1,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/4),x)","\int \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{3}{4}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(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)","\int \sqrt[4]{a^{2} + 2 a b x^{2} + b^{2} x^{4}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(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)","\int \frac{1}{\sqrt[4]{a^{2} + 2 a b x^{2} + b^{2} x^{4}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-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)","\int \frac{1}{\left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-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)","\int \frac{1}{\left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-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)","\int \frac{1}{\left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-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)","\int \frac{1}{\left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-9/4), x)","F",0
8,1,63,0,0.801883," ","integrate(1/(x**4+2*a*x**2+a**2+b),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} b^{2} + 256 b^{3}\right) - 32 t^{2} a b + 1, \left( t \mapsto t \log{\left(64 t^{3} a^{3} b + 64 t^{3} a b^{2} - 4 t a^{2} + 4 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2*b**2 + 256*b**3) - 32*_t**2*a*b + 1, Lambda(_t, _t*log(64*_t**3*a**3*b + 64*_t**3*a*b**2 - 4*_t*a**2 + 4*_t*b + x)))","A",0
9,1,257,0,0.632743," ","integrate(1/(x**4+2*a*x**2+a**2-1),x)","\frac{\sqrt{- \frac{1}{a - 1}} \log{\left(- a^{3} \left(- \frac{1}{a - 1}\right)^{\frac{3}{2}} - a^{2} \sqrt{- \frac{1}{a - 1}} + a \left(- \frac{1}{a - 1}\right)^{\frac{3}{2}} + x - \sqrt{- \frac{1}{a - 1}} \right)}}{4} - \frac{\sqrt{- \frac{1}{a - 1}} \log{\left(a^{3} \left(- \frac{1}{a - 1}\right)^{\frac{3}{2}} + a^{2} \sqrt{- \frac{1}{a - 1}} - a \left(- \frac{1}{a - 1}\right)^{\frac{3}{2}} + x + \sqrt{- \frac{1}{a - 1}} \right)}}{4} + \frac{\sqrt{- \frac{1}{a + 1}} \log{\left(- a^{3} \left(- \frac{1}{a + 1}\right)^{\frac{3}{2}} - a^{2} \sqrt{- \frac{1}{a + 1}} + a \left(- \frac{1}{a + 1}\right)^{\frac{3}{2}} + x - \sqrt{- \frac{1}{a + 1}} \right)}}{4} - \frac{\sqrt{- \frac{1}{a + 1}} \log{\left(a^{3} \left(- \frac{1}{a + 1}\right)^{\frac{3}{2}} + a^{2} \sqrt{- \frac{1}{a + 1}} - a \left(- \frac{1}{a + 1}\right)^{\frac{3}{2}} + x + \sqrt{- \frac{1}{a + 1}} \right)}}{4}"," ",0,"sqrt(-1/(a - 1))*log(-a**3*(-1/(a - 1))**(3/2) - a**2*sqrt(-1/(a - 1)) + a*(-1/(a - 1))**(3/2) + x - sqrt(-1/(a - 1)))/4 - sqrt(-1/(a - 1))*log(a**3*(-1/(a - 1))**(3/2) + a**2*sqrt(-1/(a - 1)) - a*(-1/(a - 1))**(3/2) + x + sqrt(-1/(a - 1)))/4 + sqrt(-1/(a + 1))*log(-a**3*(-1/(a + 1))**(3/2) - a**2*sqrt(-1/(a + 1)) + a*(-1/(a + 1))**(3/2) + x - sqrt(-1/(a + 1)))/4 - sqrt(-1/(a + 1))*log(a**3*(-1/(a + 1))**(3/2) + a**2*sqrt(-1/(a + 1)) - a*(-1/(a + 1))**(3/2) + x + sqrt(-1/(a + 1)))/4","B",0
10,1,48,0,0.581189," ","integrate(1/(x**4+2*a*x**2+a**2+1),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} + 256\right) - 32 t^{2} a + 1, \left( t \mapsto t \log{\left(64 t^{3} a^{3} + 64 t^{3} a - 4 t a^{2} + 4 t + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2 + 256) - 32*_t**2*a + 1, Lambda(_t, _t*log(64*_t**3*a**3 + 64*_t**3*a - 4*_t*a**2 + 4*_t + x)))","A",0
11,1,26,0,0.183104," ","integrate(1/(x**4-5*x**2+4),x)","\frac{\log{\left(x - 2 \right)}}{12} - \frac{\log{\left(x - 1 \right)}}{6} + \frac{\log{\left(x + 1 \right)}}{6} - \frac{\log{\left(x + 2 \right)}}{12}"," ",0,"log(x - 2)/12 - log(x - 1)/6 + log(x + 1)/6 - log(x + 2)/12","B",0
12,1,20,0,0.160557," ","integrate(1/(x**4+4*x**2+3),x)","\frac{\operatorname{atan}{\left(x \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{6}"," ",0,"atan(x)/2 - sqrt(3)*atan(sqrt(3)*x/3)/6","A",0
13,1,70,0,0.219423," ","integrate(1/(x**4+5*x**2+9),x)","- \frac{\log{\left(x^{2} - x + 3 \right)}}{12} + \frac{\log{\left(x^{2} + x + 3 \right)}}{12} + \frac{\sqrt{11} \operatorname{atan}{\left(\frac{2 \sqrt{11} x}{11} - \frac{\sqrt{11}}{11} \right)}}{66} + \frac{\sqrt{11} \operatorname{atan}{\left(\frac{2 \sqrt{11} x}{11} + \frac{\sqrt{11}}{11} \right)}}{66}"," ",0,"-log(x**2 - x + 3)/12 + log(x**2 + x + 3)/12 + sqrt(11)*atan(2*sqrt(11)*x/11 - sqrt(11)/11)/66 + sqrt(11)*atan(2*sqrt(11)*x/11 + sqrt(11)/11)/66","A",0
14,1,63,0,0.206125," ","integrate(1/(x**4-x**2+1),x)","- \frac{\sqrt{3} \log{\left(x^{2} - \sqrt{3} x + 1 \right)}}{12} + \frac{\sqrt{3} \log{\left(x^{2} + \sqrt{3} x + 1 \right)}}{12} + \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{2} + \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{2}"," ",0,"-sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 + sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 + atan(2*x - sqrt(3))/2 + atan(2*x + sqrt(3))/2","A",0
15,1,899,0,1.132691," ","integrate(1/(x**4+2*x**2+2),x)","\sqrt{\frac{1}{64} + \frac{\sqrt{2}}{64}} \log{\left(x^{2} + x \left(- 4 \sqrt{2} \sqrt{1 + \sqrt{2}} - \sqrt{1 + \sqrt{2}} + 3 \sqrt{1 + \sqrt{2}} \sqrt{2 \sqrt{2} + 3}\right) - 15 \sqrt{2 \sqrt{2} + 3} - 7 \sqrt{2} \sqrt{2 \sqrt{2} + 3} + 29 + 23 \sqrt{2} \right)} - \sqrt{\frac{1}{64} + \frac{\sqrt{2}}{64}} \log{\left(x^{2} + x \left(- 3 \sqrt{1 + \sqrt{2}} \sqrt{2 \sqrt{2} + 3} + \sqrt{1 + \sqrt{2}} + 4 \sqrt{2} \sqrt{1 + \sqrt{2}}\right) - 15 \sqrt{2 \sqrt{2} + 3} - 7 \sqrt{2} \sqrt{2 \sqrt{2} + 3} + 29 + 23 \sqrt{2} \right)} + 2 \sqrt{- \frac{\sqrt{2 \sqrt{2} + 3}}{32} + \frac{1}{64} + \frac{3 \sqrt{2}}{64}} \operatorname{atan}{\left(\frac{2 x}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} - \frac{4 \sqrt{2} \sqrt{1 + \sqrt{2}}}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} - \frac{\sqrt{1 + \sqrt{2}}}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} + \frac{3 \sqrt{1 + \sqrt{2}} \sqrt{2 \sqrt{2} + 3}}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} \right)} + 2 \sqrt{- \frac{\sqrt{2 \sqrt{2} + 3}}{32} + \frac{1}{64} + \frac{3 \sqrt{2}}{64}} \operatorname{atan}{\left(\frac{2 x}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} - \frac{3 \sqrt{1 + \sqrt{2}} \sqrt{2 \sqrt{2} + 3}}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} + \frac{\sqrt{1 + \sqrt{2}}}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} + \frac{4 \sqrt{2} \sqrt{1 + \sqrt{2}}}{\sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}} + \sqrt{2 \sqrt{2} + 3} \sqrt{- 2 \sqrt{2 \sqrt{2} + 3} + 1 + 3 \sqrt{2}}} \right)}"," ",0,"sqrt(1/64 + sqrt(2)/64)*log(x**2 + x*(-4*sqrt(2)*sqrt(1 + sqrt(2)) - sqrt(1 + sqrt(2)) + 3*sqrt(1 + sqrt(2))*sqrt(2*sqrt(2) + 3)) - 15*sqrt(2*sqrt(2) + 3) - 7*sqrt(2)*sqrt(2*sqrt(2) + 3) + 29 + 23*sqrt(2)) - sqrt(1/64 + sqrt(2)/64)*log(x**2 + x*(-3*sqrt(1 + sqrt(2))*sqrt(2*sqrt(2) + 3) + sqrt(1 + sqrt(2)) + 4*sqrt(2)*sqrt(1 + sqrt(2))) - 15*sqrt(2*sqrt(2) + 3) - 7*sqrt(2)*sqrt(2*sqrt(2) + 3) + 29 + 23*sqrt(2)) + 2*sqrt(-sqrt(2*sqrt(2) + 3)/32 + 1/64 + 3*sqrt(2)/64)*atan(2*x/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2))) - 4*sqrt(2)*sqrt(1 + sqrt(2))/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2))) - sqrt(1 + sqrt(2))/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2))) + 3*sqrt(1 + sqrt(2))*sqrt(2*sqrt(2) + 3)/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)))) + 2*sqrt(-sqrt(2*sqrt(2) + 3)/32 + 1/64 + 3*sqrt(2)/64)*atan(2*x/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2))) - 3*sqrt(1 + sqrt(2))*sqrt(2*sqrt(2) + 3)/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2))) + sqrt(1 + sqrt(2))/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2))) + 4*sqrt(2)*sqrt(1 + sqrt(2))/(sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2)) + sqrt(2*sqrt(2) + 3)*sqrt(-2*sqrt(2*sqrt(2) + 3) + 1 + 3*sqrt(2))))","B",0
16,0,0,0,0.000000," ","integrate(1/(-3*x**4+5*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- 3 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 4 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 3 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 2 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + x^{2} + 2}}\, dx"," ",0,"Integral(1/sqrt(-3*x**4 + x**2 + 2), x)","F",0
21,1,37,0,0.685072," ","integrate(1/(-3*x**4+2)**(1/2),x)","\frac{\sqrt{2} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{3 x^{4} e^{2 i \pi}}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(2)*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 3*x**4*exp_polar(2*I*pi)/2)/(8*gamma(5/4))","A",0
22,0,0,0,0.000000," ","integrate(1/(-3*x**4-x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- 3 x^{4} - x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 2 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 3 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 4 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 7 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 6 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 5 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 4 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 3 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 2 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + x^{2} + 3}}\, dx"," ",0,"Integral(1/sqrt(-2*x**4 + x**2 + 3), x)","F",0
34,1,37,0,0.690627," ","integrate(1/(-2*x**4+3)**(1/2),x)","\frac{\sqrt{3} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{2 x^{4} e^{2 i \pi}}{3}} \right)}}{12 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(3)*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 2*x**4*exp_polar(2*I*pi)/3)/(12*gamma(5/4))","A",0
35,0,0,0,0.000000," ","integrate(1/(-2*x**4-x**2+3)**(1/2),x)","\int \frac{1}{\sqrt{- 2 x^{4} - x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 2 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 3 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 4 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 5 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 6 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 7 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 5 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 4 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 3 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 2 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + x^{2} - 2}}\, dx"," ",0,"Integral(1/sqrt(3*x**4 + x**2 - 2), x)","F",0
47,1,34,0,0.727548," ","integrate(1/(3*x**4-2)**(1/2),x)","- \frac{\sqrt{2} i x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{3 x^{4}}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-sqrt(2)*I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 3*x**4/2)/(8*gamma(5/4))","C",0
48,0,0,0,0.000000," ","integrate(1/(3*x**4-x**2-2)**(1/2),x)","\int \frac{1}{\sqrt{3 x^{4} - x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 2 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 3 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 4 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 5 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 7 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 6 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 5 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 4 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 3 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 2 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + x^{2} - 3}}\, dx"," ",0,"Integral(1/sqrt(2*x**4 + x**2 - 3), x)","F",0
60,1,34,0,0.730366," ","integrate(1/(2*x**4-3)**(1/2),x)","- \frac{\sqrt{3} i x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{2 x^{4}}{3}} \right)}}{12 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-sqrt(3)*I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 2*x**4/3)/(12*gamma(5/4))","C",0
61,0,0,0,0.000000," ","integrate(1/(2*x**4-x**2-3)**(1/2),x)","\int \frac{1}{\sqrt{2 x^{4} - x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 2 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 3 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 4 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 5 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 4 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 3 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 2 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + x^{2} + 2}}\, dx"," ",0,"Integral(1/sqrt(3*x**4 + x**2 + 2), x)","F",0
71,1,36,0,0.705743," ","integrate(1/(3*x**4+2)**(1/2),x)","\frac{\sqrt{2} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{3 x^{4} e^{i \pi}}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(2)*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 3*x**4*exp_polar(I*pi)/2)/(8*gamma(5/4))","C",0
72,0,0,0,0.000000," ","integrate(1/(3*x**4-x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{3 x^{4} - x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 2 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 3 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 4 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} - 6 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 9 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 8 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 7 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 6 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 5 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 4 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 3 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 2 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + x^{2} + 3}}\, dx"," ",0,"Integral(1/sqrt(2*x**4 + x**2 + 3), x)","F",0
87,1,36,0,1.185760," ","integrate(1/(2*x**4+3)**(1/2),x)","\frac{\sqrt{3} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{2 x^{4} e^{i \pi}}{3}} \right)}}{12 \Gamma\left(\frac{5}{4}\right)}"," ",0,"sqrt(3)*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 2*x**4*exp_polar(I*pi)/3)/(12*gamma(5/4))","C",0
88,0,0,0,0.000000," ","integrate(1/(2*x**4-x**2+3)**(1/2),x)","\int \frac{1}{\sqrt{2 x^{4} - x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 2 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 3 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 4 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 5 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 6 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} - 7 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 7 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 6 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 5 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 4 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 3 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 2 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + x^{2} - 3}}\, dx"," ",0,"Integral(1/sqrt(-2*x**4 + x**2 - 3), x)","F",0
102,1,39,0,0.713026," ","integrate(1/(-2*x**4-3)**(1/2),x)","- \frac{\sqrt{3} i x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{2 x^{4} e^{i \pi}}{3}} \right)}}{12 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-sqrt(3)*I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 2*x**4*exp_polar(I*pi)/3)/(12*gamma(5/4))","C",0
103,0,0,0,0.000000," ","integrate(1/(-2*x**4-x**2-3)**(1/2),x)","\int \frac{1}{\sqrt{- 2 x^{4} - x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 2 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 3 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 4 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} - 5 x^{2} - 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 6 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 5 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 4 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 3 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 2 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + x^{2} - 2}}\, dx"," ",0,"Integral(1/sqrt(-3*x**4 + x**2 - 2), x)","F",0
114,1,39,0,0.702895," ","integrate(1/(-3*x**4-2)**(1/2),x)","- \frac{\sqrt{2} i x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{3 x^{4} e^{i \pi}}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}"," ",0,"-sqrt(2)*I*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), 3*x**4*exp_polar(I*pi)/2)/(8*gamma(5/4))","C",0
115,0,0,0,0.000000," ","integrate(1/(-3*x**4-x**2-2)**(1/2),x)","\int \frac{1}{\sqrt{- 3 x^{4} - x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 2 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 3 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 4 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} - 5 x^{2} - 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{5 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{4 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{3 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{2 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 2 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 3 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 4 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 5 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 6 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 7 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 8 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- 9 x^{4} + 5 x^{2} + 2}}\, dx"," ",0,"Integral(1/sqrt(-9*x**4 + 5*x**2 + 2), x)","F",0
134,1,12,0,0.073637," ","integrate(x**2*(c*x**4+b*x**2),x)","\frac{b x^{5}}{5} + \frac{c x^{7}}{7}"," ",0,"b*x**5/5 + c*x**7/7","A",0
135,1,12,0,0.064647," ","integrate(x*(c*x**4+b*x**2),x)","\frac{b x^{4}}{4} + \frac{c x^{6}}{6}"," ",0,"b*x**4/4 + c*x**6/6","A",0
136,1,12,0,0.062669," ","integrate(c*x**4+b*x**2,x)","\frac{b x^{3}}{3} + \frac{c x^{5}}{5}"," ",0,"b*x**3/3 + c*x**5/5","A",0
137,1,12,0,0.066786," ","integrate((c*x**4+b*x**2)/x,x)","\frac{b x^{2}}{2} + \frac{c x^{4}}{4}"," ",0,"b*x**2/2 + c*x**4/4","A",0
138,1,8,0,0.065250," ","integrate((c*x**4+b*x**2)/x**2,x)","b x + \frac{c x^{3}}{3}"," ",0,"b*x + c*x**3/3","A",0
139,1,10,0,0.099331," ","integrate((c*x**4+b*x**2)/x**3,x)","b \log{\left(x \right)} + \frac{c x^{2}}{2}"," ",0,"b*log(x) + c*x**2/2","A",0
140,1,5,0,0.102655," ","integrate((c*x**4+b*x**2)/x**4,x)","- \frac{b}{x} + c x"," ",0,"-b/x + c*x","A",0
141,1,10,0,0.117244," ","integrate((c*x**4+b*x**2)/x**5,x)","- \frac{b}{2 x^{2}} + c \log{\left(x \right)}"," ",0,"-b/(2*x**2) + c*log(x)","A",0
142,1,14,0,0.124805," ","integrate((c*x**4+b*x**2)/x**6,x)","\frac{- b - 3 c x^{2}}{3 x^{3}}"," ",0,"(-b - 3*c*x**2)/(3*x**3)","A",0
143,1,14,0,0.130990," ","integrate((c*x**4+b*x**2)/x**7,x)","\frac{- b - 2 c x^{2}}{4 x^{4}}"," ",0,"(-b - 2*c*x**2)/(4*x**4)","A",0
144,1,15,0,0.153716," ","integrate((c*x**4+b*x**2)/x**8,x)","\frac{- 3 b - 5 c x^{2}}{15 x^{5}}"," ",0,"(-3*b - 5*c*x**2)/(15*x**5)","A",0
145,1,26,0,0.071927," ","integrate((c*x**4+b*x**2)**2,x)","\frac{b^{2} x^{5}}{5} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9}"," ",0,"b**2*x**5/5 + 2*b*c*x**7/7 + c**2*x**9/9","A",0
146,1,24,0,0.072139," ","integrate((c*x**4+b*x**2)**2/x,x)","\frac{b^{2} x^{4}}{4} + \frac{b c x^{6}}{3} + \frac{c^{2} x^{8}}{8}"," ",0,"b**2*x**4/4 + b*c*x**6/3 + c**2*x**8/8","A",0
147,1,26,0,0.072513," ","integrate((c*x**4+b*x**2)**2/x**2,x)","\frac{b^{2} x^{3}}{3} + \frac{2 b c x^{5}}{5} + \frac{c^{2} x^{7}}{7}"," ",0,"b**2*x**3/3 + 2*b*c*x**5/5 + c**2*x**7/7","A",0
148,1,24,0,0.097099," ","integrate((c*x**4+b*x**2)**2/x**3,x)","\frac{b^{2} x^{2}}{2} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{6}}{6}"," ",0,"b**2*x**2/2 + b*c*x**4/2 + c**2*x**6/6","B",0
149,1,22,0,0.075187," ","integrate((c*x**4+b*x**2)**2/x**4,x)","b^{2} x + \frac{2 b c x^{3}}{3} + \frac{c^{2} x^{5}}{5}"," ",0,"b**2*x + 2*b*c*x**3/3 + c**2*x**5/5","A",0
150,1,20,0,0.112611," ","integrate((c*x**4+b*x**2)**2/x**5,x)","b^{2} \log{\left(x \right)} + b c x^{2} + \frac{c^{2} x^{4}}{4}"," ",0,"b**2*log(x) + b*c*x**2 + c**2*x**4/4","A",0
151,1,19,0,0.112531," ","integrate((c*x**4+b*x**2)**2/x**6,x)","- \frac{b^{2}}{x} + 2 b c x + \frac{c^{2} x^{3}}{3}"," ",0,"-b**2/x + 2*b*c*x + c**2*x**3/3","A",0
152,1,24,0,0.146919," ","integrate((c*x**4+b*x**2)**2/x**7,x)","- \frac{b^{2}}{2 x^{2}} + 2 b c \log{\left(x \right)} + \frac{c^{2} x^{2}}{2}"," ",0,"-b**2/(2*x**2) + 2*b*c*log(x) + c**2*x**2/2","A",0
153,1,22,0,0.165234," ","integrate((c*x**4+b*x**2)**2/x**8,x)","c^{2} x + \frac{- b^{2} - 6 b c x^{2}}{3 x^{3}}"," ",0,"c**2*x + (-b**2 - 6*b*c*x**2)/(3*x**3)","A",0
154,1,24,0,0.190422," ","integrate((c*x**4+b*x**2)**2/x**9,x)","c^{2} \log{\left(x \right)} + \frac{- b^{2} - 4 b c x^{2}}{4 x^{4}}"," ",0,"c**2*log(x) + (-b**2 - 4*b*c*x**2)/(4*x**4)","A",0
155,1,27,0,0.198245," ","integrate((c*x**4+b*x**2)**2/x**10,x)","\frac{- 3 b^{2} - 10 b c x^{2} - 15 c^{2} x^{4}}{15 x^{5}}"," ",0,"(-3*b**2 - 10*b*c*x**2 - 15*c**2*x**4)/(15*x**5)","A",0
156,1,26,0,0.211824," ","integrate((c*x**4+b*x**2)**2/x**11,x)","\frac{- b^{2} - 3 b c x^{2} - 3 c^{2} x^{4}}{6 x^{6}}"," ",0,"(-b**2 - 3*b*c*x**2 - 3*c**2*x**4)/(6*x**6)","A",0
157,1,27,0,0.231242," ","integrate((c*x**4+b*x**2)**2/x**12,x)","\frac{- 15 b^{2} - 42 b c x^{2} - 35 c^{2} x^{4}}{105 x^{7}}"," ",0,"(-15*b**2 - 42*b*c*x**2 - 35*c**2*x**4)/(105*x**7)","A",0
158,1,37,0,0.081804," ","integrate((c*x**4+b*x**2)**3/x**2,x)","\frac{b^{3} x^{5}}{5} + \frac{3 b^{2} c x^{7}}{7} + \frac{b c^{2} x^{9}}{3} + \frac{c^{3} x^{11}}{11}"," ",0,"b**3*x**5/5 + 3*b**2*c*x**7/7 + b*c**2*x**9/3 + c**3*x**11/11","A",0
159,1,37,0,0.077038," ","integrate((c*x**4+b*x**2)**3/x**3,x)","\frac{b^{3} x^{4}}{4} + \frac{b^{2} c x^{6}}{2} + \frac{3 b c^{2} x^{8}}{8} + \frac{c^{3} x^{10}}{10}"," ",0,"b**3*x**4/4 + b**2*c*x**6/2 + 3*b*c**2*x**8/8 + c**3*x**10/10","A",0
160,1,39,0,0.085923," ","integrate((c*x**4+b*x**2)**3/x**4,x)","\frac{b^{3} x^{3}}{3} + \frac{3 b^{2} c x^{5}}{5} + \frac{3 b c^{2} x^{7}}{7} + \frac{c^{3} x^{9}}{9}"," ",0,"b**3*x**3/3 + 3*b**2*c*x**5/5 + 3*b*c**2*x**7/7 + c**3*x**9/9","A",0
161,1,37,0,0.081538," ","integrate((c*x**4+b*x**2)**3/x**5,x)","\frac{b^{3} x^{2}}{2} + \frac{3 b^{2} c x^{4}}{4} + \frac{b c^{2} x^{6}}{2} + \frac{c^{3} x^{8}}{8}"," ",0,"b**3*x**2/2 + 3*b**2*c*x**4/4 + b*c**2*x**6/2 + c**3*x**8/8","B",0
162,1,32,0,0.081266," ","integrate((c*x**4+b*x**2)**3/x**6,x)","b^{3} x + b^{2} c x^{3} + \frac{3 b c^{2} x^{5}}{5} + \frac{c^{3} x^{7}}{7}"," ",0,"b**3*x + b**2*c*x**3 + 3*b*c**2*x**5/5 + c**3*x**7/7","A",0
163,1,37,0,0.124608," ","integrate((c*x**4+b*x**2)**3/x**7,x)","b^{3} \log{\left(x \right)} + \frac{3 b^{2} c x^{2}}{2} + \frac{3 b c^{2} x^{4}}{4} + \frac{c^{3} x^{6}}{6}"," ",0,"b**3*log(x) + 3*b**2*c*x**2/2 + 3*b*c**2*x**4/4 + c**3*x**6/6","A",0
164,1,29,0,0.123111," ","integrate((c*x**4+b*x**2)**3/x**8,x)","- \frac{b^{3}}{x} + 3 b^{2} c x + b c^{2} x^{3} + \frac{c^{3} x^{5}}{5}"," ",0,"-b**3/x + 3*b**2*c*x + b*c**2*x**3 + c**3*x**5/5","A",0
165,1,37,0,0.170370," ","integrate((c*x**4+b*x**2)**3/x**9,x)","- \frac{b^{3}}{2 x^{2}} + 3 b^{2} c \log{\left(x \right)} + \frac{3 b c^{2} x^{2}}{2} + \frac{c^{3} x^{4}}{4}"," ",0,"-b**3/(2*x**2) + 3*b**2*c*log(x) + 3*b*c**2*x**2/2 + c**3*x**4/4","A",0
166,1,36,0,0.167947," ","integrate((c*x**4+b*x**2)**3/x**10,x)","3 b c^{2} x + \frac{c^{3} x^{3}}{3} + \frac{- b^{3} - 9 b^{2} c x^{2}}{3 x^{3}}"," ",0,"3*b*c**2*x + c**3*x**3/3 + (-b**3 - 9*b**2*c*x**2)/(3*x**3)","A",0
167,1,37,0,0.225618," ","integrate((c*x**4+b*x**2)**3/x**11,x)","3 b c^{2} \log{\left(x \right)} + \frac{c^{3} x^{2}}{2} + \frac{- b^{3} - 6 b^{2} c x^{2}}{4 x^{4}}"," ",0,"3*b*c**2*log(x) + c**3*x**2/2 + (-b**3 - 6*b**2*c*x**2)/(4*x**4)","A",0
168,1,34,0,0.232293," ","integrate((c*x**4+b*x**2)**3/x**12,x)","c^{3} x + \frac{- b^{3} - 5 b^{2} c x^{2} - 15 b c^{2} x^{4}}{5 x^{5}}"," ",0,"c**3*x + (-b**3 - 5*b**2*c*x**2 - 15*b*c**2*x**4)/(5*x**5)","A",0
169,1,37,0,0.291923," ","integrate((c*x**4+b*x**2)**3/x**13,x)","c^{3} \log{\left(x \right)} + \frac{- 2 b^{3} - 9 b^{2} c x^{2} - 18 b c^{2} x^{4}}{12 x^{6}}"," ",0,"c**3*log(x) + (-2*b**3 - 9*b**2*c*x**2 - 18*b*c**2*x**4)/(12*x**6)","A",0
170,1,39,0,0.281955," ","integrate((c*x**4+b*x**2)**3/x**14,x)","\frac{- 5 b^{3} - 21 b^{2} c x^{2} - 35 b c^{2} x^{4} - 35 c^{3} x^{6}}{35 x^{7}}"," ",0,"(-5*b**3 - 21*b**2*c*x**2 - 35*b*c**2*x**4 - 35*c**3*x**6)/(35*x**7)","A",0
171,1,37,0,0.311063," ","integrate((c*x**4+b*x**2)**3/x**15,x)","\frac{- b^{3} - 4 b^{2} c x^{2} - 6 b c^{2} x^{4} - 4 c^{3} x^{6}}{8 x^{8}}"," ",0,"(-b**3 - 4*b**2*c*x**2 - 6*b*c**2*x**4 - 4*c**3*x**6)/(8*x**8)","B",0
172,1,39,0,0.303935," ","integrate((c*x**4+b*x**2)**3/x**16,x)","\frac{- 35 b^{3} - 135 b^{2} c x^{2} - 189 b c^{2} x^{4} - 105 c^{3} x^{6}}{315 x^{9}}"," ",0,"(-35*b**3 - 135*b**2*c*x**2 - 189*b*c**2*x**4 - 105*c**3*x**6)/(315*x**9)","A",0
173,1,39,0,0.324722," ","integrate((c*x**4+b*x**2)**3/x**17,x)","\frac{- 4 b^{3} - 15 b^{2} c x^{2} - 20 b c^{2} x^{4} - 10 c^{3} x^{6}}{40 x^{10}}"," ",0,"(-4*b**3 - 15*b**2*c*x**2 - 20*b*c**2*x**4 - 10*c**3*x**6)/(40*x**10)","A",0
174,1,107,0,0.224966," ","integrate(x**10/(c*x**4+b*x**2),x)","- \frac{b^{3} x}{c^{4}} + \frac{b^{2} x^{3}}{3 c^{3}} - \frac{b x^{5}}{5 c^{2}} - \frac{\sqrt{- \frac{b^{7}}{c^{9}}} \log{\left(x - \frac{c^{4} \sqrt{- \frac{b^{7}}{c^{9}}}}{b^{3}} \right)}}{2} + \frac{\sqrt{- \frac{b^{7}}{c^{9}}} \log{\left(x + \frac{c^{4} \sqrt{- \frac{b^{7}}{c^{9}}}}{b^{3}} \right)}}{2} + \frac{x^{7}}{7 c}"," ",0,"-b**3*x/c**4 + b**2*x**3/(3*c**3) - b*x**5/(5*c**2) - sqrt(-b**7/c**9)*log(x - c**4*sqrt(-b**7/c**9)/b**3)/2 + sqrt(-b**7/c**9)*log(x + c**4*sqrt(-b**7/c**9)/b**3)/2 + x**7/(7*c)","A",0
175,1,44,0,0.179923," ","integrate(x**9/(c*x**4+b*x**2),x)","- \frac{b^{3} \log{\left(b + c x^{2} \right)}}{2 c^{4}} + \frac{b^{2} x^{2}}{2 c^{3}} - \frac{b x^{4}}{4 c^{2}} + \frac{x^{6}}{6 c}"," ",0,"-b**3*log(b + c*x**2)/(2*c**4) + b**2*x**2/(2*c**3) - b*x**4/(4*c**2) + x**6/(6*c)","A",0
176,1,95,0,0.208970," ","integrate(x**8/(c*x**4+b*x**2),x)","\frac{b^{2} x}{c^{3}} - \frac{b x^{3}}{3 c^{2}} + \frac{\sqrt{- \frac{b^{5}}{c^{7}}} \log{\left(x - \frac{c^{3} \sqrt{- \frac{b^{5}}{c^{7}}}}{b^{2}} \right)}}{2} - \frac{\sqrt{- \frac{b^{5}}{c^{7}}} \log{\left(x + \frac{c^{3} \sqrt{- \frac{b^{5}}{c^{7}}}}{b^{2}} \right)}}{2} + \frac{x^{5}}{5 c}"," ",0,"b**2*x/c**3 - b*x**3/(3*c**2) + sqrt(-b**5/c**7)*log(x - c**3*sqrt(-b**5/c**7)/b**2)/2 - sqrt(-b**5/c**7)*log(x + c**3*sqrt(-b**5/c**7)/b**2)/2 + x**5/(5*c)","A",0
177,1,32,0,0.169979," ","integrate(x**7/(c*x**4+b*x**2),x)","\frac{b^{2} \log{\left(b + c x^{2} \right)}}{2 c^{3}} - \frac{b x^{2}}{2 c^{2}} + \frac{x^{4}}{4 c}"," ",0,"b**2*log(b + c*x**2)/(2*c**3) - b*x**2/(2*c**2) + x**4/(4*c)","A",0
178,1,80,0,0.193951," ","integrate(x**6/(c*x**4+b*x**2),x)","- \frac{b x}{c^{2}} - \frac{\sqrt{- \frac{b^{3}}{c^{5}}} \log{\left(x - \frac{c^{2} \sqrt{- \frac{b^{3}}{c^{5}}}}{b} \right)}}{2} + \frac{\sqrt{- \frac{b^{3}}{c^{5}}} \log{\left(x + \frac{c^{2} \sqrt{- \frac{b^{3}}{c^{5}}}}{b} \right)}}{2} + \frac{x^{3}}{3 c}"," ",0,"-b*x/c**2 - sqrt(-b**3/c**5)*log(x - c**2*sqrt(-b**3/c**5)/b)/2 + sqrt(-b**3/c**5)*log(x + c**2*sqrt(-b**3/c**5)/b)/2 + x**3/(3*c)","B",0
179,1,20,0,0.165736," ","integrate(x**5/(c*x**4+b*x**2),x)","- \frac{b \log{\left(b + c x^{2} \right)}}{2 c^{2}} + \frac{x^{2}}{2 c}"," ",0,"-b*log(b + c*x**2)/(2*c**2) + x**2/(2*c)","A",0
180,1,56,0,0.171882," ","integrate(x**4/(c*x**4+b*x**2),x)","\frac{\sqrt{- \frac{b}{c^{3}}} \log{\left(- c \sqrt{- \frac{b}{c^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{c^{3}}} \log{\left(c \sqrt{- \frac{b}{c^{3}}} + x \right)}}{2} + \frac{x}{c}"," ",0,"sqrt(-b/c**3)*log(-c*sqrt(-b/c**3) + x)/2 - sqrt(-b/c**3)*log(c*sqrt(-b/c**3) + x)/2 + x/c","B",0
181,1,10,0,0.129200," ","integrate(x**3/(c*x**4+b*x**2),x)","\frac{\log{\left(b + c x^{2} \right)}}{2 c}"," ",0,"log(b + c*x**2)/(2*c)","A",0
182,1,53,0,0.151152," ","integrate(x**2/(c*x**4+b*x**2),x)","- \frac{\sqrt{- \frac{1}{b c}} \log{\left(- b \sqrt{- \frac{1}{b c}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{b c}} \log{\left(b \sqrt{- \frac{1}{b c}} + x \right)}}{2}"," ",0,"-sqrt(-1/(b*c))*log(-b*sqrt(-1/(b*c)) + x)/2 + sqrt(-1/(b*c))*log(b*sqrt(-1/(b*c)) + x)/2","B",0
183,1,15,0,0.225989," ","integrate(x/(c*x**4+b*x**2),x)","\frac{\log{\left(x \right)}}{b} - \frac{\log{\left(\frac{b}{c} + x^{2} \right)}}{2 b}"," ",0,"log(x)/b - log(b/c + x**2)/(2*b)","A",0
184,1,65,0,0.190455," ","integrate(1/(c*x**4+b*x**2),x)","\frac{\sqrt{- \frac{c}{b^{3}}} \log{\left(- \frac{b^{2} \sqrt{- \frac{c}{b^{3}}}}{c} + x \right)}}{2} - \frac{\sqrt{- \frac{c}{b^{3}}} \log{\left(\frac{b^{2} \sqrt{- \frac{c}{b^{3}}}}{c} + x \right)}}{2} - \frac{1}{b x}"," ",0,"sqrt(-c/b**3)*log(-b**2*sqrt(-c/b**3)/c + x)/2 - sqrt(-c/b**3)*log(b**2*sqrt(-c/b**3)/c + x)/2 - 1/(b*x)","B",0
185,1,31,0,0.279978," ","integrate(1/x/(c*x**4+b*x**2),x)","- \frac{1}{2 b x^{2}} - \frac{c \log{\left(x \right)}}{b^{2}} + \frac{c \log{\left(\frac{b}{c} + x^{2} \right)}}{2 b^{2}}"," ",0,"-1/(2*b*x**2) - c*log(x)/b**2 + c*log(b/c + x**2)/(2*b**2)","A",0
186,1,87,0,0.247330," ","integrate(1/x**2/(c*x**4+b*x**2),x)","- \frac{\sqrt{- \frac{c^{3}}{b^{5}}} \log{\left(- \frac{b^{3} \sqrt{- \frac{c^{3}}{b^{5}}}}{c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{c^{3}}{b^{5}}} \log{\left(\frac{b^{3} \sqrt{- \frac{c^{3}}{b^{5}}}}{c^{2}} + x \right)}}{2} + \frac{- b + 3 c x^{2}}{3 b^{2} x^{3}}"," ",0,"-sqrt(-c**3/b**5)*log(-b**3*sqrt(-c**3/b**5)/c**2 + x)/2 + sqrt(-c**3/b**5)*log(b**3*sqrt(-c**3/b**5)/c**2 + x)/2 + (-b + 3*c*x**2)/(3*b**2*x**3)","B",0
187,1,42,0,0.356188," ","integrate(1/x**3/(c*x**4+b*x**2),x)","\frac{- b + 2 c x^{2}}{4 b^{2} x^{4}} + \frac{c^{2} \log{\left(x \right)}}{b^{3}} - \frac{c^{2} \log{\left(\frac{b}{c} + x^{2} \right)}}{2 b^{3}}"," ",0,"(-b + 2*c*x**2)/(4*b**2*x**4) + c**2*log(x)/b**3 - c**2*log(b/c + x**2)/(2*b**3)","A",0
188,1,100,0,0.281641," ","integrate(1/x**4/(c*x**4+b*x**2),x)","\frac{\sqrt{- \frac{c^{5}}{b^{7}}} \log{\left(- \frac{b^{4} \sqrt{- \frac{c^{5}}{b^{7}}}}{c^{3}} + x \right)}}{2} - \frac{\sqrt{- \frac{c^{5}}{b^{7}}} \log{\left(\frac{b^{4} \sqrt{- \frac{c^{5}}{b^{7}}}}{c^{3}} + x \right)}}{2} + \frac{- 3 b^{2} + 5 b c x^{2} - 15 c^{2} x^{4}}{15 b^{3} x^{5}}"," ",0,"sqrt(-c**5/b**7)*log(-b**4*sqrt(-c**5/b**7)/c**3 + x)/2 - sqrt(-c**5/b**7)*log(b**4*sqrt(-c**5/b**7)/c**3 + x)/2 + (-3*b**2 + 5*b*c*x**2 - 15*c**2*x**4)/(15*b**3*x**5)","B",0
189,1,56,0,0.397902," ","integrate(1/x**5/(c*x**4+b*x**2),x)","\frac{- 2 b^{2} + 3 b c x^{2} - 6 c^{2} x^{4}}{12 b^{3} x^{6}} - \frac{c^{3} \log{\left(x \right)}}{b^{4}} + \frac{c^{3} \log{\left(\frac{b}{c} + x^{2} \right)}}{2 b^{4}}"," ",0,"(-2*b**2 + 3*b*c*x**2 - 6*c**2*x**4)/(12*b**3*x**6) - c**3*log(x)/b**4 + c**3*log(b/c + x**2)/(2*b**4)","A",0
190,1,124,0,0.356900," ","integrate(x**12/(c*x**4+b*x**2)**2,x)","\frac{b^{3} x}{2 b c^{4} + 2 c^{5} x^{2}} + \frac{3 b^{2} x}{c^{4}} - \frac{2 b x^{3}}{3 c^{3}} + \frac{7 \sqrt{- \frac{b^{5}}{c^{9}}} \log{\left(x - \frac{c^{4} \sqrt{- \frac{b^{5}}{c^{9}}}}{b^{2}} \right)}}{4} - \frac{7 \sqrt{- \frac{b^{5}}{c^{9}}} \log{\left(x + \frac{c^{4} \sqrt{- \frac{b^{5}}{c^{9}}}}{b^{2}} \right)}}{4} + \frac{x^{5}}{5 c^{2}}"," ",0,"b**3*x/(2*b*c**4 + 2*c**5*x**2) + 3*b**2*x/c**4 - 2*b*x**3/(3*c**3) + 7*sqrt(-b**5/c**9)*log(x - c**4*sqrt(-b**5/c**9)/b**2)/4 - 7*sqrt(-b**5/c**9)*log(x + c**4*sqrt(-b**5/c**9)/b**2)/4 + x**5/(5*c**2)","A",0
191,1,53,0,0.299728," ","integrate(x**11/(c*x**4+b*x**2)**2,x)","\frac{b^{3}}{2 b c^{4} + 2 c^{5} x^{2}} + \frac{3 b^{2} \log{\left(b + c x^{2} \right)}}{2 c^{4}} - \frac{b x^{2}}{c^{3}} + \frac{x^{4}}{4 c^{2}}"," ",0,"b**3/(2*b*c**4 + 2*c**5*x**2) + 3*b**2*log(b + c*x**2)/(2*c**4) - b*x**2/c**3 + x**4/(4*c**2)","A",0
192,1,107,0,0.331362," ","integrate(x**10/(c*x**4+b*x**2)**2,x)","- \frac{b^{2} x}{2 b c^{3} + 2 c^{4} x^{2}} - \frac{2 b x}{c^{3}} - \frac{5 \sqrt{- \frac{b^{3}}{c^{7}}} \log{\left(x - \frac{c^{3} \sqrt{- \frac{b^{3}}{c^{7}}}}{b} \right)}}{4} + \frac{5 \sqrt{- \frac{b^{3}}{c^{7}}} \log{\left(x + \frac{c^{3} \sqrt{- \frac{b^{3}}{c^{7}}}}{b} \right)}}{4} + \frac{x^{3}}{3 c^{2}}"," ",0,"-b**2*x/(2*b*c**3 + 2*c**4*x**2) - 2*b*x/c**3 - 5*sqrt(-b**3/c**7)*log(x - c**3*sqrt(-b**3/c**7)/b)/4 + 5*sqrt(-b**3/c**7)*log(x + c**3*sqrt(-b**3/c**7)/b)/4 + x**3/(3*c**2)","A",0
193,1,39,0,0.275510," ","integrate(x**9/(c*x**4+b*x**2)**2,x)","- \frac{b^{2}}{2 b c^{3} + 2 c^{4} x^{2}} - \frac{b \log{\left(b + c x^{2} \right)}}{c^{3}} + \frac{x^{2}}{2 c^{2}}"," ",0,"-b**2/(2*b*c**3 + 2*c**4*x**2) - b*log(b + c*x**2)/c**3 + x**2/(2*c**2)","A",0
194,1,83,0,0.281958," ","integrate(x**8/(c*x**4+b*x**2)**2,x)","\frac{b x}{2 b c^{2} + 2 c^{3} x^{2}} + \frac{3 \sqrt{- \frac{b}{c^{5}}} \log{\left(- c^{2} \sqrt{- \frac{b}{c^{5}}} + x \right)}}{4} - \frac{3 \sqrt{- \frac{b}{c^{5}}} \log{\left(c^{2} \sqrt{- \frac{b}{c^{5}}} + x \right)}}{4} + \frac{x}{c^{2}}"," ",0,"b*x/(2*b*c**2 + 2*c**3*x**2) + 3*sqrt(-b/c**5)*log(-c**2*sqrt(-b/c**5) + x)/4 - 3*sqrt(-b/c**5)*log(c**2*sqrt(-b/c**5) + x)/4 + x/c**2","A",0
195,1,29,0,0.218079," ","integrate(x**7/(c*x**4+b*x**2)**2,x)","\frac{b}{2 b c^{2} + 2 c^{3} x^{2}} + \frac{\log{\left(b + c x^{2} \right)}}{2 c^{2}}"," ",0,"b/(2*b*c**2 + 2*c**3*x**2) + log(b + c*x**2)/(2*c**2)","A",0
196,1,78,0,0.232241," ","integrate(x**6/(c*x**4+b*x**2)**2,x)","- \frac{x}{2 b c + 2 c^{2} x^{2}} - \frac{\sqrt{- \frac{1}{b c^{3}}} \log{\left(- b c \sqrt{- \frac{1}{b c^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{b c^{3}}} \log{\left(b c \sqrt{- \frac{1}{b c^{3}}} + x \right)}}{4}"," ",0,"-x/(2*b*c + 2*c**2*x**2) - sqrt(-1/(b*c**3))*log(-b*c*sqrt(-1/(b*c**3)) + x)/4 + sqrt(-1/(b*c**3))*log(b*c*sqrt(-1/(b*c**3)) + x)/4","B",0
197,1,15,0,0.175090," ","integrate(x**5/(c*x**4+b*x**2)**2,x)","- \frac{1}{2 b c + 2 c^{2} x^{2}}"," ",0,"-1/(2*b*c + 2*c**2*x**2)","A",0
198,1,78,0,0.251381," ","integrate(x**4/(c*x**4+b*x**2)**2,x)","\frac{x}{2 b^{2} + 2 b c x^{2}} - \frac{\sqrt{- \frac{1}{b^{3} c}} \log{\left(- b^{2} \sqrt{- \frac{1}{b^{3} c}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{b^{3} c}} \log{\left(b^{2} \sqrt{- \frac{1}{b^{3} c}} + x \right)}}{4}"," ",0,"x/(2*b**2 + 2*b*c*x**2) - sqrt(-1/(b**3*c))*log(-b**2*sqrt(-1/(b**3*c)) + x)/4 + sqrt(-1/(b**3*c))*log(b**2*sqrt(-1/(b**3*c)) + x)/4","B",0
199,1,34,0,0.335375," ","integrate(x**3/(c*x**4+b*x**2)**2,x)","\frac{1}{2 b^{2} + 2 b c x^{2}} + \frac{\log{\left(x \right)}}{b^{2}} - \frac{\log{\left(\frac{b}{c} + x^{2} \right)}}{2 b^{2}}"," ",0,"1/(2*b**2 + 2*b*c*x**2) + log(x)/b**2 - log(b/c + x**2)/(2*b**2)","A",0
200,1,92,0,0.316856," ","integrate(x**2/(c*x**4+b*x**2)**2,x)","\frac{3 \sqrt{- \frac{c}{b^{5}}} \log{\left(- \frac{b^{3} \sqrt{- \frac{c}{b^{5}}}}{c} + x \right)}}{4} - \frac{3 \sqrt{- \frac{c}{b^{5}}} \log{\left(\frac{b^{3} \sqrt{- \frac{c}{b^{5}}}}{c} + x \right)}}{4} + \frac{- 2 b - 3 c x^{2}}{2 b^{3} x + 2 b^{2} c x^{3}}"," ",0,"3*sqrt(-c/b**5)*log(-b**3*sqrt(-c/b**5)/c + x)/4 - 3*sqrt(-c/b**5)*log(b**3*sqrt(-c/b**5)/c + x)/4 + (-2*b - 3*c*x**2)/(2*b**3*x + 2*b**2*c*x**3)","A",0
201,1,51,0,0.399089," ","integrate(x/(c*x**4+b*x**2)**2,x)","\frac{- b - 2 c x^{2}}{2 b^{3} x^{2} + 2 b^{2} c x^{4}} - \frac{2 c \log{\left(x \right)}}{b^{3}} + \frac{c \log{\left(\frac{b}{c} + x^{2} \right)}}{b^{3}}"," ",0,"(-b - 2*c*x**2)/(2*b**3*x**2 + 2*b**2*c*x**4) - 2*c*log(x)/b**3 + c*log(b/c + x**2)/b**3","A",0
202,1,114,0,0.391860," ","integrate(1/(c*x**4+b*x**2)**2,x)","- \frac{5 \sqrt{- \frac{c^{3}}{b^{7}}} \log{\left(- \frac{b^{4} \sqrt{- \frac{c^{3}}{b^{7}}}}{c^{2}} + x \right)}}{4} + \frac{5 \sqrt{- \frac{c^{3}}{b^{7}}} \log{\left(\frac{b^{4} \sqrt{- \frac{c^{3}}{b^{7}}}}{c^{2}} + x \right)}}{4} + \frac{- 2 b^{2} + 10 b c x^{2} + 15 c^{2} x^{4}}{6 b^{4} x^{3} + 6 b^{3} c x^{5}}"," ",0,"-5*sqrt(-c**3/b**7)*log(-b**4*sqrt(-c**3/b**7)/c**2 + x)/4 + 5*sqrt(-c**3/b**7)*log(b**4*sqrt(-c**3/b**7)/c**2 + x)/4 + (-2*b**2 + 10*b*c*x**2 + 15*c**2*x**4)/(6*b**4*x**3 + 6*b**3*c*x**5)","A",0
203,1,68,0,0.492019," ","integrate(1/x/(c*x**4+b*x**2)**2,x)","\frac{- b^{2} + 3 b c x^{2} + 6 c^{2} x^{4}}{4 b^{4} x^{4} + 4 b^{3} c x^{6}} + \frac{3 c^{2} \log{\left(x \right)}}{b^{4}} - \frac{3 c^{2} \log{\left(\frac{b}{c} + x^{2} \right)}}{2 b^{4}}"," ",0,"(-b**2 + 3*b*c*x**2 + 6*c**2*x**4)/(4*b**4*x**4 + 4*b**3*c*x**6) + 3*c**2*log(x)/b**4 - 3*c**2*log(b/c + x**2)/(2*b**4)","A",0
204,1,126,0,0.430840," ","integrate(1/x**2/(c*x**4+b*x**2)**2,x)","\frac{7 \sqrt{- \frac{c^{5}}{b^{9}}} \log{\left(- \frac{b^{5} \sqrt{- \frac{c^{5}}{b^{9}}}}{c^{3}} + x \right)}}{4} - \frac{7 \sqrt{- \frac{c^{5}}{b^{9}}} \log{\left(\frac{b^{5} \sqrt{- \frac{c^{5}}{b^{9}}}}{c^{3}} + x \right)}}{4} + \frac{- 6 b^{3} + 14 b^{2} c x^{2} - 70 b c^{2} x^{4} - 105 c^{3} x^{6}}{30 b^{5} x^{5} + 30 b^{4} c x^{7}}"," ",0,"7*sqrt(-c**5/b**9)*log(-b**5*sqrt(-c**5/b**9)/c**3 + x)/4 - 7*sqrt(-c**5/b**9)*log(b**5*sqrt(-c**5/b**9)/c**3 + x)/4 + (-6*b**3 + 14*b**2*c*x**2 - 70*b*c**2*x**4 - 105*c**3*x**6)/(30*b**5*x**5 + 30*b**4*c*x**7)","A",0
205,1,133,0,0.498319," ","integrate(x**14/(c*x**4+b*x**2)**3,x)","- \frac{3 b x}{c^{4}} - \frac{35 \sqrt{- \frac{b^{3}}{c^{9}}} \log{\left(x - \frac{c^{4} \sqrt{- \frac{b^{3}}{c^{9}}}}{b} \right)}}{16} + \frac{35 \sqrt{- \frac{b^{3}}{c^{9}}} \log{\left(x + \frac{c^{4} \sqrt{- \frac{b^{3}}{c^{9}}}}{b} \right)}}{16} + \frac{- 11 b^{3} x - 13 b^{2} c x^{3}}{8 b^{2} c^{4} + 16 b c^{5} x^{2} + 8 c^{6} x^{4}} + \frac{x^{3}}{3 c^{3}}"," ",0,"-3*b*x/c**4 - 35*sqrt(-b**3/c**9)*log(x - c**4*sqrt(-b**3/c**9)/b)/16 + 35*sqrt(-b**3/c**9)*log(x + c**4*sqrt(-b**3/c**9)/b)/16 + (-11*b**3*x - 13*b**2*c*x**3)/(8*b**2*c**4 + 16*b*c**5*x**2 + 8*c**6*x**4) + x**3/(3*c**3)","A",0
206,1,68,0,0.430695," ","integrate(x**13/(c*x**4+b*x**2)**3,x)","- \frac{3 b \log{\left(b + c x^{2} \right)}}{2 c^{4}} + \frac{- 5 b^{3} - 6 b^{2} c x^{2}}{4 b^{2} c^{4} + 8 b c^{5} x^{2} + 4 c^{6} x^{4}} + \frac{x^{2}}{2 c^{3}}"," ",0,"-3*b*log(b + c*x**2)/(2*c**4) + (-5*b**3 - 6*b**2*c*x**2)/(4*b**2*c**4 + 8*b*c**5*x**2 + 4*c**6*x**4) + x**2/(2*c**3)","A",0
207,1,107,0,0.458211," ","integrate(x**12/(c*x**4+b*x**2)**3,x)","\frac{15 \sqrt{- \frac{b}{c^{7}}} \log{\left(- c^{3} \sqrt{- \frac{b}{c^{7}}} + x \right)}}{16} - \frac{15 \sqrt{- \frac{b}{c^{7}}} \log{\left(c^{3} \sqrt{- \frac{b}{c^{7}}} + x \right)}}{16} + \frac{7 b^{2} x + 9 b c x^{3}}{8 b^{2} c^{3} + 16 b c^{4} x^{2} + 8 c^{5} x^{4}} + \frac{x}{c^{3}}"," ",0,"15*sqrt(-b/c**7)*log(-c**3*sqrt(-b/c**7) + x)/16 - 15*sqrt(-b/c**7)*log(c**3*sqrt(-b/c**7) + x)/16 + (7*b**2*x + 9*b*c*x**3)/(8*b**2*c**3 + 16*b*c**4*x**2 + 8*c**5*x**4) + x/c**3","A",0
208,1,53,0,0.366782," ","integrate(x**11/(c*x**4+b*x**2)**3,x)","\frac{3 b^{2} + 4 b c x^{2}}{4 b^{2} c^{3} + 8 b c^{4} x^{2} + 4 c^{5} x^{4}} + \frac{\log{\left(b + c x^{2} \right)}}{2 c^{3}}"," ",0,"(3*b**2 + 4*b*c*x**2)/(4*b**2*c**3 + 8*b*c**4*x**2 + 4*c**5*x**4) + log(b + c*x**2)/(2*c**3)","A",0
209,1,110,0,0.374362," ","integrate(x**10/(c*x**4+b*x**2)**3,x)","- \frac{3 \sqrt{- \frac{1}{b c^{5}}} \log{\left(- b c^{2} \sqrt{- \frac{1}{b c^{5}}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{b c^{5}}} \log{\left(b c^{2} \sqrt{- \frac{1}{b c^{5}}} + x \right)}}{16} + \frac{- 3 b x - 5 c x^{3}}{8 b^{2} c^{2} + 16 b c^{3} x^{2} + 8 c^{4} x^{4}}"," ",0,"-3*sqrt(-1/(b*c**5))*log(-b*c**2*sqrt(-1/(b*c**5)) + x)/16 + 3*sqrt(-1/(b*c**5))*log(b*c**2*sqrt(-1/(b*c**5)) + x)/16 + (-3*b*x - 5*c*x**3)/(8*b**2*c**2 + 16*b*c**3*x**2 + 8*c**4*x**4)","A",0
210,1,36,0,0.307300," ","integrate(x**9/(c*x**4+b*x**2)**3,x)","\frac{- b - 2 c x^{2}}{4 b^{2} c^{2} + 8 b c^{3} x^{2} + 4 c^{4} x^{4}}"," ",0,"(-b - 2*c*x**2)/(4*b**2*c**2 + 8*b*c**3*x**2 + 4*c**4*x**4)","B",0
211,1,110,0,0.352736," ","integrate(x**8/(c*x**4+b*x**2)**3,x)","- \frac{\sqrt{- \frac{1}{b^{3} c^{3}}} \log{\left(- b^{2} c \sqrt{- \frac{1}{b^{3} c^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{b^{3} c^{3}}} \log{\left(b^{2} c \sqrt{- \frac{1}{b^{3} c^{3}}} + x \right)}}{16} + \frac{- b x + c x^{3}}{8 b^{3} c + 16 b^{2} c^{2} x^{2} + 8 b c^{3} x^{4}}"," ",0,"-sqrt(-1/(b**3*c**3))*log(-b**2*c*sqrt(-1/(b**3*c**3)) + x)/16 + sqrt(-1/(b**3*c**3))*log(b**2*c*sqrt(-1/(b**3*c**3)) + x)/16 + (-b*x + c*x**3)/(8*b**3*c + 16*b**2*c**2*x**2 + 8*b*c**3*x**4)","B",0
212,1,27,0,0.270549," ","integrate(x**7/(c*x**4+b*x**2)**3,x)","- \frac{1}{4 b^{2} c + 8 b c^{2} x^{2} + 4 c^{3} x^{4}}"," ",0,"-1/(4*b**2*c + 8*b*c**2*x**2 + 4*c**3*x**4)","A",0
213,1,105,0,0.364693," ","integrate(x**6/(c*x**4+b*x**2)**3,x)","- \frac{3 \sqrt{- \frac{1}{b^{5} c}} \log{\left(- b^{3} \sqrt{- \frac{1}{b^{5} c}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{b^{5} c}} \log{\left(b^{3} \sqrt{- \frac{1}{b^{5} c}} + x \right)}}{16} + \frac{5 b x + 3 c x^{3}}{8 b^{4} + 16 b^{3} c x^{2} + 8 b^{2} c^{2} x^{4}}"," ",0,"-3*sqrt(-1/(b**5*c))*log(-b**3*sqrt(-1/(b**5*c)) + x)/16 + 3*sqrt(-1/(b**5*c))*log(b**3*sqrt(-1/(b**5*c)) + x)/16 + (5*b*x + 3*c*x**3)/(8*b**4 + 16*b**3*c*x**2 + 8*b**2*c**2*x**4)","A",0
214,1,56,0,0.454906," ","integrate(x**5/(c*x**4+b*x**2)**3,x)","\frac{3 b + 2 c x^{2}}{4 b^{4} + 8 b^{3} c x^{2} + 4 b^{2} c^{2} x^{4}} + \frac{\log{\left(x \right)}}{b^{3}} - \frac{\log{\left(\frac{b}{c} + x^{2} \right)}}{2 b^{3}}"," ",0,"(3*b + 2*c*x**2)/(4*b**4 + 8*b**3*c*x**2 + 4*b**2*c**2*x**4) + log(x)/b**3 - log(b/c + x**2)/(2*b**3)","A",0
215,1,116,0,0.452244," ","integrate(x**4/(c*x**4+b*x**2)**3,x)","\frac{15 \sqrt{- \frac{c}{b^{7}}} \log{\left(- \frac{b^{4} \sqrt{- \frac{c}{b^{7}}}}{c} + x \right)}}{16} - \frac{15 \sqrt{- \frac{c}{b^{7}}} \log{\left(\frac{b^{4} \sqrt{- \frac{c}{b^{7}}}}{c} + x \right)}}{16} + \frac{- 8 b^{2} - 25 b c x^{2} - 15 c^{2} x^{4}}{8 b^{5} x + 16 b^{4} c x^{3} + 8 b^{3} c^{2} x^{5}}"," ",0,"15*sqrt(-c/b**7)*log(-b**4*sqrt(-c/b**7)/c + x)/16 - 15*sqrt(-c/b**7)*log(b**4*sqrt(-c/b**7)/c + x)/16 + (-8*b**2 - 25*b*c*x**2 - 15*c**2*x**4)/(8*b**5*x + 16*b**4*c*x**3 + 8*b**3*c**2*x**5)","A",0
216,1,80,0,0.632161," ","integrate(x**3/(c*x**4+b*x**2)**3,x)","\frac{- 2 b^{2} - 9 b c x^{2} - 6 c^{2} x^{4}}{4 b^{5} x^{2} + 8 b^{4} c x^{4} + 4 b^{3} c^{2} x^{6}} - \frac{3 c \log{\left(x \right)}}{b^{4}} + \frac{3 c \log{\left(\frac{b}{c} + x^{2} \right)}}{2 b^{4}}"," ",0,"(-2*b**2 - 9*b*c*x**2 - 6*c**2*x**4)/(4*b**5*x**2 + 8*b**4*c*x**4 + 4*b**3*c**2*x**6) - 3*c*log(x)/b**4 + 3*c*log(b/c + x**2)/(2*b**4)","A",0
217,1,138,0,0.498581," ","integrate(x**2/(c*x**4+b*x**2)**3,x)","- \frac{35 \sqrt{- \frac{c^{3}}{b^{9}}} \log{\left(- \frac{b^{5} \sqrt{- \frac{c^{3}}{b^{9}}}}{c^{2}} + x \right)}}{16} + \frac{35 \sqrt{- \frac{c^{3}}{b^{9}}} \log{\left(\frac{b^{5} \sqrt{- \frac{c^{3}}{b^{9}}}}{c^{2}} + x \right)}}{16} + \frac{- 8 b^{3} + 56 b^{2} c x^{2} + 175 b c^{2} x^{4} + 105 c^{3} x^{6}}{24 b^{6} x^{3} + 48 b^{5} c x^{5} + 24 b^{4} c^{2} x^{7}}"," ",0,"-35*sqrt(-c**3/b**9)*log(-b**5*sqrt(-c**3/b**9)/c**2 + x)/16 + 35*sqrt(-c**3/b**9)*log(b**5*sqrt(-c**3/b**9)/c**2 + x)/16 + (-8*b**3 + 56*b**2*c*x**2 + 175*b*c**2*x**4 + 105*c**3*x**6)/(24*b**6*x**3 + 48*b**5*c*x**5 + 24*b**4*c**2*x**7)","A",0
218,1,90,0,0.569275," ","integrate(x/(c*x**4+b*x**2)**3,x)","\frac{- b^{3} + 4 b^{2} c x^{2} + 18 b c^{2} x^{4} + 12 c^{3} x^{6}}{4 b^{6} x^{4} + 8 b^{5} c x^{6} + 4 b^{4} c^{2} x^{8}} + \frac{6 c^{2} \log{\left(x \right)}}{b^{5}} - \frac{3 c^{2} \log{\left(\frac{b}{c} + x^{2} \right)}}{b^{5}}"," ",0,"(-b**3 + 4*b**2*c*x**2 + 18*b*c**2*x**4 + 12*c**3*x**6)/(4*b**6*x**4 + 8*b**5*c*x**6 + 4*b**4*c**2*x**8) + 6*c**2*log(x)/b**5 - 3*c**2*log(b/c + x**2)/b**5","A",0
219,1,150,0,0.577169," ","integrate(1/(c*x**4+b*x**2)**3,x)","\frac{63 \sqrt{- \frac{c^{5}}{b^{11}}} \log{\left(- \frac{b^{6} \sqrt{- \frac{c^{5}}{b^{11}}}}{c^{3}} + x \right)}}{16} - \frac{63 \sqrt{- \frac{c^{5}}{b^{11}}} \log{\left(\frac{b^{6} \sqrt{- \frac{c^{5}}{b^{11}}}}{c^{3}} + x \right)}}{16} + \frac{- 8 b^{4} + 24 b^{3} c x^{2} - 168 b^{2} c^{2} x^{4} - 525 b c^{3} x^{6} - 315 c^{4} x^{8}}{40 b^{7} x^{5} + 80 b^{6} c x^{7} + 40 b^{5} c^{2} x^{9}}"," ",0,"63*sqrt(-c**5/b**11)*log(-b**6*sqrt(-c**5/b**11)/c**3 + x)/16 - 63*sqrt(-c**5/b**11)*log(b**6*sqrt(-c**5/b**11)/c**3 + x)/16 + (-8*b**4 + 24*b**3*c*x**2 - 168*b**2*c**2*x**4 - 525*b*c**3*x**6 - 315*c**4*x**8)/(40*b**7*x**5 + 80*b**6*c*x**7 + 40*b**5*c**2*x**9)","A",0
220,1,104,0,0.645122," ","integrate(1/x/(c*x**4+b*x**2)**3,x)","\frac{- 2 b^{4} + 5 b^{3} c x^{2} - 20 b^{2} c^{2} x^{4} - 90 b c^{3} x^{6} - 60 c^{4} x^{8}}{12 b^{7} x^{6} + 24 b^{6} c x^{8} + 12 b^{5} c^{2} x^{10}} - \frac{10 c^{3} \log{\left(x \right)}}{b^{6}} + \frac{5 c^{3} \log{\left(\frac{b}{c} + x^{2} \right)}}{b^{6}}"," ",0,"(-2*b**4 + 5*b**3*c*x**2 - 20*b**2*c**2*x**4 - 90*b*c**3*x**6 - 60*c**4*x**8)/(12*b**7*x**6 + 24*b**6*c*x**8 + 12*b**5*c**2*x**10) - 10*c**3*log(x)/b**6 + 5*c**3*log(b/c + x**2)/b**6","A",0
221,0,0,0,0.000000," ","integrate(x**5*(c*x**4+b*x**2)**(1/2),x)","\int x^{5} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x**5*sqrt(x**2*(b + c*x**2)), x)","F",0
222,0,0,0,0.000000," ","integrate(x**3*(c*x**4+b*x**2)**(1/2),x)","\int x^{3} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x**3*sqrt(x**2*(b + c*x**2)), x)","F",0
223,0,0,0,0.000000," ","integrate(x*(c*x**4+b*x**2)**(1/2),x)","\int x \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x*sqrt(x**2*(b + c*x**2)), x)","F",0
224,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x, x)","F",0
225,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**3,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**3, x)","F",0
226,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**5,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{5}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**5, x)","F",0
227,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**7,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{7}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**7, x)","F",0
228,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**9,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{9}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**9, x)","F",0
229,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**11,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{11}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**11, x)","F",0
230,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**13,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{13}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**13, x)","F",0
231,0,0,0,0.000000," ","integrate(x**4*(c*x**4+b*x**2)**(1/2),x)","\int x^{4} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x**4*sqrt(x**2*(b + c*x**2)), x)","F",0
232,0,0,0,0.000000," ","integrate(x**2*(c*x**4+b*x**2)**(1/2),x)","\int x^{2} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x**2*sqrt(x**2*(b + c*x**2)), x)","F",0
233,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2),x)","\int \sqrt{b x^{2} + c x^{4}}\, dx"," ",0,"Integral(sqrt(b*x**2 + c*x**4), x)","F",0
234,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**2,x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{6}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{8}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**8, x)","F",0
238,0,0,0,0.000000," ","integrate(x**3*(c*x**4+b*x**2)**(3/2),x)","\int x^{3} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(x**2*(b + c*x**2))**(3/2), x)","F",0
239,0,0,0,0.000000," ","integrate(x*(c*x**4+b*x**2)**(3/2),x)","\int x \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(x**2*(b + c*x**2))**(3/2), x)","F",0
240,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x, x)","F",0
241,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**3,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**3, x)","F",0
242,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**5,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**5, x)","F",0
243,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**7,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**7, x)","F",0
244,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**9,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{9}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**9, x)","F",0
245,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**11,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{11}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**11, x)","F",0
246,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**13,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{13}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**13, x)","F",0
247,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**15,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{15}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**15, x)","F",0
248,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**17,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{17}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**17, x)","F",0
249,0,0,0,0.000000," ","integrate(x**6*(c*x**4+b*x**2)**(3/2),x)","\int x^{6} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**6*(x**2*(b + c*x**2))**(3/2), x)","F",0
250,0,0,0,0.000000," ","integrate(x**4*(c*x**4+b*x**2)**(3/2),x)","\int x^{4} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*(x**2*(b + c*x**2))**(3/2), x)","F",0
251,0,0,0,0.000000," ","integrate(x**2*(c*x**4+b*x**2)**(3/2),x)","\int x^{2} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(x**2*(b + c*x**2))**(3/2), x)","F",0
252,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2),x)","\int \left(b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*x**2 + c*x**4)**(3/2), x)","F",0
253,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**2,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**2, x)","F",0
254,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**4,x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{10}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{12}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{14}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**14, x)","F",0
260,0,0,0,0.000000," ","integrate(x**7/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{7}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**7/sqrt(x**2*(b + c*x**2)), x)","F",0
261,0,0,0,0.000000," ","integrate(x**5/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{5}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**5/sqrt(x**2*(b + c*x**2)), x)","F",0
262,0,0,0,0.000000," ","integrate(x**3/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**3/sqrt(x**2*(b + c*x**2)), x)","F",0
263,0,0,0,0.000000," ","integrate(x/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x/sqrt(x**2*(b + c*x**2)), x)","F",0
264,0,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(x**2*(b + c*x**2))), x)","F",0
265,0,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**3*sqrt(x**2*(b + c*x**2))), x)","F",0
266,0,0,0,0.000000," ","integrate(1/x**5/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{5} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**5*sqrt(x**2*(b + c*x**2))), x)","F",0
267,0,0,0,0.000000," ","integrate(1/x**7/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{7} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**7*sqrt(x**2*(b + c*x**2))), x)","F",0
268,0,0,0,0.000000," ","integrate(x**4/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{4}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**4/sqrt(x**2*(b + c*x**2)), x)","F",0
269,0,0,0,0.000000," ","integrate(x**2/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**2/sqrt(x**2*(b + c*x**2)), x)","F",0
270,0,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/sqrt(b*x**2 + c*x**4), x)","F",0
271,0,0,0,0.000000," ","integrate(1/x**2/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**2*sqrt(x**2*(b + c*x**2))), x)","F",0
272,0,0,0,0.000000," ","integrate(1/x**4/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**4*sqrt(x**2*(b + c*x**2))), x)","F",0
273,0,0,0,0.000000," ","integrate(x**9/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{9}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**9/(x**2*(b + c*x**2))**(3/2), x)","F",0
274,0,0,0,0.000000," ","integrate(x**7/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{7}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**7/(x**2*(b + c*x**2))**(3/2), x)","F",0
275,0,0,0,0.000000," ","integrate(x**5/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{5}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5/(x**2*(b + c*x**2))**(3/2), x)","F",0
276,0,0,0,0.000000," ","integrate(x**3/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{3}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(x**2*(b + c*x**2))**(3/2), x)","F",0
277,0,0,0,0.000000," ","integrate(x/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(x**2*(b + c*x**2))**(3/2), x)","F",0
278,0,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2)**(3/2),x)","\int \frac{1}{x \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(x**2*(b + c*x**2))**(3/2)), x)","F",0
279,0,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2)**(3/2),x)","\int \frac{1}{x^{3} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(x**2*(b + c*x**2))**(3/2)), x)","F",0
280,0,0,0,0.000000," ","integrate(1/x**5/(c*x**4+b*x**2)**(3/2),x)","\int \frac{1}{x^{5} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**5*(x**2*(b + c*x**2))**(3/2)), x)","F",0
281,0,0,0,0.000000," ","integrate(x**6/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{6}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**6/(x**2*(b + c*x**2))**(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate(x**4/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{4}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/(x**2*(b + c*x**2))**(3/2), x)","F",0
283,0,0,0,0.000000," ","integrate(x**2/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{2}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(x**2*(b + c*x**2))**(3/2), x)","F",0
284,0,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2)**(3/2),x)","\int \frac{1}{\left(b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*x**2 + c*x**4)**(-3/2), x)","F",0
285,0,0,0,0.000000," ","integrate(1/x**2/(c*x**4+b*x**2)**(3/2),x)","\int \frac{1}{x^{2} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(x**2*(b + c*x**2))**(3/2)), x)","F",0
286,0,0,0,0.000000," ","integrate(x**3/(-4*x**4+3*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{- x^{2} \left(4 x^{2} - 3\right)}}\, dx"," ",0,"Integral(x**3/sqrt(-x**2*(4*x**2 - 3)), x)","F",0
287,0,0,0,0.000000," ","integrate(x**3/(-4*x**4-3*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{- x^{2} \left(4 x^{2} + 3\right)}}\, dx"," ",0,"Integral(x**3/sqrt(-x**2*(4*x**2 + 3)), x)","F",0
288,0,0,0,0.000000," ","integrate(x**3/(4*x**4+3*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x^{2} \left(4 x^{2} + 3\right)}}\, dx"," ",0,"Integral(x**3/sqrt(x**2*(4*x**2 + 3)), x)","F",0
289,0,0,0,0.000000," ","integrate(x**3/(4*x**4-3*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x^{2} \left(4 x^{2} - 3\right)}}\, dx"," ",0,"Integral(x**3/sqrt(x**2*(4*x**2 - 3)), x)","F",0
290,0,0,0,0.000000," ","integrate(x**3/(b*x**4+a*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x^{2} \left(a + b x^{2}\right)}}\, dx"," ",0,"Integral(x**3/sqrt(x**2*(a + b*x**2)), x)","F",0
291,0,0,0,0.000000," ","integrate(x**3/(-b*x**4+a*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{- x^{2} \left(- a + b x^{2}\right)}}\, dx"," ",0,"Integral(x**3/sqrt(-x**2*(-a + b*x**2)), x)","F",0
292,1,19,0,11.339423," ","integrate(x**(7/2)*(c*x**4+b*x**2),x)","\frac{2 b x^{\frac{13}{2}}}{13} + \frac{2 c x^{\frac{17}{2}}}{17}"," ",0,"2*b*x**(13/2)/13 + 2*c*x**(17/2)/17","A",0
293,1,19,0,5.565233," ","integrate(x**(5/2)*(c*x**4+b*x**2),x)","\frac{2 b x^{\frac{11}{2}}}{11} + \frac{2 c x^{\frac{15}{2}}}{15}"," ",0,"2*b*x**(11/2)/11 + 2*c*x**(15/2)/15","A",0
294,1,19,0,2.525064," ","integrate(x**(3/2)*(c*x**4+b*x**2),x)","\frac{2 b x^{\frac{9}{2}}}{9} + \frac{2 c x^{\frac{13}{2}}}{13}"," ",0,"2*b*x**(9/2)/9 + 2*c*x**(13/2)/13","A",0
295,1,19,0,1.726446," ","integrate(x**(1/2)*(c*x**4+b*x**2),x)","\frac{2 b x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{11}{2}}}{11}"," ",0,"2*b*x**(7/2)/7 + 2*c*x**(11/2)/11","A",0
296,1,19,0,0.777434," ","integrate((c*x**4+b*x**2)/x**(1/2),x)","\frac{2 b x^{\frac{5}{2}}}{5} + \frac{2 c x^{\frac{9}{2}}}{9}"," ",0,"2*b*x**(5/2)/5 + 2*c*x**(9/2)/9","A",0
297,1,19,0,0.786830," ","integrate((c*x**4+b*x**2)/x**(3/2),x)","\frac{2 b x^{\frac{3}{2}}}{3} + \frac{2 c x^{\frac{7}{2}}}{7}"," ",0,"2*b*x**(3/2)/3 + 2*c*x**(7/2)/7","A",0
298,1,17,0,1.001286," ","integrate((c*x**4+b*x**2)/x**(5/2),x)","2 b \sqrt{x} + \frac{2 c x^{\frac{5}{2}}}{5}"," ",0,"2*b*sqrt(x) + 2*c*x**(5/2)/5","A",0
299,1,17,0,1.803402," ","integrate((c*x**4+b*x**2)/x**(7/2),x)","- \frac{2 b}{\sqrt{x}} + \frac{2 c x^{\frac{3}{2}}}{3}"," ",0,"-2*b/sqrt(x) + 2*c*x**(3/2)/3","A",0
300,1,34,0,35.136362," ","integrate(x**(7/2)*(c*x**4+b*x**2)**2,x)","\frac{2 b^{2} x^{\frac{17}{2}}}{17} + \frac{4 b c x^{\frac{21}{2}}}{21} + \frac{2 c^{2} x^{\frac{25}{2}}}{25}"," ",0,"2*b**2*x**(17/2)/17 + 4*b*c*x**(21/2)/21 + 2*c**2*x**(25/2)/25","A",0
301,1,34,0,20.810206," ","integrate(x**(5/2)*(c*x**4+b*x**2)**2,x)","\frac{2 b^{2} x^{\frac{15}{2}}}{15} + \frac{4 b c x^{\frac{19}{2}}}{19} + \frac{2 c^{2} x^{\frac{23}{2}}}{23}"," ",0,"2*b**2*x**(15/2)/15 + 4*b*c*x**(19/2)/19 + 2*c**2*x**(23/2)/23","A",0
302,1,34,0,11.377975," ","integrate(x**(3/2)*(c*x**4+b*x**2)**2,x)","\frac{2 b^{2} x^{\frac{13}{2}}}{13} + \frac{4 b c x^{\frac{17}{2}}}{17} + \frac{2 c^{2} x^{\frac{21}{2}}}{21}"," ",0,"2*b**2*x**(13/2)/13 + 4*b*c*x**(17/2)/17 + 2*c**2*x**(21/2)/21","A",0
303,1,34,0,2.749739," ","integrate(x**(1/2)*(c*x**4+b*x**2)**2,x)","\frac{2 b^{2} x^{\frac{11}{2}}}{11} + \frac{4 b c x^{\frac{15}{2}}}{15} + \frac{2 c^{2} x^{\frac{19}{2}}}{19}"," ",0,"2*b**2*x**(11/2)/11 + 4*b*c*x**(15/2)/15 + 2*c**2*x**(19/2)/19","A",0
304,1,34,0,4.975320," ","integrate((c*x**4+b*x**2)**2/x**(1/2),x)","\frac{2 b^{2} x^{\frac{9}{2}}}{9} + \frac{4 b c x^{\frac{13}{2}}}{13} + \frac{2 c^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*b**2*x**(9/2)/9 + 4*b*c*x**(13/2)/13 + 2*c**2*x**(17/2)/17","A",0
305,1,34,0,5.218120," ","integrate((c*x**4+b*x**2)**2/x**(3/2),x)","\frac{2 b^{2} x^{\frac{7}{2}}}{7} + \frac{4 b c x^{\frac{11}{2}}}{11} + \frac{2 c^{2} x^{\frac{15}{2}}}{15}"," ",0,"2*b**2*x**(7/2)/7 + 4*b*c*x**(11/2)/11 + 2*c**2*x**(15/2)/15","A",0
306,1,34,0,5.988225," ","integrate((c*x**4+b*x**2)**2/x**(5/2),x)","\frac{2 b^{2} x^{\frac{5}{2}}}{5} + \frac{4 b c x^{\frac{9}{2}}}{9} + \frac{2 c^{2} x^{\frac{13}{2}}}{13}"," ",0,"2*b**2*x**(5/2)/5 + 4*b*c*x**(9/2)/9 + 2*c**2*x**(13/2)/13","A",0
307,1,34,0,8.694728," ","integrate((c*x**4+b*x**2)**2/x**(7/2),x)","\frac{2 b^{2} x^{\frac{3}{2}}}{3} + \frac{4 b c x^{\frac{7}{2}}}{7} + \frac{2 c^{2} x^{\frac{11}{2}}}{11}"," ",0,"2*b**2*x**(3/2)/3 + 4*b*c*x**(7/2)/7 + 2*c**2*x**(11/2)/11","A",0
308,1,49,0,83.180057," ","integrate(x**(7/2)*(c*x**4+b*x**2)**3,x)","\frac{2 b^{3} x^{\frac{21}{2}}}{21} + \frac{6 b^{2} c x^{\frac{25}{2}}}{25} + \frac{6 b c^{2} x^{\frac{29}{2}}}{29} + \frac{2 c^{3} x^{\frac{33}{2}}}{33}"," ",0,"2*b**3*x**(21/2)/21 + 6*b**2*c*x**(25/2)/25 + 6*b*c**2*x**(29/2)/29 + 2*c**3*x**(33/2)/33","A",0
309,1,49,0,53.376182," ","integrate(x**(5/2)*(c*x**4+b*x**2)**3,x)","\frac{2 b^{3} x^{\frac{19}{2}}}{19} + \frac{6 b^{2} c x^{\frac{23}{2}}}{23} + \frac{2 b c^{2} x^{\frac{27}{2}}}{9} + \frac{2 c^{3} x^{\frac{31}{2}}}{31}"," ",0,"2*b**3*x**(19/2)/19 + 6*b**2*c*x**(23/2)/23 + 2*b*c**2*x**(27/2)/9 + 2*c**3*x**(31/2)/31","A",0
310,1,49,0,33.338266," ","integrate(x**(3/2)*(c*x**4+b*x**2)**3,x)","\frac{2 b^{3} x^{\frac{17}{2}}}{17} + \frac{2 b^{2} c x^{\frac{21}{2}}}{7} + \frac{6 b c^{2} x^{\frac{25}{2}}}{25} + \frac{2 c^{3} x^{\frac{29}{2}}}{29}"," ",0,"2*b**3*x**(17/2)/17 + 2*b**2*c*x**(21/2)/7 + 6*b*c**2*x**(25/2)/25 + 2*c**3*x**(29/2)/29","A",0
311,1,49,0,4.318372," ","integrate(x**(1/2)*(c*x**4+b*x**2)**3,x)","\frac{2 b^{3} x^{\frac{15}{2}}}{15} + \frac{6 b^{2} c x^{\frac{19}{2}}}{19} + \frac{6 b c^{2} x^{\frac{23}{2}}}{23} + \frac{2 c^{3} x^{\frac{27}{2}}}{27}"," ",0,"2*b**3*x**(15/2)/15 + 6*b**2*c*x**(19/2)/19 + 6*b*c**2*x**(23/2)/23 + 2*c**3*x**(27/2)/27","A",0
312,1,49,0,17.611500," ","integrate((c*x**4+b*x**2)**3/x**(1/2),x)","\frac{2 b^{3} x^{\frac{13}{2}}}{13} + \frac{6 b^{2} c x^{\frac{17}{2}}}{17} + \frac{2 b c^{2} x^{\frac{21}{2}}}{7} + \frac{2 c^{3} x^{\frac{25}{2}}}{25}"," ",0,"2*b**3*x**(13/2)/13 + 6*b**2*c*x**(17/2)/17 + 2*b*c**2*x**(21/2)/7 + 2*c**3*x**(25/2)/25","A",0
313,1,49,0,19.941827," ","integrate((c*x**4+b*x**2)**3/x**(3/2),x)","\frac{2 b^{3} x^{\frac{11}{2}}}{11} + \frac{2 b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 b c^{2} x^{\frac{19}{2}}}{19} + \frac{2 c^{3} x^{\frac{23}{2}}}{23}"," ",0,"2*b**3*x**(11/2)/11 + 2*b**2*c*x**(15/2)/5 + 6*b*c**2*x**(19/2)/19 + 2*c**3*x**(23/2)/23","A",0
314,1,49,0,22.203508," ","integrate((c*x**4+b*x**2)**3/x**(5/2),x)","\frac{2 b^{3} x^{\frac{9}{2}}}{9} + \frac{6 b^{2} c x^{\frac{13}{2}}}{13} + \frac{6 b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 c^{3} x^{\frac{21}{2}}}{21}"," ",0,"2*b**3*x**(9/2)/9 + 6*b**2*c*x**(13/2)/13 + 6*b*c**2*x**(17/2)/17 + 2*c**3*x**(21/2)/21","A",0
315,1,49,0,26.497913," ","integrate((c*x**4+b*x**2)**3/x**(7/2),x)","\frac{2 b^{3} x^{\frac{7}{2}}}{7} + \frac{6 b^{2} c x^{\frac{11}{2}}}{11} + \frac{2 b c^{2} x^{\frac{15}{2}}}{5} + \frac{2 c^{3} x^{\frac{19}{2}}}{19}"," ",0,"2*b**3*x**(7/2)/7 + 6*b**2*c*x**(11/2)/11 + 2*b*c**2*x**(15/2)/5 + 2*c**3*x**(19/2)/19","A",0
316,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+b*x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+b*x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,1,180,0,166.485485," ","integrate(x**(9/2)/(c*x**4+b*x**2),x)","\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: b = 0 \wedge c = 0 \\\frac{2 x^{\frac{7}{2}}}{7 b} & \text{for}\: c = 0 \\\frac{2 x^{\frac{3}{2}}}{3 c} & \text{for}\: b = 0 \\\frac{\left(-1\right)^{\frac{3}{4}} b^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} b^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c^{2} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} b^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{c^{2} \sqrt[4]{\frac{1}{c}}} + \frac{2 x^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(3/2), Eq(b, 0) & Eq(c, 0)), (2*x**(7/2)/(7*b), Eq(c, 0)), (2*x**(3/2)/(3*c), Eq(b, 0)), ((-1)**(3/4)*b**(3/4)*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2*(1/c)**(1/4)) - (-1)**(3/4)*b**(3/4)*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c**2*(1/c)**(1/4)) - (-1)**(3/4)*b**(3/4)*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/(c**2*(1/c)**(1/4)) + 2*x**(3/2)/(3*c), True))","A",0
319,1,172,0,77.501442," ","integrate(x**(7/2)/(c*x**4+b*x**2),x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: b = 0 \wedge c = 0 \\\frac{2 x^{\frac{5}{2}}}{5 b} & \text{for}\: c = 0 \\\frac{2 \sqrt{x}}{c} & \text{for}\: b = 0 \\\frac{\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c} - \frac{\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 c} + \frac{\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{c} + \frac{2 \sqrt{x}}{c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(b, 0) & Eq(c, 0)), (2*x**(5/2)/(5*b), Eq(c, 0)), (2*sqrt(x)/c, Eq(b, 0)), ((-1)**(1/4)*b**(1/4)*(1/c)**(1/4)*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c) - (-1)**(1/4)*b**(1/4)*(1/c)**(1/4)*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*c) + (-1)**(1/4)*b**(1/4)*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/c + 2*sqrt(x)/c, True))","A",0
320,1,165,0,48.273860," ","integrate(x**(5/2)/(c*x**4+b*x**2),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: b = 0 \wedge c = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b} & \text{for}\: c = 0 \\- \frac{2}{c \sqrt{x}} & \text{for}\: b = 0 \\- \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 \sqrt[4]{b} c \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 \sqrt[4]{b} c \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{\sqrt[4]{b} c \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(b, 0) & Eq(c, 0)), (2*x**(3/2)/(3*b), Eq(c, 0)), (-2/(c*sqrt(x)), Eq(b, 0)), (-(-1)**(3/4)*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(1/4)*c*(1/c)**(1/4)) + (-1)**(3/4)*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(1/4)*c*(1/c)**(1/4)) + (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/(b**(1/4)*c*(1/c)**(1/4)), True))","A",0
321,1,160,0,27.221292," ","integrate(x**(3/2)/(c*x**4+b*x**2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: b = 0 \wedge c = 0 \\- \frac{2}{3 c x^{\frac{3}{2}}} & \text{for}\: b = 0 \\\frac{2 \sqrt{x}}{b} & \text{for}\: c = 0 \\- \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{b^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(b, 0) & Eq(c, 0)), (-2/(3*c*x**(3/2)), Eq(b, 0)), (2*sqrt(x)/b, Eq(c, 0)), (-(-1)**(1/4)*(1/c)**(1/4)*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(3/4)) + (-1)**(1/4)*(1/c)**(1/4)*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(3/4)) - (-1)**(1/4)*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/b**(3/4), True))","A",0
322,1,170,0,18.319951," ","integrate(x**(1/2)/(c*x**4+b*x**2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: b = 0 \wedge c = 0 \\- \frac{2}{5 c x^{\frac{5}{2}}} & \text{for}\: b = 0 \\- \frac{2}{b \sqrt{x}} & \text{for}\: c = 0 \\- \frac{2}{b \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{b^{\frac{5}{4}} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(b, 0) & Eq(c, 0)), (-2/(5*c*x**(5/2)), Eq(b, 0)), (-2/(b*sqrt(x)), Eq(c, 0)), (-2/(b*sqrt(x)) + (-1)**(3/4)*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(5/4)*(1/c)**(1/4)) - (-1)**(3/4)*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(5/4)*(1/c)**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/(b**(5/4)*(1/c)**(1/4)), True))","A",0
323,1,178,0,27.743879," ","integrate(1/(c*x**4+b*x**2)/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: b = 0 \wedge c = 0 \\- \frac{2}{3 b x^{\frac{3}{2}}} & \text{for}\: c = 0 \\- \frac{2}{7 c x^{\frac{7}{2}}} & \text{for}\: b = 0 \\- \frac{2}{3 b x^{\frac{3}{2}}} + \frac{\sqrt[4]{-1} c \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} c \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{7}{4}}} + \frac{\sqrt[4]{-1} c \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{b^{\frac{7}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(b, 0) & Eq(c, 0)), (-2/(3*b*x**(3/2)), Eq(c, 0)), (-2/(7*c*x**(7/2)), Eq(b, 0)), (-2/(3*b*x**(3/2)) + (-1)**(1/4)*c*(1/c)**(1/4)*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(7/4)) - (-1)**(1/4)*c*(1/c)**(1/4)*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(7/4)) + (-1)**(1/4)*c*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/b**(7/4), True))","A",0
324,1,190,0,48.979751," ","integrate(1/x**(3/2)/(c*x**4+b*x**2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: b = 0 \wedge c = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: c = 0 \\- \frac{2}{9 c x^{\frac{9}{2}}} & \text{for}\: b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} + \frac{2 c}{b^{2} \sqrt{x}} - \frac{\left(-1\right)^{\frac{3}{4}} c \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{9}{4}} \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} c \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{9}{4}} \sqrt[4]{\frac{1}{c}}} + \frac{\left(-1\right)^{\frac{3}{4}} c \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{b^{\frac{9}{4}} \sqrt[4]{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(b, 0) & Eq(c, 0)), (-2/(5*b*x**(5/2)), Eq(c, 0)), (-2/(9*c*x**(9/2)), Eq(b, 0)), (-2/(5*b*x**(5/2)) + 2*c/(b**2*sqrt(x)) - (-1)**(3/4)*c*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(9/4)*(1/c)**(1/4)) + (-1)**(3/4)*c*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(9/4)*(1/c)**(1/4)) + (-1)**(3/4)*c*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/(b**(9/4)*(1/c)**(1/4)), True))","A",0
325,1,197,0,106.893346," ","integrate(1/x**(5/2)/(c*x**4+b*x**2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{11}{2}}} & \text{for}\: b = 0 \wedge c = 0 \\- \frac{2}{7 b x^{\frac{7}{2}}} & \text{for}\: c = 0 \\- \frac{2}{11 c x^{\frac{11}{2}}} & \text{for}\: b = 0 \\- \frac{2}{7 b x^{\frac{7}{2}}} + \frac{2 c}{3 b^{2} x^{\frac{3}{2}}} - \frac{\sqrt[4]{-1} c^{2} \sqrt[4]{\frac{1}{c}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{11}{4}}} + \frac{\sqrt[4]{-1} c^{2} \sqrt[4]{\frac{1}{c}} \log{\left(\sqrt[4]{-1} \sqrt[4]{b} \sqrt[4]{\frac{1}{c}} + \sqrt{x} \right)}}{2 b^{\frac{11}{4}}} - \frac{\sqrt[4]{-1} c^{2} \sqrt[4]{\frac{1}{c}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{b} \sqrt[4]{\frac{1}{c}}} \right)}}{b^{\frac{11}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(11/2), Eq(b, 0) & Eq(c, 0)), (-2/(7*b*x**(7/2)), Eq(c, 0)), (-2/(11*c*x**(11/2)), Eq(b, 0)), (-2/(7*b*x**(7/2)) + 2*c/(3*b**2*x**(3/2)) - (-1)**(1/4)*c**2*(1/c)**(1/4)*log(-(-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(11/4)) + (-1)**(1/4)*c**2*(1/c)**(1/4)*log((-1)**(1/4)*b**(1/4)*(1/c)**(1/4) + sqrt(x))/(2*b**(11/4)) - (-1)**(1/4)*c**2*(1/c)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(b**(1/4)*(1/c)**(1/4)))/b**(11/4), True))","A",0
326,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(c*x**4+b*x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate(x**(19/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate(x**(17/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate(x**(15/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2)**2/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**4+b*x**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(x**(23/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate(x**(21/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,-1,0,0,0.000000," ","integrate(x**(19/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate(x**(17/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,-1,0,0,0.000000," ","integrate(x**(15/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
345,-1,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
346,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,-1,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+b*x**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,0,0,0,0.000000," ","integrate(x**(7/2)*(c*x**4+b*x**2)**(1/2),x)","\int x^{\frac{7}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x**(7/2)*sqrt(x**2*(b + c*x**2)), x)","F",0
353,0,0,0,0.000000," ","integrate(x**(5/2)*(c*x**4+b*x**2)**(1/2),x)","\int x^{\frac{5}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x**(5/2)*sqrt(x**2*(b + c*x**2)), x)","F",0
354,0,0,0,0.000000," ","integrate(x**(3/2)*(c*x**4+b*x**2)**(1/2),x)","\int x^{\frac{3}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(x**(3/2)*sqrt(x**2*(b + c*x**2)), x)","F",0
355,0,0,0,0.000000," ","integrate(x**(1/2)*(c*x**4+b*x**2)**(1/2),x)","\int \sqrt{x} \sqrt{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral(sqrt(x)*sqrt(x**2*(b + c*x**2)), x)","F",0
356,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**(1/2),x)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{\sqrt{x}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{\frac{11}{2}}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*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)","\int \frac{\sqrt{x^{2} \left(b + c x^{2}\right)}}{x^{\frac{13}{2}}}\, dx"," ",0,"Integral(sqrt(x**2*(b + c*x**2))/x**(13/2), x)","F",0
363,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(1/2)/x**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,0,0,0,0.000000," ","integrate(x**(3/2)*(c*x**4+b*x**2)**(3/2),x)","\int x^{\frac{3}{2}} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**(3/2)*(x**2*(b + c*x**2))**(3/2), x)","F",0
365,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)*x**(1/2),x)","\int \sqrt{x} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(x)*(x**2*(b + c*x**2))**(3/2), x)","F",0
366,0,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**(1/2),x)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{\sqrt{x}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{\frac{5}{2}}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{\frac{7}{2}}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{\frac{9}{2}}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{\frac{11}{2}}}\, dx"," ",0,"Integral((x**2*(b + c*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)","\int \frac{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}{x^{\frac{13}{2}}}\, dx"," ",0,"Integral((x**2*(b + c*x**2))**(3/2)/x**(13/2), x)","F",0
373,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**(19/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**(21/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2)**(3/2)/x**(23/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+b*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,0,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{\frac{11}{2}}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**(11/2)/sqrt(x**2*(b + c*x**2)), x)","F",0
380,0,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{\frac{9}{2}}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**(9/2)/sqrt(x**2*(b + c*x**2)), x)","F",0
381,0,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{\frac{7}{2}}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**(7/2)/sqrt(x**2*(b + c*x**2)), x)","F",0
382,0,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{\frac{5}{2}}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**(5/2)/sqrt(x**2*(b + c*x**2)), x)","F",0
383,0,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{\frac{3}{2}}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**(3/2)/sqrt(x**2*(b + c*x**2)), x)","F",0
384,0,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{\sqrt{x}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(sqrt(x)/sqrt(x**2*(b + c*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)","\int \frac{1}{\sqrt{x} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(sqrt(x)*sqrt(x**2*(b + c*x**2))), x)","F",0
386,0,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{\frac{3}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**(3/2)*sqrt(x**2*(b + c*x**2))), x)","F",0
387,0,0,0,0.000000," ","integrate(1/x**(5/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{\frac{5}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**(5/2)*sqrt(x**2*(b + c*x**2))), x)","F",0
388,0,0,0,0.000000," ","integrate(1/x**(7/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{\frac{7}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**(7/2)*sqrt(x**2*(b + c*x**2))), x)","F",0
389,0,0,0,0.000000," ","integrate(1/x**(9/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{\frac{9}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**(9/2)*sqrt(x**2*(b + c*x**2))), x)","F",0
390,0,0,0,0.000000," ","integrate(1/x**(11/2)/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{\frac{11}{2}} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**(11/2)*sqrt(x**2*(b + c*x**2))), x)","F",0
391,-1,0,0,0.000000," ","integrate(x**(17/2)/(c*x**4+b*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate(x**(15/2)/(c*x**4+b*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+b*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,0,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+b*x**2)**(3/2),x)","\int \frac{x^{\frac{11}{2}}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(11/2)/(x**2*(b + c*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)","\int \frac{x^{\frac{9}{2}}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(9/2)/(x**2*(b + c*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)","\int \frac{x^{\frac{7}{2}}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(7/2)/(x**2*(b + c*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)","\int \frac{x^{\frac{5}{2}}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(5/2)/(x**2*(b + c*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)","\int \frac{x^{\frac{3}{2}}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**(3/2)/(x**2*(b + c*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)","\int \frac{\sqrt{x}}{\left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(x)/(x**2*(b + c*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)","\int \frac{1}{\sqrt{x} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(x)*(x**2*(b + c*x**2))**(3/2)), x)","F",0
401,0,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**4+b*x**2)**(3/2),x)","\int \frac{1}{x^{\frac{3}{2}} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**(3/2)*(x**2*(b + c*x**2))**(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)","\int \frac{1}{x^{\frac{5}{2}} \left(x^{2} \left(b + c x^{2}\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**(5/2)*(x**2*(b + c*x**2))**(3/2)), x)","F",0
403,1,758,0,5.284307," ","integrate((c*x)**m*(c*x**4+b*x**2)**3,x)","\begin{cases} \frac{- \frac{b^{3}}{6 x^{6}} - \frac{3 b^{2} c}{4 x^{4}} - \frac{3 b c^{2}}{2 x^{2}} + c^{3} \log{\left(x \right)}}{c^{13}} & \text{for}\: m = -13 \\\frac{- \frac{b^{3}}{4 x^{4}} - \frac{3 b^{2} c}{2 x^{2}} + 3 b c^{2} \log{\left(x \right)} + \frac{c^{3} x^{2}}{2}}{c^{11}} & \text{for}\: m = -11 \\\frac{- \frac{b^{3}}{2 x^{2}} + 3 b^{2} c \log{\left(x \right)} + \frac{3 b c^{2} x^{2}}{2} + \frac{c^{3} x^{4}}{4}}{c^{9}} & \text{for}\: m = -9 \\\frac{b^{3} \log{\left(x \right)} + \frac{3 b^{2} c x^{2}}{2} + \frac{3 b c^{2} x^{4}}{4} + \frac{c^{3} x^{6}}{6}}{c^{7}} & \text{for}\: m = -7 \\\frac{b^{3} c^{m} m^{3} x^{7} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{33 b^{3} c^{m} m^{2} x^{7} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{359 b^{3} c^{m} m x^{7} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{1287 b^{3} c^{m} x^{7} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{3 b^{2} c c^{m} m^{3} x^{9} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{93 b^{2} c c^{m} m^{2} x^{9} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{933 b^{2} c c^{m} m x^{9} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{3003 b^{2} c c^{m} x^{9} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{3 b c^{2} c^{m} m^{3} x^{11} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{87 b c^{2} c^{m} m^{2} x^{11} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{813 b c^{2} c^{m} m x^{11} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{2457 b c^{2} c^{m} x^{11} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{c^{3} c^{m} m^{3} x^{13} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{27 c^{3} c^{m} m^{2} x^{13} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{239 c^{3} c^{m} m x^{13} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} + \frac{693 c^{3} c^{m} x^{13} x^{m}}{m^{4} + 40 m^{3} + 590 m^{2} + 3800 m + 9009} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-b**3/(6*x**6) - 3*b**2*c/(4*x**4) - 3*b*c**2/(2*x**2) + c**3*log(x))/c**13, Eq(m, -13)), ((-b**3/(4*x**4) - 3*b**2*c/(2*x**2) + 3*b*c**2*log(x) + c**3*x**2/2)/c**11, Eq(m, -11)), ((-b**3/(2*x**2) + 3*b**2*c*log(x) + 3*b*c**2*x**2/2 + c**3*x**4/4)/c**9, Eq(m, -9)), ((b**3*log(x) + 3*b**2*c*x**2/2 + 3*b*c**2*x**4/4 + c**3*x**6/6)/c**7, Eq(m, -7)), (b**3*c**m*m**3*x**7*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 33*b**3*c**m*m**2*x**7*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 359*b**3*c**m*m*x**7*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 1287*b**3*c**m*x**7*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 3*b**2*c*c**m*m**3*x**9*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 93*b**2*c*c**m*m**2*x**9*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 933*b**2*c*c**m*m*x**9*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 3003*b**2*c*c**m*x**9*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 3*b*c**2*c**m*m**3*x**11*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 87*b*c**2*c**m*m**2*x**11*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 813*b*c**2*c**m*m*x**11*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 2457*b*c**2*c**m*x**11*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + c**3*c**m*m**3*x**13*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 27*c**3*c**m*m**2*x**13*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 239*c**3*c**m*m*x**13*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009) + 693*c**3*c**m*x**13*x**m/(m**4 + 40*m**3 + 590*m**2 + 3800*m + 9009), True))","A",0
404,1,352,0,2.294924," ","integrate((c*x)**m*(c*x**4+b*x**2)**2,x)","\begin{cases} \frac{- \frac{b^{2}}{4 x^{4}} - \frac{b c}{x^{2}} + c^{2} \log{\left(x \right)}}{c^{9}} & \text{for}\: m = -9 \\\frac{- \frac{b^{2}}{2 x^{2}} + 2 b c \log{\left(x \right)} + \frac{c^{2} x^{2}}{2}}{c^{7}} & \text{for}\: m = -7 \\\frac{b^{2} \log{\left(x \right)} + b c x^{2} + \frac{c^{2} x^{4}}{4}}{c^{5}} & \text{for}\: m = -5 \\\frac{b^{2} c^{m} m^{2} x^{5} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{16 b^{2} c^{m} m x^{5} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{63 b^{2} c^{m} x^{5} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{2 b c c^{m} m^{2} x^{7} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{28 b c c^{m} m x^{7} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{90 b c c^{m} x^{7} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{c^{2} c^{m} m^{2} x^{9} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{12 c^{2} c^{m} m x^{9} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} + \frac{35 c^{2} c^{m} x^{9} x^{m}}{m^{3} + 21 m^{2} + 143 m + 315} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-b**2/(4*x**4) - b*c/x**2 + c**2*log(x))/c**9, Eq(m, -9)), ((-b**2/(2*x**2) + 2*b*c*log(x) + c**2*x**2/2)/c**7, Eq(m, -7)), ((b**2*log(x) + b*c*x**2 + c**2*x**4/4)/c**5, Eq(m, -5)), (b**2*c**m*m**2*x**5*x**m/(m**3 + 21*m**2 + 143*m + 315) + 16*b**2*c**m*m*x**5*x**m/(m**3 + 21*m**2 + 143*m + 315) + 63*b**2*c**m*x**5*x**m/(m**3 + 21*m**2 + 143*m + 315) + 2*b*c*c**m*m**2*x**7*x**m/(m**3 + 21*m**2 + 143*m + 315) + 28*b*c*c**m*m*x**7*x**m/(m**3 + 21*m**2 + 143*m + 315) + 90*b*c*c**m*x**7*x**m/(m**3 + 21*m**2 + 143*m + 315) + c**2*c**m*m**2*x**9*x**m/(m**3 + 21*m**2 + 143*m + 315) + 12*c**2*c**m*m*x**9*x**m/(m**3 + 21*m**2 + 143*m + 315) + 35*c**2*c**m*x**9*x**m/(m**3 + 21*m**2 + 143*m + 315), True))","A",0
405,1,119,0,0.757331," ","integrate((c*x)**m*(c*x**4+b*x**2),x)","\begin{cases} \frac{- \frac{b}{2 x^{2}} + c \log{\left(x \right)}}{c^{5}} & \text{for}\: m = -5 \\\frac{b \log{\left(x \right)} + \frac{c x^{2}}{2}}{c^{3}} & \text{for}\: m = -3 \\\frac{b c^{m} m x^{3} x^{m}}{m^{2} + 8 m + 15} + \frac{5 b c^{m} x^{3} x^{m}}{m^{2} + 8 m + 15} + \frac{c c^{m} m x^{5} x^{m}}{m^{2} + 8 m + 15} + \frac{3 c c^{m} x^{5} x^{m}}{m^{2} + 8 m + 15} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-b/(2*x**2) + c*log(x))/c**5, Eq(m, -5)), ((b*log(x) + c*x**2/2)/c**3, Eq(m, -3)), (b*c**m*m*x**3*x**m/(m**2 + 8*m + 15) + 5*b*c**m*x**3*x**m/(m**2 + 8*m + 15) + c*c**m*m*x**5*x**m/(m**2 + 8*m + 15) + 3*c*c**m*x**5*x**m/(m**2 + 8*m + 15), True))","A",0
406,0,0,0,0.000000," ","integrate((c*x)**m/(c*x**4+b*x**2),x)","\int \frac{\left(c x\right)^{m}}{x^{2} \left(b + c x^{2}\right)}\, dx"," ",0,"Integral((c*x)**m/(x**2*(b + c*x**2)), x)","F",0
407,0,0,0,0.000000," ","integrate((c*x)**m/(c*x**4+b*x**2)**2,x)","\int \frac{\left(c x\right)^{m}}{x^{4} \left(b + c x^{2}\right)^{2}}\, dx"," ",0,"Integral((c*x)**m/(x**4*(b + c*x**2)**2), x)","F",0
408,0,0,0,0.000000," ","integrate((c*x)**m/(c*x**4+b*x**2)**3,x)","\int \frac{\left(c x\right)^{m}}{x^{6} \left(b + c x^{2}\right)^{3}}\, dx"," ",0,"Integral((c*x)**m/(x**6*(b + c*x**2)**3), x)","F",0
409,1,24,0,0.067144," ","integrate(x**3*(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}"," ",0,"a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8","A",0
410,1,26,0,0.068072," ","integrate(x**2*(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{7}}{7}"," ",0,"a**2*x**3/3 + 2*a*b*x**5/5 + b**2*x**7/7","A",0
411,1,24,0,0.066964," ","integrate(x*(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}"," ",0,"a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6","A",0
412,1,22,0,0.070495," ","integrate(b**2*x**4+2*a*b*x**2+a**2,x)","a^{2} x + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{5}}{5}"," ",0,"a**2*x + 2*a*b*x**3/3 + b**2*x**5/5","A",0
413,1,20,0,0.103636," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x,x)","a^{2} \log{\left(x \right)} + a b x^{2} + \frac{b^{2} x^{4}}{4}"," ",0,"a**2*log(x) + a*b*x**2 + b**2*x**4/4","A",0
414,1,19,0,0.096756," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x**2,x)","- \frac{a^{2}}{x} + 2 a b x + \frac{b^{2} x^{3}}{3}"," ",0,"-a**2/x + 2*a*b*x + b**2*x**3/3","A",0
415,1,24,0,0.138297," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x**3,x)","- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{2}}{2}"," ",0,"-a**2/(2*x**2) + 2*a*b*log(x) + b**2*x**2/2","A",0
416,1,22,0,0.138210," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x**4,x)","b^{2} x + \frac{- a^{2} - 6 a b x^{2}}{3 x^{3}}"," ",0,"b**2*x + (-a**2 - 6*a*b*x**2)/(3*x**3)","A",0
417,1,24,0,0.173704," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x**5,x)","b^{2} \log{\left(x \right)} + \frac{- a^{2} - 4 a b x^{2}}{4 x^{4}}"," ",0,"b**2*log(x) + (-a**2 - 4*a*b*x**2)/(4*x**4)","A",0
418,1,27,0,0.184618," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x**6,x)","\frac{- 3 a^{2} - 10 a b x^{2} - 15 b^{2} x^{4}}{15 x^{5}}"," ",0,"(-3*a**2 - 10*a*b*x**2 - 15*b**2*x**4)/(15*x**5)","A",0
419,1,26,0,0.195779," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x**7,x)","\frac{- a^{2} - 3 a b x^{2} - 3 b^{2} x^{4}}{6 x^{6}}"," ",0,"(-a**2 - 3*a*b*x**2 - 3*b**2*x**4)/(6*x**6)","A",0
420,1,27,0,0.208419," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/x**8,x)","\frac{- 15 a^{2} - 42 a b x^{2} - 35 b^{2} x^{4}}{105 x^{7}}"," ",0,"(-15*a**2 - 42*a*b*x**2 - 35*b**2*x**4)/(105*x**7)","A",0
421,1,53,0,0.080617," ","integrate(x**6*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{a^{4} x^{7}}{7} + \frac{4 a^{3} b x^{9}}{9} + \frac{6 a^{2} b^{2} x^{11}}{11} + \frac{4 a b^{3} x^{13}}{13} + \frac{b^{4} x^{15}}{15}"," ",0,"a**4*x**7/7 + 4*a**3*b*x**9/9 + 6*a**2*b**2*x**11/11 + 4*a*b**3*x**13/13 + b**4*x**15/15","A",0
422,1,49,0,0.080825," ","integrate(x**5*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{a^{4} x^{6}}{6} + \frac{a^{3} b x^{8}}{2} + \frac{3 a^{2} b^{2} x^{10}}{5} + \frac{a b^{3} x^{12}}{3} + \frac{b^{4} x^{14}}{14}"," ",0,"a**4*x**6/6 + a**3*b*x**8/2 + 3*a**2*b**2*x**10/5 + a*b**3*x**12/3 + b**4*x**14/14","A",0
423,1,53,0,0.082093," ","integrate(x**4*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{a^{4} x^{5}}{5} + \frac{4 a^{3} b x^{7}}{7} + \frac{2 a^{2} b^{2} x^{9}}{3} + \frac{4 a b^{3} x^{11}}{11} + \frac{b^{4} x^{13}}{13}"," ",0,"a**4*x**5/5 + 4*a**3*b*x**7/7 + 2*a**2*b**2*x**9/3 + 4*a*b**3*x**11/11 + b**4*x**13/13","A",0
424,1,53,0,0.080243," ","integrate(x**3*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{a^{4} x^{4}}{4} + \frac{2 a^{3} b x^{6}}{3} + \frac{3 a^{2} b^{2} x^{8}}{4} + \frac{2 a b^{3} x^{10}}{5} + \frac{b^{4} x^{12}}{12}"," ",0,"a**4*x**4/4 + 2*a**3*b*x**6/3 + 3*a**2*b**2*x**8/4 + 2*a*b**3*x**10/5 + b**4*x**12/12","A",0
425,1,53,0,0.079819," ","integrate(x**2*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{a^{4} x^{3}}{3} + \frac{4 a^{3} b x^{5}}{5} + \frac{6 a^{2} b^{2} x^{7}}{7} + \frac{4 a b^{3} x^{9}}{9} + \frac{b^{4} x^{11}}{11}"," ",0,"a**4*x**3/3 + 4*a**3*b*x**5/5 + 6*a**2*b**2*x**7/7 + 4*a*b**3*x**9/9 + b**4*x**11/11","A",0
426,1,44,0,0.079098," ","integrate(x*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{a^{4} x^{2}}{2} + a^{3} b x^{4} + a^{2} b^{2} x^{6} + \frac{a b^{3} x^{8}}{2} + \frac{b^{4} x^{10}}{10}"," ",0,"a**4*x**2/2 + a**3*b*x**4 + a**2*b**2*x**6 + a*b**3*x**8/2 + b**4*x**10/10","B",0
427,1,49,0,0.084640," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2,x)","a^{4} x + \frac{4 a^{3} b x^{3}}{3} + \frac{6 a^{2} b^{2} x^{5}}{5} + \frac{4 a b^{3} x^{7}}{7} + \frac{b^{4} x^{9}}{9}"," ",0,"a**4*x + 4*a**3*b*x**3/3 + 6*a**2*b**2*x**5/5 + 4*a*b**3*x**7/7 + b**4*x**9/9","A",0
428,1,49,0,0.133976," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x,x)","a^{4} \log{\left(x \right)} + 2 a^{3} b x^{2} + \frac{3 a^{2} b^{2} x^{4}}{2} + \frac{2 a b^{3} x^{6}}{3} + \frac{b^{4} x^{8}}{8}"," ",0,"a**4*log(x) + 2*a**3*b*x**2 + 3*a**2*b**2*x**4/2 + 2*a*b**3*x**6/3 + b**4*x**8/8","A",0
429,1,44,0,0.130016," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**2,x)","- \frac{a^{4}}{x} + 4 a^{3} b x + 2 a^{2} b^{2} x^{3} + \frac{4 a b^{3} x^{5}}{5} + \frac{b^{4} x^{7}}{7}"," ",0,"-a**4/x + 4*a**3*b*x + 2*a**2*b**2*x**3 + 4*a*b**3*x**5/5 + b**4*x**7/7","A",0
430,1,46,0,0.171843," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**3,x)","- \frac{a^{4}}{2 x^{2}} + 4 a^{3} b \log{\left(x \right)} + 3 a^{2} b^{2} x^{2} + a b^{3} x^{4} + \frac{b^{4} x^{6}}{6}"," ",0,"-a**4/(2*x**2) + 4*a**3*b*log(x) + 3*a**2*b**2*x**2 + a*b**3*x**4 + b**4*x**6/6","A",0
431,1,49,0,0.170414," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**4,x)","6 a^{2} b^{2} x + \frac{4 a b^{3} x^{3}}{3} + \frac{b^{4} x^{5}}{5} + \frac{- a^{4} - 12 a^{3} b x^{2}}{3 x^{3}}"," ",0,"6*a**2*b**2*x + 4*a*b**3*x**3/3 + b**4*x**5/5 + (-a**4 - 12*a**3*b*x**2)/(3*x**3)","A",0
432,1,49,0,0.220239," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**5,x)","6 a^{2} b^{2} \log{\left(x \right)} + 2 a b^{3} x^{2} + \frac{b^{4} x^{4}}{4} + \frac{- a^{4} - 8 a^{3} b x^{2}}{4 x^{4}}"," ",0,"6*a**2*b**2*log(x) + 2*a*b**3*x**2 + b**4*x**4/4 + (-a**4 - 8*a**3*b*x**2)/(4*x**4)","A",0
433,1,49,0,0.227421," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**6,x)","4 a b^{3} x + \frac{b^{4} x^{3}}{3} + \frac{- 3 a^{4} - 20 a^{3} b x^{2} - 90 a^{2} b^{2} x^{4}}{15 x^{5}}"," ",0,"4*a*b**3*x + b**4*x**3/3 + (-3*a**4 - 20*a**3*b*x**2 - 90*a**2*b**2*x**4)/(15*x**5)","A",0
434,1,49,0,0.303535," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**7,x)","4 a b^{3} \log{\left(x \right)} + \frac{b^{4} x^{2}}{2} + \frac{- a^{4} - 6 a^{3} b x^{2} - 18 a^{2} b^{2} x^{4}}{6 x^{6}}"," ",0,"4*a*b**3*log(x) + b**4*x**2/2 + (-a**4 - 6*a**3*b*x**2 - 18*a**2*b**2*x**4)/(6*x**6)","A",0
435,1,48,0,0.297219," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**8,x)","b^{4} x + \frac{- 5 a^{4} - 28 a^{3} b x^{2} - 70 a^{2} b^{2} x^{4} - 140 a b^{3} x^{6}}{35 x^{7}}"," ",0,"b**4*x + (-5*a**4 - 28*a**3*b*x**2 - 70*a**2*b**2*x**4 - 140*a*b**3*x**6)/(35*x**7)","A",0
436,1,49,0,0.368492," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**9,x)","b^{4} \log{\left(x \right)} + \frac{- 3 a^{4} - 16 a^{3} b x^{2} - 36 a^{2} b^{2} x^{4} - 48 a b^{3} x^{6}}{24 x^{8}}"," ",0,"b**4*log(x) + (-3*a**4 - 16*a**3*b*x**2 - 36*a**2*b**2*x**4 - 48*a*b**3*x**6)/(24*x**8)","A",0
437,1,51,0,0.369312," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**10,x)","\frac{- 35 a^{4} - 180 a^{3} b x^{2} - 378 a^{2} b^{2} x^{4} - 420 a b^{3} x^{6} - 315 b^{4} x^{8}}{315 x^{9}}"," ",0,"(-35*a**4 - 180*a**3*b*x**2 - 378*a**2*b**2*x**4 - 420*a*b**3*x**6 - 315*b**4*x**8)/(315*x**9)","A",0
438,1,49,0,0.393342," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**11,x)","\frac{- a^{4} - 5 a^{3} b x^{2} - 10 a^{2} b^{2} x^{4} - 10 a b^{3} x^{6} - 5 b^{4} x^{8}}{10 x^{10}}"," ",0,"(-a**4 - 5*a**3*b*x**2 - 10*a**2*b**2*x**4 - 10*a*b**3*x**6 - 5*b**4*x**8)/(10*x**10)","B",0
439,1,51,0,0.401132," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**12,x)","\frac{- 315 a^{4} - 1540 a^{3} b x^{2} - 2970 a^{2} b^{2} x^{4} - 2772 a b^{3} x^{6} - 1155 b^{4} x^{8}}{3465 x^{11}}"," ",0,"(-315*a**4 - 1540*a**3*b*x**2 - 2970*a**2*b**2*x**4 - 2772*a*b**3*x**6 - 1155*b**4*x**8)/(3465*x**11)","A",0
440,1,51,0,0.427554," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**13,x)","\frac{- 5 a^{4} - 24 a^{3} b x^{2} - 45 a^{2} b^{2} x^{4} - 40 a b^{3} x^{6} - 15 b^{4} x^{8}}{60 x^{12}}"," ",0,"(-5*a**4 - 24*a**3*b*x**2 - 45*a**2*b**2*x**4 - 40*a*b**3*x**6 - 15*b**4*x**8)/(60*x**12)","A",0
441,1,51,0,0.438898," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**14,x)","\frac{- 1155 a^{4} - 5460 a^{3} b x^{2} - 10010 a^{2} b^{2} x^{4} - 8580 a b^{3} x^{6} - 3003 b^{4} x^{8}}{15015 x^{13}}"," ",0,"(-1155*a**4 - 5460*a**3*b*x**2 - 10010*a**2*b**2*x**4 - 8580*a*b**3*x**6 - 3003*b**4*x**8)/(15015*x**13)","A",0
442,1,51,0,0.445225," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**15,x)","\frac{- 15 a^{4} - 70 a^{3} b x^{2} - 126 a^{2} b^{2} x^{4} - 105 a b^{3} x^{6} - 35 b^{4} x^{8}}{210 x^{14}}"," ",0,"(-15*a**4 - 70*a**3*b*x**2 - 126*a**2*b**2*x**4 - 105*a*b**3*x**6 - 35*b**4*x**8)/(210*x**14)","A",0
443,1,51,0,0.458185," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**16,x)","\frac{- 3003 a^{4} - 13860 a^{3} b x^{2} - 24570 a^{2} b^{2} x^{4} - 20020 a b^{3} x^{6} - 6435 b^{4} x^{8}}{45045 x^{15}}"," ",0,"(-3003*a**4 - 13860*a**3*b*x**2 - 24570*a**2*b**2*x**4 - 20020*a*b**3*x**6 - 6435*b**4*x**8)/(45045*x**15)","A",0
444,1,80,0,0.088737," ","integrate(x**8*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{9}}{9} + \frac{6 a^{5} b x^{11}}{11} + \frac{15 a^{4} b^{2} x^{13}}{13} + \frac{4 a^{3} b^{3} x^{15}}{3} + \frac{15 a^{2} b^{4} x^{17}}{17} + \frac{6 a b^{5} x^{19}}{19} + \frac{b^{6} x^{21}}{21}"," ",0,"a**6*x**9/9 + 6*a**5*b*x**11/11 + 15*a**4*b**2*x**13/13 + 4*a**3*b**3*x**15/3 + 15*a**2*b**4*x**17/17 + 6*a*b**5*x**19/19 + b**6*x**21/21","A",0
445,1,78,0,0.087238," ","integrate(x**7*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{8}}{8} + \frac{3 a^{5} b x^{10}}{5} + \frac{5 a^{4} b^{2} x^{12}}{4} + \frac{10 a^{3} b^{3} x^{14}}{7} + \frac{15 a^{2} b^{4} x^{16}}{16} + \frac{a b^{5} x^{18}}{3} + \frac{b^{6} x^{20}}{20}"," ",0,"a**6*x**8/8 + 3*a**5*b*x**10/5 + 5*a**4*b**2*x**12/4 + 10*a**3*b**3*x**14/7 + 15*a**2*b**4*x**16/16 + a*b**5*x**18/3 + b**6*x**20/20","A",0
446,1,76,0,0.087738," ","integrate(x**6*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{7}}{7} + \frac{2 a^{5} b x^{9}}{3} + \frac{15 a^{4} b^{2} x^{11}}{11} + \frac{20 a^{3} b^{3} x^{13}}{13} + a^{2} b^{4} x^{15} + \frac{6 a b^{5} x^{17}}{17} + \frac{b^{6} x^{19}}{19}"," ",0,"a**6*x**7/7 + 2*a**5*b*x**9/3 + 15*a**4*b**2*x**11/11 + 20*a**3*b**3*x**13/13 + a**2*b**4*x**15 + 6*a*b**5*x**17/17 + b**6*x**19/19","A",0
447,1,80,0,0.085850," ","integrate(x**5*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{6}}{6} + \frac{3 a^{5} b x^{8}}{4} + \frac{3 a^{4} b^{2} x^{10}}{2} + \frac{5 a^{3} b^{3} x^{12}}{3} + \frac{15 a^{2} b^{4} x^{14}}{14} + \frac{3 a b^{5} x^{16}}{8} + \frac{b^{6} x^{18}}{18}"," ",0,"a**6*x**6/6 + 3*a**5*b*x**8/4 + 3*a**4*b**2*x**10/2 + 5*a**3*b**3*x**12/3 + 15*a**2*b**4*x**14/14 + 3*a*b**5*x**16/8 + b**6*x**18/18","A",0
448,1,80,0,0.088950," ","integrate(x**4*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{5}}{5} + \frac{6 a^{5} b x^{7}}{7} + \frac{5 a^{4} b^{2} x^{9}}{3} + \frac{20 a^{3} b^{3} x^{11}}{11} + \frac{15 a^{2} b^{4} x^{13}}{13} + \frac{2 a b^{5} x^{15}}{5} + \frac{b^{6} x^{17}}{17}"," ",0,"a**6*x**5/5 + 6*a**5*b*x**7/7 + 5*a**4*b**2*x**9/3 + 20*a**3*b**3*x**11/11 + 15*a**2*b**4*x**13/13 + 2*a*b**5*x**15/5 + b**6*x**17/17","A",0
449,1,75,0,0.086837," ","integrate(x**3*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{4}}{4} + a^{5} b x^{6} + \frac{15 a^{4} b^{2} x^{8}}{8} + 2 a^{3} b^{3} x^{10} + \frac{5 a^{2} b^{4} x^{12}}{4} + \frac{3 a b^{5} x^{14}}{7} + \frac{b^{6} x^{16}}{16}"," ",0,"a**6*x**4/4 + a**5*b*x**6 + 15*a**4*b**2*x**8/8 + 2*a**3*b**3*x**10 + 5*a**2*b**4*x**12/4 + 3*a*b**5*x**14/7 + b**6*x**16/16","B",0
450,1,80,0,0.085931," ","integrate(x**2*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{3}}{3} + \frac{6 a^{5} b x^{5}}{5} + \frac{15 a^{4} b^{2} x^{7}}{7} + \frac{20 a^{3} b^{3} x^{9}}{9} + \frac{15 a^{2} b^{4} x^{11}}{11} + \frac{6 a b^{5} x^{13}}{13} + \frac{b^{6} x^{15}}{15}"," ",0,"a**6*x**3/3 + 6*a**5*b*x**5/5 + 15*a**4*b**2*x**7/7 + 20*a**3*b**3*x**9/9 + 15*a**2*b**4*x**11/11 + 6*a*b**5*x**13/13 + b**6*x**15/15","A",0
451,1,78,0,0.088377," ","integrate(x*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{a^{6} x^{2}}{2} + \frac{3 a^{5} b x^{4}}{2} + \frac{5 a^{4} b^{2} x^{6}}{2} + \frac{5 a^{3} b^{3} x^{8}}{2} + \frac{3 a^{2} b^{4} x^{10}}{2} + \frac{a b^{5} x^{12}}{2} + \frac{b^{6} x^{14}}{14}"," ",0,"a**6*x**2/2 + 3*a**5*b*x**4/2 + 5*a**4*b**2*x**6/2 + 5*a**3*b**3*x**8/2 + 3*a**2*b**4*x**10/2 + a*b**5*x**12/2 + b**6*x**14/14","B",0
452,1,73,0,0.083336," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3,x)","a^{6} x + 2 a^{5} b x^{3} + 3 a^{4} b^{2} x^{5} + \frac{20 a^{3} b^{3} x^{7}}{7} + \frac{5 a^{2} b^{4} x^{9}}{3} + \frac{6 a b^{5} x^{11}}{11} + \frac{b^{6} x^{13}}{13}"," ",0,"a**6*x + 2*a**5*b*x**3 + 3*a**4*b**2*x**5 + 20*a**3*b**3*x**7/7 + 5*a**2*b**4*x**9/3 + 6*a*b**5*x**11/11 + b**6*x**13/13","A",0
453,1,76,0,0.165945," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x,x)","a^{6} \log{\left(x \right)} + 3 a^{5} b x^{2} + \frac{15 a^{4} b^{2} x^{4}}{4} + \frac{10 a^{3} b^{3} x^{6}}{3} + \frac{15 a^{2} b^{4} x^{8}}{8} + \frac{3 a b^{5} x^{10}}{5} + \frac{b^{6} x^{12}}{12}"," ",0,"a**6*log(x) + 3*a**5*b*x**2 + 15*a**4*b**2*x**4/4 + 10*a**3*b**3*x**6/3 + 15*a**2*b**4*x**8/8 + 3*a*b**5*x**10/5 + b**6*x**12/12","A",0
454,1,70,0,0.158414," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**2,x)","- \frac{a^{6}}{x} + 6 a^{5} b x + 5 a^{4} b^{2} x^{3} + 4 a^{3} b^{3} x^{5} + \frac{15 a^{2} b^{4} x^{7}}{7} + \frac{2 a b^{5} x^{9}}{3} + \frac{b^{6} x^{11}}{11}"," ",0,"-a**6/x + 6*a**5*b*x + 5*a**4*b**2*x**3 + 4*a**3*b**3*x**5 + 15*a**2*b**4*x**7/7 + 2*a*b**5*x**9/3 + b**6*x**11/11","A",0
455,1,76,0,0.195968," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**3,x)","- \frac{a^{6}}{2 x^{2}} + 6 a^{5} b \log{\left(x \right)} + \frac{15 a^{4} b^{2} x^{2}}{2} + 5 a^{3} b^{3} x^{4} + \frac{5 a^{2} b^{4} x^{6}}{2} + \frac{3 a b^{5} x^{8}}{4} + \frac{b^{6} x^{10}}{10}"," ",0,"-a**6/(2*x**2) + 6*a**5*b*log(x) + 15*a**4*b**2*x**2/2 + 5*a**3*b**3*x**4 + 5*a**2*b**4*x**6/2 + 3*a*b**5*x**8/4 + b**6*x**10/10","A",0
456,1,75,0,0.206886," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**4,x)","15 a^{4} b^{2} x + \frac{20 a^{3} b^{3} x^{3}}{3} + 3 a^{2} b^{4} x^{5} + \frac{6 a b^{5} x^{7}}{7} + \frac{b^{6} x^{9}}{9} + \frac{- a^{6} - 18 a^{5} b x^{2}}{3 x^{3}}"," ",0,"15*a**4*b**2*x + 20*a**3*b**3*x**3/3 + 3*a**2*b**4*x**5 + 6*a*b**5*x**7/7 + b**6*x**9/9 + (-a**6 - 18*a**5*b*x**2)/(3*x**3)","A",0
457,1,73,0,0.253492," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**5,x)","15 a^{4} b^{2} \log{\left(x \right)} + 10 a^{3} b^{3} x^{2} + \frac{15 a^{2} b^{4} x^{4}}{4} + a b^{5} x^{6} + \frac{b^{6} x^{8}}{8} + \frac{- a^{6} - 12 a^{5} b x^{2}}{4 x^{4}}"," ",0,"15*a**4*b**2*log(x) + 10*a**3*b**3*x**2 + 15*a**2*b**4*x**4/4 + a*b**5*x**6 + b**6*x**8/8 + (-a**6 - 12*a**5*b*x**2)/(4*x**4)","A",0
458,1,73,0,0.263154," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**6,x)","20 a^{3} b^{3} x + 5 a^{2} b^{4} x^{3} + \frac{6 a b^{5} x^{5}}{5} + \frac{b^{6} x^{7}}{7} + \frac{- a^{6} - 10 a^{5} b x^{2} - 75 a^{4} b^{2} x^{4}}{5 x^{5}}"," ",0,"20*a**3*b**3*x + 5*a**2*b**4*x**3 + 6*a*b**5*x**5/5 + b**6*x**7/7 + (-a**6 - 10*a**5*b*x**2 - 75*a**4*b**2*x**4)/(5*x**5)","A",0
459,1,76,0,0.324899," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**7,x)","20 a^{3} b^{3} \log{\left(x \right)} + \frac{15 a^{2} b^{4} x^{2}}{2} + \frac{3 a b^{5} x^{4}}{2} + \frac{b^{6} x^{6}}{6} + \frac{- a^{6} - 9 a^{5} b x^{2} - 45 a^{4} b^{2} x^{4}}{6 x^{6}}"," ",0,"20*a**3*b**3*log(x) + 15*a**2*b**4*x**2/2 + 3*a*b**5*x**4/2 + b**6*x**6/6 + (-a**6 - 9*a**5*b*x**2 - 45*a**4*b**2*x**4)/(6*x**6)","A",0
460,1,73,0,0.335454," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**8,x)","15 a^{2} b^{4} x + 2 a b^{5} x^{3} + \frac{b^{6} x^{5}}{5} + \frac{- 5 a^{6} - 42 a^{5} b x^{2} - 175 a^{4} b^{2} x^{4} - 700 a^{3} b^{3} x^{6}}{35 x^{7}}"," ",0,"15*a**2*b**4*x + 2*a*b**5*x**3 + b**6*x**5/5 + (-5*a**6 - 42*a**5*b*x**2 - 175*a**4*b**2*x**4 - 700*a**3*b**3*x**6)/(35*x**7)","A",0
461,1,73,0,0.420114," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**9,x)","15 a^{2} b^{4} \log{\left(x \right)} + 3 a b^{5} x^{2} + \frac{b^{6} x^{4}}{4} + \frac{- a^{6} - 8 a^{5} b x^{2} - 30 a^{4} b^{2} x^{4} - 80 a^{3} b^{3} x^{6}}{8 x^{8}}"," ",0,"15*a**2*b**4*log(x) + 3*a*b**5*x**2 + b**6*x**4/4 + (-a**6 - 8*a**5*b*x**2 - 30*a**4*b**2*x**4 - 80*a**3*b**3*x**6)/(8*x**8)","A",0
462,1,73,0,0.435251," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**10,x)","6 a b^{5} x + \frac{b^{6} x^{3}}{3} + \frac{- 7 a^{6} - 54 a^{5} b x^{2} - 189 a^{4} b^{2} x^{4} - 420 a^{3} b^{3} x^{6} - 945 a^{2} b^{4} x^{8}}{63 x^{9}}"," ",0,"6*a*b**5*x + b**6*x**3/3 + (-7*a**6 - 54*a**5*b*x**2 - 189*a**4*b**2*x**4 - 420*a**3*b**3*x**6 - 945*a**2*b**4*x**8)/(63*x**9)","A",0
463,1,75,0,0.625983," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**11,x)","6 a b^{5} \log{\left(x \right)} + \frac{b^{6} x^{2}}{2} + \frac{- 2 a^{6} - 15 a^{5} b x^{2} - 50 a^{4} b^{2} x^{4} - 100 a^{3} b^{3} x^{6} - 150 a^{2} b^{4} x^{8}}{20 x^{10}}"," ",0,"6*a*b**5*log(x) + b**6*x**2/2 + (-2*a**6 - 15*a**5*b*x**2 - 50*a**4*b**2*x**4 - 100*a**3*b**3*x**6 - 150*a**2*b**4*x**8)/(20*x**10)","A",0
464,1,71,0,0.521158," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**12,x)","b^{6} x + \frac{- 21 a^{6} - 154 a^{5} b x^{2} - 495 a^{4} b^{2} x^{4} - 924 a^{3} b^{3} x^{6} - 1155 a^{2} b^{4} x^{8} - 1386 a b^{5} x^{10}}{231 x^{11}}"," ",0,"b**6*x + (-21*a**6 - 154*a**5*b*x**2 - 495*a**4*b**2*x**4 - 924*a**3*b**3*x**6 - 1155*a**2*b**4*x**8 - 1386*a*b**5*x**10)/(231*x**11)","A",0
465,1,73,0,0.617730," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**13,x)","b^{6} \log{\left(x \right)} + \frac{- 10 a^{6} - 72 a^{5} b x^{2} - 225 a^{4} b^{2} x^{4} - 400 a^{3} b^{3} x^{6} - 450 a^{2} b^{4} x^{8} - 360 a b^{5} x^{10}}{120 x^{12}}"," ",0,"b**6*log(x) + (-10*a**6 - 72*a**5*b*x**2 - 225*a**4*b**2*x**4 - 400*a**3*b**3*x**6 - 450*a**2*b**4*x**8 - 360*a*b**5*x**10)/(120*x**12)","A",0
466,1,75,0,0.598352," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**14,x)","\frac{- 231 a^{6} - 1638 a^{5} b x^{2} - 5005 a^{4} b^{2} x^{4} - 8580 a^{3} b^{3} x^{6} - 9009 a^{2} b^{4} x^{8} - 6006 a b^{5} x^{10} - 3003 b^{6} x^{12}}{3003 x^{13}}"," ",0,"(-231*a**6 - 1638*a**5*b*x**2 - 5005*a**4*b**2*x**4 - 8580*a**3*b**3*x**6 - 9009*a**2*b**4*x**8 - 6006*a*b**5*x**10 - 3003*b**6*x**12)/(3003*x**13)","A",0
467,1,73,0,0.628108," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**15,x)","\frac{- a^{6} - 7 a^{5} b x^{2} - 21 a^{4} b^{2} x^{4} - 35 a^{3} b^{3} x^{6} - 35 a^{2} b^{4} x^{8} - 21 a b^{5} x^{10} - 7 b^{6} x^{12}}{14 x^{14}}"," ",0,"(-a**6 - 7*a**5*b*x**2 - 21*a**4*b**2*x**4 - 35*a**3*b**3*x**6 - 35*a**2*b**4*x**8 - 21*a*b**5*x**10 - 7*b**6*x**12)/(14*x**14)","B",0
468,1,75,0,0.617092," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**16,x)","\frac{- 3003 a^{6} - 20790 a^{5} b x^{2} - 61425 a^{4} b^{2} x^{4} - 100100 a^{3} b^{3} x^{6} - 96525 a^{2} b^{4} x^{8} - 54054 a b^{5} x^{10} - 15015 b^{6} x^{12}}{45045 x^{15}}"," ",0,"(-3003*a**6 - 20790*a**5*b*x**2 - 61425*a**4*b**2*x**4 - 100100*a**3*b**3*x**6 - 96525*a**2*b**4*x**8 - 54054*a*b**5*x**10 - 15015*b**6*x**12)/(45045*x**15)","A",0
469,1,75,0,0.680447," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**17,x)","\frac{- 7 a^{6} - 48 a^{5} b x^{2} - 140 a^{4} b^{2} x^{4} - 224 a^{3} b^{3} x^{6} - 210 a^{2} b^{4} x^{8} - 112 a b^{5} x^{10} - 28 b^{6} x^{12}}{112 x^{16}}"," ",0,"(-7*a**6 - 48*a**5*b*x**2 - 140*a**4*b**2*x**4 - 224*a**3*b**3*x**6 - 210*a**2*b**4*x**8 - 112*a*b**5*x**10 - 28*b**6*x**12)/(112*x**16)","B",0
470,1,75,0,0.661469," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**18,x)","\frac{- 15015 a^{6} - 102102 a^{5} b x^{2} - 294525 a^{4} b^{2} x^{4} - 464100 a^{3} b^{3} x^{6} - 425425 a^{2} b^{4} x^{8} - 218790 a b^{5} x^{10} - 51051 b^{6} x^{12}}{255255 x^{17}}"," ",0,"(-15015*a**6 - 102102*a**5*b*x**2 - 294525*a**4*b**2*x**4 - 464100*a**3*b**3*x**6 - 425425*a**2*b**4*x**8 - 218790*a*b**5*x**10 - 51051*b**6*x**12)/(255255*x**17)","A",0
471,1,75,0,0.740551," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**19,x)","\frac{- 28 a^{6} - 189 a^{5} b x^{2} - 540 a^{4} b^{2} x^{4} - 840 a^{3} b^{3} x^{6} - 756 a^{2} b^{4} x^{8} - 378 a b^{5} x^{10} - 84 b^{6} x^{12}}{504 x^{18}}"," ",0,"(-28*a**6 - 189*a**5*b*x**2 - 540*a**4*b**2*x**4 - 840*a**3*b**3*x**6 - 756*a**2*b**4*x**8 - 378*a*b**5*x**10 - 84*b**6*x**12)/(504*x**18)","A",0
472,1,75,0,0.713824," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**20,x)","\frac{- 51051 a^{6} - 342342 a^{5} b x^{2} - 969969 a^{4} b^{2} x^{4} - 1492260 a^{3} b^{3} x^{6} - 1322685 a^{2} b^{4} x^{8} - 646646 a b^{5} x^{10} - 138567 b^{6} x^{12}}{969969 x^{19}}"," ",0,"(-51051*a**6 - 342342*a**5*b*x**2 - 969969*a**4*b**2*x**4 - 1492260*a**3*b**3*x**6 - 1322685*a**2*b**4*x**8 - 646646*a*b**5*x**10 - 138567*b**6*x**12)/(969969*x**19)","A",0
473,1,75,0,0.857143," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**21,x)","\frac{- 84 a^{6} - 560 a^{5} b x^{2} - 1575 a^{4} b^{2} x^{4} - 2400 a^{3} b^{3} x^{6} - 2100 a^{2} b^{4} x^{8} - 1008 a b^{5} x^{10} - 210 b^{6} x^{12}}{1680 x^{20}}"," ",0,"(-84*a**6 - 560*a**5*b*x**2 - 1575*a**4*b**2*x**4 - 2400*a**3*b**3*x**6 - 2100*a**2*b**4*x**8 - 1008*a*b**5*x**10 - 210*b**6*x**12)/(1680*x**20)","A",0
474,1,75,0,0.757782," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**22,x)","\frac{- 138567 a^{6} - 918918 a^{5} b x^{2} - 2567565 a^{4} b^{2} x^{4} - 3879876 a^{3} b^{3} x^{6} - 3357585 a^{2} b^{4} x^{8} - 1587222 a b^{5} x^{10} - 323323 b^{6} x^{12}}{2909907 x^{21}}"," ",0,"(-138567*a**6 - 918918*a**5*b*x**2 - 2567565*a**4*b**2*x**4 - 3879876*a**3*b**3*x**6 - 3357585*a**2*b**4*x**8 - 1587222*a*b**5*x**10 - 323323*b**6*x**12)/(2909907*x**21)","A",0
475,1,80,0,0.322871," ","integrate(x**11/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a^{5}}{2 a b^{6} + 2 b^{7} x^{2}} + \frac{5 a^{4} \log{\left(a + b x^{2} \right)}}{2 b^{6}} - \frac{2 a^{3} x^{2}}{b^{5}} + \frac{3 a^{2} x^{4}}{4 b^{4}} - \frac{a x^{6}}{3 b^{3}} + \frac{x^{8}}{8 b^{2}}"," ",0,"a**5/(2*a*b**6 + 2*b**7*x**2) + 5*a**4*log(a + b*x**2)/(2*b**6) - 2*a**3*x**2/b**5 + 3*a**2*x**4/(4*b**4) - a*x**6/(3*b**3) + x**8/(8*b**2)","A",0
476,1,66,0,0.287988," ","integrate(x**9/(b**2*x**4+2*a*b*x**2+a**2),x)","- \frac{a^{4}}{2 a b^{5} + 2 b^{6} x^{2}} - \frac{2 a^{3} \log{\left(a + b x^{2} \right)}}{b^{5}} + \frac{3 a^{2} x^{2}}{2 b^{4}} - \frac{a x^{4}}{2 b^{3}} + \frac{x^{6}}{6 b^{2}}"," ",0,"-a**4/(2*a*b**5 + 2*b**6*x**2) - 2*a**3*log(a + b*x**2)/b**5 + 3*a**2*x**2/(2*b**4) - a*x**4/(2*b**3) + x**6/(6*b**2)","A",0
477,1,53,0,0.273234," ","integrate(x**7/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a^{3}}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{3 a^{2} \log{\left(a + b x^{2} \right)}}{2 b^{4}} - \frac{a x^{2}}{b^{3}} + \frac{x^{4}}{4 b^{2}}"," ",0,"a**3/(2*a*b**4 + 2*b**5*x**2) + 3*a**2*log(a + b*x**2)/(2*b**4) - a*x**2/b**3 + x**4/(4*b**2)","A",0
478,1,39,0,0.253038," ","integrate(x**5/(b**2*x**4+2*a*b*x**2+a**2),x)","- \frac{a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{a \log{\left(a + b x^{2} \right)}}{b^{3}} + \frac{x^{2}}{2 b^{2}}"," ",0,"-a**2/(2*a*b**3 + 2*b**4*x**2) - a*log(a + b*x**2)/b**3 + x**2/(2*b**2)","A",0
479,1,29,0,0.208864," ","integrate(x**3/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{\log{\left(a + b x^{2} \right)}}{2 b^{2}}"," ",0,"a/(2*a*b**2 + 2*b**3*x**2) + log(a + b*x**2)/(2*b**2)","A",0
480,1,15,0,0.165440," ","integrate(x/(b**2*x**4+2*a*b*x**2+a**2),x)","- \frac{1}{2 a b + 2 b^{2} x^{2}}"," ",0,"-1/(2*a*b + 2*b**2*x**2)","A",0
481,1,34,0,0.321561," ","integrate(1/x/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{1}{2 a^{2} + 2 a b x^{2}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"1/(2*a**2 + 2*a*b*x**2) + log(x)/a**2 - log(a/b + x**2)/(2*a**2)","A",0
482,1,51,0,0.394251," ","integrate(1/x**3/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{- a - 2 b x^{2}}{2 a^{3} x^{2} + 2 a^{2} b x^{4}} - \frac{2 b \log{\left(x \right)}}{a^{3}} + \frac{b \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{3}}"," ",0,"(-a - 2*b*x**2)/(2*a**3*x**2 + 2*a**2*b*x**4) - 2*b*log(x)/a**3 + b*log(a/b + x**2)/a**3","A",0
483,1,68,0,0.466554," ","integrate(1/x**5/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{- a^{2} + 3 a b x^{2} + 6 b^{2} x^{4}}{4 a^{4} x^{4} + 4 a^{3} b x^{6}} + \frac{3 b^{2} \log{\left(x \right)}}{a^{4}} - \frac{3 b^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(-a**2 + 3*a*b*x**2 + 6*b**2*x**4)/(4*a**4*x**4 + 4*a**3*b*x**6) + 3*b**2*log(x)/a**4 - 3*b**2*log(a/b + x**2)/(2*a**4)","A",0
484,1,134,0,0.347618," ","integrate(x**10/(b**2*x**4+2*a*b*x**2+a**2),x)","- \frac{a^{4} x}{2 a b^{5} + 2 b^{6} x^{2}} - \frac{4 a^{3} x}{b^{5}} + \frac{a^{2} x^{3}}{b^{4}} - \frac{2 a x^{5}}{5 b^{3}} - \frac{9 \sqrt{- \frac{a^{7}}{b^{11}}} \log{\left(x - \frac{b^{5} \sqrt{- \frac{a^{7}}{b^{11}}}}{a^{3}} \right)}}{4} + \frac{9 \sqrt{- \frac{a^{7}}{b^{11}}} \log{\left(x + \frac{b^{5} \sqrt{- \frac{a^{7}}{b^{11}}}}{a^{3}} \right)}}{4} + \frac{x^{7}}{7 b^{2}}"," ",0,"-a**4*x/(2*a*b**5 + 2*b**6*x**2) - 4*a**3*x/b**5 + a**2*x**3/b**4 - 2*a*x**5/(5*b**3) - 9*sqrt(-a**7/b**11)*log(x - b**5*sqrt(-a**7/b**11)/a**3)/4 + 9*sqrt(-a**7/b**11)*log(x + b**5*sqrt(-a**7/b**11)/a**3)/4 + x**7/(7*b**2)","A",0
485,1,124,0,0.323257," ","integrate(x**8/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a^{3} x}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{3 a^{2} x}{b^{4}} - \frac{2 a x^{3}}{3 b^{3}} + \frac{7 \sqrt{- \frac{a^{5}}{b^{9}}} \log{\left(x - \frac{b^{4} \sqrt{- \frac{a^{5}}{b^{9}}}}{a^{2}} \right)}}{4} - \frac{7 \sqrt{- \frac{a^{5}}{b^{9}}} \log{\left(x + \frac{b^{4} \sqrt{- \frac{a^{5}}{b^{9}}}}{a^{2}} \right)}}{4} + \frac{x^{5}}{5 b^{2}}"," ",0,"a**3*x/(2*a*b**4 + 2*b**5*x**2) + 3*a**2*x/b**4 - 2*a*x**3/(3*b**3) + 7*sqrt(-a**5/b**9)*log(x - b**4*sqrt(-a**5/b**9)/a**2)/4 - 7*sqrt(-a**5/b**9)*log(x + b**4*sqrt(-a**5/b**9)/a**2)/4 + x**5/(5*b**2)","A",0
486,1,107,0,0.302828," ","integrate(x**6/(b**2*x**4+2*a*b*x**2+a**2),x)","- \frac{a^{2} x}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a x}{b^{3}} - \frac{5 \sqrt{- \frac{a^{3}}{b^{7}}} \log{\left(x - \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}}}{a} \right)}}{4} + \frac{5 \sqrt{- \frac{a^{3}}{b^{7}}} \log{\left(x + \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}}}{a} \right)}}{4} + \frac{x^{3}}{3 b^{2}}"," ",0,"-a**2*x/(2*a*b**3 + 2*b**4*x**2) - 2*a*x/b**3 - 5*sqrt(-a**3/b**7)*log(x - b**3*sqrt(-a**3/b**7)/a)/4 + 5*sqrt(-a**3/b**7)*log(x + b**3*sqrt(-a**3/b**7)/a)/4 + x**3/(3*b**2)","A",0
487,1,83,0,0.273253," ","integrate(x**4/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{a x}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{3 \sqrt{- \frac{a}{b^{5}}} \log{\left(- b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{4} - \frac{3 \sqrt{- \frac{a}{b^{5}}} \log{\left(b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{4} + \frac{x}{b^{2}}"," ",0,"a*x/(2*a*b**2 + 2*b**3*x**2) + 3*sqrt(-a/b**5)*log(-b**2*sqrt(-a/b**5) + x)/4 - 3*sqrt(-a/b**5)*log(b**2*sqrt(-a/b**5) + x)/4 + x/b**2","A",0
488,1,78,0,0.221923," ","integrate(x**2/(b**2*x**4+2*a*b*x**2+a**2),x)","- \frac{x}{2 a b + 2 b^{2} x^{2}} - \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(- a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4}"," ",0,"-x/(2*a*b + 2*b**2*x**2) - sqrt(-1/(a*b**3))*log(-a*b*sqrt(-1/(a*b**3)) + x)/4 + sqrt(-1/(a*b**3))*log(a*b*sqrt(-1/(a*b**3)) + x)/4","B",0
489,1,78,0,0.220051," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{x}{2 a^{2} + 2 a b x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4}"," ",0,"x/(2*a**2 + 2*a*b*x**2) - sqrt(-1/(a**3*b))*log(-a**2*sqrt(-1/(a**3*b)) + x)/4 + sqrt(-1/(a**3*b))*log(a**2*sqrt(-1/(a**3*b)) + x)/4","B",0
490,1,92,0,0.319957," ","integrate(1/x**2/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x \right)}}{4} - \frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x \right)}}{4} + \frac{- 2 a - 3 b x^{2}}{2 a^{3} x + 2 a^{2} b x^{3}}"," ",0,"3*sqrt(-b/a**5)*log(-a**3*sqrt(-b/a**5)/b + x)/4 - 3*sqrt(-b/a**5)*log(a**3*sqrt(-b/a**5)/b + x)/4 + (-2*a - 3*b*x**2)/(2*a**3*x + 2*a**2*b*x**3)","A",0
491,1,114,0,0.358326," ","integrate(1/x**4/(b**2*x**4+2*a*b*x**2+a**2),x)","- \frac{5 \sqrt{- \frac{b^{3}}{a^{7}}} \log{\left(- \frac{a^{4} \sqrt{- \frac{b^{3}}{a^{7}}}}{b^{2}} + x \right)}}{4} + \frac{5 \sqrt{- \frac{b^{3}}{a^{7}}} \log{\left(\frac{a^{4} \sqrt{- \frac{b^{3}}{a^{7}}}}{b^{2}} + x \right)}}{4} + \frac{- 2 a^{2} + 10 a b x^{2} + 15 b^{2} x^{4}}{6 a^{4} x^{3} + 6 a^{3} b x^{5}}"," ",0,"-5*sqrt(-b**3/a**7)*log(-a**4*sqrt(-b**3/a**7)/b**2 + x)/4 + 5*sqrt(-b**3/a**7)*log(a**4*sqrt(-b**3/a**7)/b**2 + x)/4 + (-2*a**2 + 10*a*b*x**2 + 15*b**2*x**4)/(6*a**4*x**3 + 6*a**3*b*x**5)","A",0
492,1,126,0,0.428017," ","integrate(1/x**6/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{7 \sqrt{- \frac{b^{5}}{a^{9}}} \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{5}}{a^{9}}}}{b^{3}} + x \right)}}{4} - \frac{7 \sqrt{- \frac{b^{5}}{a^{9}}} \log{\left(\frac{a^{5} \sqrt{- \frac{b^{5}}{a^{9}}}}{b^{3}} + x \right)}}{4} + \frac{- 6 a^{3} + 14 a^{2} b x^{2} - 70 a b^{2} x^{4} - 105 b^{3} x^{6}}{30 a^{5} x^{5} + 30 a^{4} b x^{7}}"," ",0,"7*sqrt(-b**5/a**9)*log(-a**5*sqrt(-b**5/a**9)/b**3 + x)/4 - 7*sqrt(-b**5/a**9)*log(a**5*sqrt(-b**5/a**9)/b**3 + x)/4 + (-6*a**3 + 14*a**2*b*x**2 - 70*a*b**2*x**4 - 105*b**3*x**6)/(30*a**5*x**5 + 30*a**4*b*x**7)","A",0
493,1,100,0,0.627387," ","integrate(x**11/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{5 a^{2} \log{\left(a + b x^{2} \right)}}{b^{6}} - \frac{2 a x^{2}}{b^{5}} + \frac{47 a^{5} + 105 a^{4} b x^{2} + 60 a^{3} b^{2} x^{4}}{12 a^{3} b^{6} + 36 a^{2} b^{7} x^{2} + 36 a b^{8} x^{4} + 12 b^{9} x^{6}} + \frac{x^{4}}{4 b^{4}}"," ",0,"5*a**2*log(a + b*x**2)/b**6 - 2*a*x**2/b**5 + (47*a**5 + 105*a**4*b*x**2 + 60*a**3*b**2*x**4)/(12*a**3*b**6 + 36*a**2*b**7*x**2 + 36*a*b**8*x**4 + 12*b**9*x**6) + x**4/(4*b**4)","A",0
494,1,90,0,0.586369," ","integrate(x**9/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{2 a \log{\left(a + b x^{2} \right)}}{b^{5}} + \frac{- 13 a^{4} - 30 a^{3} b x^{2} - 18 a^{2} b^{2} x^{4}}{6 a^{3} b^{5} + 18 a^{2} b^{6} x^{2} + 18 a b^{7} x^{4} + 6 b^{8} x^{6}} + \frac{x^{2}}{2 b^{4}}"," ",0,"-2*a*log(a + b*x**2)/b**5 + (-13*a**4 - 30*a**3*b*x**2 - 18*a**2*b**2*x**4)/(6*a**3*b**5 + 18*a**2*b**6*x**2 + 18*a*b**7*x**4 + 6*b**8*x**6) + x**2/(2*b**4)","A",0
495,1,76,0,0.472473," ","integrate(x**7/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{11 a^{3} + 27 a^{2} b x^{2} + 18 a b^{2} x^{4}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{\log{\left(a + b x^{2} \right)}}{2 b^{4}}"," ",0,"(11*a**3 + 27*a**2*b*x**2 + 18*a*b**2*x**4)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + log(a + b*x**2)/(2*b**4)","A",0
496,1,60,0,0.397606," ","integrate(x**5/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{- a^{2} - 3 a b x^{2} - 3 b^{2} x^{4}}{6 a^{3} b^{3} + 18 a^{2} b^{4} x^{2} + 18 a b^{5} x^{4} + 6 b^{6} x^{6}}"," ",0,"(-a**2 - 3*a*b*x**2 - 3*b**2*x**4)/(6*a**3*b**3 + 18*a**2*b**4*x**2 + 18*a*b**5*x**4 + 6*b**6*x**6)","B",0
497,1,48,0,0.366361," ","integrate(x**3/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{- a - 3 b x^{2}}{12 a^{3} b^{2} + 36 a^{2} b^{3} x^{2} + 36 a b^{4} x^{4} + 12 b^{5} x^{6}}"," ",0,"(-a - 3*b*x**2)/(12*a**3*b**2 + 36*a**2*b**3*x**2 + 36*a*b**4*x**4 + 12*b**5*x**6)","A",0
498,1,39,0,0.332896," ","integrate(x/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{1}{6 a^{3} b + 18 a^{2} b^{2} x^{2} + 18 a b^{3} x^{4} + 6 b^{4} x^{6}}"," ",0,"-1/(6*a**3*b + 18*a**2*b**2*x**2 + 18*a*b**3*x**4 + 6*b**4*x**6)","B",0
499,1,80,0,0.556000," ","integrate(1/x/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{11 a^{2} + 15 a b x^{2} + 6 b^{2} x^{4}}{12 a^{6} + 36 a^{5} b x^{2} + 36 a^{4} b^{2} x^{4} + 12 a^{3} b^{3} x^{6}} + \frac{\log{\left(x \right)}}{a^{4}} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(11*a**2 + 15*a*b*x**2 + 6*b**2*x**4)/(12*a**6 + 36*a**5*b*x**2 + 36*a**4*b**2*x**4 + 12*a**3*b**3*x**6) + log(x)/a**4 - log(a/b + x**2)/(2*a**4)","A",0
500,1,102,0,0.672991," ","integrate(1/x**3/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{- 3 a^{3} - 22 a^{2} b x^{2} - 30 a b^{2} x^{4} - 12 b^{3} x^{6}}{6 a^{7} x^{2} + 18 a^{6} b x^{4} + 18 a^{5} b^{2} x^{6} + 6 a^{4} b^{3} x^{8}} - \frac{4 b \log{\left(x \right)}}{a^{5}} + \frac{2 b \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{5}}"," ",0,"(-3*a**3 - 22*a**2*b*x**2 - 30*a*b**2*x**4 - 12*b**3*x**6)/(6*a**7*x**2 + 18*a**6*b*x**4 + 18*a**5*b**2*x**6 + 6*a**4*b**3*x**8) - 4*b*log(x)/a**5 + 2*b*log(a/b + x**2)/a**5","A",0
501,1,116,0,0.718261," ","integrate(1/x**5/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{- 3 a^{4} + 15 a^{3} b x^{2} + 110 a^{2} b^{2} x^{4} + 150 a b^{3} x^{6} + 60 b^{4} x^{8}}{12 a^{8} x^{4} + 36 a^{7} b x^{6} + 36 a^{6} b^{2} x^{8} + 12 a^{5} b^{3} x^{10}} + \frac{10 b^{2} \log{\left(x \right)}}{a^{6}} - \frac{5 b^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{6}}"," ",0,"(-3*a**4 + 15*a**3*b*x**2 + 110*a**2*b**2*x**4 + 150*a*b**3*x**6 + 60*b**4*x**8)/(12*a**8*x**4 + 36*a**7*b*x**6 + 36*a**6*b**2*x**8 + 12*a**5*b**3*x**10) + 10*b**2*log(x)/a**6 - 5*b**2*log(a/b + x**2)/a**6","A",0
502,1,172,0,0.661381," ","integrate(x**12/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{10 a^{2} x}{b^{6}} - \frac{4 a x^{3}}{3 b^{5}} + \frac{231 \sqrt{- \frac{a^{5}}{b^{13}}} \log{\left(x - \frac{b^{6} \sqrt{- \frac{a^{5}}{b^{13}}}}{a^{2}} \right)}}{32} - \frac{231 \sqrt{- \frac{a^{5}}{b^{13}}} \log{\left(x + \frac{b^{6} \sqrt{- \frac{a^{5}}{b^{13}}}}{a^{2}} \right)}}{32} + \frac{213 a^{5} x + 472 a^{4} b x^{3} + 267 a^{3} b^{2} x^{5}}{48 a^{3} b^{6} + 144 a^{2} b^{7} x^{2} + 144 a b^{8} x^{4} + 48 b^{9} x^{6}} + \frac{x^{5}}{5 b^{4}}"," ",0,"10*a**2*x/b**6 - 4*a*x**3/(3*b**5) + 231*sqrt(-a**5/b**13)*log(x - b**6*sqrt(-a**5/b**13)/a**2)/32 - 231*sqrt(-a**5/b**13)*log(x + b**6*sqrt(-a**5/b**13)/a**2)/32 + (213*a**5*x + 472*a**4*b*x**3 + 267*a**3*b**2*x**5)/(48*a**3*b**6 + 144*a**2*b**7*x**2 + 144*a*b**8*x**4 + 48*b**9*x**6) + x**5/(5*b**4)","A",0
503,1,156,0,0.628099," ","integrate(x**10/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{4 a x}{b^{5}} - \frac{105 \sqrt{- \frac{a^{3}}{b^{11}}} \log{\left(x - \frac{b^{5} \sqrt{- \frac{a^{3}}{b^{11}}}}{a} \right)}}{32} + \frac{105 \sqrt{- \frac{a^{3}}{b^{11}}} \log{\left(x + \frac{b^{5} \sqrt{- \frac{a^{3}}{b^{11}}}}{a} \right)}}{32} + \frac{- 123 a^{4} x - 280 a^{3} b x^{3} - 165 a^{2} b^{2} x^{5}}{48 a^{3} b^{5} + 144 a^{2} b^{6} x^{2} + 144 a b^{7} x^{4} + 48 b^{8} x^{6}} + \frac{x^{3}}{3 b^{4}}"," ",0,"-4*a*x/b**5 - 105*sqrt(-a**3/b**11)*log(x - b**5*sqrt(-a**3/b**11)/a)/32 + 105*sqrt(-a**3/b**11)*log(x + b**5*sqrt(-a**3/b**11)/a)/32 + (-123*a**4*x - 280*a**3*b*x**3 - 165*a**2*b**2*x**5)/(48*a**3*b**5 + 144*a**2*b**6*x**2 + 144*a*b**7*x**4 + 48*b**8*x**6) + x**3/(3*b**4)","A",0
504,1,131,0,0.572060," ","integrate(x**8/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{35 \sqrt{- \frac{a}{b^{9}}} \log{\left(- b^{4} \sqrt{- \frac{a}{b^{9}}} + x \right)}}{32} - \frac{35 \sqrt{- \frac{a}{b^{9}}} \log{\left(b^{4} \sqrt{- \frac{a}{b^{9}}} + x \right)}}{32} + \frac{57 a^{3} x + 136 a^{2} b x^{3} + 87 a b^{2} x^{5}}{48 a^{3} b^{4} + 144 a^{2} b^{5} x^{2} + 144 a b^{6} x^{4} + 48 b^{7} x^{6}} + \frac{x}{b^{4}}"," ",0,"35*sqrt(-a/b**9)*log(-b**4*sqrt(-a/b**9) + x)/32 - 35*sqrt(-a/b**9)*log(b**4*sqrt(-a/b**9) + x)/32 + (57*a**3*x + 136*a**2*b*x**3 + 87*a*b**2*x**5)/(48*a**3*b**4 + 144*a**2*b**5*x**2 + 144*a*b**6*x**4 + 48*b**7*x**6) + x/b**4","A",0
505,1,134,0,0.487442," ","integrate(x**6/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{5 \sqrt{- \frac{1}{a b^{7}}} \log{\left(- a b^{3} \sqrt{- \frac{1}{a b^{7}}} + x \right)}}{32} + \frac{5 \sqrt{- \frac{1}{a b^{7}}} \log{\left(a b^{3} \sqrt{- \frac{1}{a b^{7}}} + x \right)}}{32} + \frac{- 15 a^{2} x - 40 a b x^{3} - 33 b^{2} x^{5}}{48 a^{3} b^{3} + 144 a^{2} b^{4} x^{2} + 144 a b^{5} x^{4} + 48 b^{6} x^{6}}"," ",0,"-5*sqrt(-1/(a*b**7))*log(-a*b**3*sqrt(-1/(a*b**7)) + x)/32 + 5*sqrt(-1/(a*b**7))*log(a*b**3*sqrt(-1/(a*b**7)) + x)/32 + (-15*a**2*x - 40*a*b*x**3 - 33*b**2*x**5)/(48*a**3*b**3 + 144*a**2*b**4*x**2 + 144*a*b**5*x**4 + 48*b**6*x**6)","A",0
506,1,143,0,0.452507," ","integrate(x**4/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \log{\left(- a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \log{\left(a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} + x \right)}}{32} + \frac{- 3 a^{2} x - 8 a b x^{3} + 3 b^{2} x^{5}}{48 a^{4} b^{2} + 144 a^{3} b^{3} x^{2} + 144 a^{2} b^{4} x^{4} + 48 a b^{5} x^{6}}"," ",0,"-sqrt(-1/(a**3*b**5))*log(-a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/32 + sqrt(-1/(a**3*b**5))*log(a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/32 + (-3*a**2*x - 8*a*b*x**3 + 3*b**2*x**5)/(48*a**4*b**2 + 144*a**3*b**3*x**2 + 144*a**2*b**4*x**4 + 48*a*b**5*x**6)","B",0
507,1,139,0,0.437318," ","integrate(x**2/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \log{\left(- a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \log{\left(a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{32} + \frac{- 3 a^{2} x + 8 a b x^{3} + 3 b^{2} x^{5}}{48 a^{5} b + 144 a^{4} b^{2} x^{2} + 144 a^{3} b^{3} x^{4} + 48 a^{2} b^{4} x^{6}}"," ",0,"-sqrt(-1/(a**5*b**3))*log(-a**3*b*sqrt(-1/(a**5*b**3)) + x)/32 + sqrt(-1/(a**5*b**3))*log(a**3*b*sqrt(-1/(a**5*b**3)) + x)/32 + (-3*a**2*x + 8*a*b*x**3 + 3*b**2*x**5)/(48*a**5*b + 144*a**4*b**2*x**2 + 144*a**3*b**3*x**4 + 48*a**2*b**4*x**6)","B",0
508,1,129,0,0.444782," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{5 \sqrt{- \frac{1}{a^{7} b}} \log{\left(- a^{4} \sqrt{- \frac{1}{a^{7} b}} + x \right)}}{32} + \frac{5 \sqrt{- \frac{1}{a^{7} b}} \log{\left(a^{4} \sqrt{- \frac{1}{a^{7} b}} + x \right)}}{32} + \frac{33 a^{2} x + 40 a b x^{3} + 15 b^{2} x^{5}}{48 a^{6} + 144 a^{5} b x^{2} + 144 a^{4} b^{2} x^{4} + 48 a^{3} b^{3} x^{6}}"," ",0,"-5*sqrt(-1/(a**7*b))*log(-a**4*sqrt(-1/(a**7*b)) + x)/32 + 5*sqrt(-1/(a**7*b))*log(a**4*sqrt(-1/(a**7*b)) + x)/32 + (33*a**2*x + 40*a*b*x**3 + 15*b**2*x**5)/(48*a**6 + 144*a**5*b*x**2 + 144*a**4*b**2*x**4 + 48*a**3*b**3*x**6)","A",0
509,1,139,0,0.583691," ","integrate(1/x**2/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{35 \sqrt{- \frac{b}{a^{9}}} \log{\left(- \frac{a^{5} \sqrt{- \frac{b}{a^{9}}}}{b} + x \right)}}{32} - \frac{35 \sqrt{- \frac{b}{a^{9}}} \log{\left(\frac{a^{5} \sqrt{- \frac{b}{a^{9}}}}{b} + x \right)}}{32} + \frac{- 48 a^{3} - 231 a^{2} b x^{2} - 280 a b^{2} x^{4} - 105 b^{3} x^{6}}{48 a^{7} x + 144 a^{6} b x^{3} + 144 a^{5} b^{2} x^{5} + 48 a^{4} b^{3} x^{7}}"," ",0,"35*sqrt(-b/a**9)*log(-a**5*sqrt(-b/a**9)/b + x)/32 - 35*sqrt(-b/a**9)*log(a**5*sqrt(-b/a**9)/b + x)/32 + (-48*a**3 - 231*a**2*b*x**2 - 280*a*b**2*x**4 - 105*b**3*x**6)/(48*a**7*x + 144*a**6*b*x**3 + 144*a**5*b**2*x**5 + 48*a**4*b**3*x**7)","A",0
510,1,162,0,0.632891," ","integrate(1/x**4/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","- \frac{105 \sqrt{- \frac{b^{3}}{a^{11}}} \log{\left(- \frac{a^{6} \sqrt{- \frac{b^{3}}{a^{11}}}}{b^{2}} + x \right)}}{32} + \frac{105 \sqrt{- \frac{b^{3}}{a^{11}}} \log{\left(\frac{a^{6} \sqrt{- \frac{b^{3}}{a^{11}}}}{b^{2}} + x \right)}}{32} + \frac{- 16 a^{4} + 144 a^{3} b x^{2} + 693 a^{2} b^{2} x^{4} + 840 a b^{3} x^{6} + 315 b^{4} x^{8}}{48 a^{8} x^{3} + 144 a^{7} b x^{5} + 144 a^{6} b^{2} x^{7} + 48 a^{5} b^{3} x^{9}}"," ",0,"-105*sqrt(-b**3/a**11)*log(-a**6*sqrt(-b**3/a**11)/b**2 + x)/32 + 105*sqrt(-b**3/a**11)*log(a**6*sqrt(-b**3/a**11)/b**2 + x)/32 + (-16*a**4 + 144*a**3*b*x**2 + 693*a**2*b**2*x**4 + 840*a*b**3*x**6 + 315*b**4*x**8)/(48*a**8*x**3 + 144*a**7*b*x**5 + 144*a**6*b**2*x**7 + 48*a**5*b**3*x**9)","A",0
511,1,173,0,0.710491," ","integrate(1/x**6/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{231 \sqrt{- \frac{b^{5}}{a^{13}}} \log{\left(- \frac{a^{7} \sqrt{- \frac{b^{5}}{a^{13}}}}{b^{3}} + x \right)}}{32} - \frac{231 \sqrt{- \frac{b^{5}}{a^{13}}} \log{\left(\frac{a^{7} \sqrt{- \frac{b^{5}}{a^{13}}}}{b^{3}} + x \right)}}{32} + \frac{- 48 a^{5} + 176 a^{4} b x^{2} - 1584 a^{3} b^{2} x^{4} - 7623 a^{2} b^{3} x^{6} - 9240 a b^{4} x^{8} - 3465 b^{5} x^{10}}{240 a^{9} x^{5} + 720 a^{8} b x^{7} + 720 a^{7} b^{2} x^{9} + 240 a^{6} b^{3} x^{11}}"," ",0,"231*sqrt(-b**5/a**13)*log(-a**7*sqrt(-b**5/a**13)/b**3 + x)/32 - 231*sqrt(-b**5/a**13)*log(a**7*sqrt(-b**5/a**13)/b**3 + x)/32 + (-48*a**5 + 176*a**4*b*x**2 - 1584*a**3*b**2*x**4 - 7623*a**2*b**3*x**6 - 9240*a*b**4*x**8 - 3465*b**5*x**10)/(240*a**9*x**5 + 720*a**8*b*x**7 + 720*a**7*b**2*x**9 + 240*a**6*b**3*x**11)","A",0
512,1,150,0,0.994530," ","integrate(x**15/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{21 a^{2} \log{\left(a + b x^{2} \right)}}{2 b^{8}} - \frac{3 a x^{2}}{b^{7}} + \frac{459 a^{7} + 1995 a^{6} b x^{2} + 3290 a^{5} b^{2} x^{4} + 2450 a^{4} b^{3} x^{6} + 700 a^{3} b^{4} x^{8}}{40 a^{5} b^{8} + 200 a^{4} b^{9} x^{2} + 400 a^{3} b^{10} x^{4} + 400 a^{2} b^{11} x^{6} + 200 a b^{12} x^{8} + 40 b^{13} x^{10}} + \frac{x^{4}}{4 b^{6}}"," ",0,"21*a**2*log(a + b*x**2)/(2*b**8) - 3*a*x**2/b**7 + (459*a**7 + 1995*a**6*b*x**2 + 3290*a**5*b**2*x**4 + 2450*a**4*b**3*x**6 + 700*a**3*b**4*x**8)/(40*a**5*b**8 + 200*a**4*b**9*x**2 + 400*a**3*b**10*x**4 + 400*a**2*b**11*x**6 + 200*a*b**12*x**8 + 40*b**13*x**10) + x**4/(4*b**6)","A",0
513,1,138,0,0.973505," ","integrate(x**13/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{3 a \log{\left(a + b x^{2} \right)}}{b^{7}} + \frac{- 87 a^{6} - 385 a^{5} b x^{2} - 650 a^{4} b^{2} x^{4} - 500 a^{3} b^{3} x^{6} - 150 a^{2} b^{4} x^{8}}{20 a^{5} b^{7} + 100 a^{4} b^{8} x^{2} + 200 a^{3} b^{9} x^{4} + 200 a^{2} b^{10} x^{6} + 100 a b^{11} x^{8} + 20 b^{12} x^{10}} + \frac{x^{2}}{2 b^{6}}"," ",0,"-3*a*log(a + b*x**2)/b**7 + (-87*a**6 - 385*a**5*b*x**2 - 650*a**4*b**2*x**4 - 500*a**3*b**3*x**6 - 150*a**2*b**4*x**8)/(20*a**5*b**7 + 100*a**4*b**8*x**2 + 200*a**3*b**9*x**4 + 200*a**2*b**10*x**6 + 100*a*b**11*x**8 + 20*b**12*x**10) + x**2/(2*b**6)","A",0
514,1,124,0,0.811775," ","integrate(x**11/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{137 a^{5} + 625 a^{4} b x^{2} + 1100 a^{3} b^{2} x^{4} + 900 a^{2} b^{3} x^{6} + 300 a b^{4} x^{8}}{120 a^{5} b^{6} + 600 a^{4} b^{7} x^{2} + 1200 a^{3} b^{8} x^{4} + 1200 a^{2} b^{9} x^{6} + 600 a b^{10} x^{8} + 120 b^{11} x^{10}} + \frac{\log{\left(a + b x^{2} \right)}}{2 b^{6}}"," ",0,"(137*a**5 + 625*a**4*b*x**2 + 1100*a**3*b**2*x**4 + 900*a**2*b**3*x**6 + 300*a*b**4*x**8)/(120*a**5*b**6 + 600*a**4*b**7*x**2 + 1200*a**3*b**8*x**4 + 1200*a**2*b**9*x**6 + 600*a*b**10*x**8 + 120*b**11*x**10) + log(a + b*x**2)/(2*b**6)","A",0
515,1,107,0,0.718348," ","integrate(x**9/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{- a^{4} - 5 a^{3} b x^{2} - 10 a^{2} b^{2} x^{4} - 10 a b^{3} x^{6} - 5 b^{4} x^{8}}{10 a^{5} b^{5} + 50 a^{4} b^{6} x^{2} + 100 a^{3} b^{7} x^{4} + 100 a^{2} b^{8} x^{6} + 50 a b^{9} x^{8} + 10 b^{10} x^{10}}"," ",0,"(-a**4 - 5*a**3*b*x**2 - 10*a**2*b**2*x**4 - 10*a*b**3*x**6 - 5*b**4*x**8)/(10*a**5*b**5 + 50*a**4*b**6*x**2 + 100*a**3*b**7*x**4 + 100*a**2*b**8*x**6 + 50*a*b**9*x**8 + 10*b**10*x**10)","B",0
516,1,95,0,0.667681," ","integrate(x**7/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{- a^{3} - 5 a^{2} b x^{2} - 10 a b^{2} x^{4} - 10 b^{3} x^{6}}{40 a^{5} b^{4} + 200 a^{4} b^{5} x^{2} + 400 a^{3} b^{6} x^{4} + 400 a^{2} b^{7} x^{6} + 200 a b^{8} x^{8} + 40 b^{9} x^{10}}"," ",0,"(-a**3 - 5*a**2*b*x**2 - 10*a*b**2*x**4 - 10*b**3*x**6)/(40*a**5*b**4 + 200*a**4*b**5*x**2 + 400*a**3*b**6*x**4 + 400*a**2*b**7*x**6 + 200*a*b**8*x**8 + 40*b**9*x**10)","B",0
517,1,83,0,0.618102," ","integrate(x**5/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{- a^{2} - 5 a b x^{2} - 10 b^{2} x^{4}}{60 a^{5} b^{3} + 300 a^{4} b^{4} x^{2} + 600 a^{3} b^{5} x^{4} + 600 a^{2} b^{6} x^{6} + 300 a b^{7} x^{8} + 60 b^{8} x^{10}}"," ",0,"(-a**2 - 5*a*b*x**2 - 10*b**2*x**4)/(60*a**5*b**3 + 300*a**4*b**4*x**2 + 600*a**3*b**5*x**4 + 600*a**2*b**6*x**6 + 300*a*b**7*x**8 + 60*b**8*x**10)","A",0
518,1,71,0,0.581647," ","integrate(x**3/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{- a - 5 b x^{2}}{40 a^{5} b^{2} + 200 a^{4} b^{3} x^{2} + 400 a^{3} b^{4} x^{4} + 400 a^{2} b^{5} x^{6} + 200 a b^{6} x^{8} + 40 b^{7} x^{10}}"," ",0,"(-a - 5*b*x**2)/(40*a**5*b**2 + 200*a**4*b**3*x**2 + 400*a**3*b**4*x**4 + 400*a**2*b**5*x**6 + 200*a*b**6*x**8 + 40*b**7*x**10)","B",0
519,1,63,0,0.499872," ","integrate(x/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{1}{10 a^{5} b + 50 a^{4} b^{2} x^{2} + 100 a^{3} b^{3} x^{4} + 100 a^{2} b^{4} x^{6} + 50 a b^{5} x^{8} + 10 b^{6} x^{10}}"," ",0,"-1/(10*a**5*b + 50*a**4*b**2*x**2 + 100*a**3*b**3*x**4 + 100*a**2*b**4*x**6 + 50*a*b**5*x**8 + 10*b**6*x**10)","B",0
520,1,128,0,0.813874," ","integrate(1/x/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{137 a^{4} + 385 a^{3} b x^{2} + 470 a^{2} b^{2} x^{4} + 270 a b^{3} x^{6} + 60 b^{4} x^{8}}{120 a^{10} + 600 a^{9} b x^{2} + 1200 a^{8} b^{2} x^{4} + 1200 a^{7} b^{3} x^{6} + 600 a^{6} b^{4} x^{8} + 120 a^{5} b^{5} x^{10}} + \frac{\log{\left(x \right)}}{a^{6}} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{6}}"," ",0,"(137*a**4 + 385*a**3*b*x**2 + 470*a**2*b**2*x**4 + 270*a*b**3*x**6 + 60*b**4*x**8)/(120*a**10 + 600*a**9*b*x**2 + 1200*a**8*b**2*x**4 + 1200*a**7*b**3*x**6 + 600*a**6*b**4*x**8 + 120*a**5*b**5*x**10) + log(x)/a**6 - log(a/b + x**2)/(2*a**6)","A",0
521,1,150,0,0.901338," ","integrate(1/x**3/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{- 10 a^{5} - 137 a^{4} b x^{2} - 385 a^{3} b^{2} x^{4} - 470 a^{2} b^{3} x^{6} - 270 a b^{4} x^{8} - 60 b^{5} x^{10}}{20 a^{11} x^{2} + 100 a^{10} b x^{4} + 200 a^{9} b^{2} x^{6} + 200 a^{8} b^{3} x^{8} + 100 a^{7} b^{4} x^{10} + 20 a^{6} b^{5} x^{12}} - \frac{6 b \log{\left(x \right)}}{a^{7}} + \frac{3 b \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{7}}"," ",0,"(-10*a**5 - 137*a**4*b*x**2 - 385*a**3*b**2*x**4 - 470*a**2*b**3*x**6 - 270*a*b**4*x**8 - 60*b**5*x**10)/(20*a**11*x**2 + 100*a**10*b*x**4 + 200*a**9*b**2*x**6 + 200*a**8*b**3*x**8 + 100*a**7*b**4*x**10 + 20*a**6*b**5*x**12) - 6*b*log(x)/a**7 + 3*b*log(a/b + x**2)/a**7","A",0
522,1,165,0,0.956083," ","integrate(1/x**5/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{- 10 a^{6} + 70 a^{5} b x^{2} + 959 a^{4} b^{2} x^{4} + 2695 a^{3} b^{3} x^{6} + 3290 a^{2} b^{4} x^{8} + 1890 a b^{5} x^{10} + 420 b^{6} x^{12}}{40 a^{12} x^{4} + 200 a^{11} b x^{6} + 400 a^{10} b^{2} x^{8} + 400 a^{9} b^{3} x^{10} + 200 a^{8} b^{4} x^{12} + 40 a^{7} b^{5} x^{14}} + \frac{21 b^{2} \log{\left(x \right)}}{a^{8}} - \frac{21 b^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{8}}"," ",0,"(-10*a**6 + 70*a**5*b*x**2 + 959*a**4*b**2*x**4 + 2695*a**3*b**3*x**6 + 3290*a**2*b**4*x**8 + 1890*a*b**5*x**10 + 420*b**6*x**12)/(40*a**12*x**4 + 200*a**11*b*x**6 + 400*a**10*b**2*x**8 + 400*a**9*b**3*x**10 + 200*a**8*b**4*x**12 + 40*a**7*b**5*x**14) + 21*b**2*log(x)/a**8 - 21*b**2*log(a/b + x**2)/(2*a**8)","A",0
523,1,218,0,1.085701," ","integrate(x**16/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{21 a^{2} x}{b^{8}} - \frac{2 a x^{3}}{b^{7}} + \frac{9009 \sqrt{- \frac{a^{5}}{b^{17}}} \log{\left(x - \frac{b^{8} \sqrt{- \frac{a^{5}}{b^{17}}}}{a^{2}} \right)}}{512} - \frac{9009 \sqrt{- \frac{a^{5}}{b^{17}}} \log{\left(x + \frac{b^{8} \sqrt{- \frac{a^{5}}{b^{17}}}}{a^{2}} \right)}}{512} + \frac{18165 a^{7} x + 78370 a^{6} b x^{3} + 128128 a^{5} b^{2} x^{5} + 94430 a^{4} b^{3} x^{7} + 26635 a^{3} b^{4} x^{9}}{1280 a^{5} b^{8} + 6400 a^{4} b^{9} x^{2} + 12800 a^{3} b^{10} x^{4} + 12800 a^{2} b^{11} x^{6} + 6400 a b^{12} x^{8} + 1280 b^{13} x^{10}} + \frac{x^{5}}{5 b^{6}}"," ",0,"21*a**2*x/b**8 - 2*a*x**3/b**7 + 9009*sqrt(-a**5/b**17)*log(x - b**8*sqrt(-a**5/b**17)/a**2)/512 - 9009*sqrt(-a**5/b**17)*log(x + b**8*sqrt(-a**5/b**17)/a**2)/512 + (18165*a**7*x + 78370*a**6*b*x**3 + 128128*a**5*b**2*x**5 + 94430*a**4*b**3*x**7 + 26635*a**3*b**4*x**9)/(1280*a**5*b**8 + 6400*a**4*b**9*x**2 + 12800*a**3*b**10*x**4 + 12800*a**2*b**11*x**6 + 6400*a*b**12*x**8 + 1280*b**13*x**10) + x**5/(5*b**6)","A",0
524,1,204,0,1.031700," ","integrate(x**14/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{6 a x}{b^{7}} - \frac{3003 \sqrt{- \frac{a^{3}}{b^{15}}} \log{\left(x - \frac{b^{7} \sqrt{- \frac{a^{3}}{b^{15}}}}{a} \right)}}{512} + \frac{3003 \sqrt{- \frac{a^{3}}{b^{15}}} \log{\left(x + \frac{b^{7} \sqrt{- \frac{a^{3}}{b^{15}}}}{a} \right)}}{512} + \frac{- 22005 a^{6} x - 96290 a^{5} b x^{3} - 160384 a^{4} b^{2} x^{5} - 121310 a^{3} b^{3} x^{7} - 35595 a^{2} b^{4} x^{9}}{3840 a^{5} b^{7} + 19200 a^{4} b^{8} x^{2} + 38400 a^{3} b^{9} x^{4} + 38400 a^{2} b^{10} x^{6} + 19200 a b^{11} x^{8} + 3840 b^{12} x^{10}} + \frac{x^{3}}{3 b^{6}}"," ",0,"-6*a*x/b**7 - 3003*sqrt(-a**3/b**15)*log(x - b**7*sqrt(-a**3/b**15)/a)/512 + 3003*sqrt(-a**3/b**15)*log(x + b**7*sqrt(-a**3/b**15)/a)/512 + (-22005*a**6*x - 96290*a**5*b*x**3 - 160384*a**4*b**2*x**5 - 121310*a**3*b**3*x**7 - 35595*a**2*b**4*x**9)/(3840*a**5*b**7 + 19200*a**4*b**8*x**2 + 38400*a**3*b**9*x**4 + 38400*a**2*b**10*x**6 + 19200*a*b**11*x**8 + 3840*b**12*x**10) + x**3/(3*b**6)","A",0
525,1,178,0,0.947073," ","integrate(x**12/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{693 \sqrt{- \frac{a}{b^{13}}} \log{\left(- b^{6} \sqrt{- \frac{a}{b^{13}}} + x \right)}}{512} - \frac{693 \sqrt{- \frac{a}{b^{13}}} \log{\left(b^{6} \sqrt{- \frac{a}{b^{13}}} + x \right)}}{512} + \frac{2185 a^{5} x + 9770 a^{4} b x^{3} + 16768 a^{3} b^{2} x^{5} + 13270 a^{2} b^{3} x^{7} + 4215 a b^{4} x^{9}}{1280 a^{5} b^{6} + 6400 a^{4} b^{7} x^{2} + 12800 a^{3} b^{8} x^{4} + 12800 a^{2} b^{9} x^{6} + 6400 a b^{10} x^{8} + 1280 b^{11} x^{10}} + \frac{x}{b^{6}}"," ",0,"693*sqrt(-a/b**13)*log(-b**6*sqrt(-a/b**13) + x)/512 - 693*sqrt(-a/b**13)*log(b**6*sqrt(-a/b**13) + x)/512 + (2185*a**5*x + 9770*a**4*b*x**3 + 16768*a**3*b**2*x**5 + 13270*a**2*b**3*x**7 + 4215*a*b**4*x**9)/(1280*a**5*b**6 + 6400*a**4*b**7*x**2 + 12800*a**3*b**8*x**4 + 12800*a**2*b**9*x**6 + 6400*a*b**10*x**8 + 1280*b**11*x**10) + x/b**6","A",0
526,1,182,0,0.788820," ","integrate(x**10/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{63 \sqrt{- \frac{1}{a b^{11}}} \log{\left(- a b^{5} \sqrt{- \frac{1}{a b^{11}}} + x \right)}}{512} + \frac{63 \sqrt{- \frac{1}{a b^{11}}} \log{\left(a b^{5} \sqrt{- \frac{1}{a b^{11}}} + x \right)}}{512} + \frac{- 315 a^{4} x - 1470 a^{3} b x^{3} - 2688 a^{2} b^{2} x^{5} - 2370 a b^{3} x^{7} - 965 b^{4} x^{9}}{1280 a^{5} b^{5} + 6400 a^{4} b^{6} x^{2} + 12800 a^{3} b^{7} x^{4} + 12800 a^{2} b^{8} x^{6} + 6400 a b^{9} x^{8} + 1280 b^{10} x^{10}}"," ",0,"-63*sqrt(-1/(a*b**11))*log(-a*b**5*sqrt(-1/(a*b**11)) + x)/512 + 63*sqrt(-1/(a*b**11))*log(a*b**5*sqrt(-1/(a*b**11)) + x)/512 + (-315*a**4*x - 1470*a**3*b*x**3 - 2688*a**2*b**2*x**5 - 2370*a*b**3*x**7 - 965*b**4*x**9)/(1280*a**5*b**5 + 6400*a**4*b**6*x**2 + 12800*a**3*b**7*x**4 + 12800*a**2*b**8*x**6 + 6400*a*b**9*x**8 + 1280*b**10*x**10)","A",0
527,1,194,0,0.757399," ","integrate(x**8/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{7 \sqrt{- \frac{1}{a^{3} b^{9}}} \log{\left(- a^{2} b^{4} \sqrt{- \frac{1}{a^{3} b^{9}}} + x \right)}}{512} + \frac{7 \sqrt{- \frac{1}{a^{3} b^{9}}} \log{\left(a^{2} b^{4} \sqrt{- \frac{1}{a^{3} b^{9}}} + x \right)}}{512} + \frac{- 105 a^{4} x - 490 a^{3} b x^{3} - 896 a^{2} b^{2} x^{5} - 790 a b^{3} x^{7} + 105 b^{4} x^{9}}{3840 a^{6} b^{4} + 19200 a^{5} b^{5} x^{2} + 38400 a^{4} b^{6} x^{4} + 38400 a^{3} b^{7} x^{6} + 19200 a^{2} b^{8} x^{8} + 3840 a b^{9} x^{10}}"," ",0,"-7*sqrt(-1/(a**3*b**9))*log(-a**2*b**4*sqrt(-1/(a**3*b**9)) + x)/512 + 7*sqrt(-1/(a**3*b**9))*log(a**2*b**4*sqrt(-1/(a**3*b**9)) + x)/512 + (-105*a**4*x - 490*a**3*b*x**3 - 896*a**2*b**2*x**5 - 790*a*b**3*x**7 + 105*b**4*x**9)/(3840*a**6*b**4 + 19200*a**5*b**5*x**2 + 38400*a**4*b**6*x**4 + 38400*a**3*b**7*x**6 + 19200*a**2*b**8*x**8 + 3840*a*b**9*x**10)","A",0
528,1,196,0,0.701987," ","integrate(x**6/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{3 \sqrt{- \frac{1}{a^{5} b^{7}}} \log{\left(- a^{3} b^{3} \sqrt{- \frac{1}{a^{5} b^{7}}} + x \right)}}{512} + \frac{3 \sqrt{- \frac{1}{a^{5} b^{7}}} \log{\left(a^{3} b^{3} \sqrt{- \frac{1}{a^{5} b^{7}}} + x \right)}}{512} + \frac{- 15 a^{4} x - 70 a^{3} b x^{3} - 128 a^{2} b^{2} x^{5} + 70 a b^{3} x^{7} + 15 b^{4} x^{9}}{1280 a^{7} b^{3} + 6400 a^{6} b^{4} x^{2} + 12800 a^{5} b^{5} x^{4} + 12800 a^{4} b^{6} x^{6} + 6400 a^{3} b^{7} x^{8} + 1280 a^{2} b^{8} x^{10}}"," ",0,"-3*sqrt(-1/(a**5*b**7))*log(-a**3*b**3*sqrt(-1/(a**5*b**7)) + x)/512 + 3*sqrt(-1/(a**5*b**7))*log(a**3*b**3*sqrt(-1/(a**5*b**7)) + x)/512 + (-15*a**4*x - 70*a**3*b*x**3 - 128*a**2*b**2*x**5 + 70*a*b**3*x**7 + 15*b**4*x**9)/(1280*a**7*b**3 + 6400*a**6*b**4*x**2 + 12800*a**5*b**5*x**4 + 12800*a**4*b**6*x**6 + 6400*a**3*b**7*x**8 + 1280*a**2*b**8*x**10)","A",0
529,1,196,0,0.636112," ","integrate(x**4/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{3 \sqrt{- \frac{1}{a^{7} b^{5}}} \log{\left(- a^{4} b^{2} \sqrt{- \frac{1}{a^{7} b^{5}}} + x \right)}}{512} + \frac{3 \sqrt{- \frac{1}{a^{7} b^{5}}} \log{\left(a^{4} b^{2} \sqrt{- \frac{1}{a^{7} b^{5}}} + x \right)}}{512} + \frac{- 15 a^{4} x - 70 a^{3} b x^{3} + 128 a^{2} b^{2} x^{5} + 70 a b^{3} x^{7} + 15 b^{4} x^{9}}{1280 a^{8} b^{2} + 6400 a^{7} b^{3} x^{2} + 12800 a^{6} b^{4} x^{4} + 12800 a^{5} b^{5} x^{6} + 6400 a^{4} b^{6} x^{8} + 1280 a^{3} b^{7} x^{10}}"," ",0,"-3*sqrt(-1/(a**7*b**5))*log(-a**4*b**2*sqrt(-1/(a**7*b**5)) + x)/512 + 3*sqrt(-1/(a**7*b**5))*log(a**4*b**2*sqrt(-1/(a**7*b**5)) + x)/512 + (-15*a**4*x - 70*a**3*b*x**3 + 128*a**2*b**2*x**5 + 70*a*b**3*x**7 + 15*b**4*x**9)/(1280*a**8*b**2 + 6400*a**7*b**3*x**2 + 12800*a**6*b**4*x**4 + 12800*a**5*b**5*x**6 + 6400*a**4*b**6*x**8 + 1280*a**3*b**7*x**10)","A",0
530,1,190,0,0.624354," ","integrate(x**2/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{7 \sqrt{- \frac{1}{a^{9} b^{3}}} \log{\left(- a^{5} b \sqrt{- \frac{1}{a^{9} b^{3}}} + x \right)}}{512} + \frac{7 \sqrt{- \frac{1}{a^{9} b^{3}}} \log{\left(a^{5} b \sqrt{- \frac{1}{a^{9} b^{3}}} + x \right)}}{512} + \frac{- 105 a^{4} x + 790 a^{3} b x^{3} + 896 a^{2} b^{2} x^{5} + 490 a b^{3} x^{7} + 105 b^{4} x^{9}}{3840 a^{9} b + 19200 a^{8} b^{2} x^{2} + 38400 a^{7} b^{3} x^{4} + 38400 a^{6} b^{4} x^{6} + 19200 a^{5} b^{5} x^{8} + 3840 a^{4} b^{6} x^{10}}"," ",0,"-7*sqrt(-1/(a**9*b**3))*log(-a**5*b*sqrt(-1/(a**9*b**3)) + x)/512 + 7*sqrt(-1/(a**9*b**3))*log(a**5*b*sqrt(-1/(a**9*b**3)) + x)/512 + (-105*a**4*x + 790*a**3*b*x**3 + 896*a**2*b**2*x**5 + 490*a*b**3*x**7 + 105*b**4*x**9)/(3840*a**9*b + 19200*a**8*b**2*x**2 + 38400*a**7*b**3*x**4 + 38400*a**6*b**4*x**6 + 19200*a**5*b**5*x**8 + 3840*a**4*b**6*x**10)","A",0
531,1,177,0,0.676037," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{63 \sqrt{- \frac{1}{a^{11} b}} \log{\left(- a^{6} \sqrt{- \frac{1}{a^{11} b}} + x \right)}}{512} + \frac{63 \sqrt{- \frac{1}{a^{11} b}} \log{\left(a^{6} \sqrt{- \frac{1}{a^{11} b}} + x \right)}}{512} + \frac{965 a^{4} x + 2370 a^{3} b x^{3} + 2688 a^{2} b^{2} x^{5} + 1470 a b^{3} x^{7} + 315 b^{4} x^{9}}{1280 a^{10} + 6400 a^{9} b x^{2} + 12800 a^{8} b^{2} x^{4} + 12800 a^{7} b^{3} x^{6} + 6400 a^{6} b^{4} x^{8} + 1280 a^{5} b^{5} x^{10}}"," ",0,"-63*sqrt(-1/(a**11*b))*log(-a**6*sqrt(-1/(a**11*b)) + x)/512 + 63*sqrt(-1/(a**11*b))*log(a**6*sqrt(-1/(a**11*b)) + x)/512 + (965*a**4*x + 2370*a**3*b*x**3 + 2688*a**2*b**2*x**5 + 1470*a*b**3*x**7 + 315*b**4*x**9)/(1280*a**10 + 6400*a**9*b*x**2 + 12800*a**8*b**2*x**4 + 12800*a**7*b**3*x**6 + 6400*a**6*b**4*x**8 + 1280*a**5*b**5*x**10)","A",0
532,1,187,0,0.827696," ","integrate(1/x**2/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{693 \sqrt{- \frac{b}{a^{13}}} \log{\left(- \frac{a^{7} \sqrt{- \frac{b}{a^{13}}}}{b} + x \right)}}{512} - \frac{693 \sqrt{- \frac{b}{a^{13}}} \log{\left(\frac{a^{7} \sqrt{- \frac{b}{a^{13}}}}{b} + x \right)}}{512} + \frac{- 1280 a^{5} - 10615 a^{4} b x^{2} - 26070 a^{3} b^{2} x^{4} - 29568 a^{2} b^{3} x^{6} - 16170 a b^{4} x^{8} - 3465 b^{5} x^{10}}{1280 a^{11} x + 6400 a^{10} b x^{3} + 12800 a^{9} b^{2} x^{5} + 12800 a^{8} b^{3} x^{7} + 6400 a^{7} b^{4} x^{9} + 1280 a^{6} b^{5} x^{11}}"," ",0,"693*sqrt(-b/a**13)*log(-a**7*sqrt(-b/a**13)/b + x)/512 - 693*sqrt(-b/a**13)*log(a**7*sqrt(-b/a**13)/b + x)/512 + (-1280*a**5 - 10615*a**4*b*x**2 - 26070*a**3*b**2*x**4 - 29568*a**2*b**3*x**6 - 16170*a*b**4*x**8 - 3465*b**5*x**10)/(1280*a**11*x + 6400*a**10*b*x**3 + 12800*a**9*b**2*x**5 + 12800*a**8*b**3*x**7 + 6400*a**7*b**4*x**9 + 1280*a**6*b**5*x**11)","A",0
533,1,209,0,0.888216," ","integrate(1/x**4/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","- \frac{3003 \sqrt{- \frac{b^{3}}{a^{15}}} \log{\left(- \frac{a^{8} \sqrt{- \frac{b^{3}}{a^{15}}}}{b^{2}} + x \right)}}{512} + \frac{3003 \sqrt{- \frac{b^{3}}{a^{15}}} \log{\left(\frac{a^{8} \sqrt{- \frac{b^{3}}{a^{15}}}}{b^{2}} + x \right)}}{512} + \frac{- 1280 a^{6} + 16640 a^{5} b x^{2} + 137995 a^{4} b^{2} x^{4} + 338910 a^{3} b^{3} x^{6} + 384384 a^{2} b^{4} x^{8} + 210210 a b^{5} x^{10} + 45045 b^{6} x^{12}}{3840 a^{12} x^{3} + 19200 a^{11} b x^{5} + 38400 a^{10} b^{2} x^{7} + 38400 a^{9} b^{3} x^{9} + 19200 a^{8} b^{4} x^{11} + 3840 a^{7} b^{5} x^{13}}"," ",0,"-3003*sqrt(-b**3/a**15)*log(-a**8*sqrt(-b**3/a**15)/b**2 + x)/512 + 3003*sqrt(-b**3/a**15)*log(a**8*sqrt(-b**3/a**15)/b**2 + x)/512 + (-1280*a**6 + 16640*a**5*b*x**2 + 137995*a**4*b**2*x**4 + 338910*a**3*b**3*x**6 + 384384*a**2*b**4*x**8 + 210210*a*b**5*x**10 + 45045*b**6*x**12)/(3840*a**12*x**3 + 19200*a**11*b*x**5 + 38400*a**10*b**2*x**7 + 38400*a**9*b**3*x**9 + 19200*a**8*b**4*x**11 + 3840*a**7*b**5*x**13)","A",0
534,1,221,0,0.948706," ","integrate(1/x**6/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{9009 \sqrt{- \frac{b^{5}}{a^{17}}} \log{\left(- \frac{a^{9} \sqrt{- \frac{b^{5}}{a^{17}}}}{b^{3}} + x \right)}}{512} - \frac{9009 \sqrt{- \frac{b^{5}}{a^{17}}} \log{\left(\frac{a^{9} \sqrt{- \frac{b^{5}}{a^{17}}}}{b^{3}} + x \right)}}{512} + \frac{- 256 a^{7} + 1280 a^{6} b x^{2} - 16640 a^{5} b^{2} x^{4} - 137995 a^{4} b^{3} x^{6} - 338910 a^{3} b^{4} x^{8} - 384384 a^{2} b^{5} x^{10} - 210210 a b^{6} x^{12} - 45045 b^{7} x^{14}}{1280 a^{13} x^{5} + 6400 a^{12} b x^{7} + 12800 a^{11} b^{2} x^{9} + 12800 a^{10} b^{3} x^{11} + 6400 a^{9} b^{4} x^{13} + 1280 a^{8} b^{5} x^{15}}"," ",0,"9009*sqrt(-b**5/a**17)*log(-a**9*sqrt(-b**5/a**17)/b**3 + x)/512 - 9009*sqrt(-b**5/a**17)*log(a**9*sqrt(-b**5/a**17)/b**3 + x)/512 + (-256*a**7 + 1280*a**6*b*x**2 - 16640*a**5*b**2*x**4 - 137995*a**4*b**3*x**6 - 338910*a**3*b**4*x**8 - 384384*a**2*b**5*x**10 - 210210*a*b**6*x**12 - 45045*b**7*x**14)/(1280*a**13*x**5 + 6400*a**12*b*x**7 + 12800*a**11*b**2*x**9 + 12800*a**10*b**3*x**11 + 6400*a**9*b**4*x**13 + 1280*a**8*b**5*x**15)","A",0
535,1,12,0,0.109696," ","integrate(1/(x**4+2*x**2+1),x)","\frac{x}{2 x^{2} + 2} + \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"x/(2*x**2 + 2) + atan(x)/2","A",0
536,1,8,0,0.085829," ","integrate(x/(x**4+2*x**2+1),x)","- \frac{1}{2 x^{2} + 2}"," ",0,"-1/(2*x**2 + 2)","A",0
537,1,12,0,0.105222," ","integrate(x**2/(x**4+2*x**2+1),x)","- \frac{x}{2 x^{2} + 2} + \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"-x/(2*x**2 + 2) + atan(x)/2","A",0
538,1,15,0,0.094100," ","integrate(x**3/(x**4+2*x**2+1),x)","\frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{1}{2 x^{2} + 2}"," ",0,"log(x**2 + 1)/2 + 1/(2*x**2 + 2)","A",0
539,1,8,0,0.088064," ","integrate(x/(x**4-18*x**2+81),x)","- \frac{1}{2 x^{2} - 18}"," ",0,"-1/(2*x**2 - 18)","A",0
540,1,14,0,0.099099," ","integrate(x**3/(x**4-8*x**2+16),x)","\frac{\log{\left(x^{2} - 4 \right)}}{2} - \frac{2}{x^{2} - 4}"," ",0,"log(x**2 - 4)/2 - 2/(x**2 - 4)","A",0
541,1,12,0,0.104564," ","integrate(x**5*((b*x**2+a)**2)**(1/2),x)","\frac{a x^{6}}{6} + \frac{b x^{8}}{8}"," ",0,"a*x**6/6 + b*x**8/8","A",0
542,1,12,0,0.103486," ","integrate(x**3*((b*x**2+a)**2)**(1/2),x)","\frac{a x^{4}}{4} + \frac{b x^{6}}{6}"," ",0,"a*x**4/4 + b*x**6/6","A",0
543,1,12,0,0.098281," ","integrate(x*((b*x**2+a)**2)**(1/2),x)","\frac{a x^{2}}{2} + \frac{b x^{4}}{4}"," ",0,"a*x**2/2 + b*x**4/4","A",0
544,1,10,0,0.123372," ","integrate(((b*x**2+a)**2)**(1/2)/x,x)","a \log{\left(x \right)} + \frac{b x^{2}}{2}"," ",0,"a*log(x) + b*x**2/2","A",0
545,1,10,0,0.150372," ","integrate(((b*x**2+a)**2)**(1/2)/x**3,x)","- \frac{a}{2 x^{2}} + b \log{\left(x \right)}"," ",0,"-a/(2*x**2) + b*log(x)","A",0
546,1,14,0,0.168136," ","integrate(((b*x**2+a)**2)**(1/2)/x**5,x)","\frac{- a - 2 b x^{2}}{4 x^{4}}"," ",0,"(-a - 2*b*x**2)/(4*x**4)","A",0
547,1,15,0,0.189591," ","integrate(((b*x**2+a)**2)**(1/2)/x**7,x)","\frac{- 2 a - 3 b x^{2}}{12 x^{6}}"," ",0,"(-2*a - 3*b*x**2)/(12*x**6)","A",0
548,1,15,0,0.203261," ","integrate(((b*x**2+a)**2)**(1/2)/x**9,x)","\frac{- 3 a - 4 b x^{2}}{24 x^{8}}"," ",0,"(-3*a - 4*b*x**2)/(24*x**8)","A",0
549,1,15,0,0.215533," ","integrate(((b*x**2+a)**2)**(1/2)/x**11,x)","\frac{- 4 a - 5 b x^{2}}{40 x^{10}}"," ",0,"(-4*a - 5*b*x**2)/(40*x**10)","A",0
550,1,12,0,0.099822," ","integrate(x**4*((b*x**2+a)**2)**(1/2),x)","\frac{a x^{5}}{5} + \frac{b x^{7}}{7}"," ",0,"a*x**5/5 + b*x**7/7","A",0
551,1,12,0,0.147792," ","integrate(x**2*((b*x**2+a)**2)**(1/2),x)","\frac{a x^{3}}{3} + \frac{b x^{5}}{5}"," ",0,"a*x**3/3 + b*x**5/5","A",0
552,1,8,0,0.098966," ","integrate(((b*x**2+a)**2)**(1/2),x)","a x + \frac{b x^{3}}{3}"," ",0,"a*x + b*x**3/3","A",0
553,1,5,0,0.125200," ","integrate(((b*x**2+a)**2)**(1/2)/x**2,x)","- \frac{a}{x} + b x"," ",0,"-a/x + b*x","A",0
554,1,14,0,0.161982," ","integrate(((b*x**2+a)**2)**(1/2)/x**4,x)","\frac{- a - 3 b x^{2}}{3 x^{3}}"," ",0,"(-a - 3*b*x**2)/(3*x**3)","A",0
555,1,15,0,0.180777," ","integrate(((b*x**2+a)**2)**(1/2)/x**6,x)","\frac{- 3 a - 5 b x^{2}}{15 x^{5}}"," ",0,"(-3*a - 5*b*x**2)/(15*x**5)","A",0
556,1,15,0,0.197277," ","integrate(((b*x**2+a)**2)**(1/2)/x**8,x)","\frac{- 5 a - 7 b x^{2}}{35 x^{7}}"," ",0,"(-5*a - 7*b*x**2)/(35*x**7)","A",0
557,1,15,0,0.215411," ","integrate(((b*x**2+a)**2)**(1/2)/x**10,x)","\frac{- 7 a - 9 b x^{2}}{63 x^{9}}"," ",0,"(-7*a - 9*b*x**2)/(63*x**9)","A",0
558,0,0,0,0.000000," ","integrate(x**9*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{9} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**9*((a + b*x**2)**2)**(3/2), x)","F",0
559,0,0,0,0.000000," ","integrate(x**7*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{7} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**7*((a + b*x**2)**2)**(3/2), x)","F",0
560,0,0,0,0.000000," ","integrate(x**5*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{5} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**5*((a + b*x**2)**2)**(3/2), x)","F",0
561,0,0,0,0.000000," ","integrate(x**3*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{3} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*((a + b*x**2)**2)**(3/2), x)","F",0
562,0,0,0,0.000000," ","integrate(x*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*((a + b*x**2)**2)**(3/2), x)","F",0
563,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x, x)","F",0
564,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**3,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**3, x)","F",0
565,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**5,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**5, x)","F",0
566,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**7,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**7, x)","F",0
567,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**9,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{9}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**9, x)","F",0
568,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**11,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{11}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**11, x)","F",0
569,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**13,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{13}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**13, x)","F",0
570,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**15,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{15}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**15, x)","F",0
571,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**17,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{17}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**17, x)","F",0
572,0,0,0,0.000000," ","integrate(x**8*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{8} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**8*((a + b*x**2)**2)**(3/2), x)","F",0
573,0,0,0,0.000000," ","integrate(x**6*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{6} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**6*((a + b*x**2)**2)**(3/2), x)","F",0
574,0,0,0,0.000000," ","integrate(x**4*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{4} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*((a + b*x**2)**2)**(3/2), x)","F",0
575,0,0,0,0.000000," ","integrate(x**2*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int x^{2} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*((a + b*x**2)**2)**(3/2), x)","F",0
576,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(3/2), x)","F",0
577,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**2,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**2, x)","F",0
578,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**4,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**4, x)","F",0
579,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**6,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**6, x)","F",0
580,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**8,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**8, x)","F",0
581,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**10,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{10}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**10, x)","F",0
582,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**12,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{12}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**12, x)","F",0
583,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**14,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{14}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**14, x)","F",0
584,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/x**16,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{x^{16}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/x**16, x)","F",0
585,0,0,0,0.000000," ","integrate(x**13*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{13} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**13*((a + b*x**2)**2)**(5/2), x)","F",0
586,0,0,0,0.000000," ","integrate(x**11*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{11} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**11*((a + b*x**2)**2)**(5/2), x)","F",0
587,0,0,0,0.000000," ","integrate(x**9*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{9} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**9*((a + b*x**2)**2)**(5/2), x)","F",0
588,0,0,0,0.000000," ","integrate(x**7*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{7} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**7*((a + b*x**2)**2)**(5/2), x)","F",0
589,0,0,0,0.000000," ","integrate(x**5*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{5} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**5*((a + b*x**2)**2)**(5/2), x)","F",0
590,0,0,0,0.000000," ","integrate(x**3*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{3} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**3*((a + b*x**2)**2)**(5/2), x)","F",0
591,0,0,0,0.000000," ","integrate(x*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*((a + b*x**2)**2)**(5/2), x)","F",0
592,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x, x)","F",0
593,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**3,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**3, x)","F",0
594,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**5,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**5, x)","F",0
595,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**7,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**7, x)","F",0
596,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**9,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{9}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**9, x)","F",0
597,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**11,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{11}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**11, x)","F",0
598,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**13,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{13}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**13, x)","F",0
599,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**15,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{15}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**15, x)","F",0
600,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**17,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{17}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**17, x)","F",0
601,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**19,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{19}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**19, x)","F",0
602,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**21,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{21}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**21, x)","F",0
603,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**23,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{23}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**23, x)","F",0
604,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**25,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{25}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**25, x)","F",0
605,0,0,0,0.000000," ","integrate(x**12*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{12} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**12*((a + b*x**2)**2)**(5/2), x)","F",0
606,0,0,0,0.000000," ","integrate(x**10*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{10} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**10*((a + b*x**2)**2)**(5/2), x)","F",0
607,0,0,0,0.000000," ","integrate(x**8*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{8} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**8*((a + b*x**2)**2)**(5/2), x)","F",0
608,0,0,0,0.000000," ","integrate(x**6*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{6} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**6*((a + b*x**2)**2)**(5/2), x)","F",0
609,0,0,0,0.000000," ","integrate(x**4*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{4} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**4*((a + b*x**2)**2)**(5/2), x)","F",0
610,0,0,0,0.000000," ","integrate(x**2*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int x^{2} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**2*((a + b*x**2)**2)**(5/2), x)","F",0
611,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(5/2), x)","F",0
612,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**2,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**2, x)","F",0
613,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**4,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**4, x)","F",0
614,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**6,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**6, x)","F",0
615,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**8,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{8}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**8, x)","F",0
616,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**10,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{10}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**10, x)","F",0
617,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**12,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{12}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**12, x)","F",0
618,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**14,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{14}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**14, x)","F",0
619,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**16,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{16}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**16, x)","F",0
620,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**18,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{18}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**18, x)","F",0
621,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**20,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{20}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**20, x)","F",0
622,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**22,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{22}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**22, x)","F",0
623,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/x**24,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{x^{24}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/x**24, x)","F",0
624,1,32,0,0.196315," ","integrate(x**5/((b*x**2+a)**2)**(1/2),x)","\frac{a^{2} \log{\left(a + b x^{2} \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b}"," ",0,"a**2*log(a + b*x**2)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b)","A",0
625,1,20,0,0.182902," ","integrate(x**3/((b*x**2+a)**2)**(1/2),x)","- \frac{a \log{\left(a + b x^{2} \right)}}{2 b^{2}} + \frac{x^{2}}{2 b}"," ",0,"-a*log(a + b*x**2)/(2*b**2) + x**2/(2*b)","A",0
626,1,10,0,0.153956," ","integrate(x/((b*x**2+a)**2)**(1/2),x)","\frac{\log{\left(a + b x^{2} \right)}}{2 b}"," ",0,"log(a + b*x**2)/(2*b)","A",0
627,1,15,0,0.262463," ","integrate(1/x/((b*x**2+a)**2)**(1/2),x)","\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a}"," ",0,"log(x)/a - log(a/b + x**2)/(2*a)","A",0
628,1,31,0,0.318053," ","integrate(1/x**3/((b*x**2+a)**2)**(1/2),x)","- \frac{1}{2 a x^{2}} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"-1/(2*a*x**2) - b*log(x)/a**2 + b*log(a/b + x**2)/(2*a**2)","A",0
629,1,80,0,0.214017," ","integrate(x**4/((b*x**2+a)**2)**(1/2),x)","- \frac{a x}{b^{2}} - \frac{\sqrt{- \frac{a^{3}}{b^{5}}} \log{\left(x - \frac{b^{2} \sqrt{- \frac{a^{3}}{b^{5}}}}{a} \right)}}{2} + \frac{\sqrt{- \frac{a^{3}}{b^{5}}} \log{\left(x + \frac{b^{2} \sqrt{- \frac{a^{3}}{b^{5}}}}{a} \right)}}{2} + \frac{x^{3}}{3 b}"," ",0,"-a*x/b**2 - sqrt(-a**3/b**5)*log(x - b**2*sqrt(-a**3/b**5)/a)/2 + sqrt(-a**3/b**5)*log(x + b**2*sqrt(-a**3/b**5)/a)/2 + x**3/(3*b)","A",0
630,1,56,0,0.192929," ","integrate(x**2/((b*x**2+a)**2)**(1/2),x)","\frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(- b \sqrt{- \frac{a}{b^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(b \sqrt{- \frac{a}{b^{3}}} + x \right)}}{2} + \frac{x}{b}"," ",0,"sqrt(-a/b**3)*log(-b*sqrt(-a/b**3) + x)/2 - sqrt(-a/b**3)*log(b*sqrt(-a/b**3) + x)/2 + x/b","A",0
631,1,53,0,0.176711," ","integrate(1/((b*x**2+a)**2)**(1/2),x)","- \frac{\sqrt{- \frac{1}{a b}} \log{\left(- a \sqrt{- \frac{1}{a b}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a b}} \log{\left(a \sqrt{- \frac{1}{a b}} + x \right)}}{2}"," ",0,"-sqrt(-1/(a*b))*log(-a*sqrt(-1/(a*b)) + x)/2 + sqrt(-1/(a*b))*log(a*sqrt(-1/(a*b)) + x)/2","A",0
632,1,65,0,0.232064," ","integrate(1/x**2/((b*x**2+a)**2)**(1/2),x)","\frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(- \frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(\frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x \right)}}{2} - \frac{1}{a x}"," ",0,"sqrt(-b/a**3)*log(-a**2*sqrt(-b/a**3)/b + x)/2 - sqrt(-b/a**3)*log(a**2*sqrt(-b/a**3)/b + x)/2 - 1/(a*x)","A",0
633,1,87,0,0.279328," ","integrate(1/x**4/((b*x**2+a)**2)**(1/2),x)","- \frac{\sqrt{- \frac{b^{3}}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b^{3}}{a^{5}}}}{b^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{b^{3}}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b^{3}}{a^{5}}}}{b^{2}} + x \right)}}{2} + \frac{- a + 3 b x^{2}}{3 a^{2} x^{3}}"," ",0,"-sqrt(-b**3/a**5)*log(-a**3*sqrt(-b**3/a**5)/b**2 + x)/2 + sqrt(-b**3/a**5)*log(a**3*sqrt(-b**3/a**5)/b**2 + x)/2 + (-a + 3*b*x**2)/(3*a**2*x**3)","A",0
634,0,0,0,0.000000," ","integrate(x**7/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{x^{7}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**7/((a + b*x**2)**2)**(3/2), x)","F",0
635,0,0,0,0.000000," ","integrate(x**5/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{x^{5}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**2)**2)**(3/2), x)","F",0
636,0,0,0,0.000000," ","integrate(x**3/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{x^{3}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)**2)**(3/2), x)","F",0
637,0,0,0,0.000000," ","integrate(x/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{x}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((a + b*x**2)**2)**(3/2), x)","F",0
638,0,0,0,0.000000," ","integrate(1/x/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{1}{x \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*((a + b*x**2)**2)**(3/2)), x)","F",0
639,0,0,0,0.000000," ","integrate(1/x**3/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{1}{x^{3} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a + b*x**2)**2)**(3/2)), x)","F",0
640,0,0,0,0.000000," ","integrate(x**4/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{x^{4}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)**2)**(3/2), x)","F",0
641,0,0,0,0.000000," ","integrate(x**2/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{x^{2}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**2)**(3/2), x)","F",0
642,0,0,0,0.000000," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-3/2), x)","F",0
643,0,0,0,0.000000," ","integrate(1/x**2/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{1}{x^{2} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x**2)**2)**(3/2)), x)","F",0
644,0,0,0,0.000000," ","integrate(1/x**4/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{1}{x^{4} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*((a + b*x**2)**2)**(3/2)), x)","F",0
645,0,0,0,0.000000," ","integrate(x**11/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{11}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**11/((a + b*x**2)**2)**(5/2), x)","F",0
646,0,0,0,0.000000," ","integrate(x**9/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{9}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**9/((a + b*x**2)**2)**(5/2), x)","F",0
647,0,0,0,0.000000," ","integrate(x**7/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{7}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**7/((a + b*x**2)**2)**(5/2), x)","F",0
648,0,0,0,0.000000," ","integrate(x**5/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{5}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**2)**2)**(5/2), x)","F",0
649,0,0,0,0.000000," ","integrate(x**3/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{3}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)**2)**(5/2), x)","F",0
650,0,0,0,0.000000," ","integrate(x/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/((a + b*x**2)**2)**(5/2), x)","F",0
651,0,0,0,0.000000," ","integrate(1/x/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{1}{x \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*((a + b*x**2)**2)**(5/2)), x)","F",0
652,0,0,0,0.000000," ","integrate(1/x**3/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{1}{x^{3} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**3*((a + b*x**2)**2)**(5/2)), x)","F",0
653,0,0,0,0.000000," ","integrate(x**6/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{6}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**6/((a + b*x**2)**2)**(5/2), x)","F",0
654,0,0,0,0.000000," ","integrate(x**4/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{4}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)**2)**(5/2), x)","F",0
655,0,0,0,0.000000," ","integrate(x**2/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{x^{2}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**2)**(5/2), x)","F",0
656,0,0,0,0.000000," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{1}{\left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-5/2), x)","F",0
657,0,0,0,0.000000," ","integrate(1/x**2/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{1}{x^{2} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x**2)**2)**(5/2)), x)","F",0
658,0,0,0,0.000000," ","integrate(1/x**4/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{1}{x^{4} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**4*((a + b*x**2)**2)**(5/2)), x)","F",0
659,0,0,0,0.000000," ","integrate(x**2/(b**2*x**4+2*a*b*x**2+a**2)**(1/3),x)","\int \frac{x^{2}}{\sqrt[3]{\left(a + b x^{2}\right)^{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**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)","\int \frac{1}{\sqrt[3]{a^{2} + 2 a b x^{2} + b^{2} x^{4}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-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)","\int \frac{1}{x^{2} \sqrt[3]{\left(a + b x^{2}\right)^{2}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x**2)**2)**(1/3)), 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)","\int \frac{x^{2}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**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)","\int \frac{1}{\left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**(-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)","\int \frac{1}{x^{2} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/(x**2*((a + b*x**2)**2)**(2/3)), x)","F",0
665,1,49,0,2.671046," ","integrate((d*x)**(5/2)*(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{2 a^{2} d^{\frac{5}{2}} x^{\frac{7}{2}}}{7} + \frac{4 a b d^{\frac{5}{2}} x^{\frac{11}{2}}}{11} + \frac{2 b^{2} d^{\frac{5}{2}} x^{\frac{15}{2}}}{15}"," ",0,"2*a**2*d**(5/2)*x**(7/2)/7 + 4*a*b*d**(5/2)*x**(11/2)/11 + 2*b**2*d**(5/2)*x**(15/2)/15","A",0
666,1,49,0,1.244026," ","integrate((d*x)**(3/2)*(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{2 a^{2} d^{\frac{3}{2}} x^{\frac{5}{2}}}{5} + \frac{4 a b d^{\frac{3}{2}} x^{\frac{9}{2}}}{9} + \frac{2 b^{2} d^{\frac{3}{2}} x^{\frac{13}{2}}}{13}"," ",0,"2*a**2*d**(3/2)*x**(5/2)/5 + 4*a*b*d**(3/2)*x**(9/2)/9 + 2*b**2*d**(3/2)*x**(13/2)/13","A",0
667,1,49,0,0.482104," ","integrate((b**2*x**4+2*a*b*x**2+a**2)*(d*x)**(1/2),x)","\frac{2 a^{2} \sqrt{d} x^{\frac{3}{2}}}{3} + \frac{4 a b \sqrt{d} x^{\frac{7}{2}}}{7} + \frac{2 b^{2} \sqrt{d} x^{\frac{11}{2}}}{11}"," ",0,"2*a**2*sqrt(d)*x**(3/2)/3 + 4*a*b*sqrt(d)*x**(7/2)/7 + 2*b**2*sqrt(d)*x**(11/2)/11","A",0
668,1,48,0,0.628435," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/(d*x)**(1/2),x)","\frac{2 a^{2} \sqrt{x}}{\sqrt{d}} + \frac{4 a b x^{\frac{5}{2}}}{5 \sqrt{d}} + \frac{2 b^{2} x^{\frac{9}{2}}}{9 \sqrt{d}}"," ",0,"2*a**2*sqrt(x)/sqrt(d) + 4*a*b*x**(5/2)/(5*sqrt(d)) + 2*b**2*x**(9/2)/(9*sqrt(d))","A",0
669,1,48,0,0.664893," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/(d*x)**(3/2),x)","- \frac{2 a^{2}}{d^{\frac{3}{2}} \sqrt{x}} + \frac{4 a b x^{\frac{3}{2}}}{3 d^{\frac{3}{2}}} + \frac{2 b^{2} x^{\frac{7}{2}}}{7 d^{\frac{3}{2}}}"," ",0,"-2*a**2/(d**(3/2)*sqrt(x)) + 4*a*b*x**(3/2)/(3*d**(3/2)) + 2*b**2*x**(7/2)/(7*d**(3/2))","A",0
670,1,48,0,0.912504," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/(d*x)**(5/2),x)","- \frac{2 a^{2}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} + \frac{4 a b \sqrt{x}}{d^{\frac{5}{2}}} + \frac{2 b^{2} x^{\frac{5}{2}}}{5 d^{\frac{5}{2}}}"," ",0,"-2*a**2/(3*d**(5/2)*x**(3/2)) + 4*a*b*sqrt(x)/d**(5/2) + 2*b**2*x**(5/2)/(5*d**(5/2))","A",0
671,1,48,0,1.968773," ","integrate((b**2*x**4+2*a*b*x**2+a**2)/(d*x)**(7/2),x)","- \frac{2 a^{2}}{5 d^{\frac{7}{2}} x^{\frac{5}{2}}} - \frac{4 a b}{d^{\frac{7}{2}} \sqrt{x}} + \frac{2 b^{2} x^{\frac{3}{2}}}{3 d^{\frac{7}{2}}}"," ",0,"-2*a**2/(5*d**(7/2)*x**(5/2)) - 4*a*b/(d**(7/2)*sqrt(x)) + 2*b**2*x**(3/2)/(3*d**(7/2))","A",0
672,1,90,0,5.680502," ","integrate((d*x)**(5/2)*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{2 a^{4} d^{\frac{5}{2}} x^{\frac{7}{2}}}{7} + \frac{8 a^{3} b d^{\frac{5}{2}} x^{\frac{11}{2}}}{11} + \frac{4 a^{2} b^{2} d^{\frac{5}{2}} x^{\frac{15}{2}}}{5} + \frac{8 a b^{3} d^{\frac{5}{2}} x^{\frac{19}{2}}}{19} + \frac{2 b^{4} d^{\frac{5}{2}} x^{\frac{23}{2}}}{23}"," ",0,"2*a**4*d**(5/2)*x**(7/2)/7 + 8*a**3*b*d**(5/2)*x**(11/2)/11 + 4*a**2*b**2*d**(5/2)*x**(15/2)/5 + 8*a*b**3*d**(5/2)*x**(19/2)/19 + 2*b**4*d**(5/2)*x**(23/2)/23","A",0
673,1,90,0,2.690578," ","integrate((d*x)**(3/2)*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{2 a^{4} d^{\frac{3}{2}} x^{\frac{5}{2}}}{5} + \frac{8 a^{3} b d^{\frac{3}{2}} x^{\frac{9}{2}}}{9} + \frac{12 a^{2} b^{2} d^{\frac{3}{2}} x^{\frac{13}{2}}}{13} + \frac{8 a b^{3} d^{\frac{3}{2}} x^{\frac{17}{2}}}{17} + \frac{2 b^{4} d^{\frac{3}{2}} x^{\frac{21}{2}}}{21}"," ",0,"2*a**4*d**(3/2)*x**(5/2)/5 + 8*a**3*b*d**(3/2)*x**(9/2)/9 + 12*a**2*b**2*d**(3/2)*x**(13/2)/13 + 8*a*b**3*d**(3/2)*x**(17/2)/17 + 2*b**4*d**(3/2)*x**(21/2)/21","A",0
674,1,90,0,1.274621," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2*(d*x)**(1/2),x)","\frac{2 a^{4} \sqrt{d} x^{\frac{3}{2}}}{3} + \frac{8 a^{3} b \sqrt{d} x^{\frac{7}{2}}}{7} + \frac{12 a^{2} b^{2} \sqrt{d} x^{\frac{11}{2}}}{11} + \frac{8 a b^{3} \sqrt{d} x^{\frac{15}{2}}}{15} + \frac{2 b^{4} \sqrt{d} x^{\frac{19}{2}}}{19}"," ",0,"2*a**4*sqrt(d)*x**(3/2)/3 + 8*a**3*b*sqrt(d)*x**(7/2)/7 + 12*a**2*b**2*sqrt(d)*x**(11/2)/11 + 8*a*b**3*sqrt(d)*x**(15/2)/15 + 2*b**4*sqrt(d)*x**(19/2)/19","A",0
675,1,88,0,1.345662," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/(d*x)**(1/2),x)","\frac{2 a^{4} \sqrt{x}}{\sqrt{d}} + \frac{8 a^{3} b x^{\frac{5}{2}}}{5 \sqrt{d}} + \frac{4 a^{2} b^{2} x^{\frac{9}{2}}}{3 \sqrt{d}} + \frac{8 a b^{3} x^{\frac{13}{2}}}{13 \sqrt{d}} + \frac{2 b^{4} x^{\frac{17}{2}}}{17 \sqrt{d}}"," ",0,"2*a**4*sqrt(x)/sqrt(d) + 8*a**3*b*x**(5/2)/(5*sqrt(d)) + 4*a**2*b**2*x**(9/2)/(3*sqrt(d)) + 8*a*b**3*x**(13/2)/(13*sqrt(d)) + 2*b**4*x**(17/2)/(17*sqrt(d))","A",0
676,1,88,0,1.377382," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/(d*x)**(3/2),x)","- \frac{2 a^{4}}{d^{\frac{3}{2}} \sqrt{x}} + \frac{8 a^{3} b x^{\frac{3}{2}}}{3 d^{\frac{3}{2}}} + \frac{12 a^{2} b^{2} x^{\frac{7}{2}}}{7 d^{\frac{3}{2}}} + \frac{8 a b^{3} x^{\frac{11}{2}}}{11 d^{\frac{3}{2}}} + \frac{2 b^{4} x^{\frac{15}{2}}}{15 d^{\frac{3}{2}}}"," ",0,"-2*a**4/(d**(3/2)*sqrt(x)) + 8*a**3*b*x**(3/2)/(3*d**(3/2)) + 12*a**2*b**2*x**(7/2)/(7*d**(3/2)) + 8*a*b**3*x**(11/2)/(11*d**(3/2)) + 2*b**4*x**(15/2)/(15*d**(3/2))","A",0
677,1,88,0,1.736633," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/(d*x)**(5/2),x)","- \frac{2 a^{4}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} + \frac{8 a^{3} b \sqrt{x}}{d^{\frac{5}{2}}} + \frac{12 a^{2} b^{2} x^{\frac{5}{2}}}{5 d^{\frac{5}{2}}} + \frac{8 a b^{3} x^{\frac{9}{2}}}{9 d^{\frac{5}{2}}} + \frac{2 b^{4} x^{\frac{13}{2}}}{13 d^{\frac{5}{2}}}"," ",0,"-2*a**4/(3*d**(5/2)*x**(3/2)) + 8*a**3*b*sqrt(x)/d**(5/2) + 12*a**2*b**2*x**(5/2)/(5*d**(5/2)) + 8*a*b**3*x**(9/2)/(9*d**(5/2)) + 2*b**4*x**(13/2)/(13*d**(5/2))","A",0
678,1,87,0,2.474273," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**2/(d*x)**(7/2),x)","- \frac{2 a^{4}}{5 d^{\frac{7}{2}} x^{\frac{5}{2}}} - \frac{8 a^{3} b}{d^{\frac{7}{2}} \sqrt{x}} + \frac{4 a^{2} b^{2} x^{\frac{3}{2}}}{d^{\frac{7}{2}}} + \frac{8 a b^{3} x^{\frac{7}{2}}}{7 d^{\frac{7}{2}}} + \frac{2 b^{4} x^{\frac{11}{2}}}{11 d^{\frac{7}{2}}}"," ",0,"-2*a**4/(5*d**(7/2)*x**(5/2)) - 8*a**3*b/(d**(7/2)*sqrt(x)) + 4*a**2*b**2*x**(3/2)/d**(7/2) + 8*a*b**3*x**(7/2)/(7*d**(7/2)) + 2*b**4*x**(11/2)/(11*d**(7/2))","A",0
679,1,129,0,10.797895," ","integrate((d*x)**(5/2)*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{2 a^{6} d^{\frac{5}{2}} x^{\frac{7}{2}}}{7} + \frac{12 a^{5} b d^{\frac{5}{2}} x^{\frac{11}{2}}}{11} + 2 a^{4} b^{2} d^{\frac{5}{2}} x^{\frac{15}{2}} + \frac{40 a^{3} b^{3} d^{\frac{5}{2}} x^{\frac{19}{2}}}{19} + \frac{30 a^{2} b^{4} d^{\frac{5}{2}} x^{\frac{23}{2}}}{23} + \frac{4 a b^{5} d^{\frac{5}{2}} x^{\frac{27}{2}}}{9} + \frac{2 b^{6} d^{\frac{5}{2}} x^{\frac{31}{2}}}{31}"," ",0,"2*a**6*d**(5/2)*x**(7/2)/7 + 12*a**5*b*d**(5/2)*x**(11/2)/11 + 2*a**4*b**2*d**(5/2)*x**(15/2) + 40*a**3*b**3*d**(5/2)*x**(19/2)/19 + 30*a**2*b**4*d**(5/2)*x**(23/2)/23 + 4*a*b**5*d**(5/2)*x**(27/2)/9 + 2*b**6*d**(5/2)*x**(31/2)/31","A",0
680,1,131,0,5.337849," ","integrate((d*x)**(3/2)*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{2 a^{6} d^{\frac{3}{2}} x^{\frac{5}{2}}}{5} + \frac{4 a^{5} b d^{\frac{3}{2}} x^{\frac{9}{2}}}{3} + \frac{30 a^{4} b^{2} d^{\frac{3}{2}} x^{\frac{13}{2}}}{13} + \frac{40 a^{3} b^{3} d^{\frac{3}{2}} x^{\frac{17}{2}}}{17} + \frac{10 a^{2} b^{4} d^{\frac{3}{2}} x^{\frac{21}{2}}}{7} + \frac{12 a b^{5} d^{\frac{3}{2}} x^{\frac{25}{2}}}{25} + \frac{2 b^{6} d^{\frac{3}{2}} x^{\frac{29}{2}}}{29}"," ",0,"2*a**6*d**(3/2)*x**(5/2)/5 + 4*a**5*b*d**(3/2)*x**(9/2)/3 + 30*a**4*b**2*d**(3/2)*x**(13/2)/13 + 40*a**3*b**3*d**(3/2)*x**(17/2)/17 + 10*a**2*b**4*d**(3/2)*x**(21/2)/7 + 12*a*b**5*d**(3/2)*x**(25/2)/25 + 2*b**6*d**(3/2)*x**(29/2)/29","A",0
681,1,131,0,3.003484," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3*(d*x)**(1/2),x)","\frac{2 a^{6} \sqrt{d} x^{\frac{3}{2}}}{3} + \frac{12 a^{5} b \sqrt{d} x^{\frac{7}{2}}}{7} + \frac{30 a^{4} b^{2} \sqrt{d} x^{\frac{11}{2}}}{11} + \frac{8 a^{3} b^{3} \sqrt{d} x^{\frac{15}{2}}}{3} + \frac{30 a^{2} b^{4} \sqrt{d} x^{\frac{19}{2}}}{19} + \frac{12 a b^{5} \sqrt{d} x^{\frac{23}{2}}}{23} + \frac{2 b^{6} \sqrt{d} x^{\frac{27}{2}}}{27}"," ",0,"2*a**6*sqrt(d)*x**(3/2)/3 + 12*a**5*b*sqrt(d)*x**(7/2)/7 + 30*a**4*b**2*sqrt(d)*x**(11/2)/11 + 8*a**3*b**3*sqrt(d)*x**(15/2)/3 + 30*a**2*b**4*sqrt(d)*x**(19/2)/19 + 12*a*b**5*sqrt(d)*x**(23/2)/23 + 2*b**6*sqrt(d)*x**(27/2)/27","A",0
682,1,129,0,2.938191," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/(d*x)**(1/2),x)","\frac{2 a^{6} \sqrt{x}}{\sqrt{d}} + \frac{12 a^{5} b x^{\frac{5}{2}}}{5 \sqrt{d}} + \frac{10 a^{4} b^{2} x^{\frac{9}{2}}}{3 \sqrt{d}} + \frac{40 a^{3} b^{3} x^{\frac{13}{2}}}{13 \sqrt{d}} + \frac{30 a^{2} b^{4} x^{\frac{17}{2}}}{17 \sqrt{d}} + \frac{4 a b^{5} x^{\frac{21}{2}}}{7 \sqrt{d}} + \frac{2 b^{6} x^{\frac{25}{2}}}{25 \sqrt{d}}"," ",0,"2*a**6*sqrt(x)/sqrt(d) + 12*a**5*b*x**(5/2)/(5*sqrt(d)) + 10*a**4*b**2*x**(9/2)/(3*sqrt(d)) + 40*a**3*b**3*x**(13/2)/(13*sqrt(d)) + 30*a**2*b**4*x**(17/2)/(17*sqrt(d)) + 4*a*b**5*x**(21/2)/(7*sqrt(d)) + 2*b**6*x**(25/2)/(25*sqrt(d))","A",0
683,1,126,0,3.006126," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/(d*x)**(3/2),x)","- \frac{2 a^{6}}{d^{\frac{3}{2}} \sqrt{x}} + \frac{4 a^{5} b x^{\frac{3}{2}}}{d^{\frac{3}{2}}} + \frac{30 a^{4} b^{2} x^{\frac{7}{2}}}{7 d^{\frac{3}{2}}} + \frac{40 a^{3} b^{3} x^{\frac{11}{2}}}{11 d^{\frac{3}{2}}} + \frac{2 a^{2} b^{4} x^{\frac{15}{2}}}{d^{\frac{3}{2}}} + \frac{12 a b^{5} x^{\frac{19}{2}}}{19 d^{\frac{3}{2}}} + \frac{2 b^{6} x^{\frac{23}{2}}}{23 d^{\frac{3}{2}}}"," ",0,"-2*a**6/(d**(3/2)*sqrt(x)) + 4*a**5*b*x**(3/2)/d**(3/2) + 30*a**4*b**2*x**(7/2)/(7*d**(3/2)) + 40*a**3*b**3*x**(11/2)/(11*d**(3/2)) + 2*a**2*b**4*x**(15/2)/d**(3/2) + 12*a*b**5*x**(19/2)/(19*d**(3/2)) + 2*b**6*x**(23/2)/(23*d**(3/2))","A",0
684,1,128,0,3.571098," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/(d*x)**(5/2),x)","- \frac{2 a^{6}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} + \frac{12 a^{5} b \sqrt{x}}{d^{\frac{5}{2}}} + \frac{6 a^{4} b^{2} x^{\frac{5}{2}}}{d^{\frac{5}{2}}} + \frac{40 a^{3} b^{3} x^{\frac{9}{2}}}{9 d^{\frac{5}{2}}} + \frac{30 a^{2} b^{4} x^{\frac{13}{2}}}{13 d^{\frac{5}{2}}} + \frac{12 a b^{5} x^{\frac{17}{2}}}{17 d^{\frac{5}{2}}} + \frac{2 b^{6} x^{\frac{21}{2}}}{21 d^{\frac{5}{2}}}"," ",0,"-2*a**6/(3*d**(5/2)*x**(3/2)) + 12*a**5*b*sqrt(x)/d**(5/2) + 6*a**4*b**2*x**(5/2)/d**(5/2) + 40*a**3*b**3*x**(9/2)/(9*d**(5/2)) + 30*a**2*b**4*x**(13/2)/(13*d**(5/2)) + 12*a*b**5*x**(17/2)/(17*d**(5/2)) + 2*b**6*x**(21/2)/(21*d**(5/2))","A",0
685,1,128,0,4.556132," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**3/(d*x)**(7/2),x)","- \frac{2 a^{6}}{5 d^{\frac{7}{2}} x^{\frac{5}{2}}} - \frac{12 a^{5} b}{d^{\frac{7}{2}} \sqrt{x}} + \frac{10 a^{4} b^{2} x^{\frac{3}{2}}}{d^{\frac{7}{2}}} + \frac{40 a^{3} b^{3} x^{\frac{7}{2}}}{7 d^{\frac{7}{2}}} + \frac{30 a^{2} b^{4} x^{\frac{11}{2}}}{11 d^{\frac{7}{2}}} + \frac{4 a b^{5} x^{\frac{15}{2}}}{5 d^{\frac{7}{2}}} + \frac{2 b^{6} x^{\frac{19}{2}}}{19 d^{\frac{7}{2}}}"," ",0,"-2*a**6/(5*d**(7/2)*x**(5/2)) - 12*a**5*b/(d**(7/2)*sqrt(x)) + 10*a**4*b**2*x**(3/2)/d**(7/2) + 40*a**3*b**3*x**(7/2)/(7*d**(7/2)) + 30*a**2*b**4*x**(11/2)/(11*d**(7/2)) + 4*a*b**5*x**(15/2)/(5*d**(7/2)) + 2*b**6*x**(19/2)/(19*d**(7/2))","A",0
686,0,0,0,0.000000," ","integrate((d*x)**(11/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{\left(d x\right)^{\frac{11}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((d*x)**(11/2)/(a + b*x**2)**2, x)","F",0
687,0,0,0,0.000000," ","integrate((d*x)**(9/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{\left(d x\right)^{\frac{9}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((d*x)**(9/2)/(a + b*x**2)**2, x)","F",0
688,0,0,0,0.000000," ","integrate((d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{\left(d x\right)^{\frac{7}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((d*x)**(7/2)/(a + b*x**2)**2, x)","F",0
689,0,0,0,0.000000," ","integrate((d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{\left(d x\right)^{\frac{5}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((d*x)**(5/2)/(a + b*x**2)**2, x)","F",0
690,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((d*x)**(3/2)/(a + b*x**2)**2, x)","F",0
691,1,78,0,6.666747," ","integrate((d*x)**(1/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\frac{2 d^{3} \left(d x\right)^{\frac{3}{2}}}{4 a^{2} d^{4} + 4 a b d^{4} x^{2}} + 2 d^{3} \operatorname{RootSum} {\left(65536 t^{4} a^{5} b^{3} d^{10} + 1, \left( t \mapsto t \log{\left(4096 t^{3} a^{4} b^{2} d^{8} + \sqrt{d x} \right)} \right)\right)}"," ",0,"2*d**3*(d*x)**(3/2)/(4*a**2*d**4 + 4*a*b*d**4*x**2) + 2*d**3*RootSum(65536*_t**4*a**5*b**3*d**10 + 1, Lambda(_t, _t*log(4096*_t**3*a**4*b**2*d**8 + sqrt(d*x))))","A",0
692,0,0,0,0.000000," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2)/(d*x)**(1/2),x)","\int \frac{1}{\sqrt{d x} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*(a + b*x**2)**2), x)","F",0
693,0,0,0,0.000000," ","integrate(1/(d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*(a + b*x**2)**2), x)","F",0
694,0,0,0,0.000000," ","integrate(1/(d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{1}{\left(d x\right)^{\frac{5}{2}} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((d*x)**(5/2)*(a + b*x**2)**2), x)","F",0
695,0,0,0,0.000000," ","integrate(1/(d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{1}{\left(d x\right)^{\frac{7}{2}} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((d*x)**(7/2)*(a + b*x**2)**2), x)","F",0
696,-1,0,0,0.000000," ","integrate((d*x)**(19/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,-1,0,0,0.000000," ","integrate((d*x)**(17/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
698,-1,0,0,0.000000," ","integrate((d*x)**(15/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,0,0,0,0.000000," ","integrate((d*x)**(13/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{\left(d x\right)^{\frac{13}{2}}}{\left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((d*x)**(13/2)/(a + b*x**2)**4, x)","F",0
700,0,0,0,0.000000," ","integrate((d*x)**(11/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{\left(d x\right)^{\frac{11}{2}}}{\left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((d*x)**(11/2)/(a + b*x**2)**4, x)","F",0
701,0,0,0,0.000000," ","integrate((d*x)**(9/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{\left(d x\right)^{\frac{9}{2}}}{\left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((d*x)**(9/2)/(a + b*x**2)**4, x)","F",0
702,0,0,0,0.000000," ","integrate((d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{\left(d x\right)^{\frac{7}{2}}}{\left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((d*x)**(7/2)/(a + b*x**2)**4, x)","F",0
703,0,0,0,0.000000," ","integrate((d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{\left(d x\right)^{\frac{5}{2}}}{\left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((d*x)**(5/2)/(a + b*x**2)**4, x)","F",0
704,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((d*x)**(3/2)/(a + b*x**2)**4, x)","F",0
705,1,252,0,28.986055," ","integrate((d*x)**(1/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\frac{226 a^{2} d^{11} \left(d x\right)^{\frac{3}{2}}}{384 a^{6} d^{12} + 1152 a^{5} b d^{12} x^{2} + 1152 a^{4} b^{2} d^{12} x^{4} + 384 a^{3} b^{3} d^{12} x^{6}} + \frac{252 a b d^{9} \left(d x\right)^{\frac{7}{2}}}{384 a^{6} d^{12} + 1152 a^{5} b d^{12} x^{2} + 1152 a^{4} b^{2} d^{12} x^{4} + 384 a^{3} b^{3} d^{12} x^{6}} + \frac{90 b^{2} d^{7} \left(d x\right)^{\frac{11}{2}}}{384 a^{6} d^{12} + 1152 a^{5} b d^{12} x^{2} + 1152 a^{4} b^{2} d^{12} x^{4} + 384 a^{3} b^{3} d^{12} x^{6}} + 2 d^{7} \operatorname{RootSum} {\left(68719476736 t^{4} a^{13} b^{3} d^{26} + 50625, \left( t \mapsto t \log{\left(\frac{134217728 t^{3} a^{10} b^{2} d^{20}}{3375} + \sqrt{d x} \right)} \right)\right)}"," ",0,"226*a**2*d**11*(d*x)**(3/2)/(384*a**6*d**12 + 1152*a**5*b*d**12*x**2 + 1152*a**4*b**2*d**12*x**4 + 384*a**3*b**3*d**12*x**6) + 252*a*b*d**9*(d*x)**(7/2)/(384*a**6*d**12 + 1152*a**5*b*d**12*x**2 + 1152*a**4*b**2*d**12*x**4 + 384*a**3*b**3*d**12*x**6) + 90*b**2*d**7*(d*x)**(11/2)/(384*a**6*d**12 + 1152*a**5*b*d**12*x**2 + 1152*a**4*b**2*d**12*x**4 + 384*a**3*b**3*d**12*x**6) + 2*d**7*RootSum(68719476736*_t**4*a**13*b**3*d**26 + 50625, Lambda(_t, _t*log(134217728*_t**3*a**10*b**2*d**20/3375 + sqrt(d*x))))","A",0
706,0,0,0,0.000000," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2)**2/(d*x)**(1/2),x)","\int \frac{1}{\sqrt{d x} \left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*(a + b*x**2)**4), x)","F",0
707,0,0,0,0.000000," ","integrate(1/(d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*(a + b*x**2)**4), x)","F",0
708,0,0,0,0.000000," ","integrate(1/(d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{1}{\left(d x\right)^{\frac{5}{2}} \left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral(1/((d*x)**(5/2)*(a + b*x**2)**4), x)","F",0
709,0,0,0,0.000000," ","integrate(1/(d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\int \frac{1}{\left(d x\right)^{\frac{7}{2}} \left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral(1/((d*x)**(7/2)*(a + b*x**2)**4), x)","F",0
710,-1,0,0,0.000000," ","integrate((d*x)**(27/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
711,-1,0,0,0.000000," ","integrate((d*x)**(25/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,-1,0,0,0.000000," ","integrate((d*x)**(23/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate((d*x)**(21/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,-1,0,0,0.000000," ","integrate((d*x)**(19/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
715,-1,0,0,0.000000," ","integrate((d*x)**(17/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,-1,0,0,0.000000," ","integrate((d*x)**(15/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
717,-1,0,0,0.000000," ","integrate((d*x)**(13/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate((d*x)**(11/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate((d*x)**(9/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,0,0,0,0.000000," ","integrate((d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\int \frac{\left(d x\right)^{\frac{7}{2}}}{\left(a + b x^{2}\right)^{6}}\, dx"," ",0,"Integral((d*x)**(7/2)/(a + b*x**2)**6, x)","F",0
721,0,0,0,0.000000," ","integrate((d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\int \frac{\left(d x\right)^{\frac{5}{2}}}{\left(a + b x^{2}\right)^{6}}\, dx"," ",0,"Integral((d*x)**(5/2)/(a + b*x**2)**6, x)","F",0
722,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{6}}\, dx"," ",0,"Integral((d*x)**(3/2)/(a + b*x**2)**6, x)","F",0
723,1,547,0,89.238067," ","integrate((d*x)**(1/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\frac{75290 a^{4} d^{19} \left(d x\right)^{\frac{3}{2}}}{122880 a^{10} d^{20} + 614400 a^{9} b d^{20} x^{2} + 1228800 a^{8} b^{2} d^{20} x^{4} + 1228800 a^{7} b^{3} d^{20} x^{6} + 614400 a^{6} b^{4} d^{20} x^{8} + 122880 a^{5} b^{5} d^{20} x^{10}} + \frac{168640 a^{3} b d^{17} \left(d x\right)^{\frac{7}{2}}}{122880 a^{10} d^{20} + 614400 a^{9} b d^{20} x^{2} + 1228800 a^{8} b^{2} d^{20} x^{4} + 1228800 a^{7} b^{3} d^{20} x^{6} + 614400 a^{6} b^{4} d^{20} x^{8} + 122880 a^{5} b^{5} d^{20} x^{10}} + \frac{181220 a^{2} b^{2} d^{15} \left(d x\right)^{\frac{11}{2}}}{122880 a^{10} d^{20} + 614400 a^{9} b d^{20} x^{2} + 1228800 a^{8} b^{2} d^{20} x^{4} + 1228800 a^{7} b^{3} d^{20} x^{6} + 614400 a^{6} b^{4} d^{20} x^{8} + 122880 a^{5} b^{5} d^{20} x^{10}} + \frac{95472 a b^{3} d^{13} \left(d x\right)^{\frac{15}{2}}}{122880 a^{10} d^{20} + 614400 a^{9} b d^{20} x^{2} + 1228800 a^{8} b^{2} d^{20} x^{4} + 1228800 a^{7} b^{3} d^{20} x^{6} + 614400 a^{6} b^{4} d^{20} x^{8} + 122880 a^{5} b^{5} d^{20} x^{10}} + \frac{19890 b^{4} d^{11} \left(d x\right)^{\frac{19}{2}}}{122880 a^{10} d^{20} + 614400 a^{9} b d^{20} x^{2} + 1228800 a^{8} b^{2} d^{20} x^{4} + 1228800 a^{7} b^{3} d^{20} x^{6} + 614400 a^{6} b^{4} d^{20} x^{8} + 122880 a^{5} b^{5} d^{20} x^{10}} + 2 d^{11} \operatorname{RootSum} {\left(1152921504606846976 t^{4} a^{21} b^{3} d^{42} + 193220905761, \left( t \mapsto t \log{\left(\frac{35184372088832 t^{3} a^{16} b^{2} d^{32}}{291434247} + \sqrt{d x} \right)} \right)\right)}"," ",0,"75290*a**4*d**19*(d*x)**(3/2)/(122880*a**10*d**20 + 614400*a**9*b*d**20*x**2 + 1228800*a**8*b**2*d**20*x**4 + 1228800*a**7*b**3*d**20*x**6 + 614400*a**6*b**4*d**20*x**8 + 122880*a**5*b**5*d**20*x**10) + 168640*a**3*b*d**17*(d*x)**(7/2)/(122880*a**10*d**20 + 614400*a**9*b*d**20*x**2 + 1228800*a**8*b**2*d**20*x**4 + 1228800*a**7*b**3*d**20*x**6 + 614400*a**6*b**4*d**20*x**8 + 122880*a**5*b**5*d**20*x**10) + 181220*a**2*b**2*d**15*(d*x)**(11/2)/(122880*a**10*d**20 + 614400*a**9*b*d**20*x**2 + 1228800*a**8*b**2*d**20*x**4 + 1228800*a**7*b**3*d**20*x**6 + 614400*a**6*b**4*d**20*x**8 + 122880*a**5*b**5*d**20*x**10) + 95472*a*b**3*d**13*(d*x)**(15/2)/(122880*a**10*d**20 + 614400*a**9*b*d**20*x**2 + 1228800*a**8*b**2*d**20*x**4 + 1228800*a**7*b**3*d**20*x**6 + 614400*a**6*b**4*d**20*x**8 + 122880*a**5*b**5*d**20*x**10) + 19890*b**4*d**11*(d*x)**(19/2)/(122880*a**10*d**20 + 614400*a**9*b*d**20*x**2 + 1228800*a**8*b**2*d**20*x**4 + 1228800*a**7*b**3*d**20*x**6 + 614400*a**6*b**4*d**20*x**8 + 122880*a**5*b**5*d**20*x**10) + 2*d**11*RootSum(1152921504606846976*_t**4*a**21*b**3*d**42 + 193220905761, Lambda(_t, _t*log(35184372088832*_t**3*a**16*b**2*d**32/291434247 + sqrt(d*x))))","A",0
724,0,0,0,0.000000," ","integrate(1/(b**2*x**4+2*a*b*x**2+a**2)**3/(d*x)**(1/2),x)","\int \frac{1}{\sqrt{d x} \left(a + b x^{2}\right)^{6}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*(a + b*x**2)**6), x)","F",0
725,0,0,0,0.000000," ","integrate(1/(d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(a + b x^{2}\right)^{6}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*(a + b*x**2)**6), x)","F",0
726,-1,0,0,0.000000," ","integrate(1/(d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,-1,0,0,0.000000," ","integrate(1/(d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate((d*x)**(5/2)*((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate((d*x)**(3/2)*((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,1,27,0,133.052559," ","integrate((d*x)**(1/2)*((b*x**2+a)**2)**(1/2),x)","\frac{2 a \left(d x\right)^{\frac{3}{2}}}{3 d} + \frac{2 b \left(d x\right)^{\frac{7}{2}}}{7 d^{3}}"," ",0,"2*a*(d*x)**(3/2)/(3*d) + 2*b*(d*x)**(7/2)/(7*d**3)","A",0
731,0,0,0,0.000000," ","integrate(((b*x**2+a)**2)**(1/2)/(d*x)**(1/2),x)","\int \frac{\sqrt{\left(a + b x^{2}\right)^{2}}}{\sqrt{d x}}\, dx"," ",0,"Integral(sqrt((a + b*x**2)**2)/sqrt(d*x), x)","F",0
732,-1,0,0,0.000000," ","integrate(((b*x**2+a)**2)**(1/2)/(d*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,-1,0,0,0.000000," ","integrate(((b*x**2+a)**2)**(1/2)/(d*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,-1,0,0,0.000000," ","integrate(((b*x**2+a)**2)**(1/2)/(d*x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
735,0,0,0,0.000000," ","integrate((d*x)**(5/2)*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \left(d x\right)^{\frac{5}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**(5/2)*((a + b*x**2)**2)**(3/2), x)","F",0
736,0,0,0,0.000000," ","integrate((d*x)**(3/2)*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \left(d x\right)^{\frac{3}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**(3/2)*((a + b*x**2)**2)**(3/2), x)","F",0
737,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)*(d*x)**(1/2),x)","\int \sqrt{d x} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(d*x)*((a + b*x**2)**2)**(3/2), x)","F",0
738,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/(d*x)**(1/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{\sqrt{d x}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/sqrt(d*x), x)","F",0
739,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/(d*x)**(3/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/(d*x)**(3/2), x)","F",0
740,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/(d*x)**(5/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{\left(d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/(d*x)**(5/2), x)","F",0
741,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(3/2)/(d*x)**(7/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}{\left(d x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(3/2)/(d*x)**(7/2), x)","F",0
742,-1,0,0,0.000000," ","integrate((d*x)**(5/2)*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,0,0,0,0.000000," ","integrate((d*x)**(3/2)*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \left(d x\right)^{\frac{3}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d*x)**(3/2)*((a + b*x**2)**2)**(5/2), x)","F",0
744,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)*(d*x)**(1/2),x)","\int \sqrt{d x} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(sqrt(d*x)*((a + b*x**2)**2)**(5/2), x)","F",0
745,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/(d*x)**(1/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{\sqrt{d x}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/sqrt(d*x), x)","F",0
746,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/(d*x)**(3/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/(d*x)**(3/2), x)","F",0
747,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/(d*x)**(5/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{\left(d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/(d*x)**(5/2), x)","F",0
748,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**(5/2)/(d*x)**(7/2),x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}{\left(d x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**(5/2)/(d*x)**(7/2), x)","F",0
749,-1,0,0,0.000000," ","integrate((d*x)**(7/2)/((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate((d*x)**(5/2)/((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate((d*x)**(3/2)/((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,1,41,0,57.264651," ","integrate((d*x)**(1/2)/((b*x**2+a)**2)**(1/2),x)","2 d \operatorname{RootSum} {\left(256 t^{4} a b^{3} d^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} a b^{2} d^{2} + \sqrt{d x} \right)} \right)\right)}"," ",0,"2*d*RootSum(256*_t**4*a*b**3*d**2 + 1, Lambda(_t, _t*log(64*_t**3*a*b**2*d**2 + sqrt(d*x))))","A",0
753,0,0,0,0.000000," ","integrate(1/(d*x)**(1/2)/((b*x**2+a)**2)**(1/2),x)","\int \frac{1}{\sqrt{d x} \sqrt{\left(a + b x^{2}\right)^{2}}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*sqrt((a + b*x**2)**2)), x)","F",0
754,-1,0,0,0.000000," ","integrate(1/(d*x)**(3/2)/((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,-1,0,0,0.000000," ","integrate(1/(d*x)**(5/2)/((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
756,-1,0,0,0.000000," ","integrate(1/(d*x)**(7/2)/((b*x**2+a)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate((d*x)**(15/2)/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate((d*x)**(13/2)/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate((d*x)**(11/2)/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",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)","\int \frac{\left(d x\right)^{\frac{9}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**(9/2)/((a + b*x**2)**2)**(3/2), x)","F",0
761,0,0,0,0.000000," ","integrate((d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{\left(d x\right)^{\frac{7}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**(7/2)/((a + b*x**2)**2)**(3/2), x)","F",0
762,0,0,0,0.000000," ","integrate((d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{\left(d x\right)^{\frac{5}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**(5/2)/((a + b*x**2)**2)**(3/2), x)","F",0
763,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**(3/2)/((a + b*x**2)**2)**(3/2), x)","F",0
764,0,0,0,0.000000," ","integrate((d*x)**(1/2)/(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \frac{\sqrt{d x}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d*x)/((a + b*x**2)**2)**(3/2), x)","F",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)","\int \frac{1}{\sqrt{d x} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*((a + b*x**2)**2)**(3/2)), 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)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*((a + b*x**2)**2)**(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)","\int \frac{1}{\left(d x\right)^{\frac{5}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d*x)**(5/2)*((a + b*x**2)**2)**(3/2)), 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)","\int \frac{1}{\left(d x\right)^{\frac{7}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d*x)**(7/2)*((a + b*x**2)**2)**(3/2)), x)","F",0
769,-1,0,0,0.000000," ","integrate((d*x)**(23/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
770,-1,0,0,0.000000," ","integrate((d*x)**(21/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
771,-1,0,0,0.000000," ","integrate((d*x)**(19/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
772,-1,0,0,0.000000," ","integrate((d*x)**(17/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,-1,0,0,0.000000," ","integrate((d*x)**(15/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
774,-1,0,0,0.000000," ","integrate((d*x)**(13/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
775,-1,0,0,0.000000," ","integrate((d*x)**(11/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
776,0,0,0,0.000000," ","integrate((d*x)**(9/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{\left(d x\right)^{\frac{9}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**(9/2)/((a + b*x**2)**2)**(5/2), x)","F",0
777,0,0,0,0.000000," ","integrate((d*x)**(7/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{\left(d x\right)^{\frac{7}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**(7/2)/((a + b*x**2)**2)**(5/2), x)","F",0
778,0,0,0,0.000000," ","integrate((d*x)**(5/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{\left(d x\right)^{\frac{5}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**(5/2)/((a + b*x**2)**2)**(5/2), x)","F",0
779,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**(3/2)/((a + b*x**2)**2)**(5/2), x)","F",0
780,-1,0,0,0.000000," ","integrate((d*x)**(1/2)/(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",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)","\int \frac{1}{\sqrt{d x} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*((a + b*x**2)**2)**(5/2)), 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)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*((a + b*x**2)**2)**(5/2)), 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)","\int \frac{1}{\left(d x\right)^{\frac{5}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d*x)**(5/2)*((a + b*x**2)**2)**(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)","\int \frac{1}{\left(d x\right)^{\frac{7}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((d*x)**(7/2)*((a + b*x**2)**2)**(5/2)), x)","F",0
785,1,3188,0,7.605351," ","integrate((d*x)**m*(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\begin{cases} \frac{- \frac{a^{6}}{12 x^{12}} - \frac{3 a^{5} b}{5 x^{10}} - \frac{15 a^{4} b^{2}}{8 x^{8}} - \frac{10 a^{3} b^{3}}{3 x^{6}} - \frac{15 a^{2} b^{4}}{4 x^{4}} - \frac{3 a b^{5}}{x^{2}} + b^{6} \log{\left(x \right)}}{d^{13}} & \text{for}\: m = -13 \\\frac{- \frac{a^{6}}{10 x^{10}} - \frac{3 a^{5} b}{4 x^{8}} - \frac{5 a^{4} b^{2}}{2 x^{6}} - \frac{5 a^{3} b^{3}}{x^{4}} - \frac{15 a^{2} b^{4}}{2 x^{2}} + 6 a b^{5} \log{\left(x \right)} + \frac{b^{6} x^{2}}{2}}{d^{11}} & \text{for}\: m = -11 \\\frac{- \frac{a^{6}}{8 x^{8}} - \frac{a^{5} b}{x^{6}} - \frac{15 a^{4} b^{2}}{4 x^{4}} - \frac{10 a^{3} b^{3}}{x^{2}} + 15 a^{2} b^{4} \log{\left(x \right)} + 3 a b^{5} x^{2} + \frac{b^{6} x^{4}}{4}}{d^{9}} & \text{for}\: m = -9 \\\frac{- \frac{a^{6}}{6 x^{6}} - \frac{3 a^{5} b}{2 x^{4}} - \frac{15 a^{4} b^{2}}{2 x^{2}} + 20 a^{3} b^{3} \log{\left(x \right)} + \frac{15 a^{2} b^{4} x^{2}}{2} + \frac{3 a b^{5} x^{4}}{2} + \frac{b^{6} x^{6}}{6}}{d^{7}} & \text{for}\: m = -7 \\\frac{- \frac{a^{6}}{4 x^{4}} - \frac{3 a^{5} b}{x^{2}} + 15 a^{4} b^{2} \log{\left(x \right)} + 10 a^{3} b^{3} x^{2} + \frac{15 a^{2} b^{4} x^{4}}{4} + a b^{5} x^{6} + \frac{b^{6} x^{8}}{8}}{d^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a^{6}}{2 x^{2}} + 6 a^{5} b \log{\left(x \right)} + \frac{15 a^{4} b^{2} x^{2}}{2} + 5 a^{3} b^{3} x^{4} + \frac{5 a^{2} b^{4} x^{6}}{2} + \frac{3 a b^{5} x^{8}}{4} + \frac{b^{6} x^{10}}{10}}{d^{3}} & \text{for}\: m = -3 \\\frac{a^{6} \log{\left(x \right)} + 3 a^{5} b x^{2} + \frac{15 a^{4} b^{2} x^{4}}{4} + \frac{10 a^{3} b^{3} x^{6}}{3} + \frac{15 a^{2} b^{4} x^{8}}{8} + \frac{3 a b^{5} x^{10}}{5} + \frac{b^{6} x^{12}}{12}}{d} & \text{for}\: m = -1 \\\frac{a^{6} d^{m} m^{6} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{48 a^{6} d^{m} m^{5} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{925 a^{6} d^{m} m^{4} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{9120 a^{6} d^{m} m^{3} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{48259 a^{6} d^{m} m^{2} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{129072 a^{6} d^{m} m x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{135135 a^{6} d^{m} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{6 a^{5} b d^{m} m^{6} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{276 a^{5} b d^{m} m^{5} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{5010 a^{5} b d^{m} m^{4} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{45240 a^{5} b d^{m} m^{3} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{208554 a^{5} b d^{m} m^{2} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{438324 a^{5} b d^{m} m x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{270270 a^{5} b d^{m} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{15 a^{4} b^{2} d^{m} m^{6} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{660 a^{4} b^{2} d^{m} m^{5} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{11295 a^{4} b^{2} d^{m} m^{4} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{94200 a^{4} b^{2} d^{m} m^{3} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{389685 a^{4} b^{2} d^{m} m^{2} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{711540 a^{4} b^{2} d^{m} m x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{405405 a^{4} b^{2} d^{m} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{20 a^{3} b^{3} d^{m} m^{6} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{840 a^{3} b^{3} d^{m} m^{5} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{13580 a^{3} b^{3} d^{m} m^{4} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{105840 a^{3} b^{3} d^{m} m^{3} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{406700 a^{3} b^{3} d^{m} m^{2} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{699720 a^{3} b^{3} d^{m} m x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{386100 a^{3} b^{3} d^{m} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{15 a^{2} b^{4} d^{m} m^{6} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{600 a^{2} b^{4} d^{m} m^{5} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{9195 a^{2} b^{4} d^{m} m^{4} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{67920 a^{2} b^{4} d^{m} m^{3} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{249405 a^{2} b^{4} d^{m} m^{2} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{415320 a^{2} b^{4} d^{m} m x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{225225 a^{2} b^{4} d^{m} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{6 a b^{5} d^{m} m^{6} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{228 a b^{5} d^{m} m^{5} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3330 a b^{5} d^{m} m^{4} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{23640 a b^{5} d^{m} m^{3} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{84234 a b^{5} d^{m} m^{2} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{137412 a b^{5} d^{m} m x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{73710 a b^{5} d^{m} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{b^{6} d^{m} m^{6} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{36 b^{6} d^{m} m^{5} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{505 b^{6} d^{m} m^{4} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3480 b^{6} d^{m} m^{3} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{12139 b^{6} d^{m} m^{2} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{19524 b^{6} d^{m} m x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{10395 b^{6} d^{m} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**6/(12*x**12) - 3*a**5*b/(5*x**10) - 15*a**4*b**2/(8*x**8) - 10*a**3*b**3/(3*x**6) - 15*a**2*b**4/(4*x**4) - 3*a*b**5/x**2 + b**6*log(x))/d**13, Eq(m, -13)), ((-a**6/(10*x**10) - 3*a**5*b/(4*x**8) - 5*a**4*b**2/(2*x**6) - 5*a**3*b**3/x**4 - 15*a**2*b**4/(2*x**2) + 6*a*b**5*log(x) + b**6*x**2/2)/d**11, Eq(m, -11)), ((-a**6/(8*x**8) - a**5*b/x**6 - 15*a**4*b**2/(4*x**4) - 10*a**3*b**3/x**2 + 15*a**2*b**4*log(x) + 3*a*b**5*x**2 + b**6*x**4/4)/d**9, Eq(m, -9)), ((-a**6/(6*x**6) - 3*a**5*b/(2*x**4) - 15*a**4*b**2/(2*x**2) + 20*a**3*b**3*log(x) + 15*a**2*b**4*x**2/2 + 3*a*b**5*x**4/2 + b**6*x**6/6)/d**7, Eq(m, -7)), ((-a**6/(4*x**4) - 3*a**5*b/x**2 + 15*a**4*b**2*log(x) + 10*a**3*b**3*x**2 + 15*a**2*b**4*x**4/4 + a*b**5*x**6 + b**6*x**8/8)/d**5, Eq(m, -5)), ((-a**6/(2*x**2) + 6*a**5*b*log(x) + 15*a**4*b**2*x**2/2 + 5*a**3*b**3*x**4 + 5*a**2*b**4*x**6/2 + 3*a*b**5*x**8/4 + b**6*x**10/10)/d**3, Eq(m, -3)), ((a**6*log(x) + 3*a**5*b*x**2 + 15*a**4*b**2*x**4/4 + 10*a**3*b**3*x**6/3 + 15*a**2*b**4*x**8/8 + 3*a*b**5*x**10/5 + b**6*x**12/12)/d, Eq(m, -1)), (a**6*d**m*m**6*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 48*a**6*d**m*m**5*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 925*a**6*d**m*m**4*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 9120*a**6*d**m*m**3*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 48259*a**6*d**m*m**2*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 129072*a**6*d**m*m*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 135135*a**6*d**m*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 6*a**5*b*d**m*m**6*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 276*a**5*b*d**m*m**5*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 5010*a**5*b*d**m*m**4*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 45240*a**5*b*d**m*m**3*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 208554*a**5*b*d**m*m**2*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 438324*a**5*b*d**m*m*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 270270*a**5*b*d**m*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 15*a**4*b**2*d**m*m**6*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 660*a**4*b**2*d**m*m**5*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 11295*a**4*b**2*d**m*m**4*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 94200*a**4*b**2*d**m*m**3*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 389685*a**4*b**2*d**m*m**2*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 711540*a**4*b**2*d**m*m*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 405405*a**4*b**2*d**m*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 20*a**3*b**3*d**m*m**6*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 840*a**3*b**3*d**m*m**5*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 13580*a**3*b**3*d**m*m**4*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 105840*a**3*b**3*d**m*m**3*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 406700*a**3*b**3*d**m*m**2*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 699720*a**3*b**3*d**m*m*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 386100*a**3*b**3*d**m*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 15*a**2*b**4*d**m*m**6*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 600*a**2*b**4*d**m*m**5*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 9195*a**2*b**4*d**m*m**4*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 67920*a**2*b**4*d**m*m**3*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 249405*a**2*b**4*d**m*m**2*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 415320*a**2*b**4*d**m*m*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 225225*a**2*b**4*d**m*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 6*a*b**5*d**m*m**6*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 228*a*b**5*d**m*m**5*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3330*a*b**5*d**m*m**4*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 23640*a*b**5*d**m*m**3*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 84234*a*b**5*d**m*m**2*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 137412*a*b**5*d**m*m*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 73710*a*b**5*d**m*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + b**6*d**m*m**6*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 36*b**6*d**m*m**5*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 505*b**6*d**m*m**4*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3480*b**6*d**m*m**3*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 12139*b**6*d**m*m**2*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 19524*b**6*d**m*m*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 10395*b**6*d**m*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135), True))","A",0
786,1,1321,0,3.199953," ","integrate((d*x)**m*(b**2*x**4+2*a*b*x**2+a**2)**2,x)","\begin{cases} \frac{- \frac{a^{4}}{8 x^{8}} - \frac{2 a^{3} b}{3 x^{6}} - \frac{3 a^{2} b^{2}}{2 x^{4}} - \frac{2 a b^{3}}{x^{2}} + b^{4} \log{\left(x \right)}}{d^{9}} & \text{for}\: m = -9 \\\frac{- \frac{a^{4}}{6 x^{6}} - \frac{a^{3} b}{x^{4}} - \frac{3 a^{2} b^{2}}{x^{2}} + 4 a b^{3} \log{\left(x \right)} + \frac{b^{4} x^{2}}{2}}{d^{7}} & \text{for}\: m = -7 \\\frac{- \frac{a^{4}}{4 x^{4}} - \frac{2 a^{3} b}{x^{2}} + 6 a^{2} b^{2} \log{\left(x \right)} + 2 a b^{3} x^{2} + \frac{b^{4} x^{4}}{4}}{d^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a^{4}}{2 x^{2}} + 4 a^{3} b \log{\left(x \right)} + 3 a^{2} b^{2} x^{2} + a b^{3} x^{4} + \frac{b^{4} x^{6}}{6}}{d^{3}} & \text{for}\: m = -3 \\\frac{a^{4} \log{\left(x \right)} + 2 a^{3} b x^{2} + \frac{3 a^{2} b^{2} x^{4}}{2} + \frac{2 a b^{3} x^{6}}{3} + \frac{b^{4} x^{8}}{8}}{d} & \text{for}\: m = -1 \\\frac{a^{4} d^{m} m^{4} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{24 a^{4} d^{m} m^{3} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{206 a^{4} d^{m} m^{2} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{744 a^{4} d^{m} m x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{945 a^{4} d^{m} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{4 a^{3} b d^{m} m^{4} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{88 a^{3} b d^{m} m^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{656 a^{3} b d^{m} m^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1832 a^{3} b d^{m} m x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1260 a^{3} b d^{m} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{6 a^{2} b^{2} d^{m} m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{120 a^{2} b^{2} d^{m} m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{780 a^{2} b^{2} d^{m} m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1800 a^{2} b^{2} d^{m} m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1134 a^{2} b^{2} d^{m} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{4 a b^{3} d^{m} m^{4} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{72 a b^{3} d^{m} m^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{416 a b^{3} d^{m} m^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{888 a b^{3} d^{m} m x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{540 a b^{3} d^{m} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{b^{4} d^{m} m^{4} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{16 b^{4} d^{m} m^{3} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{86 b^{4} d^{m} m^{2} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{176 b^{4} d^{m} m x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{105 b^{4} d^{m} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**4/(8*x**8) - 2*a**3*b/(3*x**6) - 3*a**2*b**2/(2*x**4) - 2*a*b**3/x**2 + b**4*log(x))/d**9, Eq(m, -9)), ((-a**4/(6*x**6) - a**3*b/x**4 - 3*a**2*b**2/x**2 + 4*a*b**3*log(x) + b**4*x**2/2)/d**7, Eq(m, -7)), ((-a**4/(4*x**4) - 2*a**3*b/x**2 + 6*a**2*b**2*log(x) + 2*a*b**3*x**2 + b**4*x**4/4)/d**5, Eq(m, -5)), ((-a**4/(2*x**2) + 4*a**3*b*log(x) + 3*a**2*b**2*x**2 + a*b**3*x**4 + b**4*x**6/6)/d**3, Eq(m, -3)), ((a**4*log(x) + 2*a**3*b*x**2 + 3*a**2*b**2*x**4/2 + 2*a*b**3*x**6/3 + b**4*x**8/8)/d, Eq(m, -1)), (a**4*d**m*m**4*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 24*a**4*d**m*m**3*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 206*a**4*d**m*m**2*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 744*a**4*d**m*m*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 945*a**4*d**m*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 4*a**3*b*d**m*m**4*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 88*a**3*b*d**m*m**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 656*a**3*b*d**m*m**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1832*a**3*b*d**m*m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1260*a**3*b*d**m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 6*a**2*b**2*d**m*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 120*a**2*b**2*d**m*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 780*a**2*b**2*d**m*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1800*a**2*b**2*d**m*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1134*a**2*b**2*d**m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 4*a*b**3*d**m*m**4*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 72*a*b**3*d**m*m**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 416*a*b**3*d**m*m**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 888*a*b**3*d**m*m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 540*a*b**3*d**m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + b**4*d**m*m**4*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 16*b**4*d**m*m**3*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 86*b**4*d**m*m**2*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 176*b**4*d**m*m*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 105*b**4*d**m*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945), True))","A",0
787,1,345,0,1.007391," ","integrate((d*x)**m*(b**2*x**4+2*a*b*x**2+a**2),x)","\begin{cases} \frac{- \frac{a^{2}}{4 x^{4}} - \frac{a b}{x^{2}} + b^{2} \log{\left(x \right)}}{d^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + \frac{b^{2} x^{2}}{2}}{d^{3}} & \text{for}\: m = -3 \\\frac{a^{2} \log{\left(x \right)} + a b x^{2} + \frac{b^{2} x^{4}}{4}}{d} & \text{for}\: m = -1 \\\frac{a^{2} d^{m} m^{2} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{8 a^{2} d^{m} m x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{15 a^{2} d^{m} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{2 a b d^{m} m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{12 a b d^{m} m x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{10 a b d^{m} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{b^{2} d^{m} m^{2} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{4 b^{2} d^{m} m x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{3 b^{2} d^{m} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**2/(4*x**4) - a*b/x**2 + b**2*log(x))/d**5, Eq(m, -5)), ((-a**2/(2*x**2) + 2*a*b*log(x) + b**2*x**2/2)/d**3, Eq(m, -3)), ((a**2*log(x) + a*b*x**2 + b**2*x**4/4)/d, Eq(m, -1)), (a**2*d**m*m**2*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 8*a**2*d**m*m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 15*a**2*d**m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 2*a*b*d**m*m**2*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 12*a*b*d**m*m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 10*a*b*d**m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + b**2*d**m*m**2*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 4*b**2*d**m*m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 3*b**2*d**m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15), True))","A",0
788,0,0,0,0.000000," ","integrate((d*x)**m/(b**2*x**4+2*a*b*x**2+a**2),x)","\int \frac{\left(d x\right)^{m}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((d*x)**m/(a + b*x**2)**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)","\int \frac{\left(d x\right)^{m}}{\left(a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((d*x)**m/(a + b*x**2)**4, x)","F",0
790,-1,0,0,0.000000," ","integrate((d*x)**m/(b**2*x**4+2*a*b*x**2+a**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
791,0,0,0,0.000000," ","integrate((d*x)**m*(b**2*x**4+2*a*b*x**2+a**2)**(5/2),x)","\int \left(d x\right)^{m} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((d*x)**m*((a + b*x**2)**2)**(5/2), x)","F",0
792,0,0,0,0.000000," ","integrate((d*x)**m*(b**2*x**4+2*a*b*x**2+a**2)**(3/2),x)","\int \left(d x\right)^{m} \left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**m*((a + b*x**2)**2)**(3/2), x)","F",0
793,0,0,0,0.000000," ","integrate((d*x)**m*(b**2*x**4+2*a*b*x**2+a**2)**(1/2),x)","\int \left(d x\right)^{m} \sqrt{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((d*x)**m*sqrt((a + b*x**2)**2), x)","F",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)","\int \frac{\left(d x\right)^{m}}{\sqrt{\left(a + b x^{2}\right)^{2}}}\, dx"," ",0,"Integral((d*x)**m/sqrt((a + b*x**2)**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)","\int \frac{\left(d x\right)^{m}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m/((a + b*x**2)**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)","\int \frac{\left(d x\right)^{m}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**m/((a + b*x**2)**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)","\int \left(d x\right)^{m} \left(\left(a + b x^{2}\right)^{2}\right)^{p}\, dx"," ",0,"Integral((d*x)**m*((a + b*x**2)**2)**p, x)","F",0
798,0,0,0,0.000000," ","integrate(x**7*(b**2*x**4+2*a*b*x**2+a**2)**p,x)","\begin{cases} \frac{x^{8} \left(a^{2}\right)^{p}}{8} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{11 a^{3}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{27 a^{2} b x^{2}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} & \text{for}\: p = -2 \\\int \frac{x^{7}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} - \frac{3 a b^{2} x^{4}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{b^{3} x^{6}}{4 a b^{4} + 4 b^{5} x^{2}} & \text{for}\: p = -1 \\\int \frac{x^{7}}{\sqrt{\left(a + b x^{2}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\- \frac{3 a^{4} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{6 a^{3} b p x^{2} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} - \frac{6 a^{2} b^{2} p^{2} x^{4} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} - \frac{3 a^{2} b^{2} p x^{4} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{4 a b^{3} p^{3} x^{6} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{6 a b^{3} p^{2} x^{6} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{2 a b^{3} p x^{6} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{4 b^{4} p^{3} x^{8} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{12 b^{4} p^{2} x^{8} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{11 b^{4} p x^{8} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} + \frac{3 b^{4} x^{8} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{16 b^{4} p^{4} + 80 b^{4} p^{3} + 140 b^{4} p^{2} + 100 b^{4} p + 24 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**8*(a**2)**p/8, Eq(b, 0)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 11*a**3/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 27*a**2*b*x**2/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6), Eq(p, -2)), (Integral(x**7/((a + b*x**2)**2)**(3/2), x), Eq(p, -3/2)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) - 3*a*b**2*x**4/(4*a*b**4 + 4*b**5*x**2) + b**3*x**6/(4*a*b**4 + 4*b**5*x**2), Eq(p, -1)), (Integral(x**7/sqrt((a + b*x**2)**2), x), Eq(p, -1/2)), (-3*a**4*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 6*a**3*b*p*x**2*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) - 6*a**2*b**2*p**2*x**4*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) - 3*a**2*b**2*p*x**4*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 4*a*b**3*p**3*x**6*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 6*a*b**3*p**2*x**6*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 2*a*b**3*p*x**6*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 4*b**4*p**3*x**8*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 12*b**4*p**2*x**8*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 11*b**4*p*x**8*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4) + 3*b**4*x**8*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(16*b**4*p**4 + 80*b**4*p**3 + 140*b**4*p**2 + 100*b**4*p + 24*b**4), True))","F",0
799,0,0,0,0.000000," ","integrate(x**5*(b**2*x**4+2*a*b*x**2+a**2)**p,x)","\begin{cases} \frac{x^{6} \left(a^{2}\right)^{p}}{6} & \text{for}\: b = 0 \\\int \frac{x^{5}}{\left(\left(a + b x^{2}\right)^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: p = - \frac{3}{2} \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -1 \\\int \frac{x^{5}}{\sqrt{\left(a + b x^{2}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a^{3} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{3} p^{3} + 24 b^{3} p^{2} + 22 b^{3} p + 6 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{3} p^{3} + 24 b^{3} p^{2} + 22 b^{3} p + 6 b^{3}} + \frac{2 a b^{2} p^{2} x^{4} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{3} p^{3} + 24 b^{3} p^{2} + 22 b^{3} p + 6 b^{3}} + \frac{a b^{2} p x^{4} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{3} p^{3} + 24 b^{3} p^{2} + 22 b^{3} p + 6 b^{3}} + \frac{2 b^{3} p^{2} x^{6} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{3} p^{3} + 24 b^{3} p^{2} + 22 b^{3} p + 6 b^{3}} + \frac{3 b^{3} p x^{6} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{3} p^{3} + 24 b^{3} p^{2} + 22 b^{3} p + 6 b^{3}} + \frac{b^{3} x^{6} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{3} p^{3} + 24 b^{3} p^{2} + 22 b^{3} p + 6 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**6*(a**2)**p/6, Eq(b, 0)), (Integral(x**5/((a + b*x**2)**2)**(3/2), x), Eq(p, -3/2)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -1)), (Integral(x**5/sqrt((a + b*x**2)**2), x), Eq(p, -1/2)), (a**3*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**3*p**3 + 24*b**3*p**2 + 22*b**3*p + 6*b**3) - 2*a**2*b*p*x**2*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**3*p**3 + 24*b**3*p**2 + 22*b**3*p + 6*b**3) + 2*a*b**2*p**2*x**4*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**3*p**3 + 24*b**3*p**2 + 22*b**3*p + 6*b**3) + a*b**2*p*x**4*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**3*p**3 + 24*b**3*p**2 + 22*b**3*p + 6*b**3) + 2*b**3*p**2*x**6*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**3*p**3 + 24*b**3*p**2 + 22*b**3*p + 6*b**3) + 3*b**3*p*x**6*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**3*p**3 + 24*b**3*p**2 + 22*b**3*p + 6*b**3) + b**3*x**6*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**3*p**3 + 24*b**3*p**2 + 22*b**3*p + 6*b**3), True))","F",0
800,0,0,0,0.000000," ","integrate(x**3*(b**2*x**4+2*a*b*x**2+a**2)**p,x)","\begin{cases} \frac{x^{4} \left(a^{2}\right)^{p}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -1 \\\int \frac{x^{3}}{\sqrt{\left(a + b x^{2}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\- \frac{a^{2} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{2} p^{2} + 12 b^{2} p + 4 b^{2}} + \frac{2 a b p x^{2} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{2} p^{2} + 12 b^{2} p + 4 b^{2}} + \frac{2 b^{2} p x^{4} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{2} p^{2} + 12 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{8 b^{2} p^{2} + 12 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4*(a**2)**p/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -1)), (Integral(x**3/sqrt((a + b*x**2)**2), x), Eq(p, -1/2)), (-a**2*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**2*p**2 + 12*b**2*p + 4*b**2) + 2*a*b*p*x**2*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**2*p**2 + 12*b**2*p + 4*b**2) + 2*b**2*p*x**4*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**2*p**2 + 12*b**2*p + 4*b**2) + b**2*x**4*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(8*b**2*p**2 + 12*b**2*p + 4*b**2), True))","F",0
801,0,0,0,0.000000," ","integrate(x*(b**2*x**4+2*a*b*x**2+a**2)**p,x)","\begin{cases} \frac{x^{2}}{2 \sqrt{a^{2}}} & \text{for}\: b = 0 \wedge p = - \frac{1}{2} \\\frac{x^{2} \left(a^{2}\right)^{p}}{2} & \text{for}\: b = 0 \\\int \frac{x}{\sqrt{\left(a + b x^{2}\right)^{2}}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{4 b p + 2 b} + \frac{b x^{2} \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}}{4 b p + 2 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2/(2*sqrt(a**2)), Eq(b, 0) & Eq(p, -1/2)), (x**2*(a**2)**p/2, Eq(b, 0)), (Integral(x/sqrt((a + b*x**2)**2), x), Eq(p, -1/2)), (a*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(4*b*p + 2*b) + b*x**2*(a**2 + 2*a*b*x**2 + b**2*x**4)**p/(4*b*p + 2*b), True))","F",0
802,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**p/x,x)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{p}}{x}\, dx"," ",0,"Integral(((a + b*x**2)**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)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral(((a + b*x**2)**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)","\int x^{4} \left(\left(a + b x^{2}\right)^{2}\right)^{p}\, dx"," ",0,"Integral(x**4*((a + b*x**2)**2)**p, 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)","\int x^{2} \left(\left(a + b x^{2}\right)^{2}\right)^{p}\, dx"," ",0,"Integral(x**2*((a + b*x**2)**2)**p, x)","F",0
806,0,0,0,0.000000," ","integrate((b**2*x**4+2*a*b*x**2+a**2)**p,x)","\int \left(a^{2} + 2 a b x^{2} + b^{2} x^{4}\right)^{p}\, dx"," ",0,"Integral((a**2 + 2*a*b*x**2 + b**2*x**4)**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)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral(((a + b*x**2)**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)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{p}}{x^{4}}\, dx"," ",0,"Integral(((a + b*x**2)**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)","\int \left(d x\right)^{\frac{3}{2}} \left(\left(a + b x^{2}\right)^{2}\right)^{p}\, dx"," ",0,"Integral((d*x)**(3/2)*((a + b*x**2)**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)","\int \sqrt{d x} \left(\left(a + b x^{2}\right)^{2}\right)^{p}\, dx"," ",0,"Integral(sqrt(d*x)*((a + b*x**2)**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)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{p}}{\sqrt{d x}}\, dx"," ",0,"Integral(((a + b*x**2)**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)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{p}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**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)","\int \frac{\left(\left(a + b x^{2}\right)^{2}\right)^{p}}{\left(d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(((a + b*x**2)**2)**p/(d*x)**(5/2), x)","F",0
814,1,19,0,0.067762," ","integrate(x**2*(c*x**4+b*x**2+a),x)","\frac{a x^{3}}{3} + \frac{b x^{5}}{5} + \frac{c x^{7}}{7}"," ",0,"a*x**3/3 + b*x**5/5 + c*x**7/7","A",0
815,1,19,0,0.066820," ","integrate(x*(c*x**4+b*x**2+a),x)","\frac{a x^{2}}{2} + \frac{b x^{4}}{4} + \frac{c x^{6}}{6}"," ",0,"a*x**2/2 + b*x**4/4 + c*x**6/6","A",0
816,1,15,0,0.064187," ","integrate(c*x**4+b*x**2+a,x)","a x + \frac{b x^{3}}{3} + \frac{c x^{5}}{5}"," ",0,"a*x + b*x**3/3 + c*x**5/5","A",0
817,1,17,0,0.098341," ","integrate((c*x**4+b*x**2+a)/x,x)","a \log{\left(x \right)} + \frac{b x^{2}}{2} + \frac{c x^{4}}{4}"," ",0,"a*log(x) + b*x**2/2 + c*x**4/4","A",0
818,1,12,0,0.098920," ","integrate((c*x**4+b*x**2+a)/x**2,x)","- \frac{a}{x} + b x + \frac{c x^{3}}{3}"," ",0,"-a/x + b*x + c*x**3/3","A",0
819,1,17,0,0.125888," ","integrate((c*x**4+b*x**2+a)/x**3,x)","- \frac{a}{2 x^{2}} + b \log{\left(x \right)} + \frac{c x^{2}}{2}"," ",0,"-a/(2*x**2) + b*log(x) + c*x**2/2","A",0
820,1,17,0,0.133059," ","integrate((c*x**4+b*x**2+a)/x**4,x)","c x + \frac{- a - 3 b x^{2}}{3 x^{3}}"," ",0,"c*x + (-a - 3*b*x**2)/(3*x**3)","A",0
821,1,19,0,0.237173," ","integrate((c*x**4+b*x**2+a)/x**5,x)","c \log{\left(x \right)} + \frac{- a - 2 b x^{2}}{4 x^{4}}"," ",0,"c*log(x) + (-a - 2*b*x**2)/(4*x**4)","A",0
822,1,22,0,0.255768," ","integrate((c*x**4+b*x**2+a)/x**6,x)","\frac{- 3 a - 5 b x^{2} - 15 c x^{4}}{15 x^{5}}"," ",0,"(-3*a - 5*b*x**2 - 15*c*x**4)/(15*x**5)","A",0
823,1,22,0,0.340092," ","integrate((c*x**4+b*x**2+a)/x**7,x)","\frac{- 2 a - 3 b x^{2} - 6 c x^{4}}{12 x^{6}}"," ",0,"(-2*a - 3*b*x**2 - 6*c*x**4)/(12*x**6)","A",0
824,1,22,0,0.322378," ","integrate((c*x**4+b*x**2+a)/x**8,x)","\frac{- 15 a - 21 b x^{2} - 35 c x^{4}}{105 x^{7}}"," ",0,"(-15*a - 21*b*x**2 - 35*c*x**4)/(105*x**7)","A",0
825,1,51,0,0.078334," ","integrate(x**2*(c*x**4+b*x**2+a)**2,x)","\frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{2 b c x^{9}}{9} + \frac{c^{2} x^{11}}{11} + x^{7} \left(\frac{2 a c}{7} + \frac{b^{2}}{7}\right)"," ",0,"a**2*x**3/3 + 2*a*b*x**5/5 + 2*b*c*x**9/9 + c**2*x**11/11 + x**7*(2*a*c/7 + b**2/7)","A",0
826,1,46,0,0.079555," ","integrate(x*(c*x**4+b*x**2+a)**2,x)","\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b c x^{8}}{4} + \frac{c^{2} x^{10}}{10} + x^{6} \left(\frac{a c}{3} + \frac{b^{2}}{6}\right)"," ",0,"a**2*x**2/2 + a*b*x**4/2 + b*c*x**8/4 + c**2*x**10/10 + x**6*(a*c/3 + b**2/6)","A",0
827,1,48,0,0.076364," ","integrate((c*x**4+b*x**2+a)**2,x)","a^{2} x + \frac{2 a b x^{3}}{3} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} + x^{5} \left(\frac{2 a c}{5} + \frac{b^{2}}{5}\right)"," ",0,"a**2*x + 2*a*b*x**3/3 + 2*b*c*x**7/7 + c**2*x**9/9 + x**5*(2*a*c/5 + b**2/5)","A",0
828,1,42,0,0.143174," ","integrate((c*x**4+b*x**2+a)**2/x,x)","a^{2} \log{\left(x \right)} + a b x^{2} + \frac{b c x^{6}}{3} + \frac{c^{2} x^{8}}{8} + x^{4} \left(\frac{a c}{2} + \frac{b^{2}}{4}\right)"," ",0,"a**2*log(x) + a*b*x**2 + b*c*x**6/3 + c**2*x**8/8 + x**4*(a*c/2 + b**2/4)","A",0
829,1,44,0,0.135718," ","integrate((c*x**4+b*x**2+a)**2/x**2,x)","- \frac{a^{2}}{x} + 2 a b x + \frac{2 b c x^{5}}{5} + \frac{c^{2} x^{7}}{7} + x^{3} \left(\frac{2 a c}{3} + \frac{b^{2}}{3}\right)"," ",0,"-a**2/x + 2*a*b*x + 2*b*c*x**5/5 + c**2*x**7/7 + x**3*(2*a*c/3 + b**2/3)","A",0
830,1,44,0,0.168705," ","integrate((c*x**4+b*x**2+a)**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{6}}{6} + x^{2} \left(a c + \frac{b^{2}}{2}\right)"," ",0,"-a**2/(2*x**2) + 2*a*b*log(x) + b*c*x**4/2 + c**2*x**6/6 + x**2*(a*c + b**2/2)","A",0
831,1,46,0,0.180097," ","integrate((c*x**4+b*x**2+a)**2/x**4,x)","\frac{2 b c x^{3}}{3} + \frac{c^{2} x^{5}}{5} + x \left(2 a c + b^{2}\right) + \frac{- a^{2} - 6 a b x^{2}}{3 x^{3}}"," ",0,"2*b*c*x**3/3 + c**2*x**5/5 + x*(2*a*c + b**2) + (-a**2 - 6*a*b*x**2)/(3*x**3)","A",0
832,1,44,0,0.373638," ","integrate((c*x**4+b*x**2+a)**2/x**5,x)","b c x^{2} + \frac{c^{2} x^{4}}{4} + \left(2 a c + b^{2}\right) \log{\left(x \right)} + \frac{- a^{2} - 4 a b x^{2}}{4 x^{4}}"," ",0,"b*c*x**2 + c**2*x**4/4 + (2*a*c + b**2)*log(x) + (-a**2 - 4*a*b*x**2)/(4*x**4)","A",0
833,1,48,0,0.427867," ","integrate((c*x**4+b*x**2+a)**2/x**6,x)","2 b c x + \frac{c^{2} x^{3}}{3} + \frac{- 3 a^{2} - 10 a b x^{2} + x^{4} \left(- 30 a c - 15 b^{2}\right)}{15 x^{5}}"," ",0,"2*b*c*x + c**2*x**3/3 + (-3*a**2 - 10*a*b*x**2 + x**4*(-30*a*c - 15*b**2))/(15*x**5)","A",0
834,1,48,0,0.776227," ","integrate((c*x**4+b*x**2+a)**2/x**7,x)","2 b c \log{\left(x \right)} + \frac{c^{2} x^{2}}{2} + \frac{- a^{2} - 3 a b x^{2} + x^{4} \left(- 6 a c - 3 b^{2}\right)}{6 x^{6}}"," ",0,"2*b*c*log(x) + c**2*x**2/2 + (-a**2 - 3*a*b*x**2 + x**4*(-6*a*c - 3*b**2))/(6*x**6)","A",0
835,1,46,0,0.759414," ","integrate((c*x**4+b*x**2+a)**2/x**8,x)","c^{2} x + \frac{- 15 a^{2} - 42 a b x^{2} - 210 b c x^{6} + x^{4} \left(- 70 a c - 35 b^{2}\right)}{105 x^{7}}"," ",0,"c**2*x + (-15*a**2 - 42*a*b*x**2 - 210*b*c*x**6 + x**4*(-70*a*c - 35*b**2))/(105*x**7)","A",0
836,1,48,0,1.306948," ","integrate((c*x**4+b*x**2+a)**2/x**9,x)","c^{2} \log{\left(x \right)} + \frac{- 3 a^{2} - 8 a b x^{2} - 24 b c x^{6} + x^{4} \left(- 12 a c - 6 b^{2}\right)}{24 x^{8}}"," ",0,"c**2*log(x) + (-3*a**2 - 8*a*b*x**2 - 24*b*c*x**6 + x**4*(-12*a*c - 6*b**2))/(24*x**8)","A",0
837,1,49,0,1.474161," ","integrate((c*x**4+b*x**2+a)**2/x**10,x)","\frac{- 35 a^{2} - 90 a b x^{2} - 210 b c x^{6} - 315 c^{2} x^{8} + x^{4} \left(- 126 a c - 63 b^{2}\right)}{315 x^{9}}"," ",0,"(-35*a**2 - 90*a*b*x**2 - 210*b*c*x**6 - 315*c**2*x**8 + x**4*(-126*a*c - 63*b**2))/(315*x**9)","A",0
838,1,49,0,2.077564," ","integrate((c*x**4+b*x**2+a)**2/x**11,x)","\frac{- 6 a^{2} - 15 a b x^{2} - 30 b c x^{6} - 30 c^{2} x^{8} + x^{4} \left(- 20 a c - 10 b^{2}\right)}{60 x^{10}}"," ",0,"(-6*a**2 - 15*a*b*x**2 - 30*b*c*x**6 - 30*c**2*x**8 + x**4*(-20*a*c - 10*b**2))/(60*x**10)","A",0
839,1,49,0,1.957564," ","integrate((c*x**4+b*x**2+a)**2/x**12,x)","\frac{- 315 a^{2} - 770 a b x^{2} - 1386 b c x^{6} - 1155 c^{2} x^{8} + x^{4} \left(- 990 a c - 495 b^{2}\right)}{3465 x^{11}}"," ",0,"(-315*a**2 - 770*a*b*x**2 - 1386*b*c*x**6 - 1155*c**2*x**8 + x**4*(-990*a*c - 495*b**2))/(3465*x**11)","A",0
840,1,49,0,2.698200," ","integrate((c*x**4+b*x**2+a)**2/x**13,x)","\frac{- 10 a^{2} - 24 a b x^{2} - 40 b c x^{6} - 30 c^{2} x^{8} + x^{4} \left(- 30 a c - 15 b^{2}\right)}{120 x^{12}}"," ",0,"(-10*a**2 - 24*a*b*x**2 - 40*b*c*x**6 - 30*c**2*x**8 + x**4*(-30*a*c - 15*b**2))/(120*x**12)","A",0
841,1,97,0,0.094092," ","integrate(x**2*(c*x**4+b*x**2+a)**3,x)","\frac{a^{3} x^{3}}{3} + \frac{3 a^{2} b x^{5}}{5} + \frac{3 b c^{2} x^{13}}{13} + \frac{c^{3} x^{15}}{15} + x^{11} \left(\frac{3 a c^{2}}{11} + \frac{3 b^{2} c}{11}\right) + x^{9} \left(\frac{2 a b c}{3} + \frac{b^{3}}{9}\right) + x^{7} \left(\frac{3 a^{2} c}{7} + \frac{3 a b^{2}}{7}\right)"," ",0,"a**3*x**3/3 + 3*a**2*b*x**5/5 + 3*b*c**2*x**13/13 + c**3*x**15/15 + x**11*(3*a*c**2/11 + 3*b**2*c/11) + x**9*(2*a*b*c/3 + b**3/9) + x**7*(3*a**2*c/7 + 3*a*b**2/7)","A",0
842,1,92,0,0.097980," ","integrate(x*(c*x**4+b*x**2+a)**3,x)","\frac{a^{3} x^{2}}{2} + \frac{3 a^{2} b x^{4}}{4} + \frac{b c^{2} x^{12}}{4} + \frac{c^{3} x^{14}}{14} + x^{10} \left(\frac{3 a c^{2}}{10} + \frac{3 b^{2} c}{10}\right) + x^{8} \left(\frac{3 a b c}{4} + \frac{b^{3}}{8}\right) + x^{6} \left(\frac{a^{2} c}{2} + \frac{a b^{2}}{2}\right)"," ",0,"a**3*x**2/2 + 3*a**2*b*x**4/4 + b*c**2*x**12/4 + c**3*x**14/14 + x**10*(3*a*c**2/10 + 3*b**2*c/10) + x**8*(3*a*b*c/4 + b**3/8) + x**6*(a**2*c/2 + a*b**2/2)","A",0
843,1,87,0,0.094441," ","integrate((c*x**4+b*x**2+a)**3,x)","a^{3} x + a^{2} b x^{3} + \frac{3 b c^{2} x^{11}}{11} + \frac{c^{3} x^{13}}{13} + x^{9} \left(\frac{a c^{2}}{3} + \frac{b^{2} c}{3}\right) + x^{7} \left(\frac{6 a b c}{7} + \frac{b^{3}}{7}\right) + x^{5} \left(\frac{3 a^{2} c}{5} + \frac{3 a b^{2}}{5}\right)"," ",0,"a**3*x + a**2*b*x**3 + 3*b*c**2*x**11/11 + c**3*x**13/13 + x**9*(a*c**2/3 + b**2*c/3) + x**7*(6*a*b*c/7 + b**3/7) + x**5*(3*a**2*c/5 + 3*a*b**2/5)","A",0
844,1,92,0,0.221684," ","integrate((c*x**4+b*x**2+a)**3/x,x)","a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 b c^{2} x^{10}}{10} + \frac{c^{3} x^{12}}{12} + x^{8} \left(\frac{3 a c^{2}}{8} + \frac{3 b^{2} c}{8}\right) + x^{6} \left(a b c + \frac{b^{3}}{6}\right) + x^{4} \left(\frac{3 a^{2} c}{4} + \frac{3 a b^{2}}{4}\right)"," ",0,"a**3*log(x) + 3*a**2*b*x**2/2 + 3*b*c**2*x**10/10 + c**3*x**12/12 + x**8*(3*a*c**2/8 + 3*b**2*c/8) + x**6*(a*b*c + b**3/6) + x**4*(3*a**2*c/4 + 3*a*b**2/4)","A",0
845,1,82,0,0.215943," ","integrate((c*x**4+b*x**2+a)**3/x**2,x)","- \frac{a^{3}}{x} + 3 a^{2} b x + \frac{b c^{2} x^{9}}{3} + \frac{c^{3} x^{11}}{11} + x^{7} \left(\frac{3 a c^{2}}{7} + \frac{3 b^{2} c}{7}\right) + x^{5} \left(\frac{6 a b c}{5} + \frac{b^{3}}{5}\right) + x^{3} \left(a^{2} c + a b^{2}\right)"," ",0,"-a**3/x + 3*a**2*b*x + b*c**2*x**9/3 + c**3*x**11/11 + x**7*(3*a*c**2/7 + 3*b**2*c/7) + x**5*(6*a*b*c/5 + b**3/5) + x**3*(a**2*c + a*b**2)","A",0
846,1,92,0,0.266647," ","integrate((c*x**4+b*x**2+a)**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} + 3 a^{2} b \log{\left(x \right)} + \frac{3 b c^{2} x^{8}}{8} + \frac{c^{3} x^{10}}{10} + x^{6} \left(\frac{a c^{2}}{2} + \frac{b^{2} c}{2}\right) + x^{4} \left(\frac{3 a b c}{2} + \frac{b^{3}}{4}\right) + x^{2} \left(\frac{3 a^{2} c}{2} + \frac{3 a b^{2}}{2}\right)"," ",0,"-a**3/(2*x**2) + 3*a**2*b*log(x) + 3*b*c**2*x**8/8 + c**3*x**10/10 + x**6*(a*c**2/2 + b**2*c/2) + x**4*(3*a*b*c/2 + b**3/4) + x**2*(3*a**2*c/2 + 3*a*b**2/2)","A",0
847,1,90,0,0.239187," ","integrate((c*x**4+b*x**2+a)**3/x**4,x)","\frac{3 b c^{2} x^{7}}{7} + \frac{c^{3} x^{9}}{9} + x^{5} \left(\frac{3 a c^{2}}{5} + \frac{3 b^{2} c}{5}\right) + x^{3} \left(2 a b c + \frac{b^{3}}{3}\right) + x \left(3 a^{2} c + 3 a b^{2}\right) + \frac{- a^{3} - 9 a^{2} b x^{2}}{3 x^{3}}"," ",0,"3*b*c**2*x**7/7 + c**3*x**9/9 + x**5*(3*a*c**2/5 + 3*b**2*c/5) + x**3*(2*a*b*c + b**3/3) + x*(3*a**2*c + 3*a*b**2) + (-a**3 - 9*a**2*b*x**2)/(3*x**3)","A",0
848,1,391,0,2.911953," ","integrate(x**7/(c*x**4+b*x**2+a),x)","- \frac{b x^{2}}{2 c^{2}} + \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{4 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{4 c^{3}}\right) \log{\left(x^{2} + \frac{2 a^{2} c - a b^{2} + 8 a c^{3} \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{4 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{4 c^{3}}\right) - 2 b^{2} c^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{4 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{4 c^{3}}\right)}{3 a b c - b^{3}} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{4 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{4 c^{3}}\right) \log{\left(x^{2} + \frac{2 a^{2} c - a b^{2} + 8 a c^{3} \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{4 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{4 c^{3}}\right) - 2 b^{2} c^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}} \left(3 a c - b^{2}\right)}{4 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c - b^{2}}{4 c^{3}}\right)}{3 a b c - b^{3}} \right)} + \frac{x^{4}}{4 c}"," ",0,"-b*x**2/(2*c**2) + (-b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(4*c**3*(4*a*c - b**2)) - (a*c - b**2)/(4*c**3))*log(x**2 + (2*a**2*c - a*b**2 + 8*a*c**3*(-b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(4*c**3*(4*a*c - b**2)) - (a*c - b**2)/(4*c**3)) - 2*b**2*c**2*(-b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(4*c**3*(4*a*c - b**2)) - (a*c - b**2)/(4*c**3)))/(3*a*b*c - b**3)) + (b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(4*c**3*(4*a*c - b**2)) - (a*c - b**2)/(4*c**3))*log(x**2 + (2*a**2*c - a*b**2 + 8*a*c**3*(b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(4*c**3*(4*a*c - b**2)) - (a*c - b**2)/(4*c**3)) - 2*b**2*c**2*(b*sqrt(-4*a*c + b**2)*(3*a*c - b**2)/(4*c**3*(4*a*c - b**2)) - (a*c - b**2)/(4*c**3)))/(3*a*b*c - b**3)) + x**4/(4*c)","B",0
849,1,316,0,2.135289," ","integrate(x**5/(c*x**4+b*x**2+a),x)","\left(- \frac{b}{4 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{- a b - 8 a c^{2} \left(- \frac{b}{4 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) + 2 b^{2} c \left(- \frac{b}{4 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \left(- \frac{b}{4 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{- a b - 8 a c^{2} \left(- \frac{b}{4 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) + 2 b^{2} c \left(- \frac{b}{4 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \frac{x^{2}}{2 c}"," ",0,"(-b/(4*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2)))*log(x**2 + (-a*b - 8*a*c**2*(-b/(4*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))) + 2*b**2*c*(-b/(4*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + (-b/(4*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2)))*log(x**2 + (-a*b - 8*a*c**2*(-b/(4*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))) + 2*b**2*c*(-b/(4*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + x**2/(2*c)","B",0
850,1,223,0,1.032078," ","integrate(x**3/(c*x**4+b*x**2+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) \log{\left(x^{2} + \frac{- 8 a c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) + 2 a + 2 b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right)}{b} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) \log{\left(x^{2} + \frac{- 8 a c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) + 2 a + 2 b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right)}{b} \right)}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c))*log(x**2 + (-8*a*c*(-b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)) + 2*a + 2*b**2*(-b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)))/b) + (b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c))*log(x**2 + (-8*a*c*(b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)) + 2*a + 2*b**2*(b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)))/b)","B",0
851,1,131,0,0.585515," ","integrate(x/(c*x**4+b*x**2+a),x)","- \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{2} + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}}{2} + \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{2} + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} + b}{2 c} \right)}}{2}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(x**2 + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))/2 + sqrt(-1/(4*a*c - b**2))*log(x**2 + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) + b)/(2*c))/2","B",0
852,1,253,0,4.668871," ","integrate(1/x/(c*x**4+b*x**2+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) \log{\left(x^{2} + \frac{- 8 a^{2} c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) + 2 a b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) - 2 a c + b^{2}}{b c} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) \log{\left(x^{2} + \frac{- 8 a^{2} c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) + 2 a b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) - 2 a c + b^{2}}{b c} \right)} + \frac{\log{\left(x \right)}}{a}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a))*log(x**2 + (-8*a**2*c*(-b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) + 2*a*b**2*(-b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) - 2*a*c + b**2)/(b*c)) + (b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a))*log(x**2 + (-8*a**2*c*(b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) + 2*a*b**2*(b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) - 2*a*c + b**2)/(b*c)) + log(x)/a","B",0
853,1,345,0,137.798440," ","integrate(1/x**3/(c*x**4+b*x**2+a),x)","\left(\frac{b}{4 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{- 8 a^{3} c \left(\frac{b}{4 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} \left(\frac{b}{4 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) + 3 a b c - b^{3}}{2 a c^{2} - b^{2} c} \right)} + \left(\frac{b}{4 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{- 8 a^{3} c \left(\frac{b}{4 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} \left(\frac{b}{4 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) + 3 a b c - b^{3}}{2 a c^{2} - b^{2} c} \right)} - \frac{1}{2 a x^{2}} - \frac{b \log{\left(x \right)}}{a^{2}}"," ",0,"(b/(4*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2)))*log(x**2 + (-8*a**3*c*(b/(4*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) + 2*a**2*b**2*(b/(4*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) + 3*a*b*c - b**3)/(2*a*c**2 - b**2*c)) + (b/(4*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2)))*log(x**2 + (-8*a**3*c*(b/(4*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) + 2*a**2*b**2*(b/(4*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) + 3*a*b*c - b**3)/(2*a*c**2 - b**2*c)) - 1/(2*a*x**2) - b*log(x)/a**2","B",0
854,-1,0,0,0.000000," ","integrate(1/x**5/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,1,194,0,5.159836," ","integrate(x**6/(c*x**4+b*x**2+a),x)","- \frac{b x}{c^{2}} + \operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{7} - 128 a b^{2} c^{6} + 16 b^{4} c^{5}\right) + t^{2} \left(- 80 a^{3} b c^{3} + 100 a^{2} b^{3} c^{2} - 36 a b^{5} c + 4 b^{7}\right) + a^{5}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{2} c^{7} + 48 t^{3} a b^{2} c^{6} - 8 t^{3} b^{4} c^{5} + 14 t a^{3} b c^{3} - 28 t a^{2} b^{3} c^{2} + 14 t a b^{5} c - 2 t b^{7}}{a^{4} c^{2} - 3 a^{3} b^{2} c + a^{2} b^{4}} \right)} \right)\right)} + \frac{x^{3}}{3 c}"," ",0,"-b*x/c**2 + RootSum(_t**4*(256*a**2*c**7 - 128*a*b**2*c**6 + 16*b**4*c**5) + _t**2*(-80*a**3*b*c**3 + 100*a**2*b**3*c**2 - 36*a*b**5*c + 4*b**7) + a**5, Lambda(_t, _t*log(x + (-64*_t**3*a**2*c**7 + 48*_t**3*a*b**2*c**6 - 8*_t**3*b**4*c**5 + 14*_t*a**3*b*c**3 - 28*_t*a**2*b**3*c**2 + 14*_t*a*b**5*c - 2*_t*b**7)/(a**4*c**2 - 3*a**3*b**2*c + a**2*b**4)))) + x**3/(3*c)","A",0
856,1,129,0,5.505732," ","integrate(x**4/(c*x**4+b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{5} - 128 a b^{2} c^{4} + 16 b^{4} c^{3}\right) + t^{2} \left(48 a^{2} b c^{2} - 28 a b^{3} c + 4 b^{5}\right) + a^{3}, \left( t \mapsto t \log{\left(x + \frac{32 t^{3} a b c^{4} - 8 t^{3} b^{3} c^{3} - 4 t a^{2} c^{2} + 8 t a b^{2} c - 2 t b^{4}}{a^{2} c - a b^{2}} \right)} \right)\right)} + \frac{x}{c}"," ",0,"RootSum(_t**4*(256*a**2*c**5 - 128*a*b**2*c**4 + 16*b**4*c**3) + _t**2*(48*a**2*b*c**2 - 28*a*b**3*c + 4*b**5) + a**3, Lambda(_t, _t*log(x + (32*_t**3*a*b*c**4 - 8*_t**3*b**3*c**3 - 4*_t*a**2*c**2 + 8*_t*a*b**2*c - 2*_t*b**4)/(a**2*c - a*b**2)))) + x/c","A",0
857,1,75,0,2.619706," ","integrate(x**2/(c*x**4+b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{3} - 128 a b^{2} c^{2} + 16 b^{4} c\right) + t^{2} \left(- 16 a b c + 4 b^{3}\right) + a, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} - 16 t^{3} b^{2} c - 2 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2*c**3 - 128*a*b**2*c**2 + 16*b**4*c) + _t**2*(-16*a*b*c + 4*b**3) + a, Lambda(_t, _t*log(64*_t**3*a*c**2 - 16*_t**3*b**2*c - 2*_t*b + x)))","A",0
858,1,87,0,2.840032," ","integrate(1/(c*x**4+b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c^{2} - 128 a^{2} b^{2} c + 16 a b^{4}\right) + t^{2} \left(- 16 a b c + 4 b^{3}\right) + c, \left( t \mapsto t \log{\left(x + \frac{32 t^{3} a^{2} b c - 8 t^{3} a b^{3} + 4 t a c - 2 t b^{2}}{c} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**3*c**2 - 128*a**2*b**2*c + 16*a*b**4) + _t**2*(-16*a*b*c + 4*b**3) + c, Lambda(_t, _t*log(x + (32*_t**3*a**2*b*c - 8*_t**3*a*b**3 + 4*_t*a*c - 2*_t*b**2)/c)))","A",0
859,1,148,0,4.918888," ","integrate(1/x**2/(c*x**4+b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{5} c^{2} - 128 a^{4} b^{2} c + 16 a^{3} b^{4}\right) + t^{2} \left(48 a^{2} b c^{2} - 28 a b^{3} c + 4 b^{5}\right) + c^{3}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{5} c^{2} + 48 t^{3} a^{4} b^{2} c - 8 t^{3} a^{3} b^{4} - 10 t a^{2} b c^{2} + 10 t a b^{3} c - 2 t b^{5}}{a c^{3} - b^{2} c^{2}} \right)} \right)\right)} - \frac{1}{a x}"," ",0,"RootSum(_t**4*(256*a**5*c**2 - 128*a**4*b**2*c + 16*a**3*b**4) + _t**2*(48*a**2*b*c**2 - 28*a*b**3*c + 4*b**5) + c**3, Lambda(_t, _t*log(x + (-64*_t**3*a**5*c**2 + 48*_t**3*a**4*b**2*c - 8*_t**3*a**3*b**4 - 10*_t*a**2*b*c**2 + 10*_t*a*b**3*c - 2*_t*b**5)/(a*c**3 - b**2*c**2)))) - 1/(a*x)","A",0
860,1,211,0,16.671332," ","integrate(1/x**4/(c*x**4+b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{7} c^{2} - 128 a^{6} b^{2} c + 16 a^{5} b^{4}\right) + t^{2} \left(- 80 a^{3} b c^{3} + 100 a^{2} b^{3} c^{2} - 36 a b^{5} c + 4 b^{7}\right) + c^{5}, \left( t \mapsto t \log{\left(x + \frac{- 96 t^{3} a^{7} b c^{2} + 56 t^{3} a^{6} b^{3} c - 8 t^{3} a^{5} b^{5} - 4 t a^{4} c^{4} + 32 t a^{3} b^{2} c^{3} - 40 t a^{2} b^{4} c^{2} + 16 t a b^{6} c - 2 t b^{8}}{a^{2} c^{5} - 3 a b^{2} c^{4} + b^{4} c^{3}} \right)} \right)\right)} + \frac{- a + 3 b x^{2}}{3 a^{2} x^{3}}"," ",0,"RootSum(_t**4*(256*a**7*c**2 - 128*a**6*b**2*c + 16*a**5*b**4) + _t**2*(-80*a**3*b*c**3 + 100*a**2*b**3*c**2 - 36*a*b**5*c + 4*b**7) + c**5, Lambda(_t, _t*log(x + (-96*_t**3*a**7*b*c**2 + 56*_t**3*a**6*b**3*c - 8*_t**3*a**5*b**5 - 4*_t*a**4*c**4 + 32*_t*a**3*b**2*c**3 - 40*_t*a**2*b**4*c**2 + 16*_t*a*b**6*c - 2*_t*b**8)/(a**2*c**5 - 3*a*b**2*c**4 + b**4*c**3)))) + (-a + 3*b*x**2)/(3*a**2*x**3)","A",0
861,1,745,0,40.654338," ","integrate(x**7/(c*x**4+b*x**2+a)**2,x)","\left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right) \log{\left(x^{2} + \frac{- 32 a^{2} c^{3} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right) + 8 a^{2} c + 16 a b^{2} c^{2} \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right) - a b^{2} - 2 b^{4} c \left(- \frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right)}{6 a b c - b^{3}} \right)} + \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right) \log{\left(x^{2} + \frac{- 32 a^{2} c^{3} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right) + 8 a^{2} c + 16 a b^{2} c^{2} \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right) - a b^{2} - 2 b^{4} c \left(\frac{b \sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a c - b^{2}\right)}{4 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)} + \frac{1}{4 c^{2}}\right)}{6 a b c - b^{3}} \right)} + \frac{2 a^{2} c - a b^{2} + x^{2} \left(3 a b c - b^{3}\right)}{8 a^{2} c^{3} - 2 a b^{2} c^{2} + x^{4} \left(8 a c^{4} - 2 b^{2} c^{3}\right) + x^{2} \left(8 a b c^{3} - 2 b^{3} c^{2}\right)}"," ",0,"(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2))*log(x**2 + (-32*a**2*c**3*(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2)) + 8*a**2*c + 16*a*b**2*c**2*(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2)) - a*b**2 - 2*b**4*c*(-b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2)))/(6*a*b*c - b**3)) + (b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2))*log(x**2 + (-32*a**2*c**3*(b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2)) + 8*a**2*c + 16*a*b**2*c**2*(b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2)) - a*b**2 - 2*b**4*c*(b*sqrt(-(4*a*c - b**2)**3)*(6*a*c - b**2)/(4*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)) + 1/(4*c**2)))/(6*a*b*c - b**3)) + (2*a**2*c - a*b**2 + x**2*(3*a*b*c - b**3))/(8*a**2*c**3 - 2*a*b**2*c**2 + x**4*(8*a*c**4 - 2*b**2*c**3) + x**2*(8*a*b*c**3 - 2*b**3*c**2))","B",0
862,1,282,0,3.904983," ","integrate(x**5/(c*x**4+b*x**2+a)**2,x)","- a \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x^{2} + \frac{- 16 a^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a^{2} b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - a b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + a b}{2 a c} \right)} + a \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x^{2} + \frac{16 a^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a^{2} b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + a b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + a b}{2 a c} \right)} + \frac{a b + x^{2} \left(- 2 a c + b^{2}\right)}{8 a^{2} c^{2} - 2 a b^{2} c + x^{4} \left(8 a c^{3} - 2 b^{2} c^{2}\right) + x^{2} \left(8 a b c^{2} - 2 b^{3} c\right)}"," ",0,"-a*sqrt(-1/(4*a*c - b**2)**3)*log(x**2 + (-16*a**3*c**2*sqrt(-1/(4*a*c - b**2)**3) + 8*a**2*b**2*c*sqrt(-1/(4*a*c - b**2)**3) - a*b**4*sqrt(-1/(4*a*c - b**2)**3) + a*b)/(2*a*c)) + a*sqrt(-1/(4*a*c - b**2)**3)*log(x**2 + (16*a**3*c**2*sqrt(-1/(4*a*c - b**2)**3) - 8*a**2*b**2*c*sqrt(-1/(4*a*c - b**2)**3) + a*b**4*sqrt(-1/(4*a*c - b**2)**3) + a*b)/(2*a*c)) + (a*b + x**2*(-2*a*c + b**2))/(8*a**2*c**2 - 2*a*b**2*c + x**4*(8*a*c**3 - 2*b**2*c**2) + x**2*(8*a*b*c**2 - 2*b**3*c))","B",0
863,1,269,0,1.884922," ","integrate(x**3/(c*x**4+b*x**2+a)**2,x)","\frac{b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x^{2} + \frac{- 16 a^{2} b c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{3} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2}}{2 b c} \right)}}{2} - \frac{b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x^{2} + \frac{16 a^{2} b c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{3} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{2}}{2 b c} \right)}}{2} + \frac{- 2 a - b x^{2}}{8 a^{2} c - 2 a b^{2} + x^{4} \left(8 a c^{2} - 2 b^{2} c\right) + x^{2} \left(8 a b c - 2 b^{3}\right)}"," ",0,"b*sqrt(-1/(4*a*c - b**2)**3)*log(x**2 + (-16*a**2*b*c**2*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**3*c*sqrt(-1/(4*a*c - b**2)**3) - b**5*sqrt(-1/(4*a*c - b**2)**3) + b**2)/(2*b*c))/2 - b*sqrt(-1/(4*a*c - b**2)**3)*log(x**2 + (16*a**2*b*c**2*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**3*c*sqrt(-1/(4*a*c - b**2)**3) + b**5*sqrt(-1/(4*a*c - b**2)**3) + b**2)/(2*b*c))/2 + (-2*a - b*x**2)/(8*a**2*c - 2*a*b**2 + x**4*(8*a*c**2 - 2*b**2*c) + x**2*(8*a*b*c - 2*b**3))","B",0
864,1,267,0,2.777295," ","integrate(x/(c*x**4+b*x**2+a)**2,x)","- c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x^{2} + \frac{- 16 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + 8 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c}{2 c^{2}} \right)} + c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \log{\left(x^{2} + \frac{16 a^{2} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} - 8 a b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} + b c}{2 c^{2}} \right)} + \frac{b + 2 c x^{2}}{8 a^{2} c - 2 a b^{2} + x^{4} \left(8 a c^{2} - 2 b^{2} c\right) + x^{2} \left(8 a b c - 2 b^{3}\right)}"," ",0,"-c*sqrt(-1/(4*a*c - b**2)**3)*log(x**2 + (-16*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) + 8*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) - b**4*c*sqrt(-1/(4*a*c - b**2)**3) + b*c)/(2*c**2)) + c*sqrt(-1/(4*a*c - b**2)**3)*log(x**2 + (16*a**2*c**3*sqrt(-1/(4*a*c - b**2)**3) - 8*a*b**2*c**2*sqrt(-1/(4*a*c - b**2)**3) + b**4*c*sqrt(-1/(4*a*c - b**2)**3) + b*c)/(2*c**2)) + (b + 2*c*x**2)/(8*a**2*c - 2*a*b**2 + x**4*(8*a*c**2 - 2*b**2*c) + x**2*(8*a*b*c - 2*b**3))","B",0
865,-1,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate(x**8/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,1,379,0,51.729655," ","integrate(x**6/(c*x**4+b*x**2+a)**2,x)","\frac{a b x + x^{3} \left(- 2 a c + b^{2}\right)}{8 a^{2} c^{2} - 2 a b^{2} c + x^{4} \left(8 a c^{3} - 2 b^{2} c^{2}\right) + x^{2} \left(8 a b c^{2} - 2 b^{3} c\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{6} c^{9} - 1572864 a^{5} b^{2} c^{8} + 983040 a^{4} b^{4} c^{7} - 327680 a^{3} b^{6} c^{6} + 61440 a^{2} b^{8} c^{5} - 6144 a b^{10} c^{4} + 256 b^{12} c^{3}\right) + t^{2} \left(- 61440 a^{5} b c^{5} + 61440 a^{4} b^{3} c^{4} - 24064 a^{3} b^{5} c^{3} + 4608 a^{2} b^{7} c^{2} - 432 a b^{9} c + 16 b^{11}\right) + 1296 a^{5} c^{2} - 360 a^{4} b^{2} c + 25 a^{3} b^{4}, \left( t \mapsto t \log{\left(x + \frac{49152 t^{3} a^{4} c^{7} - 40960 t^{3} a^{3} b^{2} c^{6} + 12288 t^{3} a^{2} b^{4} c^{5} - 1536 t^{3} a b^{6} c^{4} + 64 t^{3} b^{8} c^{3} - 1728 t a^{3} b c^{3} + 656 t a^{2} b^{3} c^{2} - 88 t a b^{5} c + 4 t b^{7}}{324 a^{3} c^{2} - 81 a^{2} b^{2} c + 5 a b^{4}} \right)} \right)\right)}"," ",0,"(a*b*x + x**3*(-2*a*c + b**2))/(8*a**2*c**2 - 2*a*b**2*c + x**4*(8*a*c**3 - 2*b**2*c**2) + x**2*(8*a*b*c**2 - 2*b**3*c)) + RootSum(_t**4*(1048576*a**6*c**9 - 1572864*a**5*b**2*c**8 + 983040*a**4*b**4*c**7 - 327680*a**3*b**6*c**6 + 61440*a**2*b**8*c**5 - 6144*a*b**10*c**4 + 256*b**12*c**3) + _t**2*(-61440*a**5*b*c**5 + 61440*a**4*b**3*c**4 - 24064*a**3*b**5*c**3 + 4608*a**2*b**7*c**2 - 432*a*b**9*c + 16*b**11) + 1296*a**5*c**2 - 360*a**4*b**2*c + 25*a**3*b**4, Lambda(_t, _t*log(x + (49152*_t**3*a**4*c**7 - 40960*_t**3*a**3*b**2*c**6 + 12288*_t**3*a**2*b**4*c**5 - 1536*_t**3*a*b**6*c**4 + 64*_t**3*b**8*c**3 - 1728*_t*a**3*b*c**3 + 656*_t*a**2*b**3*c**2 - 88*_t*a*b**5*c + 4*_t*b**7)/(324*a**3*c**2 - 81*a**2*b**2*c + 5*a*b**4))))","A",0
869,1,296,0,9.011468," ","integrate(x**4/(c*x**4+b*x**2+a)**2,x)","\frac{- 2 a x - b x^{3}}{8 a^{2} c - 2 a b^{2} + x^{4} \left(8 a c^{2} - 2 b^{2} c\right) + x^{2} \left(8 a b c - 2 b^{3}\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{6} c^{7} - 1572864 a^{5} b^{2} c^{6} + 983040 a^{4} b^{4} c^{5} - 327680 a^{3} b^{6} c^{4} + 61440 a^{2} b^{8} c^{3} - 6144 a b^{10} c^{2} + 256 b^{12} c\right) + t^{2} \left(- 12288 a^{4} b c^{4} + 8192 a^{3} b^{3} c^{3} - 1536 a^{2} b^{5} c^{2} + 16 b^{9}\right) + 16 a^{3} c^{2} + 24 a^{2} b^{2} c + 9 a b^{4}, \left( t \mapsto t \log{\left(x + \frac{16384 t^{3} a^{3} b c^{4} - 12288 t^{3} a^{2} b^{3} c^{3} + 3072 t^{3} a b^{5} c^{2} - 256 t^{3} b^{7} c + 64 t a^{2} c^{2} - 128 t a b^{2} c - 4 t b^{4}}{4 a c + 3 b^{2}} \right)} \right)\right)}"," ",0,"(-2*a*x - b*x**3)/(8*a**2*c - 2*a*b**2 + x**4*(8*a*c**2 - 2*b**2*c) + x**2*(8*a*b*c - 2*b**3)) + RootSum(_t**4*(1048576*a**6*c**7 - 1572864*a**5*b**2*c**6 + 983040*a**4*b**4*c**5 - 327680*a**3*b**6*c**4 + 61440*a**2*b**8*c**3 - 6144*a*b**10*c**2 + 256*b**12*c) + _t**2*(-12288*a**4*b*c**4 + 8192*a**3*b**3*c**3 - 1536*a**2*b**5*c**2 + 16*b**9) + 16*a**3*c**2 + 24*a**2*b**2*c + 9*a*b**4, Lambda(_t, _t*log(x + (16384*_t**3*a**3*b*c**4 - 12288*_t**3*a**2*b**3*c**3 + 3072*_t**3*a*b**5*c**2 - 256*_t**3*b**7*c + 64*_t*a**2*c**2 - 128*_t*a*b**2*c - 4*_t*b**4)/(4*a*c + 3*b**2))))","A",0
870,1,298,0,20.749799," ","integrate(x**2/(c*x**4+b*x**2+a)**2,x)","\frac{b x + 2 c x^{3}}{8 a^{2} c - 2 a b^{2} + x^{4} \left(8 a c^{2} - 2 b^{2} c\right) + x^{2} \left(8 a b c - 2 b^{3}\right)} + \operatorname{RootSum} {\left(t^{4} \left(1048576 a^{7} c^{6} - 1572864 a^{6} b^{2} c^{5} + 983040 a^{5} b^{4} c^{4} - 327680 a^{4} b^{6} c^{3} + 61440 a^{3} b^{8} c^{2} - 6144 a^{2} b^{10} c + 256 a b^{12}\right) + t^{2} \left(- 12288 a^{4} b c^{4} + 8192 a^{3} b^{3} c^{3} - 1536 a^{2} b^{5} c^{2} + 16 b^{9}\right) + 16 a^{2} c^{3} + 24 a b^{2} c^{2} + 9 b^{4} c, \left( t \mapsto t \log{\left(x + \frac{16384 t^{3} a^{5} c^{4} - 8192 t^{3} a^{4} b^{2} c^{3} + 512 t^{3} a^{2} b^{6} c - 64 t^{3} a b^{8} - 128 t a^{2} b c^{2} - 16 t a b^{3} c - 4 t b^{5}}{4 a c^{2} + 3 b^{2} c} \right)} \right)\right)}"," ",0,"(b*x + 2*c*x**3)/(8*a**2*c - 2*a*b**2 + x**4*(8*a*c**2 - 2*b**2*c) + x**2*(8*a*b*c - 2*b**3)) + RootSum(_t**4*(1048576*a**7*c**6 - 1572864*a**6*b**2*c**5 + 983040*a**5*b**4*c**4 - 327680*a**4*b**6*c**3 + 61440*a**3*b**8*c**2 - 6144*a**2*b**10*c + 256*a*b**12) + _t**2*(-12288*a**4*b*c**4 + 8192*a**3*b**3*c**3 - 1536*a**2*b**5*c**2 + 16*b**9) + 16*a**2*c**3 + 24*a*b**2*c**2 + 9*b**4*c, Lambda(_t, _t*log(x + (16384*_t**3*a**5*c**4 - 8192*_t**3*a**4*b**2*c**3 + 512*_t**3*a**2*b**6*c - 64*_t**3*a*b**8 - 128*_t*a**2*b*c**2 - 16*_t*a*b**3*c - 4*_t*b**5)/(4*a*c**2 + 3*b**2*c))))","A",0
871,-1,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate(1/x**2/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate(x**11/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,1,554,0,4.641269," ","integrate(x**9/(c*x**4+b*x**2+a)**3,x)","- 3 a^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{- 192 a^{5} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{4} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a^{3} b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a^{2} b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a^{2} b}{6 a^{2} c} \right)} + 3 a^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{192 a^{5} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{4} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a^{3} b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 a^{2} b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a^{2} b}{6 a^{2} c} \right)} + \frac{10 a^{3} b c - a^{2} b^{3} + x^{6} \left(- 20 a^{2} c^{3} + 16 a b^{2} c^{2} - 2 b^{4} c\right) + x^{4} \left(2 a^{2} b c^{2} + 8 a b^{3} c - b^{5}\right) + x^{2} \left(- 12 a^{3} c^{2} + 20 a^{2} b^{2} c - 2 a b^{4}\right)}{64 a^{4} c^{4} - 32 a^{3} b^{2} c^{3} + 4 a^{2} b^{4} c^{2} + x^{8} \left(64 a^{2} c^{6} - 32 a b^{2} c^{5} + 4 b^{4} c^{4}\right) + x^{6} \left(128 a^{2} b c^{5} - 64 a b^{3} c^{4} + 8 b^{5} c^{3}\right) + x^{4} \left(128 a^{3} c^{5} - 24 a b^{4} c^{3} + 4 b^{6} c^{2}\right) + x^{2} \left(128 a^{3} b c^{4} - 64 a^{2} b^{3} c^{3} + 8 a b^{5} c^{2}\right)}"," ",0,"-3*a**2*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (-192*a**5*c**3*sqrt(-1/(4*a*c - b**2)**5) + 144*a**4*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5) - 36*a**3*b**4*c*sqrt(-1/(4*a*c - b**2)**5) + 3*a**2*b**6*sqrt(-1/(4*a*c - b**2)**5) + 3*a**2*b)/(6*a**2*c)) + 3*a**2*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (192*a**5*c**3*sqrt(-1/(4*a*c - b**2)**5) - 144*a**4*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5) + 36*a**3*b**4*c*sqrt(-1/(4*a*c - b**2)**5) - 3*a**2*b**6*sqrt(-1/(4*a*c - b**2)**5) + 3*a**2*b)/(6*a**2*c)) + (10*a**3*b*c - a**2*b**3 + x**6*(-20*a**2*c**3 + 16*a*b**2*c**2 - 2*b**4*c) + x**4*(2*a**2*b*c**2 + 8*a*b**3*c - b**5) + x**2*(-12*a**3*c**2 + 20*a**2*b**2*c - 2*a*b**4))/(64*a**4*c**4 - 32*a**3*b**2*c**3 + 4*a**2*b**4*c**2 + x**8*(64*a**2*c**6 - 32*a*b**2*c**5 + 4*b**4*c**4) + x**6*(128*a**2*b*c**5 - 64*a*b**3*c**4 + 8*b**5*c**3) + x**4*(128*a**3*c**5 - 24*a*b**4*c**3 + 4*b**6*c**2) + x**2*(128*a**3*b*c**4 - 64*a**2*b**3*c**3 + 8*a*b**5*c**2))","B",0
875,1,524,0,3.810791," ","integrate(x**7/(c*x**4+b*x**2+a)**3,x)","\frac{3 a b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{- 192 a^{4} b c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{3} b^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a^{2} b^{5} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a b^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a b^{2}}{6 a b c} \right)}}{2} - \frac{3 a b \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{192 a^{4} b c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{3} b^{3} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a^{2} b^{5} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 a b^{7} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 a b^{2}}{6 a b c} \right)}}{2} + \frac{- 8 a^{3} c - a^{2} b^{2} - 6 a b c^{2} x^{6} + x^{4} \left(- 16 a^{2} c^{2} - a b^{2} c - b^{4}\right) + x^{2} \left(- 10 a^{2} b c - 2 a b^{3}\right)}{64 a^{4} c^{3} - 32 a^{3} b^{2} c^{2} + 4 a^{2} b^{4} c + x^{8} \left(64 a^{2} c^{5} - 32 a b^{2} c^{4} + 4 b^{4} c^{3}\right) + x^{6} \left(128 a^{2} b c^{4} - 64 a b^{3} c^{3} + 8 b^{5} c^{2}\right) + x^{4} \left(128 a^{3} c^{4} - 24 a b^{4} c^{2} + 4 b^{6} c\right) + x^{2} \left(128 a^{3} b c^{3} - 64 a^{2} b^{3} c^{2} + 8 a b^{5} c\right)}"," ",0,"3*a*b*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (-192*a**4*b*c**3*sqrt(-1/(4*a*c - b**2)**5) + 144*a**3*b**3*c**2*sqrt(-1/(4*a*c - b**2)**5) - 36*a**2*b**5*c*sqrt(-1/(4*a*c - b**2)**5) + 3*a*b**7*sqrt(-1/(4*a*c - b**2)**5) + 3*a*b**2)/(6*a*b*c))/2 - 3*a*b*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (192*a**4*b*c**3*sqrt(-1/(4*a*c - b**2)**5) - 144*a**3*b**3*c**2*sqrt(-1/(4*a*c - b**2)**5) + 36*a**2*b**5*c*sqrt(-1/(4*a*c - b**2)**5) - 3*a*b**7*sqrt(-1/(4*a*c - b**2)**5) + 3*a*b**2)/(6*a*b*c))/2 + (-8*a**3*c - a**2*b**2 - 6*a*b*c**2*x**6 + x**4*(-16*a**2*c**2 - a*b**2*c - b**4) + x**2*(-10*a**2*b*c - 2*a*b**3))/(64*a**4*c**3 - 32*a**3*b**2*c**2 + 4*a**2*b**4*c + x**8*(64*a**2*c**5 - 32*a*b**2*c**4 + 4*b**4*c**3) + x**6*(128*a**2*b*c**4 - 64*a*b**3*c**3 + 8*b**5*c**2) + x**4*(128*a**3*c**4 - 24*a*b**4*c**2 + 4*b**6*c) + x**2*(128*a**3*b*c**3 - 64*a**2*b**3*c**2 + 8*a*b**5*c))","B",0
876,1,580,0,5.406299," ","integrate(x**5/(c*x**4+b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) \log{\left(x^{2} + \frac{- 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) - 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 2 a b c + b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + b^{3}}{4 a c^{2} + 2 b^{2} c} \right)}}{2} + \frac{\sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) \log{\left(x^{2} + \frac{64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) - 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + 2 a b c - b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(2 a c + b^{2}\right) + b^{3}}{4 a c^{2} + 2 b^{2} c} \right)}}{2} + \frac{6 a^{2} b + x^{6} \left(4 a c^{2} + 2 b^{2} c\right) + x^{4} \left(6 a b c + 3 b^{3}\right) + x^{2} \left(- 4 a^{2} c + 10 a b^{2}\right)}{64 a^{4} c^{2} - 32 a^{3} b^{2} c + 4 a^{2} b^{4} + x^{8} \left(64 a^{2} c^{4} - 32 a b^{2} c^{3} + 4 b^{4} c^{2}\right) + x^{6} \left(128 a^{2} b c^{3} - 64 a b^{3} c^{2} + 8 b^{5} c\right) + x^{4} \left(128 a^{3} c^{3} - 24 a b^{4} c + 4 b^{6}\right) + x^{2} \left(128 a^{3} b c^{2} - 64 a^{2} b^{3} c + 8 a b^{5}\right)}"," ",0,"-sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2)*log(x**2 + (-64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) - 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 2*a*b*c + b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + b**3)/(4*a*c**2 + 2*b**2*c))/2 + sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2)*log(x**2 + (64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) - 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + 2*a*b*c - b**6*sqrt(-1/(4*a*c - b**2)**5)*(2*a*c + b**2) + b**3)/(4*a*c**2 + 2*b**2*c))/2 + (6*a**2*b + x**6*(4*a*c**2 + 2*b**2*c) + x**4*(6*a*b*c + 3*b**3) + x**2*(-4*a**2*c + 10*a*b**2))/(64*a**4*c**2 - 32*a**3*b**2*c + 4*a**2*b**4 + x**8*(64*a**2*c**4 - 32*a*b**2*c**3 + 4*b**4*c**2) + x**6*(128*a**2*b*c**3 - 64*a*b**3*c**2 + 8*b**5*c) + x**4*(128*a**3*c**3 - 24*a*b**4*c + 4*b**6) + x**2*(128*a**3*b*c**2 - 64*a**2*b**3*c + 8*a*b**5))","B",0
877,1,491,0,3.041080," ","integrate(x**3/(c*x**4+b*x**2+a)**3,x)","\frac{3 b c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{- 192 a^{3} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{2} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c}{6 b c^{2}} \right)}}{2} - \frac{3 b c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{192 a^{3} b c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{2} b^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a b^{5} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 b^{7} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{2} c}{6 b c^{2}} \right)}}{2} + \frac{- 8 a^{2} c - a b^{2} - 9 b^{2} c x^{4} - 6 b c^{2} x^{6} + x^{2} \left(- 10 a b c - 2 b^{3}\right)}{64 a^{4} c^{2} - 32 a^{3} b^{2} c + 4 a^{2} b^{4} + x^{8} \left(64 a^{2} c^{4} - 32 a b^{2} c^{3} + 4 b^{4} c^{2}\right) + x^{6} \left(128 a^{2} b c^{3} - 64 a b^{3} c^{2} + 8 b^{5} c\right) + x^{4} \left(128 a^{3} c^{3} - 24 a b^{4} c + 4 b^{6}\right) + x^{2} \left(128 a^{3} b c^{2} - 64 a^{2} b^{3} c + 8 a b^{5}\right)}"," ",0,"3*b*c*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (-192*a**3*b*c**4*sqrt(-1/(4*a*c - b**2)**5) + 144*a**2*b**3*c**3*sqrt(-1/(4*a*c - b**2)**5) - 36*a*b**5*c**2*sqrt(-1/(4*a*c - b**2)**5) + 3*b**7*c*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c)/(6*b*c**2))/2 - 3*b*c*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (192*a**3*b*c**4*sqrt(-1/(4*a*c - b**2)**5) - 144*a**2*b**3*c**3*sqrt(-1/(4*a*c - b**2)**5) + 36*a*b**5*c**2*sqrt(-1/(4*a*c - b**2)**5) - 3*b**7*c*sqrt(-1/(4*a*c - b**2)**5) + 3*b**2*c)/(6*b*c**2))/2 + (-8*a**2*c - a*b**2 - 9*b**2*c*x**4 - 6*b*c**2*x**6 + x**2*(-10*a*b*c - 2*b**3))/(64*a**4*c**2 - 32*a**3*b**2*c + 4*a**2*b**4 + x**8*(64*a**2*c**4 - 32*a*b**2*c**3 + 4*b**4*c**2) + x**6*(128*a**2*b*c**3 - 64*a*b**3*c**2 + 8*b**5*c) + x**4*(128*a**3*c**3 - 24*a*b**4*c + 4*b**6) + x**2*(128*a**3*b*c**2 - 64*a**2*b**3*c + 8*a*b**5))","B",0
878,1,481,0,2.907510," ","integrate(x/(c*x**4+b*x**2+a)**3,x)","- 3 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{- 192 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 144 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 36 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b c^{2}}{6 c^{3}} \right)} + 3 c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \log{\left(x^{2} + \frac{192 a^{3} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 144 a^{2} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 36 a b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} - 3 b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} + 3 b c^{2}}{6 c^{3}} \right)} + \frac{10 a b c - b^{3} + 18 b c^{2} x^{4} + 12 c^{3} x^{6} + x^{2} \left(20 a c^{2} + 4 b^{2} c\right)}{64 a^{4} c^{2} - 32 a^{3} b^{2} c + 4 a^{2} b^{4} + x^{8} \left(64 a^{2} c^{4} - 32 a b^{2} c^{3} + 4 b^{4} c^{2}\right) + x^{6} \left(128 a^{2} b c^{3} - 64 a b^{3} c^{2} + 8 b^{5} c\right) + x^{4} \left(128 a^{3} c^{3} - 24 a b^{4} c + 4 b^{6}\right) + x^{2} \left(128 a^{3} b c^{2} - 64 a^{2} b^{3} c + 8 a b^{5}\right)}"," ",0,"-3*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (-192*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) + 144*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) - 36*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) + 3*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 3*b*c**2)/(6*c**3)) + 3*c**2*sqrt(-1/(4*a*c - b**2)**5)*log(x**2 + (192*a**3*c**5*sqrt(-1/(4*a*c - b**2)**5) - 144*a**2*b**2*c**4*sqrt(-1/(4*a*c - b**2)**5) + 36*a*b**4*c**3*sqrt(-1/(4*a*c - b**2)**5) - 3*b**6*c**2*sqrt(-1/(4*a*c - b**2)**5) + 3*b*c**2)/(6*c**3)) + (10*a*b*c - b**3 + 18*b*c**2*x**4 + 12*c**3*x**6 + x**2*(20*a*c**2 + 4*b**2*c))/(64*a**4*c**2 - 32*a**3*b**2*c + 4*a**2*b**4 + x**8*(64*a**2*c**4 - 32*a*b**2*c**3 + 4*b**4*c**2) + x**6*(128*a**2*b*c**3 - 64*a*b**3*c**2 + 8*b**5*c) + x**4*(128*a**3*c**3 - 24*a*b**4*c + 4*b**6) + x**2*(128*a**3*b*c**2 - 64*a**2*b**3*c + 8*a*b**5))","B",0
879,-1,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate(x**10/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate(x**8/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,1,627,0,23.391723," ","integrate(x**6/(c*x**4+b*x**2+a)**3,x)","\frac{12 a^{2} b x + x^{7} \left(12 a c^{2} + 3 b^{2} c\right) + x^{5} \left(16 a b c + 5 b^{3}\right) + x^{3} \left(- 4 a^{2} c + 19 a b^{2}\right)}{128 a^{4} c^{2} - 64 a^{3} b^{2} c + 8 a^{2} b^{4} + x^{8} \left(128 a^{2} c^{4} - 64 a b^{2} c^{3} + 8 b^{4} c^{2}\right) + x^{6} \left(256 a^{2} b c^{3} - 128 a b^{3} c^{2} + 16 b^{5} c\right) + x^{4} \left(256 a^{3} c^{3} - 48 a b^{4} c + 8 b^{6}\right) + x^{2} \left(256 a^{3} b c^{2} - 128 a^{2} b^{3} c + 16 a b^{5}\right)} + \operatorname{RootSum} {\left(t^{4} \left(68719476736 a^{10} c^{11} - 171798691840 a^{9} b^{2} c^{10} + 193273528320 a^{8} b^{4} c^{9} - 128849018880 a^{7} b^{6} c^{8} + 56371445760 a^{6} b^{8} c^{7} - 16911433728 a^{5} b^{10} c^{6} + 3523215360 a^{4} b^{12} c^{5} - 503316480 a^{3} b^{14} c^{4} + 47185920 a^{2} b^{16} c^{3} - 2621440 a b^{18} c^{2} + 65536 b^{20} c\right) + t^{2} \left(- 188743680 a^{7} b c^{7} + 141557760 a^{6} b^{3} c^{6} - 2359296 a^{5} b^{5} c^{5} - 26542080 a^{4} b^{7} c^{4} + 9584640 a^{3} b^{9} c^{3} - 1290240 a^{2} b^{11} c^{2} + 46080 a b^{13} c + 2304 b^{15}\right) + 20736 a^{5} c^{4} + 103680 a^{4} b^{2} c^{3} + 142560 a^{3} b^{4} c^{2} + 32400 a^{2} b^{6} c + 2025 a b^{8}, \left( t \mapsto t \log{\left(x + \frac{33554432 t^{3} a^{6} c^{7} - 16777216 t^{3} a^{5} b^{2} c^{6} - 10485760 t^{3} a^{4} b^{4} c^{5} + 10485760 t^{3} a^{3} b^{6} c^{4} - 3276800 t^{3} a^{2} b^{8} c^{3} + 458752 t^{3} a b^{10} c^{2} - 24576 t^{3} b^{12} c - 64512 t a^{3} b c^{3} - 43776 t a^{2} b^{3} c^{2} - 21312 t a b^{5} c - 144 t b^{7}}{432 a^{2} c^{2} + 1080 a b^{2} c + 135 b^{4}} \right)} \right)\right)}"," ",0,"(12*a**2*b*x + x**7*(12*a*c**2 + 3*b**2*c) + x**5*(16*a*b*c + 5*b**3) + x**3*(-4*a**2*c + 19*a*b**2))/(128*a**4*c**2 - 64*a**3*b**2*c + 8*a**2*b**4 + x**8*(128*a**2*c**4 - 64*a*b**2*c**3 + 8*b**4*c**2) + x**6*(256*a**2*b*c**3 - 128*a*b**3*c**2 + 16*b**5*c) + x**4*(256*a**3*c**3 - 48*a*b**4*c + 8*b**6) + x**2*(256*a**3*b*c**2 - 128*a**2*b**3*c + 16*a*b**5)) + RootSum(_t**4*(68719476736*a**10*c**11 - 171798691840*a**9*b**2*c**10 + 193273528320*a**8*b**4*c**9 - 128849018880*a**7*b**6*c**8 + 56371445760*a**6*b**8*c**7 - 16911433728*a**5*b**10*c**6 + 3523215360*a**4*b**12*c**5 - 503316480*a**3*b**14*c**4 + 47185920*a**2*b**16*c**3 - 2621440*a*b**18*c**2 + 65536*b**20*c) + _t**2*(-188743680*a**7*b*c**7 + 141557760*a**6*b**3*c**6 - 2359296*a**5*b**5*c**5 - 26542080*a**4*b**7*c**4 + 9584640*a**3*b**9*c**3 - 1290240*a**2*b**11*c**2 + 46080*a*b**13*c + 2304*b**15) + 20736*a**5*c**4 + 103680*a**4*b**2*c**3 + 142560*a**3*b**4*c**2 + 32400*a**2*b**6*c + 2025*a*b**8, Lambda(_t, _t*log(x + (33554432*_t**3*a**6*c**7 - 16777216*_t**3*a**5*b**2*c**6 - 10485760*_t**3*a**4*b**4*c**5 + 10485760*_t**3*a**3*b**6*c**4 - 3276800*_t**3*a**2*b**8*c**3 + 458752*_t**3*a*b**10*c**2 - 24576*_t**3*b**12*c - 64512*_t*a**3*b*c**3 - 43776*_t*a**2*b**3*c**2 - 21312*_t*a*b**5*c - 144*_t*b**7)/(432*a**2*c**2 + 1080*a*b**2*c + 135*b**4))))","B",0
884,-1,0,0,0.000000," ","integrate(x**4/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(x**2/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate(1/x**2/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,1,311,0,2.760970," ","integrate(x**5/(c*x**4-b*x**2+a),x)","\left(\frac{b}{4 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{a b - 8 a c^{2} \left(\frac{b}{4 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) + 2 b^{2} c \left(\frac{b}{4 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \left(\frac{b}{4 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{a b - 8 a c^{2} \left(\frac{b}{4 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right) + 2 b^{2} c \left(\frac{b}{4 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 c^{2} \left(4 a c - b^{2}\right)}\right)}{2 a c - b^{2}} \right)} + \frac{x^{2}}{2 c}"," ",0,"(b/(4*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2)))*log(x**2 + (a*b - 8*a*c**2*(b/(4*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))) + 2*b**2*c*(b/(4*c**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + (b/(4*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2)))*log(x**2 + (a*b - 8*a*c**2*(b/(4*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))) + 2*b**2*c*(b/(4*c**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*c**2*(4*a*c - b**2))))/(2*a*c - b**2)) + x**2/(2*c)","B",0
889,1,223,0,1.447899," ","integrate(x**3/(c*x**4-b*x**2+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) \log{\left(x^{2} + \frac{8 a c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) - 2 a - 2 b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right)}{b} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) \log{\left(x^{2} + \frac{8 a c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right) - 2 a - 2 b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 c \left(4 a c - b^{2}\right)} + \frac{1}{4 c}\right)}{b} \right)}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c))*log(x**2 + (8*a*c*(-b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)) - 2*a - 2*b**2*(-b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)))/b) + (b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c))*log(x**2 + (8*a*c*(b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)) - 2*a - 2*b**2*(b*sqrt(-4*a*c + b**2)/(4*c*(4*a*c - b**2)) + 1/(4*c)))/b)","B",0
890,1,131,0,0.720598," ","integrate(x/(c*x**4-b*x**2+a),x)","- \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{2} + \frac{- 4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} + b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} - b}{2 c} \right)}}{2} + \frac{\sqrt{- \frac{1}{4 a c - b^{2}}} \log{\left(x^{2} + \frac{4 a c \sqrt{- \frac{1}{4 a c - b^{2}}} - b^{2} \sqrt{- \frac{1}{4 a c - b^{2}}} - b}{2 c} \right)}}{2}"," ",0,"-sqrt(-1/(4*a*c - b**2))*log(x**2 + (-4*a*c*sqrt(-1/(4*a*c - b**2)) + b**2*sqrt(-1/(4*a*c - b**2)) - b)/(2*c))/2 + sqrt(-1/(4*a*c - b**2))*log(x**2 + (4*a*c*sqrt(-1/(4*a*c - b**2)) - b**2*sqrt(-1/(4*a*c - b**2)) - b)/(2*c))/2","B",0
891,1,253,0,5.742316," ","integrate(1/x/(c*x**4-b*x**2+a),x)","\left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) \log{\left(x^{2} + \frac{8 a^{2} c \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) - 2 a b^{2} \left(- \frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) + 2 a c - b^{2}}{b c} \right)} + \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) \log{\left(x^{2} + \frac{8 a^{2} c \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) - 2 a b^{2} \left(\frac{b \sqrt{- 4 a c + b^{2}}}{4 a \left(4 a c - b^{2}\right)} - \frac{1}{4 a}\right) + 2 a c - b^{2}}{b c} \right)} + \frac{\log{\left(x \right)}}{a}"," ",0,"(-b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a))*log(x**2 + (8*a**2*c*(-b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) - 2*a*b**2*(-b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) + 2*a*c - b**2)/(b*c)) + (b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a))*log(x**2 + (8*a**2*c*(b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) - 2*a*b**2*(b*sqrt(-4*a*c + b**2)/(4*a*(4*a*c - b**2)) - 1/(4*a)) + 2*a*c - b**2)/(b*c)) + log(x)/a","B",0
892,1,350,0,142.971176," ","integrate(1/x**3/(c*x**4-b*x**2+a),x)","\left(- \frac{b}{4 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{- 8 a^{3} c \left(- \frac{b}{4 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} \left(- \frac{b}{4 a^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) - 3 a b c + b^{3}}{2 a c^{2} - b^{2} c} \right)} + \left(- \frac{b}{4 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x^{2} + \frac{- 8 a^{3} c \left(- \frac{b}{4 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) + 2 a^{2} b^{2} \left(- \frac{b}{4 a^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c - b^{2}\right)}{4 a^{2} \left(4 a c - b^{2}\right)}\right) - 3 a b c + b^{3}}{2 a c^{2} - b^{2} c} \right)} - \frac{1}{2 a x^{2}} + \frac{b \log{\left(x \right)}}{a^{2}}"," ",0,"(-b/(4*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2)))*log(x**2 + (-8*a**3*c*(-b/(4*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) + 2*a**2*b**2*(-b/(4*a**2) - sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) - 3*a*b*c + b**3)/(2*a*c**2 - b**2*c)) + (-b/(4*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2)))*log(x**2 + (-8*a**3*c*(-b/(4*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) + 2*a**2*b**2*(-b/(4*a**2) + sqrt(-4*a*c + b**2)*(2*a*c - b**2)/(4*a**2*(4*a*c - b**2))) - 3*a*b*c + b**3)/(2*a*c**2 - b**2*c)) - 1/(2*a*x**2) + b*log(x)/a**2","B",0
893,1,129,0,2.775290," ","integrate(x**4/(c*x**4-b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{5} - 128 a b^{2} c^{4} + 16 b^{4} c^{3}\right) + t^{2} \left(- 48 a^{2} b c^{2} + 28 a b^{3} c - 4 b^{5}\right) + a^{3}, \left( t \mapsto t \log{\left(x + \frac{- 32 t^{3} a b c^{4} + 8 t^{3} b^{3} c^{3} - 4 t a^{2} c^{2} + 8 t a b^{2} c - 2 t b^{4}}{a^{2} c - a b^{2}} \right)} \right)\right)} + \frac{x}{c}"," ",0,"RootSum(_t**4*(256*a**2*c**5 - 128*a*b**2*c**4 + 16*b**4*c**3) + _t**2*(-48*a**2*b*c**2 + 28*a*b**3*c - 4*b**5) + a**3, Lambda(_t, _t*log(x + (-32*_t**3*a*b*c**4 + 8*_t**3*b**3*c**3 - 4*_t*a**2*c**2 + 8*_t*a*b**2*c - 2*_t*b**4)/(a**2*c - a*b**2)))) + x/c","A",0
894,1,75,0,1.245444," ","integrate(x**2/(c*x**4-b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{3} - 128 a b^{2} c^{2} + 16 b^{4} c\right) + t^{2} \left(16 a b c - 4 b^{3}\right) + a, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} - 16 t^{3} b^{2} c + 2 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2*c**3 - 128*a*b**2*c**2 + 16*b**4*c) + _t**2*(16*a*b*c - 4*b**3) + a, Lambda(_t, _t*log(64*_t**3*a*c**2 - 16*_t**3*b**2*c + 2*_t*b + x)))","A",0
895,1,87,0,1.245120," ","integrate(1/(c*x**4-b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{3} c^{2} - 128 a^{2} b^{2} c + 16 a b^{4}\right) + t^{2} \left(16 a b c - 4 b^{3}\right) + c, \left( t \mapsto t \log{\left(x + \frac{- 32 t^{3} a^{2} b c + 8 t^{3} a b^{3} + 4 t a c - 2 t b^{2}}{c} \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**3*c**2 - 128*a**2*b**2*c + 16*a*b**4) + _t**2*(16*a*b*c - 4*b**3) + c, Lambda(_t, _t*log(x + (-32*_t**3*a**2*b*c + 8*_t**3*a*b**3 + 4*_t*a*c - 2*_t*b**2)/c)))","A",0
896,1,148,0,3.834448," ","integrate(1/x**2/(c*x**4-b*x**2+a),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{5} c^{2} - 128 a^{4} b^{2} c + 16 a^{3} b^{4}\right) + t^{2} \left(- 48 a^{2} b c^{2} + 28 a b^{3} c - 4 b^{5}\right) + c^{3}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{5} c^{2} + 48 t^{3} a^{4} b^{2} c - 8 t^{3} a^{3} b^{4} + 10 t a^{2} b c^{2} - 10 t a b^{3} c + 2 t b^{5}}{a c^{3} - b^{2} c^{2}} \right)} \right)\right)} - \frac{1}{a x}"," ",0,"RootSum(_t**4*(256*a**5*c**2 - 128*a**4*b**2*c + 16*a**3*b**4) + _t**2*(-48*a**2*b*c**2 + 28*a*b**3*c - 4*b**5) + c**3, Lambda(_t, _t*log(x + (-64*_t**3*a**5*c**2 + 48*_t**3*a**4*b**2*c - 8*_t**3*a**3*b**4 + 10*_t*a**2*b*c**2 - 10*_t*a*b**3*c + 2*_t*b**5)/(a*c**3 - b**2*c**2)))) - 1/(a*x)","A",0
897,1,138,0,1.785124," ","integrate(x**5/(a*x**4+2*a*x**2+a-b),x)","\left(- \frac{1}{2 a} - \frac{\sqrt{a^{3} b} \left(a + b\right)}{4 a^{3} b}\right) \log{\left(x^{2} + \frac{- 4 a b \left(- \frac{1}{2 a} - \frac{\sqrt{a^{3} b} \left(a + b\right)}{4 a^{3} b}\right) + a - b}{a + b} \right)} + \left(- \frac{1}{2 a} + \frac{\sqrt{a^{3} b} \left(a + b\right)}{4 a^{3} b}\right) \log{\left(x^{2} + \frac{- 4 a b \left(- \frac{1}{2 a} + \frac{\sqrt{a^{3} b} \left(a + b\right)}{4 a^{3} b}\right) + a - b}{a + b} \right)} + \frac{x^{2}}{2 a}"," ",0,"(-1/(2*a) - sqrt(a**3*b)*(a + b)/(4*a**3*b))*log(x**2 + (-4*a*b*(-1/(2*a) - sqrt(a**3*b)*(a + b)/(4*a**3*b)) + a - b)/(a + b)) + (-1/(2*a) + sqrt(a**3*b)*(a + b)/(4*a**3*b))*log(x**2 + (-4*a*b*(-1/(2*a) + sqrt(a**3*b)*(a + b)/(4*a**3*b)) + a - b)/(a + b)) + x**2/(2*a)","B",0
898,1,110,0,0.844706," ","integrate(x**3/(a*x**4+2*a*x**2+a-b),x)","\left(\frac{1}{4 a} - \frac{\sqrt{a^{3} b}}{4 a^{2} b}\right) \log{\left(x^{2} + \frac{4 a b \left(\frac{1}{4 a} - \frac{\sqrt{a^{3} b}}{4 a^{2} b}\right) + a - b}{a} \right)} + \left(\frac{1}{4 a} + \frac{\sqrt{a^{3} b}}{4 a^{2} b}\right) \log{\left(x^{2} + \frac{4 a b \left(\frac{1}{4 a} + \frac{\sqrt{a^{3} b}}{4 a^{2} b}\right) + a - b}{a} \right)}"," ",0,"(1/(4*a) - sqrt(a**3*b)/(4*a**2*b))*log(x**2 + (4*a*b*(1/(4*a) - sqrt(a**3*b)/(4*a**2*b)) + a - b)/a) + (1/(4*a) + sqrt(a**3*b)/(4*a**2*b))*log(x**2 + (4*a*b*(1/(4*a) + sqrt(a**3*b)/(4*a**2*b)) + a - b)/a)","B",0
899,1,53,0,0.338986," ","integrate(x/(a*x**4+2*a*x**2+a-b),x)","\frac{\sqrt{\frac{1}{a b}} \log{\left(- b \sqrt{\frac{1}{a b}} + x^{2} + 1 \right)}}{4} - \frac{\sqrt{\frac{1}{a b}} \log{\left(b \sqrt{\frac{1}{a b}} + x^{2} + 1 \right)}}{4}"," ",0,"sqrt(1/(a*b))*log(-b*sqrt(1/(a*b)) + x**2 + 1)/4 - sqrt(1/(a*b))*log(b*sqrt(1/(a*b)) + x**2 + 1)/4","A",0
900,1,184,0,5.310875," ","integrate(1/x/(a*x**4+2*a*x**2+a-b),x)","\left(- \frac{1}{4 \left(a - b\right)} - \frac{\sqrt{a b}}{4 b \left(a - b\right)}\right) \log{\left(x^{2} + \frac{4 a b \left(- \frac{1}{4 \left(a - b\right)} - \frac{\sqrt{a b}}{4 b \left(a - b\right)}\right) + a - 4 b^{2} \left(- \frac{1}{4 \left(a - b\right)} - \frac{\sqrt{a b}}{4 b \left(a - b\right)}\right) + b}{a} \right)} + \left(- \frac{1}{4 \left(a - b\right)} + \frac{\sqrt{a b}}{4 b \left(a - b\right)}\right) \log{\left(x^{2} + \frac{4 a b \left(- \frac{1}{4 \left(a - b\right)} + \frac{\sqrt{a b}}{4 b \left(a - b\right)}\right) + a - 4 b^{2} \left(- \frac{1}{4 \left(a - b\right)} + \frac{\sqrt{a b}}{4 b \left(a - b\right)}\right) + b}{a} \right)} + \frac{\log{\left(x \right)}}{a - b}"," ",0,"(-1/(4*(a - b)) - sqrt(a*b)/(4*b*(a - b)))*log(x**2 + (4*a*b*(-1/(4*(a - b)) - sqrt(a*b)/(4*b*(a - b))) + a - 4*b**2*(-1/(4*(a - b)) - sqrt(a*b)/(4*b*(a - b))) + b)/a) + (-1/(4*(a - b)) + sqrt(a*b)/(4*b*(a - b)))*log(x**2 + (4*a*b*(-1/(4*(a - b)) + sqrt(a*b)/(4*b*(a - b))) + a - 4*b**2*(-1/(4*(a - b)) + sqrt(a*b)/(4*b*(a - b))) + b)/a) + log(x)/(a - b)","B",0
901,1,372,0,32.927510," ","integrate(1/x**3/(a*x**4+2*a*x**2+a-b),x)","- \frac{2 a \log{\left(x \right)}}{\left(a - b\right)^{2}} + \left(\frac{a}{2 \left(a - b\right)^{2}} - \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right) \log{\left(x^{2} + \frac{- 4 a^{2} b \left(\frac{a}{2 \left(a - b\right)^{2}} - \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right) + a^{2} + 8 a b^{2} \left(\frac{a}{2 \left(a - b\right)^{2}} - \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right) + 3 a b - 4 b^{3} \left(\frac{a}{2 \left(a - b\right)^{2}} - \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right)}{a^{2} + a b} \right)} + \left(\frac{a}{2 \left(a - b\right)^{2}} + \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right) \log{\left(x^{2} + \frac{- 4 a^{2} b \left(\frac{a}{2 \left(a - b\right)^{2}} + \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right) + a^{2} + 8 a b^{2} \left(\frac{a}{2 \left(a - b\right)^{2}} + \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right) + 3 a b - 4 b^{3} \left(\frac{a}{2 \left(a - b\right)^{2}} + \frac{\sqrt{a b} \left(a + b\right)}{4 b \left(a^{2} - 2 a b + b^{2}\right)}\right)}{a^{2} + a b} \right)} - \frac{1}{x^{2} \left(2 a - 2 b\right)}"," ",0,"-2*a*log(x)/(a - b)**2 + (a/(2*(a - b)**2) - sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2)))*log(x**2 + (-4*a**2*b*(a/(2*(a - b)**2) - sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2))) + a**2 + 8*a*b**2*(a/(2*(a - b)**2) - sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2))) + 3*a*b - 4*b**3*(a/(2*(a - b)**2) - sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2))))/(a**2 + a*b)) + (a/(2*(a - b)**2) + sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2)))*log(x**2 + (-4*a**2*b*(a/(2*(a - b)**2) + sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2))) + a**2 + 8*a*b**2*(a/(2*(a - b)**2) + sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2))) + 3*a*b - 4*b**3*(a/(2*(a - b)**2) + sqrt(a*b)*(a + b)/(4*b*(a**2 - 2*a*b + b**2))))/(a**2 + a*b)) - 1/(x**2*(2*a - 2*b))","B",0
902,1,105,0,2.018980," ","integrate(x**4/(a*x**4+2*a*x**2+a-b),x)","\operatorname{RootSum} {\left(256 t^{4} a^{5} b^{2} + t^{2} \left(32 a^{4} b + 96 a^{3} b^{2}\right) + a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{4} b + 4 t a^{3} + 24 t a^{2} b + 4 t a b^{2}}{3 a^{2} - 2 a b - b^{2}} \right)} \right)\right)} + \frac{x}{a}"," ",0,"RootSum(256*_t**4*a**5*b**2 + _t**2*(32*a**4*b + 96*a**3*b**2) + a**3 - 3*a**2*b + 3*a*b**2 - b**3, Lambda(_t, _t*log(x + (64*_t**3*a**4*b + 4*_t*a**3 + 24*_t*a**2*b + 4*_t*a*b**2)/(3*a**2 - 2*a*b - b**2)))) + x/a","A",0
903,1,44,0,0.595786," ","integrate(x**2/(a*x**4+2*a*x**2+a-b),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{2} + 32 t^{2} a^{2} b + a - b, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} b - 4 t a + x \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*b**2 + 32*_t**2*a**2*b + a - b, Lambda(_t, _t*log(-64*_t**3*a**2*b - 4*_t*a + x)))","A",0
904,1,63,0,0.946726," ","integrate(1/(a*x**4+2*a*x**2+a-b),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} b^{2} - 256 a b^{3}\right) + 32 t^{2} a b + 1, \left( t \mapsto t \log{\left(- 64 t^{3} a^{2} b + 64 t^{3} a b^{2} - 4 t a - 4 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2*b**2 - 256*a*b**3) + 32*_t**2*a*b + 1, Lambda(_t, _t*log(-64*_t**3*a**2*b + 64*_t**3*a*b**2 - 4*_t*a - 4*_t*b + x)))","A",0
905,1,134,0,6.143848," ","integrate(1/x**2/(a*x**4+2*a*x**2+a-b),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{3} b^{2} - 768 a^{2} b^{3} + 768 a b^{4} - 256 b^{5}\right) + t^{2} \left(32 a^{2} b + 96 a b^{2}\right) + a, \left( t \mapsto t \log{\left(x + \frac{64 t^{3} a^{4} b - 128 t^{3} a^{3} b^{2} + 128 t^{3} a b^{4} - 64 t^{3} b^{5} + 4 t a^{3} + 40 t a^{2} b + 20 t a b^{2}}{3 a^{2} + a b} \right)} \right)\right)} - \frac{1}{x \left(a - b\right)}"," ",0,"RootSum(_t**4*(256*a**3*b**2 - 768*a**2*b**3 + 768*a*b**4 - 256*b**5) + _t**2*(32*a**2*b + 96*a*b**2) + a, Lambda(_t, _t*log(x + (64*_t**3*a**4*b - 128*_t**3*a**3*b**2 + 128*_t**3*a*b**4 - 64*_t**3*b**5 + 4*_t*a**3 + 40*_t*a**2*b + 20*_t*a*b**2)/(3*a**2 + a*b)))) - 1/(x*(a - b))","A",0
906,1,144,0,1.604104," ","integrate(x**5/(a*x**4+2*a*x**2+a+b),x)","\left(- \frac{1}{2 a} - \frac{\sqrt{- a^{3} b} \left(a - b\right)}{4 a^{3} b}\right) \log{\left(x^{2} + \frac{4 a b \left(- \frac{1}{2 a} - \frac{\sqrt{- a^{3} b} \left(a - b\right)}{4 a^{3} b}\right) + a + b}{a - b} \right)} + \left(- \frac{1}{2 a} + \frac{\sqrt{- a^{3} b} \left(a - b\right)}{4 a^{3} b}\right) \log{\left(x^{2} + \frac{4 a b \left(- \frac{1}{2 a} + \frac{\sqrt{- a^{3} b} \left(a - b\right)}{4 a^{3} b}\right) + a + b}{a - b} \right)} + \frac{x^{2}}{2 a}"," ",0,"(-1/(2*a) - sqrt(-a**3*b)*(a - b)/(4*a**3*b))*log(x**2 + (4*a*b*(-1/(2*a) - sqrt(-a**3*b)*(a - b)/(4*a**3*b)) + a + b)/(a - b)) + (-1/(2*a) + sqrt(-a**3*b)*(a - b)/(4*a**3*b))*log(x**2 + (4*a*b*(-1/(2*a) + sqrt(-a**3*b)*(a - b)/(4*a**3*b)) + a + b)/(a - b)) + x**2/(2*a)","B",0
907,1,117,0,0.599705," ","integrate(x**3/(a*x**4+2*a*x**2+a+b),x)","\left(\frac{1}{4 a} - \frac{\sqrt{- a^{3} b}}{4 a^{2} b}\right) \log{\left(x^{2} + \frac{- 4 a b \left(\frac{1}{4 a} - \frac{\sqrt{- a^{3} b}}{4 a^{2} b}\right) + a + b}{a} \right)} + \left(\frac{1}{4 a} + \frac{\sqrt{- a^{3} b}}{4 a^{2} b}\right) \log{\left(x^{2} + \frac{- 4 a b \left(\frac{1}{4 a} + \frac{\sqrt{- a^{3} b}}{4 a^{2} b}\right) + a + b}{a} \right)}"," ",0,"(1/(4*a) - sqrt(-a**3*b)/(4*a**2*b))*log(x**2 + (-4*a*b*(1/(4*a) - sqrt(-a**3*b)/(4*a**2*b)) + a + b)/a) + (1/(4*a) + sqrt(-a**3*b)/(4*a**2*b))*log(x**2 + (-4*a*b*(1/(4*a) + sqrt(-a**3*b)/(4*a**2*b)) + a + b)/a)","B",0
908,1,60,0,0.459494," ","integrate(x/(a*x**4+2*a*x**2+a+b),x)","- \frac{\sqrt{- \frac{1}{a b}} \log{\left(- b \sqrt{- \frac{1}{a b}} + x^{2} + 1 \right)}}{4} + \frac{\sqrt{- \frac{1}{a b}} \log{\left(b \sqrt{- \frac{1}{a b}} + x^{2} + 1 \right)}}{4}"," ",0,"-sqrt(-1/(a*b))*log(-b*sqrt(-1/(a*b)) + x**2 + 1)/4 + sqrt(-1/(a*b))*log(b*sqrt(-1/(a*b)) + x**2 + 1)/4","B",0
909,1,194,0,5.963514," ","integrate(1/x/(a*x**4+2*a*x**2+a+b),x)","\left(- \frac{1}{4 \left(a + b\right)} - \frac{\sqrt{- a b}}{4 b \left(a + b\right)}\right) \log{\left(x^{2} + \frac{- 4 a b \left(- \frac{1}{4 \left(a + b\right)} - \frac{\sqrt{- a b}}{4 b \left(a + b\right)}\right) + a - 4 b^{2} \left(- \frac{1}{4 \left(a + b\right)} - \frac{\sqrt{- a b}}{4 b \left(a + b\right)}\right) - b}{a} \right)} + \left(- \frac{1}{4 \left(a + b\right)} + \frac{\sqrt{- a b}}{4 b \left(a + b\right)}\right) \log{\left(x^{2} + \frac{- 4 a b \left(- \frac{1}{4 \left(a + b\right)} + \frac{\sqrt{- a b}}{4 b \left(a + b\right)}\right) + a - 4 b^{2} \left(- \frac{1}{4 \left(a + b\right)} + \frac{\sqrt{- a b}}{4 b \left(a + b\right)}\right) - b}{a} \right)} + \frac{\log{\left(x \right)}}{a + b}"," ",0,"(-1/(4*(a + b)) - sqrt(-a*b)/(4*b*(a + b)))*log(x**2 + (-4*a*b*(-1/(4*(a + b)) - sqrt(-a*b)/(4*b*(a + b))) + a - 4*b**2*(-1/(4*(a + b)) - sqrt(-a*b)/(4*b*(a + b))) - b)/a) + (-1/(4*(a + b)) + sqrt(-a*b)/(4*b*(a + b)))*log(x**2 + (-4*a*b*(-1/(4*(a + b)) + sqrt(-a*b)/(4*b*(a + b))) + a - 4*b**2*(-1/(4*(a + b)) + sqrt(-a*b)/(4*b*(a + b))) - b)/a) + log(x)/(a + b)","B",0
910,1,386,0,41.751954," ","integrate(1/x**3/(a*x**4+2*a*x**2+a+b),x)","- \frac{2 a \log{\left(x \right)}}{\left(a + b\right)^{2}} + \left(\frac{a}{2 \left(a + b\right)^{2}} - \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right) \log{\left(x^{2} + \frac{4 a^{2} b \left(\frac{a}{2 \left(a + b\right)^{2}} - \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right) + a^{2} + 8 a b^{2} \left(\frac{a}{2 \left(a + b\right)^{2}} - \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right) - 3 a b + 4 b^{3} \left(\frac{a}{2 \left(a + b\right)^{2}} - \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right)}{a^{2} - a b} \right)} + \left(\frac{a}{2 \left(a + b\right)^{2}} + \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right) \log{\left(x^{2} + \frac{4 a^{2} b \left(\frac{a}{2 \left(a + b\right)^{2}} + \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right) + a^{2} + 8 a b^{2} \left(\frac{a}{2 \left(a + b\right)^{2}} + \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right) - 3 a b + 4 b^{3} \left(\frac{a}{2 \left(a + b\right)^{2}} + \frac{\sqrt{- a b} \left(a - b\right)}{4 b \left(a^{2} + 2 a b + b^{2}\right)}\right)}{a^{2} - a b} \right)} - \frac{1}{x^{2} \left(2 a + 2 b\right)}"," ",0,"-2*a*log(x)/(a + b)**2 + (a/(2*(a + b)**2) - sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2)))*log(x**2 + (4*a**2*b*(a/(2*(a + b)**2) - sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2))) + a**2 + 8*a*b**2*(a/(2*(a + b)**2) - sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2))) - 3*a*b + 4*b**3*(a/(2*(a + b)**2) - sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2))))/(a**2 - a*b)) + (a/(2*(a + b)**2) + sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2)))*log(x**2 + (4*a**2*b*(a/(2*(a + b)**2) + sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2))) + a**2 + 8*a*b**2*(a/(2*(a + b)**2) + sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2))) - 3*a*b + 4*b**3*(a/(2*(a + b)**2) + sqrt(-a*b)*(a - b)/(4*b*(a**2 + 2*a*b + b**2))))/(a**2 - a*b)) - 1/(x**2*(2*a + 2*b))","B",0
911,1,105,0,2.197205," ","integrate(x**4/(a*x**4+2*a*x**2+a+b),x)","\operatorname{RootSum} {\left(256 t^{4} a^{5} b^{2} + t^{2} \left(- 32 a^{4} b + 96 a^{3} b^{2}\right) + a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{4} b + 4 t a^{3} - 24 t a^{2} b + 4 t a b^{2}}{3 a^{2} + 2 a b - b^{2}} \right)} \right)\right)} + \frac{x}{a}"," ",0,"RootSum(256*_t**4*a**5*b**2 + _t**2*(-32*a**4*b + 96*a**3*b**2) + a**3 + 3*a**2*b + 3*a*b**2 + b**3, Lambda(_t, _t*log(x + (-64*_t**3*a**4*b + 4*_t*a**3 - 24*_t*a**2*b + 4*_t*a*b**2)/(3*a**2 + 2*a*b - b**2)))) + x/a","A",0
912,1,44,0,0.827029," ","integrate(x**2/(a*x**4+2*a*x**2+a+b),x)","\operatorname{RootSum} {\left(256 t^{4} a^{3} b^{2} - 32 t^{2} a^{2} b + a + b, \left( t \mapsto t \log{\left(64 t^{3} a^{2} b - 4 t a + x \right)} \right)\right)}"," ",0,"RootSum(256*_t**4*a**3*b**2 - 32*_t**2*a**2*b + a + b, Lambda(_t, _t*log(64*_t**3*a**2*b - 4*_t*a + x)))","A",0
913,1,63,0,1.235194," ","integrate(1/(a*x**4+2*a*x**2+a+b),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{2} b^{2} + 256 a b^{3}\right) - 32 t^{2} a b + 1, \left( t \mapsto t \log{\left(64 t^{3} a^{2} b + 64 t^{3} a b^{2} - 4 t a + 4 t b + x \right)} \right)\right)}"," ",0,"RootSum(_t**4*(256*a**2*b**2 + 256*a*b**3) - 32*_t**2*a*b + 1, Lambda(_t, _t*log(64*_t**3*a**2*b + 64*_t**3*a*b**2 - 4*_t*a + 4*_t*b + x)))","A",0
914,1,134,0,4.536751," ","integrate(1/x**2/(a*x**4+2*a*x**2+a+b),x)","\operatorname{RootSum} {\left(t^{4} \left(256 a^{3} b^{2} + 768 a^{2} b^{3} + 768 a b^{4} + 256 b^{5}\right) + t^{2} \left(- 32 a^{2} b + 96 a b^{2}\right) + a, \left( t \mapsto t \log{\left(x + \frac{- 64 t^{3} a^{4} b - 128 t^{3} a^{3} b^{2} + 128 t^{3} a b^{4} + 64 t^{3} b^{5} + 4 t a^{3} - 40 t a^{2} b + 20 t a b^{2}}{3 a^{2} - a b} \right)} \right)\right)} - \frac{1}{x \left(a + b\right)}"," ",0,"RootSum(_t**4*(256*a**3*b**2 + 768*a**2*b**3 + 768*a*b**4 + 256*b**5) + _t**2*(-32*a**2*b + 96*a*b**2) + a, Lambda(_t, _t*log(x + (-64*_t**3*a**4*b - 128*_t**3*a**3*b**2 + 128*_t**3*a*b**4 + 64*_t**3*b**5 + 4*_t*a**3 - 40*_t*a**2*b + 20*_t*a*b**2)/(3*a**2 - a*b)))) - 1/(x*(a + b))","A",0
915,1,26,0,0.167975," ","integrate(x/(x**4+x**2+1),x)","\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x^{2}}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"sqrt(3)*atan(2*sqrt(3)*x**2/3 + sqrt(3)/3)/3","A",0
916,1,10,0,0.124362," ","integrate(x/(x**4+2*x**2+10),x)","\frac{\operatorname{atan}{\left(\frac{x^{2}}{3} + \frac{1}{3} \right)}}{6}"," ",0,"atan(x**2/3 + 1/3)/6","A",0
917,1,20,0,0.209090," ","integrate(x**2/(x**4+9*x**2+20),x)","- 2 \operatorname{atan}{\left(\frac{x}{2} \right)} + \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} \right)}"," ",0,"-2*atan(x/2) + sqrt(5)*atan(sqrt(5)*x/5)","A",0
918,1,63,0,0.307553," ","integrate(x**2/(x**4-x**2+1),x)","\frac{\sqrt{3} \log{\left(x^{2} - \sqrt{3} x + 1 \right)}}{12} - \frac{\sqrt{3} \log{\left(x^{2} + \sqrt{3} x + 1 \right)}}{12} + \frac{\operatorname{atan}{\left(2 x - \sqrt{3} \right)}}{2} + \frac{\operatorname{atan}{\left(2 x + \sqrt{3} \right)}}{2}"," ",0,"sqrt(3)*log(x**2 - sqrt(3)*x + 1)/12 - sqrt(3)*log(x**2 + sqrt(3)*x + 1)/12 + atan(2*x - sqrt(3))/2 + atan(2*x + sqrt(3))/2","A",0
919,1,24,0,0.829925," ","integrate(x**2/(x**4-2*x**2+2),x)","\operatorname{RootSum} {\left(128 t^{4} + 16 t^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} + 4 t + x \right)} \right)\right)}"," ",0,"RootSum(128*_t**4 + 16*_t**2 + 1, Lambda(_t, _t*log(64*_t**3 + 4*_t + x)))","A",0
920,0,0,0,0.000000," ","integrate(x**7*(c*x**4+b*x**2+a)**(1/2),x)","\int x^{7} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(x**7*sqrt(a + b*x**2 + c*x**4), x)","F",0
921,0,0,0,0.000000," ","integrate(x**5*(c*x**4+b*x**2+a)**(1/2),x)","\int x^{5} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(x**5*sqrt(a + b*x**2 + c*x**4), x)","F",0
922,0,0,0,0.000000," ","integrate(x**3*(c*x**4+b*x**2+a)**(1/2),x)","\int x^{3} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*x**2 + c*x**4), x)","F",0
923,0,0,0,0.000000," ","integrate(x*(c*x**4+b*x**2+a)**(1/2),x)","\int x \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(x*sqrt(a + b*x**2 + c*x**4), x)","F",0
924,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x, x)","F",0
925,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**3,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**3, x)","F",0
926,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**5,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{5}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**5, x)","F",0
927,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**7,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{7}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**7, x)","F",0
928,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**9,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{9}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**9, x)","F",0
929,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**11,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{11}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**11, x)","F",0
930,0,0,0,0.000000," ","integrate(x**4*(c*x**4+b*x**2+a)**(1/2),x)","\int x^{4} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(x**4*sqrt(a + b*x**2 + c*x**4), x)","F",0
931,0,0,0,0.000000," ","integrate(x**2*(c*x**4+b*x**2+a)**(1/2),x)","\int x^{2} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*x**2 + c*x**4), x)","F",0
932,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2),x)","\int \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4), x)","F",0
933,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**2,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**2, x)","F",0
934,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**4,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**4, x)","F",0
935,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/x**6,x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{x^{6}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/x**6, x)","F",0
936,0,0,0,0.000000," ","integrate(x**7*(c*x**4+b*x**2+a)**(3/2),x)","\int x^{7} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**7*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
937,0,0,0,0.000000," ","integrate(x**5*(c*x**4+b*x**2+a)**(3/2),x)","\int x^{5} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**5*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
938,0,0,0,0.000000," ","integrate(x**3*(c*x**4+b*x**2+a)**(3/2),x)","\int x^{3} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
939,0,0,0,0.000000," ","integrate(x*(c*x**4+b*x**2+a)**(3/2),x)","\int x \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
940,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x, x)","F",0
941,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x**3,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x**3, x)","F",0
942,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x**5,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x**5, x)","F",0
943,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x**7,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x**7, x)","F",0
944,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x**9,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{9}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x**9, x)","F",0
945,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x**11,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{11}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x**11, x)","F",0
946,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x**13,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{13}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x**13, x)","F",0
947,0,0,0,0.000000," ","integrate(x**4*(c*x**4+b*x**2+a)**(3/2),x)","\int x^{4} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**4*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
948,0,0,0,0.000000," ","integrate(x**2*(c*x**4+b*x**2+a)**(3/2),x)","\int x^{2} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
949,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2),x)","\int \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2), x)","F",0
950,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/x**2,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(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)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(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)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(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)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{x^{8}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(3/2)/x**8, x)","F",0
954,0,0,0,0.000000," ","integrate((-x**4-2*x**2+3)**(1/2),x)","\int \sqrt{- x^{4} - 2 x^{2} + 3}\, dx"," ",0,"Integral(sqrt(-x**4 - 2*x**2 + 3), x)","F",0
955,0,0,0,0.000000," ","integrate(x**7/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{7}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(x**7/sqrt(a + b*x**2 + c*x**4), x)","F",0
956,0,0,0,0.000000," ","integrate(x**5/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{5}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(x**5/sqrt(a + b*x**2 + c*x**4), x)","F",0
957,0,0,0,0.000000," ","integrate(x**3/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(x**3/sqrt(a + b*x**2 + c*x**4), x)","F",0
958,0,0,0,0.000000," ","integrate(x/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(x/sqrt(a + b*x**2 + c*x**4), x)","F",0
959,0,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*x**2 + c*x**4)), x)","F",0
960,0,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + b*x**2 + c*x**4)), x)","F",0
961,0,0,0,0.000000," ","integrate(1/x**5/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x^{5} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**5*sqrt(a + b*x**2 + c*x**4)), x)","F",0
962,0,0,0,0.000000," ","integrate(1/x**7/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x^{7} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**7*sqrt(a + b*x**2 + c*x**4)), x)","F",0
963,0,0,0,0.000000," ","integrate(x**4/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{4}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(x**4/sqrt(a + b*x**2 + c*x**4), x)","F",0
964,0,0,0,0.000000," ","integrate(x**2/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*x**2 + c*x**4), x)","F",0
965,0,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/sqrt(a + b*x**2 + c*x**4), x)","F",0
966,0,0,0,0.000000," ","integrate(1/x**2/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*x**2 + c*x**4)), x)","F",0
967,0,0,0,0.000000," ","integrate(1/x**4/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(a + b*x**2 + c*x**4)), x)","F",0
968,0,0,0,0.000000," ","integrate(x**7/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{7}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(x**7/sqrt(a + b*x**2 - c*x**4), x)","F",0
969,0,0,0,0.000000," ","integrate(x**5/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{5}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(x**5/sqrt(a + b*x**2 - c*x**4), x)","F",0
970,0,0,0,0.000000," ","integrate(x**3/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(x**3/sqrt(a + b*x**2 - c*x**4), x)","F",0
971,0,0,0,0.000000," ","integrate(x/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(x/sqrt(a + b*x**2 - c*x**4), x)","F",0
972,0,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2-a)**(1/2),x)","\int \frac{1}{x \sqrt{- a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x*sqrt(-a + b*x**2 + c*x**4)), x)","F",0
973,0,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2-a)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{- a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(-a + b*x**2 + c*x**4)), x)","F",0
974,0,0,0,0.000000," ","integrate(1/x**5/(c*x**4+b*x**2-a)**(1/2),x)","\int \frac{1}{x^{5} \sqrt{- a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**5*sqrt(-a + b*x**2 + c*x**4)), x)","F",0
975,0,0,0,0.000000," ","integrate(1/x**7/(c*x**4+b*x**2-a)**(1/2),x)","\int \frac{1}{x^{7} \sqrt{- a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(x**7*sqrt(-a + b*x**2 + c*x**4)), x)","F",0
976,0,0,0,0.000000," ","integrate(x**4/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{4}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(x**4/sqrt(a + b*x**2 - c*x**4), x)","F",0
977,0,0,0,0.000000," ","integrate(x**2/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*x**2 - c*x**4), x)","F",0
978,0,0,0,0.000000," ","integrate(1/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(1/sqrt(a + b*x**2 - c*x**4), x)","F",0
979,0,0,0,0.000000," ","integrate(1/x**2/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*x**2 - c*x**4)), x)","F",0
980,0,0,0,0.000000," ","integrate(1/x**4/(-c*x**4+b*x**2+a)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{a + b x^{2} - c x^{4}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(a + b*x**2 - c*x**4)), x)","F",0
981,0,0,0,0.000000," ","integrate(x**9/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x^{9}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**9/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
982,0,0,0,0.000000," ","integrate(x**7/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x^{7}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**7/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
983,0,0,0,0.000000," ","integrate(x**5/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x^{5}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**5/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
984,0,0,0,0.000000," ","integrate(x**3/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x^{3}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
985,0,0,0,0.000000," ","integrate(x/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
986,0,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{1}{x \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*x**2 + c*x**4)**(3/2)), x)","F",0
987,0,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{1}{x^{3} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**2 + c*x**4)**(3/2)), x)","F",0
988,0,0,0,0.000000," ","integrate(1/x**5/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{1}{x^{5} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**5*(a + b*x**2 + c*x**4)**(3/2)), x)","F",0
989,0,0,0,0.000000," ","integrate(x**6/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x^{6}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**6/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
990,0,0,0,0.000000," ","integrate(x**4/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x^{4}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
991,0,0,0,0.000000," ","integrate(x**2/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{x^{2}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
992,0,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(-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)","\int \frac{1}{x^{2} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**2 + c*x**4)**(3/2)), x)","F",0
994,0,0,0,0.000000," ","integrate(x**4/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{4}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**4/sqrt(x**2*(b + c*x**2)), x)","F",0
995,0,0,0,0.000000," ","integrate(x**3/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**3/sqrt(x**2*(b + c*x**2)), x)","F",0
996,0,0,0,0.000000," ","integrate(x**2/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x**2/sqrt(x**2*(b + c*x**2)), x)","F",0
997,0,0,0,0.000000," ","integrate(x/(c*x**4+b*x**2)**(1/2),x)","\int \frac{x}{\sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(x/sqrt(x**2*(b + c*x**2)), x)","F",0
998,0,0,0,0.000000," ","integrate(1/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/sqrt(b*x**2 + c*x**4), x)","F",0
999,0,0,0,0.000000," ","integrate(1/x/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x*sqrt(x**2*(b + c*x**2))), x)","F",0
1000,0,0,0,0.000000," ","integrate(1/x**2/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**2*sqrt(x**2*(b + c*x**2))), x)","F",0
1001,0,0,0,0.000000," ","integrate(1/x**3/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**3*sqrt(x**2*(b + c*x**2))), x)","F",0
1002,0,0,0,0.000000," ","integrate(1/x**4/(c*x**4+b*x**2)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{x^{2} \left(b + c x^{2}\right)}}\, dx"," ",0,"Integral(1/(x**4*sqrt(x**2*(b + c*x**2))), x)","F",0
1003,1,37,0,1.901798," ","integrate(x**4/(c*x**4+a)**(1/2),x)","\frac{x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{9}{4}\right)}"," ",0,"x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(9/4))","C",0
1004,1,22,0,0.886385," ","integrate(x**3/(c*x**4+a)**(1/2),x)","\begin{cases} \frac{\sqrt{a + c x^{4}}}{2 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(a + c*x**4)/(2*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True))","A",0
1005,1,37,0,0.914712," ","integrate(x**2/(c*x**4+a)**(1/2),x)","\frac{x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{7}{4}\right)}"," ",0,"x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(7/4))","C",0
1006,1,20,0,1.099358," ","integrate(x/(c*x**4+a)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{c} x^{2}}{\sqrt{a}} \right)}}{2 \sqrt{c}}"," ",0,"asinh(sqrt(c)*x**2/sqrt(a))/(2*sqrt(c))","A",0
1007,1,36,0,0.855186," ","integrate(1/(c*x**4+a)**(1/2),x)","\frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} \Gamma\left(\frac{5}{4}\right)}"," ",0,"x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*gamma(5/4))","C",0
1008,1,22,0,1.251220," ","integrate(1/x/(c*x**4+a)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{c} x^{2}} \right)}}{2 \sqrt{a}}"," ",0,"-asinh(sqrt(a)/(sqrt(c)*x**2))/(2*sqrt(a))","A",0
1009,1,39,0,1.108801," ","integrate(1/x**2/(c*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x \Gamma\left(\frac{3}{4}\right)}"," ",0,"gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x*gamma(3/4))","C",0
1010,1,20,0,0.842515," ","integrate(1/x**3/(c*x**4+a)**(1/2),x)","- \frac{\sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{2 a}"," ",0,"-sqrt(c)*sqrt(a/(c*x**4) + 1)/(2*a)","A",0
1011,1,41,0,1.074938," ","integrate(1/x**4/(c*x**4+a)**(1/2),x)","\frac{\Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{c x^{4} e^{i \pi}}{a}} \right)}}{4 \sqrt{a} x^{3} \Gamma\left(\frac{1}{4}\right)}"," ",0,"gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), c*x**4*exp_polar(I*pi)/a)/(4*sqrt(a)*x**3*gamma(1/4))","C",0
1012,1,95,0,4.611983," ","integrate(x**4/(b*x**2+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} + \frac{x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(3/2)*x/(8*b**2*sqrt(1 + b*x**2/a)) - sqrt(a)*x**3/(8*b*sqrt(1 + b*x**2/a)) + 3*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) + x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
1013,1,44,0,0.545466," ","integrate(x**3/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{2 a \sqrt{a + b x^{2}}}{3 b^{2}} + \frac{x^{2} \sqrt{a + b x^{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*sqrt(a + b*x**2)/(3*b**2) + x**2*sqrt(a + b*x**2)/(3*b), Ne(b, 0)), (x**4/(4*sqrt(a)), True))","A",0
1014,1,42,0,2.910841," ","integrate(x**2/(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}}"," ",0,"sqrt(a)*x*sqrt(1 + b*x**2/a)/(2*b) - a*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2))","A",0
1015,1,20,0,0.399891," ","integrate(x/(b*x**2+a)**(1/2),x)","\begin{cases} \frac{\sqrt{a + b x^{2}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(a + b*x**2)/b, Ne(b, 0)), (x**2/(2*sqrt(a)), True))","A",0
1016,1,17,0,1.197096," ","integrate(1/(b*x**2+a)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}}"," ",0,"asinh(sqrt(b)*x/sqrt(a))/sqrt(b)","A",0
1017,1,19,0,1.202692," ","integrate(1/x/(b*x**2+a)**(1/2),x)","- \frac{\operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{\sqrt{a}}"," ",0,"-asinh(sqrt(a)/(sqrt(b)*x))/sqrt(a)","A",0
1018,1,19,0,0.748526," ","integrate(1/x**2/(b*x**2+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{a}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/a","A",0
1019,1,42,0,3.472622," ","integrate(1/x**3/(b*x**2+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 a x} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*a*x) + b*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(3/2))","A",0
1020,1,46,0,1.048519," ","integrate(1/x**4/(b*x**2+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} + \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}}"," ",0,"-sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*a*x**2) + 2*b**(3/2)*sqrt(a/(b*x**2) + 1)/(3*a**2)","A",0
1021,1,15,0,0.627371," ","integrate(x**4/(c*x**4)**(1/2),x)","\frac{x^{5}}{3 \sqrt{c} \sqrt{x^{4}}}"," ",0,"x**5/(3*sqrt(c)*sqrt(x**4))","A",0
1022,1,15,0,0.527172," ","integrate(x**3/(c*x**4)**(1/2),x)","\frac{x^{4}}{2 \sqrt{c} \sqrt{x^{4}}}"," ",0,"x**4/(2*sqrt(c)*sqrt(x**4))","A",0
1023,1,14,0,0.482181," ","integrate(x**2/(c*x**4)**(1/2),x)","\frac{x^{3}}{\sqrt{c} \sqrt{x^{4}}}"," ",0,"x**3/(sqrt(c)*sqrt(x**4))","A",0
1024,0,0,0,0.000000," ","integrate(x/(c*x**4)**(1/2),x)","\int \frac{x}{\sqrt{c x^{4}}}\, dx"," ",0,"Integral(x/sqrt(c*x**4), x)","F",0
1025,1,14,0,0.472167," ","integrate(1/(c*x**4)**(1/2),x)","- \frac{x}{\sqrt{c} \sqrt{x^{4}}}"," ",0,"-x/(sqrt(c)*sqrt(x**4))","A",0
1026,1,15,0,0.514485," ","integrate(1/x/(c*x**4)**(1/2),x)","- \frac{1}{2 \sqrt{c} \sqrt{x^{4}}}"," ",0,"-1/(2*sqrt(c)*sqrt(x**4))","A",0
1027,1,17,0,0.556208," ","integrate(1/x**2/(c*x**4)**(1/2),x)","- \frac{1}{3 \sqrt{c} x \sqrt{x^{4}}}"," ",0,"-1/(3*sqrt(c)*x*sqrt(x**4))","A",0
1028,1,19,0,0.658177," ","integrate(1/x**3/(c*x**4)**(1/2),x)","- \frac{1}{4 \sqrt{c} x^{2} \sqrt{x^{4}}}"," ",0,"-1/(4*sqrt(c)*x**2*sqrt(x**4))","A",0
1029,1,19,0,0.707816," ","integrate(1/x**4/(c*x**4)**(1/2),x)","- \frac{1}{5 \sqrt{c} x^{3} \sqrt{x^{4}}}"," ",0,"-1/(5*sqrt(c)*x**3*sqrt(x**4))","A",0
1030,1,8,0,0.066454," ","integrate(x**4/a**(1/2),x)","\frac{x^{5}}{5 \sqrt{a}}"," ",0,"x**5/(5*sqrt(a))","A",0
1031,1,8,0,0.063217," ","integrate(x**3/a**(1/2),x)","\frac{x^{4}}{4 \sqrt{a}}"," ",0,"x**4/(4*sqrt(a))","A",0
1032,1,8,0,0.066099," ","integrate(x**2/a**(1/2),x)","\frac{x^{3}}{3 \sqrt{a}}"," ",0,"x**3/(3*sqrt(a))","A",0
1033,1,8,0,0.080510," ","integrate(x/a**(1/2),x)","\frac{x^{2}}{2 \sqrt{a}}"," ",0,"x**2/(2*sqrt(a))","A",0
1034,1,5,0,0.134770," ","integrate(1/a**(1/2),x)","\frac{x}{\sqrt{a}}"," ",0,"x/sqrt(a)","A",0
1035,1,7,0,0.081282," ","integrate(1/x/a**(1/2),x)","\frac{\log{\left(x \right)}}{\sqrt{a}}"," ",0,"log(x)/sqrt(a)","A",0
1036,1,8,0,0.077216," ","integrate(1/x**2/a**(1/2),x)","- \frac{1}{\sqrt{a} x}"," ",0,"-1/(sqrt(a)*x)","A",0
1037,1,12,0,0.075096," ","integrate(1/x**3/a**(1/2),x)","- \frac{1}{2 \sqrt{a} x^{2}}"," ",0,"-1/(2*sqrt(a)*x**2)","A",0
1038,1,12,0,0.074319," ","integrate(1/x**4/a**(1/2),x)","- \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)","\int \frac{1}{\sqrt{- x^{4} - 2 x^{2} + 3}}\, dx"," ",0,"Integral(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)","\int \frac{1}{\sqrt{- x^{4} + 5 x^{2} - 1}}\, dx"," ",0,"Integral(1/sqrt(-x**4 + 5*x**2 - 1), x)","F",0
1041,1,29,0,6.724509," ","integrate(x**(5/2)*(c*x**4+b*x**2+a),x)","\frac{2 a x^{\frac{7}{2}}}{7} + \frac{2 b x^{\frac{11}{2}}}{11} + \frac{2 c x^{\frac{15}{2}}}{15}"," ",0,"2*a*x**(7/2)/7 + 2*b*x**(11/2)/11 + 2*c*x**(15/2)/15","A",0
1042,1,29,0,2.671769," ","integrate(x**(3/2)*(c*x**4+b*x**2+a),x)","\frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{9}{2}}}{9} + \frac{2 c x^{\frac{13}{2}}}{13}"," ",0,"2*a*x**(5/2)/5 + 2*b*x**(9/2)/9 + 2*c*x**(13/2)/13","A",0
1043,1,29,0,2.101589," ","integrate(x**(1/2)*(c*x**4+b*x**2+a),x)","\frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{11}{2}}}{11}"," ",0,"2*a*x**(3/2)/3 + 2*b*x**(7/2)/7 + 2*c*x**(11/2)/11","A",0
1044,1,27,0,0.817921," ","integrate((c*x**4+b*x**2+a)/x**(1/2),x)","2 a \sqrt{x} + \frac{2 b x^{\frac{5}{2}}}{5} + \frac{2 c x^{\frac{9}{2}}}{9}"," ",0,"2*a*sqrt(x) + 2*b*x**(5/2)/5 + 2*c*x**(9/2)/9","A",0
1045,1,27,0,1.041375," ","integrate((c*x**4+b*x**2+a)/x**(3/2),x)","- \frac{2 a}{\sqrt{x}} + \frac{2 b x^{\frac{3}{2}}}{3} + \frac{2 c x^{\frac{7}{2}}}{7}"," ",0,"-2*a/sqrt(x) + 2*b*x**(3/2)/3 + 2*c*x**(7/2)/7","A",0
1046,1,27,0,1.282210," ","integrate((c*x**4+b*x**2+a)/x**(5/2),x)","- \frac{2 a}{3 x^{\frac{3}{2}}} + 2 b \sqrt{x} + \frac{2 c x^{\frac{5}{2}}}{5}"," ",0,"-2*a/(3*x**(3/2)) + 2*b*sqrt(x) + 2*c*x**(5/2)/5","A",0
1047,1,27,0,1.870701," ","integrate((c*x**4+b*x**2+a)/x**(7/2),x)","- \frac{2 a}{5 x^{\frac{5}{2}}} - \frac{2 b}{\sqrt{x}} + \frac{2 c x^{\frac{3}{2}}}{3}"," ",0,"-2*a/(5*x**(5/2)) - 2*b/sqrt(x) + 2*c*x**(3/2)/3","A",0
1048,1,70,0,22.350794," ","integrate(x**(5/2)*(c*x**4+b*x**2+a)**2,x)","\frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{11}{2}}}{11} + \frac{4 a c x^{\frac{15}{2}}}{15} + \frac{2 b^{2} x^{\frac{15}{2}}}{15} + \frac{4 b c x^{\frac{19}{2}}}{19} + \frac{2 c^{2} x^{\frac{23}{2}}}{23}"," ",0,"2*a**2*x**(7/2)/7 + 4*a*b*x**(11/2)/11 + 4*a*c*x**(15/2)/15 + 2*b**2*x**(15/2)/15 + 4*b*c*x**(19/2)/19 + 2*c**2*x**(23/2)/23","A",0
1049,1,70,0,12.364730," ","integrate(x**(3/2)*(c*x**4+b*x**2+a)**2,x)","\frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b x^{\frac{9}{2}}}{9} + \frac{4 a c x^{\frac{13}{2}}}{13} + \frac{2 b^{2} x^{\frac{13}{2}}}{13} + \frac{4 b c x^{\frac{17}{2}}}{17} + \frac{2 c^{2} x^{\frac{21}{2}}}{21}"," ",0,"2*a**2*x**(5/2)/5 + 4*a*b*x**(9/2)/9 + 4*a*c*x**(13/2)/13 + 2*b**2*x**(13/2)/13 + 4*b*c*x**(17/2)/17 + 2*c**2*x**(21/2)/21","A",0
1050,1,63,0,3.454134," ","integrate(x**(1/2)*(c*x**4+b*x**2+a)**2,x)","\frac{2 a^{2} x^{\frac{3}{2}}}{3} + \frac{4 a b x^{\frac{7}{2}}}{7} + \frac{4 b c x^{\frac{15}{2}}}{15} + \frac{2 c^{2} x^{\frac{19}{2}}}{19} + \frac{2 x^{\frac{11}{2}} \left(2 a c + b^{2}\right)}{11}"," ",0,"2*a**2*x**(3/2)/3 + 4*a*b*x**(7/2)/7 + 4*b*c*x**(15/2)/15 + 2*c**2*x**(19/2)/19 + 2*x**(11/2)*(2*a*c + b**2)/11","A",0
1051,1,68,0,4.995719," ","integrate((c*x**4+b*x**2+a)**2/x**(1/2),x)","2 a^{2} \sqrt{x} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{4 a c x^{\frac{9}{2}}}{9} + \frac{2 b^{2} x^{\frac{9}{2}}}{9} + \frac{4 b c x^{\frac{13}{2}}}{13} + \frac{2 c^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*a**2*sqrt(x) + 4*a*b*x**(5/2)/5 + 4*a*c*x**(9/2)/9 + 2*b**2*x**(9/2)/9 + 4*b*c*x**(13/2)/13 + 2*c**2*x**(17/2)/17","A",0
1052,1,68,0,5.653623," ","integrate((c*x**4+b*x**2+a)**2/x**(3/2),x)","- \frac{2 a^{2}}{\sqrt{x}} + \frac{4 a b x^{\frac{3}{2}}}{3} + \frac{4 a c x^{\frac{7}{2}}}{7} + \frac{2 b^{2} x^{\frac{7}{2}}}{7} + \frac{4 b c x^{\frac{11}{2}}}{11} + \frac{2 c^{2} x^{\frac{15}{2}}}{15}"," ",0,"-2*a**2/sqrt(x) + 4*a*b*x**(3/2)/3 + 4*a*c*x**(7/2)/7 + 2*b**2*x**(7/2)/7 + 4*b*c*x**(11/2)/11 + 2*c**2*x**(15/2)/15","A",0
1053,1,68,0,6.891603," ","integrate((c*x**4+b*x**2+a)**2/x**(5/2),x)","- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + 4 a b \sqrt{x} + \frac{4 a c x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{5}{2}}}{5} + \frac{4 b c x^{\frac{9}{2}}}{9} + \frac{2 c^{2} x^{\frac{13}{2}}}{13}"," ",0,"-2*a**2/(3*x**(3/2)) + 4*a*b*sqrt(x) + 4*a*c*x**(5/2)/5 + 2*b**2*x**(5/2)/5 + 4*b*c*x**(9/2)/9 + 2*c**2*x**(13/2)/13","A",0
1054,1,68,0,9.108918," ","integrate((c*x**4+b*x**2+a)**2/x**(7/2),x)","- \frac{2 a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 a b}{\sqrt{x}} + \frac{4 a c x^{\frac{3}{2}}}{3} + \frac{2 b^{2} x^{\frac{3}{2}}}{3} + \frac{4 b c x^{\frac{7}{2}}}{7} + \frac{2 c^{2} x^{\frac{11}{2}}}{11}"," ",0,"-2*a**2/(5*x**(5/2)) - 4*a*b/sqrt(x) + 4*a*c*x**(3/2)/3 + 2*b**2*x**(3/2)/3 + 4*b*c*x**(7/2)/7 + 2*c**2*x**(11/2)/11","A",0
1055,1,129,0,60.632061," ","integrate(x**(5/2)*(c*x**4+b*x**2+a)**3,x)","\frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{6 a^{2} b x^{\frac{11}{2}}}{11} + \frac{2 a^{2} c x^{\frac{15}{2}}}{5} + \frac{2 a b^{2} x^{\frac{15}{2}}}{5} + \frac{12 a b c x^{\frac{19}{2}}}{19} + \frac{6 a c^{2} x^{\frac{23}{2}}}{23} + \frac{2 b^{3} x^{\frac{19}{2}}}{19} + \frac{6 b^{2} c x^{\frac{23}{2}}}{23} + \frac{2 b c^{2} x^{\frac{27}{2}}}{9} + \frac{2 c^{3} x^{\frac{31}{2}}}{31}"," ",0,"2*a**3*x**(7/2)/7 + 6*a**2*b*x**(11/2)/11 + 2*a**2*c*x**(15/2)/5 + 2*a*b**2*x**(15/2)/5 + 12*a*b*c*x**(19/2)/19 + 6*a*c**2*x**(23/2)/23 + 2*b**3*x**(19/2)/19 + 6*b**2*c*x**(23/2)/23 + 2*b*c**2*x**(27/2)/9 + 2*c**3*x**(31/2)/31","A",0
1056,1,129,0,39.320714," ","integrate(x**(3/2)*(c*x**4+b*x**2+a)**3,x)","\frac{2 a^{3} x^{\frac{5}{2}}}{5} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 a^{2} c x^{\frac{13}{2}}}{13} + \frac{6 a b^{2} x^{\frac{13}{2}}}{13} + \frac{12 a b c x^{\frac{17}{2}}}{17} + \frac{2 a c^{2} x^{\frac{21}{2}}}{7} + \frac{2 b^{3} x^{\frac{17}{2}}}{17} + \frac{2 b^{2} c x^{\frac{21}{2}}}{7} + \frac{6 b c^{2} x^{\frac{25}{2}}}{25} + \frac{2 c^{3} x^{\frac{29}{2}}}{29}"," ",0,"2*a**3*x**(5/2)/5 + 2*a**2*b*x**(9/2)/3 + 6*a**2*c*x**(13/2)/13 + 6*a*b**2*x**(13/2)/13 + 12*a*b*c*x**(17/2)/17 + 2*a*c**2*x**(21/2)/7 + 2*b**3*x**(17/2)/17 + 2*b**2*c*x**(21/2)/7 + 6*b*c**2*x**(25/2)/25 + 2*c**3*x**(29/2)/29","A",0
1057,1,112,0,6.047281," ","integrate(x**(1/2)*(c*x**4+b*x**2+a)**3,x)","\frac{2 a^{3} x^{\frac{3}{2}}}{3} + \frac{6 a^{2} b x^{\frac{7}{2}}}{7} + \frac{6 b c^{2} x^{\frac{23}{2}}}{23} + \frac{2 c^{3} x^{\frac{27}{2}}}{27} + \frac{2 x^{\frac{19}{2}} \left(3 a c^{2} + 3 b^{2} c\right)}{19} + \frac{2 x^{\frac{15}{2}} \left(6 a b c + b^{3}\right)}{15} + \frac{2 x^{\frac{11}{2}} \left(3 a^{2} c + 3 a b^{2}\right)}{11}"," ",0,"2*a**3*x**(3/2)/3 + 6*a**2*b*x**(7/2)/7 + 6*b*c**2*x**(23/2)/23 + 2*c**3*x**(27/2)/27 + 2*x**(19/2)*(3*a*c**2 + 3*b**2*c)/19 + 2*x**(15/2)*(6*a*b*c + b**3)/15 + 2*x**(11/2)*(3*a**2*c + 3*a*b**2)/11","A",0
1058,1,128,0,23.500606," ","integrate((c*x**4+b*x**2+a)**3/x**(1/2),x)","2 a^{3} \sqrt{x} + \frac{6 a^{2} b x^{\frac{5}{2}}}{5} + \frac{2 a^{2} c x^{\frac{9}{2}}}{3} + \frac{2 a b^{2} x^{\frac{9}{2}}}{3} + \frac{12 a b c x^{\frac{13}{2}}}{13} + \frac{6 a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 b^{3} x^{\frac{13}{2}}}{13} + \frac{6 b^{2} c x^{\frac{17}{2}}}{17} + \frac{2 b c^{2} x^{\frac{21}{2}}}{7} + \frac{2 c^{3} x^{\frac{25}{2}}}{25}"," ",0,"2*a**3*sqrt(x) + 6*a**2*b*x**(5/2)/5 + 2*a**2*c*x**(9/2)/3 + 2*a*b**2*x**(9/2)/3 + 12*a*b*c*x**(13/2)/13 + 6*a*c**2*x**(17/2)/17 + 2*b**3*x**(13/2)/13 + 6*b**2*c*x**(17/2)/17 + 2*b*c**2*x**(21/2)/7 + 2*c**3*x**(25/2)/25","A",0
1059,1,126,0,19.834948," ","integrate((c*x**4+b*x**2+a)**3/x**(3/2),x)","- \frac{2 a^{3}}{\sqrt{x}} + 2 a^{2} b x^{\frac{3}{2}} + \frac{6 a^{2} c x^{\frac{7}{2}}}{7} + \frac{6 a b^{2} x^{\frac{7}{2}}}{7} + \frac{12 a b c x^{\frac{11}{2}}}{11} + \frac{2 a c^{2} x^{\frac{15}{2}}}{5} + \frac{2 b^{3} x^{\frac{11}{2}}}{11} + \frac{2 b^{2} c x^{\frac{15}{2}}}{5} + \frac{6 b c^{2} x^{\frac{19}{2}}}{19} + \frac{2 c^{3} x^{\frac{23}{2}}}{23}"," ",0,"-2*a**3/sqrt(x) + 2*a**2*b*x**(3/2) + 6*a**2*c*x**(7/2)/7 + 6*a*b**2*x**(7/2)/7 + 12*a*b*c*x**(11/2)/11 + 2*a*c**2*x**(15/2)/5 + 2*b**3*x**(11/2)/11 + 2*b**2*c*x**(15/2)/5 + 6*b*c**2*x**(19/2)/19 + 2*c**3*x**(23/2)/23","A",0
1060,1,128,0,25.436554," ","integrate((c*x**4+b*x**2+a)**3/x**(5/2),x)","- \frac{2 a^{3}}{3 x^{\frac{3}{2}}} + 6 a^{2} b \sqrt{x} + \frac{6 a^{2} c x^{\frac{5}{2}}}{5} + \frac{6 a b^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b c x^{\frac{9}{2}}}{3} + \frac{6 a c^{2} x^{\frac{13}{2}}}{13} + \frac{2 b^{3} x^{\frac{9}{2}}}{9} + \frac{6 b^{2} c x^{\frac{13}{2}}}{13} + \frac{6 b c^{2} x^{\frac{17}{2}}}{17} + \frac{2 c^{3} x^{\frac{21}{2}}}{21}"," ",0,"-2*a**3/(3*x**(3/2)) + 6*a**2*b*sqrt(x) + 6*a**2*c*x**(5/2)/5 + 6*a*b**2*x**(5/2)/5 + 4*a*b*c*x**(9/2)/3 + 6*a*c**2*x**(13/2)/13 + 2*b**3*x**(9/2)/9 + 6*b**2*c*x**(13/2)/13 + 6*b*c**2*x**(17/2)/17 + 2*c**3*x**(21/2)/21","A",0
1061,1,124,0,31.860478," ","integrate((c*x**4+b*x**2+a)**3/x**(7/2),x)","- \frac{2 a^{3}}{5 x^{\frac{5}{2}}} - \frac{6 a^{2} b}{\sqrt{x}} + 2 a^{2} c x^{\frac{3}{2}} + 2 a b^{2} x^{\frac{3}{2}} + \frac{12 a b c x^{\frac{7}{2}}}{7} + \frac{6 a c^{2} x^{\frac{11}{2}}}{11} + \frac{2 b^{3} x^{\frac{7}{2}}}{7} + \frac{6 b^{2} c x^{\frac{11}{2}}}{11} + \frac{2 b c^{2} x^{\frac{15}{2}}}{5} + \frac{2 c^{3} x^{\frac{19}{2}}}{19}"," ",0,"-2*a**3/(5*x**(5/2)) - 6*a**2*b/sqrt(x) + 2*a**2*c*x**(3/2) + 2*a*b**2*x**(3/2) + 12*a*b*c*x**(7/2)/7 + 6*a*c**2*x**(11/2)/11 + 2*b**3*x**(7/2)/7 + 6*b**2*c*x**(11/2)/11 + 2*b*c**2*x**(15/2)/5 + 2*c**3*x**(19/2)/19","A",0
1062,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1063,-1,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1064,-1,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1065,-1,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1066,-1,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1067,-1,0,0,0.000000," ","integrate(1/x**(1/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1068,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1069,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1070,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(c*x**4+b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1071,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1072,-1,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1073,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1074,-1,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1075,-1,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1076,-1,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1077,-1,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1078,-1,0,0,0.000000," ","integrate(1/x**(1/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1079,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1080,-1,0,0,0.000000," ","integrate(x**(15/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1081,-1,0,0,0.000000," ","integrate(x**(13/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1082,-1,0,0,0.000000," ","integrate(x**(11/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1083,-1,0,0,0.000000," ","integrate(x**(9/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1084,-1,0,0,0.000000," ","integrate(x**(7/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1085,-1,0,0,0.000000," ","integrate(x**(5/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1086,-1,0,0,0.000000," ","integrate(x**(3/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1087,-1,0,0,0.000000," ","integrate(x**(1/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,-1,0,0,0.000000," ","integrate(1/x**(1/2)/(c*x**4+b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1089,0,0,0,0.000000," ","integrate((d*x)**(3/2)*(c*x**4+b*x**2+a)**(1/2),x)","\int \left(d x\right)^{\frac{3}{2}} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral((d*x)**(3/2)*sqrt(a + b*x**2 + c*x**4), x)","F",0
1090,0,0,0,0.000000," ","integrate((d*x)**(1/2)*(c*x**4+b*x**2+a)**(1/2),x)","\int \sqrt{d x} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral(sqrt(d*x)*sqrt(a + b*x**2 + c*x**4), x)","F",0
1091,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(1/2)/(d*x)**(1/2),x)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{\sqrt{d x}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/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)","\int \frac{\sqrt{a + b x^{2} + c x^{4}}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2 + c*x**4)/(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)","\int \left(d x\right)^{\frac{3}{2}} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**(3/2)*(a + b*x**2 + c*x**4)**(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)","\int \sqrt{d x} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(d*x)*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
1095,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**(3/2)/(d*x)**(1/2),x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{\sqrt{d x}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(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)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**(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)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((d*x)**(3/2)/sqrt(a + b*x**2 + c*x**4), x)","F",0
1098,0,0,0,0.000000," ","integrate((d*x)**(1/2)/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{\sqrt{d x}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(sqrt(d*x)/sqrt(a + b*x**2 + c*x**4), 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)","\int \frac{1}{\sqrt{d x} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*sqrt(a + b*x**2 + c*x**4)), 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)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*sqrt(a + b*x**2 + c*x**4)), x)","F",0
1101,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**(3/2)/(a + b*x**2 + c*x**4)**(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)","\int \frac{\sqrt{d x}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d*x)/(a + b*x**2 + c*x**4)**(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)","\int \frac{1}{\sqrt{d x} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*(a + b*x**2 + c*x**4)**(3/2)), 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)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*(a + b*x**2 + c*x**4)**(3/2)), x)","F",0
1105,1,4451,0,7.267910," ","integrate((d*x)**m*(c*x**4+b*x**2+a)**3,x)","\begin{cases} \frac{- \frac{a^{3}}{12 x^{12}} - \frac{3 a^{2} b}{10 x^{10}} - \frac{3 a^{2} c}{8 x^{8}} - \frac{3 a b^{2}}{8 x^{8}} - \frac{a b c}{x^{6}} - \frac{3 a c^{2}}{4 x^{4}} - \frac{b^{3}}{6 x^{6}} - \frac{3 b^{2} c}{4 x^{4}} - \frac{3 b c^{2}}{2 x^{2}} + c^{3} \log{\left(x \right)}}{d^{13}} & \text{for}\: m = -13 \\\frac{- \frac{a^{3}}{10 x^{10}} - \frac{3 a^{2} b}{8 x^{8}} - \frac{a^{2} c}{2 x^{6}} - \frac{a b^{2}}{2 x^{6}} - \frac{3 a b c}{2 x^{4}} - \frac{3 a c^{2}}{2 x^{2}} - \frac{b^{3}}{4 x^{4}} - \frac{3 b^{2} c}{2 x^{2}} + 3 b c^{2} \log{\left(x \right)} + \frac{c^{3} x^{2}}{2}}{d^{11}} & \text{for}\: m = -11 \\\frac{- \frac{a^{3}}{8 x^{8}} - \frac{a^{2} b}{2 x^{6}} - \frac{3 a^{2} c}{4 x^{4}} - \frac{3 a b^{2}}{4 x^{4}} - \frac{3 a b c}{x^{2}} + 3 a c^{2} \log{\left(x \right)} - \frac{b^{3}}{2 x^{2}} + 3 b^{2} c \log{\left(x \right)} + \frac{3 b c^{2} x^{2}}{2} + \frac{c^{3} x^{4}}{4}}{d^{9}} & \text{for}\: m = -9 \\\frac{- \frac{a^{3}}{6 x^{6}} - \frac{3 a^{2} b}{4 x^{4}} - \frac{3 a^{2} c}{2 x^{2}} - \frac{3 a b^{2}}{2 x^{2}} + 6 a b c \log{\left(x \right)} + \frac{3 a c^{2} x^{2}}{2} + b^{3} \log{\left(x \right)} + \frac{3 b^{2} c x^{2}}{2} + \frac{3 b c^{2} x^{4}}{4} + \frac{c^{3} x^{6}}{6}}{d^{7}} & \text{for}\: m = -7 \\\frac{- \frac{a^{3}}{4 x^{4}} - \frac{3 a^{2} b}{2 x^{2}} + 3 a^{2} c \log{\left(x \right)} + 3 a b^{2} \log{\left(x \right)} + 3 a b c x^{2} + \frac{3 a c^{2} x^{4}}{4} + \frac{b^{3} x^{2}}{2} + \frac{3 b^{2} c x^{4}}{4} + \frac{b c^{2} x^{6}}{2} + \frac{c^{3} x^{8}}{8}}{d^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a^{3}}{2 x^{2}} + 3 a^{2} b \log{\left(x \right)} + \frac{3 a^{2} c x^{2}}{2} + \frac{3 a b^{2} x^{2}}{2} + \frac{3 a b c x^{4}}{2} + \frac{a c^{2} x^{6}}{2} + \frac{b^{3} x^{4}}{4} + \frac{b^{2} c x^{6}}{2} + \frac{3 b c^{2} x^{8}}{8} + \frac{c^{3} x^{10}}{10}}{d^{3}} & \text{for}\: m = -3 \\\frac{a^{3} \log{\left(x \right)} + \frac{3 a^{2} b x^{2}}{2} + \frac{3 a^{2} c x^{4}}{4} + \frac{3 a b^{2} x^{4}}{4} + a b c x^{6} + \frac{3 a c^{2} x^{8}}{8} + \frac{b^{3} x^{6}}{6} + \frac{3 b^{2} c x^{8}}{8} + \frac{3 b c^{2} x^{10}}{10} + \frac{c^{3} x^{12}}{12}}{d} & \text{for}\: m = -1 \\\frac{a^{3} d^{m} m^{6} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{48 a^{3} d^{m} m^{5} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{925 a^{3} d^{m} m^{4} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{9120 a^{3} d^{m} m^{3} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{48259 a^{3} d^{m} m^{2} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{129072 a^{3} d^{m} m x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{135135 a^{3} d^{m} x x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3 a^{2} b d^{m} m^{6} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{138 a^{2} b d^{m} m^{5} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{2505 a^{2} b d^{m} m^{4} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{22620 a^{2} b d^{m} m^{3} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{104277 a^{2} b d^{m} m^{2} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{219162 a^{2} b d^{m} m x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{135135 a^{2} b d^{m} x^{3} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3 a^{2} c d^{m} m^{6} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{132 a^{2} c d^{m} m^{5} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{2259 a^{2} c d^{m} m^{4} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{18840 a^{2} c d^{m} m^{3} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{77937 a^{2} c d^{m} m^{2} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{142308 a^{2} c d^{m} m x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{81081 a^{2} c d^{m} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3 a b^{2} d^{m} m^{6} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{132 a b^{2} d^{m} m^{5} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{2259 a b^{2} d^{m} m^{4} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{18840 a b^{2} d^{m} m^{3} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{77937 a b^{2} d^{m} m^{2} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{142308 a b^{2} d^{m} m x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{81081 a b^{2} d^{m} x^{5} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{6 a b c d^{m} m^{6} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{252 a b c d^{m} m^{5} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{4074 a b c d^{m} m^{4} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{31752 a b c d^{m} m^{3} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{122010 a b c d^{m} m^{2} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{209916 a b c d^{m} m x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{115830 a b c d^{m} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3 a c^{2} d^{m} m^{6} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{120 a c^{2} d^{m} m^{5} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{1839 a c^{2} d^{m} m^{4} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{13584 a c^{2} d^{m} m^{3} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{49881 a c^{2} d^{m} m^{2} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{83064 a c^{2} d^{m} m x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{45045 a c^{2} d^{m} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{b^{3} d^{m} m^{6} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{42 b^{3} d^{m} m^{5} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{679 b^{3} d^{m} m^{4} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{5292 b^{3} d^{m} m^{3} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{20335 b^{3} d^{m} m^{2} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{34986 b^{3} d^{m} m x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{19305 b^{3} d^{m} x^{7} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3 b^{2} c d^{m} m^{6} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{120 b^{2} c d^{m} m^{5} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{1839 b^{2} c d^{m} m^{4} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{13584 b^{2} c d^{m} m^{3} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{49881 b^{2} c d^{m} m^{2} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{83064 b^{2} c d^{m} m x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{45045 b^{2} c d^{m} x^{9} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3 b c^{2} d^{m} m^{6} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{114 b c^{2} d^{m} m^{5} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{1665 b c^{2} d^{m} m^{4} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{11820 b c^{2} d^{m} m^{3} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{42117 b c^{2} d^{m} m^{2} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{68706 b c^{2} d^{m} m x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{36855 b c^{2} d^{m} x^{11} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{c^{3} d^{m} m^{6} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{36 c^{3} d^{m} m^{5} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{505 c^{3} d^{m} m^{4} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{3480 c^{3} d^{m} m^{3} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{12139 c^{3} d^{m} m^{2} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{19524 c^{3} d^{m} m x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} + \frac{10395 c^{3} d^{m} x^{13} x^{m}}{m^{7} + 49 m^{6} + 973 m^{5} + 10045 m^{4} + 57379 m^{3} + 177331 m^{2} + 264207 m + 135135} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**3/(12*x**12) - 3*a**2*b/(10*x**10) - 3*a**2*c/(8*x**8) - 3*a*b**2/(8*x**8) - a*b*c/x**6 - 3*a*c**2/(4*x**4) - b**3/(6*x**6) - 3*b**2*c/(4*x**4) - 3*b*c**2/(2*x**2) + c**3*log(x))/d**13, Eq(m, -13)), ((-a**3/(10*x**10) - 3*a**2*b/(8*x**8) - a**2*c/(2*x**6) - a*b**2/(2*x**6) - 3*a*b*c/(2*x**4) - 3*a*c**2/(2*x**2) - b**3/(4*x**4) - 3*b**2*c/(2*x**2) + 3*b*c**2*log(x) + c**3*x**2/2)/d**11, Eq(m, -11)), ((-a**3/(8*x**8) - a**2*b/(2*x**6) - 3*a**2*c/(4*x**4) - 3*a*b**2/(4*x**4) - 3*a*b*c/x**2 + 3*a*c**2*log(x) - b**3/(2*x**2) + 3*b**2*c*log(x) + 3*b*c**2*x**2/2 + c**3*x**4/4)/d**9, Eq(m, -9)), ((-a**3/(6*x**6) - 3*a**2*b/(4*x**4) - 3*a**2*c/(2*x**2) - 3*a*b**2/(2*x**2) + 6*a*b*c*log(x) + 3*a*c**2*x**2/2 + b**3*log(x) + 3*b**2*c*x**2/2 + 3*b*c**2*x**4/4 + c**3*x**6/6)/d**7, Eq(m, -7)), ((-a**3/(4*x**4) - 3*a**2*b/(2*x**2) + 3*a**2*c*log(x) + 3*a*b**2*log(x) + 3*a*b*c*x**2 + 3*a*c**2*x**4/4 + b**3*x**2/2 + 3*b**2*c*x**4/4 + b*c**2*x**6/2 + c**3*x**8/8)/d**5, Eq(m, -5)), ((-a**3/(2*x**2) + 3*a**2*b*log(x) + 3*a**2*c*x**2/2 + 3*a*b**2*x**2/2 + 3*a*b*c*x**4/2 + a*c**2*x**6/2 + b**3*x**4/4 + b**2*c*x**6/2 + 3*b*c**2*x**8/8 + c**3*x**10/10)/d**3, Eq(m, -3)), ((a**3*log(x) + 3*a**2*b*x**2/2 + 3*a**2*c*x**4/4 + 3*a*b**2*x**4/4 + a*b*c*x**6 + 3*a*c**2*x**8/8 + b**3*x**6/6 + 3*b**2*c*x**8/8 + 3*b*c**2*x**10/10 + c**3*x**12/12)/d, Eq(m, -1)), (a**3*d**m*m**6*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 48*a**3*d**m*m**5*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 925*a**3*d**m*m**4*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 9120*a**3*d**m*m**3*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 48259*a**3*d**m*m**2*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 129072*a**3*d**m*m*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 135135*a**3*d**m*x*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3*a**2*b*d**m*m**6*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 138*a**2*b*d**m*m**5*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 2505*a**2*b*d**m*m**4*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 22620*a**2*b*d**m*m**3*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 104277*a**2*b*d**m*m**2*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 219162*a**2*b*d**m*m*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 135135*a**2*b*d**m*x**3*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3*a**2*c*d**m*m**6*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 132*a**2*c*d**m*m**5*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 2259*a**2*c*d**m*m**4*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 18840*a**2*c*d**m*m**3*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 77937*a**2*c*d**m*m**2*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 142308*a**2*c*d**m*m*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 81081*a**2*c*d**m*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3*a*b**2*d**m*m**6*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 132*a*b**2*d**m*m**5*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 2259*a*b**2*d**m*m**4*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 18840*a*b**2*d**m*m**3*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 77937*a*b**2*d**m*m**2*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 142308*a*b**2*d**m*m*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 81081*a*b**2*d**m*x**5*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 6*a*b*c*d**m*m**6*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 252*a*b*c*d**m*m**5*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 4074*a*b*c*d**m*m**4*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 31752*a*b*c*d**m*m**3*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 122010*a*b*c*d**m*m**2*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 209916*a*b*c*d**m*m*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 115830*a*b*c*d**m*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3*a*c**2*d**m*m**6*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 120*a*c**2*d**m*m**5*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 1839*a*c**2*d**m*m**4*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 13584*a*c**2*d**m*m**3*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 49881*a*c**2*d**m*m**2*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 83064*a*c**2*d**m*m*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 45045*a*c**2*d**m*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + b**3*d**m*m**6*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 42*b**3*d**m*m**5*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 679*b**3*d**m*m**4*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 5292*b**3*d**m*m**3*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 20335*b**3*d**m*m**2*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 34986*b**3*d**m*m*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 19305*b**3*d**m*x**7*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3*b**2*c*d**m*m**6*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 120*b**2*c*d**m*m**5*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 1839*b**2*c*d**m*m**4*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 13584*b**2*c*d**m*m**3*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 49881*b**2*c*d**m*m**2*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 83064*b**2*c*d**m*m*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 45045*b**2*c*d**m*x**9*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3*b*c**2*d**m*m**6*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 114*b*c**2*d**m*m**5*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 1665*b*c**2*d**m*m**4*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 11820*b*c**2*d**m*m**3*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 42117*b*c**2*d**m*m**2*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 68706*b*c**2*d**m*m*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 36855*b*c**2*d**m*x**11*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + c**3*d**m*m**6*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 36*c**3*d**m*m**5*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 505*c**3*d**m*m**4*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 3480*c**3*d**m*m**3*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 12139*c**3*d**m*m**2*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 19524*c**3*d**m*m*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135) + 10395*c**3*d**m*x**13*x**m/(m**7 + 49*m**6 + 973*m**5 + 10045*m**4 + 57379*m**3 + 177331*m**2 + 264207*m + 135135), True))","A",0
1106,1,1486,0,2.871179," ","integrate((d*x)**m*(c*x**4+b*x**2+a)**2,x)","\begin{cases} \frac{- \frac{a^{2}}{8 x^{8}} - \frac{a b}{3 x^{6}} - \frac{a c}{2 x^{4}} - \frac{b^{2}}{4 x^{4}} - \frac{b c}{x^{2}} + c^{2} \log{\left(x \right)}}{d^{9}} & \text{for}\: m = -9 \\\frac{- \frac{a^{2}}{6 x^{6}} - \frac{a b}{2 x^{4}} - \frac{a c}{x^{2}} - \frac{b^{2}}{2 x^{2}} + 2 b c \log{\left(x \right)} + \frac{c^{2} x^{2}}{2}}{d^{7}} & \text{for}\: m = -7 \\\frac{- \frac{a^{2}}{4 x^{4}} - \frac{a b}{x^{2}} + 2 a c \log{\left(x \right)} + b^{2} \log{\left(x \right)} + b c x^{2} + \frac{c^{2} x^{4}}{4}}{d^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a^{2}}{2 x^{2}} + 2 a b \log{\left(x \right)} + a c x^{2} + \frac{b^{2} x^{2}}{2} + \frac{b c x^{4}}{2} + \frac{c^{2} x^{6}}{6}}{d^{3}} & \text{for}\: m = -3 \\\frac{a^{2} \log{\left(x \right)} + a b x^{2} + \frac{a c x^{4}}{2} + \frac{b^{2} x^{4}}{4} + \frac{b c x^{6}}{3} + \frac{c^{2} x^{8}}{8}}{d} & \text{for}\: m = -1 \\\frac{a^{2} d^{m} m^{4} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{24 a^{2} d^{m} m^{3} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{206 a^{2} d^{m} m^{2} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{744 a^{2} d^{m} m x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{945 a^{2} d^{m} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{2 a b d^{m} m^{4} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{44 a b d^{m} m^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{328 a b d^{m} m^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{916 a b d^{m} m x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{630 a b d^{m} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{2 a c d^{m} m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{40 a c d^{m} m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{260 a c d^{m} m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{600 a c d^{m} m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{378 a c d^{m} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{b^{2} d^{m} m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{20 b^{2} d^{m} m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{130 b^{2} d^{m} m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{300 b^{2} d^{m} m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{189 b^{2} d^{m} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{2 b c d^{m} m^{4} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{36 b c d^{m} m^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{208 b c d^{m} m^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{444 b c d^{m} m x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{270 b c d^{m} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{c^{2} d^{m} m^{4} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{16 c^{2} d^{m} m^{3} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{86 c^{2} d^{m} m^{2} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{176 c^{2} d^{m} m x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{105 c^{2} d^{m} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a**2/(8*x**8) - a*b/(3*x**6) - a*c/(2*x**4) - b**2/(4*x**4) - b*c/x**2 + c**2*log(x))/d**9, Eq(m, -9)), ((-a**2/(6*x**6) - a*b/(2*x**4) - a*c/x**2 - b**2/(2*x**2) + 2*b*c*log(x) + c**2*x**2/2)/d**7, Eq(m, -7)), ((-a**2/(4*x**4) - a*b/x**2 + 2*a*c*log(x) + b**2*log(x) + b*c*x**2 + c**2*x**4/4)/d**5, Eq(m, -5)), ((-a**2/(2*x**2) + 2*a*b*log(x) + a*c*x**2 + b**2*x**2/2 + b*c*x**4/2 + c**2*x**6/6)/d**3, Eq(m, -3)), ((a**2*log(x) + a*b*x**2 + a*c*x**4/2 + b**2*x**4/4 + b*c*x**6/3 + c**2*x**8/8)/d, Eq(m, -1)), (a**2*d**m*m**4*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 24*a**2*d**m*m**3*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 206*a**2*d**m*m**2*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 744*a**2*d**m*m*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 945*a**2*d**m*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 2*a*b*d**m*m**4*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 44*a*b*d**m*m**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 328*a*b*d**m*m**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 916*a*b*d**m*m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 630*a*b*d**m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 2*a*c*d**m*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 40*a*c*d**m*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 260*a*c*d**m*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 600*a*c*d**m*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 378*a*c*d**m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + b**2*d**m*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 20*b**2*d**m*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 130*b**2*d**m*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 300*b**2*d**m*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 189*b**2*d**m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 2*b*c*d**m*m**4*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 36*b*c*d**m*m**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 208*b*c*d**m*m**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 444*b*c*d**m*m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 270*b*c*d**m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + c**2*d**m*m**4*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 16*c**2*d**m*m**3*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 86*c**2*d**m*m**2*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 176*c**2*d**m*m*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 105*c**2*d**m*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945), True))","A",0
1107,1,314,0,0.989267," ","integrate((d*x)**m*(c*x**4+b*x**2+a),x)","\begin{cases} \frac{- \frac{a}{4 x^{4}} - \frac{b}{2 x^{2}} + c \log{\left(x \right)}}{d^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a}{2 x^{2}} + b \log{\left(x \right)} + \frac{c x^{2}}{2}}{d^{3}} & \text{for}\: m = -3 \\\frac{a \log{\left(x \right)} + \frac{b x^{2}}{2} + \frac{c x^{4}}{4}}{d} & \text{for}\: m = -1 \\\frac{a d^{m} m^{2} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{8 a d^{m} m x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{15 a d^{m} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{b d^{m} m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{6 b d^{m} m x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{5 b d^{m} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{c d^{m} m^{2} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{4 c d^{m} m x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{3 c d^{m} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a/(4*x**4) - b/(2*x**2) + c*log(x))/d**5, Eq(m, -5)), ((-a/(2*x**2) + b*log(x) + c*x**2/2)/d**3, Eq(m, -3)), ((a*log(x) + b*x**2/2 + c*x**4/4)/d, Eq(m, -1)), (a*d**m*m**2*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 8*a*d**m*m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 15*a*d**m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + b*d**m*m**2*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 6*b*d**m*m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 5*b*d**m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + c*d**m*m**2*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 4*c*d**m*m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 3*c*d**m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15), True))","A",0
1108,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**4+b*x**2+a),x)","\int \frac{\left(d x\right)^{m}}{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral((d*x)**m/(a + b*x**2 + c*x**4), x)","F",0
1109,-1,0,0,0.000000," ","integrate((d*x)**m/(c*x**4+b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**4+b*x**2+a)**(3/2),x)","\int \left(d x\right)^{m} \left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*x)**m*(a + b*x**2 + c*x**4)**(3/2), x)","F",0
1111,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**4+b*x**2+a)**(1/2),x)","\int \left(d x\right)^{m} \sqrt{a + b x^{2} + c x^{4}}\, dx"," ",0,"Integral((d*x)**m*sqrt(a + b*x**2 + c*x**4), x)","F",0
1112,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**4+b*x**2+a)**(1/2),x)","\int \frac{\left(d x\right)^{m}}{\sqrt{a + b x^{2} + c x^{4}}}\, dx"," ",0,"Integral((d*x)**m/sqrt(a + b*x**2 + c*x**4), x)","F",0
1113,0,0,0,0.000000," ","integrate((d*x)**m/(c*x**4+b*x**2+a)**(3/2),x)","\int \frac{\left(d x\right)^{m}}{\left(a + b x^{2} + c x^{4}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m/(a + b*x**2 + c*x**4)**(3/2), x)","F",0
1114,-1,0,0,0.000000," ","integrate((d*x)**m*(c*x**4+b*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1115,0,0,0,0.000000," ","integrate(x**7*(c*x**4+b*x**2+a)**p,x)","\int x^{7} \left(a + b x^{2} + c x^{4}\right)^{p}\, dx"," ",0,"Integral(x**7*(a + b*x**2 + c*x**4)**p, x)","F",0
1116,0,0,0,0.000000," ","integrate(x**5*(c*x**4+b*x**2+a)**p,x)","\int x^{5} \left(a + b x^{2} + c x^{4}\right)^{p}\, dx"," ",0,"Integral(x**5*(a + b*x**2 + c*x**4)**p, x)","F",0
1117,0,0,0,0.000000," ","integrate(x**3*(c*x**4+b*x**2+a)**p,x)","\int x^{3} \left(a + b x^{2} + c x^{4}\right)^{p}\, dx"," ",0,"Integral(x**3*(a + b*x**2 + c*x**4)**p, x)","F",0
1118,0,0,0,0.000000," ","integrate(x*(c*x**4+b*x**2+a)**p,x)","\int x \left(a + b x^{2} + c x^{4}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*x**2 + c*x**4)**p, x)","F",0
1119,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**p/x,x)","\int \frac{\left(a + b x^{2} + c x^{4}\right)^{p}}{x}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**p/x, x)","F",0
1120,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**p/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1121,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**p/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1122,0,0,0,0.000000," ","integrate(x**4*(c*x**4+b*x**2+a)**p,x)","\int x^{4} \left(a + b x^{2} + c x^{4}\right)^{p}\, dx"," ",0,"Integral(x**4*(a + b*x**2 + c*x**4)**p, x)","F",0
1123,0,0,0,0.000000," ","integrate(x**2*(c*x**4+b*x**2+a)**p,x)","\int x^{2} \left(a + b x^{2} + c x^{4}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*x**2 + c*x**4)**p, x)","F",0
1124,0,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**p,x)","\int \left(a + b x^{2} + c x^{4}\right)^{p}\, dx"," ",0,"Integral((a + b*x**2 + c*x**4)**p, x)","F",0
1125,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**p/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,-1,0,0,0.000000," ","integrate((c*x**4+b*x**2+a)**p/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
