1,1,128,0,0.0308191,"\int \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4),x]","\frac{3 a x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}{8 \left(a+b x^2\right)}+\frac{1}{4} x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}+\frac{3 \sqrt{a} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/2}}","\frac{3 a x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}{8 \left(a+b x^2\right)}+\frac{1}{4} x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}+\frac{3 \sqrt{a} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/2}}",1,"(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4))/4 + (3*a*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4))/(8*(a + b*x^2)) + (3*Sqrt[a]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4)*ArcSinh[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[b]*(1 + (b*x^2)/a)^(3/2))","A",4,3,22,0.1364,1,"{1089, 195, 215}"
2,1,91,0,0.0195423,"\int \sqrt[4]{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4),x]","\frac{1}{2} x \sqrt[4]{a^2+2 a b x^2+b^2 x^4}+\frac{\sqrt{a} \sqrt[4]{a^2+2 a b x^2+b^2 x^4} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{b} \sqrt{\frac{b x^2}{a}+1}}","\frac{1}{2} x \sqrt[4]{a^2+2 a b x^2+b^2 x^4}+\frac{\sqrt{a} \sqrt[4]{a^2+2 a b x^2+b^2 x^4} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{b} \sqrt{\frac{b x^2}{a}+1}}",1,"(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4))/2 + (Sqrt[a]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4)*ArcSinh[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[b]*Sqrt[1 + (b*x^2)/a])","A",3,3,22,0.1364,1,"{1089, 195, 215}"
3,1,60,0,0.0122802,"\int \frac{1}{\sqrt[4]{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-1/4),x]","\frac{\sqrt{a} \sqrt{\frac{b x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}","\frac{\sqrt{a} \sqrt{\frac{b x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}",1,"(Sqrt[a]*Sqrt[1 + (b*x^2)/a]*ArcSinh[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[b]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4))","A",2,2,22,0.09091,1,"{1089, 215}"
4,1,34,0,0.0084038,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-3/4),x]","\frac{x \left(a+b x^2\right)}{a \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}","\frac{x \left(a+b x^2\right)}{a \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}",1,"(x*(a + b*x^2))/(a*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4))","A",2,2,22,0.09091,1,"{1089, 191}"
5,1,70,0,0.0161971,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/4}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-5/4),x]","\frac{x}{3 a \left(a+b x^2\right) \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}+\frac{2 x}{3 a^2 \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}","\frac{2 x}{3 a^2 \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}+\frac{x \left(a+b x^2\right)}{3 a \left(a^2+2 a b x^2+b^2 x^4\right)^{5/4}}",1,"(2*x)/(3*a^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4)) + x/(3*a*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4))","A",3,3,22,0.1364,1,"{1089, 192, 191}"
6,1,107,0,0.0236083,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^{7/4}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-7/4),x]","\frac{8 x \left(a+b x^2\right)}{15 a^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}+\frac{x}{5 a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}+\frac{4 x}{15 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}","\frac{8 x \left(a+b x^2\right)}{15 a^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}+\frac{4 x}{15 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/4}}+\frac{x \left(a+b x^2\right)}{5 a \left(a^2+2 a b x^2+b^2 x^4\right)^{7/4}}",1,"(4*x)/(15*a^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4)) + x/(5*a*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4)) + (8*x*(a + b*x^2))/(15*a^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/4))","A",4,3,22,0.1364,1,"{1089, 192, 191}"
7,1,148,0,0.0432201,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^{9/4}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-9/4),x]","\frac{8 x}{35 a^3 \left(a+b x^2\right) \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}+\frac{6 x}{35 a^2 \left(a+b x^2\right)^2 \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}+\frac{x}{7 a \left(a+b x^2\right)^3 \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}+\frac{16 x}{35 a^4 \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}","\frac{16 x}{35 a^4 \sqrt[4]{a^2+2 a b x^2+b^2 x^4}}+\frac{8 x \left(a+b x^2\right)}{35 a^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/4}}+\frac{6 x}{35 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/4}}+\frac{x \left(a+b x^2\right)}{7 a \left(a^2+2 a b x^2+b^2 x^4\right)^{9/4}}",1,"(16*x)/(35*a^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4)) + x/(7*a*(a + b*x^2)^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4)) + (6*x)/(35*a^2*(a + b*x^2)^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4)) + (8*x)/(35*a^3*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/4))","A",5,3,22,0.1364,1,"{1089, 192, 191}"
8,1,299,0,0.3121861,"\int \frac{1}{a^2+b+2 a x^2+x^4} \, dx","Int[(a^2 + b + 2*a*x^2 + x^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} x \sqrt{\sqrt{a^2+b}-a}+\sqrt{a^2+b}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}-a}}+\frac{\log \left(\sqrt{2} x \sqrt{\sqrt{a^2+b}-a}+\sqrt{a^2+b}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}-a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b}-a}-\sqrt{2} x}{\sqrt{\sqrt{a^2+b}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}+a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b}-a}+\sqrt{2} x}{\sqrt{\sqrt{a^2+b}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}+a}}","-\frac{\log \left(-\sqrt{2} x \sqrt{\sqrt{a^2+b}-a}+\sqrt{a^2+b}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}-a}}+\frac{\log \left(\sqrt{2} x \sqrt{\sqrt{a^2+b}-a}+\sqrt{a^2+b}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}-a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b}-a}-\sqrt{2} x}{\sqrt{\sqrt{a^2+b}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}+a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b}-a}+\sqrt{2} x}{\sqrt{\sqrt{a^2+b}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+b} \sqrt{\sqrt{a^2+b}+a}}",1,"-ArcTan[(Sqrt[-a + Sqrt[a^2 + b]] - Sqrt[2]*x)/Sqrt[a + Sqrt[a^2 + b]]]/(2*Sqrt[2]*Sqrt[a^2 + b]*Sqrt[a + Sqrt[a^2 + b]]) + ArcTan[(Sqrt[-a + Sqrt[a^2 + b]] + Sqrt[2]*x)/Sqrt[a + Sqrt[a^2 + b]]]/(2*Sqrt[2]*Sqrt[a^2 + b]*Sqrt[a + Sqrt[a^2 + b]]) - Log[Sqrt[a^2 + b] - Sqrt[2]*Sqrt[-a + Sqrt[a^2 + b]]*x + x^2]/(4*Sqrt[2]*Sqrt[a^2 + b]*Sqrt[-a + Sqrt[a^2 + b]]) + Log[Sqrt[a^2 + b] + Sqrt[2]*Sqrt[-a + Sqrt[a^2 + b]]*x + x^2]/(4*Sqrt[2]*Sqrt[a^2 + b]*Sqrt[-a + Sqrt[a^2 + b]])","A",9,5,16,0.3125,1,"{1094, 634, 618, 204, 628}"
9,1,47,0,0.0263606,"\int \frac{1}{-1+a^2+2 a x^2+x^4} \, dx","Int[(-1 + a^2 + 2*a*x^2 + x^4)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{a+1}}\right)}{2 \sqrt{a+1}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{1-a}}\right)}{2 \sqrt{1-a}}","-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{a+1}}\right)}{2 \sqrt{a+1}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt{1-a}}\right)}{2 \sqrt{1-a}}",1,"-ArcTan[x/Sqrt[1 + a]]/(2*Sqrt[1 + a]) - ArcTanh[x/Sqrt[1 - a]]/(2*Sqrt[1 - a])","A",3,3,16,0.1875,1,"{1093, 207, 203}"
10,1,299,0,0.3078039,"\int \frac{1}{1+a^2+2 a x^2+x^4} \, dx","Int[(1 + a^2 + 2*a*x^2 + x^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt{\sqrt{a^2+1}-a} x+\sqrt{a^2+1}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}-a}}+\frac{\log \left(\sqrt{2} \sqrt{\sqrt{a^2+1}-a} x+\sqrt{a^2+1}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}-a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+1}-a}-\sqrt{2} x}{\sqrt{\sqrt{a^2+1}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}+a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+1}-a}+\sqrt{2} x}{\sqrt{\sqrt{a^2+1}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}+a}}","-\frac{\log \left(-\sqrt{2} \sqrt{\sqrt{a^2+1}-a} x+\sqrt{a^2+1}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}-a}}+\frac{\log \left(\sqrt{2} \sqrt{\sqrt{a^2+1}-a} x+\sqrt{a^2+1}+x^2\right)}{4 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}-a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+1}-a}-\sqrt{2} x}{\sqrt{\sqrt{a^2+1}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}+a}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a^2+1}-a}+\sqrt{2} x}{\sqrt{\sqrt{a^2+1}+a}}\right)}{2 \sqrt{2} \sqrt{a^2+1} \sqrt{\sqrt{a^2+1}+a}}",1,"-ArcTan[(Sqrt[-a + Sqrt[1 + a^2]] - Sqrt[2]*x)/Sqrt[a + Sqrt[1 + a^2]]]/(2*Sqrt[2]*Sqrt[1 + a^2]*Sqrt[a + Sqrt[1 + a^2]]) + ArcTan[(Sqrt[-a + Sqrt[1 + a^2]] + Sqrt[2]*x)/Sqrt[a + Sqrt[1 + a^2]]]/(2*Sqrt[2]*Sqrt[1 + a^2]*Sqrt[a + Sqrt[1 + a^2]]) - Log[Sqrt[1 + a^2] - Sqrt[2]*Sqrt[-a + Sqrt[1 + a^2]]*x + x^2]/(4*Sqrt[2]*Sqrt[1 + a^2]*Sqrt[-a + Sqrt[1 + a^2]]) + Log[Sqrt[1 + a^2] + Sqrt[2]*Sqrt[-a + Sqrt[1 + a^2]]*x + x^2]/(4*Sqrt[2]*Sqrt[1 + a^2]*Sqrt[-a + Sqrt[1 + a^2]])","A",9,5,16,0.3125,1,"{1094, 634, 618, 204, 628}"
11,1,17,0,0.0079561,"\int \frac{1}{4-5 x^2+x^4} \, dx","Int[(4 - 5*x^2 + x^4)^(-1),x]","\frac{1}{3} \tanh ^{-1}(x)-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{2}\right)","\frac{1}{3} \tanh ^{-1}(x)-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{2}\right)",1,"-ArcTanh[x/2]/6 + ArcTanh[x]/3","A",3,2,12,0.1667,1,"{1093, 207}"
12,1,24,0,0.0150571,"\int \frac{1}{3+4 x^2+x^4} \, dx","Int[(3 + 4*x^2 + x^4)^(-1),x]","\frac{1}{2} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{1}{2} \tan ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"ArcTan[x]/2 - ArcTan[x/Sqrt[3]]/(2*Sqrt[3])","A",3,2,12,0.1667,1,"{1093, 203}"
13,1,67,0,0.049631,"\int \frac{1}{9+5 x^2+x^4} \, dx","Int[(9 + 5*x^2 + x^4)^(-1),x]","-\frac{1}{12} \log \left(x^2-x+3\right)+\frac{1}{12} \log \left(x^2+x+3\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{11}}\right)}{6 \sqrt{11}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{11}}\right)}{6 \sqrt{11}}","-\frac{1}{12} \log \left(x^2-x+3\right)+\frac{1}{12} \log \left(x^2+x+3\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{11}}\right)}{6 \sqrt{11}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{11}}\right)}{6 \sqrt{11}}",1,"-ArcTan[(1 - 2*x)/Sqrt[11]]/(6*Sqrt[11]) + ArcTan[(1 + 2*x)/Sqrt[11]]/(6*Sqrt[11]) - Log[3 - x + x^2]/12 + Log[3 + x + x^2]/12","A",9,5,12,0.4167,1,"{1094, 634, 618, 204, 628}"
14,1,74,0,0.0489245,"\int \frac{1}{1-x^2+x^4} \, dx","Int[(1 - x^2 + x^4)^(-1),x]","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{2} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{2} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-ArcTan[Sqrt[3] - 2*x]/2 + ArcTan[Sqrt[3] + 2*x]/2 - Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) + Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",9,5,12,0.4167,1,"{1094, 634, 618, 204, 628}"
15,1,176,0,0.1617052,"\int \frac{1}{2+2 x^2+x^4} \, dx","Int[(2 + 2*x^2 + x^4)^(-1),x]","-\frac{\log \left(x^2-\sqrt{2 \left(\sqrt{2}-1\right)} x+\sqrt{2}\right)}{8 \sqrt{\sqrt{2}-1}}+\frac{\log \left(x^2+\sqrt{2 \left(\sqrt{2}-1\right)} x+\sqrt{2}\right)}{8 \sqrt{\sqrt{2}-1}}-\frac{1}{4} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)+\frac{1}{4} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{2}-1\right)}}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)","-\frac{\log \left(x^2-\sqrt{2 \left(\sqrt{2}-1\right)} x+\sqrt{2}\right)}{8 \sqrt{\sqrt{2}-1}}+\frac{\log \left(x^2+\sqrt{2 \left(\sqrt{2}-1\right)} x+\sqrt{2}\right)}{8 \sqrt{\sqrt{2}-1}}-\frac{1}{4} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\sqrt{2 \left(\sqrt{2}-1\right)}-2 x}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)+\frac{1}{4} \sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(\sqrt{2}-1\right)}}{\sqrt{2 \left(1+\sqrt{2}\right)}}\right)",1,"-(Sqrt[-1 + Sqrt[2]]*ArcTan[(Sqrt[2*(-1 + Sqrt[2])] - 2*x)/Sqrt[2*(1 + Sqrt[2])]])/4 + (Sqrt[-1 + Sqrt[2]]*ArcTan[(Sqrt[2*(-1 + Sqrt[2])] + 2*x)/Sqrt[2*(1 + Sqrt[2])]])/4 - Log[Sqrt[2] - Sqrt[2*(-1 + Sqrt[2])]*x + x^2]/(8*Sqrt[-1 + Sqrt[2]]) + Log[Sqrt[2] + Sqrt[2*(-1 + Sqrt[2])]*x + x^2]/(8*Sqrt[-1 + Sqrt[2]])","A",9,5,12,0.4167,1,"{1094, 634, 618, 204, 628}"
16,1,10,0,0.0157512,"\int \frac{1}{\sqrt{2+5 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 3*x^4],x]","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-6\right)","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-6\right)",1,"EllipticF[ArcSin[x/Sqrt[2]], -6]","A",2,2,16,0.1250,1,"{1095, 419}"
17,1,48,0,0.1335883,"\int \frac{1}{\sqrt{2+4 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 + 4*x^2 - 3*x^4],x]","\sqrt{\frac{1}{6} \left(2+\sqrt{10}\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{2} \left(-2+\sqrt{10}\right)} x\right)|\frac{1}{3} \left(-7-2 \sqrt{10}\right)\right)","\sqrt{\frac{1}{6} \left(2+\sqrt{10}\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{2} \left(-2+\sqrt{10}\right)} x\right)|\frac{1}{3} \left(-7-2 \sqrt{10}\right)\right)",1,"Sqrt[(2 + Sqrt[10])/6]*EllipticF[ArcSin[Sqrt[(-2 + Sqrt[10])/2]*x], (-7 - 2*Sqrt[10])/3]","A",2,2,16,0.1250,1,"{1095, 419}"
18,1,48,0,0.1043776,"\int \frac{1}{\sqrt{2+3 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 + 3*x^2 - 3*x^4],x]","\sqrt{\frac{2}{\sqrt{33}-3}} F\left(\sin ^{-1}\left(\sqrt{\frac{6}{3+\sqrt{33}}} x\right)|\frac{1}{4} \left(-7-\sqrt{33}\right)\right)","\sqrt{\frac{2}{\sqrt{33}-3}} F\left(\sin ^{-1}\left(\sqrt{\frac{6}{3+\sqrt{33}}} x\right)|\frac{1}{4} \left(-7-\sqrt{33}\right)\right)",1,"Sqrt[2/(-3 + Sqrt[33])]*EllipticF[ArcSin[Sqrt[6/(3 + Sqrt[33])]*x], (-7 - Sqrt[33])/4]","A",2,2,16,0.1250,1,"{1095, 419}"
19,1,44,0,0.0674992,"\int \frac{1}{\sqrt{2+2 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 + 2*x^2 - 3*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4-\sqrt{7}\right)\right)}{\sqrt{\sqrt{7}-1}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4-\sqrt{7}\right)\right)}{\sqrt{\sqrt{7}-1}}",1,"EllipticF[ArcSin[Sqrt[3/(1 + Sqrt[7])]*x], (-4 - Sqrt[7])/3]/Sqrt[-1 + Sqrt[7]]","A",2,2,16,0.1250,1,"{1095, 419}"
20,1,12,0,0.0119981,"\int \frac{1}{\sqrt{2+x^2-3 x^4}} \, dx","Int[1/Sqrt[2 + x^2 - 3*x^4],x]","\frac{F\left(\sin ^{-1}(x)|-\frac{3}{2}\right)}{\sqrt{2}}","\frac{F\left(\sin ^{-1}(x)|-\frac{3}{2}\right)}{\sqrt{2}}",1,"EllipticF[ArcSin[x], -3/2]/Sqrt[2]","A",2,2,14,0.1429,1,"{1095, 419}"
21,1,18,0,0.0101381,"\int \frac{1}{\sqrt{2-3 x^4}} \, dx","Int[1/Sqrt[2 - 3*x^4],x]","\frac{F\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)\right|-1\right)}{\sqrt[4]{6}}","\frac{F\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)\right|-1\right)}{\sqrt[4]{6}}",1,"EllipticF[ArcSin[(3/2)^(1/4)*x], -1]/6^(1/4)","A",1,1,11,0.09091,1,"{221}"
22,1,20,0,0.0111094,"\int \frac{1}{\sqrt{2-x^2-3 x^4}} \, dx","Int[1/Sqrt[2 - x^2 - 3*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{2}{3}\right)}{\sqrt{3}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{2}{3}\right)}{\sqrt{3}}",1,"EllipticF[ArcSin[Sqrt[3/2]*x], -2/3]/Sqrt[3]","A",2,2,16,0.1250,1,"{1095, 419}"
23,1,42,0,0.064737,"\int \frac{1}{\sqrt{2-2 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 - 2*x^2 - 3*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{-1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4+\sqrt{7}\right)\right)}{\sqrt{1+\sqrt{7}}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{-1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4+\sqrt{7}\right)\right)}{\sqrt{1+\sqrt{7}}}",1,"EllipticF[ArcSin[Sqrt[3/(-1 + Sqrt[7])]*x], (-4 + Sqrt[7])/3]/Sqrt[1 + Sqrt[7]]","A",2,2,16,0.1250,1,"{1095, 419}"
24,1,46,0,0.0889233,"\int \frac{1}{\sqrt{2-3 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 - 3*x^2 - 3*x^4],x]","\sqrt{\frac{2}{3+\sqrt{33}}} F\left(\sin ^{-1}\left(\sqrt{\frac{6}{-3+\sqrt{33}}} x\right)|\frac{1}{4} \left(-7+\sqrt{33}\right)\right)","\sqrt{\frac{2}{3+\sqrt{33}}} F\left(\sin ^{-1}\left(\sqrt{\frac{6}{-3+\sqrt{33}}} x\right)|\frac{1}{4} \left(-7+\sqrt{33}\right)\right)",1,"Sqrt[2/(3 + Sqrt[33])]*EllipticF[ArcSin[Sqrt[6/(-3 + Sqrt[33])]*x], (-7 + Sqrt[33])/4]","A",2,2,16,0.1250,1,"{1095, 419}"
25,1,48,0,0.0938131,"\int \frac{1}{\sqrt{2-4 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 - 4*x^2 - 3*x^4],x]","\sqrt{\frac{1}{6} \left(\sqrt{10}-2\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{2} \left(2+\sqrt{10}\right)} x\right)|\frac{1}{3} \left(-7+2 \sqrt{10}\right)\right)","\sqrt{\frac{1}{6} \left(\sqrt{10}-2\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{2} \left(2+\sqrt{10}\right)} x\right)|\frac{1}{3} \left(-7+2 \sqrt{10}\right)\right)",1,"Sqrt[(-2 + Sqrt[10])/6]*EllipticF[ArcSin[Sqrt[(2 + Sqrt[10])/2]*x], (-7 + 2*Sqrt[10])/3]","A",2,2,16,0.1250,1,"{1095, 419}"
26,1,18,0,0.0145935,"\int \frac{1}{\sqrt{2-5 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 - 5*x^2 - 3*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{3} x\right)|-\frac{1}{6}\right)}{\sqrt{6}}","\frac{F\left(\sin ^{-1}\left(\sqrt{3} x\right)|-\frac{1}{6}\right)}{\sqrt{6}}",1,"EllipticF[ArcSin[Sqrt[3]*x], -1/6]/Sqrt[6]","A",2,2,16,0.1250,1,"{1095, 419}"
27,1,45,0,0.064989,"\int \frac{1}{\sqrt{3+7 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 + 7*x^2 - 2*x^4],x]","\sqrt{\frac{2}{\sqrt{73}-7}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{7+\sqrt{73}}}\right)|\frac{1}{12} \left(-61-7 \sqrt{73}\right)\right)","\sqrt{\frac{2}{\sqrt{73}-7}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{7+\sqrt{73}}}\right)|\frac{1}{12} \left(-61-7 \sqrt{73}\right)\right)",1,"Sqrt[2/(-7 + Sqrt[73])]*EllipticF[ArcSin[(2*x)/Sqrt[7 + Sqrt[73]]], (-61 - 7*Sqrt[73])/12]","A",2,2,16,0.1250,1,"{1095, 419}"
28,1,44,0,0.132986,"\int \frac{1}{\sqrt{3+6 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 + 6*x^2 - 2*x^4],x]","\sqrt{\frac{1}{6} \left(3+\sqrt{15}\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{3} \left(-3+\sqrt{15}\right)} x\right)|-4-\sqrt{15}\right)","\sqrt{\frac{1}{6} \left(3+\sqrt{15}\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{3} \left(-3+\sqrt{15}\right)} x\right)|-4-\sqrt{15}\right)",1,"Sqrt[(3 + Sqrt[15])/6]*EllipticF[ArcSin[Sqrt[(-3 + Sqrt[15])/3]*x], -4 - Sqrt[15]]","A",2,2,16,0.1250,1,"{1095, 419}"
29,1,10,0,0.0105851,"\int \frac{1}{\sqrt{3+5 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 + 5*x^2 - 2*x^4],x]","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right|-6\right)","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right|-6\right)",1,"EllipticF[ArcSin[x/Sqrt[3]], -6]","A",2,2,16,0.1250,1,"{1095, 419}"
30,1,44,0,0.0766136,"\int \frac{1}{\sqrt{3+4 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 + 4*x^2 - 2*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{2+\sqrt{10}}} x\right)|\frac{1}{3} \left(-7-2 \sqrt{10}\right)\right)}{\sqrt{\sqrt{10}-2}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{2+\sqrt{10}}} x\right)|\frac{1}{3} \left(-7-2 \sqrt{10}\right)\right)}{\sqrt{\sqrt{10}-2}}",1,"EllipticF[ArcSin[Sqrt[2/(2 + Sqrt[10])]*x], (-7 - 2*Sqrt[10])/3]/Sqrt[-2 + Sqrt[10]]","A",2,2,16,0.1250,1,"{1095, 419}"
31,1,45,0,0.0672437,"\int \frac{1}{\sqrt{3+3 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 + 3*x^2 - 2*x^4],x]","\sqrt{\frac{2}{\sqrt{33}-3}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{33}}}\right)|\frac{1}{4} \left(-7-\sqrt{33}\right)\right)","\sqrt{\frac{2}{\sqrt{33}-3}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{33}}}\right)|\frac{1}{4} \left(-7-\sqrt{33}\right)\right)",1,"Sqrt[2/(-3 + Sqrt[33])]*EllipticF[ArcSin[(2*x)/Sqrt[3 + Sqrt[33]]], (-7 - Sqrt[33])/4]","A",2,2,16,0.1250,1,"{1095, 419}"
32,1,44,0,0.0620457,"\int \frac{1}{\sqrt{3+2 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 + 2*x^2 - 2*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4-\sqrt{7}\right)\right)}{\sqrt{\sqrt{7}-1}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4-\sqrt{7}\right)\right)}{\sqrt{\sqrt{7}-1}}",1,"EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[7])]*x], (-4 - Sqrt[7])/3]/Sqrt[-1 + Sqrt[7]]","A",2,2,16,0.1250,1,"{1095, 419}"
33,1,20,0,0.0110002,"\int \frac{1}{\sqrt{3+x^2-2 x^4}} \, dx","Int[1/Sqrt[3 + x^2 - 2*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{3}} x\right)|-\frac{3}{2}\right)}{\sqrt{2}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{3}} x\right)|-\frac{3}{2}\right)}{\sqrt{2}}",1,"EllipticF[ArcSin[Sqrt[2/3]*x], -3/2]/Sqrt[2]","A",2,2,14,0.1429,1,"{1095, 419}"
34,1,18,0,0.0060963,"\int \frac{1}{\sqrt{3-2 x^4}} \, dx","Int[1/Sqrt[3 - 2*x^4],x]","\frac{F\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)\right|-1\right)}{\sqrt[4]{6}}","\frac{F\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)\right|-1\right)}{\sqrt[4]{6}}",1,"EllipticF[ArcSin[(2/3)^(1/4)*x], -1]/6^(1/4)","A",1,1,11,0.09091,1,"{221}"
35,1,12,0,0.010715,"\int \frac{1}{\sqrt{3-x^2-2 x^4}} \, dx","Int[1/Sqrt[3 - x^2 - 2*x^4],x]","\frac{F\left(\sin ^{-1}(x)|-\frac{2}{3}\right)}{\sqrt{3}}","\frac{F\left(\sin ^{-1}(x)|-\frac{2}{3}\right)}{\sqrt{3}}",1,"EllipticF[ArcSin[x], -2/3]/Sqrt[3]","A",2,2,16,0.1250,1,"{1095, 419}"
36,1,42,0,0.0473294,"\int \frac{1}{\sqrt{3-2 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 - 2*x^2 - 2*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4+\sqrt{7}\right)\right)}{\sqrt{1+\sqrt{7}}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{7}}} x\right)|\frac{1}{3} \left(-4+\sqrt{7}\right)\right)}{\sqrt{1+\sqrt{7}}}",1,"EllipticF[ArcSin[Sqrt[2/(-1 + Sqrt[7])]*x], (-4 + Sqrt[7])/3]/Sqrt[1 + Sqrt[7]]","A",2,2,16,0.1250,1,"{1095, 419}"
37,1,43,0,0.0314177,"\int \frac{1}{\sqrt{3-3 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 - 3*x^2 - 2*x^4],x]","\sqrt{\frac{2}{3+\sqrt{33}}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{33}}}\right)|\frac{1}{4} \left(-7+\sqrt{33}\right)\right)","\sqrt{\frac{2}{3+\sqrt{33}}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-3+\sqrt{33}}}\right)|\frac{1}{4} \left(-7+\sqrt{33}\right)\right)",1,"Sqrt[2/(3 + Sqrt[33])]*EllipticF[ArcSin[(2*x)/Sqrt[-3 + Sqrt[33]]], (-7 + Sqrt[33])/4]","A",2,2,16,0.1250,1,"{1095, 419}"
38,1,44,0,0.0679591,"\int \frac{1}{\sqrt{3-4 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 - 4*x^2 - 2*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-2+\sqrt{10}}} x\right)|\frac{1}{3} \left(-7+2 \sqrt{10}\right)\right)}{\sqrt{2+\sqrt{10}}}","\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-2+\sqrt{10}}} x\right)|\frac{1}{3} \left(-7+2 \sqrt{10}\right)\right)}{\sqrt{2+\sqrt{10}}}",1,"EllipticF[ArcSin[Sqrt[2/(-2 + Sqrt[10])]*x], (-7 + 2*Sqrt[10])/3]/Sqrt[2 + Sqrt[10]]","A",2,2,16,0.1250,1,"{1095, 419}"
39,1,18,0,0.0122699,"\int \frac{1}{\sqrt{3-5 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 - 5*x^2 - 2*x^4],x]","\frac{F\left(\sin ^{-1}\left(\sqrt{2} x\right)|-\frac{1}{6}\right)}{\sqrt{6}}","\frac{F\left(\sin ^{-1}\left(\sqrt{2} x\right)|-\frac{1}{6}\right)}{\sqrt{6}}",1,"EllipticF[ArcSin[Sqrt[2]*x], -1/6]/Sqrt[6]","A",2,2,16,0.1250,1,"{1095, 419}"
40,1,42,0,0.0958311,"\int \frac{1}{\sqrt{3-6 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 - 6*x^2 - 2*x^4],x]","\sqrt{\frac{1}{6} \left(\sqrt{15}-3\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{3} \left(3+\sqrt{15}\right)} x\right)|-4+\sqrt{15}\right)","\sqrt{\frac{1}{6} \left(\sqrt{15}-3\right)} F\left(\sin ^{-1}\left(\sqrt{\frac{1}{3} \left(3+\sqrt{15}\right)} x\right)|-4+\sqrt{15}\right)",1,"Sqrt[(-3 + Sqrt[15])/6]*EllipticF[ArcSin[Sqrt[(3 + Sqrt[15])/3]*x], -4 + Sqrt[15]]","A",2,2,16,0.1250,1,"{1095, 419}"
41,1,45,0,0.0478908,"\int \frac{1}{\sqrt{3-7 x^2-2 x^4}} \, dx","Int[1/Sqrt[3 - 7*x^2 - 2*x^4],x]","\sqrt{\frac{2}{7+\sqrt{73}}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-7+\sqrt{73}}}\right)|\frac{1}{12} \left(-61+7 \sqrt{73}\right)\right)","\sqrt{\frac{2}{7+\sqrt{73}}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{-7+\sqrt{73}}}\right)|\frac{1}{12} \left(-61+7 \sqrt{73}\right)\right)",1,"Sqrt[2/(7 + Sqrt[73])]*EllipticF[ArcSin[(2*x)/Sqrt[-7 + Sqrt[73]]], (-61 + 7*Sqrt[73])/12]","A",2,2,16,0.1250,1,"{1095, 419}"
42,1,67,0,0.0082686,"\int \frac{1}{\sqrt{-2+5 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 + 5*x^2 + 3*x^4],x]","\frac{\sqrt{x^2+2} \sqrt{3 x^2-1} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{7}{2}} x}{\sqrt{3 x^2-1}}\right)|\frac{6}{7}\right)}{\sqrt{7} \sqrt{3 x^4+5 x^2-2}}","\frac{\sqrt{x^2+2} \sqrt{3 x^2-1} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{7}{2}} x}{\sqrt{3 x^2-1}}\right)|\frac{6}{7}\right)}{\sqrt{7} \sqrt{3 x^4+5 x^2-2}}",1,"(Sqrt[2 + x^2]*Sqrt[-1 + 3*x^2]*EllipticF[ArcSin[(Sqrt[7/2]*x)/Sqrt[-1 + 3*x^2]], 6/7])/(Sqrt[7]*Sqrt[-2 + 5*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1097}"
43,1,141,0,0.0347325,"\int \frac{1}{\sqrt{-2+4 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 + 4*x^2 + 3*x^4],x]","\frac{\sqrt{\frac{2-\left(2-\sqrt{10}\right) x^2}{2-\left(2+\sqrt{10}\right) x^2}} \sqrt{\left(2+\sqrt{10}\right) x^2-2} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{\left(2+\sqrt{10}\right) x^2-2}}\right)|\frac{1}{10} \left(5+\sqrt{10}\right)\right)}{2 \sqrt[4]{10} \sqrt{\frac{1}{2-\left(2+\sqrt{10}\right) x^2}} \sqrt{3 x^4+4 x^2-2}}","\frac{\sqrt{\frac{2-\left(2-\sqrt{10}\right) x^2}{2-\left(2+\sqrt{10}\right) x^2}} \sqrt{\left(2+\sqrt{10}\right) x^2-2} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{\left(2+\sqrt{10}\right) x^2-2}}\right)|\frac{1}{10} \left(5+\sqrt{10}\right)\right)}{2 \sqrt[4]{10} \sqrt{\frac{1}{2-\left(2+\sqrt{10}\right) x^2}} \sqrt{3 x^4+4 x^2-2}}",1,"(Sqrt[(2 - (2 - Sqrt[10])*x^2)/(2 - (2 + Sqrt[10])*x^2)]*Sqrt[-2 + (2 + Sqrt[10])*x^2]*EllipticF[ArcSin[(2^(3/4)*5^(1/4)*x)/Sqrt[-2 + (2 + Sqrt[10])*x^2]], (5 + Sqrt[10])/10])/(2*10^(1/4)*Sqrt[(2 - (2 + Sqrt[10])*x^2)^(-1)]*Sqrt[-2 + 4*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1098}"
44,1,146,0,0.0385048,"\int \frac{1}{\sqrt{-2+3 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 + 3*x^2 + 3*x^4],x]","\frac{\sqrt{\frac{4-\left(3-\sqrt{33}\right) x^2}{4-\left(3+\sqrt{33}\right) x^2}} \sqrt{\left(3+\sqrt{33}\right) x^2-4} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{\left(3+\sqrt{33}\right) x^2-4}}\right)|\frac{1}{22} \left(11+\sqrt{33}\right)\right)}{2 \sqrt{2} \sqrt[4]{33} \sqrt{\frac{1}{4-\left(3+\sqrt{33}\right) x^2}} \sqrt{3 x^4+3 x^2-2}}","\frac{\sqrt{\frac{4-\left(3-\sqrt{33}\right) x^2}{4-\left(3+\sqrt{33}\right) x^2}} \sqrt{\left(3+\sqrt{33}\right) x^2-4} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{\left(3+\sqrt{33}\right) x^2-4}}\right)|\frac{1}{22} \left(11+\sqrt{33}\right)\right)}{2 \sqrt{2} \sqrt[4]{33} \sqrt{\frac{1}{4-\left(3+\sqrt{33}\right) x^2}} \sqrt{3 x^4+3 x^2-2}}",1,"(Sqrt[(4 - (3 - Sqrt[33])*x^2)/(4 - (3 + Sqrt[33])*x^2)]*Sqrt[-4 + (3 + Sqrt[33])*x^2]*EllipticF[ArcSin[(Sqrt[2]*33^(1/4)*x)/Sqrt[-4 + (3 + Sqrt[33])*x^2]], (11 + Sqrt[33])/22])/(2*Sqrt[2]*33^(1/4)*Sqrt[(4 - (3 + Sqrt[33])*x^2)^(-1)]*Sqrt[-2 + 3*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1098}"
45,1,141,0,0.0302293,"\int \frac{1}{\sqrt{-2+2 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 + 2*x^2 + 3*x^4],x]","\frac{\sqrt{\frac{2-\left(1-\sqrt{7}\right) x^2}{2-\left(1+\sqrt{7}\right) x^2}} \sqrt{\left(1+\sqrt{7}\right) x^2-2} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{\left(1+\sqrt{7}\right) x^2-2}}\right)|\frac{1}{14} \left(7+\sqrt{7}\right)\right)}{2 \sqrt[4]{7} \sqrt{\frac{1}{2-\left(1+\sqrt{7}\right) x^2}} \sqrt{3 x^4+2 x^2-2}}","\frac{\sqrt{\frac{2-\left(1-\sqrt{7}\right) x^2}{2-\left(1+\sqrt{7}\right) x^2}} \sqrt{\left(1+\sqrt{7}\right) x^2-2} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{\left(1+\sqrt{7}\right) x^2-2}}\right)|\frac{1}{14} \left(7+\sqrt{7}\right)\right)}{2 \sqrt[4]{7} \sqrt{\frac{1}{2-\left(1+\sqrt{7}\right) x^2}} \sqrt{3 x^4+2 x^2-2}}",1,"(Sqrt[(2 - (1 - Sqrt[7])*x^2)/(2 - (1 + Sqrt[7])*x^2)]*Sqrt[-2 + (1 + Sqrt[7])*x^2]*EllipticF[ArcSin[(Sqrt[2]*7^(1/4)*x)/Sqrt[-2 + (1 + Sqrt[7])*x^2]], (7 + Sqrt[7])/14])/(2*7^(1/4)*Sqrt[(2 - (1 + Sqrt[7])*x^2)^(-1)]*Sqrt[-2 + 2*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1098}"
46,1,63,0,0.0077939,"\int \frac{1}{\sqrt{-2+x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 + x^2 + 3*x^4],x]","\frac{\sqrt{x^2+1} \sqrt{3 x^2-2} F\left(\sin ^{-1}\left(\frac{\sqrt{5} x}{\sqrt{3 x^2-2}}\right)|\frac{3}{5}\right)}{\sqrt{5} \sqrt{3 x^4+x^2-2}}","\frac{\sqrt{x^2+1} \sqrt{3 x^2-2} F\left(\sin ^{-1}\left(\frac{\sqrt{5} x}{\sqrt{3 x^2-2}}\right)|\frac{3}{5}\right)}{\sqrt{5} \sqrt{3 x^4+x^2-2}}",1,"(Sqrt[1 + x^2]*Sqrt[-2 + 3*x^2]*EllipticF[ArcSin[(Sqrt[5]*x)/Sqrt[-2 + 3*x^2]], 3/5])/(Sqrt[5]*Sqrt[-2 + x^2 + 3*x^4])","A",1,1,14,0.07143,1,"{1097}"
47,1,115,0,0.016283,"\int \frac{1}{\sqrt{-2+3 x^4}} \, dx","Int[1/Sqrt[-2 + 3*x^4],x]","\frac{\sqrt{\sqrt{6} x^2-2} \sqrt{\frac{\sqrt{6} x^2+2}{2-\sqrt{6} x^2}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt{\sqrt{6} x^2-2}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{\frac{1}{2-\sqrt{6} x^2}} \sqrt{3 x^4-2}}","\frac{\sqrt{\sqrt{6} x^2-2} \sqrt{\frac{\sqrt{6} x^2+2}{2-\sqrt{6} x^2}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt{\sqrt{6} x^2-2}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{\frac{1}{2-\sqrt{6} x^2}} \sqrt{3 x^4-2}}",1,"(Sqrt[-2 + Sqrt[6]*x^2]*Sqrt[(2 + Sqrt[6]*x^2)/(2 - Sqrt[6]*x^2)]*EllipticF[ArcSin[(2^(3/4)*3^(1/4)*x)/Sqrt[-2 + Sqrt[6]*x^2]], 1/2])/(2*6^(1/4)*Sqrt[(2 - Sqrt[6]*x^2)^(-1)]*Sqrt[-2 + 3*x^4])","A",1,1,11,0.09091,1,"{223}"
48,1,65,0,0.006997,"\int \frac{1}{\sqrt{-2-x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 - x^2 + 3*x^4],x]","\frac{\sqrt{x^2-1} \sqrt{3 x^2+2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{2}} x}{\sqrt{x^2-1}}\right)|\frac{2}{5}\right)}{\sqrt{5} \sqrt{3 x^4-x^2-2}}","\frac{\sqrt{x^2-1} \sqrt{3 x^2+2} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{2}} x}{\sqrt{x^2-1}}\right)|\frac{2}{5}\right)}{\sqrt{5} \sqrt{3 x^4-x^2-2}}",1,"(Sqrt[-1 + x^2]*Sqrt[2 + 3*x^2]*EllipticF[ArcSin[(Sqrt[5/2]*x)/Sqrt[-1 + x^2]], 2/5])/(Sqrt[5]*Sqrt[-2 - x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1097}"
49,1,148,0,0.02631,"\int \frac{1}{\sqrt{-2-2 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 - 2*x^2 + 3*x^4],x]","\frac{\sqrt{-\left(1-\sqrt{7}\right) x^2-2} \sqrt{\frac{\left(1+\sqrt{7}\right) x^2+2}{\left(1-\sqrt{7}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{-\left(1-\sqrt{7}\right) x^2-2}}\right)|\frac{1}{14} \left(7-\sqrt{7}\right)\right)}{2 \sqrt[4]{7} \sqrt{\frac{1}{\left(1-\sqrt{7}\right) x^2+2}} \sqrt{3 x^4-2 x^2-2}}","\frac{\sqrt{-\left(1-\sqrt{7}\right) x^2-2} \sqrt{\frac{\left(1+\sqrt{7}\right) x^2+2}{\left(1-\sqrt{7}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{-\left(1-\sqrt{7}\right) x^2-2}}\right)|\frac{1}{14} \left(7-\sqrt{7}\right)\right)}{2 \sqrt[4]{7} \sqrt{\frac{1}{\left(1-\sqrt{7}\right) x^2+2}} \sqrt{3 x^4-2 x^2-2}}",1,"(Sqrt[-2 - (1 - Sqrt[7])*x^2]*Sqrt[(2 + (1 + Sqrt[7])*x^2)/(2 + (1 - Sqrt[7])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*7^(1/4)*x)/Sqrt[-2 - (1 - Sqrt[7])*x^2]], (7 - Sqrt[7])/14])/(2*7^(1/4)*Sqrt[(2 + (1 - Sqrt[7])*x^2)^(-1)]*Sqrt[-2 - 2*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1098}"
50,1,153,0,0.030337,"\int \frac{1}{\sqrt{-2-3 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 - 3*x^2 + 3*x^4],x]","\frac{\sqrt{-\left(3-\sqrt{33}\right) x^2-4} \sqrt{\frac{\left(3+\sqrt{33}\right) x^2+4}{\left(3-\sqrt{33}\right) x^2+4}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{-\left(3-\sqrt{33}\right) x^2-4}}\right)|\frac{1}{22} \left(11-\sqrt{33}\right)\right)}{2 \sqrt{2} \sqrt[4]{33} \sqrt{\frac{1}{\left(3-\sqrt{33}\right) x^2+4}} \sqrt{3 x^4-3 x^2-2}}","\frac{\sqrt{-\left(3-\sqrt{33}\right) x^2-4} \sqrt{\frac{\left(3+\sqrt{33}\right) x^2+4}{\left(3-\sqrt{33}\right) x^2+4}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{-\left(3-\sqrt{33}\right) x^2-4}}\right)|\frac{1}{22} \left(11-\sqrt{33}\right)\right)}{2 \sqrt{2} \sqrt[4]{33} \sqrt{\frac{1}{\left(3-\sqrt{33}\right) x^2+4}} \sqrt{3 x^4-3 x^2-2}}",1,"(Sqrt[-4 - (3 - Sqrt[33])*x^2]*Sqrt[(4 + (3 + Sqrt[33])*x^2)/(4 + (3 - Sqrt[33])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*33^(1/4)*x)/Sqrt[-4 - (3 - Sqrt[33])*x^2]], (11 - Sqrt[33])/22])/(2*Sqrt[2]*33^(1/4)*Sqrt[(4 + (3 - Sqrt[33])*x^2)^(-1)]*Sqrt[-2 - 3*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1098}"
51,1,148,0,0.0288026,"\int \frac{1}{\sqrt{-2-4 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 - 4*x^2 + 3*x^4],x]","\frac{\sqrt{-\left(2-\sqrt{10}\right) x^2-2} \sqrt{\frac{\left(2+\sqrt{10}\right) x^2+2}{\left(2-\sqrt{10}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{-\left(2-\sqrt{10}\right) x^2-2}}\right)|\frac{1}{10} \left(5-\sqrt{10}\right)\right)}{2 \sqrt[4]{10} \sqrt{\frac{1}{\left(2-\sqrt{10}\right) x^2+2}} \sqrt{3 x^4-4 x^2-2}}","\frac{\sqrt{-\left(2-\sqrt{10}\right) x^2-2} \sqrt{\frac{\left(2+\sqrt{10}\right) x^2+2}{\left(2-\sqrt{10}\right) x^2+2}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{-\left(2-\sqrt{10}\right) x^2-2}}\right)|\frac{1}{10} \left(5-\sqrt{10}\right)\right)}{2 \sqrt[4]{10} \sqrt{\frac{1}{\left(2-\sqrt{10}\right) x^2+2}} \sqrt{3 x^4-4 x^2-2}}",1,"(Sqrt[-2 - (2 - Sqrt[10])*x^2]*Sqrt[(2 + (2 + Sqrt[10])*x^2)/(2 + (2 - Sqrt[10])*x^2)]*EllipticF[ArcSin[(2^(3/4)*5^(1/4)*x)/Sqrt[-2 - (2 - Sqrt[10])*x^2]], (5 - Sqrt[10])/10])/(2*10^(1/4)*Sqrt[(2 + (2 - Sqrt[10])*x^2)^(-1)]*Sqrt[-2 - 4*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1098}"
52,1,63,0,0.0069716,"\int \frac{1}{\sqrt{-2-5 x^2+3 x^4}} \, dx","Int[1/Sqrt[-2 - 5*x^2 + 3*x^4],x]","\frac{\sqrt{x^2-2} \sqrt{3 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{7} x}{\sqrt{x^2-2}}\right)|\frac{1}{7}\right)}{\sqrt{7} \sqrt{3 x^4-5 x^2-2}}","\frac{\sqrt{x^2-2} \sqrt{3 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{7} x}{\sqrt{x^2-2}}\right)|\frac{1}{7}\right)}{\sqrt{7} \sqrt{3 x^4-5 x^2-2}}",1,"(Sqrt[-2 + x^2]*Sqrt[1 + 3*x^2]*EllipticF[ArcSin[(Sqrt[7]*x)/Sqrt[-2 + x^2]], 1/7])/(Sqrt[7]*Sqrt[-2 - 5*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1097}"
53,1,148,0,0.02914,"\int \frac{1}{\sqrt{-3+7 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 + 7*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{6-\left(7-\sqrt{73}\right) x^2}{6-\left(7+\sqrt{73}\right) x^2}} \sqrt{\left(7+\sqrt{73}\right) x^2-6} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{73} x}{\sqrt{\left(7+\sqrt{73}\right) x^2-6}}\right)|\frac{1}{146} \left(73+7 \sqrt{73}\right)\right)}{2 \sqrt{3} \sqrt[4]{73} \sqrt{\frac{1}{6-\left(7+\sqrt{73}\right) x^2}} \sqrt{2 x^4+7 x^2-3}}","\frac{\sqrt{\frac{6-\left(7-\sqrt{73}\right) x^2}{6-\left(7+\sqrt{73}\right) x^2}} \sqrt{\left(7+\sqrt{73}\right) x^2-6} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{73} x}{\sqrt{\left(7+\sqrt{73}\right) x^2-6}}\right)|\frac{1}{146} \left(73+7 \sqrt{73}\right)\right)}{2 \sqrt{3} \sqrt[4]{73} \sqrt{\frac{1}{6-\left(7+\sqrt{73}\right) x^2}} \sqrt{2 x^4+7 x^2-3}}",1,"(Sqrt[(6 - (7 - Sqrt[73])*x^2)/(6 - (7 + Sqrt[73])*x^2)]*Sqrt[-6 + (7 + Sqrt[73])*x^2]*EllipticF[ArcSin[(Sqrt[2]*73^(1/4)*x)/Sqrt[-6 + (7 + Sqrt[73])*x^2]], (73 + 7*Sqrt[73])/146])/(2*Sqrt[3]*73^(1/4)*Sqrt[(6 - (7 + Sqrt[73])*x^2)^(-1)]*Sqrt[-3 + 7*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
54,1,148,0,0.0397224,"\int \frac{1}{\sqrt{-3+6 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 + 6*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{3-\left(3-\sqrt{15}\right) x^2}{3-\left(3+\sqrt{15}\right) x^2}} \sqrt{\left(3+\sqrt{15}\right) x^2-3} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{15} x}{\sqrt{\left(3+\sqrt{15}\right) x^2-3}}\right)|\frac{1}{10} \left(5+\sqrt{15}\right)\right)}{\sqrt{2} 3^{3/4} \sqrt[4]{5} \sqrt{\frac{1}{3-\left(3+\sqrt{15}\right) x^2}} \sqrt{2 x^4+6 x^2-3}}","\frac{\sqrt{\frac{3-\left(3-\sqrt{15}\right) x^2}{3-\left(3+\sqrt{15}\right) x^2}} \sqrt{\left(3+\sqrt{15}\right) x^2-3} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{15} x}{\sqrt{\left(3+\sqrt{15}\right) x^2-3}}\right)|\frac{1}{10} \left(5+\sqrt{15}\right)\right)}{\sqrt{2} 3^{3/4} \sqrt[4]{5} \sqrt{\frac{1}{3-\left(3+\sqrt{15}\right) x^2}} \sqrt{2 x^4+6 x^2-3}}",1,"(Sqrt[(3 - (3 - Sqrt[15])*x^2)/(3 - (3 + Sqrt[15])*x^2)]*Sqrt[-3 + (3 + Sqrt[15])*x^2]*EllipticF[ArcSin[(Sqrt[2]*15^(1/4)*x)/Sqrt[-3 + (3 + Sqrt[15])*x^2]], (5 + Sqrt[15])/10])/(Sqrt[2]*3^(3/4)*5^(1/4)*Sqrt[(3 - (3 + Sqrt[15])*x^2)^(-1)]*Sqrt[-3 + 6*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
55,1,67,0,0.0083515,"\int \frac{1}{\sqrt{-3+5 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 + 5*x^2 + 2*x^4],x]","\frac{\sqrt{x^2+3} \sqrt{2 x^2-1} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{7}{3}} x}{\sqrt{2 x^2-1}}\right)|\frac{6}{7}\right)}{\sqrt{7} \sqrt{2 x^4+5 x^2-3}}","\frac{\sqrt{x^2+3} \sqrt{2 x^2-1} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{7}{3}} x}{\sqrt{2 x^2-1}}\right)|\frac{6}{7}\right)}{\sqrt{7} \sqrt{2 x^4+5 x^2-3}}",1,"(Sqrt[3 + x^2]*Sqrt[-1 + 2*x^2]*EllipticF[ArcSin[(Sqrt[7/3]*x)/Sqrt[-1 + 2*x^2]], 6/7])/(Sqrt[7]*Sqrt[-3 + 5*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1097}"
56,1,148,0,0.0271006,"\int \frac{1}{\sqrt{-3+4 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 + 4*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{3-\left(2-\sqrt{10}\right) x^2}{3-\left(2+\sqrt{10}\right) x^2}} \sqrt{\left(2+\sqrt{10}\right) x^2-3} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{\left(2+\sqrt{10}\right) x^2-3}}\right)|\frac{1}{10} \left(5+\sqrt{10}\right)\right)}{2^{3/4} \sqrt{3} \sqrt[4]{5} \sqrt{\frac{1}{3-\left(2+\sqrt{10}\right) x^2}} \sqrt{2 x^4+4 x^2-3}}","\frac{\sqrt{\frac{3-\left(2-\sqrt{10}\right) x^2}{3-\left(2+\sqrt{10}\right) x^2}} \sqrt{\left(2+\sqrt{10}\right) x^2-3} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{\left(2+\sqrt{10}\right) x^2-3}}\right)|\frac{1}{10} \left(5+\sqrt{10}\right)\right)}{2^{3/4} \sqrt{3} \sqrt[4]{5} \sqrt{\frac{1}{3-\left(2+\sqrt{10}\right) x^2}} \sqrt{2 x^4+4 x^2-3}}",1,"(Sqrt[(3 - (2 - Sqrt[10])*x^2)/(3 - (2 + Sqrt[10])*x^2)]*Sqrt[-3 + (2 + Sqrt[10])*x^2]*EllipticF[ArcSin[(2^(3/4)*5^(1/4)*x)/Sqrt[-3 + (2 + Sqrt[10])*x^2]], (5 + Sqrt[10])/10])/(2^(3/4)*Sqrt[3]*5^(1/4)*Sqrt[(3 - (2 + Sqrt[10])*x^2)^(-1)]*Sqrt[-3 + 4*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
57,1,146,0,0.0266953,"\int \frac{1}{\sqrt{-3+3 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 + 3*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{6-\left(3-\sqrt{33}\right) x^2}{6-\left(3+\sqrt{33}\right) x^2}} \sqrt{\left(3+\sqrt{33}\right) x^2-6} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{\left(3+\sqrt{33}\right) x^2-6}}\right)|\frac{1}{22} \left(11+\sqrt{33}\right)\right)}{2\ 3^{3/4} \sqrt[4]{11} \sqrt{\frac{1}{6-\left(3+\sqrt{33}\right) x^2}} \sqrt{2 x^4+3 x^2-3}}","\frac{\sqrt{\frac{6-\left(3-\sqrt{33}\right) x^2}{6-\left(3+\sqrt{33}\right) x^2}} \sqrt{\left(3+\sqrt{33}\right) x^2-6} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{\left(3+\sqrt{33}\right) x^2-6}}\right)|\frac{1}{22} \left(11+\sqrt{33}\right)\right)}{2\ 3^{3/4} \sqrt[4]{11} \sqrt{\frac{1}{6-\left(3+\sqrt{33}\right) x^2}} \sqrt{2 x^4+3 x^2-3}}",1,"(Sqrt[(6 - (3 - Sqrt[33])*x^2)/(6 - (3 + Sqrt[33])*x^2)]*Sqrt[-6 + (3 + Sqrt[33])*x^2]*EllipticF[ArcSin[(Sqrt[2]*33^(1/4)*x)/Sqrt[-6 + (3 + Sqrt[33])*x^2]], (11 + Sqrt[33])/22])/(2*3^(3/4)*11^(1/4)*Sqrt[(6 - (3 + Sqrt[33])*x^2)^(-1)]*Sqrt[-3 + 3*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
58,1,143,0,0.0233424,"\int \frac{1}{\sqrt{-3+2 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 + 2*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{3-\left(1-\sqrt{7}\right) x^2}{3-\left(1+\sqrt{7}\right) x^2}} \sqrt{\left(1+\sqrt{7}\right) x^2-3} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{\left(1+\sqrt{7}\right) x^2-3}}\right)|\frac{1}{14} \left(7+\sqrt{7}\right)\right)}{\sqrt{6} \sqrt[4]{7} \sqrt{\frac{1}{3-\left(1+\sqrt{7}\right) x^2}} \sqrt{2 x^4+2 x^2-3}}","\frac{\sqrt{\frac{3-\left(1-\sqrt{7}\right) x^2}{3-\left(1+\sqrt{7}\right) x^2}} \sqrt{\left(1+\sqrt{7}\right) x^2-3} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{\left(1+\sqrt{7}\right) x^2-3}}\right)|\frac{1}{14} \left(7+\sqrt{7}\right)\right)}{\sqrt{6} \sqrt[4]{7} \sqrt{\frac{1}{3-\left(1+\sqrt{7}\right) x^2}} \sqrt{2 x^4+2 x^2-3}}",1,"(Sqrt[(3 - (1 - Sqrt[7])*x^2)/(3 - (1 + Sqrt[7])*x^2)]*Sqrt[-3 + (1 + Sqrt[7])*x^2]*EllipticF[ArcSin[(Sqrt[2]*7^(1/4)*x)/Sqrt[-3 + (1 + Sqrt[7])*x^2]], (7 + Sqrt[7])/14])/(Sqrt[6]*7^(1/4)*Sqrt[(3 - (1 + Sqrt[7])*x^2)^(-1)]*Sqrt[-3 + 2*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
59,1,63,0,0.0074047,"\int \frac{1}{\sqrt{-3+x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 + x^2 + 2*x^4],x]","\frac{\sqrt{x^2-1} \sqrt{2 x^2+3} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{x^2-1}}\right)|\frac{3}{5}\right)}{\sqrt{5} \sqrt{2 x^4+x^2-3}}","\frac{\sqrt{x^2-1} \sqrt{2 x^2+3} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{x^2-1}}\right)|\frac{3}{5}\right)}{\sqrt{5} \sqrt{2 x^4+x^2-3}}",1,"(Sqrt[-1 + x^2]*Sqrt[3 + 2*x^2]*EllipticF[ArcSin[(Sqrt[5/3]*x)/Sqrt[-1 + x^2]], 3/5])/(Sqrt[5]*Sqrt[-3 + x^2 + 2*x^4])","A",1,1,14,0.07143,1,"{1097}"
60,1,112,0,0.0154549,"\int \frac{1}{\sqrt{-3+2 x^4}} \, dx","Int[1/Sqrt[-3 + 2*x^4],x]","\frac{\sqrt{\sqrt{6} x^2-3} \sqrt{\frac{\sqrt{6} x^2+3}{3-\sqrt{6} x^2}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt{\sqrt{6} x^2-3}}\right)|\frac{1}{2}\right)}{6^{3/4} \sqrt{\frac{1}{3-\sqrt{6} x^2}} \sqrt{2 x^4-3}}","\frac{\sqrt{\sqrt{6} x^2-3} \sqrt{\frac{\sqrt{6} x^2+3}{3-\sqrt{6} x^2}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{3} x}{\sqrt{\sqrt{6} x^2-3}}\right)|\frac{1}{2}\right)}{6^{3/4} \sqrt{\frac{1}{3-\sqrt{6} x^2}} \sqrt{2 x^4-3}}",1,"(Sqrt[-3 + Sqrt[6]*x^2]*Sqrt[(3 + Sqrt[6]*x^2)/(3 - Sqrt[6]*x^2)]*EllipticF[ArcSin[(2^(3/4)*3^(1/4)*x)/Sqrt[-3 + Sqrt[6]*x^2]], 1/2])/(6^(3/4)*Sqrt[(3 - Sqrt[6]*x^2)^(-1)]*Sqrt[-3 + 2*x^4])","A",1,1,11,0.09091,1,"{223}"
61,1,65,0,0.0068685,"\int \frac{1}{\sqrt{-3-x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 - x^2 + 2*x^4],x]","\frac{\sqrt{x^2+1} \sqrt{2 x^2-3} F\left(\sin ^{-1}\left(\frac{\sqrt{5} x}{\sqrt{2 x^2-3}}\right)|\frac{2}{5}\right)}{\sqrt{5} \sqrt{2 x^4-x^2-3}}","\frac{\sqrt{x^2+1} \sqrt{2 x^2-3} F\left(\sin ^{-1}\left(\frac{\sqrt{5} x}{\sqrt{2 x^2-3}}\right)|\frac{2}{5}\right)}{\sqrt{5} \sqrt{2 x^4-x^2-3}}",1,"(Sqrt[1 + x^2]*Sqrt[-3 + 2*x^2]*EllipticF[ArcSin[(Sqrt[5]*x)/Sqrt[-3 + 2*x^2]], 2/5])/(Sqrt[5]*Sqrt[-3 - x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1097}"
62,1,150,0,0.0212946,"\int \frac{1}{\sqrt{-3-2 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 - 2*x^2 + 2*x^4],x]","\frac{\sqrt{-\left(1-\sqrt{7}\right) x^2-3} \sqrt{\frac{\left(1+\sqrt{7}\right) x^2+3}{\left(1-\sqrt{7}\right) x^2+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{-\left(1-\sqrt{7}\right) x^2-3}}\right)|\frac{1}{14} \left(7-\sqrt{7}\right)\right)}{\sqrt{6} \sqrt[4]{7} \sqrt{\frac{1}{\left(1-\sqrt{7}\right) x^2+3}} \sqrt{2 x^4-2 x^2-3}}","\frac{\sqrt{-\left(1-\sqrt{7}\right) x^2-3} \sqrt{\frac{\left(1+\sqrt{7}\right) x^2+3}{\left(1-\sqrt{7}\right) x^2+3}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{7} x}{\sqrt{-\left(1-\sqrt{7}\right) x^2-3}}\right)|\frac{1}{14} \left(7-\sqrt{7}\right)\right)}{\sqrt{6} \sqrt[4]{7} \sqrt{\frac{1}{\left(1-\sqrt{7}\right) x^2+3}} \sqrt{2 x^4-2 x^2-3}}",1,"(Sqrt[-3 - (1 - Sqrt[7])*x^2]*Sqrt[(3 + (1 + Sqrt[7])*x^2)/(3 + (1 - Sqrt[7])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*7^(1/4)*x)/Sqrt[-3 - (1 - Sqrt[7])*x^2]], (7 - Sqrt[7])/14])/(Sqrt[6]*7^(1/4)*Sqrt[(3 + (1 - Sqrt[7])*x^2)^(-1)]*Sqrt[-3 - 2*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
63,1,153,0,0.0235416,"\int \frac{1}{\sqrt{-3-3 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 - 3*x^2 + 2*x^4],x]","\frac{\sqrt{-\left(3-\sqrt{33}\right) x^2-6} \sqrt{\frac{\left(3+\sqrt{33}\right) x^2+6}{\left(3-\sqrt{33}\right) x^2+6}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{-\left(3-\sqrt{33}\right) x^2-6}}\right)|\frac{1}{22} \left(11-\sqrt{33}\right)\right)}{2\ 3^{3/4} \sqrt[4]{11} \sqrt{\frac{1}{\left(3-\sqrt{33}\right) x^2+6}} \sqrt{2 x^4-3 x^2-3}}","\frac{\sqrt{-\left(3-\sqrt{33}\right) x^2-6} \sqrt{\frac{\left(3+\sqrt{33}\right) x^2+6}{\left(3-\sqrt{33}\right) x^2+6}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{33} x}{\sqrt{-\left(3-\sqrt{33}\right) x^2-6}}\right)|\frac{1}{22} \left(11-\sqrt{33}\right)\right)}{2\ 3^{3/4} \sqrt[4]{11} \sqrt{\frac{1}{\left(3-\sqrt{33}\right) x^2+6}} \sqrt{2 x^4-3 x^2-3}}",1,"(Sqrt[-6 - (3 - Sqrt[33])*x^2]*Sqrt[(6 + (3 + Sqrt[33])*x^2)/(6 + (3 - Sqrt[33])*x^2)]*EllipticF[ArcSin[(Sqrt[2]*33^(1/4)*x)/Sqrt[-6 - (3 - Sqrt[33])*x^2]], (11 - Sqrt[33])/22])/(2*3^(3/4)*11^(1/4)*Sqrt[(6 + (3 - Sqrt[33])*x^2)^(-1)]*Sqrt[-3 - 3*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
64,1,155,0,0.0236497,"\int \frac{1}{\sqrt{-3-4 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 - 4*x^2 + 2*x^4],x]","\frac{\sqrt{-\left(2-\sqrt{10}\right) x^2-3} \sqrt{\frac{\left(2+\sqrt{10}\right) x^2+3}{\left(2-\sqrt{10}\right) x^2+3}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{-\left(2-\sqrt{10}\right) x^2-3}}\right)|\frac{1}{10} \left(5-\sqrt{10}\right)\right)}{2^{3/4} \sqrt{3} \sqrt[4]{5} \sqrt{\frac{1}{\left(2-\sqrt{10}\right) x^2+3}} \sqrt{2 x^4-4 x^2-3}}","\frac{\sqrt{-\left(2-\sqrt{10}\right) x^2-3} \sqrt{\frac{\left(2+\sqrt{10}\right) x^2+3}{\left(2-\sqrt{10}\right) x^2+3}} F\left(\sin ^{-1}\left(\frac{2^{3/4} \sqrt[4]{5} x}{\sqrt{-\left(2-\sqrt{10}\right) x^2-3}}\right)|\frac{1}{10} \left(5-\sqrt{10}\right)\right)}{2^{3/4} \sqrt{3} \sqrt[4]{5} \sqrt{\frac{1}{\left(2-\sqrt{10}\right) x^2+3}} \sqrt{2 x^4-4 x^2-3}}",1,"(Sqrt[-3 - (2 - Sqrt[10])*x^2]*Sqrt[(3 + (2 + Sqrt[10])*x^2)/(3 + (2 - Sqrt[10])*x^2)]*EllipticF[ArcSin[(2^(3/4)*5^(1/4)*x)/Sqrt[-3 - (2 - Sqrt[10])*x^2]], (5 - Sqrt[10])/10])/(2^(3/4)*Sqrt[3]*5^(1/4)*Sqrt[(3 + (2 - Sqrt[10])*x^2)^(-1)]*Sqrt[-3 - 4*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1098}"
65,1,63,0,0.0064966,"\int \frac{1}{\sqrt{-3-5 x^2+2 x^4}} \, dx","Int[1/Sqrt[-3 - 5*x^2 + 2*x^4],x]","\frac{\sqrt{x^2-3} \sqrt{2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{7} x}{\sqrt{x^2-3}}\right)|\frac{1}{7}\right)}{\sqrt{7} \sqrt{2 x^4-5 x^2-3}}","\frac{\sqrt{x^2-3} \sqrt{2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{7} x}{\sqrt{x^2-3}}\right)|\frac{1}{7}\right)}{\sqrt{7} \sqrt{2 x^4-5 x^2-3}}",1,"(Sqrt[-3 + x^2]*Sqrt[1 + 2*x^2]*EllipticF[ArcSin[(Sqrt[7]*x)/Sqrt[-3 + x^2]], 1/7])/(Sqrt[7]*Sqrt[-3 - 5*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1097}"
66,1,52,0,0.007413,"\int \frac{1}{\sqrt{2+5 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 + 3*x^4],x]","\frac{\left(x^2+1\right) \sqrt{\frac{3 x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^4+5 x^2+2}}","\frac{\left(x^2+1\right) \sqrt{\frac{3 x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^4+5 x^2+2}}",1,"((1 + x^2)*Sqrt[(2 + 3*x^2)/(1 + x^2)]*EllipticF[ArcTan[x], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1100}"
67,1,90,0,0.0212167,"\int \frac{1}{\sqrt{2+4 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 + 4*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+4 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+4 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 4*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], 1/2 - 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[2 + 4*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
68,1,92,0,0.0160884,"\int \frac{1}{\sqrt{2+3 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 + 3*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+3 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+3 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 3*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (4 - Sqrt[6])/8])/(2*6^(1/4)*Sqrt[2 + 3*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
69,1,92,0,0.0159053,"\int \frac{1}{\sqrt{2+2 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 + 2*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+2 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+2 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 2*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (6 - Sqrt[6])/12])/(2*6^(1/4)*Sqrt[2 + 2*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
70,1,88,0,0.0138713,"\int \frac{1}{\sqrt{2+x^2+3 x^4}} \, dx","Int[1/Sqrt[2 + x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (12 - Sqrt[6])/24])/(2*6^(1/4)*Sqrt[2 + x^2 + 3*x^4])","A",1,1,14,0.07143,1,"{1103}"
71,1,72,0,0.0072882,"\int \frac{1}{\sqrt{2+3 x^4}} \, dx","Int[1/Sqrt[2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{3 x^4+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], 1/2])/(2*6^(1/4)*Sqrt[2 + 3*x^4])","A",1,1,11,0.09091,1,"{220}"
72,1,90,0,0.0154063,"\int \frac{1}{\sqrt{2-x^2+3 x^4}} \, dx","Int[1/Sqrt[2 - x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (12 + Sqrt[6])/24])/(2*6^(1/4)*Sqrt[2 - x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
73,1,90,0,0.0151346,"\int \frac{1}{\sqrt{2-2 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 - 2*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-2 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-2 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 2*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (6 + Sqrt[6])/12])/(2*6^(1/4)*Sqrt[2 - 2*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
74,1,90,0,0.0156303,"\int \frac{1}{\sqrt{2-3 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 - 3*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-3 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-3 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 3*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (4 + Sqrt[6])/8])/(2*6^(1/4)*Sqrt[2 - 3*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
75,1,88,0,0.0115275,"\int \frac{1}{\sqrt{2-4 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 - 4*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-4 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-4 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 4*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], 1/2 + 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[2 - 4*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
76,1,92,0,0.0151634,"\int \frac{1}{\sqrt{2-5 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 - 5*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-5 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12+5 \sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-5 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-5 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12+5 \sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-5 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 5*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (12 + 5*Sqrt[6])/24])/(2*6^(1/4)*Sqrt[2 - 5*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1096}"
77,1,90,0,0.0163397,"\int \frac{1}{\sqrt{2-6 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 - 6*x^2 + 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-6 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{4} \left(2+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-6 x^2+2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-6 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{4} \left(2+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{3 x^4-6 x^2+2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 6*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (2 + Sqrt[6])/4])/(2*6^(1/4)*Sqrt[2 - 6*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1096}"
78,1,110,0,0.091197,"\int \frac{1}{\sqrt{3+9 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 9*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{\left(9-\sqrt{57}\right) x^2+6}{\left(9+\sqrt{57}\right) x^2+6}} \left(\left(9+\sqrt{57}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(9+\sqrt{57}\right)} x\right)|\frac{1}{4} \left(-19+3 \sqrt{57}\right)\right)}{\sqrt{6 \left(9+\sqrt{57}\right)} \sqrt{2 x^4+9 x^2+3}}","\frac{\sqrt{\frac{\left(9-\sqrt{57}\right) x^2+6}{\left(9+\sqrt{57}\right) x^2+6}} \left(\left(9+\sqrt{57}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(9+\sqrt{57}\right)} x\right)|\frac{1}{4} \left(-19+3 \sqrt{57}\right)\right)}{\sqrt{6 \left(9+\sqrt{57}\right)} \sqrt{2 x^4+9 x^2+3}}",1,"(Sqrt[(6 + (9 - Sqrt[57])*x^2)/(6 + (9 + Sqrt[57])*x^2)]*(6 + (9 + Sqrt[57])*x^2)*EllipticF[ArcTan[Sqrt[(9 + Sqrt[57])/6]*x], (-19 + 3*Sqrt[57])/4])/(Sqrt[6*(9 + Sqrt[57])]*Sqrt[3 + 9*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1099}"
79,1,110,0,0.0757186,"\int \frac{1}{\sqrt{3+8 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 8*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{\left(4-\sqrt{10}\right) x^2+3}{\left(4+\sqrt{10}\right) x^2+3}} \left(\left(4+\sqrt{10}\right) x^2+3\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{3} \left(4+\sqrt{10}\right)} x\right)|-\frac{2}{3} \left(5-2 \sqrt{10}\right)\right)}{\sqrt{3 \left(4+\sqrt{10}\right)} \sqrt{2 x^4+8 x^2+3}}","\frac{\sqrt{\frac{\left(4-\sqrt{10}\right) x^2+3}{\left(4+\sqrt{10}\right) x^2+3}} \left(\left(4+\sqrt{10}\right) x^2+3\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{3} \left(4+\sqrt{10}\right)} x\right)|-\frac{2}{3} \left(5-2 \sqrt{10}\right)\right)}{\sqrt{3 \left(4+\sqrt{10}\right)} \sqrt{2 x^4+8 x^2+3}}",1,"(Sqrt[(3 + (4 - Sqrt[10])*x^2)/(3 + (4 + Sqrt[10])*x^2)]*(3 + (4 + Sqrt[10])*x^2)*EllipticF[ArcTan[Sqrt[(4 + Sqrt[10])/3]*x], (-2*(5 - 2*Sqrt[10]))/3])/(Sqrt[3*(4 + Sqrt[10])]*Sqrt[3 + 8*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1099}"
80,1,60,0,0.0074505,"\int \frac{1}{\sqrt{3+7 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 7*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{x^2+3}{2 x^2+1}} \left(2 x^2+1\right) F\left(\tan ^{-1}\left(\sqrt{2} x\right)|\frac{5}{6}\right)}{\sqrt{6} \sqrt{2 x^4+7 x^2+3}}","\frac{\sqrt{\frac{x^2+3}{2 x^2+1}} \left(2 x^2+1\right) F\left(\tan ^{-1}\left(\sqrt{2} x\right)|\frac{5}{6}\right)}{\sqrt{6} \sqrt{2 x^4+7 x^2+3}}",1,"(Sqrt[(3 + x^2)/(1 + 2*x^2)]*(1 + 2*x^2)*EllipticF[ArcTan[Sqrt[2]*x], 5/6])/(Sqrt[6]*Sqrt[3 + 7*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1099}"
81,1,104,0,0.0642674,"\int \frac{1}{\sqrt{3+6 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 6*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{\left(3-\sqrt{3}\right) x^2+3}{\left(3+\sqrt{3}\right) x^2+3}} \left(\left(3+\sqrt{3}\right) x^2+3\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{3} \left(3+\sqrt{3}\right)} x\right)|-1+\sqrt{3}\right)}{\sqrt{3 \left(3+\sqrt{3}\right)} \sqrt{2 x^4+6 x^2+3}}","\frac{\sqrt{\frac{\left(3-\sqrt{3}\right) x^2+3}{\left(3+\sqrt{3}\right) x^2+3}} \left(\left(3+\sqrt{3}\right) x^2+3\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{3} \left(3+\sqrt{3}\right)} x\right)|-1+\sqrt{3}\right)}{\sqrt{3 \left(3+\sqrt{3}\right)} \sqrt{2 x^4+6 x^2+3}}",1,"(Sqrt[(3 + (3 - Sqrt[3])*x^2)/(3 + (3 + Sqrt[3])*x^2)]*(3 + (3 + Sqrt[3])*x^2)*EllipticF[ArcTan[Sqrt[(3 + Sqrt[3])/3]*x], -1 + Sqrt[3]])/(Sqrt[3*(3 + Sqrt[3])]*Sqrt[3 + 6*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1099}"
82,1,52,0,0.006334,"\int \frac{1}{\sqrt{3+5 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 5*x^2 + 2*x^4],x]","\frac{\left(x^2+1\right) \sqrt{\frac{2 x^2+3}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{3}\right)}{\sqrt{3} \sqrt{2 x^4+5 x^2+3}}","\frac{\left(x^2+1\right) \sqrt{\frac{2 x^2+3}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{3}\right)}{\sqrt{3} \sqrt{2 x^4+5 x^2+3}}",1,"((1 + x^2)*Sqrt[(3 + 2*x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/3])/(Sqrt[3]*Sqrt[3 + 5*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1099}"
83,1,90,0,0.0163867,"\int \frac{1}{\sqrt{3+4 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 4*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+4 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+4 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 4*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], 1/2 - 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[3 + 4*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
84,1,92,0,0.0099577,"\int \frac{1}{\sqrt{3+3 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 3*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+3 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+3 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 3*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (4 - Sqrt[6])/8])/(2*6^(1/4)*Sqrt[3 + 3*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
85,1,92,0,0.0095349,"\int \frac{1}{\sqrt{3+2 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + 2*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+2 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+2 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 2*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (6 - Sqrt[6])/12])/(2*6^(1/4)*Sqrt[3 + 2*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
86,1,88,0,0.0119184,"\int \frac{1}{\sqrt{3+x^2+2 x^4}} \, dx","Int[1/Sqrt[3 + x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (12 - Sqrt[6])/24])/(2*6^(1/4)*Sqrt[3 + x^2 + 2*x^4])","A",1,1,14,0.07143,1,"{1103}"
87,1,72,0,0.0073546,"\int \frac{1}{\sqrt{3+2 x^4}} \, dx","Int[1/Sqrt[3 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{2 x^4+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], 1/2])/(2*6^(1/4)*Sqrt[3 + 2*x^4])","A",1,1,11,0.09091,1,"{220}"
88,1,90,0,0.0096487,"\int \frac{1}{\sqrt{3-x^2+2 x^4}} \, dx","Int[1/Sqrt[3 - x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (12 + Sqrt[6])/24])/(2*6^(1/4)*Sqrt[3 - x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
89,1,90,0,0.0096703,"\int \frac{1}{\sqrt{3-2 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 - 2*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-2 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-2 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 2*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (6 + Sqrt[6])/12])/(2*6^(1/4)*Sqrt[3 - 2*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
90,1,90,0,0.0092666,"\int \frac{1}{\sqrt{3-3 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 - 3*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-3 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-3 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 3*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (4 + Sqrt[6])/8])/(2*6^(1/4)*Sqrt[3 - 3*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
91,1,88,0,0.0095326,"\int \frac{1}{\sqrt{3-4 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 - 4*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-4 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-4 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 4*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], 1/2 + 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[3 - 4*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
92,1,92,0,0.0091571,"\int \frac{1}{\sqrt{3-5 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 - 5*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-5 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+5 \sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-5 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-5 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+5 \sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-5 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 5*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (12 + 5*Sqrt[6])/24])/(2*6^(1/4)*Sqrt[3 - 5*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1096}"
93,1,90,0,0.0095625,"\int \frac{1}{\sqrt{3-6 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 - 6*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-6 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{4} \left(2+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-6 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-6 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{4} \left(2+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-6 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 6*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (2 + Sqrt[6])/4])/(2*6^(1/4)*Sqrt[3 - 6*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1096}"
94,1,92,0,0.013894,"\int \frac{1}{\sqrt{3-7 x^2+2 x^4}} \, dx","Int[1/Sqrt[3 - 7*x^2 + 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-7 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+7 \sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-7 x^2+3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-7 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+7 \sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{2 x^4-7 x^2+3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 7*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (12 + 7*Sqrt[6])/24])/(2*6^(1/4)*Sqrt[3 - 7*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1096}"
95,1,19,0,0.0119673,"\int \frac{1}{\sqrt{-3+7 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 + 7*x^2 - 2*x^4],x]","-\frac{F\left(\cos ^{-1}\left(\frac{x}{\sqrt{3}}\right)|\frac{6}{5}\right)}{\sqrt{5}}","-\frac{F\left(\cos ^{-1}\left(\frac{x}{\sqrt{3}}\right)|\frac{6}{5}\right)}{\sqrt{5}}",1,"-(EllipticF[ArcCos[x/Sqrt[3]], 6/5]/Sqrt[5])","A",2,2,16,0.1250,1,"{1095, 420}"
96,1,44,0,0.0607096,"\int \frac{1}{\sqrt{-3+6 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 + 6*x^2 - 2*x^4],x]","-\frac{F\left(\cos ^{-1}\left(\sqrt{\frac{1}{3} \left(3-\sqrt{3}\right)} x\right)|\frac{1}{2} \left(1+\sqrt{3}\right)\right)}{\sqrt{2} \sqrt[4]{3}}","-\frac{F\left(\cos ^{-1}\left(\sqrt{\frac{1}{3} \left(3-\sqrt{3}\right)} x\right)|\frac{1}{2} \left(1+\sqrt{3}\right)\right)}{\sqrt{2} \sqrt[4]{3}}",1,"-(EllipticF[ArcCos[Sqrt[(3 - Sqrt[3])/3]*x], (1 + Sqrt[3])/2]/(Sqrt[2]*3^(1/4)))","A",2,2,16,0.1250,1,"{1095, 420}"
97,1,14,0,0.0116204,"\int \frac{1}{\sqrt{-3+5 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 + 5*x^2 - 2*x^4],x]","-F\left(\left.\cos ^{-1}\left(\sqrt{\frac{2}{3}} x\right)\right|3\right)","-F\left(\left.\cos ^{-1}\left(\sqrt{\frac{2}{3}} x\right)\right|3\right)",1,"-EllipticF[ArcCos[Sqrt[2/3]*x], 3]","A",2,2,16,0.1250,1,"{1095, 420}"
98,1,88,0,0.010028,"\int \frac{1}{\sqrt{-3+4 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 + 4*x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+4 x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+4 x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 4*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], 1/2 + 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[-3 + 4*x^2 - 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
99,1,90,0,0.0102385,"\int \frac{1}{\sqrt{-3+3 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 + 3*x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+3 x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+3 x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 3*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (4 + Sqrt[6])/8])/(2*6^(1/4)*Sqrt[-3 + 3*x^2 - 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
100,1,90,0,0.0096004,"\int \frac{1}{\sqrt{-3+2 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 + 2*x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+2 x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+2 x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - 2*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (6 + Sqrt[6])/12])/(2*6^(1/4)*Sqrt[-3 + 2*x^2 - 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
101,1,88,0,0.00898,"\int \frac{1}{\sqrt{-3+x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 + x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4-x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4+x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 - x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (12 + Sqrt[6])/24])/(2*6^(1/4)*Sqrt[-3 + x^2 - 2*x^4])","A",1,1,14,0.07143,1,"{1103}"
102,1,72,0,0.0070373,"\int \frac{1}{\sqrt{-3-2 x^4}} \, dx","Int[1/Sqrt[-3 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], 1/2])/(2*6^(1/4)*Sqrt[-3 - 2*x^4])","A",1,1,11,0.09091,1,"{220}"
103,1,90,0,0.0100277,"\int \frac{1}{\sqrt{-3-x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 - x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (12 - Sqrt[6])/24])/(2*6^(1/4)*Sqrt[-3 - x^2 - 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
104,1,92,0,0.010235,"\int \frac{1}{\sqrt{-3-2 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 - 2*x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-2 x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+2 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-2 x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 2*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (6 - Sqrt[6])/12])/(2*6^(1/4)*Sqrt[-3 - 2*x^2 - 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
105,1,92,0,0.009903,"\int \frac{1}{\sqrt{-3-3 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 - 3*x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-3 x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+3 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-3 x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 3*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], (4 - Sqrt[6])/8])/(2*6^(1/4)*Sqrt[-3 - 3*x^2 - 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
106,1,90,0,0.0093564,"\int \frac{1}{\sqrt{-3-4 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 - 4*x^2 - 2*x^4],x]","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-4 x^2-3}}","\frac{\left(\sqrt{6} x^2+3\right) \sqrt{\frac{2 x^4+4 x^2+3}{\left(\sqrt{6} x^2+3\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{2}{3}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-2 x^4-4 x^2-3}}",1,"((3 + Sqrt[6]*x^2)*Sqrt[(3 + 4*x^2 + 2*x^4)/(3 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(2/3)^(1/4)*x], 1/2 - 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[-3 - 4*x^2 - 2*x^4])","A",1,1,16,0.06250,1,"{1103}"
107,1,53,0,0.0161595,"\int \frac{1}{\sqrt{-3-5 x^2-2 x^4}} \, dx","Int[1/Sqrt[-3 - 5*x^2 - 2*x^4],x]","\frac{\sqrt{2 x^2+3} F\left(\tan ^{-1}(x)|\frac{1}{3}\right)}{\sqrt{3} \sqrt{-x^2-1} \sqrt{\frac{2 x^2+3}{x^2+1}}}","\frac{\sqrt{2 x^2+3} F\left(\tan ^{-1}(x)|\frac{1}{3}\right)}{\sqrt{3} \sqrt{-x^2-1} \sqrt{\frac{2 x^2+3}{x^2+1}}}",1,"(Sqrt[3 + 2*x^2]*EllipticF[ArcTan[x], 1/3])/(Sqrt[3]*Sqrt[-1 - x^2]*Sqrt[(3 + 2*x^2)/(1 + x^2)])","A",2,2,16,0.1250,1,"{1095, 418}"
108,1,42,0,0.0520854,"\int \frac{1}{\sqrt{-2+6 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 + 6*x^2 - 3*x^4],x]","-\frac{F\left(\cos ^{-1}\left(\sqrt{\frac{3}{3+\sqrt{3}}} x\right)|\frac{1}{2} \left(1+\sqrt{3}\right)\right)}{\sqrt{2} \sqrt[4]{3}}","-\frac{F\left(\cos ^{-1}\left(\sqrt{\frac{3}{3+\sqrt{3}}} x\right)|\frac{1}{2} \left(1+\sqrt{3}\right)\right)}{\sqrt{2} \sqrt[4]{3}}",1,"-(EllipticF[ArcCos[Sqrt[3/(3 + Sqrt[3])]*x], (1 + Sqrt[3])/2]/(Sqrt[2]*3^(1/4)))","A",2,2,16,0.1250,1,"{1095, 420}"
109,1,6,0,0.0104999,"\int \frac{1}{\sqrt{-2+5 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 + 5*x^2 - 3*x^4],x]","-F\left(\left.\cos ^{-1}(x)\right|3\right)","-F\left(\left.\cos ^{-1}(x)\right|3\right)",1,"-EllipticF[ArcCos[x], 3]","A",2,2,16,0.1250,1,"{1095, 420}"
110,1,88,0,0.0095612,"\int \frac{1}{\sqrt{-2+4 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 + 4*x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+4 x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}+\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+4 x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 4*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], 1/2 + 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[-2 + 4*x^2 - 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
111,1,90,0,0.0094841,"\int \frac{1}{\sqrt{-2+3 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 + 3*x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+3 x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+3 x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 3*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (4 + Sqrt[6])/8])/(2*6^(1/4)*Sqrt[-2 + 3*x^2 - 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
112,1,90,0,0.0139037,"\int \frac{1}{\sqrt{-2+2 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 + 2*x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+2 x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+2 x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - 2*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (6 + Sqrt[6])/12])/(2*6^(1/4)*Sqrt[-2 + 2*x^2 - 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
113,1,88,0,0.0093471,"\int \frac{1}{\sqrt{-2+x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 + x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4-x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12+\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4+x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 - x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (12 + Sqrt[6])/24])/(2*6^(1/4)*Sqrt[-2 + x^2 - 3*x^4])","A",1,1,14,0.07143,1,"{1103}"
114,1,72,0,0.0079274,"\int \frac{1}{\sqrt{-2-3 x^4}} \, dx","Int[1/Sqrt[-2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], 1/2])/(2*6^(1/4)*Sqrt[-2 - 3*x^4])","A",1,1,11,0.09091,1,"{220}"
115,1,90,0,0.0097881,"\int \frac{1}{\sqrt{-2-x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 - x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{24} \left(12-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (12 - Sqrt[6])/24])/(2*6^(1/4)*Sqrt[-2 - x^2 - 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
116,1,92,0,0.0102529,"\int \frac{1}{\sqrt{-2-2 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 - 2*x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-2 x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+2 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{12} \left(6-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-2 x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 2*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (6 - Sqrt[6])/12])/(2*6^(1/4)*Sqrt[-2 - 2*x^2 - 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
117,1,92,0,0.0095006,"\int \frac{1}{\sqrt{-2-3 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 - 3*x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-3 x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+3 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{8} \left(4-\sqrt{6}\right)\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-3 x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 3*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], (4 - Sqrt[6])/8])/(2*6^(1/4)*Sqrt[-2 - 3*x^2 - 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
118,1,90,0,0.0094641,"\int \frac{1}{\sqrt{-2-4 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 - 4*x^2 - 3*x^4],x]","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-4 x^2-2}}","\frac{\left(\sqrt{6} x^2+2\right) \sqrt{\frac{3 x^4+4 x^2+2}{\left(\sqrt{6} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{3}{2}} x\right)|\frac{1}{2}-\frac{1}{\sqrt{6}}\right)}{2 \sqrt[4]{6} \sqrt{-3 x^4-4 x^2-2}}",1,"((2 + Sqrt[6]*x^2)*Sqrt[(2 + 4*x^2 + 3*x^4)/(2 + Sqrt[6]*x^2)^2]*EllipticF[2*ArcTan[(3/2)^(1/4)*x], 1/2 - 1/Sqrt[6]])/(2*6^(1/4)*Sqrt[-2 - 4*x^2 - 3*x^4])","A",1,1,16,0.06250,1,"{1103}"
119,1,52,0,0.0167469,"\int \frac{1}{\sqrt{-2-5 x^2-3 x^4}} \, dx","Int[1/Sqrt[-2 - 5*x^2 - 3*x^4],x]","-\frac{\sqrt{-3 x^2-2} F\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^2+1} \sqrt{\frac{3 x^2+2}{x^2+1}}}","-\frac{\sqrt{-3 x^2-2} F\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^2+1} \sqrt{\frac{3 x^2+2}{x^2+1}}}",1,"-((Sqrt[-2 - 3*x^2]*EllipticF[ArcTan[x], -1/2])/(Sqrt[2]*Sqrt[1 + x^2]*Sqrt[(2 + 3*x^2)/(1 + x^2)]))","A",2,2,16,0.1250,1,"{1095, 418}"
120,1,92,0,0.0258335,"\int \frac{1}{\sqrt{2+5 x^2+5 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 + 5*x^4],x]","\frac{\left(\sqrt{10} x^2+2\right) \sqrt{\frac{5 x^4+5 x^2+2}{\left(\sqrt{10} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{5}{2}} x\right)|\frac{1}{8} \left(4-\sqrt{10}\right)\right)}{2 \sqrt[4]{10} \sqrt{5 x^4+5 x^2+2}}","\frac{\left(\sqrt{10} x^2+2\right) \sqrt{\frac{5 x^4+5 x^2+2}{\left(\sqrt{10} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{\frac{5}{2}} x\right)|\frac{1}{8} \left(4-\sqrt{10}\right)\right)}{2 \sqrt[4]{10} \sqrt{5 x^4+5 x^2+2}}",1,"((2 + Sqrt[10]*x^2)*Sqrt[(2 + 5*x^2 + 5*x^4)/(2 + Sqrt[10]*x^2)^2]*EllipticF[2*ArcTan[(5/2)^(1/4)*x], (4 - Sqrt[10])/8])/(2*10^(1/4)*Sqrt[2 + 5*x^2 + 5*x^4])","A",1,1,16,0.06250,1,"{1103}"
121,1,90,0,0.0189061,"\int \frac{1}{\sqrt{2+5 x^2+4 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 + 4*x^4],x]","\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{4 x^4+5 x^2+2}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{16} \left(8-5 \sqrt{2}\right)\right)}{2\ 2^{3/4} \sqrt{4 x^4+5 x^2+2}}","\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{4 x^4+5 x^2+2}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{16} \left(8-5 \sqrt{2}\right)\right)}{2\ 2^{3/4} \sqrt{4 x^4+5 x^2+2}}",1,"((1 + Sqrt[2]*x^2)*Sqrt[(2 + 5*x^2 + 4*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (8 - 5*Sqrt[2])/16])/(2*2^(3/4)*Sqrt[2 + 5*x^2 + 4*x^4])","A",1,1,16,0.06250,1,"{1103}"
122,1,52,0,0.0072609,"\int \frac{1}{\sqrt{2+5 x^2+3 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 + 3*x^4],x]","\frac{\left(x^2+1\right) \sqrt{\frac{3 x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^4+5 x^2+2}}","\frac{\left(x^2+1\right) \sqrt{\frac{3 x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^4+5 x^2+2}}",1,"((1 + x^2)*Sqrt[(2 + 3*x^2)/(1 + x^2)]*EllipticF[ArcTan[x], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x^2 + 3*x^4])","A",1,1,16,0.06250,1,"{1100}"
123,1,58,0,0.0071399,"\int \frac{1}{\sqrt{2+5 x^2+2 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 + 2*x^4],x]","\frac{\sqrt{\frac{x^2+2}{2 x^2+1}} \left(2 x^2+1\right) F\left(\tan ^{-1}\left(\sqrt{2} x\right)|\frac{3}{4}\right)}{2 \sqrt{2 x^4+5 x^2+2}}","\frac{\sqrt{\frac{x^2+2}{2 x^2+1}} \left(2 x^2+1\right) F\left(\tan ^{-1}\left(\sqrt{2} x\right)|\frac{3}{4}\right)}{2 \sqrt{2 x^4+5 x^2+2}}",1,"(Sqrt[(2 + x^2)/(1 + 2*x^2)]*(1 + 2*x^2)*EllipticF[ArcTan[Sqrt[2]*x], 3/4])/(2*Sqrt[2 + 5*x^2 + 2*x^4])","A",1,1,16,0.06250,1,"{1099}"
124,1,108,0,0.0420829,"\int \frac{1}{\sqrt{2+5 x^2+x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 + x^4],x]","\frac{\sqrt{\frac{\left(5-\sqrt{17}\right) x^2+4}{\left(5+\sqrt{17}\right) x^2+4}} \left(\left(5+\sqrt{17}\right) x^2+4\right) F\left(\tan ^{-1}\left(\frac{1}{2} \sqrt{5+\sqrt{17}} x\right)|\frac{1}{4} \left(-17+5 \sqrt{17}\right)\right)}{2 \sqrt{5+\sqrt{17}} \sqrt{x^4+5 x^2+2}}","\frac{\sqrt{\frac{\left(5-\sqrt{17}\right) x^2+4}{\left(5+\sqrt{17}\right) x^2+4}} \left(\left(5+\sqrt{17}\right) x^2+4\right) F\left(\tan ^{-1}\left(\frac{1}{2} \sqrt{5+\sqrt{17}} x\right)|\frac{1}{4} \left(-17+5 \sqrt{17}\right)\right)}{2 \sqrt{5+\sqrt{17}} \sqrt{x^4+5 x^2+2}}",1,"(Sqrt[(4 + (5 - Sqrt[17])*x^2)/(4 + (5 + Sqrt[17])*x^2)]*(4 + (5 + Sqrt[17])*x^2)*EllipticF[ArcTan[(Sqrt[5 + Sqrt[17]]*x)/2], (-17 + 5*Sqrt[17])/4])/(2*Sqrt[5 + Sqrt[17]]*Sqrt[2 + 5*x^2 + x^4])","A",1,1,14,0.07143,1,"{1099}"
125,1,48,0,0.0983492,"\int \frac{1}{\sqrt{2+5 x^2-x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - x^4],x]","\sqrt{\frac{2}{\sqrt{33}-5}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{33}}} x\right)|\frac{1}{4} \left(-29-5 \sqrt{33}\right)\right)","\sqrt{\frac{2}{\sqrt{33}-5}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{33}}} x\right)|\frac{1}{4} \left(-29-5 \sqrt{33}\right)\right)",1,"Sqrt[2/(-5 + Sqrt[33])]*EllipticF[ArcSin[Sqrt[2/(5 + Sqrt[33])]*x], (-29 - 5*Sqrt[33])/4]","A",2,2,16,0.1250,1,"{1095, 419}"
126,1,45,0,0.062061,"\int \frac{1}{\sqrt{2+5 x^2-2 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 2*x^4],x]","\sqrt{\frac{2}{\sqrt{41}-5}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{5+\sqrt{41}}}\right)|\frac{1}{8} \left(-33-5 \sqrt{41}\right)\right)","\sqrt{\frac{2}{\sqrt{41}-5}} F\left(\sin ^{-1}\left(\frac{2 x}{\sqrt{5+\sqrt{41}}}\right)|\frac{1}{8} \left(-33-5 \sqrt{41}\right)\right)",1,"Sqrt[2/(-5 + Sqrt[41])]*EllipticF[ArcSin[(2*x)/Sqrt[5 + Sqrt[41]]], (-33 - 5*Sqrt[41])/8]","A",2,2,16,0.1250,1,"{1095, 419}"
127,1,10,0,0.011636,"\int \frac{1}{\sqrt{2+5 x^2-3 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 3*x^4],x]","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-6\right)","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-6\right)",1,"EllipticF[ArcSin[x/Sqrt[2]], -6]","A",2,2,16,0.1250,1,"{1095, 419}"
128,1,49,0,0.1037511,"\int \frac{1}{\sqrt{2+5 x^2-4 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 4*x^4],x]","\sqrt{\frac{2}{\sqrt{57}-5}} F\left(\sin ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{57}}} x\right)|\frac{1}{16} \left(-41-5 \sqrt{57}\right)\right)","\sqrt{\frac{2}{\sqrt{57}-5}} F\left(\sin ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{57}}} x\right)|\frac{1}{16} \left(-41-5 \sqrt{57}\right)\right)",1,"Sqrt[2/(-5 + Sqrt[57])]*EllipticF[ArcSin[2*Sqrt[2/(5 + Sqrt[57])]*x], (-41 - 5*Sqrt[57])/16]","A",2,2,16,0.1250,1,"{1095, 419}"
129,1,48,0,0.1042495,"\int \frac{1}{\sqrt{2+5 x^2-5 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 5*x^4],x]","\sqrt{\frac{2}{\sqrt{65}-5}} F\left(\sin ^{-1}\left(\sqrt{\frac{10}{5+\sqrt{65}}} x\right)|\frac{1}{4} \left(-9-\sqrt{65}\right)\right)","\sqrt{\frac{2}{\sqrt{65}-5}} F\left(\sin ^{-1}\left(\sqrt{\frac{10}{5+\sqrt{65}}} x\right)|\frac{1}{4} \left(-9-\sqrt{65}\right)\right)",1,"Sqrt[2/(-5 + Sqrt[65])]*EllipticF[ArcSin[Sqrt[10/(5 + Sqrt[65])]*x], (-9 - Sqrt[65])/4]","A",2,2,16,0.1250,1,"{1095, 419}"
130,1,49,0,0.0782031,"\int \frac{1}{\sqrt{2+5 x^2-6 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 6*x^4],x]","\sqrt{\frac{2}{\sqrt{73}-5}} F\left(\sin ^{-1}\left(2 \sqrt{\frac{3}{5+\sqrt{73}}} x\right)|\frac{1}{24} \left(-49-5 \sqrt{73}\right)\right)","\sqrt{\frac{2}{\sqrt{73}-5}} F\left(\sin ^{-1}\left(2 \sqrt{\frac{3}{5+\sqrt{73}}} x\right)|\frac{1}{24} \left(-49-5 \sqrt{73}\right)\right)",1,"Sqrt[2/(-5 + Sqrt[73])]*EllipticF[ArcSin[2*Sqrt[3/(5 + Sqrt[73])]*x], (-49 - 5*Sqrt[73])/24]","A",2,2,16,0.1250,1,"{1095, 419}"
131,1,12,0,0.011929,"\int \frac{1}{\sqrt{2+5 x^2-7 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 7*x^4],x]","\frac{F\left(\sin ^{-1}(x)|-\frac{7}{2}\right)}{\sqrt{2}}","\frac{F\left(\sin ^{-1}(x)|-\frac{7}{2}\right)}{\sqrt{2}}",1,"EllipticF[ArcSin[x], -7/2]/Sqrt[2]","A",2,2,16,0.1250,1,"{1095, 419}"
132,1,45,0,0.0696016,"\int \frac{1}{\sqrt{2+5 x^2-8 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 8*x^4],x]","\sqrt{\frac{2}{\sqrt{89}-5}} F\left(\sin ^{-1}\left(\frac{4 x}{\sqrt{5+\sqrt{89}}}\right)|\frac{1}{32} \left(-57-5 \sqrt{89}\right)\right)","\sqrt{\frac{2}{\sqrt{89}-5}} F\left(\sin ^{-1}\left(\frac{4 x}{\sqrt{5+\sqrt{89}}}\right)|\frac{1}{32} \left(-57-5 \sqrt{89}\right)\right)",1,"Sqrt[2/(-5 + Sqrt[89])]*EllipticF[ArcSin[(4*x)/Sqrt[5 + Sqrt[89]]], (-57 - 5*Sqrt[89])/32]","A",2,2,16,0.1250,1,"{1095, 419}"
133,1,49,0,0.0785738,"\int \frac{1}{\sqrt{2+5 x^2-9 x^4}} \, dx","Int[1/Sqrt[2 + 5*x^2 - 9*x^4],x]","\sqrt{\frac{2}{\sqrt{97}-5}} F\left(\sin ^{-1}\left(3 \sqrt{\frac{2}{5+\sqrt{97}}} x\right)|\frac{1}{36} \left(-61-5 \sqrt{97}\right)\right)","\sqrt{\frac{2}{\sqrt{97}-5}} F\left(\sin ^{-1}\left(3 \sqrt{\frac{2}{5+\sqrt{97}}} x\right)|\frac{1}{36} \left(-61-5 \sqrt{97}\right)\right)",1,"Sqrt[2/(-5 + Sqrt[97])]*EllipticF[ArcSin[3*Sqrt[2/(5 + Sqrt[97])]*x], (-61 - 5*Sqrt[97])/36]","A",2,2,16,0.1250,1,"{1095, 419}"
134,1,17,0,0.0058893,"\int x^2 \left(b x^2+c x^4\right) \, dx","Int[x^2*(b*x^2 + c*x^4),x]","\frac{b x^5}{5}+\frac{c x^7}{7}","\frac{b x^5}{5}+\frac{c x^7}{7}",1,"(b*x^5)/5 + (c*x^7)/7","A",2,1,15,0.06667,1,"{14}"
135,1,17,0,0.0056222,"\int x \left(b x^2+c x^4\right) \, dx","Int[x*(b*x^2 + c*x^4),x]","\frac{b x^4}{4}+\frac{c x^6}{6}","\frac{b x^4}{4}+\frac{c x^6}{6}",1,"(b*x^4)/4 + (c*x^6)/6","A",2,1,13,0.07692,1,"{14}"
136,1,17,0,0.0030681,"\int \left(b x^2+c x^4\right) \, dx","Int[b*x^2 + c*x^4,x]","\frac{b x^3}{3}+\frac{c x^5}{5}","\frac{b x^3}{3}+\frac{c x^5}{5}",1,"(b*x^3)/3 + (c*x^5)/5","A",1,0,11,0,1,"{}"
137,1,17,0,0.0049654,"\int \frac{b x^2+c x^4}{x} \, dx","Int[(b*x^2 + c*x^4)/x,x]","\frac{b x^2}{2}+\frac{c x^4}{4}","\frac{b x^2}{2}+\frac{c x^4}{4}",1,"(b*x^2)/2 + (c*x^4)/4","A",2,1,15,0.06667,1,"{14}"
138,1,12,0,0.0044172,"\int \frac{b x^2+c x^4}{x^2} \, dx","Int[(b*x^2 + c*x^4)/x^2,x]","b x+\frac{c x^3}{3}","b x+\frac{c x^3}{3}",1,"b*x + (c*x^3)/3","A",2,1,15,0.06667,1,"{14}"
139,1,13,0,0.0053259,"\int \frac{b x^2+c x^4}{x^3} \, dx","Int[(b*x^2 + c*x^4)/x^3,x]","b \log (x)+\frac{c x^2}{2}","b \log (x)+\frac{c x^2}{2}",1,"(c*x^2)/2 + b*Log[x]","A",2,1,15,0.06667,1,"{14}"
140,1,10,0,0.0052681,"\int \frac{b x^2+c x^4}{x^4} \, dx","Int[(b*x^2 + c*x^4)/x^4,x]","c x-\frac{b}{x}","c x-\frac{b}{x}",1,"-(b/x) + c*x","A",2,1,15,0.06667,1,"{14}"
141,1,13,0,0.00563,"\int \frac{b x^2+c x^4}{x^5} \, dx","Int[(b*x^2 + c*x^4)/x^5,x]","c \log (x)-\frac{b}{2 x^2}","c \log (x)-\frac{b}{2 x^2}",1,"-b/(2*x^2) + c*Log[x]","A",2,1,15,0.06667,1,"{14}"
142,1,15,0,0.0056849,"\int \frac{b x^2+c x^4}{x^6} \, dx","Int[(b*x^2 + c*x^4)/x^6,x]","-\frac{b}{3 x^3}-\frac{c}{x}","-\frac{b}{3 x^3}-\frac{c}{x}",1,"-b/(3*x^3) - c/x","A",2,1,15,0.06667,1,"{14}"
143,1,17,0,0.0060832,"\int \frac{b x^2+c x^4}{x^7} \, dx","Int[(b*x^2 + c*x^4)/x^7,x]","-\frac{b}{4 x^4}-\frac{c}{2 x^2}","-\frac{b}{4 x^4}-\frac{c}{2 x^2}",1,"-b/(4*x^4) - c/(2*x^2)","A",2,1,15,0.06667,1,"{14}"
144,1,17,0,0.0056135,"\int \frac{b x^2+c x^4}{x^8} \, dx","Int[(b*x^2 + c*x^4)/x^8,x]","-\frac{b}{5 x^5}-\frac{c}{3 x^3}","-\frac{b}{5 x^5}-\frac{c}{3 x^3}",1,"-b/(5*x^5) - c/(3*x^3)","A",2,1,15,0.06667,1,"{14}"
145,1,30,0,0.0131603,"\int \left(b x^2+c x^4\right)^2 \, dx","Int[(b*x^2 + c*x^4)^2,x]","\frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9}","\frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9}",1,"(b^2*x^5)/5 + (2*b*c*x^7)/7 + (c^2*x^9)/9","A",3,2,13,0.1538,1,"{1593, 270}"
146,1,30,0,0.0253981,"\int \frac{\left(b x^2+c x^4\right)^2}{x} \, dx","Int[(b*x^2 + c*x^4)^2/x,x]","\frac{b^2 x^4}{4}+\frac{1}{3} b c x^6+\frac{c^2 x^8}{8}","\frac{b^2 x^4}{4}+\frac{1}{3} b c x^6+\frac{c^2 x^8}{8}",1,"(b^2*x^4)/4 + (b*c*x^6)/3 + (c^2*x^8)/8","A",4,3,17,0.1765,1,"{1584, 266, 43}"
147,1,30,0,0.0172618,"\int \frac{\left(b x^2+c x^4\right)^2}{x^2} \, dx","Int[(b*x^2 + c*x^4)^2/x^2,x]","\frac{b^2 x^3}{3}+\frac{2}{5} b c x^5+\frac{c^2 x^7}{7}","\frac{b^2 x^3}{3}+\frac{2}{5} b c x^5+\frac{c^2 x^7}{7}",1,"(b^2*x^3)/3 + (2*b*c*x^5)/5 + (c^2*x^7)/7","A",3,2,17,0.1176,1,"{1584, 270}"
148,1,16,0,0.0086475,"\int \frac{\left(b x^2+c x^4\right)^2}{x^3} \, dx","Int[(b*x^2 + c*x^4)^2/x^3,x]","\frac{\left(b+c x^2\right)^3}{6 c}","\frac{\left(b+c x^2\right)^3}{6 c}",1,"(b + c*x^2)^3/(6*c)","A",2,2,17,0.1176,1,"{1584, 261}"
149,1,25,0,0.0131654,"\int \frac{\left(b x^2+c x^4\right)^2}{x^4} \, dx","Int[(b*x^2 + c*x^4)^2/x^4,x]","b^2 x+\frac{2}{3} b c x^3+\frac{c^2 x^5}{5}","b^2 x+\frac{2}{3} b c x^3+\frac{c^2 x^5}{5}",1,"b^2*x + (2*b*c*x^3)/3 + (c^2*x^5)/5","A",3,2,17,0.1176,1,"{1584, 194}"
150,1,23,0,0.0186775,"\int \frac{\left(b x^2+c x^4\right)^2}{x^5} \, dx","Int[(b*x^2 + c*x^4)^2/x^5,x]","b^2 \log (x)+b c x^2+\frac{c^2 x^4}{4}","b^2 \log (x)+b c x^2+\frac{c^2 x^4}{4}",1,"b*c*x^2 + (c^2*x^4)/4 + b^2*Log[x]","A",4,3,17,0.1765,1,"{1584, 266, 43}"
151,1,24,0,0.0167236,"\int \frac{\left(b x^2+c x^4\right)^2}{x^6} \, dx","Int[(b*x^2 + c*x^4)^2/x^6,x]","-\frac{b^2}{x}+2 b c x+\frac{c^2 x^3}{3}","-\frac{b^2}{x}+2 b c x+\frac{c^2 x^3}{3}",1,"-(b^2/x) + 2*b*c*x + (c^2*x^3)/3","A",3,2,17,0.1176,1,"{1584, 270}"
152,1,27,0,0.0211402,"\int \frac{\left(b x^2+c x^4\right)^2}{x^7} \, dx","Int[(b*x^2 + c*x^4)^2/x^7,x]","-\frac{b^2}{2 x^2}+2 b c \log (x)+\frac{c^2 x^2}{2}","-\frac{b^2}{2 x^2}+2 b c \log (x)+\frac{c^2 x^2}{2}",1,"-b^2/(2*x^2) + (c^2*x^2)/2 + 2*b*c*Log[x]","A",4,3,17,0.1765,1,"{1584, 266, 43}"
153,1,23,0,0.0180535,"\int \frac{\left(b x^2+c x^4\right)^2}{x^8} \, dx","Int[(b*x^2 + c*x^4)^2/x^8,x]","-\frac{b^2}{3 x^3}-\frac{2 b c}{x}+c^2 x","-\frac{b^2}{3 x^3}-\frac{2 b c}{x}+c^2 x",1,"-b^2/(3*x^3) - (2*b*c)/x + c^2*x","A",3,2,17,0.1176,1,"{1584, 270}"
154,1,24,0,0.0185294,"\int \frac{\left(b x^2+c x^4\right)^2}{x^9} \, dx","Int[(b*x^2 + c*x^4)^2/x^9,x]","-\frac{b^2}{4 x^4}-\frac{b c}{x^2}+c^2 \log (x)","-\frac{b^2}{4 x^4}-\frac{b c}{x^2}+c^2 \log (x)",1,"-b^2/(4*x^4) - (b*c)/x^2 + c^2*Log[x]","A",4,3,17,0.1765,1,"{1584, 266, 43}"
155,1,28,0,0.0164468,"\int \frac{\left(b x^2+c x^4\right)^2}{x^{10}} \, dx","Int[(b*x^2 + c*x^4)^2/x^10,x]","-\frac{b^2}{5 x^5}-\frac{2 b c}{3 x^3}-\frac{c^2}{x}","-\frac{b^2}{5 x^5}-\frac{2 b c}{3 x^3}-\frac{c^2}{x}",1,"-b^2/(5*x^5) - (2*b*c)/(3*x^3) - c^2/x","A",3,2,17,0.1176,1,"{1584, 270}"
156,1,19,0,0.009546,"\int \frac{\left(b x^2+c x^4\right)^2}{x^{11}} \, dx","Int[(b*x^2 + c*x^4)^2/x^11,x]","-\frac{\left(b+c x^2\right)^3}{6 b x^6}","-\frac{\left(b+c x^2\right)^3}{6 b x^6}",1,"-(b + c*x^2)^3/(6*b*x^6)","A",2,2,17,0.1176,1,"{1584, 264}"
157,1,30,0,0.0159052,"\int \frac{\left(b x^2+c x^4\right)^2}{x^{12}} \, dx","Int[(b*x^2 + c*x^4)^2/x^12,x]","-\frac{b^2}{7 x^7}-\frac{2 b c}{5 x^5}-\frac{c^2}{3 x^3}","-\frac{b^2}{7 x^7}-\frac{2 b c}{5 x^5}-\frac{c^2}{3 x^3}",1,"-b^2/(7*x^7) - (2*b*c)/(5*x^5) - c^2/(3*x^3)","A",3,2,17,0.1176,1,"{1584, 270}"
158,1,43,0,0.023521,"\int \frac{\left(b x^2+c x^4\right)^3}{x^2} \, dx","Int[(b*x^2 + c*x^4)^3/x^2,x]","\frac{3}{7} b^2 c x^7+\frac{b^3 x^5}{5}+\frac{1}{3} b c^2 x^9+\frac{c^3 x^{11}}{11}","\frac{3}{7} b^2 c x^7+\frac{b^3 x^5}{5}+\frac{1}{3} b c^2 x^9+\frac{c^3 x^{11}}{11}",1,"(b^3*x^5)/5 + (3*b^2*c*x^7)/7 + (b*c^2*x^9)/3 + (c^3*x^11)/11","A",3,2,17,0.1176,1,"{1584, 270}"
159,1,34,0,0.0387291,"\int \frac{\left(b x^2+c x^4\right)^3}{x^3} \, dx","Int[(b*x^2 + c*x^4)^3/x^3,x]","\frac{\left(b+c x^2\right)^5}{10 c^2}-\frac{b \left(b+c x^2\right)^4}{8 c^2}","\frac{\left(b+c x^2\right)^5}{10 c^2}-\frac{b \left(b+c x^2\right)^4}{8 c^2}",1,"-(b*(b + c*x^2)^4)/(8*c^2) + (b + c*x^2)^5/(10*c^2)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
160,1,43,0,0.0208536,"\int \frac{\left(b x^2+c x^4\right)^3}{x^4} \, dx","Int[(b*x^2 + c*x^4)^3/x^4,x]","\frac{3}{5} b^2 c x^5+\frac{b^3 x^3}{3}+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9}","\frac{3}{5} b^2 c x^5+\frac{b^3 x^3}{3}+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9}",1,"(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",3,2,17,0.1176,1,"{1584, 270}"
161,1,16,0,0.0088485,"\int \frac{\left(b x^2+c x^4\right)^3}{x^5} \, dx","Int[(b*x^2 + c*x^4)^3/x^5,x]","\frac{\left(b+c x^2\right)^4}{8 c}","\frac{\left(b+c x^2\right)^4}{8 c}",1,"(b + c*x^2)^4/(8*c)","A",2,2,17,0.1176,1,"{1584, 261}"
162,1,35,0,0.0172534,"\int \frac{\left(b x^2+c x^4\right)^3}{x^6} \, dx","Int[(b*x^2 + c*x^4)^3/x^6,x]","b^2 c x^3+b^3 x+\frac{3}{5} b c^2 x^5+\frac{c^3 x^7}{7}","b^2 c x^3+b^3 x+\frac{3}{5} b c^2 x^5+\frac{c^3 x^7}{7}",1,"b^3*x + b^2*c*x^3 + (3*b*c^2*x^5)/5 + (c^3*x^7)/7","A",3,2,17,0.1176,1,"{1584, 194}"
163,1,39,0,0.0259172,"\int \frac{\left(b x^2+c x^4\right)^3}{x^7} \, dx","Int[(b*x^2 + c*x^4)^3/x^7,x]","\frac{3}{2} b^2 c x^2+b^3 \log (x)+\frac{3}{4} b c^2 x^4+\frac{c^3 x^6}{6}","\frac{3}{2} b^2 c x^2+b^3 \log (x)+\frac{3}{4} b c^2 x^4+\frac{c^3 x^6}{6}",1,"(3*b^2*c*x^2)/2 + (3*b*c^2*x^4)/4 + (c^3*x^6)/6 + b^3*Log[x]","A",4,3,17,0.1765,1,"{1584, 266, 43}"
164,1,34,0,0.0194427,"\int \frac{\left(b x^2+c x^4\right)^3}{x^8} \, dx","Int[(b*x^2 + c*x^4)^3/x^8,x]","3 b^2 c x-\frac{b^3}{x}+b c^2 x^3+\frac{c^3 x^5}{5}","3 b^2 c x-\frac{b^3}{x}+b c^2 x^3+\frac{c^3 x^5}{5}",1,"-(b^3/x) + 3*b^2*c*x + b*c^2*x^3 + (c^3*x^5)/5","A",3,2,17,0.1176,1,"{1584, 270}"
165,1,40,0,0.0291111,"\int \frac{\left(b x^2+c x^4\right)^3}{x^9} \, dx","Int[(b*x^2 + c*x^4)^3/x^9,x]","3 b^2 c \log (x)-\frac{b^3}{2 x^2}+\frac{3}{2} b c^2 x^2+\frac{c^3 x^4}{4}","3 b^2 c \log (x)-\frac{b^3}{2 x^2}+\frac{3}{2} b c^2 x^2+\frac{c^3 x^4}{4}",1,"-b^3/(2*x^2) + (3*b*c^2*x^2)/2 + (c^3*x^4)/4 + 3*b^2*c*Log[x]","A",4,3,17,0.1765,1,"{1584, 266, 43}"
166,1,37,0,0.0193349,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{10}} \, dx","Int[(b*x^2 + c*x^4)^3/x^10,x]","-\frac{3 b^2 c}{x}-\frac{b^3}{3 x^3}+3 b c^2 x+\frac{c^3 x^3}{3}","-\frac{3 b^2 c}{x}-\frac{b^3}{3 x^3}+3 b c^2 x+\frac{c^3 x^3}{3}",1,"-b^3/(3*x^3) - (3*b^2*c)/x + 3*b*c^2*x + (c^3*x^3)/3","A",3,2,17,0.1176,1,"{1584, 270}"
167,1,40,0,0.0256056,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{11}} \, dx","Int[(b*x^2 + c*x^4)^3/x^11,x]","-\frac{3 b^2 c}{2 x^2}-\frac{b^3}{4 x^4}+3 b c^2 \log (x)+\frac{c^3 x^2}{2}","-\frac{3 b^2 c}{2 x^2}-\frac{b^3}{4 x^4}+3 b c^2 \log (x)+\frac{c^3 x^2}{2}",1,"-b^3/(4*x^4) - (3*b^2*c)/(2*x^2) + (c^3*x^2)/2 + 3*b*c^2*Log[x]","A",4,3,17,0.1765,1,"{1584, 266, 43}"
168,1,34,0,0.0202517,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{12}} \, dx","Int[(b*x^2 + c*x^4)^3/x^12,x]","-\frac{b^2 c}{x^3}-\frac{b^3}{5 x^5}-\frac{3 b c^2}{x}+c^3 x","-\frac{b^2 c}{x^3}-\frac{b^3}{5 x^5}-\frac{3 b c^2}{x}+c^3 x",1,"-b^3/(5*x^5) - (b^2*c)/x^3 - (3*b*c^2)/x + c^3*x","A",3,2,17,0.1176,1,"{1584, 270}"
169,1,39,0,0.0262622,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{13}} \, dx","Int[(b*x^2 + c*x^4)^3/x^13,x]","-\frac{3 b^2 c}{4 x^4}-\frac{b^3}{6 x^6}-\frac{3 b c^2}{2 x^2}+c^3 \log (x)","-\frac{3 b^2 c}{4 x^4}-\frac{b^3}{6 x^6}-\frac{3 b c^2}{2 x^2}+c^3 \log (x)",1,"-b^3/(6*x^6) - (3*b^2*c)/(4*x^4) - (3*b*c^2)/(2*x^2) + c^3*Log[x]","A",4,3,17,0.1765,1,"{1584, 266, 43}"
170,1,39,0,0.0213671,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{14}} \, dx","Int[(b*x^2 + c*x^4)^3/x^14,x]","-\frac{3 b^2 c}{5 x^5}-\frac{b^3}{7 x^7}-\frac{b c^2}{x^3}-\frac{c^3}{x}","-\frac{3 b^2 c}{5 x^5}-\frac{b^3}{7 x^7}-\frac{b c^2}{x^3}-\frac{c^3}{x}",1,"-b^3/(7*x^7) - (3*b^2*c)/(5*x^5) - (b*c^2)/x^3 - c^3/x","A",3,2,17,0.1176,1,"{1584, 270}"
171,1,19,0,0.0097317,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{15}} \, dx","Int[(b*x^2 + c*x^4)^3/x^15,x]","-\frac{\left(b+c x^2\right)^4}{8 b x^8}","-\frac{\left(b+c x^2\right)^4}{8 b x^8}",1,"-(b + c*x^2)^4/(8*b*x^8)","A",2,2,17,0.1176,1,"{1584, 264}"
172,1,43,0,0.0213949,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{16}} \, dx","Int[(b*x^2 + c*x^4)^3/x^16,x]","-\frac{3 b^2 c}{7 x^7}-\frac{b^3}{9 x^9}-\frac{3 b c^2}{5 x^5}-\frac{c^3}{3 x^3}","-\frac{3 b^2 c}{7 x^7}-\frac{b^3}{9 x^9}-\frac{3 b c^2}{5 x^5}-\frac{c^3}{3 x^3}",1,"-b^3/(9*x^9) - (3*b^2*c)/(7*x^7) - (3*b*c^2)/(5*x^5) - c^3/(3*x^3)","A",3,2,17,0.1176,1,"{1584, 270}"
173,1,40,0,0.0232954,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{17}} \, dx","Int[(b*x^2 + c*x^4)^3/x^17,x]","\frac{c \left(b+c x^2\right)^4}{40 b^2 x^8}-\frac{\left(b+c x^2\right)^4}{10 b x^{10}}","\frac{c \left(b+c x^2\right)^4}{40 b^2 x^8}-\frac{\left(b+c x^2\right)^4}{10 b x^{10}}",1,"-(b + c*x^2)^4/(10*b*x^10) + (c*(b + c*x^2)^4)/(40*b^2*x^8)","A",4,4,17,0.2353,1,"{1584, 266, 45, 37}"
174,1,68,0,0.0382052,"\int \frac{x^{10}}{b x^2+c x^4} \, dx","Int[x^10/(b*x^2 + c*x^4),x]","\frac{b^2 x^3}{3 c^3}-\frac{b^3 x}{c^4}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{9/2}}-\frac{b x^5}{5 c^2}+\frac{x^7}{7 c}","\frac{b^2 x^3}{3 c^3}-\frac{b^3 x}{c^4}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{9/2}}-\frac{b x^5}{5 c^2}+\frac{x^7}{7 c}",1,"-((b^3*x)/c^4) + (b^2*x^3)/(3*c^3) - (b*x^5)/(5*c^2) + x^7/(7*c) + (b^(7/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(9/2)","A",4,3,17,0.1765,1,"{1584, 302, 205}"
175,1,53,0,0.0452063,"\int \frac{x^9}{b x^2+c x^4} \, dx","Int[x^9/(b*x^2 + c*x^4),x]","\frac{b^2 x^2}{2 c^3}-\frac{b^3 \log \left(b+c x^2\right)}{2 c^4}-\frac{b x^4}{4 c^2}+\frac{x^6}{6 c}","\frac{b^2 x^2}{2 c^3}-\frac{b^3 \log \left(b+c x^2\right)}{2 c^4}-\frac{b x^4}{4 c^2}+\frac{x^6}{6 c}",1,"(b^2*x^2)/(2*c^3) - (b*x^4)/(4*c^2) + x^6/(6*c) - (b^3*Log[b + c*x^2])/(2*c^4)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
176,1,55,0,0.0326585,"\int \frac{x^8}{b x^2+c x^4} \, dx","Int[x^8/(b*x^2 + c*x^4),x]","\frac{b^2 x}{c^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{7/2}}-\frac{b x^3}{3 c^2}+\frac{x^5}{5 c}","\frac{b^2 x}{c^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{7/2}}-\frac{b x^3}{3 c^2}+\frac{x^5}{5 c}",1,"(b^2*x)/c^3 - (b*x^3)/(3*c^2) + x^5/(5*c) - (b^(5/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(7/2)","A",4,3,17,0.1765,1,"{1584, 302, 205}"
177,1,40,0,0.0337389,"\int \frac{x^7}{b x^2+c x^4} \, dx","Int[x^7/(b*x^2 + c*x^4),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}","\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}",1,"-(b*x^2)/(2*c^2) + x^4/(4*c) + (b^2*Log[b + c*x^2])/(2*c^3)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
178,1,42,0,0.0266642,"\int \frac{x^6}{b x^2+c x^4} \, dx","Int[x^6/(b*x^2 + c*x^4),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{5/2}}-\frac{b x}{c^2}+\frac{x^3}{3 c}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{5/2}}-\frac{b x}{c^2}+\frac{x^3}{3 c}",1,"-((b*x)/c^2) + x^3/(3*c) + (b^(3/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(5/2)","A",4,3,17,0.1765,1,"{1584, 302, 205}"
179,1,27,0,0.0266021,"\int \frac{x^5}{b x^2+c x^4} \, dx","Int[x^5/(b*x^2 + c*x^4),x]","\frac{x^2}{2 c}-\frac{b \log \left(b+c x^2\right)}{2 c^2}","\frac{x^2}{2 c}-\frac{b \log \left(b+c x^2\right)}{2 c^2}",1,"x^2/(2*c) - (b*Log[b + c*x^2])/(2*c^2)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
180,1,31,0,0.0181689,"\int \frac{x^4}{b x^2+c x^4} \, dx","Int[x^4/(b*x^2 + c*x^4),x]","\frac{x}{c}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{3/2}}","\frac{x}{c}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{3/2}}",1,"x/c - (Sqrt[b]*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(3/2)","A",3,3,17,0.1765,1,"{1584, 321, 205}"
181,1,15,0,0.0089441,"\int \frac{x^3}{b x^2+c x^4} \, dx","Int[x^3/(b*x^2 + c*x^4),x]","\frac{\log \left(b+c x^2\right)}{2 c}","\frac{\log \left(b+c x^2\right)}{2 c}",1,"Log[b + c*x^2]/(2*c)","A",2,2,17,0.1176,1,"{1584, 260}"
182,1,24,0,0.0117432,"\int \frac{x^2}{b x^2+c x^4} \, dx","Int[x^2/(b*x^2 + c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{c}}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{c}}",1,"ArcTan[(Sqrt[c]*x)/Sqrt[b]]/(Sqrt[b]*Sqrt[c])","A",2,2,17,0.1176,1,"{1584, 205}"
183,1,22,0,0.0160743,"\int \frac{x}{b x^2+c x^4} \, dx","Int[x/(b*x^2 + c*x^4),x]","\frac{\log (x)}{b}-\frac{\log \left(b+c x^2\right)}{2 b}","\frac{\log (x)}{b}-\frac{\log \left(b+c x^2\right)}{2 b}",1,"Log[x]/b - Log[b + c*x^2]/(2*b)","A",5,5,15,0.3333,1,"{1584, 266, 36, 29, 31}"
184,1,34,0,0.0142081,"\int \frac{1}{b x^2+c x^4} \, dx","Int[(b*x^2 + c*x^4)^(-1),x]","-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{3/2}}-\frac{1}{b x}","-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{3/2}}-\frac{1}{b x}",1,"-(1/(b*x)) - (Sqrt[c]*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/b^(3/2)","A",3,3,13,0.2308,1,"{1593, 325, 205}"
185,1,35,0,0.0275042,"\int \frac{1}{x \left(b x^2+c x^4\right)} \, dx","Int[1/(x*(b*x^2 + c*x^4)),x]","\frac{c \log \left(b+c x^2\right)}{2 b^2}-\frac{c \log (x)}{b^2}-\frac{1}{2 b x^2}","\frac{c \log \left(b+c x^2\right)}{2 b^2}-\frac{c \log (x)}{b^2}-\frac{1}{2 b x^2}",1,"-1/(2*b*x^2) - (c*Log[x])/b^2 + (c*Log[b + c*x^2])/(2*b^2)","A",4,3,17,0.1765,1,"{1584, 266, 44}"
186,1,43,0,0.0226364,"\int \frac{1}{x^2 \left(b x^2+c x^4\right)} \, dx","Int[1/(x^2*(b*x^2 + c*x^4)),x]","\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{5/2}}+\frac{c}{b^2 x}-\frac{1}{3 b x^3}","\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{5/2}}+\frac{c}{b^2 x}-\frac{1}{3 b x^3}",1,"-1/(3*b*x^3) + c/(b^2*x) + (c^(3/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/b^(5/2)","A",4,3,17,0.1765,1,"{1584, 325, 205}"
187,1,49,0,0.0350715,"\int \frac{1}{x^3 \left(b x^2+c x^4\right)} \, dx","Int[1/(x^3*(b*x^2 + c*x^4)),x]","-\frac{c^2 \log \left(b+c x^2\right)}{2 b^3}+\frac{c^2 \log (x)}{b^3}+\frac{c}{2 b^2 x^2}-\frac{1}{4 b x^4}","-\frac{c^2 \log \left(b+c x^2\right)}{2 b^3}+\frac{c^2 \log (x)}{b^3}+\frac{c}{2 b^2 x^2}-\frac{1}{4 b x^4}",1,"-1/(4*b*x^4) + c/(2*b^2*x^2) + (c^2*Log[x])/b^3 - (c^2*Log[b + c*x^2])/(2*b^3)","A",4,3,17,0.1765,1,"{1584, 266, 44}"
188,1,58,0,0.0362493,"\int \frac{1}{x^4 \left(b x^2+c x^4\right)} \, dx","Int[1/(x^4*(b*x^2 + c*x^4)),x]","-\frac{c^2}{b^3 x}-\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{7/2}}+\frac{c}{3 b^2 x^3}-\frac{1}{5 b x^5}","-\frac{c^2}{b^3 x}-\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{7/2}}+\frac{c}{3 b^2 x^3}-\frac{1}{5 b x^5}",1,"-1/(5*b*x^5) + c/(3*b^2*x^3) - c^2/(b^3*x) - (c^(5/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/b^(7/2)","A",5,3,17,0.1765,1,"{1584, 325, 205}"
189,1,63,0,0.0410101,"\int \frac{1}{x^5 \left(b x^2+c x^4\right)} \, dx","Int[1/(x^5*(b*x^2 + c*x^4)),x]","-\frac{c^2}{2 b^3 x^2}+\frac{c^3 \log \left(b+c x^2\right)}{2 b^4}-\frac{c^3 \log (x)}{b^4}+\frac{c}{4 b^2 x^4}-\frac{1}{6 b x^6}","-\frac{c^2}{2 b^3 x^2}+\frac{c^3 \log \left(b+c x^2\right)}{2 b^4}-\frac{c^3 \log (x)}{b^4}+\frac{c}{4 b^2 x^4}-\frac{1}{6 b x^6}",1,"-1/(6*b*x^6) + c/(4*b^2*x^4) - c^2/(2*b^3*x^2) - (c^3*Log[x])/b^4 + (c^3*Log[b + c*x^2])/(2*b^4)","A",4,3,17,0.1765,1,"{1584, 266, 44}"
190,1,79,0,0.0387618,"\int \frac{x^{12}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^12/(b*x^2 + c*x^4)^2,x]","\frac{7 b^2 x}{2 c^4}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{9/2}}-\frac{7 b x^3}{6 c^3}-\frac{x^7}{2 c \left(b+c x^2\right)}+\frac{7 x^5}{10 c^2}","\frac{7 b^2 x}{2 c^4}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{9/2}}-\frac{7 b x^3}{6 c^3}-\frac{x^7}{2 c \left(b+c x^2\right)}+\frac{7 x^5}{10 c^2}",1,"(7*b^2*x)/(2*c^4) - (7*b*x^3)/(6*c^3) + (7*x^5)/(10*c^2) - x^7/(2*c*(b + c*x^2)) - (7*b^(5/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*c^(9/2))","A",5,4,17,0.2353,1,"{1584, 288, 302, 205}"
191,1,57,0,0.0513479,"\int \frac{x^{11}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^11/(b*x^2 + c*x^4)^2,x]","\frac{b^3}{2 c^4 \left(b+c x^2\right)}+\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}","\frac{b^3}{2 c^4 \left(b+c x^2\right)}+\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}",1,"-((b*x^2)/c^3) + x^4/(4*c^2) + b^3/(2*c^4*(b + c*x^2)) + (3*b^2*Log[b + c*x^2])/(2*c^4)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
192,1,66,0,0.0347578,"\int \frac{x^{10}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^10/(b*x^2 + c*x^4)^2,x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{7/2}}-\frac{5 b x}{2 c^3}-\frac{x^5}{2 c \left(b+c x^2\right)}+\frac{5 x^3}{6 c^2}","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{7/2}}-\frac{5 b x}{2 c^3}-\frac{x^5}{2 c \left(b+c x^2\right)}+\frac{5 x^3}{6 c^2}",1,"(-5*b*x)/(2*c^3) + (5*x^3)/(6*c^2) - x^5/(2*c*(b + c*x^2)) + (5*b^(3/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*c^(7/2))","A",5,4,17,0.2353,1,"{1584, 288, 302, 205}"
193,1,44,0,0.0370274,"\int \frac{x^9}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^9/(b*x^2 + c*x^4)^2,x]","-\frac{b^2}{2 c^3 \left(b+c x^2\right)}-\frac{b \log \left(b+c x^2\right)}{c^3}+\frac{x^2}{2 c^2}","-\frac{b^2}{2 c^3 \left(b+c x^2\right)}-\frac{b \log \left(b+c x^2\right)}{c^3}+\frac{x^2}{2 c^2}",1,"x^2/(2*c^2) - b^2/(2*c^3*(b + c*x^2)) - (b*Log[b + c*x^2])/c^3","A",4,3,17,0.1765,1,"{1584, 266, 43}"
194,1,55,0,0.0244315,"\int \frac{x^8}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^8/(b*x^2 + c*x^4)^2,x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{5/2}}-\frac{x^3}{2 c \left(b+c x^2\right)}+\frac{3 x}{2 c^2}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{5/2}}-\frac{x^3}{2 c \left(b+c x^2\right)}+\frac{3 x}{2 c^2}",1,"(3*x)/(2*c^2) - x^3/(2*c*(b + c*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*c^(5/2))","A",4,4,17,0.2353,1,"{1584, 288, 321, 205}"
195,1,33,0,0.0319761,"\int \frac{x^7}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^7/(b*x^2 + c*x^4)^2,x]","\frac{b}{2 c^2 \left(b+c x^2\right)}+\frac{\log \left(b+c x^2\right)}{2 c^2}","\frac{b}{2 c^2 \left(b+c x^2\right)}+\frac{\log \left(b+c x^2\right)}{2 c^2}",1,"b/(2*c^2*(b + c*x^2)) + Log[b + c*x^2]/(2*c^2)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
196,1,45,0,0.0188261,"\int \frac{x^6}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^6/(b*x^2 + c*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 \sqrt{b} c^{3/2}}-\frac{x}{2 c \left(b+c x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 \sqrt{b} c^{3/2}}-\frac{x}{2 c \left(b+c x^2\right)}",1,"-x/(2*c*(b + c*x^2)) + ArcTan[(Sqrt[c]*x)/Sqrt[b]]/(2*Sqrt[b]*c^(3/2))","A",3,3,17,0.1765,1,"{1584, 288, 205}"
197,1,16,0,0.0093297,"\int \frac{x^5}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^5/(b*x^2 + c*x^4)^2,x]","-\frac{1}{2 c \left(b+c x^2\right)}","-\frac{1}{2 c \left(b+c x^2\right)}",1,"-1/(2*c*(b + c*x^2))","A",2,2,17,0.1176,1,"{1584, 261}"
198,1,45,0,0.0173041,"\int \frac{x^4}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^4/(b*x^2 + c*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{3/2} \sqrt{c}}+\frac{x}{2 b \left(b+c x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{3/2} \sqrt{c}}+\frac{x}{2 b \left(b+c x^2\right)}",1,"x/(2*b*(b + c*x^2)) + ArcTan[(Sqrt[c]*x)/Sqrt[b]]/(2*b^(3/2)*Sqrt[c])","A",3,3,17,0.1765,1,"{1584, 199, 205}"
199,1,38,0,0.0347204,"\int \frac{x^3}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^3/(b*x^2 + c*x^4)^2,x]","-\frac{\log \left(b+c x^2\right)}{2 b^2}+\frac{\log (x)}{b^2}+\frac{1}{2 b \left(b+c x^2\right)}","-\frac{\log \left(b+c x^2\right)}{2 b^2}+\frac{\log (x)}{b^2}+\frac{1}{2 b \left(b+c x^2\right)}",1,"1/(2*b*(b + c*x^2)) + Log[x]/b^2 - Log[b + c*x^2]/(2*b^2)","A",4,3,17,0.1765,1,"{1584, 266, 44}"
200,1,57,0,0.025463,"\int \frac{x^2}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^2/(b*x^2 + c*x^4)^2,x]","-\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{5/2}}-\frac{3}{2 b^2 x}+\frac{1}{2 b x \left(b+c x^2\right)}","-\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{5/2}}-\frac{3}{2 b^2 x}+\frac{1}{2 b x \left(b+c x^2\right)}",1,"-3/(2*b^2*x) + 1/(2*b*x*(b + c*x^2)) - (3*Sqrt[c]*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*b^(5/2))","A",4,4,17,0.2353,1,"{1584, 290, 325, 205}"
201,1,49,0,0.0405369,"\int \frac{x}{\left(b x^2+c x^4\right)^2} \, dx","Int[x/(b*x^2 + c*x^4)^2,x]","-\frac{c}{2 b^2 \left(b+c x^2\right)}+\frac{c \log \left(b+c x^2\right)}{b^3}-\frac{2 c \log (x)}{b^3}-\frac{1}{2 b^2 x^2}","-\frac{c}{2 b^2 \left(b+c x^2\right)}+\frac{c \log \left(b+c x^2\right)}{b^3}-\frac{2 c \log (x)}{b^3}-\frac{1}{2 b^2 x^2}",1,"-1/(2*b^2*x^2) - c/(2*b^2*(b + c*x^2)) - (2*c*Log[x])/b^3 + (c*Log[b + c*x^2])/b^3","A",4,3,15,0.2000,1,"{1584, 266, 44}"
202,1,68,0,0.029305,"\int \frac{1}{\left(b x^2+c x^4\right)^2} \, dx","Int[(b*x^2 + c*x^4)^(-2),x]","\frac{5 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{7/2}}+\frac{5 c}{2 b^3 x}-\frac{5}{6 b^2 x^3}+\frac{1}{2 b x^3 \left(b+c x^2\right)}","\frac{5 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{7/2}}+\frac{5 c}{2 b^3 x}-\frac{5}{6 b^2 x^3}+\frac{1}{2 b x^3 \left(b+c x^2\right)}",1,"-5/(6*b^2*x^3) + (5*c)/(2*b^3*x) + 1/(2*b*x^3*(b + c*x^2)) + (5*c^(3/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*b^(7/2))","A",5,4,13,0.3077,1,"{1593, 290, 325, 205}"
203,1,66,0,0.054881,"\int \frac{1}{x \left(b x^2+c x^4\right)^2} \, dx","Int[1/(x*(b*x^2 + c*x^4)^2),x]","\frac{c^2}{2 b^3 \left(b+c x^2\right)}-\frac{3 c^2 \log \left(b+c x^2\right)}{2 b^4}+\frac{3 c^2 \log (x)}{b^4}+\frac{c}{b^3 x^2}-\frac{1}{4 b^2 x^4}","\frac{c^2}{2 b^3 \left(b+c x^2\right)}-\frac{3 c^2 \log \left(b+c x^2\right)}{2 b^4}+\frac{3 c^2 \log (x)}{b^4}+\frac{c}{b^3 x^2}-\frac{1}{4 b^2 x^4}",1,"-1/(4*b^2*x^4) + c/(b^3*x^2) + c^2/(2*b^3*(b + c*x^2)) + (3*c^2*Log[x])/b^4 - (3*c^2*Log[b + c*x^2])/(2*b^4)","A",4,3,17,0.1765,1,"{1584, 266, 44}"
204,1,81,0,0.0454493,"\int \frac{1}{x^2 \left(b x^2+c x^4\right)^2} \, dx","Int[1/(x^2*(b*x^2 + c*x^4)^2),x]","-\frac{7 c^2}{2 b^4 x}-\frac{7 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{9/2}}+\frac{7 c}{6 b^3 x^3}-\frac{7}{10 b^2 x^5}+\frac{1}{2 b x^5 \left(b+c x^2\right)}","-\frac{7 c^2}{2 b^4 x}-\frac{7 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{9/2}}+\frac{7 c}{6 b^3 x^3}-\frac{7}{10 b^2 x^5}+\frac{1}{2 b x^5 \left(b+c x^2\right)}",1,"-7/(10*b^2*x^5) + (7*c)/(6*b^3*x^3) - (7*c^2)/(2*b^4*x) + 1/(2*b*x^5*(b + c*x^2)) - (7*c^(5/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*b^(9/2))","A",6,4,17,0.2353,1,"{1584, 290, 325, 205}"
205,1,85,0,0.0424448,"\int \frac{x^{14}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^14/(b*x^2 + c*x^4)^3,x]","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{9/2}}-\frac{7 x^5}{8 c^2 \left(b+c x^2\right)}-\frac{35 b x}{8 c^4}-\frac{x^7}{4 c \left(b+c x^2\right)^2}+\frac{35 x^3}{24 c^3}","\frac{35 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{9/2}}-\frac{7 x^5}{8 c^2 \left(b+c x^2\right)}-\frac{35 b x}{8 c^4}-\frac{x^7}{4 c \left(b+c x^2\right)^2}+\frac{35 x^3}{24 c^3}",1,"(-35*b*x)/(8*c^4) + (35*x^3)/(24*c^3) - x^7/(4*c*(b + c*x^2)^2) - (7*x^5)/(8*c^2*(b + c*x^2)) + (35*b^(3/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*c^(9/2))","A",6,4,17,0.2353,1,"{1584, 288, 302, 205}"
206,1,65,0,0.0541817,"\int \frac{x^{13}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^13/(b*x^2 + c*x^4)^3,x]","\frac{b^3}{4 c^4 \left(b+c x^2\right)^2}-\frac{3 b^2}{2 c^4 \left(b+c x^2\right)}-\frac{3 b \log \left(b+c x^2\right)}{2 c^4}+\frac{x^2}{2 c^3}","\frac{b^3}{4 c^4 \left(b+c x^2\right)^2}-\frac{3 b^2}{2 c^4 \left(b+c x^2\right)}-\frac{3 b \log \left(b+c x^2\right)}{2 c^4}+\frac{x^2}{2 c^3}",1,"x^2/(2*c^3) + b^3/(4*c^4*(b + c*x^2)^2) - (3*b^2)/(2*c^4*(b + c*x^2)) - (3*b*Log[b + c*x^2])/(2*c^4)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
207,1,74,0,0.0324637,"\int \frac{x^{12}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^12/(b*x^2 + c*x^4)^3,x]","-\frac{5 x^3}{8 c^2 \left(b+c x^2\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{7/2}}-\frac{x^5}{4 c \left(b+c x^2\right)^2}+\frac{15 x}{8 c^3}","-\frac{5 x^3}{8 c^2 \left(b+c x^2\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{7/2}}-\frac{x^5}{4 c \left(b+c x^2\right)^2}+\frac{15 x}{8 c^3}",1,"(15*x)/(8*c^3) - x^5/(4*c*(b + c*x^2)^2) - (5*x^3)/(8*c^2*(b + c*x^2)) - (15*Sqrt[b]*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*c^(7/2))","A",5,4,17,0.2353,1,"{1584, 288, 321, 205}"
208,1,49,0,0.0447711,"\int \frac{x^{11}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^11/(b*x^2 + c*x^4)^3,x]","-\frac{b^2}{4 c^3 \left(b+c x^2\right)^2}+\frac{b}{c^3 \left(b+c x^2\right)}+\frac{\log \left(b+c x^2\right)}{2 c^3}","-\frac{b^2}{4 c^3 \left(b+c x^2\right)^2}+\frac{b}{c^3 \left(b+c x^2\right)}+\frac{\log \left(b+c x^2\right)}{2 c^3}",1,"-b^2/(4*c^3*(b + c*x^2)^2) + b/(c^3*(b + c*x^2)) + Log[b + c*x^2]/(2*c^3)","A",4,3,17,0.1765,1,"{1584, 266, 43}"
209,1,64,0,0.0255314,"\int \frac{x^{10}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^10/(b*x^2 + c*x^4)^3,x]","-\frac{3 x}{8 c^2 \left(b+c x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 \sqrt{b} c^{5/2}}-\frac{x^3}{4 c \left(b+c x^2\right)^2}","-\frac{3 x}{8 c^2 \left(b+c x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 \sqrt{b} c^{5/2}}-\frac{x^3}{4 c \left(b+c x^2\right)^2}",1,"-x^3/(4*c*(b + c*x^2)^2) - (3*x)/(8*c^2*(b + c*x^2)) + (3*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*Sqrt[b]*c^(5/2))","A",4,3,17,0.1765,1,"{1584, 288, 205}"
210,1,19,0,0.0110066,"\int \frac{x^9}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^9/(b*x^2 + c*x^4)^3,x]","\frac{x^4}{4 b \left(b+c x^2\right)^2}","\frac{x^4}{4 b \left(b+c x^2\right)^2}",1,"x^4/(4*b*(b + c*x^2)^2)","A",2,2,17,0.1176,1,"{1584, 264}"
211,1,65,0,0.0249015,"\int \frac{x^8}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^8/(b*x^2 + c*x^4)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{3/2} c^{3/2}}+\frac{x}{8 b c \left(b+c x^2\right)}-\frac{x}{4 c \left(b+c x^2\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{3/2} c^{3/2}}+\frac{x}{8 b c \left(b+c x^2\right)}-\frac{x}{4 c \left(b+c x^2\right)^2}",1,"-x/(4*c*(b + c*x^2)^2) + x/(8*b*c*(b + c*x^2)) + ArcTan[(Sqrt[c]*x)/Sqrt[b]]/(8*b^(3/2)*c^(3/2))","A",4,4,17,0.2353,1,"{1584, 288, 199, 205}"
212,1,16,0,0.0094585,"\int \frac{x^7}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^7/(b*x^2 + c*x^4)^3,x]","-\frac{1}{4 c \left(b+c x^2\right)^2}","-\frac{1}{4 c \left(b+c x^2\right)^2}",1,"-1/(4*c*(b + c*x^2)^2)","A",2,2,17,0.1176,1,"{1584, 261}"
213,1,62,0,0.0234265,"\int \frac{x^6}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^6/(b*x^2 + c*x^4)^3,x]","\frac{3 x}{8 b^2 \left(b+c x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{5/2} \sqrt{c}}+\frac{x}{4 b \left(b+c x^2\right)^2}","\frac{3 x}{8 b^2 \left(b+c x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{5/2} \sqrt{c}}+\frac{x}{4 b \left(b+c x^2\right)^2}",1,"x/(4*b*(b + c*x^2)^2) + (3*x)/(8*b^2*(b + c*x^2)) + (3*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(5/2)*Sqrt[c])","A",4,3,17,0.1765,1,"{1584, 199, 205}"
214,1,54,0,0.0441454,"\int \frac{x^5}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^5/(b*x^2 + c*x^4)^3,x]","\frac{1}{2 b^2 \left(b+c x^2\right)}-\frac{\log \left(b+c x^2\right)}{2 b^3}+\frac{\log (x)}{b^3}+\frac{1}{4 b \left(b+c x^2\right)^2}","\frac{1}{2 b^2 \left(b+c x^2\right)}-\frac{\log \left(b+c x^2\right)}{2 b^3}+\frac{\log (x)}{b^3}+\frac{1}{4 b \left(b+c x^2\right)^2}",1,"1/(4*b*(b + c*x^2)^2) + 1/(2*b^2*(b + c*x^2)) + Log[x]/b^3 - Log[b + c*x^2]/(2*b^3)","A",4,3,17,0.1765,1,"{1584, 266, 44}"
215,1,76,0,0.0356755,"\int \frac{x^4}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^4/(b*x^2 + c*x^4)^3,x]","\frac{5}{8 b^2 x \left(b+c x^2\right)}-\frac{15 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{7/2}}-\frac{15}{8 b^3 x}+\frac{1}{4 b x \left(b+c x^2\right)^2}","\frac{5}{8 b^2 x \left(b+c x^2\right)}-\frac{15 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{7/2}}-\frac{15}{8 b^3 x}+\frac{1}{4 b x \left(b+c x^2\right)^2}",1,"-15/(8*b^3*x) + 1/(4*b*x*(b + c*x^2)^2) + 5/(8*b^2*x*(b + c*x^2)) - (15*Sqrt[c]*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(7/2))","A",5,4,17,0.2353,1,"{1584, 290, 325, 205}"
216,1,67,0,0.0605118,"\int \frac{x^3}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^3/(b*x^2 + c*x^4)^3,x]","-\frac{c}{b^3 \left(b+c x^2\right)}-\frac{c}{4 b^2 \left(b+c x^2\right)^2}+\frac{3 c \log \left(b+c x^2\right)}{2 b^4}-\frac{3 c \log (x)}{b^4}-\frac{1}{2 b^3 x^2}","-\frac{c}{b^3 \left(b+c x^2\right)}-\frac{c}{4 b^2 \left(b+c x^2\right)^2}+\frac{3 c \log \left(b+c x^2\right)}{2 b^4}-\frac{3 c \log (x)}{b^4}-\frac{1}{2 b^3 x^2}",1,"-1/(2*b^3*x^2) - c/(4*b^2*(b + c*x^2)^2) - c/(b^3*(b + c*x^2)) - (3*c*Log[x])/b^4 + (3*c*Log[b + c*x^2])/(2*b^4)","A",4,3,17,0.1765,1,"{1584, 266, 44}"
217,1,87,0,0.0418952,"\int \frac{x^2}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^2/(b*x^2 + c*x^4)^3,x]","\frac{35 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{9/2}}+\frac{7}{8 b^2 x^3 \left(b+c x^2\right)}+\frac{35 c}{8 b^4 x}-\frac{35}{24 b^3 x^3}+\frac{1}{4 b x^3 \left(b+c x^2\right)^2}","\frac{35 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{9/2}}+\frac{7}{8 b^2 x^3 \left(b+c x^2\right)}+\frac{35 c}{8 b^4 x}-\frac{35}{24 b^3 x^3}+\frac{1}{4 b x^3 \left(b+c x^2\right)^2}",1,"-35/(24*b^3*x^3) + (35*c)/(8*b^4*x) + 1/(4*b*x^3*(b + c*x^2)^2) + 7/(8*b^2*x^3*(b + c*x^2)) + (35*c^(3/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(9/2))","A",6,4,17,0.2353,1,"{1584, 290, 325, 205}"
218,1,86,0,0.0718563,"\int \frac{x}{\left(b x^2+c x^4\right)^3} \, dx","Int[x/(b*x^2 + c*x^4)^3,x]","\frac{3 c^2}{2 b^4 \left(b+c x^2\right)}+\frac{c^2}{4 b^3 \left(b+c x^2\right)^2}-\frac{3 c^2 \log \left(b+c x^2\right)}{b^5}+\frac{6 c^2 \log (x)}{b^5}+\frac{3 c}{2 b^4 x^2}-\frac{1}{4 b^3 x^4}","\frac{3 c^2}{2 b^4 \left(b+c x^2\right)}+\frac{c^2}{4 b^3 \left(b+c x^2\right)^2}-\frac{3 c^2 \log \left(b+c x^2\right)}{b^5}+\frac{6 c^2 \log (x)}{b^5}+\frac{3 c}{2 b^4 x^2}-\frac{1}{4 b^3 x^4}",1,"-1/(4*b^3*x^4) + (3*c)/(2*b^4*x^2) + c^2/(4*b^3*(b + c*x^2)^2) + (3*c^2)/(2*b^4*(b + c*x^2)) + (6*c^2*Log[x])/b^5 - (3*c^2*Log[b + c*x^2])/b^5","A",4,3,15,0.2000,1,"{1584, 266, 44}"
219,1,100,0,0.0491003,"\int \frac{1}{\left(b x^2+c x^4\right)^3} \, dx","Int[(b*x^2 + c*x^4)^(-3),x]","-\frac{63 c^2}{8 b^5 x}-\frac{63 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{11/2}}+\frac{21 c}{8 b^4 x^3}+\frac{9}{8 b^2 x^5 \left(b+c x^2\right)}-\frac{63}{40 b^3 x^5}+\frac{1}{4 b x^5 \left(b+c x^2\right)^2}","-\frac{63 c^2}{8 b^5 x}-\frac{63 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{11/2}}+\frac{21 c}{8 b^4 x^3}+\frac{9}{8 b^2 x^5 \left(b+c x^2\right)}-\frac{63}{40 b^3 x^5}+\frac{1}{4 b x^5 \left(b+c x^2\right)^2}",1,"-63/(40*b^3*x^5) + (21*c)/(8*b^4*x^3) - (63*c^2)/(8*b^5*x) + 1/(4*b*x^5*(b + c*x^2)^2) + 9/(8*b^2*x^5*(b + c*x^2)) - (63*c^(5/2)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(11/2))","A",7,4,13,0.3077,1,"{1593, 290, 325, 205}"
220,1,95,0,0.0847774,"\int \frac{1}{x \left(b x^2+c x^4\right)^3} \, dx","Int[1/(x*(b*x^2 + c*x^4)^3),x]","-\frac{2 c^3}{b^5 \left(b+c x^2\right)}-\frac{c^3}{4 b^4 \left(b+c x^2\right)^2}-\frac{3 c^2}{b^5 x^2}+\frac{5 c^3 \log \left(b+c x^2\right)}{b^6}-\frac{10 c^3 \log (x)}{b^6}+\frac{3 c}{4 b^4 x^4}-\frac{1}{6 b^3 x^6}","-\frac{2 c^3}{b^5 \left(b+c x^2\right)}-\frac{c^3}{4 b^4 \left(b+c x^2\right)^2}-\frac{3 c^2}{b^5 x^2}+\frac{5 c^3 \log \left(b+c x^2\right)}{b^6}-\frac{10 c^3 \log (x)}{b^6}+\frac{3 c}{4 b^4 x^4}-\frac{1}{6 b^3 x^6}",1,"-1/(6*b^3*x^6) + (3*c)/(4*b^4*x^4) - (3*c^2)/(b^5*x^2) - c^3/(4*b^4*(b + c*x^2)^2) - (2*c^3)/(b^5*(b + c*x^2)) - (10*c^3*Log[x])/b^6 + (5*c^3*Log[b + c*x^2])/b^6","A",4,3,17,0.1765,1,"{1584, 266, 44}"
221,1,119,0,0.1307578,"\int x^5 \sqrt{b x^2+c x^4} \, dx","Int[x^5*Sqrt[b*x^2 + c*x^4],x]","\frac{5 b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{128 c^3}-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{7/2}}-\frac{5 b \left(b x^2+c x^4\right)^{3/2}}{48 c^2}+\frac{x^2 \left(b x^2+c x^4\right)^{3/2}}{8 c}","\frac{5 b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{128 c^3}-\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{7/2}}-\frac{5 b \left(b x^2+c x^4\right)^{3/2}}{48 c^2}+\frac{x^2 \left(b x^2+c x^4\right)^{3/2}}{8 c}",1,"(5*b^2*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(128*c^3) - (5*b*(b*x^2 + c*x^4)^(3/2))/(48*c^2) + (x^2*(b*x^2 + c*x^4)^(3/2))/(8*c) - (5*b^4*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(128*c^(7/2))","A",6,6,19,0.3158,1,"{2018, 670, 640, 612, 620, 206}"
222,1,91,0,0.0996667,"\int x^3 \sqrt{b x^2+c x^4} \, dx","Int[x^3*Sqrt[b*x^2 + c*x^4],x]","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{16 c^2}+\frac{\left(b x^2+c x^4\right)^{3/2}}{6 c}","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{16 c^2}+\frac{\left(b x^2+c x^4\right)^{3/2}}{6 c}",1,"-(b*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(16*c^2) + (b*x^2 + c*x^4)^(3/2)/(6*c) + (b^3*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(16*c^(5/2))","A",5,5,19,0.2632,1,"{2018, 640, 612, 620, 206}"
223,1,68,0,0.0638366,"\int x \sqrt{b x^2+c x^4} \, dx","Int[x*Sqrt[b*x^2 + c*x^4],x]","\frac{\left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{8 c}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{3/2}}","\frac{\left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{8 c}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{3/2}}",1,"((b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(8*c) - (b^2*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*c^(3/2))","A",4,4,17,0.2353,1,"{2013, 612, 620, 206}"
224,1,55,0,0.0714512,"\int \frac{\sqrt{b x^2+c x^4}}{x} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x,x]","\frac{1}{2} \sqrt{b x^2+c x^4}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{c}}","\frac{1}{2} \sqrt{b x^2+c x^4}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{c}}",1,"Sqrt[b*x^2 + c*x^4]/2 + (b*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2*Sqrt[c])","A",4,4,19,0.2105,1,"{2018, 664, 620, 206}"
225,1,52,0,0.0770799,"\int \frac{\sqrt{b x^2+c x^4}}{x^3} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^3,x]","\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{\sqrt{b x^2+c x^4}}{x^2}","\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{\sqrt{b x^2+c x^4}}{x^2}",1,"-(Sqrt[b*x^2 + c*x^4]/x^2) + Sqrt[c]*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]]","A",4,4,19,0.2105,1,"{2018, 662, 620, 206}"
226,1,25,0,0.0393856,"\int \frac{\sqrt{b x^2+c x^4}}{x^5} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^5,x]","-\frac{\left(b x^2+c x^4\right)^{3/2}}{3 b x^6}","-\frac{\left(b x^2+c x^4\right)^{3/2}}{3 b x^6}",1,"-(b*x^2 + c*x^4)^(3/2)/(3*b*x^6)","A",1,1,19,0.05263,1,"{2014}"
227,1,52,0,0.0831615,"\int \frac{\sqrt{b x^2+c x^4}}{x^7} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^7,x]","\frac{2 c \left(b x^2+c x^4\right)^{3/2}}{15 b^2 x^6}-\frac{\left(b x^2+c x^4\right)^{3/2}}{5 b x^8}","\frac{2 c \left(b x^2+c x^4\right)^{3/2}}{15 b^2 x^6}-\frac{\left(b x^2+c x^4\right)^{3/2}}{5 b x^8}",1,"-(b*x^2 + c*x^4)^(3/2)/(5*b*x^8) + (2*c*(b*x^2 + c*x^4)^(3/2))/(15*b^2*x^6)","A",2,2,19,0.1053,1,"{2016, 2014}"
228,1,80,0,0.1198066,"\int \frac{\sqrt{b x^2+c x^4}}{x^9} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^9,x]","-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2}}{105 b^3 x^6}+\frac{4 c \left(b x^2+c x^4\right)^{3/2}}{35 b^2 x^8}-\frac{\left(b x^2+c x^4\right)^{3/2}}{7 b x^{10}}","-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2}}{105 b^3 x^6}+\frac{4 c \left(b x^2+c x^4\right)^{3/2}}{35 b^2 x^8}-\frac{\left(b x^2+c x^4\right)^{3/2}}{7 b x^{10}}",1,"-(b*x^2 + c*x^4)^(3/2)/(7*b*x^10) + (4*c*(b*x^2 + c*x^4)^(3/2))/(35*b^2*x^8) - (8*c^2*(b*x^2 + c*x^4)^(3/2))/(105*b^3*x^6)","A",3,2,19,0.1053,1,"{2016, 2014}"
229,1,108,0,0.163684,"\int \frac{\sqrt{b x^2+c x^4}}{x^{11}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^11,x]","\frac{16 c^3 \left(b x^2+c x^4\right)^{3/2}}{315 b^4 x^6}-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2}}{105 b^3 x^8}+\frac{2 c \left(b x^2+c x^4\right)^{3/2}}{21 b^2 x^{10}}-\frac{\left(b x^2+c x^4\right)^{3/2}}{9 b x^{12}}","\frac{16 c^3 \left(b x^2+c x^4\right)^{3/2}}{315 b^4 x^6}-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2}}{105 b^3 x^8}+\frac{2 c \left(b x^2+c x^4\right)^{3/2}}{21 b^2 x^{10}}-\frac{\left(b x^2+c x^4\right)^{3/2}}{9 b x^{12}}",1,"-(b*x^2 + c*x^4)^(3/2)/(9*b*x^12) + (2*c*(b*x^2 + c*x^4)^(3/2))/(21*b^2*x^10) - (8*c^2*(b*x^2 + c*x^4)^(3/2))/(105*b^3*x^8) + (16*c^3*(b*x^2 + c*x^4)^(3/2))/(315*b^4*x^6)","A",4,2,19,0.1053,1,"{2016, 2014}"
230,1,136,0,0.2140099,"\int \frac{\sqrt{b x^2+c x^4}}{x^{13}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^13,x]","-\frac{128 c^4 \left(b x^2+c x^4\right)^{3/2}}{3465 b^5 x^6}+\frac{64 c^3 \left(b x^2+c x^4\right)^{3/2}}{1155 b^4 x^8}-\frac{16 c^2 \left(b x^2+c x^4\right)^{3/2}}{231 b^3 x^{10}}+\frac{8 c \left(b x^2+c x^4\right)^{3/2}}{99 b^2 x^{12}}-\frac{\left(b x^2+c x^4\right)^{3/2}}{11 b x^{14}}","-\frac{128 c^4 \left(b x^2+c x^4\right)^{3/2}}{3465 b^5 x^6}+\frac{64 c^3 \left(b x^2+c x^4\right)^{3/2}}{1155 b^4 x^8}-\frac{16 c^2 \left(b x^2+c x^4\right)^{3/2}}{231 b^3 x^{10}}+\frac{8 c \left(b x^2+c x^4\right)^{3/2}}{99 b^2 x^{12}}-\frac{\left(b x^2+c x^4\right)^{3/2}}{11 b x^{14}}",1,"-(b*x^2 + c*x^4)^(3/2)/(11*b*x^14) + (8*c*(b*x^2 + c*x^4)^(3/2))/(99*b^2*x^12) - (16*c^2*(b*x^2 + c*x^4)^(3/2))/(231*b^3*x^10) + (64*c^3*(b*x^2 + c*x^4)^(3/2))/(1155*b^4*x^8) - (128*c^4*(b*x^2 + c*x^4)^(3/2))/(3465*b^5*x^6)","A",5,2,19,0.1053,1,"{2016, 2014}"
231,1,78,0,0.0942747,"\int x^4 \sqrt{b x^2+c x^4} \, dx","Int[x^4*Sqrt[b*x^2 + c*x^4],x]","\frac{8 b^2 \left(b x^2+c x^4\right)^{3/2}}{105 c^3 x^3}-\frac{4 b \left(b x^2+c x^4\right)^{3/2}}{35 c^2 x}+\frac{x \left(b x^2+c x^4\right)^{3/2}}{7 c}","\frac{8 b^2 \left(b x^2+c x^4\right)^{3/2}}{105 c^3 x^3}-\frac{4 b \left(b x^2+c x^4\right)^{3/2}}{35 c^2 x}+\frac{x \left(b x^2+c x^4\right)^{3/2}}{7 c}",1,"(8*b^2*(b*x^2 + c*x^4)^(3/2))/(105*c^3*x^3) - (4*b*(b*x^2 + c*x^4)^(3/2))/(35*c^2*x) + (x*(b*x^2 + c*x^4)^(3/2))/(7*c)","A",3,2,19,0.1053,1,"{2016, 2000}"
232,1,52,0,0.0486033,"\int x^2 \sqrt{b x^2+c x^4} \, dx","Int[x^2*Sqrt[b*x^2 + c*x^4],x]","\frac{\left(b x^2+c x^4\right)^{3/2}}{5 c x}-\frac{2 b \left(b x^2+c x^4\right)^{3/2}}{15 c^2 x^3}","\frac{\left(b x^2+c x^4\right)^{3/2}}{5 c x}-\frac{2 b \left(b x^2+c x^4\right)^{3/2}}{15 c^2 x^3}",1,"(-2*b*(b*x^2 + c*x^4)^(3/2))/(15*c^2*x^3) + (b*x^2 + c*x^4)^(3/2)/(5*c*x)","A",2,2,19,0.1053,1,"{2016, 2000}"
233,1,25,0,0.0058113,"\int \sqrt{b x^2+c x^4} \, dx","Int[Sqrt[b*x^2 + c*x^4],x]","\frac{\left(b x^2+c x^4\right)^{3/2}}{3 c x^3}","\frac{\left(b x^2+c x^4\right)^{3/2}}{3 c x^3}",1,"(b*x^2 + c*x^4)^(3/2)/(3*c*x^3)","A",1,1,15,0.06667,1,"{2000}"
234,1,50,0,0.0491527,"\int \frac{\sqrt{b x^2+c x^4}}{x^2} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^2,x]","\frac{\sqrt{b x^2+c x^4}}{x}-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)","\frac{\sqrt{b x^2+c x^4}}{x}-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)",1,"Sqrt[b*x^2 + c*x^4]/x - Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]]","A",3,3,19,0.1579,1,"{2021, 2008, 206}"
235,1,56,0,0.0521658,"\int \frac{\sqrt{b x^2+c x^4}}{x^4} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^4,x]","-\frac{\sqrt{b x^2+c x^4}}{2 x^3}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{b}}","-\frac{\sqrt{b x^2+c x^4}}{2 x^3}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{b}}",1,"-Sqrt[b*x^2 + c*x^4]/(2*x^3) - (c*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(2*Sqrt[b])","A",3,3,19,0.1579,1,"{2020, 2008, 206}"
236,1,84,0,0.0980381,"\int \frac{\sqrt{b x^2+c x^4}}{x^6} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^6,x]","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{3/2}}-\frac{c \sqrt{b x^2+c x^4}}{8 b x^3}-\frac{\sqrt{b x^2+c x^4}}{4 x^5}","\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{3/2}}-\frac{c \sqrt{b x^2+c x^4}}{8 b x^3}-\frac{\sqrt{b x^2+c x^4}}{4 x^5}",1,"-Sqrt[b*x^2 + c*x^4]/(4*x^5) - (c*Sqrt[b*x^2 + c*x^4])/(8*b*x^3) + (c^2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*b^(3/2))","A",4,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
237,1,112,0,0.1448865,"\int \frac{\sqrt{b x^2+c x^4}}{x^8} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^8,x]","\frac{c^2 \sqrt{b x^2+c x^4}}{16 b^2 x^3}-\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{16 b^{5/2}}-\frac{c \sqrt{b x^2+c x^4}}{24 b x^5}-\frac{\sqrt{b x^2+c x^4}}{6 x^7}","\frac{c^2 \sqrt{b x^2+c x^4}}{16 b^2 x^3}-\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{16 b^{5/2}}-\frac{c \sqrt{b x^2+c x^4}}{24 b x^5}-\frac{\sqrt{b x^2+c x^4}}{6 x^7}",1,"-Sqrt[b*x^2 + c*x^4]/(6*x^7) - (c*Sqrt[b*x^2 + c*x^4])/(24*b*x^5) + (c^2*Sqrt[b*x^2 + c*x^4])/(16*b^2*x^3) - (c^3*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(16*b^(5/2))","A",5,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
238,1,124,0,0.1322811,"\int x^3 \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^3*(b*x^2 + c*x^4)^(3/2),x]","\frac{3 b^3 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{256 c^3}-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{256 c^{7/2}}-\frac{b \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2}}{32 c^2}+\frac{\left(b x^2+c x^4\right)^{5/2}}{10 c}","\frac{3 b^3 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{256 c^3}-\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{256 c^{7/2}}-\frac{b \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2}}{32 c^2}+\frac{\left(b x^2+c x^4\right)^{5/2}}{10 c}",1,"(3*b^3*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(256*c^3) - (b*(b + 2*c*x^2)*(b*x^2 + c*x^4)^(3/2))/(32*c^2) + (b*x^2 + c*x^4)^(5/2)/(10*c) - (3*b^5*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(256*c^(7/2))","A",6,5,19,0.2632,1,"{2018, 640, 612, 620, 206}"
239,1,101,0,0.0922218,"\int x \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x*(b*x^2 + c*x^4)^(3/2),x]","-\frac{3 b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{128 c^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{5/2}}+\frac{\left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2}}{16 c}","-\frac{3 b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{128 c^2}+\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{5/2}}+\frac{\left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2}}{16 c}",1,"(-3*b^2*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(128*c^2) + ((b + 2*c*x^2)*(b*x^2 + c*x^4)^(3/2))/(16*c) + (3*b^4*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(128*c^(5/2))","A",5,4,17,0.2353,1,"{2013, 612, 620, 206}"
240,1,88,0,0.0991041,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x,x]","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{3/2}}+\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{16 c}+\frac{1}{6} \left(b x^2+c x^4\right)^{3/2}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{3/2}}+\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4}}{16 c}+\frac{1}{6} \left(b x^2+c x^4\right)^{3/2}",1,"(b*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(16*c) + (b*x^2 + c*x^4)^(3/2)/6 - (b^3*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(16*c^(3/2))","A",5,5,19,0.2632,1,"{2018, 664, 612, 620, 206}"
241,1,80,0,0.0999827,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^3} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^3,x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{c}}+\frac{3}{8} b \sqrt{b x^2+c x^4}+\frac{\left(b x^2+c x^4\right)^{3/2}}{4 x^2}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{c}}+\frac{3}{8} b \sqrt{b x^2+c x^4}+\frac{\left(b x^2+c x^4\right)^{3/2}}{4 x^2}",1,"(3*b*Sqrt[b*x^2 + c*x^4])/8 + (b*x^2 + c*x^4)^(3/2)/(4*x^2) + (3*b^2*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*Sqrt[c])","A",5,4,19,0.2105,1,"{2018, 664, 620, 206}"
242,1,76,0,0.1108273,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^5} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^5,x]","-\frac{\left(b x^2+c x^4\right)^{3/2}}{x^4}+\frac{3}{2} c \sqrt{b x^2+c x^4}+\frac{3}{2} b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)","-\frac{\left(b x^2+c x^4\right)^{3/2}}{x^4}+\frac{3}{2} c \sqrt{b x^2+c x^4}+\frac{3}{2} b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)",1,"(3*c*Sqrt[b*x^2 + c*x^4])/2 - (b*x^2 + c*x^4)^(3/2)/x^4 + (3*b*Sqrt[c]*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/2","A",5,5,19,0.2632,1,"{2018, 662, 664, 620, 206}"
243,1,75,0,0.103917,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^7} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^7,x]","c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{c \sqrt{b x^2+c x^4}}{x^2}-\frac{\left(b x^2+c x^4\right)^{3/2}}{3 x^6}","c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{c \sqrt{b x^2+c x^4}}{x^2}-\frac{\left(b x^2+c x^4\right)^{3/2}}{3 x^6}",1,"-((c*Sqrt[b*x^2 + c*x^4])/x^2) - (b*x^2 + c*x^4)^(3/2)/(3*x^6) + c^(3/2)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]]","A",5,4,19,0.2105,1,"{2018, 662, 620, 206}"
244,1,25,0,0.0459559,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^9} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^9,x]","-\frac{\left(b x^2+c x^4\right)^{5/2}}{5 b x^{10}}","-\frac{\left(b x^2+c x^4\right)^{5/2}}{5 b x^{10}}",1,"-(b*x^2 + c*x^4)^(5/2)/(5*b*x^10)","A",1,1,19,0.05263,1,"{2014}"
245,1,52,0,0.0930483,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{11}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^11,x]","\frac{2 c \left(b x^2+c x^4\right)^{5/2}}{35 b^2 x^{10}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{7 b x^{12}}","\frac{2 c \left(b x^2+c x^4\right)^{5/2}}{35 b^2 x^{10}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{7 b x^{12}}",1,"-(b*x^2 + c*x^4)^(5/2)/(7*b*x^12) + (2*c*(b*x^2 + c*x^4)^(5/2))/(35*b^2*x^10)","A",2,2,19,0.1053,1,"{2016, 2014}"
246,1,80,0,0.1405985,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{13}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^13,x]","-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2}}{315 b^3 x^{10}}+\frac{4 c \left(b x^2+c x^4\right)^{5/2}}{63 b^2 x^{12}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{9 b x^{14}}","-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2}}{315 b^3 x^{10}}+\frac{4 c \left(b x^2+c x^4\right)^{5/2}}{63 b^2 x^{12}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{9 b x^{14}}",1,"-(b*x^2 + c*x^4)^(5/2)/(9*b*x^14) + (4*c*(b*x^2 + c*x^4)^(5/2))/(63*b^2*x^12) - (8*c^2*(b*x^2 + c*x^4)^(5/2))/(315*b^3*x^10)","A",3,2,19,0.1053,1,"{2016, 2014}"
247,1,108,0,0.1839431,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{15}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^15,x]","\frac{16 c^3 \left(b x^2+c x^4\right)^{5/2}}{1155 b^4 x^{10}}-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2}}{231 b^3 x^{12}}+\frac{2 c \left(b x^2+c x^4\right)^{5/2}}{33 b^2 x^{14}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{11 b x^{16}}","\frac{16 c^3 \left(b x^2+c x^4\right)^{5/2}}{1155 b^4 x^{10}}-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2}}{231 b^3 x^{12}}+\frac{2 c \left(b x^2+c x^4\right)^{5/2}}{33 b^2 x^{14}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{11 b x^{16}}",1,"-(b*x^2 + c*x^4)^(5/2)/(11*b*x^16) + (2*c*(b*x^2 + c*x^4)^(5/2))/(33*b^2*x^14) - (8*c^2*(b*x^2 + c*x^4)^(5/2))/(231*b^3*x^12) + (16*c^3*(b*x^2 + c*x^4)^(5/2))/(1155*b^4*x^10)","A",4,2,19,0.1053,1,"{2016, 2014}"
248,1,136,0,0.2620114,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{17}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^17,x]","-\frac{128 c^4 \left(b x^2+c x^4\right)^{5/2}}{15015 b^5 x^{10}}+\frac{64 c^3 \left(b x^2+c x^4\right)^{5/2}}{3003 b^4 x^{12}}-\frac{16 c^2 \left(b x^2+c x^4\right)^{5/2}}{429 b^3 x^{14}}+\frac{8 c \left(b x^2+c x^4\right)^{5/2}}{143 b^2 x^{16}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{13 b x^{18}}","-\frac{128 c^4 \left(b x^2+c x^4\right)^{5/2}}{15015 b^5 x^{10}}+\frac{64 c^3 \left(b x^2+c x^4\right)^{5/2}}{3003 b^4 x^{12}}-\frac{16 c^2 \left(b x^2+c x^4\right)^{5/2}}{429 b^3 x^{14}}+\frac{8 c \left(b x^2+c x^4\right)^{5/2}}{143 b^2 x^{16}}-\frac{\left(b x^2+c x^4\right)^{5/2}}{13 b x^{18}}",1,"-(b*x^2 + c*x^4)^(5/2)/(13*b*x^18) + (8*c*(b*x^2 + c*x^4)^(5/2))/(143*b^2*x^16) - (16*c^2*(b*x^2 + c*x^4)^(5/2))/(429*b^3*x^14) + (64*c^3*(b*x^2 + c*x^4)^(5/2))/(3003*b^4*x^12) - (128*c^4*(b*x^2 + c*x^4)^(5/2))/(15015*b^5*x^10)","A",5,2,19,0.1053,1,"{2016, 2014}"
249,1,134,0,0.2526843,"\int x^6 \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^6*(b*x^2 + c*x^4)^(3/2),x]","\frac{128 b^4 \left(b x^2+c x^4\right)^{5/2}}{15015 c^5 x^5}-\frac{64 b^3 \left(b x^2+c x^4\right)^{5/2}}{3003 c^4 x^3}+\frac{16 b^2 \left(b x^2+c x^4\right)^{5/2}}{429 c^3 x}-\frac{8 b x \left(b x^2+c x^4\right)^{5/2}}{143 c^2}+\frac{x^3 \left(b x^2+c x^4\right)^{5/2}}{13 c}","\frac{128 b^4 \left(b x^2+c x^4\right)^{5/2}}{15015 c^5 x^5}-\frac{64 b^3 \left(b x^2+c x^4\right)^{5/2}}{3003 c^4 x^3}+\frac{16 b^2 \left(b x^2+c x^4\right)^{5/2}}{429 c^3 x}-\frac{8 b x \left(b x^2+c x^4\right)^{5/2}}{143 c^2}+\frac{x^3 \left(b x^2+c x^4\right)^{5/2}}{13 c}",1,"(128*b^4*(b*x^2 + c*x^4)^(5/2))/(15015*c^5*x^5) - (64*b^3*(b*x^2 + c*x^4)^(5/2))/(3003*c^4*x^3) + (16*b^2*(b*x^2 + c*x^4)^(5/2))/(429*c^3*x) - (8*b*x*(b*x^2 + c*x^4)^(5/2))/(143*c^2) + (x^3*(b*x^2 + c*x^4)^(5/2))/(13*c)","A",5,3,19,0.1579,1,"{2016, 2002, 2014}"
250,1,106,0,0.1956255,"\int x^4 \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^4*(b*x^2 + c*x^4)^(3/2),x]","-\frac{16 b^3 \left(b x^2+c x^4\right)^{5/2}}{1155 c^4 x^5}+\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2}}{231 c^3 x^3}-\frac{2 b \left(b x^2+c x^4\right)^{5/2}}{33 c^2 x}+\frac{x \left(b x^2+c x^4\right)^{5/2}}{11 c}","-\frac{16 b^3 \left(b x^2+c x^4\right)^{5/2}}{1155 c^4 x^5}+\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2}}{231 c^3 x^3}-\frac{2 b \left(b x^2+c x^4\right)^{5/2}}{33 c^2 x}+\frac{x \left(b x^2+c x^4\right)^{5/2}}{11 c}",1,"(-16*b^3*(b*x^2 + c*x^4)^(5/2))/(1155*c^4*x^5) + (8*b^2*(b*x^2 + c*x^4)^(5/2))/(231*c^3*x^3) - (2*b*(b*x^2 + c*x^4)^(5/2))/(33*c^2*x) + (x*(b*x^2 + c*x^4)^(5/2))/(11*c)","A",4,3,19,0.1579,1,"{2016, 2002, 2014}"
251,1,80,0,0.1113752,"\int x^2 \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^2*(b*x^2 + c*x^4)^(3/2),x]","\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2}}{315 c^3 x^5}-\frac{4 b \left(b x^2+c x^4\right)^{5/2}}{63 c^2 x^3}+\frac{\left(b x^2+c x^4\right)^{5/2}}{9 c x}","\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2}}{315 c^3 x^5}-\frac{4 b \left(b x^2+c x^4\right)^{5/2}}{63 c^2 x^3}+\frac{\left(b x^2+c x^4\right)^{5/2}}{9 c x}",1,"(8*b^2*(b*x^2 + c*x^4)^(5/2))/(315*c^3*x^5) - (4*b*(b*x^2 + c*x^4)^(5/2))/(63*c^2*x^3) + (b*x^2 + c*x^4)^(5/2)/(9*c*x)","A",3,3,19,0.1579,1,"{2016, 2002, 2014}"
252,1,52,0,0.0540039,"\int \left(b x^2+c x^4\right)^{3/2} \, dx","Int[(b*x^2 + c*x^4)^(3/2),x]","\frac{\left(b x^2+c x^4\right)^{5/2}}{7 c x^3}-\frac{2 b \left(b x^2+c x^4\right)^{5/2}}{35 c^2 x^5}","\frac{\left(b x^2+c x^4\right)^{5/2}}{7 c x^3}-\frac{2 b \left(b x^2+c x^4\right)^{5/2}}{35 c^2 x^5}",1,"(-2*b*(b*x^2 + c*x^4)^(5/2))/(35*c^2*x^5) + (b*x^2 + c*x^4)^(5/2)/(7*c*x^3)","A",2,2,15,0.1333,1,"{2002, 2014}"
253,1,25,0,0.0475792,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^2} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^2,x]","\frac{\left(b x^2+c x^4\right)^{5/2}}{5 c x^5}","\frac{\left(b x^2+c x^4\right)^{5/2}}{5 c x^5}",1,"(b*x^2 + c*x^4)^(5/2)/(5*c*x^5)","A",1,1,19,0.05263,1,"{2014}"
254,1,73,0,0.1104632,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^4} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^4,x]","b^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)\right)+\frac{b \sqrt{b x^2+c x^4}}{x}+\frac{\left(b x^2+c x^4\right)^{3/2}}{3 x^3}","b^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)\right)+\frac{b \sqrt{b x^2+c x^4}}{x}+\frac{\left(b x^2+c x^4\right)^{3/2}}{3 x^3}",1,"(b*Sqrt[b*x^2 + c*x^4])/x + (b*x^2 + c*x^4)^(3/2)/(3*x^3) - b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]]","A",4,3,19,0.1579,1,"{2021, 2008, 206}"
255,1,79,0,0.1183445,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^6} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^6,x]","-\frac{\left(b x^2+c x^4\right)^{3/2}}{2 x^5}+\frac{3 c \sqrt{b x^2+c x^4}}{2 x}-\frac{3}{2} \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)","-\frac{\left(b x^2+c x^4\right)^{3/2}}{2 x^5}+\frac{3 c \sqrt{b x^2+c x^4}}{2 x}-\frac{3}{2} \sqrt{b} c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)",1,"(3*c*Sqrt[b*x^2 + c*x^4])/(2*x) - (b*x^2 + c*x^4)^(3/2)/(2*x^5) - (3*Sqrt[b]*c*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/2","A",4,4,19,0.2105,1,"{2020, 2021, 2008, 206}"
256,1,81,0,0.1145523,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^8} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^8,x]","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{b}}-\frac{3 c \sqrt{b x^2+c x^4}}{8 x^3}-\frac{\left(b x^2+c x^4\right)^{3/2}}{4 x^7}","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{b}}-\frac{3 c \sqrt{b x^2+c x^4}}{8 x^3}-\frac{\left(b x^2+c x^4\right)^{3/2}}{4 x^7}",1,"(-3*c*Sqrt[b*x^2 + c*x^4])/(8*x^3) - (b*x^2 + c*x^4)^(3/2)/(4*x^7) - (3*c^2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*Sqrt[b])","A",4,3,19,0.1579,1,"{2020, 2008, 206}"
257,1,109,0,0.1642607,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{10}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^10,x]","\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{16 b^{3/2}}-\frac{c^2 \sqrt{b x^2+c x^4}}{16 b x^3}-\frac{c \sqrt{b x^2+c x^4}}{8 x^5}-\frac{\left(b x^2+c x^4\right)^{3/2}}{6 x^9}","\frac{c^3 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{16 b^{3/2}}-\frac{c^2 \sqrt{b x^2+c x^4}}{16 b x^3}-\frac{c \sqrt{b x^2+c x^4}}{8 x^5}-\frac{\left(b x^2+c x^4\right)^{3/2}}{6 x^9}",1,"-(c*Sqrt[b*x^2 + c*x^4])/(8*x^5) - (c^2*Sqrt[b*x^2 + c*x^4])/(16*b*x^3) - (b*x^2 + c*x^4)^(3/2)/(6*x^9) + (c^3*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(16*b^(3/2))","A",5,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
258,1,137,0,0.2034884,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{12}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^12,x]","\frac{3 c^3 \sqrt{b x^2+c x^4}}{128 b^2 x^3}-\frac{3 c^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{128 b^{5/2}}-\frac{c^2 \sqrt{b x^2+c x^4}}{64 b x^5}-\frac{c \sqrt{b x^2+c x^4}}{16 x^7}-\frac{\left(b x^2+c x^4\right)^{3/2}}{8 x^{11}}","\frac{3 c^3 \sqrt{b x^2+c x^4}}{128 b^2 x^3}-\frac{3 c^4 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{128 b^{5/2}}-\frac{c^2 \sqrt{b x^2+c x^4}}{64 b x^5}-\frac{c \sqrt{b x^2+c x^4}}{16 x^7}-\frac{\left(b x^2+c x^4\right)^{3/2}}{8 x^{11}}",1,"-(c*Sqrt[b*x^2 + c*x^4])/(16*x^7) - (c^2*Sqrt[b*x^2 + c*x^4])/(64*b*x^5) + (3*c^3*Sqrt[b*x^2 + c*x^4])/(128*b^2*x^3) - (b*x^2 + c*x^4)^(3/2)/(8*x^11) - (3*c^4*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(128*b^(5/2))","A",6,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
259,1,165,0,0.2549284,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{14}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^14,x]","-\frac{3 c^4 \sqrt{b x^2+c x^4}}{256 b^3 x^3}+\frac{c^3 \sqrt{b x^2+c x^4}}{128 b^2 x^5}+\frac{3 c^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{256 b^{7/2}}-\frac{c^2 \sqrt{b x^2+c x^4}}{160 b x^7}-\frac{3 c \sqrt{b x^2+c x^4}}{80 x^9}-\frac{\left(b x^2+c x^4\right)^{3/2}}{10 x^{13}}","-\frac{3 c^4 \sqrt{b x^2+c x^4}}{256 b^3 x^3}+\frac{c^3 \sqrt{b x^2+c x^4}}{128 b^2 x^5}+\frac{3 c^5 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{256 b^{7/2}}-\frac{c^2 \sqrt{b x^2+c x^4}}{160 b x^7}-\frac{3 c \sqrt{b x^2+c x^4}}{80 x^9}-\frac{\left(b x^2+c x^4\right)^{3/2}}{10 x^{13}}",1,"(-3*c*Sqrt[b*x^2 + c*x^4])/(80*x^9) - (c^2*Sqrt[b*x^2 + c*x^4])/(160*b*x^7) + (c^3*Sqrt[b*x^2 + c*x^4])/(128*b^2*x^5) - (3*c^4*Sqrt[b*x^2 + c*x^4])/(256*b^3*x^3) - (b*x^2 + c*x^4)^(3/2)/(10*x^13) + (3*c^5*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(256*b^(7/2))","A",7,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
260,1,114,0,0.1293402,"\int \frac{x^7}{\sqrt{b x^2+c x^4}} \, dx","Int[x^7/Sqrt[b*x^2 + c*x^4],x]","\frac{5 b^2 \sqrt{b x^2+c x^4}}{16 c^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{7/2}}-\frac{5 b x^2 \sqrt{b x^2+c x^4}}{24 c^2}+\frac{x^4 \sqrt{b x^2+c x^4}}{6 c}","\frac{5 b^2 \sqrt{b x^2+c x^4}}{16 c^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{7/2}}-\frac{5 b x^2 \sqrt{b x^2+c x^4}}{24 c^2}+\frac{x^4 \sqrt{b x^2+c x^4}}{6 c}",1,"(5*b^2*Sqrt[b*x^2 + c*x^4])/(16*c^3) - (5*b*x^2*Sqrt[b*x^2 + c*x^4])/(24*c^2) + (x^4*Sqrt[b*x^2 + c*x^4])/(6*c) - (5*b^3*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(16*c^(7/2))","A",6,5,19,0.2632,1,"{2018, 670, 640, 620, 206}"
261,1,86,0,0.1033469,"\int \frac{x^5}{\sqrt{b x^2+c x^4}} \, dx","Int[x^5/Sqrt[b*x^2 + c*x^4],x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{5/2}}-\frac{3 b \sqrt{b x^2+c x^4}}{8 c^2}+\frac{x^2 \sqrt{b x^2+c x^4}}{4 c}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{5/2}}-\frac{3 b \sqrt{b x^2+c x^4}}{8 c^2}+\frac{x^2 \sqrt{b x^2+c x^4}}{4 c}",1,"(-3*b*Sqrt[b*x^2 + c*x^4])/(8*c^2) + (x^2*Sqrt[b*x^2 + c*x^4])/(4*c) + (3*b^2*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*c^(5/2))","A",5,5,19,0.2632,1,"{2018, 670, 640, 620, 206}"
262,1,58,0,0.0831443,"\int \frac{x^3}{\sqrt{b x^2+c x^4}} \, dx","Int[x^3/Sqrt[b*x^2 + c*x^4],x]","\frac{\sqrt{b x^2+c x^4}}{2 c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{3/2}}","\frac{\sqrt{b x^2+c x^4}}{2 c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{3/2}}",1,"Sqrt[b*x^2 + c*x^4]/(2*c) - (b*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2*c^(3/2))","A",4,4,19,0.2105,1,"{2018, 640, 620, 206}"
263,1,31,0,0.0541314,"\int \frac{x}{\sqrt{b x^2+c x^4}} \, dx","Int[x/Sqrt[b*x^2 + c*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{c}}",1,"ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]]/Sqrt[c]","A",3,3,17,0.1765,1,"{2013, 620, 206}"
264,1,23,0,0.0405952,"\int \frac{1}{x \sqrt{b x^2+c x^4}} \, dx","Int[1/(x*Sqrt[b*x^2 + c*x^4]),x]","-\frac{\sqrt{b x^2+c x^4}}{b x^2}","-\frac{\sqrt{b x^2+c x^4}}{b x^2}",1,"-(Sqrt[b*x^2 + c*x^4]/(b*x^2))","A",1,1,19,0.05263,1,"{2014}"
265,1,52,0,0.0825069,"\int \frac{1}{x^3 \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^3*Sqrt[b*x^2 + c*x^4]),x]","\frac{2 c \sqrt{b x^2+c x^4}}{3 b^2 x^2}-\frac{\sqrt{b x^2+c x^4}}{3 b x^4}","\frac{2 c \sqrt{b x^2+c x^4}}{3 b^2 x^2}-\frac{\sqrt{b x^2+c x^4}}{3 b x^4}",1,"-Sqrt[b*x^2 + c*x^4]/(3*b*x^4) + (2*c*Sqrt[b*x^2 + c*x^4])/(3*b^2*x^2)","A",2,2,19,0.1053,1,"{2016, 2014}"
266,1,80,0,0.1253818,"\int \frac{1}{x^5 \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^5*Sqrt[b*x^2 + c*x^4]),x]","-\frac{8 c^2 \sqrt{b x^2+c x^4}}{15 b^3 x^2}+\frac{4 c \sqrt{b x^2+c x^4}}{15 b^2 x^4}-\frac{\sqrt{b x^2+c x^4}}{5 b x^6}","-\frac{8 c^2 \sqrt{b x^2+c x^4}}{15 b^3 x^2}+\frac{4 c \sqrt{b x^2+c x^4}}{15 b^2 x^4}-\frac{\sqrt{b x^2+c x^4}}{5 b x^6}",1,"-Sqrt[b*x^2 + c*x^4]/(5*b*x^6) + (4*c*Sqrt[b*x^2 + c*x^4])/(15*b^2*x^4) - (8*c^2*Sqrt[b*x^2 + c*x^4])/(15*b^3*x^2)","A",3,2,19,0.1053,1,"{2016, 2014}"
267,1,108,0,0.1693806,"\int \frac{1}{x^7 \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^7*Sqrt[b*x^2 + c*x^4]),x]","\frac{16 c^3 \sqrt{b x^2+c x^4}}{35 b^4 x^2}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{35 b^3 x^4}+\frac{6 c \sqrt{b x^2+c x^4}}{35 b^2 x^6}-\frac{\sqrt{b x^2+c x^4}}{7 b x^8}","\frac{16 c^3 \sqrt{b x^2+c x^4}}{35 b^4 x^2}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{35 b^3 x^4}+\frac{6 c \sqrt{b x^2+c x^4}}{35 b^2 x^6}-\frac{\sqrt{b x^2+c x^4}}{7 b x^8}",1,"-Sqrt[b*x^2 + c*x^4]/(7*b*x^8) + (6*c*Sqrt[b*x^2 + c*x^4])/(35*b^2*x^6) - (8*c^2*Sqrt[b*x^2 + c*x^4])/(35*b^3*x^4) + (16*c^3*Sqrt[b*x^2 + c*x^4])/(35*b^4*x^2)","A",4,2,19,0.1053,1,"{2016, 2014}"
268,1,50,0,0.078702,"\int \frac{x^4}{\sqrt{b x^2+c x^4}} \, dx","Int[x^4/Sqrt[b*x^2 + c*x^4],x]","\frac{x \sqrt{b x^2+c x^4}}{3 c}-\frac{2 b \sqrt{b x^2+c x^4}}{3 c^2 x}","\frac{x \sqrt{b x^2+c x^4}}{3 c}-\frac{2 b \sqrt{b x^2+c x^4}}{3 c^2 x}",1,"(-2*b*Sqrt[b*x^2 + c*x^4])/(3*c^2*x) + (x*Sqrt[b*x^2 + c*x^4])/(3*c)","A",2,2,19,0.1053,1,"{2016, 1588}"
269,1,22,0,0.0168739,"\int \frac{x^2}{\sqrt{b x^2+c x^4}} \, dx","Int[x^2/Sqrt[b*x^2 + c*x^4],x]","\frac{\sqrt{b x^2+c x^4}}{c x}","\frac{\sqrt{b x^2+c x^4}}{c x}",1,"Sqrt[b*x^2 + c*x^4]/(c*x)","A",1,1,19,0.05263,1,"{1588}"
270,1,30,0,0.0089355,"\int \frac{1}{\sqrt{b x^2+c x^4}} \, dx","Int[1/Sqrt[b*x^2 + c*x^4],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{b}}",1,"-(ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]]/Sqrt[b])","A",2,2,15,0.1333,1,"{2008, 206}"
271,1,59,0,0.055138,"\int \frac{1}{x^2 \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^2*Sqrt[b*x^2 + c*x^4]),x]","\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{3/2}}-\frac{\sqrt{b x^2+c x^4}}{2 b x^3}","\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{3/2}}-\frac{\sqrt{b x^2+c x^4}}{2 b x^3}",1,"-Sqrt[b*x^2 + c*x^4]/(2*b*x^3) + (c*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(2*b^(3/2))","A",3,3,19,0.1579,1,"{2025, 2008, 206}"
272,1,87,0,0.0974708,"\int \frac{1}{x^4 \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^4*Sqrt[b*x^2 + c*x^4]),x]","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{5/2}}+\frac{3 c \sqrt{b x^2+c x^4}}{8 b^2 x^3}-\frac{\sqrt{b x^2+c x^4}}{4 b x^5}","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{5/2}}+\frac{3 c \sqrt{b x^2+c x^4}}{8 b^2 x^3}-\frac{\sqrt{b x^2+c x^4}}{4 b x^5}",1,"-Sqrt[b*x^2 + c*x^4]/(4*b*x^5) + (3*c*Sqrt[b*x^2 + c*x^4])/(8*b^2*x^3) - (3*c^2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*b^(5/2))","A",4,3,19,0.1579,1,"{2025, 2008, 206}"
273,1,109,0,0.1287512,"\int \frac{x^9}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^9/(b*x^2 + c*x^4)^(3/2),x]","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{7/2}}+\frac{5 x^2 \sqrt{b x^2+c x^4}}{4 c^2}-\frac{15 b \sqrt{b x^2+c x^4}}{8 c^3}-\frac{x^6}{c \sqrt{b x^2+c x^4}}","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{7/2}}+\frac{5 x^2 \sqrt{b x^2+c x^4}}{4 c^2}-\frac{15 b \sqrt{b x^2+c x^4}}{8 c^3}-\frac{x^6}{c \sqrt{b x^2+c x^4}}",1,"-(x^6/(c*Sqrt[b*x^2 + c*x^4])) - (15*b*Sqrt[b*x^2 + c*x^4])/(8*c^3) + (5*x^2*Sqrt[b*x^2 + c*x^4])/(4*c^2) + (15*b^2*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*c^(7/2))","A",6,6,19,0.3158,1,"{2018, 668, 670, 640, 620, 206}"
274,1,81,0,0.1089313,"\int \frac{x^7}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^7/(b*x^2 + c*x^4)^(3/2),x]","\frac{3 \sqrt{b x^2+c x^4}}{2 c^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{5/2}}-\frac{x^4}{c \sqrt{b x^2+c x^4}}","\frac{3 \sqrt{b x^2+c x^4}}{2 c^2}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{5/2}}-\frac{x^4}{c \sqrt{b x^2+c x^4}}",1,"-(x^4/(c*Sqrt[b*x^2 + c*x^4])) + (3*Sqrt[b*x^2 + c*x^4])/(2*c^2) - (3*b*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2*c^(5/2))","A",5,5,19,0.2632,1,"{2018, 668, 640, 620, 206}"
275,1,55,0,0.0920113,"\int \frac{x^5}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^5/(b*x^2 + c*x^4)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{c^{3/2}}-\frac{x^2}{c \sqrt{b x^2+c x^4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{c^{3/2}}-\frac{x^2}{c \sqrt{b x^2+c x^4}}",1,"-(x^2/(c*Sqrt[b*x^2 + c*x^4])) + ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]]/c^(3/2)","A",4,4,19,0.2105,1,"{2018, 652, 620, 206}"
276,1,22,0,0.0553208,"\int \frac{x^3}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^3/(b*x^2 + c*x^4)^(3/2),x]","\frac{x^2}{b \sqrt{b x^2+c x^4}}","\frac{x^2}{b \sqrt{b x^2+c x^4}}",1,"x^2/(b*Sqrt[b*x^2 + c*x^4])","A",1,1,19,0.05263,1,"{2014}"
277,1,28,0,0.0464225,"\int \frac{x}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x/(b*x^2 + c*x^4)^(3/2),x]","-\frac{b+2 c x^2}{b^2 \sqrt{b x^2+c x^4}}","-\frac{b+2 c x^2}{b^2 \sqrt{b x^2+c x^4}}",1,"-((b + 2*c*x^2)/(b^2*Sqrt[b*x^2 + c*x^4]))","A",2,2,17,0.1176,1,"{2013, 613}"
278,1,74,0,0.1292869,"\int \frac{1}{x \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x*(b*x^2 + c*x^4)^(3/2)),x]","\frac{8 c \sqrt{b x^2+c x^4}}{3 b^3 x^2}-\frac{4 \sqrt{b x^2+c x^4}}{3 b^2 x^4}+\frac{1}{b x^2 \sqrt{b x^2+c x^4}}","\frac{8 c \sqrt{b x^2+c x^4}}{3 b^3 x^2}-\frac{4 \sqrt{b x^2+c x^4}}{3 b^2 x^4}+\frac{1}{b x^2 \sqrt{b x^2+c x^4}}",1,"1/(b*x^2*Sqrt[b*x^2 + c*x^4]) - (4*Sqrt[b*x^2 + c*x^4])/(3*b^2*x^4) + (8*c*Sqrt[b*x^2 + c*x^4])/(3*b^3*x^2)","A",3,3,19,0.1579,1,"{2015, 2016, 2014}"
279,1,102,0,0.1848751,"\int \frac{1}{x^3 \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^3*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{16 c^2 \sqrt{b x^2+c x^4}}{5 b^4 x^2}+\frac{8 c \sqrt{b x^2+c x^4}}{5 b^3 x^4}-\frac{6 \sqrt{b x^2+c x^4}}{5 b^2 x^6}+\frac{1}{b x^4 \sqrt{b x^2+c x^4}}","-\frac{16 c^2 \sqrt{b x^2+c x^4}}{5 b^4 x^2}+\frac{8 c \sqrt{b x^2+c x^4}}{5 b^3 x^4}-\frac{6 \sqrt{b x^2+c x^4}}{5 b^2 x^6}+\frac{1}{b x^4 \sqrt{b x^2+c x^4}}",1,"1/(b*x^4*Sqrt[b*x^2 + c*x^4]) - (6*Sqrt[b*x^2 + c*x^4])/(5*b^2*x^6) + (8*c*Sqrt[b*x^2 + c*x^4])/(5*b^3*x^4) - (16*c^2*Sqrt[b*x^2 + c*x^4])/(5*b^4*x^2)","A",4,3,19,0.1579,1,"{2015, 2016, 2014}"
280,1,130,0,0.2333261,"\int \frac{1}{x^5 \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^5*(b*x^2 + c*x^4)^(3/2)),x]","\frac{128 c^3 \sqrt{b x^2+c x^4}}{35 b^5 x^2}-\frac{64 c^2 \sqrt{b x^2+c x^4}}{35 b^4 x^4}+\frac{48 c \sqrt{b x^2+c x^4}}{35 b^3 x^6}-\frac{8 \sqrt{b x^2+c x^4}}{7 b^2 x^8}+\frac{1}{b x^6 \sqrt{b x^2+c x^4}}","\frac{128 c^3 \sqrt{b x^2+c x^4}}{35 b^5 x^2}-\frac{64 c^2 \sqrt{b x^2+c x^4}}{35 b^4 x^4}+\frac{48 c \sqrt{b x^2+c x^4}}{35 b^3 x^6}-\frac{8 \sqrt{b x^2+c x^4}}{7 b^2 x^8}+\frac{1}{b x^6 \sqrt{b x^2+c x^4}}",1,"1/(b*x^6*Sqrt[b*x^2 + c*x^4]) - (8*Sqrt[b*x^2 + c*x^4])/(7*b^2*x^8) + (48*c*Sqrt[b*x^2 + c*x^4])/(35*b^3*x^6) - (64*c^2*Sqrt[b*x^2 + c*x^4])/(35*b^4*x^4) + (128*c^3*Sqrt[b*x^2 + c*x^4])/(35*b^5*x^2)","A",5,3,19,0.1579,1,"{2015, 2016, 2014}"
281,1,47,0,0.067865,"\int \frac{x^6}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^6/(b*x^2 + c*x^4)^(3/2),x]","\frac{2 \sqrt{b x^2+c x^4}}{c^2 x}-\frac{x^3}{c \sqrt{b x^2+c x^4}}","\frac{2 \sqrt{b x^2+c x^4}}{c^2 x}-\frac{x^3}{c \sqrt{b x^2+c x^4}}",1,"-(x^3/(c*Sqrt[b*x^2 + c*x^4])) + (2*Sqrt[b*x^2 + c*x^4])/(c^2*x)","A",2,2,19,0.1053,1,"{2015, 1588}"
282,1,21,0,0.0194372,"\int \frac{x^4}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^4/(b*x^2 + c*x^4)^(3/2),x]","-\frac{x}{c \sqrt{b x^2+c x^4}}","-\frac{x}{c \sqrt{b x^2+c x^4}}",1,"-(x/(c*Sqrt[b*x^2 + c*x^4]))","A",1,1,19,0.05263,1,"{1588}"
283,1,51,0,0.0618186,"\int \frac{x^2}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^2/(b*x^2 + c*x^4)^(3/2),x]","\frac{x}{b \sqrt{b x^2+c x^4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{b^{3/2}}","\frac{x}{b \sqrt{b x^2+c x^4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{b^{3/2}}",1,"x/(b*Sqrt[b*x^2 + c*x^4]) - ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]]/b^(3/2)","A",3,3,19,0.1579,1,"{2023, 2008, 206}"
284,1,81,0,0.0646457,"\int \frac{1}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(b*x^2 + c*x^4)^(-3/2),x]","-\frac{3 \sqrt{b x^2+c x^4}}{2 b^2 x^3}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{5/2}}+\frac{1}{b x \sqrt{b x^2+c x^4}}","-\frac{3 \sqrt{b x^2+c x^4}}{2 b^2 x^3}+\frac{3 c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{5/2}}+\frac{1}{b x \sqrt{b x^2+c x^4}}",1,"1/(b*x*Sqrt[b*x^2 + c*x^4]) - (3*Sqrt[b*x^2 + c*x^4])/(2*b^2*x^3) + (3*c*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(2*b^(5/2))","A",4,4,15,0.2667,1,"{2006, 2025, 2008, 206}"
285,1,109,0,0.1534494,"\int \frac{1}{x^2 \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^2*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{15 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{7/2}}+\frac{15 c \sqrt{b x^2+c x^4}}{8 b^3 x^3}-\frac{5 \sqrt{b x^2+c x^4}}{4 b^2 x^5}+\frac{1}{b x^3 \sqrt{b x^2+c x^4}}","-\frac{15 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{7/2}}+\frac{15 c \sqrt{b x^2+c x^4}}{8 b^3 x^3}-\frac{5 \sqrt{b x^2+c x^4}}{4 b^2 x^5}+\frac{1}{b x^3 \sqrt{b x^2+c x^4}}",1,"1/(b*x^3*Sqrt[b*x^2 + c*x^4]) - (5*Sqrt[b*x^2 + c*x^4])/(4*b^2*x^5) + (15*c*Sqrt[b*x^2 + c*x^4])/(8*b^3*x^3) - (15*c^2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*b^(7/2))","A",5,4,19,0.2105,1,"{2023, 2025, 2008, 206}"
286,1,34,0,0.0582664,"\int \frac{x^3}{\sqrt{3 x^2-4 x^4}} \, dx","Int[x^3/Sqrt[3*x^2 - 4*x^4],x]","-\frac{1}{8} \sqrt{3 x^2-4 x^4}-\frac{3}{32} \sin ^{-1}\left(1-\frac{8 x^2}{3}\right)","-\frac{1}{8} \sqrt{3 x^2-4 x^4}-\frac{3}{32} \sin ^{-1}\left(1-\frac{8 x^2}{3}\right)",1,"-Sqrt[3*x^2 - 4*x^4]/8 - (3*ArcSin[1 - (8*x^2)/3])/32","A",4,4,19,0.2105,1,"{2018, 640, 619, 216}"
287,1,34,0,0.0572119,"\int \frac{x^3}{\sqrt{-3 x^2-4 x^4}} \, dx","Int[x^3/Sqrt[-3*x^2 - 4*x^4],x]","-\frac{1}{8} \sqrt{-4 x^4-3 x^2}-\frac{3}{32} \sin ^{-1}\left(\frac{8 x^2}{3}+1\right)","-\frac{1}{8} \sqrt{-4 x^4-3 x^2}-\frac{3}{32} \sin ^{-1}\left(\frac{8 x^2}{3}+1\right)",1,"-Sqrt[-3*x^2 - 4*x^4]/8 - (3*ArcSin[1 + (8*x^2)/3])/32","A",4,4,19,0.2105,1,"{2018, 640, 619, 216}"
288,1,45,0,0.0561752,"\int \frac{x^3}{\sqrt{3 x^2+4 x^4}} \, dx","Int[x^3/Sqrt[3*x^2 + 4*x^4],x]","\frac{1}{8} \sqrt{4 x^4+3 x^2}-\frac{3}{16} \tanh ^{-1}\left(\frac{2 x^2}{\sqrt{4 x^4+3 x^2}}\right)","\frac{1}{8} \sqrt{4 x^4+3 x^2}-\frac{3}{16} \tanh ^{-1}\left(\frac{2 x^2}{\sqrt{4 x^4+3 x^2}}\right)",1,"Sqrt[3*x^2 + 4*x^4]/8 - (3*ArcTanh[(2*x^2)/Sqrt[3*x^2 + 4*x^4]])/16","A",4,4,19,0.2105,1,"{2018, 640, 620, 206}"
289,1,45,0,0.0567401,"\int \frac{x^3}{\sqrt{-3 x^2+4 x^4}} \, dx","Int[x^3/Sqrt[-3*x^2 + 4*x^4],x]","\frac{1}{8} \sqrt{4 x^4-3 x^2}+\frac{3}{16} \tanh ^{-1}\left(\frac{2 x^2}{\sqrt{4 x^4-3 x^2}}\right)","\frac{1}{8} \sqrt{4 x^4-3 x^2}+\frac{3}{16} \tanh ^{-1}\left(\frac{2 x^2}{\sqrt{4 x^4-3 x^2}}\right)",1,"Sqrt[-3*x^2 + 4*x^4]/8 + (3*ArcTanh[(2*x^2)/Sqrt[-3*x^2 + 4*x^4]])/16","A",4,4,19,0.2105,1,"{2018, 640, 620, 206}"
290,1,58,0,0.0827262,"\int \frac{x^3}{\sqrt{a x^2+b x^4}} \, dx","Int[x^3/Sqrt[a*x^2 + b*x^4],x]","\frac{\sqrt{a x^2+b x^4}}{2 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^2+b x^4}}\right)}{2 b^{3/2}}","\frac{\sqrt{a x^2+b x^4}}{2 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^2+b x^4}}\right)}{2 b^{3/2}}",1,"Sqrt[a*x^2 + b*x^4]/(2*b) - (a*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a*x^2 + b*x^4]])/(2*b^(3/2))","A",4,4,19,0.2105,1,"{2018, 640, 620, 206}"
291,1,60,0,0.0816661,"\int \frac{x^3}{\sqrt{a x^2-b x^4}} \, dx","Int[x^3/Sqrt[a*x^2 - b*x^4],x]","\frac{a \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^2-b x^4}}\right)}{2 b^{3/2}}-\frac{\sqrt{a x^2-b x^4}}{2 b}","\frac{a \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^2-b x^4}}\right)}{2 b^{3/2}}-\frac{\sqrt{a x^2-b x^4}}{2 b}",1,"-Sqrt[a*x^2 - b*x^4]/(2*b) + (a*ArcTan[(Sqrt[b]*x^2)/Sqrt[a*x^2 - b*x^4]])/(2*b^(3/2))","A",4,4,20,0.2000,1,"{2018, 640, 620, 203}"
292,1,21,0,0.0047629,"\int x^{7/2} \left(b x^2+c x^4\right) \, dx","Int[x^(7/2)*(b*x^2 + c*x^4),x]","\frac{2}{13} b x^{13/2}+\frac{2}{17} c x^{17/2}","\frac{2}{13} b x^{13/2}+\frac{2}{17} c x^{17/2}",1,"(2*b*x^(13/2))/13 + (2*c*x^(17/2))/17","A",2,1,17,0.05882,1,"{14}"
293,1,21,0,0.0053335,"\int x^{5/2} \left(b x^2+c x^4\right) \, dx","Int[x^(5/2)*(b*x^2 + c*x^4),x]","\frac{2}{11} b x^{11/2}+\frac{2}{15} c x^{15/2}","\frac{2}{11} b x^{11/2}+\frac{2}{15} c x^{15/2}",1,"(2*b*x^(11/2))/11 + (2*c*x^(15/2))/15","A",2,1,17,0.05882,1,"{14}"
294,1,21,0,0.0049,"\int x^{3/2} \left(b x^2+c x^4\right) \, dx","Int[x^(3/2)*(b*x^2 + c*x^4),x]","\frac{2}{9} b x^{9/2}+\frac{2}{13} c x^{13/2}","\frac{2}{9} b x^{9/2}+\frac{2}{13} c x^{13/2}",1,"(2*b*x^(9/2))/9 + (2*c*x^(13/2))/13","A",2,1,17,0.05882,1,"{14}"
295,1,21,0,0.0047368,"\int \sqrt{x} \left(b x^2+c x^4\right) \, dx","Int[Sqrt[x]*(b*x^2 + c*x^4),x]","\frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2}","\frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2}",1,"(2*b*x^(7/2))/7 + (2*c*x^(11/2))/11","A",2,1,17,0.05882,1,"{14}"
296,1,21,0,0.0050601,"\int \frac{b x^2+c x^4}{\sqrt{x}} \, dx","Int[(b*x^2 + c*x^4)/Sqrt[x],x]","\frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2}","\frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2}",1,"(2*b*x^(5/2))/5 + (2*c*x^(9/2))/9","A",2,1,17,0.05882,1,"{14}"
297,1,21,0,0.0051502,"\int \frac{b x^2+c x^4}{x^{3/2}} \, dx","Int[(b*x^2 + c*x^4)/x^(3/2),x]","\frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2}","\frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2}",1,"(2*b*x^(3/2))/3 + (2*c*x^(7/2))/7","A",2,1,17,0.05882,1,"{14}"
298,1,19,0,0.0047181,"\int \frac{b x^2+c x^4}{x^{5/2}} \, dx","Int[(b*x^2 + c*x^4)/x^(5/2),x]","2 b \sqrt{x}+\frac{2}{5} c x^{5/2}","2 b \sqrt{x}+\frac{2}{5} c x^{5/2}",1,"2*b*Sqrt[x] + (2*c*x^(5/2))/5","A",2,1,17,0.05882,1,"{14}"
299,1,19,0,0.0050894,"\int \frac{b x^2+c x^4}{x^{7/2}} \, dx","Int[(b*x^2 + c*x^4)/x^(7/2),x]","\frac{2}{3} c x^{3/2}-\frac{2 b}{\sqrt{x}}","\frac{2}{3} c x^{3/2}-\frac{2 b}{\sqrt{x}}",1,"(-2*b)/Sqrt[x] + (2*c*x^(3/2))/3","A",2,1,17,0.05882,1,"{14}"
300,1,36,0,0.0160419,"\int x^{7/2} \left(b x^2+c x^4\right)^2 \, dx","Int[x^(7/2)*(b*x^2 + c*x^4)^2,x]","\frac{2}{17} b^2 x^{17/2}+\frac{4}{21} b c x^{21/2}+\frac{2}{25} c^2 x^{25/2}","\frac{2}{17} b^2 x^{17/2}+\frac{4}{21} b c x^{21/2}+\frac{2}{25} c^2 x^{25/2}",1,"(2*b^2*x^(17/2))/17 + (4*b*c*x^(21/2))/21 + (2*c^2*x^(25/2))/25","A",3,2,19,0.1053,1,"{1584, 270}"
301,1,36,0,0.0179989,"\int x^{5/2} \left(b x^2+c x^4\right)^2 \, dx","Int[x^(5/2)*(b*x^2 + c*x^4)^2,x]","\frac{2}{15} b^2 x^{15/2}+\frac{4}{19} b c x^{19/2}+\frac{2}{23} c^2 x^{23/2}","\frac{2}{15} b^2 x^{15/2}+\frac{4}{19} b c x^{19/2}+\frac{2}{23} c^2 x^{23/2}",1,"(2*b^2*x^(15/2))/15 + (4*b*c*x^(19/2))/19 + (2*c^2*x^(23/2))/23","A",3,2,19,0.1053,1,"{1584, 270}"
302,1,36,0,0.0149835,"\int x^{3/2} \left(b x^2+c x^4\right)^2 \, dx","Int[x^(3/2)*(b*x^2 + c*x^4)^2,x]","\frac{2}{13} b^2 x^{13/2}+\frac{4}{17} b c x^{17/2}+\frac{2}{21} c^2 x^{21/2}","\frac{2}{13} b^2 x^{13/2}+\frac{4}{17} b c x^{17/2}+\frac{2}{21} c^2 x^{21/2}",1,"(2*b^2*x^(13/2))/13 + (4*b*c*x^(17/2))/17 + (2*c^2*x^(21/2))/21","A",3,2,19,0.1053,1,"{1584, 270}"
303,1,36,0,0.0139267,"\int \sqrt{x} \left(b x^2+c x^4\right)^2 \, dx","Int[Sqrt[x]*(b*x^2 + c*x^4)^2,x]","\frac{2}{11} b^2 x^{11/2}+\frac{4}{15} b c x^{15/2}+\frac{2}{19} c^2 x^{19/2}","\frac{2}{11} b^2 x^{11/2}+\frac{4}{15} b c x^{15/2}+\frac{2}{19} c^2 x^{19/2}",1,"(2*b^2*x^(11/2))/11 + (4*b*c*x^(15/2))/15 + (2*c^2*x^(19/2))/19","A",3,2,19,0.1053,1,"{1584, 270}"
304,1,36,0,0.0143971,"\int \frac{\left(b x^2+c x^4\right)^2}{\sqrt{x}} \, dx","Int[(b*x^2 + c*x^4)^2/Sqrt[x],x]","\frac{2}{9} b^2 x^{9/2}+\frac{4}{13} b c x^{13/2}+\frac{2}{17} c^2 x^{17/2}","\frac{2}{9} b^2 x^{9/2}+\frac{4}{13} b c x^{13/2}+\frac{2}{17} c^2 x^{17/2}",1,"(2*b^2*x^(9/2))/9 + (4*b*c*x^(13/2))/13 + (2*c^2*x^(17/2))/17","A",3,2,19,0.1053,1,"{1584, 270}"
305,1,36,0,0.0157798,"\int \frac{\left(b x^2+c x^4\right)^2}{x^{3/2}} \, dx","Int[(b*x^2 + c*x^4)^2/x^(3/2),x]","\frac{2}{7} b^2 x^{7/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2}","\frac{2}{7} b^2 x^{7/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2}",1,"(2*b^2*x^(7/2))/7 + (4*b*c*x^(11/2))/11 + (2*c^2*x^(15/2))/15","A",3,2,19,0.1053,1,"{1584, 270}"
306,1,36,0,0.0150283,"\int \frac{\left(b x^2+c x^4\right)^2}{x^{5/2}} \, dx","Int[(b*x^2 + c*x^4)^2/x^(5/2),x]","\frac{2}{5} b^2 x^{5/2}+\frac{4}{9} b c x^{9/2}+\frac{2}{13} c^2 x^{13/2}","\frac{2}{5} b^2 x^{5/2}+\frac{4}{9} b c x^{9/2}+\frac{2}{13} c^2 x^{13/2}",1,"(2*b^2*x^(5/2))/5 + (4*b*c*x^(9/2))/9 + (2*c^2*x^(13/2))/13","A",3,2,19,0.1053,1,"{1584, 270}"
307,1,36,0,0.0162743,"\int \frac{\left(b x^2+c x^4\right)^2}{x^{7/2}} \, dx","Int[(b*x^2 + c*x^4)^2/x^(7/2),x]","\frac{2}{3} b^2 x^{3/2}+\frac{4}{7} b c x^{7/2}+\frac{2}{11} c^2 x^{11/2}","\frac{2}{3} b^2 x^{3/2}+\frac{4}{7} b c x^{7/2}+\frac{2}{11} c^2 x^{11/2}",1,"(2*b^2*x^(3/2))/3 + (4*b*c*x^(7/2))/7 + (2*c^2*x^(11/2))/11","A",3,2,19,0.1053,1,"{1584, 270}"
308,1,51,0,0.0212143,"\int x^{7/2} \left(b x^2+c x^4\right)^3 \, dx","Int[x^(7/2)*(b*x^2 + c*x^4)^3,x]","\frac{6}{25} b^2 c x^{25/2}+\frac{2}{21} b^3 x^{21/2}+\frac{6}{29} b c^2 x^{29/2}+\frac{2}{33} c^3 x^{33/2}","\frac{6}{25} b^2 c x^{25/2}+\frac{2}{21} b^3 x^{21/2}+\frac{6}{29} b c^2 x^{29/2}+\frac{2}{33} c^3 x^{33/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
309,1,51,0,0.0204168,"\int x^{5/2} \left(b x^2+c x^4\right)^3 \, dx","Int[x^(5/2)*(b*x^2 + c*x^4)^3,x]","\frac{6}{23} b^2 c x^{23/2}+\frac{2}{19} b^3 x^{19/2}+\frac{2}{9} b c^2 x^{27/2}+\frac{2}{31} c^3 x^{31/2}","\frac{6}{23} b^2 c x^{23/2}+\frac{2}{19} b^3 x^{19/2}+\frac{2}{9} b c^2 x^{27/2}+\frac{2}{31} c^3 x^{31/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
310,1,51,0,0.019643,"\int x^{3/2} \left(b x^2+c x^4\right)^3 \, dx","Int[x^(3/2)*(b*x^2 + c*x^4)^3,x]","\frac{2}{7} b^2 c x^{21/2}+\frac{2}{17} b^3 x^{17/2}+\frac{6}{25} b c^2 x^{25/2}+\frac{2}{29} c^3 x^{29/2}","\frac{2}{7} b^2 c x^{21/2}+\frac{2}{17} b^3 x^{17/2}+\frac{6}{25} b c^2 x^{25/2}+\frac{2}{29} c^3 x^{29/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
311,1,51,0,0.0191347,"\int \sqrt{x} \left(b x^2+c x^4\right)^3 \, dx","Int[Sqrt[x]*(b*x^2 + c*x^4)^3,x]","\frac{6}{19} b^2 c x^{19/2}+\frac{2}{15} b^3 x^{15/2}+\frac{6}{23} b c^2 x^{23/2}+\frac{2}{27} c^3 x^{27/2}","\frac{6}{19} b^2 c x^{19/2}+\frac{2}{15} b^3 x^{15/2}+\frac{6}{23} b c^2 x^{23/2}+\frac{2}{27} c^3 x^{27/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
312,1,51,0,0.0202165,"\int \frac{\left(b x^2+c x^4\right)^3}{\sqrt{x}} \, dx","Int[(b*x^2 + c*x^4)^3/Sqrt[x],x]","\frac{6}{17} b^2 c x^{17/2}+\frac{2}{13} b^3 x^{13/2}+\frac{2}{7} b c^2 x^{21/2}+\frac{2}{25} c^3 x^{25/2}","\frac{6}{17} b^2 c x^{17/2}+\frac{2}{13} b^3 x^{13/2}+\frac{2}{7} b c^2 x^{21/2}+\frac{2}{25} c^3 x^{25/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
313,1,51,0,0.0200503,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{3/2}} \, dx","Int[(b*x^2 + c*x^4)^3/x^(3/2),x]","\frac{2}{5} b^2 c x^{15/2}+\frac{2}{11} b^3 x^{11/2}+\frac{6}{19} b c^2 x^{19/2}+\frac{2}{23} c^3 x^{23/2}","\frac{2}{5} b^2 c x^{15/2}+\frac{2}{11} b^3 x^{11/2}+\frac{6}{19} b c^2 x^{19/2}+\frac{2}{23} c^3 x^{23/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
314,1,51,0,0.0189882,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{5/2}} \, dx","Int[(b*x^2 + c*x^4)^3/x^(5/2),x]","\frac{6}{13} b^2 c x^{13/2}+\frac{2}{9} b^3 x^{9/2}+\frac{6}{17} b c^2 x^{17/2}+\frac{2}{21} c^3 x^{21/2}","\frac{6}{13} b^2 c x^{13/2}+\frac{2}{9} b^3 x^{9/2}+\frac{6}{17} b c^2 x^{17/2}+\frac{2}{21} c^3 x^{21/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
315,1,51,0,0.0222626,"\int \frac{\left(b x^2+c x^4\right)^3}{x^{7/2}} \, dx","Int[(b*x^2 + c*x^4)^3/x^(7/2),x]","\frac{6}{11} b^2 c x^{11/2}+\frac{2}{7} b^3 x^{7/2}+\frac{2}{5} b c^2 x^{15/2}+\frac{2}{19} c^3 x^{19/2}","\frac{6}{11} b^2 c x^{11/2}+\frac{2}{7} b^3 x^{7/2}+\frac{2}{5} b c^2 x^{15/2}+\frac{2}{19} c^3 x^{19/2}",1,"(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",3,2,19,0.1053,1,"{1584, 270}"
316,1,217,0,0.2322598,"\int \frac{x^{13/2}}{b x^2+c x^4} \, dx","Int[x^(13/2)/(b*x^2 + c*x^4),x]","\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{11/4}}+\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{11/4}}-\frac{2 b x^{3/2}}{3 c^2}+\frac{2 x^{7/2}}{7 c}","\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{11/4}}+\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{11/4}}-\frac{2 b x^{3/2}}{3 c^2}+\frac{2 x^{7/2}}{7 c}",1,"(-2*b*x^(3/2))/(3*c^2) + (2*x^(7/2))/(7*c) - (b^(7/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(11/4)) + (b^(7/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(11/4)) + (b^(7/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(11/4)) - (b^(7/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(11/4))","A",13,9,19,0.4737,1,"{1584, 321, 329, 297, 1162, 617, 204, 1165, 628}"
317,1,215,0,0.1937613,"\int \frac{x^{11/2}}{b x^2+c x^4} \, dx","Int[x^(11/2)/(b*x^2 + c*x^4),x]","-\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}+\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}-\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{9/4}}+\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{9/4}}-\frac{2 b \sqrt{x}}{c^2}+\frac{2 x^{5/2}}{5 c}","-\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}+\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}-\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{9/4}}+\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{9/4}}-\frac{2 b \sqrt{x}}{c^2}+\frac{2 x^{5/2}}{5 c}",1,"(-2*b*Sqrt[x])/c^2 + (2*x^(5/2))/(5*c) - (b^(5/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(9/4)) + (b^(5/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(9/4)) - (b^(5/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(9/4)) + (b^(5/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(9/4))","A",13,9,19,0.4737,1,"{1584, 321, 329, 211, 1165, 628, 1162, 617, 204}"
318,1,204,0,0.1858774,"\int \frac{x^{9/2}}{b x^2+c x^4} \, dx","Int[x^(9/2)/(b*x^2 + c*x^4),x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{7/4}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{7/4}}+\frac{2 x^{3/2}}{3 c}","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{7/4}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{7/4}}+\frac{2 x^{3/2}}{3 c}",1,"(2*x^(3/2))/(3*c) + (b^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(7/4)) - (b^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(7/4)) - (b^(3/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(7/4)) + (b^(3/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(7/4))","A",12,9,19,0.4737,1,"{1584, 321, 329, 297, 1162, 617, 204, 1165, 628}"
319,1,202,0,0.1849836,"\int \frac{x^{7/2}}{b x^2+c x^4} \, dx","Int[x^(7/2)/(b*x^2 + c*x^4),x]","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{5/4}}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{5/4}}+\frac{2 \sqrt{x}}{c}","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{5/4}}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{5/4}}+\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{5/4}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{5/4}}+\frac{2 \sqrt{x}}{c}",1,"(2*Sqrt[x])/c + (b^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(5/4)) - (b^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(5/4)) + (b^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(5/4)) - (b^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(5/4))","A",12,9,19,0.4737,1,"{1584, 321, 329, 211, 1165, 628, 1162, 617, 204}"
320,1,192,0,0.1420385,"\int \frac{x^{5/2}}{b x^2+c x^4} \, dx","Int[x^(5/2)/(b*x^2 + c*x^4),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} \sqrt[4]{b} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} \sqrt[4]{b} c^{3/4}}","\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} \sqrt[4]{b} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} \sqrt[4]{b} c^{3/4}}",1,"-(ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(Sqrt[2]*b^(1/4)*c^(3/4))) + ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(Sqrt[2]*b^(1/4)*c^(3/4)) + Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(2*Sqrt[2]*b^(1/4)*c^(3/4)) - Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(2*Sqrt[2]*b^(1/4)*c^(3/4))","A",11,8,19,0.4211,1,"{1584, 329, 297, 1162, 617, 204, 1165, 628}"
321,1,192,0,0.1386914,"\int \frac{x^{3/2}}{b x^2+c x^4} \, dx","Int[x^(3/2)/(b*x^2 + c*x^4),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{3/4} \sqrt[4]{c}}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{3/4} \sqrt[4]{c}}",1,"-(ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(Sqrt[2]*b^(3/4)*c^(1/4))) + ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(Sqrt[2]*b^(3/4)*c^(1/4)) - Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(2*Sqrt[2]*b^(3/4)*c^(1/4)) + Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(2*Sqrt[2]*b^(3/4)*c^(1/4))","A",11,8,19,0.4211,1,"{1584, 329, 211, 1165, 628, 1162, 617, 204}"
322,1,202,0,0.1642145,"\int \frac{\sqrt{x}}{b x^2+c x^4} \, dx","Int[Sqrt[x]/(b*x^2 + c*x^4),x]","-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{5/4}}-\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{5/4}}-\frac{2}{b \sqrt{x}}","-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4}}+\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{5/4}}-\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{5/4}}-\frac{2}{b \sqrt{x}}",1,"-2/(b*Sqrt[x]) + (c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(5/4)) - (c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(5/4)) - (c^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(5/4)) + (c^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(5/4))","A",12,9,19,0.4737,1,"{1584, 325, 329, 297, 1162, 617, 204, 1165, 628}"
323,1,204,0,0.1671329,"\int \frac{1}{\sqrt{x} \left(b x^2+c x^4\right)} \, dx","Int[1/(Sqrt[x]*(b*x^2 + c*x^4)),x]","\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4}}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4}}+\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{7/4}}-\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{7/4}}-\frac{2}{3 b x^{3/2}}","\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4}}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4}}+\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{7/4}}-\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{7/4}}-\frac{2}{3 b x^{3/2}}",1,"-2/(3*b*x^(3/2)) + (c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(7/4)) - (c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(7/4)) + (c^(3/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(7/4)) - (c^(3/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(7/4))","A",12,9,19,0.4737,1,"{1584, 325, 329, 211, 1165, 628, 1162, 617, 204}"
324,1,215,0,0.1876659,"\int \frac{1}{x^{3/2} \left(b x^2+c x^4\right)} \, dx","Int[1/(x^(3/2)*(b*x^2 + c*x^4)),x]","\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{9/4}}+\frac{c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{9/4}}+\frac{2 c}{b^2 \sqrt{x}}-\frac{2}{5 b x^{5/2}}","\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{9/4}}+\frac{c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{9/4}}+\frac{2 c}{b^2 \sqrt{x}}-\frac{2}{5 b x^{5/2}}",1,"-2/(5*b*x^(5/2)) + (2*c)/(b^2*Sqrt[x]) - (c^(5/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(9/4)) + (c^(5/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(9/4)) + (c^(5/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(9/4)) - (c^(5/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(9/4))","A",13,9,19,0.4737,1,"{1584, 325, 329, 297, 1162, 617, 204, 1165, 628}"
325,1,217,0,0.1821576,"\int \frac{1}{x^{5/2} \left(b x^2+c x^4\right)} \, dx","Int[1/(x^(5/2)*(b*x^2 + c*x^4)),x]","-\frac{c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{c^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}-\frac{c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{11/4}}+\frac{c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{11/4}}+\frac{2 c}{3 b^2 x^{3/2}}-\frac{2}{7 b x^{7/2}}","-\frac{c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{c^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}-\frac{c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{11/4}}+\frac{c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{11/4}}+\frac{2 c}{3 b^2 x^{3/2}}-\frac{2}{7 b x^{7/2}}",1,"-2/(7*b*x^(7/2)) + (2*c)/(3*b^2*x^(3/2)) - (c^(7/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(11/4)) + (c^(7/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(11/4)) - (c^(7/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(11/4)) + (c^(7/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(11/4))","A",13,9,19,0.4737,1,"{1584, 325, 329, 211, 1165, 628, 1162, 617, 204}"
326,1,230,0,0.219664,"\int \frac{1}{x^{7/2} \left(b x^2+c x^4\right)} \, dx","Int[1/(x^(7/2)*(b*x^2 + c*x^4)),x]","-\frac{2 c^2}{b^3 \sqrt{x}}-\frac{c^{9/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}+\frac{c^{9/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}+\frac{c^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{13/4}}-\frac{c^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{13/4}}+\frac{2 c}{5 b^2 x^{5/2}}-\frac{2}{9 b x^{9/2}}","-\frac{2 c^2}{b^3 \sqrt{x}}-\frac{c^{9/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}+\frac{c^{9/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}+\frac{c^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{13/4}}-\frac{c^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{13/4}}+\frac{2 c}{5 b^2 x^{5/2}}-\frac{2}{9 b x^{9/2}}",1,"-2/(9*b*x^(9/2)) + (2*c)/(5*b^2*x^(5/2)) - (2*c^2)/(b^3*Sqrt[x]) + (c^(9/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(13/4)) - (c^(9/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(13/4)) - (c^(9/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(13/4)) + (c^(9/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(13/4))","A",14,9,19,0.4737,1,"{1584, 325, 329, 297, 1162, 617, 204, 1165, 628}"
327,1,243,0,0.2100415,"\int \frac{x^{19/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(19/2)/(b*x^2 + c*x^4)^2,x]","-\frac{9 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}+\frac{9 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}-\frac{9 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{13/4}}+\frac{9 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{13/4}}-\frac{9 b \sqrt{x}}{2 c^3}-\frac{x^{9/2}}{2 c \left(b+c x^2\right)}+\frac{9 x^{5/2}}{10 c^2}","-\frac{9 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}+\frac{9 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}-\frac{9 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{13/4}}+\frac{9 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{13/4}}-\frac{9 b \sqrt{x}}{2 c^3}-\frac{x^{9/2}}{2 c \left(b+c x^2\right)}+\frac{9 x^{5/2}}{10 c^2}",1,"(-9*b*Sqrt[x])/(2*c^3) + (9*x^(5/2))/(10*c^2) - x^(9/2)/(2*c*(b + c*x^2)) - (9*b^(5/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(13/4)) + (9*b^(5/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(13/4)) - (9*b^(5/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(13/4)) + (9*b^(5/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(13/4))","A",14,10,19,0.5263,1,"{1584, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
328,1,230,0,0.1821539,"\int \frac{x^{17/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(17/2)/(b*x^2 + c*x^4)^2,x]","-\frac{7 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{11/4}}+\frac{7 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{11/4}}+\frac{7 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{11/4}}-\frac{7 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{11/4}}-\frac{x^{7/2}}{2 c \left(b+c x^2\right)}+\frac{7 x^{3/2}}{6 c^2}","-\frac{7 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{11/4}}+\frac{7 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{11/4}}+\frac{7 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{11/4}}-\frac{7 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{11/4}}-\frac{x^{7/2}}{2 c \left(b+c x^2\right)}+\frac{7 x^{3/2}}{6 c^2}",1,"(7*x^(3/2))/(6*c^2) - x^(7/2)/(2*c*(b + c*x^2)) + (7*b^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(11/4)) - (7*b^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(11/4)) - (7*b^(3/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(11/4)) + (7*b^(3/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(11/4))","A",13,10,19,0.5263,1,"{1584, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
329,1,230,0,0.1819837,"\int \frac{x^{15/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(15/2)/(b*x^2 + c*x^4)^2,x]","\frac{5 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{9/4}}-\frac{5 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{9/4}}+\frac{5 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{9/4}}-\frac{5 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{9/4}}-\frac{x^{5/2}}{2 c \left(b+c x^2\right)}+\frac{5 \sqrt{x}}{2 c^2}","\frac{5 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{9/4}}-\frac{5 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{9/4}}+\frac{5 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{9/4}}-\frac{5 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{9/4}}-\frac{x^{5/2}}{2 c \left(b+c x^2\right)}+\frac{5 \sqrt{x}}{2 c^2}",1,"(5*Sqrt[x])/(2*c^2) - x^(5/2)/(2*c*(b + c*x^2)) + (5*b^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(9/4)) - (5*b^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(9/4)) + (5*b^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(9/4)) - (5*b^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(9/4))","A",13,10,19,0.5263,1,"{1584, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
330,1,218,0,0.1656188,"\int \frac{x^{13/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(13/2)/(b*x^2 + c*x^4)^2,x]","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{x^{3/2}}{2 c \left(b+c x^2\right)}","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{x^{3/2}}{2 c \left(b+c x^2\right)}",1,"-x^(3/2)/(2*c*(b + c*x^2)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(1/4)*c^(7/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(1/4)*c^(7/4)) + (3*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(1/4)*c^(7/4)) - (3*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(1/4)*c^(7/4))","A",12,9,19,0.4737,1,"{1584, 288, 329, 297, 1162, 617, 204, 1165, 628}"
331,1,218,0,0.1598237,"\int \frac{x^{11/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(11/2)/(b*x^2 + c*x^4)^2,x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{3/4} c^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{3/4} c^{5/4}}-\frac{\sqrt{x}}{2 c \left(b+c x^2\right)}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{5/4}}+\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{5/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{3/4} c^{5/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{3/4} c^{5/4}}-\frac{\sqrt{x}}{2 c \left(b+c x^2\right)}",1,"-Sqrt[x]/(2*c*(b + c*x^2)) - ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(4*Sqrt[2]*b^(3/4)*c^(5/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(4*Sqrt[2]*b^(3/4)*c^(5/4)) - Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(8*Sqrt[2]*b^(3/4)*c^(5/4)) + Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(8*Sqrt[2]*b^(3/4)*c^(5/4))","A",12,9,19,0.4737,1,"{1584, 288, 329, 211, 1165, 628, 1162, 617, 204}"
332,1,218,0,0.1632096,"\int \frac{x^{9/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(9/2)/(b*x^2 + c*x^4)^2,x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{5/4} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{5/4} c^{3/4}}+\frac{x^{3/2}}{2 b \left(b+c x^2\right)}","\frac{\log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{3/4}}-\frac{\log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{3/4}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{5/4} c^{3/4}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{5/4} c^{3/4}}+\frac{x^{3/2}}{2 b \left(b+c x^2\right)}",1,"x^(3/2)/(2*b*(b + c*x^2)) - ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(4*Sqrt[2]*b^(5/4)*c^(3/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)]/(4*Sqrt[2]*b^(5/4)*c^(3/4)) + Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(8*Sqrt[2]*b^(5/4)*c^(3/4)) - Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x]/(8*Sqrt[2]*b^(5/4)*c^(3/4))","A",12,9,19,0.4737,1,"{1584, 290, 329, 297, 1162, 617, 204, 1165, 628}"
333,1,218,0,0.169269,"\int \frac{x^{7/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(7/2)/(b*x^2 + c*x^4)^2,x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{\sqrt{x}}{2 b \left(b+c x^2\right)}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{\sqrt{x}}{2 b \left(b+c x^2\right)}",1,"Sqrt[x]/(2*b*(b + c*x^2)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(7/4)*c^(1/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(7/4)*c^(1/4)) - (3*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(7/4)*c^(1/4)) + (3*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(7/4)*c^(1/4))","A",12,9,19,0.4737,1,"{1584, 290, 329, 211, 1165, 628, 1162, 617, 204}"
334,1,230,0,0.1903828,"\int \frac{x^{5/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(5/2)/(b*x^2 + c*x^4)^2,x]","-\frac{5 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{9/4}}-\frac{5}{2 b^2 \sqrt{x}}+\frac{1}{2 b \sqrt{x} \left(b+c x^2\right)}","-\frac{5 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{9/4}}-\frac{5}{2 b^2 \sqrt{x}}+\frac{1}{2 b \sqrt{x} \left(b+c x^2\right)}",1,"-5/(2*b^2*Sqrt[x]) + 1/(2*b*Sqrt[x]*(b + c*x^2)) + (5*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(9/4)) - (5*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(9/4)) - (5*c^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(9/4)) + (5*c^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(9/4))","A",13,10,19,0.5263,1,"{1584, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
335,1,230,0,0.1849467,"\int \frac{x^{3/2}}{\left(b x^2+c x^4\right)^2} \, dx","Int[x^(3/2)/(b*x^2 + c*x^4)^2,x]","\frac{7 c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4}}-\frac{7 c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4}}+\frac{7 c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{11/4}}-\frac{7 c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{11/4}}-\frac{7}{6 b^2 x^{3/2}}+\frac{1}{2 b x^{3/2} \left(b+c x^2\right)}","\frac{7 c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4}}-\frac{7 c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4}}+\frac{7 c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{11/4}}-\frac{7 c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{11/4}}-\frac{7}{6 b^2 x^{3/2}}+\frac{1}{2 b x^{3/2} \left(b+c x^2\right)}",1,"-7/(6*b^2*x^(3/2)) + 1/(2*b*x^(3/2)*(b + c*x^2)) + (7*c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(11/4)) - (7*c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(11/4)) + (7*c^(3/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(11/4)) - (7*c^(3/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(11/4))","A",13,10,19,0.5263,1,"{1584, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
336,1,243,0,0.2172968,"\int \frac{\sqrt{x}}{\left(b x^2+c x^4\right)^2} \, dx","Int[Sqrt[x]/(b*x^2 + c*x^4)^2,x]","\frac{9 c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{9 c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{9 c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{13/4}}+\frac{9 c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{13/4}}+\frac{9 c}{2 b^3 \sqrt{x}}-\frac{9}{10 b^2 x^{5/2}}+\frac{1}{2 b x^{5/2} \left(b+c x^2\right)}","\frac{9 c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{9 c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{9 c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{13/4}}+\frac{9 c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{13/4}}+\frac{9 c}{2 b^3 \sqrt{x}}-\frac{9}{10 b^2 x^{5/2}}+\frac{1}{2 b x^{5/2} \left(b+c x^2\right)}",1,"-9/(10*b^2*x^(5/2)) + (9*c)/(2*b^3*Sqrt[x]) + 1/(2*b*x^(5/2)*(b + c*x^2)) - (9*c^(5/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(13/4)) + (9*c^(5/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(13/4)) + (9*c^(5/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(13/4)) - (9*c^(5/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(13/4))","A",14,10,19,0.5263,1,"{1584, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
337,1,243,0,0.2073842,"\int \frac{1}{\sqrt{x} \left(b x^2+c x^4\right)^2} \, dx","Int[1/(Sqrt[x]*(b*x^2 + c*x^4)^2),x]","-\frac{11 c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}+\frac{11 c^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}-\frac{11 c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{15/4}}+\frac{11 c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{15/4}}+\frac{11 c}{6 b^3 x^{3/2}}-\frac{11}{14 b^2 x^{7/2}}+\frac{1}{2 b x^{7/2} \left(b+c x^2\right)}","-\frac{11 c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}+\frac{11 c^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}-\frac{11 c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{15/4}}+\frac{11 c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{15/4}}+\frac{11 c}{6 b^3 x^{3/2}}-\frac{11}{14 b^2 x^{7/2}}+\frac{1}{2 b x^{7/2} \left(b+c x^2\right)}",1,"-11/(14*b^2*x^(7/2)) + (11*c)/(6*b^3*x^(3/2)) + 1/(2*b*x^(7/2)*(b + c*x^2)) - (11*c^(7/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(15/4)) + (11*c^(7/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(15/4)) - (11*c^(7/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(15/4)) + (11*c^(7/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(15/4))","A",14,10,19,0.5263,1,"{1584, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
338,1,258,0,0.2348885,"\int \frac{1}{x^{3/2} \left(b x^2+c x^4\right)^2} \, dx","Int[1/(x^(3/2)*(b*x^2 + c*x^4)^2),x]","-\frac{13 c^2}{2 b^4 \sqrt{x}}-\frac{13 c^{9/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}+\frac{13 c^{9/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}+\frac{13 c^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{17/4}}-\frac{13 c^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{17/4}}+\frac{13 c}{10 b^3 x^{5/2}}-\frac{13}{18 b^2 x^{9/2}}+\frac{1}{2 b x^{9/2} \left(b+c x^2\right)}","-\frac{13 c^2}{2 b^4 \sqrt{x}}-\frac{13 c^{9/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}+\frac{13 c^{9/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}+\frac{13 c^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{17/4}}-\frac{13 c^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{17/4}}+\frac{13 c}{10 b^3 x^{5/2}}-\frac{13}{18 b^2 x^{9/2}}+\frac{1}{2 b x^{9/2} \left(b+c x^2\right)}",1,"-13/(18*b^2*x^(9/2)) + (13*c)/(10*b^3*x^(5/2)) - (13*c^2)/(2*b^4*Sqrt[x]) + 1/(2*b*x^(9/2)*(b + c*x^2)) + (13*c^(9/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(17/4)) - (13*c^(9/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(17/4)) - (13*c^(9/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(17/4)) + (13*c^(9/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(17/4))","A",15,10,19,0.5263,1,"{1584, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
339,1,251,0,0.2106248,"\int \frac{x^{23/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(23/2)/(b*x^2 + c*x^4)^3,x]","-\frac{9 x^{5/2}}{16 c^2 \left(b+c x^2\right)}+\frac{45 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{13/4}}-\frac{45 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{13/4}}+\frac{45 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} c^{13/4}}-\frac{45 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} c^{13/4}}-\frac{x^{9/2}}{4 c \left(b+c x^2\right)^2}+\frac{45 \sqrt{x}}{16 c^3}","-\frac{9 x^{5/2}}{16 c^2 \left(b+c x^2\right)}+\frac{45 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{13/4}}-\frac{45 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{13/4}}+\frac{45 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} c^{13/4}}-\frac{45 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} c^{13/4}}-\frac{x^{9/2}}{4 c \left(b+c x^2\right)^2}+\frac{45 \sqrt{x}}{16 c^3}",1,"(45*Sqrt[x])/(16*c^3) - x^(9/2)/(4*c*(b + c*x^2)^2) - (9*x^(5/2))/(16*c^2*(b + c*x^2)) + (45*b^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*c^(13/4)) - (45*b^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*c^(13/4)) + (45*b^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*c^(13/4)) - (45*b^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*c^(13/4))","A",14,10,19,0.5263,1,"{1584, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
340,1,239,0,0.2029119,"\int \frac{x^{21/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(21/2)/(b*x^2 + c*x^4)^3,x]","-\frac{7 x^{3/2}}{16 c^2 \left(b+c x^2\right)}+\frac{21 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{21 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} \sqrt[4]{b} c^{11/4}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{x^{7/2}}{4 c \left(b+c x^2\right)^2}","-\frac{7 x^{3/2}}{16 c^2 \left(b+c x^2\right)}+\frac{21 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{21 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} \sqrt[4]{b} c^{11/4}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{x^{7/2}}{4 c \left(b+c x^2\right)^2}",1,"-x^(7/2)/(4*c*(b + c*x^2)^2) - (7*x^(3/2))/(16*c^2*(b + c*x^2)) - (21*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(1/4)*c^(11/4)) + (21*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(1/4)*c^(11/4)) + (21*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(1/4)*c^(11/4)) - (21*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(1/4)*c^(11/4))","A",13,9,19,0.4737,1,"{1584, 288, 329, 297, 1162, 617, 204, 1165, 628}"
341,1,239,0,0.1893252,"\int \frac{x^{19/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(19/2)/(b*x^2 + c*x^4)^3,x]","-\frac{5 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{9/4}}+\frac{5 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{9/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{3/4} c^{9/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{3/4} c^{9/4}}-\frac{5 \sqrt{x}}{16 c^2 \left(b+c x^2\right)}-\frac{x^{5/2}}{4 c \left(b+c x^2\right)^2}","-\frac{5 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{9/4}}+\frac{5 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{9/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{3/4} c^{9/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{3/4} c^{9/4}}-\frac{5 \sqrt{x}}{16 c^2 \left(b+c x^2\right)}-\frac{x^{5/2}}{4 c \left(b+c x^2\right)^2}",1,"-x^(5/2)/(4*c*(b + c*x^2)^2) - (5*Sqrt[x])/(16*c^2*(b + c*x^2)) - (5*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(3/4)*c^(9/4)) + (5*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(3/4)*c^(9/4)) - (5*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(3/4)*c^(9/4)) + (5*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(3/4)*c^(9/4))","A",13,9,19,0.4737,1,"{1584, 288, 329, 211, 1165, 628, 1162, 617, 204}"
342,1,242,0,0.1884277,"\int \frac{x^{17/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(17/2)/(b*x^2 + c*x^4)^3,x]","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{5/4} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{5/4} c^{7/4}}+\frac{3 x^{3/2}}{16 b c \left(b+c x^2\right)}-\frac{x^{3/2}}{4 c \left(b+c x^2\right)^2}","\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{7/4}}-\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{7/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{5/4} c^{7/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{5/4} c^{7/4}}+\frac{3 x^{3/2}}{16 b c \left(b+c x^2\right)}-\frac{x^{3/2}}{4 c \left(b+c x^2\right)^2}",1,"-x^(3/2)/(4*c*(b + c*x^2)^2) + (3*x^(3/2))/(16*b*c*(b + c*x^2)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(5/4)*c^(7/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(5/4)*c^(7/4)) + (3*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(5/4)*c^(7/4)) - (3*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(5/4)*c^(7/4))","A",13,10,19,0.5263,1,"{1584, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
343,1,242,0,0.183075,"\int \frac{x^{15/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(15/2)/(b*x^2 + c*x^4)^3,x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{5/4}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{5/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{7/4} c^{5/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{7/4} c^{5/4}}+\frac{\sqrt{x}}{16 b c \left(b+c x^2\right)}-\frac{\sqrt{x}}{4 c \left(b+c x^2\right)^2}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{5/4}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{5/4}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{7/4} c^{5/4}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{7/4} c^{5/4}}+\frac{\sqrt{x}}{16 b c \left(b+c x^2\right)}-\frac{\sqrt{x}}{4 c \left(b+c x^2\right)^2}",1,"-Sqrt[x]/(4*c*(b + c*x^2)^2) + Sqrt[x]/(16*b*c*(b + c*x^2)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(7/4)*c^(5/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(7/4)*c^(5/4)) - (3*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(7/4)*c^(5/4)) + (3*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(7/4)*c^(5/4))","A",13,10,19,0.5263,1,"{1584, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
344,1,239,0,0.1848585,"\int \frac{x^{13/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(13/2)/(b*x^2 + c*x^4)^3,x]","\frac{5 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{3/4}}-\frac{5 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{3/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{9/4} c^{3/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{9/4} c^{3/4}}+\frac{5 x^{3/2}}{16 b^2 \left(b+c x^2\right)}+\frac{x^{3/2}}{4 b \left(b+c x^2\right)^2}","\frac{5 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{3/4}}-\frac{5 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{3/4}}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{9/4} c^{3/4}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{9/4} c^{3/4}}+\frac{5 x^{3/2}}{16 b^2 \left(b+c x^2\right)}+\frac{x^{3/2}}{4 b \left(b+c x^2\right)^2}",1,"x^(3/2)/(4*b*(b + c*x^2)^2) + (5*x^(3/2))/(16*b^2*(b + c*x^2)) - (5*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(9/4)*c^(3/4)) + (5*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(9/4)*c^(3/4)) + (5*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(9/4)*c^(3/4)) - (5*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(9/4)*c^(3/4))","A",13,9,19,0.4737,1,"{1584, 290, 329, 297, 1162, 617, 204, 1165, 628}"
345,1,239,0,0.1861449,"\int \frac{x^{11/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(11/2)/(b*x^2 + c*x^4)^3,x]","\frac{7 \sqrt{x}}{16 b^2 \left(b+c x^2\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} \sqrt[4]{c}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{\sqrt{x}}{4 b \left(b+c x^2\right)^2}","\frac{7 \sqrt{x}}{16 b^2 \left(b+c x^2\right)}-\frac{21 \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{21 \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} \sqrt[4]{c}}-\frac{21 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{21 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{\sqrt{x}}{4 b \left(b+c x^2\right)^2}",1,"Sqrt[x]/(4*b*(b + c*x^2)^2) + (7*Sqrt[x])/(16*b^2*(b + c*x^2)) - (21*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(11/4)*c^(1/4)) + (21*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(11/4)*c^(1/4)) - (21*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(11/4)*c^(1/4)) + (21*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(11/4)*c^(1/4))","A",13,9,19,0.4737,1,"{1584, 290, 329, 211, 1165, 628, 1162, 617, 204}"
346,1,251,0,0.2168559,"\int \frac{x^{9/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(9/2)/(b*x^2 + c*x^4)^3,x]","\frac{9}{16 b^2 \sqrt{x} \left(b+c x^2\right)}-\frac{45 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4}}+\frac{45 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4}}+\frac{45 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{13/4}}-\frac{45 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{13/4}}-\frac{45}{16 b^3 \sqrt{x}}+\frac{1}{4 b \sqrt{x} \left(b+c x^2\right)^2}","\frac{9}{16 b^2 \sqrt{x} \left(b+c x^2\right)}-\frac{45 \sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4}}+\frac{45 \sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4}}+\frac{45 \sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{13/4}}-\frac{45 \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{13/4}}-\frac{45}{16 b^3 \sqrt{x}}+\frac{1}{4 b \sqrt{x} \left(b+c x^2\right)^2}",1,"-45/(16*b^3*Sqrt[x]) + 1/(4*b*Sqrt[x]*(b + c*x^2)^2) + 9/(16*b^2*Sqrt[x]*(b + c*x^2)) + (45*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(13/4)) - (45*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(13/4)) - (45*c^(1/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(13/4)) + (45*c^(1/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(13/4))","A",14,10,19,0.5263,1,"{1584, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
347,1,251,0,0.2136609,"\int \frac{x^{7/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(7/2)/(b*x^2 + c*x^4)^3,x]","\frac{77 c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4}}-\frac{77 c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4}}+\frac{77 c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{15/4}}-\frac{77 c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{15/4}}+\frac{11}{16 b^2 x^{3/2} \left(b+c x^2\right)}-\frac{77}{48 b^3 x^{3/2}}+\frac{1}{4 b x^{3/2} \left(b+c x^2\right)^2}","\frac{77 c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4}}-\frac{77 c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4}}+\frac{77 c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{15/4}}-\frac{77 c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{15/4}}+\frac{11}{16 b^2 x^{3/2} \left(b+c x^2\right)}-\frac{77}{48 b^3 x^{3/2}}+\frac{1}{4 b x^{3/2} \left(b+c x^2\right)^2}",1,"-77/(48*b^3*x^(3/2)) + 1/(4*b*x^(3/2)*(b + c*x^2)^2) + 11/(16*b^2*x^(3/2)*(b + c*x^2)) + (77*c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(15/4)) - (77*c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(15/4)) + (77*c^(3/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(15/4)) - (77*c^(3/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(15/4))","A",14,10,19,0.5263,1,"{1584, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
348,1,264,0,0.2331975,"\int \frac{x^{5/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(5/2)/(b*x^2 + c*x^4)^3,x]","\frac{117 c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}-\frac{117 c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}-\frac{117 c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{17/4}}+\frac{117 c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{17/4}}+\frac{13}{16 b^2 x^{5/2} \left(b+c x^2\right)}+\frac{117 c}{16 b^4 \sqrt{x}}-\frac{117}{80 b^3 x^{5/2}}+\frac{1}{4 b x^{5/2} \left(b+c x^2\right)^2}","\frac{117 c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}-\frac{117 c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}-\frac{117 c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{17/4}}+\frac{117 c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{17/4}}+\frac{13}{16 b^2 x^{5/2} \left(b+c x^2\right)}+\frac{117 c}{16 b^4 \sqrt{x}}-\frac{117}{80 b^3 x^{5/2}}+\frac{1}{4 b x^{5/2} \left(b+c x^2\right)^2}",1,"-117/(80*b^3*x^(5/2)) + (117*c)/(16*b^4*Sqrt[x]) + 1/(4*b*x^(5/2)*(b + c*x^2)^2) + 13/(16*b^2*x^(5/2)*(b + c*x^2)) - (117*c^(5/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(17/4)) + (117*c^(5/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(17/4)) + (117*c^(5/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(17/4)) - (117*c^(5/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(17/4))","A",15,10,19,0.5263,1,"{1584, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
349,1,264,0,0.2314277,"\int \frac{x^{3/2}}{\left(b x^2+c x^4\right)^3} \, dx","Int[x^(3/2)/(b*x^2 + c*x^4)^3,x]","-\frac{165 c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}+\frac{165 c^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}-\frac{165 c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{19/4}}+\frac{165 c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{19/4}}+\frac{55 c}{16 b^4 x^{3/2}}+\frac{15}{16 b^2 x^{7/2} \left(b+c x^2\right)}-\frac{165}{112 b^3 x^{7/2}}+\frac{1}{4 b x^{7/2} \left(b+c x^2\right)^2}","-\frac{165 c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}+\frac{165 c^{7/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}-\frac{165 c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{19/4}}+\frac{165 c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{19/4}}+\frac{55 c}{16 b^4 x^{3/2}}+\frac{15}{16 b^2 x^{7/2} \left(b+c x^2\right)}-\frac{165}{112 b^3 x^{7/2}}+\frac{1}{4 b x^{7/2} \left(b+c x^2\right)^2}",1,"-165/(112*b^3*x^(7/2)) + (55*c)/(16*b^4*x^(3/2)) + 1/(4*b*x^(7/2)*(b + c*x^2)^2) + 15/(16*b^2*x^(7/2)*(b + c*x^2)) - (165*c^(7/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(19/4)) + (165*c^(7/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(19/4)) - (165*c^(7/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(19/4)) + (165*c^(7/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(19/4))","A",15,10,19,0.5263,1,"{1584, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
350,1,279,0,0.2679867,"\int \frac{\sqrt{x}}{\left(b x^2+c x^4\right)^3} \, dx","Int[Sqrt[x]/(b*x^2 + c*x^4)^3,x]","-\frac{221 c^2}{16 b^5 \sqrt{x}}-\frac{221 c^{9/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}+\frac{221 c^{9/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}+\frac{221 c^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{21/4}}-\frac{221 c^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{21/4}}+\frac{221 c}{80 b^4 x^{5/2}}+\frac{17}{16 b^2 x^{9/2} \left(b+c x^2\right)}-\frac{221}{144 b^3 x^{9/2}}+\frac{1}{4 b x^{9/2} \left(b+c x^2\right)^2}","-\frac{221 c^2}{16 b^5 \sqrt{x}}-\frac{221 c^{9/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}+\frac{221 c^{9/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}+\frac{221 c^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{21/4}}-\frac{221 c^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{21/4}}+\frac{221 c}{80 b^4 x^{5/2}}+\frac{17}{16 b^2 x^{9/2} \left(b+c x^2\right)}-\frac{221}{144 b^3 x^{9/2}}+\frac{1}{4 b x^{9/2} \left(b+c x^2\right)^2}",1,"-221/(144*b^3*x^(9/2)) + (221*c)/(80*b^4*x^(5/2)) - (221*c^2)/(16*b^5*Sqrt[x]) + 1/(4*b*x^(9/2)*(b + c*x^2)^2) + 17/(16*b^2*x^(9/2)*(b + c*x^2)) + (221*c^(9/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(21/4)) - (221*c^(9/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(21/4)) - (221*c^(9/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(21/4)) + (221*c^(9/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(21/4))","A",16,10,19,0.5263,1,"{1584, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
351,1,279,0,0.2601745,"\int \frac{1}{\sqrt{x} \left(b x^2+c x^4\right)^3} \, dx","Int[1/(Sqrt[x]*(b*x^2 + c*x^4)^3),x]","-\frac{95 c^2}{16 b^5 x^{3/2}}+\frac{285 c^{11/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}-\frac{285 c^{11/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}+\frac{285 c^{11/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{23/4}}-\frac{285 c^{11/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{23/4}}+\frac{285 c}{112 b^4 x^{7/2}}+\frac{19}{16 b^2 x^{11/2} \left(b+c x^2\right)}-\frac{285}{176 b^3 x^{11/2}}+\frac{1}{4 b x^{11/2} \left(b+c x^2\right)^2}","-\frac{95 c^2}{16 b^5 x^{3/2}}+\frac{285 c^{11/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}-\frac{285 c^{11/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}+\frac{285 c^{11/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{23/4}}-\frac{285 c^{11/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{23/4}}+\frac{285 c}{112 b^4 x^{7/2}}+\frac{19}{16 b^2 x^{11/2} \left(b+c x^2\right)}-\frac{285}{176 b^3 x^{11/2}}+\frac{1}{4 b x^{11/2} \left(b+c x^2\right)^2}",1,"-285/(176*b^3*x^(11/2)) + (285*c)/(112*b^4*x^(7/2)) - (95*c^2)/(16*b^5*x^(3/2)) + 1/(4*b*x^(11/2)*(b + c*x^2)^2) + 19/(16*b^2*x^(11/2)*(b + c*x^2)) + (285*c^(11/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(23/4)) - (285*c^(11/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(23/4)) + (285*c^(11/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(23/4)) - (285*c^(11/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(23/4))","A",16,10,19,0.5263,1,"{1584, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
352,1,323,0,0.3830178,"\int x^{7/2} \sqrt{b x^2+c x^4} \, dx","Int[x^(7/2)*Sqrt[b*x^2 + c*x^4],x]","\frac{28 b^3 x^{3/2} \left(b+c x^2\right)}{195 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{28 b^2 \sqrt{x} \sqrt{b x^2+c x^4}}{585 c^2}+\frac{14 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{28 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{2}{13} x^{9/2} \sqrt{b x^2+c x^4}+\frac{4 b x^{5/2} \sqrt{b x^2+c x^4}}{117 c}","\frac{28 b^3 x^{3/2} \left(b+c x^2\right)}{195 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{28 b^2 \sqrt{x} \sqrt{b x^2+c x^4}}{585 c^2}+\frac{14 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{28 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{2}{13} x^{9/2} \sqrt{b x^2+c x^4}+\frac{4 b x^{5/2} \sqrt{b x^2+c x^4}}{117 c}",1,"(28*b^3*x^(3/2)*(b + c*x^2))/(195*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (28*b^2*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(585*c^2) + (4*b*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(117*c) + (2*x^(9/2)*Sqrt[b*x^2 + c*x^4])/13 - (28*b^(13/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(11/4)*Sqrt[b*x^2 + c*x^4]) + (14*b^(13/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,21,0.3333,1,"{2021, 2024, 2032, 329, 305, 220, 1196}"
353,1,176,0,0.2488868,"\int x^{5/2} \sqrt{b x^2+c x^4} \, dx","Int[x^(5/2)*Sqrt[b*x^2 + c*x^4],x]","-\frac{20 b^2 \sqrt{b x^2+c x^4}}{231 c^2 \sqrt{x}}+\frac{10 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}+\frac{2}{11} x^{7/2} \sqrt{b x^2+c x^4}+\frac{4 b x^{3/2} \sqrt{b x^2+c x^4}}{77 c}","-\frac{20 b^2 \sqrt{b x^2+c x^4}}{231 c^2 \sqrt{x}}+\frac{10 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}+\frac{2}{11} x^{7/2} \sqrt{b x^2+c x^4}+\frac{4 b x^{3/2} \sqrt{b x^2+c x^4}}{77 c}",1,"(-20*b^2*Sqrt[b*x^2 + c*x^4])/(231*c^2*Sqrt[x]) + (4*b*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(77*c) + (2*x^(7/2)*Sqrt[b*x^2 + c*x^4])/11 + (10*b^(11/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,21,0.2381,1,"{2021, 2024, 2032, 329, 220}"
354,1,293,0,0.3069506,"\int x^{3/2} \sqrt{b x^2+c x^4} \, dx","Int[x^(3/2)*Sqrt[b*x^2 + c*x^4],x]","-\frac{4 b^2 x^{3/2} \left(b+c x^2\right)}{15 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{2}{9} x^{5/2} \sqrt{b x^2+c x^4}+\frac{4 b \sqrt{x} \sqrt{b x^2+c x^4}}{45 c}","-\frac{4 b^2 x^{3/2} \left(b+c x^2\right)}{15 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{2}{9} x^{5/2} \sqrt{b x^2+c x^4}+\frac{4 b \sqrt{x} \sqrt{b x^2+c x^4}}{45 c}",1,"(-4*b^2*x^(3/2)*(b + c*x^2))/(15*c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (4*b*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(45*c) + (2*x^(5/2)*Sqrt[b*x^2 + c*x^4])/9 + (4*b^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[b*x^2 + c*x^4]) - (2*b^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,21,0.3333,1,"{2021, 2024, 2032, 329, 305, 220, 1196}"
355,1,146,0,0.1849864,"\int \sqrt{x} \sqrt{b x^2+c x^4} \, dx","Int[Sqrt[x]*Sqrt[b*x^2 + c*x^4],x]","-\frac{2 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt{b x^2+c x^4}}+\frac{4 b \sqrt{b x^2+c x^4}}{21 c \sqrt{x}}+\frac{2}{7} x^{3/2} \sqrt{b x^2+c x^4}","-\frac{2 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt{b x^2+c x^4}}+\frac{4 b \sqrt{b x^2+c x^4}}{21 c \sqrt{x}}+\frac{2}{7} x^{3/2} \sqrt{b x^2+c x^4}",1,"(4*b*Sqrt[b*x^2 + c*x^4])/(21*c*Sqrt[x]) + (2*x^(3/2)*Sqrt[b*x^2 + c*x^4])/7 - (2*b^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,21,0.2381,1,"{2021, 2024, 2032, 329, 220}"
356,1,263,0,0.2382266,"\int \frac{\sqrt{b x^2+c x^4}}{\sqrt{x}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/Sqrt[x],x]","\frac{2 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 b x^{3/2} \left(b+c x^2\right)}{5 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2}{5} \sqrt{x} \sqrt{b x^2+c x^4}","\frac{2 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 b x^{3/2} \left(b+c x^2\right)}{5 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2}{5} \sqrt{x} \sqrt{b x^2+c x^4}",1,"(4*b*x^(3/2)*(b + c*x^2))/(5*Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (2*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/5 - (4*b^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[b*x^2 + c*x^4]) + (2*b^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,21,0.2857,1,"{2021, 2032, 329, 305, 220, 1196}"
357,1,118,0,0.1331092,"\int \frac{\sqrt{b x^2+c x^4}}{x^{3/2}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^(3/2),x]","\frac{2 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{b x^2+c x^4}}{3 \sqrt{x}}","\frac{2 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{b x^2+c x^4}}{3 \sqrt{x}}",1,"(2*Sqrt[b*x^2 + c*x^4])/(3*Sqrt[x]) + (2*b^(3/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,21,0.1905,1,"{2021, 2032, 329, 220}"
358,1,254,0,0.2379516,"\int \frac{\sqrt{b x^2+c x^4}}{x^{5/2}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^(5/2),x]","\frac{4 \sqrt{c} x^{3/2} \left(b+c x^2\right)}{\left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{x^{3/2}}+\frac{2 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{b x^2+c x^4}}-\frac{4 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{b x^2+c x^4}}","\frac{4 \sqrt{c} x^{3/2} \left(b+c x^2\right)}{\left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{x^{3/2}}+\frac{2 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{b x^2+c x^4}}-\frac{4 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{b x^2+c x^4}}",1,"(4*Sqrt[c]*x^(3/2)*(b + c*x^2))/((Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*Sqrt[b*x^2 + c*x^4])/x^(3/2) - (4*b^(1/4)*c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/Sqrt[b*x^2 + c*x^4] + (2*b^(1/4)*c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/Sqrt[b*x^2 + c*x^4]","A",6,6,21,0.2857,1,"{2020, 2032, 329, 305, 220, 1196}"
359,1,118,0,0.1320031,"\int \frac{\sqrt{b x^2+c x^4}}{x^{7/2}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^(7/2),x]","\frac{2 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{3 x^{5/2}}","\frac{2 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{3 x^{5/2}}",1,"(-2*Sqrt[b*x^2 + c*x^4])/(3*x^(5/2)) + (2*c^(3/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*b^(1/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,21,0.1905,1,"{2020, 2032, 329, 220}"
360,1,293,0,0.2993941,"\int \frac{\sqrt{b x^2+c x^4}}{x^{9/2}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^(9/2),x]","\frac{2 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{5 b x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4}}{5 x^{7/2}}","\frac{2 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{5 b x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4}}{5 x^{7/2}}",1,"(4*c^(3/2)*x^(3/2)*(b + c*x^2))/(5*b*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*Sqrt[b*x^2 + c*x^4])/(5*x^(7/2)) - (4*c*Sqrt[b*x^2 + c*x^4])/(5*b*x^(3/2)) - (4*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^2 + c*x^4]) + (2*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,21,0.3333,1,"{2020, 2025, 2032, 329, 305, 220, 1196}"
361,1,146,0,0.1823914,"\int \frac{\sqrt{b x^2+c x^4}}{x^{11/2}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^(11/2),x]","-\frac{2 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{21 b x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4}}{7 x^{9/2}}","-\frac{2 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{21 b x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4}}{7 x^{9/2}}",1,"(-2*Sqrt[b*x^2 + c*x^4])/(7*x^(9/2)) - (4*c*Sqrt[b*x^2 + c*x^4])/(21*b*x^(5/2)) - (2*c^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*b^(5/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,21,0.2381,1,"{2020, 2025, 2032, 329, 220}"
362,1,323,0,0.3658633,"\int \frac{\sqrt{b x^2+c x^4}}{x^{13/2}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^(13/2),x]","-\frac{4 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{4 c^2 \sqrt{b x^2+c x^4}}{15 b^2 x^{3/2}}-\frac{2 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{4 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{45 b x^{7/2}}-\frac{2 \sqrt{b x^2+c x^4}}{9 x^{11/2}}","-\frac{4 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{4 c^2 \sqrt{b x^2+c x^4}}{15 b^2 x^{3/2}}-\frac{2 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{4 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{45 b x^{7/2}}-\frac{2 \sqrt{b x^2+c x^4}}{9 x^{11/2}}",1,"(-4*c^(5/2)*x^(3/2)*(b + c*x^2))/(15*b^2*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*Sqrt[b*x^2 + c*x^4])/(9*x^(11/2)) - (4*c*Sqrt[b*x^2 + c*x^4])/(45*b*x^(7/2)) + (4*c^2*Sqrt[b*x^2 + c*x^4])/(15*b^2*x^(3/2)) + (4*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[b*x^2 + c*x^4]) - (2*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,21,0.3333,1,"{2020, 2025, 2032, 329, 305, 220, 1196}"
363,1,176,0,0.23427,"\int \frac{\sqrt{b x^2+c x^4}}{x^{15/2}} \, dx","Int[Sqrt[b*x^2 + c*x^4]/x^(15/2),x]","\frac{20 c^2 \sqrt{b x^2+c x^4}}{231 b^2 x^{5/2}}+\frac{10 c^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{77 b x^{9/2}}-\frac{2 \sqrt{b x^2+c x^4}}{11 x^{13/2}}","\frac{20 c^2 \sqrt{b x^2+c x^4}}{231 b^2 x^{5/2}}+\frac{10 c^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{77 b x^{9/2}}-\frac{2 \sqrt{b x^2+c x^4}}{11 x^{13/2}}",1,"(-2*Sqrt[b*x^2 + c*x^4])/(11*x^(13/2)) - (4*c*Sqrt[b*x^2 + c*x^4])/(77*b*x^(9/2)) + (20*c^2*Sqrt[b*x^2 + c*x^4])/(231*b^2*x^(5/2)) + (10*c^(11/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*b^(9/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,21,0.2381,1,"{2020, 2025, 2032, 329, 220}"
364,1,350,0,0.4335558,"\int x^{3/2} \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^(3/2)*(b*x^2 + c*x^4)^(3/2),x]","\frac{56 b^4 x^{3/2} \left(b+c x^2\right)}{1105 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{56 b^3 \sqrt{x} \sqrt{b x^2+c x^4}}{3315 c^2}+\frac{28 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{56 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 x^{5/2} \sqrt{b x^2+c x^4}}{663 c}+\frac{12}{221} b x^{9/2} \sqrt{b x^2+c x^4}+\frac{2}{17} x^{5/2} \left(b x^2+c x^4\right)^{3/2}","\frac{56 b^4 x^{3/2} \left(b+c x^2\right)}{1105 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{56 b^3 \sqrt{x} \sqrt{b x^2+c x^4}}{3315 c^2}+\frac{28 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{56 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 x^{5/2} \sqrt{b x^2+c x^4}}{663 c}+\frac{12}{221} b x^{9/2} \sqrt{b x^2+c x^4}+\frac{2}{17} x^{5/2} \left(b x^2+c x^4\right)^{3/2}",1,"(56*b^4*x^(3/2)*(b + c*x^2))/(1105*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (56*b^3*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(3315*c^2) + (8*b^2*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(663*c) + (12*b*x^(9/2)*Sqrt[b*x^2 + c*x^4])/221 + (2*x^(5/2)*(b*x^2 + c*x^4)^(3/2))/17 - (56*b^(17/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(1105*c^(11/4)*Sqrt[b*x^2 + c*x^4]) + (28*b^(17/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(1105*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",9,7,21,0.3333,1,"{2021, 2024, 2032, 329, 305, 220, 1196}"
365,1,203,0,0.2892788,"\int \sqrt{x} \left(b x^2+c x^4\right)^{3/2} \, dx","Int[Sqrt[x]*(b*x^2 + c*x^4)^(3/2),x]","-\frac{8 b^3 \sqrt{b x^2+c x^4}}{231 c^2 \sqrt{x}}+\frac{4 b^{15/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 x^{3/2} \sqrt{b x^2+c x^4}}{385 c}+\frac{4}{55} b x^{7/2} \sqrt{b x^2+c x^4}+\frac{2}{15} x^{3/2} \left(b x^2+c x^4\right)^{3/2}","-\frac{8 b^3 \sqrt{b x^2+c x^4}}{231 c^2 \sqrt{x}}+\frac{4 b^{15/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 x^{3/2} \sqrt{b x^2+c x^4}}{385 c}+\frac{4}{55} b x^{7/2} \sqrt{b x^2+c x^4}+\frac{2}{15} x^{3/2} \left(b x^2+c x^4\right)^{3/2}",1,"(-8*b^3*Sqrt[b*x^2 + c*x^4])/(231*c^2*Sqrt[x]) + (8*b^2*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(385*c) + (4*b*x^(7/2)*Sqrt[b*x^2 + c*x^4])/55 + (2*x^(3/2)*(b*x^2 + c*x^4)^(3/2))/15 + (4*b^(15/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",7,5,21,0.2381,1,"{2021, 2024, 2032, 329, 220}"
366,1,320,0,0.3699913,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{\sqrt{x}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/Sqrt[x],x]","-\frac{8 b^3 x^{3/2} \left(b+c x^2\right)}{65 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{4 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 \sqrt{x} \sqrt{b x^2+c x^4}}{195 c}+\frac{4}{39} b x^{5/2} \sqrt{b x^2+c x^4}+\frac{2}{13} \sqrt{x} \left(b x^2+c x^4\right)^{3/2}","-\frac{8 b^3 x^{3/2} \left(b+c x^2\right)}{65 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{4 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 \sqrt{x} \sqrt{b x^2+c x^4}}{195 c}+\frac{4}{39} b x^{5/2} \sqrt{b x^2+c x^4}+\frac{2}{13} \sqrt{x} \left(b x^2+c x^4\right)^{3/2}",1,"(-8*b^3*x^(3/2)*(b + c*x^2))/(65*c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (8*b^2*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(195*c) + (4*b*x^(5/2)*Sqrt[b*x^2 + c*x^4])/39 + (2*Sqrt[x]*(b*x^2 + c*x^4)^(3/2))/13 + (8*b^(13/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(65*c^(7/4)*Sqrt[b*x^2 + c*x^4]) - (4*b^(13/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(65*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,21,0.3333,1,"{2021, 2024, 2032, 329, 305, 220, 1196}"
367,1,173,0,0.2355174,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{3/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(3/2),x]","-\frac{4 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{5/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 \sqrt{b x^2+c x^4}}{77 c \sqrt{x}}+\frac{12}{77} b x^{3/2} \sqrt{b x^2+c x^4}+\frac{2 \left(b x^2+c x^4\right)^{3/2}}{11 \sqrt{x}}","-\frac{4 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{5/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 \sqrt{b x^2+c x^4}}{77 c \sqrt{x}}+\frac{12}{77} b x^{3/2} \sqrt{b x^2+c x^4}+\frac{2 \left(b x^2+c x^4\right)^{3/2}}{11 \sqrt{x}}",1,"(8*b^2*Sqrt[b*x^2 + c*x^4])/(77*c*Sqrt[x]) + (12*b*x^(3/2)*Sqrt[b*x^2 + c*x^4])/77 + (2*(b*x^2 + c*x^4)^(3/2))/(11*Sqrt[x]) - (4*b^(11/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(77*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,21,0.2381,1,"{2021, 2024, 2032, 329, 220}"
368,1,290,0,0.2986593,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{5/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(5/2),x]","\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 x^{3/2} \left(b+c x^2\right)}{15 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{4}{15} b \sqrt{x} \sqrt{b x^2+c x^4}+\frac{2 \left(b x^2+c x^4\right)^{3/2}}{9 x^{3/2}}","\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{8 b^2 x^{3/2} \left(b+c x^2\right)}{15 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{4}{15} b \sqrt{x} \sqrt{b x^2+c x^4}+\frac{2 \left(b x^2+c x^4\right)^{3/2}}{9 x^{3/2}}",1,"(8*b^2*x^(3/2)*(b + c*x^2))/(15*Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (4*b*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/15 + (2*(b*x^2 + c*x^4)^(3/2))/(9*x^(3/2)) - (8*b^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[b*x^2 + c*x^4]) + (4*b^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",7,6,21,0.2857,1,"{2021, 2032, 329, 305, 220, 1196}"
369,1,143,0,0.1848489,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{7/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(7/2),x]","\frac{4 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{4 b \sqrt{b x^2+c x^4}}{7 \sqrt{x}}+\frac{2 \left(b x^2+c x^4\right)^{3/2}}{7 x^{5/2}}","\frac{4 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{4 b \sqrt{b x^2+c x^4}}{7 \sqrt{x}}+\frac{2 \left(b x^2+c x^4\right)^{3/2}}{7 x^{5/2}}",1,"(4*b*Sqrt[b*x^2 + c*x^4])/(7*Sqrt[x]) + (2*(b*x^2 + c*x^4)^(3/2))/(7*x^(5/2)) + (4*b^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(7*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",5,4,21,0.1905,1,"{2021, 2032, 329, 220}"
370,1,286,0,0.3010893,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{9/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(9/2),x]","\frac{12 b^{5/4} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{24 b^{5/4} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}+\frac{24 b \sqrt{c} x^{3/2} \left(b+c x^2\right)}{5 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{12}{5} c \sqrt{x} \sqrt{b x^2+c x^4}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{x^{7/2}}","\frac{12 b^{5/4} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{24 b^{5/4} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}+\frac{24 b \sqrt{c} x^{3/2} \left(b+c x^2\right)}{5 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{12}{5} c \sqrt{x} \sqrt{b x^2+c x^4}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{x^{7/2}}",1,"(24*b*Sqrt[c]*x^(3/2)*(b + c*x^2))/(5*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (12*c*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/5 - (2*(b*x^2 + c*x^4)^(3/2))/x^(7/2) - (24*b^(5/4)*c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*Sqrt[b*x^2 + c*x^4]) + (12*b^(5/4)*c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*Sqrt[b*x^2 + c*x^4])","A",7,7,21,0.3333,1,"{2020, 2021, 2032, 329, 305, 220, 1196}"
371,1,143,0,0.1879462,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{11/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(11/2),x]","\frac{4 b^{3/4} c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{3 x^{9/2}}+\frac{4 c \sqrt{b x^2+c x^4}}{3 \sqrt{x}}","\frac{4 b^{3/4} c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{3 x^{9/2}}+\frac{4 c \sqrt{b x^2+c x^4}}{3 \sqrt{x}}",1,"(4*c*Sqrt[b*x^2 + c*x^4])/(3*Sqrt[x]) - (2*(b*x^2 + c*x^4)^(3/2))/(3*x^(9/2)) + (4*b^(3/4)*c^(3/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*Sqrt[b*x^2 + c*x^4])","A",5,5,21,0.2381,1,"{2020, 2021, 2032, 329, 220}"
372,1,287,0,0.3045923,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{13/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(13/2),x]","\frac{24 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{12 \sqrt[4]{b} c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{24 \sqrt[4]{b} c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{12 c \sqrt{b x^2+c x^4}}{5 x^{3/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{5 x^{11/2}}","\frac{24 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{12 \sqrt[4]{b} c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{24 \sqrt[4]{b} c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{12 c \sqrt{b x^2+c x^4}}{5 x^{3/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{5 x^{11/2}}",1,"(24*c^(3/2)*x^(3/2)*(b + c*x^2))/(5*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (12*c*Sqrt[b*x^2 + c*x^4])/(5*x^(3/2)) - (2*(b*x^2 + c*x^4)^(3/2))/(5*x^(11/2)) - (24*b^(1/4)*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*Sqrt[b*x^2 + c*x^4]) + (12*b^(1/4)*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*Sqrt[b*x^2 + c*x^4])","A",7,6,21,0.2857,1,"{2020, 2032, 329, 305, 220, 1196}"
373,1,143,0,0.1833804,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{15/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(15/2),x]","\frac{4 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{7 x^{5/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{7 x^{13/2}}","\frac{4 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4}}{7 x^{5/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{7 x^{13/2}}",1,"(-4*c*Sqrt[b*x^2 + c*x^4])/(7*x^(5/2)) - (2*(b*x^2 + c*x^4)^(3/2))/(7*x^(13/2)) + (4*c^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(7*b^(1/4)*Sqrt[b*x^2 + c*x^4])","A",5,4,21,0.1905,1,"{2020, 2032, 329, 220}"
374,1,320,0,0.3598145,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{17/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(17/2),x]","\frac{4 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{8 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{15 b x^{3/2}}-\frac{4 c \sqrt{b x^2+c x^4}}{15 x^{7/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{9 x^{15/2}}","\frac{4 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{8 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{15 b x^{3/2}}-\frac{4 c \sqrt{b x^2+c x^4}}{15 x^{7/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{9 x^{15/2}}",1,"(8*c^(5/2)*x^(3/2)*(b + c*x^2))/(15*b*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (4*c*Sqrt[b*x^2 + c*x^4])/(15*x^(7/2)) - (8*c^2*Sqrt[b*x^2 + c*x^4])/(15*b*x^(3/2)) - (2*(b*x^2 + c*x^4)^(3/2))/(9*x^(15/2)) - (8*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[b*x^2 + c*x^4]) + (4*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,21,0.3333,1,"{2020, 2025, 2032, 329, 305, 220, 1196}"
375,1,173,0,0.2371281,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{19/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(19/2),x]","-\frac{4 c^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{77 b x^{5/2}}-\frac{12 c \sqrt{b x^2+c x^4}}{77 x^{9/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{11 x^{17/2}}","-\frac{4 c^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{77 b x^{5/2}}-\frac{12 c \sqrt{b x^2+c x^4}}{77 x^{9/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{11 x^{17/2}}",1,"(-12*c*Sqrt[b*x^2 + c*x^4])/(77*x^(9/2)) - (8*c^2*Sqrt[b*x^2 + c*x^4])/(77*b*x^(5/2)) - (2*(b*x^2 + c*x^4)^(3/2))/(11*x^(17/2)) - (4*c^(11/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(77*b^(5/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,21,0.2381,1,"{2020, 2025, 2032, 329, 220}"
376,1,350,0,0.4262435,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{21/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(21/2),x]","-\frac{8 c^{7/2} x^{3/2} \left(b+c x^2\right)}{65 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{8 c^3 \sqrt{b x^2+c x^4}}{65 b^2 x^{3/2}}-\frac{4 c^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 c^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{195 b x^{7/2}}-\frac{4 c \sqrt{b x^2+c x^4}}{39 x^{11/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{13 x^{19/2}}","-\frac{8 c^{7/2} x^{3/2} \left(b+c x^2\right)}{65 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{8 c^3 \sqrt{b x^2+c x^4}}{65 b^2 x^{3/2}}-\frac{4 c^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 c^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{195 b x^{7/2}}-\frac{4 c \sqrt{b x^2+c x^4}}{39 x^{11/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{13 x^{19/2}}",1,"(-8*c^(7/2)*x^(3/2)*(b + c*x^2))/(65*b^2*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (4*c*Sqrt[b*x^2 + c*x^4])/(39*x^(11/2)) - (8*c^2*Sqrt[b*x^2 + c*x^4])/(195*b*x^(7/2)) + (8*c^3*Sqrt[b*x^2 + c*x^4])/(65*b^2*x^(3/2)) - (2*(b*x^2 + c*x^4)^(3/2))/(13*x^(19/2)) + (8*c^(13/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(65*b^(7/4)*Sqrt[b*x^2 + c*x^4]) - (4*c^(13/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(65*b^(7/4)*Sqrt[b*x^2 + c*x^4])","A",9,7,21,0.3333,1,"{2020, 2025, 2032, 329, 305, 220, 1196}"
377,1,203,0,0.2957409,"\int \frac{\left(b x^2+c x^4\right)^{3/2}}{x^{23/2}} \, dx","Int[(b*x^2 + c*x^4)^(3/2)/x^(23/2),x]","\frac{8 c^3 \sqrt{b x^2+c x^4}}{231 b^2 x^{5/2}}+\frac{4 c^{15/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{385 b x^{9/2}}-\frac{4 c \sqrt{b x^2+c x^4}}{55 x^{13/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{15 x^{21/2}}","\frac{8 c^3 \sqrt{b x^2+c x^4}}{231 b^2 x^{5/2}}+\frac{4 c^{15/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{8 c^2 \sqrt{b x^2+c x^4}}{385 b x^{9/2}}-\frac{4 c \sqrt{b x^2+c x^4}}{55 x^{13/2}}-\frac{2 \left(b x^2+c x^4\right)^{3/2}}{15 x^{21/2}}",1,"(-4*c*Sqrt[b*x^2 + c*x^4])/(55*x^(13/2)) - (8*c^2*Sqrt[b*x^2 + c*x^4])/(385*b*x^(9/2)) + (8*c^3*Sqrt[b*x^2 + c*x^4])/(231*b^2*x^(5/2)) - (2*(b*x^2 + c*x^4)^(3/2))/(15*x^(21/2)) + (4*c^(15/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*b^(9/4)*Sqrt[b*x^2 + c*x^4])","A",7,5,21,0.2381,1,"{2020, 2025, 2032, 329, 220}"
378,1,179,0,0.2440539,"\int \frac{x^{13/2}}{\sqrt{b x^2+c x^4}} \, dx","Int[x^(13/2)/Sqrt[b*x^2 + c*x^4],x]","\frac{30 b^2 \sqrt{b x^2+c x^4}}{77 c^3 \sqrt{x}}-\frac{15 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{18 b x^{3/2} \sqrt{b x^2+c x^4}}{77 c^2}+\frac{2 x^{7/2} \sqrt{b x^2+c x^4}}{11 c}","\frac{30 b^2 \sqrt{b x^2+c x^4}}{77 c^3 \sqrt{x}}-\frac{15 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{18 b x^{3/2} \sqrt{b x^2+c x^4}}{77 c^2}+\frac{2 x^{7/2} \sqrt{b x^2+c x^4}}{11 c}",1,"(30*b^2*Sqrt[b*x^2 + c*x^4])/(77*c^3*Sqrt[x]) - (18*b*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(77*c^2) + (2*x^(7/2)*Sqrt[b*x^2 + c*x^4])/(11*c) - (15*b^(11/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(77*c^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,4,21,0.1905,1,"{2024, 2032, 329, 220}"
379,1,296,0,0.2978917,"\int \frac{x^{11/2}}{\sqrt{b x^2+c x^4}} \, dx","Int[x^(11/2)/Sqrt[b*x^2 + c*x^4],x]","\frac{14 b^2 x^{3/2} \left(b+c x^2\right)}{15 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{7 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{14 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{14 b \sqrt{x} \sqrt{b x^2+c x^4}}{45 c^2}+\frac{2 x^{5/2} \sqrt{b x^2+c x^4}}{9 c}","\frac{14 b^2 x^{3/2} \left(b+c x^2\right)}{15 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{7 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{14 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{14 b \sqrt{x} \sqrt{b x^2+c x^4}}{45 c^2}+\frac{2 x^{5/2} \sqrt{b x^2+c x^4}}{9 c}",1,"(14*b^2*x^(3/2)*(b + c*x^2))/(15*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (14*b*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(45*c^2) + (2*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(9*c) - (14*b^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(11/4)*Sqrt[b*x^2 + c*x^4]) + (7*b^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",7,6,21,0.2857,1,"{2024, 2032, 329, 305, 220, 1196}"
380,1,149,0,0.1834992,"\int \frac{x^{9/2}}{\sqrt{b x^2+c x^4}} \, dx","Int[x^(9/2)/Sqrt[b*x^2 + c*x^4],x]","\frac{5 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{10 b \sqrt{b x^2+c x^4}}{21 c^2 \sqrt{x}}+\frac{2 x^{3/2} \sqrt{b x^2+c x^4}}{7 c}","\frac{5 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{10 b \sqrt{b x^2+c x^4}}{21 c^2 \sqrt{x}}+\frac{2 x^{3/2} \sqrt{b x^2+c x^4}}{7 c}",1,"(-10*b*Sqrt[b*x^2 + c*x^4])/(21*c^2*Sqrt[x]) + (2*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(7*c) + (5*b^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",5,4,21,0.1905,1,"{2024, 2032, 329, 220}"
381,1,266,0,0.2366163,"\int \frac{x^{7/2}}{\sqrt{b x^2+c x^4}} \, dx","Int[x^(7/2)/Sqrt[b*x^2 + c*x^4],x]","-\frac{3 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{6 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{6 b x^{3/2} \left(b+c x^2\right)}{5 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{x} \sqrt{b x^2+c x^4}}{5 c}","-\frac{3 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{6 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{6 b x^{3/2} \left(b+c x^2\right)}{5 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{x} \sqrt{b x^2+c x^4}}{5 c}",1,"(-6*b*x^(3/2)*(b + c*x^2))/(5*c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (2*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(5*c) + (6*b^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(7/4)*Sqrt[b*x^2 + c*x^4]) - (3*b^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,21,0.2857,1,"{2024, 2032, 329, 305, 220, 1196}"
382,1,121,0,0.1310165,"\int \frac{x^{5/2}}{\sqrt{b x^2+c x^4}} \, dx","Int[x^(5/2)/Sqrt[b*x^2 + c*x^4],x]","\frac{2 \sqrt{b x^2+c x^4}}{3 c \sqrt{x}}-\frac{b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 c^{5/4} \sqrt{b x^2+c x^4}}","\frac{2 \sqrt{b x^2+c x^4}}{3 c \sqrt{x}}-\frac{b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 c^{5/4} \sqrt{b x^2+c x^4}}",1,"(2*Sqrt[b*x^2 + c*x^4])/(3*c*Sqrt[x]) - (b^(3/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,21,0.1905,1,"{2024, 2032, 329, 220}"
383,1,231,0,0.1762289,"\int \frac{x^{3/2}}{\sqrt{b x^2+c x^4}} \, dx","Int[x^(3/2)/Sqrt[b*x^2 + c*x^4],x]","\frac{\sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 x^{3/2} \left(b+c x^2\right)}{\sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}","\frac{\sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 x^{3/2} \left(b+c x^2\right)}{\sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}",1,"(2*x^(3/2)*(b + c*x^2))/(Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*b^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(c^(3/4)*Sqrt[b*x^2 + c*x^4]) + (b^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,21,0.2381,1,"{2032, 329, 305, 220, 1196}"
384,1,90,0,0.0890293,"\int \frac{\sqrt{x}}{\sqrt{b x^2+c x^4}} \, dx","Int[Sqrt[x]/Sqrt[b*x^2 + c*x^4],x]","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b} \sqrt[4]{c} \sqrt{b x^2+c x^4}}","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{b} \sqrt[4]{c} \sqrt{b x^2+c x^4}}",1,"(x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(1/4)*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",3,3,21,0.1429,1,"{2032, 329, 220}"
385,1,259,0,0.2315564,"\int \frac{1}{\sqrt{x} \sqrt{b x^2+c x^4}} \, dx","Int[1/(Sqrt[x]*Sqrt[b*x^2 + c*x^4]),x]","\frac{\sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{c} x^{3/2} \left(b+c x^2\right)}{b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{b x^{3/2}}","\frac{\sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{c} x^{3/2} \left(b+c x^2\right)}{b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{b x^{3/2}}",1,"(2*Sqrt[c]*x^(3/2)*(b + c*x^2))/(b*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*Sqrt[b*x^2 + c*x^4])/(b*x^(3/2)) - (2*c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(3/4)*Sqrt[b*x^2 + c*x^4]) + (c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(3/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,21,0.2857,1,"{2025, 2032, 329, 305, 220, 1196}"
386,1,121,0,0.1334157,"\int \frac{1}{x^{3/2} \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^(3/2)*Sqrt[b*x^2 + c*x^4]),x]","-\frac{c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{3 b x^{5/2}}","-\frac{c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4}}{3 b x^{5/2}}",1,"(-2*Sqrt[b*x^2 + c*x^4])/(3*b*x^(5/2)) - (c^(3/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*b^(5/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,21,0.1905,1,"{2025, 2032, 329, 220}"
387,1,296,0,0.2936967,"\int \frac{1}{x^{5/2} \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^(5/2)*Sqrt[b*x^2 + c*x^4]),x]","-\frac{6 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{3 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{6 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{6 c \sqrt{b x^2+c x^4}}{5 b^2 x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4}}{5 b x^{7/2}}","-\frac{6 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{3 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{6 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}+\frac{6 c \sqrt{b x^2+c x^4}}{5 b^2 x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4}}{5 b x^{7/2}}",1,"(-6*c^(3/2)*x^(3/2)*(b + c*x^2))/(5*b^2*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*Sqrt[b*x^2 + c*x^4])/(5*b*x^(7/2)) + (6*c*Sqrt[b*x^2 + c*x^4])/(5*b^2*x^(3/2)) + (6*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[b*x^2 + c*x^4]) - (3*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[b*x^2 + c*x^4])","A",7,6,21,0.2857,1,"{2025, 2032, 329, 305, 220, 1196}"
388,1,149,0,0.1816347,"\int \frac{1}{x^{7/2} \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^(7/2)*Sqrt[b*x^2 + c*x^4]),x]","\frac{5 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{b x^2+c x^4}}+\frac{10 c \sqrt{b x^2+c x^4}}{21 b^2 x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4}}{7 b x^{9/2}}","\frac{5 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{b x^2+c x^4}}+\frac{10 c \sqrt{b x^2+c x^4}}{21 b^2 x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4}}{7 b x^{9/2}}",1,"(-2*Sqrt[b*x^2 + c*x^4])/(7*b*x^(9/2)) + (10*c*Sqrt[b*x^2 + c*x^4])/(21*b^2*x^(5/2)) + (5*c^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*b^(9/4)*Sqrt[b*x^2 + c*x^4])","A",5,4,21,0.1905,1,"{2025, 2032, 329, 220}"
389,1,326,0,0.3586235,"\int \frac{1}{x^{9/2} \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^(9/2)*Sqrt[b*x^2 + c*x^4]),x]","\frac{14 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{14 c^2 \sqrt{b x^2+c x^4}}{15 b^3 x^{3/2}}+\frac{7 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}-\frac{14 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{14 c \sqrt{b x^2+c x^4}}{45 b^2 x^{7/2}}-\frac{2 \sqrt{b x^2+c x^4}}{9 b x^{11/2}}","\frac{14 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{14 c^2 \sqrt{b x^2+c x^4}}{15 b^3 x^{3/2}}+\frac{7 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}-\frac{14 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{14 c \sqrt{b x^2+c x^4}}{45 b^2 x^{7/2}}-\frac{2 \sqrt{b x^2+c x^4}}{9 b x^{11/2}}",1,"(14*c^(5/2)*x^(3/2)*(b + c*x^2))/(15*b^3*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*Sqrt[b*x^2 + c*x^4])/(9*b*x^(11/2)) + (14*c*Sqrt[b*x^2 + c*x^4])/(45*b^2*x^(7/2)) - (14*c^2*Sqrt[b*x^2 + c*x^4])/(15*b^3*x^(3/2)) - (14*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(11/4)*Sqrt[b*x^2 + c*x^4]) + (7*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(11/4)*Sqrt[b*x^2 + c*x^4])","A",8,6,21,0.2857,1,"{2025, 2032, 329, 305, 220, 1196}"
390,1,179,0,0.2331158,"\int \frac{1}{x^{11/2} \sqrt{b x^2+c x^4}} \, dx","Int[1/(x^(11/2)*Sqrt[b*x^2 + c*x^4]),x]","-\frac{30 c^2 \sqrt{b x^2+c x^4}}{77 b^3 x^{5/2}}-\frac{15 c^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{13/4} \sqrt{b x^2+c x^4}}+\frac{18 c \sqrt{b x^2+c x^4}}{77 b^2 x^{9/2}}-\frac{2 \sqrt{b x^2+c x^4}}{11 b x^{13/2}}","-\frac{30 c^2 \sqrt{b x^2+c x^4}}{77 b^3 x^{5/2}}-\frac{15 c^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{13/4} \sqrt{b x^2+c x^4}}+\frac{18 c \sqrt{b x^2+c x^4}}{77 b^2 x^{9/2}}-\frac{2 \sqrt{b x^2+c x^4}}{11 b x^{13/2}}",1,"(-2*Sqrt[b*x^2 + c*x^4])/(11*b*x^(13/2)) + (18*c*Sqrt[b*x^2 + c*x^4])/(77*b^2*x^(9/2)) - (30*c^2*Sqrt[b*x^2 + c*x^4])/(77*b^3*x^(5/2)) - (15*c^(11/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(77*b^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,4,21,0.1905,1,"{2025, 2032, 329, 220}"
391,1,174,0,0.2424468,"\int \frac{x^{17/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(17/2)/(b*x^2 + c*x^4)^(3/2),x]","\frac{15 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14 c^{13/4} \sqrt{b x^2+c x^4}}+\frac{9 x^{3/2} \sqrt{b x^2+c x^4}}{7 c^2}-\frac{15 b \sqrt{b x^2+c x^4}}{7 c^3 \sqrt{x}}-\frac{x^{11/2}}{c \sqrt{b x^2+c x^4}}","\frac{15 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14 c^{13/4} \sqrt{b x^2+c x^4}}+\frac{9 x^{3/2} \sqrt{b x^2+c x^4}}{7 c^2}-\frac{15 b \sqrt{b x^2+c x^4}}{7 c^3 \sqrt{x}}-\frac{x^{11/2}}{c \sqrt{b x^2+c x^4}}",1,"-(x^(11/2)/(c*Sqrt[b*x^2 + c*x^4])) - (15*b*Sqrt[b*x^2 + c*x^4])/(7*c^3*Sqrt[x]) + (9*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(7*c^2) + (15*b^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(14*c^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,21,0.2381,1,"{2022, 2024, 2032, 329, 220}"
392,1,291,0,0.2964801,"\int \frac{x^{15/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(15/2)/(b*x^2 + c*x^4)^(3/2),x]","-\frac{21 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{21 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{21 b x^{3/2} \left(b+c x^2\right)}{5 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{7 \sqrt{x} \sqrt{b x^2+c x^4}}{5 c^2}-\frac{x^{9/2}}{c \sqrt{b x^2+c x^4}}","-\frac{21 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{21 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{21 b x^{3/2} \left(b+c x^2\right)}{5 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{7 \sqrt{x} \sqrt{b x^2+c x^4}}{5 c^2}-\frac{x^{9/2}}{c \sqrt{b x^2+c x^4}}",1,"-(x^(9/2)/(c*Sqrt[b*x^2 + c*x^4])) - (21*b*x^(3/2)*(b + c*x^2))/(5*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (7*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(5*c^2) + (21*b^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(11/4)*Sqrt[b*x^2 + c*x^4]) - (21*b^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(10*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,21,0.3333,1,"{2022, 2024, 2032, 329, 305, 220, 1196}"
393,1,146,0,0.1850856,"\int \frac{x^{13/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(13/2)/(b*x^2 + c*x^4)^(3/2),x]","-\frac{5 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 c^{9/4} \sqrt{b x^2+c x^4}}+\frac{5 \sqrt{b x^2+c x^4}}{3 c^2 \sqrt{x}}-\frac{x^{7/2}}{c \sqrt{b x^2+c x^4}}","-\frac{5 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 c^{9/4} \sqrt{b x^2+c x^4}}+\frac{5 \sqrt{b x^2+c x^4}}{3 c^2 \sqrt{x}}-\frac{x^{7/2}}{c \sqrt{b x^2+c x^4}}",1,"-(x^(7/2)/(c*Sqrt[b*x^2 + c*x^4])) + (5*Sqrt[b*x^2 + c*x^4])/(3*c^2*Sqrt[x]) - (5*b^(3/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(6*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,21,0.2381,1,"{2022, 2024, 2032, 329, 220}"
394,1,259,0,0.2340802,"\int \frac{x^{11/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(11/2)/(b*x^2 + c*x^4)^(3/2),x]","\frac{3 x^{3/2} \left(b+c x^2\right)}{c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt{b x^2+c x^4}}-\frac{x^{5/2}}{c \sqrt{b x^2+c x^4}}","\frac{3 x^{3/2} \left(b+c x^2\right)}{c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt{b x^2+c x^4}}-\frac{x^{5/2}}{c \sqrt{b x^2+c x^4}}",1,"-(x^(5/2)/(c*Sqrt[b*x^2 + c*x^4])) + (3*x^(3/2)*(b + c*x^2))/(c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (3*b^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(c^(7/4)*Sqrt[b*x^2 + c*x^4]) + (3*b^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,21,0.2857,1,"{2022, 2032, 329, 305, 220, 1196}"
395,1,119,0,0.1382635,"\int \frac{x^{9/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(9/2)/(b*x^2 + c*x^4)^(3/2),x]","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} c^{5/4} \sqrt{b x^2+c x^4}}-\frac{x^{3/2}}{c \sqrt{b x^2+c x^4}}","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{b} c^{5/4} \sqrt{b x^2+c x^4}}-\frac{x^{3/2}}{c \sqrt{b x^2+c x^4}}",1,"-(x^(3/2)/(c*Sqrt[b*x^2 + c*x^4])) + (x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*b^(1/4)*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,21,0.1905,1,"{2022, 2032, 329, 220}"
396,1,260,0,0.2368345,"\int \frac{x^{7/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(7/2)/(b*x^2 + c*x^4)^(3/2),x]","-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x^{5/2}}{b \sqrt{b x^2+c x^4}}-\frac{x^{3/2} \left(b+c x^2\right)}{b \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}","-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x^{5/2}}{b \sqrt{b x^2+c x^4}}-\frac{x^{3/2} \left(b+c x^2\right)}{b \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}",1,"x^(5/2)/(b*Sqrt[b*x^2 + c*x^4]) - (x^(3/2)*(b + c*x^2))/(b*Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(3/4)*c^(3/4)*Sqrt[b*x^2 + c*x^4]) - (x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*b^(3/4)*c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,21,0.2857,1,"{2023, 2032, 329, 305, 220, 1196}"
397,1,118,0,0.1364536,"\int \frac{x^{5/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(5/2)/(b*x^2 + c*x^4)^(3/2),x]","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{5/4} \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{x^{3/2}}{b \sqrt{b x^2+c x^4}}","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{5/4} \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{x^{3/2}}{b \sqrt{b x^2+c x^4}}",1,"x^(3/2)/(b*Sqrt[b*x^2 + c*x^4]) + (x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*b^(5/4)*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,21,0.1905,1,"{2023, 2032, 329, 220}"
398,1,286,0,0.298486,"\int \frac{x^{3/2}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[x^(3/2)/(b*x^2 + c*x^4)^(3/2),x]","\frac{3 \sqrt{c} x^{3/2} \left(b+c x^2\right)}{b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{3 \sqrt{b x^2+c x^4}}{b^2 x^{3/2}}+\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{7/4} \sqrt{b x^2+c x^4}}+\frac{\sqrt{x}}{b \sqrt{b x^2+c x^4}}","\frac{3 \sqrt{c} x^{3/2} \left(b+c x^2\right)}{b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{3 \sqrt{b x^2+c x^4}}{b^2 x^{3/2}}+\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{7/4} \sqrt{b x^2+c x^4}}+\frac{\sqrt{x}}{b \sqrt{b x^2+c x^4}}",1,"Sqrt[x]/(b*Sqrt[b*x^2 + c*x^4]) + (3*Sqrt[c]*x^(3/2)*(b + c*x^2))/(b^2*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (3*Sqrt[b*x^2 + c*x^4])/(b^2*x^(3/2)) - (3*c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(7/4)*Sqrt[b*x^2 + c*x^4]) + (3*c^(1/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*b^(7/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,21,0.3333,1,"{2023, 2025, 2032, 329, 305, 220, 1196}"
399,1,145,0,0.1846253,"\int \frac{\sqrt{x}}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[Sqrt[x]/(b*x^2 + c*x^4)^(3/2),x]","-\frac{5 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{5 \sqrt{b x^2+c x^4}}{3 b^2 x^{5/2}}+\frac{1}{b \sqrt{x} \sqrt{b x^2+c x^4}}","-\frac{5 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{5 \sqrt{b x^2+c x^4}}{3 b^2 x^{5/2}}+\frac{1}{b \sqrt{x} \sqrt{b x^2+c x^4}}",1,"1/(b*Sqrt[x]*Sqrt[b*x^2 + c*x^4]) - (5*Sqrt[b*x^2 + c*x^4])/(3*b^2*x^(5/2)) - (5*c^(3/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(6*b^(9/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,21,0.2381,1,"{2023, 2025, 2032, 329, 220}"
400,1,320,0,0.3640853,"\int \frac{1}{\sqrt{x} \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(Sqrt[x]*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{21 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{21 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{21 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{21 c \sqrt{b x^2+c x^4}}{5 b^3 x^{3/2}}-\frac{7 \sqrt{b x^2+c x^4}}{5 b^2 x^{7/2}}+\frac{1}{b x^{3/2} \sqrt{b x^2+c x^4}}","-\frac{21 c^{3/2} x^{3/2} \left(b+c x^2\right)}{5 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{21 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{21 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{21 c \sqrt{b x^2+c x^4}}{5 b^3 x^{3/2}}-\frac{7 \sqrt{b x^2+c x^4}}{5 b^2 x^{7/2}}+\frac{1}{b x^{3/2} \sqrt{b x^2+c x^4}}",1,"1/(b*x^(3/2)*Sqrt[b*x^2 + c*x^4]) - (21*c^(3/2)*x^(3/2)*(b + c*x^2))/(5*b^3*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (7*Sqrt[b*x^2 + c*x^4])/(5*b^2*x^(7/2)) + (21*c*Sqrt[b*x^2 + c*x^4])/(5*b^3*x^(3/2)) + (21*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(11/4)*Sqrt[b*x^2 + c*x^4]) - (21*c^(5/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(10*b^(11/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,21,0.3333,1,"{2023, 2025, 2032, 329, 305, 220, 1196}"
401,1,173,0,0.2332874,"\int \frac{1}{x^{3/2} \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^(3/2)*(b*x^2 + c*x^4)^(3/2)),x]","\frac{15 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14 b^{13/4} \sqrt{b x^2+c x^4}}+\frac{15 c \sqrt{b x^2+c x^4}}{7 b^3 x^{5/2}}-\frac{9 \sqrt{b x^2+c x^4}}{7 b^2 x^{9/2}}+\frac{1}{b x^{5/2} \sqrt{b x^2+c x^4}}","\frac{15 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14 b^{13/4} \sqrt{b x^2+c x^4}}+\frac{15 c \sqrt{b x^2+c x^4}}{7 b^3 x^{5/2}}-\frac{9 \sqrt{b x^2+c x^4}}{7 b^2 x^{9/2}}+\frac{1}{b x^{5/2} \sqrt{b x^2+c x^4}}",1,"1/(b*x^(5/2)*Sqrt[b*x^2 + c*x^4]) - (9*Sqrt[b*x^2 + c*x^4])/(7*b^2*x^(9/2)) + (15*c*Sqrt[b*x^2 + c*x^4])/(7*b^3*x^(5/2)) + (15*c^(7/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(14*b^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,21,0.2381,1,"{2023, 2025, 2032, 329, 220}"
402,1,350,0,0.4268548,"\int \frac{1}{x^{5/2} \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^(5/2)*(b*x^2 + c*x^4)^(3/2)),x]","\frac{77 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b^4 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{77 c^2 \sqrt{b x^2+c x^4}}{15 b^4 x^{3/2}}+\frac{77 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{30 b^{15/4} \sqrt{b x^2+c x^4}}-\frac{77 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{15/4} \sqrt{b x^2+c x^4}}+\frac{77 c \sqrt{b x^2+c x^4}}{45 b^3 x^{7/2}}-\frac{11 \sqrt{b x^2+c x^4}}{9 b^2 x^{11/2}}+\frac{1}{b x^{7/2} \sqrt{b x^2+c x^4}}","\frac{77 c^{5/2} x^{3/2} \left(b+c x^2\right)}{15 b^4 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{77 c^2 \sqrt{b x^2+c x^4}}{15 b^4 x^{3/2}}+\frac{77 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{30 b^{15/4} \sqrt{b x^2+c x^4}}-\frac{77 c^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{15/4} \sqrt{b x^2+c x^4}}+\frac{77 c \sqrt{b x^2+c x^4}}{45 b^3 x^{7/2}}-\frac{11 \sqrt{b x^2+c x^4}}{9 b^2 x^{11/2}}+\frac{1}{b x^{7/2} \sqrt{b x^2+c x^4}}",1,"1/(b*x^(7/2)*Sqrt[b*x^2 + c*x^4]) + (77*c^(5/2)*x^(3/2)*(b + c*x^2))/(15*b^4*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (11*Sqrt[b*x^2 + c*x^4])/(9*b^2*x^(11/2)) + (77*c*Sqrt[b*x^2 + c*x^4])/(45*b^3*x^(7/2)) - (77*c^2*Sqrt[b*x^2 + c*x^4])/(15*b^4*x^(3/2)) - (77*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(15/4)*Sqrt[b*x^2 + c*x^4]) + (77*c^(9/4)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(30*b^(15/4)*Sqrt[b*x^2 + c*x^4])","A",9,7,21,0.3333,1,"{2023, 2025, 2032, 329, 305, 220, 1196}"
403,1,73,0,0.0498427,"\int (c x)^m \left(b x^2+c x^4\right)^3 \, dx","Int[(c*x)^m*(b*x^2 + c*x^4)^3,x]","\frac{3 b^2 c x^9 (c x)^m}{m+9}+\frac{b^3 x^7 (c x)^m}{m+7}+\frac{3 b c^2 x^{11} (c x)^m}{m+11}+\frac{c^3 x^{13} (c x)^m}{m+13}","\frac{3 b^2 c x^9 (c x)^m}{m+9}+\frac{b^3 x^7 (c x)^m}{m+7}+\frac{3 b c^2 x^{11} (c x)^m}{m+11}+\frac{c^3 x^{13} (c x)^m}{m+13}",1,"(b^3*x^7*(c*x)^m)/(7 + m) + (3*b^2*c*x^9*(c*x)^m)/(9 + m) + (3*b*c^2*x^11*(c*x)^m)/(11 + m) + (c^3*x^13*(c*x)^m)/(13 + m)","A",4,3,19,0.1579,1,"{1142, 1584, 270}"
404,1,52,0,0.0394327,"\int (c x)^m \left(b x^2+c x^4\right)^2 \, dx","Int[(c*x)^m*(b*x^2 + c*x^4)^2,x]","\frac{b^2 x^5 (c x)^m}{m+5}+\frac{2 b c x^7 (c x)^m}{m+7}+\frac{c^2 x^9 (c x)^m}{m+9}","\frac{b^2 x^5 (c x)^m}{m+5}+\frac{2 b c x^7 (c x)^m}{m+7}+\frac{c^2 x^9 (c x)^m}{m+9}",1,"(b^2*x^5*(c*x)^m)/(5 + m) + (2*b*c*x^7*(c*x)^m)/(7 + m) + (c^2*x^9*(c*x)^m)/(9 + m)","A",4,3,19,0.1579,1,"{1142, 1584, 270}"
405,1,34,0,0.014332,"\int (c x)^m \left(b x^2+c x^4\right) \, dx","Int[(c*x)^m*(b*x^2 + c*x^4),x]","\frac{b (c x)^{m+3}}{c^3 (m+3)}+\frac{(c x)^{m+5}}{c^4 (m+5)}","\frac{b (c x)^{m+3}}{c^3 (m+3)}+\frac{(c x)^{m+5}}{c^4 (m+5)}",1,"(b*(c*x)^(3 + m))/(c^3*(3 + m)) + (c*x)^(5 + m)/(c^4*(5 + m))","A",2,1,17,0.05882,1,"{14}"
406,1,45,0,0.0322719,"\int \frac{(c x)^m}{b x^2+c x^4} \, dx","Int[(c*x)^m/(b*x^2 + c*x^4),x]","-\frac{(c x)^m \, _2F_1\left(1,\frac{m-1}{2};\frac{m+1}{2};-\frac{c x^2}{b}\right)}{b (1-m) x}","-\frac{(c x)^m \, _2F_1\left(1,\frac{m-1}{2};\frac{m+1}{2};-\frac{c x^2}{b}\right)}{b (1-m) x}",1,"-(((c*x)^m*Hypergeometric2F1[1, (-1 + m)/2, (1 + m)/2, -((c*x^2)/b)])/(b*(1 - m)*x))","A",3,3,19,0.1579,1,"{1142, 1584, 364}"
407,1,45,0,0.0307726,"\int \frac{(c x)^m}{\left(b x^2+c x^4\right)^2} \, dx","Int[(c*x)^m/(b*x^2 + c*x^4)^2,x]","-\frac{(c x)^m \, _2F_1\left(2,\frac{m-3}{2};\frac{m-1}{2};-\frac{c x^2}{b}\right)}{b^2 (3-m) x^3}","-\frac{(c x)^m \, _2F_1\left(2,\frac{m-3}{2};\frac{m-1}{2};-\frac{c x^2}{b}\right)}{b^2 (3-m) x^3}",1,"-(((c*x)^m*Hypergeometric2F1[2, (-3 + m)/2, (-1 + m)/2, -((c*x^2)/b)])/(b^2*(3 - m)*x^3))","A",3,3,19,0.1579,1,"{1142, 1584, 364}"
408,1,45,0,0.0314853,"\int \frac{(c x)^m}{\left(b x^2+c x^4\right)^3} \, dx","Int[(c*x)^m/(b*x^2 + c*x^4)^3,x]","-\frac{(c x)^m \, _2F_1\left(3,\frac{m-5}{2};\frac{m-3}{2};-\frac{c x^2}{b}\right)}{b^3 (5-m) x^5}","-\frac{(c x)^m \, _2F_1\left(3,\frac{m-5}{2};\frac{m-3}{2};-\frac{c x^2}{b}\right)}{b^3 (5-m) x^5}",1,"-(((c*x)^m*Hypergeometric2F1[3, (-5 + m)/2, (-3 + m)/2, -((c*x^2)/b)])/(b^3*(5 - m)*x^5))","A",3,3,19,0.1579,1,"{1142, 1584, 364}"
409,1,30,0,0.0095719,"\int x^3 \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[x^3*(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8}","\frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8}",1,"(a^2*x^4)/4 + (a*b*x^6)/3 + (b^2*x^8)/8","A",2,1,22,0.04545,1,"{14}"
410,1,30,0,0.0090823,"\int x^2 \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[x^2*(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}","\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}",1,"(a^2*x^3)/3 + (2*a*b*x^5)/5 + (b^2*x^7)/7","A",2,1,22,0.04545,1,"{14}"
411,1,30,0,0.0094222,"\int x \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[x*(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{a^2 x^2}{2}+\frac{1}{2} a b x^4+\frac{b^2 x^6}{6}","\frac{a^2 x^2}{2}+\frac{1}{2} a b x^4+\frac{b^2 x^6}{6}",1,"(a^2*x^2)/2 + (a*b*x^4)/2 + (b^2*x^6)/6","A",2,1,20,0.05000,1,"{14}"
412,1,25,0,0.0049772,"\int \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[a^2 + 2*a*b*x^2 + b^2*x^4,x]","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}",1,"a^2*x + (2*a*b*x^3)/3 + (b^2*x^5)/5","A",1,0,18,0,1,"{}"
413,1,23,0,0.0072947,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x,x]","a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4}","a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4}",1,"a*b*x^2 + (b^2*x^4)/4 + a^2*Log[x]","A",2,1,22,0.04545,1,"{14}"
414,1,24,0,0.008317,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x^2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x^2,x]","-\frac{a^2}{x}+2 a b x+\frac{b^2 x^3}{3}","-\frac{a^2}{x}+2 a b x+\frac{b^2 x^3}{3}",1,"-(a^2/x) + 2*a*b*x + (b^2*x^3)/3","A",2,1,22,0.04545,1,"{14}"
415,1,27,0,0.0091011,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x^3} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x^3,x]","-\frac{a^2}{2 x^2}+2 a b \log (x)+\frac{b^2 x^2}{2}","-\frac{a^2}{2 x^2}+2 a b \log (x)+\frac{b^2 x^2}{2}",1,"-a^2/(2*x^2) + (b^2*x^2)/2 + 2*a*b*Log[x]","A",2,1,22,0.04545,1,"{14}"
416,1,23,0,0.0089646,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x^4,x]","-\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x","-\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x",1,"-a^2/(3*x^3) - (2*a*b)/x + b^2*x","A",2,1,22,0.04545,1,"{14}"
417,1,24,0,0.009459,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x^5} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x^5,x]","-\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x)","-\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x)",1,"-a^2/(4*x^4) - (a*b)/x^2 + b^2*Log[x]","A",2,1,22,0.04545,1,"{14}"
418,1,28,0,0.0096647,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x^6} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x^6,x]","-\frac{a^2}{5 x^5}-\frac{2 a b}{3 x^3}-\frac{b^2}{x}","-\frac{a^2}{5 x^5}-\frac{2 a b}{3 x^3}-\frac{b^2}{x}",1,"-a^2/(5*x^5) - (2*a*b)/(3*x^3) - b^2/x","A",2,1,22,0.04545,1,"{14}"
419,1,30,0,0.0089832,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x^7} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x^7,x]","-\frac{a^2}{6 x^6}-\frac{a b}{2 x^4}-\frac{b^2}{2 x^2}","-\frac{a^2}{6 x^6}-\frac{a b}{2 x^4}-\frac{b^2}{2 x^2}",1,"-a^2/(6*x^6) - (a*b)/(2*x^4) - b^2/(2*x^2)","A",2,1,22,0.04545,1,"{14}"
420,1,30,0,0.0094775,"\int \frac{a^2+2 a b x^2+b^2 x^4}{x^8} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/x^8,x]","-\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3}","-\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3}",1,"-a^2/(7*x^7) - (2*a*b)/(5*x^5) - b^2/(3*x^3)","A",2,1,22,0.04545,1,"{14}"
421,1,56,0,0.0283449,"\int x^6 \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{6}{11} a^2 b^2 x^{11}+\frac{4}{9} a^3 b x^9+\frac{a^4 x^7}{7}+\frac{4}{13} a b^3 x^{13}+\frac{b^4 x^{15}}{15}","\frac{6}{11} a^2 b^2 x^{11}+\frac{4}{9} a^3 b x^9+\frac{a^4 x^7}{7}+\frac{4}{13} a b^3 x^{13}+\frac{b^4 x^{15}}{15}",1,"(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",3,2,24,0.08333,1,"{28, 270}"
422,1,53,0,0.070219,"\int x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{a^2 \left(a+b x^2\right)^5}{10 b^3}+\frac{\left(a+b x^2\right)^7}{14 b^3}-\frac{a \left(a+b x^2\right)^6}{6 b^3}","\frac{a^2 \left(a+b x^2\right)^5}{10 b^3}+\frac{\left(a+b x^2\right)^7}{14 b^3}-\frac{a \left(a+b x^2\right)^6}{6 b^3}",1,"(a^2*(a + b*x^2)^5)/(10*b^3) - (a*(a + b*x^2)^6)/(6*b^3) + (a + b*x^2)^7/(14*b^3)","A",4,3,24,0.1250,1,"{28, 266, 43}"
423,1,56,0,0.0272856,"\int x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{2}{3} a^2 b^2 x^9+\frac{4}{7} a^3 b x^7+\frac{a^4 x^5}{5}+\frac{4}{11} a b^3 x^{11}+\frac{b^4 x^{13}}{13}","\frac{2}{3} a^2 b^2 x^9+\frac{4}{7} a^3 b x^7+\frac{a^4 x^5}{5}+\frac{4}{11} a b^3 x^{11}+\frac{b^4 x^{13}}{13}",1,"(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",3,2,24,0.08333,1,"{28, 270}"
424,1,34,0,0.0395182,"\int x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{\left(a+b x^2\right)^6}{12 b^2}-\frac{a \left(a+b x^2\right)^5}{10 b^2}","\frac{\left(a+b x^2\right)^6}{12 b^2}-\frac{a \left(a+b x^2\right)^5}{10 b^2}",1,"-(a*(a + b*x^2)^5)/(10*b^2) + (a + b*x^2)^6/(12*b^2)","A",4,3,24,0.1250,1,"{28, 266, 43}"
425,1,56,0,0.0288531,"\int x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{6}{7} a^2 b^2 x^7+\frac{4}{5} a^3 b x^5+\frac{a^4 x^3}{3}+\frac{4}{9} a b^3 x^9+\frac{b^4 x^{11}}{11}","\frac{6}{7} a^2 b^2 x^7+\frac{4}{5} a^3 b x^5+\frac{a^4 x^3}{3}+\frac{4}{9} a b^3 x^9+\frac{b^4 x^{11}}{11}",1,"(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",3,2,24,0.08333,1,"{28, 270}"
426,1,16,0,0.0048408,"\int x \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[x*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{\left(a+b x^2\right)^5}{10 b}","\frac{\left(a+b x^2\right)^5}{10 b}",1,"(a + b*x^2)^5/(10*b)","A",2,2,22,0.09091,1,"{28, 261}"
427,1,51,0,0.0238017,"\int \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{6}{5} a^2 b^2 x^5+\frac{4}{3} a^3 b x^3+a^4 x+\frac{4}{7} a b^3 x^7+\frac{b^4 x^9}{9}","\frac{6}{5} a^2 b^2 x^5+\frac{4}{3} a^3 b x^3+a^4 x+\frac{4}{7} a b^3 x^7+\frac{b^4 x^9}{9}",1,"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",3,2,20,0.1000,1,"{28, 194}"
428,1,50,0,0.0337603,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x,x]","\frac{3}{2} a^2 b^2 x^4+2 a^3 b x^2+a^4 \log (x)+\frac{2}{3} a b^3 x^6+\frac{b^4 x^8}{8}","\frac{3}{2} a^2 b^2 x^4+2 a^3 b x^2+a^4 \log (x)+\frac{2}{3} a b^3 x^6+\frac{b^4 x^8}{8}",1,"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^4*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
429,1,48,0,0.0255003,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^2,x]","2 a^2 b^2 x^3+4 a^3 b x-\frac{a^4}{x}+\frac{4}{5} a b^3 x^5+\frac{b^4 x^7}{7}","2 a^2 b^2 x^3+4 a^3 b x-\frac{a^4}{x}+\frac{4}{5} a b^3 x^5+\frac{b^4 x^7}{7}",1,"-(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",3,2,24,0.08333,1,"{28, 270}"
430,1,48,0,0.0372027,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^3} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^3,x]","3 a^2 b^2 x^2+4 a^3 b \log (x)-\frac{a^4}{2 x^2}+a b^3 x^4+\frac{b^4 x^6}{6}","3 a^2 b^2 x^2+4 a^3 b \log (x)-\frac{a^4}{2 x^2}+a b^3 x^4+\frac{b^4 x^6}{6}",1,"-a^4/(2*x^2) + 3*a^2*b^2*x^2 + a*b^3*x^4 + (b^4*x^6)/6 + 4*a^3*b*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
431,1,50,0,0.0261702,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^4,x]","6 a^2 b^2 x-\frac{4 a^3 b}{x}-\frac{a^4}{3 x^3}+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5}","6 a^2 b^2 x-\frac{4 a^3 b}{x}-\frac{a^4}{3 x^3}+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5}",1,"-a^4/(3*x^3) - (4*a^3*b)/x + 6*a^2*b^2*x + (4*a*b^3*x^3)/3 + (b^4*x^5)/5","A",3,2,24,0.08333,1,"{28, 270}"
432,1,49,0,0.0356296,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^5} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^5,x]","6 a^2 b^2 \log (x)-\frac{2 a^3 b}{x^2}-\frac{a^4}{4 x^4}+2 a b^3 x^2+\frac{b^4 x^4}{4}","6 a^2 b^2 \log (x)-\frac{2 a^3 b}{x^2}-\frac{a^4}{4 x^4}+2 a b^3 x^2+\frac{b^4 x^4}{4}",1,"-a^4/(4*x^4) - (2*a^3*b)/x^2 + 2*a*b^3*x^2 + (b^4*x^4)/4 + 6*a^2*b^2*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
433,1,50,0,0.0263534,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^6} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^6,x]","-\frac{6 a^2 b^2}{x}-\frac{4 a^3 b}{3 x^3}-\frac{a^4}{5 x^5}+4 a b^3 x+\frac{b^4 x^3}{3}","-\frac{6 a^2 b^2}{x}-\frac{4 a^3 b}{3 x^3}-\frac{a^4}{5 x^5}+4 a b^3 x+\frac{b^4 x^3}{3}",1,"-a^4/(5*x^5) - (4*a^3*b)/(3*x^3) - (6*a^2*b^2)/x + 4*a*b^3*x + (b^4*x^3)/3","A",3,2,24,0.08333,1,"{28, 270}"
434,1,49,0,0.0326376,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^7} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^7,x]","-\frac{3 a^2 b^2}{x^2}-\frac{a^3 b}{x^4}-\frac{a^4}{6 x^6}+4 a b^3 \log (x)+\frac{b^4 x^2}{2}","-\frac{3 a^2 b^2}{x^2}-\frac{a^3 b}{x^4}-\frac{a^4}{6 x^6}+4 a b^3 \log (x)+\frac{b^4 x^2}{2}",1,"-a^4/(6*x^6) - (a^3*b)/x^4 - (3*a^2*b^2)/x^2 + (b^4*x^2)/2 + 4*a*b^3*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
435,1,47,0,0.02538,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^8} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^8,x]","-\frac{2 a^2 b^2}{x^3}-\frac{4 a^3 b}{5 x^5}-\frac{a^4}{7 x^7}-\frac{4 a b^3}{x}+b^4 x","-\frac{2 a^2 b^2}{x^3}-\frac{4 a^3 b}{5 x^5}-\frac{a^4}{7 x^7}-\frac{4 a b^3}{x}+b^4 x",1,"-a^4/(7*x^7) - (4*a^3*b)/(5*x^5) - (2*a^2*b^2)/x^3 - (4*a*b^3)/x + b^4*x","A",3,2,24,0.08333,1,"{28, 270}"
436,1,50,0,0.0326616,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^9} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^9,x]","-\frac{3 a^2 b^2}{2 x^4}-\frac{2 a^3 b}{3 x^6}-\frac{a^4}{8 x^8}-\frac{2 a b^3}{x^2}+b^4 \log (x)","-\frac{3 a^2 b^2}{2 x^4}-\frac{2 a^3 b}{3 x^6}-\frac{a^4}{8 x^8}-\frac{2 a b^3}{x^2}+b^4 \log (x)",1,"-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]","A",4,3,24,0.1250,1,"{28, 266, 43}"
437,1,54,0,0.0261705,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^{10}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^10,x]","-\frac{6 a^2 b^2}{5 x^5}-\frac{4 a^3 b}{7 x^7}-\frac{a^4}{9 x^9}-\frac{4 a b^3}{3 x^3}-\frac{b^4}{x}","-\frac{6 a^2 b^2}{5 x^5}-\frac{4 a^3 b}{7 x^7}-\frac{a^4}{9 x^9}-\frac{4 a b^3}{3 x^3}-\frac{b^4}{x}",1,"-a^4/(9*x^9) - (4*a^3*b)/(7*x^7) - (6*a^2*b^2)/(5*x^5) - (4*a*b^3)/(3*x^3) - b^4/x","A",3,2,24,0.08333,1,"{28, 270}"
438,1,19,0,0.0061135,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^{11}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^11,x]","-\frac{\left(a+b x^2\right)^5}{10 a x^{10}}","-\frac{\left(a+b x^2\right)^5}{10 a x^{10}}",1,"-(a + b*x^2)^5/(10*a*x^10)","A",2,2,24,0.08333,1,"{28, 264}"
439,1,56,0,0.0263073,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^{12}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^12,x]","-\frac{6 a^2 b^2}{7 x^7}-\frac{4 a^3 b}{9 x^9}-\frac{a^4}{11 x^{11}}-\frac{4 a b^3}{5 x^5}-\frac{b^4}{3 x^3}","-\frac{6 a^2 b^2}{7 x^7}-\frac{4 a^3 b}{9 x^9}-\frac{a^4}{11 x^{11}}-\frac{4 a b^3}{5 x^5}-\frac{b^4}{3 x^3}",1,"-a^4/(11*x^11) - (4*a^3*b)/(9*x^9) - (6*a^2*b^2)/(7*x^7) - (4*a*b^3)/(5*x^5) - b^4/(3*x^3)","A",3,2,24,0.08333,1,"{28, 270}"
440,1,40,0,0.0245002,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^{13}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^13,x]","\frac{b \left(a+b x^2\right)^5}{60 a^2 x^{10}}-\frac{\left(a+b x^2\right)^5}{12 a x^{12}}","\frac{b \left(a+b x^2\right)^5}{60 a^2 x^{10}}-\frac{\left(a+b x^2\right)^5}{12 a x^{12}}",1,"-(a + b*x^2)^5/(12*a*x^12) + (b*(a + b*x^2)^5)/(60*a^2*x^10)","A",4,4,24,0.1667,1,"{28, 266, 45, 37}"
441,1,56,0,0.0274963,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^{14}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^14,x]","-\frac{2 a^2 b^2}{3 x^9}-\frac{4 a^3 b}{11 x^{11}}-\frac{a^4}{13 x^{13}}-\frac{4 a b^3}{7 x^7}-\frac{b^4}{5 x^5}","-\frac{2 a^2 b^2}{3 x^9}-\frac{4 a^3 b}{11 x^{11}}-\frac{a^4}{13 x^{13}}-\frac{4 a b^3}{7 x^7}-\frac{b^4}{5 x^5}",1,"-a^4/(13*x^13) - (4*a^3*b)/(11*x^11) - (2*a^2*b^2)/(3*x^9) - (4*a*b^3)/(7*x^7) - b^4/(5*x^5)","A",3,2,24,0.08333,1,"{28, 270}"
442,1,56,0,0.0364443,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^{15}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^15,x]","-\frac{3 a^2 b^2}{5 x^{10}}-\frac{a^3 b}{3 x^{12}}-\frac{a^4}{14 x^{14}}-\frac{a b^3}{2 x^8}-\frac{b^4}{6 x^6}","-\frac{3 a^2 b^2}{5 x^{10}}-\frac{a^3 b}{3 x^{12}}-\frac{a^4}{14 x^{14}}-\frac{a b^3}{2 x^8}-\frac{b^4}{6 x^6}",1,"-a^4/(14*x^14) - (a^3*b)/(3*x^12) - (3*a^2*b^2)/(5*x^10) - (a*b^3)/(2*x^8) - b^4/(6*x^6)","A",4,3,24,0.1250,1,"{28, 266, 43}"
443,1,56,0,0.0252742,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{x^{16}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^16,x]","-\frac{6 a^2 b^2}{11 x^{11}}-\frac{4 a^3 b}{13 x^{13}}-\frac{a^4}{15 x^{15}}-\frac{4 a b^3}{9 x^9}-\frac{b^4}{7 x^7}","-\frac{6 a^2 b^2}{11 x^{11}}-\frac{4 a^3 b}{13 x^{13}}-\frac{a^4}{15 x^{15}}-\frac{4 a b^3}{9 x^9}-\frac{b^4}{7 x^7}",1,"-a^4/(15*x^15) - (4*a^3*b)/(13*x^13) - (6*a^2*b^2)/(11*x^11) - (4*a*b^3)/(9*x^9) - b^4/(7*x^7)","A",3,2,24,0.08333,1,"{28, 270}"
444,1,82,0,0.0456947,"\int x^8 \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x^8*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{15}{17} a^2 b^4 x^{17}+\frac{4}{3} a^3 b^3 x^{15}+\frac{15}{13} a^4 b^2 x^{13}+\frac{6}{11} a^5 b x^{11}+\frac{a^6 x^9}{9}+\frac{6}{19} a b^5 x^{19}+\frac{b^6 x^{21}}{21}","\frac{15}{17} a^2 b^4 x^{17}+\frac{4}{3} a^3 b^3 x^{15}+\frac{15}{13} a^4 b^2 x^{13}+\frac{6}{11} a^5 b x^{11}+\frac{a^6 x^9}{9}+\frac{6}{19} a b^5 x^{19}+\frac{b^6 x^{21}}{21}",1,"(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",3,2,24,0.08333,1,"{28, 270}"
445,1,72,0,0.1169906,"\int x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x^7*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{3 a^2 \left(a+b x^2\right)^8}{16 b^4}-\frac{a^3 \left(a+b x^2\right)^7}{14 b^4}+\frac{\left(a+b x^2\right)^{10}}{20 b^4}-\frac{a \left(a+b x^2\right)^9}{6 b^4}","\frac{3 a^2 \left(a+b x^2\right)^8}{16 b^4}-\frac{a^3 \left(a+b x^2\right)^7}{14 b^4}+\frac{\left(a+b x^2\right)^{10}}{20 b^4}-\frac{a \left(a+b x^2\right)^9}{6 b^4}",1,"-(a^3*(a + b*x^2)^7)/(14*b^4) + (3*a^2*(a + b*x^2)^8)/(16*b^4) - (a*(a + b*x^2)^9)/(6*b^4) + (a + b*x^2)^10/(20*b^4)","A",4,3,24,0.1250,1,"{28, 266, 43}"
446,1,79,0,0.0380232,"\int x^6 \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","a^2 b^4 x^{15}+\frac{20}{13} a^3 b^3 x^{13}+\frac{15}{11} a^4 b^2 x^{11}+\frac{2}{3} a^5 b x^9+\frac{a^6 x^7}{7}+\frac{6}{17} a b^5 x^{17}+\frac{b^6 x^{19}}{19}","a^2 b^4 x^{15}+\frac{20}{13} a^3 b^3 x^{13}+\frac{15}{11} a^4 b^2 x^{11}+\frac{2}{3} a^5 b x^9+\frac{a^6 x^7}{7}+\frac{6}{17} a b^5 x^{17}+\frac{b^6 x^{19}}{19}",1,"(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",3,2,24,0.08333,1,"{28, 270}"
447,1,53,0,0.0853567,"\int x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{a^2 \left(a+b x^2\right)^7}{14 b^3}+\frac{\left(a+b x^2\right)^9}{18 b^3}-\frac{a \left(a+b x^2\right)^8}{8 b^3}","\frac{a^2 \left(a+b x^2\right)^7}{14 b^3}+\frac{\left(a+b x^2\right)^9}{18 b^3}-\frac{a \left(a+b x^2\right)^8}{8 b^3}",1,"(a^2*(a + b*x^2)^7)/(14*b^3) - (a*(a + b*x^2)^8)/(8*b^3) + (a + b*x^2)^9/(18*b^3)","A",4,3,24,0.1250,1,"{28, 266, 43}"
448,1,82,0,0.0398535,"\int x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{15}{13} a^2 b^4 x^{13}+\frac{20}{11} a^3 b^3 x^{11}+\frac{5}{3} a^4 b^2 x^9+\frac{6}{7} a^5 b x^7+\frac{a^6 x^5}{5}+\frac{2}{5} a b^5 x^{15}+\frac{b^6 x^{17}}{17}","\frac{15}{13} a^2 b^4 x^{13}+\frac{20}{11} a^3 b^3 x^{11}+\frac{5}{3} a^4 b^2 x^9+\frac{6}{7} a^5 b x^7+\frac{a^6 x^5}{5}+\frac{2}{5} a b^5 x^{15}+\frac{b^6 x^{17}}{17}",1,"(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",3,2,24,0.08333,1,"{28, 270}"
449,1,34,0,0.0456321,"\int x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{\left(a+b x^2\right)^8}{16 b^2}-\frac{a \left(a+b x^2\right)^7}{14 b^2}","\frac{\left(a+b x^2\right)^8}{16 b^2}-\frac{a \left(a+b x^2\right)^7}{14 b^2}",1,"-(a*(a + b*x^2)^7)/(14*b^2) + (a + b*x^2)^8/(16*b^2)","A",4,3,24,0.1250,1,"{28, 266, 43}"
450,1,82,0,0.0384399,"\int x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{15}{11} a^2 b^4 x^{11}+\frac{20}{9} a^3 b^3 x^9+\frac{15}{7} a^4 b^2 x^7+\frac{6}{5} a^5 b x^5+\frac{a^6 x^3}{3}+\frac{6}{13} a b^5 x^{13}+\frac{b^6 x^{15}}{15}","\frac{15}{11} a^2 b^4 x^{11}+\frac{20}{9} a^3 b^3 x^9+\frac{15}{7} a^4 b^2 x^7+\frac{6}{5} a^5 b x^5+\frac{a^6 x^3}{3}+\frac{6}{13} a b^5 x^{13}+\frac{b^6 x^{15}}{15}",1,"(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",3,2,24,0.08333,1,"{28, 270}"
451,1,16,0,0.0048827,"\int x \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[x*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{\left(a+b x^2\right)^7}{14 b}","\frac{\left(a+b x^2\right)^7}{14 b}",1,"(a + b*x^2)^7/(14*b)","A",2,2,22,0.09091,1,"{28, 261}"
452,1,73,0,0.0343958,"\int \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{5}{3} a^2 b^4 x^9+\frac{20}{7} a^3 b^3 x^7+3 a^4 b^2 x^5+2 a^5 b x^3+a^6 x+\frac{6}{11} a b^5 x^{11}+\frac{b^6 x^{13}}{13}","\frac{5}{3} a^2 b^4 x^9+\frac{20}{7} a^3 b^3 x^7+3 a^4 b^2 x^5+2 a^5 b x^3+a^6 x+\frac{6}{11} a b^5 x^{11}+\frac{b^6 x^{13}}{13}",1,"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",3,2,20,0.1000,1,"{28, 194}"
453,1,76,0,0.0545137,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x,x]","\frac{15}{8} a^2 b^4 x^8+\frac{10}{3} a^3 b^3 x^6+\frac{15}{4} a^4 b^2 x^4+3 a^5 b x^2+a^6 \log (x)+\frac{3}{5} a b^5 x^{10}+\frac{b^6 x^{12}}{12}","\frac{15}{8} a^2 b^4 x^8+\frac{10}{3} a^3 b^3 x^6+\frac{15}{4} a^4 b^2 x^4+3 a^5 b x^2+a^6 \log (x)+\frac{3}{5} a b^5 x^{10}+\frac{b^6 x^{12}}{12}",1,"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^6*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
454,1,72,0,0.0392213,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^2,x]","\frac{15}{7} a^2 b^4 x^7+4 a^3 b^3 x^5+5 a^4 b^2 x^3+6 a^5 b x-\frac{a^6}{x}+\frac{2}{3} a b^5 x^9+\frac{b^6 x^{11}}{11}","\frac{15}{7} a^2 b^4 x^7+4 a^3 b^3 x^5+5 a^4 b^2 x^3+6 a^5 b x-\frac{a^6}{x}+\frac{2}{3} a b^5 x^9+\frac{b^6 x^{11}}{11}",1,"-(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",3,2,24,0.08333,1,"{28, 270}"
455,1,77,0,0.0562668,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^3} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^3,x]","\frac{5}{2} a^2 b^4 x^6+5 a^3 b^3 x^4+\frac{15}{2} a^4 b^2 x^2+6 a^5 b \log (x)-\frac{a^6}{2 x^2}+\frac{3}{4} a b^5 x^8+\frac{b^6 x^{10}}{10}","\frac{5}{2} a^2 b^4 x^6+5 a^3 b^3 x^4+\frac{15}{2} a^4 b^2 x^2+6 a^5 b \log (x)-\frac{a^6}{2 x^2}+\frac{3}{4} a b^5 x^8+\frac{b^6 x^{10}}{10}",1,"-a^6/(2*x^2) + (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 + 6*a^5*b*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
456,1,74,0,0.0364336,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^4,x]","3 a^2 b^4 x^5+\frac{20}{3} a^3 b^3 x^3+15 a^4 b^2 x-\frac{6 a^5 b}{x}-\frac{a^6}{3 x^3}+\frac{6}{7} a b^5 x^7+\frac{b^6 x^9}{9}","3 a^2 b^4 x^5+\frac{20}{3} a^3 b^3 x^3+15 a^4 b^2 x-\frac{6 a^5 b}{x}-\frac{a^6}{3 x^3}+\frac{6}{7} a b^5 x^7+\frac{b^6 x^9}{9}",1,"-a^6/(3*x^3) - (6*a^5*b)/x + 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",3,2,24,0.08333,1,"{28, 270}"
457,1,72,0,0.052438,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^5} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^5,x]","\frac{15}{4} a^2 b^4 x^4+10 a^3 b^3 x^2+15 a^4 b^2 \log (x)-\frac{3 a^5 b}{x^2}-\frac{a^6}{4 x^4}+a b^5 x^6+\frac{b^6 x^8}{8}","\frac{15}{4} a^2 b^4 x^4+10 a^3 b^3 x^2+15 a^4 b^2 \log (x)-\frac{3 a^5 b}{x^2}-\frac{a^6}{4 x^4}+a b^5 x^6+\frac{b^6 x^8}{8}",1,"-a^6/(4*x^4) - (3*a^5*b)/x^2 + 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 + 15*a^4*b^2*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
458,1,72,0,0.0408074,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^6} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^6,x]","5 a^2 b^4 x^3+20 a^3 b^3 x-\frac{15 a^4 b^2}{x}-\frac{2 a^5 b}{x^3}-\frac{a^6}{5 x^5}+\frac{6}{5} a b^5 x^5+\frac{b^6 x^7}{7}","5 a^2 b^4 x^3+20 a^3 b^3 x-\frac{15 a^4 b^2}{x}-\frac{2 a^5 b}{x^3}-\frac{a^6}{5 x^5}+\frac{6}{5} a b^5 x^5+\frac{b^6 x^7}{7}",1,"-a^6/(5*x^5) - (2*a^5*b)/x^3 - (15*a^4*b^2)/x + 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",3,2,24,0.08333,1,"{28, 270}"
459,1,79,0,0.0505286,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^7} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^7,x]","-\frac{15 a^4 b^2}{2 x^2}+\frac{15}{2} a^2 b^4 x^2+20 a^3 b^3 \log (x)-\frac{3 a^5 b}{2 x^4}-\frac{a^6}{6 x^6}+\frac{3}{2} a b^5 x^4+\frac{b^6 x^6}{6}","-\frac{15 a^4 b^2}{2 x^2}+\frac{15}{2} a^2 b^4 x^2+20 a^3 b^3 \log (x)-\frac{3 a^5 b}{2 x^4}-\frac{a^6}{6 x^6}+\frac{3}{2} a b^5 x^4+\frac{b^6 x^6}{6}",1,"-a^6/(6*x^6) - (3*a^5*b)/(2*x^4) - (15*a^4*b^2)/(2*x^2) + (15*a^2*b^4*x^2)/2 + (3*a*b^5*x^4)/2 + (b^6*x^6)/6 + 20*a^3*b^3*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
460,1,72,0,0.0369146,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^8} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^8,x]","-\frac{5 a^4 b^2}{x^3}-\frac{20 a^3 b^3}{x}+15 a^2 b^4 x-\frac{6 a^5 b}{5 x^5}-\frac{a^6}{7 x^7}+2 a b^5 x^3+\frac{b^6 x^5}{5}","-\frac{5 a^4 b^2}{x^3}-\frac{20 a^3 b^3}{x}+15 a^2 b^4 x-\frac{6 a^5 b}{5 x^5}-\frac{a^6}{7 x^7}+2 a b^5 x^3+\frac{b^6 x^5}{5}",1,"-a^6/(7*x^7) - (6*a^5*b)/(5*x^5) - (5*a^4*b^2)/x^3 - (20*a^3*b^3)/x + 15*a^2*b^4*x + 2*a*b^5*x^3 + (b^6*x^5)/5","A",3,2,24,0.08333,1,"{28, 270}"
461,1,73,0,0.0520787,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^9} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^9,x]","-\frac{15 a^4 b^2}{4 x^4}-\frac{10 a^3 b^3}{x^2}+15 a^2 b^4 \log (x)-\frac{a^5 b}{x^6}-\frac{a^6}{8 x^8}+3 a b^5 x^2+\frac{b^6 x^4}{4}","-\frac{15 a^4 b^2}{4 x^4}-\frac{10 a^3 b^3}{x^2}+15 a^2 b^4 \log (x)-\frac{a^5 b}{x^6}-\frac{a^6}{8 x^8}+3 a b^5 x^2+\frac{b^6 x^4}{4}",1,"-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 + 3*a*b^5*x^2 + (b^6*x^4)/4 + 15*a^2*b^4*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
462,1,74,0,0.0393374,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{10}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^10,x]","-\frac{3 a^4 b^2}{x^5}-\frac{20 a^3 b^3}{3 x^3}-\frac{15 a^2 b^4}{x}-\frac{6 a^5 b}{7 x^7}-\frac{a^6}{9 x^9}+6 a b^5 x+\frac{b^6 x^3}{3}","-\frac{3 a^4 b^2}{x^5}-\frac{20 a^3 b^3}{3 x^3}-\frac{15 a^2 b^4}{x}-\frac{6 a^5 b}{7 x^7}-\frac{a^6}{9 x^9}+6 a b^5 x+\frac{b^6 x^3}{3}",1,"-a^6/(9*x^9) - (6*a^5*b)/(7*x^7) - (3*a^4*b^2)/x^5 - (20*a^3*b^3)/(3*x^3) - (15*a^2*b^4)/x + 6*a*b^5*x + (b^6*x^3)/3","A",3,2,24,0.08333,1,"{28, 270}"
463,1,77,0,0.0511226,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{11}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^11,x]","-\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}-\frac{3 a^5 b}{4 x^8}-\frac{a^6}{10 x^{10}}+6 a b^5 \log (x)+\frac{b^6 x^2}{2}","-\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}-\frac{3 a^5 b}{4 x^8}-\frac{a^6}{10 x^{10}}+6 a b^5 \log (x)+\frac{b^6 x^2}{2}",1,"-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) + (b^6*x^2)/2 + 6*a*b^5*Log[x]","A",4,3,24,0.1250,1,"{28, 266, 43}"
464,1,71,0,0.0370139,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{12}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^12,x]","-\frac{15 a^4 b^2}{7 x^7}-\frac{4 a^3 b^3}{x^5}-\frac{5 a^2 b^4}{x^3}-\frac{2 a^5 b}{3 x^9}-\frac{a^6}{11 x^{11}}-\frac{6 a b^5}{x}+b^6 x","-\frac{15 a^4 b^2}{7 x^7}-\frac{4 a^3 b^3}{x^5}-\frac{5 a^2 b^4}{x^3}-\frac{2 a^5 b}{3 x^9}-\frac{a^6}{11 x^{11}}-\frac{6 a b^5}{x}+b^6 x",1,"-a^6/(11*x^11) - (2*a^5*b)/(3*x^9) - (15*a^4*b^2)/(7*x^7) - (4*a^3*b^3)/x^5 - (5*a^2*b^4)/x^3 - (6*a*b^5)/x + b^6*x","A",3,2,24,0.08333,1,"{28, 270}"
465,1,76,0,0.0486256,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{13}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^13,x]","-\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^5 b}{5 x^{10}}-\frac{a^6}{12 x^{12}}-\frac{3 a b^5}{x^2}+b^6 \log (x)","-\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^5 b}{5 x^{10}}-\frac{a^6}{12 x^{12}}-\frac{3 a b^5}{x^2}+b^6 \log (x)",1,"-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]","A",4,3,24,0.1250,1,"{28, 266, 43}"
466,1,76,0,0.0401458,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{14}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^14,x]","-\frac{5 a^4 b^2}{3 x^9}-\frac{20 a^3 b^3}{7 x^7}-\frac{3 a^2 b^4}{x^5}-\frac{6 a^5 b}{11 x^{11}}-\frac{a^6}{13 x^{13}}-\frac{2 a b^5}{x^3}-\frac{b^6}{x}","-\frac{5 a^4 b^2}{3 x^9}-\frac{20 a^3 b^3}{7 x^7}-\frac{3 a^2 b^4}{x^5}-\frac{6 a^5 b}{11 x^{11}}-\frac{a^6}{13 x^{13}}-\frac{2 a b^5}{x^3}-\frac{b^6}{x}",1,"-a^6/(13*x^13) - (6*a^5*b)/(11*x^11) - (5*a^4*b^2)/(3*x^9) - (20*a^3*b^3)/(7*x^7) - (3*a^2*b^4)/x^5 - (2*a*b^5)/x^3 - b^6/x","A",3,2,24,0.08333,1,"{28, 270}"
467,1,19,0,0.0066284,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{15}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^15,x]","-\frac{\left(a+b x^2\right)^7}{14 a x^{14}}","-\frac{\left(a+b x^2\right)^7}{14 a x^{14}}",1,"-(a + b*x^2)^7/(14*a*x^14)","A",2,2,24,0.08333,1,"{28, 264}"
468,1,82,0,0.0383924,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{16}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^16,x]","-\frac{15 a^4 b^2}{11 x^{11}}-\frac{20 a^3 b^3}{9 x^9}-\frac{15 a^2 b^4}{7 x^7}-\frac{6 a^5 b}{13 x^{13}}-\frac{a^6}{15 x^{15}}-\frac{6 a b^5}{5 x^5}-\frac{b^6}{3 x^3}","-\frac{15 a^4 b^2}{11 x^{11}}-\frac{20 a^3 b^3}{9 x^9}-\frac{15 a^2 b^4}{7 x^7}-\frac{6 a^5 b}{13 x^{13}}-\frac{a^6}{15 x^{15}}-\frac{6 a b^5}{5 x^5}-\frac{b^6}{3 x^3}",1,"-a^6/(15*x^15) - (6*a^5*b)/(13*x^13) - (15*a^4*b^2)/(11*x^11) - (20*a^3*b^3)/(9*x^9) - (15*a^2*b^4)/(7*x^7) - (6*a*b^5)/(5*x^5) - b^6/(3*x^3)","A",3,2,24,0.08333,1,"{28, 270}"
469,1,40,0,0.0251543,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{17}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^17,x]","\frac{b \left(a+b x^2\right)^7}{112 a^2 x^{14}}-\frac{\left(a+b x^2\right)^7}{16 a x^{16}}","\frac{b \left(a+b x^2\right)^7}{112 a^2 x^{14}}-\frac{\left(a+b x^2\right)^7}{16 a x^{16}}",1,"-(a + b*x^2)^7/(16*a*x^16) + (b*(a + b*x^2)^7)/(112*a^2*x^14)","A",4,4,24,0.1667,1,"{28, 266, 45, 37}"
470,1,82,0,0.0377724,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{18}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^18,x]","-\frac{15 a^4 b^2}{13 x^{13}}-\frac{20 a^3 b^3}{11 x^{11}}-\frac{5 a^2 b^4}{3 x^9}-\frac{2 a^5 b}{5 x^{15}}-\frac{a^6}{17 x^{17}}-\frac{6 a b^5}{7 x^7}-\frac{b^6}{5 x^5}","-\frac{15 a^4 b^2}{13 x^{13}}-\frac{20 a^3 b^3}{11 x^{11}}-\frac{5 a^2 b^4}{3 x^9}-\frac{2 a^5 b}{5 x^{15}}-\frac{a^6}{17 x^{17}}-\frac{6 a b^5}{7 x^7}-\frac{b^6}{5 x^5}",1,"-a^6/(17*x^17) - (2*a^5*b)/(5*x^15) - (15*a^4*b^2)/(13*x^13) - (20*a^3*b^3)/(11*x^11) - (5*a^2*b^4)/(3*x^9) - (6*a*b^5)/(7*x^7) - b^6/(5*x^5)","A",3,2,24,0.08333,1,"{28, 270}"
471,1,62,0,0.0386362,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{19}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^19,x]","-\frac{b^2 \left(a+b x^2\right)^7}{504 a^3 x^{14}}+\frac{b \left(a+b x^2\right)^7}{72 a^2 x^{16}}-\frac{\left(a+b x^2\right)^7}{18 a x^{18}}","-\frac{b^2 \left(a+b x^2\right)^7}{504 a^3 x^{14}}+\frac{b \left(a+b x^2\right)^7}{72 a^2 x^{16}}-\frac{\left(a+b x^2\right)^7}{18 a x^{18}}",1,"-(a + b*x^2)^7/(18*a*x^18) + (b*(a + b*x^2)^7)/(72*a^2*x^16) - (b^2*(a + b*x^2)^7)/(504*a^3*x^14)","A",5,4,24,0.1667,1,"{28, 266, 45, 37}"
472,1,80,0,0.0375387,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{20}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^20,x]","-\frac{a^4 b^2}{x^{15}}-\frac{20 a^3 b^3}{13 x^{13}}-\frac{15 a^2 b^4}{11 x^{11}}-\frac{6 a^5 b}{17 x^{17}}-\frac{a^6}{19 x^{19}}-\frac{2 a b^5}{3 x^9}-\frac{b^6}{7 x^7}","-\frac{a^4 b^2}{x^{15}}-\frac{20 a^3 b^3}{13 x^{13}}-\frac{15 a^2 b^4}{11 x^{11}}-\frac{6 a^5 b}{17 x^{17}}-\frac{a^6}{19 x^{19}}-\frac{2 a b^5}{3 x^9}-\frac{b^6}{7 x^7}",1,"-a^6/(19*x^19) - (6*a^5*b)/(17*x^17) - (a^4*b^2)/x^15 - (20*a^3*b^3)/(13*x^13) - (15*a^2*b^4)/(11*x^11) - (2*a*b^5)/(3*x^9) - b^6/(7*x^7)","A",3,2,24,0.08333,1,"{28, 270}"
473,1,84,0,0.056049,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{21}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^21,x]","\frac{b^3 \left(a+b x^2\right)^7}{1680 a^4 x^{14}}-\frac{b^2 \left(a+b x^2\right)^7}{240 a^3 x^{16}}+\frac{b \left(a+b x^2\right)^7}{60 a^2 x^{18}}-\frac{\left(a+b x^2\right)^7}{20 a x^{20}}","\frac{b^3 \left(a+b x^2\right)^7}{1680 a^4 x^{14}}-\frac{b^2 \left(a+b x^2\right)^7}{240 a^3 x^{16}}+\frac{b \left(a+b x^2\right)^7}{60 a^2 x^{18}}-\frac{\left(a+b x^2\right)^7}{20 a x^{20}}",1,"-(a + b*x^2)^7/(20*a*x^20) + (b*(a + b*x^2)^7)/(60*a^2*x^18) - (b^2*(a + b*x^2)^7)/(240*a^3*x^16) + (b^3*(a + b*x^2)^7)/(1680*a^4*x^14)","A",6,4,24,0.1667,1,"{28, 266, 45, 37}"
474,1,82,0,0.0397837,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{x^{22}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^22,x]","-\frac{15 a^4 b^2}{17 x^{17}}-\frac{4 a^3 b^3}{3 x^{15}}-\frac{15 a^2 b^4}{13 x^{13}}-\frac{6 a^5 b}{19 x^{19}}-\frac{a^6}{21 x^{21}}-\frac{6 a b^5}{11 x^{11}}-\frac{b^6}{9 x^9}","-\frac{15 a^4 b^2}{17 x^{17}}-\frac{4 a^3 b^3}{3 x^{15}}-\frac{15 a^2 b^4}{13 x^{13}}-\frac{6 a^5 b}{19 x^{19}}-\frac{a^6}{21 x^{21}}-\frac{6 a b^5}{11 x^{11}}-\frac{b^6}{9 x^9}",1,"-a^6/(21*x^21) - (6*a^5*b)/(19*x^19) - (15*a^4*b^2)/(17*x^17) - (4*a^3*b^3)/(3*x^15) - (15*a^2*b^4)/(13*x^13) - (6*a*b^5)/(11*x^11) - b^6/(9*x^9)","A",3,2,24,0.08333,1,"{28, 270}"
475,1,83,0,0.0821507,"\int \frac{x^{11}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^11/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{3 a^2 x^4}{4 b^4}-\frac{2 a^3 x^2}{b^5}+\frac{a^5}{2 b^6 \left(a+b x^2\right)}+\frac{5 a^4 \log \left(a+b x^2\right)}{2 b^6}-\frac{a x^6}{3 b^3}+\frac{x^8}{8 b^2}","\frac{3 a^2 x^4}{4 b^4}-\frac{2 a^3 x^2}{b^5}+\frac{a^5}{2 b^6 \left(a+b x^2\right)}+\frac{5 a^4 \log \left(a+b x^2\right)}{2 b^6}-\frac{a x^6}{3 b^3}+\frac{x^8}{8 b^2}",1,"(-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^5/(2*b^6*(a + b*x^2)) + (5*a^4*Log[a + b*x^2])/(2*b^6)","A",4,3,24,0.1250,1,"{28, 266, 43}"
476,1,70,0,0.0625934,"\int \frac{x^9}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^9/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{3 a^2 x^2}{2 b^4}-\frac{a^4}{2 b^5 \left(a+b x^2\right)}-\frac{2 a^3 \log \left(a+b x^2\right)}{b^5}-\frac{a x^4}{2 b^3}+\frac{x^6}{6 b^2}","\frac{3 a^2 x^2}{2 b^4}-\frac{a^4}{2 b^5 \left(a+b x^2\right)}-\frac{2 a^3 \log \left(a+b x^2\right)}{b^5}-\frac{a x^4}{2 b^3}+\frac{x^6}{6 b^2}",1,"(3*a^2*x^2)/(2*b^4) - (a*x^4)/(2*b^3) + x^6/(6*b^2) - a^4/(2*b^5*(a + b*x^2)) - (2*a^3*Log[a + b*x^2])/b^5","A",4,3,24,0.1250,1,"{28, 266, 43}"
477,1,57,0,0.0524434,"\int \frac{x^7}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^7/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{a^3}{2 b^4 \left(a+b x^2\right)}+\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}","\frac{a^3}{2 b^4 \left(a+b x^2\right)}+\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}",1,"-((a*x^2)/b^3) + x^4/(4*b^2) + a^3/(2*b^4*(a + b*x^2)) + (3*a^2*Log[a + b*x^2])/(2*b^4)","A",4,3,24,0.1250,1,"{28, 266, 43}"
478,1,44,0,0.037158,"\int \frac{x^5}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^5/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","-\frac{a^2}{2 b^3 \left(a+b x^2\right)}-\frac{a \log \left(a+b x^2\right)}{b^3}+\frac{x^2}{2 b^2}","-\frac{a^2}{2 b^3 \left(a+b x^2\right)}-\frac{a \log \left(a+b x^2\right)}{b^3}+\frac{x^2}{2 b^2}",1,"x^2/(2*b^2) - a^2/(2*b^3*(a + b*x^2)) - (a*Log[a + b*x^2])/b^3","A",4,3,24,0.1250,1,"{28, 266, 43}"
479,1,33,0,0.0284405,"\int \frac{x^3}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^3/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{a}{2 b^2 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^2}","\frac{a}{2 b^2 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^2}",1,"a/(2*b^2*(a + b*x^2)) + Log[a + b*x^2]/(2*b^2)","A",4,3,24,0.1250,1,"{28, 266, 43}"
480,1,16,0,0.0053895,"\int \frac{x}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","-\frac{1}{2 b \left(a+b x^2\right)}","-\frac{1}{2 b \left(a+b x^2\right)}",1,"-1/(2*b*(a + b*x^2))","A",2,2,22,0.09091,1,"{28, 261}"
481,1,38,0,0.0382369,"\int \frac{1}{x \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/(x*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","-\frac{\log \left(a+b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a+b x^2\right)}","-\frac{\log \left(a+b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a+b x^2\right)}",1,"1/(2*a*(a + b*x^2)) + Log[x]/a^2 - Log[a + b*x^2]/(2*a^2)","A",4,3,24,0.1250,1,"{28, 266, 44}"
482,1,49,0,0.0489452,"\int \frac{1}{x^3 \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","-\frac{b}{2 a^2 \left(a+b x^2\right)}+\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}","-\frac{b}{2 a^2 \left(a+b x^2\right)}+\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}",1,"-1/(2*a^2*x^2) - b/(2*a^2*(a + b*x^2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x^2])/a^3","A",4,3,24,0.1250,1,"{28, 266, 44}"
483,1,66,0,0.0537842,"\int \frac{1}{x^5 \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/(x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","\frac{b^2}{2 a^3 \left(a+b x^2\right)}-\frac{3 b^2 \log \left(a+b x^2\right)}{2 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{b}{a^3 x^2}-\frac{1}{4 a^2 x^4}","\frac{b^2}{2 a^3 \left(a+b x^2\right)}-\frac{3 b^2 \log \left(a+b x^2\right)}{2 a^4}+\frac{3 b^2 \log (x)}{a^4}+\frac{b}{a^3 x^2}-\frac{1}{4 a^2 x^4}",1,"-1/(4*a^2*x^4) + b/(a^3*x^2) + b^2/(2*a^3*(a + b*x^2)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x^2])/(2*a^4)","A",4,3,24,0.1250,1,"{28, 266, 44}"
484,1,92,0,0.0555928,"\int \frac{x^{10}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^10/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{3 a^2 x^3}{2 b^4}-\frac{9 a^3 x}{2 b^5}+\frac{9 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}-\frac{9 a x^5}{10 b^3}-\frac{x^9}{2 b \left(a+b x^2\right)}+\frac{9 x^7}{14 b^2}","\frac{3 a^2 x^3}{2 b^4}-\frac{9 a^3 x}{2 b^5}+\frac{9 a^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}-\frac{9 a x^5}{10 b^3}-\frac{x^9}{2 b \left(a+b x^2\right)}+\frac{9 x^7}{14 b^2}",1,"(-9*a^3*x)/(2*b^5) + (3*a^2*x^3)/(2*b^4) - (9*a*x^5)/(10*b^3) + (9*x^7)/(14*b^2) - x^9/(2*b*(a + b*x^2)) + (9*a^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(11/2))","A",5,4,24,0.1667,1,"{28, 288, 302, 205}"
485,1,79,0,0.0452181,"\int \frac{x^8}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^8/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{7 a^2 x}{2 b^4}-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}-\frac{7 a x^3}{6 b^3}-\frac{x^7}{2 b \left(a+b x^2\right)}+\frac{7 x^5}{10 b^2}","\frac{7 a^2 x}{2 b^4}-\frac{7 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}-\frac{7 a x^3}{6 b^3}-\frac{x^7}{2 b \left(a+b x^2\right)}+\frac{7 x^5}{10 b^2}",1,"(7*a^2*x)/(2*b^4) - (7*a*x^3)/(6*b^3) + (7*x^5)/(10*b^2) - x^7/(2*b*(a + b*x^2)) - (7*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(9/2))","A",5,4,24,0.1667,1,"{28, 288, 302, 205}"
486,1,66,0,0.037731,"\int \frac{x^6}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^6/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}-\frac{5 a x}{2 b^3}-\frac{x^5}{2 b \left(a+b x^2\right)}+\frac{5 x^3}{6 b^2}","\frac{5 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}-\frac{5 a x}{2 b^3}-\frac{x^5}{2 b \left(a+b x^2\right)}+\frac{5 x^3}{6 b^2}",1,"(-5*a*x)/(2*b^3) + (5*x^3)/(6*b^2) - x^5/(2*b*(a + b*x^2)) + (5*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(7/2))","A",5,4,24,0.1667,1,"{28, 288, 302, 205}"
487,1,55,0,0.0273325,"\int \frac{x^4}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^4/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{5/2}}-\frac{x^3}{2 b \left(a+b x^2\right)}+\frac{3 x}{2 b^2}","-\frac{3 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{5/2}}-\frac{x^3}{2 b \left(a+b x^2\right)}+\frac{3 x}{2 b^2}",1,"(3*x)/(2*b^2) - x^3/(2*b*(a + b*x^2)) - (3*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(5/2))","A",4,4,24,0.1667,1,"{28, 288, 321, 205}"
488,1,45,0,0.0172016,"\int \frac{x^2}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^2/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{x}{2 b \left(a+b x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{x}{2 b \left(a+b x^2\right)}",1,"-x/(2*b*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(2*Sqrt[a]*b^(3/2))","A",3,3,24,0.1250,1,"{28, 288, 205}"
489,1,45,0,0.017064,"\int \frac{1}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b x^2\right)}",1,"x/(2*a*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(2*a^(3/2)*Sqrt[b])","A",3,3,20,0.1500,1,"{28, 199, 205}"
490,1,57,0,0.0274065,"\int \frac{1}{x^2 \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a+b x^2\right)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a+b x^2\right)}",1,"-3/(2*a^2*x) + 1/(2*a*x*(a + b*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",4,4,24,0.1667,1,"{28, 290, 325, 205}"
491,1,68,0,0.0359153,"\int \frac{1}{x^4 \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/(x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{5 b}{2 a^3 x}-\frac{5}{6 a^2 x^3}+\frac{1}{2 a x^3 \left(a+b x^2\right)}","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{5 b}{2 a^3 x}-\frac{5}{6 a^2 x^3}+\frac{1}{2 a x^3 \left(a+b x^2\right)}",1,"-5/(6*a^2*x^3) + (5*b)/(2*a^3*x) + 1/(2*a*x^3*(a + b*x^2)) + (5*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2))","A",5,4,24,0.1667,1,"{28, 290, 325, 205}"
492,1,81,0,0.0460682,"\int \frac{1}{x^6 \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/(x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","-\frac{7 b^2}{2 a^4 x}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}+\frac{7 b}{6 a^3 x^3}-\frac{7}{10 a^2 x^5}+\frac{1}{2 a x^5 \left(a+b x^2\right)}","-\frac{7 b^2}{2 a^4 x}-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}+\frac{7 b}{6 a^3 x^3}-\frac{7}{10 a^2 x^5}+\frac{1}{2 a x^5 \left(a+b x^2\right)}",1,"-7/(10*a^2*x^5) + (7*b)/(6*a^3*x^3) - (7*b^2)/(2*a^4*x) + 1/(2*a*x^5*(a + b*x^2)) - (7*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(9/2))","A",6,4,24,0.1667,1,"{28, 290, 325, 205}"
493,1,91,0,0.0926364,"\int \frac{x^{11}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^11/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{a^5}{6 b^6 \left(a+b x^2\right)^3}-\frac{5 a^4}{4 b^6 \left(a+b x^2\right)^2}+\frac{5 a^3}{b^6 \left(a+b x^2\right)}+\frac{5 a^2 \log \left(a+b x^2\right)}{b^6}-\frac{2 a x^2}{b^5}+\frac{x^4}{4 b^4}","\frac{a^5}{6 b^6 \left(a+b x^2\right)^3}-\frac{5 a^4}{4 b^6 \left(a+b x^2\right)^2}+\frac{5 a^3}{b^6 \left(a+b x^2\right)}+\frac{5 a^2 \log \left(a+b x^2\right)}{b^6}-\frac{2 a x^2}{b^5}+\frac{x^4}{4 b^4}",1,"(-2*a*x^2)/b^5 + x^4/(4*b^4) + a^5/(6*b^6*(a + b*x^2)^3) - (5*a^4)/(4*b^6*(a + b*x^2)^2) + (5*a^3)/(b^6*(a + b*x^2)) + (5*a^2*Log[a + b*x^2])/b^6","A",4,3,24,0.1250,1,"{28, 266, 43}"
494,1,77,0,0.0733187,"\int \frac{x^9}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^9/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{a^4}{6 b^5 \left(a+b x^2\right)^3}+\frac{a^3}{b^5 \left(a+b x^2\right)^2}-\frac{3 a^2}{b^5 \left(a+b x^2\right)}-\frac{2 a \log \left(a+b x^2\right)}{b^5}+\frac{x^2}{2 b^4}","-\frac{a^4}{6 b^5 \left(a+b x^2\right)^3}+\frac{a^3}{b^5 \left(a+b x^2\right)^2}-\frac{3 a^2}{b^5 \left(a+b x^2\right)}-\frac{2 a \log \left(a+b x^2\right)}{b^5}+\frac{x^2}{2 b^4}",1,"x^2/(2*b^4) - a^4/(6*b^5*(a + b*x^2)^3) + a^3/(b^5*(a + b*x^2)^2) - (3*a^2)/(b^5*(a + b*x^2)) - (2*a*Log[a + b*x^2])/b^5","A",4,3,24,0.1250,1,"{28, 266, 43}"
495,1,71,0,0.0636041,"\int \frac{x^7}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^7/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{a^3}{6 b^4 \left(a+b x^2\right)^3}-\frac{3 a^2}{4 b^4 \left(a+b x^2\right)^2}+\frac{3 a}{2 b^4 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^4}","\frac{a^3}{6 b^4 \left(a+b x^2\right)^3}-\frac{3 a^2}{4 b^4 \left(a+b x^2\right)^2}+\frac{3 a}{2 b^4 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^4}",1,"a^3/(6*b^4*(a + b*x^2)^3) - (3*a^2)/(4*b^4*(a + b*x^2)^2) + (3*a)/(2*b^4*(a + b*x^2)) + Log[a + b*x^2]/(2*b^4)","A",4,3,24,0.1250,1,"{28, 266, 43}"
496,1,19,0,0.006774,"\int \frac{x^5}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^5/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{x^6}{6 a \left(a+b x^2\right)^3}","\frac{x^6}{6 a \left(a+b x^2\right)^3}",1,"x^6/(6*a*(a + b*x^2)^3)","A",2,2,24,0.08333,1,"{28, 264}"
497,1,34,0,0.0292993,"\int \frac{x^3}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^3/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{a}{6 b^2 \left(a+b x^2\right)^3}-\frac{1}{4 b^2 \left(a+b x^2\right)^2}","\frac{a}{6 b^2 \left(a+b x^2\right)^3}-\frac{1}{4 b^2 \left(a+b x^2\right)^2}",1,"a/(6*b^2*(a + b*x^2)^3) - 1/(4*b^2*(a + b*x^2)^2)","A",4,3,24,0.1250,1,"{28, 266, 43}"
498,1,16,0,0.0049299,"\int \frac{x}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{1}{6 b \left(a+b x^2\right)^3}","-\frac{1}{6 b \left(a+b x^2\right)^3}",1,"-1/(6*b*(a + b*x^2)^3)","A",2,2,22,0.09091,1,"{28, 261}"
499,1,70,0,0.0758043,"\int \frac{1}{x \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","\frac{1}{2 a^3 \left(a+b x^2\right)}+\frac{1}{4 a^2 \left(a+b x^2\right)^2}-\frac{\log \left(a+b x^2\right)}{2 a^4}+\frac{\log (x)}{a^4}+\frac{1}{6 a \left(a+b x^2\right)^3}","\frac{1}{2 a^3 \left(a+b x^2\right)}+\frac{1}{4 a^2 \left(a+b x^2\right)^2}-\frac{\log \left(a+b x^2\right)}{2 a^4}+\frac{\log (x)}{a^4}+\frac{1}{6 a \left(a+b x^2\right)^3}",1,"1/(6*a*(a + b*x^2)^3) + 1/(4*a^2*(a + b*x^2)^2) + 1/(2*a^3*(a + b*x^2)) + Log[x]/a^4 - Log[a + b*x^2]/(2*a^4)","A",4,3,24,0.1250,1,"{28, 266, 44}"
500,1,84,0,0.0856393,"\int \frac{1}{x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","-\frac{3 b}{2 a^4 \left(a+b x^2\right)}-\frac{b}{2 a^3 \left(a+b x^2\right)^2}-\frac{b}{6 a^2 \left(a+b x^2\right)^3}+\frac{2 b \log \left(a+b x^2\right)}{a^5}-\frac{4 b \log (x)}{a^5}-\frac{1}{2 a^4 x^2}","-\frac{3 b}{2 a^4 \left(a+b x^2\right)}-\frac{b}{2 a^3 \left(a+b x^2\right)^2}-\frac{b}{6 a^2 \left(a+b x^2\right)^3}+\frac{2 b \log \left(a+b x^2\right)}{a^5}-\frac{4 b \log (x)}{a^5}-\frac{1}{2 a^4 x^2}",1,"-1/(2*a^4*x^2) - b/(6*a^2*(a + b*x^2)^3) - b/(2*a^3*(a + b*x^2)^2) - (3*b)/(2*a^4*(a + b*x^2)) - (4*b*Log[x])/a^5 + (2*b*Log[a + b*x^2])/a^5","A",4,3,24,0.1250,1,"{28, 266, 44}"
501,1,101,0,0.0981371,"\int \frac{1}{x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/(x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","\frac{3 b^2}{a^5 \left(a+b x^2\right)}+\frac{3 b^2}{4 a^4 \left(a+b x^2\right)^2}+\frac{b^2}{6 a^3 \left(a+b x^2\right)^3}-\frac{5 b^2 \log \left(a+b x^2\right)}{a^6}+\frac{10 b^2 \log (x)}{a^6}+\frac{2 b}{a^5 x^2}-\frac{1}{4 a^4 x^4}","\frac{3 b^2}{a^5 \left(a+b x^2\right)}+\frac{3 b^2}{4 a^4 \left(a+b x^2\right)^2}+\frac{b^2}{6 a^3 \left(a+b x^2\right)^3}-\frac{5 b^2 \log \left(a+b x^2\right)}{a^6}+\frac{10 b^2 \log (x)}{a^6}+\frac{2 b}{a^5 x^2}-\frac{1}{4 a^4 x^4}",1,"-1/(4*a^4*x^4) + (2*b)/(a^5*x^2) + b^2/(6*a^3*(a + b*x^2)^3) + (3*b^2)/(4*a^4*(a + b*x^2)^2) + (3*b^2)/(a^5*(a + b*x^2)) + (10*b^2*Log[x])/a^6 - (5*b^2*Log[a + b*x^2])/a^6","A",4,3,24,0.1250,1,"{28, 266, 44}"
502,1,117,0,0.072478,"\int \frac{x^{12}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^12/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{231 a^2 x}{16 b^6}-\frac{231 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 b^{13/2}}-\frac{11 x^9}{24 b^2 \left(a+b x^2\right)^2}-\frac{33 x^7}{16 b^3 \left(a+b x^2\right)}-\frac{77 a x^3}{16 b^5}-\frac{x^{11}}{6 b \left(a+b x^2\right)^3}+\frac{231 x^5}{80 b^4}","\frac{231 a^2 x}{16 b^6}-\frac{231 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 b^{13/2}}-\frac{11 x^9}{24 b^2 \left(a+b x^2\right)^2}-\frac{33 x^7}{16 b^3 \left(a+b x^2\right)}-\frac{77 a x^3}{16 b^5}-\frac{x^{11}}{6 b \left(a+b x^2\right)^3}+\frac{231 x^5}{80 b^4}",1,"(231*a^2*x)/(16*b^6) - (77*a*x^3)/(16*b^5) + (231*x^5)/(80*b^4) - x^11/(6*b*(a + b*x^2)^3) - (11*x^9)/(24*b^2*(a + b*x^2)^2) - (33*x^7)/(16*b^3*(a + b*x^2)) - (231*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*b^(13/2))","A",7,4,24,0.1667,1,"{28, 288, 302, 205}"
503,1,104,0,0.0594884,"\int \frac{x^{10}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^10/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{105 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 b^{11/2}}-\frac{3 x^7}{8 b^2 \left(a+b x^2\right)^2}-\frac{21 x^5}{16 b^3 \left(a+b x^2\right)}-\frac{105 a x}{16 b^5}-\frac{x^9}{6 b \left(a+b x^2\right)^3}+\frac{35 x^3}{16 b^4}","\frac{105 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 b^{11/2}}-\frac{3 x^7}{8 b^2 \left(a+b x^2\right)^2}-\frac{21 x^5}{16 b^3 \left(a+b x^2\right)}-\frac{105 a x}{16 b^5}-\frac{x^9}{6 b \left(a+b x^2\right)^3}+\frac{35 x^3}{16 b^4}",1,"(-105*a*x)/(16*b^5) + (35*x^3)/(16*b^4) - x^9/(6*b*(a + b*x^2)^3) - (3*x^7)/(8*b^2*(a + b*x^2)^2) - (21*x^5)/(16*b^3*(a + b*x^2)) + (105*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*b^(11/2))","A",7,4,24,0.1667,1,"{28, 288, 302, 205}"
504,1,93,0,0.0466813,"\int \frac{x^8}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^8/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{7 x^5}{24 b^2 \left(a+b x^2\right)^2}-\frac{35 x^3}{48 b^3 \left(a+b x^2\right)}-\frac{35 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 b^{9/2}}-\frac{x^7}{6 b \left(a+b x^2\right)^3}+\frac{35 x}{16 b^4}","-\frac{7 x^5}{24 b^2 \left(a+b x^2\right)^2}-\frac{35 x^3}{48 b^3 \left(a+b x^2\right)}-\frac{35 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 b^{9/2}}-\frac{x^7}{6 b \left(a+b x^2\right)^3}+\frac{35 x}{16 b^4}",1,"(35*x)/(16*b^4) - x^7/(6*b*(a + b*x^2)^3) - (7*x^5)/(24*b^2*(a + b*x^2)^2) - (35*x^3)/(48*b^3*(a + b*x^2)) - (35*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*b^(9/2))","A",6,4,24,0.1667,1,"{28, 288, 321, 205}"
505,1,83,0,0.039702,"\int \frac{x^6}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^6/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{5 x^3}{24 b^2 \left(a+b x^2\right)^2}-\frac{5 x}{16 b^3 \left(a+b x^2\right)}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 \sqrt{a} b^{7/2}}-\frac{x^5}{6 b \left(a+b x^2\right)^3}","-\frac{5 x^3}{24 b^2 \left(a+b x^2\right)^2}-\frac{5 x}{16 b^3 \left(a+b x^2\right)}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 \sqrt{a} b^{7/2}}-\frac{x^5}{6 b \left(a+b x^2\right)^3}",1,"-x^5/(6*b*(a + b*x^2)^3) - (5*x^3)/(24*b^2*(a + b*x^2)^2) - (5*x)/(16*b^3*(a + b*x^2)) + (5*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*Sqrt[a]*b^(7/2))","A",5,3,24,0.1250,1,"{28, 288, 205}"
506,1,84,0,0.0411935,"\int \frac{x^4}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^4/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{3/2} b^{5/2}}+\frac{x}{16 a b^2 \left(a+b x^2\right)}-\frac{x}{8 b^2 \left(a+b x^2\right)^2}-\frac{x^3}{6 b \left(a+b x^2\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{3/2} b^{5/2}}+\frac{x}{16 a b^2 \left(a+b x^2\right)}-\frac{x}{8 b^2 \left(a+b x^2\right)^2}-\frac{x^3}{6 b \left(a+b x^2\right)^3}",1,"-x^3/(6*b*(a + b*x^2)^3) - x/(8*b^2*(a + b*x^2)^2) + x/(16*a*b^2*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(16*a^(3/2)*b^(5/2))","A",5,4,24,0.1667,1,"{28, 288, 199, 205}"
507,1,85,0,0.0426251,"\int \frac{x^2}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[x^2/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x}{16 a^2 b \left(a+b x^2\right)}+\frac{x}{24 a b \left(a+b x^2\right)^2}-\frac{x}{6 b \left(a+b x^2\right)^3}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{5/2} b^{3/2}}+\frac{x}{16 a^2 b \left(a+b x^2\right)}+\frac{x}{24 a b \left(a+b x^2\right)^2}-\frac{x}{6 b \left(a+b x^2\right)^3}",1,"-x/(6*b*(a + b*x^2)^3) + x/(24*a*b*(a + b*x^2)^2) + x/(16*a^2*b*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(16*a^(5/2)*b^(3/2))","A",5,4,24,0.1667,1,"{28, 288, 199, 205}"
508,1,79,0,0.036823,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-2),x]","\frac{5 x}{16 a^3 \left(a+b x^2\right)}+\frac{5 x}{24 a^2 \left(a+b x^2\right)^2}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{7/2} \sqrt{b}}+\frac{x}{6 a \left(a+b x^2\right)^3}","\frac{5 x}{16 a^3 \left(a+b x^2\right)}+\frac{5 x}{24 a^2 \left(a+b x^2\right)^2}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{7/2} \sqrt{b}}+\frac{x}{6 a \left(a+b x^2\right)^3}",1,"x/(6*a*(a + b*x^2)^3) + (5*x)/(24*a^2*(a + b*x^2)^2) + (5*x)/(16*a^3*(a + b*x^2)) + (5*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*a^(7/2)*Sqrt[b])","A",5,3,20,0.1500,1,"{28, 199, 205}"
509,1,95,0,0.0560155,"\int \frac{1}{x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","\frac{35}{48 a^3 x \left(a+b x^2\right)}+\frac{7}{24 a^2 x \left(a+b x^2\right)^2}-\frac{35 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{9/2}}-\frac{35}{16 a^4 x}+\frac{1}{6 a x \left(a+b x^2\right)^3}","\frac{35}{48 a^3 x \left(a+b x^2\right)}+\frac{7}{24 a^2 x \left(a+b x^2\right)^2}-\frac{35 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{9/2}}-\frac{35}{16 a^4 x}+\frac{1}{6 a x \left(a+b x^2\right)^3}",1,"-35/(16*a^4*x) + 1/(6*a*x*(a + b*x^2)^3) + 7/(24*a^2*x*(a + b*x^2)^2) + 35/(48*a^3*x*(a + b*x^2)) - (35*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*a^(9/2))","A",6,4,24,0.1667,1,"{28, 290, 325, 205}"
510,1,106,0,0.0661874,"\int \frac{1}{x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/(x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","\frac{105 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{11/2}}+\frac{21}{16 a^3 x^3 \left(a+b x^2\right)}+\frac{3}{8 a^2 x^3 \left(a+b x^2\right)^2}+\frac{105 b}{16 a^5 x}-\frac{35}{16 a^4 x^3}+\frac{1}{6 a x^3 \left(a+b x^2\right)^3}","\frac{105 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{11/2}}+\frac{21}{16 a^3 x^3 \left(a+b x^2\right)}+\frac{3}{8 a^2 x^3 \left(a+b x^2\right)^2}+\frac{105 b}{16 a^5 x}-\frac{35}{16 a^4 x^3}+\frac{1}{6 a x^3 \left(a+b x^2\right)^3}",1,"-35/(16*a^4*x^3) + (105*b)/(16*a^5*x) + 1/(6*a*x^3*(a + b*x^2)^3) + 3/(8*a^2*x^3*(a + b*x^2)^2) + 21/(16*a^3*x^3*(a + b*x^2)) + (105*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*a^(11/2))","A",7,4,24,0.1667,1,"{28, 290, 325, 205}"
511,1,119,0,0.0785271,"\int \frac{1}{x^6 \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/(x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","-\frac{231 b^2}{16 a^6 x}-\frac{231 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{13/2}}+\frac{77 b}{16 a^5 x^3}+\frac{33}{16 a^3 x^5 \left(a+b x^2\right)}+\frac{11}{24 a^2 x^5 \left(a+b x^2\right)^2}-\frac{231}{80 a^4 x^5}+\frac{1}{6 a x^5 \left(a+b x^2\right)^3}","-\frac{231 b^2}{16 a^6 x}-\frac{231 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{16 a^{13/2}}+\frac{77 b}{16 a^5 x^3}+\frac{33}{16 a^3 x^5 \left(a+b x^2\right)}+\frac{11}{24 a^2 x^5 \left(a+b x^2\right)^2}-\frac{231}{80 a^4 x^5}+\frac{1}{6 a x^5 \left(a+b x^2\right)^3}",1,"-231/(80*a^4*x^5) + (77*b)/(16*a^5*x^3) - (231*b^2)/(16*a^6*x) + 1/(6*a*x^5*(a + b*x^2)^3) + 11/(24*a^2*x^5*(a + b*x^2)^2) + 33/(16*a^3*x^5*(a + b*x^2)) - (231*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(16*a^(13/2))","A",8,4,24,0.1667,1,"{28, 290, 325, 205}"
512,1,133,0,0.1427241,"\int \frac{x^{15}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^15/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{a^7}{10 b^8 \left(a+b x^2\right)^5}-\frac{7 a^6}{8 b^8 \left(a+b x^2\right)^4}+\frac{7 a^5}{2 b^8 \left(a+b x^2\right)^3}-\frac{35 a^4}{4 b^8 \left(a+b x^2\right)^2}+\frac{35 a^3}{2 b^8 \left(a+b x^2\right)}+\frac{21 a^2 \log \left(a+b x^2\right)}{2 b^8}-\frac{3 a x^2}{b^7}+\frac{x^4}{4 b^6}","\frac{a^7}{10 b^8 \left(a+b x^2\right)^5}-\frac{7 a^6}{8 b^8 \left(a+b x^2\right)^4}+\frac{7 a^5}{2 b^8 \left(a+b x^2\right)^3}-\frac{35 a^4}{4 b^8 \left(a+b x^2\right)^2}+\frac{35 a^3}{2 b^8 \left(a+b x^2\right)}+\frac{21 a^2 \log \left(a+b x^2\right)}{2 b^8}-\frac{3 a x^2}{b^7}+\frac{x^4}{4 b^6}",1,"(-3*a*x^2)/b^7 + x^4/(4*b^6) + a^7/(10*b^8*(a + b*x^2)^5) - (7*a^6)/(8*b^8*(a + b*x^2)^4) + (7*a^5)/(2*b^8*(a + b*x^2)^3) - (35*a^4)/(4*b^8*(a + b*x^2)^2) + (35*a^3)/(2*b^8*(a + b*x^2)) + (21*a^2*Log[a + b*x^2])/(2*b^8)","A",4,3,24,0.1250,1,"{28, 266, 43}"
513,1,118,0,0.1144869,"\int \frac{x^{13}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^13/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{a^6}{10 b^7 \left(a+b x^2\right)^5}+\frac{3 a^5}{4 b^7 \left(a+b x^2\right)^4}-\frac{5 a^4}{2 b^7 \left(a+b x^2\right)^3}+\frac{5 a^3}{b^7 \left(a+b x^2\right)^2}-\frac{15 a^2}{2 b^7 \left(a+b x^2\right)}-\frac{3 a \log \left(a+b x^2\right)}{b^7}+\frac{x^2}{2 b^6}","-\frac{a^6}{10 b^7 \left(a+b x^2\right)^5}+\frac{3 a^5}{4 b^7 \left(a+b x^2\right)^4}-\frac{5 a^4}{2 b^7 \left(a+b x^2\right)^3}+\frac{5 a^3}{b^7 \left(a+b x^2\right)^2}-\frac{15 a^2}{2 b^7 \left(a+b x^2\right)}-\frac{3 a \log \left(a+b x^2\right)}{b^7}+\frac{x^2}{2 b^6}",1,"x^2/(2*b^6) - a^6/(10*b^7*(a + b*x^2)^5) + (3*a^5)/(4*b^7*(a + b*x^2)^4) - (5*a^4)/(2*b^7*(a + b*x^2)^3) + (5*a^3)/(b^7*(a + b*x^2)^2) - (15*a^2)/(2*b^7*(a + b*x^2)) - (3*a*Log[a + b*x^2])/b^7","A",4,3,24,0.1250,1,"{28, 266, 43}"
514,1,109,0,0.1023031,"\int \frac{x^{11}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^11/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{a^5}{10 b^6 \left(a+b x^2\right)^5}-\frac{5 a^4}{8 b^6 \left(a+b x^2\right)^4}+\frac{5 a^3}{3 b^6 \left(a+b x^2\right)^3}-\frac{5 a^2}{2 b^6 \left(a+b x^2\right)^2}+\frac{5 a}{2 b^6 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^6}","\frac{a^5}{10 b^6 \left(a+b x^2\right)^5}-\frac{5 a^4}{8 b^6 \left(a+b x^2\right)^4}+\frac{5 a^3}{3 b^6 \left(a+b x^2\right)^3}-\frac{5 a^2}{2 b^6 \left(a+b x^2\right)^2}+\frac{5 a}{2 b^6 \left(a+b x^2\right)}+\frac{\log \left(a+b x^2\right)}{2 b^6}",1,"a^5/(10*b^6*(a + b*x^2)^5) - (5*a^4)/(8*b^6*(a + b*x^2)^4) + (5*a^3)/(3*b^6*(a + b*x^2)^3) - (5*a^2)/(2*b^6*(a + b*x^2)^2) + (5*a)/(2*b^6*(a + b*x^2)) + Log[a + b*x^2]/(2*b^6)","A",4,3,24,0.1250,1,"{28, 266, 43}"
515,1,19,0,0.0067681,"\int \frac{x^9}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^9/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{x^{10}}{10 a \left(a+b x^2\right)^5}","\frac{x^{10}}{10 a \left(a+b x^2\right)^5}",1,"x^10/(10*a*(a + b*x^2)^5)","A",2,2,24,0.08333,1,"{28, 264}"
516,1,39,0,0.0261123,"\int \frac{x^7}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^7/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{x^8}{40 a^2 \left(a+b x^2\right)^4}+\frac{x^8}{10 a \left(a+b x^2\right)^5}","\frac{x^8}{40 a^2 \left(a+b x^2\right)^4}+\frac{x^8}{10 a \left(a+b x^2\right)^5}",1,"x^8/(10*a*(a + b*x^2)^5) + x^8/(40*a^2*(a + b*x^2)^4)","A",4,4,24,0.1667,1,"{28, 266, 45, 37}"
517,1,53,0,0.0453038,"\int \frac{x^5}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^5/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{a^2}{10 b^3 \left(a+b x^2\right)^5}+\frac{a}{4 b^3 \left(a+b x^2\right)^4}-\frac{1}{6 b^3 \left(a+b x^2\right)^3}","-\frac{a^2}{10 b^3 \left(a+b x^2\right)^5}+\frac{a}{4 b^3 \left(a+b x^2\right)^4}-\frac{1}{6 b^3 \left(a+b x^2\right)^3}",1,"-a^2/(10*b^3*(a + b*x^2)^5) + a/(4*b^3*(a + b*x^2)^4) - 1/(6*b^3*(a + b*x^2)^3)","A",4,3,24,0.1250,1,"{28, 266, 43}"
518,1,34,0,0.0307099,"\int \frac{x^3}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^3/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{a}{10 b^2 \left(a+b x^2\right)^5}-\frac{1}{8 b^2 \left(a+b x^2\right)^4}","\frac{a}{10 b^2 \left(a+b x^2\right)^5}-\frac{1}{8 b^2 \left(a+b x^2\right)^4}",1,"a/(10*b^2*(a + b*x^2)^5) - 1/(8*b^2*(a + b*x^2)^4)","A",4,3,24,0.1250,1,"{28, 266, 43}"
519,1,16,0,0.0053067,"\int \frac{x}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{1}{10 b \left(a+b x^2\right)^5}","-\frac{1}{10 b \left(a+b x^2\right)^5}",1,"-1/(10*b*(a + b*x^2)^5)","A",2,2,22,0.09091,1,"{28, 261}"
520,1,102,0,0.1051261,"\int \frac{1}{x \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","\frac{1}{2 a^5 \left(a+b x^2\right)}+\frac{1}{4 a^4 \left(a+b x^2\right)^2}+\frac{1}{6 a^3 \left(a+b x^2\right)^3}+\frac{1}{8 a^2 \left(a+b x^2\right)^4}-\frac{\log \left(a+b x^2\right)}{2 a^6}+\frac{\log (x)}{a^6}+\frac{1}{10 a \left(a+b x^2\right)^5}","\frac{1}{2 a^5 \left(a+b x^2\right)}+\frac{1}{4 a^4 \left(a+b x^2\right)^2}+\frac{1}{6 a^3 \left(a+b x^2\right)^3}+\frac{1}{8 a^2 \left(a+b x^2\right)^4}-\frac{\log \left(a+b x^2\right)}{2 a^6}+\frac{\log (x)}{a^6}+\frac{1}{10 a \left(a+b x^2\right)^5}",1,"1/(10*a*(a + b*x^2)^5) + 1/(8*a^2*(a + b*x^2)^4) + 1/(6*a^3*(a + b*x^2)^3) + 1/(4*a^4*(a + b*x^2)^2) + 1/(2*a^5*(a + b*x^2)) + Log[x]/a^6 - Log[a + b*x^2]/(2*a^6)","A",4,3,24,0.1250,1,"{28, 266, 44}"
521,1,116,0,0.125673,"\int \frac{1}{x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","-\frac{5 b}{2 a^6 \left(a+b x^2\right)}-\frac{b}{a^5 \left(a+b x^2\right)^2}-\frac{b}{2 a^4 \left(a+b x^2\right)^3}-\frac{b}{4 a^3 \left(a+b x^2\right)^4}-\frac{b}{10 a^2 \left(a+b x^2\right)^5}+\frac{3 b \log \left(a+b x^2\right)}{a^7}-\frac{6 b \log (x)}{a^7}-\frac{1}{2 a^6 x^2}","-\frac{5 b}{2 a^6 \left(a+b x^2\right)}-\frac{b}{a^5 \left(a+b x^2\right)^2}-\frac{b}{2 a^4 \left(a+b x^2\right)^3}-\frac{b}{4 a^3 \left(a+b x^2\right)^4}-\frac{b}{10 a^2 \left(a+b x^2\right)^5}+\frac{3 b \log \left(a+b x^2\right)}{a^7}-\frac{6 b \log (x)}{a^7}-\frac{1}{2 a^6 x^2}",1,"-1/(2*a^6*x^2) - b/(10*a^2*(a + b*x^2)^5) - b/(4*a^3*(a + b*x^2)^4) - b/(2*a^4*(a + b*x^2)^3) - b/(a^5*(a + b*x^2)^2) - (5*b)/(2*a^6*(a + b*x^2)) - (6*b*Log[x])/a^7 + (3*b*Log[a + b*x^2])/a^7","A",4,3,24,0.1250,1,"{28, 266, 44}"
522,1,140,0,0.1446785,"\int \frac{1}{x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/(x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","\frac{15 b^2}{2 a^7 \left(a+b x^2\right)}+\frac{5 b^2}{2 a^6 \left(a+b x^2\right)^2}+\frac{b^2}{a^5 \left(a+b x^2\right)^3}+\frac{3 b^2}{8 a^4 \left(a+b x^2\right)^4}+\frac{b^2}{10 a^3 \left(a+b x^2\right)^5}-\frac{21 b^2 \log \left(a+b x^2\right)}{2 a^8}+\frac{21 b^2 \log (x)}{a^8}+\frac{3 b}{a^7 x^2}-\frac{1}{4 a^6 x^4}","\frac{15 b^2}{2 a^7 \left(a+b x^2\right)}+\frac{5 b^2}{2 a^6 \left(a+b x^2\right)^2}+\frac{b^2}{a^5 \left(a+b x^2\right)^3}+\frac{3 b^2}{8 a^4 \left(a+b x^2\right)^4}+\frac{b^2}{10 a^3 \left(a+b x^2\right)^5}-\frac{21 b^2 \log \left(a+b x^2\right)}{2 a^8}+\frac{21 b^2 \log (x)}{a^8}+\frac{3 b}{a^7 x^2}-\frac{1}{4 a^6 x^4}",1,"-1/(4*a^6*x^4) + (3*b)/(a^7*x^2) + b^2/(10*a^3*(a + b*x^2)^5) + (3*b^2)/(8*a^4*(a + b*x^2)^4) + b^2/(a^5*(a + b*x^2)^3) + (5*b^2)/(2*a^6*(a + b*x^2)^2) + (15*b^2)/(2*a^7*(a + b*x^2)) + (21*b^2*Log[x])/a^8 - (21*b^2*Log[a + b*x^2])/(2*a^8)","A",4,3,24,0.1250,1,"{28, 266, 44}"
523,1,155,0,0.1056124,"\int \frac{x^{16}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^16/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{9009 a^2 x}{256 b^8}-\frac{9009 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 b^{17/2}}-\frac{3 x^{13}}{16 b^2 \left(a+b x^2\right)^4}-\frac{13 x^{11}}{32 b^3 \left(a+b x^2\right)^3}-\frac{143 x^9}{128 b^4 \left(a+b x^2\right)^2}-\frac{1287 x^7}{256 b^5 \left(a+b x^2\right)}-\frac{3003 a x^3}{256 b^7}-\frac{x^{15}}{10 b \left(a+b x^2\right)^5}+\frac{9009 x^5}{1280 b^6}","\frac{9009 a^2 x}{256 b^8}-\frac{9009 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 b^{17/2}}-\frac{3 x^{13}}{16 b^2 \left(a+b x^2\right)^4}-\frac{13 x^{11}}{32 b^3 \left(a+b x^2\right)^3}-\frac{143 x^9}{128 b^4 \left(a+b x^2\right)^2}-\frac{1287 x^7}{256 b^5 \left(a+b x^2\right)}-\frac{3003 a x^3}{256 b^7}-\frac{x^{15}}{10 b \left(a+b x^2\right)^5}+\frac{9009 x^5}{1280 b^6}",1,"(9009*a^2*x)/(256*b^8) - (3003*a*x^3)/(256*b^7) + (9009*x^5)/(1280*b^6) - x^15/(10*b*(a + b*x^2)^5) - (3*x^13)/(16*b^2*(a + b*x^2)^4) - (13*x^11)/(32*b^3*(a + b*x^2)^3) - (143*x^9)/(128*b^4*(a + b*x^2)^2) - (1287*x^7)/(256*b^5*(a + b*x^2)) - (9009*a^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*b^(17/2))","A",9,4,24,0.1667,1,"{28, 288, 302, 205}"
524,1,142,0,0.0927995,"\int \frac{x^{14}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^14/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{3003 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 b^{15/2}}-\frac{13 x^{11}}{80 b^2 \left(a+b x^2\right)^4}-\frac{143 x^9}{480 b^3 \left(a+b x^2\right)^3}-\frac{429 x^7}{640 b^4 \left(a+b x^2\right)^2}-\frac{3003 x^5}{1280 b^5 \left(a+b x^2\right)}-\frac{3003 a x}{256 b^7}-\frac{x^{13}}{10 b \left(a+b x^2\right)^5}+\frac{1001 x^3}{256 b^6}","\frac{3003 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 b^{15/2}}-\frac{13 x^{11}}{80 b^2 \left(a+b x^2\right)^4}-\frac{143 x^9}{480 b^3 \left(a+b x^2\right)^3}-\frac{429 x^7}{640 b^4 \left(a+b x^2\right)^2}-\frac{3003 x^5}{1280 b^5 \left(a+b x^2\right)}-\frac{3003 a x}{256 b^7}-\frac{x^{13}}{10 b \left(a+b x^2\right)^5}+\frac{1001 x^3}{256 b^6}",1,"(-3003*a*x)/(256*b^7) + (1001*x^3)/(256*b^6) - x^13/(10*b*(a + b*x^2)^5) - (13*x^11)/(80*b^2*(a + b*x^2)^4) - (143*x^9)/(480*b^3*(a + b*x^2)^3) - (429*x^7)/(640*b^4*(a + b*x^2)^2) - (3003*x^5)/(1280*b^5*(a + b*x^2)) + (3003*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*b^(15/2))","A",9,4,24,0.1667,1,"{28, 288, 302, 205}"
525,1,131,0,0.0777952,"\int \frac{x^{12}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^12/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{11 x^9}{80 b^2 \left(a+b x^2\right)^4}-\frac{33 x^7}{160 b^3 \left(a+b x^2\right)^3}-\frac{231 x^5}{640 b^4 \left(a+b x^2\right)^2}-\frac{231 x^3}{256 b^5 \left(a+b x^2\right)}-\frac{693 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 b^{13/2}}-\frac{x^{11}}{10 b \left(a+b x^2\right)^5}+\frac{693 x}{256 b^6}","-\frac{11 x^9}{80 b^2 \left(a+b x^2\right)^4}-\frac{33 x^7}{160 b^3 \left(a+b x^2\right)^3}-\frac{231 x^5}{640 b^4 \left(a+b x^2\right)^2}-\frac{231 x^3}{256 b^5 \left(a+b x^2\right)}-\frac{693 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 b^{13/2}}-\frac{x^{11}}{10 b \left(a+b x^2\right)^5}+\frac{693 x}{256 b^6}",1,"(693*x)/(256*b^6) - x^11/(10*b*(a + b*x^2)^5) - (11*x^9)/(80*b^2*(a + b*x^2)^4) - (33*x^7)/(160*b^3*(a + b*x^2)^3) - (231*x^5)/(640*b^4*(a + b*x^2)^2) - (231*x^3)/(256*b^5*(a + b*x^2)) - (693*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*b^(13/2))","A",8,4,24,0.1667,1,"{28, 288, 321, 205}"
526,1,121,0,0.0688564,"\int \frac{x^{10}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^10/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{9 x^7}{80 b^2 \left(a+b x^2\right)^4}-\frac{21 x^5}{160 b^3 \left(a+b x^2\right)^3}-\frac{21 x^3}{128 b^4 \left(a+b x^2\right)^2}-\frac{63 x}{256 b^5 \left(a+b x^2\right)}+\frac{63 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 \sqrt{a} b^{11/2}}-\frac{x^9}{10 b \left(a+b x^2\right)^5}","-\frac{9 x^7}{80 b^2 \left(a+b x^2\right)^4}-\frac{21 x^5}{160 b^3 \left(a+b x^2\right)^3}-\frac{21 x^3}{128 b^4 \left(a+b x^2\right)^2}-\frac{63 x}{256 b^5 \left(a+b x^2\right)}+\frac{63 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 \sqrt{a} b^{11/2}}-\frac{x^9}{10 b \left(a+b x^2\right)^5}",1,"-x^9/(10*b*(a + b*x^2)^5) - (9*x^7)/(80*b^2*(a + b*x^2)^4) - (21*x^5)/(160*b^3*(a + b*x^2)^3) - (21*x^3)/(128*b^4*(a + b*x^2)^2) - (63*x)/(256*b^5*(a + b*x^2)) + (63*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*Sqrt[a]*b^(11/2))","A",7,3,24,0.1250,1,"{28, 288, 205}"
527,1,122,0,0.0721806,"\int \frac{x^8}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^8/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{7 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{3/2} b^{9/2}}-\frac{7 x^5}{80 b^2 \left(a+b x^2\right)^4}-\frac{7 x^3}{96 b^3 \left(a+b x^2\right)^3}+\frac{7 x}{256 a b^4 \left(a+b x^2\right)}-\frac{7 x}{128 b^4 \left(a+b x^2\right)^2}-\frac{x^7}{10 b \left(a+b x^2\right)^5}","\frac{7 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{3/2} b^{9/2}}-\frac{7 x^5}{80 b^2 \left(a+b x^2\right)^4}-\frac{7 x^3}{96 b^3 \left(a+b x^2\right)^3}+\frac{7 x}{256 a b^4 \left(a+b x^2\right)}-\frac{7 x}{128 b^4 \left(a+b x^2\right)^2}-\frac{x^7}{10 b \left(a+b x^2\right)^5}",1,"-x^7/(10*b*(a + b*x^2)^5) - (7*x^5)/(80*b^2*(a + b*x^2)^4) - (7*x^3)/(96*b^3*(a + b*x^2)^3) - (7*x)/(128*b^4*(a + b*x^2)^2) + (7*x)/(256*a*b^4*(a + b*x^2)) + (7*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(3/2)*b^(9/2))","A",7,4,24,0.1667,1,"{28, 288, 199, 205}"
528,1,123,0,0.0721446,"\int \frac{x^6}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^6/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{3 x}{256 a^2 b^3 \left(a+b x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{5/2} b^{7/2}}-\frac{x^3}{16 b^2 \left(a+b x^2\right)^4}+\frac{x}{128 a b^3 \left(a+b x^2\right)^2}-\frac{x}{32 b^3 \left(a+b x^2\right)^3}-\frac{x^5}{10 b \left(a+b x^2\right)^5}","\frac{3 x}{256 a^2 b^3 \left(a+b x^2\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{5/2} b^{7/2}}-\frac{x^3}{16 b^2 \left(a+b x^2\right)^4}+\frac{x}{128 a b^3 \left(a+b x^2\right)^2}-\frac{x}{32 b^3 \left(a+b x^2\right)^3}-\frac{x^5}{10 b \left(a+b x^2\right)^5}",1,"-x^5/(10*b*(a + b*x^2)^5) - x^3/(16*b^2*(a + b*x^2)^4) - x/(32*b^3*(a + b*x^2)^3) + x/(128*a*b^3*(a + b*x^2)^2) + (3*x)/(256*a^2*b^3*(a + b*x^2)) + (3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(5/2)*b^(7/2))","A",7,4,24,0.1667,1,"{28, 288, 199, 205}"
529,1,124,0,0.0729037,"\int \frac{x^4}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^4/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{3 x}{256 a^3 b^2 \left(a+b x^2\right)}+\frac{x}{128 a^2 b^2 \left(a+b x^2\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{7/2} b^{5/2}}+\frac{x}{160 a b^2 \left(a+b x^2\right)^3}-\frac{3 x}{80 b^2 \left(a+b x^2\right)^4}-\frac{x^3}{10 b \left(a+b x^2\right)^5}","\frac{3 x}{256 a^3 b^2 \left(a+b x^2\right)}+\frac{x}{128 a^2 b^2 \left(a+b x^2\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{7/2} b^{5/2}}+\frac{x}{160 a b^2 \left(a+b x^2\right)^3}-\frac{3 x}{80 b^2 \left(a+b x^2\right)^4}-\frac{x^3}{10 b \left(a+b x^2\right)^5}",1,"-x^3/(10*b*(a + b*x^2)^5) - (3*x)/(80*b^2*(a + b*x^2)^4) + x/(160*a*b^2*(a + b*x^2)^3) + x/(128*a^2*b^2*(a + b*x^2)^2) + (3*x)/(256*a^3*b^2*(a + b*x^2)) + (3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(7/2)*b^(5/2))","A",7,4,24,0.1667,1,"{28, 288, 199, 205}"
530,1,125,0,0.0746596,"\int \frac{x^2}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[x^2/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{7 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{9/2} b^{3/2}}+\frac{7 x}{256 a^4 b \left(a+b x^2\right)}+\frac{7 x}{384 a^3 b \left(a+b x^2\right)^2}+\frac{7 x}{480 a^2 b \left(a+b x^2\right)^3}+\frac{x}{80 a b \left(a+b x^2\right)^4}-\frac{x}{10 b \left(a+b x^2\right)^5}","\frac{7 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{9/2} b^{3/2}}+\frac{7 x}{256 a^4 b \left(a+b x^2\right)}+\frac{7 x}{384 a^3 b \left(a+b x^2\right)^2}+\frac{7 x}{480 a^2 b \left(a+b x^2\right)^3}+\frac{x}{80 a b \left(a+b x^2\right)^4}-\frac{x}{10 b \left(a+b x^2\right)^5}",1,"-x/(10*b*(a + b*x^2)^5) + x/(80*a*b*(a + b*x^2)^4) + (7*x)/(480*a^2*b*(a + b*x^2)^3) + (7*x)/(384*a^3*b*(a + b*x^2)^2) + (7*x)/(256*a^4*b*(a + b*x^2)) + (7*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(9/2)*b^(3/2))","A",7,4,24,0.1667,1,"{28, 288, 199, 205}"
531,1,113,0,0.0663419,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-3),x]","\frac{63 x}{256 a^5 \left(a+b x^2\right)}+\frac{21 x}{128 a^4 \left(a+b x^2\right)^2}+\frac{21 x}{160 a^3 \left(a+b x^2\right)^3}+\frac{9 x}{80 a^2 \left(a+b x^2\right)^4}+\frac{63 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{11/2} \sqrt{b}}+\frac{x}{10 a \left(a+b x^2\right)^5}","\frac{63 x}{256 a^5 \left(a+b x^2\right)}+\frac{21 x}{128 a^4 \left(a+b x^2\right)^2}+\frac{21 x}{160 a^3 \left(a+b x^2\right)^3}+\frac{9 x}{80 a^2 \left(a+b x^2\right)^4}+\frac{63 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{11/2} \sqrt{b}}+\frac{x}{10 a \left(a+b x^2\right)^5}",1,"x/(10*a*(a + b*x^2)^5) + (9*x)/(80*a^2*(a + b*x^2)^4) + (21*x)/(160*a^3*(a + b*x^2)^3) + (21*x)/(128*a^4*(a + b*x^2)^2) + (63*x)/(256*a^5*(a + b*x^2)) + (63*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(11/2)*Sqrt[b])","A",7,3,20,0.1500,1,"{28, 199, 205}"
532,1,133,0,0.0893844,"\int \frac{1}{x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","\frac{231}{256 a^5 x \left(a+b x^2\right)}+\frac{231}{640 a^4 x \left(a+b x^2\right)^2}+\frac{33}{160 a^3 x \left(a+b x^2\right)^3}+\frac{11}{80 a^2 x \left(a+b x^2\right)^4}-\frac{693 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{13/2}}-\frac{693}{256 a^6 x}+\frac{1}{10 a x \left(a+b x^2\right)^5}","\frac{231}{256 a^5 x \left(a+b x^2\right)}+\frac{231}{640 a^4 x \left(a+b x^2\right)^2}+\frac{33}{160 a^3 x \left(a+b x^2\right)^3}+\frac{11}{80 a^2 x \left(a+b x^2\right)^4}-\frac{693 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{13/2}}-\frac{693}{256 a^6 x}+\frac{1}{10 a x \left(a+b x^2\right)^5}",1,"-693/(256*a^6*x) + 1/(10*a*x*(a + b*x^2)^5) + 11/(80*a^2*x*(a + b*x^2)^4) + 33/(160*a^3*x*(a + b*x^2)^3) + 231/(640*a^4*x*(a + b*x^2)^2) + 231/(256*a^5*x*(a + b*x^2)) - (693*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(13/2))","A",8,4,24,0.1667,1,"{28, 290, 325, 205}"
533,1,144,0,0.1030983,"\int \frac{1}{x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/(x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","\frac{3003 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{15/2}}+\frac{3003}{1280 a^5 x^3 \left(a+b x^2\right)}+\frac{429}{640 a^4 x^3 \left(a+b x^2\right)^2}+\frac{143}{480 a^3 x^3 \left(a+b x^2\right)^3}+\frac{13}{80 a^2 x^3 \left(a+b x^2\right)^4}+\frac{3003 b}{256 a^7 x}-\frac{1001}{256 a^6 x^3}+\frac{1}{10 a x^3 \left(a+b x^2\right)^5}","\frac{3003 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{15/2}}+\frac{3003}{1280 a^5 x^3 \left(a+b x^2\right)}+\frac{429}{640 a^4 x^3 \left(a+b x^2\right)^2}+\frac{143}{480 a^3 x^3 \left(a+b x^2\right)^3}+\frac{13}{80 a^2 x^3 \left(a+b x^2\right)^4}+\frac{3003 b}{256 a^7 x}-\frac{1001}{256 a^6 x^3}+\frac{1}{10 a x^3 \left(a+b x^2\right)^5}",1,"-1001/(256*a^6*x^3) + (3003*b)/(256*a^7*x) + 1/(10*a*x^3*(a + b*x^2)^5) + 13/(80*a^2*x^3*(a + b*x^2)^4) + 143/(480*a^3*x^3*(a + b*x^2)^3) + 429/(640*a^4*x^3*(a + b*x^2)^2) + 3003/(1280*a^5*x^3*(a + b*x^2)) + (3003*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(15/2))","A",9,4,24,0.1667,1,"{28, 290, 325, 205}"
534,1,157,0,0.1221919,"\int \frac{1}{x^6 \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/(x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","-\frac{9009 b^2}{256 a^8 x}-\frac{9009 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{17/2}}+\frac{3003 b}{256 a^7 x^3}+\frac{1287}{256 a^5 x^5 \left(a+b x^2\right)}+\frac{143}{128 a^4 x^5 \left(a+b x^2\right)^2}+\frac{13}{32 a^3 x^5 \left(a+b x^2\right)^3}+\frac{3}{16 a^2 x^5 \left(a+b x^2\right)^4}-\frac{9009}{1280 a^6 x^5}+\frac{1}{10 a x^5 \left(a+b x^2\right)^5}","-\frac{9009 b^2}{256 a^8 x}-\frac{9009 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 a^{17/2}}+\frac{3003 b}{256 a^7 x^3}+\frac{1287}{256 a^5 x^5 \left(a+b x^2\right)}+\frac{143}{128 a^4 x^5 \left(a+b x^2\right)^2}+\frac{13}{32 a^3 x^5 \left(a+b x^2\right)^3}+\frac{3}{16 a^2 x^5 \left(a+b x^2\right)^4}-\frac{9009}{1280 a^6 x^5}+\frac{1}{10 a x^5 \left(a+b x^2\right)^5}",1,"-9009/(1280*a^6*x^5) + (3003*b)/(256*a^7*x^3) - (9009*b^2)/(256*a^8*x) + 1/(10*a*x^5*(a + b*x^2)^5) + 3/(16*a^2*x^5*(a + b*x^2)^4) + 13/(32*a^3*x^5*(a + b*x^2)^3) + 143/(128*a^4*x^5*(a + b*x^2)^2) + 1287/(256*a^5*x^5*(a + b*x^2)) - (9009*b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(256*a^(17/2))","A",10,4,24,0.1667,1,"{28, 290, 325, 205}"
535,1,19,0,0.0031113,"\int \frac{1}{1+2 x^2+x^4} \, dx","Int[(1 + 2*x^2 + x^4)^(-1),x]","\frac{x}{2 \left(x^2+1\right)}+\frac{1}{2} \tan ^{-1}(x)","\frac{x}{2 \left(x^2+1\right)}+\frac{1}{2} \tan ^{-1}(x)",1,"x/(2*(1 + x^2)) + ArcTan[x]/2","A",3,3,12,0.2500,1,"{28, 199, 203}"
536,1,11,0,0.0021301,"\int \frac{x}{1+2 x^2+x^4} \, dx","Int[x/(1 + 2*x^2 + x^4),x]","-\frac{1}{2 \left(x^2+1\right)}","-\frac{1}{2 \left(x^2+1\right)}",1,"-1/(2*(1 + x^2))","A",2,2,14,0.1429,1,"{28, 261}"
537,1,19,0,0.0048065,"\int \frac{x^2}{1+2 x^2+x^4} \, dx","Int[x^2/(1 + 2*x^2 + x^4),x]","\frac{1}{2} \tan ^{-1}(x)-\frac{x}{2 \left(x^2+1\right)}","\frac{1}{2} \tan ^{-1}(x)-\frac{x}{2 \left(x^2+1\right)}",1,"-x/(2*(1 + x^2)) + ArcTan[x]/2","A",3,3,16,0.1875,1,"{28, 288, 203}"
538,1,22,0,0.0108123,"\int \frac{x^3}{1+2 x^2+x^4} \, dx","Int[x^3/(1 + 2*x^2 + x^4),x]","\frac{1}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)","\frac{1}{2 \left(x^2+1\right)}+\frac{1}{2} \log \left(x^2+1\right)",1,"1/(2*(1 + x^2)) + Log[1 + x^2]/2","A",4,3,16,0.1875,1,"{28, 266, 43}"
539,1,13,0,0.0021261,"\int \frac{x}{81-18 x^2+x^4} \, dx","Int[x/(81 - 18*x^2 + x^4),x]","\frac{1}{2 \left(9-x^2\right)}","\frac{1}{2 \left(9-x^2\right)}",1,"1/(2*(9 - x^2))","A",2,2,14,0.1429,1,"{28, 261}"
540,1,24,0,0.0147868,"\int \frac{x^3}{16-8 x^2+x^4} \, dx","Int[x^3/(16 - 8*x^2 + x^4),x]","\frac{2}{4-x^2}+\frac{1}{2} \log \left(4-x^2\right)","\frac{2}{4-x^2}+\frac{1}{2} \log \left(4-x^2\right)",1,"2/(4 - x^2) + Log[4 - x^2]/2","A",4,3,16,0.1875,1,"{28, 266, 43}"
541,1,79,0,0.0643209,"\int x^5 \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{b x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{a x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}","\frac{b x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{a x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}",1,"(a*x^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*(a + b*x^2)) + (b*x^8*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
542,1,67,0,0.0516276,"\int x^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{6 b^2}-\frac{a \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 b^2}","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{6 b^2}-\frac{a \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 b^2}",1,"-(a*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*b^2) + (a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/(6*b^2)","A",3,3,26,0.1154,1,"{1111, 640, 609}"
543,1,36,0,0.0255502,"\int x \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 b}","\frac{\left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 b}",1,"((a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*b)","A",2,2,24,0.08333,1,"{1107, 609}"
544,1,75,0,0.0219498,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x,x]","\frac{b x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{a \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","\frac{b x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{a \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"(b*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",3,2,26,0.07692,1,"{1112, 14}"
545,1,75,0,0.0218993,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^3} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^3,x]","\frac{b \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}","\frac{b \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^2*(a + b*x^2)) + (b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",3,2,26,0.07692,1,"{1112, 14}"
546,1,39,0,0.0382253,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^5,x]","-\frac{\left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 a x^4}","-\frac{\left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 a x^4}",1,"-((a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*a*x^4)","A",3,3,26,0.1154,1,"{1111, 646, 37}"
547,1,72,0,0.0155318,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^7} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^7,x]","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{12 a^2 x^6}-\frac{\left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 a x^6}","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{12 a^2 x^6}-\frac{\left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 a x^6}",1,"-((a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*a*x^6) + (a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/(12*a^2*x^6)","A",1,1,26,0.03846,1,"{1110}"
548,1,79,0,0.0594119,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^9} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^9,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^8*(a + b*x^2)) - (b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*x^6*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
549,1,79,0,0.0581569,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^{11}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^11,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*x^10*(a + b*x^2)) - (b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^8*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
550,1,79,0,0.0226354,"\int x^4 \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{b x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}","\frac{b x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}",1,"(a*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*(a + b*x^2)) + (b*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 14}"
551,1,79,0,0.023179,"\int x^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{b x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}+\frac{a x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}","\frac{b x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}+\frac{a x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}",1,"(a*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (b*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 14}"
552,1,74,0,0.0136244,"\int \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{b x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{a x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","\frac{b x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{a x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"(a*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (b*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2))","A",2,1,22,0.04545,1,"{1088}"
553,1,72,0,0.0203706,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^2} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^2,x]","\frac{b x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}","\frac{b x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}",1,"-((a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2))) + (b*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2)","A",3,2,26,0.07692,1,"{1112, 14}"
554,1,77,0,0.0230154,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^4} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^4,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2)) - (b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 14}"
555,1,79,0,0.0205168,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^6} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^6,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2)) - (b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 14}"
556,1,79,0,0.0216657,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^8} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^8,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 14}"
557,1,79,0,0.0222312,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{x^{10}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/x^10,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2)) - (b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 14}"
558,1,167,0,0.1136162,"\int x^9 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^9*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{b^3 x^{16} \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 \left(a+b x^2\right)}+\frac{3 a b^2 x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}+\frac{a^2 b x^{12} \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{a^3 x^{10} \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 \left(a+b x^2\right)}","\frac{b^3 x^{16} \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 \left(a+b x^2\right)}+\frac{3 a b^2 x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}+\frac{a^2 b x^{12} \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{a^3 x^{10} \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 \left(a+b x^2\right)}",1,"(a^3*x^10*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*(a + b*x^2)) + (a^2*b*x^12*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*(a + b*x^2)) + (3*a*b^2*x^14*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*(a + b*x^2)) + (b^3*x^16*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
559,1,167,0,0.1138621,"\int x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^7*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{b^3 x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}+\frac{a b^2 x^{12} \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{3 a^2 b x^{10} \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 \left(a+b x^2\right)}+\frac{a^3 x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}","\frac{b^3 x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}+\frac{a b^2 x^{12} \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{3 a^2 b x^{10} \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 \left(a+b x^2\right)}+\frac{a^3 x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}",1,"(a^3*x^8*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*(a + b*x^2)) + (3*a^2*b*x^10*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*(a + b*x^2)) + (a*b^2*x^12*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*(a + b*x^2)) + (b^3*x^14*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
560,1,119,0,0.0834046,"\int x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{12 b^3}-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^4}{5 b^3}+\frac{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^3}{8 b^3}","\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{12 b^3}-\frac{a \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{5 b^3}+\frac{a^2 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{8 b^3}",1,"(a^2*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*b^3) - (a*(a + b*x^2)^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*b^3) + ((a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*b^3)","A",3,2,26,0.07692,1,"{1111, 645}"
561,1,67,0,0.0509264,"\int x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{10 b^2}-\frac{a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{8 b^2}","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{10 b^2}-\frac{a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{8 b^2}",1,"-(a*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))/(8*b^2) + (a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/(10*b^2)","A",3,3,26,0.1154,1,"{1111, 640, 609}"
562,1,36,0,0.0259699,"\int x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{8 b}","\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{8 b}",1,"((a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))/(8*b)","A",2,2,24,0.08333,1,"{1107, 609}"
563,1,163,0,0.0492274,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x,x]","\frac{b^3 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}+\frac{3 a b^2 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{3 a^2 b x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","\frac{b^3 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}+\frac{3 a b^2 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{3 a^2 b x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"(3*a^2*b*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (3*a*b^2*x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*(a + b*x^2)) + (b^3*x^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*(a + b*x^2)) + (a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
564,1,164,0,0.0470999,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^3} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^3,x]","\frac{b^3 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{3 a b^2 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{3 a^2 b \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","\frac{b^3 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{3 a b^2 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{3 a^2 b \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^2*(a + b*x^2)) + (3*a*b^2*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (b^3*x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*(a + b*x^2)) + (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
565,1,164,0,0.0487639,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^5} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^5,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{b^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{3 a b^2 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{b^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{3 a b^2 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*x^4*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^2*(a + b*x^2)) + (b^3*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
566,1,163,0,0.0461357,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^7} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^7,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{b^3 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{b^3 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*x^6*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*x^4*(a + b*x^2)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^2*(a + b*x^2)) + (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
567,1,41,0,0.0394895,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^9} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^9,x]","-\frac{\left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 a x^8}","-\frac{\left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 a x^8}",1,"-((a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*a*x^8)","A",3,3,26,0.1154,1,"{1111, 646, 37}"
568,1,72,0,0.0167922,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{11}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^11,x]","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{40 a^2 x^{10}}-\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{8 a x^{10}}","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{40 a^2 x^{10}}-\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{8 a x^{10}}",1,"-((a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))/(8*a*x^10) + (a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/(40*a^2*x^10)","A",1,1,26,0.03846,1,"{1110}"
569,1,167,0,0.1049705,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{13}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^13,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 x^{12} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 x^{12} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*x^12*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*x^10*(a + b*x^2)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^8*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*x^6*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
570,1,167,0,0.1058185,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{15}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^15,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^{12} \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^{12} \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*x^14*(a + b*x^2)) - (a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*x^12*(a + b*x^2)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*x^10*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^8*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
571,1,167,0,0.1045887,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{17}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^17,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 x^{16} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^{12} \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 x^{16} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^{12} \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*x^16*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*x^14*(a + b*x^2)) - (a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*x^12*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*x^10*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
572,1,167,0,0.0420411,"\int x^8 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^8*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{b^3 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 \left(a+b x^2\right)}+\frac{3 a b^2 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{3 a^2 b x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a^3 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}","\frac{b^3 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 \left(a+b x^2\right)}+\frac{3 a b^2 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{3 a^2 b x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a^3 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}",1,"(a^3*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2)) + (3*a^2*b*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2)) + (3*a*b^2*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2)) + (b^3*x^15*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(15*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
573,1,167,0,0.0405747,"\int x^6 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{b^3 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{3 a b^2 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a^2 b x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{a^3 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}","\frac{b^3 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{3 a b^2 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a^2 b x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{a^3 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}",1,"(a^3*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2)) + (a^2*b*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (3*a*b^2*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2)) + (b^3*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
574,1,167,0,0.0432692,"\int x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{b^3 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a b^2 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{3 a^2 b x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a^3 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}","\frac{b^3 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a b^2 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{3 a^2 b x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a^3 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}",1,"(a^3*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*(a + b*x^2)) + (3*a^2*b*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2)) + (a*b^2*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (b^3*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
575,1,167,0,0.0407834,"\int x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{b^3 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{3 a b^2 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{3 a^2 b x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}+\frac{a^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}","\frac{b^3 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{3 a b^2 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{3 a^2 b x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}+\frac{a^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}",1,"(a^3*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (3*a^2*b*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*(a + b*x^2)) + (3*a*b^2*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2)) + (b^3*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
576,1,159,0,0.0332733,"\int \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{b^3 x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{7 \left(a+b x^2\right)^3}+\frac{3 a b^2 x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{5 \left(a+b x^2\right)^3}+\frac{a^2 b x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{\left(a+b x^2\right)^3}+\frac{a^3 x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{\left(a+b x^2\right)^3}","\frac{b^3 x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{7 \left(a+b x^2\right)^3}+\frac{3 a b^2 x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{5 \left(a+b x^2\right)^3}+\frac{a^2 b x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{\left(a+b x^2\right)^3}+\frac{a^3 x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{\left(a+b x^2\right)^3}",1,"(a^3*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))/(a + b*x^2)^3 + (a^2*b*x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))/(a + b*x^2)^3 + (3*a*b^2*x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))/(5*(a + b*x^2)^3) + (b^3*x^7*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))/(7*(a + b*x^2)^3)","A",3,2,22,0.09091,1,"{1088, 194}"
577,1,158,0,0.0397997,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^2,x]","\frac{b^3 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}+\frac{a b^2 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{3 a^2 b x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}","\frac{b^3 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}+\frac{a b^2 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{3 a^2 b x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}",1,"-((a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2))) + (3*a^2*b*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (a*b^2*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (b^3*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
578,1,161,0,0.0403986,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^4,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{3 a b^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{b^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{3 a b^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{b^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2)) + (3*a*b^2*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (b^3*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
579,1,158,0,0.0403273,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^6} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^6,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^3 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{b^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^3 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{b^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2)) - (a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^3*(a + b*x^2)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2)) + (b^3*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2)","A",3,2,26,0.07692,1,"{1112, 270}"
580,1,163,0,0.0432572,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^8} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^8,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^3 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^3 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2)) - (a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^3*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
581,1,167,0,0.0394533,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{10}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^10,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
582,1,167,0,0.0439584,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{12}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^12,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^9 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^9 \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^9*(a + b*x^2)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
583,1,167,0,0.0403642,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{14}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^14,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^9 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^9 \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^9*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
584,1,167,0,0.0411472,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{x^{16}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/x^16,x]","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 x^{15} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 x^{15} \left(a+b x^2\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(15*x^15*(a + b*x^2)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
585,1,255,0,0.1616853,"\int x^{13} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^13*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{24} \sqrt{a^2+2 a b x^2+b^2 x^4}}{24 \left(a+b x^2\right)}+\frac{5 a b^4 x^{22} \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 \left(a+b x^2\right)}+\frac{a^2 b^3 x^{20} \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^{18} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a^4 b x^{16} \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 \left(a+b x^2\right)}+\frac{a^5 x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}","\frac{b^5 x^{24} \sqrt{a^2+2 a b x^2+b^2 x^4}}{24 \left(a+b x^2\right)}+\frac{5 a b^4 x^{22} \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 \left(a+b x^2\right)}+\frac{a^2 b^3 x^{20} \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^{18} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a^4 b x^{16} \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 \left(a+b x^2\right)}+\frac{a^5 x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}",1,"(a^5*x^14*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*(a + b*x^2)) + (5*a^4*b*x^16*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*(a + b*x^2)) + (5*a^3*b^2*x^18*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2)) + (a^2*b^3*x^20*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (5*a*b^4*x^22*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(22*(a + b*x^2)) + (b^5*x^24*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(24*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
586,1,255,0,0.1589803,"\int x^{11} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^11*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{22} \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 \left(a+b x^2\right)}+\frac{a b^4 x^{20} \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^{18} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^{16} \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{5 a^4 b x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}+\frac{a^5 x^{12} \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 \left(a+b x^2\right)}","\frac{b^5 x^{22} \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 \left(a+b x^2\right)}+\frac{a b^4 x^{20} \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^{18} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^{16} \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{5 a^4 b x^{14} \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 \left(a+b x^2\right)}+\frac{a^5 x^{12} \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 \left(a+b x^2\right)}",1,"(a^5*x^12*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*(a + b*x^2)) + (5*a^4*b*x^14*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*(a + b*x^2)) + (5*a^3*b^2*x^16*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*(a + b*x^2)) + (5*a^2*b^3*x^18*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2)) + (a*b^4*x^20*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*(a + b*x^2)) + (b^5*x^22*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(22*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
587,1,201,0,0.1315248,"\int x^9 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^9*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^9}{20 b^5}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^8}{9 b^5}+\frac{3 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^7}{8 b^5}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^6}{7 b^5}+\frac{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{12 b^5}","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^9}{20 b^5}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^8}{9 b^5}+\frac{3 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^7}{8 b^5}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^6}{7 b^5}+\frac{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{12 b^5}",1,"(a^4*(a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*b^5) - (2*a^3*(a + b*x^2)^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*b^5) + (3*a^2*(a + b*x^2)^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*b^5) - (2*a*(a + b*x^2)^8*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*b^5) + ((a + b*x^2)^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(20*b^5)","A",3,2,26,0.07692,1,"{1111, 645}"
588,1,160,0,0.1183275,"\int x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^7*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^8}{18 b^4}-\frac{3 a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^7}{16 b^4}+\frac{3 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^6}{14 b^4}-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{12 b^4}","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^8}{18 b^4}-\frac{3 a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^7}{16 b^4}+\frac{3 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^6}{14 b^4}-\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{12 b^4}",1,"-(a^3*(a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*b^4) + (3*a^2*(a + b*x^2)^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*b^4) - (3*a*(a + b*x^2)^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*b^4) + ((a + b*x^2)^8*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(18*b^4)","A",4,3,26,0.1154,1,"{1111, 646, 43}"
589,1,119,0,0.0971745,"\int x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^7}{16 b^3}-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^6}{7 b^3}+\frac{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{12 b^3}","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^7}{16 b^3}-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^6}{7 b^3}+\frac{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{12 b^3}",1,"(a^2*(a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*b^3) - (a*(a + b*x^2)^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*b^3) + ((a + b*x^2)^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*b^3)","A",4,3,26,0.1154,1,"{1111, 646, 43}"
590,1,67,0,0.0516458,"\int x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{7/2}}{14 b^2}-\frac{a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{12 b^2}","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{7/2}}{14 b^2}-\frac{a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{12 b^2}",1,"-(a*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(12*b^2) + (a^2 + 2*a*b*x^2 + b^2*x^4)^(7/2)/(14*b^2)","A",3,3,26,0.1154,1,"{1111, 640, 609}"
591,1,36,0,0.0258815,"\int x \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{12 b}","\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{12 b}",1,"((a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(12*b)","A",2,2,24,0.08333,1,"{1107, 609}"
592,1,251,0,0.070981,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x,x]","\frac{b^5 x^{10} \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 \left(a+b x^2\right)}+\frac{5 a b^4 x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a^4 b x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{a^5 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","\frac{b^5 x^{10} \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 \left(a+b x^2\right)}+\frac{5 a b^4 x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a^4 b x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{a^5 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"(5*a^4*b*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (5*a^3*b^2*x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (5*a^2*b^3*x^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (5*a*b^4*x^8*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*(a + b*x^2)) + (b^5*x^10*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*(a + b*x^2)) + (a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
593,1,250,0,0.0714932,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^3} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^3,x]","\frac{b^5 x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{5 a b^4 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{5 a^4 b \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","\frac{b^5 x^8 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 \left(a+b x^2\right)}+\frac{5 a b^4 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a^3 b^2 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{5 a^4 b \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^2*(a + b*x^2)) + (5*a^3*b^2*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (5*a^2*b^3*x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (5*a*b^4*x^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*(a + b*x^2)) + (b^5*x^8*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*(a + b*x^2)) + (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
594,1,250,0,0.0700548,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^5} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^5,x]","\frac{b^5 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}+\frac{5 a b^4 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}+\frac{10 a^3 b^2 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","\frac{b^5 x^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 \left(a+b x^2\right)}+\frac{5 a b^4 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{5 a^2 b^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}+\frac{10 a^3 b^2 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*x^4*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^2*(a + b*x^2)) + (5*a^2*b^3*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (5*a*b^4*x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*(a + b*x^2)) + (b^5*x^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*(a + b*x^2)) + (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
595,1,250,0,0.0724194,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^7} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^7,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^2 \left(a+b x^2\right)}+\frac{5 a b^4 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{b^5 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{10 a^2 b^3 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^4 \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^2 \left(a+b x^2\right)}+\frac{5 a b^4 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{b^5 x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 \left(a+b x^2\right)}+\frac{10 a^2 b^3 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*x^6*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*x^4*(a + b*x^2)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^2*(a + b*x^2)) + (5*a*b^4*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (b^5*x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*(a + b*x^2)) + (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
596,1,250,0,0.0707543,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^9} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^9,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^4 \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^2 \left(a+b x^2\right)}+\frac{b^5 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a b^4 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^6 \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^4 \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^2 \left(a+b x^2\right)}+\frac{b^5 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 \left(a+b x^2\right)}+\frac{5 a b^4 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^8*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*x^6*(a + b*x^2)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^4*(a + b*x^2)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^2*(a + b*x^2)) + (b^5*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*(a + b*x^2)) + (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
597,1,251,0,0.0682964,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{11}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^11,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^6 \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^4 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{b^5 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^6 \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^4 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{b^5 \log (x) \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*x^10*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^8*(a + b*x^2)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^6*(a + b*x^2)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^4*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^2*(a + b*x^2)) + (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*Log[x])/(a + b*x^2)","A",4,3,26,0.1154,1,"{1112, 266, 43}"
598,1,41,0,0.0392379,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{13}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^13,x]","-\frac{\left(a+b x^2\right)^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 a x^{12}}","-\frac{\left(a+b x^2\right)^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 a x^{12}}",1,"-((a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*a*x^12)","A",3,3,26,0.1154,1,"{1111, 646, 37}"
599,1,72,0,0.0168661,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{15}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^15,x]","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{7/2}}{84 a^2 x^{14}}-\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{12 a x^{14}}","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{7/2}}{84 a^2 x^{14}}-\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{12 a x^{14}}",1,"-((a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(12*a*x^14) + (a^2 + 2*a*b*x^2 + b^2*x^4)^(7/2)/(84*a^2*x^14)","A",1,1,26,0.03846,1,"{1110}"
600,1,128,0,0.0911089,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{17}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^17,x]","-\frac{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{336 a^3 x^{12}}+\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{56 a^2 x^{14}}-\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{16 a x^{16}}","-\frac{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{336 a^3 x^{12}}+\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{56 a^2 x^{14}}-\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^5}{16 a x^{16}}",1,"-((a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*a*x^16) + (b*(a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(56*a^2*x^14) - (b^2*(a + b*x^2)^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(336*a^3*x^12)","A",5,4,26,0.1538,1,"{1111, 646, 45, 37}"
601,1,255,0,0.15505,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{19}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^19,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{18 x^{18} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 x^{16} \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^{14} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^{12} \left(a+b x^2\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^{10} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{18 x^{18} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 x^{16} \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^{14} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{6 x^{12} \left(a+b x^2\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^{10} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^8 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(18*x^18*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*x^16*(a + b*x^2)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^14*(a + b*x^2)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*x^12*(a + b*x^2)) - (a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^10*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^8*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
602,1,255,0,0.1510456,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{21}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^21,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{20 x^{20} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{18 x^{18} \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^{16} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^{14} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 x^{12} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{20 x^{20} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{18 x^{18} \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^{16} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^{14} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 x^{12} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{10 x^{10} \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(20*x^20*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(18*x^18*(a + b*x^2)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^16*(a + b*x^2)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^14*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*x^12*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(10*x^10*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
603,1,255,0,0.1533093,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{23}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^23,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 x^{22} \left(a+b x^2\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^{20} \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^{18} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^{16} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 x^{12} \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 x^{22} \left(a+b x^2\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{4 x^{20} \left(a+b x^2\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^{18} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{8 x^{16} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{12 x^{12} \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(22*x^22*(a + b*x^2)) - (a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*x^20*(a + b*x^2)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^18*(a + b*x^2)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*x^16*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*x^14*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(12*x^12*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
604,1,255,0,0.1512869,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{25}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^25,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{24 x^{24} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 x^{22} \left(a+b x^2\right)}-\frac{a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^{20} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^{18} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 x^{16} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{24 x^{24} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{22 x^{22} \left(a+b x^2\right)}-\frac{a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 x^{20} \left(a+b x^2\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^{18} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{16 x^{16} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{14 x^{14} \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(24*x^24*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(22*x^22*(a + b*x^2)) - (a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*x^20*(a + b*x^2)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^18*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*x^16*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(14*x^14*(a + b*x^2))","A",4,3,26,0.1154,1,"{1111, 646, 43}"
605,1,255,0,0.0621528,"\int x^{12} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^12*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{23} \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 \left(a+b x^2\right)}+\frac{5 a b^4 x^{21} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{19} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{a^4 b x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{a^5 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}","\frac{b^5 x^{23} \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 \left(a+b x^2\right)}+\frac{5 a b^4 x^{21} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{19} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{a^4 b x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{a^5 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}",1,"(a^5*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2)) + (a^4*b*x^15*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (10*a^3*b^2*x^17*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*(a + b*x^2)) + (10*a^2*b^3*x^19*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*(a + b*x^2)) + (5*a*b^4*x^21*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(21*(a + b*x^2)) + (b^5*x^23*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(23*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
606,1,255,0,0.0577635,"\int x^{10} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^10*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{21} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 \left(a+b x^2\right)}+\frac{5 a b^4 x^{19} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{2 a^3 b^2 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{5 a^4 b x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{a^5 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}","\frac{b^5 x^{21} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 \left(a+b x^2\right)}+\frac{5 a b^4 x^{19} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{2 a^3 b^2 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{5 a^4 b x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{a^5 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}",1,"(a^5*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2)) + (5*a^4*b*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2)) + (2*a^3*b^2*x^15*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (10*a^2*b^3*x^17*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*(a + b*x^2)) + (5*a*b^4*x^19*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*(a + b*x^2)) + (b^5*x^21*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(21*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
607,1,255,0,0.0608189,"\int x^8 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^8*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{19} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 \left(a+b x^2\right)}+\frac{5 a b^4 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{2 a^2 b^3 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{5 a^4 b x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a^5 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}","\frac{b^5 x^{19} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 \left(a+b x^2\right)}+\frac{5 a b^4 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{2 a^2 b^3 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{5 a^4 b x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{a^5 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}",1,"(a^5*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2)) + (5*a^4*b*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2)) + (10*a^3*b^2*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2)) + (2*a^2*b^3*x^15*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (5*a*b^4*x^17*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*(a + b*x^2)) + (b^5*x^19*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
608,1,255,0,0.0584595,"\int x^6 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{a b^4 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{5 a^4 b x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{a^5 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}","\frac{b^5 x^{17} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 \left(a+b x^2\right)}+\frac{a b^4 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{5 a^4 b x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{a^5 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}",1,"(a^5*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2)) + (5*a^4*b*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2)) + (10*a^3*b^2*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2)) + (10*a^2*b^3*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2)) + (a*b^4*x^15*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (b^5*x^17*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
609,1,255,0,0.0594737,"\int x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 \left(a+b x^2\right)}+\frac{5 a b^4 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a^4 b x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a^5 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}","\frac{b^5 x^{15} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 \left(a+b x^2\right)}+\frac{5 a b^4 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a^4 b x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a^5 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}",1,"(a^5*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*(a + b*x^2)) + (5*a^4*b*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2)) + (10*a^3*b^2*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2)) + (10*a^2*b^3*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2)) + (5*a*b^4*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2)) + (b^5*x^15*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(15*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
610,1,252,0,0.0598965,"\int x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{5 a b^4 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a^4 b x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{a^5 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}","\frac{b^5 x^{13} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 \left(a+b x^2\right)}+\frac{5 a b^4 x^{11} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 \left(a+b x^2\right)}+\frac{10 a^2 b^3 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a^4 b x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{a^5 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}",1,"(a^5*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (a^4*b*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (10*a^3*b^2*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2)) + (10*a^2*b^3*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2)) + (5*a*b^4*x^11*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*(a + b*x^2)) + (b^5*x^13*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
611,1,248,0,0.051071,"\int \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{b^5 x^{11} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{11 \left(a+b x^2\right)^5}+\frac{5 a b^4 x^9 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{9 \left(a+b x^2\right)^5}+\frac{10 a^2 b^3 x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{7 \left(a+b x^2\right)^5}+\frac{2 a^3 b^2 x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{\left(a+b x^2\right)^5}+\frac{5 a^4 b x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{3 \left(a+b x^2\right)^5}+\frac{a^5 x \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{\left(a+b x^2\right)^5}","\frac{b^5 x^{11} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{11 \left(a+b x^2\right)^5}+\frac{5 a b^4 x^9 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{9 \left(a+b x^2\right)^5}+\frac{10 a^2 b^3 x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{7 \left(a+b x^2\right)^5}+\frac{2 a^3 b^2 x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{\left(a+b x^2\right)^5}+\frac{5 a^4 b x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{3 \left(a+b x^2\right)^5}+\frac{a^5 x \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{\left(a+b x^2\right)^5}",1,"(a^5*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(a + b*x^2)^5 + (5*a^4*b*x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(3*(a + b*x^2)^5) + (2*a^3*b^2*x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(a + b*x^2)^5 + (10*a^2*b^3*x^7*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(7*(a + b*x^2)^5) + (5*a*b^4*x^9*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(9*(a + b*x^2)^5) + (b^5*x^11*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))/(11*(a + b*x^2)^5)","A",3,2,22,0.09091,1,"{1088, 194}"
612,1,247,0,0.0581297,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^2,x]","\frac{b^5 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a b^4 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{2 a^2 b^3 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{10 a^3 b^2 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{5 a^4 b x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}","\frac{b^5 x^9 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 \left(a+b x^2\right)}+\frac{5 a b^4 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{2 a^2 b^3 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{10 a^3 b^2 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{5 a^4 b x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}",1,"-((a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2))) + (5*a^4*b*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (10*a^3*b^2*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (2*a^2*b^3*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (5*a*b^4*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2)) + (b^5*x^9*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
613,1,246,0,0.06027,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^4,x]","\frac{b^5 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a b^4 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{10 a^2 b^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}","\frac{b^5 x^7 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 \left(a+b x^2\right)}+\frac{a b^4 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{10 a^2 b^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{10 a^3 b^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2)) + (10*a^3*b^2*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (10*a^2*b^3*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (a*b^4*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (b^5*x^7*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
614,1,249,0,0.0578224,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^6} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^6,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{10 a^2 b^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{5 a b^4 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{b^5 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{10 a^2 b^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{5 a b^4 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}+\frac{b^5 x^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2)) + (10*a^2*b^3*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (5*a*b^4*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2)) + (b^5*x^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
615,1,247,0,0.0583021,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^8} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^8,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{5 a b^4 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{b^5 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{5 a b^4 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}+\frac{b^5 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^5*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2)) + (5*a*b^4*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (b^5*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
616,1,246,0,0.0580791,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{10}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^10,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{2 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{b^5 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{2 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}+\frac{b^5 x \sqrt{a^2+2 a b x^2+b^2 x^4}}{a+b x^2}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (2*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^5*(a + b*x^2)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2)) + (b^5*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2)","A",3,2,26,0.07692,1,"{1112, 270}"
617,1,251,0,0.0584969,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{12}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^12,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{2 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{2 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (2*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^5*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
618,1,253,0,0.0601616,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{14}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^14,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^5 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^3 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(x^5*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^3*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
619,1,255,0,0.0580007,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{16}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^16,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 x^{15} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 x^{15} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 x^5 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(15*x^15*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*x^5*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
620,1,255,0,0.0588274,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{18}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^18,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 x^7 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*x^17*(a + b*x^2)) - (a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^15*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*x^7*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
621,1,255,0,0.0582526,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{20}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^20,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 x^{19} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{2 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 x^{19} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{2 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 x^9 \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*x^19*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*x^17*(a + b*x^2)) - (2*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^15*(a + b*x^2)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*x^9*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
622,1,255,0,0.0575609,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{22}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^22,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 x^{21} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 x^{19} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{2 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 x^{21} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 x^{19} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{2 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 x^{11} \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(21*x^21*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*x^19*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*x^17*(a + b*x^2)) - (2*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^15*(a + b*x^2)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*x^11*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
623,1,255,0,0.0576959,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{x^{24}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/x^24,x]","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 x^{23} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 x^{21} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 x^{19} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 x^{23} \left(a+b x^2\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 x^{21} \left(a+b x^2\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 x^{19} \left(a+b x^2\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 x^{17} \left(a+b x^2\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 x^{15} \left(a+b x^2\right)}-\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 x^{13} \left(a+b x^2\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(23*x^23*(a + b*x^2)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(21*x^21*(a + b*x^2)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*x^19*(a + b*x^2)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*x^17*(a + b*x^2)) - (a*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*x^15*(a + b*x^2)) - (b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*x^13*(a + b*x^2))","A",3,2,26,0.07692,1,"{1112, 270}"
624,1,127,0,0.1015959,"\int \frac{x^5}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[x^5/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{x^4 \left(a+b x^2\right)}{4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a x^2 \left(a+b x^2\right)}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^2 \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x^4 \left(a+b x^2\right)}{4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a x^2 \left(a+b x^2\right)}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^2 \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-(a*x^2*(a + b*x^2))/(2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (x^4*(a + b*x^2))/(4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^2*(a + b*x^2)*Log[a + b*x^2])/(2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1111, 646, 43}"
625,1,75,0,0.0559249,"\int \frac{x^3}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[x^3/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{2 b^2}-\frac{a \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{2 b^2}-\frac{a \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/(2*b^2) - (a*(a + b*x^2)*Log[a + b*x^2])/(2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,4,26,0.1538,1,"{1111, 640, 608, 31}"
626,1,44,0,0.0316934,"\int \frac{x}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[x/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((a + b*x^2)*Log[a + b*x^2])/(2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,24,0.1250,1,"{1107, 608, 31}"
627,1,80,0,0.0337835,"\int \frac{1}{x \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/(x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","\frac{\log (x) \left(a+b x^2\right)}{a \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\log (x) \left(a+b x^2\right)}{a \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((a + b*x^2)*Log[x])/(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((a + b*x^2)*Log[a + b*x^2])/(2*a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",5,5,26,0.1923,1,"{1112, 266, 36, 29, 31}"
628,1,122,0,0.0496018,"\int \frac{1}{x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/(x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","-\frac{a+b x^2}{2 a x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b \log (x) \left(a+b x^2\right)}{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{a+b x^2}{2 a x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b \log (x) \left(a+b x^2\right)}{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-(a + b*x^2)/(2*a*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b*(a + b*x^2)*Log[x])/(a^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b*(a + b*x^2)*Log[a + b*x^2])/(2*a^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 266, 44}"
629,1,129,0,0.0460382,"\int \frac{x^4}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[x^4/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{x^3 \left(a+b x^2\right)}{3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a x \left(a+b x^2\right)}{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x^3 \left(a+b x^2\right)}{3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a x \left(a+b x^2\right)}{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-((a*x*(a + b*x^2))/(b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])) + (x^3*(a + b*x^2))/(3*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^(3/2)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 302, 205}"
630,1,89,0,0.031588,"\int \frac{x^2}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[x^2/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{x \left(a+b x^2\right)}{b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{a} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x \left(a+b x^2\right)}{b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{a} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(x*(a + b*x^2))/(b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (Sqrt[a]*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,26,0.1154,1,"{1112, 321, 205}"
631,1,53,0,0.0150325,"\int \frac{1}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",2,2,22,0.09091,1,"{1088, 205}"
632,1,92,0,0.0333592,"\int \frac{1}{x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/(x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","-\frac{a+b x^2}{a x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{a+b x^2}{a x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-((a + b*x^2)/(a*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])) - (Sqrt[b]*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,26,0.1154,1,"{1112, 325, 205}"
633,1,130,0,0.0434308,"\int \frac{1}{x^4 \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/(x^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","\frac{b \left(a+b x^2\right)}{a^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a+b x^2}{3 a x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{b \left(a+b x^2\right)}{a^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a+b x^2}{3 a x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-(a + b*x^2)/(3*a*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b*(a + b*x^2))/(a^2*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b^(3/2)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 325, 205}"
634,1,158,0,0.1313242,"\int \frac{x^7}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[x^7/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{a^3}{4 b^4 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 a^2}{2 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x^2 \left(a+b x^2\right)}{2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 a \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{a^3}{4 b^4 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 a^2}{2 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x^2 \left(a+b x^2\right)}{2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 a \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-3*a^2)/(2*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + a^3/(4*b^4*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (x^2*(a + b*x^2))/(2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*a*(a + b*x^2)*Log[a + b*x^2])/(2*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1111, 646, 43}"
635,1,113,0,0.0983267,"\int \frac{x^5}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[x^5/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{a^2}{4 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a}{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{a^2}{4 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a}{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"a/(b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - a^2/(4*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((a + b*x^2)*Log[a + b*x^2])/(2*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1111, 646, 43}"
636,1,69,0,0.0501704,"\int \frac{x^3}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[x^3/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{a}{4 b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x^4}{4 a \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-1/(2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + a/(4*b^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,26,0.1154,1,"{1111, 640, 607}"
637,1,38,0,0.0257146,"\int \frac{x}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[x/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{1}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{1}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-1/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",2,2,24,0.08333,1,"{1107, 607}"
638,1,147,0,0.0826822,"\int \frac{1}{x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","\frac{1}{4 a \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\log (x) \left(a+b x^2\right)}{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{1}{4 a \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\log (x) \left(a+b x^2\right)}{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"1/(2*a^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(4*a*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((a + b*x^2)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((a + b*x^2)*Log[a + b*x^2])/(2*a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 266, 44}"
639,1,189,0,0.095797,"\int \frac{1}{x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","-\frac{b}{4 a^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b}{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a+b x^2}{2 a^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 b \log (x) \left(a+b x^2\right)}{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 b \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{b}{4 a^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b}{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a+b x^2}{2 a^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 b \log (x) \left(a+b x^2\right)}{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 b \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-(b/(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])) - b/(4*a^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a + b*x^2)/(2*a^3*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*b*(a + b*x^2)*Log[x])/(a^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3*b*(a + b*x^2)*Log[a + b*x^2])/(2*a^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 266, 44}"
640,1,128,0,0.0526389,"\int \frac{x^4}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[x^4/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{x^3}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 x}{8 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{x^3}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 x}{8 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-3*x)/(8*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - x^3/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[a]*b^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 288, 205}"
641,1,129,0,0.0492152,"\int \frac{x^2}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[x^2/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{x}{8 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x}{8 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"x/(8*a*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - x/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(3/2)*b^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,4,26,0.1538,1,"{1112, 288, 199, 205}"
642,1,135,0,0.0383879,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-3/2),x]","\frac{3 x \left(a+b x^2\right)^2}{8 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}+\frac{x \left(a+b x^2\right)}{4 a \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}+\frac{3 \left(a+b x^2\right)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}","\frac{3 x \left(a+b x^2\right)^2}{8 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}+\frac{x \left(a+b x^2\right)}{4 a \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}+\frac{3 \left(a+b x^2\right)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}",1,"(x*(a + b*x^2))/(4*a*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)) + (3*x*(a + b*x^2)^2)/(8*a^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)) + (3*(a + b*x^2)^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))","A",4,3,22,0.1364,1,"{1088, 199, 205}"
643,1,169,0,0.0653457,"\int \frac{1}{x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","-\frac{15 \left(a+b x^2\right)}{8 a^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5}{8 a^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}-\frac{15 \sqrt{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{15 \left(a+b x^2\right)}{8 a^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5}{8 a^2 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}-\frac{15 \sqrt{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"5/(8*a^2*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(4*a*x*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (15*(a + b*x^2))/(8*a^3*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (15*Sqrt[b]*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",5,4,26,0.1538,1,"{1112, 290, 325, 205}"
644,1,209,0,0.0791235,"\int \frac{1}{x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/(x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","\frac{35 b \left(a+b x^2\right)}{8 a^4 x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 \left(a+b x^2\right)}{24 a^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a x^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7}{8 a^2 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 b^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{35 b \left(a+b x^2\right)}{8 a^4 x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 \left(a+b x^2\right)}{24 a^3 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a x^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7}{8 a^2 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 b^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"7/(8*a^2*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(4*a*x^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (35*(a + b*x^2))/(24*a^3*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (35*b*(a + b*x^2))/(8*a^4*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (35*b^(3/2)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",6,4,26,0.1538,1,"{1112, 290, 325, 205}"
645,1,238,0,0.1894691,"\int \frac{x^{11}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^11/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{a^5}{8 b^6 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 a^4}{6 b^6 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 a^3}{2 b^6 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 a^2}{b^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x^2 \left(a+b x^2\right)}{2 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 a \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{a^5}{8 b^6 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 a^4}{6 b^6 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 a^3}{2 b^6 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 a^2}{b^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x^2 \left(a+b x^2\right)}{2 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 a \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-5*a^2)/(b^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + a^5/(8*b^6*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*a^4)/(6*b^6*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*a^3)/(2*b^6*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (x^2*(a + b*x^2))/(2*b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*a*(a + b*x^2)*Log[a + b*x^2])/(2*b^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1111, 646, 43}"
646,1,196,0,0.1621374,"\int \frac{x^9}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^9/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{a^4}{8 b^5 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 a^3}{3 b^5 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 a^2}{2 b^5 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 a}{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{a^4}{8 b^5 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 a^3}{3 b^5 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 a^2}{2 b^5 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 a}{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(2*a)/(b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - a^4/(8*b^5*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (2*a^3)/(3*b^5*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*a^2)/(2*b^5*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((a + b*x^2)*Log[a + b*x^2])/(2*b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1111, 646, 43}"
647,1,41,0,0.0404306,"\int \frac{x^7}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^7/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{x^8}{8 a \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x^8}{8 a \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"x^8/(8*a*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,26,0.1154,1,"{1111, 646, 37}"
648,1,74,0,0.0158215,"\int \frac{x^5}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^5/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{x^6}{8 a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}+\frac{x^6}{24 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}","\frac{x^6}{8 a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}+\frac{x^6}{24 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}",1,"x^6/(24*a^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)) + x^6/(8*a*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))","A",1,1,26,0.03846,1,"{1109}"
649,1,69,0,0.0537152,"\int \frac{x^3}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^3/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{a}{8 b^2 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}-\frac{1}{6 b^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}","\frac{a}{8 b^2 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}-\frac{1}{6 b^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}",1,"-1/(6*b^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)) + a/(8*b^2*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))","A",3,3,26,0.1154,1,"{1111, 640, 607}"
650,1,38,0,0.0251851,"\int \frac{x}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{1}{8 b \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}","-\frac{1}{8 b \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}",1,"-1/(8*b*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2))","A",2,2,24,0.08333,1,"{1107, 607}"
651,1,223,0,0.1207666,"\int \frac{1}{x \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","\frac{1}{4 a^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{6 a^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{8 a \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{2 a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\log (x) \left(a+b x^2\right)}{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{1}{4 a^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{6 a^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{8 a \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{2 a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\log (x) \left(a+b x^2\right)}{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"1/(2*a^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(8*a*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(6*a^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(4*a^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((a + b*x^2)*Log[x])/(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((a + b*x^2)*Log[a + b*x^2])/(2*a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 266, 44}"
652,1,267,0,0.1419488,"\int \frac{1}{x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","-\frac{3 b}{4 a^4 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b}{3 a^3 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b}{8 a^2 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 b}{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a+b x^2}{2 a^5 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 b \log (x) \left(a+b x^2\right)}{a^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 b \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{3 b}{4 a^4 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b}{3 a^3 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b}{8 a^2 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 b}{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a+b x^2}{2 a^5 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 b \log (x) \left(a+b x^2\right)}{a^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 b \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-2*b)/(a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - b/(8*a^2*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - b/(3*a^3*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*b)/(4*a^4*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a + b*x^2)/(2*a^5*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*b*(a + b*x^2)*Log[x])/(a^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*b*(a + b*x^2)*Log[a + b*x^2])/(2*a^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,26,0.1154,1,"{1112, 266, 44}"
653,1,211,0,0.0845826,"\int \frac{x^6}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^6/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{x^5}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 x^3}{48 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 x}{64 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 x}{128 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{3/2} b^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{x^5}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 x^3}{48 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 x}{64 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 x}{128 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{3/2} b^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(5*x)/(128*a*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - x^5/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*x^3)/(48*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*x)/(64*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(3/2)*b^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",6,4,26,0.1538,1,"{1112, 288, 199, 205}"
654,1,212,0,0.0878467,"\int \frac{x^4}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^4/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{x^3}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x}{64 a b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 x}{128 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x}{16 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{5/2} b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{x^3}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x}{64 a b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 x}{128 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x}{16 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{5/2} b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(3*x)/(128*a^2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - x^3/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - x/(16*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + x/(64*a*b^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(5/2)*b^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",6,4,26,0.1538,1,"{1112, 288, 199, 205}"
655,1,213,0,0.0835851,"\int \frac{x^2}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[x^2/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{5 x}{128 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 x}{192 a^2 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x}{48 a b \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{7/2} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{5 x}{128 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 x}{192 a^2 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x}{48 a b \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{7/2} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(5*x)/(128*a^3*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - x/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + x/(48*a*b*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*x)/(192*a^2*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(7/2)*b^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",6,4,26,0.1538,1,"{1112, 288, 199, 205}"
656,1,213,0,0.07216,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-5/2),x]","\frac{35 x \left(a+b x^2\right)^4}{128 a^4 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{35 x \left(a+b x^2\right)^3}{192 a^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{7 x \left(a+b x^2\right)^2}{48 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{x \left(a+b x^2\right)}{8 a \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{35 \left(a+b x^2\right)^5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{9/2} \sqrt{b} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}","\frac{35 x \left(a+b x^2\right)^4}{128 a^4 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{35 x \left(a+b x^2\right)^3}{192 a^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{7 x \left(a+b x^2\right)^2}{48 a^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{x \left(a+b x^2\right)}{8 a \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}+\frac{35 \left(a+b x^2\right)^5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{9/2} \sqrt{b} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}",1,"(x*(a + b*x^2))/(8*a*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)) + (7*x*(a + b*x^2)^2)/(48*a^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)) + (35*x*(a + b*x^2)^3)/(192*a^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)) + (35*x*(a + b*x^2)^4)/(128*a^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)) + (35*(a + b*x^2)^5*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(9/2)*Sqrt[b]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2))","A",6,3,22,0.1364,1,"{1088, 199, 205}"
657,1,251,0,0.1093763,"\int \frac{1}{x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","-\frac{315 \left(a+b x^2\right)}{128 a^5 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{105}{128 a^4 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21}{64 a^3 x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}+\frac{3}{16 a^2 x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^2}+\frac{1}{8 a x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^3}-\frac{315 \sqrt{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{315 \left(a+b x^2\right)}{128 a^5 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{105}{128 a^4 x \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21}{64 a^3 x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}+\frac{3}{16 a^2 x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^2}+\frac{1}{8 a x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^3}-\frac{315 \sqrt{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"105/(128*a^4*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(8*a*x*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 3/(16*a^2*x*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 21/(64*a^3*x*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (315*(a + b*x^2))/(128*a^5*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (315*Sqrt[b]*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",7,4,26,0.1538,1,"{1112, 290, 325, 205}"
658,1,291,0,0.1248139,"\int \frac{1}{x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/(x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","\frac{1155 b \left(a+b x^2\right)}{128 a^6 x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{385 \left(a+b x^2\right)}{128 a^5 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{33}{64 a^3 x^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{11}{48 a^2 x^3 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{231}{128 a^4 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{8 a x^3 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 b^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{1155 b \left(a+b x^2\right)}{128 a^6 x \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{385 \left(a+b x^2\right)}{128 a^5 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{33}{64 a^3 x^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{11}{48 a^2 x^3 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{231}{128 a^4 x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{8 a x^3 \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 b^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 a^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"231/(128*a^4*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(8*a*x^3*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 11/(48*a^2*x^3*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 33/(64*a^3*x^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (385*(a + b*x^2))/(128*a^5*x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (1155*b*(a + b*x^2))/(128*a^6*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (1155*b^(3/2)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(128*a^(13/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",8,4,26,0.1538,1,"{1112, 290, 325, 205}"
659,1,298,0,0.2294793,"\int \frac{x^2}{\sqrt[3]{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[x^2/(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/3),x]","\frac{3 x \left(a+b x^2\right)}{5 b \sqrt[3]{a^2+2 a b x^2+b^2 x^4}}+\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\frac{b x^2}{a}+1\right)^{2/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 b^2 x \sqrt[3]{a^2+2 a b x^2+b^2 x^4} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}","\frac{3 x \left(a+b x^2\right)}{5 b \sqrt[3]{a^2+2 a b x^2+b^2 x^4}}+\frac{3\ 3^{3/4} \sqrt{2-\sqrt{3}} a^2 \left(\frac{b x^2}{a}+1\right)^{2/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 b^2 x \sqrt[3]{a^2+2 a b x^2+b^2 x^4} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}",1,"(3*x*(a + b*x^2))/(5*b*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/3)) + (3*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^2*(1 + (b*x^2)/a)^(2/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(5*b^2*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)])","A",4,4,26,0.1538,1,"{1113, 321, 236, 219}"
660,1,256,0,0.1231404,"\int \frac{1}{\sqrt[3]{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-1/3),x]","-\frac{3^{3/4} \sqrt{2-\sqrt{3}} a \left(\frac{b x^2}{a}+1\right)^{2/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt[3]{a^2+2 a b x^2+b^2 x^4} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}","-\frac{3^{3/4} \sqrt{2-\sqrt{3}} a \left(\frac{b x^2}{a}+1\right)^{2/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{b x \sqrt[3]{a^2+2 a b x^2+b^2 x^4} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}",1,"-((3^(3/4)*Sqrt[2 - Sqrt[3]]*a*(1 + (b*x^2)/a)^(2/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(b*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)]))","A",3,3,22,0.1364,1,"{1089, 236, 219}"
661,1,289,0,0.1578682,"\int \frac{1}{x^2 \sqrt[3]{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/3)),x]","\frac{\sqrt{2-\sqrt{3}} \left(\frac{b x^2}{a}+1\right)^{2/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt[3]{a^2+2 a b x^2+b^2 x^4} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}-\frac{a+b x^2}{a x \sqrt[3]{a^2+2 a b x^2+b^2 x^4}}","\frac{\sqrt{2-\sqrt{3}} \left(\frac{b x^2}{a}+1\right)^{2/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt[3]{a^2+2 a b x^2+b^2 x^4} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}-\frac{a+b x^2}{a x \sqrt[3]{a^2+2 a b x^2+b^2 x^4}}",1,"-((a + b*x^2)/(a*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/3))) + (Sqrt[2 - Sqrt[3]]*(1 + (b*x^2)/a)^(2/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(3^(1/4)*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(1/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)])","A",4,4,26,0.1538,1,"{1113, 325, 236, 219}"
662,1,618,0,0.4119556,"\int \frac{x^2}{\left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}} \, dx","Int[x^2/(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3),x]","-\frac{9 a x \left(\frac{b x^2}{a}+1\right)^{4/3}}{2 b \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)}-\frac{3 x \left(a+b x^2\right)}{2 b \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}-\frac{3\ 3^{3/4} a^2 \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b^2 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}+\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^2 \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}","-\frac{9 a x \left(\frac{b x^2}{a}+1\right)^{4/3}}{2 b \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)}-\frac{3 x \left(a+b x^2\right)}{2 b \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}-\frac{3\ 3^{3/4} a^2 \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b^2 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}+\frac{9 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a^2 \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b^2 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}",1,"(-3*x*(a + b*x^2))/(2*b*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)) - (9*a*x*(1 + (b*x^2)/a)^(4/3))/(2*b*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))) + (9*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^2*(1 + (b*x^2)/a)^(4/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(4*b^2*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)]) - (3*3^(3/4)*a^2*(1 + (b*x^2)/a)^(4/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*b^2*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)])","A",6,6,26,0.2308,1,"{1113, 288, 235, 304, 219, 1879}"
663,1,609,0,0.3661572,"\int \frac{1}{\left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(-2/3),x]","\frac{3 x \left(\frac{b x^2}{a}+1\right)^{4/3}}{2 \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)}+\frac{3 x \left(a+b x^2\right)}{2 a \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}+\frac{3^{3/4} a \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} \left(\frac{b x^2}{a}+1\right)^{4/3} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} \left(\frac{b x^2}{a}+1\right)^{4/3} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}","\frac{3 x \left(\frac{b x^2}{a}+1\right)^{4/3}}{2 \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)}+\frac{3 x \left(a+b x^2\right)}{2 a \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}+\frac{3^{3/4} a \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} \left(\frac{b x^2}{a}+1\right)^{4/3} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} b x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} a \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} \left(\frac{b x^2}{a}+1\right)^{4/3} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 b x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}",1,"(3*x*(a + b*x^2))/(2*a*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)) + (3*x*(1 + (b*x^2)/a)^(4/3))/(2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*a*(1 + (b*x^2)/a)^(4/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(4*b*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)]) + (3^(3/4)*a*(1 + (b*x^2)/a)^(4/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*b*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)])","A",6,6,22,0.2727,1,"{1089, 199, 235, 304, 219, 1879}"
664,1,649,0,0.4442505,"\int \frac{1}{x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)),x]","-\frac{5 \left(a+b x^2\right)^2}{2 a^2 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}+\frac{3 \left(a+b x^2\right)}{2 a x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}-\frac{5 b x \left(\frac{b x^2}{a}+1\right)^{4/3}}{2 a \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)}-\frac{5 \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} \sqrt[4]{3} x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}+\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}","-\frac{5 \left(a+b x^2\right)^2}{2 a^2 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}+\frac{3 \left(a+b x^2\right)}{2 a x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3}}-\frac{5 b x \left(\frac{b x^2}{a}+1\right)^{4/3}}{2 a \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)}-\frac{5 \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{2} \sqrt[4]{3} x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}+\frac{5 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(\frac{b x^2}{a}+1\right)^{4/3} \left(1-\sqrt[3]{\frac{b x^2}{a}+1}\right) \sqrt{\frac{\left(\frac{b x^2}{a}+1\right)^{2/3}+\sqrt[3]{\frac{b x^2}{a}+1}+1}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{\frac{b x^2}{a}+1}+\sqrt{3}+1}{-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 x \left(a^2+2 a b x^2+b^2 x^4\right)^{2/3} \sqrt{-\frac{1-\sqrt[3]{\frac{b x^2}{a}+1}}{\left(-\sqrt[3]{\frac{b x^2}{a}+1}-\sqrt{3}+1\right)^2}}}",1,"(3*(a + b*x^2))/(2*a*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)) - (5*(a + b*x^2)^2)/(2*a^2*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)) - (5*b*x*(1 + (b*x^2)/a)^(4/3))/(2*a*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))) + (5*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + (b*x^2)/a)^(4/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(4*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)]) - (5*(1 + (b*x^2)/a)^(4/3)*(1 - (1 + (b*x^2)/a)^(1/3))*Sqrt[(1 + (1 + (b*x^2)/a)^(1/3) + (1 + (b*x^2)/a)^(2/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))], -7 + 4*Sqrt[3]])/(Sqrt[2]*3^(1/4)*x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(2/3)*Sqrt[-((1 - (1 + (b*x^2)/a)^(1/3))/(1 - Sqrt[3] - (1 + (b*x^2)/a)^(1/3))^2)])","A",7,7,26,0.2692,1,"{1113, 290, 325, 235, 304, 219, 1879}"
665,1,51,0,0.0136195,"\int (d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[(d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{2 a^2 (d x)^{7/2}}{7 d}+\frac{4 a b (d x)^{11/2}}{11 d^3}+\frac{2 b^2 (d x)^{15/2}}{15 d^5}","\frac{2 a^2 (d x)^{7/2}}{7 d}+\frac{4 a b (d x)^{11/2}}{11 d^3}+\frac{2 b^2 (d x)^{15/2}}{15 d^5}",1,"(2*a^2*(d*x)^(7/2))/(7*d) + (4*a*b*(d*x)^(11/2))/(11*d^3) + (2*b^2*(d*x)^(15/2))/(15*d^5)","A",2,1,26,0.03846,1,"{14}"
666,1,51,0,0.0142823,"\int (d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[(d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{2 a^2 (d x)^{5/2}}{5 d}+\frac{4 a b (d x)^{9/2}}{9 d^3}+\frac{2 b^2 (d x)^{13/2}}{13 d^5}","\frac{2 a^2 (d x)^{5/2}}{5 d}+\frac{4 a b (d x)^{9/2}}{9 d^3}+\frac{2 b^2 (d x)^{13/2}}{13 d^5}",1,"(2*a^2*(d*x)^(5/2))/(5*d) + (4*a*b*(d*x)^(9/2))/(9*d^3) + (2*b^2*(d*x)^(13/2))/(13*d^5)","A",2,1,26,0.03846,1,"{14}"
667,1,51,0,0.0130496,"\int \sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{2 a^2 (d x)^{3/2}}{3 d}+\frac{4 a b (d x)^{7/2}}{7 d^3}+\frac{2 b^2 (d x)^{11/2}}{11 d^5}","\frac{2 a^2 (d x)^{3/2}}{3 d}+\frac{4 a b (d x)^{7/2}}{7 d^3}+\frac{2 b^2 (d x)^{11/2}}{11 d^5}",1,"(2*a^2*(d*x)^(3/2))/(3*d) + (4*a*b*(d*x)^(7/2))/(7*d^3) + (2*b^2*(d*x)^(11/2))/(11*d^5)","A",2,1,26,0.03846,1,"{14}"
668,1,49,0,0.0131858,"\int \frac{a^2+2 a b x^2+b^2 x^4}{\sqrt{d x}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/Sqrt[d*x],x]","\frac{2 a^2 \sqrt{d x}}{d}+\frac{4 a b (d x)^{5/2}}{5 d^3}+\frac{2 b^2 (d x)^{9/2}}{9 d^5}","\frac{2 a^2 \sqrt{d x}}{d}+\frac{4 a b (d x)^{5/2}}{5 d^3}+\frac{2 b^2 (d x)^{9/2}}{9 d^5}",1,"(2*a^2*Sqrt[d*x])/d + (4*a*b*(d*x)^(5/2))/(5*d^3) + (2*b^2*(d*x)^(9/2))/(9*d^5)","A",2,1,26,0.03846,1,"{14}"
669,1,49,0,0.0149061,"\int \frac{a^2+2 a b x^2+b^2 x^4}{(d x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/(d*x)^(3/2),x]","-\frac{2 a^2}{d \sqrt{d x}}+\frac{4 a b (d x)^{3/2}}{3 d^3}+\frac{2 b^2 (d x)^{7/2}}{7 d^5}","-\frac{2 a^2}{d \sqrt{d x}}+\frac{4 a b (d x)^{3/2}}{3 d^3}+\frac{2 b^2 (d x)^{7/2}}{7 d^5}",1,"(-2*a^2)/(d*Sqrt[d*x]) + (4*a*b*(d*x)^(3/2))/(3*d^3) + (2*b^2*(d*x)^(7/2))/(7*d^5)","A",2,1,26,0.03846,1,"{14}"
670,1,49,0,0.0144974,"\int \frac{a^2+2 a b x^2+b^2 x^4}{(d x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/(d*x)^(5/2),x]","-\frac{2 a^2}{3 d (d x)^{3/2}}+\frac{4 a b \sqrt{d x}}{d^3}+\frac{2 b^2 (d x)^{5/2}}{5 d^5}","-\frac{2 a^2}{3 d (d x)^{3/2}}+\frac{4 a b \sqrt{d x}}{d^3}+\frac{2 b^2 (d x)^{5/2}}{5 d^5}",1,"(-2*a^2)/(3*d*(d*x)^(3/2)) + (4*a*b*Sqrt[d*x])/d^3 + (2*b^2*(d*x)^(5/2))/(5*d^5)","A",2,1,26,0.03846,1,"{14}"
671,1,49,0,0.0130246,"\int \frac{a^2+2 a b x^2+b^2 x^4}{(d x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/(d*x)^(7/2),x]","-\frac{2 a^2}{5 d (d x)^{5/2}}-\frac{4 a b}{d^3 \sqrt{d x}}+\frac{2 b^2 (d x)^{3/2}}{3 d^5}","-\frac{2 a^2}{5 d (d x)^{5/2}}-\frac{4 a b}{d^3 \sqrt{d x}}+\frac{2 b^2 (d x)^{3/2}}{3 d^5}",1,"(-2*a^2)/(5*d*(d*x)^(5/2)) - (4*a*b)/(d^3*Sqrt[d*x]) + (2*b^2*(d*x)^(3/2))/(3*d^5)","A",2,1,26,0.03846,1,"{14}"
672,1,91,0,0.0448823,"\int (d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[(d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{4 a^2 b^2 (d x)^{15/2}}{5 d^5}+\frac{8 a^3 b (d x)^{11/2}}{11 d^3}+\frac{2 a^4 (d x)^{7/2}}{7 d}+\frac{8 a b^3 (d x)^{19/2}}{19 d^7}+\frac{2 b^4 (d x)^{23/2}}{23 d^9}","\frac{4 a^2 b^2 (d x)^{15/2}}{5 d^5}+\frac{8 a^3 b (d x)^{11/2}}{11 d^3}+\frac{2 a^4 (d x)^{7/2}}{7 d}+\frac{8 a b^3 (d x)^{19/2}}{19 d^7}+\frac{2 b^4 (d x)^{23/2}}{23 d^9}",1,"(2*a^4*(d*x)^(7/2))/(7*d) + (8*a^3*b*(d*x)^(11/2))/(11*d^3) + (4*a^2*b^2*(d*x)^(15/2))/(5*d^5) + (8*a*b^3*(d*x)^(19/2))/(19*d^7) + (2*b^4*(d*x)^(23/2))/(23*d^9)","A",3,2,28,0.07143,1,"{28, 270}"
673,1,91,0,0.0439847,"\int (d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[(d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{12 a^2 b^2 (d x)^{13/2}}{13 d^5}+\frac{8 a^3 b (d x)^{9/2}}{9 d^3}+\frac{2 a^4 (d x)^{5/2}}{5 d}+\frac{8 a b^3 (d x)^{17/2}}{17 d^7}+\frac{2 b^4 (d x)^{21/2}}{21 d^9}","\frac{12 a^2 b^2 (d x)^{13/2}}{13 d^5}+\frac{8 a^3 b (d x)^{9/2}}{9 d^3}+\frac{2 a^4 (d x)^{5/2}}{5 d}+\frac{8 a b^3 (d x)^{17/2}}{17 d^7}+\frac{2 b^4 (d x)^{21/2}}{21 d^9}",1,"(2*a^4*(d*x)^(5/2))/(5*d) + (8*a^3*b*(d*x)^(9/2))/(9*d^3) + (12*a^2*b^2*(d*x)^(13/2))/(13*d^5) + (8*a*b^3*(d*x)^(17/2))/(17*d^7) + (2*b^4*(d*x)^(21/2))/(21*d^9)","A",3,2,28,0.07143,1,"{28, 270}"
674,1,91,0,0.040864,"\int \sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{12 a^2 b^2 (d x)^{11/2}}{11 d^5}+\frac{8 a^3 b (d x)^{7/2}}{7 d^3}+\frac{2 a^4 (d x)^{3/2}}{3 d}+\frac{8 a b^3 (d x)^{15/2}}{15 d^7}+\frac{2 b^4 (d x)^{19/2}}{19 d^9}","\frac{12 a^2 b^2 (d x)^{11/2}}{11 d^5}+\frac{8 a^3 b (d x)^{7/2}}{7 d^3}+\frac{2 a^4 (d x)^{3/2}}{3 d}+\frac{8 a b^3 (d x)^{15/2}}{15 d^7}+\frac{2 b^4 (d x)^{19/2}}{19 d^9}",1,"(2*a^4*(d*x)^(3/2))/(3*d) + (8*a^3*b*(d*x)^(7/2))/(7*d^3) + (12*a^2*b^2*(d*x)^(11/2))/(11*d^5) + (8*a*b^3*(d*x)^(15/2))/(15*d^7) + (2*b^4*(d*x)^(19/2))/(19*d^9)","A",3,2,28,0.07143,1,"{28, 270}"
675,1,89,0,0.0413977,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{\sqrt{d x}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/Sqrt[d*x],x]","\frac{4 a^2 b^2 (d x)^{9/2}}{3 d^5}+\frac{8 a^3 b (d x)^{5/2}}{5 d^3}+\frac{2 a^4 \sqrt{d x}}{d}+\frac{8 a b^3 (d x)^{13/2}}{13 d^7}+\frac{2 b^4 (d x)^{17/2}}{17 d^9}","\frac{4 a^2 b^2 (d x)^{9/2}}{3 d^5}+\frac{8 a^3 b (d x)^{5/2}}{5 d^3}+\frac{2 a^4 \sqrt{d x}}{d}+\frac{8 a b^3 (d x)^{13/2}}{13 d^7}+\frac{2 b^4 (d x)^{17/2}}{17 d^9}",1,"(2*a^4*Sqrt[d*x])/d + (8*a^3*b*(d*x)^(5/2))/(5*d^3) + (4*a^2*b^2*(d*x)^(9/2))/(3*d^5) + (8*a*b^3*(d*x)^(13/2))/(13*d^7) + (2*b^4*(d*x)^(17/2))/(17*d^9)","A",3,2,28,0.07143,1,"{28, 270}"
676,1,89,0,0.0420059,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{(d x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/(d*x)^(3/2),x]","\frac{12 a^2 b^2 (d x)^{7/2}}{7 d^5}+\frac{8 a^3 b (d x)^{3/2}}{3 d^3}-\frac{2 a^4}{d \sqrt{d x}}+\frac{8 a b^3 (d x)^{11/2}}{11 d^7}+\frac{2 b^4 (d x)^{15/2}}{15 d^9}","\frac{12 a^2 b^2 (d x)^{7/2}}{7 d^5}+\frac{8 a^3 b (d x)^{3/2}}{3 d^3}-\frac{2 a^4}{d \sqrt{d x}}+\frac{8 a b^3 (d x)^{11/2}}{11 d^7}+\frac{2 b^4 (d x)^{15/2}}{15 d^9}",1,"(-2*a^4)/(d*Sqrt[d*x]) + (8*a^3*b*(d*x)^(3/2))/(3*d^3) + (12*a^2*b^2*(d*x)^(7/2))/(7*d^5) + (8*a*b^3*(d*x)^(11/2))/(11*d^7) + (2*b^4*(d*x)^(15/2))/(15*d^9)","A",3,2,28,0.07143,1,"{28, 270}"
677,1,89,0,0.0418703,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{(d x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/(d*x)^(5/2),x]","\frac{12 a^2 b^2 (d x)^{5/2}}{5 d^5}+\frac{8 a^3 b \sqrt{d x}}{d^3}-\frac{2 a^4}{3 d (d x)^{3/2}}+\frac{8 a b^3 (d x)^{9/2}}{9 d^7}+\frac{2 b^4 (d x)^{13/2}}{13 d^9}","\frac{12 a^2 b^2 (d x)^{5/2}}{5 d^5}+\frac{8 a^3 b \sqrt{d x}}{d^3}-\frac{2 a^4}{3 d (d x)^{3/2}}+\frac{8 a b^3 (d x)^{9/2}}{9 d^7}+\frac{2 b^4 (d x)^{13/2}}{13 d^9}",1,"(-2*a^4)/(3*d*(d*x)^(3/2)) + (8*a^3*b*Sqrt[d*x])/d^3 + (12*a^2*b^2*(d*x)^(5/2))/(5*d^5) + (8*a*b^3*(d*x)^(9/2))/(9*d^7) + (2*b^4*(d*x)^(13/2))/(13*d^9)","A",3,2,28,0.07143,1,"{28, 270}"
678,1,87,0,0.0415425,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^2}{(d x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/(d*x)^(7/2),x]","\frac{4 a^2 b^2 (d x)^{3/2}}{d^5}-\frac{8 a^3 b}{d^3 \sqrt{d x}}-\frac{2 a^4}{5 d (d x)^{5/2}}+\frac{8 a b^3 (d x)^{7/2}}{7 d^7}+\frac{2 b^4 (d x)^{11/2}}{11 d^9}","\frac{4 a^2 b^2 (d x)^{3/2}}{d^5}-\frac{8 a^3 b}{d^3 \sqrt{d x}}-\frac{2 a^4}{5 d (d x)^{5/2}}+\frac{8 a b^3 (d x)^{7/2}}{7 d^7}+\frac{2 b^4 (d x)^{11/2}}{11 d^9}",1,"(-2*a^4)/(5*d*(d*x)^(5/2)) - (8*a^3*b)/(d^3*Sqrt[d*x]) + (4*a^2*b^2*(d*x)^(3/2))/d^5 + (8*a*b^3*(d*x)^(7/2))/(7*d^7) + (2*b^4*(d*x)^(11/2))/(11*d^9)","A",3,2,28,0.07143,1,"{28, 270}"
679,1,129,0,0.066312,"\int (d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[(d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{30 a^2 b^4 (d x)^{23/2}}{23 d^9}+\frac{40 a^3 b^3 (d x)^{19/2}}{19 d^7}+\frac{2 a^4 b^2 (d x)^{15/2}}{d^5}+\frac{12 a^5 b (d x)^{11/2}}{11 d^3}+\frac{2 a^6 (d x)^{7/2}}{7 d}+\frac{4 a b^5 (d x)^{27/2}}{9 d^{11}}+\frac{2 b^6 (d x)^{31/2}}{31 d^{13}}","\frac{30 a^2 b^4 (d x)^{23/2}}{23 d^9}+\frac{40 a^3 b^3 (d x)^{19/2}}{19 d^7}+\frac{2 a^4 b^2 (d x)^{15/2}}{d^5}+\frac{12 a^5 b (d x)^{11/2}}{11 d^3}+\frac{2 a^6 (d x)^{7/2}}{7 d}+\frac{4 a b^5 (d x)^{27/2}}{9 d^{11}}+\frac{2 b^6 (d x)^{31/2}}{31 d^{13}}",1,"(2*a^6*(d*x)^(7/2))/(7*d) + (12*a^5*b*(d*x)^(11/2))/(11*d^3) + (2*a^4*b^2*(d*x)^(15/2))/d^5 + (40*a^3*b^3*(d*x)^(19/2))/(19*d^7) + (30*a^2*b^4*(d*x)^(23/2))/(23*d^9) + (4*a*b^5*(d*x)^(27/2))/(9*d^11) + (2*b^6*(d*x)^(31/2))/(31*d^13)","A",3,2,28,0.07143,1,"{28, 270}"
680,1,131,0,0.0613499,"\int (d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[(d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{10 a^2 b^4 (d x)^{21/2}}{7 d^9}+\frac{40 a^3 b^3 (d x)^{17/2}}{17 d^7}+\frac{30 a^4 b^2 (d x)^{13/2}}{13 d^5}+\frac{4 a^5 b (d x)^{9/2}}{3 d^3}+\frac{2 a^6 (d x)^{5/2}}{5 d}+\frac{12 a b^5 (d x)^{25/2}}{25 d^{11}}+\frac{2 b^6 (d x)^{29/2}}{29 d^{13}}","\frac{10 a^2 b^4 (d x)^{21/2}}{7 d^9}+\frac{40 a^3 b^3 (d x)^{17/2}}{17 d^7}+\frac{30 a^4 b^2 (d x)^{13/2}}{13 d^5}+\frac{4 a^5 b (d x)^{9/2}}{3 d^3}+\frac{2 a^6 (d x)^{5/2}}{5 d}+\frac{12 a b^5 (d x)^{25/2}}{25 d^{11}}+\frac{2 b^6 (d x)^{29/2}}{29 d^{13}}",1,"(2*a^6*(d*x)^(5/2))/(5*d) + (4*a^5*b*(d*x)^(9/2))/(3*d^3) + (30*a^4*b^2*(d*x)^(13/2))/(13*d^5) + (40*a^3*b^3*(d*x)^(17/2))/(17*d^7) + (10*a^2*b^4*(d*x)^(21/2))/(7*d^9) + (12*a*b^5*(d*x)^(25/2))/(25*d^11) + (2*b^6*(d*x)^(29/2))/(29*d^13)","A",3,2,28,0.07143,1,"{28, 270}"
681,1,131,0,0.0610318,"\int \sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{30 a^2 b^4 (d x)^{19/2}}{19 d^9}+\frac{8 a^3 b^3 (d x)^{15/2}}{3 d^7}+\frac{30 a^4 b^2 (d x)^{11/2}}{11 d^5}+\frac{12 a^5 b (d x)^{7/2}}{7 d^3}+\frac{2 a^6 (d x)^{3/2}}{3 d}+\frac{12 a b^5 (d x)^{23/2}}{23 d^{11}}+\frac{2 b^6 (d x)^{27/2}}{27 d^{13}}","\frac{30 a^2 b^4 (d x)^{19/2}}{19 d^9}+\frac{8 a^3 b^3 (d x)^{15/2}}{3 d^7}+\frac{30 a^4 b^2 (d x)^{11/2}}{11 d^5}+\frac{12 a^5 b (d x)^{7/2}}{7 d^3}+\frac{2 a^6 (d x)^{3/2}}{3 d}+\frac{12 a b^5 (d x)^{23/2}}{23 d^{11}}+\frac{2 b^6 (d x)^{27/2}}{27 d^{13}}",1,"(2*a^6*(d*x)^(3/2))/(3*d) + (12*a^5*b*(d*x)^(7/2))/(7*d^3) + (30*a^4*b^2*(d*x)^(11/2))/(11*d^5) + (8*a^3*b^3*(d*x)^(15/2))/(3*d^7) + (30*a^2*b^4*(d*x)^(19/2))/(19*d^9) + (12*a*b^5*(d*x)^(23/2))/(23*d^11) + (2*b^6*(d*x)^(27/2))/(27*d^13)","A",3,2,28,0.07143,1,"{28, 270}"
682,1,129,0,0.0597216,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{\sqrt{d x}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/Sqrt[d*x],x]","\frac{30 a^2 b^4 (d x)^{17/2}}{17 d^9}+\frac{40 a^3 b^3 (d x)^{13/2}}{13 d^7}+\frac{10 a^4 b^2 (d x)^{9/2}}{3 d^5}+\frac{12 a^5 b (d x)^{5/2}}{5 d^3}+\frac{2 a^6 \sqrt{d x}}{d}+\frac{4 a b^5 (d x)^{21/2}}{7 d^{11}}+\frac{2 b^6 (d x)^{25/2}}{25 d^{13}}","\frac{30 a^2 b^4 (d x)^{17/2}}{17 d^9}+\frac{40 a^3 b^3 (d x)^{13/2}}{13 d^7}+\frac{10 a^4 b^2 (d x)^{9/2}}{3 d^5}+\frac{12 a^5 b (d x)^{5/2}}{5 d^3}+\frac{2 a^6 \sqrt{d x}}{d}+\frac{4 a b^5 (d x)^{21/2}}{7 d^{11}}+\frac{2 b^6 (d x)^{25/2}}{25 d^{13}}",1,"(2*a^6*Sqrt[d*x])/d + (12*a^5*b*(d*x)^(5/2))/(5*d^3) + (10*a^4*b^2*(d*x)^(9/2))/(3*d^5) + (40*a^3*b^3*(d*x)^(13/2))/(13*d^7) + (30*a^2*b^4*(d*x)^(17/2))/(17*d^9) + (4*a*b^5*(d*x)^(21/2))/(7*d^11) + (2*b^6*(d*x)^(25/2))/(25*d^13)","A",3,2,28,0.07143,1,"{28, 270}"
683,1,125,0,0.0598052,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{(d x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/(d*x)^(3/2),x]","\frac{2 a^2 b^4 (d x)^{15/2}}{d^9}+\frac{40 a^3 b^3 (d x)^{11/2}}{11 d^7}+\frac{30 a^4 b^2 (d x)^{7/2}}{7 d^5}+\frac{4 a^5 b (d x)^{3/2}}{d^3}-\frac{2 a^6}{d \sqrt{d x}}+\frac{12 a b^5 (d x)^{19/2}}{19 d^{11}}+\frac{2 b^6 (d x)^{23/2}}{23 d^{13}}","\frac{2 a^2 b^4 (d x)^{15/2}}{d^9}+\frac{40 a^3 b^3 (d x)^{11/2}}{11 d^7}+\frac{30 a^4 b^2 (d x)^{7/2}}{7 d^5}+\frac{4 a^5 b (d x)^{3/2}}{d^3}-\frac{2 a^6}{d \sqrt{d x}}+\frac{12 a b^5 (d x)^{19/2}}{19 d^{11}}+\frac{2 b^6 (d x)^{23/2}}{23 d^{13}}",1,"(-2*a^6)/(d*Sqrt[d*x]) + (4*a^5*b*(d*x)^(3/2))/d^3 + (30*a^4*b^2*(d*x)^(7/2))/(7*d^5) + (40*a^3*b^3*(d*x)^(11/2))/(11*d^7) + (2*a^2*b^4*(d*x)^(15/2))/d^9 + (12*a*b^5*(d*x)^(19/2))/(19*d^11) + (2*b^6*(d*x)^(23/2))/(23*d^13)","A",3,2,28,0.07143,1,"{28, 270}"
684,1,127,0,0.0621556,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{(d x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/(d*x)^(5/2),x]","\frac{30 a^2 b^4 (d x)^{13/2}}{13 d^9}+\frac{40 a^3 b^3 (d x)^{9/2}}{9 d^7}+\frac{6 a^4 b^2 (d x)^{5/2}}{d^5}+\frac{12 a^5 b \sqrt{d x}}{d^3}-\frac{2 a^6}{3 d (d x)^{3/2}}+\frac{12 a b^5 (d x)^{17/2}}{17 d^{11}}+\frac{2 b^6 (d x)^{21/2}}{21 d^{13}}","\frac{30 a^2 b^4 (d x)^{13/2}}{13 d^9}+\frac{40 a^3 b^3 (d x)^{9/2}}{9 d^7}+\frac{6 a^4 b^2 (d x)^{5/2}}{d^5}+\frac{12 a^5 b \sqrt{d x}}{d^3}-\frac{2 a^6}{3 d (d x)^{3/2}}+\frac{12 a b^5 (d x)^{17/2}}{17 d^{11}}+\frac{2 b^6 (d x)^{21/2}}{21 d^{13}}",1,"(-2*a^6)/(3*d*(d*x)^(3/2)) + (12*a^5*b*Sqrt[d*x])/d^3 + (6*a^4*b^2*(d*x)^(5/2))/d^5 + (40*a^3*b^3*(d*x)^(9/2))/(9*d^7) + (30*a^2*b^4*(d*x)^(13/2))/(13*d^9) + (12*a*b^5*(d*x)^(17/2))/(17*d^11) + (2*b^6*(d*x)^(21/2))/(21*d^13)","A",3,2,28,0.07143,1,"{28, 270}"
685,1,127,0,0.0637789,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^3}{(d x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/(d*x)^(7/2),x]","\frac{30 a^2 b^4 (d x)^{11/2}}{11 d^9}+\frac{40 a^3 b^3 (d x)^{7/2}}{7 d^7}+\frac{10 a^4 b^2 (d x)^{3/2}}{d^5}-\frac{12 a^5 b}{d^3 \sqrt{d x}}-\frac{2 a^6}{5 d (d x)^{5/2}}+\frac{4 a b^5 (d x)^{15/2}}{5 d^{11}}+\frac{2 b^6 (d x)^{19/2}}{19 d^{13}}","\frac{30 a^2 b^4 (d x)^{11/2}}{11 d^9}+\frac{40 a^3 b^3 (d x)^{7/2}}{7 d^7}+\frac{10 a^4 b^2 (d x)^{3/2}}{d^5}-\frac{12 a^5 b}{d^3 \sqrt{d x}}-\frac{2 a^6}{5 d (d x)^{5/2}}+\frac{4 a b^5 (d x)^{15/2}}{5 d^{11}}+\frac{2 b^6 (d x)^{19/2}}{19 d^{13}}",1,"(-2*a^6)/(5*d*(d*x)^(5/2)) - (12*a^5*b)/(d^3*Sqrt[d*x]) + (10*a^4*b^2*(d*x)^(3/2))/d^5 + (40*a^3*b^3*(d*x)^(7/2))/(7*d^7) + (30*a^2*b^4*(d*x)^(11/2))/(11*d^9) + (4*a*b^5*(d*x)^(15/2))/(5*d^11) + (2*b^6*(d*x)^(19/2))/(19*d^13)","A",3,2,28,0.07143,1,"{28, 270}"
686,1,316,0,0.383407,"\int \frac{(d x)^{11/2}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^(11/2)/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","-\frac{9 a^{5/4} d^{11/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{9 a^{5/4} d^{11/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{9 a^{5/4} d^{11/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} b^{13/4}}+\frac{9 a^{5/4} d^{11/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} b^{13/4}}-\frac{9 a d^5 \sqrt{d x}}{2 b^3}-\frac{d (d x)^{9/2}}{2 b \left(a+b x^2\right)}+\frac{9 d^3 (d x)^{5/2}}{10 b^2}","-\frac{9 a^{5/4} d^{11/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{9 a^{5/4} d^{11/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{9 a^{5/4} d^{11/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} b^{13/4}}+\frac{9 a^{5/4} d^{11/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} b^{13/4}}-\frac{9 a d^5 \sqrt{d x}}{2 b^3}-\frac{d (d x)^{9/2}}{2 b \left(a+b x^2\right)}+\frac{9 d^3 (d x)^{5/2}}{10 b^2}",1,"(-9*a*d^5*Sqrt[d*x])/(2*b^3) + (9*d^3*(d*x)^(5/2))/(10*b^2) - (d*(d*x)^(9/2))/(2*b*(a + b*x^2)) - (9*a^(5/4)*d^(11/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*b^(13/4)) + (9*a^(5/4)*d^(11/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*b^(13/4)) - (9*a^(5/4)*d^(11/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*b^(13/4)) + (9*a^(5/4)*d^(11/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*b^(13/4))","A",14,10,28,0.3571,1,"{28, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
687,1,298,0,0.2990314,"\int \frac{(d x)^{9/2}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^(9/2)/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","-\frac{7 a^{3/4} d^{9/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{11/4}}+\frac{7 a^{3/4} d^{9/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{11/4}}+\frac{7 a^{3/4} d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} b^{11/4}}-\frac{7 a^{3/4} d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} b^{11/4}}-\frac{d (d x)^{7/2}}{2 b \left(a+b x^2\right)}+\frac{7 d^3 (d x)^{3/2}}{6 b^2}","-\frac{7 a^{3/4} d^{9/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{11/4}}+\frac{7 a^{3/4} d^{9/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{11/4}}+\frac{7 a^{3/4} d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} b^{11/4}}-\frac{7 a^{3/4} d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} b^{11/4}}-\frac{d (d x)^{7/2}}{2 b \left(a+b x^2\right)}+\frac{7 d^3 (d x)^{3/2}}{6 b^2}",1,"(7*d^3*(d*x)^(3/2))/(6*b^2) - (d*(d*x)^(7/2))/(2*b*(a + b*x^2)) + (7*a^(3/4)*d^(9/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*b^(11/4)) - (7*a^(3/4)*d^(9/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*b^(11/4)) - (7*a^(3/4)*d^(9/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*b^(11/4)) + (7*a^(3/4)*d^(9/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*b^(11/4))","A",13,10,28,0.3571,1,"{28, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
688,1,298,0,0.2948554,"\int \frac{(d x)^{7/2}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^(7/2)/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{5 \sqrt[4]{a} d^{7/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} d^{7/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{a} d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} b^{9/4}}-\frac{d (d x)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{5 d^3 \sqrt{d x}}{2 b^2}","\frac{5 \sqrt[4]{a} d^{7/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} d^{7/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} b^{9/4}}+\frac{5 \sqrt[4]{a} d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} b^{9/4}}-\frac{5 \sqrt[4]{a} d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} b^{9/4}}-\frac{d (d x)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{5 d^3 \sqrt{d x}}{2 b^2}",1,"(5*d^3*Sqrt[d*x])/(2*b^2) - (d*(d*x)^(5/2))/(2*b*(a + b*x^2)) + (5*a^(1/4)*d^(7/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*b^(9/4)) - (5*a^(1/4)*d^(7/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*b^(9/4)) + (5*a^(1/4)*d^(7/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*b^(9/4)) - (5*a^(1/4)*d^(7/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*b^(9/4))","A",13,10,28,0.3571,1,"{28, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
689,1,281,0,0.2798582,"\int \frac{(d x)^{5/2}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^(5/2)/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{3 d^{5/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 d^{5/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{d (d x)^{3/2}}{2 b \left(a+b x^2\right)}","\frac{3 d^{5/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 d^{5/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{3 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{d (d x)^{3/2}}{2 b \left(a+b x^2\right)}",1,"-(d*(d*x)^(3/2))/(2*b*(a + b*x^2)) - (3*d^(5/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(1/4)*b^(7/4)) + (3*d^(5/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(1/4)*b^(7/4)) + (3*d^(5/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(1/4)*b^(7/4)) - (3*d^(5/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(1/4)*b^(7/4))","A",12,9,28,0.3214,1,"{28, 288, 329, 297, 1162, 617, 204, 1165, 628}"
690,1,281,0,0.2603894,"\int \frac{(d x)^{3/2}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^(3/2)/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","-\frac{d^{3/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d^{3/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{d \sqrt{d x}}{2 b \left(a+b x^2\right)}","-\frac{d^{3/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d^{3/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{3/4} b^{5/4}}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{3/4} b^{5/4}}-\frac{d \sqrt{d x}}{2 b \left(a+b x^2\right)}",1,"-(d*Sqrt[d*x])/(2*b*(a + b*x^2)) - (d^(3/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(3/4)*b^(5/4)) + (d^(3/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(3/4)*b^(5/4)) - (d^(3/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(3/4)*b^(5/4)) + (d^(3/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(3/4)*b^(5/4))","A",12,9,28,0.3214,1,"{28, 288, 329, 211, 1165, 628, 1162, 617, 204}"
691,1,283,0,0.2714932,"\int \frac{\sqrt{d x}}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[Sqrt[d*x]/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{\sqrt{d} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\sqrt{d} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{(d x)^{3/2}}{2 a d \left(a+b x^2\right)}","\frac{\sqrt{d} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\sqrt{d} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{5/4} b^{3/4}}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{5/4} b^{3/4}}+\frac{(d x)^{3/2}}{2 a d \left(a+b x^2\right)}",1,"(d*x)^(3/2)/(2*a*d*(a + b*x^2)) - (Sqrt[d]*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(5/4)*b^(3/4)) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(5/4)*b^(3/4)) + (Sqrt[d]*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(5/4)*b^(3/4)) - (Sqrt[d]*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(5/4)*b^(3/4))","A",12,9,28,0.3214,1,"{28, 290, 329, 297, 1162, 617, 204, 1165, 628}"
692,1,283,0,0.2649792,"\int \frac{1}{\sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/(Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}+\frac{\sqrt{d x}}{2 a d \left(a+b x^2\right)}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{7/4} \sqrt[4]{b} \sqrt{d}}+\frac{\sqrt{d x}}{2 a d \left(a+b x^2\right)}",1,"Sqrt[d*x]/(2*a*d*(a + b*x^2)) - (3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(7/4)*b^(1/4)*Sqrt[d]) + (3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(7/4)*b^(1/4)*Sqrt[d]) - (3*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(7/4)*b^(1/4)*Sqrt[d]) + (3*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(7/4)*b^(1/4)*Sqrt[d])","A",12,9,28,0.3214,1,"{28, 290, 329, 211, 1165, 628, 1162, 617, 204}"
693,1,300,0,0.3231685,"\int \frac{1}{(d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/((d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","-\frac{5 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{9/4} d^{3/2}}+\frac{5 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{9/4} d^{3/2}}+\frac{5 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{9/4} d^{3/2}}-\frac{5 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{9/4} d^{3/2}}-\frac{5}{2 a^2 d \sqrt{d x}}+\frac{1}{2 a d \sqrt{d x} \left(a+b x^2\right)}","-\frac{5 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{9/4} d^{3/2}}+\frac{5 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{9/4} d^{3/2}}+\frac{5 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{9/4} d^{3/2}}-\frac{5 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{9/4} d^{3/2}}-\frac{5}{2 a^2 d \sqrt{d x}}+\frac{1}{2 a d \sqrt{d x} \left(a+b x^2\right)}",1,"-5/(2*a^2*d*Sqrt[d*x]) + 1/(2*a*d*Sqrt[d*x]*(a + b*x^2)) + (5*b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(9/4)*d^(3/2)) - (5*b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(9/4)*d^(3/2)) - (5*b^(1/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(9/4)*d^(3/2)) + (5*b^(1/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(9/4)*d^(3/2))","A",13,10,28,0.3571,1,"{28, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
694,1,300,0,0.2991235,"\int \frac{1}{(d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/((d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","\frac{7 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{11/4} d^{5/2}}-\frac{7 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{11/4} d^{5/2}}+\frac{7 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{11/4} d^{5/2}}-\frac{7 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{11/4} d^{5/2}}-\frac{7}{6 a^2 d (d x)^{3/2}}+\frac{1}{2 a d (d x)^{3/2} \left(a+b x^2\right)}","\frac{7 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{11/4} d^{5/2}}-\frac{7 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{11/4} d^{5/2}}+\frac{7 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{11/4} d^{5/2}}-\frac{7 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{11/4} d^{5/2}}-\frac{7}{6 a^2 d (d x)^{3/2}}+\frac{1}{2 a d (d x)^{3/2} \left(a+b x^2\right)}",1,"-7/(6*a^2*d*(d*x)^(3/2)) + 1/(2*a*d*(d*x)^(3/2)*(a + b*x^2)) + (7*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(11/4)*d^(5/2)) - (7*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(11/4)*d^(5/2)) + (7*b^(3/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(11/4)*d^(5/2)) - (7*b^(3/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(11/4)*d^(5/2))","A",13,10,28,0.3571,1,"{28, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
695,1,318,0,0.342626,"\int \frac{1}{(d x)^{7/2} \left(a^2+2 a b x^2+b^2 x^4\right)} \, dx","Int[1/((d*x)^(7/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)),x]","\frac{9 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{13/4} d^{7/2}}-\frac{9 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{13/4} d^{7/2}}-\frac{9 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{13/4} d^{7/2}}+\frac{9 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{13/4} d^{7/2}}+\frac{9 b}{2 a^3 d^3 \sqrt{d x}}-\frac{9}{10 a^2 d (d x)^{5/2}}+\frac{1}{2 a d (d x)^{5/2} \left(a+b x^2\right)}","\frac{9 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{13/4} d^{7/2}}-\frac{9 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{8 \sqrt{2} a^{13/4} d^{7/2}}-\frac{9 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{4 \sqrt{2} a^{13/4} d^{7/2}}+\frac{9 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{4 \sqrt{2} a^{13/4} d^{7/2}}+\frac{9 b}{2 a^3 d^3 \sqrt{d x}}-\frac{9}{10 a^2 d (d x)^{5/2}}+\frac{1}{2 a d (d x)^{5/2} \left(a+b x^2\right)}",1,"-9/(10*a^2*d*(d*x)^(5/2)) + (9*b)/(2*a^3*d^3*Sqrt[d*x]) + 1/(2*a*d*(d*x)^(5/2)*(a + b*x^2)) - (9*b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(13/4)*d^(7/2)) + (9*b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(4*Sqrt[2]*a^(13/4)*d^(7/2)) + (9*b^(5/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(13/4)*d^(7/2)) - (9*b^(5/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(8*Sqrt[2]*a^(13/4)*d^(7/2))","A",14,10,28,0.3571,1,"{28, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
696,1,368,0,0.4182136,"\int \frac{(d x)^{19/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(19/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{663 a^{5/4} d^{19/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{21/4}}+\frac{663 a^{5/4} d^{19/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{21/4}}-\frac{663 a^{5/4} d^{19/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} b^{21/4}}+\frac{663 a^{5/4} d^{19/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} b^{21/4}}-\frac{221 d^5 (d x)^{9/2}}{192 b^3 \left(a+b x^2\right)}-\frac{17 d^3 (d x)^{13/2}}{48 b^2 \left(a+b x^2\right)^2}-\frac{663 a d^9 \sqrt{d x}}{64 b^5}-\frac{d (d x)^{17/2}}{6 b \left(a+b x^2\right)^3}+\frac{663 d^7 (d x)^{5/2}}{320 b^4}","-\frac{663 a^{5/4} d^{19/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{21/4}}+\frac{663 a^{5/4} d^{19/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{21/4}}-\frac{663 a^{5/4} d^{19/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} b^{21/4}}+\frac{663 a^{5/4} d^{19/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} b^{21/4}}-\frac{221 d^5 (d x)^{9/2}}{192 b^3 \left(a+b x^2\right)}-\frac{17 d^3 (d x)^{13/2}}{48 b^2 \left(a+b x^2\right)^2}-\frac{663 a d^9 \sqrt{d x}}{64 b^5}-\frac{d (d x)^{17/2}}{6 b \left(a+b x^2\right)^3}+\frac{663 d^7 (d x)^{5/2}}{320 b^4}",1,"(-663*a*d^9*Sqrt[d*x])/(64*b^5) + (663*d^7*(d*x)^(5/2))/(320*b^4) - (d*(d*x)^(17/2))/(6*b*(a + b*x^2)^3) - (17*d^3*(d*x)^(13/2))/(48*b^2*(a + b*x^2)^2) - (221*d^5*(d*x)^(9/2))/(192*b^3*(a + b*x^2)) - (663*a^(5/4)*d^(19/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*b^(21/4)) + (663*a^(5/4)*d^(19/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*b^(21/4)) - (663*a^(5/4)*d^(19/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*b^(21/4)) + (663*a^(5/4)*d^(19/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*b^(21/4))","A",16,10,28,0.3571,1,"{28, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
697,1,350,0,0.3929449,"\int \frac{(d x)^{17/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(17/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{385 a^{3/4} d^{17/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{19/4}}+\frac{385 a^{3/4} d^{17/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{19/4}}+\frac{385 a^{3/4} d^{17/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} b^{19/4}}-\frac{385 a^{3/4} d^{17/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} b^{19/4}}-\frac{55 d^5 (d x)^{7/2}}{64 b^3 \left(a+b x^2\right)}-\frac{5 d^3 (d x)^{11/2}}{16 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{15/2}}{6 b \left(a+b x^2\right)^3}+\frac{385 d^7 (d x)^{3/2}}{192 b^4}","-\frac{385 a^{3/4} d^{17/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{19/4}}+\frac{385 a^{3/4} d^{17/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{19/4}}+\frac{385 a^{3/4} d^{17/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} b^{19/4}}-\frac{385 a^{3/4} d^{17/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} b^{19/4}}-\frac{55 d^5 (d x)^{7/2}}{64 b^3 \left(a+b x^2\right)}-\frac{5 d^3 (d x)^{11/2}}{16 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{15/2}}{6 b \left(a+b x^2\right)^3}+\frac{385 d^7 (d x)^{3/2}}{192 b^4}",1,"(385*d^7*(d*x)^(3/2))/(192*b^4) - (d*(d*x)^(15/2))/(6*b*(a + b*x^2)^3) - (5*d^3*(d*x)^(11/2))/(16*b^2*(a + b*x^2)^2) - (55*d^5*(d*x)^(7/2))/(64*b^3*(a + b*x^2)) + (385*a^(3/4)*d^(17/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*b^(19/4)) - (385*a^(3/4)*d^(17/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*b^(19/4)) - (385*a^(3/4)*d^(17/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*b^(19/4)) + (385*a^(3/4)*d^(17/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*b^(19/4))","A",15,10,28,0.3571,1,"{28, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
698,1,350,0,0.3819976,"\int \frac{(d x)^{15/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(15/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{39 d^5 (d x)^{5/2}}{64 b^3 \left(a+b x^2\right)}-\frac{13 d^3 (d x)^{9/2}}{48 b^2 \left(a+b x^2\right)^2}+\frac{195 \sqrt[4]{a} d^{15/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{17/4}}-\frac{195 \sqrt[4]{a} d^{15/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{17/4}}+\frac{195 \sqrt[4]{a} d^{15/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} b^{17/4}}-\frac{195 \sqrt[4]{a} d^{15/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} b^{17/4}}-\frac{d (d x)^{13/2}}{6 b \left(a+b x^2\right)^3}+\frac{195 d^7 \sqrt{d x}}{64 b^4}","-\frac{39 d^5 (d x)^{5/2}}{64 b^3 \left(a+b x^2\right)}-\frac{13 d^3 (d x)^{9/2}}{48 b^2 \left(a+b x^2\right)^2}+\frac{195 \sqrt[4]{a} d^{15/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{17/4}}-\frac{195 \sqrt[4]{a} d^{15/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} b^{17/4}}+\frac{195 \sqrt[4]{a} d^{15/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} b^{17/4}}-\frac{195 \sqrt[4]{a} d^{15/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} b^{17/4}}-\frac{d (d x)^{13/2}}{6 b \left(a+b x^2\right)^3}+\frac{195 d^7 \sqrt{d x}}{64 b^4}",1,"(195*d^7*Sqrt[d*x])/(64*b^4) - (d*(d*x)^(13/2))/(6*b*(a + b*x^2)^3) - (13*d^3*(d*x)^(9/2))/(48*b^2*(a + b*x^2)^2) - (39*d^5*(d*x)^(5/2))/(64*b^3*(a + b*x^2)) + (195*a^(1/4)*d^(15/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*b^(17/4)) - (195*a^(1/4)*d^(15/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*b^(17/4)) + (195*a^(1/4)*d^(15/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*b^(17/4)) - (195*a^(1/4)*d^(15/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*b^(17/4))","A",15,10,28,0.3571,1,"{28, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
699,1,333,0,0.3450975,"\int \frac{(d x)^{13/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(13/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{77 d^5 (d x)^{3/2}}{192 b^3 \left(a+b x^2\right)}-\frac{11 d^3 (d x)^{7/2}}{48 b^2 \left(a+b x^2\right)^2}+\frac{77 d^{13/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{77 d^{13/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{77 d^{13/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} \sqrt[4]{a} b^{15/4}}+\frac{77 d^{13/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{d (d x)^{11/2}}{6 b \left(a+b x^2\right)^3}","-\frac{77 d^5 (d x)^{3/2}}{192 b^3 \left(a+b x^2\right)}-\frac{11 d^3 (d x)^{7/2}}{48 b^2 \left(a+b x^2\right)^2}+\frac{77 d^{13/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{77 d^{13/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{77 d^{13/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} \sqrt[4]{a} b^{15/4}}+\frac{77 d^{13/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{d (d x)^{11/2}}{6 b \left(a+b x^2\right)^3}",1,"-(d*(d*x)^(11/2))/(6*b*(a + b*x^2)^3) - (11*d^3*(d*x)^(7/2))/(48*b^2*(a + b*x^2)^2) - (77*d^5*(d*x)^(3/2))/(192*b^3*(a + b*x^2)) - (77*d^(13/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(1/4)*b^(15/4)) + (77*d^(13/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(1/4)*b^(15/4)) + (77*d^(13/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(1/4)*b^(15/4)) - (77*d^(13/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(1/4)*b^(15/4))","A",14,9,28,0.3214,1,"{28, 288, 329, 297, 1162, 617, 204, 1165, 628}"
700,1,333,0,0.3445787,"\int \frac{(d x)^{11/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(11/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{15 d^{11/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{3/4} b^{13/4}}+\frac{15 d^{11/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{3/4} b^{13/4}}-\frac{15 d^{11/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{3/4} b^{13/4}}+\frac{15 d^{11/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{3/4} b^{13/4}}-\frac{15 d^5 \sqrt{d x}}{64 b^3 \left(a+b x^2\right)}-\frac{3 d^3 (d x)^{5/2}}{16 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{9/2}}{6 b \left(a+b x^2\right)^3}","-\frac{15 d^{11/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{3/4} b^{13/4}}+\frac{15 d^{11/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{3/4} b^{13/4}}-\frac{15 d^{11/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{3/4} b^{13/4}}+\frac{15 d^{11/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{3/4} b^{13/4}}-\frac{15 d^5 \sqrt{d x}}{64 b^3 \left(a+b x^2\right)}-\frac{3 d^3 (d x)^{5/2}}{16 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{9/2}}{6 b \left(a+b x^2\right)^3}",1,"-(d*(d*x)^(9/2))/(6*b*(a + b*x^2)^3) - (3*d^3*(d*x)^(5/2))/(16*b^2*(a + b*x^2)^2) - (15*d^5*Sqrt[d*x])/(64*b^3*(a + b*x^2)) - (15*d^(11/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(3/4)*b^(13/4)) + (15*d^(11/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(3/4)*b^(13/4)) - (15*d^(11/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(3/4)*b^(13/4)) + (15*d^(11/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(3/4)*b^(13/4))","A",14,9,28,0.3214,1,"{28, 288, 329, 211, 1165, 628, 1162, 617, 204}"
701,1,336,0,0.3514594,"\int \frac{(d x)^{9/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(9/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{7 d^{9/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{5/4} b^{11/4}}-\frac{7 d^{9/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{5/4} b^{11/4}}-\frac{7 d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{5/4} b^{11/4}}+\frac{7 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{5/4} b^{11/4}}+\frac{7 d^3 (d x)^{3/2}}{64 a b^2 \left(a+b x^2\right)}-\frac{7 d^3 (d x)^{3/2}}{48 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{7/2}}{6 b \left(a+b x^2\right)^3}","\frac{7 d^{9/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{5/4} b^{11/4}}-\frac{7 d^{9/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{5/4} b^{11/4}}-\frac{7 d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{5/4} b^{11/4}}+\frac{7 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{5/4} b^{11/4}}+\frac{7 d^3 (d x)^{3/2}}{64 a b^2 \left(a+b x^2\right)}-\frac{7 d^3 (d x)^{3/2}}{48 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{7/2}}{6 b \left(a+b x^2\right)^3}",1,"-(d*(d*x)^(7/2))/(6*b*(a + b*x^2)^3) - (7*d^3*(d*x)^(3/2))/(48*b^2*(a + b*x^2)^2) + (7*d^3*(d*x)^(3/2))/(64*a*b^2*(a + b*x^2)) - (7*d^(9/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(5/4)*b^(11/4)) + (7*d^(9/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(5/4)*b^(11/4)) + (7*d^(9/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(5/4)*b^(11/4)) - (7*d^(9/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(5/4)*b^(11/4))","A",14,10,28,0.3571,1,"{28, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
702,1,336,0,0.3410189,"\int \frac{(d x)^{7/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(7/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{5 d^{7/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{7/4} b^{9/4}}+\frac{5 d^{7/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{7/4} b^{9/4}}-\frac{5 d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{7/4} b^{9/4}}+\frac{5 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{7/4} b^{9/4}}+\frac{5 d^3 \sqrt{d x}}{192 a b^2 \left(a+b x^2\right)}-\frac{5 d^3 \sqrt{d x}}{48 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{5/2}}{6 b \left(a+b x^2\right)^3}","-\frac{5 d^{7/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{7/4} b^{9/4}}+\frac{5 d^{7/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{7/4} b^{9/4}}-\frac{5 d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{7/4} b^{9/4}}+\frac{5 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{7/4} b^{9/4}}+\frac{5 d^3 \sqrt{d x}}{192 a b^2 \left(a+b x^2\right)}-\frac{5 d^3 \sqrt{d x}}{48 b^2 \left(a+b x^2\right)^2}-\frac{d (d x)^{5/2}}{6 b \left(a+b x^2\right)^3}",1,"-(d*(d*x)^(5/2))/(6*b*(a + b*x^2)^3) - (5*d^3*Sqrt[d*x])/(48*b^2*(a + b*x^2)^2) + (5*d^3*Sqrt[d*x])/(192*a*b^2*(a + b*x^2)) - (5*d^(7/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(7/4)*b^(9/4)) + (5*d^(7/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(7/4)*b^(9/4)) - (5*d^(7/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(7/4)*b^(9/4)) + (5*d^(7/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(7/4)*b^(9/4))","A",14,10,28,0.3571,1,"{28, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
703,1,335,0,0.3483549,"\int \frac{(d x)^{5/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(5/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{5 d^{5/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{9/4} b^{7/4}}-\frac{5 d^{5/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{9/4} b^{7/4}}-\frac{5 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{9/4} b^{7/4}}+\frac{5 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{9/4} b^{7/4}}+\frac{5 d (d x)^{3/2}}{64 a^2 b \left(a+b x^2\right)}+\frac{d (d x)^{3/2}}{16 a b \left(a+b x^2\right)^2}-\frac{d (d x)^{3/2}}{6 b \left(a+b x^2\right)^3}","\frac{5 d^{5/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{9/4} b^{7/4}}-\frac{5 d^{5/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{9/4} b^{7/4}}-\frac{5 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{9/4} b^{7/4}}+\frac{5 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{9/4} b^{7/4}}+\frac{5 d (d x)^{3/2}}{64 a^2 b \left(a+b x^2\right)}+\frac{d (d x)^{3/2}}{16 a b \left(a+b x^2\right)^2}-\frac{d (d x)^{3/2}}{6 b \left(a+b x^2\right)^3}",1,"-(d*(d*x)^(3/2))/(6*b*(a + b*x^2)^3) + (d*(d*x)^(3/2))/(16*a*b*(a + b*x^2)^2) + (5*d*(d*x)^(3/2))/(64*a^2*b*(a + b*x^2)) - (5*d^(5/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(9/4)*b^(7/4)) + (5*d^(5/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(9/4)*b^(7/4)) + (5*d^(5/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(9/4)*b^(7/4)) - (5*d^(5/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(9/4)*b^(7/4))","A",14,10,28,0.3571,1,"{28, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
704,1,335,0,0.3466789,"\int \frac{(d x)^{3/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^(3/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","-\frac{7 d^{3/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{11/4} b^{5/4}}+\frac{7 d^{3/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{11/4} b^{5/4}}-\frac{7 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{7 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{7 d \sqrt{d x}}{192 a^2 b \left(a+b x^2\right)}+\frac{d \sqrt{d x}}{48 a b \left(a+b x^2\right)^2}-\frac{d \sqrt{d x}}{6 b \left(a+b x^2\right)^3}","-\frac{7 d^{3/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{11/4} b^{5/4}}+\frac{7 d^{3/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{11/4} b^{5/4}}-\frac{7 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{7 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{11/4} b^{5/4}}+\frac{7 d \sqrt{d x}}{192 a^2 b \left(a+b x^2\right)}+\frac{d \sqrt{d x}}{48 a b \left(a+b x^2\right)^2}-\frac{d \sqrt{d x}}{6 b \left(a+b x^2\right)^3}",1,"-(d*Sqrt[d*x])/(6*b*(a + b*x^2)^3) + (d*Sqrt[d*x])/(48*a*b*(a + b*x^2)^2) + (7*d*Sqrt[d*x])/(192*a^2*b*(a + b*x^2)) - (7*d^(3/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(11/4)*b^(5/4)) + (7*d^(3/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(11/4)*b^(5/4)) - (7*d^(3/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(11/4)*b^(5/4)) + (7*d^(3/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(11/4)*b^(5/4))","A",14,10,28,0.3571,1,"{28, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
705,1,335,0,0.3518357,"\int \frac{\sqrt{d x}}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[Sqrt[d*x]/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{15 \sqrt{d} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{13/4} b^{3/4}}-\frac{15 \sqrt{d} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{13/4} b^{3/4}}-\frac{15 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{13/4} b^{3/4}}+\frac{15 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{13/4} b^{3/4}}+\frac{15 (d x)^{3/2}}{64 a^3 d \left(a+b x^2\right)}+\frac{3 (d x)^{3/2}}{16 a^2 d \left(a+b x^2\right)^2}+\frac{(d x)^{3/2}}{6 a d \left(a+b x^2\right)^3}","\frac{15 \sqrt{d} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{13/4} b^{3/4}}-\frac{15 \sqrt{d} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{13/4} b^{3/4}}-\frac{15 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{13/4} b^{3/4}}+\frac{15 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{13/4} b^{3/4}}+\frac{15 (d x)^{3/2}}{64 a^3 d \left(a+b x^2\right)}+\frac{3 (d x)^{3/2}}{16 a^2 d \left(a+b x^2\right)^2}+\frac{(d x)^{3/2}}{6 a d \left(a+b x^2\right)^3}",1,"(d*x)^(3/2)/(6*a*d*(a + b*x^2)^3) + (3*(d*x)^(3/2))/(16*a^2*d*(a + b*x^2)^2) + (15*(d*x)^(3/2))/(64*a^3*d*(a + b*x^2)) - (15*Sqrt[d]*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(13/4)*b^(3/4)) + (15*Sqrt[d]*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(13/4)*b^(3/4)) + (15*Sqrt[d]*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(13/4)*b^(3/4)) - (15*Sqrt[d]*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(13/4)*b^(3/4))","A",14,9,28,0.3214,1,"{28, 290, 329, 297, 1162, 617, 204, 1165, 628}"
706,1,335,0,0.3478136,"\int \frac{1}{\sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/(Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","\frac{77 \sqrt{d x}}{192 a^3 d \left(a+b x^2\right)}+\frac{11 \sqrt{d x}}{48 a^2 d \left(a+b x^2\right)^2}-\frac{77 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}+\frac{77 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}-\frac{77 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}+\frac{77 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}+\frac{\sqrt{d x}}{6 a d \left(a+b x^2\right)^3}","\frac{77 \sqrt{d x}}{192 a^3 d \left(a+b x^2\right)}+\frac{11 \sqrt{d x}}{48 a^2 d \left(a+b x^2\right)^2}-\frac{77 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}+\frac{77 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}-\frac{77 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}+\frac{77 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{15/4} \sqrt[4]{b} \sqrt{d}}+\frac{\sqrt{d x}}{6 a d \left(a+b x^2\right)^3}",1,"Sqrt[d*x]/(6*a*d*(a + b*x^2)^3) + (11*Sqrt[d*x])/(48*a^2*d*(a + b*x^2)^2) + (77*Sqrt[d*x])/(192*a^3*d*(a + b*x^2)) - (77*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(15/4)*b^(1/4)*Sqrt[d]) + (77*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(15/4)*b^(1/4)*Sqrt[d]) - (77*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(15/4)*b^(1/4)*Sqrt[d]) + (77*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(15/4)*b^(1/4)*Sqrt[d])","A",14,9,28,0.3214,1,"{28, 290, 329, 211, 1165, 628, 1162, 617, 204}"
707,1,352,0,0.4024529,"\int \frac{1}{(d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/((d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","-\frac{195 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{17/4} d^{3/2}}+\frac{195 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{17/4} d^{3/2}}+\frac{195 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{17/4} d^{3/2}}-\frac{195 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{17/4} d^{3/2}}+\frac{39}{64 a^3 d \sqrt{d x} \left(a+b x^2\right)}+\frac{13}{48 a^2 d \sqrt{d x} \left(a+b x^2\right)^2}-\frac{195}{64 a^4 d \sqrt{d x}}+\frac{1}{6 a d \sqrt{d x} \left(a+b x^2\right)^3}","-\frac{195 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{17/4} d^{3/2}}+\frac{195 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{17/4} d^{3/2}}+\frac{195 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{17/4} d^{3/2}}-\frac{195 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{17/4} d^{3/2}}+\frac{39}{64 a^3 d \sqrt{d x} \left(a+b x^2\right)}+\frac{13}{48 a^2 d \sqrt{d x} \left(a+b x^2\right)^2}-\frac{195}{64 a^4 d \sqrt{d x}}+\frac{1}{6 a d \sqrt{d x} \left(a+b x^2\right)^3}",1,"-195/(64*a^4*d*Sqrt[d*x]) + 1/(6*a*d*Sqrt[d*x]*(a + b*x^2)^3) + 13/(48*a^2*d*Sqrt[d*x]*(a + b*x^2)^2) + 39/(64*a^3*d*Sqrt[d*x]*(a + b*x^2)) + (195*b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(17/4)*d^(3/2)) - (195*b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(17/4)*d^(3/2)) - (195*b^(1/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(17/4)*d^(3/2)) + (195*b^(1/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(17/4)*d^(3/2))","A",15,10,28,0.3571,1,"{28, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
708,1,352,0,0.3877435,"\int \frac{1}{(d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/((d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","\frac{385 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{19/4} d^{5/2}}-\frac{385 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{19/4} d^{5/2}}+\frac{385 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{19/4} d^{5/2}}-\frac{385 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{19/4} d^{5/2}}+\frac{55}{64 a^3 d (d x)^{3/2} \left(a+b x^2\right)}+\frac{5}{16 a^2 d (d x)^{3/2} \left(a+b x^2\right)^2}-\frac{385}{192 a^4 d (d x)^{3/2}}+\frac{1}{6 a d (d x)^{3/2} \left(a+b x^2\right)^3}","\frac{385 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{19/4} d^{5/2}}-\frac{385 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{19/4} d^{5/2}}+\frac{385 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{19/4} d^{5/2}}-\frac{385 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{19/4} d^{5/2}}+\frac{55}{64 a^3 d (d x)^{3/2} \left(a+b x^2\right)}+\frac{5}{16 a^2 d (d x)^{3/2} \left(a+b x^2\right)^2}-\frac{385}{192 a^4 d (d x)^{3/2}}+\frac{1}{6 a d (d x)^{3/2} \left(a+b x^2\right)^3}",1,"-385/(192*a^4*d*(d*x)^(3/2)) + 1/(6*a*d*(d*x)^(3/2)*(a + b*x^2)^3) + 5/(16*a^2*d*(d*x)^(3/2)*(a + b*x^2)^2) + 55/(64*a^3*d*(d*x)^(3/2)*(a + b*x^2)) + (385*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(19/4)*d^(5/2)) - (385*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(19/4)*d^(5/2)) + (385*b^(3/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(19/4)*d^(5/2)) - (385*b^(3/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(19/4)*d^(5/2))","A",15,10,28,0.3571,1,"{28, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
709,1,370,0,0.4469969,"\int \frac{1}{(d x)^{7/2} \left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[1/((d*x)^(7/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^2),x]","\frac{663 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{21/4} d^{7/2}}-\frac{663 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{21/4} d^{7/2}}-\frac{663 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{21/4} d^{7/2}}+\frac{663 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{21/4} d^{7/2}}+\frac{663 b}{64 a^5 d^3 \sqrt{d x}}+\frac{221}{192 a^3 d (d x)^{5/2} \left(a+b x^2\right)}+\frac{17}{48 a^2 d (d x)^{5/2} \left(a+b x^2\right)^2}-\frac{663}{320 a^4 d (d x)^{5/2}}+\frac{1}{6 a d (d x)^{5/2} \left(a+b x^2\right)^3}","\frac{663 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{21/4} d^{7/2}}-\frac{663 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{256 \sqrt{2} a^{21/4} d^{7/2}}-\frac{663 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{128 \sqrt{2} a^{21/4} d^{7/2}}+\frac{663 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{128 \sqrt{2} a^{21/4} d^{7/2}}+\frac{663 b}{64 a^5 d^3 \sqrt{d x}}+\frac{221}{192 a^3 d (d x)^{5/2} \left(a+b x^2\right)}+\frac{17}{48 a^2 d (d x)^{5/2} \left(a+b x^2\right)^2}-\frac{663}{320 a^4 d (d x)^{5/2}}+\frac{1}{6 a d (d x)^{5/2} \left(a+b x^2\right)^3}",1,"-663/(320*a^4*d*(d*x)^(5/2)) + (663*b)/(64*a^5*d^3*Sqrt[d*x]) + 1/(6*a*d*(d*x)^(5/2)*(a + b*x^2)^3) + 17/(48*a^2*d*(d*x)^(5/2)*(a + b*x^2)^2) + 221/(192*a^3*d*(d*x)^(5/2)*(a + b*x^2)) - (663*b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(21/4)*d^(7/2)) + (663*b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(128*Sqrt[2]*a^(21/4)*d^(7/2)) + (663*b^(5/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(21/4)*d^(7/2)) - (663*b^(5/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(256*Sqrt[2]*a^(21/4)*d^(7/2))","A",16,10,28,0.3571,1,"{28, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
710,1,420,0,0.5291273,"\int \frac{(d x)^{27/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(27/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{69615 a^{5/4} d^{27/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{29/4}}+\frac{69615 a^{5/4} d^{27/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{29/4}}-\frac{69615 a^{5/4} d^{27/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} b^{29/4}}+\frac{69615 a^{5/4} d^{27/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} b^{29/4}}-\frac{7735 d^9 (d x)^{9/2}}{4096 b^5 \left(a+b x^2\right)}-\frac{595 d^7 (d x)^{13/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{35 d^5 (d x)^{17/2}}{128 b^3 \left(a+b x^2\right)^3}-\frac{5 d^3 (d x)^{21/2}}{32 b^2 \left(a+b x^2\right)^4}-\frac{69615 a d^{13} \sqrt{d x}}{4096 b^7}-\frac{d (d x)^{25/2}}{10 b \left(a+b x^2\right)^5}+\frac{13923 d^{11} (d x)^{5/2}}{4096 b^6}","-\frac{69615 a^{5/4} d^{27/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{29/4}}+\frac{69615 a^{5/4} d^{27/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{29/4}}-\frac{69615 a^{5/4} d^{27/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} b^{29/4}}+\frac{69615 a^{5/4} d^{27/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} b^{29/4}}-\frac{7735 d^9 (d x)^{9/2}}{4096 b^5 \left(a+b x^2\right)}-\frac{595 d^7 (d x)^{13/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{35 d^5 (d x)^{17/2}}{128 b^3 \left(a+b x^2\right)^3}-\frac{5 d^3 (d x)^{21/2}}{32 b^2 \left(a+b x^2\right)^4}-\frac{69615 a d^{13} \sqrt{d x}}{4096 b^7}-\frac{d (d x)^{25/2}}{10 b \left(a+b x^2\right)^5}+\frac{13923 d^{11} (d x)^{5/2}}{4096 b^6}",1,"(-69615*a*d^13*Sqrt[d*x])/(4096*b^7) + (13923*d^11*(d*x)^(5/2))/(4096*b^6) - (d*(d*x)^(25/2))/(10*b*(a + b*x^2)^5) - (5*d^3*(d*x)^(21/2))/(32*b^2*(a + b*x^2)^4) - (35*d^5*(d*x)^(17/2))/(128*b^3*(a + b*x^2)^3) - (595*d^7*(d*x)^(13/2))/(1024*b^4*(a + b*x^2)^2) - (7735*d^9*(d*x)^(9/2))/(4096*b^5*(a + b*x^2)) - (69615*a^(5/4)*d^(27/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*b^(29/4)) + (69615*a^(5/4)*d^(27/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*b^(29/4)) - (69615*a^(5/4)*d^(27/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*b^(29/4)) + (69615*a^(5/4)*d^(27/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*b^(29/4))","A",18,10,28,0.3571,1,"{28, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
711,1,402,0,0.4685385,"\int \frac{(d x)^{25/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(25/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{33649 a^{3/4} d^{25/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{27/4}}+\frac{33649 a^{3/4} d^{25/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{27/4}}+\frac{33649 a^{3/4} d^{25/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} b^{27/4}}-\frac{33649 a^{3/4} d^{25/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} b^{27/4}}-\frac{4807 d^9 (d x)^{7/2}}{4096 b^5 \left(a+b x^2\right)}-\frac{437 d^7 (d x)^{11/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{437 d^5 (d x)^{15/2}}{1920 b^3 \left(a+b x^2\right)^3}-\frac{23 d^3 (d x)^{19/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{23/2}}{10 b \left(a+b x^2\right)^5}+\frac{33649 d^{11} (d x)^{3/2}}{12288 b^6}","-\frac{33649 a^{3/4} d^{25/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{27/4}}+\frac{33649 a^{3/4} d^{25/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{27/4}}+\frac{33649 a^{3/4} d^{25/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} b^{27/4}}-\frac{33649 a^{3/4} d^{25/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} b^{27/4}}-\frac{4807 d^9 (d x)^{7/2}}{4096 b^5 \left(a+b x^2\right)}-\frac{437 d^7 (d x)^{11/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{437 d^5 (d x)^{15/2}}{1920 b^3 \left(a+b x^2\right)^3}-\frac{23 d^3 (d x)^{19/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{23/2}}{10 b \left(a+b x^2\right)^5}+\frac{33649 d^{11} (d x)^{3/2}}{12288 b^6}",1,"(33649*d^11*(d*x)^(3/2))/(12288*b^6) - (d*(d*x)^(23/2))/(10*b*(a + b*x^2)^5) - (23*d^3*(d*x)^(19/2))/(160*b^2*(a + b*x^2)^4) - (437*d^5*(d*x)^(15/2))/(1920*b^3*(a + b*x^2)^3) - (437*d^7*(d*x)^(11/2))/(1024*b^4*(a + b*x^2)^2) - (4807*d^9*(d*x)^(7/2))/(4096*b^5*(a + b*x^2)) + (33649*a^(3/4)*d^(25/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*b^(27/4)) - (33649*a^(3/4)*d^(25/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*b^(27/4)) - (33649*a^(3/4)*d^(25/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*b^(27/4)) + (33649*a^(3/4)*d^(25/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*b^(27/4))","A",17,10,28,0.3571,1,"{28, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
712,1,402,0,0.4855375,"\int \frac{(d x)^{23/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(23/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{13923 d^9 (d x)^{5/2}}{20480 b^5 \left(a+b x^2\right)}-\frac{1547 d^7 (d x)^{9/2}}{5120 b^4 \left(a+b x^2\right)^2}-\frac{119 d^5 (d x)^{13/2}}{640 b^3 \left(a+b x^2\right)^3}-\frac{21 d^3 (d x)^{17/2}}{160 b^2 \left(a+b x^2\right)^4}+\frac{13923 \sqrt[4]{a} d^{23/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{25/4}}-\frac{13923 \sqrt[4]{a} d^{23/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{25/4}}+\frac{13923 \sqrt[4]{a} d^{23/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} b^{25/4}}-\frac{13923 \sqrt[4]{a} d^{23/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} b^{25/4}}-\frac{d (d x)^{21/2}}{10 b \left(a+b x^2\right)^5}+\frac{13923 d^{11} \sqrt{d x}}{4096 b^6}","-\frac{13923 d^9 (d x)^{5/2}}{20480 b^5 \left(a+b x^2\right)}-\frac{1547 d^7 (d x)^{9/2}}{5120 b^4 \left(a+b x^2\right)^2}-\frac{119 d^5 (d x)^{13/2}}{640 b^3 \left(a+b x^2\right)^3}-\frac{21 d^3 (d x)^{17/2}}{160 b^2 \left(a+b x^2\right)^4}+\frac{13923 \sqrt[4]{a} d^{23/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{25/4}}-\frac{13923 \sqrt[4]{a} d^{23/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} b^{25/4}}+\frac{13923 \sqrt[4]{a} d^{23/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} b^{25/4}}-\frac{13923 \sqrt[4]{a} d^{23/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} b^{25/4}}-\frac{d (d x)^{21/2}}{10 b \left(a+b x^2\right)^5}+\frac{13923 d^{11} \sqrt{d x}}{4096 b^6}",1,"(13923*d^11*Sqrt[d*x])/(4096*b^6) - (d*(d*x)^(21/2))/(10*b*(a + b*x^2)^5) - (21*d^3*(d*x)^(17/2))/(160*b^2*(a + b*x^2)^4) - (119*d^5*(d*x)^(13/2))/(640*b^3*(a + b*x^2)^3) - (1547*d^7*(d*x)^(9/2))/(5120*b^4*(a + b*x^2)^2) - (13923*d^9*(d*x)^(5/2))/(20480*b^5*(a + b*x^2)) + (13923*a^(1/4)*d^(23/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*b^(25/4)) - (13923*a^(1/4)*d^(23/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*b^(25/4)) + (13923*a^(1/4)*d^(23/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*b^(25/4)) - (13923*a^(1/4)*d^(23/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*b^(25/4))","A",17,10,28,0.3571,1,"{28, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
713,1,385,0,0.4480267,"\int \frac{(d x)^{21/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(21/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{1463 d^9 (d x)^{3/2}}{4096 b^5 \left(a+b x^2\right)}-\frac{209 d^7 (d x)^{7/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{19 d^5 (d x)^{11/2}}{128 b^3 \left(a+b x^2\right)^3}-\frac{19 d^3 (d x)^{15/2}}{160 b^2 \left(a+b x^2\right)^4}+\frac{4389 d^{21/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} \sqrt[4]{a} b^{23/4}}-\frac{4389 d^{21/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} \sqrt[4]{a} b^{23/4}}-\frac{4389 d^{21/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} \sqrt[4]{a} b^{23/4}}+\frac{4389 d^{21/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} \sqrt[4]{a} b^{23/4}}-\frac{d (d x)^{19/2}}{10 b \left(a+b x^2\right)^5}","-\frac{1463 d^9 (d x)^{3/2}}{4096 b^5 \left(a+b x^2\right)}-\frac{209 d^7 (d x)^{7/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{19 d^5 (d x)^{11/2}}{128 b^3 \left(a+b x^2\right)^3}-\frac{19 d^3 (d x)^{15/2}}{160 b^2 \left(a+b x^2\right)^4}+\frac{4389 d^{21/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} \sqrt[4]{a} b^{23/4}}-\frac{4389 d^{21/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} \sqrt[4]{a} b^{23/4}}-\frac{4389 d^{21/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} \sqrt[4]{a} b^{23/4}}+\frac{4389 d^{21/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} \sqrt[4]{a} b^{23/4}}-\frac{d (d x)^{19/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(19/2))/(10*b*(a + b*x^2)^5) - (19*d^3*(d*x)^(15/2))/(160*b^2*(a + b*x^2)^4) - (19*d^5*(d*x)^(11/2))/(128*b^3*(a + b*x^2)^3) - (209*d^7*(d*x)^(7/2))/(1024*b^4*(a + b*x^2)^2) - (1463*d^9*(d*x)^(3/2))/(4096*b^5*(a + b*x^2)) - (4389*d^(21/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(1/4)*b^(23/4)) + (4389*d^(21/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(1/4)*b^(23/4)) + (4389*d^(21/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(1/4)*b^(23/4)) - (4389*d^(21/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(1/4)*b^(23/4))","A",16,9,28,0.3214,1,"{28, 288, 329, 297, 1162, 617, 204, 1165, 628}"
714,1,385,0,0.445966,"\int \frac{(d x)^{19/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(19/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{663 d^{19/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{3/4} b^{21/4}}+\frac{663 d^{19/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{3/4} b^{21/4}}-\frac{663 d^{19/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{3/4} b^{21/4}}+\frac{663 d^{19/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{3/4} b^{21/4}}-\frac{663 d^9 \sqrt{d x}}{4096 b^5 \left(a+b x^2\right)}-\frac{663 d^7 (d x)^{5/2}}{5120 b^4 \left(a+b x^2\right)^2}-\frac{221 d^5 (d x)^{9/2}}{1920 b^3 \left(a+b x^2\right)^3}-\frac{17 d^3 (d x)^{13/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{17/2}}{10 b \left(a+b x^2\right)^5}","-\frac{663 d^{19/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{3/4} b^{21/4}}+\frac{663 d^{19/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{3/4} b^{21/4}}-\frac{663 d^{19/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{3/4} b^{21/4}}+\frac{663 d^{19/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{3/4} b^{21/4}}-\frac{663 d^9 \sqrt{d x}}{4096 b^5 \left(a+b x^2\right)}-\frac{663 d^7 (d x)^{5/2}}{5120 b^4 \left(a+b x^2\right)^2}-\frac{221 d^5 (d x)^{9/2}}{1920 b^3 \left(a+b x^2\right)^3}-\frac{17 d^3 (d x)^{13/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{17/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(17/2))/(10*b*(a + b*x^2)^5) - (17*d^3*(d*x)^(13/2))/(160*b^2*(a + b*x^2)^4) - (221*d^5*(d*x)^(9/2))/(1920*b^3*(a + b*x^2)^3) - (663*d^7*(d*x)^(5/2))/(5120*b^4*(a + b*x^2)^2) - (663*d^9*Sqrt[d*x])/(4096*b^5*(a + b*x^2)) - (663*d^(19/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(3/4)*b^(21/4)) + (663*d^(19/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(3/4)*b^(21/4)) - (663*d^(19/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(3/4)*b^(21/4)) + (663*d^(19/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(3/4)*b^(21/4))","A",16,9,28,0.3214,1,"{28, 288, 329, 211, 1165, 628, 1162, 617, 204}"
715,1,388,0,0.4488173,"\int \frac{(d x)^{17/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(17/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{231 d^{17/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{5/4} b^{19/4}}-\frac{231 d^{17/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{5/4} b^{19/4}}-\frac{231 d^{17/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{5/4} b^{19/4}}+\frac{231 d^{17/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{5/4} b^{19/4}}+\frac{231 d^7 (d x)^{3/2}}{4096 a b^4 \left(a+b x^2\right)}-\frac{77 d^7 (d x)^{3/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{11 d^5 (d x)^{7/2}}{128 b^3 \left(a+b x^2\right)^3}-\frac{3 d^3 (d x)^{11/2}}{32 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{15/2}}{10 b \left(a+b x^2\right)^5}","\frac{231 d^{17/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{5/4} b^{19/4}}-\frac{231 d^{17/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{5/4} b^{19/4}}-\frac{231 d^{17/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{5/4} b^{19/4}}+\frac{231 d^{17/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{5/4} b^{19/4}}+\frac{231 d^7 (d x)^{3/2}}{4096 a b^4 \left(a+b x^2\right)}-\frac{77 d^7 (d x)^{3/2}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{11 d^5 (d x)^{7/2}}{128 b^3 \left(a+b x^2\right)^3}-\frac{3 d^3 (d x)^{11/2}}{32 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{15/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(15/2))/(10*b*(a + b*x^2)^5) - (3*d^3*(d*x)^(11/2))/(32*b^2*(a + b*x^2)^4) - (11*d^5*(d*x)^(7/2))/(128*b^3*(a + b*x^2)^3) - (77*d^7*(d*x)^(3/2))/(1024*b^4*(a + b*x^2)^2) + (231*d^7*(d*x)^(3/2))/(4096*a*b^4*(a + b*x^2)) - (231*d^(17/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(5/4)*b^(19/4)) + (231*d^(17/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(5/4)*b^(19/4)) + (231*d^(17/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(5/4)*b^(19/4)) - (231*d^(17/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(5/4)*b^(19/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
716,1,388,0,0.4458775,"\int \frac{(d x)^{15/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(15/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{117 d^{15/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{7/4} b^{17/4}}+\frac{117 d^{15/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{7/4} b^{17/4}}-\frac{117 d^{15/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{7/4} b^{17/4}}+\frac{117 d^{15/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{7/4} b^{17/4}}+\frac{39 d^7 \sqrt{d x}}{4096 a b^4 \left(a+b x^2\right)}-\frac{39 d^7 \sqrt{d x}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{39 d^5 (d x)^{5/2}}{640 b^3 \left(a+b x^2\right)^3}-\frac{13 d^3 (d x)^{9/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{13/2}}{10 b \left(a+b x^2\right)^5}","-\frac{117 d^{15/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{7/4} b^{17/4}}+\frac{117 d^{15/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{7/4} b^{17/4}}-\frac{117 d^{15/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{7/4} b^{17/4}}+\frac{117 d^{15/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{7/4} b^{17/4}}+\frac{39 d^7 \sqrt{d x}}{4096 a b^4 \left(a+b x^2\right)}-\frac{39 d^7 \sqrt{d x}}{1024 b^4 \left(a+b x^2\right)^2}-\frac{39 d^5 (d x)^{5/2}}{640 b^3 \left(a+b x^2\right)^3}-\frac{13 d^3 (d x)^{9/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{13/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(13/2))/(10*b*(a + b*x^2)^5) - (13*d^3*(d*x)^(9/2))/(160*b^2*(a + b*x^2)^4) - (39*d^5*(d*x)^(5/2))/(640*b^3*(a + b*x^2)^3) - (39*d^7*Sqrt[d*x])/(1024*b^4*(a + b*x^2)^2) + (39*d^7*Sqrt[d*x])/(4096*a*b^4*(a + b*x^2)) - (117*d^(15/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(7/4)*b^(17/4)) + (117*d^(15/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(7/4)*b^(17/4)) - (117*d^(15/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(7/4)*b^(17/4)) + (117*d^(15/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(7/4)*b^(17/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
717,1,391,0,0.4790261,"\int \frac{(d x)^{13/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(13/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{77 d^5 (d x)^{3/2}}{4096 a^2 b^3 \left(a+b x^2\right)}+\frac{77 d^{13/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{9/4} b^{15/4}}-\frac{77 d^{13/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{9/4} b^{15/4}}-\frac{77 d^{13/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{9/4} b^{15/4}}+\frac{77 d^{13/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{9/4} b^{15/4}}+\frac{77 d^5 (d x)^{3/2}}{5120 a b^3 \left(a+b x^2\right)^2}-\frac{77 d^5 (d x)^{3/2}}{1920 b^3 \left(a+b x^2\right)^3}-\frac{11 d^3 (d x)^{7/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{11/2}}{10 b \left(a+b x^2\right)^5}","\frac{77 d^5 (d x)^{3/2}}{4096 a^2 b^3 \left(a+b x^2\right)}+\frac{77 d^{13/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{9/4} b^{15/4}}-\frac{77 d^{13/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{9/4} b^{15/4}}-\frac{77 d^{13/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{9/4} b^{15/4}}+\frac{77 d^{13/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{9/4} b^{15/4}}+\frac{77 d^5 (d x)^{3/2}}{5120 a b^3 \left(a+b x^2\right)^2}-\frac{77 d^5 (d x)^{3/2}}{1920 b^3 \left(a+b x^2\right)^3}-\frac{11 d^3 (d x)^{7/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{11/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(11/2))/(10*b*(a + b*x^2)^5) - (11*d^3*(d*x)^(7/2))/(160*b^2*(a + b*x^2)^4) - (77*d^5*(d*x)^(3/2))/(1920*b^3*(a + b*x^2)^3) + (77*d^5*(d*x)^(3/2))/(5120*a*b^3*(a + b*x^2)^2) + (77*d^5*(d*x)^(3/2))/(4096*a^2*b^3*(a + b*x^2)) - (77*d^(13/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(9/4)*b^(15/4)) + (77*d^(13/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(9/4)*b^(15/4)) + (77*d^(13/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(9/4)*b^(15/4)) - (77*d^(13/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(9/4)*b^(15/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
718,1,391,0,0.4730322,"\int \frac{(d x)^{11/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(11/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{21 d^5 \sqrt{d x}}{4096 a^2 b^3 \left(a+b x^2\right)}-\frac{63 d^{11/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{11/4} b^{13/4}}+\frac{63 d^{11/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{11/4} b^{13/4}}-\frac{63 d^{11/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{11/4} b^{13/4}}+\frac{63 d^{11/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{11/4} b^{13/4}}+\frac{3 d^5 \sqrt{d x}}{1024 a b^3 \left(a+b x^2\right)^2}-\frac{3 d^5 \sqrt{d x}}{128 b^3 \left(a+b x^2\right)^3}-\frac{9 d^3 (d x)^{5/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{9/2}}{10 b \left(a+b x^2\right)^5}","\frac{21 d^5 \sqrt{d x}}{4096 a^2 b^3 \left(a+b x^2\right)}-\frac{63 d^{11/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{11/4} b^{13/4}}+\frac{63 d^{11/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{11/4} b^{13/4}}-\frac{63 d^{11/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{11/4} b^{13/4}}+\frac{63 d^{11/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{11/4} b^{13/4}}+\frac{3 d^5 \sqrt{d x}}{1024 a b^3 \left(a+b x^2\right)^2}-\frac{3 d^5 \sqrt{d x}}{128 b^3 \left(a+b x^2\right)^3}-\frac{9 d^3 (d x)^{5/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{9/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(9/2))/(10*b*(a + b*x^2)^5) - (9*d^3*(d*x)^(5/2))/(160*b^2*(a + b*x^2)^4) - (3*d^5*Sqrt[d*x])/(128*b^3*(a + b*x^2)^3) + (3*d^5*Sqrt[d*x])/(1024*a*b^3*(a + b*x^2)^2) + (21*d^5*Sqrt[d*x])/(4096*a^2*b^3*(a + b*x^2)) - (63*d^(11/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(11/4)*b^(13/4)) + (63*d^(11/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(11/4)*b^(13/4)) - (63*d^(11/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(11/4)*b^(13/4)) + (63*d^(11/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(11/4)*b^(13/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
719,1,394,0,0.4610545,"\int \frac{(d x)^{9/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(9/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{63 d^3 (d x)^{3/2}}{4096 a^3 b^2 \left(a+b x^2\right)}+\frac{63 d^3 (d x)^{3/2}}{5120 a^2 b^2 \left(a+b x^2\right)^2}+\frac{63 d^{9/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{13/4} b^{11/4}}-\frac{63 d^{9/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{13/4} b^{11/4}}-\frac{63 d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{13/4} b^{11/4}}+\frac{63 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{13/4} b^{11/4}}+\frac{7 d^3 (d x)^{3/2}}{640 a b^2 \left(a+b x^2\right)^3}-\frac{7 d^3 (d x)^{3/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{7/2}}{10 b \left(a+b x^2\right)^5}","\frac{63 d^3 (d x)^{3/2}}{4096 a^3 b^2 \left(a+b x^2\right)}+\frac{63 d^3 (d x)^{3/2}}{5120 a^2 b^2 \left(a+b x^2\right)^2}+\frac{63 d^{9/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{13/4} b^{11/4}}-\frac{63 d^{9/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{13/4} b^{11/4}}-\frac{63 d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{13/4} b^{11/4}}+\frac{63 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{13/4} b^{11/4}}+\frac{7 d^3 (d x)^{3/2}}{640 a b^2 \left(a+b x^2\right)^3}-\frac{7 d^3 (d x)^{3/2}}{160 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{7/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(7/2))/(10*b*(a + b*x^2)^5) - (7*d^3*(d*x)^(3/2))/(160*b^2*(a + b*x^2)^4) + (7*d^3*(d*x)^(3/2))/(640*a*b^2*(a + b*x^2)^3) + (63*d^3*(d*x)^(3/2))/(5120*a^2*b^2*(a + b*x^2)^2) + (63*d^3*(d*x)^(3/2))/(4096*a^3*b^2*(a + b*x^2)) - (63*d^(9/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(13/4)*b^(11/4)) + (63*d^(9/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(13/4)*b^(11/4)) + (63*d^(9/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(13/4)*b^(11/4)) - (63*d^(9/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(13/4)*b^(11/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
720,1,394,0,0.4487441,"\int \frac{(d x)^{7/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(7/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{77 d^3 \sqrt{d x}}{12288 a^3 b^2 \left(a+b x^2\right)}+\frac{11 d^3 \sqrt{d x}}{3072 a^2 b^2 \left(a+b x^2\right)^2}-\frac{77 d^{7/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{15/4} b^{9/4}}+\frac{77 d^{7/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{15/4} b^{9/4}}-\frac{77 d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{15/4} b^{9/4}}+\frac{77 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{15/4} b^{9/4}}+\frac{d^3 \sqrt{d x}}{384 a b^2 \left(a+b x^2\right)^3}-\frac{d^3 \sqrt{d x}}{32 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{5/2}}{10 b \left(a+b x^2\right)^5}","\frac{77 d^3 \sqrt{d x}}{12288 a^3 b^2 \left(a+b x^2\right)}+\frac{11 d^3 \sqrt{d x}}{3072 a^2 b^2 \left(a+b x^2\right)^2}-\frac{77 d^{7/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{15/4} b^{9/4}}+\frac{77 d^{7/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{15/4} b^{9/4}}-\frac{77 d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{15/4} b^{9/4}}+\frac{77 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{15/4} b^{9/4}}+\frac{d^3 \sqrt{d x}}{384 a b^2 \left(a+b x^2\right)^3}-\frac{d^3 \sqrt{d x}}{32 b^2 \left(a+b x^2\right)^4}-\frac{d (d x)^{5/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(5/2))/(10*b*(a + b*x^2)^5) - (d^3*Sqrt[d*x])/(32*b^2*(a + b*x^2)^4) + (d^3*Sqrt[d*x])/(384*a*b^2*(a + b*x^2)^3) + (11*d^3*Sqrt[d*x])/(3072*a^2*b^2*(a + b*x^2)^2) + (77*d^3*Sqrt[d*x])/(12288*a^3*b^2*(a + b*x^2)) - (77*d^(7/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(15/4)*b^(9/4)) + (77*d^(7/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(15/4)*b^(9/4)) - (77*d^(7/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(15/4)*b^(9/4)) + (77*d^(7/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(15/4)*b^(9/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
721,1,389,0,0.4552393,"\int \frac{(d x)^{5/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(5/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{117 d^{5/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{17/4} b^{7/4}}-\frac{117 d^{5/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{17/4} b^{7/4}}-\frac{117 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{17/4} b^{7/4}}+\frac{117 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{17/4} b^{7/4}}+\frac{117 d (d x)^{3/2}}{4096 a^4 b \left(a+b x^2\right)}+\frac{117 d (d x)^{3/2}}{5120 a^3 b \left(a+b x^2\right)^2}+\frac{13 d (d x)^{3/2}}{640 a^2 b \left(a+b x^2\right)^3}+\frac{3 d (d x)^{3/2}}{160 a b \left(a+b x^2\right)^4}-\frac{d (d x)^{3/2}}{10 b \left(a+b x^2\right)^5}","\frac{117 d^{5/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{17/4} b^{7/4}}-\frac{117 d^{5/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{17/4} b^{7/4}}-\frac{117 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{17/4} b^{7/4}}+\frac{117 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{17/4} b^{7/4}}+\frac{117 d (d x)^{3/2}}{4096 a^4 b \left(a+b x^2\right)}+\frac{117 d (d x)^{3/2}}{5120 a^3 b \left(a+b x^2\right)^2}+\frac{13 d (d x)^{3/2}}{640 a^2 b \left(a+b x^2\right)^3}+\frac{3 d (d x)^{3/2}}{160 a b \left(a+b x^2\right)^4}-\frac{d (d x)^{3/2}}{10 b \left(a+b x^2\right)^5}",1,"-(d*(d*x)^(3/2))/(10*b*(a + b*x^2)^5) + (3*d*(d*x)^(3/2))/(160*a*b*(a + b*x^2)^4) + (13*d*(d*x)^(3/2))/(640*a^2*b*(a + b*x^2)^3) + (117*d*(d*x)^(3/2))/(5120*a^3*b*(a + b*x^2)^2) + (117*d*(d*x)^(3/2))/(4096*a^4*b*(a + b*x^2)) - (117*d^(5/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(17/4)*b^(7/4)) + (117*d^(5/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(17/4)*b^(7/4)) + (117*d^(5/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(17/4)*b^(7/4)) - (117*d^(5/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(17/4)*b^(7/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
722,1,389,0,0.4987208,"\int \frac{(d x)^{3/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^(3/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","-\frac{231 d^{3/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{19/4} b^{5/4}}+\frac{231 d^{3/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{19/4} b^{5/4}}-\frac{231 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{19/4} b^{5/4}}+\frac{231 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{19/4} b^{5/4}}+\frac{77 d \sqrt{d x}}{4096 a^4 b \left(a+b x^2\right)}+\frac{11 d \sqrt{d x}}{1024 a^3 b \left(a+b x^2\right)^2}+\frac{d \sqrt{d x}}{128 a^2 b \left(a+b x^2\right)^3}+\frac{d \sqrt{d x}}{160 a b \left(a+b x^2\right)^4}-\frac{d \sqrt{d x}}{10 b \left(a+b x^2\right)^5}","-\frac{231 d^{3/2} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{19/4} b^{5/4}}+\frac{231 d^{3/2} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{19/4} b^{5/4}}-\frac{231 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{19/4} b^{5/4}}+\frac{231 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{19/4} b^{5/4}}+\frac{77 d \sqrt{d x}}{4096 a^4 b \left(a+b x^2\right)}+\frac{11 d \sqrt{d x}}{1024 a^3 b \left(a+b x^2\right)^2}+\frac{d \sqrt{d x}}{128 a^2 b \left(a+b x^2\right)^3}+\frac{d \sqrt{d x}}{160 a b \left(a+b x^2\right)^4}-\frac{d \sqrt{d x}}{10 b \left(a+b x^2\right)^5}",1,"-(d*Sqrt[d*x])/(10*b*(a + b*x^2)^5) + (d*Sqrt[d*x])/(160*a*b*(a + b*x^2)^4) + (d*Sqrt[d*x])/(128*a^2*b*(a + b*x^2)^3) + (11*d*Sqrt[d*x])/(1024*a^3*b*(a + b*x^2)^2) + (77*d*Sqrt[d*x])/(4096*a^4*b*(a + b*x^2)) - (231*d^(3/2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(19/4)*b^(5/4)) + (231*d^(3/2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(19/4)*b^(5/4)) - (231*d^(3/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(19/4)*b^(5/4)) + (231*d^(3/2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(19/4)*b^(5/4))","A",16,10,28,0.3571,1,"{28, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
723,1,387,0,0.4902225,"\int \frac{\sqrt{d x}}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[Sqrt[d*x]/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{663 \sqrt{d} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{21/4} b^{3/4}}-\frac{663 \sqrt{d} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{21/4} b^{3/4}}-\frac{663 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{21/4} b^{3/4}}+\frac{663 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{21/4} b^{3/4}}+\frac{663 (d x)^{3/2}}{4096 a^5 d \left(a+b x^2\right)}+\frac{663 (d x)^{3/2}}{5120 a^4 d \left(a+b x^2\right)^2}+\frac{221 (d x)^{3/2}}{1920 a^3 d \left(a+b x^2\right)^3}+\frac{17 (d x)^{3/2}}{160 a^2 d \left(a+b x^2\right)^4}+\frac{(d x)^{3/2}}{10 a d \left(a+b x^2\right)^5}","\frac{663 \sqrt{d} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{21/4} b^{3/4}}-\frac{663 \sqrt{d} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{21/4} b^{3/4}}-\frac{663 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{21/4} b^{3/4}}+\frac{663 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{21/4} b^{3/4}}+\frac{663 (d x)^{3/2}}{4096 a^5 d \left(a+b x^2\right)}+\frac{663 (d x)^{3/2}}{5120 a^4 d \left(a+b x^2\right)^2}+\frac{221 (d x)^{3/2}}{1920 a^3 d \left(a+b x^2\right)^3}+\frac{17 (d x)^{3/2}}{160 a^2 d \left(a+b x^2\right)^4}+\frac{(d x)^{3/2}}{10 a d \left(a+b x^2\right)^5}",1,"(d*x)^(3/2)/(10*a*d*(a + b*x^2)^5) + (17*(d*x)^(3/2))/(160*a^2*d*(a + b*x^2)^4) + (221*(d*x)^(3/2))/(1920*a^3*d*(a + b*x^2)^3) + (663*(d*x)^(3/2))/(5120*a^4*d*(a + b*x^2)^2) + (663*(d*x)^(3/2))/(4096*a^5*d*(a + b*x^2)) - (663*Sqrt[d]*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(21/4)*b^(3/4)) + (663*Sqrt[d]*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(21/4)*b^(3/4)) + (663*Sqrt[d]*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(21/4)*b^(3/4)) - (663*Sqrt[d]*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(21/4)*b^(3/4))","A",16,9,28,0.3214,1,"{28, 290, 329, 297, 1162, 617, 204, 1165, 628}"
724,1,387,0,0.4958582,"\int \frac{1}{\sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/(Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","\frac{1463 \sqrt{d x}}{4096 a^5 d \left(a+b x^2\right)}+\frac{209 \sqrt{d x}}{1024 a^4 d \left(a+b x^2\right)^2}+\frac{19 \sqrt{d x}}{128 a^3 d \left(a+b x^2\right)^3}+\frac{19 \sqrt{d x}}{160 a^2 d \left(a+b x^2\right)^4}-\frac{4389 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}+\frac{4389 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}-\frac{4389 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}+\frac{4389 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}+\frac{\sqrt{d x}}{10 a d \left(a+b x^2\right)^5}","\frac{1463 \sqrt{d x}}{4096 a^5 d \left(a+b x^2\right)}+\frac{209 \sqrt{d x}}{1024 a^4 d \left(a+b x^2\right)^2}+\frac{19 \sqrt{d x}}{128 a^3 d \left(a+b x^2\right)^3}+\frac{19 \sqrt{d x}}{160 a^2 d \left(a+b x^2\right)^4}-\frac{4389 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}+\frac{4389 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}-\frac{4389 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}+\frac{4389 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{23/4} \sqrt[4]{b} \sqrt{d}}+\frac{\sqrt{d x}}{10 a d \left(a+b x^2\right)^5}",1,"Sqrt[d*x]/(10*a*d*(a + b*x^2)^5) + (19*Sqrt[d*x])/(160*a^2*d*(a + b*x^2)^4) + (19*Sqrt[d*x])/(128*a^3*d*(a + b*x^2)^3) + (209*Sqrt[d*x])/(1024*a^4*d*(a + b*x^2)^2) + (1463*Sqrt[d*x])/(4096*a^5*d*(a + b*x^2)) - (4389*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(23/4)*b^(1/4)*Sqrt[d]) + (4389*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(23/4)*b^(1/4)*Sqrt[d]) - (4389*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(23/4)*b^(1/4)*Sqrt[d]) + (4389*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(23/4)*b^(1/4)*Sqrt[d])","A",16,9,28,0.3214,1,"{28, 290, 329, 211, 1165, 628, 1162, 617, 204}"
725,1,404,0,0.5293828,"\int \frac{1}{(d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/((d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","-\frac{13923 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{25/4} d^{3/2}}+\frac{13923 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{25/4} d^{3/2}}+\frac{13923 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{25/4} d^{3/2}}-\frac{13923 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{25/4} d^{3/2}}+\frac{13923}{20480 a^5 d \sqrt{d x} \left(a+b x^2\right)}+\frac{1547}{5120 a^4 d \sqrt{d x} \left(a+b x^2\right)^2}+\frac{119}{640 a^3 d \sqrt{d x} \left(a+b x^2\right)^3}+\frac{21}{160 a^2 d \sqrt{d x} \left(a+b x^2\right)^4}-\frac{13923}{4096 a^6 d \sqrt{d x}}+\frac{1}{10 a d \sqrt{d x} \left(a+b x^2\right)^5}","-\frac{13923 \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{25/4} d^{3/2}}+\frac{13923 \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{25/4} d^{3/2}}+\frac{13923 \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{25/4} d^{3/2}}-\frac{13923 \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{25/4} d^{3/2}}+\frac{13923}{20480 a^5 d \sqrt{d x} \left(a+b x^2\right)}+\frac{1547}{5120 a^4 d \sqrt{d x} \left(a+b x^2\right)^2}+\frac{119}{640 a^3 d \sqrt{d x} \left(a+b x^2\right)^3}+\frac{21}{160 a^2 d \sqrt{d x} \left(a+b x^2\right)^4}-\frac{13923}{4096 a^6 d \sqrt{d x}}+\frac{1}{10 a d \sqrt{d x} \left(a+b x^2\right)^5}",1,"-13923/(4096*a^6*d*Sqrt[d*x]) + 1/(10*a*d*Sqrt[d*x]*(a + b*x^2)^5) + 21/(160*a^2*d*Sqrt[d*x]*(a + b*x^2)^4) + 119/(640*a^3*d*Sqrt[d*x]*(a + b*x^2)^3) + 1547/(5120*a^4*d*Sqrt[d*x]*(a + b*x^2)^2) + 13923/(20480*a^5*d*Sqrt[d*x]*(a + b*x^2)) + (13923*b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(25/4)*d^(3/2)) - (13923*b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(25/4)*d^(3/2)) - (13923*b^(1/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(25/4)*d^(3/2)) + (13923*b^(1/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(25/4)*d^(3/2))","A",17,10,28,0.3571,1,"{28, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
726,1,404,0,0.5092424,"\int \frac{1}{(d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/((d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","\frac{33649 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{27/4} d^{5/2}}-\frac{33649 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{27/4} d^{5/2}}+\frac{33649 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{27/4} d^{5/2}}-\frac{33649 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{27/4} d^{5/2}}+\frac{4807}{4096 a^5 d (d x)^{3/2} \left(a+b x^2\right)}+\frac{437}{1024 a^4 d (d x)^{3/2} \left(a+b x^2\right)^2}+\frac{437}{1920 a^3 d (d x)^{3/2} \left(a+b x^2\right)^3}+\frac{23}{160 a^2 d (d x)^{3/2} \left(a+b x^2\right)^4}-\frac{33649}{12288 a^6 d (d x)^{3/2}}+\frac{1}{10 a d (d x)^{3/2} \left(a+b x^2\right)^5}","\frac{33649 b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{27/4} d^{5/2}}-\frac{33649 b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{27/4} d^{5/2}}+\frac{33649 b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{27/4} d^{5/2}}-\frac{33649 b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{27/4} d^{5/2}}+\frac{4807}{4096 a^5 d (d x)^{3/2} \left(a+b x^2\right)}+\frac{437}{1024 a^4 d (d x)^{3/2} \left(a+b x^2\right)^2}+\frac{437}{1920 a^3 d (d x)^{3/2} \left(a+b x^2\right)^3}+\frac{23}{160 a^2 d (d x)^{3/2} \left(a+b x^2\right)^4}-\frac{33649}{12288 a^6 d (d x)^{3/2}}+\frac{1}{10 a d (d x)^{3/2} \left(a+b x^2\right)^5}",1,"-33649/(12288*a^6*d*(d*x)^(3/2)) + 1/(10*a*d*(d*x)^(3/2)*(a + b*x^2)^5) + 23/(160*a^2*d*(d*x)^(3/2)*(a + b*x^2)^4) + 437/(1920*a^3*d*(d*x)^(3/2)*(a + b*x^2)^3) + 437/(1024*a^4*d*(d*x)^(3/2)*(a + b*x^2)^2) + 4807/(4096*a^5*d*(d*x)^(3/2)*(a + b*x^2)) + (33649*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(27/4)*d^(5/2)) - (33649*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(27/4)*d^(5/2)) + (33649*b^(3/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(27/4)*d^(5/2)) - (33649*b^(3/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(27/4)*d^(5/2))","A",17,10,28,0.3571,1,"{28, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
727,1,422,0,0.554436,"\int \frac{1}{(d x)^{7/2} \left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[1/((d*x)^(7/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^3),x]","\frac{69615 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{29/4} d^{7/2}}-\frac{69615 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{29/4} d^{7/2}}-\frac{69615 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{29/4} d^{7/2}}+\frac{69615 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{29/4} d^{7/2}}+\frac{69615 b}{4096 a^7 d^3 \sqrt{d x}}+\frac{7735}{4096 a^5 d (d x)^{5/2} \left(a+b x^2\right)}+\frac{595}{1024 a^4 d (d x)^{5/2} \left(a+b x^2\right)^2}+\frac{35}{128 a^3 d (d x)^{5/2} \left(a+b x^2\right)^3}+\frac{5}{32 a^2 d (d x)^{5/2} \left(a+b x^2\right)^4}-\frac{13923}{4096 a^6 d (d x)^{5/2}}+\frac{1}{10 a d (d x)^{5/2} \left(a+b x^2\right)^5}","\frac{69615 b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{29/4} d^{7/2}}-\frac{69615 b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{16384 \sqrt{2} a^{29/4} d^{7/2}}-\frac{69615 b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{8192 \sqrt{2} a^{29/4} d^{7/2}}+\frac{69615 b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{8192 \sqrt{2} a^{29/4} d^{7/2}}+\frac{69615 b}{4096 a^7 d^3 \sqrt{d x}}+\frac{7735}{4096 a^5 d (d x)^{5/2} \left(a+b x^2\right)}+\frac{595}{1024 a^4 d (d x)^{5/2} \left(a+b x^2\right)^2}+\frac{35}{128 a^3 d (d x)^{5/2} \left(a+b x^2\right)^3}+\frac{5}{32 a^2 d (d x)^{5/2} \left(a+b x^2\right)^4}-\frac{13923}{4096 a^6 d (d x)^{5/2}}+\frac{1}{10 a d (d x)^{5/2} \left(a+b x^2\right)^5}",1,"-13923/(4096*a^6*d*(d*x)^(5/2)) + (69615*b)/(4096*a^7*d^3*Sqrt[d*x]) + 1/(10*a*d*(d*x)^(5/2)*(a + b*x^2)^5) + 5/(32*a^2*d*(d*x)^(5/2)*(a + b*x^2)^4) + 35/(128*a^3*d*(d*x)^(5/2)*(a + b*x^2)^3) + 595/(1024*a^4*d*(d*x)^(5/2)*(a + b*x^2)^2) + 7735/(4096*a^5*d*(d*x)^(5/2)*(a + b*x^2)) - (69615*b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(29/4)*d^(7/2)) + (69615*b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(8192*Sqrt[2]*a^(29/4)*d^(7/2)) + (69615*b^(5/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(29/4)*d^(7/2)) - (69615*b^(5/4)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(16384*Sqrt[2]*a^(29/4)*d^(7/2))","A",18,10,28,0.3571,1,"{28, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
728,1,93,0,0.0297022,"\int (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{2 b (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^3 \left(a+b x^2\right)}+\frac{2 a (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d \left(a+b x^2\right)}","\frac{2 b (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^3 \left(a+b x^2\right)}+\frac{2 a (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d \left(a+b x^2\right)}",1,"(2*a*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d*(a + b*x^2)) + (2*b*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^3*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 14}"
729,1,93,0,0.0288275,"\int (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{2 b (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^3 \left(a+b x^2\right)}+\frac{2 a (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d \left(a+b x^2\right)}","\frac{2 b (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^3 \left(a+b x^2\right)}+\frac{2 a (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d \left(a+b x^2\right)}",1,"(2*a*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d*(a + b*x^2)) + (2*b*(d*x)^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*d^3*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 14}"
730,1,93,0,0.0290742,"\int \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{2 b (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^3 \left(a+b x^2\right)}+\frac{2 a (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d \left(a+b x^2\right)}","\frac{2 b (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^3 \left(a+b x^2\right)}+\frac{2 a (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d \left(a+b x^2\right)}",1,"(2*a*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d*(a + b*x^2)) + (2*b*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d^3*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 14}"
731,1,91,0,0.0283024,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{\sqrt{d x}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/Sqrt[d*x],x]","\frac{2 b (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^3 \left(a+b x^2\right)}+\frac{2 a \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \left(a+b x^2\right)}","\frac{2 b (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^3 \left(a+b x^2\right)}+\frac{2 a \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \left(a+b x^2\right)}",1,"(2*a*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*(a + b*x^2)) + (2*b*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d^3*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 14}"
732,1,91,0,0.0279233,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{(d x)^{3/2}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/(d*x)^(3/2),x]","\frac{2 b (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^3 \left(a+b x^2\right)}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \sqrt{d x} \left(a+b x^2\right)}","\frac{2 b (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^3 \left(a+b x^2\right)}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \sqrt{d x} \left(a+b x^2\right)}",1,"(-2*a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*Sqrt[d*x]*(a + b*x^2)) + (2*b*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^3*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 14}"
733,1,91,0,0.0280979,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{(d x)^{5/2}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/(d*x)^(5/2),x]","\frac{2 b \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d (d x)^{3/2} \left(a+b x^2\right)}","\frac{2 b \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d (d x)^{3/2} \left(a+b x^2\right)}",1,"(-2*a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d*(d*x)^(3/2)*(a + b*x^2)) + (2*b*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 14}"
734,1,91,0,0.0287815,"\int \frac{\sqrt{a^2+2 a b x^2+b^2 x^4}}{(d x)^{7/2}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]/(d*x)^(7/2),x]","-\frac{2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \sqrt{d x} \left(a+b x^2\right)}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d (d x)^{5/2} \left(a+b x^2\right)}","-\frac{2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \sqrt{d x} \left(a+b x^2\right)}-\frac{2 a \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d (d x)^{5/2} \left(a+b x^2\right)}",1,"(-2*a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d*(d*x)^(5/2)*(a + b*x^2)) - (2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*Sqrt[d*x]*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 14}"
735,1,195,0,0.0594125,"\int (d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[(d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{2 b^3 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^7 \left(a+b x^2\right)}+\frac{2 a b^2 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^3 \left(a+b x^2\right)}+\frac{2 a^3 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d \left(a+b x^2\right)}","\frac{2 b^3 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^7 \left(a+b x^2\right)}+\frac{2 a b^2 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^3 \left(a+b x^2\right)}+\frac{2 a^3 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d \left(a+b x^2\right)}",1,"(2*a^3*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d*(a + b*x^2)) + (6*a^2*b*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^3*(a + b*x^2)) + (2*a*b^2*(d*x)^(15/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d^5*(a + b*x^2)) + (2*b^3*(d*x)^(19/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*d^7*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
736,1,195,0,0.0583482,"\int (d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[(d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{2 b^3 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^5 \left(a+b x^2\right)}+\frac{2 a^2 b (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^3 \left(a+b x^2\right)}+\frac{2 a^3 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d \left(a+b x^2\right)}","\frac{2 b^3 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^5 \left(a+b x^2\right)}+\frac{2 a^2 b (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^3 \left(a+b x^2\right)}+\frac{2 a^3 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d \left(a+b x^2\right)}",1,"(2*a^3*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d*(a + b*x^2)) + (2*a^2*b*(d*x)^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^3*(a + b*x^2)) + (6*a*b^2*(d*x)^(13/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*d^5*(a + b*x^2)) + (2*b^3*(d*x)^(17/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*d^7*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
737,1,195,0,0.0547496,"\int \sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{2 b^3 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^3 \left(a+b x^2\right)}+\frac{2 a^3 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d \left(a+b x^2\right)}","\frac{2 b^3 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^3 \left(a+b x^2\right)}+\frac{2 a^3 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d \left(a+b x^2\right)}",1,"(2*a^3*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d*(a + b*x^2)) + (6*a^2*b*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d^3*(a + b*x^2)) + (6*a*b^2*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^5*(a + b*x^2)) + (2*b^3*(d*x)^(15/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(15*d^7*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
738,1,193,0,0.0544002,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{\sqrt{d x}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/Sqrt[d*x],x]","\frac{2 b^3 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^7 \left(a+b x^2\right)}+\frac{2 a b^2 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^3 \left(a+b x^2\right)}+\frac{2 a^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \left(a+b x^2\right)}","\frac{2 b^3 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^7 \left(a+b x^2\right)}+\frac{2 a b^2 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^3 \left(a+b x^2\right)}+\frac{2 a^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \left(a+b x^2\right)}",1,"(2*a^3*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*(a + b*x^2)) + (6*a^2*b*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d^3*(a + b*x^2)) + (2*a*b^2*(d*x)^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^5*(a + b*x^2)) + (2*b^3*(d*x)^(13/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*d^7*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
739,1,191,0,0.0576898,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{(d x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/(d*x)^(3/2),x]","\frac{2 b^3 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^5 \left(a+b x^2\right)}+\frac{2 a^2 b (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \sqrt{d x} \left(a+b x^2\right)}","\frac{2 b^3 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^5 \left(a+b x^2\right)}+\frac{2 a^2 b (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \sqrt{d x} \left(a+b x^2\right)}",1,"(-2*a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*Sqrt[d*x]*(a + b*x^2)) + (2*a^2*b*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(a + b*x^2)) + (6*a*b^2*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d^5*(a + b*x^2)) + (2*b^3*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^7*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
740,1,193,0,0.0547985,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{(d x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/(d*x)^(5/2),x]","\frac{2 b^3 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d (d x)^{3/2} \left(a+b x^2\right)}","\frac{2 b^3 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^7 \left(a+b x^2\right)}+\frac{6 a b^2 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d^5 \left(a+b x^2\right)}+\frac{6 a^2 b \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d (d x)^{3/2} \left(a+b x^2\right)}",1,"(-2*a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d*(d*x)^(3/2)*(a + b*x^2)) + (6*a^2*b*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(a + b*x^2)) + (6*a*b^2*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d^5*(a + b*x^2)) + (2*b^3*(d*x)^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*d^7*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
741,1,191,0,0.0552309,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}}{(d x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)/(d*x)^(7/2),x]","\frac{2 b^3 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^7 \left(a+b x^2\right)}+\frac{2 a b^2 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^5 \left(a+b x^2\right)}-\frac{6 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \sqrt{d x} \left(a+b x^2\right)}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d (d x)^{5/2} \left(a+b x^2\right)}","\frac{2 b^3 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^7 \left(a+b x^2\right)}+\frac{2 a b^2 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^5 \left(a+b x^2\right)}-\frac{6 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \sqrt{d x} \left(a+b x^2\right)}-\frac{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d (d x)^{5/2} \left(a+b x^2\right)}",1,"(-2*a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d*(d*x)^(5/2)*(a + b*x^2)) - (6*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*Sqrt[d*x]*(a + b*x^2)) + (2*a*b^2*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^5*(a + b*x^2)) + (2*b^3*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d^7*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
742,1,297,0,0.0823243,"\int (d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[(d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{2 b^5 (d x)^{27/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{27 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{23/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^7 \left(a+b x^2\right)}+\frac{4 a^3 b^2 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^3 \left(a+b x^2\right)}+\frac{2 a^5 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d \left(a+b x^2\right)}","\frac{2 b^5 (d x)^{27/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{27 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{23/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^7 \left(a+b x^2\right)}+\frac{4 a^3 b^2 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^3 \left(a+b x^2\right)}+\frac{2 a^5 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d \left(a+b x^2\right)}",1,"(2*a^5*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d*(a + b*x^2)) + (10*a^4*b*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^3*(a + b*x^2)) + (4*a^3*b^2*(d*x)^(15/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^5*(a + b*x^2)) + (20*a^2*b^3*(d*x)^(19/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*d^7*(a + b*x^2)) + (10*a*b^4*(d*x)^(23/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(23*d^9*(a + b*x^2)) + (2*b^5*(d*x)^(27/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(27*d^11*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
743,1,297,0,0.0772811,"\int (d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[(d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{2 b^5 (d x)^{25/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{25 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{21/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^3 \left(a+b x^2\right)}+\frac{2 a^5 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d \left(a+b x^2\right)}","\frac{2 b^5 (d x)^{25/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{25 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{21/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^3 \left(a+b x^2\right)}+\frac{2 a^5 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d \left(a+b x^2\right)}",1,"(2*a^5*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d*(a + b*x^2)) + (10*a^4*b*(d*x)^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*d^3*(a + b*x^2)) + (20*a^3*b^2*(d*x)^(13/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*d^5*(a + b*x^2)) + (20*a^2*b^3*(d*x)^(17/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*d^7*(a + b*x^2)) + (10*a*b^4*(d*x)^(21/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(21*d^9*(a + b*x^2)) + (2*b^5*(d*x)^(25/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(25*d^11*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
744,1,297,0,0.0812924,"\int \sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{2 b^5 (d x)^{23/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^9 \left(a+b x^2\right)}+\frac{4 a^2 b^3 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^3 \left(a+b x^2\right)}+\frac{2 a^5 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d \left(a+b x^2\right)}","\frac{2 b^5 (d x)^{23/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{23 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^9 \left(a+b x^2\right)}+\frac{4 a^2 b^3 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^3 \left(a+b x^2\right)}+\frac{2 a^5 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d \left(a+b x^2\right)}",1,"(2*a^5*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d*(a + b*x^2)) + (10*a^4*b*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d^3*(a + b*x^2)) + (20*a^3*b^2*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^5*(a + b*x^2)) + (4*a^2*b^3*(d*x)^(15/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^7*(a + b*x^2)) + (10*a*b^4*(d*x)^(19/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*d^9*(a + b*x^2)) + (2*b^5*(d*x)^(23/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(23*d^11*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
745,1,293,0,0.078523,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{\sqrt{d x}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/Sqrt[d*x],x]","\frac{2 b^5 (d x)^{21/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^5 \left(a+b x^2\right)}+\frac{2 a^4 b (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}+\frac{2 a^5 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \left(a+b x^2\right)}","\frac{2 b^5 (d x)^{21/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{21 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^5 \left(a+b x^2\right)}+\frac{2 a^4 b (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}+\frac{2 a^5 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \left(a+b x^2\right)}",1,"(2*a^5*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*(a + b*x^2)) + (2*a^4*b*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(a + b*x^2)) + (20*a^3*b^2*(d*x)^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*d^5*(a + b*x^2)) + (20*a^2*b^3*(d*x)^(13/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*d^7*(a + b*x^2)) + (10*a*b^4*(d*x)^(17/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*d^9*(a + b*x^2)) + (2*b^5*(d*x)^(21/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(21*d^11*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
746,1,295,0,0.079362,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{(d x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/(d*x)^(3/2),x]","\frac{2 b^5 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^{11} \left(a+b x^2\right)}+\frac{2 a b^4 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^3 \left(a+b x^2\right)}-\frac{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \sqrt{d x} \left(a+b x^2\right)}","\frac{2 b^5 (d x)^{19/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{19 d^{11} \left(a+b x^2\right)}+\frac{2 a b^4 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^5 \left(a+b x^2\right)}+\frac{10 a^4 b (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^3 \left(a+b x^2\right)}-\frac{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{d \sqrt{d x} \left(a+b x^2\right)}",1,"(-2*a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*Sqrt[d*x]*(a + b*x^2)) + (10*a^4*b*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^3*(a + b*x^2)) + (20*a^3*b^2*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d^5*(a + b*x^2)) + (20*a^2*b^3*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^7*(a + b*x^2)) + (2*a*b^4*(d*x)^(15/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^9*(a + b*x^2)) + (2*b^5*(d*x)^(19/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(19*d^11*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
747,1,293,0,0.0819537,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{(d x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/(d*x)^(5/2),x]","\frac{2 b^5 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^7 \left(a+b x^2\right)}+\frac{4 a^3 b^2 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^5 \left(a+b x^2\right)}+\frac{10 a^4 b \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d (d x)^{3/2} \left(a+b x^2\right)}","\frac{2 b^5 (d x)^{17/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{17 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{13/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{13 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{9/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{9 d^7 \left(a+b x^2\right)}+\frac{4 a^3 b^2 (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^5 \left(a+b x^2\right)}+\frac{10 a^4 b \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \left(a+b x^2\right)}-\frac{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d (d x)^{3/2} \left(a+b x^2\right)}",1,"(-2*a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d*(d*x)^(3/2)*(a + b*x^2)) + (10*a^4*b*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(a + b*x^2)) + (4*a^3*b^2*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^5*(a + b*x^2)) + (20*a^2*b^3*(d*x)^(9/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(9*d^7*(a + b*x^2)) + (10*a*b^4*(d*x)^(13/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(13*d^9*(a + b*x^2)) + (2*b^5*(d*x)^(17/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(17*d^11*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
748,1,295,0,0.0792314,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}}{(d x)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)/(d*x)^(7/2),x]","\frac{2 b^5 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^5 \left(a+b x^2\right)}-\frac{10 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \sqrt{d x} \left(a+b x^2\right)}-\frac{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d (d x)^{5/2} \left(a+b x^2\right)}","\frac{2 b^5 (d x)^{15/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{15 d^{11} \left(a+b x^2\right)}+\frac{10 a b^4 (d x)^{11/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{11 d^9 \left(a+b x^2\right)}+\frac{20 a^2 b^3 (d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{7 d^7 \left(a+b x^2\right)}+\frac{20 a^3 b^2 (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{3 d^5 \left(a+b x^2\right)}-\frac{10 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4}}{d^3 \sqrt{d x} \left(a+b x^2\right)}-\frac{2 a^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}{5 d (d x)^{5/2} \left(a+b x^2\right)}",1,"(-2*a^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d*(d*x)^(5/2)*(a + b*x^2)) - (10*a^4*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*Sqrt[d*x]*(a + b*x^2)) + (20*a^3*b^2*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^5*(a + b*x^2)) + (20*a^2*b^3*(d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(7*d^7*(a + b*x^2)) + (10*a*b^4*(d*x)^(11/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(11*d^9*(a + b*x^2)) + (2*b^5*(d*x)^(15/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(15*d^11*(a + b*x^2))","A",3,2,30,0.06667,1,"{1112, 270}"
749,1,457,0,0.324991,"\int \frac{(d x)^{7/2}}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d*x)^(7/2)/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","-\frac{2 a d^3 \sqrt{d x} \left(a+b x^2\right)}{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 d (d x)^{5/2} \left(a+b x^2\right)}{5 b \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{2 a d^3 \sqrt{d x} \left(a+b x^2\right)}{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{5/4} d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 d (d x)^{5/2} \left(a+b x^2\right)}{5 b \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-2*a*d^3*Sqrt[d*x]*(a + b*x^2))/(b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (2*d*(d*x)^(5/2)*(a + b*x^2))/(5*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a^(5/4)*d^(7/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^(5/4)*d^(7/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a^(5/4)*d^(7/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^(5/4)*d^(7/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,9,30,0.3000,1,"{1112, 321, 329, 211, 1165, 628, 1162, 617, 204}"
750,1,412,0,0.2861507,"\int \frac{(d x)^{5/2}}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d*x)^(5/2)/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","-\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 d (d x)^{3/2} \left(a+b x^2\right)}{3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{a^{3/4} d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 d (d x)^{3/2} \left(a+b x^2\right)}{3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(2*d*(d*x)^(3/2)*(a + b*x^2))/(3*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^(3/4)*d^(5/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a^(3/4)*d^(5/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a^(3/4)*d^(5/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^(3/4)*d^(5/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",12,9,30,0.3000,1,"{1112, 321, 329, 297, 1162, 617, 204, 1165, 628}"
751,1,410,0,0.2754398,"\int \frac{(d x)^{3/2}}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d*x)^(3/2)/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 d \sqrt{d x} \left(a+b x^2\right)}{b \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt[4]{a} d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{2 d \sqrt{d x} \left(a+b x^2\right)}{b \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(2*d*Sqrt[d*x]*(a + b*x^2))/(b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^(1/4)*d^(3/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a^(1/4)*d^(3/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (a^(1/4)*d^(3/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (a^(1/4)*d^(3/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",12,9,30,0.3000,1,"{1112, 321, 329, 211, 1165, 628, 1162, 617, 204}"
752,1,368,0,0.2460735,"\int \frac{\sqrt{d x}}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[Sqrt[d*x]/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\sqrt{d} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{d} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\sqrt{d} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{d} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-((Sqrt[d]*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(1/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])) + (Sqrt[d]*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(1/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (Sqrt[d]*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(1/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (Sqrt[d]*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(1/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",11,8,30,0.2667,1,"{1112, 329, 297, 1162, 617, 204, 1165, 628}"
753,1,368,0,0.2375985,"\int \frac{1}{\sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/(Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","-\frac{\left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{\left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{3/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-(((a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(3/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])) + ((a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(3/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(3/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(3/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",11,8,30,0.2667,1,"{1112, 329, 211, 1165, 628, 1162, 617, 204}"
754,1,412,0,0.2786175,"\int \frac{1}{(d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/((d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","-\frac{\sqrt[4]{b} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt[4]{b} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 \left(a+b x^2\right)}{a d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{\sqrt[4]{b} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt[4]{b} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{5/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 \left(a+b x^2\right)}{a d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-2*(a + b*x^2))/(a*d*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b^(1/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(5/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b^(1/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(5/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b^(1/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(5/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b^(1/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(5/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",12,9,30,0.3000,1,"{1112, 325, 329, 297, 1162, 617, 204, 1165, 628}"
755,1,414,0,0.2762575,"\int \frac{1}{(d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/((d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","\frac{b^{3/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{3/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 \left(a+b x^2\right)}{3 a d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{b^{3/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{3/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{7/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 \left(a+b x^2\right)}{3 a d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-2*(a + b*x^2))/(3*a*d*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b^(3/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(7/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b^(3/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(7/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b^(3/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(7/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b^(3/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(7/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",12,9,30,0.3000,1,"{1112, 325, 329, 211, 1165, 628, 1162, 617, 204}"
756,1,459,0,0.3267333,"\int \frac{1}{(d x)^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[1/((d*x)^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","\frac{2 b \left(a+b x^2\right)}{a^2 d^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{5/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{5/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 \left(a+b x^2\right)}{5 a d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{2 b \left(a+b x^2\right)}{a^2 d^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{5/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{5/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{2 \sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{\sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{\sqrt{2} a^{9/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 \left(a+b x^2\right)}{5 a d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-2*(a + b*x^2))/(5*a*d*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (2*b*(a + b*x^2))/(a^2*d^3*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b^(5/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(9/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b^(5/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(Sqrt[2]*a^(9/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b^(5/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(9/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b^(5/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(2*Sqrt[2]*a^(9/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,9,30,0.3000,1,"{1112, 325, 329, 297, 1162, 617, 204, 1165, 628}"
757,1,551,0,0.3987195,"\int \frac{(d x)^{15/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^(15/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{117 a d^7 \sqrt{d x} \left(a+b x^2\right)}{16 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 d^5 (d x)^{5/2} \left(a+b x^2\right)}{80 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13 d^3 (d x)^{9/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{13/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{117 a d^7 \sqrt{d x} \left(a+b x^2\right)}{16 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 d^5 (d x)^{5/2} \left(a+b x^2\right)}{80 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13 d^3 (d x)^{9/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 a^{5/4} d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{13/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-13*d^3*(d*x)^(9/2))/(16*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(13/2))/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (117*a*d^7*Sqrt[d*x]*(a + b*x^2))/(16*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (117*d^5*(d*x)^(5/2)*(a + b*x^2))/(80*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (117*a^(5/4)*d^(15/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (117*a^(5/4)*d^(15/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (117*a^(5/4)*d^(15/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (117*a^(5/4)*d^(15/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
758,1,504,0,0.3688431,"\int \frac{(d x)^{13/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^(13/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{77 d^5 (d x)^{3/2} \left(a+b x^2\right)}{48 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{11 d^3 (d x)^{7/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{11/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{77 d^5 (d x)^{3/2} \left(a+b x^2\right)}{48 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{11 d^3 (d x)^{7/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 a^{3/4} d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{11/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-11*d^3*(d*x)^(7/2))/(16*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(11/2))/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*d^5*(d*x)^(3/2)*(a + b*x^2))/(48*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*a^(3/4)*d^(13/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*a^(3/4)*d^(13/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*a^(3/4)*d^(13/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*a^(3/4)*d^(13/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",14,10,30,0.3333,1,"{1112, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
759,1,504,0,0.3714316,"\int \frac{(d x)^{11/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^(11/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{45 d^5 \sqrt{d x} \left(a+b x^2\right)}{16 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{9 d^3 (d x)^{5/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{9/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{45 d^5 \sqrt{d x} \left(a+b x^2\right)}{16 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{9 d^3 (d x)^{5/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \sqrt[4]{a} d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{9/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-9*d^3*(d*x)^(5/2))/(16*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(9/2))/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*d^5*Sqrt[d*x]*(a + b*x^2))/(16*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*a^(1/4)*d^(11/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*a^(1/4)*d^(11/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*a^(1/4)*d^(11/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*a^(1/4)*d^(11/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",14,10,30,0.3333,1,"{1112, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
760,1,458,0,0.3334219,"\int \frac{(d x)^{9/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^(9/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{7 d^3 (d x)^{3/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 d^{9/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 d^{9/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{7/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{7 d^3 (d x)^{3/2}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 d^{9/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 d^{9/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} \sqrt[4]{a} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{7/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-7*d^3*(d*x)^(3/2))/(16*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(7/2))/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (21*d^(9/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(1/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (21*d^(9/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(1/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (21*d^(9/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(1/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (21*d^(9/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(1/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,9,30,0.3000,1,"{1112, 288, 329, 297, 1162, 617, 204, 1165, 628}"
761,1,458,0,0.3221869,"\int \frac{(d x)^{7/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^(7/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{5 d^3 \sqrt{d x}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^{7/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 d^{7/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{5/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{5 d^3 \sqrt{d x}}{16 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^{7/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 d^{7/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{3/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{5/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-5*d^3*Sqrt[d*x])/(16*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(5/2))/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*d^(7/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(3/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*d^(7/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(3/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*d^(7/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(3/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*d^(7/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(3/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,9,30,0.3000,1,"{1112, 288, 329, 211, 1165, 628, 1162, 617, 204}"
762,1,459,0,0.3331421,"\int \frac{(d x)^{5/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^(5/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{3 d^{5/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^{5/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d (d x)^{3/2}}{16 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{3/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{3 d^{5/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^{5/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{5/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d (d x)^{3/2}}{16 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{3/2}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(3*d*(d*x)^(3/2))/(16*a*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(3/2))/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*d^(5/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(5/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3*d^(5/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(5/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3*d^(5/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(5/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*d^(5/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(5/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,10,30,0.3333,1,"{1112, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
763,1,459,0,0.3266633,"\int \frac{(d x)^{3/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^(3/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{3 d^{3/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d^{3/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d \sqrt{d x}}{16 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \sqrt{d x}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{3 d^{3/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d^{3/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{7/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d \sqrt{d x}}{16 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \sqrt{d x}}{4 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(d*Sqrt[d*x])/(16*a*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*Sqrt[d*x])/(4*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*d^(3/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(7/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3*d^(3/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(7/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*d^(3/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(7/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3*d^(3/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(7/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,10,30,0.3333,1,"{1112, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
764,1,460,0,0.3329145,"\int \frac{\sqrt{d x}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[Sqrt[d*x]/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{5 (d x)^{3/2}}{16 a^2 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{(d x)^{3/2}}{4 a d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \sqrt{d} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 \sqrt{d} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{5 (d x)^{3/2}}{16 a^2 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{(d x)^{3/2}}{4 a d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \sqrt{d} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 \sqrt{d} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{9/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(5*(d*x)^(3/2))/(16*a^2*d*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (d*x)^(3/2)/(4*a*d*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*Sqrt[d]*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(9/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*Sqrt[d]*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(9/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*Sqrt[d]*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(9/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*Sqrt[d]*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(9/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,9,30,0.3000,1,"{1112, 290, 329, 297, 1162, 617, 204, 1165, 628}"
765,1,460,0,0.3359742,"\int \frac{1}{\sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/(Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","\frac{7 \sqrt{d x}}{16 a^2 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt{d x}}{4 a d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{7 \sqrt{d x}}{16 a^2 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt{d x}}{4 a d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{21 \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{21 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{11/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(7*Sqrt[d*x])/(16*a^2*d*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + Sqrt[d*x]/(4*a*d*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (21*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(11/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (21*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(11/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (21*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(11/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (21*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(11/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",13,9,30,0.3000,1,"{1112, 290, 329, 211, 1165, 628, 1162, 617, 204}"
766,1,506,0,0.3842983,"\int \frac{1}{(d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/((d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","-\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \left(a+b x^2\right)}{16 a^3 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{9}{16 a^2 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}","-\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{13/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 \left(a+b x^2\right)}{16 a^3 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{9}{16 a^2 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}",1,"9/(16*a^2*d*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(4*a*d*Sqrt[d*x]*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*(a + b*x^2))/(16*a^3*d*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*b^(1/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(13/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*b^(1/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(13/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*b^(1/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(13/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*b^(1/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(13/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",14,10,30,0.3333,1,"{1112, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
767,1,506,0,0.3761968,"\int \frac{1}{(d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/((d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","\frac{77 b^{3/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 b^{3/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 \left(a+b x^2\right)}{48 a^3 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{11}{16 a^2 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}","\frac{77 b^{3/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 b^{3/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{15/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 \left(a+b x^2\right)}{48 a^3 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{11}{16 a^2 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}",1,"11/(16*a^2*d*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(4*a*d*(d*x)^(3/2)*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*(a + b*x^2))/(48*a^3*d*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*b^(3/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(15/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*b^(3/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(15/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*b^(3/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(15/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*b^(3/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(15/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",14,10,30,0.3333,1,"{1112, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
768,1,553,0,0.4323066,"\int \frac{1}{(d x)^{7/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[1/((d*x)^(7/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","\frac{117 b \left(a+b x^2\right)}{16 a^4 d^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 b^{5/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 b^{5/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 \left(a+b x^2\right)}{80 a^3 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a d (d x)^{5/2} \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13}{16 a^2 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{117 b \left(a+b x^2\right)}{16 a^4 d^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 b^{5/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 b^{5/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{64 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{32 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{117 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{32 \sqrt{2} a^{17/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{117 \left(a+b x^2\right)}{80 a^3 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{4 a d (d x)^{5/2} \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13}{16 a^2 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"13/(16*a^2*d*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(4*a*d*(d*x)^(5/2)*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (117*(a + b*x^2))/(80*a^3*d*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (117*b*(a + b*x^2))/(16*a^4*d^3*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (117*b^(5/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(17/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (117*b^(5/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(32*Sqrt[2]*a^(17/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (117*b^(5/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(17/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (117*b^(5/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(64*Sqrt[2]*a^(17/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
769,1,647,0,0.5088112,"\int \frac{(d x)^{23/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(23/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{13923 a d^{11} \sqrt{d x} \left(a+b x^2\right)}{1024 b^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 d^9 (d x)^{5/2} \left(a+b x^2\right)}{5120 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1547 d^7 (d x)^{9/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{119 d^5 (d x)^{13/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7 d^3 (d x)^{17/2}}{32 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{21/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{13923 a d^{11} \sqrt{d x} \left(a+b x^2\right)}{1024 b^6 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 d^9 (d x)^{5/2} \left(a+b x^2\right)}{5120 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1547 d^7 (d x)^{9/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{119 d^5 (d x)^{13/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7 d^3 (d x)^{17/2}}{32 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 a^{5/4} d^{23/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} b^{25/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{21/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-1547*d^7*(d*x)^(9/2))/(1024*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(21/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (7*d^3*(d*x)^(17/2))/(32*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (119*d^5*(d*x)^(13/2))/(256*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (13923*a*d^11*Sqrt[d*x]*(a + b*x^2))/(1024*b^6*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (13923*d^9*(d*x)^(5/2)*(a + b*x^2))/(5120*b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (13923*a^(5/4)*d^(23/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*b^(25/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (13923*a^(5/4)*d^(23/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*b^(25/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (13923*a^(5/4)*d^(23/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*b^(25/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (13923*a^(5/4)*d^(23/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*b^(25/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",17,10,30,0.3333,1,"{1112, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
770,1,600,0,0.4683361,"\int \frac{(d x)^{21/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(21/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{7315 d^9 (d x)^{3/2} \left(a+b x^2\right)}{3072 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1045 d^7 (d x)^{7/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{95 d^5 (d x)^{11/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{19 d^3 (d x)^{15/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{19/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{7315 d^9 (d x)^{3/2} \left(a+b x^2\right)}{3072 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1045 d^7 (d x)^{7/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{95 d^5 (d x)^{11/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{19 d^3 (d x)^{15/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 a^{3/4} d^{21/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} b^{23/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{19/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-1045*d^7*(d*x)^(7/2))/(1024*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(19/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (19*d^3*(d*x)^(15/2))/(96*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (95*d^5*(d*x)^(11/2))/(256*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (7315*d^9*(d*x)^(3/2)*(a + b*x^2))/(3072*b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (7315*a^(3/4)*d^(21/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*b^(23/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (7315*a^(3/4)*d^(21/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*b^(23/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (7315*a^(3/4)*d^(21/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*b^(23/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (7315*a^(3/4)*d^(21/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*b^(23/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",16,10,30,0.3333,1,"{1112, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
771,1,600,0,0.4631173,"\int \frac{(d x)^{19/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(19/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{3315 d^9 \sqrt{d x} \left(a+b x^2\right)}{1024 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{663 d^7 (d x)^{5/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{221 d^5 (d x)^{9/2}}{768 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{17 d^3 (d x)^{13/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{17/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{3315 d^9 \sqrt{d x} \left(a+b x^2\right)}{1024 b^5 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{663 d^7 (d x)^{5/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{221 d^5 (d x)^{9/2}}{768 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{17 d^3 (d x)^{13/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \sqrt[4]{a} d^{19/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} b^{21/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{17/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-663*d^7*(d*x)^(5/2))/(1024*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(17/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (17*d^3*(d*x)^(13/2))/(96*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (221*d^5*(d*x)^(9/2))/(768*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3315*d^9*Sqrt[d*x]*(a + b*x^2))/(1024*b^5*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3315*a^(1/4)*d^(19/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*b^(21/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3315*a^(1/4)*d^(19/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*b^(21/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3315*a^(1/4)*d^(19/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*b^(21/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3315*a^(1/4)*d^(19/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*b^(21/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",16,10,30,0.3333,1,"{1112, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
772,1,554,0,0.4194761,"\int \frac{(d x)^{17/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(17/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{385 d^7 (d x)^{3/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{55 d^5 (d x)^{7/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^3 (d x)^{11/2}}{32 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 d^{17/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 d^{17/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 d^{17/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 d^{17/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{15/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{385 d^7 (d x)^{3/2}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{55 d^5 (d x)^{7/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^3 (d x)^{11/2}}{32 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 d^{17/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 d^{17/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 d^{17/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 d^{17/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} \sqrt[4]{a} b^{19/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{15/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-385*d^7*(d*x)^(3/2))/(1024*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(15/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*d^3*(d*x)^(11/2))/(32*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (55*d^5*(d*x)^(7/2))/(256*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (1155*d^(17/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(1/4)*b^(19/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (1155*d^(17/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(1/4)*b^(19/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (1155*d^(17/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(1/4)*b^(19/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (1155*d^(17/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(1/4)*b^(19/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,9,30,0.3000,1,"{1112, 288, 329, 297, 1162, 617, 204, 1165, 628}"
773,1,554,0,0.4222049,"\int \frac{(d x)^{15/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(15/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{195 d^7 \sqrt{d x}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{39 d^5 (d x)^{5/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13 d^3 (d x)^{9/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 d^{15/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 d^{15/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{13/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{195 d^7 \sqrt{d x}}{1024 b^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{39 d^5 (d x)^{5/2}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13 d^3 (d x)^{9/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 d^{15/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 d^{15/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 d^{15/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{3/4} b^{17/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{13/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(-195*d^7*Sqrt[d*x])/(1024*b^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(13/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (13*d^3*(d*x)^(9/2))/(96*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (39*d^5*(d*x)^(5/2))/(256*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (195*d^(15/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(3/4)*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (195*d^(15/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(3/4)*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (195*d^(15/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(3/4)*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (195*d^(15/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(3/4)*b^(17/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,9,30,0.3000,1,"{1112, 288, 329, 211, 1165, 628, 1162, 617, 204}"
774,1,557,0,0.4252918,"\int \frac{(d x)^{13/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(13/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{77 d^5 (d x)^{3/2}}{1024 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^5 (d x)^{3/2}}{768 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{11 d^3 (d x)^{7/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{13/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^{13/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{11/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{77 d^5 (d x)^{3/2}}{1024 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^5 (d x)^{3/2}}{768 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{11 d^3 (d x)^{7/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{13/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^{13/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{13/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{5/4} b^{15/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{11/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(77*d^5*(d*x)^(3/2))/(1024*a*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(11/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (11*d^3*(d*x)^(7/2))/(96*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*d^5*(d*x)^(3/2))/(768*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*d^(13/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(5/4)*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*d^(13/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(5/4)*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*d^(13/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(5/4)*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*d^(13/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(5/4)*b^(15/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
775,1,557,0,0.4302483,"\int \frac{(d x)^{11/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(11/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{15 d^5 \sqrt{d x}}{1024 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{15 d^5 \sqrt{d x}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^3 (d x)^{5/2}}{32 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{11/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d^{11/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{9/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{15 d^5 \sqrt{d x}}{1024 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{15 d^5 \sqrt{d x}}{256 b^3 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 d^3 (d x)^{5/2}}{32 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{11/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d^{11/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d^{11/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{7/4} b^{13/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{9/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(15*d^5*Sqrt[d*x])/(1024*a*b^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(9/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*d^3*(d*x)^(5/2))/(32*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (15*d^5*Sqrt[d*x])/(256*b^3*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*d^(11/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(7/4)*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*d^(11/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(7/4)*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*d^(11/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(7/4)*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*d^(11/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(7/4)*b^(13/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
776,1,560,0,0.4239486,"\int \frac{(d x)^{9/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(9/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{35 d^3 (d x)^{3/2}}{1024 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7 d^3 (d x)^{3/2}}{256 a b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7 d^3 (d x)^{3/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{9/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{9/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{7/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{35 d^3 (d x)^{3/2}}{1024 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7 d^3 (d x)^{3/2}}{256 a b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7 d^3 (d x)^{3/2}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{9/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{9/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{9/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{9/4} b^{11/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{7/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(35*d^3*(d*x)^(3/2))/(1024*a^2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(7/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (7*d^3*(d*x)^(3/2))/(96*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (7*d^3*(d*x)^(3/2))/(256*a*b^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (35*d^(9/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(9/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (35*d^(9/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(9/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (35*d^(9/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(9/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (35*d^(9/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(9/4)*b^(11/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
777,1,560,0,0.438324,"\int \frac{(d x)^{7/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(7/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{35 d^3 \sqrt{d x}}{3072 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 d^3 \sqrt{d x}}{768 a b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^3 \sqrt{d x}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{7/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{7/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{5/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{35 d^3 \sqrt{d x}}{3072 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 d^3 \sqrt{d x}}{768 a b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{5 d^3 \sqrt{d x}}{96 b^2 \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{7/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{7/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{35 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{35 d^{7/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{11/4} b^{9/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{5/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(35*d^3*Sqrt[d*x])/(3072*a^2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(5/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (5*d^3*Sqrt[d*x])/(96*b^2*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*d^3*Sqrt[d*x])/(768*a*b^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (35*d^(7/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(11/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (35*d^(7/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(11/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (35*d^(7/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(11/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (35*d^(7/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(11/4)*b^(9/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
778,1,557,0,0.4538247,"\int \frac{(d x)^{5/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(5/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{45 d^{5/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{5/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d (d x)^{3/2}}{1024 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{9 d (d x)^{3/2}}{256 a^2 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d (d x)^{3/2}}{32 a b \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{3/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{45 d^{5/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{5/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{45 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d^{5/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{13/4} b^{7/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{45 d (d x)^{3/2}}{1024 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{9 d (d x)^{3/2}}{256 a^2 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d (d x)^{3/2}}{32 a b \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d (d x)^{3/2}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(45*d*(d*x)^(3/2))/(1024*a^3*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(d*x)^(3/2))/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (d*(d*x)^(3/2))/(32*a*b*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (9*d*(d*x)^(3/2))/(256*a^2*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*d^(5/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(13/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*d^(5/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(13/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (45*d^(5/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(13/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (45*d^(5/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(13/4)*b^(7/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 288, 290, 329, 297, 1162, 617, 204, 1165, 628}"
779,1,557,0,0.4261466,"\int \frac{(d x)^{3/2}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^(3/2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","-\frac{77 d^{3/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{3/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d \sqrt{d x}}{3072 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{11 d \sqrt{d x}}{768 a^2 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d \sqrt{d x}}{96 a b \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \sqrt{d x}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{77 d^{3/2} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{3/2} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{77 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d^{3/2} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{15/4} b^{5/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{77 d \sqrt{d x}}{3072 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{11 d \sqrt{d x}}{768 a^2 b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d \sqrt{d x}}{96 a b \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \sqrt{d x}}{8 b \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(77*d*Sqrt[d*x])/(3072*a^3*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*Sqrt[d*x])/(8*b*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (d*Sqrt[d*x])/(96*a*b*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (11*d*Sqrt[d*x])/(768*a^2*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*d^(3/2)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(15/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*d^(3/2)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(15/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (77*d^(3/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(15/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (77*d^(3/2)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(15/4)*b^(5/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,10,30,0.3333,1,"{1112, 288, 290, 329, 211, 1165, 628, 1162, 617, 204}"
780,1,556,0,0.4337815,"\int \frac{\sqrt{d x}}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[Sqrt[d*x]/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{195 (d x)^{3/2}}{1024 a^4 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{39 (d x)^{3/2}}{256 a^3 d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13 (d x)^{3/2}}{96 a^2 d \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{(d x)^{3/2}}{8 a d \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 \sqrt{d} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 \sqrt{d} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{195 (d x)^{3/2}}{1024 a^4 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{39 (d x)^{3/2}}{256 a^3 d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13 (d x)^{3/2}}{96 a^2 d \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{(d x)^{3/2}}{8 a d \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 \sqrt{d} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 \sqrt{d} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{195 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{195 \sqrt{d} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{17/4} b^{3/4} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(195*(d*x)^(3/2))/(1024*a^4*d*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (d*x)^(3/2)/(8*a*d*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (13*(d*x)^(3/2))/(96*a^2*d*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (39*(d*x)^(3/2))/(256*a^3*d*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (195*Sqrt[d]*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(17/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (195*Sqrt[d]*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(17/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (195*Sqrt[d]*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(17/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (195*Sqrt[d]*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(17/4)*b^(3/4)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,9,30,0.3000,1,"{1112, 290, 329, 297, 1162, 617, 204, 1165, 628}"
781,1,556,0,0.429213,"\int \frac{1}{\sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/(Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","\frac{385 \sqrt{d x}}{1024 a^4 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{55 \sqrt{d x}}{256 a^3 d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \sqrt{d x}}{32 a^2 d \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt{d x}}{8 a d \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{385 \sqrt{d x}}{1024 a^4 d \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{55 \sqrt{d x}}{256 a^3 d \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{5 \sqrt{d x}}{32 a^2 d \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\sqrt{d x}}{8 a d \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{1155 \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1155 \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{19/4} \sqrt[4]{b} \sqrt{d} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(385*Sqrt[d*x])/(1024*a^4*d*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + Sqrt[d*x]/(8*a*d*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (5*Sqrt[d*x])/(32*a^2*d*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (55*Sqrt[d*x])/(256*a^3*d*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (1155*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(19/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (1155*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(19/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (1155*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(19/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (1155*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(19/4)*b^(1/4)*Sqrt[d]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",15,9,30,0.3000,1,"{1112, 290, 329, 211, 1165, 628, 1162, 617, 204}"
782,1,602,0,0.485422,"\int \frac{1}{(d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/((d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","-\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \left(a+b x^2\right)}{1024 a^5 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{663}{1024 a^4 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{221}{768 a^3 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}+\frac{17}{96 a^2 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^2}+\frac{1}{8 a d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^3}","-\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \sqrt[4]{b} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{21/4} d^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3315 \left(a+b x^2\right)}{1024 a^5 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{663}{1024 a^4 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{221}{768 a^3 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}+\frac{17}{96 a^2 d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^2}+\frac{1}{8 a d \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^3}",1,"663/(1024*a^4*d*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(8*a*d*Sqrt[d*x]*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 17/(96*a^2*d*Sqrt[d*x]*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 221/(768*a^3*d*Sqrt[d*x]*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3315*(a + b*x^2))/(1024*a^5*d*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3315*b^(1/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(21/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3315*b^(1/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(21/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3315*b^(1/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(21/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (3315*b^(1/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(21/4)*d^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",16,10,30,0.3333,1,"{1112, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
783,1,602,0,0.4836476,"\int \frac{1}{(d x)^{5/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/((d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","\frac{7315 b^{3/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 b^{3/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7315 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 \left(a+b x^2\right)}{3072 a^5 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1045}{1024 a^4 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{95}{256 a^3 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}+\frac{19}{96 a^2 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^2}+\frac{1}{8 a d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^3}","\frac{7315 b^{3/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 b^{3/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7315 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 b^{3/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{23/4} d^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{7315 \left(a+b x^2\right)}{3072 a^5 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1045}{1024 a^4 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{95}{256 a^3 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)}+\frac{19}{96 a^2 d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^2}+\frac{1}{8 a d (d x)^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4} \left(a+b x^2\right)^3}",1,"1045/(1024*a^4*d*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(8*a*d*(d*x)^(3/2)*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 19/(96*a^2*d*(d*x)^(3/2)*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 95/(256*a^3*d*(d*x)^(3/2)*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (7315*(a + b*x^2))/(3072*a^5*d*(d*x)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (7315*b^(3/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(23/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (7315*b^(3/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(23/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (7315*b^(3/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(23/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (7315*b^(3/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(23/4)*d^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",16,10,30,0.3333,1,"{1112, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
784,1,649,0,0.5344276,"\int \frac{1}{(d x)^{7/2} \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[1/((d*x)^(7/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2)),x]","\frac{13923 b \left(a+b x^2\right)}{1024 a^6 d^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 b^{5/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 b^{5/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 \left(a+b x^2\right)}{5120 a^5 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{119}{256 a^3 d (d x)^{5/2} \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7}{32 a^2 d (d x)^{5/2} \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1547}{1024 a^4 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{8 a d (d x)^{5/2} \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{13923 b \left(a+b x^2\right)}{1024 a^6 d^3 \sqrt{d x} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 b^{5/4} \left(a+b x^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 b^{5/4} \left(a+b x^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{d x}+\sqrt{a} \sqrt{d}+\sqrt{b} \sqrt{d} x\right)}{4096 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}\right)}{2048 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{13923 b^{5/4} \left(a+b x^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{d x}}{\sqrt[4]{a} \sqrt{d}}+1\right)}{2048 \sqrt{2} a^{25/4} d^{7/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{13923 \left(a+b x^2\right)}{5120 a^5 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{119}{256 a^3 d (d x)^{5/2} \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{7}{32 a^2 d (d x)^{5/2} \left(a+b x^2\right)^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1547}{1024 a^4 d (d x)^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{1}{8 a d (d x)^{5/2} \left(a+b x^2\right)^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"1547/(1024*a^4*d*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 1/(8*a*d*(d*x)^(5/2)*(a + b*x^2)^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 7/(32*a^2*d*(d*x)^(5/2)*(a + b*x^2)^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + 119/(256*a^3*d*(d*x)^(5/2)*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (13923*(a + b*x^2))/(5120*a^5*d*(d*x)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (13923*b*(a + b*x^2))/(1024*a^6*d^3*Sqrt[d*x]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (13923*b^(5/4)*(a + b*x^2)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(25/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (13923*b^(5/4)*(a + b*x^2)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[d*x])/(a^(1/4)*Sqrt[d])])/(2048*Sqrt[2]*a^(25/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (13923*b^(5/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(25/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (13923*b^(5/4)*(a + b*x^2)*Log[Sqrt[a]*Sqrt[d] + Sqrt[b]*Sqrt[d]*x + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[d*x]])/(4096*Sqrt[2]*a^(25/4)*d^(7/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",17,10,30,0.3333,1,"{1112, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
785,1,150,0,0.1206094,"\int (d x)^m \left(a^2+2 a b x^2+b^2 x^4\right)^3 \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{15 a^4 b^2 (d x)^{m+5}}{d^5 (m+5)}+\frac{20 a^3 b^3 (d x)^{m+7}}{d^7 (m+7)}+\frac{15 a^2 b^4 (d x)^{m+9}}{d^9 (m+9)}+\frac{6 a^5 b (d x)^{m+3}}{d^3 (m+3)}+\frac{a^6 (d x)^{m+1}}{d (m+1)}+\frac{6 a b^5 (d x)^{m+11}}{d^{11} (m+11)}+\frac{b^6 (d x)^{m+13}}{d^{13} (m+13)}","\frac{15 a^4 b^2 (d x)^{m+5}}{d^5 (m+5)}+\frac{20 a^3 b^3 (d x)^{m+7}}{d^7 (m+7)}+\frac{15 a^2 b^4 (d x)^{m+9}}{d^9 (m+9)}+\frac{6 a^5 b (d x)^{m+3}}{d^3 (m+3)}+\frac{a^6 (d x)^{m+1}}{d (m+1)}+\frac{6 a b^5 (d x)^{m+11}}{d^{11} (m+11)}+\frac{b^6 (d x)^{m+13}}{d^{13} (m+13)}",1,"(a^6*(d*x)^(1 + m))/(d*(1 + m)) + (6*a^5*b*(d*x)^(3 + m))/(d^3*(3 + m)) + (15*a^4*b^2*(d*x)^(5 + m))/(d^5*(5 + m)) + (20*a^3*b^3*(d*x)^(7 + m))/(d^7*(7 + m)) + (15*a^2*b^4*(d*x)^(9 + m))/(d^9*(9 + m)) + (6*a*b^5*(d*x)^(11 + m))/(d^11*(11 + m)) + (b^6*(d*x)^(13 + m))/(d^13*(13 + m))","A",3,2,26,0.07692,1,"{28, 270}"
786,1,104,0,0.074949,"\int (d x)^m \left(a^2+2 a b x^2+b^2 x^4\right)^2 \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{6 a^2 b^2 (d x)^{m+5}}{d^5 (m+5)}+\frac{4 a^3 b (d x)^{m+3}}{d^3 (m+3)}+\frac{a^4 (d x)^{m+1}}{d (m+1)}+\frac{4 a b^3 (d x)^{m+7}}{d^7 (m+7)}+\frac{b^4 (d x)^{m+9}}{d^9 (m+9)}","\frac{6 a^2 b^2 (d x)^{m+5}}{d^5 (m+5)}+\frac{4 a^3 b (d x)^{m+3}}{d^3 (m+3)}+\frac{a^4 (d x)^{m+1}}{d (m+1)}+\frac{4 a b^3 (d x)^{m+7}}{d^7 (m+7)}+\frac{b^4 (d x)^{m+9}}{d^9 (m+9)}",1,"(a^4*(d*x)^(1 + m))/(d*(1 + m)) + (4*a^3*b*(d*x)^(3 + m))/(d^3*(3 + m)) + (6*a^2*b^2*(d*x)^(5 + m))/(d^5*(5 + m)) + (4*a*b^3*(d*x)^(7 + m))/(d^7*(7 + m)) + (b^4*(d*x)^(9 + m))/(d^9*(9 + m))","A",3,2,26,0.07692,1,"{28, 270}"
787,1,58,0,0.0232997,"\int (d x)^m \left(a^2+2 a b x^2+b^2 x^4\right) \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{2 a b (d x)^{m+3}}{d^3 (m+3)}+\frac{b^2 (d x)^{m+5}}{d^5 (m+5)}","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{2 a b (d x)^{m+3}}{d^3 (m+3)}+\frac{b^2 (d x)^{m+5}}{d^5 (m+5)}",1,"(a^2*(d*x)^(1 + m))/(d*(1 + m)) + (2*a*b*(d*x)^(3 + m))/(d^3*(3 + m)) + (b^2*(d*x)^(5 + m))/(d^5*(5 + m))","A",2,1,24,0.04167,1,"{14}"
788,1,44,0,0.0176527,"\int \frac{(d x)^m}{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^2 + b^2*x^4),x]","\frac{(d x)^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^2 d (m+1)}","\frac{(d x)^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^2 d (m+1)}",1,"((d*x)^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^2*d*(1 + m))","A",2,2,26,0.07692,1,"{28, 364}"
789,1,44,0,0.0169372,"\int \frac{(d x)^m}{\left(a^2+2 a b x^2+b^2 x^4\right)^2} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]","\frac{(d x)^{m+1} \, _2F_1\left(4,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^4 d (m+1)}","\frac{(d x)^{m+1} \, _2F_1\left(4,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^4 d (m+1)}",1,"((d*x)^(1 + m)*Hypergeometric2F1[4, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^4*d*(1 + m))","A",2,2,26,0.07692,1,"{28, 364}"
790,1,44,0,0.0174174,"\int \frac{(d x)^m}{\left(a^2+2 a b x^2+b^2 x^4\right)^3} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]","\frac{(d x)^{m+1} \, _2F_1\left(6,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^6 d (m+1)}","\frac{(d x)^{m+1} \, _2F_1\left(6,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^6 d (m+1)}",1,"((d*x)^(1 + m)*Hypergeometric2F1[6, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^6*d*(1 + m))","A",2,2,26,0.07692,1,"{28, 364}"
791,1,313,0,0.1203122,"\int (d x)^m \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+3}}{d^3 (m+3) \left(a+b x^2\right)}+\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+5}}{d^5 (m+5) \left(a+b x^2\right)}+\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^2\right)}+\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+9}}{d^9 (m+9) \left(a+b x^2\right)}+\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+11}}{d^{11} (m+11) \left(a+b x^2\right)}+\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+1}}{d (m+1) \left(a+b x^2\right)}","\frac{5 a^4 b \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+3}}{d^3 (m+3) \left(a+b x^2\right)}+\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+5}}{d^5 (m+5) \left(a+b x^2\right)}+\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^2\right)}+\frac{5 a b^4 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+9}}{d^9 (m+9) \left(a+b x^2\right)}+\frac{b^5 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+11}}{d^{11} (m+11) \left(a+b x^2\right)}+\frac{a^5 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+1}}{d (m+1) \left(a+b x^2\right)}",1,"(a^5*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*(1 + m)*(a + b*x^2)) + (5*a^4*b*(d*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(3 + m)*(a + b*x^2)) + (10*a^3*b^2*(d*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^5*(5 + m)*(a + b*x^2)) + (10*a^2*b^3*(d*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^7*(7 + m)*(a + b*x^2)) + (5*a*b^4*(d*x)^(9 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^9*(9 + m)*(a + b*x^2)) + (b^5*(d*x)^(11 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^11*(11 + m)*(a + b*x^2))","A",3,2,28,0.07143,1,"{1112, 270}"
792,1,205,0,0.0758189,"\int (d x)^m \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+3}}{d^3 (m+3) \left(a+b x^2\right)}+\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+5}}{d^5 (m+5) \left(a+b x^2\right)}+\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^2\right)}+\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+1}}{d (m+1) \left(a+b x^2\right)}","\frac{3 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+3}}{d^3 (m+3) \left(a+b x^2\right)}+\frac{3 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+5}}{d^5 (m+5) \left(a+b x^2\right)}+\frac{b^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^2\right)}+\frac{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+1}}{d (m+1) \left(a+b x^2\right)}",1,"(a^3*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*(1 + m)*(a + b*x^2)) + (3*a^2*b*(d*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(3 + m)*(a + b*x^2)) + (3*a*b^2*(d*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^5*(5 + m)*(a + b*x^2)) + (b^3*(d*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^7*(7 + m)*(a + b*x^2))","A",3,2,28,0.07143,1,"{1112, 270}"
793,1,97,0,0.0337345,"\int (d x)^m \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(d*x)^m*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+3}}{d^3 (m+3) \left(a+b x^2\right)}+\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+1}}{d (m+1) \left(a+b x^2\right)}","\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+3}}{d^3 (m+3) \left(a+b x^2\right)}+\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} (d x)^{m+1}}{d (m+1) \left(a+b x^2\right)}",1,"(a*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d*(1 + m)*(a + b*x^2)) + (b*(d*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(d^3*(3 + m)*(a + b*x^2))","A",3,2,28,0.07143,1,"{1112, 14}"
794,1,73,0,0.0308932,"\int \frac{(d x)^m}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d*x)^m/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a+b x^2\right) (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a d (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a d (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((d*x)^(1 + m)*(a + b*x^2)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",2,2,28,0.07143,1,"{1112, 364}"
795,1,73,0,0.0339412,"\int \frac{(d x)^m}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{\left(a+b x^2\right) (d x)^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^3 d (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) (d x)^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^3 d (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((d*x)^(1 + m)*(a + b*x^2)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^3*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",2,2,28,0.07143,1,"{1112, 364}"
796,1,73,0,0.0327895,"\int \frac{(d x)^m}{\left(a^2+2 a b x^2+b^2 x^4\right)^{5/2}} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{\left(a+b x^2\right) (d x)^{m+1} \, _2F_1\left(5,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^5 d (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) (d x)^{m+1} \, _2F_1\left(5,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a^5 d (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((d*x)^(1 + m)*(a + b*x^2)*Hypergeometric2F1[5, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a^5*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",2,2,28,0.07143,1,"{1112, 364}"
797,1,77,0,0.0263096,"\int (d x)^m \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{(d x)^{m+1} \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{m+1}{2},-2 p;\frac{m+3}{2};-\frac{b x^2}{a}\right)}{d (m+1)}","\frac{\left(a+b x^2\right) (d x)^{m+1} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(1,\frac{1}{2} (m+4 p+3);\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a d (m+1)}",1,"((d*x)^(1 + m)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[(1 + m)/2, -2*p, (3 + m)/2, -((b*x^2)/a)])/(d*(1 + m)*(1 + (b*x^2)/a)^(2*p))","A",2,2,26,0.07692,1,"{1113, 364}"
798,1,174,0,0.1086855,"\int x^7 \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x^7*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{\left(a+b x^2\right)^4 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^4 (p+2)}-\frac{3 a \left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^4 (2 p+3)}+\frac{3 a^2 \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^4 (p+1)}-\frac{a^3 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^4 (2 p+1)}","\frac{\left(a+b x^2\right)^4 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^4 (p+2)}-\frac{3 a \left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^4 (2 p+3)}+\frac{3 a^2 \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^4 (p+1)}-\frac{a^3 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^4 (2 p+1)}",1,"-(a^3*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b^4*(1 + 2*p)) + (3*a^2*(a + b*x^2)^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(4*b^4*(1 + p)) - (3*a*(a + b*x^2)^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b^4*(3 + 2*p)) + ((a + b*x^2)^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(4*b^4*(2 + p))","A",4,3,24,0.1250,1,"{1113, 266, 43}"
799,1,130,0,0.081633,"\int x^5 \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{\left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^3 (2 p+3)}-\frac{a \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^3 (p+1)}+\frac{a^2 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^3 (2 p+1)}","\frac{\left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^3 (2 p+3)}-\frac{a \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^3 (p+1)}+\frac{a^2 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^3 (2 p+1)}",1,"(a^2*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b^3*(1 + 2*p)) - (a*(a + b*x^2)^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b^3*(1 + p)) + ((a + b*x^2)^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b^3*(3 + 2*p))","A",4,3,24,0.1250,1,"{1113, 266, 43}"
800,1,84,0,0.0566805,"\int x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{\left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^2 (p+1)}-\frac{a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^2 (2 p+1)}","\frac{\left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^2 (p+1)}-\frac{a \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^2 (2 p+1)}",1,"-(a*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b^2*(1 + 2*p)) + ((a + b*x^2)^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(4*b^2*(1 + p))","A",4,3,24,0.1250,1,"{1113, 266, 43}"
801,1,41,0,0.0249834,"\int x \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b (2 p+1)}","\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b (2 p+1)}",1,"((a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b*(1 + 2*p))","A",2,2,22,0.09091,1,"{1107, 609}"
802,1,63,0,0.036719,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^p}{x} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p/x,x]","-\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);\frac{b x^2}{a}+1\right)}{2 a (2 p+1)}","-\frac{\left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);\frac{b x^2}{a}+1\right)}{2 a (2 p+1)}",1,"-((a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[1, 1 + 2*p, 2*(1 + p), 1 + (b*x^2)/a])/(2*a*(1 + 2*p))","A",3,3,24,0.1250,1,"{1113, 266, 65}"
803,1,64,0,0.03992,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^p}{x^3} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p/x^3,x]","\frac{b \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);\frac{b x^2}{a}+1\right)}{2 a^2 (2 p+1)}","\frac{b \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);\frac{b x^2}{a}+1\right)}{2 a^2 (2 p+1)}",1,"(b*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[2, 1 + 2*p, 2*(1 + p), 1 + (b*x^2)/a])/(2*a^2*(1 + 2*p))","A",3,3,24,0.1250,1,"{1113, 266, 65}"
804,1,60,0,0.0190635,"\int x^4 \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{1}{5} x^5 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{5}{2},-2 p;\frac{7}{2};-\frac{b x^2}{a}\right)","\frac{1}{5} x^5 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{5}{2},-2 p;\frac{7}{2};-\frac{b x^2}{a}\right)",1,"(x^5*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[5/2, -2*p, 7/2, -((b*x^2)/a)])/(5*(1 + (b*x^2)/a)^(2*p))","A",2,2,24,0.08333,1,"{1113, 364}"
805,1,60,0,0.0181595,"\int x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{1}{3} x^3 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{3}{2},-2 p;\frac{5}{2};-\frac{b x^2}{a}\right)","\frac{1}{3} x^3 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{3}{2},-2 p;\frac{5}{2};-\frac{b x^2}{a}\right)",1,"(x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[3/2, -2*p, 5/2, -((b*x^2)/a)])/(3*(1 + (b*x^2)/a)^(2*p))","A",2,2,24,0.08333,1,"{1113, 364}"
806,1,55,0,0.0118,"\int \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","x \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{1}{2},-2 p;\frac{3}{2};-\frac{b x^2}{a}\right)","x \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{1}{2},-2 p;\frac{3}{2};-\frac{b x^2}{a}\right)",1,"(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[1/2, -2*p, 3/2, -((b*x^2)/a)])/(1 + (b*x^2)/a)^(2*p)","A",2,2,20,0.1000,1,"{1089, 245}"
807,1,58,0,0.0184011,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^p}{x^2} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p/x^2,x]","-\frac{\left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{1}{2},-2 p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}","-\frac{\left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{1}{2},-2 p;\frac{1}{2};-\frac{b x^2}{a}\right)}{x}",1,"-(((a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[-1/2, -2*p, 1/2, -((b*x^2)/a)])/(x*(1 + (b*x^2)/a)^(2*p)))","A",2,2,24,0.08333,1,"{1113, 364}"
808,1,60,0,0.0179137,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^p}{x^4} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p/x^4,x]","-\frac{\left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{3}{2},-2 p;-\frac{1}{2};-\frac{b x^2}{a}\right)}{3 x^3}","-\frac{\left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{3}{2},-2 p;-\frac{1}{2};-\frac{b x^2}{a}\right)}{3 x^3}",1,"-((a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[-3/2, -2*p, -1/2, -((b*x^2)/a)])/(3*x^3*(1 + (b*x^2)/a)^(2*p))","A",2,2,24,0.08333,1,"{1113, 364}"
809,1,67,0,0.0211025,"\int (d x)^{3/2} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[(d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{2 (d x)^{5/2} \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{5}{4},-2 p;\frac{9}{4};-\frac{b x^2}{a}\right)}{5 d}","\frac{2 (d x)^{5/2} \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{5}{4},-2 p;\frac{9}{4};-\frac{b x^2}{a}\right)}{5 d}",1,"(2*(d*x)^(5/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[5/4, -2*p, 9/4, -((b*x^2)/a)])/(5*d*(1 + (b*x^2)/a)^(2*p))","A",2,2,28,0.07143,1,"{1113, 364}"
810,1,67,0,0.0204767,"\int \sqrt{d x} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{2 (d x)^{3/2} \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{3}{4},-2 p;\frac{7}{4};-\frac{b x^2}{a}\right)}{3 d}","\frac{2 (d x)^{3/2} \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{3}{4},-2 p;\frac{7}{4};-\frac{b x^2}{a}\right)}{3 d}",1,"(2*(d*x)^(3/2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[3/4, -2*p, 7/4, -((b*x^2)/a)])/(3*d*(1 + (b*x^2)/a)^(2*p))","A",2,2,28,0.07143,1,"{1113, 364}"
811,1,65,0,0.0206416,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^p}{\sqrt{d x}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p/Sqrt[d*x],x]","\frac{2 \sqrt{d x} \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{1}{4},-2 p;\frac{5}{4};-\frac{b x^2}{a}\right)}{d}","\frac{2 \sqrt{d x} \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(\frac{1}{4},-2 p;\frac{5}{4};-\frac{b x^2}{a}\right)}{d}",1,"(2*Sqrt[d*x]*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[1/4, -2*p, 5/4, -((b*x^2)/a)])/(d*(1 + (b*x^2)/a)^(2*p))","A",2,2,28,0.07143,1,"{1113, 364}"
812,1,65,0,0.0221593,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^p}{(d x)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p/(d*x)^(3/2),x]","-\frac{2 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{1}{4},-2 p;\frac{3}{4};-\frac{b x^2}{a}\right)}{d \sqrt{d x}}","-\frac{2 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{1}{4},-2 p;\frac{3}{4};-\frac{b x^2}{a}\right)}{d \sqrt{d x}}",1,"(-2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[-1/4, -2*p, 3/4, -((b*x^2)/a)])/(d*Sqrt[d*x]*(1 + (b*x^2)/a)^(2*p))","A",2,2,28,0.07143,1,"{1113, 364}"
813,1,67,0,0.021957,"\int \frac{\left(a^2+2 a b x^2+b^2 x^4\right)^p}{(d x)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^p/(d*x)^(5/2),x]","-\frac{2 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{3}{4},-2 p;\frac{1}{4};-\frac{b x^2}{a}\right)}{3 d (d x)^{3/2}}","-\frac{2 \left(\frac{b x^2}{a}+1\right)^{-2 p} \left(a^2+2 a b x^2+b^2 x^4\right)^p \, _2F_1\left(-\frac{3}{4},-2 p;\frac{1}{4};-\frac{b x^2}{a}\right)}{3 d (d x)^{3/2}}",1,"(-2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p*Hypergeometric2F1[-3/4, -2*p, 1/4, -((b*x^2)/a)])/(3*d*(d*x)^(3/2)*(1 + (b*x^2)/a)^(2*p))","A",2,2,28,0.07143,1,"{1113, 364}"
814,1,25,0,0.0070952,"\int x^2 \left(a+b x^2+c x^4\right) \, dx","Int[x^2*(a + b*x^2 + c*x^4),x]","\frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7}","\frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7}",1,"(a*x^3)/3 + (b*x^5)/5 + (c*x^7)/7","A",2,1,16,0.06250,1,"{14}"
815,1,25,0,0.0071979,"\int x \left(a+b x^2+c x^4\right) \, dx","Int[x*(a + b*x^2 + c*x^4),x]","\frac{a x^2}{2}+\frac{b x^4}{4}+\frac{c x^6}{6}","\frac{a x^2}{2}+\frac{b x^4}{4}+\frac{c x^6}{6}",1,"(a*x^2)/2 + (b*x^4)/4 + (c*x^6)/6","A",2,1,14,0.07143,1,"{14}"
816,1,20,0,0.0034928,"\int \left(a+b x^2+c x^4\right) \, dx","Int[a + b*x^2 + c*x^4,x]","a x+\frac{b x^3}{3}+\frac{c x^5}{5}","a x+\frac{b x^3}{3}+\frac{c x^5}{5}",1,"a*x + (b*x^3)/3 + (c*x^5)/5","A",1,0,12,0,1,"{}"
817,1,21,0,0.005449,"\int \frac{a+b x^2+c x^4}{x} \, dx","Int[(a + b*x^2 + c*x^4)/x,x]","a \log (x)+\frac{b x^2}{2}+\frac{c x^4}{4}","a \log (x)+\frac{b x^2}{2}+\frac{c x^4}{4}",1,"(b*x^2)/2 + (c*x^4)/4 + a*Log[x]","A",2,1,16,0.06250,1,"{14}"
818,1,18,0,0.0066606,"\int \frac{a+b x^2+c x^4}{x^2} \, dx","Int[(a + b*x^2 + c*x^4)/x^2,x]","-\frac{a}{x}+b x+\frac{c x^3}{3}","-\frac{a}{x}+b x+\frac{c x^3}{3}",1,"-(a/x) + b*x + (c*x^3)/3","A",2,1,16,0.06250,1,"{14}"
819,1,21,0,0.0069357,"\int \frac{a+b x^2+c x^4}{x^3} \, dx","Int[(a + b*x^2 + c*x^4)/x^3,x]","-\frac{a}{2 x^2}+b \log (x)+\frac{c x^2}{2}","-\frac{a}{2 x^2}+b \log (x)+\frac{c x^2}{2}",1,"-a/(2*x^2) + (c*x^2)/2 + b*Log[x]","A",2,1,16,0.06250,1,"{14}"
820,1,18,0,0.0066929,"\int \frac{a+b x^2+c x^4}{x^4} \, dx","Int[(a + b*x^2 + c*x^4)/x^4,x]","-\frac{a}{3 x^3}-\frac{b}{x}+c x","-\frac{a}{3 x^3}-\frac{b}{x}+c x",1,"-a/(3*x^3) - b/x + c*x","A",2,1,16,0.06250,1,"{14}"
821,1,21,0,0.0069292,"\int \frac{a+b x^2+c x^4}{x^5} \, dx","Int[(a + b*x^2 + c*x^4)/x^5,x]","-\frac{a}{4 x^4}-\frac{b}{2 x^2}+c \log (x)","-\frac{a}{4 x^4}-\frac{b}{2 x^2}+c \log (x)",1,"-a/(4*x^4) - b/(2*x^2) + c*Log[x]","A",2,1,16,0.06250,1,"{14}"
822,1,23,0,0.0068175,"\int \frac{a+b x^2+c x^4}{x^6} \, dx","Int[(a + b*x^2 + c*x^4)/x^6,x]","-\frac{a}{5 x^5}-\frac{b}{3 x^3}-\frac{c}{x}","-\frac{a}{5 x^5}-\frac{b}{3 x^3}-\frac{c}{x}",1,"-a/(5*x^5) - b/(3*x^3) - c/x","A",2,1,16,0.06250,1,"{14}"
823,1,25,0,0.0069301,"\int \frac{a+b x^2+c x^4}{x^7} \, dx","Int[(a + b*x^2 + c*x^4)/x^7,x]","-\frac{a}{6 x^6}-\frac{b}{4 x^4}-\frac{c}{2 x^2}","-\frac{a}{6 x^6}-\frac{b}{4 x^4}-\frac{c}{2 x^2}",1,"-a/(6*x^6) - b/(4*x^4) - c/(2*x^2)","A",2,1,16,0.06250,1,"{14}"
824,1,25,0,0.0066146,"\int \frac{a+b x^2+c x^4}{x^8} \, dx","Int[(a + b*x^2 + c*x^4)/x^8,x]","-\frac{a}{7 x^7}-\frac{b}{5 x^5}-\frac{c}{3 x^3}","-\frac{a}{7 x^7}-\frac{b}{5 x^5}-\frac{c}{3 x^3}",1,"-a/(7*x^7) - b/(5*x^5) - c/(3*x^3)","A",2,1,16,0.06250,1,"{14}"
825,1,54,0,0.0301173,"\int x^2 \left(a+b x^2+c x^4\right)^2 \, dx","Int[x^2*(a + b*x^2 + c*x^4)^2,x]","\frac{a^2 x^3}{3}+\frac{1}{7} x^7 \left(2 a c+b^2\right)+\frac{2}{5} a b x^5+\frac{2}{9} b c x^9+\frac{c^2 x^{11}}{11}","\frac{a^2 x^3}{3}+\frac{1}{7} x^7 \left(2 a c+b^2\right)+\frac{2}{5} a b x^5+\frac{2}{9} b c x^9+\frac{c^2 x^{11}}{11}",1,"(a^2*x^3)/3 + (2*a*b*x^5)/5 + ((b^2 + 2*a*c)*x^7)/7 + (2*b*c*x^9)/9 + (c^2*x^11)/11","A",2,1,18,0.05556,1,"{1108}"
826,1,54,0,0.0383747,"\int x \left(a+b x^2+c x^4\right)^2 \, dx","Int[x*(a + b*x^2 + c*x^4)^2,x]","\frac{a^2 x^2}{2}+\frac{1}{6} x^6 \left(2 a c+b^2\right)+\frac{1}{2} a b x^4+\frac{1}{4} b c x^8+\frac{c^2 x^{10}}{10}","\frac{a^2 x^2}{2}+\frac{1}{6} x^6 \left(2 a c+b^2\right)+\frac{1}{2} a b x^4+\frac{1}{4} b c x^8+\frac{c^2 x^{10}}{10}",1,"(a^2*x^2)/2 + (a*b*x^4)/2 + ((b^2 + 2*a*c)*x^6)/6 + (b*c*x^8)/4 + (c^2*x^10)/10","A",3,2,16,0.1250,1,"{1107, 611}"
827,1,49,0,0.0207458,"\int \left(a+b x^2+c x^4\right)^2 \, dx","Int[(a + b*x^2 + c*x^4)^2,x]","a^2 x+\frac{1}{5} x^5 \left(2 a c+b^2\right)+\frac{2}{3} a b x^3+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9}","a^2 x+\frac{1}{5} x^5 \left(2 a c+b^2\right)+\frac{2}{3} a b x^3+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9}",1,"a^2*x + (2*a*b*x^3)/3 + ((b^2 + 2*a*c)*x^5)/5 + (2*b*c*x^7)/7 + (c^2*x^9)/9","A",2,1,14,0.07143,1,"{1090}"
828,1,47,0,0.0413996,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x} \, dx","Int[(a + b*x^2 + c*x^4)^2/x,x]","a^2 \log (x)+\frac{1}{4} x^4 \left(2 a c+b^2\right)+a b x^2+\frac{1}{3} b c x^6+\frac{c^2 x^8}{8}","a^2 \log (x)+\frac{1}{4} x^4 \left(2 a c+b^2\right)+a b x^2+\frac{1}{3} b c x^6+\frac{c^2 x^8}{8}",1,"a*b*x^2 + ((b^2 + 2*a*c)*x^4)/4 + (b*c*x^6)/3 + (c^2*x^8)/8 + a^2*Log[x]","A",3,2,18,0.1111,1,"{1114, 698}"
829,1,48,0,0.021085,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^2} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^2,x]","-\frac{a^2}{x}+\frac{1}{3} x^3 \left(2 a c+b^2\right)+2 a b x+\frac{2}{5} b c x^5+\frac{c^2 x^7}{7}","-\frac{a^2}{x}+\frac{1}{3} x^3 \left(2 a c+b^2\right)+2 a b x+\frac{2}{5} b c x^5+\frac{c^2 x^7}{7}",1,"-(a^2/x) + 2*a*b*x + ((b^2 + 2*a*c)*x^3)/3 + (2*b*c*x^5)/5 + (c^2*x^7)/7","A",2,1,18,0.05556,1,"{1108}"
830,1,51,0,0.0408121,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^3} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^3,x]","-\frac{a^2}{2 x^2}+\frac{1}{2} x^2 \left(2 a c+b^2\right)+2 a b \log (x)+\frac{1}{2} b c x^4+\frac{c^2 x^6}{6}","-\frac{a^2}{2 x^2}+\frac{1}{2} x^2 \left(2 a c+b^2\right)+2 a b \log (x)+\frac{1}{2} b c x^4+\frac{c^2 x^6}{6}",1,"-a^2/(2*x^2) + ((b^2 + 2*a*c)*x^2)/2 + (b*c*x^4)/2 + (c^2*x^6)/6 + 2*a*b*Log[x]","A",3,2,18,0.1111,1,"{1114, 698}"
831,1,47,0,0.023734,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^4} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^4,x]","-\frac{a^2}{3 x^3}+x \left(2 a c+b^2\right)-\frac{2 a b}{x}+\frac{2}{3} b c x^3+\frac{c^2 x^5}{5}","-\frac{a^2}{3 x^3}+x \left(2 a c+b^2\right)-\frac{2 a b}{x}+\frac{2}{3} b c x^3+\frac{c^2 x^5}{5}",1,"-a^2/(3*x^3) - (2*a*b)/x + (b^2 + 2*a*c)*x + (2*b*c*x^3)/3 + (c^2*x^5)/5","A",2,1,18,0.05556,1,"{1108}"
832,1,45,0,0.0375199,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^5} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^5,x]","-\frac{a^2}{4 x^4}+\log (x) \left(2 a c+b^2\right)-\frac{a b}{x^2}+b c x^2+\frac{c^2 x^4}{4}","-\frac{a^2}{4 x^4}+\log (x) \left(2 a c+b^2\right)-\frac{a b}{x^2}+b c x^2+\frac{c^2 x^4}{4}",1,"-a^2/(4*x^4) - (a*b)/x^2 + b*c*x^2 + (c^2*x^4)/4 + (b^2 + 2*a*c)*Log[x]","A",3,2,18,0.1111,1,"{1114, 698}"
833,1,48,0,0.0230556,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^6} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^6,x]","-\frac{a^2}{5 x^5}-\frac{2 a c+b^2}{x}-\frac{2 a b}{3 x^3}+2 b c x+\frac{c^2 x^3}{3}","-\frac{a^2}{5 x^5}-\frac{2 a c+b^2}{x}-\frac{2 a b}{3 x^3}+2 b c x+\frac{c^2 x^3}{3}",1,"-a^2/(5*x^5) - (2*a*b)/(3*x^3) - (b^2 + 2*a*c)/x + 2*b*c*x + (c^2*x^3)/3","A",2,1,18,0.05556,1,"{1108}"
834,1,51,0,0.036362,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^7} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^7,x]","-\frac{a^2}{6 x^6}-\frac{2 a c+b^2}{2 x^2}-\frac{a b}{2 x^4}+2 b c \log (x)+\frac{c^2 x^2}{2}","-\frac{a^2}{6 x^6}-\frac{2 a c+b^2}{2 x^2}-\frac{a b}{2 x^4}+2 b c \log (x)+\frac{c^2 x^2}{2}",1,"-a^2/(6*x^6) - (a*b)/(2*x^4) - (b^2 + 2*a*c)/(2*x^2) + (c^2*x^2)/2 + 2*b*c*Log[x]","A",3,2,18,0.1111,1,"{1114, 698}"
835,1,47,0,0.0240573,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^8} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^8,x]","-\frac{a^2}{7 x^7}-\frac{2 a c+b^2}{3 x^3}-\frac{2 a b}{5 x^5}-\frac{2 b c}{x}+c^2 x","-\frac{a^2}{7 x^7}-\frac{2 a c+b^2}{3 x^3}-\frac{2 a b}{5 x^5}-\frac{2 b c}{x}+c^2 x",1,"-a^2/(7*x^7) - (2*a*b)/(5*x^5) - (b^2 + 2*a*c)/(3*x^3) - (2*b*c)/x + c^2*x","A",2,1,18,0.05556,1,"{1108}"
836,1,48,0,0.0350476,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^9} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^9,x]","-\frac{a^2}{8 x^8}-\frac{2 a c+b^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b c}{x^2}+c^2 \log (x)","-\frac{a^2}{8 x^8}-\frac{2 a c+b^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b c}{x^2}+c^2 \log (x)",1,"-a^2/(8*x^8) - (a*b)/(3*x^6) - (b^2 + 2*a*c)/(4*x^4) - (b*c)/x^2 + c^2*Log[x]","A",3,2,18,0.1111,1,"{1114, 698}"
837,1,52,0,0.0246766,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^{10}} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^10,x]","-\frac{a^2}{9 x^9}-\frac{2 a c+b^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{2 b c}{3 x^3}-\frac{c^2}{x}","-\frac{a^2}{9 x^9}-\frac{2 a c+b^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{2 b c}{3 x^3}-\frac{c^2}{x}",1,"-a^2/(9*x^9) - (2*a*b)/(7*x^7) - (b^2 + 2*a*c)/(5*x^5) - (2*b*c)/(3*x^3) - c^2/x","A",2,1,18,0.05556,1,"{1108}"
838,1,54,0,0.0374664,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^{11}} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^11,x]","-\frac{a^2}{10 x^{10}}-\frac{2 a c+b^2}{6 x^6}-\frac{a b}{4 x^8}-\frac{b c}{2 x^4}-\frac{c^2}{2 x^2}","-\frac{a^2}{10 x^{10}}-\frac{2 a c+b^2}{6 x^6}-\frac{a b}{4 x^8}-\frac{b c}{2 x^4}-\frac{c^2}{2 x^2}",1,"-a^2/(10*x^10) - (a*b)/(4*x^8) - (b^2 + 2*a*c)/(6*x^6) - (b*c)/(2*x^4) - c^2/(2*x^2)","A",3,2,18,0.1111,1,"{1114, 698}"
839,1,54,0,0.0248372,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^{12}} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^12,x]","-\frac{a^2}{11 x^{11}}-\frac{2 a c+b^2}{7 x^7}-\frac{2 a b}{9 x^9}-\frac{2 b c}{5 x^5}-\frac{c^2}{3 x^3}","-\frac{a^2}{11 x^{11}}-\frac{2 a c+b^2}{7 x^7}-\frac{2 a b}{9 x^9}-\frac{2 b c}{5 x^5}-\frac{c^2}{3 x^3}",1,"-a^2/(11*x^11) - (2*a*b)/(9*x^9) - (b^2 + 2*a*c)/(7*x^7) - (2*b*c)/(5*x^5) - c^2/(3*x^3)","A",2,1,18,0.05556,1,"{1108}"
840,1,54,0,0.0353243,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^{13}} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^13,x]","-\frac{a^2}{12 x^{12}}-\frac{2 a c+b^2}{8 x^8}-\frac{a b}{5 x^{10}}-\frac{b c}{3 x^6}-\frac{c^2}{4 x^4}","-\frac{a^2}{12 x^{12}}-\frac{2 a c+b^2}{8 x^8}-\frac{a b}{5 x^{10}}-\frac{b c}{3 x^6}-\frac{c^2}{4 x^4}",1,"-a^2/(12*x^12) - (a*b)/(5*x^10) - (b^2 + 2*a*c)/(8*x^8) - (b*c)/(3*x^6) - c^2/(4*x^4)","A",3,2,18,0.1111,1,"{1114, 698}"
841,1,89,0,0.0594182,"\int x^2 \left(a+b x^2+c x^4\right)^3 \, dx","Int[x^2*(a + b*x^2 + c*x^4)^3,x]","\frac{3}{5} a^2 b x^5+\frac{a^3 x^3}{3}+\frac{3}{11} c x^{11} \left(a c+b^2\right)+\frac{1}{9} b x^9 \left(6 a c+b^2\right)+\frac{3}{7} a x^7 \left(a c+b^2\right)+\frac{3}{13} b c^2 x^{13}+\frac{c^3 x^{15}}{15}","\frac{3}{5} a^2 b x^5+\frac{a^3 x^3}{3}+\frac{3}{11} c x^{11} \left(a c+b^2\right)+\frac{1}{9} b x^9 \left(6 a c+b^2\right)+\frac{3}{7} a x^7 \left(a c+b^2\right)+\frac{3}{13} b c^2 x^{13}+\frac{c^3 x^{15}}{15}",1,"(a^3*x^3)/3 + (3*a^2*b*x^5)/5 + (3*a*(b^2 + a*c)*x^7)/7 + (b*(b^2 + 6*a*c)*x^9)/9 + (3*c*(b^2 + a*c)*x^11)/11 + (3*b*c^2*x^13)/13 + (c^3*x^15)/15","A",2,1,18,0.05556,1,"{1108}"
842,1,89,0,0.0830906,"\int x \left(a+b x^2+c x^4\right)^3 \, dx","Int[x*(a + b*x^2 + c*x^4)^3,x]","\frac{3}{4} a^2 b x^4+\frac{a^3 x^2}{2}+\frac{3}{10} c x^{10} \left(a c+b^2\right)+\frac{1}{8} b x^8 \left(6 a c+b^2\right)+\frac{1}{2} a x^6 \left(a c+b^2\right)+\frac{1}{4} b c^2 x^{12}+\frac{c^3 x^{14}}{14}","\frac{3}{4} a^2 b x^4+\frac{a^3 x^2}{2}+\frac{3}{10} c x^{10} \left(a c+b^2\right)+\frac{1}{8} b x^8 \left(6 a c+b^2\right)+\frac{1}{2} a x^6 \left(a c+b^2\right)+\frac{1}{4} b c^2 x^{12}+\frac{c^3 x^{14}}{14}",1,"(a^3*x^2)/2 + (3*a^2*b*x^4)/4 + (a*(b^2 + a*c)*x^6)/2 + (b*(b^2 + 6*a*c)*x^8)/8 + (3*c*(b^2 + a*c)*x^10)/10 + (b*c^2*x^12)/4 + (c^3*x^14)/14","A",3,2,16,0.1250,1,"{1107, 611}"
843,1,81,0,0.0447497,"\int \left(a+b x^2+c x^4\right)^3 \, dx","Int[(a + b*x^2 + c*x^4)^3,x]","a^2 b x^3+a^3 x+\frac{1}{3} c x^9 \left(a c+b^2\right)+\frac{1}{7} b x^7 \left(6 a c+b^2\right)+\frac{3}{5} a x^5 \left(a c+b^2\right)+\frac{3}{11} b c^2 x^{11}+\frac{c^3 x^{13}}{13}","a^2 b x^3+a^3 x+\frac{1}{3} c x^9 \left(a c+b^2\right)+\frac{1}{7} b x^7 \left(6 a c+b^2\right)+\frac{3}{5} a x^5 \left(a c+b^2\right)+\frac{3}{11} b c^2 x^{11}+\frac{c^3 x^{13}}{13}",1,"a^3*x + a^2*b*x^3 + (3*a*(b^2 + a*c)*x^5)/5 + (b*(b^2 + 6*a*c)*x^7)/7 + (c*(b^2 + a*c)*x^9)/3 + (3*b*c^2*x^11)/11 + (c^3*x^13)/13","A",2,1,14,0.07143,1,"{1090}"
844,1,85,0,0.0742707,"\int \frac{\left(a+b x^2+c x^4\right)^3}{x} \, dx","Int[(a + b*x^2 + c*x^4)^3/x,x]","\frac{3}{2} a^2 b x^2+a^3 \log (x)+\frac{3}{8} c x^8 \left(a c+b^2\right)+\frac{1}{6} b x^6 \left(6 a c+b^2\right)+\frac{3}{4} a x^4 \left(a c+b^2\right)+\frac{3}{10} b c^2 x^{10}+\frac{c^3 x^{12}}{12}","\frac{3}{2} a^2 b x^2+a^3 \log (x)+\frac{3}{8} c x^8 \left(a c+b^2\right)+\frac{1}{6} b x^6 \left(6 a c+b^2\right)+\frac{3}{4} a x^4 \left(a c+b^2\right)+\frac{3}{10} b c^2 x^{10}+\frac{c^3 x^{12}}{12}",1,"(3*a^2*b*x^2)/2 + (3*a*(b^2 + a*c)*x^4)/4 + (b*(b^2 + 6*a*c)*x^6)/6 + (3*c*(b^2 + a*c)*x^8)/8 + (3*b*c^2*x^10)/10 + (c^3*x^12)/12 + a^3*Log[x]","A",3,2,18,0.1111,1,"{1114, 698}"
845,1,80,0,0.039367,"\int \frac{\left(a+b x^2+c x^4\right)^3}{x^2} \, dx","Int[(a + b*x^2 + c*x^4)^3/x^2,x]","3 a^2 b x-\frac{a^3}{x}+\frac{3}{7} c x^7 \left(a c+b^2\right)+\frac{1}{5} b x^5 \left(6 a c+b^2\right)+a x^3 \left(a c+b^2\right)+\frac{1}{3} b c^2 x^9+\frac{c^3 x^{11}}{11}","3 a^2 b x-\frac{a^3}{x}+\frac{3}{7} c x^7 \left(a c+b^2\right)+\frac{1}{5} b x^5 \left(6 a c+b^2\right)+a x^3 \left(a c+b^2\right)+\frac{1}{3} b c^2 x^9+\frac{c^3 x^{11}}{11}",1,"-(a^3/x) + 3*a^2*b*x + a*(b^2 + a*c)*x^3 + (b*(b^2 + 6*a*c)*x^5)/5 + (3*c*(b^2 + a*c)*x^7)/7 + (b*c^2*x^9)/3 + (c^3*x^11)/11","A",2,1,18,0.05556,1,"{1108}"
846,1,86,0,0.0778557,"\int \frac{\left(a+b x^2+c x^4\right)^3}{x^3} \, dx","Int[(a + b*x^2 + c*x^4)^3/x^3,x]","3 a^2 b \log (x)-\frac{a^3}{2 x^2}+\frac{1}{2} c x^6 \left(a c+b^2\right)+\frac{1}{4} b x^4 \left(6 a c+b^2\right)+\frac{3}{2} a x^2 \left(a c+b^2\right)+\frac{3}{8} b c^2 x^8+\frac{c^3 x^{10}}{10}","3 a^2 b \log (x)-\frac{a^3}{2 x^2}+\frac{1}{2} c x^6 \left(a c+b^2\right)+\frac{1}{4} b x^4 \left(6 a c+b^2\right)+\frac{3}{2} a x^2 \left(a c+b^2\right)+\frac{3}{8} b c^2 x^8+\frac{c^3 x^{10}}{10}",1,"-a^3/(2*x^2) + (3*a*(b^2 + a*c)*x^2)/2 + (b*(b^2 + 6*a*c)*x^4)/4 + (c*(b^2 + a*c)*x^6)/2 + (3*b*c^2*x^8)/8 + (c^3*x^10)/10 + 3*a^2*b*Log[x]","A",3,2,18,0.1111,1,"{1114, 698}"
847,1,83,0,0.0406804,"\int \frac{\left(a+b x^2+c x^4\right)^3}{x^4} \, dx","Int[(a + b*x^2 + c*x^4)^3/x^4,x]","-\frac{3 a^2 b}{x}-\frac{a^3}{3 x^3}+\frac{3}{5} c x^5 \left(a c+b^2\right)+\frac{1}{3} b x^3 \left(6 a c+b^2\right)+3 a x \left(a c+b^2\right)+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9}","-\frac{3 a^2 b}{x}-\frac{a^3}{3 x^3}+\frac{3}{5} c x^5 \left(a c+b^2\right)+\frac{1}{3} b x^3 \left(6 a c+b^2\right)+3 a x \left(a c+b^2\right)+\frac{3}{7} b c^2 x^7+\frac{c^3 x^9}{9}",1,"-a^3/(3*x^3) - (3*a^2*b)/x + 3*a*(b^2 + a*c)*x + (b*(b^2 + 6*a*c)*x^3)/3 + (3*c*(b^2 + a*c)*x^5)/5 + (3*b*c^2*x^7)/7 + (c^3*x^9)/9","A",2,1,18,0.05556,1,"{1108}"
848,1,100,0,0.117027,"\int \frac{x^7}{a+b x^2+c x^4} \, dx","Int[x^7/(a + b*x^2 + c*x^4),x]","\frac{\left(b^2-a c\right) \log \left(a+b x^2+c x^4\right)}{4 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c}}-\frac{b x^2}{2 c^2}+\frac{x^4}{4 c}","\frac{\left(b^2-a c\right) \log \left(a+b x^2+c x^4\right)}{4 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c}}-\frac{b x^2}{2 c^2}+\frac{x^4}{4 c}",1,"-(b*x^2)/(2*c^2) + x^4/(4*c) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*Sqrt[b^2 - 4*a*c]) + ((b^2 - a*c)*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",7,6,18,0.3333,1,"{1114, 701, 634, 618, 206, 628}"
849,1,81,0,0.0799677,"\int \frac{x^5}{a+b x^2+c x^4} \, dx","Int[x^5/(a + b*x^2 + c*x^4),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{x^2}{2 c}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{x^2}{2 c}",1,"x^2/(2*c) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) - (b*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",6,6,18,0.3333,1,"{1114, 703, 634, 618, 206, 628}"
850,1,63,0,0.0549137,"\int \frac{x^3}{a+b x^2+c x^4} \, dx","Int[x^3/(a + b*x^2 + c*x^4),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c}",1,"(b*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + Log[a + b*x^2 + c*x^4]/(4*c)","A",5,5,18,0.2778,1,"{1114, 634, 618, 206, 628}"
851,1,36,0,0.033514,"\int \frac{x}{a+b x^2+c x^4} \, dx","Int[x/(a + b*x^2 + c*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"-(ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]]/Sqrt[b^2 - 4*a*c])","A",3,3,16,0.1875,1,"{1107, 618, 206}"
852,1,69,0,0.0699097,"\int \frac{1}{x \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x*(a + b*x^2 + c*x^4)),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]) + Log[x]/a - Log[a + b*x^2 + c*x^4]/(4*a)","A",7,7,18,0.3889,1,"{1114, 705, 29, 634, 618, 206, 628}"
853,1,89,0,0.1306867,"\int \frac{1}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]) - (b*Log[x])/a^2 + (b*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",8,7,18,0.3889,1,"{1114, 709, 800, 634, 618, 206, 628}"
854,1,114,0,0.1962357,"\int \frac{1}{x^5 \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^5*(a + b*x^2 + c*x^4)),x]","-\frac{\left(b^2-a c\right) \log \left(a+b x^2+c x^4\right)}{4 a^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \sqrt{b^2-4 a c}}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b}{2 a^2 x^2}-\frac{1}{4 a x^4}","-\frac{\left(b^2-a c\right) \log \left(a+b x^2+c x^4\right)}{4 a^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \sqrt{b^2-4 a c}}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b}{2 a^2 x^2}-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) + b/(2*a^2*x^2) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*Sqrt[b^2 - 4*a*c]) + ((b^2 - a*c)*Log[x])/a^3 - ((b^2 - a*c)*Log[a + b*x^2 + c*x^4])/(4*a^3)","A",8,7,18,0.3889,1,"{1114, 709, 800, 634, 618, 206, 628}"
855,1,203,0,0.6701223,"\int \frac{x^6}{a+b x^2+c x^4} \, dx","Int[x^6/(a + b*x^2 + c*x^4),x]","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{b x}{c^2}+\frac{x^3}{3 c}","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{b x}{c^2}+\frac{x^3}{3 c}",1,"-((b*x)/c^2) + x^3/(3*c) + ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1122, 1279, 1166, 205}"
856,1,179,0,0.2687754,"\int \frac{x^4}{a+b x^2+c x^4} \, dx","Int[x^4/(a + b*x^2 + c*x^4),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}",1,"x/c - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,18,0.1667,1,"{1122, 1166, 205}"
857,1,150,0,0.1094898,"\int \frac{x^2}{a+b x^2+c x^4} \, dx","Int[x^2/(a + b*x^2 + c*x^4),x]","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}",1,"-((Sqrt[b - Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])) + (Sqrt[b + Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",3,2,18,0.1111,1,"{1130, 205}"
858,1,150,0,0.0862244,"\int \frac{1}{a+b x^2+c x^4} \, dx","Int[(a + b*x^2 + c*x^4)^(-1),x]","\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[2]*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",3,2,14,0.1429,1,"{1093, 205}"
859,1,174,0,0.2217747,"\int \frac{1}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}",1,"-(1/(a*x)) - (Sqrt[c]*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,18,0.1667,1,"{1123, 1166, 205}"
860,1,196,0,0.4228243,"\int \frac{1}{x^4 \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^4*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b}{a^2 x}-\frac{1}{3 a x^3}","\frac{\sqrt{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b}{a^2 x}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + b/(a^2*x) + (Sqrt[c]*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1123, 1281, 1166, 205}"
861,1,132,0,0.1681108,"\int \frac{x^7}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^7/(a + b*x^2 + c*x^4)^2,x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^4 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^2}{2 c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c^2}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^4 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^2}{2 c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c^2}",1,"-(b*x^2)/(2*c*(b^2 - 4*a*c)) + (x^4*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*(b^2 - 4*a*c)^(3/2)) + Log[a + b*x^2 + c*x^4]/(4*c^2)","A",7,7,18,0.3889,1,"{1114, 738, 773, 634, 618, 206, 628}"
862,1,78,0,0.0656601,"\int \frac{x^5}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^5/(a + b*x^2 + c*x^4)^2,x]","\frac{x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 a \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 a \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(x^2*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (2*a*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,18,0.2222,1,"{1114, 722, 618, 206}"
863,1,75,0,0.0612293,"\int \frac{x^3}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^3/(a + b*x^2 + c*x^4)^2,x]","\frac{2 a+b x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{2 a+b x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(2*a + b*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (b*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,18,0.2222,1,"{1114, 638, 618, 206}"
864,1,74,0,0.0579318,"\int \frac{x}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x/(a + b*x^2 + c*x^4)^2,x]","\frac{2 c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{2 c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x^2}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(b + 2*c*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (2*c*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,16,0.2500,1,"{1107, 614, 618, 206}"
865,1,122,0,0.197928,"\int \frac{1}{x \left(a+b x^2+c x^4\right)^2} \, dx","Int[1/(x*(a + b*x^2 + c*x^4)^2),x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x^2}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x^2}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)) + Log[x]/a^2 - Log[a + b*x^2 + c*x^4]/(4*a^2)","A",8,7,18,0.3889,1,"{1114, 740, 800, 634, 618, 206, 628}"
866,1,162,0,0.2505504,"\int \frac{1}{x^3 \left(a+b x^2+c x^4\right)^2} \, dx","Int[1/(x^3*(a + b*x^2 + c*x^4)^2),x]","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 x^2 \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x^2+c x^4\right)}{2 a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x^2}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 x^2 \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x^2+c x^4\right)}{2 a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x^2}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-((b^2 - 3*a*c)/(a^2*(b^2 - 4*a*c)*x^2)) + (b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*x^2*(a + b*x^2 + c*x^4)) - ((b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(3/2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x^2 + c*x^4])/(2*a^3)","A",8,7,18,0.3889,1,"{1114, 740, 800, 634, 618, 206, 628}"
867,1,331,0,0.8441443,"\int \frac{x^8}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^8/(a + b*x^2 + c*x^4)^2,x]","-\frac{\left(-\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(3 b^2-10 a c\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{x^5 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^3}{2 c \left(b^2-4 a c\right)}","-\frac{\left(-\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 c^2-19 a b^2 c+3 b^4}{\sqrt{b^2-4 a c}}-13 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(3 b^2-10 a c\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{x^5 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^3}{2 c \left(b^2-4 a c\right)}",1,"((3*b^2 - 10*a*c)*x)/(2*c^2*(b^2 - 4*a*c)) - (b*x^3)/(2*c*(b^2 - 4*a*c)) + (x^5*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((3*b^3 - 13*a*b*c - (3*b^4 - 19*a*b^2*c + 20*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^3 - 13*a*b*c + (3*b^4 - 19*a*b^2*c + 20*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,18,0.2222,1,"{1120, 1279, 1166, 205}"
868,1,271,0,0.5719019,"\int \frac{x^6}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^6/(a + b*x^2 + c*x^4)^2,x]","\frac{\left(-\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^3 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x}{2 c \left(b^2-4 a c\right)}","\frac{\left(-\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b \left(b^2-8 a c\right)}{\sqrt{b^2-4 a c}}-6 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^3 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x}{2 c \left(b^2-4 a c\right)}",1,"-(b*x)/(2*c*(b^2 - 4*a*c)) + (x^3*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b^2 - 6*a*c - (b*(b^2 - 8*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2 - 6*a*c + (b*(b^2 - 8*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1120, 1279, 1166, 205}"
869,1,237,0,0.4109976,"\int \frac{x^4}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^4/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b - (b^2 + 4*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2 + 4*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,18,0.1667,1,"{1120, 1166, 205}"
870,1,221,0,0.2595115,"\int \frac{x^2}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^2/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{x \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(x*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(2*b - Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(2*b + Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,18,0.1667,1,"{1119, 1166, 205}"
871,1,252,0,0.5130733,"\int \frac{1}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)^(-2),x]","\frac{x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(b^2 - 12*a*c - b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,14,0.2143,1,"{1092, 1166, 205}"
872,1,308,0,1.4427557,"\int \frac{1}{x^2 \left(a+b x^2+c x^4\right)^2} \, dx","Int[1/(x^2*(a + b*x^2 + c*x^4)^2),x]","-\frac{3 b^2-10 a c}{2 a^2 x \left(b^2-4 a c\right)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c x^2}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{3 b^2-10 a c}{2 a^2 x \left(b^2-4 a c\right)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c x^2}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(3*b^2 - 10*a*c)/(2*a^2*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*x*(a + b*x^2 + c*x^4)) - (Sqrt[c]*(3*b^3 - 16*a*b*c + (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(3*b^3 - 16*a*b*c - (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1121, 1281, 1166, 205}"
873,1,209,0,0.40082,"\int \frac{x^{11}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^11/(a + b*x^2 + c*x^4)^3,x]","\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{b x^2 \left(b^2-7 a c\right)}{2 c^2 \left(b^2-4 a c\right)^2}+\frac{x^8 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^4 \left(b x^2 \left(b^2-10 a c\right)+a \left(b^2-16 a c\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c^3}","\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{b x^2 \left(b^2-7 a c\right)}{2 c^2 \left(b^2-4 a c\right)^2}+\frac{x^8 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^4 \left(b x^2 \left(b^2-10 a c\right)+a \left(b^2-16 a c\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\log \left(a+b x^2+c x^4\right)}{4 c^3}",1,"-(b*(b^2 - 7*a*c)*x^2)/(2*c^2*(b^2 - 4*a*c)^2) + (x^8*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x^4*(a*(b^2 - 16*a*c) + b*(b^2 - 10*a*c)*x^2))/(4*c*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (b*(b^4 - 10*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*(b^2 - 4*a*c)^(5/2)) + Log[a + b*x^2 + c*x^4]/(4*c^3)","A",8,8,18,0.4444,1,"{1114, 738, 818, 773, 634, 618, 206, 628}"
874,1,121,0,0.1119312,"\int \frac{x^9}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^9/(a + b*x^2 + c*x^4)^3,x]","-\frac{6 a^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{x^6 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 a x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}","-\frac{6 a^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{x^6 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 a x^2 \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}",1,"(x^6*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (3*a*x^2*(2*a + b*x^2))/(2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - (6*a^2*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,4,18,0.2222,1,"{1114, 722, 618, 206}"
875,1,119,0,0.1037845,"\int \frac{x^7}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^7/(a + b*x^2 + c*x^4)^3,x]","-\frac{x^6 \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 b x^2 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 a b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","-\frac{x^6 \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 b x^2 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 a b \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(x^6*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*b*x^2*(2*a + b*x^2))/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*a*b*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,18,0.2778,1,"{1114, 728, 722, 618, 206}"
876,1,130,0,0.1294465,"\int \frac{x^5}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^5/(a + b*x^2 + c*x^4)^3,x]","\frac{x^2 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^2 \left(2 a c+b^2\right)+3 a b}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{\left(2 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{x^2 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^2 \left(2 a c+b^2\right)+3 a b}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{\left(2 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"(x^2*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*a*b + (b^2 + 2*a*c)*x^2)/(2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - ((b^2 + 2*a*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,18,0.2778,1,"{1114, 738, 638, 618, 206}"
877,1,113,0,0.0903027,"\int \frac{x^3}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^3/(a + b*x^2 + c*x^4)^3,x]","\frac{2 a+b x^2}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 b \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 b c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{2 a+b x^2}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 b \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 b c \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"(2*a + b*x^2)/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (3*b*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*b*c*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,18,0.2778,1,"{1114, 638, 614, 618, 206}"
878,1,113,0,0.0875405,"\int \frac{x}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x/(a + b*x^2 + c*x^4)^3,x]","-\frac{6 c^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{3 c \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{b+2 c x^2}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","-\frac{6 c^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{3 c \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{b+2 c x^2}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"-(b + 2*c*x^2)/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*c*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - (6*c^2*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,4,16,0.2500,1,"{1107, 614, 618, 206}"
879,1,200,0,0.2984898,"\int \frac{1}{x \left(a+b x^2+c x^4\right)^3} \, dx","Int[1/(x*(a + b*x^2 + c*x^4)^3),x]","\frac{16 a^2 c^2+2 b c x^2 \left(b^2-7 a c\right)-15 a b^2 c+2 b^4}{4 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a^3}+\frac{\log (x)}{a^3}+\frac{-2 a c+b^2+b c x^2}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{16 a^2 c^2+2 b c x^2 \left(b^2-7 a c\right)-15 a b^2 c+2 b^4}{4 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b x^2+c x^4\right)}{4 a^3}+\frac{\log (x)}{a^3}+\frac{-2 a c+b^2+b c x^2}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(b^2 - 2*a*c + b*c*x^2)/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (2*b^4 - 15*a*b^2*c + 16*a^2*c^2 + 2*b*c*(b^2 - 7*a*c)*x^2)/(4*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (b*(b^4 - 10*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*(b^2 - 4*a*c)^(5/2)) + Log[x]/a^3 - Log[a + b*x^2 + c*x^4]/(4*a^3)","A",9,8,18,0.4444,1,"{1114, 740, 822, 800, 634, 618, 206, 628}"
880,1,255,0,0.3913439,"\int \frac{1}{x^3 \left(a+b x^2+c x^4\right)^3} \, dx","Int[1/(x^3*(a + b*x^2 + c*x^4)^3),x]","\frac{20 a^2 c^2+3 b c x^2 \left(b^2-6 a c\right)-20 a b^2 c+3 b^4}{4 a^2 x^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{2 a^3 x^2 \left(b^2-4 a c\right)^2}+\frac{3 b \log \left(a+b x^2+c x^4\right)}{4 a^4}-\frac{3 b \log (x)}{a^4}+\frac{-2 a c+b^2+b c x^2}{4 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{20 a^2 c^2+3 b c x^2 \left(b^2-6 a c\right)-20 a b^2 c+3 b^4}{4 a^2 x^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{2 a^3 x^2 \left(b^2-4 a c\right)^2}+\frac{3 b \log \left(a+b x^2+c x^4\right)}{4 a^4}-\frac{3 b \log (x)}{a^4}+\frac{-2 a c+b^2+b c x^2}{4 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(-3*(b^2 - 5*a*c)*(b^2 - 2*a*c))/(2*a^3*(b^2 - 4*a*c)^2*x^2) + (b^2 - 2*a*c + b*c*x^2)/(4*a*(b^2 - 4*a*c)*x^2*(a + b*x^2 + c*x^4)^2) + (3*b^4 - 20*a*b^2*c + 20*a^2*c^2 + 3*b*c*(b^2 - 6*a*c)*x^2)/(4*a^2*(b^2 - 4*a*c)^2*x^2*(a + b*x^2 + c*x^4)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^4*(b^2 - 4*a*c)^(5/2)) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x^2 + c*x^4])/(4*a^4)","A",9,8,18,0.4444,1,"{1114, 740, 822, 800, 634, 618, 206, 628}"
881,1,400,0,1.7272255,"\int \frac{x^{10}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^10/(a + b*x^2 + c*x^4)^3,x]","\frac{3 \left(-\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 b x \left(b^2-8 a c\right)}{8 c^2 \left(b^2-4 a c\right)^2}+\frac{x^7 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^5 \left(12 a b-x^2 \left(b^2-28 a c\right)\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^3 \left(b^2-28 a c\right)}{8 c \left(b^2-4 a c\right)^2}","\frac{3 \left(-\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{44 a^2 b c^2-11 a b^3 c+b^5}{\sqrt{b^2-4 a c}}+28 a^2 c^2-9 a b^2 c+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 b x \left(b^2-8 a c\right)}{8 c^2 \left(b^2-4 a c\right)^2}+\frac{x^7 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^5 \left(12 a b-x^2 \left(b^2-28 a c\right)\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^3 \left(b^2-28 a c\right)}{8 c \left(b^2-4 a c\right)^2}",1,"(-3*b*(b^2 - 8*a*c)*x)/(8*c^2*(b^2 - 4*a*c)^2) + ((b^2 - 28*a*c)*x^3)/(8*c*(b^2 - 4*a*c)^2) + (x^7*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x^5*(12*a*b - (b^2 - 28*a*c)*x^2))/(8*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*(b^4 - 9*a*b^2*c + 28*a^2*c^2 - (b^5 - 11*a*b^3*c + 44*a^2*b*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*(b^4 - 9*a*b^2*c + 28*a^2*c^2 + (b^5 - 11*a*b^3*c + 44*a^2*b*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,5,18,0.2778,1,"{1120, 1275, 1279, 1166, 205}"
882,1,348,0,0.8858948,"\int \frac{x^8}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^8/(a + b*x^2 + c*x^4)^3,x]","\frac{\left(-\frac{-40 a^2 c^2-18 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-16 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 c^2-18 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-16 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^5 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^3 \left(x^2 \left(20 a c+b^2\right)+12 a b\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x \left(20 a c+b^2\right)}{8 c \left(b^2-4 a c\right)^2}","\frac{\left(-\frac{-40 a^2 c^2-18 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-16 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 c^2-18 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-16 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^5 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^3 \left(x^2 \left(20 a c+b^2\right)+12 a b\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x \left(20 a c+b^2\right)}{8 c \left(b^2-4 a c\right)^2}",1,"-((b^2 + 20*a*c)*x)/(8*c*(b^2 - 4*a*c)^2) + (x^5*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x^3*(12*a*b + (b^2 + 20*a*c)*x^2))/(8*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((b^3 - 16*a*b*c - (b^4 - 18*a*b^2*c - 40*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^3 - 16*a*b*c + (b^4 - 18*a*b^2*c - 40*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,18,0.2778,1,"{1120, 1275, 1279, 1166, 205}"
883,1,298,0,0.6829667,"\int \frac{x^6}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^6/(a + b*x^2 + c*x^4)^3,x]","\frac{x^3 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x \left(x^2 \left(4 a c+b^2\right)+4 a b\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 \left(-\frac{b \left(12 a c+b^2\right)}{\sqrt{b^2-4 a c}}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{b \left(12 a c+b^2\right)}{\sqrt{b^2-4 a c}}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x^3 \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x \left(x^2 \left(4 a c+b^2\right)+4 a b\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 \left(-\frac{b \left(12 a c+b^2\right)}{\sqrt{b^2-4 a c}}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{b \left(12 a c+b^2\right)}{\sqrt{b^2-4 a c}}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x^3*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*x*(4*a*b + (b^2 + 4*a*c)*x^2))/(8*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*(b^2 + 4*a*c - (b*(b^2 + 12*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*(b^2 + 4*a*c + (b*(b^2 + 12*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1120, 1275, 1166, 205}"
884,1,289,0,0.7054258,"\int \frac{x^4}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^4/(a + b*x^2 + c*x^4)^3,x]","\frac{x \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x \left(-4 a c+7 b^2+12 b c x^2\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 \sqrt{c} \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x \left(-4 a c+7 b^2+12 b c x^2\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 \sqrt{c} \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (x*(7*b^2 - 4*a*c + 12*b*c*x^2))/(8*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*Sqrt[c]*(3*b^2 + 4*a*c - 2*b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (3*Sqrt[c]*(3*b^2 + 4*a*c + 2*b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1120, 1178, 1166, 205}"
885,1,311,0,0.700862,"\int \frac{x^2}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^2/(a + b*x^2 + c*x^4)^3,x]","-\frac{x \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x \left(c x^2 \left(20 a c+b^2\right)+b \left(8 a c+b^2\right)\right)}{8 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{x \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x \left(c x^2 \left(20 a c+b^2\right)+b \left(8 a c+b^2\right)\right)}{8 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(x*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x*(b*(b^2 + 8*a*c) + c*(b^2 + 20*a*c)*x^2))/(8*a*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b^2 + 20*a*c + (b*(b^2 - 52*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(b^2 + 20*a*c - (b*(b^2 - 52*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1119, 1178, 1166, 205}"
886,1,355,0,1.8383218,"\int \frac{1}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(a + b*x^2 + c*x^4)^(-3),x]","\frac{3 \sqrt{c} \left(56 a^2 c^2-10 a b^2 c+b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \sqrt{c} \left(-\frac{56 a^2 c^2-10 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-8 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(3 b c x^2 \left(b^2-8 a c\right)+\left(b^2-7 a c\right) \left(3 b^2-4 a c\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{3 \sqrt{c} \left(56 a^2 c^2-10 a b^2 c+b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \sqrt{c} \left(-\frac{56 a^2 c^2-10 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-8 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(3 b c x^2 \left(b^2-8 a c\right)+\left(b^2-7 a c\right) \left(3 b^2-4 a c\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(x*(b^2 - 2*a*c + b*c*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x*((b^2 - 7*a*c)*(3*b^2 - 4*a*c) + 3*b*c*(b^2 - 8*a*c)*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*Sqrt[c]*(b^4 - 10*a*b^2*c + 56*a^2*c^2 + b*(b^2 - 8*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*Sqrt[c]*(b^3 - 8*a*b*c - (b^4 - 10*a*b^2*c + 56*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,14,0.2857,1,"{1092, 1178, 1166, 205}"
887,1,425,0,0.9629724,"\int \frac{1}{x^2 \left(a+b x^2+c x^4\right)^3} \, dx","Int[1/(x^2*(a + b*x^2 + c*x^4)^3),x]","\frac{36 a^2 c^2+b c x^2 \left(5 b^2-32 a c\right)-35 a b^2 c+5 b^4}{8 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \sqrt{c} \left(\frac{b \left(124 a^2 c^2-47 a b^2 c+5 b^4\right)}{\sqrt{b^2-4 a c}}+\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^3 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)-\frac{124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^3 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{8 a^3 x \left(b^2-4 a c\right)^2}+\frac{-2 a c+b^2+b c x^2}{4 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{36 a^2 c^2+b c x^2 \left(5 b^2-32 a c\right)-35 a b^2 c+5 b^4}{8 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \sqrt{c} \left(\frac{b \left(124 a^2 c^2-47 a b^2 c+5 b^4\right)}{\sqrt{b^2-4 a c}}+\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^3 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)-\frac{124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^3 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{8 a^3 x \left(b^2-4 a c\right)^2}+\frac{-2 a c+b^2+b c x^2}{4 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(-3*(5*b^2 - 12*a*c)*(b^2 - 5*a*c))/(8*a^3*(b^2 - 4*a*c)^2*x) + (b^2 - 2*a*c + b*c*x^2)/(4*a*(b^2 - 4*a*c)*x*(a + b*x^2 + c*x^4)^2) + (5*b^4 - 35*a*b^2*c + 36*a^2*c^2 + b*c*(5*b^2 - 32*a*c)*x^2)/(8*a^2*(b^2 - 4*a*c)^2*x*(a + b*x^2 + c*x^4)) - (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) + (b*(5*b^4 - 47*a*b^2*c + 124*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) - (5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,18,0.2778,1,"{1121, 1277, 1281, 1166, 205}"
888,1,82,0,0.091598,"\int \frac{x^5}{a-b x^2+c x^4} \, dx","Int[x^5/(a - b*x^2 + c*x^4),x]","\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a-b x^2+c x^4\right)}{4 c^2}+\frac{x^2}{2 c}","\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a-b x^2+c x^4\right)}{4 c^2}+\frac{x^2}{2 c}",1,"x^2/(2*c) + ((b^2 - 2*a*c)*ArcTanh[(b - 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) + (b*Log[a - b*x^2 + c*x^4])/(4*c^2)","A",6,6,19,0.3158,1,"{1114, 703, 634, 618, 206, 628}"
889,1,64,0,0.0621696,"\int \frac{x^3}{a-b x^2+c x^4} \, dx","Int[x^3/(a - b*x^2 + c*x^4),x]","\frac{b \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{\log \left(a-b x^2+c x^4\right)}{4 c}","\frac{b \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{\log \left(a-b x^2+c x^4\right)}{4 c}",1,"(b*ArcTanh[(b - 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + Log[a - b*x^2 + c*x^4]/(4*c)","A",5,5,19,0.2632,1,"{1114, 634, 618, 206, 628}"
890,1,35,0,0.0430031,"\int \frac{x}{a-b x^2+c x^4} \, dx","Int[x/(a - b*x^2 + c*x^4),x]","\frac{\tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{\tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"ArcTanh[(b - 2*c*x^2)/Sqrt[b^2 - 4*a*c]]/Sqrt[b^2 - 4*a*c]","A",3,3,17,0.1765,1,"{1107, 618, 206}"
891,1,70,0,0.0837868,"\int \frac{1}{x \left(a-b x^2+c x^4\right)} \, dx","Int[1/(x*(a - b*x^2 + c*x^4)),x]","\frac{b \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{\log \left(a-b x^2+c x^4\right)}{4 a}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{\log \left(a-b x^2+c x^4\right)}{4 a}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b - 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]) + Log[x]/a - Log[a - b*x^2 + c*x^4]/(4*a)","A",7,7,19,0.3684,1,"{1114, 705, 29, 634, 618, 206, 628}"
892,1,89,0,0.139838,"\int \frac{1}{x^3 \left(a-b x^2+c x^4\right)} \, dx","Int[1/(x^3*(a - b*x^2 + c*x^4)),x]","\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a-b x^2+c x^4\right)}{4 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}","\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b-2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a-b x^2+c x^4\right)}{4 a^2}+\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + ((b^2 - 2*a*c)*ArcTanh[(b - 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]) + (b*Log[x])/a^2 - (b*Log[a - b*x^2 + c*x^4])/(4*a^2)","A",8,7,19,0.3684,1,"{1114, 709, 800, 634, 618, 206, 628}"
893,1,179,0,0.3645239,"\int \frac{x^4}{a-b x^2+c x^4} \, dx","Int[x^4/(a - b*x^2 + c*x^4),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}",1,"x/c - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,19,0.1579,1,"{1122, 1166, 208}"
894,1,150,0,0.1087311,"\int \frac{x^2}{a-b x^2+c x^4} \, dx","Int[x^2/(a - b*x^2 + c*x^4),x]","\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}","\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}",1,"(Sqrt[b - Sqrt[b^2 - 4*a*c]]*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]) - (Sqrt[b + Sqrt[b^2 - 4*a*c]]*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",3,2,19,0.1053,1,"{1130, 208}"
895,1,150,0,0.0724572,"\int \frac{1}{a-b x^2+c x^4} \, dx","Int[(a - b*x^2 + c*x^4)^(-1),x]","\frac{\sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",3,2,15,0.1333,1,"{1093, 208}"
896,1,172,0,0.2033555,"\int \frac{1}{x^2 \left(a-b x^2+c x^4\right)} \, dx","Int[1/(x^2*(a - b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}","\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}",1,"-(1/(a*x)) + (Sqrt[c]*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,19,0.1579,1,"{1123, 1166, 208}"
897,1,69,0,0.0840896,"\int \frac{x^5}{a-b+2 a x^2+a x^4} \, dx","Int[x^5/(a - b + 2*a*x^2 + a*x^4),x]","-\frac{(a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 a^{3/2} \sqrt{b}}-\frac{\log \left(a x^4+2 a x^2+a-b\right)}{2 a}+\frac{x^2}{2 a}","-\frac{(a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 a^{3/2} \sqrt{b}}-\frac{\log \left(a x^4+2 a x^2+a-b\right)}{2 a}+\frac{x^2}{2 a}",1,"x^2/(2*a) - ((a + b)*ArcTanh[(Sqrt[a]*(1 + x^2))/Sqrt[b]])/(2*a^(3/2)*Sqrt[b]) - Log[a - b + 2*a*x^2 + a*x^4]/(2*a)","A",6,6,22,0.2727,1,"{1114, 703, 634, 618, 206, 628}"
898,1,56,0,0.0489732,"\int \frac{x^3}{a-b+2 a x^2+a x^4} \, dx","Int[x^3/(a - b + 2*a*x^2 + a*x^4),x]","\frac{\log \left(a x^4+2 a x^2+a-b\right)}{4 a}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}","\frac{\log \left(a x^4+2 a x^2+a-b\right)}{4 a}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"ArcTanh[(Sqrt[a]*(1 + x^2))/Sqrt[b]]/(2*Sqrt[a]*Sqrt[b]) + Log[a - b + 2*a*x^2 + a*x^4]/(4*a)","A",5,5,22,0.2273,1,"{1114, 634, 618, 206, 628}"
899,1,31,0,0.028482,"\int \frac{x}{a-b+2 a x^2+a x^4} \, dx","Int[x/(a - b + 2*a*x^2 + a*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"-ArcTanh[(Sqrt[a]*(1 + x^2))/Sqrt[b]]/(2*Sqrt[a]*Sqrt[b])","A",3,3,20,0.1500,1,"{1107, 618, 206}"
900,1,77,0,0.0717382,"\int \frac{1}{x \left(a-b+2 a x^2+a x^4\right)} \, dx","Int[1/(x*(a - b + 2*a*x^2 + a*x^4)),x]","-\frac{\log \left(a x^4+2 a x^2+a-b\right)}{4 (a-b)}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a-b)}+\frac{\log (x)}{a-b}","-\frac{\log \left(a x^4+2 a x^2+a-b\right)}{4 (a-b)}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a-b)}+\frac{\log (x)}{a-b}",1,"(Sqrt[a]*ArcTanh[(Sqrt[a]*(1 + x^2))/Sqrt[b]])/(2*(a - b)*Sqrt[b]) + Log[x]/(a - b) - Log[a - b + 2*a*x^2 + a*x^4]/(4*(a - b))","A",7,7,22,0.3182,1,"{1114, 705, 29, 634, 618, 206, 628}"
901,1,97,0,0.1407643,"\int \frac{1}{x^3 \left(a-b+2 a x^2+a x^4\right)} \, dx","Int[1/(x^3*(a - b + 2*a*x^2 + a*x^4)),x]","-\frac{1}{2 x^2 (a-b)}+\frac{a \log \left(a x^4+2 a x^2+a-b\right)}{2 (a-b)^2}-\frac{\sqrt{a} (a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a-b)^2}-\frac{2 a \log (x)}{(a-b)^2}","-\frac{1}{2 x^2 (a-b)}+\frac{a \log \left(a x^4+2 a x^2+a-b\right)}{2 (a-b)^2}-\frac{\sqrt{a} (a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a-b)^2}-\frac{2 a \log (x)}{(a-b)^2}",1,"-1/(2*(a - b)*x^2) - (Sqrt[a]*(a + b)*ArcTanh[(Sqrt[a]*(1 + x^2))/Sqrt[b]])/(2*(a - b)^2*Sqrt[b]) - (2*a*Log[x])/(a - b)^2 + (a*Log[a - b + 2*a*x^2 + a*x^4])/(2*(a - b)^2)","A",8,7,22,0.3182,1,"{1114, 709, 800, 634, 618, 206, 628}"
902,1,114,0,0.165205,"\int \frac{x^4}{a-b+2 a x^2+a x^4} \, dx","Int[x^4/(a - b + 2*a*x^2 + a*x^4),x]","\frac{\left(\sqrt{a}-\sqrt{b}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{5/4} \sqrt{b}}-\frac{\left(\sqrt{a}+\sqrt{b}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{5/4} \sqrt{b}}+\frac{x}{a}","\frac{\left(\sqrt{a}-\sqrt{b}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{5/4} \sqrt{b}}-\frac{\left(\sqrt{a}+\sqrt{b}\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{5/4} \sqrt{b}}+\frac{x}{a}",1,"x/a + ((Sqrt[a] - Sqrt[b])^(3/2)*ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*a^(5/4)*Sqrt[b]) - ((Sqrt[a] + Sqrt[b])^(3/2)*ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*a^(5/4)*Sqrt[b])","A",4,3,22,0.1364,1,"{1122, 1166, 205}"
903,1,109,0,0.0537356,"\int \frac{x^2}{a-b+2 a x^2+a x^4} \, dx","Int[x^2/(a - b + 2*a*x^2 + a*x^4),x]","\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{b}}-\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{b}}","\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{b}}-\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{b}}",1,"-(Sqrt[Sqrt[a] - Sqrt[b]]*ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*a^(3/4)*Sqrt[b]) + (Sqrt[Sqrt[a] + Sqrt[b]]*ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*a^(3/4)*Sqrt[b])","A",3,2,22,0.09091,1,"{1130, 205}"
904,1,109,0,0.0467918,"\int \frac{1}{a-b+2 a x^2+a x^4} \, dx","Int[(a - b + 2*a*x^2 + a*x^4)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 \sqrt[4]{a} \sqrt{b} \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 \sqrt[4]{a} \sqrt{b} \sqrt{\sqrt{a}+\sqrt{b}}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 \sqrt[4]{a} \sqrt{b} \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 \sqrt[4]{a} \sqrt{b} \sqrt{\sqrt{a}+\sqrt{b}}}",1,"ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] - Sqrt[b]]]/(2*a^(1/4)*Sqrt[Sqrt[a] - Sqrt[b]]*Sqrt[b]) - ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[b]]]/(2*a^(1/4)*Sqrt[Sqrt[a] + Sqrt[b]]*Sqrt[b])","A",3,2,18,0.1111,1,"{1093, 205}"
905,1,121,0,0.1128508,"\int \frac{1}{x^2 \left(a-b+2 a x^2+a x^4\right)} \, dx","Int[1/(x^2*(a - b + 2*a*x^2 + a*x^4)),x]","-\frac{1}{x (a-b)}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 \sqrt{b} \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 \sqrt{b} \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}","-\frac{1}{x (a-b)}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 \sqrt{b} \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} x}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 \sqrt{b} \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}",1,"-(1/((a - b)*x)) - (a^(1/4)*ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*(Sqrt[a] - Sqrt[b])^(3/2)*Sqrt[b]) + (a^(1/4)*ArcTan[(a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*(Sqrt[a] + Sqrt[b])^(3/2)*Sqrt[b])","A",4,3,22,0.1364,1,"{1123, 1166, 205}"
906,1,69,0,0.0757646,"\int \frac{x^5}{a+b+2 a x^2+a x^4} \, dx","Int[x^5/(a + b + 2*a*x^2 + a*x^4),x]","\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 a^{3/2} \sqrt{b}}-\frac{\log \left(a x^4+2 a x^2+a+b\right)}{2 a}+\frac{x^2}{2 a}","\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 a^{3/2} \sqrt{b}}-\frac{\log \left(a x^4+2 a x^2+a+b\right)}{2 a}+\frac{x^2}{2 a}",1,"x^2/(2*a) + ((a - b)*ArcTan[(Sqrt[a]*(1 + x^2))/Sqrt[b]])/(2*a^(3/2)*Sqrt[b]) - Log[a + b + 2*a*x^2 + a*x^4]/(2*a)","A",6,6,20,0.3000,1,"{1114, 703, 634, 618, 204, 628}"
907,1,54,0,0.0449957,"\int \frac{x^3}{a+b+2 a x^2+a x^4} \, dx","Int[x^3/(a + b + 2*a*x^2 + a*x^4),x]","\frac{\log \left(a x^4+2 a x^2+a+b\right)}{4 a}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}","\frac{\log \left(a x^4+2 a x^2+a+b\right)}{4 a}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"-ArcTan[(Sqrt[a]*(1 + x^2))/Sqrt[b]]/(2*Sqrt[a]*Sqrt[b]) + Log[a + b + 2*a*x^2 + a*x^4]/(4*a)","A",5,5,20,0.2500,1,"{1114, 634, 618, 204, 628}"
908,1,31,0,0.0255772,"\int \frac{x}{a+b+2 a x^2+a x^4} \, dx","Int[x/(a + b + 2*a*x^2 + a*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[a]*(1 + x^2))/Sqrt[b]]/(2*Sqrt[a]*Sqrt[b])","A",3,3,18,0.1667,1,"{1107, 618, 204}"
909,1,69,0,0.067098,"\int \frac{1}{x \left(a+b+2 a x^2+a x^4\right)} \, dx","Int[1/(x*(a + b + 2*a*x^2 + a*x^4)),x]","-\frac{\log \left(a x^4+2 a x^2+a+b\right)}{4 (a+b)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a+b)}+\frac{\log (x)}{a+b}","-\frac{\log \left(a x^4+2 a x^2+a+b\right)}{4 (a+b)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a+b)}+\frac{\log (x)}{a+b}",1,"-(Sqrt[a]*ArcTan[(Sqrt[a]*(1 + x^2))/Sqrt[b]])/(2*Sqrt[b]*(a + b)) + Log[x]/(a + b) - Log[a + b + 2*a*x^2 + a*x^4]/(4*(a + b))","A",7,7,20,0.3500,1,"{1114, 705, 29, 634, 618, 204, 628}"
910,1,89,0,0.131711,"\int \frac{1}{x^3 \left(a+b+2 a x^2+a x^4\right)} \, dx","Int[1/(x^3*(a + b + 2*a*x^2 + a*x^4)),x]","-\frac{1}{2 x^2 (a+b)}+\frac{a \log \left(a x^4+2 a x^2+a+b\right)}{2 (a+b)^2}+\frac{\sqrt{a} (a-b) \tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a+b)^2}-\frac{2 a \log (x)}{(a+b)^2}","-\frac{1}{2 x^2 (a+b)}+\frac{a \log \left(a x^4+2 a x^2+a+b\right)}{2 (a+b)^2}+\frac{\sqrt{a} (a-b) \tan ^{-1}\left(\frac{\sqrt{a} \left(x^2+1\right)}{\sqrt{b}}\right)}{2 \sqrt{b} (a+b)^2}-\frac{2 a \log (x)}{(a+b)^2}",1,"-1/(2*(a + b)*x^2) + (Sqrt[a]*(a - b)*ArcTan[(Sqrt[a]*(1 + x^2))/Sqrt[b]])/(2*Sqrt[b]*(a + b)^2) - (2*a*Log[x])/(a + b)^2 + (a*Log[a + b + 2*a*x^2 + a*x^4])/(2*(a + b)^2)","A",8,7,20,0.3500,1,"{1114, 709, 800, 634, 618, 204, 628}"
911,1,432,0,0.8905869,"\int \frac{x^4}{a+b+2 a x^2+a x^4} \, dx","Int[x^4/(a + b + 2*a*x^2 + a*x^4),x]","\frac{\left(-2 \sqrt{a} \sqrt{a+b}+a+b\right) \log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\left(-2 \sqrt{a} \sqrt{a+b}+a+b\right) \log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}+\frac{\left(2 \sqrt{a} \sqrt{a+b}+a+b\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}-\frac{\left(2 \sqrt{a} \sqrt{a+b}+a+b\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}+\frac{x}{a}","\frac{\left(-2 \sqrt{a} \sqrt{a+b}+a+b\right) \log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\left(-2 \sqrt{a} \sqrt{a+b}+a+b\right) \log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}+\frac{\left(2 \sqrt{a} \sqrt{a+b}+a+b\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}-\frac{\left(2 \sqrt{a} \sqrt{a+b}+a+b\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{5/4} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}+\frac{x}{a}",1,"x/a + ((a + b + 2*Sqrt[a]*Sqrt[a + b])*ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] - Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]])/(2*Sqrt[2]*a^(5/4)*Sqrt[a + b]*Sqrt[Sqrt[a] + Sqrt[a + b]]) - ((a + b + 2*Sqrt[a]*Sqrt[a + b])*ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] + Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]])/(2*Sqrt[2]*a^(5/4)*Sqrt[a + b]*Sqrt[Sqrt[a] + Sqrt[a + b]]) + ((a + b - 2*Sqrt[a]*Sqrt[a + b])*Log[Sqrt[a + b] - Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2])/(4*Sqrt[2]*a^(5/4)*Sqrt[a + b]*Sqrt[-Sqrt[a] + Sqrt[a + b]]) - ((a + b - 2*Sqrt[a]*Sqrt[a + b])*Log[Sqrt[a + b] + Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2])/(4*Sqrt[2]*a^(5/4)*Sqrt[a + b]*Sqrt[-Sqrt[a] + Sqrt[a + b]])","A",10,6,20,0.3000,1,"{1122, 1169, 634, 618, 204, 628}"
912,1,331,0,0.2555473,"\int \frac{x^2}{a+b+2 a x^2+a x^4} \, dx","Int[x^2/(a + b + 2*a*x^2 + a*x^4),x]","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}+\sqrt{a}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}+\sqrt{a}}}","\frac{\log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}+\sqrt{a}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} a^{3/4} \sqrt{\sqrt{a+b}+\sqrt{a}}}",1,"-ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] - Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]]/(2*Sqrt[2]*a^(3/4)*Sqrt[Sqrt[a] + Sqrt[a + b]]) + ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] + Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]]/(2*Sqrt[2]*a^(3/4)*Sqrt[Sqrt[a] + Sqrt[a + b]]) + Log[Sqrt[a + b] - Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2]/(4*Sqrt[2]*a^(3/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]) - Log[Sqrt[a + b] + Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2]/(4*Sqrt[2]*a^(3/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]])","A",9,5,20,0.2500,1,"{1129, 634, 618, 204, 628}"
913,1,359,0,0.261469,"\int \frac{1}{a+b+2 a x^2+a x^4} \, dx","Int[(a + b + 2*a*x^2 + a*x^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} \sqrt[4]{a} \sqrt{a+b} \sqrt{\sqrt{a+b}+\sqrt{a}}}",1,"-ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] - Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]]/(2*Sqrt[2]*a^(1/4)*Sqrt[a + b]*Sqrt[Sqrt[a] + Sqrt[a + b]]) + ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] + Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]]/(2*Sqrt[2]*a^(1/4)*Sqrt[a + b]*Sqrt[Sqrt[a] + Sqrt[a + b]]) - Log[Sqrt[a + b] - Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2]/(4*Sqrt[2]*a^(1/4)*Sqrt[a + b]*Sqrt[-Sqrt[a] + Sqrt[a + b]]) + Log[Sqrt[a + b] + Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2]/(4*Sqrt[2]*a^(1/4)*Sqrt[a + b]*Sqrt[-Sqrt[a] + Sqrt[a + b]])","A",9,5,16,0.3125,1,"{1094, 634, 618, 204, 628}"
914,1,433,0,0.5187214,"\int \frac{1}{x^2 \left(a+b+2 a x^2+a x^4\right)} \, dx","Int[1/(x^2*(a + b + 2*a*x^2 + a*x^4)),x]","\frac{\sqrt[4]{a} \left(2 \sqrt{a}-\sqrt{a+b}\right) \log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\sqrt[4]{a} \left(2 \sqrt{a}-\sqrt{a+b}\right) \log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{1}{x (a+b)}+\frac{\sqrt[4]{a} \left(\sqrt{a+b}+2 \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}+\sqrt{a}}}-\frac{\sqrt[4]{a} \left(\sqrt{a+b}+2 \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}+\sqrt{a}}}","\frac{\sqrt[4]{a} \left(2 \sqrt{a}-\sqrt{a+b}\right) \log \left(-\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{\sqrt[4]{a} \left(2 \sqrt{a}-\sqrt{a+b}\right) \log \left(\sqrt{2} \sqrt[4]{a} x \sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{a+b}+\sqrt{a} x^2\right)}{4 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}-\sqrt{a}}}-\frac{1}{x (a+b)}+\frac{\sqrt[4]{a} \left(\sqrt{a+b}+2 \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}-\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}+\sqrt{a}}}-\frac{\sqrt[4]{a} \left(\sqrt{a+b}+2 \sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{\sqrt{a+b}-\sqrt{a}}+\sqrt{2} \sqrt[4]{a} x}{\sqrt{\sqrt{a+b}+\sqrt{a}}}\right)}{2 \sqrt{2} (a+b)^{3/2} \sqrt{\sqrt{a+b}+\sqrt{a}}}",1,"-(1/((a + b)*x)) + (a^(1/4)*(2*Sqrt[a] + Sqrt[a + b])*ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] - Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]])/(2*Sqrt[2]*(a + b)^(3/2)*Sqrt[Sqrt[a] + Sqrt[a + b]]) - (a^(1/4)*(2*Sqrt[a] + Sqrt[a + b])*ArcTan[(Sqrt[-Sqrt[a] + Sqrt[a + b]] + Sqrt[2]*a^(1/4)*x)/Sqrt[Sqrt[a] + Sqrt[a + b]]])/(2*Sqrt[2]*(a + b)^(3/2)*Sqrt[Sqrt[a] + Sqrt[a + b]]) + (a^(1/4)*(2*Sqrt[a] - Sqrt[a + b])*Log[Sqrt[a + b] - Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2])/(4*Sqrt[2]*(a + b)^(3/2)*Sqrt[-Sqrt[a] + Sqrt[a + b]]) - (a^(1/4)*(2*Sqrt[a] - Sqrt[a + b])*Log[Sqrt[a + b] + Sqrt[2]*a^(1/4)*Sqrt[-Sqrt[a] + Sqrt[a + b]]*x + Sqrt[a]*x^2])/(4*Sqrt[2]*(a + b)^(3/2)*Sqrt[-Sqrt[a] + Sqrt[a + b]])","A",10,6,20,0.3000,1,"{1123, 1169, 634, 618, 204, 628}"
915,1,20,0,0.0198906,"\int \frac{x}{1+x^2+x^4} \, dx","Int[x/(1 + x^2 + x^4),x]","\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTan[(1 + 2*x^2)/Sqrt[3]]/Sqrt[3]","A",3,3,12,0.2500,1,"{1107, 618, 204}"
916,1,14,0,0.0155259,"\int \frac{x}{10+2 x^2+x^4} \, dx","Int[x/(10 + 2*x^2 + x^4),x]","\frac{1}{6} \tan ^{-1}\left(\frac{1}{3} \left(x^2+1\right)\right)","\frac{1}{6} \tan ^{-1}\left(\frac{1}{3} \left(x^2+1\right)\right)",1,"ArcTan[(1 + x^2)/3]/6","A",3,3,14,0.2143,1,"{1107, 618, 204}"
917,1,23,0,0.0124621,"\int \frac{x^2}{20+9 x^2+x^4} \, dx","Int[x^2/(20 + 9*x^2 + x^4),x]","\sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)-2 \tan ^{-1}\left(\frac{x}{2}\right)","\sqrt{5} \tan ^{-1}\left(\frac{x}{\sqrt{5}}\right)-2 \tan ^{-1}\left(\frac{x}{2}\right)",1,"-2*ArcTan[x/2] + Sqrt[5]*ArcTan[x/Sqrt[5]]","A",3,2,16,0.1250,1,"{1130, 203}"
918,1,74,0,0.0502575,"\int \frac{x^2}{1-x^2+x^4} \, dx","Int[x^2/(1 - x^2 + x^4),x]","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{2} \tan ^{-1}\left(2 x+\sqrt{3}\right)","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{1}{2} \tan ^{-1}\left(\sqrt{3}-2 x\right)+\frac{1}{2} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-ArcTan[Sqrt[3] - 2*x]/2 + ArcTan[Sqrt[3] + 2*x]/2 + Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",9,6,16,0.3750,1,"{1127, 1161, 618, 204, 1164, 628}"
919,1,188,0,0.177248,"\int \frac{x^2}{2-2 x^2+x^4} \, dx","Int[x^2/(2 - 2*x^2 + x^4),x]","\frac{\log \left(x^2-\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 x}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)","\frac{\log \left(x^2-\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{\log \left(x^2+\sqrt{2 \left(1+\sqrt{2}\right)} x+\sqrt{2}\right)}{4 \sqrt{2 \left(1+\sqrt{2}\right)}}-\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 x}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\frac{1}{2} \sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)",1,"-(Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*x)/Sqrt[2*(-1 + Sqrt[2])]])/2 + (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*x)/Sqrt[2*(-1 + Sqrt[2])]])/2 + Log[Sqrt[2] - Sqrt[2*(1 + Sqrt[2])]*x + x^2]/(4*Sqrt[2*(1 + Sqrt[2])]) - Log[Sqrt[2] + Sqrt[2*(1 + Sqrt[2])]*x + x^2]/(4*Sqrt[2*(1 + Sqrt[2])])","A",9,6,16,0.3750,1,"{1127, 1161, 618, 204, 1164, 628}"
920,1,171,0,0.1552709,"\int x^7 \sqrt{a+b x^2+c x^4} \, dx","Int[x^7*Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(-32 a c+35 b^2-42 b c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{480 c^3}-\frac{b \left(7 b^2-12 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{256 c^4}+\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{9/2}}+\frac{x^4 \left(a+b x^2+c x^4\right)^{3/2}}{10 c}","\frac{\left(-32 a c+35 b^2-42 b c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{480 c^3}-\frac{b \left(7 b^2-12 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{256 c^4}+\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{9/2}}+\frac{x^4 \left(a+b x^2+c x^4\right)^{3/2}}{10 c}",1,"-(b*(7*b^2 - 12*a*c)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(256*c^4) + (x^4*(a + b*x^2 + c*x^4)^(3/2))/(10*c) + ((35*b^2 - 32*a*c - 42*b*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(480*c^3) + (b*(7*b^2 - 12*a*c)*(b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(512*c^(9/2))","A",6,6,20,0.3000,1,"{1114, 742, 779, 612, 621, 206}"
921,1,153,0,0.1293592,"\int x^5 \sqrt{a+b x^2+c x^4} \, dx","Int[x^5*Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(5 b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{128 c^3}-\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{7/2}}-\frac{5 b \left(a+b x^2+c x^4\right)^{3/2}}{48 c^2}+\frac{x^2 \left(a+b x^2+c x^4\right)^{3/2}}{8 c}","\frac{\left(5 b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{128 c^3}-\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{7/2}}-\frac{5 b \left(a+b x^2+c x^4\right)^{3/2}}{48 c^2}+\frac{x^2 \left(a+b x^2+c x^4\right)^{3/2}}{8 c}",1,"((5*b^2 - 4*a*c)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(128*c^3) - (5*b*(a + b*x^2 + c*x^4)^(3/2))/(48*c^2) + (x^2*(a + b*x^2 + c*x^4)^(3/2))/(8*c) - ((b^2 - 4*a*c)*(5*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(256*c^(7/2))","A",6,6,20,0.3000,1,"{1114, 742, 640, 612, 621, 206}"
922,1,108,0,0.0807406,"\int x^3 \sqrt{a+b x^2+c x^4} \, dx","Int[x^3*Sqrt[a + b*x^2 + c*x^4],x]","\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{5/2}}-\frac{b \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{16 c^2}+\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 c}","\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{5/2}}-\frac{b \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{16 c^2}+\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 c}",1,"-(b*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*c^2) + (a + b*x^2 + c*x^4)^(3/2)/(6*c) + (b*(b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(5/2))","A",5,5,20,0.2500,1,"{1114, 640, 612, 621, 206}"
923,1,83,0,0.0546726,"\int x \sqrt{a+b x^2+c x^4} \, dx","Int[x*Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{8 c}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{3/2}}","\frac{\left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{8 c}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{3/2}}",1,"((b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*c) - ((b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*c^(3/2))","A",4,4,18,0.2222,1,"{1107, 612, 621, 206}"
924,1,109,0,0.1090707,"\int \frac{\sqrt{a+b x^2+c x^4}}{x} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x,x]","\frac{1}{2} \sqrt{a+b x^2+c x^4}-\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)+\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c}}","\frac{1}{2} \sqrt{a+b x^2+c x^4}-\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)+\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c}}",1,"Sqrt[a + b*x^2 + c*x^4]/2 - (Sqrt[a]*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/2 + (b*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[c])","A",7,6,20,0.3000,1,"{1114, 734, 843, 621, 206, 724}"
925,1,112,0,0.1037658,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^3} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^3,x]","-\frac{\sqrt{a+b x^2+c x^4}}{2 x^2}-\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{a}}+\frac{1}{2} \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)","-\frac{\sqrt{a+b x^2+c x^4}}{2 x^2}-\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{a}}+\frac{1}{2} \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)",1,"-Sqrt[a + b*x^2 + c*x^4]/(2*x^2) - (b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[a]) + (Sqrt[c]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/2","A",7,6,20,0.3000,1,"{1114, 732, 843, 621, 206, 724}"
926,1,88,0,0.0709131,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^5} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^5,x]","\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{3/2}}-\frac{\left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{8 a x^4}","\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{3/2}}-\frac{\left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{8 a x^4}",1,"-((2*a + b*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*a*x^4) + ((b^2 - 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(16*a^(3/2))","A",4,4,20,0.2000,1,"{1114, 720, 724, 206}"
927,1,116,0,0.0964375,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^7} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^7,x]","-\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{5/2}}+\frac{b \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{16 a^2 x^4}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 a x^6}","-\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{5/2}}+\frac{b \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{16 a^2 x^4}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 a x^6}",1,"(b*(2*a + b*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*a^2*x^4) - (a + b*x^2 + c*x^4)^(3/2)/(6*a*x^6) - (b*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(32*a^(5/2))","A",5,5,20,0.2500,1,"{1114, 730, 720, 724, 206}"
928,1,161,0,0.1497051,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^9} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^9,x]","-\frac{\left(5 b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{128 a^3 x^4}+\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{256 a^{7/2}}+\frac{5 b \left(a+b x^2+c x^4\right)^{3/2}}{48 a^2 x^6}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{8 a x^8}","-\frac{\left(5 b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{128 a^3 x^4}+\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{256 a^{7/2}}+\frac{5 b \left(a+b x^2+c x^4\right)^{3/2}}{48 a^2 x^6}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{8 a x^8}",1,"-((5*b^2 - 4*a*c)*(2*a + b*x^2)*Sqrt[a + b*x^2 + c*x^4])/(128*a^3*x^4) - (a + b*x^2 + c*x^4)^(3/2)/(8*a*x^8) + (5*b*(a + b*x^2 + c*x^4)^(3/2))/(48*a^2*x^6) + ((b^2 - 4*a*c)*(5*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(256*a^(7/2))","A",6,6,20,0.3000,1,"{1114, 744, 806, 720, 724, 206}"
929,1,199,0,0.2290353,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^{11}} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^11,x]","-\frac{\left(35 b^2-32 a c\right) \left(a+b x^2+c x^4\right)^{3/2}}{480 a^3 x^6}+\frac{b \left(7 b^2-12 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{256 a^4 x^4}-\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{512 a^{9/2}}+\frac{7 b \left(a+b x^2+c x^4\right)^{3/2}}{80 a^2 x^8}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{10 a x^{10}}","-\frac{\left(35 b^2-32 a c\right) \left(a+b x^2+c x^4\right)^{3/2}}{480 a^3 x^6}+\frac{b \left(7 b^2-12 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{256 a^4 x^4}-\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{512 a^{9/2}}+\frac{7 b \left(a+b x^2+c x^4\right)^{3/2}}{80 a^2 x^8}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{10 a x^{10}}",1,"(b*(7*b^2 - 12*a*c)*(2*a + b*x^2)*Sqrt[a + b*x^2 + c*x^4])/(256*a^4*x^4) - (a + b*x^2 + c*x^4)^(3/2)/(10*a*x^10) + (7*b*(a + b*x^2 + c*x^4)^(3/2))/(80*a^2*x^8) - ((35*b^2 - 32*a*c)*(a + b*x^2 + c*x^4)^(3/2))/(480*a^3*x^6) - (b*(7*b^2 - 12*a*c)*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(512*a^(9/2))","A",7,7,20,0.3500,1,"{1114, 744, 834, 806, 720, 724, 206}"
930,1,395,0,0.2510718,"\int x^4 \sqrt{a+b x^2+c x^4} \, dx","Int[x^4*Sqrt[a + b*x^2 + c*x^4],x]","-\frac{2 x \left(2 b^2-5 a c\right) \sqrt{a+b x^2+c x^4}}{105 c^2}+\frac{b x \left(8 b^2-29 a c\right) \sqrt{a+b x^2+c x^4}}{105 c^{5/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c} \left(2 b^2-5 a c\right)-29 a b c+8 b^3\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{210 c^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} b \left(8 b^2-29 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{105 c^{11/4} \sqrt{a+b x^2+c x^4}}+\frac{x^3 \left(b+5 c x^2\right) \sqrt{a+b x^2+c x^4}}{35 c}","-\frac{2 x \left(2 b^2-5 a c\right) \sqrt{a+b x^2+c x^4}}{105 c^2}+\frac{b x \left(8 b^2-29 a c\right) \sqrt{a+b x^2+c x^4}}{105 c^{5/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c} \left(2 b^2-5 a c\right)-29 a b c+8 b^3\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{210 c^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} b \left(8 b^2-29 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{105 c^{11/4} \sqrt{a+b x^2+c x^4}}+\frac{x^3 \left(b+5 c x^2\right) \sqrt{a+b x^2+c x^4}}{35 c}",1,"(-2*(2*b^2 - 5*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(105*c^2) + (b*(8*b^2 - 29*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(105*c^(5/2)*(Sqrt[a] + Sqrt[c]*x^2)) + (x^3*(b + 5*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(35*c) - (a^(1/4)*b*(8*b^2 - 29*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(105*c^(11/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(8*b^3 - 29*a*b*c + 2*Sqrt[a]*Sqrt[c]*(2*b^2 - 5*a*c))*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(210*c^(11/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1116, 1279, 1197, 1103, 1195}"
931,1,342,0,0.1414416,"\int x^2 \sqrt{a+b x^2+c x^4} \, dx","Int[x^2*Sqrt[a + b*x^2 + c*x^4],x]","-\frac{2 x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{15 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{30 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{a} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{x \left(b+3 c x^2\right) \sqrt{a+b x^2+c x^4}}{15 c}","-\frac{2 x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{15 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{30 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{a} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{x \left(b+3 c x^2\right) \sqrt{a+b x^2+c x^4}}{15 c}",1,"(-2*(b^2 - 3*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(15*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) + (x*(b + 3*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(15*c) + (2*a^(1/4)*(b^2 - 3*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*c^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - (a^(1/4)*(2*b^2 + Sqrt[a]*b*Sqrt[c] - 6*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(30*c^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,20,0.2000,1,"{1116, 1197, 1103, 1195}"
932,1,309,0,0.1007352,"\int \sqrt{a+b x^2+c x^4} \, dx","Int[Sqrt[a + b*x^2 + c*x^4],x]","\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} b \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{b x \sqrt{a+b x^2+c x^4}}{3 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{1}{3} x \sqrt{a+b x^2+c x^4}","\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} b \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{b x \sqrt{a+b x^2+c x^4}}{3 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{1}{3} x \sqrt{a+b x^2+c x^4}",1,"(x*Sqrt[a + b*x^2 + c*x^4])/3 + (b*x*Sqrt[a + b*x^2 + c*x^4])/(3*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*b*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*c^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(b + 2*Sqrt[a]*Sqrt[c])*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*c^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,16,0.2500,1,"{1091, 1197, 1103, 1195}"
933,1,303,0,0.0843806,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^2} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^2,x]","\frac{2 \sqrt{c} x \sqrt{a+b x^2+c x^4}}{\sqrt{a}+\sqrt{c} x^2}-\frac{\sqrt{a+b x^2+c x^4}}{x}+\frac{\left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{\sqrt{a+b x^2+c x^4}}","\frac{2 \sqrt{c} x \sqrt{a+b x^2+c x^4}}{\sqrt{a}+\sqrt{c} x^2}-\frac{\sqrt{a+b x^2+c x^4}}{x}+\frac{\left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{\sqrt{a+b x^2+c x^4}}",1,"-(Sqrt[a + b*x^2 + c*x^4]/x) + (2*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(Sqrt[a] + Sqrt[c]*x^2) - (2*a^(1/4)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/Sqrt[a + b*x^2 + c*x^4] + ((b + 2*Sqrt[a]*Sqrt[c])*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(1/4)*c^(1/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,20,0.2000,1,"{1117, 1197, 1103, 1195}"
934,1,341,0,0.1551286,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^4} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^4,x]","\frac{\sqrt[4]{c} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{a+b x^2+c x^4}}{3 a x}+\frac{b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{3 a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt{a+b x^2+c x^4}}{3 x^3}","\frac{\sqrt[4]{c} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{a+b x^2+c x^4}}{3 a x}+\frac{b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{3 a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt{a+b x^2+c x^4}}{3 x^3}",1,"-Sqrt[a + b*x^2 + c*x^4]/(3*x^3) - (b*Sqrt[a + b*x^2 + c*x^4])/(3*a*x) + (b*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(3*a*(Sqrt[a] + Sqrt[c]*x^2)) - (b*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*a^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + ((b + 2*Sqrt[a]*Sqrt[c])*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*a^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1117, 1281, 1197, 1103, 1195}"
935,1,397,0,0.2611001,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^6} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/x^6,x]","\frac{2 \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{15 a^2 x}-\frac{2 \sqrt{c} x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{15 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{30 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{c} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{a+b x^2+c x^4}}{15 a x^3}-\frac{\sqrt{a+b x^2+c x^4}}{5 x^5}","\frac{2 \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{15 a^2 x}-\frac{2 \sqrt{c} x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{15 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{30 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{c} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{a+b x^2+c x^4}}{15 a x^3}-\frac{\sqrt{a+b x^2+c x^4}}{5 x^5}",1,"-Sqrt[a + b*x^2 + c*x^4]/(5*x^5) - (b*Sqrt[a + b*x^2 + c*x^4])/(15*a*x^3) + (2*(b^2 - 3*a*c)*Sqrt[a + b*x^2 + c*x^4])/(15*a^2*x) - (2*Sqrt[c]*(b^2 - 3*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(15*a^2*(Sqrt[a] + Sqrt[c]*x^2)) + (2*c^(1/4)*(b^2 - 3*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*a^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - (c^(1/4)*(2*b^2 + Sqrt[a]*b*Sqrt[c] - 6*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(30*a^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",6,5,20,0.2500,1,"{1117, 1281, 1197, 1103, 1195}"
936,1,223,0,0.2117534,"\int x^7 \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[x^7*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{\left(-16 a c+21 b^2-30 b c x^2\right) \left(a+b x^2+c x^4\right)^{5/2}}{560 c^3}-\frac{b \left(3 b^2-4 a c\right) \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{256 c^4}+\frac{3 b \left(b^2-4 a c\right) \left(3 b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{2048 c^5}-\frac{3 b \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4096 c^{11/2}}+\frac{x^4 \left(a+b x^2+c x^4\right)^{5/2}}{14 c}","\frac{\left(-16 a c+21 b^2-30 b c x^2\right) \left(a+b x^2+c x^4\right)^{5/2}}{560 c^3}-\frac{b \left(3 b^2-4 a c\right) \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{256 c^4}+\frac{3 b \left(b^2-4 a c\right) \left(3 b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{2048 c^5}-\frac{3 b \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4096 c^{11/2}}+\frac{x^4 \left(a+b x^2+c x^4\right)^{5/2}}{14 c}",1,"(3*b*(b^2 - 4*a*c)*(3*b^2 - 4*a*c)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(2048*c^5) - (b*(3*b^2 - 4*a*c)*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(256*c^4) + (x^4*(a + b*x^2 + c*x^4)^(5/2))/(14*c) + ((21*b^2 - 16*a*c - 30*b*c*x^2)*(a + b*x^2 + c*x^4)^(5/2))/(560*c^3) - (3*b*(b^2 - 4*a*c)^2*(3*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4096*c^(11/2))","A",7,6,20,0.3000,1,"{1114, 742, 779, 612, 621, 206}"
937,1,204,0,0.1823419,"\int x^5 \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[x^5*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{\left(7 b^2-4 a c\right) \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{384 c^3}-\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{1024 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2048 c^{9/2}}-\frac{7 b \left(a+b x^2+c x^4\right)^{5/2}}{120 c^2}+\frac{x^2 \left(a+b x^2+c x^4\right)^{5/2}}{12 c}","\frac{\left(7 b^2-4 a c\right) \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{384 c^3}-\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{1024 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2048 c^{9/2}}-\frac{7 b \left(a+b x^2+c x^4\right)^{5/2}}{120 c^2}+\frac{x^2 \left(a+b x^2+c x^4\right)^{5/2}}{12 c}",1,"-((b^2 - 4*a*c)*(7*b^2 - 4*a*c)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(1024*c^4) + ((7*b^2 - 4*a*c)*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(384*c^3) - (7*b*(a + b*x^2 + c*x^4)^(5/2))/(120*c^2) + (x^2*(a + b*x^2 + c*x^4)^(5/2))/(12*c) + ((b^2 - 4*a*c)^2*(7*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(2048*c^(9/2))","A",7,6,20,0.3000,1,"{1114, 742, 640, 612, 621, 206}"
938,1,150,0,0.1169777,"\int x^3 \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[x^3*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{3 b \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{256 c^3}-\frac{3 b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2}}-\frac{b \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{32 c^2}+\frac{\left(a+b x^2+c x^4\right)^{5/2}}{10 c}","\frac{3 b \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{256 c^3}-\frac{3 b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2}}-\frac{b \left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{32 c^2}+\frac{\left(a+b x^2+c x^4\right)^{5/2}}{10 c}",1,"(3*b*(b^2 - 4*a*c)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(256*c^3) - (b*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(32*c^2) + (a + b*x^2 + c*x^4)^(5/2)/(10*c) - (3*b*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(512*c^(7/2))","A",6,5,20,0.2500,1,"{1114, 640, 612, 621, 206}"
939,1,124,0,0.0855727,"\int x \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[x*(a + b*x^2 + c*x^4)^(3/2),x]","-\frac{3 \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{128 c^2}+\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{5/2}}+\frac{\left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{16 c}","-\frac{3 \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{128 c^2}+\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{5/2}}+\frac{\left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{16 c}",1,"(-3*(b^2 - 4*a*c)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(128*c^2) + ((b + 2*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(16*c) + (3*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(256*c^(5/2))","A",5,4,18,0.2222,1,"{1107, 612, 621, 206}"
940,1,155,0,0.1842346,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x,x]","-\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)-\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2}}+\frac{\left(8 a c+b^2+2 b c x^2\right) \sqrt{a+b x^2+c x^4}}{16 c}+\frac{1}{6} \left(a+b x^2+c x^4\right)^{3/2}","-\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)-\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2}}+\frac{\left(8 a c+b^2+2 b c x^2\right) \sqrt{a+b x^2+c x^4}}{16 c}+\frac{1}{6} \left(a+b x^2+c x^4\right)^{3/2}",1,"((b^2 + 8*a*c + 2*b*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*c) + (a + b*x^2 + c*x^4)^(3/2)/6 - (a^(3/2)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/2 - (b*(b^2 - 12*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(3/2))","A",8,7,20,0.3500,1,"{1114, 734, 814, 843, 621, 206, 724}"
941,1,150,0,0.1692452,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^3} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^3,x]","\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{c}}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{2 x^2}+\frac{3}{8} \left(3 b+2 c x^2\right) \sqrt{a+b x^2+c x^4}-\frac{3}{4} \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)","\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{c}}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{2 x^2}+\frac{3}{8} \left(3 b+2 c x^2\right) \sqrt{a+b x^2+c x^4}-\frac{3}{4} \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)",1,"(3*(3*b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/8 - (a + b*x^2 + c*x^4)^(3/2)/(2*x^2) - (3*Sqrt[a]*b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/4 + (3*(b^2 + 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*Sqrt[c])","A",8,7,20,0.3500,1,"{1114, 732, 814, 843, 621, 206, 724}"
942,1,151,0,0.1630266,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^5} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^5,x]","-\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{a}}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{4 x^4}-\frac{3 \left(b-2 c x^2\right) \sqrt{a+b x^2+c x^4}}{8 x^2}+\frac{3}{4} b \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)","-\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{a}}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{4 x^4}-\frac{3 \left(b-2 c x^2\right) \sqrt{a+b x^2+c x^4}}{8 x^2}+\frac{3}{4} b \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)",1,"(-3*(b - 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*x^2) - (a + b*x^2 + c*x^4)^(3/2)/(4*x^4) - (3*(b^2 + 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(16*Sqrt[a]) + (3*b*Sqrt[c]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/4","A",8,7,20,0.3500,1,"{1114, 732, 812, 843, 621, 206, 724}"
943,1,163,0,0.1837869,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^7} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^7,x]","\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{3/2}}-\frac{\left(x^2 \left(8 a c+b^2\right)+2 a b\right) \sqrt{a+b x^2+c x^4}}{16 a x^4}+\frac{1}{2} c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 x^6}","\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{3/2}}-\frac{\left(x^2 \left(8 a c+b^2\right)+2 a b\right) \sqrt{a+b x^2+c x^4}}{16 a x^4}+\frac{1}{2} c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 x^6}",1,"-((2*a*b + (b^2 + 8*a*c)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*a*x^4) - (a + b*x^2 + c*x^4)^(3/2)/(6*x^6) + (b*(b^2 - 12*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(32*a^(3/2)) + (c^(3/2)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/2","A",8,7,20,0.3500,1,"{1114, 732, 810, 843, 621, 206, 724}"
944,1,133,0,0.1165173,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^9} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^9,x]","\frac{3 \left(b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{128 a^2 x^4}-\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{256 a^{5/2}}-\frac{\left(2 a+b x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{16 a x^8}","\frac{3 \left(b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{128 a^2 x^4}-\frac{3 \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{256 a^{5/2}}-\frac{\left(2 a+b x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{16 a x^8}",1,"(3*(b^2 - 4*a*c)*(2*a + b*x^2)*Sqrt[a + b*x^2 + c*x^4])/(128*a^2*x^4) - ((2*a + b*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(16*a*x^8) - (3*(b^2 - 4*a*c)^2*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(256*a^(5/2))","A",5,4,20,0.2000,1,"{1114, 720, 724, 206}"
945,1,162,0,0.1401098,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^{11}} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^11,x]","-\frac{3 b \left(b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{256 a^3 x^4}+\frac{3 b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{512 a^{7/2}}+\frac{b \left(2 a+b x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{32 a^2 x^8}-\frac{\left(a+b x^2+c x^4\right)^{5/2}}{10 a x^{10}}","-\frac{3 b \left(b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{256 a^3 x^4}+\frac{3 b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{512 a^{7/2}}+\frac{b \left(2 a+b x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{32 a^2 x^8}-\frac{\left(a+b x^2+c x^4\right)^{5/2}}{10 a x^{10}}",1,"(-3*b*(b^2 - 4*a*c)*(2*a + b*x^2)*Sqrt[a + b*x^2 + c*x^4])/(256*a^3*x^4) + (b*(2*a + b*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(32*a^2*x^8) - (a + b*x^2 + c*x^4)^(5/2)/(10*a*x^10) + (3*b*(b^2 - 4*a*c)^2*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(512*a^(7/2))","A",6,5,20,0.2500,1,"{1114, 730, 720, 724, 206}"
946,1,216,0,0.2170457,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^{13}} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^13,x]","-\frac{\left(7 b^2-4 a c\right) \left(2 a+b x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{384 a^3 x^8}+\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{1024 a^4 x^4}-\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2048 a^{9/2}}+\frac{7 b \left(a+b x^2+c x^4\right)^{5/2}}{120 a^2 x^{10}}-\frac{\left(a+b x^2+c x^4\right)^{5/2}}{12 a x^{12}}","-\frac{\left(7 b^2-4 a c\right) \left(2 a+b x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{384 a^3 x^8}+\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(2 a+b x^2\right) \sqrt{a+b x^2+c x^4}}{1024 a^4 x^4}-\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2048 a^{9/2}}+\frac{7 b \left(a+b x^2+c x^4\right)^{5/2}}{120 a^2 x^{10}}-\frac{\left(a+b x^2+c x^4\right)^{5/2}}{12 a x^{12}}",1,"((b^2 - 4*a*c)*(7*b^2 - 4*a*c)*(2*a + b*x^2)*Sqrt[a + b*x^2 + c*x^4])/(1024*a^4*x^4) - ((7*b^2 - 4*a*c)*(2*a + b*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(384*a^3*x^8) - (a + b*x^2 + c*x^4)^(5/2)/(12*a*x^12) + (7*b*(a + b*x^2 + c*x^4)^(5/2))/(120*a^2*x^10) - ((b^2 - 4*a*c)^2*(7*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2048*a^(9/2))","A",7,6,20,0.3000,1,"{1114, 744, 806, 720, 724, 206}"
947,1,495,0,0.4404377,"\int x^4 \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[x^4*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{x \left(60 a^2 c^2-51 a b^2 c+8 b^4\right) \sqrt{a+b x^2+c x^4}}{1155 c^3}-\frac{\sqrt[4]{a} \left(\sqrt{a} \sqrt{c} \left(60 a^2 c^2-51 a b^2 c+8 b^4\right)+8 b \left(2 b^2-9 a c\right) \left(b^2-3 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2310 c^{15/4} \sqrt{a+b x^2+c x^4}}-\frac{x^3 \left(10 c x^2 \left(b^2-3 a c\right)+b \left(a c+2 b^2\right)\right) \sqrt{a+b x^2+c x^4}}{385 c^2}-\frac{8 b x \left(2 b^2-9 a c\right) \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{1155 c^{7/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{8 \sqrt[4]{a} b \left(2 b^2-9 a c\right) \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{1155 c^{15/4} \sqrt{a+b x^2+c x^4}}+\frac{x^3 \left(b+3 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{33 c}","\frac{x \left(60 a^2 c^2-51 a b^2 c+8 b^4\right) \sqrt{a+b x^2+c x^4}}{1155 c^3}-\frac{\sqrt[4]{a} \left(\sqrt{a} \sqrt{c} \left(60 a^2 c^2-51 a b^2 c+8 b^4\right)+8 b \left(2 b^2-9 a c\right) \left(b^2-3 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2310 c^{15/4} \sqrt{a+b x^2+c x^4}}-\frac{x^3 \left(10 c x^2 \left(b^2-3 a c\right)+b \left(a c+2 b^2\right)\right) \sqrt{a+b x^2+c x^4}}{385 c^2}-\frac{8 b x \left(2 b^2-9 a c\right) \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{1155 c^{7/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{8 \sqrt[4]{a} b \left(2 b^2-9 a c\right) \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{1155 c^{15/4} \sqrt{a+b x^2+c x^4}}+\frac{x^3 \left(b+3 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{33 c}",1,"((8*b^4 - 51*a*b^2*c + 60*a^2*c^2)*x*Sqrt[a + b*x^2 + c*x^4])/(1155*c^3) - (8*b*(2*b^2 - 9*a*c)*(b^2 - 3*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(1155*c^(7/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (x^3*(b*(2*b^2 + a*c) + 10*c*(b^2 - 3*a*c)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(385*c^2) + (x^3*(b + 3*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(33*c) + (8*a^(1/4)*b*(2*b^2 - 9*a*c)*(b^2 - 3*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(1155*c^(15/4)*Sqrt[a + b*x^2 + c*x^4]) - (a^(1/4)*(8*b*(2*b^2 - 9*a*c)*(b^2 - 3*a*c) + Sqrt[a]*Sqrt[c]*(8*b^4 - 51*a*b^2*c + 60*a^2*c^2))*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2310*c^(15/4)*Sqrt[a + b*x^2 + c*x^4])","A",6,6,20,0.3000,1,"{1116, 1273, 1279, 1197, 1103, 1195}"
948,1,443,0,0.2849678,"\int x^2 \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[x^2*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{x \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \sqrt{a+b x^2+c x^4}}{315 c^{5/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \left(84 a^2 c^2-57 a b^2 c+4 \sqrt{a} b \sqrt{c} \left(b^2-6 a c\right)+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{630 c^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{x \left(6 c x^2 \left(2 b^2-7 a c\right)+b \left(4 b^2-9 a c\right)\right) \sqrt{a+b x^2+c x^4}}{315 c^2}+\frac{x \left(3 b+7 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{63 c}","\frac{x \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \sqrt{a+b x^2+c x^4}}{315 c^{5/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \left(84 a^2 c^2-57 a b^2 c+4 \sqrt{a} b \sqrt{c} \left(b^2-6 a c\right)+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{630 c^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(84 a^2 c^2-57 a b^2 c+8 b^4\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{315 c^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{x \left(6 c x^2 \left(2 b^2-7 a c\right)+b \left(4 b^2-9 a c\right)\right) \sqrt{a+b x^2+c x^4}}{315 c^2}+\frac{x \left(3 b+7 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{63 c}",1,"((8*b^4 - 57*a*b^2*c + 84*a^2*c^2)*x*Sqrt[a + b*x^2 + c*x^4])/(315*c^(5/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (x*(b*(4*b^2 - 9*a*c) + 6*c*(2*b^2 - 7*a*c)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(315*c^2) + (x*(3*b + 7*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(63*c) - (a^(1/4)*(8*b^4 - 57*a*b^2*c + 84*a^2*c^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(315*c^(11/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(8*b^4 - 57*a*b^2*c + 84*a^2*c^2 + 4*Sqrt[a]*b*Sqrt[c]*(b^2 - 6*a*c))*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(630*c^(11/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1116, 1176, 1197, 1103, 1195}"
949,1,381,0,0.2510148,"\int \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2),x]","-\frac{2 b x \left(b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{35 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a} \sqrt{c} \left(b^2-20 a c\right)+2 b \left(b^2-8 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{70 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{a} b \left(b^2-8 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{35 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{x \left(10 a c+b^2+3 b c x^2\right) \sqrt{a+b x^2+c x^4}}{35 c}+\frac{1}{7} x \left(a+b x^2+c x^4\right)^{3/2}","-\frac{2 b x \left(b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{35 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a} \sqrt{c} \left(b^2-20 a c\right)+2 b \left(b^2-8 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{70 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{a} b \left(b^2-8 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{35 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{x \left(10 a c+b^2+3 b c x^2\right) \sqrt{a+b x^2+c x^4}}{35 c}+\frac{1}{7} x \left(a+b x^2+c x^4\right)^{3/2}",1,"(-2*b*(b^2 - 8*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(35*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) + (x*(b^2 + 10*a*c + 3*b*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(35*c) + (x*(a + b*x^2 + c*x^4)^(3/2))/7 + (2*a^(1/4)*b*(b^2 - 8*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(35*c^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - (a^(1/4)*(Sqrt[a]*Sqrt[c]*(b^2 - 20*a*c) + 2*b*(b^2 - 8*a*c))*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(70*c^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,16,0.3125,1,"{1091, 1176, 1197, 1103, 1195}"
950,1,361,0,0.2063455,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^2} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^2,x]","\frac{\sqrt[4]{a} \left(8 \sqrt{a} b \sqrt{c}+12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{10 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{5 c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{x \left(12 a c+b^2\right) \sqrt{a+b x^2+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{x}+\frac{1}{5} x \left(7 b+6 c x^2\right) \sqrt{a+b x^2+c x^4}","\frac{\sqrt[4]{a} \left(8 \sqrt{a} b \sqrt{c}+12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{10 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{5 c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{x \left(12 a c+b^2\right) \sqrt{a+b x^2+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{x}+\frac{1}{5} x \left(7 b+6 c x^2\right) \sqrt{a+b x^2+c x^4}",1,"((b^2 + 12*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(5*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + (x*(7*b + 6*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/5 - (a + b*x^2 + c*x^4)^(3/2)/x - (a^(1/4)*(b^2 + 12*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(5*c^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(b^2 + 8*Sqrt[a]*b*Sqrt[c] + 12*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(10*c^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1117, 1176, 1197, 1103, 1195}"
951,1,353,0,0.1528889,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^4} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^4,x]","\frac{\left(8 \sqrt{a} b \sqrt{c}+4 a c+3 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{3 x^3}-\frac{\left(3 b-2 c x^2\right) \sqrt{a+b x^2+c x^4}}{3 x}+\frac{8 b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{3 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{8 \sqrt[4]{a} b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 \sqrt{a+b x^2+c x^4}}","\frac{\left(8 \sqrt{a} b \sqrt{c}+4 a c+3 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{3 x^3}-\frac{\left(3 b-2 c x^2\right) \sqrt{a+b x^2+c x^4}}{3 x}+\frac{8 b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{3 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{8 \sqrt[4]{a} b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 \sqrt{a+b x^2+c x^4}}",1,"(8*b*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(3*(Sqrt[a] + Sqrt[c]*x^2)) - ((3*b - 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(3*x) - (a + b*x^2 + c*x^4)^(3/2)/(3*x^3) - (8*a^(1/4)*b*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*Sqrt[a + b*x^2 + c*x^4]) + ((3*b^2 + 8*Sqrt[a]*b*Sqrt[c] + 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*a^(1/4)*c^(1/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1117, 1271, 1197, 1103, 1195}"
952,1,400,0,0.2509145,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^6} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^6,x]","\frac{\sqrt[4]{c} \left(8 \sqrt{a} b \sqrt{c}+12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{10 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{c} \left(12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{5 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\left(12 a c+b^2\right) \sqrt{a+b x^2+c x^4}}{5 a x}+\frac{\sqrt{c} x \left(12 a c+b^2\right) \sqrt{a+b x^2+c x^4}}{5 a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{5 x^5}-\frac{\left(b-6 c x^2\right) \sqrt{a+b x^2+c x^4}}{5 x^3}","\frac{\sqrt[4]{c} \left(8 \sqrt{a} b \sqrt{c}+12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{10 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{c} \left(12 a c+b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{5 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\left(12 a c+b^2\right) \sqrt{a+b x^2+c x^4}}{5 a x}+\frac{\sqrt{c} x \left(12 a c+b^2\right) \sqrt{a+b x^2+c x^4}}{5 a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{5 x^5}-\frac{\left(b-6 c x^2\right) \sqrt{a+b x^2+c x^4}}{5 x^3}",1,"-((b^2 + 12*a*c)*Sqrt[a + b*x^2 + c*x^4])/(5*a*x) + (Sqrt[c]*(b^2 + 12*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(5*a*(Sqrt[a] + Sqrt[c]*x^2)) - ((b - 6*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(5*x^3) - (a + b*x^2 + c*x^4)^(3/2)/(5*x^5) - (c^(1/4)*(b^2 + 12*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(5*a^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + (c^(1/4)*(b^2 + 8*Sqrt[a]*b*Sqrt[c] + 12*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(10*a^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",6,6,20,0.3000,1,"{1117, 1271, 1281, 1197, 1103, 1195}"
953,1,447,0,0.3949062,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^8} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/x^8,x]","\frac{2 b \left(b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{35 a^2 x}-\frac{2 b \sqrt{c} x \left(b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{35 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a} \sqrt{c} \left(b^2-20 a c\right)+2 b \left(b^2-8 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{70 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 b \sqrt[4]{c} \left(b^2-8 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{35 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{\left(b^2-20 a c\right) \sqrt{a+b x^2+c x^4}}{35 a x^3}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{7 x^7}-\frac{3 \left(b+10 c x^2\right) \sqrt{a+b x^2+c x^4}}{35 x^5}","\frac{2 b \left(b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{35 a^2 x}-\frac{2 b \sqrt{c} x \left(b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{35 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a} \sqrt{c} \left(b^2-20 a c\right)+2 b \left(b^2-8 a c\right)\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{70 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 b \sqrt[4]{c} \left(b^2-8 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{35 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{\left(b^2-20 a c\right) \sqrt{a+b x^2+c x^4}}{35 a x^3}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{7 x^7}-\frac{3 \left(b+10 c x^2\right) \sqrt{a+b x^2+c x^4}}{35 x^5}",1,"-((b^2 - 20*a*c)*Sqrt[a + b*x^2 + c*x^4])/(35*a*x^3) + (2*b*(b^2 - 8*a*c)*Sqrt[a + b*x^2 + c*x^4])/(35*a^2*x) - (2*b*Sqrt[c]*(b^2 - 8*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(35*a^2*(Sqrt[a] + Sqrt[c]*x^2)) - (3*(b + 10*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(35*x^5) - (a + b*x^2 + c*x^4)^(3/2)/(7*x^7) + (2*b*c^(1/4)*(b^2 - 8*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(35*a^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - (c^(1/4)*(Sqrt[a]*Sqrt[c]*(b^2 - 20*a*c) + 2*b*(b^2 - 8*a*c))*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(70*a^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",7,6,20,0.3000,1,"{1117, 1271, 1281, 1197, 1103, 1195}"
954,1,48,0,0.0425514,"\int \sqrt{3-2 x^2-x^4} \, dx","Int[Sqrt[3 - 2*x^2 - x^4],x]","\frac{1}{3} \sqrt{-x^4-2 x^2+3} x+\frac{4 F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}-\frac{2 E\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}","\frac{1}{3} \sqrt{-x^4-2 x^2+3} x+\frac{4 F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}-\frac{2 E\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"(x*Sqrt[3 - 2*x^2 - x^4])/3 - (2*EllipticE[ArcSin[x], -1/3])/Sqrt[3] + (4*EllipticF[ArcSin[x], -1/3])/Sqrt[3]","A",5,5,16,0.3125,1,"{1091, 1180, 524, 424, 419}"
955,1,121,0,0.1143965,"\int \frac{x^7}{\sqrt{a+b x^2+c x^4}} \, dx","Int[x^7/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(-16 a c+15 b^2-10 b c x^2\right) \sqrt{a+b x^2+c x^4}}{48 c^3}-\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{7/2}}+\frac{x^4 \sqrt{a+b x^2+c x^4}}{6 c}","\frac{\left(-16 a c+15 b^2-10 b c x^2\right) \sqrt{a+b x^2+c x^4}}{48 c^3}-\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{7/2}}+\frac{x^4 \sqrt{a+b x^2+c x^4}}{6 c}",1,"(x^4*Sqrt[a + b*x^2 + c*x^4])/(6*c) + ((15*b^2 - 16*a*c - 10*b*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(48*c^3) - (b*(5*b^2 - 12*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(7/2))","A",5,5,20,0.2500,1,"{1114, 742, 779, 621, 206}"
956,1,104,0,0.0990005,"\int \frac{x^5}{\sqrt{a+b x^2+c x^4}} \, dx","Int[x^5/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{3 b \sqrt{a+b x^2+c x^4}}{8 c^2}+\frac{x^2 \sqrt{a+b x^2+c x^4}}{4 c}","\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{3 b \sqrt{a+b x^2+c x^4}}{8 c^2}+\frac{x^2 \sqrt{a+b x^2+c x^4}}{4 c}",1,"(-3*b*Sqrt[a + b*x^2 + c*x^4])/(8*c^2) + (x^2*Sqrt[a + b*x^2 + c*x^4])/(4*c) + ((3*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*c^(5/2))","A",5,5,20,0.2500,1,"{1114, 742, 640, 621, 206}"
957,1,68,0,0.0539312,"\int \frac{x^3}{\sqrt{a+b x^2+c x^4}} \, dx","Int[x^3/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\sqrt{a+b x^2+c x^4}}{2 c}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2}}","\frac{\sqrt{a+b x^2+c x^4}}{2 c}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2}}",1,"Sqrt[a + b*x^2 + c*x^4]/(2*c) - (b*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*c^(3/2))","A",4,4,20,0.2000,1,"{1114, 640, 621, 206}"
958,1,43,0,0.031136,"\int \frac{x}{\sqrt{a+b x^2+c x^4}} \, dx","Int[x/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c}}",1,"ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])]/(2*Sqrt[c])","A",3,3,18,0.1667,1,"{1107, 621, 206}"
959,1,44,0,0.0409892,"\int \frac{1}{x \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])]/(2*Sqrt[a])","A",3,3,20,0.1500,1,"{1114, 724, 206}"
960,1,72,0,0.0611296,"\int \frac{1}{x^3 \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x^3*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{3/2}}-\frac{\sqrt{a+b x^2+c x^4}}{2 a x^2}","\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{3/2}}-\frac{\sqrt{a+b x^2+c x^4}}{2 a x^2}",1,"-Sqrt[a + b*x^2 + c*x^4]/(2*a*x^2) + (b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*a^(3/2))","A",4,4,20,0.2000,1,"{1114, 730, 724, 206}"
961,1,108,0,0.1054004,"\int \frac{1}{x^5 \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x^5*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{5/2}}+\frac{3 b \sqrt{a+b x^2+c x^4}}{8 a^2 x^2}-\frac{\sqrt{a+b x^2+c x^4}}{4 a x^4}","-\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{5/2}}+\frac{3 b \sqrt{a+b x^2+c x^4}}{8 a^2 x^2}-\frac{\sqrt{a+b x^2+c x^4}}{4 a x^4}",1,"-Sqrt[a + b*x^2 + c*x^4]/(4*a*x^4) + (3*b*Sqrt[a + b*x^2 + c*x^4])/(8*a^2*x^2) - ((3*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(16*a^(5/2))","A",5,5,20,0.2500,1,"{1114, 744, 806, 724, 206}"
962,1,145,0,0.1659684,"\int \frac{1}{x^7 \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x^7*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{\left(15 b^2-16 a c\right) \sqrt{a+b x^2+c x^4}}{48 a^3 x^2}+\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{7/2}}+\frac{5 b \sqrt{a+b x^2+c x^4}}{24 a^2 x^4}-\frac{\sqrt{a+b x^2+c x^4}}{6 a x^6}","-\frac{\left(15 b^2-16 a c\right) \sqrt{a+b x^2+c x^4}}{48 a^3 x^2}+\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{7/2}}+\frac{5 b \sqrt{a+b x^2+c x^4}}{24 a^2 x^4}-\frac{\sqrt{a+b x^2+c x^4}}{6 a x^6}",1,"-Sqrt[a + b*x^2 + c*x^4]/(6*a*x^6) + (5*b*Sqrt[a + b*x^2 + c*x^4])/(24*a^2*x^4) - ((15*b^2 - 16*a*c)*Sqrt[a + b*x^2 + c*x^4])/(48*a^3*x^2) + (b*(5*b^2 - 12*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(32*a^(7/2))","A",6,6,20,0.3000,1,"{1114, 744, 834, 806, 724, 206}"
963,1,313,0,0.1134609,"\int \frac{x^4}{\sqrt{a+b x^2+c x^4}} \, dx","Int[x^4/Sqrt[a + b*x^2 + c*x^4],x]","-\frac{2 b x \sqrt{a+b x^2+c x^4}}{3 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a} \sqrt{c}+2 b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{a} b \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{x \sqrt{a+b x^2+c x^4}}{3 c}","-\frac{2 b x \sqrt{a+b x^2+c x^4}}{3 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a} \sqrt{c}+2 b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 \sqrt[4]{a} b \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{x \sqrt{a+b x^2+c x^4}}{3 c}",1,"(x*Sqrt[a + b*x^2 + c*x^4])/(3*c) - (2*b*x*Sqrt[a + b*x^2 + c*x^4])/(3*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) + (2*a^(1/4)*b*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*c^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - (a^(1/4)*(2*b + Sqrt[a]*Sqrt[c])*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*c^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,20,0.2000,1,"{1122, 1197, 1103, 1195}"
964,1,267,0,0.0689026,"\int \frac{x^2}{\sqrt{a+b x^2+c x^4}} \, dx","Int[x^2/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(x*Sqrt[a + b*x^2 + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(c^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*c^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",3,3,20,0.1500,1,"{1139, 1103, 1195}"
965,1,114,0,0.0138488,"\int \frac{1}{\sqrt{a+b x^2+c x^4}} \, dx","Int[1/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}",1,"((Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(1/4)*c^(1/4)*Sqrt[a + b*x^2 + c*x^4])","A",1,1,16,0.06250,1,"{1103}"
966,1,294,0,0.1164595,"\int \frac{1}{x^2 \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x^2*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{\sqrt{c} x \sqrt{a+b x^2+c x^4}}{a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt{a+b x^2+c x^4}}{a x}","\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{\sqrt{c} x \sqrt{a+b x^2+c x^4}}{a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt{a+b x^2+c x^4}}{a x}",1,"-(Sqrt[a + b*x^2 + c*x^4]/(a*x)) + (Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(a*(Sqrt[a] + Sqrt[c]*x^2)) - (c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + (c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1123, 12, 1139, 1103, 1195}"
967,1,345,0,0.1564359,"\int \frac{1}{x^4 \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x^4*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{2 b \sqrt{a+b x^2+c x^4}}{3 a^2 x}-\frac{2 b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{3 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a} \sqrt{c}+2 b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt{a+b x^2+c x^4}}{3 a x^3}","\frac{2 b \sqrt{a+b x^2+c x^4}}{3 a^2 x}-\frac{2 b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{3 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a} \sqrt{c}+2 b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{6 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{2 b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt{a+b x^2+c x^4}}{3 a x^3}",1,"-Sqrt[a + b*x^2 + c*x^4]/(3*a*x^3) + (2*b*Sqrt[a + b*x^2 + c*x^4])/(3*a^2*x) - (2*b*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(3*a^2*(Sqrt[a] + Sqrt[c]*x^2)) + (2*b*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*a^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - ((2*b + Sqrt[a]*Sqrt[c])*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*a^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1123, 1281, 1197, 1103, 1195}"
968,1,124,0,0.1130008,"\int \frac{x^7}{\sqrt{a+b x^2-c x^4}} \, dx","Int[x^7/Sqrt[a + b*x^2 - c*x^4],x]","-\frac{\left(16 a c+15 b^2+10 b c x^2\right) \sqrt{a+b x^2-c x^4}}{48 c^3}-\frac{b \left(12 a c+5 b^2\right) \tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{32 c^{7/2}}-\frac{x^4 \sqrt{a+b x^2-c x^4}}{6 c}","-\frac{\left(16 a c+15 b^2+10 b c x^2\right) \sqrt{a+b x^2-c x^4}}{48 c^3}-\frac{b \left(12 a c+5 b^2\right) \tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{32 c^{7/2}}-\frac{x^4 \sqrt{a+b x^2-c x^4}}{6 c}",1,"-(x^4*Sqrt[a + b*x^2 - c*x^4])/(6*c) - ((15*b^2 + 16*a*c + 10*b*c*x^2)*Sqrt[a + b*x^2 - c*x^4])/(48*c^3) - (b*(5*b^2 + 12*a*c)*ArcTan[(b - 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4])])/(32*c^(7/2))","A",5,5,21,0.2381,1,"{1114, 742, 779, 621, 204}"
969,1,107,0,0.0927536,"\int \frac{x^5}{\sqrt{a+b x^2-c x^4}} \, dx","Int[x^5/Sqrt[a + b*x^2 - c*x^4],x]","-\frac{\left(4 a c+3 b^2\right) \tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{16 c^{5/2}}-\frac{3 b \sqrt{a+b x^2-c x^4}}{8 c^2}-\frac{x^2 \sqrt{a+b x^2-c x^4}}{4 c}","-\frac{\left(4 a c+3 b^2\right) \tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{16 c^{5/2}}-\frac{3 b \sqrt{a+b x^2-c x^4}}{8 c^2}-\frac{x^2 \sqrt{a+b x^2-c x^4}}{4 c}",1,"(-3*b*Sqrt[a + b*x^2 - c*x^4])/(8*c^2) - (x^2*Sqrt[a + b*x^2 - c*x^4])/(4*c) - ((3*b^2 + 4*a*c)*ArcTan[(b - 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4])])/(16*c^(5/2))","A",5,5,21,0.2381,1,"{1114, 742, 640, 621, 204}"
970,1,70,0,0.0581514,"\int \frac{x^3}{\sqrt{a+b x^2-c x^4}} \, dx","Int[x^3/Sqrt[a + b*x^2 - c*x^4],x]","-\frac{b \tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{4 c^{3/2}}-\frac{\sqrt{a+b x^2-c x^4}}{2 c}","-\frac{b \tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{4 c^{3/2}}-\frac{\sqrt{a+b x^2-c x^4}}{2 c}",1,"-Sqrt[a + b*x^2 - c*x^4]/(2*c) - (b*ArcTan[(b - 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4])])/(4*c^(3/2))","A",4,4,21,0.1905,1,"{1114, 640, 621, 204}"
971,1,44,0,0.0382176,"\int \frac{x}{\sqrt{a+b x^2-c x^4}} \, dx","Int[x/Sqrt[a + b*x^2 - c*x^4],x]","-\frac{\tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{2 \sqrt{c}}","-\frac{\tan ^{-1}\left(\frac{b-2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2-c x^4}}\right)}{2 \sqrt{c}}",1,"-ArcTan[(b - 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4])]/(2*Sqrt[c])","A",3,3,19,0.1579,1,"{1107, 621, 204}"
972,1,47,0,0.042422,"\int \frac{1}{x \sqrt{-a+b x^2+c x^4}} \, dx","Int[1/(x*Sqrt[-a + b*x^2 + c*x^4]),x]","-\frac{\tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{2 \sqrt{a}}","-\frac{\tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{2 \sqrt{a}}",1,"-ArcTan[(2*a - b*x^2)/(2*Sqrt[a]*Sqrt[-a + b*x^2 + c*x^4])]/(2*Sqrt[a])","A",3,3,22,0.1364,1,"{1114, 724, 204}"
973,1,77,0,0.0619014,"\int \frac{1}{x^3 \sqrt{-a+b x^2+c x^4}} \, dx","Int[1/(x^3*Sqrt[-a + b*x^2 + c*x^4]),x]","\frac{\sqrt{-a+b x^2+c x^4}}{2 a x^2}-\frac{b \tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{4 a^{3/2}}","\frac{\sqrt{-a+b x^2+c x^4}}{2 a x^2}-\frac{b \tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{4 a^{3/2}}",1,"Sqrt[-a + b*x^2 + c*x^4]/(2*a*x^2) - (b*ArcTan[(2*a - b*x^2)/(2*Sqrt[a]*Sqrt[-a + b*x^2 + c*x^4])])/(4*a^(3/2))","A",4,4,22,0.1818,1,"{1114, 730, 724, 204}"
974,1,115,0,0.1234754,"\int \frac{1}{x^5 \sqrt{-a+b x^2+c x^4}} \, dx","Int[1/(x^5*Sqrt[-a + b*x^2 + c*x^4]),x]","-\frac{\left(4 a c+3 b^2\right) \tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{16 a^{5/2}}+\frac{3 b \sqrt{-a+b x^2+c x^4}}{8 a^2 x^2}+\frac{\sqrt{-a+b x^2+c x^4}}{4 a x^4}","-\frac{\left(4 a c+3 b^2\right) \tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{16 a^{5/2}}+\frac{3 b \sqrt{-a+b x^2+c x^4}}{8 a^2 x^2}+\frac{\sqrt{-a+b x^2+c x^4}}{4 a x^4}",1,"Sqrt[-a + b*x^2 + c*x^4]/(4*a*x^4) + (3*b*Sqrt[-a + b*x^2 + c*x^4])/(8*a^2*x^2) - ((3*b^2 + 4*a*c)*ArcTan[(2*a - b*x^2)/(2*Sqrt[a]*Sqrt[-a + b*x^2 + c*x^4])])/(16*a^(5/2))","A",5,5,22,0.2273,1,"{1114, 744, 806, 724, 204}"
975,1,154,0,0.1716208,"\int \frac{1}{x^7 \sqrt{-a+b x^2+c x^4}} \, dx","Int[1/(x^7*Sqrt[-a + b*x^2 + c*x^4]),x]","\frac{\left(16 a c+15 b^2\right) \sqrt{-a+b x^2+c x^4}}{48 a^3 x^2}-\frac{b \left(12 a c+5 b^2\right) \tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{32 a^{7/2}}+\frac{5 b \sqrt{-a+b x^2+c x^4}}{24 a^2 x^4}+\frac{\sqrt{-a+b x^2+c x^4}}{6 a x^6}","\frac{\left(16 a c+15 b^2\right) \sqrt{-a+b x^2+c x^4}}{48 a^3 x^2}-\frac{b \left(12 a c+5 b^2\right) \tan ^{-1}\left(\frac{2 a-b x^2}{2 \sqrt{a} \sqrt{-a+b x^2+c x^4}}\right)}{32 a^{7/2}}+\frac{5 b \sqrt{-a+b x^2+c x^4}}{24 a^2 x^4}+\frac{\sqrt{-a+b x^2+c x^4}}{6 a x^6}",1,"Sqrt[-a + b*x^2 + c*x^4]/(6*a*x^6) + (5*b*Sqrt[-a + b*x^2 + c*x^4])/(24*a^2*x^4) + ((15*b^2 + 16*a*c)*Sqrt[-a + b*x^2 + c*x^4])/(48*a^3*x^2) - (b*(5*b^2 + 12*a*c)*ArcTan[(2*a - b*x^2)/(2*Sqrt[a]*Sqrt[-a + b*x^2 + c*x^4])])/(32*a^(7/2))","A",6,6,22,0.2727,1,"{1114, 744, 834, 806, 724, 204}"
976,1,409,0,0.5875494,"\int \frac{x^4}{\sqrt{a+b x^2-c x^4}} \, dx","Int[x^4/Sqrt[a + b*x^2 - c*x^4],x]","\frac{\sqrt{\sqrt{4 a c+b^2}+b} \left(-b \sqrt{4 a c+b^2}+a c+b^2\right) \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} c^{5/2} \sqrt{a+b x^2-c x^4}}-\frac{b \left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} c^{5/2} \sqrt{a+b x^2-c x^4}}-\frac{x \sqrt{a+b x^2-c x^4}}{3 c}","\frac{\sqrt{\sqrt{4 a c+b^2}+b} \left(-b \sqrt{4 a c+b^2}+a c+b^2\right) \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} c^{5/2} \sqrt{a+b x^2-c x^4}}-\frac{b \left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} c^{5/2} \sqrt{a+b x^2-c x^4}}-\frac{x \sqrt{a+b x^2-c x^4}}{3 c}",1,"-(x*Sqrt[a + b*x^2 - c*x^4])/(3*c) - (b*(b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticE[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(3*Sqrt[2]*c^(5/2)*Sqrt[a + b*x^2 - c*x^4]) + (Sqrt[b + Sqrt[b^2 + 4*a*c]]*(b^2 + a*c - b*Sqrt[b^2 + 4*a*c])*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(3*Sqrt[2]*c^(5/2)*Sqrt[a + b*x^2 - c*x^4])","A",5,5,21,0.2381,1,"{1122, 1202, 524, 424, 419}"
977,1,377,0,0.24461,"\int \frac{x^2}{\sqrt{a+b x^2-c x^4}} \, dx","Int[x^2/Sqrt[a + b*x^2 - c*x^4],x]","\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{a+b x^2-c x^4}}-\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{a+b x^2-c x^4}}","\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{a+b x^2-c x^4}}-\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{a+b x^2-c x^4}}",1,"-((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticE[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(2*Sqrt[2]*c^(3/2)*Sqrt[a + b*x^2 - c*x^4]) + ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(2*Sqrt[2]*c^(3/2)*Sqrt[a + b*x^2 - c*x^4])","A",4,4,21,0.1905,1,"{1140, 493, 424, 419}"
978,1,169,0,0.0663954,"\int \frac{1}{\sqrt{a+b x^2-c x^4}} \, dx","Int[1/Sqrt[a + b*x^2 - c*x^4],x]","\frac{\sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{a+b x^2-c x^4}}","\frac{\sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{a+b x^2-c x^4}}",1,"(Sqrt[b + Sqrt[b^2 + 4*a*c]]*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(Sqrt[2]*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4])","A",2,2,17,0.1176,1,"{1104, 419}"
979,1,408,0,0.3317773,"\int \frac{1}{x^2 \sqrt{a+b x^2-c x^4}} \, dx","Int[1/(x^2*Sqrt[a + b*x^2 - c*x^4]),x]","-\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} a \sqrt{c} \sqrt{a+b x^2-c x^4}}+\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} a \sqrt{c} \sqrt{a+b x^2-c x^4}}-\frac{\sqrt{a+b x^2-c x^4}}{a x}","-\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} a \sqrt{c} \sqrt{a+b x^2-c x^4}}+\frac{\left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} a \sqrt{c} \sqrt{a+b x^2-c x^4}}-\frac{\sqrt{a+b x^2-c x^4}}{a x}",1,"-(Sqrt[a + b*x^2 - c*x^4]/(a*x)) + ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticE[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(2*Sqrt[2]*a*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4]) - ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(2*Sqrt[2]*a*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4])","A",6,6,21,0.2857,1,"{1123, 12, 1140, 493, 424, 419}"
980,1,445,0,0.4694041,"\int \frac{1}{x^4 \sqrt{a+b x^2-c x^4}} \, dx","Int[1/(x^4*Sqrt[a + b*x^2 - c*x^4]),x]","\frac{\sqrt{\sqrt{4 a c+b^2}+b} \left(-b \sqrt{4 a c+b^2}+a c+b^2\right) \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} a^2 \sqrt{c} \sqrt{a+b x^2-c x^4}}-\frac{b \left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} a^2 \sqrt{c} \sqrt{a+b x^2-c x^4}}+\frac{2 b \sqrt{a+b x^2-c x^4}}{3 a^2 x}-\frac{\sqrt{a+b x^2-c x^4}}{3 a x^3}","\frac{\sqrt{\sqrt{4 a c+b^2}+b} \left(-b \sqrt{4 a c+b^2}+a c+b^2\right) \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} a^2 \sqrt{c} \sqrt{a+b x^2-c x^4}}-\frac{b \left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \sqrt{1-\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}} \sqrt{1-\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|\frac{b+\sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{3 \sqrt{2} a^2 \sqrt{c} \sqrt{a+b x^2-c x^4}}+\frac{2 b \sqrt{a+b x^2-c x^4}}{3 a^2 x}-\frac{\sqrt{a+b x^2-c x^4}}{3 a x^3}",1,"-Sqrt[a + b*x^2 - c*x^4]/(3*a*x^3) + (2*b*Sqrt[a + b*x^2 - c*x^4])/(3*a^2*x) - (b*(b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticE[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(3*Sqrt[2]*a^2*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4]) + (Sqrt[b + Sqrt[b^2 + 4*a*c]]*(b^2 + a*c - b*Sqrt[b^2 + 4*a*c])*Sqrt[1 - (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])]*Sqrt[1 - (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c])]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (b + Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(3*Sqrt[2]*a^2*Sqrt[c]*Sqrt[a + b*x^2 - c*x^4])","A",6,6,21,0.2857,1,"{1123, 1281, 1202, 524, 424, 419}"
981,1,190,0,0.2371954,"\int \frac{x^9}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^9/(a + b*x^2 + c*x^4)^(3/2),x]","-\frac{\left(b \left(15 b^2-52 a c\right)-2 c x^2 \left(5 b^2-12 a c\right)\right) \sqrt{a+b x^2+c x^4}}{8 c^3 \left(b^2-4 a c\right)}+\frac{3 \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{7/2}}+\frac{x^6 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b x^4 \sqrt{a+b x^2+c x^4}}{c \left(b^2-4 a c\right)}","-\frac{\left(b \left(15 b^2-52 a c\right)-2 c x^2 \left(5 b^2-12 a c\right)\right) \sqrt{a+b x^2+c x^4}}{8 c^3 \left(b^2-4 a c\right)}+\frac{3 \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{7/2}}+\frac{x^6 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b x^4 \sqrt{a+b x^2+c x^4}}{c \left(b^2-4 a c\right)}",1,"(x^6*(2*a + b*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (b*x^4*Sqrt[a + b*x^2 + c*x^4])/(c*(b^2 - 4*a*c)) - ((b*(15*b^2 - 52*a*c) - 2*c*(5*b^2 - 12*a*c)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*c^3*(b^2 - 4*a*c)) + (3*(5*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*c^(7/2))","A",6,6,20,0.3000,1,"{1114, 738, 832, 779, 621, 206}"
982,1,134,0,0.1112916,"\int \frac{x^7}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^7/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{\left(-8 a c+3 b^2-2 b c x^2\right) \sqrt{a+b x^2+c x^4}}{2 c^2 \left(b^2-4 a c\right)}+\frac{x^4 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{3 b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{5/2}}","\frac{\left(-8 a c+3 b^2-2 b c x^2\right) \sqrt{a+b x^2+c x^4}}{2 c^2 \left(b^2-4 a c\right)}+\frac{x^4 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{3 b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{5/2}}",1,"(x^4*(2*a + b*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) + ((3*b^2 - 8*a*c - 2*b*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(2*c^2*(b^2 - 4*a*c)) - (3*b*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*c^(5/2))","A",5,5,20,0.2500,1,"{1114, 738, 779, 621, 206}"
983,1,115,0,0.0922341,"\int \frac{x^5}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^5/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{x^2 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{a+b x^2+c x^4}}{c \left(b^2-4 a c\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 c^{3/2}}","\frac{x^2 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{a+b x^2+c x^4}}{c \left(b^2-4 a c\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 c^{3/2}}",1,"(x^2*(2*a + b*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (b*Sqrt[a + b*x^2 + c*x^4])/(c*(b^2 - 4*a*c)) + ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])]/(2*c^(3/2))","A",5,5,20,0.2500,1,"{1114, 738, 640, 621, 206}"
984,1,36,0,0.028675,"\int \frac{x^3}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^3/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 a+b x^2}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","\frac{2 a+b x^2}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(2*a + b*x^2)/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])","A",2,2,20,0.1000,1,"{1114, 636}"
985,1,36,0,0.0231567,"\int \frac{x}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x/(a + b*x^2 + c*x^4)^(3/2),x]","-\frac{b+2 c x^2}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","-\frac{b+2 c x^2}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"-((b + 2*c*x^2)/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]))","A",2,2,18,0.1111,1,"{1107, 613}"
986,1,89,0,0.0808448,"\int \frac{1}{x \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{-2 a c+b^2+b c x^2}{a \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 a^{3/2}}","\frac{-2 a c+b^2+b c x^2}{a \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 a^{3/2}}",1,"(b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])]/(2*a^(3/2))","A",5,5,20,0.2500,1,"{1114, 740, 12, 724, 206}"
987,1,139,0,0.1259077,"\int \frac{1}{x^3 \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^2 + c*x^4)^(3/2)),x]","-\frac{\left(3 b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{2 a^2 x^2 \left(b^2-4 a c\right)}+\frac{3 b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{5/2}}+\frac{-2 a c+b^2+b c x^2}{a x^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","-\frac{\left(3 b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{2 a^2 x^2 \left(b^2-4 a c\right)}+\frac{3 b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{5/2}}+\frac{-2 a c+b^2+b c x^2}{a x^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*x^2*Sqrt[a + b*x^2 + c*x^4]) - ((3*b^2 - 8*a*c)*Sqrt[a + b*x^2 + c*x^4])/(2*a^2*(b^2 - 4*a*c)*x^2) + (3*b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*a^(5/2))","A",5,5,20,0.2500,1,"{1114, 740, 806, 724, 206}"
988,1,195,0,0.2112984,"\int \frac{1}{x^5 \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^5*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{b \left(15 b^2-52 a c\right) \sqrt{a+b x^2+c x^4}}{8 a^3 x^2 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-12 a c\right) \sqrt{a+b x^2+c x^4}}{4 a^2 x^4 \left(b^2-4 a c\right)}-\frac{3 \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{7/2}}+\frac{-2 a c+b^2+b c x^2}{a x^4 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","\frac{b \left(15 b^2-52 a c\right) \sqrt{a+b x^2+c x^4}}{8 a^3 x^2 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-12 a c\right) \sqrt{a+b x^2+c x^4}}{4 a^2 x^4 \left(b^2-4 a c\right)}-\frac{3 \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{7/2}}+\frac{-2 a c+b^2+b c x^2}{a x^4 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*x^4*Sqrt[a + b*x^2 + c*x^4]) - ((5*b^2 - 12*a*c)*Sqrt[a + b*x^2 + c*x^4])/(4*a^2*(b^2 - 4*a*c)*x^4) + (b*(15*b^2 - 52*a*c)*Sqrt[a + b*x^2 + c*x^4])/(8*a^3*(b^2 - 4*a*c)*x^2) - (3*(5*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(16*a^(7/2))","A",6,6,20,0.3000,1,"{1114, 740, 834, 806, 724, 206}"
989,1,408,0,0.2097125,"\int \frac{x^6}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^6/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{c^{3/2} \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{a} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{x^3 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b x \sqrt{a+b x^2+c x^4}}{c \left(b^2-4 a c\right)}","\frac{2 x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{c^{3/2} \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{a} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{x^3 \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b x \sqrt{a+b x^2+c x^4}}{c \left(b^2-4 a c\right)}",1,"(x^3*(2*a + b*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (b*x*Sqrt[a + b*x^2 + c*x^4])/(c*(b^2 - 4*a*c)) + (2*(b^2 - 3*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(c^(3/2)*(b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)) - (2*a^(1/4)*(b^2 - 3*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(c^(7/4)*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(2*b^2 + Sqrt[a]*b*Sqrt[c] - 6*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*c^(7/4)*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1120, 1279, 1197, 1103, 1195}"
990,1,342,0,0.1300481,"\int \frac{x^4}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^4/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{\sqrt[4]{a} b \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{x \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}","\frac{\sqrt[4]{a} b \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{b x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{x \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}",1,"(x*(2*a + b*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (b*x*Sqrt[a + b*x^2 + c*x^4])/(Sqrt[c]*(b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)) + (a^(1/4)*b*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(c^(3/4)*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (a^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*(b - 2*Sqrt[a]*Sqrt[c])*c^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,20,0.2000,1,"{1120, 1197, 1103, 1195}"
991,1,341,0,0.1252425,"\int \frac{x^2}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^2/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 \sqrt{c} x \sqrt{a+b x^2+c x^4}}{\left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{x \left(b+2 c x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}","\frac{2 \sqrt{c} x \sqrt{a+b x^2+c x^4}}{\left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{x \left(b+2 c x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}",1,"-((x*(b + 2*c*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])) + (2*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/((b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)) - (2*a^(1/4)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) + ((Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(1/4)*(b - 2*Sqrt[a]*Sqrt[c])*c^(1/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,20,0.2000,1,"{1119, 1197, 1103, 1195}"
992,1,353,0,0.1351209,"\int \frac{1}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(a + b*x^2 + c*x^4)^(-3/2),x]","\frac{b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{a \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{x \left(-2 a c+b^2+b c x^2\right)}{a \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","\frac{b \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}-\frac{b \sqrt{c} x \sqrt{a+b x^2+c x^4}}{a \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{x \left(-2 a c+b^2+b c x^2\right)}{a \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(x*(b^2 - 2*a*c + b*c*x^2))/(a*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (b*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(a*(b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)) + (b*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(3/4)*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(3/4)*(b - 2*Sqrt[a]*Sqrt[c])*Sqrt[a + b*x^2 + c*x^4])","A",4,4,16,0.2500,1,"{1092, 1197, 1103, 1195}"
993,1,428,0,0.2169414,"\int \frac{1}{x^2 \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^2 + c*x^4)^(3/2)),x]","-\frac{2 \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{a^2 x \left(b^2-4 a c\right)}+\frac{2 \sqrt{c} x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{a^2 \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{c} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{-2 a c+b^2+b c x^2}{a x \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","-\frac{2 \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{a^2 x \left(b^2-4 a c\right)}+\frac{2 \sqrt{c} x \left(b^2-3 a c\right) \sqrt{a+b x^2+c x^4}}{a^2 \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{a} b \sqrt{c}-6 a c+2 b^2\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{2 \sqrt[4]{c} \left(b^2-3 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{7/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{-2 a c+b^2+b c x^2}{a x \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*x*Sqrt[a + b*x^2 + c*x^4]) - (2*(b^2 - 3*a*c)*Sqrt[a + b*x^2 + c*x^4])/(a^2*(b^2 - 4*a*c)*x) + (2*Sqrt[c]*(b^2 - 3*a*c)*x*Sqrt[a + b*x^2 + c*x^4])/(a^2*(b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)) - (2*c^(1/4)*(b^2 - 3*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(7/4)*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) + (c^(1/4)*(2*b^2 + Sqrt[a]*b*Sqrt[c] - 6*a*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(7/4)*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,20,0.2500,1,"{1121, 1281, 1197, 1103, 1195}"
994,1,50,0,0.0677387,"\int \frac{x^4}{\sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[x^4/Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4],x]","\frac{x \sqrt{b x^2+c x^4}}{3 c}-\frac{2 b \sqrt{b x^2+c x^4}}{3 c^2 x}","\frac{x \sqrt{b x^2+c x^4}}{3 c}-\frac{2 b \sqrt{b x^2+c x^4}}{3 c^2 x}",1,"(-2*b*Sqrt[b*x^2 + c*x^4])/(3*c^2*x) + (x*Sqrt[b*x^2 + c*x^4])/(3*c)","A",3,3,28,0.1071,1,"{3, 2016, 1588}"
995,1,58,0,0.0836604,"\int \frac{x^3}{\sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[x^3/Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4],x]","\frac{\sqrt{b x^2+c x^4}}{2 c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{3/2}}","\frac{\sqrt{b x^2+c x^4}}{2 c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{3/2}}",1,"Sqrt[b*x^2 + c*x^4]/(2*c) - (b*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2*c^(3/2))","A",5,5,28,0.1786,1,"{3, 2018, 640, 620, 206}"
996,1,22,0,0.0174382,"\int \frac{x^2}{\sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[x^2/Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4],x]","\frac{\sqrt{b x^2+c x^4}}{c x}","\frac{\sqrt{b x^2+c x^4}}{c x}",1,"Sqrt[b*x^2 + c*x^4]/(c*x)","A",2,2,28,0.07143,1,"{3, 1588}"
997,1,31,0,0.0489377,"\int \frac{x}{\sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[x/Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{c}}",1,"ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]]/Sqrt[c]","A",4,4,26,0.1538,1,"{3, 2013, 620, 206}"
998,1,30,0,0.0099777,"\int \frac{1}{\sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[1/Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{b}}",1,"-(ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]]/Sqrt[b])","A",3,3,24,0.1250,1,"{3, 2008, 206}"
999,1,23,0,0.0400943,"\int \frac{1}{x \sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[1/(x*Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4]),x]","-\frac{\sqrt{b x^2+c x^4}}{b x^2}","-\frac{\sqrt{b x^2+c x^4}}{b x^2}",1,"-(Sqrt[b*x^2 + c*x^4]/(b*x^2))","A",2,2,28,0.07143,1,"{3, 2014}"
1000,1,59,0,0.05555,"\int \frac{1}{x^2 \sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[1/(x^2*Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4]),x]","\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{3/2}}-\frac{\sqrt{b x^2+c x^4}}{2 b x^3}","\frac{c \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{3/2}}-\frac{\sqrt{b x^2+c x^4}}{2 b x^3}",1,"-Sqrt[b*x^2 + c*x^4]/(2*b*x^3) + (c*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(2*b^(3/2))","A",4,4,28,0.1429,1,"{3, 2025, 2008, 206}"
1001,1,52,0,0.0837913,"\int \frac{1}{x^3 \sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[1/(x^3*Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4]),x]","\frac{2 c \sqrt{b x^2+c x^4}}{3 b^2 x^2}-\frac{\sqrt{b x^2+c x^4}}{3 b x^4}","\frac{2 c \sqrt{b x^2+c x^4}}{3 b^2 x^2}-\frac{\sqrt{b x^2+c x^4}}{3 b x^4}",1,"-Sqrt[b*x^2 + c*x^4]/(3*b*x^4) + (2*c*Sqrt[b*x^2 + c*x^4])/(3*b^2*x^2)","A",3,3,28,0.1071,1,"{3, 2016, 2014}"
1002,1,87,0,0.0995023,"\int \frac{1}{x^4 \sqrt{2+2 a-2 (1+a)+b x^2+c x^4}} \, dx","Int[1/(x^4*Sqrt[2 + 2*a - 2*(1 + a) + b*x^2 + c*x^4]),x]","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{5/2}}+\frac{3 c \sqrt{b x^2+c x^4}}{8 b^2 x^3}-\frac{\sqrt{b x^2+c x^4}}{4 b x^5}","-\frac{3 c^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{5/2}}+\frac{3 c \sqrt{b x^2+c x^4}}{8 b^2 x^3}-\frac{\sqrt{b x^2+c x^4}}{4 b x^5}",1,"-Sqrt[b*x^2 + c*x^4]/(4*b*x^5) + (3*c*Sqrt[b*x^2 + c*x^4])/(8*b^2*x^3) - (3*c^2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*b^(5/2))","A",5,4,28,0.1429,1,"{3, 2025, 2008, 206}"
1003,1,108,0,0.0251027,"\int \frac{x^4}{\sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[x^4/Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4],x]","\frac{x \sqrt{a+c x^4}}{3 c}-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 c^{5/4} \sqrt{a+c x^4}}","\frac{x \sqrt{a+c x^4}}{3 c}-\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 c^{5/4} \sqrt{a+c x^4}}",1,"(x*Sqrt[a + c*x^4])/(3*c) - (a^(3/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(6*c^(5/4)*Sqrt[a + c*x^4])","A",3,3,29,0.1034,1,"{4, 321, 220}"
1004,1,18,0,0.0044898,"\int \frac{x^3}{\sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[x^3/Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4],x]","\frac{\sqrt{a+c x^4}}{2 c}","\frac{\sqrt{a+c x^4}}{2 c}",1,"Sqrt[a + c*x^4]/(2*c)","A",2,2,29,0.06897,1,"{4, 261}"
1005,1,210,0,0.0533998,"\int \frac{x^2}{\sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[x^2/Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{3/4} \sqrt{a+c x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{a+c x^4}}+\frac{x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{3/4} \sqrt{a+c x^4}}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{a+c x^4}}+\frac{x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(x*Sqrt[a + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(c^(3/4)*Sqrt[a + c*x^4]) + (a^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*c^(3/4)*Sqrt[a + c*x^4])","A",4,4,29,0.1379,1,"{4, 305, 220, 1196}"
1006,1,30,0,0.0161084,"\int \frac{x}{\sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[x/Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}",1,"ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]]/(2*Sqrt[c])","A",4,4,27,0.1481,1,"{4, 275, 217, 206}"
1007,1,88,0,0.0097947,"\int \frac{1}{\sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[1/Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4],x]","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+c x^4}}","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+c x^4}}",1,"((Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*c^(1/4)*Sqrt[a + c*x^4])","A",2,2,25,0.08000,1,"{4, 220}"
1008,1,27,0,0.0199715,"\int \frac{1}{x \sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[1/(x*Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+c x^4}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[Sqrt[a + c*x^4]/Sqrt[a]]/(2*Sqrt[a])","A",4,4,29,0.1379,1,"{4, 266, 63, 208}"
1009,1,232,0,0.0717008,"\int \frac{1}{x^2 \sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[1/(x^2*Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4]),x]","\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt{a+c x^4}}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+c x^4}}+\frac{\sqrt{c} x \sqrt{a+c x^4}}{a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt{a+c x^4}}{a x}","\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} \sqrt{a+c x^4}}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a+c x^4}}+\frac{\sqrt{c} x \sqrt{a+c x^4}}{a \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt{a+c x^4}}{a x}",1,"-(Sqrt[a + c*x^4]/(a*x)) + (Sqrt[c]*x*Sqrt[a + c*x^4])/(a*(Sqrt[a] + Sqrt[c]*x^2)) - (c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a + c*x^4]) + (c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*Sqrt[a + c*x^4])","A",5,5,29,0.1724,1,"{4, 325, 305, 220, 1196}"
1010,1,21,0,0.0046456,"\int \frac{1}{x^3 \sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[1/(x^3*Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4]),x]","-\frac{\sqrt{a+c x^4}}{2 a x^2}","-\frac{\sqrt{a+c x^4}}{2 a x^2}",1,"-Sqrt[a + c*x^4]/(2*a*x^2)","A",2,2,29,0.06897,1,"{4, 264}"
1011,1,110,0,0.022057,"\int \frac{1}{x^4 \sqrt{a+(2+2 b-2 (1+b)) x^2+c x^4}} \, dx","Int[1/(x^4*Sqrt[a + (2 + 2*b - 2*(1 + b))*x^2 + c*x^4]),x]","-\frac{c^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+c x^4}}-\frac{\sqrt{a+c x^4}}{3 a x^3}","-\frac{c^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{5/4} \sqrt{a+c x^4}}-\frac{\sqrt{a+c x^4}}{3 a x^3}",1,"-Sqrt[a + c*x^4]/(3*a*x^3) - (c^(3/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(6*a^(5/4)*Sqrt[a + c*x^4])","A",3,3,29,0.1034,1,"{4, 325, 220}"
1012,1,73,0,0.022045,"\int \frac{x^4}{\sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x^4/Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}-\frac{3 a x \sqrt{a+b x^2}}{8 b^2}+\frac{x^3 \sqrt{a+b x^2}}{4 b}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}-\frac{3 a x \sqrt{a+b x^2}}{8 b^2}+\frac{x^3 \sqrt{a+b x^2}}{4 b}",1,"(-3*a*x*Sqrt[a + b*x^2])/(8*b^2) + (x^3*Sqrt[a + b*x^2])/(4*b) + (3*a^2*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(5/2))","A",5,4,29,0.1379,1,"{5, 321, 217, 206}"
1013,1,36,0,0.0225047,"\int \frac{x^3}{\sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x^3/Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{\left(a+b x^2\right)^{3/2}}{3 b^2}-\frac{a \sqrt{a+b x^2}}{b^2}","\frac{\left(a+b x^2\right)^{3/2}}{3 b^2}-\frac{a \sqrt{a+b x^2}}{b^2}",1,"-((a*Sqrt[a + b*x^2])/b^2) + (a + b*x^2)^(3/2)/(3*b^2)","A",4,3,29,0.1034,1,"{5, 266, 43}"
1014,1,49,0,0.0128613,"\int \frac{x^2}{\sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x^2/Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{x \sqrt{a+b x^2}}{2 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}","\frac{x \sqrt{a+b x^2}}{2 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}",1,"(x*Sqrt[a + b*x^2])/(2*b) - (a*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(3/2))","A",4,4,29,0.1379,1,"{5, 321, 217, 206}"
1015,1,15,0,0.0033684,"\int \frac{x}{\sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x/Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{\sqrt{a+b x^2}}{b}","\frac{\sqrt{a+b x^2}}{b}",1,"Sqrt[a + b*x^2]/b","A",2,2,27,0.07407,1,"{5, 261}"
1016,1,25,0,0.0058784,"\int \frac{1}{\sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]/Sqrt[b]","A",3,3,25,0.1200,1,"{5, 217, 206}"
1017,1,25,0,0.01713,"\int \frac{1}{x \sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x*Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]/Sqrt[a])","A",4,4,29,0.1379,1,"{5, 266, 63, 208}"
1018,1,19,0,0.0044502,"\int \frac{1}{x^2 \sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x^2*Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4]),x]","-\frac{\sqrt{a+b x^2}}{a x}","-\frac{\sqrt{a+b x^2}}{a x}",1,"-(Sqrt[a + b*x^2]/(a*x))","A",2,2,29,0.06897,1,"{5, 264}"
1019,1,50,0,0.0269898,"\int \frac{1}{x^3 \sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x^3*Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{\sqrt{a+b x^2}}{2 a x^2}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{\sqrt{a+b x^2}}{2 a x^2}",1,"-Sqrt[a + b*x^2]/(2*a*x^2) + (b*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(3/2))","A",5,5,29,0.1724,1,"{5, 266, 51, 63, 208}"
1020,1,44,0,0.0104717,"\int \frac{1}{x^4 \sqrt{a+b x^2+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x^4*Sqrt[a + b*x^2 + (2 + 2*c - 2*(1 + c))*x^4]),x]","\frac{2 b \sqrt{a+b x^2}}{3 a^2 x}-\frac{\sqrt{a+b x^2}}{3 a x^3}","\frac{2 b \sqrt{a+b x^2}}{3 a^2 x}-\frac{\sqrt{a+b x^2}}{3 a x^3}",1,"-Sqrt[a + b*x^2]/(3*a*x^3) + (2*b*Sqrt[a + b*x^2])/(3*a^2*x)","A",3,3,29,0.1034,1,"{5, 271, 264}"
1021,1,16,0,0.0015658,"\int \frac{x^4}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[x^4/Sqrt[2 + 2*a - 2*(1 + a) + c*x^4],x]","\frac{x^5}{3 \sqrt{c x^4}}","\frac{x^5}{3 \sqrt{c x^4}}",1,"x^5/(3*Sqrt[c*x^4])","A",3,3,23,0.1304,1,"{1, 15, 30}"
1022,1,16,0,0.0017394,"\int \frac{x^3}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[x^3/Sqrt[2 + 2*a - 2*(1 + a) + c*x^4],x]","\frac{x^4}{2 \sqrt{c x^4}}","\frac{x^4}{2 \sqrt{c x^4}}",1,"x^4/(2*Sqrt[c*x^4])","A",3,3,23,0.1304,1,"{1, 15, 30}"
1023,1,13,0,0.0011957,"\int \frac{x^2}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[x^2/Sqrt[2 + 2*a - 2*(1 + a) + c*x^4],x]","\frac{x^3}{\sqrt{c x^4}}","\frac{x^3}{\sqrt{c x^4}}",1,"x^3/Sqrt[c*x^4]","A",3,3,23,0.1304,1,"{1, 15, 8}"
1024,1,15,0,0.0013116,"\int \frac{x}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[x/Sqrt[2 + 2*a - 2*(1 + a) + c*x^4],x]","\frac{x^2 \log (x)}{\sqrt{c x^4}}","\frac{x^2 \log (x)}{\sqrt{c x^4}}",1,"(x^2*Log[x])/Sqrt[c*x^4]","A",3,3,21,0.1429,1,"{1, 15, 29}"
1025,1,12,0,0.0014219,"\int \frac{1}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[1/Sqrt[2 + 2*a - 2*(1 + a) + c*x^4],x]","-\frac{x}{\sqrt{c x^4}}","-\frac{x}{\sqrt{c x^4}}",1,"-(x/Sqrt[c*x^4])","A",3,3,19,0.1579,1,"{1, 15, 30}"
1026,1,13,0,0.0013866,"\int \frac{1}{x \sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[1/(x*Sqrt[2 + 2*a - 2*(1 + a) + c*x^4]),x]","-\frac{1}{2 \sqrt{c x^4}}","-\frac{1}{2 \sqrt{c x^4}}",1,"-1/(2*Sqrt[c*x^4])","A",3,3,23,0.1304,1,"{1, 15, 30}"
1027,1,16,0,0.0014903,"\int \frac{1}{x^2 \sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[1/(x^2*Sqrt[2 + 2*a - 2*(1 + a) + c*x^4]),x]","-\frac{1}{3 x \sqrt{c x^4}}","-\frac{1}{3 x \sqrt{c x^4}}",1,"-1/(3*x*Sqrt[c*x^4])","A",3,3,23,0.1304,1,"{1, 15, 30}"
1028,1,16,0,0.0016737,"\int \frac{1}{x^3 \sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[1/(x^3*Sqrt[2 + 2*a - 2*(1 + a) + c*x^4]),x]","-\frac{1}{4 x^2 \sqrt{c x^4}}","-\frac{1}{4 x^2 \sqrt{c x^4}}",1,"-1/(4*x^2*Sqrt[c*x^4])","A",3,3,23,0.1304,1,"{1, 15, 30}"
1029,1,16,0,0.0016077,"\int \frac{1}{x^4 \sqrt{2+2 a-2 (1+a)+c x^4}} \, dx","Int[1/(x^4*Sqrt[2 + 2*a - 2*(1 + a) + c*x^4]),x]","-\frac{1}{5 x^3 \sqrt{c x^4}}","-\frac{1}{5 x^3 \sqrt{c x^4}}",1,"-1/(5*x^3*Sqrt[c*x^4])","A",3,3,23,0.1304,1,"{1, 15, 30}"
1030,1,12,0,0.0014659,"\int \frac{x^4}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x^4/Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{x^5}{5 \sqrt{a}}","\frac{x^5}{5 \sqrt{a}}",1,"x^5/(5*Sqrt[a])","A",3,3,24,0.1250,1,"{2, 12, 30}"
1031,1,12,0,0.0013625,"\int \frac{x^3}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x^3/Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{x^4}{4 \sqrt{a}}","\frac{x^4}{4 \sqrt{a}}",1,"x^4/(4*Sqrt[a])","A",3,3,24,0.1250,1,"{2, 12, 30}"
1032,1,12,0,0.0014377,"\int \frac{x^2}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x^2/Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{x^3}{3 \sqrt{a}}","\frac{x^3}{3 \sqrt{a}}",1,"x^3/(3*Sqrt[a])","A",3,3,24,0.1250,1,"{2, 12, 30}"
1033,1,12,0,0.0012983,"\int \frac{x}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[x/Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{x^2}{2 \sqrt{a}}","\frac{x^2}{2 \sqrt{a}}",1,"x^2/(2*Sqrt[a])","A",3,3,22,0.1364,1,"{2, 12, 30}"
1034,1,7,0,0.000861,"\int \frac{1}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4],x]","\frac{x}{\sqrt{a}}","\frac{x}{\sqrt{a}}",1,"x/Sqrt[a]","A",2,2,20,0.1000,1,"{2, 8}"
1035,1,8,0,0.001119,"\int \frac{1}{x \sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x*Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4]),x]","\frac{\log (x)}{\sqrt{a}}","\frac{\log (x)}{\sqrt{a}}",1,"Log[x]/Sqrt[a]","A",3,3,24,0.1250,1,"{2, 12, 29}"
1036,1,10,0,0.0014484,"\int \frac{1}{x^2 \sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x^2*Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4]),x]","-\frac{1}{\sqrt{a} x}","-\frac{1}{\sqrt{a} x}",1,"-(1/(Sqrt[a]*x))","A",3,3,24,0.1250,1,"{2, 12, 30}"
1037,1,12,0,0.001611,"\int \frac{1}{x^3 \sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x^3*Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4]),x]","-\frac{1}{2 \sqrt{a} x^2}","-\frac{1}{2 \sqrt{a} x^2}",1,"-1/(2*Sqrt[a]*x^2)","A",3,3,24,0.1250,1,"{2, 12, 30}"
1038,1,12,0,0.0014429,"\int \frac{1}{x^4 \sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx","Int[1/(x^4*Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4]),x]","-\frac{1}{3 \sqrt{a} x^3}","-\frac{1}{3 \sqrt{a} x^3}",1,"-1/(3*Sqrt[a]*x^3)","A",3,3,24,0.1250,1,"{2, 12, 30}"
1039,1,12,0,0.0103334,"\int \frac{1}{\sqrt{3-2 x^2-x^4}} \, dx","Int[1/Sqrt[3 - 2*x^2 - x^4],x]","\frac{F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}","\frac{F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"EllipticF[ArcSin[x], -1/3]/Sqrt[3]","A",2,2,16,0.1250,1,"{1095, 419}"
1040,1,39,0,0.0725563,"\int \frac{1}{\sqrt{-1+5 x^2-x^4}} \, dx","Int[1/Sqrt[-1 + 5*x^2 - x^4],x]","-\frac{F\left(\cos ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{21}}} x\right)|\frac{1}{42} \left(21+5 \sqrt{21}\right)\right)}{\sqrt[4]{21}}","-\frac{F\left(\cos ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{21}}} x\right)|\frac{1}{42} \left(21+5 \sqrt{21}\right)\right)}{\sqrt[4]{21}}",1,"-(EllipticF[ArcCos[Sqrt[2/(5 + Sqrt[21])]*x], (21 + 5*Sqrt[21])/42]/21^(1/4))","A",2,2,16,0.1250,1,"{1095, 420}"
1041,1,31,0,0.0061682,"\int x^{5/2} \left(a+b x^2+c x^4\right) \, dx","Int[x^(5/2)*(a + b*x^2 + c*x^4),x]","\frac{2}{7} a x^{7/2}+\frac{2}{11} b x^{11/2}+\frac{2}{15} c x^{15/2}","\frac{2}{7} a x^{7/2}+\frac{2}{11} b x^{11/2}+\frac{2}{15} c x^{15/2}",1,"(2*a*x^(7/2))/7 + (2*b*x^(11/2))/11 + (2*c*x^(15/2))/15","A",2,1,18,0.05556,1,"{14}"
1042,1,31,0,0.0065908,"\int x^{3/2} \left(a+b x^2+c x^4\right) \, dx","Int[x^(3/2)*(a + b*x^2 + c*x^4),x]","\frac{2}{5} a x^{5/2}+\frac{2}{9} b x^{9/2}+\frac{2}{13} c x^{13/2}","\frac{2}{5} a x^{5/2}+\frac{2}{9} b x^{9/2}+\frac{2}{13} c x^{13/2}",1,"(2*a*x^(5/2))/5 + (2*b*x^(9/2))/9 + (2*c*x^(13/2))/13","A",2,1,18,0.05556,1,"{14}"
1043,1,31,0,0.0066384,"\int \sqrt{x} \left(a+b x^2+c x^4\right) \, dx","Int[Sqrt[x]*(a + b*x^2 + c*x^4),x]","\frac{2}{3} a x^{3/2}+\frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2}","\frac{2}{3} a x^{3/2}+\frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2}",1,"(2*a*x^(3/2))/3 + (2*b*x^(7/2))/7 + (2*c*x^(11/2))/11","A",2,1,18,0.05556,1,"{14}"
1044,1,29,0,0.0062927,"\int \frac{a+b x^2+c x^4}{\sqrt{x}} \, dx","Int[(a + b*x^2 + c*x^4)/Sqrt[x],x]","2 a \sqrt{x}+\frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2}","2 a \sqrt{x}+\frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2}",1,"2*a*Sqrt[x] + (2*b*x^(5/2))/5 + (2*c*x^(9/2))/9","A",2,1,18,0.05556,1,"{14}"
1045,1,29,0,0.0062198,"\int \frac{a+b x^2+c x^4}{x^{3/2}} \, dx","Int[(a + b*x^2 + c*x^4)/x^(3/2),x]","-\frac{2 a}{\sqrt{x}}+\frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2}","-\frac{2 a}{\sqrt{x}}+\frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2}",1,"(-2*a)/Sqrt[x] + (2*b*x^(3/2))/3 + (2*c*x^(7/2))/7","A",2,1,18,0.05556,1,"{14}"
1046,1,29,0,0.0059993,"\int \frac{a+b x^2+c x^4}{x^{5/2}} \, dx","Int[(a + b*x^2 + c*x^4)/x^(5/2),x]","-\frac{2 a}{3 x^{3/2}}+2 b \sqrt{x}+\frac{2}{5} c x^{5/2}","-\frac{2 a}{3 x^{3/2}}+2 b \sqrt{x}+\frac{2}{5} c x^{5/2}",1,"(-2*a)/(3*x^(3/2)) + 2*b*Sqrt[x] + (2*c*x^(5/2))/5","A",2,1,18,0.05556,1,"{14}"
1047,1,29,0,0.0062878,"\int \frac{a+b x^2+c x^4}{x^{7/2}} \, dx","Int[(a + b*x^2 + c*x^4)/x^(7/2),x]","-\frac{2 a}{5 x^{5/2}}-\frac{2 b}{\sqrt{x}}+\frac{2}{3} c x^{3/2}","-\frac{2 a}{5 x^{5/2}}-\frac{2 b}{\sqrt{x}}+\frac{2}{3} c x^{3/2}",1,"(-2*a)/(5*x^(5/2)) - (2*b)/Sqrt[x] + (2*c*x^(3/2))/3","A",2,1,18,0.05556,1,"{14}"
1048,1,64,0,0.0229386,"\int x^{5/2} \left(a+b x^2+c x^4\right)^2 \, dx","Int[x^(5/2)*(a + b*x^2 + c*x^4)^2,x]","\frac{2}{7} a^2 x^{7/2}+\frac{2}{15} x^{15/2} \left(2 a c+b^2\right)+\frac{4}{11} a b x^{11/2}+\frac{4}{19} b c x^{19/2}+\frac{2}{23} c^2 x^{23/2}","\frac{2}{7} a^2 x^{7/2}+\frac{2}{15} x^{15/2} \left(2 a c+b^2\right)+\frac{4}{11} a b x^{11/2}+\frac{4}{19} b c x^{19/2}+\frac{2}{23} c^2 x^{23/2}",1,"(2*a^2*x^(7/2))/7 + (4*a*b*x^(11/2))/11 + (2*(b^2 + 2*a*c)*x^(15/2))/15 + (4*b*c*x^(19/2))/19 + (2*c^2*x^(23/2))/23","A",2,1,20,0.05000,1,"{1108}"
1049,1,64,0,0.0222693,"\int x^{3/2} \left(a+b x^2+c x^4\right)^2 \, dx","Int[x^(3/2)*(a + b*x^2 + c*x^4)^2,x]","\frac{2}{5} a^2 x^{5/2}+\frac{2}{13} x^{13/2} \left(2 a c+b^2\right)+\frac{4}{9} a b x^{9/2}+\frac{4}{17} b c x^{17/2}+\frac{2}{21} c^2 x^{21/2}","\frac{2}{5} a^2 x^{5/2}+\frac{2}{13} x^{13/2} \left(2 a c+b^2\right)+\frac{4}{9} a b x^{9/2}+\frac{4}{17} b c x^{17/2}+\frac{2}{21} c^2 x^{21/2}",1,"(2*a^2*x^(5/2))/5 + (4*a*b*x^(9/2))/9 + (2*(b^2 + 2*a*c)*x^(13/2))/13 + (4*b*c*x^(17/2))/17 + (2*c^2*x^(21/2))/21","A",2,1,20,0.05000,1,"{1108}"
1050,1,64,0,0.0230685,"\int \sqrt{x} \left(a+b x^2+c x^4\right)^2 \, dx","Int[Sqrt[x]*(a + b*x^2 + c*x^4)^2,x]","\frac{2}{3} a^2 x^{3/2}+\frac{2}{11} x^{11/2} \left(2 a c+b^2\right)+\frac{4}{7} a b x^{7/2}+\frac{4}{15} b c x^{15/2}+\frac{2}{19} c^2 x^{19/2}","\frac{2}{3} a^2 x^{3/2}+\frac{2}{11} x^{11/2} \left(2 a c+b^2\right)+\frac{4}{7} a b x^{7/2}+\frac{4}{15} b c x^{15/2}+\frac{2}{19} c^2 x^{19/2}",1,"(2*a^2*x^(3/2))/3 + (4*a*b*x^(7/2))/7 + (2*(b^2 + 2*a*c)*x^(11/2))/11 + (4*b*c*x^(15/2))/15 + (2*c^2*x^(19/2))/19","A",2,1,20,0.05000,1,"{1108}"
1051,1,62,0,0.022,"\int \frac{\left(a+b x^2+c x^4\right)^2}{\sqrt{x}} \, dx","Int[(a + b*x^2 + c*x^4)^2/Sqrt[x],x]","2 a^2 \sqrt{x}+\frac{2}{9} x^{9/2} \left(2 a c+b^2\right)+\frac{4}{5} a b x^{5/2}+\frac{4}{13} b c x^{13/2}+\frac{2}{17} c^2 x^{17/2}","2 a^2 \sqrt{x}+\frac{2}{9} x^{9/2} \left(2 a c+b^2\right)+\frac{4}{5} a b x^{5/2}+\frac{4}{13} b c x^{13/2}+\frac{2}{17} c^2 x^{17/2}",1,"2*a^2*Sqrt[x] + (4*a*b*x^(5/2))/5 + (2*(b^2 + 2*a*c)*x^(9/2))/9 + (4*b*c*x^(13/2))/13 + (2*c^2*x^(17/2))/17","A",2,1,20,0.05000,1,"{1108}"
1052,1,62,0,0.0222581,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^{3/2}} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^(3/2),x]","-\frac{2 a^2}{\sqrt{x}}+\frac{2}{7} x^{7/2} \left(2 a c+b^2\right)+\frac{4}{3} a b x^{3/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2}","-\frac{2 a^2}{\sqrt{x}}+\frac{2}{7} x^{7/2} \left(2 a c+b^2\right)+\frac{4}{3} a b x^{3/2}+\frac{4}{11} b c x^{11/2}+\frac{2}{15} c^2 x^{15/2}",1,"(-2*a^2)/Sqrt[x] + (4*a*b*x^(3/2))/3 + (2*(b^2 + 2*a*c)*x^(7/2))/7 + (4*b*c*x^(11/2))/11 + (2*c^2*x^(15/2))/15","A",2,1,20,0.05000,1,"{1108}"
1053,1,62,0,0.0220935,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^{5/2}} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^(5/2),x]","-\frac{2 a^2}{3 x^{3/2}}+\frac{2}{5} x^{5/2} \left(2 a c+b^2\right)+4 a b \sqrt{x}+\frac{4}{9} b c x^{9/2}+\frac{2}{13} c^2 x^{13/2}","-\frac{2 a^2}{3 x^{3/2}}+\frac{2}{5} x^{5/2} \left(2 a c+b^2\right)+4 a b \sqrt{x}+\frac{4}{9} b c x^{9/2}+\frac{2}{13} c^2 x^{13/2}",1,"(-2*a^2)/(3*x^(3/2)) + 4*a*b*Sqrt[x] + (2*(b^2 + 2*a*c)*x^(5/2))/5 + (4*b*c*x^(9/2))/9 + (2*c^2*x^(13/2))/13","A",2,1,20,0.05000,1,"{1108}"
1054,1,62,0,0.0229676,"\int \frac{\left(a+b x^2+c x^4\right)^2}{x^{7/2}} \, dx","Int[(a + b*x^2 + c*x^4)^2/x^(7/2),x]","-\frac{2 a^2}{5 x^{5/2}}+\frac{2}{3} x^{3/2} \left(2 a c+b^2\right)-\frac{4 a b}{\sqrt{x}}+\frac{4}{7} b c x^{7/2}+\frac{2}{11} c^2 x^{11/2}","-\frac{2 a^2}{5 x^{5/2}}+\frac{2}{3} x^{3/2} \left(2 a c+b^2\right)-\frac{4 a b}{\sqrt{x}}+\frac{4}{7} b c x^{7/2}+\frac{2}{11} c^2 x^{11/2}",1,"(-2*a^2)/(5*x^(5/2)) - (4*a*b)/Sqrt[x] + (2*(b^2 + 2*a*c)*x^(3/2))/3 + (4*b*c*x^(7/2))/7 + (2*c^2*x^(11/2))/11","A",2,1,20,0.05000,1,"{1108}"
1055,1,103,0,0.0484514,"\int x^{5/2} \left(a+b x^2+c x^4\right)^3 \, dx","Int[x^(5/2)*(a + b*x^2 + c*x^4)^3,x]","\frac{6}{11} a^2 b x^{11/2}+\frac{2}{7} a^3 x^{7/2}+\frac{6}{23} c x^{23/2} \left(a c+b^2\right)+\frac{2}{19} b x^{19/2} \left(6 a c+b^2\right)+\frac{2}{5} a x^{15/2} \left(a c+b^2\right)+\frac{2}{9} b c^2 x^{27/2}+\frac{2}{31} c^3 x^{31/2}","\frac{6}{11} a^2 b x^{11/2}+\frac{2}{7} a^3 x^{7/2}+\frac{6}{23} c x^{23/2} \left(a c+b^2\right)+\frac{2}{19} b x^{19/2} \left(6 a c+b^2\right)+\frac{2}{5} a x^{15/2} \left(a c+b^2\right)+\frac{2}{9} b c^2 x^{27/2}+\frac{2}{31} c^3 x^{31/2}",1,"(2*a^3*x^(7/2))/7 + (6*a^2*b*x^(11/2))/11 + (2*a*(b^2 + a*c)*x^(15/2))/5 + (2*b*(b^2 + 6*a*c)*x^(19/2))/19 + (6*c*(b^2 + a*c)*x^(23/2))/23 + (2*b*c^2*x^(27/2))/9 + (2*c^3*x^(31/2))/31","A",2,1,20,0.05000,1,"{1108}"
1056,1,103,0,0.0434847,"\int x^{3/2} \left(a+b x^2+c x^4\right)^3 \, dx","Int[x^(3/2)*(a + b*x^2 + c*x^4)^3,x]","\frac{2}{3} a^2 b x^{9/2}+\frac{2}{5} a^3 x^{5/2}+\frac{2}{7} c x^{21/2} \left(a c+b^2\right)+\frac{2}{17} b x^{17/2} \left(6 a c+b^2\right)+\frac{6}{13} a x^{13/2} \left(a c+b^2\right)+\frac{6}{25} b c^2 x^{25/2}+\frac{2}{29} c^3 x^{29/2}","\frac{2}{3} a^2 b x^{9/2}+\frac{2}{5} a^3 x^{5/2}+\frac{2}{7} c x^{21/2} \left(a c+b^2\right)+\frac{2}{17} b x^{17/2} \left(6 a c+b^2\right)+\frac{6}{13} a x^{13/2} \left(a c+b^2\right)+\frac{6}{25} b c^2 x^{25/2}+\frac{2}{29} c^3 x^{29/2}",1,"(2*a^3*x^(5/2))/5 + (2*a^2*b*x^(9/2))/3 + (6*a*(b^2 + a*c)*x^(13/2))/13 + (2*b*(b^2 + 6*a*c)*x^(17/2))/17 + (2*c*(b^2 + a*c)*x^(21/2))/7 + (6*b*c^2*x^(25/2))/25 + (2*c^3*x^(29/2))/29","A",2,1,20,0.05000,1,"{1108}"
1057,1,103,0,0.0416628,"\int \sqrt{x} \left(a+b x^2+c x^4\right)^3 \, dx","Int[Sqrt[x]*(a + b*x^2 + c*x^4)^3,x]","\frac{6}{7} a^2 b x^{7/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{19} c x^{19/2} \left(a c+b^2\right)+\frac{2}{15} b x^{15/2} \left(6 a c+b^2\right)+\frac{6}{11} a x^{11/2} \left(a c+b^2\right)+\frac{6}{23} b c^2 x^{23/2}+\frac{2}{27} c^3 x^{27/2}","\frac{6}{7} a^2 b x^{7/2}+\frac{2}{3} a^3 x^{3/2}+\frac{6}{19} c x^{19/2} \left(a c+b^2\right)+\frac{2}{15} b x^{15/2} \left(6 a c+b^2\right)+\frac{6}{11} a x^{11/2} \left(a c+b^2\right)+\frac{6}{23} b c^2 x^{23/2}+\frac{2}{27} c^3 x^{27/2}",1,"(2*a^3*x^(3/2))/3 + (6*a^2*b*x^(7/2))/7 + (6*a*(b^2 + a*c)*x^(11/2))/11 + (2*b*(b^2 + 6*a*c)*x^(15/2))/15 + (6*c*(b^2 + a*c)*x^(19/2))/19 + (6*b*c^2*x^(23/2))/23 + (2*c^3*x^(27/2))/27","A",2,1,20,0.05000,1,"{1108}"
1058,1,101,0,0.0437411,"\int \frac{\left(a+b x^2+c x^4\right)^3}{\sqrt{x}} \, dx","Int[(a + b*x^2 + c*x^4)^3/Sqrt[x],x]","\frac{6}{5} a^2 b x^{5/2}+2 a^3 \sqrt{x}+\frac{6}{17} c x^{17/2} \left(a c+b^2\right)+\frac{2}{13} b x^{13/2} \left(6 a c+b^2\right)+\frac{2}{3} a x^{9/2} \left(a c+b^2\right)+\frac{2}{7} b c^2 x^{21/2}+\frac{2}{25} c^3 x^{25/2}","\frac{6}{5} a^2 b x^{5/2}+2 a^3 \sqrt{x}+\frac{6}{17} c x^{17/2} \left(a c+b^2\right)+\frac{2}{13} b x^{13/2} \left(6 a c+b^2\right)+\frac{2}{3} a x^{9/2} \left(a c+b^2\right)+\frac{2}{7} b c^2 x^{21/2}+\frac{2}{25} c^3 x^{25/2}",1,"2*a^3*Sqrt[x] + (6*a^2*b*x^(5/2))/5 + (2*a*(b^2 + a*c)*x^(9/2))/3 + (2*b*(b^2 + 6*a*c)*x^(13/2))/13 + (6*c*(b^2 + a*c)*x^(17/2))/17 + (2*b*c^2*x^(21/2))/7 + (2*c^3*x^(25/2))/25","A",2,1,20,0.05000,1,"{1108}"
1059,1,99,0,0.0425691,"\int \frac{\left(a+b x^2+c x^4\right)^3}{x^{3/2}} \, dx","Int[(a + b*x^2 + c*x^4)^3/x^(3/2),x]","2 a^2 b x^{3/2}-\frac{2 a^3}{\sqrt{x}}+\frac{2}{5} c x^{15/2} \left(a c+b^2\right)+\frac{2}{11} b x^{11/2} \left(6 a c+b^2\right)+\frac{6}{7} a x^{7/2} \left(a c+b^2\right)+\frac{6}{19} b c^2 x^{19/2}+\frac{2}{23} c^3 x^{23/2}","2 a^2 b x^{3/2}-\frac{2 a^3}{\sqrt{x}}+\frac{2}{5} c x^{15/2} \left(a c+b^2\right)+\frac{2}{11} b x^{11/2} \left(6 a c+b^2\right)+\frac{6}{7} a x^{7/2} \left(a c+b^2\right)+\frac{6}{19} b c^2 x^{19/2}+\frac{2}{23} c^3 x^{23/2}",1,"(-2*a^3)/Sqrt[x] + 2*a^2*b*x^(3/2) + (6*a*(b^2 + a*c)*x^(7/2))/7 + (2*b*(b^2 + 6*a*c)*x^(11/2))/11 + (2*c*(b^2 + a*c)*x^(15/2))/5 + (6*b*c^2*x^(19/2))/19 + (2*c^3*x^(23/2))/23","A",2,1,20,0.05000,1,"{1108}"
1060,1,101,0,0.0439858,"\int \frac{\left(a+b x^2+c x^4\right)^3}{x^{5/2}} \, dx","Int[(a + b*x^2 + c*x^4)^3/x^(5/2),x]","6 a^2 b \sqrt{x}-\frac{2 a^3}{3 x^{3/2}}+\frac{6}{13} c x^{13/2} \left(a c+b^2\right)+\frac{2}{9} b x^{9/2} \left(6 a c+b^2\right)+\frac{6}{5} a x^{5/2} \left(a c+b^2\right)+\frac{6}{17} b c^2 x^{17/2}+\frac{2}{21} c^3 x^{21/2}","6 a^2 b \sqrt{x}-\frac{2 a^3}{3 x^{3/2}}+\frac{6}{13} c x^{13/2} \left(a c+b^2\right)+\frac{2}{9} b x^{9/2} \left(6 a c+b^2\right)+\frac{6}{5} a x^{5/2} \left(a c+b^2\right)+\frac{6}{17} b c^2 x^{17/2}+\frac{2}{21} c^3 x^{21/2}",1,"(-2*a^3)/(3*x^(3/2)) + 6*a^2*b*Sqrt[x] + (6*a*(b^2 + a*c)*x^(5/2))/5 + (2*b*(b^2 + 6*a*c)*x^(9/2))/9 + (6*c*(b^2 + a*c)*x^(13/2))/13 + (6*b*c^2*x^(17/2))/17 + (2*c^3*x^(21/2))/21","A",2,1,20,0.05000,1,"{1108}"
1061,1,99,0,0.0416287,"\int \frac{\left(a+b x^2+c x^4\right)^3}{x^{7/2}} \, dx","Int[(a + b*x^2 + c*x^4)^3/x^(7/2),x]","-\frac{6 a^2 b}{\sqrt{x}}-\frac{2 a^3}{5 x^{5/2}}+\frac{6}{11} c x^{11/2} \left(a c+b^2\right)+\frac{2}{7} b x^{7/2} \left(6 a c+b^2\right)+2 a x^{3/2} \left(a c+b^2\right)+\frac{2}{5} b c^2 x^{15/2}+\frac{2}{19} c^3 x^{19/2}","-\frac{6 a^2 b}{\sqrt{x}}-\frac{2 a^3}{5 x^{5/2}}+\frac{6}{11} c x^{11/2} \left(a c+b^2\right)+\frac{2}{7} b x^{7/2} \left(6 a c+b^2\right)+2 a x^{3/2} \left(a c+b^2\right)+\frac{2}{5} b c^2 x^{15/2}+\frac{2}{19} c^3 x^{19/2}",1,"(-2*a^3)/(5*x^(5/2)) - (6*a^2*b)/Sqrt[x] + 2*a*(b^2 + a*c)*x^(3/2) + (2*b*(b^2 + 6*a*c)*x^(7/2))/7 + (6*c*(b^2 + a*c)*x^(11/2))/11 + (2*b*c^2*x^(15/2))/5 + (2*c^3*x^(19/2))/19","A",2,1,20,0.05000,1,"{1108}"
1062,1,389,0,0.8599195,"\int \frac{x^{9/2}}{a+b x^2+c x^4} \, dx","Int[x^(9/2)/(a + b*x^2 + c*x^4),x]","-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{2 x^{3/2}}{3 c}","-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{2 x^{3/2}}{3 c}",1,"(2*x^(3/2))/(3*c) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(7/4)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(7/4)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(7/4)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(7/4)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",9,6,20,0.3000,1,"{1115, 1367, 1510, 298, 205, 208}"
1063,1,385,0,0.7973523,"\int \frac{x^{7/2}}{a+b x^2+c x^4} \, dx","Int[x^(7/2)/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{2 \sqrt{x}}{c}","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{2 \sqrt{x}}{c}",1,"(2*Sqrt[x])/c + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",9,6,20,0.3000,1,"{1115, 1367, 1422, 212, 208, 205}"
1064,1,331,0,0.4422593,"\int \frac{x^{5/2}}{a+b x^2+c x^4} \, dx","Int[x^(5/2)/(a + b*x^2 + c*x^4),x]","-\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}","-\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}",1,"-(((-b - Sqrt[b^2 - 4*a*c])^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c])) + ((-b + Sqrt[b^2 - 4*a*c])^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c]) + ((-b - Sqrt[b^2 - 4*a*c])^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c]) - ((-b + Sqrt[b^2 - 4*a*c])^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c])","A",8,5,20,0.2500,1,"{1115, 1374, 298, 205, 208}"
1065,1,331,0,0.403399,"\int \frac{x^{3/2}}{a+b x^2+c x^4} \, dx","Int[x^(3/2)/(a + b*x^2 + c*x^4),x]","\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}","\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}",1,"((-b - Sqrt[b^2 - 4*a*c])^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c]) - ((-b + Sqrt[b^2 - 4*a*c])^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c]) + ((-b - Sqrt[b^2 - 4*a*c])^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c]) - ((-b + Sqrt[b^2 - 4*a*c])^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c])","A",8,5,20,0.2500,1,"{1115, 1374, 212, 208, 205}"
1066,1,331,0,0.3664688,"\int \frac{\sqrt{x}}{a+b x^2+c x^4} \, dx","Int[Sqrt[x]/(a + b*x^2 + c*x^4),x]","-\frac{\sqrt[4]{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{2} \sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{2} \sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}","-\frac{\sqrt[4]{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{2} \sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{2} \sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{2} \sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}",1,"-((2^(1/4)*c^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(1/4))) + (2^(1/4)*c^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (2^(1/4)*c^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (2^(1/4)*c^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",8,5,20,0.2500,1,"{1115, 1375, 298, 205, 208}"
1067,1,331,0,0.4151092,"\int \frac{1}{\sqrt{x} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(Sqrt[x]*(a + b*x^2 + c*x^4)),x]","\frac{2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}","\frac{2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}",1,"(2^(3/4)*c^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (2^(3/4)*c^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (2^(3/4)*c^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (2^(3/4)*c^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",8,5,20,0.2500,1,"{1115, 1347, 212, 208, 205}"
1068,1,371,0,0.5673781,"\int \frac{1}{x^{3/2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^(3/2)*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{2}{a \sqrt{x}}","-\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{2}{a \sqrt{x}}",1,"-2/(a*Sqrt[x]) - (c^(1/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",9,6,20,0.3000,1,"{1115, 1368, 1510, 298, 205, 208}"
1069,1,371,0,0.5121351,"\int \frac{1}{x^{5/2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^(5/2)*(a + b*x^2 + c*x^4)),x]","\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2}{3 a x^{3/2}}","\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2}{3 a x^{3/2}}",1,"-2/(3*a*x^(3/2)) + (c^(3/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",9,6,20,0.3000,1,"{1115, 1368, 1422, 212, 208, 205}"
1070,1,412,0,0.9811749,"\int \frac{1}{x^{7/2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^(7/2)*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt[4]{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{2 b}{a^2 \sqrt{x}}-\frac{2}{5 a x^{5/2}}","\frac{\sqrt[4]{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} a^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{2 b}{a^2 \sqrt{x}}-\frac{2}{5 a x^{5/2}}",1,"-2/(5*a*x^(5/2)) + (2*b)/(a^2*Sqrt[x]) + (c^(1/4)*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*a^2*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",10,7,20,0.3500,1,"{1115, 1368, 1504, 1510, 298, 205, 208}"
1071,1,544,0,2.5773415,"\int \frac{x^{13/2}}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^(13/2)/(a + b*x^2 + c*x^4)^2,x]","\frac{\left(\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(-\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(-\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{7/2} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^{3/2}}{2 c \left(b^2-4 a c\right)}","\frac{\left(\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(-\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(-\left(3 b^2-14 a c\right) \sqrt{b^2-4 a c}-20 a b c+3 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{7/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{7/2} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b x^{3/2}}{2 c \left(b^2-4 a c\right)}",1,"-(b*x^(3/2))/(2*c*(b^2 - 4*a*c)) + (x^(7/2)*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((3*b^3 - 20*a*b*c + (3*b^2 - 14*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(7/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - ((3*b^3 - 20*a*b*c - (3*b^2 - 14*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(7/4)*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - ((3*b^3 - 20*a*b*c + (3*b^2 - 14*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(7/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + ((3*b^3 - 20*a*b*c - (3*b^2 - 14*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(7/4)*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",10,7,20,0.3500,1,"{1115, 1365, 1502, 1510, 298, 205, 208}"
1072,1,520,0,1.3705812,"\int \frac{x^{11/2}}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^(11/2)/(a + b*x^2 + c*x^4)^2,x]","-\frac{\left(\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x^{5/2} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b \sqrt{x}}{2 c \left(b^2-4 a c\right)}","-\frac{\left(\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(-\frac{b \left(b^2-12 a c\right)}{\sqrt{b^2-4 a c}}-10 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x^{5/2} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{b \sqrt{x}}{2 c \left(b^2-4 a c\right)}",1,"-(b*Sqrt[x])/(2*c*(b^2 - 4*a*c)) + (x^(5/2)*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((b^2 - 10*a*c + (b*(b^2 - 12*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - ((b^2 - 10*a*c - (b*(b^2 - 12*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) - ((b^2 - 10*a*c + (b*(b^2 - 12*a*c))/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - ((b^2 - 10*a*c - (b*(b^2 - 12*a*c))/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",10,7,20,0.3500,1,"{1115, 1365, 1502, 1422, 212, 208, 205}"
1073,1,471,0,0.9173517,"\int \frac{x^{9/2}}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^(9/2)/(a + b*x^2 + c*x^4)^2,x]","\frac{\left(b \sqrt{b^2-4 a c}+12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(b-\frac{12 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(b \sqrt{b^2-4 a c}+12 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(b-\frac{12 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{3/2} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{\left(b \sqrt{b^2-4 a c}+12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(b-\frac{12 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(b \sqrt{b^2-4 a c}+12 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(b-\frac{12 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{3/2} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(x^(3/2)*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b^2 + 12*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + ((b - (b^2 + 12*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - ((b^2 + 12*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - ((b - (b^2 + 12*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",9,6,20,0.3000,1,"{1115, 1365, 1510, 298, 205, 208}"
1074,1,483,0,1.0317861,"\int \frac{x^{7/2}}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^(7/2)/(a + b*x^2 + c*x^4)^2,x]","\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(-3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(-3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}","\frac{\sqrt{x} \left(2 a+b x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\left(3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(-3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\left(3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(-3 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}",1,"(Sqrt[x]*(2*a + b*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((3*b^2 + 4*a*c + 3*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((3*b^2 + 4*a*c - 3*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) - ((3*b^2 + 4*a*c + 3*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((3*b^2 + 4*a*c - 3*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",9,6,20,0.3000,1,"{1115, 1365, 1422, 212, 208, 205}"
1075,1,450,0,0.7097118,"\int \frac{x^{5/2}}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^(5/2)/(a + b*x^2 + c*x^4)^2,x]","-\frac{x^{3/2} \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\sqrt[4]{c} \left(\sqrt{b^2-4 a c}+4 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(4 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\sqrt{b^2-4 a c}+4 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(4 b-\sqrt{b^2-4 a c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}","-\frac{x^{3/2} \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{\sqrt[4]{c} \left(\sqrt{b^2-4 a c}+4 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(4 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\sqrt{b^2-4 a c}+4 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(4 b-\sqrt{b^2-4 a c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}",1,"-(x^(3/2)*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (c^(1/4)*(4*b + Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(4*b - Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(4*b + Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(4*b - Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",9,6,20,0.3000,1,"{1115, 1364, 1510, 298, 205, 208}"
1076,1,442,0,0.7046182,"\int \frac{x^{3/2}}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[x^(3/2)/(a + b*x^2 + c*x^4)^2,x]","\frac{c^{3/4} \left(\frac{4 b}{\sqrt{b^2-4 a c}}+3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(3-\frac{4 b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{4 b}{\sqrt{b^2-4 a c}}+3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(3-\frac{4 b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\sqrt{x} \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{c^{3/4} \left(\frac{4 b}{\sqrt{b^2-4 a c}}+3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(3-\frac{4 b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{4 b}{\sqrt{b^2-4 a c}}+3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(3-\frac{4 b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\sqrt{x} \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(Sqrt[x]*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (c^(3/4)*(3 + (4*b)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*(b^2 - 4*a*c)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(3 - (4*b)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(3 + (4*b)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*(b^2 - 4*a*c)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(3 - (4*b)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",9,6,20,0.3000,1,"{1115, 1364, 1422, 212, 208, 205}"
1077,1,489,0,0.9979343,"\int \frac{\sqrt{x}}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[Sqrt[x]/(a + b*x^2 + c*x^4)^2,x]","\frac{x^{3/2} \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt[4]{c} \left(b-\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(b-\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}","\frac{x^{3/2} \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt[4]{c} \left(b-\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(b-\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b^2-20 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a \left(b^2-4 a c\right) \sqrt[4]{\sqrt{b^2-4 a c}-b}}",1,"(x^(3/2)*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (c^(1/4)*(b - (b^2 - 20*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a*(b^2 - 4*a*c)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(b + (b^2 - 20*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(b - (b^2 - 20*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a*(b^2 - 4*a*c)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(b + (b^2 - 20*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a*(b^2 - 4*a*c)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",9,6,20,0.3000,1,"{1115, 1366, 1510, 298, 205, 208}"
1078,1,503,0,1.2755951,"\int \frac{1}{\sqrt{x} \left(a+b x^2+c x^4\right)^2} \, dx","Int[1/(Sqrt[x]*(a + b*x^2 + c*x^4)^2),x]","\frac{c^{3/4} \left(-3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(-3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\sqrt{x} \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{c^{3/4} \left(-3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(-3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(3 b \sqrt{b^2-4 a c}-28 a c+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4 \sqrt[4]{2} a \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\sqrt{x} \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(Sqrt[x]*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (c^(3/4)*(3*b^2 - 28*a*c - 3*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*a*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*(3*b^2 - 28*a*c + 3*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*a*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(3*b^2 - 28*a*c - 3*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*a*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*(3*b^2 - 28*a*c + 3*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(1/4)*a*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",9,6,20,0.3000,1,"{1115, 1345, 1422, 212, 208, 205}"
1079,1,573,0,2.4463832,"\int \frac{1}{x^{3/2} \left(a+b x^2+c x^4\right)^2} \, dx","Int[1/(x^(3/2)*(a + b*x^2 + c*x^4)^2),x]","-\frac{5 b^2-18 a c}{2 a^2 \sqrt{x} \left(b^2-4 a c\right)}+\frac{\sqrt[4]{c} \left(-\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(-\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{-2 a c+b^2+b c x^2}{2 a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{5 b^2-18 a c}{2 a^2 \sqrt{x} \left(b^2-4 a c\right)}+\frac{\sqrt[4]{c} \left(-\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(-\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\left(5 b^2-18 a c\right) \sqrt{b^2-4 a c}-28 a b c+5 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{4\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{-2 a c+b^2+b c x^2}{2 a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(5*b^2 - 18*a*c)/(2*a^2*(b^2 - 4*a*c)*Sqrt[x]) + (b^2 - 2*a*c + b*c*x^2)/(2*a*(b^2 - 4*a*c)*Sqrt[x]*(a + b*x^2 + c*x^4)) + (c^(1/4)*(5*b^3 - 28*a*b*c - (5*b^2 - 18*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a^2*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(5*b^3 - 28*a*b*c + (5*b^2 - 18*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a^2*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(5*b^3 - 28*a*b*c - (5*b^2 - 18*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a^2*(b^2 - 4*a*c)^(3/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(5*b^3 - 28*a*b*c + (5*b^2 - 18*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(4*2^(3/4)*a^2*(b^2 - 4*a*c)^(3/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",10,7,20,0.3500,1,"{1115, 1366, 1504, 1510, 298, 205, 208}"
1080,1,621,0,1.7718131,"\int \frac{x^{15/2}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^(15/2)/(a + b*x^2 + c*x^4)^3,x]","-\frac{3 \left(\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x^{9/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x^{5/2} \left(x^2 \left(12 a c+b^2\right)+8 a b\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \sqrt{x} \left(12 a c+b^2\right)}{16 c \left(b^2-4 a c\right)^2}","-\frac{3 \left(\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{-24 a^2 c^2-30 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-28 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} c^{5/4} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x^{9/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x^{5/2} \left(x^2 \left(12 a c+b^2\right)+8 a b\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \sqrt{x} \left(12 a c+b^2\right)}{16 c \left(b^2-4 a c\right)^2}",1,"(-3*(b^2 + 12*a*c)*Sqrt[x])/(16*c*(b^2 - 4*a*c)^2) + (x^(9/2)*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*x^(5/2)*(8*a*b + (b^2 + 12*a*c)*x^2))/(16*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - (3*(b^3 - 28*a*b*c + (b^4 - 30*a*b^2*c - 24*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)^2*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*(b^3 - 28*a*b*c - (b^4 - 30*a*b^2*c - 24*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)^2*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) - (3*(b^3 - 28*a*b*c + (b^4 - 30*a*b^2*c - 24*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)^2*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*(b^3 - 28*a*b*c - (b^4 - 30*a*b^2*c - 24*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(5/4)*(b^2 - 4*a*c)^2*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",11,8,20,0.4000,1,"{1115, 1365, 1498, 1502, 1422, 212, 208, 205}"
1081,1,569,0,1.9079703,"\int \frac{x^{13/2}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^(13/2)/(a + b*x^2 + c*x^4)^3,x]","\frac{\left(\sqrt{b^2-4 a c} \left(28 a c+5 b^2\right)+172 a b c+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(-\frac{172 a b c+5 b^3}{\sqrt{b^2-4 a c}}+28 a c+5 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(\sqrt{b^2-4 a c} \left(28 a c+5 b^2\right)+172 a b c+5 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(-\frac{172 a b c+5 b^3}{\sqrt{b^2-4 a c}}+28 a c+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{7/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^{3/2} \left(x^2 \left(28 a c+5 b^2\right)+24 a b\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}","\frac{\left(\sqrt{b^2-4 a c} \left(28 a c+5 b^2\right)+172 a b c+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(-\frac{172 a b c+5 b^3}{\sqrt{b^2-4 a c}}+28 a c+5 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{\left(\sqrt{b^2-4 a c} \left(28 a c+5 b^2\right)+172 a b c+5 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(-\frac{172 a b c+5 b^3}{\sqrt{b^2-4 a c}}+28 a c+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} c^{3/4} \left(b^2-4 a c\right)^2 \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{7/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{x^{3/2} \left(x^2 \left(28 a c+5 b^2\right)+24 a b\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}",1,"(x^(7/2)*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x^(3/2)*(24*a*b + (5*b^2 + 28*a*c)*x^2))/(16*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((5*b^3 + 172*a*b*c + Sqrt[b^2 - 4*a*c]*(5*b^2 + 28*a*c))*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + ((5*b^2 + 28*a*c - (5*b^3 + 172*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)^2*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - ((5*b^3 + 172*a*b*c + Sqrt[b^2 - 4*a*c]*(5*b^2 + 28*a*c))*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - ((5*b^2 + 28*a*c - (5*b^3 + 172*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*c^(3/4)*(b^2 - 4*a*c)^2*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",10,7,20,0.3500,1,"{1115, 1365, 1498, 1510, 298, 205, 208}"
1082,1,569,0,1.9645723,"\int \frac{x^{11/2}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^(11/2)/(a + b*x^2 + c*x^4)^3,x]","\frac{x^{5/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\sqrt{x} \left(x^2 \left(20 a c+7 b^2\right)+24 a b\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \left(\sqrt{b^2-4 a c} \left(20 a c+7 b^2\right)+36 a b c+7 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{36 a b c+7 b^3}{\sqrt{b^2-4 a c}}+20 a c+7 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(\sqrt{b^2-4 a c} \left(20 a c+7 b^2\right)+36 a b c+7 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{36 a b c+7 b^3}{\sqrt{b^2-4 a c}}+20 a c+7 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}","\frac{x^{5/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\sqrt{x} \left(x^2 \left(20 a c+7 b^2\right)+24 a b\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{3 \left(\sqrt{b^2-4 a c} \left(20 a c+7 b^2\right)+36 a b c+7 b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{36 a b c+7 b^3}{\sqrt{b^2-4 a c}}+20 a c+7 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(\sqrt{b^2-4 a c} \left(20 a c+7 b^2\right)+36 a b c+7 b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 \left(-\frac{36 a b c+7 b^3}{\sqrt{b^2-4 a c}}+20 a c+7 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} \sqrt[4]{c} \left(b^2-4 a c\right)^2 \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}",1,"(x^(5/2)*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (Sqrt[x]*(24*a*b + (7*b^2 + 20*a*c)*x^2))/(16*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - (3*(7*b^3 + 36*a*b*c + Sqrt[b^2 - 4*a*c]*(7*b^2 + 20*a*c))*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*(7*b^2 + 20*a*c - (7*b^3 + 36*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^2*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) - (3*(7*b^3 + 36*a*b*c + Sqrt[b^2 - 4*a*c]*(7*b^2 + 20*a*c))*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*(7*b^2 + 20*a*c - (7*b^3 + 36*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*c^(1/4)*(b^2 - 4*a*c)^2*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",10,7,20,0.3500,1,"{1115, 1365, 1498, 1422, 212, 208, 205}"
1083,1,533,0,1.4519245,"\int \frac{x^{9/2}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^(9/2)/(a + b*x^2 + c*x^4)^3,x]","-\frac{3 x^{3/2} \left(-4 a c+5 b^2+8 b c x^2\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^{3/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 \sqrt[4]{c} \left(4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{3 \sqrt[4]{c} \left(-4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{3 \sqrt[4]{c} \left(4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{3 \sqrt[4]{c} \left(-4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}","-\frac{3 x^{3/2} \left(-4 a c+5 b^2+8 b c x^2\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^{3/2} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 \sqrt[4]{c} \left(4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{3 \sqrt[4]{c} \left(-4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{3 \sqrt[4]{c} \left(4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{3 \sqrt[4]{c} \left(-4 b \sqrt{b^2-4 a c}+20 a c+11 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16\ 2^{3/4} \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}",1,"(x^(3/2)*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (3*x^(3/2)*(5*b^2 - 4*a*c + 8*b*c*x^2))/(16*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - (3*c^(1/4)*(11*b^2 + 20*a*c + 4*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(3/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (3*c^(1/4)*(11*b^2 + 20*a*c - 4*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(3/4)*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (3*c^(1/4)*(11*b^2 + 20*a*c + 4*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(3/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (3*c^(1/4)*(11*b^2 + 20*a*c - 4*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(3/4)*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",10,7,20,0.3500,1,"{1115, 1365, 1500, 1510, 298, 205, 208}"
1084,1,533,0,1.3630083,"\int \frac{x^{7/2}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^(7/2)/(a + b*x^2 + c*x^4)^3,x]","\frac{c^{3/4} \left(36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(-36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(-36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\sqrt{x} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{\sqrt{x} \left(-4 a c+13 b^2+24 b c x^2\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}","\frac{c^{3/4} \left(36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(-36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \left(-36 b \sqrt{b^2-4 a c}+28 a c+41 b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{16 \sqrt[4]{2} \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\sqrt{x} \left(2 a+b x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{\sqrt{x} \left(-4 a c+13 b^2+24 b c x^2\right)}{16 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}",1,"(Sqrt[x]*(2*a + b*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (Sqrt[x]*(13*b^2 - 4*a*c + 24*b*c*x^2))/(16*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (c^(3/4)*(41*b^2 + 28*a*c + 36*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*(41*b^2 + 28*a*c - 36*b*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(41*b^2 + 28*a*c + 36*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*(41*b^2 + 28*a*c - 36*b*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(16*2^(1/4)*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",10,7,20,0.3500,1,"{1115, 1365, 1430, 1422, 212, 208, 205}"
1085,1,594,0,2.3101999,"\int \frac{x^{5/2}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^(5/2)/(a + b*x^2 + c*x^4)^3,x]","\frac{3 x^{3/2} \left(c x^2 \left(12 a c+b^2\right)+b \left(4 a c+b^2\right)\right)}{16 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x^{3/2} \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 \sqrt[4]{c} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{3 \sqrt[4]{c} \left(\sqrt{b^2-4 a c} \left(12 a c+b^2\right)-68 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{3 \sqrt[4]{c} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+12 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{3 \sqrt[4]{c} \left(\sqrt{b^2-4 a c} \left(12 a c+b^2\right)-68 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}","\frac{3 x^{3/2} \left(c x^2 \left(12 a c+b^2\right)+b \left(4 a c+b^2\right)\right)}{16 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x^{3/2} \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 \sqrt[4]{c} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{3 \sqrt[4]{c} \left(\sqrt{b^2-4 a c} \left(12 a c+b^2\right)-68 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{3 \sqrt[4]{c} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+12 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^2 \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{3 \sqrt[4]{c} \left(\sqrt{b^2-4 a c} \left(12 a c+b^2\right)-68 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}",1,"-(x^(3/2)*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*x^(3/2)*(b*(b^2 + 4*a*c) + c*(b^2 + 12*a*c)*x^2))/(16*a*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*c^(1/4)*(b^2 + 12*a*c - b^3/Sqrt[b^2 - 4*a*c] + (68*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a*(b^2 - 4*a*c)^2*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (3*c^(1/4)*(b^3 - 68*a*b*c + Sqrt[b^2 - 4*a*c]*(b^2 + 12*a*c))*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) - (3*c^(1/4)*(b^2 + 12*a*c - b^3/Sqrt[b^2 - 4*a*c] + (68*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a*(b^2 - 4*a*c)^2*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (3*c^(1/4)*(b^3 - 68*a*b*c + Sqrt[b^2 - 4*a*c]*(b^2 + 12*a*c))*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",10,7,20,0.3500,1,"{1115, 1364, 1500, 1510, 298, 205, 208}"
1086,1,594,0,2.3660648,"\int \frac{x^{3/2}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[x^(3/2)/(a + b*x^2 + c*x^4)^3,x]","-\frac{3 c^{3/4} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+44 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(\sqrt{b^2-4 a c} \left(44 a c+b^2\right)-68 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+44 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(\sqrt{b^2-4 a c} \left(44 a c+b^2\right)-68 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\sqrt{x} \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\sqrt{x} \left(c x^2 \left(44 a c+b^2\right)+b \left(20 a c+b^2\right)\right)}{16 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}","-\frac{3 c^{3/4} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+44 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(\sqrt{b^2-4 a c} \left(44 a c+b^2\right)-68 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{68 a b c}{\sqrt{b^2-4 a c}}+44 a c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^2 \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(\sqrt{b^2-4 a c} \left(44 a c+b^2\right)-68 a b c+b^3\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{\sqrt{x} \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\sqrt{x} \left(c x^2 \left(44 a c+b^2\right)+b \left(20 a c+b^2\right)\right)}{16 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}",1,"-(Sqrt[x]*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (Sqrt[x]*(b*(b^2 + 20*a*c) + c*(b^2 + 44*a*c)*x^2))/(16*a*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - (3*c^(3/4)*(b^2 + 44*a*c - b^3/Sqrt[b^2 - 4*a*c] + (68*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a*(b^2 - 4*a*c)^2*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*c^(3/4)*(b^3 - 68*a*b*c + Sqrt[b^2 - 4*a*c]*(b^2 + 44*a*c))*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) - (3*c^(3/4)*(b^2 + 44*a*c - b^3/Sqrt[b^2 - 4*a*c] + (68*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a*(b^2 - 4*a*c)^2*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*c^(3/4)*(b^3 - 68*a*b*c + Sqrt[b^2 - 4*a*c]*(b^2 + 44*a*c))*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",10,7,20,0.3500,1,"{1115, 1364, 1430, 1422, 212, 208, 205}"
1087,1,658,0,5.4845627,"\int \frac{\sqrt{x}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[Sqrt[x]/(a + b*x^2 + c*x^4)^3,x]","\frac{x^{3/2} \left(52 a^2 c^2+b c x^2 \left(5 b^2-44 a c\right)-45 a b^2 c+5 b^4\right)}{16 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c-b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c+b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c-b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c+b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{3/2} \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{x^{3/2} \left(52 a^2 c^2+b c x^2 \left(5 b^2-44 a c\right)-45 a b^2 c+5 b^4\right)}{16 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c-b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c+b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c-b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(520 a^2 c^2-54 a b^2 c+b \left(5 b^2-44 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32\ 2^{3/4} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^{3/2} \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(x^(3/2)*(b^2 - 2*a*c + b*c*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x^(3/2)*(5*b^4 - 45*a*b^2*c + 52*a^2*c^2 + b*c*(5*b^2 - 44*a*c)*x^2))/(16*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - (c^(1/4)*(5*b^4 - 54*a*b^2*c + 520*a^2*c^2 - b*(5*b^2 - 44*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(5*b^4 - 54*a*b^2*c + 520*a^2*c^2 + b*(5*b^2 - 44*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(5*b^4 - 54*a*b^2*c + 520*a^2*c^2 - b*(5*b^2 - 44*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(5*b^4 - 54*a*b^2*c + 520*a^2*c^2 + b*(5*b^2 - 44*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(3/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",10,7,20,0.3500,1,"{1115, 1366, 1500, 1510, 298, 205, 208}"
1088,1,658,0,5.7917886,"\int \frac{1}{\sqrt{x} \left(a+b x^2+c x^4\right)^3} \, dx","Int[1/(Sqrt[x]*(a + b*x^2 + c*x^4)^3),x]","\frac{\sqrt{x} \left(60 a^2 c^2+b c x^2 \left(7 b^2-52 a c\right)-55 a b^2 c+7 b^4\right)}{16 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c-b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c+b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c-b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c+b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\sqrt{x} \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{\sqrt{x} \left(60 a^2 c^2+b c x^2 \left(7 b^2-52 a c\right)-55 a b^2 c+7 b^4\right)}{16 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c-b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c+b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c-b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{3 c^{3/4} \left(280 a^2 c^2-66 a b^2 c+b \left(7 b^2-52 a c\right) \sqrt{b^2-4 a c}+7 b^4\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{32 \sqrt[4]{2} a^2 \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\sqrt{x} \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(Sqrt[x]*(b^2 - 2*a*c + b*c*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (Sqrt[x]*(7*b^4 - 55*a*b^2*c + 60*a^2*c^2 + b*c*(7*b^2 - 52*a*c)*x^2))/(16*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*c^(3/4)*(7*b^4 - 66*a*b^2*c + 280*a^2*c^2 - b*(7*b^2 - 52*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*c^(3/4)*(7*b^4 - 66*a*b^2*c + 280*a^2*c^2 + b*(7*b^2 - 52*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (3*c^(3/4)*(7*b^4 - 66*a*b^2*c + 280*a^2*c^2 - b*(7*b^2 - 52*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (3*c^(3/4)*(7*b^4 - 66*a*b^2*c + 280*a^2*c^2 + b*(7*b^2 - 52*a*c)*Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[x])/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(32*2^(1/4)*a^2*(b^2 - 4*a*c)^(5/2)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",10,7,20,0.3500,1,"{1115, 1345, 1430, 1422, 212, 208, 205}"
1089,1,147,0,0.2074925,"\int (d x)^{3/2} \sqrt{a+b x^2+c x^4} \, dx","Int[(d*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 (d x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{1}{2},-\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 (d x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{1}{2},-\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*(d*x)^(5/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[5/4, -1/2, -1/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1090,1,147,0,0.1256796,"\int \sqrt{d x} \sqrt{a+b x^2+c x^4} \, dx","Int[Sqrt[d*x]*Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 (d x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{1}{2},-\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 (d x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{1}{2},-\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*(d*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[3/4, -1/2, -1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1091,1,145,0,0.1246216,"\int \frac{\sqrt{a+b x^2+c x^4}}{\sqrt{d x}} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/Sqrt[d*x],x]","\frac{2 \sqrt{d x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 \sqrt{d x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*Sqrt[d*x]*Sqrt[a + b*x^2 + c*x^4]*AppellF1[1/4, -1/2, -1/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1092,1,145,0,0.1261132,"\int \frac{\sqrt{a+b x^2+c x^4}}{(d x)^{3/2}} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/(d*x)^(3/2),x]","-\frac{2 \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{2 \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(-2*Sqrt[a + b*x^2 + c*x^4]*AppellF1[-1/4, -1/2, -1/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*Sqrt[d*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1093,1,148,0,0.127711,"\int (d x)^{3/2} \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[(d*x)^(3/2)*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 a (d x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{3}{2},-\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 a (d x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{3}{2},-\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*a*(d*x)^(5/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[5/4, -3/2, -3/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1094,1,148,0,0.1300433,"\int \sqrt{d x} \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[Sqrt[d*x]*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 a (d x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{3}{2},-\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 a (d x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{3}{2},-\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*a*(d*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[3/4, -3/2, -3/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1095,1,146,0,0.1274114,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{\sqrt{d x}} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/Sqrt[d*x],x]","\frac{2 a \sqrt{d x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 a \sqrt{d x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*a*Sqrt[d*x]*Sqrt[a + b*x^2 + c*x^4]*AppellF1[1/4, -3/2, -3/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1096,1,146,0,0.1293582,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{(d x)^{3/2}} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/(d*x)^(3/2),x]","-\frac{2 a \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{2 a \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(-2*a*Sqrt[a + b*x^2 + c*x^4]*AppellF1[-1/4, -3/2, -3/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*Sqrt[d*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1141, 510}"
1097,1,147,0,0.1260729,"\int \frac{(d x)^{3/2}}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(d*x)^(3/2)/Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 (d x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{1}{2},\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 d \sqrt{a+b x^2+c x^4}}","\frac{2 (d x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{1}{2},\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 d \sqrt{a+b x^2+c x^4}}",1,"(2*(d*x)^(5/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[5/4, 1/2, 1/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*d*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1098,1,147,0,0.1213961,"\int \frac{\sqrt{d x}}{\sqrt{a+b x^2+c x^4}} \, dx","Int[Sqrt[d*x]/Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 (d x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 d \sqrt{a+b x^2+c x^4}}","\frac{2 (d x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 d \sqrt{a+b x^2+c x^4}}",1,"(2*(d*x)^(3/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 1/2, 1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*d*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1099,1,145,0,0.1222566,"\int \frac{1}{\sqrt{d x} \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(Sqrt[d*x]*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{2 \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{a+b x^2+c x^4}}","\frac{2 \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{a+b x^2+c x^4}}",1,"(2*Sqrt[d*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/4, 1/2, 1/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1100,1,145,0,0.1248654,"\int \frac{1}{(d x)^{3/2} \sqrt{a+b x^2+c x^4}} \, dx","Int[1/((d*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{d x} \sqrt{a+b x^2+c x^4}}","-\frac{2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d \sqrt{d x} \sqrt{a+b x^2+c x^4}}",1,"(-2*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-1/4, 1/2, 1/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*Sqrt[d*x]*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1101,1,150,0,0.1283438,"\int \frac{(d x)^{3/2}}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(d*x)^(3/2)/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 (d x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{3}{2},\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 a d \sqrt{a+b x^2+c x^4}}","\frac{2 (d x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{3}{2},\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 a d \sqrt{a+b x^2+c x^4}}",1,"(2*(d*x)^(5/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[5/4, 3/2, 3/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*a*d*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1102,1,150,0,0.1260615,"\int \frac{\sqrt{d x}}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[Sqrt[d*x]/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 (d x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{3}{2},\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 a d \sqrt{a+b x^2+c x^4}}","\frac{2 (d x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{3}{2},\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 a d \sqrt{a+b x^2+c x^4}}",1,"(2*(d*x)^(3/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 3/2, 3/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*a*d*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1103,1,148,0,0.1257958,"\int \frac{1}{\sqrt{d x} \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(Sqrt[d*x]*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{2 \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a d \sqrt{a+b x^2+c x^4}}","\frac{2 \sqrt{d x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a d \sqrt{a+b x^2+c x^4}}",1,"(2*Sqrt[d*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/4, 3/2, 3/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(a*d*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1104,1,148,0,0.1274192,"\int \frac{1}{(d x)^{3/2} \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/((d*x)^(3/2)*(a + b*x^2 + c*x^4)^(3/2)),x]","-\frac{2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a d \sqrt{d x} \sqrt{a+b x^2+c x^4}}","-\frac{2 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a d \sqrt{d x} \sqrt{a+b x^2+c x^4}}",1,"(-2*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-1/4, 3/2, 3/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(a*d*Sqrt[d*x]*Sqrt[a + b*x^2 + c*x^4])","A",2,2,24,0.08333,1,"{1141, 510}"
1105,1,156,0,0.0999336,"\int (d x)^m \left(a+b x^2+c x^4\right)^3 \, dx","Int[(d*x)^m*(a + b*x^2 + c*x^4)^3,x]","\frac{3 a^2 b (d x)^{m+3}}{d^3 (m+3)}+\frac{a^3 (d x)^{m+1}}{d (m+1)}+\frac{3 a \left(a c+b^2\right) (d x)^{m+5}}{d^5 (m+5)}+\frac{b \left(6 a c+b^2\right) (d x)^{m+7}}{d^7 (m+7)}+\frac{3 c \left(a c+b^2\right) (d x)^{m+9}}{d^9 (m+9)}+\frac{3 b c^2 (d x)^{m+11}}{d^{11} (m+11)}+\frac{c^3 (d x)^{m+13}}{d^{13} (m+13)}","\frac{3 a^2 b (d x)^{m+3}}{d^3 (m+3)}+\frac{a^3 (d x)^{m+1}}{d (m+1)}+\frac{3 a \left(a c+b^2\right) (d x)^{m+5}}{d^5 (m+5)}+\frac{b \left(6 a c+b^2\right) (d x)^{m+7}}{d^7 (m+7)}+\frac{3 c \left(a c+b^2\right) (d x)^{m+9}}{d^9 (m+9)}+\frac{3 b c^2 (d x)^{m+11}}{d^{11} (m+11)}+\frac{c^3 (d x)^{m+13}}{d^{13} (m+13)}",1,"(a^3*(d*x)^(1 + m))/(d*(1 + m)) + (3*a^2*b*(d*x)^(3 + m))/(d^3*(3 + m)) + (3*a*(b^2 + a*c)*(d*x)^(5 + m))/(d^5*(5 + m)) + (b*(b^2 + 6*a*c)*(d*x)^(7 + m))/(d^7*(7 + m)) + (3*c*(b^2 + a*c)*(d*x)^(9 + m))/(d^9*(9 + m)) + (3*b*c^2*(d*x)^(11 + m))/(d^11*(11 + m)) + (c^3*(d*x)^(13 + m))/(d^13*(13 + m))","A",2,1,20,0.05000,1,"{1108}"
1106,1,101,0,0.0528217,"\int (d x)^m \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d*x)^m*(a + b*x^2 + c*x^4)^2,x]","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{\left(2 a c+b^2\right) (d x)^{m+5}}{d^5 (m+5)}+\frac{2 a b (d x)^{m+3}}{d^3 (m+3)}+\frac{2 b c (d x)^{m+7}}{d^7 (m+7)}+\frac{c^2 (d x)^{m+9}}{d^9 (m+9)}","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{\left(2 a c+b^2\right) (d x)^{m+5}}{d^5 (m+5)}+\frac{2 a b (d x)^{m+3}}{d^3 (m+3)}+\frac{2 b c (d x)^{m+7}}{d^7 (m+7)}+\frac{c^2 (d x)^{m+9}}{d^9 (m+9)}",1,"(a^2*(d*x)^(1 + m))/(d*(1 + m)) + (2*a*b*(d*x)^(3 + m))/(d^3*(3 + m)) + ((b^2 + 2*a*c)*(d*x)^(5 + m))/(d^5*(5 + m)) + (2*b*c*(d*x)^(7 + m))/(d^7*(7 + m)) + (c^2*(d*x)^(9 + m))/(d^9*(9 + m))","A",2,1,20,0.05000,1,"{1108}"
1107,1,52,0,0.0195031,"\int (d x)^m \left(a+b x^2+c x^4\right) \, dx","Int[(d*x)^m*(a + b*x^2 + c*x^4),x]","\frac{a (d x)^{m+1}}{d (m+1)}+\frac{b (d x)^{m+3}}{d^3 (m+3)}+\frac{c (d x)^{m+5}}{d^5 (m+5)}","\frac{a (d x)^{m+1}}{d (m+1)}+\frac{b (d x)^{m+3}}{d^3 (m+3)}+\frac{c (d x)^{m+5}}{d^5 (m+5)}",1,"(a*(d*x)^(1 + m))/(d*(1 + m)) + (b*(d*x)^(3 + m))/(d^3*(3 + m)) + (c*(d*x)^(5 + m))/(d^5*(5 + m))","A",2,1,18,0.05556,1,"{14}"
1108,1,173,0,0.2508731,"\int \frac{(d x)^m}{a+b x^2+c x^4} \, dx","Int[(d*x)^m/(a + b*x^2 + c*x^4),x]","\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"(2*c*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)) - (2*c*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m))","A",3,2,20,0.1000,1,"{1131, 364}"
1109,1,315,0,0.6955677,"\int \frac{(d x)^m}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d*x)^m/(a + b*x^2 + c*x^4)^2,x]","\frac{c (d x)^{m+1} \left(b (1-m) \sqrt{b^2-4 a c}-4 a c (3-m)+b^2 (1-m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(-b (1-m) \sqrt{b^2-4 a c}-4 a c (3-m)+b^2 (1-m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^2\right)}{2 a d \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{c (d x)^{m+1} \left(b (1-m) \sqrt{b^2-4 a c}-4 a c (3-m)+b^2 (1-m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(-b (1-m) \sqrt{b^2-4 a c}-4 a c (3-m)+b^2 (1-m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^2\right)}{2 a d \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"((d*x)^(1 + m)*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*d*(a + b*x^2 + c*x^4)) + (c*(b^2*(1 - m) + b*Sqrt[b^2 - 4*a*c]*(1 - m) - 4*a*c*(3 - m))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)) - (c*(b^2*(1 - m) - b*Sqrt[b^2 - 4*a*c]*(1 - m) - 4*a*c*(3 - m))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m))","A",4,3,20,0.1500,1,"{1121, 1285, 364}"
1110,1,158,0,0.1455069,"\int (d x)^m \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[(d*x)^m*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{a (d x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{3}{2},-\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a (d x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{3}{2},-\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*(d*x)^(1 + m)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[(1 + m)/2, -3/2, -3/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1141, 510}"
1111,1,157,0,0.1364122,"\int (d x)^m \sqrt{a+b x^2+c x^4} \, dx","Int[(d*x)^m*Sqrt[a + b*x^2 + c*x^4],x]","\frac{(d x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{1}{2},-\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{(d x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{1}{2},-\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"((d*x)^(1 + m)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[(1 + m)/2, -1/2, -1/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1141, 510}"
1112,1,157,0,0.135529,"\int \frac{(d x)^m}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(d*x)^m/Sqrt[a + b*x^2 + c*x^4],x]","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{1}{2},\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{a+b x^2+c x^4}}","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{1}{2},\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{a+b x^2+c x^4}}",1,"((d*x)^(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/2, 1/2, 1/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[a + b*x^2 + c*x^4])","A",2,2,22,0.09091,1,"{1141, 510}"
1113,1,160,0,0.1422622,"\int \frac{(d x)^m}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(d*x)^m/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{3}{2},\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) \sqrt{a+b x^2+c x^4}}","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{3}{2},\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) \sqrt{a+b x^2+c x^4}}",1,"((d*x)^(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/2, 3/2, 3/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(a*d*(1 + m)*Sqrt[a + b*x^2 + c*x^4])","A",2,2,22,0.09091,1,"{1141, 510}"
1114,1,155,0,0.1019733,"\int (d x)^m \left(a+b x^2+c x^4\right)^p \, dx","Int[(d*x)^m*(a + b*x^2 + c*x^4)^p,x]","\frac{(d x)^{m+1} \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{m+1}{2};-p,-p;\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}","\frac{(d x)^{m+1} \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{m+1}{2};-p,-p;\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}",1,"((d*x)^(1 + m)*(a + b*x^2 + c*x^4)^p*AppellF1[(1 + m)/2, -p, -p, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*(1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,20,0.1000,1,"{1141, 510}"
1115,1,257,0,0.3733156,"\int x^7 \left(a+b x^2+c x^4\right)^p \, dx","Int[x^7*(a + b*x^2 + c*x^4)^p,x]","-\frac{b 2^{p-2} \left(6 a c-b^2 (p+3)\right) \left(a+b x^2+c x^4\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^3 (p+1) (2 p+3) \sqrt{b^2-4 a c}}+\frac{\left(-2 a c (2 p+3)+b^2 (p+2) (p+3)-2 b c (p+1) (p+3) x^2\right) \left(a+b x^2+c x^4\right)^{p+1}}{8 c^3 (p+1) (p+2) (2 p+3)}+\frac{x^4 \left(a+b x^2+c x^4\right)^{p+1}}{4 c (p+2)}","-\frac{b 2^{p-2} \left(6 a c-b^2 (p+3)\right) \left(a+b x^2+c x^4\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^3 (p+1) (2 p+3) \sqrt{b^2-4 a c}}+\frac{\left(-2 a c (2 p+3)+b^2 (p+2) (p+3)-2 b c (p+1) (p+3) x^2\right) \left(a+b x^2+c x^4\right)^{p+1}}{8 c^3 (p+1) (p+2) (2 p+3)}+\frac{x^4 \left(a+b x^2+c x^4\right)^{p+1}}{4 c (p+2)}",1,"(x^4*(a + b*x^2 + c*x^4)^(1 + p))/(4*c*(2 + p)) + ((b^2*(2 + p)*(3 + p) - 2*a*c*(3 + 2*p) - 2*b*c*(1 + p)*(3 + p)*x^2)*(a + b*x^2 + c*x^4)^(1 + p))/(8*c^3*(1 + p)*(2 + p)*(3 + 2*p)) - (2^(-2 + p)*b*(6*a*c - b^2*(3 + p))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x^2 + c*x^4)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(2*Sqrt[b^2 - 4*a*c])])/(c^3*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p))","A",4,4,18,0.2222,1,"{1114, 742, 779, 624}"
1116,1,223,0,0.2111606,"\int x^5 \left(a+b x^2+c x^4\right)^p \, dx","Int[x^5*(a + b*x^2 + c*x^4)^p,x]","\frac{2^{p-1} \left(2 a c-b^2 (p+2)\right) \left(a+b x^2+c x^4\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{b (p+2) \left(a+b x^2+c x^4\right)^{p+1}}{4 c^2 (p+1) (2 p+3)}+\frac{x^2 \left(a+b x^2+c x^4\right)^{p+1}}{2 c (2 p+3)}","\frac{2^{p-1} \left(2 a c-b^2 (p+2)\right) \left(a+b x^2+c x^4\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{b (p+2) \left(a+b x^2+c x^4\right)^{p+1}}{4 c^2 (p+1) (2 p+3)}+\frac{x^2 \left(a+b x^2+c x^4\right)^{p+1}}{2 c (2 p+3)}",1,"-(b*(2 + p)*(a + b*x^2 + c*x^4)^(1 + p))/(4*c^2*(1 + p)*(3 + 2*p)) + (x^2*(a + b*x^2 + c*x^4)^(1 + p))/(2*c*(3 + 2*p)) + (2^(-1 + p)*(2*a*c - b^2*(2 + p))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x^2 + c*x^4)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(2*Sqrt[b^2 - 4*a*c])])/(c^2*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p))","A",4,4,18,0.2222,1,"{1114, 742, 640, 624}"
1117,1,160,0,0.1254839,"\int x^3 \left(a+b x^2+c x^4\right)^p \, dx","Int[x^3*(a + b*x^2 + c*x^4)^p,x]","\frac{b 2^{p-1} \left(a+b x^2+c x^4\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c (p+1) \sqrt{b^2-4 a c}}+\frac{\left(a+b x^2+c x^4\right)^{p+1}}{4 c (p+1)}","\frac{b 2^{p-1} \left(a+b x^2+c x^4\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c (p+1) \sqrt{b^2-4 a c}}+\frac{\left(a+b x^2+c x^4\right)^{p+1}}{4 c (p+1)}",1,"(a + b*x^2 + c*x^4)^(1 + p)/(4*c*(1 + p)) + (2^(-1 + p)*b*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x^2 + c*x^4)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(2*Sqrt[b^2 - 4*a*c])])/(c*Sqrt[b^2 - 4*a*c]*(1 + p))","A",3,3,18,0.1667,1,"{1114, 640, 624}"
1118,1,126,0,0.0757463,"\int x \left(a+b x^2+c x^4\right)^p \, dx","Int[x*(a + b*x^2 + c*x^4)^p,x]","-\frac{2^p \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x^2+c x^4\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}","-\frac{2^p \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x^2+c x^4\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^2+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}",1,"-((2^p*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x^2 + c*x^4)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(2*Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(1 + p)))","A",2,2,16,0.1250,1,"{1107, 624}"
1119,1,152,0,0.148887,"\int \frac{\left(a+b x^2+c x^4\right)^p}{x} \, dx","Int[(a + b*x^2 + c*x^4)^p/x,x]","\frac{4^{p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^2},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^2}\right)}{p}","\frac{4^{p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^2},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^2}\right)}{p}",1,"(4^(-1 + p)*(a + b*x^2 + c*x^4)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, -(b - Sqrt[b^2 - 4*a*c])/(2*c*x^2), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x^2)])/(p*((b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(c*x^2))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(c*x^2))^p)","A",3,3,18,0.1667,1,"{1114, 758, 133}"
1120,1,166,0,0.130781,"\int \frac{\left(a+b x^2+c x^4\right)^p}{x^3} \, dx","Int[(a + b*x^2 + c*x^4)^p/x^3,x]","-\frac{2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(1-2 p;-p,-p;2 (1-p);-\frac{b-\sqrt{b^2-4 a c}}{2 c x^2},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^2}\right)}{(1-2 p) x^2}","-\frac{2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(1-2 p;-p,-p;2 (1-p);-\frac{b-\sqrt{b^2-4 a c}}{2 c x^2},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^2}\right)}{(1-2 p) x^2}",1,"-((2^(-1 + 2*p)*(a + b*x^2 + c*x^4)^p*AppellF1[1 - 2*p, -p, -p, 2*(1 - p), -(b - Sqrt[b^2 - 4*a*c])/(2*c*x^2), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x^2)])/((1 - 2*p)*x^2*((b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(c*x^2))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(c*x^2))^p))","A",3,3,18,0.1667,1,"{1114, 758, 133}"
1121,1,164,0,0.1330079,"\int \frac{\left(a+b x^2+c x^4\right)^p}{x^5} \, dx","Int[(a + b*x^2 + c*x^4)^p/x^5,x]","-\frac{4^{p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(2 (1-p);-p,-p;3-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^2},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^2}\right)}{(1-p) x^4}","-\frac{4^{p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^2}{c x^2}\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(2 (1-p);-p,-p;3-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^2},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^2}\right)}{(1-p) x^4}",1,"-((4^(-1 + p)*(a + b*x^2 + c*x^4)^p*AppellF1[2*(1 - p), -p, -p, 3 - 2*p, -(b - Sqrt[b^2 - 4*a*c])/(2*c*x^2), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x^2)])/((1 - p)*x^4*((b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(c*x^2))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x^2)/(c*x^2))^p))","A",3,3,18,0.1667,1,"{1114, 758, 133}"
1122,1,138,0,0.1035316,"\int x^4 \left(a+b x^2+c x^4\right)^p \, dx","Int[x^4*(a + b*x^2 + c*x^4)^p,x]","\frac{1}{5} x^5 \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{5}{2};-p,-p;\frac{7}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)","\frac{1}{5} x^5 \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{5}{2};-p,-p;\frac{7}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)",1,"(x^5*(a + b*x^2 + c*x^4)^p*AppellF1[5/2, -p, -p, 7/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*(1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1141, 510}"
1123,1,138,0,0.0913095,"\int x^2 \left(a+b x^2+c x^4\right)^p \, dx","Int[x^2*(a + b*x^2 + c*x^4)^p,x]","\frac{1}{3} x^3 \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)","\frac{1}{3} x^3 \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)",1,"(x^3*(a + b*x^2 + c*x^4)^p*AppellF1[3/2, -p, -p, 5/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*(1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1141, 510}"
1124,1,133,0,0.0600732,"\int \left(a+b x^2+c x^4\right)^p \, dx","Int[(a + b*x^2 + c*x^4)^p,x]","x \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)","x \left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)",1,"(x*(a + b*x^2 + c*x^4)^p*AppellF1[1/2, -p, -p, 3/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/((1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,14,0.1429,1,"{1105, 429}"
1125,1,136,0,0.0856047,"\int \frac{\left(a+b x^2+c x^4\right)^p}{x^2} \, dx","Int[(a + b*x^2 + c*x^4)^p/x^2,x]","-\frac{\left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(-\frac{1}{2};-p,-p;\frac{1}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{x}","-\frac{\left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(-\frac{1}{2};-p,-p;\frac{1}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{x}",1,"-(((a + b*x^2 + c*x^4)^p*AppellF1[-1/2, -p, -p, 1/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(x*(1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]))^p))","A",2,2,18,0.1111,1,"{1141, 510}"
1126,1,138,0,0.0870568,"\int \frac{\left(a+b x^2+c x^4\right)^p}{x^4} \, dx","Int[(a + b*x^2 + c*x^4)^p/x^4,x]","-\frac{\left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(-\frac{3}{2};-p,-p;-\frac{1}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 x^3}","-\frac{\left(\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^2+c x^4\right)^p F_1\left(-\frac{3}{2};-p,-p;-\frac{1}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 x^3}",1,"-((a + b*x^2 + c*x^4)^p*AppellF1[-3/2, -p, -p, -1/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*x^3*(1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1141, 510}"