{6 \, b^{2} x^{4} + 9 \, a b x^{2} + 2 \, a^{2}}{4 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{4} + a^{5} x^{2}\right)}} + \frac{3 \, b \log\left(b x^{2} + a\right)}{2 \, a^{4}} - \frac{3 \, b \log\left(x\right)}{a^{4}}"," ",0,"-1/4*(6*b^2*x^4 + 9*a*b*x^2 + 2*a^2)/(a^3*b^2*x^6 + 2*a^4*b*x^4 + a^5*x^2) + 3/2*b*log(b*x^2 + a)/a^4 - 3*b*log(x)/a^4","A",0
640,1,59,0,3.030695," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{5 \, b x^{3} + 3 \, a x}{8 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}} + \frac{3 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{2}}"," ",0,"-1/8*(5*b*x^3 + 3*a*x)/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2) + 3/8*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2)","A",0
641,1,62,0,2.934516," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{b x^{3} - a x}{8 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)}} + \frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b}"," ",0,"1/8*(b*x^3 - a*x)/(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b) + 1/8*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
642,1,58,0,2.986672," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{3 \, b x^{3} + 5 \, a x}{8 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}} + \frac{3 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2}}"," ",0,"1/8*(3*b*x^3 + 5*a*x)/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4) + 3/8*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2)","A",0
643,1,71,0,2.978569," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{15 \, b^{2} x^{4} + 25 \, a b x^{2} + 8 \, a^{2}}{8 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}} - \frac{15 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3}}"," ",0,"-1/8*(15*b^2*x^4 + 25*a*b*x^2 + 8*a^2)/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x) - 15/8*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3)","A",0
644,1,86,0,3.034600," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{105 \, b^{3} x^{6} + 175 \, a b^{2} x^{4} + 56 \, a^{2} b x^{2} - 8 \, a^{3}}{24 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}} + \frac{35 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{4}}"," ",0,"1/24*(105*b^3*x^6 + 175*a*b^2*x^4 + 56*a^2*b*x^2 - 8*a^3)/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3) + 35/8*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4)","A",0
645,1,110,0,1.383144," ","integrate(x^11/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\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^{10} x^{8} + 4 \, a b^{9} x^{6} + 6 \, a^{2} b^{8} x^{4} + 4 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)}} + \frac{x^{2}}{2 \, b^{5}} - \frac{5 \, a \log\left(b x^{2} + a\right)}{2 \, b^{6}}"," ",0,"-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^10*x^8 + 4*a*b^9*x^6 + 6*a^2*b^8*x^4 + 4*a^3*b^7*x^2 + a^4*b^6) + 1/2*x^2/b^5 - 5/2*a*log(b*x^2 + a)/b^6","A",0
646,1,99,0,1.458076," ","integrate(x^9/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{48 \, a b^{3} x^{6} + 108 \, a^{2} b^{2} x^{4} + 88 \, a^{3} b x^{2} + 25 \, a^{4}}{24 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}} + \frac{\log\left(b x^{2} + a\right)}{2 \, b^{5}}"," ",0,"1/24*(48*a*b^3*x^6 + 108*a^2*b^2*x^4 + 88*a^3*b*x^2 + 25*a^4)/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5) + 1/2*log(b*x^2 + a)/b^5","A",0
647,1,80,0,1.403585," ","integrate(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}}"," ",0,"-1/8*(4*b^3*x^6 + 6*a*b^2*x^4 + 4*a^2*b*x^2 + a^3)/(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4)","B",0
648,1,69,0,1.788285," ","integrate(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{6 \, b^{2} x^{4} + 4 \, a b x^{2} + a^{2}}{24 \, {\left(b^{7} x^{8} + 4 \, a b^{6} x^{6} + 6 \, a^{2} b^{5} x^{4} + 4 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}"," ",0,"-1/24*(6*b^2*x^4 + 4*a*b*x^2 + a^2)/(b^7*x^8 + 4*a*b^6*x^6 + 6*a^2*b^5*x^4 + 4*a^3*b^4*x^2 + a^4*b^3)","A",0
649,1,58,0,1.363792," ","integrate(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{4 \, b x^{2} + a}{24 \, {\left(b^{6} x^{8} + 4 \, a b^{5} x^{6} + 6 \, a^{2} b^{4} x^{4} + 4 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}}"," ",0,"-1/24*(4*b*x^2 + a)/(b^6*x^8 + 4*a*b^5*x^6 + 6*a^2*b^4*x^4 + 4*a^3*b^3*x^2 + a^4*b^2)","A",0
650,1,48,0,1.315781," ","integrate(x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{1}{8 \, {\left(b^{5} x^{8} + 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} + 4 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}"," ",0,"-1/8/(b^5*x^8 + 4*a*b^4*x^6 + 6*a^2*b^3*x^4 + 4*a^3*b^2*x^2 + a^4*b)","A",0
651,1,101,0,1.438635," ","integrate(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{12 \, b^{3} x^{6} + 42 \, a b^{2} x^{4} + 52 \, a^{2} b x^{2} + 25 \, a^{3}}{24 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)}} - \frac{\log\left(b x^{2} + a\right)}{2 \, a^{5}} + \frac{\log\left(x\right)}{a^{5}}"," ",0,"1/24*(12*b^3*x^6 + 42*a*b^2*x^4 + 52*a^2*b*x^2 + 25*a^3)/(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8) - 1/2*log(b*x^2 + a)/a^5 + log(x)/a^5","A",0
652,1,119,0,1.420980," ","integrate(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{60 \, b^{4} x^{8} + 210 \, a b^{3} x^{6} + 260 \, a^{2} b^{2} x^{4} + 125 \, a^{3} b x^{2} + 12 \, a^{4}}{24 \, {\left(a^{5} b^{4} x^{10} + 4 \, a^{6} b^{3} x^{8} + 6 \, a^{7} b^{2} x^{6} + 4 \, a^{8} b x^{4} + a^{9} x^{2}\right)}} + \frac{5 \, b \log\left(b x^{2} + a\right)}{2 \, a^{6}} - \frac{5 \, b \log\left(x\right)}{a^{6}}"," ",0,"-1/24*(60*b^4*x^8 + 210*a*b^3*x^6 + 260*a^2*b^2*x^4 + 125*a^3*b*x^2 + 12*a^4)/(a^5*b^4*x^10 + 4*a^6*b^3*x^8 + 6*a^7*b^2*x^6 + 4*a^8*b*x^4 + a^9*x^2) + 5/2*b*log(b*x^2 + a)/a^6 - 5*b*log(x)/a^6","A",0
653,1,109,0,3.032669," ","integrate(x^6/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{15 \, b^{3} x^{7} - 73 \, a b^{2} x^{5} - 55 \, a^{2} b x^{3} - 15 \, a^{3} x}{384 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}} + \frac{5 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a b^{3}}"," ",0,"1/384*(15*b^3*x^7 - 73*a*b^2*x^5 - 55*a^2*b*x^3 - 15*a^3*x)/(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3) + 5/128*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^3)","A",0
654,1,111,0,2.993506," ","integrate(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{3 \, b^{3} x^{7} + 11 \, a b^{2} x^{5} - 11 \, a^{2} b x^{3} - 3 \, a^{3} x}{128 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)}} + \frac{3 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{2} b^{2}}"," ",0,"1/128*(3*b^3*x^7 + 11*a*b^2*x^5 - 11*a^2*b*x^3 - 3*a^3*x)/(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2) + 3/128*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^2)","A",0
655,1,109,0,2.901908," ","integrate(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{15 \, b^{3} x^{7} + 55 \, a b^{2} x^{5} + 73 \, a^{2} b x^{3} - 15 \, a^{3} x}{384 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)}} + \frac{5 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{3} b}"," ",0,"1/384*(15*b^3*x^7 + 55*a*b^2*x^5 + 73*a^2*b*x^3 - 15*a^3*x)/(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b) + 5/128*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b)","A",0
656,1,102,0,3.050643," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{105 \, b^{3} x^{7} + 385 \, a b^{2} x^{5} + 511 \, a^{2} b x^{3} + 279 \, a^{3} x}{384 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)}} + \frac{35 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{4}}"," ",0,"1/384*(105*b^3*x^7 + 385*a*b^2*x^5 + 511*a^2*b*x^3 + 279*a^3*x)/(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8) + 35/128*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4)","A",0
657,1,115,0,3.038829," ","integrate(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{315 \, b^{4} x^{8} + 1155 \, a b^{3} x^{6} + 1533 \, a^{2} b^{2} x^{4} + 837 \, a^{3} b x^{2} + 128 \, a^{4}}{128 \, {\left(a^{5} b^{4} x^{9} + 4 \, a^{6} b^{3} x^{7} + 6 \, a^{7} b^{2} x^{5} + 4 \, a^{8} b x^{3} + a^{9} x\right)}} - \frac{315 \, b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{5}}"," ",0,"-1/128*(315*b^4*x^8 + 1155*a*b^3*x^6 + 1533*a^2*b^2*x^4 + 837*a^3*b*x^2 + 128*a^4)/(a^5*b^4*x^9 + 4*a^6*b^3*x^7 + 6*a^7*b^2*x^5 + 4*a^8*b*x^3 + a^9*x) - 315/128*b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5)","A",0
658,1,130,0,3.134603," ","integrate(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{3465 \, b^{5} x^{10} + 12705 \, a b^{4} x^{8} + 16863 \, a^{2} b^{3} x^{6} + 9207 \, a^{3} b^{2} x^{4} + 1408 \, a^{4} b x^{2} - 128 \, a^{5}}{384 \, {\left(a^{6} b^{4} x^{11} + 4 \, a^{7} b^{3} x^{9} + 6 \, a^{8} b^{2} x^{7} + 4 \, a^{9} b x^{5} + a^{10} x^{3}\right)}} + \frac{1155 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, \sqrt{a b} a^{6}}"," ",0,"1/384*(3465*b^5*x^10 + 12705*a*b^4*x^8 + 16863*a^2*b^3*x^6 + 9207*a^3*b^2*x^4 + 1408*a^4*b*x^2 - 128*a^5)/(a^6*b^4*x^11 + 4*a^7*b^3*x^9 + 6*a^8*b^2*x^7 + 4*a^9*b*x^5 + a^10*x^3) + 1155/128*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6)","A",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
665,1,41,0,1.304901," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{2 \, {\left(77 \, \left(d x\right)^{\frac{15}{2}} b^{2} + 210 \, \left(d x\right)^{\frac{11}{2}} a b d^{2} + 165 \, \left(d x\right)^{\frac{7}{2}} a^{2} d^{4}\right)}}{1155 \, d^{5}}"," ",0,"2/1155*(77*(d*x)^(15/2)*b^2 + 210*(d*x)^(11/2)*a*b*d^2 + 165*(d*x)^(7/2)*a^2*d^4)/d^5","A",0
666,1,41,0,1.341444," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{2 \, {\left(45 \, \left(d x\right)^{\frac{13}{2}} b^{2} + 130 \, \left(d x\right)^{\frac{9}{2}} a b d^{2} + 117 \, \left(d x\right)^{\frac{5}{2}} a^{2} d^{4}\right)}}{585 \, d^{5}}"," ",0,"2/585*(45*(d*x)^(13/2)*b^2 + 130*(d*x)^(9/2)*a*b*d^2 + 117*(d*x)^(5/2)*a^2*d^4)/d^5","A",0
667,1,41,0,1.363910," ","integrate((b^2*x^4+2*a*b*x^2+a^2)*(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(21 \, \left(d x\right)^{\frac{11}{2}} b^{2} + 66 \, \left(d x\right)^{\frac{7}{2}} a b d^{2} + 77 \, \left(d x\right)^{\frac{3}{2}} a^{2} d^{4}\right)}}{231 \, d^{5}}"," ",0,"2/231*(21*(d*x)^(11/2)*b^2 + 66*(d*x)^(7/2)*a*b*d^2 + 77*(d*x)^(3/2)*a^2*d^4)/d^5","A",0
668,1,41,0,1.273889," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(45 \, \sqrt{d x} a^{2} + \frac{5 \, \left(d x\right)^{\frac{9}{2}} b^{2}}{d^{4}} + \frac{18 \, \left(d x\right)^{\frac{5}{2}} a b}{d^{2}}\right)}}{45 \, d}"," ",0,"2/45*(45*sqrt(d*x)*a^2 + 5*(d*x)^(9/2)*b^2/d^4 + 18*(d*x)^(5/2)*a*b/d^2)/d","A",0
669,1,44,0,1.356823," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{21 \, a^{2}}{\sqrt{d x}} - \frac{3 \, \left(d x\right)^{\frac{7}{2}} b^{2} + 14 \, \left(d x\right)^{\frac{3}{2}} a b d^{2}}{d^{4}}\right)}}{21 \, d}"," ",0,"-2/21*(21*a^2/sqrt(d*x) - (3*(d*x)^(7/2)*b^2 + 14*(d*x)^(3/2)*a*b*d^2)/d^4)/d","A",0
670,1,43,0,1.403123," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, a^{2}}{\left(d x\right)^{\frac{3}{2}}} - \frac{3 \, {\left(\left(d x\right)^{\frac{5}{2}} b^{2} + 10 \, \sqrt{d x} a b d^{2}\right)}}{d^{4}}\right)}}{15 \, d}"," ",0,"-2/15*(5*a^2/(d*x)^(3/2) - 3*((d*x)^(5/2)*b^2 + 10*sqrt(d*x)*a*b*d^2)/d^4)/d","A",0
671,1,47,0,1.301362," ","integrate((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{5 \, \left(d x\right)^{\frac{3}{2}} b^{2}}{d^{4}} - \frac{3 \, {\left(10 \, a b d^{2} x^{2} + a^{2} d^{2}\right)}}{\left(d x\right)^{\frac{5}{2}} d^{2}}\right)}}{15 \, d}"," ",0,"2/15*(5*(d*x)^(3/2)*b^2/d^4 - 3*(10*a*b*d^2*x^2 + a^2*d^2)/((d*x)^(5/2)*d^2))/d","A",0
672,1,73,0,1.350420," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(7315 \, \left(d x\right)^{\frac{23}{2}} b^{4} + 35420 \, \left(d x\right)^{\frac{19}{2}} a b^{3} d^{2} + 67298 \, \left(d x\right)^{\frac{15}{2}} a^{2} b^{2} d^{4} + 61180 \, \left(d x\right)^{\frac{11}{2}} a^{3} b d^{6} + 24035 \, \left(d x\right)^{\frac{7}{2}} a^{4} d^{8}\right)}}{168245 \, d^{9}}"," ",0,"2/168245*(7315*(d*x)^(23/2)*b^4 + 35420*(d*x)^(19/2)*a*b^3*d^2 + 67298*(d*x)^(15/2)*a^2*b^2*d^4 + 61180*(d*x)^(11/2)*a^3*b*d^6 + 24035*(d*x)^(7/2)*a^4*d^8)/d^9","A",0
673,1,73,0,1.349540," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(3315 \, \left(d x\right)^{\frac{21}{2}} b^{4} + 16380 \, \left(d x\right)^{\frac{17}{2}} a b^{3} d^{2} + 32130 \, \left(d x\right)^{\frac{13}{2}} a^{2} b^{2} d^{4} + 30940 \, \left(d x\right)^{\frac{9}{2}} a^{3} b d^{6} + 13923 \, \left(d x\right)^{\frac{5}{2}} a^{4} d^{8}\right)}}{69615 \, d^{9}}"," ",0,"2/69615*(3315*(d*x)^(21/2)*b^4 + 16380*(d*x)^(17/2)*a*b^3*d^2 + 32130*(d*x)^(13/2)*a^2*b^2*d^4 + 30940*(d*x)^(9/2)*a^3*b*d^6 + 13923*(d*x)^(5/2)*a^4*d^8)/d^9","A",0
674,1,73,0,1.332723," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2*(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(1155 \, \left(d x\right)^{\frac{19}{2}} b^{4} + 5852 \, \left(d x\right)^{\frac{15}{2}} a b^{3} d^{2} + 11970 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{2} d^{4} + 12540 \, \left(d x\right)^{\frac{7}{2}} a^{3} b d^{6} + 7315 \, \left(d x\right)^{\frac{3}{2}} a^{4} d^{8}\right)}}{21945 \, d^{9}}"," ",0,"2/21945*(1155*(d*x)^(19/2)*b^4 + 5852*(d*x)^(15/2)*a*b^3*d^2 + 11970*(d*x)^(11/2)*a^2*b^2*d^4 + 12540*(d*x)^(7/2)*a^3*b*d^6 + 7315*(d*x)^(3/2)*a^4*d^8)/d^9","A",0
675,1,90,0,1.356748," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(9945 \, \sqrt{d x} a^{4} + \frac{585 \, \left(d x\right)^{\frac{17}{2}} b^{4}}{d^{8}} + \frac{3060 \, \left(d x\right)^{\frac{13}{2}} a b^{3}}{d^{6}} + \frac{4420 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2}}{d^{4}} + 442 \, {\left(\frac{5 \, \left(d x\right)^{\frac{9}{2}} b^{2}}{d^{4}} + \frac{18 \, \left(d x\right)^{\frac{5}{2}} a b}{d^{2}}\right)} a^{2}\right)}}{9945 \, d}"," ",0,"2/9945*(9945*sqrt(d*x)*a^4 + 585*(d*x)^(17/2)*b^4/d^8 + 3060*(d*x)^(13/2)*a*b^3/d^6 + 4420*(d*x)^(9/2)*a^2*b^2/d^4 + 442*(5*(d*x)^(9/2)*b^2/d^4 + 18*(d*x)^(5/2)*a*b/d^2)*a^2)/d","A",0
676,1,76,0,1.210987," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{1155 \, a^{4}}{\sqrt{d x}} - \frac{77 \, \left(d x\right)^{\frac{15}{2}} b^{4} + 420 \, \left(d x\right)^{\frac{11}{2}} a b^{3} d^{2} + 990 \, \left(d x\right)^{\frac{7}{2}} a^{2} b^{2} d^{4} + 1540 \, \left(d x\right)^{\frac{3}{2}} a^{3} b d^{6}}{d^{8}}\right)}}{1155 \, d}"," ",0,"-2/1155*(1155*a^4/sqrt(d*x) - (77*(d*x)^(15/2)*b^4 + 420*(d*x)^(11/2)*a*b^3*d^2 + 990*(d*x)^(7/2)*a^2*b^2*d^4 + 1540*(d*x)^(3/2)*a^3*b*d^6)/d^8)/d","A",0
677,1,76,0,1.354557," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{195 \, a^{4}}{\left(d x\right)^{\frac{3}{2}}} - \frac{45 \, \left(d x\right)^{\frac{13}{2}} b^{4} + 260 \, \left(d x\right)^{\frac{9}{2}} a b^{3} d^{2} + 702 \, \left(d x\right)^{\frac{5}{2}} a^{2} b^{2} d^{4} + 2340 \, \sqrt{d x} a^{3} b d^{6}}{d^{8}}\right)}}{585 \, d}"," ",0,"-2/585*(195*a^4/(d*x)^(3/2) - (45*(d*x)^(13/2)*b^4 + 260*(d*x)^(9/2)*a*b^3*d^2 + 702*(d*x)^(5/2)*a^2*b^2*d^4 + 2340*sqrt(d*x)*a^3*b*d^6)/d^8)/d","A",0
678,1,82,0,1.437894," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{77 \, {\left(20 \, a^{3} b d^{2} x^{2} + a^{4} d^{2}\right)}}{\left(d x\right)^{\frac{5}{2}} d^{2}} - \frac{5 \, {\left(7 \, \left(d x\right)^{\frac{11}{2}} b^{4} + 44 \, \left(d x\right)^{\frac{7}{2}} a b^{3} d^{2} + 154 \, \left(d x\right)^{\frac{3}{2}} a^{2} b^{2} d^{4}\right)}}{d^{8}}\right)}}{385 \, d}"," ",0,"-2/385*(77*(20*a^3*b*d^2*x^2 + a^4*d^2)/((d*x)^(5/2)*d^2) - 5*(7*(d*x)^(11/2)*b^4 + 44*(d*x)^(7/2)*a*b^3*d^2 + 154*(d*x)^(3/2)*a^2*b^2*d^4)/d^8)/d","A",0
679,1,105,0,1.400784," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(302841 \, \left(d x\right)^{\frac{31}{2}} b^{6} + 2086238 \, \left(d x\right)^{\frac{27}{2}} a b^{5} d^{2} + 6122655 \, \left(d x\right)^{\frac{23}{2}} a^{2} b^{4} d^{4} + 9882180 \, \left(d x\right)^{\frac{19}{2}} a^{3} b^{3} d^{6} + 9388071 \, \left(d x\right)^{\frac{15}{2}} a^{4} b^{2} d^{8} + 5120766 \, \left(d x\right)^{\frac{11}{2}} a^{5} b d^{10} + 1341153 \, \left(d x\right)^{\frac{7}{2}} a^{6} d^{12}\right)}}{9388071 \, d^{13}}"," ",0,"2/9388071*(302841*(d*x)^(31/2)*b^6 + 2086238*(d*x)^(27/2)*a*b^5*d^2 + 6122655*(d*x)^(23/2)*a^2*b^4*d^4 + 9882180*(d*x)^(19/2)*a^3*b^3*d^6 + 9388071*(d*x)^(15/2)*a^4*b^2*d^8 + 5120766*(d*x)^(11/2)*a^5*b*d^10 + 1341153*(d*x)^(7/2)*a^6*d^12)/d^13","A",0
680,1,105,0,1.333025," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(116025 \, \left(d x\right)^{\frac{29}{2}} b^{6} + 807534 \, \left(d x\right)^{\frac{25}{2}} a b^{5} d^{2} + 2403375 \, \left(d x\right)^{\frac{21}{2}} a^{2} b^{4} d^{4} + 3958500 \, \left(d x\right)^{\frac{17}{2}} a^{3} b^{3} d^{6} + 3882375 \, \left(d x\right)^{\frac{13}{2}} a^{4} b^{2} d^{8} + 2243150 \, \left(d x\right)^{\frac{9}{2}} a^{5} b d^{10} + 672945 \, \left(d x\right)^{\frac{5}{2}} a^{6} d^{12}\right)}}{3364725 \, d^{13}}"," ",0,"2/3364725*(116025*(d*x)^(29/2)*b^6 + 807534*(d*x)^(25/2)*a*b^5*d^2 + 2403375*(d*x)^(21/2)*a^2*b^4*d^4 + 3958500*(d*x)^(17/2)*a^3*b^3*d^6 + 3882375*(d*x)^(13/2)*a^4*b^2*d^8 + 2243150*(d*x)^(9/2)*a^5*b*d^10 + 672945*(d*x)^(5/2)*a^6*d^12)/d^13","A",0
681,1,105,0,1.391870," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3*(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(33649 \, \left(d x\right)^{\frac{27}{2}} b^{6} + 237006 \, \left(d x\right)^{\frac{23}{2}} a b^{5} d^{2} + 717255 \, \left(d x\right)^{\frac{19}{2}} a^{2} b^{4} d^{4} + 1211364 \, \left(d x\right)^{\frac{15}{2}} a^{3} b^{3} d^{6} + 1238895 \, \left(d x\right)^{\frac{11}{2}} a^{4} b^{2} d^{8} + 778734 \, \left(d x\right)^{\frac{7}{2}} a^{5} b d^{10} + 302841 \, \left(d x\right)^{\frac{3}{2}} a^{6} d^{12}\right)}}{908523 \, d^{13}}"," ",0,"2/908523*(33649*(d*x)^(27/2)*b^6 + 237006*(d*x)^(23/2)*a*b^5*d^2 + 717255*(d*x)^(19/2)*a^2*b^4*d^4 + 1211364*(d*x)^(15/2)*a^3*b^3*d^6 + 1238895*(d*x)^(11/2)*a^4*b^2*d^8 + 778734*(d*x)^(7/2)*a^5*b*d^10 + 302841*(d*x)^(3/2)*a^6*d^12)/d^13","A",0
682,1,155,0,1.360528," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(116025 \, \sqrt{d x} a^{6} + \frac{4641 \, \left(d x\right)^{\frac{25}{2}} b^{6}}{d^{12}} + \frac{33150 \, \left(d x\right)^{\frac{21}{2}} a b^{5}}{d^{10}} + \frac{81900 \, \left(d x\right)^{\frac{17}{2}} a^{2} b^{4}}{d^{8}} + \frac{71400 \, \left(d x\right)^{\frac{13}{2}} a^{3} b^{3}}{d^{6}} + 7735 \, {\left(\frac{5 \, \left(d x\right)^{\frac{9}{2}} b^{2}}{d^{4}} + \frac{18 \, \left(d x\right)^{\frac{5}{2}} a b}{d^{2}}\right)} a^{4} + 175 \, {\left(\frac{117 \, \left(d x\right)^{\frac{17}{2}} b^{4}}{d^{8}} + \frac{612 \, \left(d x\right)^{\frac{13}{2}} a b^{3}}{d^{6}} + \frac{884 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2}}{d^{4}}\right)} a^{2}\right)}}{116025 \, d}"," ",0,"2/116025*(116025*sqrt(d*x)*a^6 + 4641*(d*x)^(25/2)*b^6/d^12 + 33150*(d*x)^(21/2)*a*b^5/d^10 + 81900*(d*x)^(17/2)*a^2*b^4/d^8 + 71400*(d*x)^(13/2)*a^3*b^3/d^6 + 7735*(5*(d*x)^(9/2)*b^2/d^4 + 18*(d*x)^(5/2)*a*b/d^2)*a^4 + 175*(117*(d*x)^(17/2)*b^4/d^8 + 612*(d*x)^(13/2)*a*b^3/d^6 + 884*(d*x)^(9/2)*a^2*b^2/d^4)*a^2)/d","A",0
683,1,108,0,1.388976," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{33649 \, a^{6}}{\sqrt{d x}} - \frac{1463 \, \left(d x\right)^{\frac{23}{2}} b^{6} + 10626 \, \left(d x\right)^{\frac{19}{2}} a b^{5} d^{2} + 33649 \, \left(d x\right)^{\frac{15}{2}} a^{2} b^{4} d^{4} + 61180 \, \left(d x\right)^{\frac{11}{2}} a^{3} b^{3} d^{6} + 72105 \, \left(d x\right)^{\frac{7}{2}} a^{4} b^{2} d^{8} + 67298 \, \left(d x\right)^{\frac{3}{2}} a^{5} b d^{10}}{d^{12}}\right)}}{33649 \, d}"," ",0,"-2/33649*(33649*a^6/sqrt(d*x) - (1463*(d*x)^(23/2)*b^6 + 10626*(d*x)^(19/2)*a*b^5*d^2 + 33649*(d*x)^(15/2)*a^2*b^4*d^4 + 61180*(d*x)^(11/2)*a^3*b^3*d^6 + 72105*(d*x)^(7/2)*a^4*b^2*d^8 + 67298*(d*x)^(3/2)*a^5*b*d^10)/d^12)/d","A",0
684,1,108,0,1.387749," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{4641 \, a^{6}}{\left(d x\right)^{\frac{3}{2}}} - \frac{663 \, \left(d x\right)^{\frac{21}{2}} b^{6} + 4914 \, \left(d x\right)^{\frac{17}{2}} a b^{5} d^{2} + 16065 \, \left(d x\right)^{\frac{13}{2}} a^{2} b^{4} d^{4} + 30940 \, \left(d x\right)^{\frac{9}{2}} a^{3} b^{3} d^{6} + 41769 \, \left(d x\right)^{\frac{5}{2}} a^{4} b^{2} d^{8} + 83538 \, \sqrt{d x} a^{5} b d^{10}}{d^{12}}\right)}}{13923 \, d}"," ",0,"-2/13923*(4641*a^6/(d*x)^(3/2) - (663*(d*x)^(21/2)*b^6 + 4914*(d*x)^(17/2)*a*b^5*d^2 + 16065*(d*x)^(13/2)*a^2*b^4*d^4 + 30940*(d*x)^(9/2)*a^3*b^3*d^6 + 41769*(d*x)^(5/2)*a^4*b^2*d^8 + 83538*sqrt(d*x)*a^5*b*d^10)/d^12)/d","A",0
685,1,114,0,1.346473," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{1463 \, {\left(30 \, a^{5} b d^{2} x^{2} + a^{6} d^{2}\right)}}{\left(d x\right)^{\frac{5}{2}} d^{2}} - \frac{385 \, \left(d x\right)^{\frac{19}{2}} b^{6} + 2926 \, \left(d x\right)^{\frac{15}{2}} a b^{5} d^{2} + 9975 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{4} d^{4} + 20900 \, \left(d x\right)^{\frac{7}{2}} a^{3} b^{3} d^{6} + 36575 \, \left(d x\right)^{\frac{3}{2}} a^{4} b^{2} d^{8}}{d^{12}}\right)}}{7315 \, d}"," ",0,"-2/7315*(1463*(30*a^5*b*d^2*x^2 + a^6*d^2)/((d*x)^(5/2)*d^2) - (385*(d*x)^(19/2)*b^6 + 2926*(d*x)^(15/2)*a*b^5*d^2 + 9975*(d*x)^(11/2)*a^2*b^4*d^4 + 20900*(d*x)^(7/2)*a^3*b^3*d^6 + 36575*(d*x)^(3/2)*a^4*b^2*d^8)/d^12)/d","A",0
686,1,300,0,3.036773," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{\frac{40 \, \sqrt{d x} a^{2} d^{8}}{b^{4} d^{2} x^{2} + a b^{3} d^{2}} - \frac{45 \, {\left(\frac{\sqrt{2} d^{8} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{8} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{7} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{7} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a^{2}}{b^{3}} - \frac{32 \, {\left(\left(d x\right)^{\frac{5}{2}} b d^{4} - 10 \, \sqrt{d x} a d^{6}\right)}}{b^{3}}}{80 \, d}"," ",0,"-1/80*(40*sqrt(d*x)*a^2*d^8/(b^4*d^2*x^2 + a*b^3*d^2) - 45*(sqrt(2)*d^8*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^8*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^7*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^7*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a^2/b^3 - 32*((d*x)^(5/2)*b*d^4 - 10*sqrt(d*x)*a*d^6)/b^3)/d","A",0
687,1,273,0,3.122975," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{\frac{24 \, \left(d x\right)^{\frac{3}{2}} a d^{6}}{b^{3} d^{2} x^{2} + a b^{2} d^{2}} - \frac{21 \, a d^{6} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{b^{2}} + \frac{32 \, \left(d x\right)^{\frac{3}{2}} d^{4}}{b^{2}}}{48 \, d}"," ",0,"1/48*(24*(d*x)^(3/2)*a*d^6/(b^3*d^2*x^2 + a*b^2*d^2) - 21*a*d^6*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/b^2 + 32*(d*x)^(3/2)*d^4/b^2)/d","A",0
688,1,282,0,3.029166," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{\frac{8 \, \sqrt{d x} a d^{6}}{b^{3} d^{2} x^{2} + a b^{2} d^{2}} + \frac{32 \, \sqrt{d x} d^{4}}{b^{2}} - \frac{5 \, {\left(\frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a}{b^{2}}}{16 \, d}"," ",0,"1/16*(8*sqrt(d*x)*a*d^6/(b^3*d^2*x^2 + a*b^2*d^2) + 32*sqrt(d*x)*d^4/b^2 - 5*(sqrt(2)*d^6*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^6*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^5*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a/b^2)/d","A",0
689,1,256,0,3.103449," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, \left(d x\right)^{\frac{3}{2}} d^{4}}{b^{2} d^{2} x^{2} + a b d^{2}} - \frac{3 \, d^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{b}}{16 \, d}"," ",0,"-1/16*(8*(d*x)^(3/2)*d^4/(b^2*d^2*x^2 + a*b*d^2) - 3*d^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/b)/d","A",0
690,1,265,0,3.058769," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, \sqrt{d x} d^{4}}{b^{2} d^{2} x^{2} + a b d^{2}} - \frac{\frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}}{b}}{16 \, d}"," ",0,"-1/16*(8*sqrt(d*x)*d^4/(b^2*d^2*x^2 + a*b*d^2) - (sqrt(2)*d^4*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^4*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/b)/d","A",0
691,1,255,0,3.055171," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{\frac{8 \, \left(d x\right)^{\frac{3}{2}} d^{2}}{a b d^{2} x^{2} + a^{2} d^{2}} + \frac{d^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a}}{16 \, d}"," ",0,"1/16*(8*(d*x)^(3/2)*d^2/(a*b*d^2*x^2 + a^2*d^2) + d^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/a)/d","A",0
692,1,261,0,3.000968," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{\frac{8 \, \sqrt{d x} d^{2}}{a b d^{2} x^{2} + a^{2} d^{2}} + \frac{3 \, {\left(\frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a}}{16 \, d}"," ",0,"1/16*(8*sqrt(d*x)*d^2/(a*b*d^2*x^2 + a^2*d^2) + 3*(sqrt(2)*d^2*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^2*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/a)/d","A",0
693,1,268,0,3.122450," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(5 \, b d^{2} x^{2} + 4 \, a d^{2}\right)}}{\left(d x\right)^{\frac{5}{2}} a^{2} b + \sqrt{d x} a^{3} d^{2}} + \frac{5 \, b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{2}}}{16 \, d}"," ",0,"-1/16*(8*(5*b*d^2*x^2 + 4*a*d^2)/((d*x)^(5/2)*a^2*b + sqrt(d*x)*a^3*d^2) + 5*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/a^2)/d","A",0
694,1,275,0,3.076526," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(7 \, b d^{2} x^{2} + 4 \, a d^{2}\right)}}{\left(d x\right)^{\frac{7}{2}} a^{2} b + \left(d x\right)^{\frac{3}{2}} a^{3} d^{2}} + \frac{21 \, {\left(\frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d}\right)}}{a^{2}}}{48 \, d}"," ",0,"-1/48*(8*(7*b*d^2*x^2 + 4*a*d^2)/((d*x)^(7/2)*a^2*b + (d*x)^(3/2)*a^3*d^2) + 21*(sqrt(2)*b^(3/4)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) - sqrt(2)*b^(3/4)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) + 2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d))/a^2)/d","A",0
695,1,290,0,3.007713," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(45 \, b^{2} d^{4} x^{4} + 36 \, a b d^{4} x^{2} - 4 \, a^{2} d^{4}\right)}}{\left(d x\right)^{\frac{9}{2}} a^{3} b d^{2} + \left(d x\right)^{\frac{5}{2}} a^{4} d^{4}} + \frac{45 \, b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{3} d^{2}}}{80 \, d}"," ",0,"1/80*(8*(45*b^2*d^4*x^4 + 36*a*b*d^4*x^2 - 4*a^2*d^4)/((d*x)^(9/2)*a^3*b*d^2 + (d*x)^(5/2)*a^4*d^4) + 45*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^3*d^2))/d","A",0
696,1,361,0,3.103263," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{\frac{40 \, {\left(617 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2} d^{12} + 1038 \, \left(d x\right)^{\frac{5}{2}} a^{3} b d^{14} + 453 \, \sqrt{d x} a^{4} d^{16}\right)}}{b^{8} d^{6} x^{6} + 3 \, a b^{7} d^{6} x^{4} + 3 \, a^{2} b^{6} d^{6} x^{2} + a^{3} b^{5} d^{6}} - \frac{9945 \, {\left(\frac{\sqrt{2} d^{12} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{12} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{11} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{11} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a^{2}}{b^{5}} - \frac{3072 \, {\left(\left(d x\right)^{\frac{5}{2}} b d^{8} - 20 \, \sqrt{d x} a d^{10}\right)}}{b^{5}}}{7680 \, d}"," ",0,"-1/7680*(40*(617*(d*x)^(9/2)*a^2*b^2*d^12 + 1038*(d*x)^(5/2)*a^3*b*d^14 + 453*sqrt(d*x)*a^4*d^16)/(b^8*d^6*x^6 + 3*a*b^7*d^6*x^4 + 3*a^2*b^6*d^6*x^2 + a^3*b^5*d^6) - 9945*(sqrt(2)*d^12*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^12*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^11*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^11*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a^2/b^5 - 3072*((d*x)^(5/2)*b*d^8 - 20*sqrt(d*x)*a*d^10)/b^5)/d","A",0
697,1,334,0,3.082996," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{\frac{1155 \, a d^{10} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{b^{4}} - \frac{1024 \, \left(d x\right)^{\frac{3}{2}} d^{8}}{b^{4}} - \frac{8 \, {\left(381 \, \left(d x\right)^{\frac{11}{2}} a b^{2} d^{10} + 606 \, \left(d x\right)^{\frac{7}{2}} a^{2} b d^{12} + 257 \, \left(d x\right)^{\frac{3}{2}} a^{3} d^{14}\right)}}{b^{7} d^{6} x^{6} + 3 \, a b^{6} d^{6} x^{4} + 3 \, a^{2} b^{5} d^{6} x^{2} + a^{3} b^{4} d^{6}}}{1536 \, d}"," ",0,"-1/1536*(1155*a*d^10*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/b^4 - 1024*(d*x)^(3/2)*d^8/b^4 - 8*(381*(d*x)^(11/2)*a*b^2*d^10 + 606*(d*x)^(7/2)*a^2*b*d^12 + 257*(d*x)^(3/2)*a^3*d^14)/(b^7*d^6*x^6 + 3*a*b^6*d^6*x^4 + 3*a^2*b^5*d^6*x^2 + a^3*b^4*d^6))/d","A",0
698,1,343,0,3.140501," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{3072 \, \sqrt{d x} d^{8}}{b^{4}} + \frac{8 \, {\left(317 \, \left(d x\right)^{\frac{9}{2}} a b^{2} d^{10} + 486 \, \left(d x\right)^{\frac{5}{2}} a^{2} b d^{12} + 201 \, \sqrt{d x} a^{3} d^{14}\right)}}{b^{7} d^{6} x^{6} + 3 \, a b^{6} d^{6} x^{4} + 3 \, a^{2} b^{5} d^{6} x^{2} + a^{3} b^{4} d^{6}} - \frac{585 \, {\left(\frac{\sqrt{2} d^{10} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{10} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{9} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{9} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a}{b^{4}}}{1536 \, d}"," ",0,"1/1536*(3072*sqrt(d*x)*d^8/b^4 + 8*(317*(d*x)^(9/2)*a*b^2*d^10 + 486*(d*x)^(5/2)*a^2*b*d^12 + 201*sqrt(d*x)*a^3*d^14)/(b^7*d^6*x^6 + 3*a*b^6*d^6*x^4 + 3*a^2*b^5*d^6*x^2 + a^3*b^4*d^6) - 585*(sqrt(2)*d^10*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^10*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^9*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^9*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a/b^4)/d","A",0
699,1,317,0,3.443942," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{231 \, d^{8} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{b^{3}} - \frac{8 \, {\left(153 \, \left(d x\right)^{\frac{11}{2}} b^{2} d^{8} + 198 \, \left(d x\right)^{\frac{7}{2}} a b d^{10} + 77 \, \left(d x\right)^{\frac{3}{2}} a^{2} d^{12}\right)}}{b^{6} d^{6} x^{6} + 3 \, a b^{5} d^{6} x^{4} + 3 \, a^{2} b^{4} d^{6} x^{2} + a^{3} b^{3} d^{6}}}{1536 \, d}"," ",0,"1/1536*(231*d^8*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/b^3 - 8*(153*(d*x)^(11/2)*b^2*d^8 + 198*(d*x)^(7/2)*a*b*d^10 + 77*(d*x)^(3/2)*a^2*d^12)/(b^6*d^6*x^6 + 3*a*b^5*d^6*x^4 + 3*a^2*b^4*d^6*x^2 + a^3*b^3*d^6))/d","A",0
700,1,326,0,3.131289," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(113 \, \left(d x\right)^{\frac{9}{2}} b^{2} d^{8} + 126 \, \left(d x\right)^{\frac{5}{2}} a b d^{10} + 45 \, \sqrt{d x} a^{2} d^{12}\right)}}{b^{6} d^{6} x^{6} + 3 \, a b^{5} d^{6} x^{4} + 3 \, a^{2} b^{4} d^{6} x^{2} + a^{3} b^{3} d^{6}} - \frac{45 \, {\left(\frac{\sqrt{2} d^{8} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{8} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{7} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{7} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{b^{3}}}{1536 \, d}"," ",0,"-1/1536*(8*(113*(d*x)^(9/2)*b^2*d^8 + 126*(d*x)^(5/2)*a*b*d^10 + 45*sqrt(d*x)*a^2*d^12)/(b^6*d^6*x^6 + 3*a*b^5*d^6*x^4 + 3*a^2*b^4*d^6*x^2 + a^3*b^3*d^6) - 45*(sqrt(2)*d^8*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^8*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^7*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^7*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/b^3)/d","A",0
701,1,323,0,3.017079," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{21 \, d^{6} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a b^{2}} + \frac{8 \, {\left(21 \, \left(d x\right)^{\frac{11}{2}} b^{2} d^{6} - 18 \, \left(d x\right)^{\frac{7}{2}} a b d^{8} - 7 \, \left(d x\right)^{\frac{3}{2}} a^{2} d^{10}\right)}}{a b^{5} d^{6} x^{6} + 3 \, a^{2} b^{4} d^{6} x^{4} + 3 \, a^{3} b^{3} d^{6} x^{2} + a^{4} b^{2} d^{6}}}{1536 \, d}"," ",0,"1/1536*(21*d^6*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a*b^2) + 8*(21*(d*x)^(11/2)*b^2*d^6 - 18*(d*x)^(7/2)*a*b*d^8 - 7*(d*x)^(3/2)*a^2*d^10)/(a*b^5*d^6*x^6 + 3*a^2*b^4*d^6*x^4 + 3*a^3*b^3*d^6*x^2 + a^4*b^2*d^6))/d","A",0
702,1,332,0,2.961737," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(5 \, \left(d x\right)^{\frac{9}{2}} b^{2} d^{6} - 42 \, \left(d x\right)^{\frac{5}{2}} a b d^{8} - 15 \, \sqrt{d x} a^{2} d^{10}\right)}}{a b^{5} d^{6} x^{6} + 3 \, a^{2} b^{4} d^{6} x^{4} + 3 \, a^{3} b^{3} d^{6} x^{2} + a^{4} b^{2} d^{6}} + \frac{15 \, {\left(\frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a b^{2}}}{1536 \, d}"," ",0,"1/1536*(8*(5*(d*x)^(9/2)*b^2*d^6 - 42*(d*x)^(5/2)*a*b*d^8 - 15*sqrt(d*x)*a^2*d^10)/(a*b^5*d^6*x^6 + 3*a^2*b^4*d^6*x^4 + 3*a^3*b^3*d^6*x^2 + a^4*b^2*d^6) + 15*(sqrt(2)*d^6*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^6*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^5*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/(a*b^2))/d","A",0
703,1,323,0,3.019151," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{15 \, d^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{2} b} + \frac{8 \, {\left(15 \, \left(d x\right)^{\frac{11}{2}} b^{2} d^{4} + 42 \, \left(d x\right)^{\frac{7}{2}} a b d^{6} - 5 \, \left(d x\right)^{\frac{3}{2}} a^{2} d^{8}\right)}}{a^{2} b^{4} d^{6} x^{6} + 3 \, a^{3} b^{3} d^{6} x^{4} + 3 \, a^{4} b^{2} d^{6} x^{2} + a^{5} b d^{6}}}{1536 \, d}"," ",0,"1/1536*(15*d^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^2*b) + 8*(15*(d*x)^(11/2)*b^2*d^4 + 42*(d*x)^(7/2)*a*b*d^6 - 5*(d*x)^(3/2)*a^2*d^8)/(a^2*b^4*d^6*x^6 + 3*a^3*b^3*d^6*x^4 + 3*a^4*b^2*d^6*x^2 + a^5*b*d^6))/d","A",0
704,1,332,0,3.019407," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(7 \, \left(d x\right)^{\frac{9}{2}} b^{2} d^{4} + 18 \, \left(d x\right)^{\frac{5}{2}} a b d^{6} - 21 \, \sqrt{d x} a^{2} d^{8}\right)}}{a^{2} b^{4} d^{6} x^{6} + 3 \, a^{3} b^{3} d^{6} x^{4} + 3 \, a^{4} b^{2} d^{6} x^{2} + a^{5} b d^{6}} + \frac{21 \, {\left(\frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a^{2} b}}{1536 \, d}"," ",0,"1/1536*(8*(7*(d*x)^(9/2)*b^2*d^4 + 18*(d*x)^(5/2)*a*b*d^6 - 21*sqrt(d*x)*a^2*d^8)/(a^2*b^4*d^6*x^6 + 3*a^3*b^3*d^6*x^4 + 3*a^4*b^2*d^6*x^2 + a^5*b*d^6) + 21*(sqrt(2)*d^4*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^4*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/(a^2*b))/d","A",0
705,1,317,0,2.983374," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(45 \, \left(d x\right)^{\frac{11}{2}} b^{2} d^{2} + 126 \, \left(d x\right)^{\frac{7}{2}} a b d^{4} + 113 \, \left(d x\right)^{\frac{3}{2}} a^{2} d^{6}\right)}}{a^{3} b^{3} d^{6} x^{6} + 3 \, a^{4} b^{2} d^{6} x^{4} + 3 \, a^{5} b d^{6} x^{2} + a^{6} d^{6}} + \frac{45 \, d^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{3}}}{1536 \, d}"," ",0,"1/1536*(8*(45*(d*x)^(11/2)*b^2*d^2 + 126*(d*x)^(7/2)*a*b*d^4 + 113*(d*x)^(3/2)*a^2*d^6)/(a^3*b^3*d^6*x^6 + 3*a^4*b^2*d^6*x^4 + 3*a^5*b*d^6*x^2 + a^6*d^6) + 45*d^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/a^3)/d","A",0
706,1,322,0,3.090660," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(77 \, \left(d x\right)^{\frac{9}{2}} b^{2} d^{2} + 198 \, \left(d x\right)^{\frac{5}{2}} a b d^{4} + 153 \, \sqrt{d x} a^{2} d^{6}\right)}}{a^{3} b^{3} d^{6} x^{6} + 3 \, a^{4} b^{2} d^{6} x^{4} + 3 \, a^{5} b d^{6} x^{2} + a^{6} d^{6}} + \frac{231 \, {\left(\frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a^{3}}}{1536 \, d}"," ",0,"1/1536*(8*(77*(d*x)^(9/2)*b^2*d^2 + 198*(d*x)^(5/2)*a*b*d^4 + 153*sqrt(d*x)*a^2*d^6)/(a^3*b^3*d^6*x^6 + 3*a^4*b^2*d^6*x^4 + 3*a^5*b*d^6*x^2 + a^6*d^6) + 231*(sqrt(2)*d^2*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^2*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/a^3)/d","A",0
707,1,328,0,3.071092," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(585 \, b^{3} d^{6} x^{6} + 1638 \, a b^{2} d^{6} x^{4} + 1469 \, a^{2} b d^{6} x^{2} + 384 \, a^{3} d^{6}\right)}}{\left(d x\right)^{\frac{13}{2}} a^{4} b^{3} + 3 \, \left(d x\right)^{\frac{9}{2}} a^{5} b^{2} d^{2} + 3 \, \left(d x\right)^{\frac{5}{2}} a^{6} b d^{4} + \sqrt{d x} a^{7} d^{6}} + \frac{585 \, b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{4}}}{1536 \, d}"," ",0,"-1/1536*(8*(585*b^3*d^6*x^6 + 1638*a*b^2*d^6*x^4 + 1469*a^2*b*d^6*x^2 + 384*a^3*d^6)/((d*x)^(13/2)*a^4*b^3 + 3*(d*x)^(9/2)*a^5*b^2*d^2 + 3*(d*x)^(5/2)*a^6*b*d^4 + sqrt(d*x)*a^7*d^6) + 585*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/a^4)/d","A",0
708,1,335,0,3.071073," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(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}\right)}}{\left(d x\right)^{\frac{15}{2}} a^{4} b^{3} + 3 \, \left(d x\right)^{\frac{11}{2}} a^{5} b^{2} d^{2} + 3 \, \left(d x\right)^{\frac{7}{2}} a^{6} b d^{4} + \left(d x\right)^{\frac{3}{2}} a^{7} d^{6}} + \frac{1155 \, {\left(\frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d}\right)}}{a^{4}}}{1536 \, d}"," ",0,"-1/1536*(8*(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)/((d*x)^(15/2)*a^4*b^3 + 3*(d*x)^(11/2)*a^5*b^2*d^2 + 3*(d*x)^(7/2)*a^6*b*d^4 + (d*x)^(3/2)*a^7*d^6) + 1155*(sqrt(2)*b^(3/4)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) - sqrt(2)*b^(3/4)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) + 2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d))/a^4)/d","A",0
709,1,350,0,3.172711," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(9945 \, b^{4} d^{8} x^{8} + 27846 \, a b^{3} d^{8} x^{6} + 24973 \, a^{2} b^{2} d^{8} x^{4} + 6528 \, a^{3} b d^{8} x^{2} - 384 \, a^{4} d^{8}\right)}}{\left(d x\right)^{\frac{17}{2}} a^{5} b^{3} d^{2} + 3 \, \left(d x\right)^{\frac{13}{2}} a^{6} b^{2} d^{4} + 3 \, \left(d x\right)^{\frac{9}{2}} a^{7} b d^{6} + \left(d x\right)^{\frac{5}{2}} a^{8} d^{8}} + \frac{9945 \, b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{5} d^{2}}}{7680 \, d}"," ",0,"1/7680*(8*(9945*b^4*d^8*x^8 + 27846*a*b^3*d^8*x^6 + 24973*a^2*b^2*d^8*x^4 + 6528*a^3*b*d^8*x^2 - 384*a^4*d^8)/((d*x)^(17/2)*a^5*b^3*d^2 + 3*(d*x)^(13/2)*a^6*b^2*d^4 + 3*(d*x)^(9/2)*a^7*b*d^6 + (d*x)^(5/2)*a^8*d^8) + 9945*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^5*d^2))/d","A",0
710,1,421,0,3.181134," ","integrate((d*x)^(27/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(170695 \, \left(d x\right)^{\frac{17}{2}} a^{2} b^{4} d^{16} + 575520 \, \left(d x\right)^{\frac{13}{2}} a^{3} b^{3} d^{18} + 754710 \, \left(d x\right)^{\frac{9}{2}} a^{4} b^{2} d^{20} + 450152 \, \left(d x\right)^{\frac{5}{2}} a^{5} b d^{22} + 102315 \, \sqrt{d x} a^{6} d^{24}\right)}}{b^{12} d^{10} x^{10} + 5 \, a b^{11} d^{10} x^{8} + 10 \, a^{2} b^{10} d^{10} x^{6} + 10 \, a^{3} b^{9} d^{10} x^{4} + 5 \, a^{4} b^{8} d^{10} x^{2} + a^{5} b^{7} d^{10}} - \frac{348075 \, {\left(\frac{\sqrt{2} d^{16} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{16} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{15} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{15} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a^{2}}{b^{7}} - \frac{65536 \, {\left(\left(d x\right)^{\frac{5}{2}} b d^{12} - 30 \, \sqrt{d x} a d^{14}\right)}}{b^{7}}}{163840 \, d}"," ",0,"-1/163840*(8*(170695*(d*x)^(17/2)*a^2*b^4*d^16 + 575520*(d*x)^(13/2)*a^3*b^3*d^18 + 754710*(d*x)^(9/2)*a^4*b^2*d^20 + 450152*(d*x)^(5/2)*a^5*b*d^22 + 102315*sqrt(d*x)*a^6*d^24)/(b^12*d^10*x^10 + 5*a*b^11*d^10*x^8 + 10*a^2*b^10*d^10*x^6 + 10*a^3*b^9*d^10*x^4 + 5*a^4*b^8*d^10*x^2 + a^5*b^7*d^10) - 348075*(sqrt(2)*d^16*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^16*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^15*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^15*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a^2/b^7 - 65536*((d*x)^(5/2)*b*d^12 - 30*sqrt(d*x)*a*d^14)/b^7)/d","A",0
711,1,394,0,3.204127," ","integrate((d*x)^(25/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{\frac{504735 \, a d^{14} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{b^{6}} - \frac{327680 \, \left(d x\right)^{\frac{3}{2}} d^{12}}{b^{6}} - \frac{8 \, {\left(232545 \, \left(d x\right)^{\frac{19}{2}} a b^{4} d^{14} + 747576 \, \left(d x\right)^{\frac{15}{2}} a^{2} b^{3} d^{16} + 958210 \, \left(d x\right)^{\frac{11}{2}} a^{3} b^{2} d^{18} + 564320 \, \left(d x\right)^{\frac{7}{2}} a^{4} b d^{20} + 127285 \, \left(d x\right)^{\frac{3}{2}} a^{5} d^{22}\right)}}{b^{11} d^{10} x^{10} + 5 \, a b^{10} d^{10} x^{8} + 10 \, a^{2} b^{9} d^{10} x^{6} + 10 \, a^{3} b^{8} d^{10} x^{4} + 5 \, a^{4} b^{7} d^{10} x^{2} + a^{5} b^{6} d^{10}}}{491520 \, d}"," ",0,"-1/491520*(504735*a*d^14*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/b^6 - 327680*(d*x)^(3/2)*d^12/b^6 - 8*(232545*(d*x)^(19/2)*a*b^4*d^14 + 747576*(d*x)^(15/2)*a^2*b^3*d^16 + 958210*(d*x)^(11/2)*a^3*b^2*d^18 + 564320*(d*x)^(7/2)*a^4*b*d^20 + 127285*(d*x)^(3/2)*a^5*d^22)/(b^11*d^10*x^10 + 5*a*b^10*d^10*x^8 + 10*a^2*b^9*d^10*x^6 + 10*a^3*b^8*d^10*x^4 + 5*a^4*b^7*d^10*x^2 + a^5*b^6*d^10))/d","A",0
712,1,403,0,3.225900," ","integrate((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{327680 \, \sqrt{d x} d^{12}}{b^{6}} + \frac{8 \, {\left(58715 \, \left(d x\right)^{\frac{17}{2}} a b^{4} d^{14} + 180640 \, \left(d x\right)^{\frac{13}{2}} a^{2} b^{3} d^{16} + 224670 \, \left(d x\right)^{\frac{9}{2}} a^{3} b^{2} d^{18} + 129352 \, \left(d x\right)^{\frac{5}{2}} a^{4} b d^{20} + 28655 \, \sqrt{d x} a^{5} d^{22}\right)}}{b^{11} d^{10} x^{10} + 5 \, a b^{10} d^{10} x^{8} + 10 \, a^{2} b^{9} d^{10} x^{6} + 10 \, a^{3} b^{8} d^{10} x^{4} + 5 \, a^{4} b^{7} d^{10} x^{2} + a^{5} b^{6} d^{10}} - \frac{69615 \, {\left(\frac{\sqrt{2} d^{14} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{14} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{13} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{13} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a}{b^{6}}}{163840 \, d}"," ",0,"1/163840*(327680*sqrt(d*x)*d^12/b^6 + 8*(58715*(d*x)^(17/2)*a*b^4*d^14 + 180640*(d*x)^(13/2)*a^2*b^3*d^16 + 224670*(d*x)^(9/2)*a^3*b^2*d^18 + 129352*(d*x)^(5/2)*a^4*b*d^20 + 28655*sqrt(d*x)*a^5*d^22)/(b^11*d^10*x^10 + 5*a*b^10*d^10*x^8 + 10*a^2*b^9*d^10*x^6 + 10*a^3*b^8*d^10*x^4 + 5*a^4*b^7*d^10*x^2 + a^5*b^6*d^10) - 69615*(sqrt(2)*d^14*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^14*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^13*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^13*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a/b^6)/d","A",0
713,1,377,0,3.160617," ","integrate((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{21945 \, d^{12} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{b^{5}} - \frac{8 \, {\left(19015 \, \left(d x\right)^{\frac{19}{2}} b^{4} d^{12} + 50312 \, \left(d x\right)^{\frac{15}{2}} a b^{3} d^{14} + 59470 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{2} d^{16} + 33440 \, \left(d x\right)^{\frac{7}{2}} a^{3} b d^{18} + 7315 \, \left(d x\right)^{\frac{3}{2}} a^{4} d^{20}\right)}}{b^{10} d^{10} x^{10} + 5 \, a b^{9} d^{10} x^{8} + 10 \, a^{2} b^{8} d^{10} x^{6} + 10 \, a^{3} b^{7} d^{10} x^{4} + 5 \, a^{4} b^{6} d^{10} x^{2} + a^{5} b^{5} d^{10}}}{163840 \, d}"," ",0,"1/163840*(21945*d^12*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/b^5 - 8*(19015*(d*x)^(19/2)*b^4*d^12 + 50312*(d*x)^(15/2)*a*b^3*d^14 + 59470*(d*x)^(11/2)*a^2*b^2*d^16 + 33440*(d*x)^(7/2)*a^3*b*d^18 + 7315*(d*x)^(3/2)*a^4*d^20)/(b^10*d^10*x^10 + 5*a*b^9*d^10*x^8 + 10*a^2*b^8*d^10*x^6 + 10*a^3*b^7*d^10*x^4 + 5*a^4*b^6*d^10*x^2 + a^5*b^5*d^10))/d","A",0
714,1,386,0,3.113649," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(37645 \, \left(d x\right)^{\frac{17}{2}} b^{4} d^{12} + 84320 \, \left(d x\right)^{\frac{13}{2}} a b^{3} d^{14} + 90610 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2} d^{16} + 47736 \, \left(d x\right)^{\frac{5}{2}} a^{3} b d^{18} + 9945 \, \sqrt{d x} a^{4} d^{20}\right)}}{b^{10} d^{10} x^{10} + 5 \, a b^{9} d^{10} x^{8} + 10 \, a^{2} b^{8} d^{10} x^{6} + 10 \, a^{3} b^{7} d^{10} x^{4} + 5 \, a^{4} b^{6} d^{10} x^{2} + a^{5} b^{5} d^{10}} - \frac{9945 \, {\left(\frac{\sqrt{2} d^{12} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{12} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{11} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{11} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{b^{5}}}{491520 \, d}"," ",0,"-1/491520*(8*(37645*(d*x)^(17/2)*b^4*d^12 + 84320*(d*x)^(13/2)*a*b^3*d^14 + 90610*(d*x)^(9/2)*a^2*b^2*d^16 + 47736*(d*x)^(5/2)*a^3*b*d^18 + 9945*sqrt(d*x)*a^4*d^20)/(b^10*d^10*x^10 + 5*a*b^9*d^10*x^8 + 10*a^2*b^8*d^10*x^6 + 10*a^3*b^7*d^10*x^4 + 5*a^4*b^6*d^10*x^2 + a^5*b^5*d^10) - 9945*(sqrt(2)*d^12*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^12*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^11*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^11*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/b^5)/d","A",0
715,1,383,0,3.043267," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{1155 \, d^{10} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a b^{4}} + \frac{8 \, {\left(1155 \, \left(d x\right)^{\frac{19}{2}} b^{4} d^{10} - 2648 \, \left(d x\right)^{\frac{15}{2}} a b^{3} d^{12} - 3130 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{2} d^{14} - 1760 \, \left(d x\right)^{\frac{7}{2}} a^{3} b d^{16} - 385 \, \left(d x\right)^{\frac{3}{2}} a^{4} d^{18}\right)}}{a b^{9} d^{10} x^{10} + 5 \, a^{2} b^{8} d^{10} x^{8} + 10 \, a^{3} b^{7} d^{10} x^{6} + 10 \, a^{4} b^{6} d^{10} x^{4} + 5 \, a^{5} b^{5} d^{10} x^{2} + a^{6} b^{4} d^{10}}}{163840 \, d}"," ",0,"1/163840*(1155*d^10*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a*b^4) + 8*(1155*(d*x)^(19/2)*b^4*d^10 - 2648*(d*x)^(15/2)*a*b^3*d^12 - 3130*(d*x)^(11/2)*a^2*b^2*d^14 - 1760*(d*x)^(7/2)*a^3*b*d^16 - 385*(d*x)^(3/2)*a^4*d^18)/(a*b^9*d^10*x^10 + 5*a^2*b^8*d^10*x^8 + 10*a^3*b^7*d^10*x^6 + 10*a^4*b^6*d^10*x^4 + 5*a^5*b^5*d^10*x^2 + a^6*b^4*d^10))/d","A",0
716,1,392,0,3.220560," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(195 \, \left(d x\right)^{\frac{17}{2}} b^{4} d^{10} - 4960 \, \left(d x\right)^{\frac{13}{2}} a b^{3} d^{12} - 5330 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2} d^{14} - 2808 \, \left(d x\right)^{\frac{5}{2}} a^{3} b d^{16} - 585 \, \sqrt{d x} a^{4} d^{18}\right)}}{a b^{9} d^{10} x^{10} + 5 \, a^{2} b^{8} d^{10} x^{8} + 10 \, a^{3} b^{7} d^{10} x^{6} + 10 \, a^{4} b^{6} d^{10} x^{4} + 5 \, a^{5} b^{5} d^{10} x^{2} + a^{6} b^{4} d^{10}} + \frac{585 \, {\left(\frac{\sqrt{2} d^{10} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{10} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{9} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{9} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a b^{4}}}{163840 \, d}"," ",0,"1/163840*(8*(195*(d*x)^(17/2)*b^4*d^10 - 4960*(d*x)^(13/2)*a*b^3*d^12 - 5330*(d*x)^(9/2)*a^2*b^2*d^14 - 2808*(d*x)^(5/2)*a^3*b*d^16 - 585*sqrt(d*x)*a^4*d^18)/(a*b^9*d^10*x^10 + 5*a^2*b^8*d^10*x^8 + 10*a^3*b^7*d^10*x^6 + 10*a^4*b^6*d^10*x^4 + 5*a^5*b^5*d^10*x^2 + a^6*b^4*d^10) + 585*(sqrt(2)*d^10*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^10*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^9*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^9*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/(a*b^4))/d","A",0
717,1,385,0,3.002633," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{1155 \, d^{8} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{2} b^{3}} + \frac{8 \, {\left(1155 \, \left(d x\right)^{\frac{19}{2}} b^{4} d^{8} + 5544 \, \left(d x\right)^{\frac{15}{2}} a b^{3} d^{10} - 3130 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{2} d^{12} - 1760 \, \left(d x\right)^{\frac{7}{2}} a^{3} b d^{14} - 385 \, \left(d x\right)^{\frac{3}{2}} a^{4} d^{16}\right)}}{a^{2} b^{8} d^{10} x^{10} + 5 \, a^{3} b^{7} d^{10} x^{8} + 10 \, a^{4} b^{6} d^{10} x^{6} + 10 \, a^{5} b^{5} d^{10} x^{4} + 5 \, a^{6} b^{4} d^{10} x^{2} + a^{7} b^{3} d^{10}}}{491520 \, d}"," ",0,"1/491520*(1155*d^8*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^2*b^3) + 8*(1155*(d*x)^(19/2)*b^4*d^8 + 5544*(d*x)^(15/2)*a*b^3*d^10 - 3130*(d*x)^(11/2)*a^2*b^2*d^12 - 1760*(d*x)^(7/2)*a^3*b*d^14 - 385*(d*x)^(3/2)*a^4*d^16)/(a^2*b^8*d^10*x^10 + 5*a^3*b^7*d^10*x^8 + 10*a^4*b^6*d^10*x^6 + 10*a^5*b^5*d^10*x^4 + 5*a^6*b^4*d^10*x^2 + a^7*b^3*d^10))/d","A",0
718,1,394,0,3.161854," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(105 \, \left(d x\right)^{\frac{17}{2}} b^{4} d^{8} + 480 \, \left(d x\right)^{\frac{13}{2}} a b^{3} d^{10} - 2870 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2} d^{12} - 1512 \, \left(d x\right)^{\frac{5}{2}} a^{3} b d^{14} - 315 \, \sqrt{d x} a^{4} d^{16}\right)}}{a^{2} b^{8} d^{10} x^{10} + 5 \, a^{3} b^{7} d^{10} x^{8} + 10 \, a^{4} b^{6} d^{10} x^{6} + 10 \, a^{5} b^{5} d^{10} x^{4} + 5 \, a^{6} b^{4} d^{10} x^{2} + a^{7} b^{3} d^{10}} + \frac{315 \, {\left(\frac{\sqrt{2} d^{8} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{8} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{7} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{7} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a^{2} b^{3}}}{163840 \, d}"," ",0,"1/163840*(8*(105*(d*x)^(17/2)*b^4*d^8 + 480*(d*x)^(13/2)*a*b^3*d^10 - 2870*(d*x)^(9/2)*a^2*b^2*d^12 - 1512*(d*x)^(5/2)*a^3*b*d^14 - 315*sqrt(d*x)*a^4*d^16)/(a^2*b^8*d^10*x^10 + 5*a^3*b^7*d^10*x^8 + 10*a^4*b^6*d^10*x^6 + 10*a^5*b^5*d^10*x^4 + 5*a^6*b^4*d^10*x^2 + a^7*b^3*d^10) + 315*(sqrt(2)*d^8*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^8*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^7*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^7*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/(a^2*b^3))/d","A",0
719,1,385,0,3.173361," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{315 \, d^{6} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{3} b^{2}} + \frac{8 \, {\left(315 \, \left(d x\right)^{\frac{19}{2}} b^{4} d^{6} + 1512 \, \left(d x\right)^{\frac{15}{2}} a b^{3} d^{8} + 2870 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{2} d^{10} - 480 \, \left(d x\right)^{\frac{7}{2}} a^{3} b d^{12} - 105 \, \left(d x\right)^{\frac{3}{2}} a^{4} d^{14}\right)}}{a^{3} b^{7} d^{10} x^{10} + 5 \, a^{4} b^{6} d^{10} x^{8} + 10 \, a^{5} b^{5} d^{10} x^{6} + 10 \, a^{6} b^{4} d^{10} x^{4} + 5 \, a^{7} b^{3} d^{10} x^{2} + a^{8} b^{2} d^{10}}}{163840 \, d}"," ",0,"1/163840*(315*d^6*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^3*b^2) + 8*(315*(d*x)^(19/2)*b^4*d^6 + 1512*(d*x)^(15/2)*a*b^3*d^8 + 2870*(d*x)^(11/2)*a^2*b^2*d^10 - 480*(d*x)^(7/2)*a^3*b*d^12 - 105*(d*x)^(3/2)*a^4*d^14)/(a^3*b^7*d^10*x^10 + 5*a^4*b^6*d^10*x^8 + 10*a^5*b^5*d^10*x^6 + 10*a^6*b^4*d^10*x^4 + 5*a^7*b^3*d^10*x^2 + a^8*b^2*d^10))/d","A",0
720,1,394,0,3.149232," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(385 \, \left(d x\right)^{\frac{17}{2}} b^{4} d^{6} + 1760 \, \left(d x\right)^{\frac{13}{2}} a b^{3} d^{8} + 3130 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2} d^{10} - 5544 \, \left(d x\right)^{\frac{5}{2}} a^{3} b d^{12} - 1155 \, \sqrt{d x} a^{4} d^{14}\right)}}{a^{3} b^{7} d^{10} x^{10} + 5 \, a^{4} b^{6} d^{10} x^{8} + 10 \, a^{5} b^{5} d^{10} x^{6} + 10 \, a^{6} b^{4} d^{10} x^{4} + 5 \, a^{7} b^{3} d^{10} x^{2} + a^{8} b^{2} d^{10}} + \frac{1155 \, {\left(\frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a^{3} b^{2}}}{491520 \, d}"," ",0,"1/491520*(8*(385*(d*x)^(17/2)*b^4*d^6 + 1760*(d*x)^(13/2)*a*b^3*d^8 + 3130*(d*x)^(9/2)*a^2*b^2*d^10 - 5544*(d*x)^(5/2)*a^3*b*d^12 - 1155*sqrt(d*x)*a^4*d^14)/(a^3*b^7*d^10*x^10 + 5*a^4*b^6*d^10*x^8 + 10*a^5*b^5*d^10*x^6 + 10*a^6*b^4*d^10*x^4 + 5*a^7*b^3*d^10*x^2 + a^8*b^2*d^10) + 1155*(sqrt(2)*d^6*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^6*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^5*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/(a^3*b^2))/d","A",0
721,1,383,0,3.155657," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(585 \, \left(d x\right)^{\frac{19}{2}} b^{4} d^{4} + 2808 \, \left(d x\right)^{\frac{15}{2}} a b^{3} d^{6} + 5330 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{2} d^{8} + 4960 \, \left(d x\right)^{\frac{7}{2}} a^{3} b d^{10} - 195 \, \left(d x\right)^{\frac{3}{2}} a^{4} d^{12}\right)}}{a^{4} b^{6} d^{10} x^{10} + 5 \, a^{5} b^{5} d^{10} x^{8} + 10 \, a^{6} b^{4} d^{10} x^{6} + 10 \, a^{7} b^{3} d^{10} x^{4} + 5 \, a^{8} b^{2} d^{10} x^{2} + a^{9} b d^{10}} + \frac{585 \, d^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{4} b}}{163840 \, d}"," ",0,"1/163840*(8*(585*(d*x)^(19/2)*b^4*d^4 + 2808*(d*x)^(15/2)*a*b^3*d^6 + 5330*(d*x)^(11/2)*a^2*b^2*d^8 + 4960*(d*x)^(7/2)*a^3*b*d^10 - 195*(d*x)^(3/2)*a^4*d^12)/(a^4*b^6*d^10*x^10 + 5*a^5*b^5*d^10*x^8 + 10*a^6*b^4*d^10*x^6 + 10*a^7*b^3*d^10*x^4 + 5*a^8*b^2*d^10*x^2 + a^9*b*d^10) + 585*d^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^4*b))/d","A",0
722,1,392,0,3.232020," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(385 \, \left(d x\right)^{\frac{17}{2}} b^{4} d^{4} + 1760 \, \left(d x\right)^{\frac{13}{2}} a b^{3} d^{6} + 3130 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2} d^{8} + 2648 \, \left(d x\right)^{\frac{5}{2}} a^{3} b d^{10} - 1155 \, \sqrt{d x} a^{4} d^{12}\right)}}{a^{4} b^{6} d^{10} x^{10} + 5 \, a^{5} b^{5} d^{10} x^{8} + 10 \, a^{6} b^{4} d^{10} x^{6} + 10 \, a^{7} b^{3} d^{10} x^{4} + 5 \, a^{8} b^{2} d^{10} x^{2} + a^{9} b d^{10}} + \frac{1155 \, {\left(\frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a^{4} b}}{163840 \, d}"," ",0,"1/163840*(8*(385*(d*x)^(17/2)*b^4*d^4 + 1760*(d*x)^(13/2)*a*b^3*d^6 + 3130*(d*x)^(9/2)*a^2*b^2*d^8 + 2648*(d*x)^(5/2)*a^3*b*d^10 - 1155*sqrt(d*x)*a^4*d^12)/(a^4*b^6*d^10*x^10 + 5*a^5*b^5*d^10*x^8 + 10*a^6*b^4*d^10*x^6 + 10*a^7*b^3*d^10*x^4 + 5*a^8*b^2*d^10*x^2 + a^9*b*d^10) + 1155*(sqrt(2)*d^4*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^4*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/(a^4*b))/d","A",0
723,1,377,0,3.191721," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(9945 \, \left(d x\right)^{\frac{19}{2}} b^{4} d^{2} + 47736 \, \left(d x\right)^{\frac{15}{2}} a b^{3} d^{4} + 90610 \, \left(d x\right)^{\frac{11}{2}} a^{2} b^{2} d^{6} + 84320 \, \left(d x\right)^{\frac{7}{2}} a^{3} b d^{8} + 37645 \, \left(d x\right)^{\frac{3}{2}} a^{4} d^{10}\right)}}{a^{5} b^{5} d^{10} x^{10} + 5 \, a^{6} b^{4} d^{10} x^{8} + 10 \, a^{7} b^{3} d^{10} x^{6} + 10 \, a^{8} b^{2} d^{10} x^{4} + 5 \, a^{9} b d^{10} x^{2} + a^{10} d^{10}} + \frac{9945 \, d^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{5}}}{491520 \, d}"," ",0,"1/491520*(8*(9945*(d*x)^(19/2)*b^4*d^2 + 47736*(d*x)^(15/2)*a*b^3*d^4 + 90610*(d*x)^(11/2)*a^2*b^2*d^6 + 84320*(d*x)^(7/2)*a^3*b*d^8 + 37645*(d*x)^(3/2)*a^4*d^10)/(a^5*b^5*d^10*x^10 + 5*a^6*b^4*d^10*x^8 + 10*a^7*b^3*d^10*x^6 + 10*a^8*b^2*d^10*x^4 + 5*a^9*b*d^10*x^2 + a^10*d^10) + 9945*d^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/a^5)/d","A",0
724,1,382,0,3.105533," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(7315 \, \left(d x\right)^{\frac{17}{2}} b^{4} d^{2} + 33440 \, \left(d x\right)^{\frac{13}{2}} a b^{3} d^{4} + 59470 \, \left(d x\right)^{\frac{9}{2}} a^{2} b^{2} d^{6} + 50312 \, \left(d x\right)^{\frac{5}{2}} a^{3} b d^{8} + 19015 \, \sqrt{d x} a^{4} d^{10}\right)}}{a^{5} b^{5} d^{10} x^{10} + 5 \, a^{6} b^{4} d^{10} x^{8} + 10 \, a^{7} b^{3} d^{10} x^{6} + 10 \, a^{8} b^{2} d^{10} x^{4} + 5 \, a^{9} b d^{10} x^{2} + a^{10} d^{10}} + \frac{21945 \, {\left(\frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)}}{a^{5}}}{163840 \, d}"," ",0,"1/163840*(8*(7315*(d*x)^(17/2)*b^4*d^2 + 33440*(d*x)^(13/2)*a*b^3*d^4 + 59470*(d*x)^(9/2)*a^2*b^2*d^6 + 50312*(d*x)^(5/2)*a^3*b*d^8 + 19015*sqrt(d*x)*a^4*d^10)/(a^5*b^5*d^10*x^10 + 5*a^6*b^4*d^10*x^8 + 10*a^7*b^3*d^10*x^6 + 10*a^8*b^2*d^10*x^4 + 5*a^9*b*d^10*x^2 + a^10*d^10) + 21945*(sqrt(2)*d^2*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^2*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/a^5)/d","A",0
725,1,388,0,3.229453," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(69615 \, b^{5} d^{10} x^{10} + 334152 \, a b^{4} d^{10} x^{8} + 634270 \, a^{2} b^{3} d^{10} x^{6} + 590240 \, a^{3} b^{2} d^{10} x^{4} + 263515 \, a^{4} b d^{10} x^{2} + 40960 \, a^{5} d^{10}\right)}}{\left(d x\right)^{\frac{21}{2}} a^{6} b^{5} + 5 \, \left(d x\right)^{\frac{17}{2}} a^{7} b^{4} d^{2} + 10 \, \left(d x\right)^{\frac{13}{2}} a^{8} b^{3} d^{4} + 10 \, \left(d x\right)^{\frac{9}{2}} a^{9} b^{2} d^{6} + 5 \, \left(d x\right)^{\frac{5}{2}} a^{10} b d^{8} + \sqrt{d x} a^{11} d^{10}} + \frac{69615 \, b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{6}}}{163840 \, d}"," ",0,"-1/163840*(8*(69615*b^5*d^10*x^10 + 334152*a*b^4*d^10*x^8 + 634270*a^2*b^3*d^10*x^6 + 590240*a^3*b^2*d^10*x^4 + 263515*a^4*b*d^10*x^2 + 40960*a^5*d^10)/((d*x)^(21/2)*a^6*b^5 + 5*(d*x)^(17/2)*a^7*b^4*d^2 + 10*(d*x)^(13/2)*a^8*b^3*d^4 + 10*(d*x)^(9/2)*a^9*b^2*d^6 + 5*(d*x)^(5/2)*a^10*b*d^8 + sqrt(d*x)*a^11*d^10) + 69615*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/a^6)/d","A",0
726,1,395,0,3.233565," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(168245 \, b^{5} d^{10} x^{10} + 769120 \, a b^{4} d^{10} x^{8} + 1367810 \, a^{2} b^{3} d^{10} x^{6} + 1157176 \, a^{3} b^{2} d^{10} x^{4} + 437345 \, a^{4} b d^{10} x^{2} + 40960 \, a^{5} d^{10}\right)}}{\left(d x\right)^{\frac{23}{2}} a^{6} b^{5} + 5 \, \left(d x\right)^{\frac{19}{2}} a^{7} b^{4} d^{2} + 10 \, \left(d x\right)^{\frac{15}{2}} a^{8} b^{3} d^{4} + 10 \, \left(d x\right)^{\frac{11}{2}} a^{9} b^{2} d^{6} + 5 \, \left(d x\right)^{\frac{7}{2}} a^{10} b d^{8} + \left(d x\right)^{\frac{3}{2}} a^{11} d^{10}} + \frac{504735 \, {\left(\frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d}\right)}}{a^{6}}}{491520 \, d}"," ",0,"-1/491520*(8*(168245*b^5*d^10*x^10 + 769120*a*b^4*d^10*x^8 + 1367810*a^2*b^3*d^10*x^6 + 1157176*a^3*b^2*d^10*x^4 + 437345*a^4*b*d^10*x^2 + 40960*a^5*d^10)/((d*x)^(23/2)*a^6*b^5 + 5*(d*x)^(19/2)*a^7*b^4*d^2 + 10*(d*x)^(15/2)*a^8*b^3*d^4 + 10*(d*x)^(11/2)*a^9*b^2*d^6 + 5*(d*x)^(7/2)*a^10*b*d^8 + (d*x)^(3/2)*a^11*d^10) + 504735*(sqrt(2)*b^(3/4)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) - sqrt(2)*b^(3/4)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) + 2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d))/a^6)/d","A",0
727,1,410,0,3.316933," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(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}\right)}}{\left(d x\right)^{\frac{25}{2}} a^{7} b^{5} d^{2} + 5 \, \left(d x\right)^{\frac{21}{2}} a^{8} b^{4} d^{4} + 10 \, \left(d x\right)^{\frac{17}{2}} a^{9} b^{3} d^{6} + 10 \, \left(d x\right)^{\frac{13}{2}} a^{10} b^{2} d^{8} + 5 \, \left(d x\right)^{\frac{9}{2}} a^{11} b d^{10} + \left(d x\right)^{\frac{5}{2}} a^{12} d^{12}} + \frac{348075 \, b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{7} d^{2}}}{163840 \, d}"," ",0,"1/163840*(8*(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)/((d*x)^(25/2)*a^7*b^5*d^2 + 5*(d*x)^(21/2)*a^8*b^4*d^4 + 10*(d*x)^(17/2)*a^9*b^3*d^6 + 10*(d*x)^(13/2)*a^10*b^2*d^8 + 5*(d*x)^(9/2)*a^11*b*d^10 + (d*x)^(5/2)*a^12*d^12) + 348075*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^7*d^2))/d","A",0
728,1,25,0,1.324950," ","integrate((d*x)^(5/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, \left(d x\right)^{\frac{11}{2}} b + 11 \, \left(d x\right)^{\frac{7}{2}} a d^{2}\right)}}{77 \, d^{3}}"," ",0,"2/77*(7*(d*x)^(11/2)*b + 11*(d*x)^(7/2)*a*d^2)/d^3","A",0
729,1,25,0,1.252091," ","integrate((d*x)^(3/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, \left(d x\right)^{\frac{9}{2}} b + 9 \, \left(d x\right)^{\frac{5}{2}} a d^{2}\right)}}{45 \, d^{3}}"," ",0,"2/45*(5*(d*x)^(9/2)*b + 9*(d*x)^(5/2)*a*d^2)/d^3","A",0
730,1,25,0,1.396808," ","integrate((d*x)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, \left(d x\right)^{\frac{7}{2}} b + 7 \, \left(d x\right)^{\frac{3}{2}} a d^{2}\right)}}{21 \, d^{3}}"," ",0,"2/21*(3*(d*x)^(7/2)*b + 7*(d*x)^(3/2)*a*d^2)/d^3","A",0
731,1,24,0,1.370094," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, \sqrt{d x} a + \frac{\left(d x\right)^{\frac{5}{2}} b}{d^{2}}\right)}}{5 \, d}"," ",0,"2/5*(5*sqrt(d*x)*a + (d*x)^(5/2)*b/d^2)/d","A",0
732,1,25,0,1.355283," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, a}{\sqrt{d x}} - \frac{\left(d x\right)^{\frac{3}{2}} b}{d^{2}}\right)}}{3 \, d}"," ",0,"-2/3*(3*a/sqrt(d*x) - (d*x)^(3/2)*b/d^2)/d","A",0
733,1,24,0,1.403149," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a}{\left(d x\right)^{\frac{3}{2}}} - \frac{3 \, \sqrt{d x} b}{d^{2}}\right)}}{3 \, d}"," ",0,"-2/3*(a/(d*x)^(3/2) - 3*sqrt(d*x)*b/d^2)/d","A",0
734,1,25,0,1.269854," ","integrate(((b*x^2+a)^2)^(1/2)/(d*x)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, b d^{2} x^{2} + a d^{2}\right)}}{5 \, \left(d x\right)^{\frac{5}{2}} d^{3}}"," ",0,"-2/5*(5*b*d^2*x^2 + a*d^2)/((d*x)^(5/2)*d^3)","A",0
735,1,83,0,1.458146," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{2}{285} \, {\left(15 \, b^{3} d^{\frac{5}{2}} x^{3} + 19 \, a b^{2} d^{\frac{5}{2}} x\right)} x^{\frac{13}{2}} + \frac{4}{165} \, {\left(11 \, a b^{2} d^{\frac{5}{2}} x^{3} + 15 \, a^{2} b d^{\frac{5}{2}} x\right)} x^{\frac{9}{2}} + \frac{2}{77} \, {\left(7 \, a^{2} b d^{\frac{5}{2}} x^{3} + 11 \, a^{3} d^{\frac{5}{2}} x\right)} x^{\frac{5}{2}}"," ",0,"2/285*(15*b^3*d^(5/2)*x^3 + 19*a*b^2*d^(5/2)*x)*x^(13/2) + 4/165*(11*a*b^2*d^(5/2)*x^3 + 15*a^2*b*d^(5/2)*x)*x^(9/2) + 2/77*(7*a^2*b*d^(5/2)*x^3 + 11*a^3*d^(5/2)*x)*x^(5/2)","A",0
736,1,83,0,1.408680," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{2}{221} \, {\left(13 \, b^{3} d^{\frac{3}{2}} x^{3} + 17 \, a b^{2} d^{\frac{3}{2}} x\right)} x^{\frac{11}{2}} + \frac{4}{117} \, {\left(9 \, a b^{2} d^{\frac{3}{2}} x^{3} + 13 \, a^{2} b d^{\frac{3}{2}} x\right)} x^{\frac{7}{2}} + \frac{2}{45} \, {\left(5 \, a^{2} b d^{\frac{3}{2}} x^{3} + 9 \, a^{3} d^{\frac{3}{2}} x\right)} x^{\frac{3}{2}}"," ",0,"2/221*(13*b^3*d^(3/2)*x^3 + 17*a*b^2*d^(3/2)*x)*x^(11/2) + 4/117*(9*a*b^2*d^(3/2)*x^3 + 13*a^2*b*d^(3/2)*x)*x^(7/2) + 2/45*(5*a^2*b*d^(3/2)*x^3 + 9*a^3*d^(3/2)*x)*x^(3/2)","A",0
737,1,83,0,1.436494," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)*(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2}{165} \, {\left(11 \, b^{3} \sqrt{d} x^{3} + 15 \, a b^{2} \sqrt{d} x\right)} x^{\frac{9}{2}} + \frac{4}{77} \, {\left(7 \, a b^{2} \sqrt{d} x^{3} + 11 \, a^{2} b \sqrt{d} x\right)} x^{\frac{5}{2}} + \frac{2}{21} \, {\left(3 \, a^{2} b \sqrt{d} x^{3} + 7 \, a^{3} \sqrt{d} x\right)} \sqrt{x}"," ",0,"2/165*(11*b^3*sqrt(d)*x^3 + 15*a*b^2*sqrt(d)*x)*x^(9/2) + 4/77*(7*a*b^2*sqrt(d)*x^3 + 11*a^2*b*sqrt(d)*x)*x^(5/2) + 2/21*(3*a^2*b*sqrt(d)*x^3 + 7*a^3*sqrt(d)*x)*sqrt(x)","A",0
738,1,87,0,1.459450," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, {\left(9 \, b^{3} \sqrt{d} x^{3} + 13 \, a b^{2} \sqrt{d} x\right)} x^{\frac{7}{2}} + 26 \, {\left(5 \, a b^{2} \sqrt{d} x^{3} + 9 \, a^{2} b \sqrt{d} x\right)} x^{\frac{3}{2}} + \frac{117 \, {\left(a^{2} b \sqrt{d} x^{3} + 5 \, a^{3} \sqrt{d} x\right)}}{\sqrt{x}}\right)}}{585 \, d}"," ",0,"2/585*(5*(9*b^3*sqrt(d)*x^3 + 13*a*b^2*sqrt(d)*x)*x^(7/2) + 26*(5*a*b^2*sqrt(d)*x^3 + 9*a^2*b*sqrt(d)*x)*x^(3/2) + 117*(a^2*b*sqrt(d)*x^3 + 5*a^3*sqrt(d)*x)/sqrt(x))/d","A",0
739,1,87,0,1.424156," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, {\left(7 \, b^{3} \sqrt{d} x^{3} + 11 \, a b^{2} \sqrt{d} x\right)} x^{\frac{5}{2}} + 22 \, {\left(3 \, a b^{2} \sqrt{d} x^{3} + 7 \, a^{2} b \sqrt{d} x\right)} \sqrt{x} + \frac{77 \, {\left(a^{2} b \sqrt{d} x^{3} - 3 \, a^{3} \sqrt{d} x\right)}}{x^{\frac{3}{2}}}\right)}}{231 \, d^{2}}"," ",0,"2/231*(3*(7*b^3*sqrt(d)*x^3 + 11*a*b^2*sqrt(d)*x)*x^(5/2) + 22*(3*a*b^2*sqrt(d)*x^3 + 7*a^2*b*sqrt(d)*x)*sqrt(x) + 77*(a^2*b*sqrt(d)*x^3 - 3*a^3*sqrt(d)*x)/x^(3/2))/d^2","A",0
740,1,86,0,1.474799," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(5 \, b^{3} \sqrt{d} x^{3} + 9 \, a b^{2} \sqrt{d} x\right)} x^{\frac{3}{2}} + \frac{18 \, {\left(a b^{2} \sqrt{d} x^{3} + 5 \, a^{2} b \sqrt{d} x\right)}}{\sqrt{x}} + \frac{15 \, {\left(3 \, a^{2} b \sqrt{d} x^{3} - a^{3} \sqrt{d} x\right)}}{x^{\frac{5}{2}}}\right)}}{45 \, d^{3}}"," ",0,"2/45*((5*b^3*sqrt(d)*x^3 + 9*a*b^2*sqrt(d)*x)*x^(3/2) + 18*(a*b^2*sqrt(d)*x^3 + 5*a^2*b*sqrt(d)*x)/sqrt(x) + 15*(3*a^2*b*sqrt(d)*x^3 - a^3*sqrt(d)*x)/x^(5/2))/d^3","A",0
741,1,86,0,1.451977," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, {\left(3 \, b^{3} \sqrt{d} x^{3} + 7 \, a b^{2} \sqrt{d} x\right)} \sqrt{x} + \frac{70 \, {\left(a b^{2} \sqrt{d} x^{3} - 3 \, a^{2} b \sqrt{d} x\right)}}{x^{\frac{3}{2}}} - \frac{21 \, {\left(5 \, a^{2} b \sqrt{d} x^{3} + a^{3} \sqrt{d} x\right)}}{x^{\frac{7}{2}}}\right)}}{105 \, d^{4}}"," ",0,"2/105*(5*(3*b^3*sqrt(d)*x^3 + 7*a*b^2*sqrt(d)*x)*sqrt(x) + 70*(a*b^2*sqrt(d)*x^3 - 3*a^2*b*sqrt(d)*x)/x^(3/2) - 21*(5*a^2*b*sqrt(d)*x^3 + a^3*sqrt(d)*x)/x^(7/2))/d^4","A",0
742,1,147,0,1.471377," ","integrate((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{2}{621} \, {\left(23 \, b^{5} d^{\frac{5}{2}} x^{3} + 27 \, a b^{4} d^{\frac{5}{2}} x\right)} x^{\frac{21}{2}} + \frac{8}{437} \, {\left(19 \, a b^{4} d^{\frac{5}{2}} x^{3} + 23 \, a^{2} b^{3} d^{\frac{5}{2}} x\right)} x^{\frac{17}{2}} + \frac{4}{95} \, {\left(15 \, a^{2} b^{3} d^{\frac{5}{2}} x^{3} + 19 \, a^{3} b^{2} d^{\frac{5}{2}} x\right)} x^{\frac{13}{2}} + \frac{8}{165} \, {\left(11 \, a^{3} b^{2} d^{\frac{5}{2}} x^{3} + 15 \, a^{4} b d^{\frac{5}{2}} x\right)} x^{\frac{9}{2}} + \frac{2}{77} \, {\left(7 \, a^{4} b d^{\frac{5}{2}} x^{3} + 11 \, a^{5} d^{\frac{5}{2}} x\right)} x^{\frac{5}{2}}"," ",0,"2/621*(23*b^5*d^(5/2)*x^3 + 27*a*b^4*d^(5/2)*x)*x^(21/2) + 8/437*(19*a*b^4*d^(5/2)*x^3 + 23*a^2*b^3*d^(5/2)*x)*x^(17/2) + 4/95*(15*a^2*b^3*d^(5/2)*x^3 + 19*a^3*b^2*d^(5/2)*x)*x^(13/2) + 8/165*(11*a^3*b^2*d^(5/2)*x^3 + 15*a^4*b*d^(5/2)*x)*x^(9/2) + 2/77*(7*a^4*b*d^(5/2)*x^3 + 11*a^5*d^(5/2)*x)*x^(5/2)","A",0
743,1,147,0,1.415760," ","integrate((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{2}{525} \, {\left(21 \, b^{5} d^{\frac{3}{2}} x^{3} + 25 \, a b^{4} d^{\frac{3}{2}} x\right)} x^{\frac{19}{2}} + \frac{8}{357} \, {\left(17 \, a b^{4} d^{\frac{3}{2}} x^{3} + 21 \, a^{2} b^{3} d^{\frac{3}{2}} x\right)} x^{\frac{15}{2}} + \frac{12}{221} \, {\left(13 \, a^{2} b^{3} d^{\frac{3}{2}} x^{3} + 17 \, a^{3} b^{2} d^{\frac{3}{2}} x\right)} x^{\frac{11}{2}} + \frac{8}{117} \, {\left(9 \, a^{3} b^{2} d^{\frac{3}{2}} x^{3} + 13 \, a^{4} b d^{\frac{3}{2}} x\right)} x^{\frac{7}{2}} + \frac{2}{45} \, {\left(5 \, a^{4} b d^{\frac{3}{2}} x^{3} + 9 \, a^{5} d^{\frac{3}{2}} x\right)} x^{\frac{3}{2}}"," ",0,"2/525*(21*b^5*d^(3/2)*x^3 + 25*a*b^4*d^(3/2)*x)*x^(19/2) + 8/357*(17*a*b^4*d^(3/2)*x^3 + 21*a^2*b^3*d^(3/2)*x)*x^(15/2) + 12/221*(13*a^2*b^3*d^(3/2)*x^3 + 17*a^3*b^2*d^(3/2)*x)*x^(11/2) + 8/117*(9*a^3*b^2*d^(3/2)*x^3 + 13*a^4*b*d^(3/2)*x)*x^(7/2) + 2/45*(5*a^4*b*d^(3/2)*x^3 + 9*a^5*d^(3/2)*x)*x^(3/2)","A",0
744,1,147,0,1.526050," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)*(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2}{437} \, {\left(19 \, b^{5} \sqrt{d} x^{3} + 23 \, a b^{4} \sqrt{d} x\right)} x^{\frac{17}{2}} + \frac{8}{285} \, {\left(15 \, a b^{4} \sqrt{d} x^{3} + 19 \, a^{2} b^{3} \sqrt{d} x\right)} x^{\frac{13}{2}} + \frac{4}{55} \, {\left(11 \, a^{2} b^{3} \sqrt{d} x^{3} + 15 \, a^{3} b^{2} \sqrt{d} x\right)} x^{\frac{9}{2}} + \frac{8}{77} \, {\left(7 \, a^{3} b^{2} \sqrt{d} x^{3} + 11 \, a^{4} b \sqrt{d} x\right)} x^{\frac{5}{2}} + \frac{2}{21} \, {\left(3 \, a^{4} b \sqrt{d} x^{3} + 7 \, a^{5} \sqrt{d} x\right)} \sqrt{x}"," ",0,"2/437*(19*b^5*sqrt(d)*x^3 + 23*a*b^4*sqrt(d)*x)*x^(17/2) + 8/285*(15*a*b^4*sqrt(d)*x^3 + 19*a^2*b^3*sqrt(d)*x)*x^(13/2) + 4/55*(11*a^2*b^3*sqrt(d)*x^3 + 15*a^3*b^2*sqrt(d)*x)*x^(9/2) + 8/77*(7*a^3*b^2*sqrt(d)*x^3 + 11*a^4*b*sqrt(d)*x)*x^(5/2) + 2/21*(3*a^4*b*sqrt(d)*x^3 + 7*a^5*sqrt(d)*x)*sqrt(x)","A",0
745,1,151,0,1.449554," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(195 \, {\left(17 \, b^{5} \sqrt{d} x^{3} + 21 \, a b^{4} \sqrt{d} x\right)} x^{\frac{15}{2}} + 1260 \, {\left(13 \, a b^{4} \sqrt{d} x^{3} + 17 \, a^{2} b^{3} \sqrt{d} x\right)} x^{\frac{11}{2}} + 3570 \, {\left(9 \, a^{2} b^{3} \sqrt{d} x^{3} + 13 \, a^{3} b^{2} \sqrt{d} x\right)} x^{\frac{7}{2}} + 6188 \, {\left(5 \, a^{3} b^{2} \sqrt{d} x^{3} + 9 \, a^{4} b \sqrt{d} x\right)} x^{\frac{3}{2}} + \frac{13923 \, {\left(a^{4} b \sqrt{d} x^{3} + 5 \, a^{5} \sqrt{d} x\right)}}{\sqrt{x}}\right)}}{69615 \, d}"," ",0,"2/69615*(195*(17*b^5*sqrt(d)*x^3 + 21*a*b^4*sqrt(d)*x)*x^(15/2) + 1260*(13*a*b^4*sqrt(d)*x^3 + 17*a^2*b^3*sqrt(d)*x)*x^(11/2) + 3570*(9*a^2*b^3*sqrt(d)*x^3 + 13*a^3*b^2*sqrt(d)*x)*x^(7/2) + 6188*(5*a^3*b^2*sqrt(d)*x^3 + 9*a^4*b*sqrt(d)*x)*x^(3/2) + 13923*(a^4*b*sqrt(d)*x^3 + 5*a^5*sqrt(d)*x)/sqrt(x))/d","A",0
746,1,151,0,1.503716," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(77 \, {\left(15 \, b^{5} \sqrt{d} x^{3} + 19 \, a b^{4} \sqrt{d} x\right)} x^{\frac{13}{2}} + 532 \, {\left(11 \, a b^{4} \sqrt{d} x^{3} + 15 \, a^{2} b^{3} \sqrt{d} x\right)} x^{\frac{9}{2}} + 1710 \, {\left(7 \, a^{2} b^{3} \sqrt{d} x^{3} + 11 \, a^{3} b^{2} \sqrt{d} x\right)} x^{\frac{5}{2}} + 4180 \, {\left(3 \, a^{3} b^{2} \sqrt{d} x^{3} + 7 \, a^{4} b \sqrt{d} x\right)} \sqrt{x} + \frac{7315 \, {\left(a^{4} b \sqrt{d} x^{3} - 3 \, a^{5} \sqrt{d} x\right)}}{x^{\frac{3}{2}}}\right)}}{21945 \, d^{2}}"," ",0,"2/21945*(77*(15*b^5*sqrt(d)*x^3 + 19*a*b^4*sqrt(d)*x)*x^(13/2) + 532*(11*a*b^4*sqrt(d)*x^3 + 15*a^2*b^3*sqrt(d)*x)*x^(9/2) + 1710*(7*a^2*b^3*sqrt(d)*x^3 + 11*a^3*b^2*sqrt(d)*x)*x^(5/2) + 4180*(3*a^3*b^2*sqrt(d)*x^3 + 7*a^4*b*sqrt(d)*x)*sqrt(x) + 7315*(a^4*b*sqrt(d)*x^3 - 3*a^5*sqrt(d)*x)/x^(3/2))/d^2","A",0
747,1,151,0,1.537243," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(45 \, {\left(13 \, b^{5} \sqrt{d} x^{3} + 17 \, a b^{4} \sqrt{d} x\right)} x^{\frac{11}{2}} + 340 \, {\left(9 \, a b^{4} \sqrt{d} x^{3} + 13 \, a^{2} b^{3} \sqrt{d} x\right)} x^{\frac{7}{2}} + 1326 \, {\left(5 \, a^{2} b^{3} \sqrt{d} x^{3} + 9 \, a^{3} b^{2} \sqrt{d} x\right)} x^{\frac{3}{2}} + \frac{7956 \, {\left(a^{3} b^{2} \sqrt{d} x^{3} + 5 \, a^{4} b \sqrt{d} x\right)}}{\sqrt{x}} + \frac{3315 \, {\left(3 \, a^{4} b \sqrt{d} x^{3} - a^{5} \sqrt{d} x\right)}}{x^{\frac{5}{2}}}\right)}}{9945 \, d^{3}}"," ",0,"2/9945*(45*(13*b^5*sqrt(d)*x^3 + 17*a*b^4*sqrt(d)*x)*x^(11/2) + 340*(9*a*b^4*sqrt(d)*x^3 + 13*a^2*b^3*sqrt(d)*x)*x^(7/2) + 1326*(5*a^2*b^3*sqrt(d)*x^3 + 9*a^3*b^2*sqrt(d)*x)*x^(3/2) + 7956*(a^3*b^2*sqrt(d)*x^3 + 5*a^4*b*sqrt(d)*x)/sqrt(x) + 3315*(3*a^4*b*sqrt(d)*x^3 - a^5*sqrt(d)*x)/x^(5/2))/d^3","A",0
748,1,150,0,1.554233," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, {\left(11 \, b^{5} \sqrt{d} x^{3} + 15 \, a b^{4} \sqrt{d} x\right)} x^{\frac{9}{2}} + 60 \, {\left(7 \, a b^{4} \sqrt{d} x^{3} + 11 \, a^{2} b^{3} \sqrt{d} x\right)} x^{\frac{5}{2}} + 330 \, {\left(3 \, a^{2} b^{3} \sqrt{d} x^{3} + 7 \, a^{3} b^{2} \sqrt{d} x\right)} \sqrt{x} + \frac{1540 \, {\left(a^{3} b^{2} \sqrt{d} x^{3} - 3 \, a^{4} b \sqrt{d} x\right)}}{x^{\frac{3}{2}}} - \frac{231 \, {\left(5 \, a^{4} b \sqrt{d} x^{3} + a^{5} \sqrt{d} x\right)}}{x^{\frac{7}{2}}}\right)}}{1155 \, d^{4}}"," ",0,"2/1155*(7*(11*b^5*sqrt(d)*x^3 + 15*a*b^4*sqrt(d)*x)*x^(9/2) + 60*(7*a*b^4*sqrt(d)*x^3 + 11*a^2*b^3*sqrt(d)*x)*x^(5/2) + 330*(3*a^2*b^3*sqrt(d)*x^3 + 7*a^3*b^2*sqrt(d)*x)*sqrt(x) + 1540*(a^3*b^2*sqrt(d)*x^3 - 3*a^4*b*sqrt(d)*x)/x^(3/2) - 231*(5*a^4*b*sqrt(d)*x^3 + a^5*sqrt(d)*x)/x^(7/2))/d^4","A",0
749,1,266,0,2.942862," ","integrate((d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{5 \, {\left(\frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{6} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a^{2}}{b^{2}} + \frac{8 \, {\left(\left(d x\right)^{\frac{5}{2}} b d^{2} - 5 \, \sqrt{d x} a d^{4}\right)}}{b^{2}}}{20 \, d}"," ",0,"1/20*(5*(sqrt(2)*d^6*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^6*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^5*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a^2/b^2 + 8*((d*x)^(5/2)*b*d^2 - 5*sqrt(d*x)*a*d^4)/b^2)/d","A",0
750,1,241,0,2.971267," ","integrate((d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, a d^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{b} - \frac{8 \, \left(d x\right)^{\frac{3}{2}} d^{2}}{b}}{12 \, d}"," ",0,"-1/12*(3*a*d^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/b - 8*(d*x)^(3/2)*d^2/b)/d","A",0
751,1,250,0,3.102976," ","integrate((d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{8 \, \sqrt{d x} d^{2}}{b} - \frac{{\left(\frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{4} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}\right)} a}{b}}{4 \, d}"," ",0,"1/4*(8*sqrt(d*x)*d^2/b - (sqrt(2)*d^4*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^4*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))*a/b)/d","A",0
752,1,216,0,3.004571," ","integrate((d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, d {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}"," ",0,"1/4*d*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))","A",0
753,1,226,0,3.056012," ","integrate(1/(d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} d^{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}} b^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}} + \frac{2 \, \sqrt{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a}}}{4 \, d}"," ",0,"1/4*(sqrt(2)*d^2*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) - sqrt(2)*d^2*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(3/4)*b^(1/4)) + 2*sqrt(2)*d*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)) + 2*sqrt(2)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)))/d","A",0
754,1,234,0,3.255057," ","integrate(1/(d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a} + \frac{8}{\sqrt{d x} a}}{4 \, d}"," ",0,"-1/4*(b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/a + 8/(sqrt(d*x)*a))/d","A",0
755,1,242,0,3.076189," ","integrate(1/(d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(\frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{a} d}\right)}}{a} + \frac{8}{\left(d x\right)^{\frac{3}{2}} a}}{12 \, d}"," ",0,"-1/12*(3*(sqrt(2)*b^(3/4)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) - sqrt(2)*b^(3/4)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/(a*d^2)^(3/4) + 2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(a)*d))/a + 8/((d*x)^(3/2)*a))/d","A",0
756,1,259,0,3.033512," ","integrate(1/(d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{5 \, b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{d x} \sqrt{b}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b} d}}\right)}{\sqrt{\sqrt{a} \sqrt{b} d} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{b} d x + \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{b} d x - \sqrt{2} \left(a d^{2}\right)^{\frac{1}{4}} \sqrt{d x} b^{\frac{1}{4}} + \sqrt{a} d\right)}{\left(a d^{2}\right)^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{a^{2} d^{2}} + \frac{8 \, {\left(5 \, b d^{2} x^{2} - a d^{2}\right)}}{\left(d x\right)^{\frac{5}{2}} a^{2} d^{2}}}{20 \, d}"," ",0,"1/20*(5*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) + 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a*d^2)^(1/4)*b^(1/4) - 2*sqrt(d*x)*sqrt(b))/sqrt(sqrt(a)*sqrt(b)*d))/(sqrt(sqrt(a)*sqrt(b)*d)*sqrt(b)) - sqrt(2)*log(sqrt(b)*d*x + sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)) + sqrt(2)*log(sqrt(b)*d*x - sqrt(2)*(a*d^2)^(1/4)*sqrt(d*x)*b^(1/4) + sqrt(a)*d)/((a*d^2)^(1/4)*b^(3/4)))/(a^2*d^2) + 8*(5*b*d^2*x^2 - a*d^2)/((d*x)^(5/2)*a^2*d^2))/d","A",0
757,0,0,0,0.000000," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{a^{2} d^{\frac{15}{2}} x^{\frac{5}{2}}}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3} + {\left(b^{5} x^{2} + a b^{4}\right)} x^{2}\right)}} - 2 \, a d^{\frac{15}{2}} \int \frac{x^{\frac{3}{2}}}{b^{4} x^{2} + a b^{3}}\,{d x} + d^{\frac{15}{2}} \int \frac{x^{\frac{7}{2}}}{b^{3} x^{2} + a b^{2}}\,{d x} + \frac{21 \, {\left(\frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}\right)} d^{\frac{15}{2}}}{128 \, b^{4}} - \frac{17 \, a^{2} b d^{\frac{15}{2}} x^{\frac{5}{2}} + 21 \, a^{3} d^{\frac{15}{2}} \sqrt{x}}{16 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}"," ",0,"-1/2*a^2*d^(15/2)*x^(5/2)/(a*b^4*x^2 + a^2*b^3 + (b^5*x^2 + a*b^4)*x^2) - 2*a*d^(15/2)*integrate(x^(3/2)/(b^4*x^2 + a*b^3), x) + d^(15/2)*integrate(x^(7/2)/(b^3*x^2 + a*b^2), x) + 21/128*(2*sqrt(2)*a^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*a^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(5/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(5/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))*d^(15/2)/b^4 - 1/16*(17*a^2*b*d^(15/2)*x^(5/2) + 21*a^3*d^(15/2)*sqrt(x))/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)","F",0
758,0,0,0,0.000000," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{a^{2} d^{\frac{13}{2}} x^{\frac{3}{2}}}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3} + {\left(b^{5} x^{2} + a b^{4}\right)} x^{2}\right)}} - 2 \, a d^{\frac{13}{2}} \int \frac{\sqrt{x}}{b^{4} x^{2} + a b^{3}}\,{d x} + d^{\frac{13}{2}} \int \frac{x^{\frac{5}{2}}}{b^{3} x^{2} + a b^{2}}\,{d x} + \frac{19 \, a d^{\frac{13}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, b^{3}} + \frac{19 \, a b d^{\frac{13}{2}} x^{\frac{7}{2}} + 23 \, a^{2} d^{\frac{13}{2}} x^{\frac{3}{2}}}{16 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"-1/2*a^2*d^(13/2)*x^(3/2)/(a*b^4*x^2 + a^2*b^3 + (b^5*x^2 + a*b^4)*x^2) - 2*a*d^(13/2)*integrate(sqrt(x)/(b^4*x^2 + a*b^3), x) + d^(13/2)*integrate(x^(5/2)/(b^3*x^2 + a*b^2), x) + 19/128*a*d^(13/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^3 + 1/16*(19*a*b*d^(13/2)*x^(7/2) + 23*a^2*d^(13/2)*x^(3/2))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","F",0
759,0,0,0,0.000000," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{a d^{\frac{11}{2}} x^{\frac{5}{2}}}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2} + {\left(b^{4} x^{2} + a b^{3}\right)} x^{2}\right)}} + d^{\frac{11}{2}} \int \frac{x^{\frac{3}{2}}}{b^{3} x^{2} + a b^{2}}\,{d x} - \frac{13 \, {\left(\frac{2 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{a} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{1}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{1}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}\right)} d^{\frac{11}{2}}}{128 \, b^{3}} + \frac{9 \, a b d^{\frac{11}{2}} x^{\frac{5}{2}} + 13 \, a^{2} d^{\frac{11}{2}} \sqrt{x}}{16 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/2*a*d^(11/2)*x^(5/2)/(a*b^3*x^2 + a^2*b^2 + (b^4*x^2 + a*b^3)*x^2) + d^(11/2)*integrate(x^(3/2)/(b^3*x^2 + a*b^2), x) - 13/128*(2*sqrt(2)*sqrt(a)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*sqrt(a)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(1/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(1/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))*d^(11/2)/b^3 + 1/16*(9*a*b*d^(11/2)*x^(5/2) + 13*a^2*d^(11/2)*sqrt(x))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","F",0
760,0,0,0,0.000000," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{a d^{\frac{9}{2}} x^{\frac{3}{2}}}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2} + {\left(b^{4} x^{2} + a b^{3}\right)} x^{2}\right)}} + d^{\frac{9}{2}} \int \frac{\sqrt{x}}{b^{3} x^{2} + a b^{2}}\,{d x} - \frac{11 \, d^{\frac{9}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, b^{2}} - \frac{11 \, b d^{\frac{9}{2}} x^{\frac{7}{2}} + 15 \, a d^{\frac{9}{2}} x^{\frac{3}{2}}}{16 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"1/2*a*d^(9/2)*x^(3/2)/(a*b^3*x^2 + a^2*b^2 + (b^4*x^2 + a*b^3)*x^2) + d^(9/2)*integrate(sqrt(x)/(b^3*x^2 + a*b^2), x) - 11/128*d^(9/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^2 - 1/16*(11*b*d^(9/2)*x^(7/2) + 15*a*d^(9/2)*x^(3/2))/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","F",0
761,1,279,0,3.229766," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{d^{\frac{7}{2}} x^{\frac{5}{2}}}{2 \, {\left(a b^{2} x^{2} + a^{2} b + {\left(b^{3} x^{2} + a b^{2}\right)} x^{2}\right)}} + \frac{5 \, d^{3} {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{128 \, b^{2}} - \frac{b d^{\frac{7}{2}} x^{\frac{5}{2}} + 5 \, a d^{\frac{7}{2}} \sqrt{x}}{16 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/2*d^(7/2)*x^(5/2)/(a*b^2*x^2 + a^2*b + (b^3*x^2 + a*b^2)*x^2) + 5/128*d^3*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^2 - 1/16*(b*d^(7/2)*x^(5/2) + 5*a*d^(7/2)*sqrt(x))/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
762,1,272,0,3.185588," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{d^{\frac{5}{2}} x^{\frac{3}{2}}}{2 \, {\left(a b^{2} x^{2} + a^{2} b + {\left(b^{3} x^{2} + a b^{2}\right)} x^{2}\right)}} + \frac{3 \, d^{\frac{5}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a b} + \frac{3 \, b d^{\frac{5}{2}} x^{\frac{7}{2}} + 7 \, a d^{\frac{5}{2}} x^{\frac{3}{2}}}{16 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"-1/2*d^(5/2)*x^(3/2)/(a*b^2*x^2 + a^2*b + (b^3*x^2 + a*b^2)*x^2) + 3/128*d^(5/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b) + 1/16*(3*b*d^(5/2)*x^(7/2) + 7*a*d^(5/2)*x^(3/2))/(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)","A",0
763,1,281,0,3.220150," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{d^{\frac{3}{2}} x^{\frac{5}{2}}}{2 \, {\left(a^{2} b x^{2} + a^{3} + {\left(a b^{2} x^{2} + a^{2} b\right)} x^{2}\right)}} - \frac{7 \, b d^{\frac{3}{2}} x^{\frac{5}{2}} + 3 \, a d^{\frac{3}{2}} \sqrt{x}}{16 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)}} + \frac{3 \, d {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{128 \, a b}"," ",0,"1/2*d^(3/2)*x^(5/2)/(a^2*b*x^2 + a^3 + (a*b^2*x^2 + a^2*b)*x^2) - 1/16*(7*b*d^(3/2)*x^(5/2) + 3*a*d^(3/2)*sqrt(x))/(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b) + 3/128*d*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b)","A",0
764,1,265,0,3.205123," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{d} x^{\frac{3}{2}}}{2 \, {\left(a^{2} b x^{2} + a^{3} + {\left(a b^{2} x^{2} + a^{2} b\right)} x^{2}\right)}} + \frac{5 \, b \sqrt{d} x^{\frac{7}{2}} + a \sqrt{d} x^{\frac{3}{2}}}{16 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}} + \frac{5 \, \sqrt{d} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a^{2}}"," ",0,"1/2*sqrt(d)*x^(3/2)/(a^2*b*x^2 + a^3 + (a*b^2*x^2 + a^2*b)*x^2) + 1/16*(5*b*sqrt(d)*x^(7/2) + a*sqrt(d)*x^(3/2))/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4) + 5/128*sqrt(d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^2","A",0
765,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x, algorithm=""maxima"")","-\frac{b \sqrt{d} x^{\frac{5}{2}}}{2 \, {\left(a^{3} b d x^{2} + a^{4} d + {\left(a^{2} b^{2} d x^{2} + a^{3} b d\right)} x^{2}\right)}} + \frac{15 \, b x^{\frac{5}{2}} + 11 \, a \sqrt{x}}{16 \, {\left(a^{2} b^{2} \sqrt{d} x^{4} + 2 \, a^{3} b \sqrt{d} x^{2} + a^{4} \sqrt{d}\right)}} - \frac{11 \, {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{128 \, a^{2} d} + \int \frac{1}{{\left(a^{2} b \sqrt{d} x^{2} + a^{3} \sqrt{d}\right)} \sqrt{x}}\,{d x}"," ",0,"-1/2*b*sqrt(d)*x^(5/2)/(a^3*b*d*x^2 + a^4*d + (a^2*b^2*d*x^2 + a^3*b*d)*x^2) + 1/16*(15*b*x^(5/2) + 11*a*sqrt(x))/(a^2*b^2*sqrt(d)*x^4 + 2*a^3*b*sqrt(d)*x^2 + a^4*sqrt(d)) - 11/128*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^2*d) + integrate(1/((a^2*b*sqrt(d)*x^2 + a^3*sqrt(d))*sqrt(x)), x)","F",0
766,0,0,0,0.000000," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","-\frac{b x^{\frac{3}{2}}}{2 \, {\left(a^{3} b d^{\frac{3}{2}} x^{2} + a^{4} d^{\frac{3}{2}} + {\left(a^{2} b^{2} d^{\frac{3}{2}} x^{2} + a^{3} b d^{\frac{3}{2}}\right)} x^{2}\right)}} - \frac{13 \, b^{2} x^{\frac{7}{2}} + 9 \, a b x^{\frac{3}{2}}}{16 \, {\left(a^{3} b^{2} d^{\frac{3}{2}} x^{4} + 2 \, a^{4} b d^{\frac{3}{2}} x^{2} + a^{5} d^{\frac{3}{2}}\right)}} - \frac{13 \, b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a^{3} d^{\frac{3}{2}}} + \int \frac{1}{{\left(a^{2} b d^{\frac{3}{2}} x^{2} + a^{3} d^{\frac{3}{2}}\right)} x^{\frac{3}{2}}}\,{d x}"," ",0,"-1/2*b*x^(3/2)/(a^3*b*d^(3/2)*x^2 + a^4*d^(3/2) + (a^2*b^2*d^(3/2)*x^2 + a^3*b*d^(3/2))*x^2) - 1/16*(13*b^2*x^(7/2) + 9*a*b*x^(3/2))/(a^3*b^2*d^(3/2)*x^4 + 2*a^4*b*d^(3/2)*x^2 + a^5*d^(3/2)) - 13/128*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^3*d^(3/2)) + integrate(1/((a^2*b*d^(3/2)*x^2 + a^3*d^(3/2))*x^(3/2)), x)","F",0
767,0,0,0,0.000000," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{\frac{5}{2}}}{2 \, {\left(a^{4} b d^{\frac{5}{2}} x^{2} + a^{5} d^{\frac{5}{2}} + {\left(a^{3} b^{2} d^{\frac{5}{2}} x^{2} + a^{4} b d^{\frac{5}{2}}\right)} x^{2}\right)}} - 2 \, b \int \frac{1}{{\left(a^{3} b d^{\frac{5}{2}} x^{2} + a^{4} d^{\frac{5}{2}}\right)} \sqrt{x}}\,{d x} - \frac{23 \, b^{2} x^{\frac{5}{2}} + 19 \, a b \sqrt{x}}{16 \, {\left(a^{3} b^{2} d^{\frac{5}{2}} x^{4} + 2 \, a^{4} b d^{\frac{5}{2}} x^{2} + a^{5} d^{\frac{5}{2}}\right)}} + \frac{19 \, {\left(\frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}\right)}}{128 \, a^{3} d^{\frac{5}{2}}} + \int \frac{1}{{\left(a^{2} b d^{\frac{5}{2}} x^{2} + a^{3} d^{\frac{5}{2}}\right)} x^{\frac{5}{2}}}\,{d x}"," ",0,"1/2*b^2*x^(5/2)/(a^4*b*d^(5/2)*x^2 + a^5*d^(5/2) + (a^3*b^2*d^(5/2)*x^2 + a^4*b*d^(5/2))*x^2) - 2*b*integrate(1/((a^3*b*d^(5/2)*x^2 + a^4*d^(5/2))*sqrt(x)), x) - 1/16*(23*b^2*x^(5/2) + 19*a*b*sqrt(x))/(a^3*b^2*d^(5/2)*x^4 + 2*a^4*b*d^(5/2)*x^2 + a^5*d^(5/2)) + 19/128*(2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(3/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(3/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(a^3*d^(5/2)) + integrate(1/((a^2*b*d^(5/2)*x^2 + a^3*d^(5/2))*x^(5/2)), x)","F",0
768,0,0,0,0.000000," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{\frac{3}{2}}}{2 \, {\left(a^{4} b d^{\frac{7}{2}} x^{2} + a^{5} d^{\frac{7}{2}} + {\left(a^{3} b^{2} d^{\frac{7}{2}} x^{2} + a^{4} b d^{\frac{7}{2}}\right)} x^{2}\right)}} - 2 \, b \int \frac{1}{{\left(a^{3} b d^{\frac{7}{2}} x^{2} + a^{4} d^{\frac{7}{2}}\right)} x^{\frac{3}{2}}}\,{d x} + \frac{21 \, b^{3} x^{\frac{7}{2}} + 17 \, a b^{2} x^{\frac{3}{2}}}{16 \, {\left(a^{4} b^{2} d^{\frac{7}{2}} x^{4} + 2 \, a^{5} b d^{\frac{7}{2}} x^{2} + a^{6} d^{\frac{7}{2}}\right)}} + \frac{21 \, b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a^{4} d^{\frac{7}{2}}} + \int \frac{1}{{\left(a^{2} b d^{\frac{7}{2}} x^{2} + a^{3} d^{\frac{7}{2}}\right)} x^{\frac{7}{2}}}\,{d x}"," ",0,"1/2*b^2*x^(3/2)/(a^4*b*d^(7/2)*x^2 + a^5*d^(7/2) + (a^3*b^2*d^(7/2)*x^2 + a^4*b*d^(7/2))*x^2) - 2*b*integrate(1/((a^3*b*d^(7/2)*x^2 + a^4*d^(7/2))*x^(3/2)), x) + 1/16*(21*b^3*x^(7/2) + 17*a*b^2*x^(3/2))/(a^4*b^2*d^(7/2)*x^4 + 2*a^5*b*d^(7/2)*x^2 + a^6*d^(7/2)) + 21/128*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^4*d^(7/2)) + integrate(1/((a^2*b*d^(7/2)*x^2 + a^3*d^(7/2))*x^(7/2)), x)","F",0
769,0,0,0,0.000000," ","integrate((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-4 \, a d^{\frac{23}{2}} \int \frac{x^{\frac{3}{2}}}{b^{6} x^{2} + a b^{5}}\,{d x} + d^{\frac{23}{2}} \int \frac{x^{\frac{7}{2}}}{b^{5} x^{2} + a b^{4}}\,{d x} + \frac{3683 \, {\left(\frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}\right)} d^{\frac{23}{2}}}{8192 \, b^{6}} - \frac{6925 \, a^{2} b^{3} d^{\frac{23}{2}} x^{\frac{13}{2}} + 23395 \, a^{3} b^{2} d^{\frac{23}{2}} x^{\frac{9}{2}} + 27135 \, a^{4} b d^{\frac{23}{2}} x^{\frac{5}{2}} + 11049 \, a^{5} d^{\frac{23}{2}} \sqrt{x}}{3072 \, {\left(b^{10} x^{8} + 4 \, a b^{9} x^{6} + 6 \, a^{2} b^{8} x^{4} + 4 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)}} - \frac{{\left(617 \, a^{2} b^{4} d^{\frac{23}{2}} x^{5} + 1386 \, a^{3} b^{3} d^{\frac{23}{2}} x^{3} + 801 \, a^{4} b^{2} d^{\frac{23}{2}} x\right)} x^{\frac{11}{2}} + 2 \, {\left(519 \, a^{3} b^{3} d^{\frac{23}{2}} x^{5} + 1182 \, a^{4} b^{2} d^{\frac{23}{2}} x^{3} + 695 \, a^{5} b d^{\frac{23}{2}} x\right)} x^{\frac{7}{2}} + {\left(453 \, a^{4} b^{2} d^{\frac{23}{2}} x^{5} + 1042 \, a^{5} b d^{\frac{23}{2}} x^{3} + 621 \, a^{6} d^{\frac{23}{2}} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{3} b^{8} x^{6} + 3 \, a^{4} b^{7} x^{4} + 3 \, a^{5} b^{6} x^{2} + a^{6} b^{5} + {\left(b^{11} x^{6} + 3 \, a b^{10} x^{4} + 3 \, a^{2} b^{9} x^{2} + a^{3} b^{8}\right)} x^{6} + 3 \, {\left(a b^{10} x^{6} + 3 \, a^{2} b^{9} x^{4} + 3 \, a^{3} b^{8} x^{2} + a^{4} b^{7}\right)} x^{4} + 3 \, {\left(a^{2} b^{9} x^{6} + 3 \, a^{3} b^{8} x^{4} + 3 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} x^{2}\right)}}"," ",0,"-4*a*d^(23/2)*integrate(x^(3/2)/(b^6*x^2 + a*b^5), x) + d^(23/2)*integrate(x^(7/2)/(b^5*x^2 + a*b^4), x) + 3683/8192*(2*sqrt(2)*a^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*a^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(5/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(5/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))*d^(23/2)/b^6 - 1/3072*(6925*a^2*b^3*d^(23/2)*x^(13/2) + 23395*a^3*b^2*d^(23/2)*x^(9/2) + 27135*a^4*b*d^(23/2)*x^(5/2) + 11049*a^5*d^(23/2)*sqrt(x))/(b^10*x^8 + 4*a*b^9*x^6 + 6*a^2*b^8*x^4 + 4*a^3*b^7*x^2 + a^4*b^6) - 1/192*((617*a^2*b^4*d^(23/2)*x^5 + 1386*a^3*b^3*d^(23/2)*x^3 + 801*a^4*b^2*d^(23/2)*x)*x^(11/2) + 2*(519*a^3*b^3*d^(23/2)*x^5 + 1182*a^4*b^2*d^(23/2)*x^3 + 695*a^5*b*d^(23/2)*x)*x^(7/2) + (453*a^4*b^2*d^(23/2)*x^5 + 1042*a^5*b*d^(23/2)*x^3 + 621*a^6*d^(23/2)*x)*x^(3/2))/(a^3*b^8*x^6 + 3*a^4*b^7*x^4 + 3*a^5*b^6*x^2 + a^6*b^5 + (b^11*x^6 + 3*a*b^10*x^4 + 3*a^2*b^9*x^2 + a^3*b^8)*x^6 + 3*(a*b^10*x^6 + 3*a^2*b^9*x^4 + 3*a^3*b^8*x^2 + a^4*b^7)*x^4 + 3*(a^2*b^9*x^6 + 3*a^3*b^8*x^4 + 3*a^4*b^7*x^2 + a^5*b^6)*x^2)","F",0
770,0,0,0,0.000000," ","integrate((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-4 \, a d^{\frac{21}{2}} \int \frac{\sqrt{x}}{b^{6} x^{2} + a b^{5}}\,{d x} + d^{\frac{21}{2}} \int \frac{x^{\frac{5}{2}}}{b^{5} x^{2} + a b^{4}}\,{d x} + \frac{2925 \, a d^{\frac{21}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, b^{5}} + \frac{8775 \, a b^{3} d^{\frac{21}{2}} x^{\frac{15}{2}} + 29649 \, a^{2} b^{2} d^{\frac{21}{2}} x^{\frac{11}{2}} + 34285 \, a^{3} b d^{\frac{21}{2}} x^{\frac{7}{2}} + 13795 \, a^{4} d^{\frac{21}{2}} x^{\frac{3}{2}}}{3072 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}} - \frac{{\left(537 \, a^{2} b^{4} d^{\frac{21}{2}} x^{5} + 1210 \, a^{3} b^{3} d^{\frac{21}{2}} x^{3} + 705 \, a^{4} b^{2} d^{\frac{21}{2}} x\right)} x^{\frac{9}{2}} + 2 \, {\left(443 \, a^{3} b^{3} d^{\frac{21}{2}} x^{5} + 1014 \, a^{4} b^{2} d^{\frac{21}{2}} x^{3} + 603 \, a^{5} b d^{\frac{21}{2}} x\right)} x^{\frac{5}{2}} + {\left(381 \, a^{4} b^{2} d^{\frac{21}{2}} x^{5} + 882 \, a^{5} b d^{\frac{21}{2}} x^{3} + 533 \, a^{6} d^{\frac{21}{2}} x\right)} \sqrt{x}}{192 \, {\left(a^{3} b^{8} x^{6} + 3 \, a^{4} b^{7} x^{4} + 3 \, a^{5} b^{6} x^{2} + a^{6} b^{5} + {\left(b^{11} x^{6} + 3 \, a b^{10} x^{4} + 3 \, a^{2} b^{9} x^{2} + a^{3} b^{8}\right)} x^{6} + 3 \, {\left(a b^{10} x^{6} + 3 \, a^{2} b^{9} x^{4} + 3 \, a^{3} b^{8} x^{2} + a^{4} b^{7}\right)} x^{4} + 3 \, {\left(a^{2} b^{9} x^{6} + 3 \, a^{3} b^{8} x^{4} + 3 \, a^{4} b^{7} x^{2} + a^{5} b^{6}\right)} x^{2}\right)}}"," ",0,"-4*a*d^(21/2)*integrate(sqrt(x)/(b^6*x^2 + a*b^5), x) + d^(21/2)*integrate(x^(5/2)/(b^5*x^2 + a*b^4), x) + 2925/8192*a*d^(21/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^5 + 1/3072*(8775*a*b^3*d^(21/2)*x^(15/2) + 29649*a^2*b^2*d^(21/2)*x^(11/2) + 34285*a^3*b*d^(21/2)*x^(7/2) + 13795*a^4*d^(21/2)*x^(3/2))/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5) - 1/192*((537*a^2*b^4*d^(21/2)*x^5 + 1210*a^3*b^3*d^(21/2)*x^3 + 705*a^4*b^2*d^(21/2)*x)*x^(9/2) + 2*(443*a^3*b^3*d^(21/2)*x^5 + 1014*a^4*b^2*d^(21/2)*x^3 + 603*a^5*b*d^(21/2)*x)*x^(5/2) + (381*a^4*b^2*d^(21/2)*x^5 + 882*a^5*b*d^(21/2)*x^3 + 533*a^6*d^(21/2)*x)*sqrt(x))/(a^3*b^8*x^6 + 3*a^4*b^7*x^4 + 3*a^5*b^6*x^2 + a^6*b^5 + (b^11*x^6 + 3*a*b^10*x^4 + 3*a^2*b^9*x^2 + a^3*b^8)*x^6 + 3*(a*b^10*x^6 + 3*a^2*b^9*x^4 + 3*a^3*b^8*x^2 + a^4*b^7)*x^4 + 3*(a^2*b^9*x^6 + 3*a^3*b^8*x^4 + 3*a^4*b^7*x^2 + a^5*b^6)*x^2)","F",0
771,0,0,0,0.000000," ","integrate((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","d^{\frac{19}{2}} \int \frac{x^{\frac{3}{2}}}{b^{5} x^{2} + a b^{4}}\,{d x} - \frac{1267 \, {\left(\frac{2 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{a} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{1}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{1}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}\right)} d^{\frac{19}{2}}}{8192 \, b^{5}} + \frac{1853 \, a b^{3} d^{\frac{19}{2}} x^{\frac{13}{2}} + 6515 \, a^{2} b^{2} d^{\frac{19}{2}} x^{\frac{9}{2}} + 8079 \, a^{3} b d^{\frac{19}{2}} x^{\frac{5}{2}} + 3801 \, a^{4} d^{\frac{19}{2}} \sqrt{x}}{3072 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}} + \frac{{\left(317 \, a b^{4} d^{\frac{19}{2}} x^{5} + 738 \, a^{2} b^{3} d^{\frac{19}{2}} x^{3} + 453 \, a^{3} b^{2} d^{\frac{19}{2}} x\right)} x^{\frac{11}{2}} + 2 \, {\left(243 \, a^{2} b^{3} d^{\frac{19}{2}} x^{5} + 582 \, a^{3} b^{2} d^{\frac{19}{2}} x^{3} + 371 \, a^{4} b d^{\frac{19}{2}} x\right)} x^{\frac{7}{2}} + {\left(201 \, a^{3} b^{2} d^{\frac{19}{2}} x^{5} + 490 \, a^{4} b d^{\frac{19}{2}} x^{3} + 321 \, a^{5} d^{\frac{19}{2}} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{3} b^{7} x^{6} + 3 \, a^{4} b^{6} x^{4} + 3 \, a^{5} b^{5} x^{2} + a^{6} b^{4} + {\left(b^{10} x^{6} + 3 \, a b^{9} x^{4} + 3 \, a^{2} b^{8} x^{2} + a^{3} b^{7}\right)} x^{6} + 3 \, {\left(a b^{9} x^{6} + 3 \, a^{2} b^{8} x^{4} + 3 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)} x^{4} + 3 \, {\left(a^{2} b^{8} x^{6} + 3 \, a^{3} b^{7} x^{4} + 3 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} x^{2}\right)}}"," ",0,"d^(19/2)*integrate(x^(3/2)/(b^5*x^2 + a*b^4), x) - 1267/8192*(2*sqrt(2)*sqrt(a)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*sqrt(a)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(1/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(1/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))*d^(19/2)/b^5 + 1/3072*(1853*a*b^3*d^(19/2)*x^(13/2) + 6515*a^2*b^2*d^(19/2)*x^(9/2) + 8079*a^3*b*d^(19/2)*x^(5/2) + 3801*a^4*d^(19/2)*sqrt(x))/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5) + 1/192*((317*a*b^4*d^(19/2)*x^5 + 738*a^2*b^3*d^(19/2)*x^3 + 453*a^3*b^2*d^(19/2)*x)*x^(11/2) + 2*(243*a^2*b^3*d^(19/2)*x^5 + 582*a^3*b^2*d^(19/2)*x^3 + 371*a^4*b*d^(19/2)*x)*x^(7/2) + (201*a^3*b^2*d^(19/2)*x^5 + 490*a^4*b*d^(19/2)*x^3 + 321*a^5*d^(19/2)*x)*x^(3/2))/(a^3*b^7*x^6 + 3*a^4*b^6*x^4 + 3*a^5*b^5*x^2 + a^6*b^4 + (b^10*x^6 + 3*a*b^9*x^4 + 3*a^2*b^8*x^2 + a^3*b^7)*x^6 + 3*(a*b^9*x^6 + 3*a^2*b^8*x^4 + 3*a^3*b^7*x^2 + a^4*b^6)*x^4 + 3*(a^2*b^8*x^6 + 3*a^3*b^7*x^4 + 3*a^4*b^6*x^2 + a^5*b^5)*x^2)","F",0
772,0,0,0,0.000000," ","integrate((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","d^{\frac{17}{2}} \int \frac{\sqrt{x}}{b^{5} x^{2} + a b^{4}}\,{d x} - \frac{893 \, d^{\frac{17}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, b^{4}} - \frac{2679 \, b^{3} d^{\frac{17}{2}} x^{\frac{15}{2}} + 9441 \, a b^{2} d^{\frac{17}{2}} x^{\frac{11}{2}} + 11645 \, a^{2} b d^{\frac{17}{2}} x^{\frac{7}{2}} + 5267 \, a^{3} d^{\frac{17}{2}} x^{\frac{3}{2}}}{3072 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}} + \frac{{\left(261 \, a b^{4} d^{\frac{17}{2}} x^{5} + 610 \, a^{2} b^{3} d^{\frac{17}{2}} x^{3} + 381 \, a^{3} b^{2} d^{\frac{17}{2}} x\right)} x^{\frac{9}{2}} + 2 \, {\left(191 \, a^{2} b^{3} d^{\frac{17}{2}} x^{5} + 462 \, a^{3} b^{2} d^{\frac{17}{2}} x^{3} + 303 \, a^{4} b d^{\frac{17}{2}} x\right)} x^{\frac{5}{2}} + {\left(153 \, a^{3} b^{2} d^{\frac{17}{2}} x^{5} + 378 \, a^{4} b d^{\frac{17}{2}} x^{3} + 257 \, a^{5} d^{\frac{17}{2}} x\right)} \sqrt{x}}{192 \, {\left(a^{3} b^{7} x^{6} + 3 \, a^{4} b^{6} x^{4} + 3 \, a^{5} b^{5} x^{2} + a^{6} b^{4} + {\left(b^{10} x^{6} + 3 \, a b^{9} x^{4} + 3 \, a^{2} b^{8} x^{2} + a^{3} b^{7}\right)} x^{6} + 3 \, {\left(a b^{9} x^{6} + 3 \, a^{2} b^{8} x^{4} + 3 \, a^{3} b^{7} x^{2} + a^{4} b^{6}\right)} x^{4} + 3 \, {\left(a^{2} b^{8} x^{6} + 3 \, a^{3} b^{7} x^{4} + 3 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)} x^{2}\right)}}"," ",0,"d^(17/2)*integrate(sqrt(x)/(b^5*x^2 + a*b^4), x) - 893/8192*d^(17/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^4 - 1/3072*(2679*b^3*d^(17/2)*x^(15/2) + 9441*a*b^2*d^(17/2)*x^(11/2) + 11645*a^2*b*d^(17/2)*x^(7/2) + 5267*a^3*d^(17/2)*x^(3/2))/(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4) + 1/192*((261*a*b^4*d^(17/2)*x^5 + 610*a^2*b^3*d^(17/2)*x^3 + 381*a^3*b^2*d^(17/2)*x)*x^(9/2) + 2*(191*a^2*b^3*d^(17/2)*x^5 + 462*a^3*b^2*d^(17/2)*x^3 + 303*a^4*b*d^(17/2)*x)*x^(5/2) + (153*a^3*b^2*d^(17/2)*x^5 + 378*a^4*b*d^(17/2)*x^3 + 257*a^5*d^(17/2)*x)*sqrt(x))/(a^3*b^7*x^6 + 3*a^4*b^6*x^4 + 3*a^5*b^5*x^2 + a^6*b^4 + (b^10*x^6 + 3*a*b^9*x^4 + 3*a^2*b^8*x^2 + a^3*b^7)*x^6 + 3*(a*b^9*x^6 + 3*a^2*b^8*x^4 + 3*a^3*b^7*x^2 + a^4*b^6)*x^4 + 3*(a^2*b^8*x^6 + 3*a^3*b^7*x^4 + 3*a^4*b^6*x^2 + a^5*b^5)*x^2)","F",0
773,1,583,0,3.762048," ","integrate((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{195 \, d^{7} {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{8192 \, b^{4}} - \frac{15 \, b^{3} d^{\frac{15}{2}} x^{\frac{13}{2}} + 65 \, a b^{2} d^{\frac{15}{2}} x^{\frac{9}{2}} + 117 \, a^{2} b d^{\frac{15}{2}} x^{\frac{5}{2}} + 195 \, a^{3} d^{\frac{15}{2}} \sqrt{x}}{1024 \, {\left(b^{8} x^{8} + 4 \, a b^{7} x^{6} + 6 \, a^{2} b^{6} x^{4} + 4 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}} - \frac{{\left(113 \, b^{4} d^{\frac{15}{2}} x^{5} + 282 \, a b^{3} d^{\frac{15}{2}} x^{3} + 201 \, a^{2} b^{2} d^{\frac{15}{2}} x\right)} x^{\frac{11}{2}} + 2 \, {\left(63 \, a b^{3} d^{\frac{15}{2}} x^{5} + 174 \, a^{2} b^{2} d^{\frac{15}{2}} x^{3} + 143 \, a^{3} b d^{\frac{15}{2}} x\right)} x^{\frac{7}{2}} + {\left(45 \, a^{2} b^{2} d^{\frac{15}{2}} x^{5} + 130 \, a^{3} b d^{\frac{15}{2}} x^{3} + 117 \, a^{4} d^{\frac{15}{2}} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3} + {\left(b^{9} x^{6} + 3 \, a b^{8} x^{4} + 3 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)} x^{6} + 3 \, {\left(a b^{8} x^{6} + 3 \, a^{2} b^{7} x^{4} + 3 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} x^{4} + 3 \, {\left(a^{2} b^{7} x^{6} + 3 \, a^{3} b^{6} x^{4} + 3 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)} x^{2}\right)}}"," ",0,"195/8192*d^7*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^4 - 1/1024*(15*b^3*d^(15/2)*x^(13/2) + 65*a*b^2*d^(15/2)*x^(9/2) + 117*a^2*b*d^(15/2)*x^(5/2) + 195*a^3*d^(15/2)*sqrt(x))/(b^8*x^8 + 4*a*b^7*x^6 + 6*a^2*b^6*x^4 + 4*a^3*b^5*x^2 + a^4*b^4) - 1/192*((113*b^4*d^(15/2)*x^5 + 282*a*b^3*d^(15/2)*x^3 + 201*a^2*b^2*d^(15/2)*x)*x^(11/2) + 2*(63*a*b^3*d^(15/2)*x^5 + 174*a^2*b^2*d^(15/2)*x^3 + 143*a^3*b*d^(15/2)*x)*x^(7/2) + (45*a^2*b^2*d^(15/2)*x^5 + 130*a^3*b*d^(15/2)*x^3 + 117*a^4*d^(15/2)*x)*x^(3/2))/(a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3 + (b^9*x^6 + 3*a*b^8*x^4 + 3*a^2*b^7*x^2 + a^3*b^6)*x^6 + 3*(a*b^8*x^6 + 3*a^2*b^7*x^4 + 3*a^3*b^6*x^2 + a^4*b^5)*x^4 + 3*(a^2*b^7*x^6 + 3*a^3*b^6*x^4 + 3*a^4*b^5*x^2 + a^5*b^4)*x^2)","A",0
774,1,577,0,3.751885," ","integrate((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{77 \, d^{\frac{13}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, a b^{3}} + \frac{77 \, b^{3} d^{\frac{13}{2}} x^{\frac{15}{2}} + 315 \, a b^{2} d^{\frac{13}{2}} x^{\frac{11}{2}} + 495 \, a^{2} b d^{\frac{13}{2}} x^{\frac{7}{2}} + 385 \, a^{3} d^{\frac{13}{2}} x^{\frac{3}{2}}}{1024 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}} - \frac{{\left(81 \, b^{4} d^{\frac{13}{2}} x^{5} + 202 \, a b^{3} d^{\frac{13}{2}} x^{3} + 153 \, a^{2} b^{2} d^{\frac{13}{2}} x\right)} x^{\frac{9}{2}} + 2 \, {\left(35 \, a b^{3} d^{\frac{13}{2}} x^{5} + 102 \, a^{2} b^{2} d^{\frac{13}{2}} x^{3} + 99 \, a^{3} b d^{\frac{13}{2}} x\right)} x^{\frac{5}{2}} + {\left(21 \, a^{2} b^{2} d^{\frac{13}{2}} x^{5} + 66 \, a^{3} b d^{\frac{13}{2}} x^{3} + 77 \, a^{4} d^{\frac{13}{2}} x\right)} \sqrt{x}}{192 \, {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3} + {\left(b^{9} x^{6} + 3 \, a b^{8} x^{4} + 3 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)} x^{6} + 3 \, {\left(a b^{8} x^{6} + 3 \, a^{2} b^{7} x^{4} + 3 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} x^{4} + 3 \, {\left(a^{2} b^{7} x^{6} + 3 \, a^{3} b^{6} x^{4} + 3 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)} x^{2}\right)}}"," ",0,"77/8192*d^(13/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^3) + 1/1024*(77*b^3*d^(13/2)*x^(15/2) + 315*a*b^2*d^(13/2)*x^(11/2) + 495*a^2*b*d^(13/2)*x^(7/2) + 385*a^3*d^(13/2)*x^(3/2))/(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3) - 1/192*((81*b^4*d^(13/2)*x^5 + 202*a*b^3*d^(13/2)*x^3 + 153*a^2*b^2*d^(13/2)*x)*x^(9/2) + 2*(35*a*b^3*d^(13/2)*x^5 + 102*a^2*b^2*d^(13/2)*x^3 + 99*a^3*b*d^(13/2)*x)*x^(5/2) + (21*a^2*b^2*d^(13/2)*x^5 + 66*a^3*b*d^(13/2)*x^3 + 77*a^4*d^(13/2)*x)*sqrt(x))/(a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3 + (b^9*x^6 + 3*a*b^8*x^4 + 3*a^2*b^7*x^2 + a^3*b^6)*x^6 + 3*(a*b^8*x^6 + 3*a^2*b^7*x^4 + 3*a^3*b^6*x^2 + a^4*b^5)*x^4 + 3*(a^2*b^7*x^6 + 3*a^3*b^6*x^4 + 3*a^4*b^5*x^2 + a^5*b^4)*x^2)","A",0
775,1,595,0,3.709690," ","integrate((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{45 \, d^{5} {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{8192 \, a b^{3}} - \frac{35 \, b^{3} d^{\frac{11}{2}} x^{\frac{13}{2}} + 173 \, a b^{2} d^{\frac{11}{2}} x^{\frac{9}{2}} + 657 \, a^{2} b d^{\frac{11}{2}} x^{\frac{5}{2}} + 135 \, a^{3} d^{\frac{11}{2}} \sqrt{x}}{3072 \, {\left(a b^{7} x^{8} + 4 \, a^{2} b^{6} x^{6} + 6 \, a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{2} + a^{5} b^{3}\right)}} + \frac{{\left(5 \, b^{4} d^{\frac{11}{2}} x^{5} + 18 \, a b^{3} d^{\frac{11}{2}} x^{3} + 45 \, a^{2} b^{2} d^{\frac{11}{2}} x\right)} x^{\frac{11}{2}} - 2 \, {\left(21 \, a b^{3} d^{\frac{11}{2}} x^{5} + 42 \, a^{2} b^{2} d^{\frac{11}{2}} x^{3} - 11 \, a^{3} b d^{\frac{11}{2}} x\right)} x^{\frac{7}{2}} - {\left(15 \, a^{2} b^{2} d^{\frac{11}{2}} x^{5} + 38 \, a^{3} b d^{\frac{11}{2}} x^{3} - 9 \, a^{4} d^{\frac{11}{2}} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{4} b^{5} x^{6} + 3 \, a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{2} + a^{7} b^{2} + {\left(a b^{8} x^{6} + 3 \, a^{2} b^{7} x^{4} + 3 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} x^{6} + 3 \, {\left(a^{2} b^{7} x^{6} + 3 \, a^{3} b^{6} x^{4} + 3 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)} x^{4} + 3 \, {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)} x^{2}\right)}}"," ",0,"45/8192*d^5*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^3) - 1/3072*(35*b^3*d^(11/2)*x^(13/2) + 173*a*b^2*d^(11/2)*x^(9/2) + 657*a^2*b*d^(11/2)*x^(5/2) + 135*a^3*d^(11/2)*sqrt(x))/(a*b^7*x^8 + 4*a^2*b^6*x^6 + 6*a^3*b^5*x^4 + 4*a^4*b^4*x^2 + a^5*b^3) + 1/192*((5*b^4*d^(11/2)*x^5 + 18*a*b^3*d^(11/2)*x^3 + 45*a^2*b^2*d^(11/2)*x)*x^(11/2) - 2*(21*a*b^3*d^(11/2)*x^5 + 42*a^2*b^2*d^(11/2)*x^3 - 11*a^3*b*d^(11/2)*x)*x^(7/2) - (15*a^2*b^2*d^(11/2)*x^5 + 38*a^3*b*d^(11/2)*x^3 - 9*a^4*d^(11/2)*x)*x^(3/2))/(a^4*b^5*x^6 + 3*a^5*b^4*x^4 + 3*a^6*b^3*x^2 + a^7*b^2 + (a*b^8*x^6 + 3*a^2*b^7*x^4 + 3*a^3*b^6*x^2 + a^4*b^5)*x^6 + 3*(a^2*b^7*x^6 + 3*a^3*b^6*x^4 + 3*a^4*b^5*x^2 + a^5*b^4)*x^4 + 3*(a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3)*x^2)","A",0
776,1,584,0,3.687512," ","integrate((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{35 \, d^{\frac{9}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, a^{2} b^{2}} + \frac{105 \, b^{3} d^{\frac{9}{2}} x^{\frac{15}{2}} + 447 \, a b^{2} d^{\frac{9}{2}} x^{\frac{11}{2}} + 803 \, a^{2} b d^{\frac{9}{2}} x^{\frac{7}{2}} + 77 \, a^{3} d^{\frac{9}{2}} x^{\frac{3}{2}}}{3072 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)}} - \frac{{\left(3 \, b^{4} d^{\frac{9}{2}} x^{5} + 14 \, a b^{3} d^{\frac{9}{2}} x^{3} - 21 \, a^{2} b^{2} d^{\frac{9}{2}} x\right)} x^{\frac{9}{2}} + 2 \, {\left(25 \, a b^{3} d^{\frac{9}{2}} x^{5} + 66 \, a^{2} b^{2} d^{\frac{9}{2}} x^{3} + 9 \, a^{3} b d^{\frac{9}{2}} x\right)} x^{\frac{5}{2}} + {\left(15 \, a^{2} b^{2} d^{\frac{9}{2}} x^{5} + 54 \, a^{3} b d^{\frac{9}{2}} x^{3} + 7 \, a^{4} d^{\frac{9}{2}} x\right)} \sqrt{x}}{192 \, {\left(a^{4} b^{5} x^{6} + 3 \, a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{2} + a^{7} b^{2} + {\left(a b^{8} x^{6} + 3 \, a^{2} b^{7} x^{4} + 3 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)} x^{6} + 3 \, {\left(a^{2} b^{7} x^{6} + 3 \, a^{3} b^{6} x^{4} + 3 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)} x^{4} + 3 \, {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)} x^{2}\right)}}"," ",0,"35/8192*d^(9/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^2*b^2) + 1/3072*(105*b^3*d^(9/2)*x^(15/2) + 447*a*b^2*d^(9/2)*x^(11/2) + 803*a^2*b*d^(9/2)*x^(7/2) + 77*a^3*d^(9/2)*x^(3/2))/(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2) - 1/192*((3*b^4*d^(9/2)*x^5 + 14*a*b^3*d^(9/2)*x^3 - 21*a^2*b^2*d^(9/2)*x)*x^(9/2) + 2*(25*a*b^3*d^(9/2)*x^5 + 66*a^2*b^2*d^(9/2)*x^3 + 9*a^3*b*d^(9/2)*x)*x^(5/2) + (15*a^2*b^2*d^(9/2)*x^5 + 54*a^3*b*d^(9/2)*x^3 + 7*a^4*d^(9/2)*x)*sqrt(x))/(a^4*b^5*x^6 + 3*a^5*b^4*x^4 + 3*a^6*b^3*x^2 + a^7*b^2 + (a*b^8*x^6 + 3*a^2*b^7*x^4 + 3*a^3*b^6*x^2 + a^4*b^5)*x^6 + 3*(a^2*b^7*x^6 + 3*a^3*b^6*x^4 + 3*a^4*b^5*x^2 + a^5*b^4)*x^4 + 3*(a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3)*x^2)","A",0
777,1,597,0,3.810887," ","integrate((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{77 \, b^{3} d^{\frac{7}{2}} x^{\frac{13}{2}} + 803 \, a b^{2} d^{\frac{7}{2}} x^{\frac{9}{2}} + 447 \, a^{2} b d^{\frac{7}{2}} x^{\frac{5}{2}} + 105 \, a^{3} d^{\frac{7}{2}} \sqrt{x}}{3072 \, {\left(a^{2} b^{6} x^{8} + 4 \, a^{3} b^{5} x^{6} + 6 \, a^{4} b^{4} x^{4} + 4 \, a^{5} b^{3} x^{2} + a^{6} b^{2}\right)}} + \frac{{\left(7 \, b^{4} d^{\frac{7}{2}} x^{5} + 54 \, a b^{3} d^{\frac{7}{2}} x^{3} + 15 \, a^{2} b^{2} d^{\frac{7}{2}} x\right)} x^{\frac{11}{2}} + 2 \, {\left(9 \, a b^{3} d^{\frac{7}{2}} x^{5} + 66 \, a^{2} b^{2} d^{\frac{7}{2}} x^{3} + 25 \, a^{3} b d^{\frac{7}{2}} x\right)} x^{\frac{7}{2}} - {\left(21 \, a^{2} b^{2} d^{\frac{7}{2}} x^{5} - 14 \, a^{3} b d^{\frac{7}{2}} x^{3} - 3 \, a^{4} d^{\frac{7}{2}} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{5} b^{4} x^{6} + 3 \, a^{6} b^{3} x^{4} + 3 \, a^{7} b^{2} x^{2} + a^{8} b + {\left(a^{2} b^{7} x^{6} + 3 \, a^{3} b^{6} x^{4} + 3 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)} x^{6} + 3 \, {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)} x^{4} + 3 \, {\left(a^{4} b^{5} x^{6} + 3 \, a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{2} + a^{7} b^{2}\right)} x^{2}\right)}} + \frac{35 \, d^{3} {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{8192 \, a^{2} b^{2}}"," ",0,"-1/3072*(77*b^3*d^(7/2)*x^(13/2) + 803*a*b^2*d^(7/2)*x^(9/2) + 447*a^2*b*d^(7/2)*x^(5/2) + 105*a^3*d^(7/2)*sqrt(x))/(a^2*b^6*x^8 + 4*a^3*b^5*x^6 + 6*a^4*b^4*x^4 + 4*a^5*b^3*x^2 + a^6*b^2) + 1/192*((7*b^4*d^(7/2)*x^5 + 54*a*b^3*d^(7/2)*x^3 + 15*a^2*b^2*d^(7/2)*x)*x^(11/2) + 2*(9*a*b^3*d^(7/2)*x^5 + 66*a^2*b^2*d^(7/2)*x^3 + 25*a^3*b*d^(7/2)*x)*x^(7/2) - (21*a^2*b^2*d^(7/2)*x^5 - 14*a^3*b*d^(7/2)*x^3 - 3*a^4*d^(7/2)*x)*x^(3/2))/(a^5*b^4*x^6 + 3*a^6*b^3*x^4 + 3*a^7*b^2*x^2 + a^8*b + (a^2*b^7*x^6 + 3*a^3*b^6*x^4 + 3*a^4*b^5*x^2 + a^5*b^4)*x^6 + 3*(a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3)*x^4 + 3*(a^4*b^5*x^6 + 3*a^5*b^4*x^4 + 3*a^6*b^3*x^2 + a^7*b^2)*x^2) + 35/8192*d^3*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^2*b^2)","A",0
778,1,582,0,3.707906," ","integrate((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{135 \, b^{3} d^{\frac{5}{2}} x^{\frac{15}{2}} + 657 \, a b^{2} d^{\frac{5}{2}} x^{\frac{11}{2}} + 173 \, a^{2} b d^{\frac{5}{2}} x^{\frac{7}{2}} + 35 \, a^{3} d^{\frac{5}{2}} x^{\frac{3}{2}}}{3072 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)}} - \frac{{\left(9 \, b^{4} d^{\frac{5}{2}} x^{5} - 38 \, a b^{3} d^{\frac{5}{2}} x^{3} - 15 \, a^{2} b^{2} d^{\frac{5}{2}} x\right)} x^{\frac{9}{2}} + 2 \, {\left(11 \, a b^{3} d^{\frac{5}{2}} x^{5} - 42 \, a^{2} b^{2} d^{\frac{5}{2}} x^{3} - 21 \, a^{3} b d^{\frac{5}{2}} x\right)} x^{\frac{5}{2}} + {\left(45 \, a^{2} b^{2} d^{\frac{5}{2}} x^{5} + 18 \, a^{3} b d^{\frac{5}{2}} x^{3} + 5 \, a^{4} d^{\frac{5}{2}} x\right)} \sqrt{x}}{192 \, {\left(a^{5} b^{4} x^{6} + 3 \, a^{6} b^{3} x^{4} + 3 \, a^{7} b^{2} x^{2} + a^{8} b + {\left(a^{2} b^{7} x^{6} + 3 \, a^{3} b^{6} x^{4} + 3 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)} x^{6} + 3 \, {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)} x^{4} + 3 \, {\left(a^{4} b^{5} x^{6} + 3 \, a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{2} + a^{7} b^{2}\right)} x^{2}\right)}} + \frac{45 \, d^{\frac{5}{2}} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, a^{3} b}"," ",0,"1/3072*(135*b^3*d^(5/2)*x^(15/2) + 657*a*b^2*d^(5/2)*x^(11/2) + 173*a^2*b*d^(5/2)*x^(7/2) + 35*a^3*d^(5/2)*x^(3/2))/(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b) - 1/192*((9*b^4*d^(5/2)*x^5 - 38*a*b^3*d^(5/2)*x^3 - 15*a^2*b^2*d^(5/2)*x)*x^(9/2) + 2*(11*a*b^3*d^(5/2)*x^5 - 42*a^2*b^2*d^(5/2)*x^3 - 21*a^3*b*d^(5/2)*x)*x^(5/2) + (45*a^2*b^2*d^(5/2)*x^5 + 18*a^3*b*d^(5/2)*x^3 + 5*a^4*d^(5/2)*x)*sqrt(x))/(a^5*b^4*x^6 + 3*a^6*b^3*x^4 + 3*a^7*b^2*x^2 + a^8*b + (a^2*b^7*x^6 + 3*a^3*b^6*x^4 + 3*a^4*b^5*x^2 + a^5*b^4)*x^6 + 3*(a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3)*x^4 + 3*(a^4*b^5*x^6 + 3*a^5*b^4*x^4 + 3*a^6*b^3*x^2 + a^7*b^2)*x^2) + 45/8192*d^(5/2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^3*b)","A",0
779,1,586,0,3.638021," ","integrate((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{385 \, b^{3} d^{\frac{3}{2}} x^{\frac{13}{2}} + 495 \, a b^{2} d^{\frac{3}{2}} x^{\frac{9}{2}} + 315 \, a^{2} b d^{\frac{3}{2}} x^{\frac{5}{2}} + 77 \, a^{3} d^{\frac{3}{2}} \sqrt{x}}{1024 \, {\left(a^{3} b^{5} x^{8} + 4 \, a^{4} b^{4} x^{6} + 6 \, a^{5} b^{3} x^{4} + 4 \, a^{6} b^{2} x^{2} + a^{7} b\right)}} + \frac{{\left(77 \, b^{4} d^{\frac{3}{2}} x^{5} + 66 \, a b^{3} d^{\frac{3}{2}} x^{3} + 21 \, a^{2} b^{2} d^{\frac{3}{2}} x\right)} x^{\frac{11}{2}} + 2 \, {\left(99 \, a b^{3} d^{\frac{3}{2}} x^{5} + 102 \, a^{2} b^{2} d^{\frac{3}{2}} x^{3} + 35 \, a^{3} b d^{\frac{3}{2}} x\right)} x^{\frac{7}{2}} + {\left(153 \, a^{2} b^{2} d^{\frac{3}{2}} x^{5} + 202 \, a^{3} b d^{\frac{3}{2}} x^{3} + 81 \, a^{4} d^{\frac{3}{2}} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{6} b^{3} x^{6} + 3 \, a^{7} b^{2} x^{4} + 3 \, a^{8} b x^{2} + a^{9} + {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)} x^{6} + 3 \, {\left(a^{4} b^{5} x^{6} + 3 \, a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{2} + a^{7} b^{2}\right)} x^{4} + 3 \, {\left(a^{5} b^{4} x^{6} + 3 \, a^{6} b^{3} x^{4} + 3 \, a^{7} b^{2} x^{2} + a^{8} b\right)} x^{2}\right)}} + \frac{77 \, d {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{8192 \, a^{3} b}"," ",0,"-1/1024*(385*b^3*d^(3/2)*x^(13/2) + 495*a*b^2*d^(3/2)*x^(9/2) + 315*a^2*b*d^(3/2)*x^(5/2) + 77*a^3*d^(3/2)*sqrt(x))/(a^3*b^5*x^8 + 4*a^4*b^4*x^6 + 6*a^5*b^3*x^4 + 4*a^6*b^2*x^2 + a^7*b) + 1/192*((77*b^4*d^(3/2)*x^5 + 66*a*b^3*d^(3/2)*x^3 + 21*a^2*b^2*d^(3/2)*x)*x^(11/2) + 2*(99*a*b^3*d^(3/2)*x^5 + 102*a^2*b^2*d^(3/2)*x^3 + 35*a^3*b*d^(3/2)*x)*x^(7/2) + (153*a^2*b^2*d^(3/2)*x^5 + 202*a^3*b*d^(3/2)*x^3 + 81*a^4*d^(3/2)*x)*x^(3/2))/(a^6*b^3*x^6 + 3*a^7*b^2*x^4 + 3*a^8*b*x^2 + a^9 + (a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3)*x^6 + 3*(a^4*b^5*x^6 + 3*a^5*b^4*x^4 + 3*a^6*b^3*x^2 + a^7*b^2)*x^4 + 3*(a^5*b^4*x^6 + 3*a^6*b^3*x^4 + 3*a^7*b^2*x^2 + a^8*b)*x^2) + 77/8192*d*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^3*b)","A",0
780,1,569,0,3.788902," ","integrate((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{195 \, b^{3} \sqrt{d} x^{\frac{15}{2}} + 117 \, a b^{2} \sqrt{d} x^{\frac{11}{2}} + 65 \, a^{2} b \sqrt{d} x^{\frac{7}{2}} + 15 \, a^{3} \sqrt{d} x^{\frac{3}{2}}}{1024 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)}} + \frac{{\left(117 \, b^{4} \sqrt{d} x^{5} + 130 \, a b^{3} \sqrt{d} x^{3} + 45 \, a^{2} b^{2} \sqrt{d} x\right)} x^{\frac{9}{2}} + 2 \, {\left(143 \, a b^{3} \sqrt{d} x^{5} + 174 \, a^{2} b^{2} \sqrt{d} x^{3} + 63 \, a^{3} b \sqrt{d} x\right)} x^{\frac{5}{2}} + {\left(201 \, a^{2} b^{2} \sqrt{d} x^{5} + 282 \, a^{3} b \sqrt{d} x^{3} + 113 \, a^{4} \sqrt{d} x\right)} \sqrt{x}}{192 \, {\left(a^{6} b^{3} x^{6} + 3 \, a^{7} b^{2} x^{4} + 3 \, a^{8} b x^{2} + a^{9} + {\left(a^{3} b^{6} x^{6} + 3 \, a^{4} b^{5} x^{4} + 3 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)} x^{6} + 3 \, {\left(a^{4} b^{5} x^{6} + 3 \, a^{5} b^{4} x^{4} + 3 \, a^{6} b^{3} x^{2} + a^{7} b^{2}\right)} x^{4} + 3 \, {\left(a^{5} b^{4} x^{6} + 3 \, a^{6} b^{3} x^{4} + 3 \, a^{7} b^{2} x^{2} + a^{8} b\right)} x^{2}\right)}} + \frac{195 \, \sqrt{d} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, a^{4}}"," ",0,"1/1024*(195*b^3*sqrt(d)*x^(15/2) + 117*a*b^2*sqrt(d)*x^(11/2) + 65*a^2*b*sqrt(d)*x^(7/2) + 15*a^3*sqrt(d)*x^(3/2))/(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8) + 1/192*((117*b^4*sqrt(d)*x^5 + 130*a*b^3*sqrt(d)*x^3 + 45*a^2*b^2*sqrt(d)*x)*x^(9/2) + 2*(143*a*b^3*sqrt(d)*x^5 + 174*a^2*b^2*sqrt(d)*x^3 + 63*a^3*b*sqrt(d)*x)*x^(5/2) + (201*a^2*b^2*sqrt(d)*x^5 + 282*a^3*b*sqrt(d)*x^3 + 113*a^4*sqrt(d)*x)*sqrt(x))/(a^6*b^3*x^6 + 3*a^7*b^2*x^4 + 3*a^8*b*x^2 + a^9 + (a^3*b^6*x^6 + 3*a^4*b^5*x^4 + 3*a^5*b^4*x^2 + a^6*b^3)*x^6 + 3*(a^4*b^5*x^6 + 3*a^5*b^4*x^4 + 3*a^6*b^3*x^2 + a^7*b^2)*x^4 + 3*(a^5*b^4*x^6 + 3*a^6*b^3*x^4 + 3*a^7*b^2*x^2 + a^8*b)*x^2) + 195/8192*sqrt(d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^4","A",0
781,0,0,0,0.000000," ","integrate(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{5267 \, b^{3} x^{\frac{13}{2}} + 11645 \, a b^{2} x^{\frac{9}{2}} + 9441 \, a^{2} b x^{\frac{5}{2}} + 2679 \, a^{3} \sqrt{x}}{3072 \, {\left(a^{4} b^{4} \sqrt{d} x^{8} + 4 \, a^{5} b^{3} \sqrt{d} x^{6} + 6 \, a^{6} b^{2} \sqrt{d} x^{4} + 4 \, a^{7} b \sqrt{d} x^{2} + a^{8} \sqrt{d}\right)}} - \frac{{\left(257 \, b^{5} \sqrt{d} x^{5} + 378 \, a b^{4} \sqrt{d} x^{3} + 153 \, a^{2} b^{3} \sqrt{d} x\right)} x^{\frac{11}{2}} + 2 \, {\left(303 \, a b^{4} \sqrt{d} x^{5} + 462 \, a^{2} b^{3} \sqrt{d} x^{3} + 191 \, a^{3} b^{2} \sqrt{d} x\right)} x^{\frac{7}{2}} + {\left(381 \, a^{2} b^{3} \sqrt{d} x^{5} + 610 \, a^{3} b^{2} \sqrt{d} x^{3} + 261 \, a^{4} b \sqrt{d} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{7} b^{3} d x^{6} + 3 \, a^{8} b^{2} d x^{4} + 3 \, a^{9} b d x^{2} + a^{10} d + {\left(a^{4} b^{6} d x^{6} + 3 \, a^{5} b^{5} d x^{4} + 3 \, a^{6} b^{4} d x^{2} + a^{7} b^{3} d\right)} x^{6} + 3 \, {\left(a^{5} b^{5} d x^{6} + 3 \, a^{6} b^{4} d x^{4} + 3 \, a^{7} b^{3} d x^{2} + a^{8} b^{2} d\right)} x^{4} + 3 \, {\left(a^{6} b^{4} d x^{6} + 3 \, a^{7} b^{3} d x^{4} + 3 \, a^{8} b^{2} d x^{2} + a^{9} b d\right)} x^{2}\right)}} - \frac{893 \, {\left(\frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{8192 \, a^{4} d} + \int \frac{1}{{\left(a^{4} b \sqrt{d} x^{2} + a^{5} \sqrt{d}\right)} \sqrt{x}}\,{d x}"," ",0,"1/3072*(5267*b^3*x^(13/2) + 11645*a*b^2*x^(9/2) + 9441*a^2*b*x^(5/2) + 2679*a^3*sqrt(x))/(a^4*b^4*sqrt(d)*x^8 + 4*a^5*b^3*sqrt(d)*x^6 + 6*a^6*b^2*sqrt(d)*x^4 + 4*a^7*b*sqrt(d)*x^2 + a^8*sqrt(d)) - 1/192*((257*b^5*sqrt(d)*x^5 + 378*a*b^4*sqrt(d)*x^3 + 153*a^2*b^3*sqrt(d)*x)*x^(11/2) + 2*(303*a*b^4*sqrt(d)*x^5 + 462*a^2*b^3*sqrt(d)*x^3 + 191*a^3*b^2*sqrt(d)*x)*x^(7/2) + (381*a^2*b^3*sqrt(d)*x^5 + 610*a^3*b^2*sqrt(d)*x^3 + 261*a^4*b*sqrt(d)*x)*x^(3/2))/(a^7*b^3*d*x^6 + 3*a^8*b^2*d*x^4 + 3*a^9*b*d*x^2 + a^10*d + (a^4*b^6*d*x^6 + 3*a^5*b^5*d*x^4 + 3*a^6*b^4*d*x^2 + a^7*b^3*d)*x^6 + 3*(a^5*b^5*d*x^6 + 3*a^6*b^4*d*x^4 + 3*a^7*b^3*d*x^2 + a^8*b^2*d)*x^4 + 3*(a^6*b^4*d*x^6 + 3*a^7*b^3*d*x^4 + 3*a^8*b^2*d*x^2 + a^9*b*d)*x^2) - 893/8192*(2*sqrt(2)*sqrt(d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*sqrt(d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*sqrt(d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*sqrt(d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^4*d) + integrate(1/((a^4*b*sqrt(d)*x^2 + a^5*sqrt(d))*sqrt(x)), x)","F",0
782,0,0,0,0.000000," ","integrate(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-\frac{3801 \, b^{4} x^{\frac{15}{2}} + 8079 \, a b^{3} x^{\frac{11}{2}} + 6515 \, a^{2} b^{2} x^{\frac{7}{2}} + 1853 \, a^{3} b x^{\frac{3}{2}}}{3072 \, {\left(a^{5} b^{4} d^{\frac{3}{2}} x^{8} + 4 \, a^{6} b^{3} d^{\frac{3}{2}} x^{6} + 6 \, a^{7} b^{2} d^{\frac{3}{2}} x^{4} + 4 \, a^{8} b d^{\frac{3}{2}} x^{2} + a^{9} d^{\frac{3}{2}}\right)}} - \frac{{\left(321 \, b^{5} \sqrt{d} x^{5} + 490 \, a b^{4} \sqrt{d} x^{3} + 201 \, a^{2} b^{3} \sqrt{d} x\right)} x^{\frac{9}{2}} + 2 \, {\left(371 \, a b^{4} \sqrt{d} x^{5} + 582 \, a^{2} b^{3} \sqrt{d} x^{3} + 243 \, a^{3} b^{2} \sqrt{d} x\right)} x^{\frac{5}{2}} + {\left(453 \, a^{2} b^{3} \sqrt{d} x^{5} + 738 \, a^{3} b^{2} \sqrt{d} x^{3} + 317 \, a^{4} b \sqrt{d} x\right)} \sqrt{x}}{192 \, {\left(a^{7} b^{3} d^{2} x^{6} + 3 \, a^{8} b^{2} d^{2} x^{4} + 3 \, a^{9} b d^{2} x^{2} + a^{10} d^{2} + {\left(a^{4} b^{6} d^{2} x^{6} + 3 \, a^{5} b^{5} d^{2} x^{4} + 3 \, a^{6} b^{4} d^{2} x^{2} + a^{7} b^{3} d^{2}\right)} x^{6} + 3 \, {\left(a^{5} b^{5} d^{2} x^{6} + 3 \, a^{6} b^{4} d^{2} x^{4} + 3 \, a^{7} b^{3} d^{2} x^{2} + a^{8} b^{2} d^{2}\right)} x^{4} + 3 \, {\left(a^{6} b^{4} d^{2} x^{6} + 3 \, a^{7} b^{3} d^{2} x^{4} + 3 \, a^{8} b^{2} d^{2} x^{2} + a^{9} b d^{2}\right)} x^{2}\right)}} - \frac{1267 \, b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, a^{5} d^{\frac{3}{2}}} + \int \frac{1}{{\left(a^{4} b d^{\frac{3}{2}} x^{2} + a^{5} d^{\frac{3}{2}}\right)} x^{\frac{3}{2}}}\,{d x}"," ",0,"-1/3072*(3801*b^4*x^(15/2) + 8079*a*b^3*x^(11/2) + 6515*a^2*b^2*x^(7/2) + 1853*a^3*b*x^(3/2))/(a^5*b^4*d^(3/2)*x^8 + 4*a^6*b^3*d^(3/2)*x^6 + 6*a^7*b^2*d^(3/2)*x^4 + 4*a^8*b*d^(3/2)*x^2 + a^9*d^(3/2)) - 1/192*((321*b^5*sqrt(d)*x^5 + 490*a*b^4*sqrt(d)*x^3 + 201*a^2*b^3*sqrt(d)*x)*x^(9/2) + 2*(371*a*b^4*sqrt(d)*x^5 + 582*a^2*b^3*sqrt(d)*x^3 + 243*a^3*b^2*sqrt(d)*x)*x^(5/2) + (453*a^2*b^3*sqrt(d)*x^5 + 738*a^3*b^2*sqrt(d)*x^3 + 317*a^4*b*sqrt(d)*x)*sqrt(x))/(a^7*b^3*d^2*x^6 + 3*a^8*b^2*d^2*x^4 + 3*a^9*b*d^2*x^2 + a^10*d^2 + (a^4*b^6*d^2*x^6 + 3*a^5*b^5*d^2*x^4 + 3*a^6*b^4*d^2*x^2 + a^7*b^3*d^2)*x^6 + 3*(a^5*b^5*d^2*x^6 + 3*a^6*b^4*d^2*x^4 + 3*a^7*b^3*d^2*x^2 + a^8*b^2*d^2)*x^4 + 3*(a^6*b^4*d^2*x^6 + 3*a^7*b^3*d^2*x^4 + 3*a^8*b^2*d^2*x^2 + a^9*b*d^2)*x^2) - 1267/8192*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^5*d^(3/2)) + integrate(1/((a^4*b*d^(3/2)*x^2 + a^5*d^(3/2))*x^(3/2)), x)","F",0
783,0,0,0,0.000000," ","integrate(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-4 \, b \int \frac{1}{{\left(a^{5} b d^{\frac{5}{2}} x^{2} + a^{6} d^{\frac{5}{2}}\right)} \sqrt{x}}\,{d x} - \frac{13795 \, b^{4} x^{\frac{13}{2}} + 34285 \, a b^{3} x^{\frac{9}{2}} + 29649 \, a^{2} b^{2} x^{\frac{5}{2}} + 8775 \, a^{3} b \sqrt{x}}{3072 \, {\left(a^{5} b^{4} d^{\frac{5}{2}} x^{8} + 4 \, a^{6} b^{3} d^{\frac{5}{2}} x^{6} + 6 \, a^{7} b^{2} d^{\frac{5}{2}} x^{4} + 4 \, a^{8} b d^{\frac{5}{2}} x^{2} + a^{9} d^{\frac{5}{2}}\right)}} + \frac{{\left(533 \, b^{6} x^{5} + 882 \, a b^{5} x^{3} + 381 \, a^{2} b^{4} x\right)} x^{\frac{11}{2}} + 2 \, {\left(603 \, a b^{5} x^{5} + 1014 \, a^{2} b^{4} x^{3} + 443 \, a^{3} b^{3} x\right)} x^{\frac{7}{2}} + {\left(705 \, a^{2} b^{4} x^{5} + 1210 \, a^{3} b^{3} x^{3} + 537 \, a^{4} b^{2} x\right)} x^{\frac{3}{2}}}{192 \, {\left(a^{8} b^{3} d^{\frac{5}{2}} x^{6} + 3 \, a^{9} b^{2} d^{\frac{5}{2}} x^{4} + 3 \, a^{10} b d^{\frac{5}{2}} x^{2} + a^{11} d^{\frac{5}{2}} + {\left(a^{5} b^{6} d^{\frac{5}{2}} x^{6} + 3 \, a^{6} b^{5} d^{\frac{5}{2}} x^{4} + 3 \, a^{7} b^{4} d^{\frac{5}{2}} x^{2} + a^{8} b^{3} d^{\frac{5}{2}}\right)} x^{6} + 3 \, {\left(a^{6} b^{5} d^{\frac{5}{2}} x^{6} + 3 \, a^{7} b^{4} d^{\frac{5}{2}} x^{4} + 3 \, a^{8} b^{3} d^{\frac{5}{2}} x^{2} + a^{9} b^{2} d^{\frac{5}{2}}\right)} x^{4} + 3 \, {\left(a^{7} b^{4} d^{\frac{5}{2}} x^{6} + 3 \, a^{8} b^{3} d^{\frac{5}{2}} x^{4} + 3 \, a^{9} b^{2} d^{\frac{5}{2}} x^{2} + a^{10} b d^{\frac{5}{2}}\right)} x^{2}\right)}} + \frac{2925 \, {\left(\frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}\right)}}{8192 \, a^{5} d^{\frac{5}{2}}} + \int \frac{1}{{\left(a^{4} b d^{\frac{5}{2}} x^{2} + a^{5} d^{\frac{5}{2}}\right)} x^{\frac{5}{2}}}\,{d x}"," ",0,"-4*b*integrate(1/((a^5*b*d^(5/2)*x^2 + a^6*d^(5/2))*sqrt(x)), x) - 1/3072*(13795*b^4*x^(13/2) + 34285*a*b^3*x^(9/2) + 29649*a^2*b^2*x^(5/2) + 8775*a^3*b*sqrt(x))/(a^5*b^4*d^(5/2)*x^8 + 4*a^6*b^3*d^(5/2)*x^6 + 6*a^7*b^2*d^(5/2)*x^4 + 4*a^8*b*d^(5/2)*x^2 + a^9*d^(5/2)) + 1/192*((533*b^6*x^5 + 882*a*b^5*x^3 + 381*a^2*b^4*x)*x^(11/2) + 2*(603*a*b^5*x^5 + 1014*a^2*b^4*x^3 + 443*a^3*b^3*x)*x^(7/2) + (705*a^2*b^4*x^5 + 1210*a^3*b^3*x^3 + 537*a^4*b^2*x)*x^(3/2))/(a^8*b^3*d^(5/2)*x^6 + 3*a^9*b^2*d^(5/2)*x^4 + 3*a^10*b*d^(5/2)*x^2 + a^11*d^(5/2) + (a^5*b^6*d^(5/2)*x^6 + 3*a^6*b^5*d^(5/2)*x^4 + 3*a^7*b^4*d^(5/2)*x^2 + a^8*b^3*d^(5/2))*x^6 + 3*(a^6*b^5*d^(5/2)*x^6 + 3*a^7*b^4*d^(5/2)*x^4 + 3*a^8*b^3*d^(5/2)*x^2 + a^9*b^2*d^(5/2))*x^4 + 3*(a^7*b^4*d^(5/2)*x^6 + 3*a^8*b^3*d^(5/2)*x^4 + 3*a^9*b^2*d^(5/2)*x^2 + a^10*b*d^(5/2))*x^2) + 2925/8192*(2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(3/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(3/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(a^5*d^(5/2)) + integrate(1/((a^4*b*d^(5/2)*x^2 + a^5*d^(5/2))*x^(5/2)), x)","F",0
784,0,0,0,0.000000," ","integrate(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","-4 \, b \int \frac{1}{{\left(a^{5} b d^{\frac{7}{2}} x^{2} + a^{6} d^{\frac{7}{2}}\right)} x^{\frac{3}{2}}}\,{d x} + \frac{11049 \, b^{5} x^{\frac{15}{2}} + 27135 \, a b^{4} x^{\frac{11}{2}} + 23395 \, a^{2} b^{3} x^{\frac{7}{2}} + 6925 \, a^{3} b^{2} x^{\frac{3}{2}}}{3072 \, {\left(a^{6} b^{4} d^{\frac{7}{2}} x^{8} + 4 \, a^{7} b^{3} d^{\frac{7}{2}} x^{6} + 6 \, a^{8} b^{2} d^{\frac{7}{2}} x^{4} + 4 \, a^{9} b d^{\frac{7}{2}} x^{2} + a^{10} d^{\frac{7}{2}}\right)}} + \frac{{\left(621 \, b^{6} x^{5} + 1042 \, a b^{5} x^{3} + 453 \, a^{2} b^{4} x\right)} x^{\frac{9}{2}} + 2 \, {\left(695 \, a b^{5} x^{5} + 1182 \, a^{2} b^{4} x^{3} + 519 \, a^{3} b^{3} x\right)} x^{\frac{5}{2}} + {\left(801 \, a^{2} b^{4} x^{5} + 1386 \, a^{3} b^{3} x^{3} + 617 \, a^{4} b^{2} x\right)} \sqrt{x}}{192 \, {\left(a^{8} b^{3} d^{\frac{7}{2}} x^{6} + 3 \, a^{9} b^{2} d^{\frac{7}{2}} x^{4} + 3 \, a^{10} b d^{\frac{7}{2}} x^{2} + a^{11} d^{\frac{7}{2}} + {\left(a^{5} b^{6} d^{\frac{7}{2}} x^{6} + 3 \, a^{6} b^{5} d^{\frac{7}{2}} x^{4} + 3 \, a^{7} b^{4} d^{\frac{7}{2}} x^{2} + a^{8} b^{3} d^{\frac{7}{2}}\right)} x^{6} + 3 \, {\left(a^{6} b^{5} d^{\frac{7}{2}} x^{6} + 3 \, a^{7} b^{4} d^{\frac{7}{2}} x^{4} + 3 \, a^{8} b^{3} d^{\frac{7}{2}} x^{2} + a^{9} b^{2} d^{\frac{7}{2}}\right)} x^{4} + 3 \, {\left(a^{7} b^{4} d^{\frac{7}{2}} x^{6} + 3 \, a^{8} b^{3} d^{\frac{7}{2}} x^{4} + 3 \, a^{9} b^{2} d^{\frac{7}{2}} x^{2} + a^{10} b d^{\frac{7}{2}}\right)} x^{2}\right)}} + \frac{3683 \, b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{8192 \, a^{6} d^{\frac{7}{2}}} + \int \frac{1}{{\left(a^{4} b d^{\frac{7}{2}} x^{2} + a^{5} d^{\frac{7}{2}}\right)} x^{\frac{7}{2}}}\,{d x}"," ",0,"-4*b*integrate(1/((a^5*b*d^(7/2)*x^2 + a^6*d^(7/2))*x^(3/2)), x) + 1/3072*(11049*b^5*x^(15/2) + 27135*a*b^4*x^(11/2) + 23395*a^2*b^3*x^(7/2) + 6925*a^3*b^2*x^(3/2))/(a^6*b^4*d^(7/2)*x^8 + 4*a^7*b^3*d^(7/2)*x^6 + 6*a^8*b^2*d^(7/2)*x^4 + 4*a^9*b*d^(7/2)*x^2 + a^10*d^(7/2)) + 1/192*((621*b^6*x^5 + 1042*a*b^5*x^3 + 453*a^2*b^4*x)*x^(9/2) + 2*(695*a*b^5*x^5 + 1182*a^2*b^4*x^3 + 519*a^3*b^3*x)*x^(5/2) + (801*a^2*b^4*x^5 + 1386*a^3*b^3*x^3 + 617*a^4*b^2*x)*sqrt(x))/(a^8*b^3*d^(7/2)*x^6 + 3*a^9*b^2*d^(7/2)*x^4 + 3*a^10*b*d^(7/2)*x^2 + a^11*d^(7/2) + (a^5*b^6*d^(7/2)*x^6 + 3*a^6*b^5*d^(7/2)*x^4 + 3*a^7*b^4*d^(7/2)*x^2 + a^8*b^3*d^(7/2))*x^6 + 3*(a^6*b^5*d^(7/2)*x^6 + 3*a^7*b^4*d^(7/2)*x^4 + 3*a^8*b^3*d^(7/2)*x^2 + a^9*b^2*d^(7/2))*x^4 + 3*(a^7*b^4*d^(7/2)*x^6 + 3*a^8*b^3*d^(7/2)*x^4 + 3*a^9*b^2*d^(7/2)*x^2 + a^10*b*d^(7/2))*x^2) + 3683/8192*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^6*d^(7/2)) + integrate(1/((a^4*b*d^(7/2)*x^2 + a^5*d^(7/2))*x^(7/2)), x)","F",0
785,1,144,0,1.541906," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^3,x, algorithm=""maxima"")","\frac{b^{6} d^{m} x^{13} x^{m}}{m + 13} + \frac{6 \, a b^{5} d^{m} x^{11} x^{m}}{m + 11} + \frac{15 \, a^{2} b^{4} d^{m} x^{9} x^{m}}{m + 9} + \frac{20 \, a^{3} b^{3} d^{m} x^{7} x^{m}}{m + 7} + \frac{15 \, a^{4} b^{2} d^{m} x^{5} x^{m}}{m + 5} + \frac{6 \, a^{5} b d^{m} x^{3} x^{m}}{m + 3} + \frac{\left(d x\right)^{m + 1} a^{6}}{d {\left(m + 1\right)}}"," ",0,"b^6*d^m*x^13*x^m/(m + 13) + 6*a*b^5*d^m*x^11*x^m/(m + 11) + 15*a^2*b^4*d^m*x^9*x^m/(m + 9) + 20*a^3*b^3*d^m*x^7*x^m/(m + 7) + 15*a^4*b^2*d^m*x^5*x^m/(m + 5) + 6*a^5*b*d^m*x^3*x^m/(m + 3) + (d*x)^(m + 1)*a^6/(d*(m + 1))","A",0
786,1,100,0,1.487056," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^2,x, algorithm=""maxima"")","\frac{b^{4} d^{m} x^{9} x^{m}}{m + 9} + \frac{4 \, a b^{3} d^{m} x^{7} x^{m}}{m + 7} + \frac{6 \, a^{2} b^{2} d^{m} x^{5} x^{m}}{m + 5} + \frac{4 \, a^{3} b d^{m} x^{3} x^{m}}{m + 3} + \frac{\left(d x\right)^{m + 1} a^{4}}{d {\left(m + 1\right)}}"," ",0,"b^4*d^m*x^9*x^m/(m + 9) + 4*a*b^3*d^m*x^7*x^m/(m + 7) + 6*a^2*b^2*d^m*x^5*x^m/(m + 5) + 4*a^3*b*d^m*x^3*x^m/(m + 3) + (d*x)^(m + 1)*a^4/(d*(m + 1))","A",0
787,1,56,0,1.396957," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\frac{b^{2} d^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, a b d^{m} x^{3} x^{m}}{m + 3} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}}"," ",0,"b^2*d^m*x^5*x^m/(m + 5) + 2*a*b*d^m*x^3*x^m/(m + 3) + (d*x)^(m + 1)*a^2/(d*(m + 1))","A",0
788,0,0,0,0.000000," ","integrate((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
791,1,243,0,1.414380," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""maxima"")","\frac{{\left({\left(m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945\right)} b^{5} d^{m} x^{11} + 5 \, {\left(m^{5} + 27 \, m^{4} + 262 \, m^{3} + 1122 \, m^{2} + 2041 \, m + 1155\right)} a b^{4} d^{m} x^{9} + 10 \, {\left(m^{5} + 29 \, m^{4} + 302 \, m^{3} + 1366 \, m^{2} + 2577 \, m + 1485\right)} a^{2} b^{3} d^{m} x^{7} + 10 \, {\left(m^{5} + 31 \, m^{4} + 350 \, m^{3} + 1730 \, m^{2} + 3489 \, m + 2079\right)} a^{3} b^{2} d^{m} x^{5} + 5 \, {\left(m^{5} + 33 \, m^{4} + 406 \, m^{3} + 2262 \, m^{2} + 5353 \, m + 3465\right)} a^{4} b d^{m} x^{3} + {\left(m^{5} + 35 \, m^{4} + 470 \, m^{3} + 3010 \, m^{2} + 9129 \, m + 10395\right)} a^{5} d^{m} x\right)} x^{m}}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)*b^5*d^m*x^11 + 5*(m^5 + 27*m^4 + 262*m^3 + 1122*m^2 + 2041*m + 1155)*a*b^4*d^m*x^9 + 10*(m^5 + 29*m^4 + 302*m^3 + 1366*m^2 + 2577*m + 1485)*a^2*b^3*d^m*x^7 + 10*(m^5 + 31*m^4 + 350*m^3 + 1730*m^2 + 3489*m + 2079)*a^3*b^2*d^m*x^5 + 5*(m^5 + 33*m^4 + 406*m^3 + 2262*m^2 + 5353*m + 3465)*a^4*b*d^m*x^3 + (m^5 + 35*m^4 + 470*m^3 + 3010*m^2 + 9129*m + 10395)*a^5*d^m*x)*x^m/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","A",0
792,1,119,0,1.443266," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b^{3} d^{m} x^{7} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} a b^{2} d^{m} x^{5} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} a^{2} b d^{m} x^{3} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} a^{3} d^{m} x\right)} x^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((m^3 + 9*m^2 + 23*m + 15)*b^3*d^m*x^7 + 3*(m^3 + 11*m^2 + 31*m + 21)*a*b^2*d^m*x^5 + 3*(m^3 + 13*m^2 + 47*m + 35)*a^2*b*d^m*x^3 + (m^3 + 15*m^2 + 71*m + 105)*a^3*d^m*x)*x^m/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","A",0
793,1,35,0,1.397943," ","integrate((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b d^{m} {\left(m + 1\right)} x^{3} + a d^{m} {\left(m + 3\right)} x\right)} x^{m}}{m^{2} + 4 \, m + 3}"," ",0,"(b*d^m*(m + 1)*x^3 + a*d^m*(m + 3)*x)*x^m/(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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
798,1,115,0,1.459243," ","integrate(x^7*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""maxima"")","\frac{{\left({\left(4 \, p^{3} + 12 \, p^{2} + 11 \, p + 3\right)} b^{4} x^{8} + 2 \, {\left(2 \, p^{3} + 3 \, p^{2} + p\right)} a b^{3} x^{6} - 3 \, {\left(2 \, p^{2} + p\right)} a^{2} b^{2} x^{4} + 6 \, a^{3} b p x^{2} - 3 \, a^{4}\right)} {\left(b x^{2} + a\right)}^{2 \, p}}{4 \, {\left(4 \, p^{4} + 20 \, p^{3} + 35 \, p^{2} + 25 \, p + 6\right)} b^{4}}"," ",0,"1/4*((4*p^3 + 12*p^2 + 11*p + 3)*b^4*x^8 + 2*(2*p^3 + 3*p^2 + p)*a*b^3*x^6 - 3*(2*p^2 + p)*a^2*b^2*x^4 + 6*a^3*b*p*x^2 - 3*a^4)*(b*x^2 + a)^(2*p)/((4*p^4 + 20*p^3 + 35*p^2 + 25*p + 6)*b^4)","A",0
799,1,79,0,1.436686," ","integrate(x^5*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""maxima"")","\frac{{\left({\left(2 \, p^{2} + 3 \, p + 1\right)} b^{3} x^{6} + {\left(2 \, p^{2} + p\right)} a b^{2} x^{4} - 2 \, a^{2} b p x^{2} + a^{3}\right)} {\left(b x^{2} + a\right)}^{2 \, p}}{2 \, {\left(4 \, p^{3} + 12 \, p^{2} + 11 \, p + 3\right)} b^{3}}"," ",0,"1/2*((2*p^2 + 3*p + 1)*b^3*x^6 + (2*p^2 + p)*a*b^2*x^4 - 2*a^2*b*p*x^2 + a^3)*(b*x^2 + a)^(2*p)/((4*p^3 + 12*p^2 + 11*p + 3)*b^3)","A",0
800,1,54,0,1.431109," ","integrate(x^3*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""maxima"")","\frac{{\left(b^{2} {\left(2 \, p + 1\right)} x^{4} + 2 \, a b p x^{2} - a^{2}\right)} {\left(b x^{2} + a\right)}^{2 \, p}}{4 \, {\left(2 \, p^{2} + 3 \, p + 1\right)} b^{2}}"," ",0,"1/4*(b^2*(2*p + 1)*x^4 + 2*a*b*p*x^2 - a^2)*(b*x^2 + a)^(2*p)/((2*p^2 + 3*p + 1)*b^2)","A",0
801,1,30,0,1.324398," ","integrate(x*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)} {\left(b x^{2} + a\right)}^{2 \, p}}{2 \, b {\left(2 \, p + 1\right)}}"," ",0,"1/2*(b*x^2 + a)*(b*x^2 + a)^(2*p)/(b*(2*p + 1))","A",0
802,0,0,0,0.000000," ","integrate((b^2*x^4+2*a*b*x^2+a^2)^p/x,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
814,1,19,0,1.331718," ","integrate(x^2*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\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
815,1,19,0,1.385283," ","integrate(x*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\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
816,1,16,0,1.351630," ","integrate(c*x^4+b*x^2+a,x, algorithm=""maxima"")","\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
817,1,20,0,1.359554," ","integrate((c*x^4+b*x^2+a)/x,x, algorithm=""maxima"")","\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
818,1,16,0,1.385053," ","integrate((c*x^4+b*x^2+a)/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, c x^{3} + b x - \frac{a}{x}"," ",0,"1/3*c*x^3 + b*x - a/x","A",0
819,1,20,0,1.336970," ","integrate((c*x^4+b*x^2+a)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, c x^{2} + \frac{1}{2} \, b \log\left(x^{2}\right) - \frac{a}{2 \, x^{2}}"," ",0,"1/2*c*x^2 + 1/2*b*log(x^2) - 1/2*a/x^2","A",0
820,1,17,0,1.369328," ","integrate((c*x^4+b*x^2+a)/x^4,x, algorithm=""maxima"")","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
821,1,21,0,1.305007," ","integrate((c*x^4+b*x^2+a)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, c \log\left(x^{2}\right) - \frac{2 \, b x^{2} + a}{4 \, x^{4}}"," ",0,"1/2*c*log(x^2) - 1/4*(2*b*x^2 + a)/x^4","A",0
822,1,21,0,1.361694," ","integrate((c*x^4+b*x^2+a)/x^6,x, algorithm=""maxima"")","-\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
823,1,21,0,1.295115," ","integrate((c*x^4+b*x^2+a)/x^7,x, algorithm=""maxima"")","-\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
824,1,21,0,1.344184," ","integrate((c*x^4+b*x^2+a)/x^8,x, algorithm=""maxima"")","-\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
825,1,44,0,1.312615," ","integrate(x^2*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{11} \, c^{2} x^{11} + \frac{2}{9} \, b c x^{9} + \frac{1}{7} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^7 + 2/5*a*b*x^5 + 1/3*a^2*x^3","A",0
826,1,44,0,1.378024," ","integrate(x*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{10} \, c^{2} x^{10} + \frac{1}{4} \, b c x^{8} + \frac{1}{6} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^6 + 1/2*a*b*x^4 + 1/2*a^2*x^2","A",0
827,1,45,0,1.328696," ","integrate((c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} + a^{2} x + \frac{2}{15} \, {\left(3 \, c x^{5} + 5 \, b x^{3}\right)} a"," ",0,"1/9*c^2*x^9 + 2/7*b*c*x^7 + 1/5*b^2*x^5 + a^2*x + 2/15*(3*c*x^5 + 5*b*x^3)*a","A",0
828,1,44,0,1.339033," ","integrate((c*x^4+b*x^2+a)^2/x,x, algorithm=""maxima"")","\frac{1}{8} \, c^{2} x^{8} + \frac{1}{3} \, b c x^{6} + \frac{1}{4} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^4 + a*b*x^2 + 1/2*a^2*log(x^2)","A",0
829,1,42,0,1.220224," ","integrate((c*x^4+b*x^2+a)^2/x^2,x, algorithm=""maxima"")","\frac{1}{7} \, c^{2} x^{7} + \frac{2}{5} \, b c x^{5} + \frac{1}{3} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^3 + 2*a*b*x - a^2/x","A",0
830,1,44,0,1.374269," ","integrate((c*x^4+b*x^2+a)^2/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, c^{2} x^{6} + \frac{1}{2} \, b c x^{4} + \frac{1}{2} \, {\left(b^{2} + 2 \, a c\right)} x^{2} + a b \log\left(x^{2}\right) - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/6*c^2*x^6 + 1/2*b*c*x^4 + 1/2*(b^2 + 2*a*c)*x^2 + a*b*log(x^2) - 1/2*a^2/x^2","A",0
831,1,42,0,1.371017," ","integrate((c*x^4+b*x^2+a)^2/x^4,x, algorithm=""maxima"")","\frac{1}{5} \, c^{2} x^{5} + \frac{2}{3} \, b c x^{3} + {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x - 1/3*(6*a*b*x^2 + a^2)/x^3","A",0
832,1,45,0,1.335676," ","integrate((c*x^4+b*x^2+a)^2/x^5,x, algorithm=""maxima"")","\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{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*(4*a*b*x^2 + a^2)/x^4","A",0
833,1,45,0,1.322743," ","integrate((c*x^4+b*x^2+a)^2/x^6,x, algorithm=""maxima"")","\frac{1}{3} \, c^{2} x^{3} + 2 \, b c x - \frac{15 \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^4 + 10*a*b*x^2 + 3*a^2)/x^5","A",0
834,1,45,0,1.337600," ","integrate((c*x^4+b*x^2+a)^2/x^7,x, algorithm=""maxima"")","\frac{1}{2} \, c^{2} x^{2} + b c \log\left(x^{2}\right) - \frac{3 \, {\left(b^{2} + 2 \, a c\right)} 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*(3*(b^2 + 2*a*c)*x^4 + 3*a*b*x^2 + a^2)/x^6","A",0
835,1,44,0,1.342134," ","integrate((c*x^4+b*x^2+a)^2/x^8,x, algorithm=""maxima"")","c^{2} x - \frac{210 \, b c x^{6} + 35 \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^4 + 42*a*b*x^2 + 15*a^2)/x^7","A",0
836,1,48,0,1.364293," ","integrate((c*x^4+b*x^2+a)^2/x^9,x, algorithm=""maxima"")","\frac{1}{2} \, c^{2} \log\left(x^{2}\right) - \frac{24 \, b c x^{6} + 6 \, {\left(b^{2} + 2 \, a c\right)} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}}"," ",0,"1/2*c^2*log(x^2) - 1/24*(24*b*c*x^6 + 6*(b^2 + 2*a*c)*x^4 + 8*a*b*x^2 + 3*a^2)/x^8","A",0
837,1,46,0,1.330165," ","integrate((c*x^4+b*x^2+a)^2/x^10,x, algorithm=""maxima"")","-\frac{315 \, c^{2} x^{8} + 210 \, b c x^{6} + 63 \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^4 + 90*a*b*x^2 + 35*a^2)/x^9","A",0
838,1,46,0,1.278512," ","integrate((c*x^4+b*x^2+a)^2/x^11,x, algorithm=""maxima"")","-\frac{30 \, c^{2} x^{8} + 30 \, b c x^{6} + 10 \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^4 + 15*a*b*x^2 + 6*a^2)/x^10","A",0
839,1,46,0,1.379704," ","integrate((c*x^4+b*x^2+a)^2/x^12,x, algorithm=""maxima"")","-\frac{1155 \, c^{2} x^{8} + 1386 \, b c x^{6} + 495 \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^4 + 770*a*b*x^2 + 315*a^2)/x^11","A",0
840,1,46,0,1.340902," ","integrate((c*x^4+b*x^2+a)^2/x^13,x, algorithm=""maxima"")","-\frac{30 \, c^{2} x^{8} + 40 \, b c x^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^4 + 24*a*b*x^2 + 10*a^2)/x^12","A",0
841,1,81,0,1.385321," ","integrate(x^2*(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{1}{15} \, c^{3} x^{15} + \frac{3}{13} \, b c^{2} x^{13} + \frac{3}{11} \, {\left(b^{2} c + a c^{2}\right)} x^{11} + \frac{1}{9} \, {\left(b^{3} + 6 \, a b c\right)} x^{9} + \frac{3}{5} \, a^{2} b x^{5} + \frac{3}{7} \, {\left(a b^{2} + a^{2} c\right)} x^{7} + \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 + a*c^2)*x^11 + 1/9*(b^3 + 6*a*b*c)*x^9 + 3/5*a^2*b*x^5 + 3/7*(a*b^2 + a^2*c)*x^7 + 1/3*a^3*x^3","A",0
842,1,81,0,1.365446," ","integrate(x*(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{1}{14} \, c^{3} x^{14} + \frac{1}{4} \, b c^{2} x^{12} + \frac{3}{10} \, {\left(b^{2} c + a c^{2}\right)} x^{10} + \frac{1}{8} \, {\left(b^{3} + 6 \, a b c\right)} x^{8} + \frac{3}{4} \, a^{2} b x^{4} + \frac{1}{2} \, {\left(a b^{2} + a^{2} c\right)} x^{6} + \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 + a*c^2)*x^10 + 1/8*(b^3 + 6*a*b*c)*x^8 + 3/4*a^2*b*x^4 + 1/2*(a*b^2 + a^2*c)*x^6 + 1/2*a^3*x^2","A",0
843,1,85,0,1.354550," ","integrate((c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\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}{7} \, b^{3} x^{7} + a^{3} x + \frac{1}{5} \, {\left(3 \, c x^{5} + 5 \, b x^{3}\right)} a^{2} + \frac{1}{105} \, {\left(35 \, c^{2} x^{9} + 90 \, b c x^{7} + 63 \, b^{2} x^{5}\right)} a"," ",0,"1/13*c^3*x^13 + 3/11*b*c^2*x^11 + 1/3*b^2*c*x^9 + 1/7*b^3*x^7 + a^3*x + 1/5*(3*c*x^5 + 5*b*x^3)*a^2 + 1/105*(35*c^2*x^9 + 90*b*c*x^7 + 63*b^2*x^5)*a","A",0
844,1,82,0,1.386901," ","integrate((c*x^4+b*x^2+a)^3/x,x, algorithm=""maxima"")","\frac{1}{12} \, c^{3} x^{12} + \frac{3}{10} \, b c^{2} x^{10} + \frac{3}{8} \, {\left(b^{2} c + a c^{2}\right)} x^{8} + \frac{1}{6} \, {\left(b^{3} + 6 \, a b c\right)} x^{6} + \frac{3}{2} \, a^{2} b x^{2} + \frac{3}{4} \, {\left(a b^{2} + a^{2} c\right)} x^{4} + \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 + a*c^2)*x^8 + 1/6*(b^3 + 6*a*b*c)*x^6 + 3/2*a^2*b*x^2 + 3/4*(a*b^2 + a^2*c)*x^4 + 1/2*a^3*log(x^2)","A",0
845,1,78,0,1.362170," ","integrate((c*x^4+b*x^2+a)^3/x^2,x, algorithm=""maxima"")","\frac{1}{11} \, c^{3} x^{11} + \frac{1}{3} \, b c^{2} x^{9} + \frac{3}{7} \, {\left(b^{2} c + a c^{2}\right)} x^{7} + \frac{1}{5} \, {\left(b^{3} + 6 \, a b c\right)} x^{5} + 3 \, a^{2} b x + {\left(a b^{2} + a^{2} c\right)} x^{3} - \frac{a^{3}}{x}"," ",0,"1/11*c^3*x^11 + 1/3*b*c^2*x^9 + 3/7*(b^2*c + a*c^2)*x^7 + 1/5*(b^3 + 6*a*b*c)*x^5 + 3*a^2*b*x + (a*b^2 + a^2*c)*x^3 - a^3/x","A",0
846,1,82,0,1.365653," ","integrate((c*x^4+b*x^2+a)^3/x^3,x, algorithm=""maxima"")","\frac{1}{10} \, c^{3} x^{10} + \frac{3}{8} \, b c^{2} x^{8} + \frac{1}{2} \, {\left(b^{2} c + a c^{2}\right)} x^{6} + \frac{1}{4} \, {\left(b^{3} + 6 \, a b c\right)} x^{4} + \frac{3}{2} \, a^{2} b \log\left(x^{2}\right) + \frac{3}{2} \, {\left(a b^{2} + a^{2} c\right)} x^{2} - \frac{a^{3}}{2 \, x^{2}}"," ",0,"1/10*c^3*x^10 + 3/8*b*c^2*x^8 + 1/2*(b^2*c + a*c^2)*x^6 + 1/4*(b^3 + 6*a*b*c)*x^4 + 3/2*a^2*b*log(x^2) + 3/2*(a*b^2 + a^2*c)*x^2 - 1/2*a^3/x^2","A",0
847,1,80,0,1.345019," ","integrate((c*x^4+b*x^2+a)^3/x^4,x, algorithm=""maxima"")","\frac{1}{9} \, c^{3} x^{9} + \frac{3}{7} \, b c^{2} x^{7} + \frac{3}{5} \, {\left(b^{2} c + a c^{2}\right)} x^{5} + \frac{1}{3} \, {\left(b^{3} + 6 \, a b c\right)} x^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} 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 + a*c^2)*x^5 + 1/3*(b^3 + 6*a*b*c)*x^3 + 3*(a*b^2 + a^2*c)*x - 1/3*(9*a^2*b*x^2 + a^3)/x^3","A",0
848,-2,0,0,0.000000," ","integrate(x^7/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
849,-2,0,0,0.000000," ","integrate(x^5/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
850,-2,0,0,0.000000," ","integrate(x^3/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
851,-2,0,0,0.000000," ","integrate(x/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
852,-2,0,0,0.000000," ","integrate(1/x/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
853,-2,0,0,0.000000," ","integrate(1/x^3/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
854,-2,0,0,0.000000," ","integrate(1/x^5/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
855,0,0,0,0.000000," ","integrate(x^6/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{c x^{3} - 3 \, b x}{3 \, c^{2}} - \frac{-\int \frac{{\left(b^{2} - a c\right)} x^{2} + a b}{c x^{4} + b x^{2} + a}\,{d x}}{c^{2}}"," ",0,"1/3*(c*x^3 - 3*b*x)/c^2 - integrate(-((b^2 - a*c)*x^2 + a*b)/(c*x^4 + b*x^2 + a), x)/c^2","F",0
856,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{x}{c} - \frac{\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(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)} c} + \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(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)} c}}{c}"," ",0,"x/c - integrate((b*x^2 + a)/(c*x^4 + b*x^2 + a), x)/c","F",0
857,0,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{x^{2}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate(x^2/(c*x^4 + b*x^2 + a), x)","F",0
858,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{1}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate(1/(c*x^4 + b*x^2 + a), x)","F",0
859,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","-\frac{\frac{{\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} + 2 \, b^{4} 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} - 12 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 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 - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 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^{2} + 2 \, \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^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\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)} c} + \frac{{\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} - 2 \, b^{4} 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} + 12 \, a b^{2} c^{3} - 16 \, a^{2} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 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 + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 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^{2} - 2 \, \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^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\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)} c}}{a} - \frac{1}{a x}"," ",0,"-integrate((c*x^2 + b)/(c*x^4 + b*x^2 + a), x)/a - 1/(a*x)","F",0
860,0,0,0,0.000000," ","integrate(1/x^4/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{\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{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)} c} + \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{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)} c}}{a^{2}} + \frac{3 \, b x^{2} - a}{3 \, a^{2} x^{3}}"," ",0,"integrate((b*c*x^2 + b^2 - a*c)/(c*x^4 + b*x^2 + a), x)/a^2 + 1/3*(3*b*x^2 - a)/(a^2*x^3)","F",0
861,-2,0,0,0.000000," ","integrate(x^7/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
862,-2,0,0,0.000000," ","integrate(x^5/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
863,-2,0,0,0.000000," ","integrate(x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
864,-2,0,0,0.000000," ","integrate(x/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
865,-2,0,0,0.000000," ","integrate(1/x/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
866,-2,0,0,0.000000," ","integrate(1/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
867,0,0,0,0.000000," ","integrate(x^8/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} - 3 \, a b c\right)} x^{3} + {\left(a b^{2} - 2 \, a^{2} c\right)} x}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)}} + \frac{-\int \frac{3 \, a b^{2} - 10 \, a^{2} c + {\left(3 \, b^{3} - 13 \, a b c\right)} x^{2}}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}} + \frac{x}{c^{2}}"," ",0,"1/2*((b^3 - 3*a*b*c)*x^3 + (a*b^2 - 2*a^2*c)*x)/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2) + 1/2*integrate(-(3*a*b^2 - 10*a^2*c + (3*b^3 - 13*a*b*c)*x^2)/(c*x^4 + b*x^2 + a), x)/(b^2*c^2 - 4*a*c^3) + x/c^2","F",0
868,0,0,0,0.000000," ","integrate(x^6/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} - 2 \, a c\right)} x^{3} + a b x}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}} - \frac{-\int \frac{{\left(b^{2} - 6 \, a c\right)} x^{2} + a b}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}"," ",0,"-1/2*((b^2 - 2*a*c)*x^3 + a*b*x)/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2) - 1/2*integrate(-((b^2 - 6*a*c)*x^2 + a*b)/(c*x^4 + b*x^2 + a), x)/(b^2*c - 4*a*c^2)","F",0
869,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b x^{3} + 2 \, a x}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}} + \frac{-\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} + 4 \, 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} - 16 \, a b c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - 2 \, \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} - 4 \, {\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)}{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)} c} - \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} - 4 \, 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} + 16 \, a b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 2 \, \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} + 4 \, {\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)}{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)} c}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(b*x^3 + 2*a*x)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2) + 1/2*integrate((b*x^2 - 2*a)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
870,0,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, c x^{3} + b x}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}} - \frac{-\frac{{\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} + 2 \, b^{4} 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} - 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} + 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^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 2 \, {\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 + \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)} c} - \frac{{\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} - 2 \, b^{4} 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} + 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} - 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^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} + 2 \, {\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 - \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)} c}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-1/2*(2*c*x^3 + b*x)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2) - 1/2*integrate((2*c*x^2 - b)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
871,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b c x^{3} + {\left(b^{2} - 2 \, a c\right)} x}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} + \frac{\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \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 + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \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} + 28 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 128 \, a^{2} b^{2} c^{3} - 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 192 \, a^{3} c^{4} + 64 \, 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} + 12 \, \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 - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 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^{2} + 8 \, \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 - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\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)} c} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \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 + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \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} - 28 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 128 \, a^{2} b^{2} c^{3} + 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 192 \, a^{3} c^{4} - 64 \, 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} - 12 \, \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 + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 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^{2} - 8 \, \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 + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\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)} c}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"1/2*(b*c*x^3 + (b^2 - 2*a*c)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) + 1/2*integrate((b*c*x^2 + b^2 - 6*a*c)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
872,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, b^{2} c - 10 \, a c^{2}\right)} x^{4} + 2 \, a b^{2} - 8 \, a^{2} c + {\left(3 \, b^{3} - 11 \, a b c\right)} x^{2}}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}} + \frac{-\int \frac{3 \, b^{3} - 13 \, a b c + {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} x^{2}}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}}"," ",0,"-1/2*((3*b^2*c - 10*a*c^2)*x^4 + 2*a*b^2 - 8*a^2*c + (3*b^3 - 11*a*b*c)*x^2)/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x) + 1/2*integrate(-(3*b^3 - 13*a*b*c + (3*b^2*c - 10*a*c^2)*x^2)/(c*x^4 + b*x^2 + a), x)/(a^2*b^2 - 4*a^3*c)","F",0
873,-2,0,0,0.000000," ","integrate(x^11/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
874,-2,0,0,0.000000," ","integrate(x^9/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
875,-2,0,0,0.000000," ","integrate(x^7/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
876,-2,0,0,0.000000," ","integrate(x^5/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
877,-2,0,0,0.000000," ","integrate(x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
878,-2,0,0,0.000000," ","integrate(x/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
879,-2,0,0,0.000000," ","integrate(1/x/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
880,-2,0,0,0.000000," ","integrate(1/x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
881,0,0,0,0.000000," ","integrate(x^10/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(5 \, b^{4} c - 37 \, a b^{2} c^{2} + 44 \, a^{2} c^{3}\right)} x^{7} + {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{5} + {\left(6 \, a b^{4} - 49 \, a^{2} b^{2} c + 28 \, a^{3} c^{2}\right)} x^{3} + 3 \, {\left(a^{2} b^{3} - 8 \, a^{3} b c\right)} x}{8 \, {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)}} + \frac{3 \, {\left(\frac{{\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 + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\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)} c} + \frac{{\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 - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\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)} c}\right)}}{8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}"," ",0,"-1/8*((5*b^4*c - 37*a*b^2*c^2 + 44*a^2*c^3)*x^7 + (3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*x^5 + (6*a*b^4 - 49*a^2*b^2*c + 28*a^3*c^2)*x^3 + 3*(a^2*b^3 - 8*a^3*b*c)*x)/((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2) + 3/8*integrate((a*b^3 - 8*a^2*b*c + (b^4 - 9*a*b^2*c + 28*a^2*c^2)*x^2)/(c*x^4 + b*x^2 + a), x)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)","F",0
882,0,0,0,0.000000," ","integrate(x^8/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(b^{3} c - 16 \, a b c^{2}\right)} x^{7} - {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} x^{5} - 2 \, {\left(a b^{3} + 14 \, a^{2} b c\right)} x^{3} - {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x}{8 \, {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)}} - \frac{-\int \frac{a b^{2} + 20 \, a^{2} c + {\left(b^{3} - 16 \, a b c\right)} x^{2}}{c x^{4} + b x^{2} + a}\,{d x}}{8 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}"," ",0,"1/8*((b^3*c - 16*a*b*c^2)*x^7 - (b^4 + 5*a*b^2*c + 36*a^2*c^2)*x^5 - 2*(a*b^3 + 14*a^2*b*c)*x^3 - (a^2*b^2 + 20*a^3*c)*x)/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2) - 1/8*integrate(-(a*b^2 + 20*a^2*c + (b^3 - 16*a*b*c)*x^2)/(c*x^4 + b*x^2 + a), x)/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)","F",0
883,0,0,0,0.000000," ","integrate(x^6/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{2} c + 4 \, a c^{2}\right)} x^{7} + {\left(5 \, b^{3} + 16 \, a b c\right)} x^{5} + 12 \, a^{2} b x + {\left(19 \, a b^{2} - 4 \, a^{2} c\right)} x^{3}}{8 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}} + \frac{3 \, {\left(-\frac{{\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 + \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)} c} - \frac{{\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 - \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)} c}\right)}}{8 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"1/8*(3*(b^2*c + 4*a*c^2)*x^7 + (5*b^3 + 16*a*b*c)*x^5 + 12*a^2*b*x + (19*a*b^2 - 4*a^2*c)*x^3)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2) + 3/8*integrate(((b^2 + 4*a*c)*x^2 - 4*a*b)/(c*x^4 + b*x^2 + a), x)/(b^4 - 8*a*b^2*c + 16*a^2*c^2)","F",0
884,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{12 \, b c^{2} x^{7} + {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} x^{5} + {\left(5 \, b^{3} + 16 \, a b c\right)} x^{3} + 3 \, {\left(a b^{2} + 4 \, a^{2} c\right)} x}{8 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}} - \frac{3 \, {\left(-\frac{{\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 + \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)} c} - \frac{{\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 - \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)} c}\right)}}{8 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"-1/8*(12*b*c^2*x^7 + (19*b^2*c - 4*a*c^2)*x^5 + (5*b^3 + 16*a*b*c)*x^3 + 3*(a*b^2 + 4*a^2*c)*x)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2) - 3/8*integrate((4*b*c*x^2 - b^2 - 4*a*c)/(c*x^4 + b*x^2 + a), x)/(b^4 - 8*a*b^2*c + 16*a^2*c^2)","F",0
885,0,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x^{7} + 2 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} x^{5} + {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} x^{3} - {\left(a b^{3} - 16 \, a^{2} b c\right)} x}{8 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}} + \frac{\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 24 \, \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 + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 40 \, \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} + 48 \, a b^{5} c^{2} + 2 \, b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 288 \, a^{2} b^{3} c^{3} - 44 \, a b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 512 \, a^{3} b c^{4} + 64 \, a^{2} b^{2} c^{4} + 320 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 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 - 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} - 36 \, \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} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 40 \, \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 - 40 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 36 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\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)} c} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 24 \, \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 + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 40 \, \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} - 48 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 288 \, a^{2} b^{3} c^{3} + 44 \, a b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 512 \, a^{3} b c^{4} - 64 \, a^{2} b^{2} c^{4} - 320 \, a^{3} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 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 + 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} + 36 \, \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} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 40 \, \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 + 40 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\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)} c}}{8 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}}"," ",0,"1/8*((b^2*c^2 + 20*a*c^3)*x^7 + 2*(b^3*c + 14*a*b*c^2)*x^5 + (b^4 + 5*a*b^2*c + 36*a^2*c^2)*x^3 - (a*b^3 - 16*a^2*b*c)*x)/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2) + 1/8*integrate((b^3 - 16*a*b*c + (b^2*c + 20*a*c^2)*x^2)/(c*x^4 + b*x^2 + a), x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)","F",0
886,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} x^{7} + {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} x^{5} + {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{3} + {\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} x}{8 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} - \frac{-3 \, \int \frac{b^{4} - 9 \, a b^{2} c + 28 \, a^{2} c^{2} + {\left(b^{3} c - 8 \, a b c^{2}\right)} x^{2}}{c x^{4} + b x^{2} + a}\,{d x}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}}"," ",0,"1/8*(3*(b^3*c^2 - 8*a*b*c^3)*x^7 + (6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*x^5 + (3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*x^3 + (5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) - 3/8*integrate(-(b^4 - 9*a*b^2*c + 28*a^2*c^2 + (b^3*c - 8*a*b*c^2)*x^2)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)","F",0
887,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} x^{8} + {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} x^{6} + 8 \, a^{2} b^{4} - 64 \, a^{3} b^{2} c + 128 \, a^{4} c^{2} + {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} x^{4} + {\left(25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2}\right)} x^{2}}{8 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)}} - \frac{3 \, {\left(\frac{{\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} - 82 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c - 10 \, b^{9} c + 508 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 124 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 164 \, a b^{7} c^{2} + 10 \, b^{8} c^{2} - 1408 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 520 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 62 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 1016 \, a^{2} b^{5} c^{3} - 144 \, a b^{6} c^{3} + 1472 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 736 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 260 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 2816 \, a^{3} b^{3} c^{4} + 748 \, a^{2} b^{4} c^{4} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 2944 \, a^{4} b c^{5} - 1568 \, a^{3} b^{2} c^{5} + 960 \, a^{4} c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} + 72 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 374 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 784 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 332 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 480 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 166 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c - 124 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{2} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{2} + 520 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} + 104 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 736 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4} - 332 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 240 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\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)} c} + \frac{{\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} - 82 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c + 10 \, b^{9} c + 508 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 124 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} - 164 \, a b^{7} c^{2} - 10 \, b^{8} c^{2} - 1408 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 520 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 62 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 1016 \, a^{2} b^{5} c^{3} + 144 \, a b^{6} c^{3} + 1472 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 736 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 260 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 2816 \, a^{3} b^{3} c^{4} - 748 \, a^{2} b^{4} c^{4} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 2944 \, a^{4} b c^{5} + 1568 \, a^{3} b^{2} c^{5} - 960 \, a^{4} c^{6} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 72 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 374 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 784 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 332 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 480 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 166 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c + 124 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{2} - 520 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} - 104 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 736 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4} + 332 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 240 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\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)} c}\right)}}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}}"," ",0,"-1/8*(3*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*x^8 + (30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*x^6 + 8*a^2*b^4 - 64*a^3*b^2*c + 128*a^4*c^2 + (15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*x^4 + (25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2)*x^2)/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x) - 3/8*integrate((5*b^5 - 42*a*b^3*c + 92*a^2*b*c^2 + (5*b^4*c - 37*a*b^2*c^2 + 60*a^2*c^3)*x^2)/(c*x^4 + b*x^2 + a), x)/(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)","F",0
888,-2,0,0,0.000000," ","integrate(x^5/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
889,-2,0,0,0.000000," ","integrate(x^3/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
890,-2,0,0,0.000000," ","integrate(x/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
891,-2,0,0,0.000000," ","integrate(1/x/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
892,-2,0,0,0.000000," ","integrate(1/x^3/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
893,0,0,0,0.000000," ","integrate(x^4/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\frac{x}{c} + \frac{-\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(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)} c} - \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(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)} c}}{c}"," ",0,"x/c + integrate((b*x^2 - a)/(c*x^4 - b*x^2 + a), x)/c","F",0
894,0,0,0,0.000000," ","integrate(x^2/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\int \frac{x^{2}}{c x^{4} - b x^{2} + a}\,{d x}"," ",0,"integrate(x^2/(c*x^4 - b*x^2 + a), x)","F",0
895,0,0,0,0.000000," ","integrate(1/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","\int \frac{1}{c x^{4} - b x^{2} + a}\,{d x}"," ",0,"integrate(1/(c*x^4 - b*x^2 + a), x)","F",0
896,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4-b*x^2+a),x, algorithm=""maxima"")","-\frac{-\frac{{\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} + 2 \, b^{4} 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} - 12 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 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 - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 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^{2} + 2 \, \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^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\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)} c} - \frac{{\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} - 2 \, b^{4} 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} + 12 \, a b^{2} c^{3} - 16 \, a^{2} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 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 + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 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^{2} - 2 \, \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^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\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)} c}}{a} - \frac{1}{a x}"," ",0,"-integrate((c*x^2 - b)/(c*x^4 - b*x^2 + a), x)/a - 1/(a*x)","F",0
897,1,74,0,2.998022," ","integrate(x^5/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","\frac{x^{2}}{2 \, a} + \frac{{\left(a + b\right)} \log\left(\frac{a x^{2} + a - \sqrt{a b}}{a x^{2} + a + \sqrt{a b}}\right)}{4 \, \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 + 1/4*(a + b)*log((a*x^2 + a - sqrt(a*b))/(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
898,1,60,0,2.970521," ","integrate(x^3/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","-\frac{\log\left(\frac{a x^{2} + a - \sqrt{a b}}{a x^{2} + a + \sqrt{a b}}\right)}{4 \, \sqrt{a b}} + \frac{\log\left(a x^{4} + 2 \, a x^{2} + a - b\right)}{4 \, a}"," ",0,"-1/4*log((a*x^2 + a - sqrt(a*b))/(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
899,1,37,0,3.015070," ","integrate(x/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","\frac{\log\left(\frac{a x^{2} + a - \sqrt{a b}}{a x^{2} + a + \sqrt{a b}}\right)}{4 \, \sqrt{a b}}"," ",0,"1/4*log((a*x^2 + a - sqrt(a*b))/(a*x^2 + a + sqrt(a*b)))/sqrt(a*b)","A",0
900,1,85,0,3.125474," ","integrate(1/x/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","-\frac{a \log\left(\frac{a x^{2} + a - \sqrt{a b}}{a x^{2} + a + \sqrt{a b}}\right)}{4 \, \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,"-1/4*a*log((a*x^2 + a - sqrt(a*b))/(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
901,1,123,0,2.969982," ","integrate(1/x^3/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","\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)} \log\left(\frac{a x^{2} + a - \sqrt{a b}}{a x^{2} + a + \sqrt{a b}}\right)}{4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{1}{2 \, {\left(a - b\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) + 1/4*(a^2 + a*b)*log((a*x^2 + a - sqrt(a*b))/(a*x^2 + a + sqrt(a*b)))/((a^2 - 2*a*b + b^2)*sqrt(a*b)) - 1/2/((a - b)*x^2)","A",0
902,0,0,0,0.000000," ","integrate(x^4/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","\frac{x}{a} - \frac{\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)} a \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} 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)} a \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)}}}{a}"," ",0,"x/a - integrate((2*a*x^2 + a - b)/(a*x^4 + 2*a*x^2 + a - b), x)/a","F",0
903,0,0,0,0.000000," ","integrate(x^2/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","\int \frac{x^{2}}{a x^{4} + 2 \, a x^{2} + a - b}\,{d x}"," ",0,"integrate(x^2/(a*x^4 + 2*a*x^2 + a - b), x)","F",0
904,0,0,0,0.000000," ","integrate(1/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","\int \frac{1}{a x^{4} + 2 \, a x^{2} + a - b}\,{d x}"," ",0,"integrate(1/(a*x^4 + 2*a*x^2 + a - b), x)","F",0
905,0,0,0,0.000000," ","integrate(1/x^2/(a*x^4+2*a*x^2+a-b),x, algorithm=""maxima"")","-\frac{\frac{1}{2} \, {\left(\frac{{\left(6 \, \sqrt{a^{2} + \sqrt{a b} a} a^{2} b - 8 \, \sqrt{a^{2} + \sqrt{a b} a} a b^{2} - 3 \, \sqrt{a^{2} + \sqrt{a b} a} \sqrt{a b} a^{2} + \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 \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)}{3 \, a^{5} b - 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}} + \frac{{\left(6 \, \sqrt{a^{2} - \sqrt{a b} a} a^{2} b - 8 \, \sqrt{a^{2} - \sqrt{a b} a} a b^{2} + 3 \, \sqrt{a^{2} - \sqrt{a b} a} \sqrt{a b} a^{2} - \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 \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)}{3 \, a^{5} b - 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}}\right)} a}{a - b} - \frac{1}{{\left(a - b\right)} x}"," ",0,"-a*integrate((x^2 + 2)/(a*x^4 + 2*a*x^2 + a - b), x)/(a - b) - 1/((a - b)*x)","F",0
906,1,58,0,3.028105," ","integrate(x^5/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","\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
907,1,42,0,2.874877," ","integrate(x^3/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","-\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
908,1,21,0,2.939919," ","integrate(x/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","\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
909,1,61,0,3.013037," ","integrate(1/x/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","-\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
910,1,104,0,2.904338," ","integrate(1/x^3/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","\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{1}{2 \, {\left(a + b\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/((a + b)*x^2)","A",0
911,0,0,0,0.000000," ","integrate(x^4/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","\frac{x}{a} - \frac{\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)} a \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} 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)} a \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)}}}{a}"," ",0,"x/a - integrate((2*a*x^2 + a + b)/(a*x^4 + 2*a*x^2 + a + b), x)/a","F",0
912,0,0,0,0.000000," ","integrate(x^2/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","\int \frac{x^{2}}{a x^{4} + 2 \, a x^{2} + a + b}\,{d x}"," ",0,"integrate(x^2/(a*x^4 + 2*a*x^2 + a + b), x)","F",0
913,0,0,0,0.000000," ","integrate(1/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","\int \frac{1}{a x^{4} + 2 \, a x^{2} + a + b}\,{d x}"," ",0,"integrate(1/(a*x^4 + 2*a*x^2 + a + b), x)","F",0
914,0,0,0,0.000000," ","integrate(1/x^2/(a*x^4+2*a*x^2+a+b),x, algorithm=""maxima"")","-\frac{\frac{1}{2} \, {\left(\frac{{\left(6 \, \sqrt{a^{2} + \sqrt{-a b} a} a^{2} b + 8 \, \sqrt{a^{2} + \sqrt{-a b} a} a b^{2} + 3 \, \sqrt{a^{2} + \sqrt{-a b} a} \sqrt{-a b} a^{2} + \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 \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)}{3 \, a^{5} b + 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}} + \frac{{\left(6 \, \sqrt{a^{2} - \sqrt{-a b} a} a^{2} b + 8 \, \sqrt{a^{2} - \sqrt{-a b} a} a b^{2} - 3 \, \sqrt{a^{2} - \sqrt{-a b} a} \sqrt{-a b} a^{2} - \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 \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)}{3 \, a^{5} b + 7 \, a^{4} b^{2} + 4 \, a^{3} b^{3}}\right)} a}{a + b} - \frac{1}{{\left(a + b\right)} x}"," ",0,"-a*integrate((x^2 + 2)/(a*x^4 + 2*a*x^2 + a + b), x)/(a + b) - 1/((a + b)*x)","F",0
915,1,18,0,2.836626," ","integrate(x/(x^4+x^2+1),x, algorithm=""maxima"")","\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
916,1,10,0,2.920021," ","integrate(x/(x^4+2*x^2+10),x, algorithm=""maxima"")","\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
917,1,18,0,2.982048," ","integrate(x^2/(x^4+9*x^2+20),x, algorithm=""maxima"")","\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
918,0,0,0,0.000000," ","integrate(x^2/(x^4-x^2+1),x, algorithm=""maxima"")","\int \frac{x^{2}}{x^{4} - x^{2} + 1}\,{d x}"," ",0,"integrate(x^2/(x^4 - x^2 + 1), x)","F",0
919,0,0,0,0.000000," ","integrate(x^2/(x^4-2*x^2+2),x, algorithm=""maxima"")","\int \frac{x^{2}}{x^{4} - 2 \, x^{2} + 2}\,{d x}"," ",0,"integrate(x^2/(x^4 - 2*x^2 + 2), x)","F",0
920,-2,0,0,0.000000," ","integrate(x^7*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
921,-2,0,0,0.000000," ","integrate(x^5*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
922,-2,0,0,0.000000," ","integrate(x^3*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
923,-2,0,0,0.000000," ","integrate(x*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
924,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
925,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
926,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
927,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^7,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
928,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^9,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
929,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^11,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
930,0,0,0,0.000000," ","integrate(x^4*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(x^7*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
937,-2,0,0,0.000000," ","integrate(x^5*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
938,-2,0,0,0.000000," ","integrate(x^3*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
939,-2,0,0,0.000000," ","integrate(x*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
940,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
941,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
942,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
943,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^7,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
944,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^9,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
945,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^11,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
946,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^13,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
947,0,0,0,0.000000," ","integrate(x^4*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\int \sqrt{-x^{4} - 2 \, x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(-x^4 - 2*x^2 + 3), x)","F",0
955,-2,0,0,0.000000," ","integrate(x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
956,-2,0,0,0.000000," ","integrate(x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
957,-2,0,0,0.000000," ","integrate(x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
958,-2,0,0,0.000000," ","integrate(x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
959,-2,0,0,0.000000," ","integrate(1/x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
960,-2,0,0,0.000000," ","integrate(1/x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
961,-2,0,0,0.000000," ","integrate(1/x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
962,-2,0,0,0.000000," ","integrate(1/x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
963,0,0,0,0.000000," ","integrate(x^4/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
968,1,153,0,2.430367," ","integrate(x^7/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-c x^{4} + b x^{2} + a} x^{4}}{6 \, c} - \frac{5 \, \sqrt{-c x^{4} + b x^{2} + a} b x^{2}}{24 \, c^{2}} - \frac{5 \, b^{3} \arcsin\left(-\frac{2 \, c x^{2} - b}{\sqrt{b^{2} + 4 \, a c}}\right)}{32 \, c^{\frac{7}{2}}} - \frac{3 \, a b \arcsin\left(-\frac{2 \, c x^{2} - b}{\sqrt{b^{2} + 4 \, a c}}\right)}{8 \, c^{\frac{5}{2}}} - \frac{5 \, \sqrt{-c x^{4} + b x^{2} + a} b^{2}}{16 \, c^{3}} - \frac{\sqrt{-c x^{4} + b x^{2} + a} a}{3 \, c^{2}}"," ",0,"-1/6*sqrt(-c*x^4 + b*x^2 + a)*x^4/c - 5/24*sqrt(-c*x^4 + b*x^2 + a)*b*x^2/c^2 - 5/32*b^3*arcsin(-(2*c*x^2 - b)/sqrt(b^2 + 4*a*c))/c^(7/2) - 3/8*a*b*arcsin(-(2*c*x^2 - b)/sqrt(b^2 + 4*a*c))/c^(5/2) - 5/16*sqrt(-c*x^4 + b*x^2 + a)*b^2/c^3 - 1/3*sqrt(-c*x^4 + b*x^2 + a)*a/c^2","A",0
969,1,105,0,2.419876," ","integrate(x^5/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-c x^{4} + b x^{2} + a} x^{2}}{4 \, c} - \frac{3 \, b^{2} \arcsin\left(-\frac{2 \, c x^{2} - b}{\sqrt{b^{2} + 4 \, a c}}\right)}{16 \, c^{\frac{5}{2}}} - \frac{a \arcsin\left(-\frac{2 \, c x^{2} - b}{\sqrt{b^{2} + 4 \, a c}}\right)}{4 \, c^{\frac{3}{2}}} - \frac{3 \, \sqrt{-c x^{4} + b x^{2} + a} b}{8 \, c^{2}}"," ",0,"-1/4*sqrt(-c*x^4 + b*x^2 + a)*x^2/c - 3/16*b^2*arcsin(-(2*c*x^2 - b)/sqrt(b^2 + 4*a*c))/c^(5/2) - 1/4*a*arcsin(-(2*c*x^2 - b)/sqrt(b^2 + 4*a*c))/c^(3/2) - 3/8*sqrt(-c*x^4 + b*x^2 + a)*b/c^2","A",0
970,1,50,0,2.466394," ","integrate(x^3/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{b \arcsin\left(-\frac{2 \, c x^{2} - b}{\sqrt{b^{2} + 4 \, a c}}\right)}{4 \, c^{\frac{3}{2}}} - \frac{\sqrt{-c x^{4} + b x^{2} + a}}{2 \, c}"," ",0,"-1/4*b*arcsin(-(2*c*x^2 - b)/sqrt(b^2 + 4*a*c))/c^(3/2) - 1/2*sqrt(-c*x^4 + b*x^2 + a)/c","A",0
971,1,28,0,2.393834," ","integrate(x/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(-\frac{2 \, c x^{2} - b}{\sqrt{b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{c}}"," ",0,"-1/2*arcsin(-(2*c*x^2 - b)/sqrt(b^2 + 4*a*c))/sqrt(c)","A",0
972,1,36,0,2.329858," ","integrate(1/x/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(-\frac{b}{\sqrt{b^{2} + 4 \, a c}} + \frac{2 \, a}{\sqrt{b^{2} + 4 \, a c} x^{2}}\right)}{2 \, \sqrt{a}}"," ",0,"-1/2*arcsin(-b/sqrt(b^2 + 4*a*c) + 2*a/(sqrt(b^2 + 4*a*c)*x^2))/sqrt(a)","A",0
973,1,62,0,2.410405," ","integrate(1/x^3/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""maxima"")","-\frac{b \arcsin\left(-\frac{b}{\sqrt{b^{2} + 4 \, a c}} + \frac{2 \, a}{\sqrt{b^{2} + 4 \, a c} x^{2}}\right)}{4 \, a^{\frac{3}{2}}} + \frac{\sqrt{c x^{4} + b x^{2} - a}}{2 \, a x^{2}}"," ",0,"-1/4*b*arcsin(-b/sqrt(b^2 + 4*a*c) + 2*a/(sqrt(b^2 + 4*a*c)*x^2))/a^(3/2) + 1/2*sqrt(c*x^4 + b*x^2 - a)/(a*x^2)","A",0
974,1,126,0,2.432175," ","integrate(1/x^5/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""maxima"")","-\frac{3 \, b^{2} \arcsin\left(-\frac{b}{\sqrt{b^{2} + 4 \, a c}} + \frac{2 \, a}{\sqrt{b^{2} + 4 \, a c} x^{2}}\right)}{16 \, a^{\frac{5}{2}}} - \frac{c \arcsin\left(-\frac{b}{\sqrt{b^{2} + 4 \, a c}} + \frac{2 \, a}{\sqrt{b^{2} + 4 \, a c} x^{2}}\right)}{4 \, a^{\frac{3}{2}}} + \frac{3 \, \sqrt{c x^{4} + b x^{2} - a} b}{8 \, a^{2} x^{2}} + \frac{\sqrt{c x^{4} + b x^{2} - a}}{4 \, a x^{4}}"," ",0,"-3/16*b^2*arcsin(-b/sqrt(b^2 + 4*a*c) + 2*a/(sqrt(b^2 + 4*a*c)*x^2))/a^(5/2) - 1/4*c*arcsin(-b/sqrt(b^2 + 4*a*c) + 2*a/(sqrt(b^2 + 4*a*c)*x^2))/a^(3/2) + 3/8*sqrt(c*x^4 + b*x^2 - a)*b/(a^2*x^2) + 1/4*sqrt(c*x^4 + b*x^2 - a)/(a*x^4)","A",0
975,1,179,0,2.258424," ","integrate(1/x^7/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""maxima"")","-\frac{5 \, b^{3} \arcsin\left(-\frac{b}{\sqrt{b^{2} + 4 \, a c}} + \frac{2 \, a}{\sqrt{b^{2} + 4 \, a c} x^{2}}\right)}{32 \, a^{\frac{7}{2}}} - \frac{3 \, b c \arcsin\left(-\frac{b}{\sqrt{b^{2} + 4 \, a c}} + \frac{2 \, a}{\sqrt{b^{2} + 4 \, a c} x^{2}}\right)}{8 \, a^{\frac{5}{2}}} + \frac{5 \, \sqrt{c x^{4} + b x^{2} - a} b^{2}}{16 \, a^{3} x^{2}} + \frac{\sqrt{c x^{4} + b x^{2} - a} c}{3 \, a^{2} x^{2}} + \frac{5 \, \sqrt{c x^{4} + b x^{2} - a} b}{24 \, a^{2} x^{4}} + \frac{\sqrt{c x^{4} + b x^{2} - a}}{6 \, a x^{6}}"," ",0,"-5/32*b^3*arcsin(-b/sqrt(b^2 + 4*a*c) + 2*a/(sqrt(b^2 + 4*a*c)*x^2))/a^(7/2) - 3/8*b*c*arcsin(-b/sqrt(b^2 + 4*a*c) + 2*a/(sqrt(b^2 + 4*a*c)*x^2))/a^(5/2) + 5/16*sqrt(c*x^4 + b*x^2 - a)*b^2/(a^3*x^2) + 1/3*sqrt(c*x^4 + b*x^2 - a)*c/(a^2*x^2) + 5/24*sqrt(c*x^4 + b*x^2 - a)*b/(a^2*x^4) + 1/6*sqrt(c*x^4 + b*x^2 - a)/(a*x^6)","A",0
976,0,0,0,0.000000," ","integrate(x^4/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(x^9/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
982,-2,0,0,0.000000," ","integrate(x^7/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
983,-2,0,0,0.000000," ","integrate(x^5/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
984,-2,0,0,0.000000," ","integrate(x^3/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
985,-2,0,0,0.000000," ","integrate(x/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 zero or nonzero?","F(-2)",0
986,-2,0,0,0.000000," ","integrate(1/x/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
987,-2,0,0,0.000000," ","integrate(1/x^3/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
988,-2,0,0,0.000000," ","integrate(1/x^5/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive, negative or zero?","F(-2)",0
989,0,0,0,0.000000," ","integrate(x^6/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
994,1,34,0,1.263750," ","integrate(x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{c^{2} x^{4} - b c x^{2} - 2 \, b^{2}}{3 \, \sqrt{c x^{2} + b} c^{2}}"," ",0,"1/3*(c^2*x^4 - b*c*x^2 - 2*b^2)/(sqrt(c*x^2 + b)*c^2)","A",0
995,1,52,0,1.157095," ","integrate(x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{b \log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{4 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{4} + b x^{2}}}{2 \, c}"," ",0,"-1/4*b*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/c^(3/2) + 1/2*sqrt(c*x^4 + b*x^2)/c","A",0
996,1,13,0,1.219075," ","integrate(x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{2} + b}}{c}"," ",0,"sqrt(c*x^2 + b)/c","A",0
997,1,32,0,1.055162," ","integrate(x/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(2 \, c x^{2} + b + 2 \, \sqrt{c x^{4} + b x^{2}} \sqrt{c}\right)}{2 \, \sqrt{c}}"," ",0,"1/2*log(2*c*x^2 + b + 2*sqrt(c*x^4 + b*x^2)*sqrt(c))/sqrt(c)","A",0
998,0,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^4 + b*x^2), x)","F",0
999,1,21,0,1.022495," ","integrate(1/x/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{4} + b x^{2}}}{b x^{2}}"," ",0,"-sqrt(c*x^4 + b*x^2)/(b*x^2)","A",0
1000,0,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^2), x)","F",0
1001,1,44,0,1.086041," ","integrate(1/x^3/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{c x^{4} + b x^{2}} c}{3 \, b^{2} x^{2}} - \frac{\sqrt{c x^{4} + b x^{2}}}{3 \, b x^{4}}"," ",0,"2/3*sqrt(c*x^4 + b*x^2)*c/(b^2*x^2) - 1/3*sqrt(c*x^4 + b*x^2)/(b*x^4)","A",0
1002,0,0,0,0.000000," ","integrate(1/x^4/(c*x^4+b*x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2}} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2)*x^4), x)","F",0
1003,0,0,0,0.000000," ","integrate(x^4/(c*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate(x^4/sqrt(c*x^4 + a), x)","F",0
1004,1,14,0,0.969093," ","integrate(x^3/(c*x^4+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\int \frac{x^{2}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(c*x^4 + a), x)","F",0
1006,1,45,0,2.425866," ","integrate(x/(c*x^4+a)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(-\frac{\sqrt{c} - \frac{\sqrt{c x^{4} + a}}{x^{2}}}{\sqrt{c} + \frac{\sqrt{c x^{4} + a}}{x^{2}}}\right)}{4 \, \sqrt{c}}"," ",0,"-1/4*log(-(sqrt(c) - sqrt(c*x^4 + a)/x^2)/(sqrt(c) + sqrt(c*x^4 + a)/x^2))/sqrt(c)","B",0
1007,0,0,0,0.000000," ","integrate(1/(c*x^4+a)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^4 + a), x)","F",0
1008,1,37,0,2.293698," ","integrate(1/x/(c*x^4+a)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sqrt{c x^{4} + a} - \sqrt{a}}{\sqrt{c x^{4} + a} + \sqrt{a}}\right)}{4 \, \sqrt{a}}"," ",0,"1/4*log((sqrt(c*x^4 + a) - sqrt(a))/(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=""maxima"")","\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
1010,1,17,0,1.080933," ","integrate(1/x^3/(c*x^4+a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{4} + a}}{2 \, a x^{2}}"," ",0,"-1/2*sqrt(c*x^4 + a)/(a*x^2)","A",0
1011,0,0,0,0.000000," ","integrate(1/x^4/(c*x^4+a)^(1/2),x, algorithm=""maxima"")","\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
1012,1,51,0,0.971221," ","integrate(x^4/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} x^{3}}{4 \, b} - \frac{3 \, \sqrt{b x^{2} + a} a x}{8 \, b^{2}} + \frac{3 \, a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}}"," ",0,"1/4*sqrt(b*x^2 + a)*x^3/b - 3/8*sqrt(b*x^2 + a)*a*x/b^2 + 3/8*a^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
1013,1,33,0,1.022369," ","integrate(x^3/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} x^{2}}{3 \, b} - \frac{2 \, \sqrt{b x^{2} + a} a}{3 \, b^{2}}"," ",0,"1/3*sqrt(b*x^2 + a)*x^2/b - 2/3*sqrt(b*x^2 + a)*a/b^2","A",0
1014,1,31,0,1.023872," ","integrate(x^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} x}{2 \, b} - \frac{a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/2*sqrt(b*x^2 + a)*x/b - 1/2*a*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
1015,1,13,0,1.047758," ","integrate(x/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a}}{b}"," ",0,"sqrt(b*x^2 + a)/b","A",0
1016,1,13,0,1.017770," ","integrate(1/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}}"," ",0,"arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
1017,1,17,0,1.079401," ","integrate(1/x/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{\operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}}"," ",0,"-arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a)","A",0
1018,1,17,0,1.005264," ","integrate(1/x^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{b x^{2} + a}}{a x}"," ",0,"-sqrt(b*x^2 + a)/(a*x)","A",0
1019,1,36,0,1.029202," ","integrate(1/x^3/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{\sqrt{b x^{2} + a}}{2 \, a x^{2}}"," ",0,"1/2*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - 1/2*sqrt(b*x^2 + a)/(a*x^2)","A",0
1020,1,36,0,1.000108," ","integrate(1/x^4/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b x^{2} + a} b}{3 \, a^{2} x} - \frac{\sqrt{b x^{2} + a}}{3 \, a x^{3}}"," ",0,"2/3*sqrt(b*x^2 + a)*b/(a^2*x) - 1/3*sqrt(b*x^2 + a)/(a*x^3)","A",0
1021,1,12,0,0.964751," ","integrate(x^4/(c*x^4)^(1/2),x, algorithm=""maxima"")","\frac{x^{5}}{3 \, \sqrt{c x^{4}}}"," ",0,"1/3*x^5/sqrt(c*x^4)","A",0
1022,1,12,0,1.037502," ","integrate(x^3/(c*x^4)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c x^{4}}}{2 \, c}"," ",0,"1/2*sqrt(c*x^4)/c","A",0
1023,1,11,0,0.984179," ","integrate(x^2/(c*x^4)^(1/2),x, algorithm=""maxima"")","\frac{x^{3}}{\sqrt{c x^{4}}}"," ",0,"x^3/sqrt(c*x^4)","A",0
1024,1,13,0,0.984672," ","integrate(x/(c*x^4)^(1/2),x, algorithm=""maxima"")","\frac{x^{2} \log\left(x\right)}{\sqrt{c x^{4}}}"," ",0,"x^2*log(x)/sqrt(c*x^4)","A",0
1025,1,10,0,0.977251," ","integrate(1/(c*x^4)^(1/2),x, algorithm=""maxima"")","-\frac{x}{\sqrt{c x^{4}}}"," ",0,"-x/sqrt(c*x^4)","A",0
1026,1,9,0,1.025947," ","integrate(1/x/(c*x^4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2 \, \sqrt{c x^{4}}}"," ",0,"-1/2/sqrt(c*x^4)","A",0
1027,1,12,0,1.075464," ","integrate(1/x^2/(c*x^4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3 \, \sqrt{c x^{4}} x}"," ",0,"-1/3/(sqrt(c*x^4)*x)","A",0
1028,1,12,0,1.047980," ","integrate(1/x^3/(c*x^4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4 \, \sqrt{c x^{4}} x^{2}}"," ",0,"-1/4/(sqrt(c*x^4)*x^2)","A",0
1029,1,12,0,1.064004," ","integrate(1/x^4/(c*x^4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{5 \, \sqrt{c x^{4}} x^{3}}"," ",0,"-1/5/(sqrt(c*x^4)*x^3)","A",0
1030,1,8,0,1.008820," ","integrate(x^4/a^(1/2),x, algorithm=""maxima"")","\frac{x^{5}}{5 \, \sqrt{a}}"," ",0,"1/5*x^5/sqrt(a)","A",0
1031,1,8,0,1.040001," ","integrate(x^3/a^(1/2),x, algorithm=""maxima"")","\frac{x^{4}}{4 \, \sqrt{a}}"," ",0,"1/4*x^4/sqrt(a)","A",0
1032,1,8,0,0.949180," ","integrate(x^2/a^(1/2),x, algorithm=""maxima"")","\frac{x^{3}}{3 \, \sqrt{a}}"," ",0,"1/3*x^3/sqrt(a)","A",0
1033,1,8,0,1.074294," ","integrate(x/a^(1/2),x, algorithm=""maxima"")","\frac{x^{2}}{2 \, \sqrt{a}}"," ",0,"1/2*x^2/sqrt(a)","A",0
1034,1,5,0,0.980844," ","integrate(1/a^(1/2),x, algorithm=""maxima"")","\frac{x}{\sqrt{a}}"," ",0,"x/sqrt(a)","A",0
1035,1,6,0,1.032416," ","integrate(1/x/a^(1/2),x, algorithm=""maxima"")","\frac{\log\left(x\right)}{\sqrt{a}}"," ",0,"log(x)/sqrt(a)","A",0
1036,1,8,0,0.881868," ","integrate(1/x^2/a^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{a} x}"," ",0,"-1/(sqrt(a)*x)","A",0
1037,1,8,0,1.038414," ","integrate(1/x^3/a^(1/2),x, algorithm=""maxima"")","-\frac{1}{2 \, \sqrt{a} x^{2}}"," ",0,"-1/2/(sqrt(a)*x^2)","A",0
1038,1,8,0,1.003288," ","integrate(1/x^4/a^(1/2),x, algorithm=""maxima"")","-\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=""maxima"")","\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=""maxima"")","\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
1041,1,19,0,0.978709," ","integrate(x^(5/2)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\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
1042,1,19,0,1.041573," ","integrate(x^(3/2)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\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
1043,1,19,0,1.013260," ","integrate(x^(1/2)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\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
1044,1,19,0,1.028213," ","integrate((c*x^4+b*x^2+a)/x^(1/2),x, algorithm=""maxima"")","\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
1045,1,19,0,1.094856," ","integrate((c*x^4+b*x^2+a)/x^(3/2),x, algorithm=""maxima"")","\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
1046,1,19,0,1.023312," ","integrate((c*x^4+b*x^2+a)/x^(5/2),x, algorithm=""maxima"")","\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
1047,1,20,0,1.080592," ","integrate((c*x^4+b*x^2+a)/x^(7/2),x, algorithm=""maxima"")","\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
1048,1,44,0,1.025775," ","integrate(x^(5/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{19} \, b c x^{\frac{19}{2}} + \frac{2}{15} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^(15/2) + 4/11*a*b*x^(11/2) + 2/7*a^2*x^(7/2)","A",0
1049,1,44,0,1.159710," ","integrate(x^(3/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{17} \, b c x^{\frac{17}{2}} + \frac{2}{13} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^(13/2) + 4/9*a*b*x^(9/2) + 2/5*a^2*x^(5/2)","A",0
1050,1,44,0,1.112356," ","integrate(x^(1/2)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{2}{19} \, c^{2} x^{\frac{19}{2}} + \frac{4}{15} \, b c x^{\frac{15}{2}} + \frac{2}{11} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^(11/2) + 4/7*a*b*x^(7/2) + 2/3*a^2*x^(3/2)","A",0
1051,1,48,0,1.139143," ","integrate((c*x^4+b*x^2+a)^2/x^(1/2),x, algorithm=""maxima"")","\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}} + 2 \, a^{2} \sqrt{x} + \frac{4}{45} \, {\left(5 \, c x^{\frac{9}{2}} + 9 \, b x^{\frac{5}{2}}\right)} a"," ",0,"2/17*c^2*x^(17/2) + 4/13*b*c*x^(13/2) + 2/9*b^2*x^(9/2) + 2*a^2*sqrt(x) + 4/45*(5*c*x^(9/2) + 9*b*x^(5/2))*a","A",0
1052,1,44,0,1.113371," ","integrate((c*x^4+b*x^2+a)^2/x^(3/2),x, algorithm=""maxima"")","\frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b c x^{\frac{11}{2}} + \frac{2}{7} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^(7/2) + 4/3*a*b*x^(3/2) - 2*a^2/sqrt(x)","A",0
1053,1,44,0,1.129887," ","integrate((c*x^4+b*x^2+a)^2/x^(5/2),x, algorithm=""maxima"")","\frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{9} \, b c x^{\frac{9}{2}} + \frac{2}{5} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^(5/2) + 4*a*b*sqrt(x) - 2/3*a^2/x^(3/2)","A",0
1054,1,45,0,1.117770," ","integrate((c*x^4+b*x^2+a)^2/x^(7/2),x, algorithm=""maxima"")","\frac{2}{11} \, c^{2} x^{\frac{11}{2}} + \frac{4}{7} \, b c x^{\frac{7}{2}} + \frac{2}{3} \, {\left(b^{2} + 2 \, a c\right)} 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 + 2*a*c)*x^(3/2) - 2/5*(10*a*b*x^2 + a^2)/x^(5/2)","A",0
1055,1,81,0,0.999485," ","integrate(x^(5/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{2}{31} \, c^{3} x^{\frac{31}{2}} + \frac{2}{9} \, b c^{2} x^{\frac{27}{2}} + \frac{6}{23} \, {\left(b^{2} c + a c^{2}\right)} x^{\frac{23}{2}} + \frac{2}{19} \, {\left(b^{3} + 6 \, a b c\right)} x^{\frac{19}{2}} + \frac{6}{11} \, a^{2} b x^{\frac{11}{2}} + \frac{2}{5} \, {\left(a b^{2} + a^{2} c\right)} x^{\frac{15}{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 + a*c^2)*x^(23/2) + 2/19*(b^3 + 6*a*b*c)*x^(19/2) + 6/11*a^2*b*x^(11/2) + 2/5*(a*b^2 + a^2*c)*x^(15/2) + 2/7*a^3*x^(7/2)","A",0
1056,1,81,0,1.060715," ","integrate(x^(3/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{2}{29} \, c^{3} x^{\frac{29}{2}} + \frac{6}{25} \, b c^{2} x^{\frac{25}{2}} + \frac{2}{7} \, {\left(b^{2} c + a c^{2}\right)} x^{\frac{21}{2}} + \frac{2}{17} \, {\left(b^{3} + 6 \, a b c\right)} x^{\frac{17}{2}} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{6}{13} \, {\left(a b^{2} + a^{2} c\right)} x^{\frac{13}{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 + a*c^2)*x^(21/2) + 2/17*(b^3 + 6*a*b*c)*x^(17/2) + 2/3*a^2*b*x^(9/2) + 6/13*(a*b^2 + a^2*c)*x^(13/2) + 2/5*a^3*x^(5/2)","A",0
1057,1,81,0,1.042744," ","integrate(x^(1/2)*(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{2}{27} \, c^{3} x^{\frac{27}{2}} + \frac{6}{23} \, b c^{2} x^{\frac{23}{2}} + \frac{6}{19} \, {\left(b^{2} c + a c^{2}\right)} x^{\frac{19}{2}} + \frac{2}{15} \, {\left(b^{3} + 6 \, a b c\right)} x^{\frac{15}{2}} + \frac{6}{7} \, a^{2} b x^{\frac{7}{2}} + \frac{6}{11} \, {\left(a b^{2} + a^{2} c\right)} x^{\frac{11}{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 + a*c^2)*x^(19/2) + 2/15*(b^3 + 6*a*b*c)*x^(15/2) + 6/7*a^2*b*x^(7/2) + 6/11*(a*b^2 + a^2*c)*x^(11/2) + 2/3*a^3*x^(3/2)","A",0
1058,1,88,0,1.042765," ","integrate((c*x^4+b*x^2+a)^3/x^(1/2),x, algorithm=""maxima"")","\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}} + 2 \, a^{3} \sqrt{x} + \frac{2}{15} \, {\left(5 \, c x^{\frac{9}{2}} + 9 \, b x^{\frac{5}{2}}\right)} a^{2} + \frac{2}{663} \, {\left(117 \, c^{2} x^{\frac{17}{2}} + 306 \, b c x^{\frac{13}{2}} + 221 \, b^{2} x^{\frac{9}{2}}\right)} a"," ",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) + 2*a^3*sqrt(x) + 2/15*(5*c*x^(9/2) + 9*b*x^(5/2))*a^2 + 2/663*(117*c^2*x^(17/2) + 306*b*c*x^(13/2) + 221*b^2*x^(9/2))*a","A",0
1059,1,81,0,0.982371," ","integrate((c*x^4+b*x^2+a)^3/x^(3/2),x, algorithm=""maxima"")","\frac{2}{23} \, c^{3} x^{\frac{23}{2}} + \frac{6}{19} \, b c^{2} x^{\frac{19}{2}} + \frac{2}{5} \, {\left(b^{2} c + a c^{2}\right)} x^{\frac{15}{2}} + \frac{2}{11} \, {\left(b^{3} + 6 \, a b c\right)} x^{\frac{11}{2}} + 2 \, a^{2} b x^{\frac{3}{2}} + \frac{6}{7} \, {\left(a b^{2} + a^{2} c\right)} x^{\frac{7}{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 + a*c^2)*x^(15/2) + 2/11*(b^3 + 6*a*b*c)*x^(11/2) + 2*a^2*b*x^(3/2) + 6/7*(a*b^2 + a^2*c)*x^(7/2) - 2*a^3/sqrt(x)","A",0
1060,1,81,0,1.063378," ","integrate((c*x^4+b*x^2+a)^3/x^(5/2),x, algorithm=""maxima"")","\frac{2}{21} \, c^{3} x^{\frac{21}{2}} + \frac{6}{17} \, b c^{2} x^{\frac{17}{2}} + \frac{6}{13} \, {\left(b^{2} c + a c^{2}\right)} x^{\frac{13}{2}} + \frac{2}{9} \, {\left(b^{3} + 6 \, a b c\right)} x^{\frac{9}{2}} + 6 \, a^{2} b \sqrt{x} + \frac{6}{5} \, {\left(a b^{2} + a^{2} c\right)} x^{\frac{5}{2}} - \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 + a*c^2)*x^(13/2) + 2/9*(b^3 + 6*a*b*c)*x^(9/2) + 6*a^2*b*sqrt(x) + 6/5*(a*b^2 + a^2*c)*x^(5/2) - 2/3*a^3/x^(3/2)","A",0
1061,1,82,0,1.054904," ","integrate((c*x^4+b*x^2+a)^3/x^(7/2),x, algorithm=""maxima"")","\frac{2}{19} \, c^{3} x^{\frac{19}{2}} + \frac{2}{5} \, b c^{2} x^{\frac{15}{2}} + \frac{6}{11} \, {\left(b^{2} c + a c^{2}\right)} x^{\frac{11}{2}} + \frac{2}{7} \, {\left(b^{3} + 6 \, a b c\right)} x^{\frac{7}{2}} + 2 \, {\left(a b^{2} + a^{2} c\right)} 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 + a*c^2)*x^(11/2) + 2/7*(b^3 + 6*a*b*c)*x^(7/2) + 2*(a*b^2 + a^2*c)*x^(3/2) - 2/5*(15*a^2*b*x^2 + a^3)/x^(5/2)","A",0
1062,0,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, x^{\frac{3}{2}}}{3 \, c} - \int \frac{b x^{\frac{5}{2}} + a \sqrt{x}}{c^{2} x^{4} + b c x^{2} + a c}\,{d x}"," ",0,"2/3*x^(3/2)/c - integrate((b*x^(5/2) + a*sqrt(x))/(c^2*x^4 + b*c*x^2 + a*c), x)","F",0
1063,0,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{x^{\frac{7}{2}}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate(x^(7/2)/(c*x^4 + b*x^2 + a), x)","F",0
1064,0,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\frac{2 \, \sqrt{x}}{a} - \int \frac{c x^{\frac{7}{2}} + b x^{\frac{3}{2}}}{a c x^{4} + a b x^{2} + a^{2}}\,{d x}"," ",0,"2*sqrt(x)/a - integrate((c*x^(7/2) + b*x^(3/2))/(a*c*x^4 + a*b*x^2 + a^2), x)","F",0
1068,0,0,0,0.000000," ","integrate(1/x^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","-\frac{2}{a \sqrt{x}} - \int \frac{c x^{\frac{5}{2}} + b \sqrt{x}}{a c x^{4} + a b x^{2} + a^{2}}\,{d x}"," ",0,"-2/(a*sqrt(x)) - integrate((c*x^(5/2) + b*sqrt(x))/(a*c*x^4 + a*b*x^2 + a^2), x)","F",0
1069,0,0,0,0.000000," ","integrate(1/x^(5/2)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, b \sqrt{x} + \frac{a}{x^{\frac{3}{2}}}\right)}}{3 \, a^{2}} + \int \frac{b c x^{\frac{7}{2}} + {\left(b^{2} - a c\right)} x^{\frac{3}{2}}}{a^{2} c x^{4} + a^{2} b x^{2} + a^{3}}\,{d x}"," ",0,"-2/3*(3*b*sqrt(x) + a/x^(3/2))/a^2 + integrate((b*c*x^(7/2) + (b^2 - a*c)*x^(3/2))/(a^2*c*x^4 + a^2*b*x^2 + a^3), x)","F",0
1070,0,0,0,0.000000," ","integrate(1/x^(7/2)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{5 \, b}{\sqrt{x}} - \frac{a}{x^{\frac{5}{2}}}\right)}}{5 \, a^{2}} + \int \frac{b c x^{\frac{5}{2}} + {\left(b^{2} - a c\right)} \sqrt{x}}{a^{2} c x^{4} + a^{2} b x^{2} + a^{3}}\,{d x}"," ",0,"2/5*(5*b/sqrt(x) - a/x^(5/2))/a^2 + integrate((b*c*x^(5/2) + (b^2 - a*c)*sqrt(x))/(a^2*c*x^4 + a^2*b*x^2 + a^3), x)","F",0
1071,0,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} - 2 \, a c\right)} x^{\frac{7}{2}} + a b x^{\frac{3}{2}}}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}} + \int \frac{{\left(3 \, b^{2} - 14 \, a c\right)} x^{\frac{5}{2}} + 3 \, a b \sqrt{x}}{4 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"-1/2*((b^2 - 2*a*c)*x^(7/2) + a*b*x^(3/2))/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2) + integrate(1/4*((3*b^2 - 14*a*c)*x^(5/2) + 3*a*b*sqrt(x))/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2), x)","F",0
1072,0,0,0,0.000000," ","integrate(x^(11/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b x^{\frac{9}{2}} + 2 \, a x^{\frac{5}{2}}}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}} + \int -\frac{b x^{\frac{7}{2}} + 10 \, a x^{\frac{3}{2}}}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}}\,{d x}"," ",0,"1/2*(b*x^(9/2) + 2*a*x^(5/2))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2) + integrate(-1/4*(b*x^(7/2) + 10*a*x^(3/2))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2), x)","F",0
1073,0,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b x^{\frac{7}{2}} + 2 \, a x^{\frac{3}{2}}}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}} - \int -\frac{b x^{\frac{5}{2}} - 6 \, a \sqrt{x}}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}}\,{d x}"," ",0,"1/2*(b*x^(7/2) + 2*a*x^(3/2))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2) - integrate(-1/4*(b*x^(5/2) - 6*a*sqrt(x))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2), x)","F",0
1074,0,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, c x^{\frac{9}{2}} + b x^{\frac{5}{2}}}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}} - \int -\frac{2 \, c x^{\frac{7}{2}} + 5 \, b x^{\frac{3}{2}}}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}}\,{d x}"," ",0,"-1/2*(2*c*x^(9/2) + b*x^(5/2))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2) - integrate(-1/4*(2*c*x^(7/2) + 5*b*x^(3/2))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2), x)","F",0
1075,0,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, c x^{\frac{7}{2}} + b x^{\frac{3}{2}}}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}} + \int -\frac{2 \, c x^{\frac{5}{2}} - 3 \, b \sqrt{x}}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}}\,{d x}"," ",0,"-1/2*(2*c*x^(7/2) + b*x^(3/2))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2) + integrate(-1/4*(2*c*x^(5/2) - 3*b*sqrt(x))/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2), x)","F",0
1076,0,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b c x^{\frac{9}{2}} + {\left(b^{2} - 2 \, a c\right)} x^{\frac{5}{2}}}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} + \int -\frac{b c x^{\frac{7}{2}} + {\left(b^{2} + 6 \, a c\right)} x^{\frac{3}{2}}}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}}\,{d x}"," ",0,"1/2*(b*c*x^(9/2) + (b^2 - 2*a*c)*x^(5/2))/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) + integrate(-1/4*(b*c*x^(7/2) + (b^2 + 6*a*c)*x^(3/2))/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2), x)","F",0
1077,0,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b c x^{\frac{7}{2}} + {\left(b^{2} - 2 \, a c\right)} x^{\frac{3}{2}}}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} - \int -\frac{b c x^{\frac{5}{2}} + {\left(b^{2} - 10 \, a c\right)} \sqrt{x}}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}}\,{d x}"," ",0,"1/2*(b*c*x^(7/2) + (b^2 - 2*a*c)*x^(3/2))/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) - integrate(-1/4*(b*c*x^(5/2) + (b^2 - 10*a*c)*sqrt(x))/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2), x)","F",0
1078,0,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{2} c - 14 \, a c^{2}\right)} x^{\frac{9}{2}} + {\left(3 \, b^{3} - 13 \, a b c\right)} x^{\frac{5}{2}} + 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{x}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)}} - \int \frac{{\left(3 \, b^{2} c - 14 \, a c^{2}\right)} x^{\frac{7}{2}} + {\left(3 \, b^{3} - 17 \, a b c\right)} x^{\frac{3}{2}}}{4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)}}\,{d x}"," ",0,"1/2*((3*b^2*c - 14*a*c^2)*x^(9/2) + (3*b^3 - 13*a*b*c)*x^(5/2) + 4*(a*b^2 - 4*a^2*c)*sqrt(x))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2) - integrate(1/4*((3*b^2*c - 14*a*c^2)*x^(7/2) + (3*b^3 - 17*a*b*c)*x^(3/2))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2), x)","F",0
1079,0,0,0,0.000000," ","integrate(1/x^(3/2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(5 \, b^{2} c - 18 \, a c^{2}\right)} x^{\frac{7}{2}} + {\left(5 \, b^{3} - 19 \, a b c\right)} x^{\frac{3}{2}} + \frac{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}{\sqrt{x}}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)}} - \int \frac{{\left(5 \, b^{2} c - 18 \, a c^{2}\right)} x^{\frac{5}{2}} + {\left(5 \, b^{3} - 23 \, a b c\right)} \sqrt{x}}{4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{2}\right)}}\,{d x}"," ",0,"-1/2*((5*b^2*c - 18*a*c^2)*x^(7/2) + (5*b^3 - 19*a*b*c)*x^(3/2) + 4*(a*b^2 - 4*a^2*c)/sqrt(x))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2) - integrate(1/4*((5*b^2*c - 18*a*c^2)*x^(5/2) + (5*b^3 - 23*a*b*c)*sqrt(x))/(a^3*b^2 - 4*a^4*c + (a^2*b^2*c - 4*a^3*c^2)*x^4 + (a^2*b^3 - 4*a^3*b*c)*x^2), x)","F",0
1080,0,0,0,0.000000," ","integrate(x^(15/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{2} c + 12 \, a c^{2}\right)} x^{\frac{17}{2}} + {\left(7 \, b^{3} + 44 \, a b c\right)} x^{\frac{13}{2}} + 24 \, a^{2} b x^{\frac{5}{2}} + {\left(35 \, a b^{2} + 4 \, a^{2} c\right)} x^{\frac{9}{2}}}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}} - \int \frac{3 \, {\left({\left(b^{2} + 12 \, a c\right)} x^{\frac{7}{2}} + 40 \, a b x^{\frac{3}{2}}\right)}}{32 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"1/16*(3*(b^2*c + 12*a*c^2)*x^(17/2) + (7*b^3 + 44*a*b*c)*x^(13/2) + 24*a^2*b*x^(5/2) + (35*a*b^2 + 4*a^2*c)*x^(9/2))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2) - integrate(3/32*((b^2 + 12*a*c)*x^(7/2) + 40*a*b*x^(3/2))/(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)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2), x)","F",0
1081,0,0,0,0.000000," ","integrate(x^(13/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(5 \, b^{2} c + 28 \, a c^{2}\right)} x^{\frac{15}{2}} + 9 \, {\left(b^{3} + 4 \, a b c\right)} x^{\frac{11}{2}} + 24 \, a^{2} b x^{\frac{3}{2}} + {\left(37 \, a b^{2} - 4 \, a^{2} c\right)} x^{\frac{7}{2}}}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}} + \int \frac{{\left(5 \, b^{2} + 28 \, a c\right)} x^{\frac{5}{2}} - 72 \, a b \sqrt{x}}{32 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"1/16*((5*b^2*c + 28*a*c^2)*x^(15/2) + 9*(b^3 + 4*a*b*c)*x^(11/2) + 24*a^2*b*x^(3/2) + (37*a*b^2 - 4*a^2*c)*x^(7/2))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2) + integrate(1/32*((5*b^2 + 28*a*c)*x^(5/2) - 72*a*b*sqrt(x))/(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)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2), x)","F",0
1082,0,0,0,0.000000," ","integrate(x^(11/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{24 \, b c^{2} x^{\frac{17}{2}} + {\left(41 \, b^{2} c - 20 \, a c^{2}\right)} x^{\frac{13}{2}} + {\left(13 \, b^{3} + 20 \, a b c\right)} x^{\frac{9}{2}} + 3 \, {\left(3 \, a b^{2} + 4 \, a^{2} c\right)} x^{\frac{5}{2}}}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}} + \int \frac{3 \, {\left(8 \, b c x^{\frac{7}{2}} + 5 \, {\left(3 \, b^{2} + 4 \, a c\right)} x^{\frac{3}{2}}\right)}}{32 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"-1/16*(24*b*c^2*x^(17/2) + (41*b^2*c - 20*a*c^2)*x^(13/2) + (13*b^3 + 20*a*b*c)*x^(9/2) + 3*(3*a*b^2 + 4*a^2*c)*x^(5/2))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2) + integrate(3/32*(8*b*c*x^(7/2) + 5*(3*b^2 + 4*a*c)*x^(3/2))/(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)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2), x)","F",0
1083,0,0,0,0.000000," ","integrate(x^(9/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{24 \, b c^{2} x^{\frac{15}{2}} + 3 \, {\left(13 \, b^{2} c - 4 \, a c^{2}\right)} x^{\frac{11}{2}} + {\left(11 \, b^{3} + 28 \, a b c\right)} x^{\frac{7}{2}} + {\left(7 \, a b^{2} + 20 \, a^{2} c\right)} x^{\frac{3}{2}}}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}} - \int \frac{3 \, {\left(8 \, b c x^{\frac{5}{2}} - {\left(7 \, b^{2} + 20 \, a c\right)} \sqrt{x}\right)}}{32 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"-1/16*(24*b*c^2*x^(15/2) + 3*(13*b^2*c - 4*a*c^2)*x^(11/2) + (11*b^3 + 28*a*b*c)*x^(7/2) + (7*a*b^2 + 20*a^2*c)*x^(3/2))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2) - integrate(3/32*(8*b*c*x^(5/2) - (7*b^2 + 20*a*c)*sqrt(x))/(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)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2), x)","F",0
1084,0,0,0,0.000000," ","integrate(x^(7/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(5 \, b^{2} c^{2} + 28 \, a c^{3}\right)} x^{\frac{17}{2}} + 2 \, {\left(5 \, b^{3} c + 16 \, a b c^{2}\right)} x^{\frac{13}{2}} + {\left(5 \, b^{4} + a b^{2} c + 60 \, a^{2} c^{2}\right)} x^{\frac{9}{2}} + {\left(a b^{3} + 20 \, a^{2} b c\right)} x^{\frac{5}{2}}}{16 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}} - \int \frac{{\left(5 \, b^{2} c + 28 \, a c^{2}\right)} x^{\frac{7}{2}} + 5 \, {\left(b^{3} + 20 \, a b c\right)} x^{\frac{3}{2}}}{32 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} x^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"1/16*((5*b^2*c^2 + 28*a*c^3)*x^(17/2) + 2*(5*b^3*c + 16*a*b*c^2)*x^(13/2) + (5*b^4 + a*b^2*c + 60*a^2*c^2)*x^(9/2) + (a*b^3 + 20*a^2*b*c)*x^(5/2))/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2) - integrate(1/32*((5*b^2*c + 28*a*c^2)*x^(7/2) + 5*(b^3 + 20*a*b*c)*x^(3/2))/(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)*x^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2), x)","F",0
1085,0,0,0,0.000000," ","integrate(x^(5/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{2} c^{2} + 12 \, a c^{3}\right)} x^{\frac{15}{2}} + 6 \, {\left(b^{3} c + 8 \, a b c^{2}\right)} x^{\frac{11}{2}} + {\left(3 \, b^{4} + 7 \, a b^{2} c + 68 \, a^{2} c^{2}\right)} x^{\frac{7}{2}} - {\left(a b^{3} - 28 \, a^{2} b c\right)} x^{\frac{3}{2}}}{16 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}} + \int \frac{3 \, {\left({\left(b^{2} c + 12 \, a c^{2}\right)} x^{\frac{5}{2}} + {\left(b^{3} - 28 \, a b c\right)} \sqrt{x}\right)}}{32 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} x^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"1/16*(3*(b^2*c^2 + 12*a*c^3)*x^(15/2) + 6*(b^3*c + 8*a*b*c^2)*x^(11/2) + (3*b^4 + 7*a*b^2*c + 68*a^2*c^2)*x^(7/2) - (a*b^3 - 28*a^2*b*c)*x^(3/2))/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2) + integrate(3/32*((b^2*c + 12*a*c^2)*x^(5/2) + (b^3 - 28*a*b*c)*sqrt(x))/(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)*x^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2), x)","F",0
1086,0,0,0,0.000000," ","integrate(x^(3/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{3} c^{2} - 12 \, a b c^{3}\right)} x^{\frac{17}{2}} + {\left(6 \, b^{4} c - 71 \, a b^{2} c^{2} + 44 \, a^{2} c^{3}\right)} x^{\frac{13}{2}} + {\left(3 \, b^{5} - 28 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} x^{\frac{9}{2}} + {\left(7 \, a b^{4} - 59 \, a^{2} b^{2} c + 76 \, a^{3} c^{2}\right)} x^{\frac{5}{2}}}{16 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} + \int -\frac{3 \, {\left({\left(b^{3} c - 12 \, a b c^{2}\right)} x^{\frac{7}{2}} + {\left(b^{4} - 13 \, a b^{2} c - 44 \, a^{2} c^{2}\right)} x^{\frac{3}{2}}\right)}}{32 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"1/16*(3*(b^3*c^2 - 12*a*b*c^3)*x^(17/2) + (6*b^4*c - 71*a*b^2*c^2 + 44*a^2*c^3)*x^(13/2) + (3*b^5 - 28*a*b^3*c - 8*a^2*b*c^2)*x^(9/2) + (7*a*b^4 - 59*a^2*b^2*c + 76*a^3*c^2)*x^(5/2))/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) + integrate(-3/32*((b^3*c - 12*a*b*c^2)*x^(7/2) + (b^4 - 13*a*b^2*c - 44*a^2*c^2)*x^(3/2))/(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)*x^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2), x)","F",0
1087,0,0,0,0.000000," ","integrate(x^(1/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(5 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} x^{\frac{15}{2}} + {\left(10 \, b^{4} c - 89 \, a b^{2} c^{2} + 52 \, a^{2} c^{3}\right)} x^{\frac{11}{2}} + {\left(5 \, b^{5} - 36 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} x^{\frac{7}{2}} + 3 \, {\left(3 \, a b^{4} - 23 \, a^{2} b^{2} c + 28 \, a^{3} c^{2}\right)} x^{\frac{3}{2}}}{16 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} - \int -\frac{{\left(5 \, b^{3} c - 44 \, a b c^{2}\right)} x^{\frac{5}{2}} + {\left(5 \, b^{4} - 49 \, a b^{2} c + 260 \, a^{2} c^{2}\right)} \sqrt{x}}{32 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"1/16*((5*b^3*c^2 - 44*a*b*c^3)*x^(15/2) + (10*b^4*c - 89*a*b^2*c^2 + 52*a^2*c^3)*x^(11/2) + (5*b^5 - 36*a*b^3*c - 8*a^2*b*c^2)*x^(7/2) + 3*(3*a*b^4 - 23*a^2*b^2*c + 28*a^3*c^2)*x^(3/2))/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) - integrate(-1/32*((5*b^3*c - 44*a*b*c^2)*x^(5/2) + (5*b^4 - 49*a*b^2*c + 260*a^2*c^2)*sqrt(x))/(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)*x^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2), x)","F",0
1088,0,0,0,0.000000," ","integrate(1/x^(1/2)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(7 \, b^{4} c^{2} - 59 \, a b^{2} c^{3} + 140 \, a^{2} c^{4}\right)} x^{\frac{17}{2}} + {\left(42 \, b^{5} c - 347 \, a b^{3} c^{2} + 788 \, a^{2} b c^{3}\right)} x^{\frac{13}{2}} + {\left(21 \, b^{6} - 121 \, a b^{4} c - 41 \, a^{2} b^{2} c^{2} + 900 \, a^{3} c^{3}\right)} x^{\frac{9}{2}} + {\left(49 \, a b^{5} - 398 \, a^{2} b^{3} c + 832 \, a^{3} b c^{2}\right)} x^{\frac{5}{2}} + 32 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} \sqrt{x}}{16 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2}\right)}} - \int \frac{3 \, {\left({\left(7 \, b^{4} c - 59 \, a b^{2} c^{2} + 140 \, a^{2} c^{3}\right)} x^{\frac{7}{2}} + {\left(7 \, b^{5} - 66 \, a b^{3} c + 192 \, a^{2} b c^{2}\right)} x^{\frac{3}{2}}\right)}}{32 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{4} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}}\,{d x}"," ",0,"1/16*(3*(7*b^4*c^2 - 59*a*b^2*c^3 + 140*a^2*c^4)*x^(17/2) + (42*b^5*c - 347*a*b^3*c^2 + 788*a^2*b*c^3)*x^(13/2) + (21*b^6 - 121*a*b^4*c - 41*a^2*b^2*c^2 + 900*a^3*c^3)*x^(9/2) + (49*a*b^5 - 398*a^2*b^3*c + 832*a^3*b*c^2)*x^(5/2) + 32*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*sqrt(x))/(a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2) - integrate(3/32*((7*b^4*c - 59*a*b^2*c^2 + 140*a^2*c^3)*x^(7/2) + (7*b^5 - 66*a*b^3*c + 192*a^2*b*c^2)*x^(3/2))/(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)*x^4 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2), x)","F",0
1089,0,0,0,0.000000," ","integrate((d*x)^(3/2)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
1105,1,195,0,1.308094," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{c^{3} d^{m} x^{13} x^{m}}{m + 13} + \frac{3 \, b c^{2} d^{m} x^{11} x^{m}}{m + 11} + \frac{3 \, b^{2} c d^{m} x^{9} x^{m}}{m + 9} + \frac{3 \, a c^{2} d^{m} x^{9} x^{m}}{m + 9} + \frac{b^{3} d^{m} x^{7} x^{m}}{m + 7} + \frac{6 \, a b c d^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, a b^{2} d^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, a^{2} c d^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, a^{2} b d^{m} x^{3} x^{m}}{m + 3} + \frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}}"," ",0,"c^3*d^m*x^13*x^m/(m + 13) + 3*b*c^2*d^m*x^11*x^m/(m + 11) + 3*b^2*c*d^m*x^9*x^m/(m + 9) + 3*a*c^2*d^m*x^9*x^m/(m + 9) + b^3*d^m*x^7*x^m/(m + 7) + 6*a*b*c*d^m*x^7*x^m/(m + 7) + 3*a*b^2*d^m*x^5*x^m/(m + 5) + 3*a^2*c*d^m*x^5*x^m/(m + 5) + 3*a^2*b*d^m*x^3*x^m/(m + 3) + (d*x)^(m + 1)*a^3/(d*(m + 1))","A",0
1106,1,110,0,1.107244," ","integrate((d*x)^m*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{c^{2} d^{m} x^{9} x^{m}}{m + 9} + \frac{2 \, b c d^{m} x^{7} x^{m}}{m + 7} + \frac{b^{2} d^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, a c d^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, a b d^{m} x^{3} x^{m}}{m + 3} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}}"," ",0,"c^2*d^m*x^9*x^m/(m + 9) + 2*b*c*d^m*x^7*x^m/(m + 7) + b^2*d^m*x^5*x^m/(m + 5) + 2*a*c*d^m*x^5*x^m/(m + 5) + 2*a*b*d^m*x^3*x^m/(m + 3) + (d*x)^(m + 1)*a^2/(d*(m + 1))","A",0
1107,1,50,0,1.087255," ","integrate((d*x)^m*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{c d^{m} x^{5} x^{m}}{m + 5} + \frac{b d^{m} x^{3} x^{m}}{m + 3} + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"c*d^m*x^5*x^m/(m + 5) + b*d^m*x^3*x^m/(m + 3) + (d*x)^(m + 1)*a/(d*(m + 1))","A",0
1108,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
