1,1,405,0,0.3893785,"\int \frac{1}{(d+e x) \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x)*Sqrt[a + c*x^4]),x]","\frac{e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 \sqrt{-a e^4-c d^4}}-\frac{e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 \sqrt{a e^4+c d^4}}+\frac{\sqrt[4]{c} d \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{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} d \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}","\frac{e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 \sqrt{-a e^4-c d^4}}-\frac{e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 \sqrt{a e^4+c d^4}}+\frac{\sqrt[4]{c} d \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{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} d \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}",1,"(e*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(2*Sqrt[-(c*d^4) - a*e^4]) - (e*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(2*Sqrt[c*d^4 + a*e^4]) + (c^(1/4)*d*(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)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4]) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c^(1/4)*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4])","A",7,7,19,0.3684,1,"{1725, 1217, 220, 1707, 1248, 725, 206}"
2,1,610,0,0.8000657,"\int \frac{1}{(d+e x)^2 \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x)^2*Sqrt[a + c*x^4]),x]","-\frac{c^{3/4} d^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \left(a e^4+c d^4\right)}-\frac{e^3 \sqrt{a+c x^4}}{(d+e x) \left(a e^4+c d^4\right)}+\frac{\sqrt{c} e^2 x \sqrt{a+c x^4}}{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^4+c d^4\right)}-\frac{c d^3 e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{\left(-a e^4-c d^4\right)^{3/2}}-\frac{c d^3 e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{\left(a e^4+c d^4\right)^{3/2}}+\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 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} e^2 \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)}{\sqrt{a+c x^4} \left(a e^4+c d^4\right)}","-\frac{c^{3/4} d^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \left(a e^4+c d^4\right)}-\frac{e^3 \sqrt{a+c x^4}}{(d+e x) \left(a e^4+c d^4\right)}+\frac{\sqrt{c} e^2 x \sqrt{a+c x^4}}{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^4+c d^4\right)}-\frac{c d^3 e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{\left(-a e^4-c d^4\right)^{3/2}}-\frac{c d^3 e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{\left(a e^4+c d^4\right)^{3/2}}+\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 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} e^2 \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)}{\sqrt{a+c x^4} \left(a e^4+c d^4\right)}",1,"-((e^3*Sqrt[a + c*x^4])/((c*d^4 + a*e^4)*(d + e*x))) + (Sqrt[c]*e^2*x*Sqrt[a + c*x^4])/((c*d^4 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)) - (c*d^3*e*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(-(c*d^4) - a*e^4)^(3/2) - (c*d^3*e*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(c*d^4 + a*e^4)^(3/2) - (a^(1/4)*c^(1/4)*e^2*(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*d^4 + a*e^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^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4]) - (c^(3/4)*d^2*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*(c*d^4 + a*e^4)*Sqrt[a + c*x^4])","A",11,11,19,0.5789,1,"{1727, 1742, 12, 1248, 725, 206, 1715, 1196, 1709, 220, 1707}"
3,1,518,0,0.5329253,"\int \frac{1}{(d+e x) \sqrt{a+b x^2+c x^4}} \, dx","Int[1/((d + e*x)*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-b d^2 e^2-c d^4}}{d e \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{-a e^4-b d^2 e^2-c d^4}}-\frac{e \tanh ^{-1}\left(\frac{2 a e^2+x^2 \left(b e^2+2 c d^2\right)+b d^2}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^4+b d^2 e^2+c d^4}}\right)}{2 \sqrt{a e^4+b d^2 e^2+c d^4}}+\frac{\sqrt[4]{c} d \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{a+b x^2+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\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}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};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)}{4 \sqrt[4]{a} \sqrt[4]{c} d \sqrt{a+b x^2+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}","\frac{e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-b d^2 e^2-c d^4}}{d e \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{-a e^4-b d^2 e^2-c d^4}}-\frac{e \tanh ^{-1}\left(\frac{2 a e^2+x^2 \left(b e^2+2 c d^2\right)+b d^2}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^4+b d^2 e^2+c d^4}}\right)}{2 \sqrt{a e^4+b d^2 e^2+c d^4}}+\frac{\sqrt[4]{c} d \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{a+b x^2+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\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}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};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)}{4 \sqrt[4]{a} \sqrt[4]{c} d \sqrt{a+b x^2+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}",1,"(e*ArcTan[(Sqrt[-(c*d^4) - b*d^2*e^2 - a*e^4]*x)/(d*e*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[-(c*d^4) - b*d^2*e^2 - a*e^4]) - (e*ArcTanh[(b*d^2 + 2*a*e^2 + (2*c*d^2 + b*e^2)*x^2)/(2*Sqrt[c*d^4 + b*d^2*e^2 + a*e^4]*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[c*d^4 + b*d^2*e^2 + a*e^4]) + (c^(1/4)*d*(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)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + b*x^2 + c*x^4]) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(4*a^(1/4)*c^(1/4)*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + b*x^2 + c*x^4])","A",7,7,24,0.2917,1,"{1724, 1216, 1103, 1706, 1247, 724, 206}"
4,1,822,0,1.2563974,"\int \frac{1}{(d+e x)^2 \sqrt{a+b x^2+c x^4}} \, dx","Int[1/((d + e*x)^2*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{\sqrt{c x^4+b x^2+a} e^3}{\left(c d^4+b e^2 d^2+a e^4\right) (d+e x)}-\frac{\sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+b x^2+a}{\left(\sqrt{c} x^2+\sqrt{a}\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) e^2}{\left(c d^4+b e^2 d^2+a e^4\right) \sqrt{c x^4+b x^2+a}}+\frac{\sqrt{c} x \sqrt{c x^4+b x^2+a} e^2}{\left(c d^4+b e^2 d^2+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right)}-\frac{d \left(2 c d^2+b e^2\right) \tan ^{-1}\left(\frac{\sqrt{-c d^4-b e^2 d^2-a e^4} x}{d e \sqrt{c x^4+b x^2+a}}\right) e}{2 \left(-c d^4-b e^2 d^2-a e^4\right)^{3/2}}-\frac{d \left(2 c d^2+b e^2\right) \tanh ^{-1}\left(\frac{b d^2+2 a e^2+\left(2 c d^2+b e^2\right) x^2}{2 \sqrt{c d^4+b e^2 d^2+a e^4} \sqrt{c x^4+b x^2+a}}\right) e}{2 \left(c d^4+b e^2 d^2+a e^4\right)^{3/2}}+\frac{\sqrt[4]{c} \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+b x^2+a}{\left(\sqrt{c} x^2+\sqrt{a}\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} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \sqrt{c x^4+b x^2+a}}-\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(2 c d^2+b e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+b x^2+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};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)}{4 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(c d^4+b e^2 d^2+a e^4\right) \sqrt{c x^4+b x^2+a}}","-\frac{\sqrt{c x^4+b x^2+a} e^3}{\left(c d^4+b e^2 d^2+a e^4\right) (d+e x)}-\frac{\sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+b x^2+a}{\left(\sqrt{c} x^2+\sqrt{a}\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) e^2}{\left(c d^4+b e^2 d^2+a e^4\right) \sqrt{c x^4+b x^2+a}}+\frac{\sqrt{c} x \sqrt{c x^4+b x^2+a} e^2}{\left(c d^4+b e^2 d^2+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right)}-\frac{d \left(2 c d^2+b e^2\right) \tan ^{-1}\left(\frac{\sqrt{-c d^4-b e^2 d^2-a e^4} x}{d e \sqrt{c x^4+b x^2+a}}\right) e}{2 \left(-c d^4-b e^2 d^2-a e^4\right)^{3/2}}-\frac{d \left(2 c d^2+b e^2\right) \tanh ^{-1}\left(\frac{b d^2+2 a e^2+\left(2 c d^2+b e^2\right) x^2}{2 \sqrt{c d^4+b e^2 d^2+a e^4} \sqrt{c x^4+b x^2+a}}\right) e}{2 \left(c d^4+b e^2 d^2+a e^4\right)^{3/2}}+\frac{\sqrt[4]{c} \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+b x^2+a}{\left(\sqrt{c} x^2+\sqrt{a}\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} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \sqrt{c x^4+b x^2+a}}-\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(2 c d^2+b e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+b x^2+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};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)}{4 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(c d^4+b e^2 d^2+a e^4\right) \sqrt{c x^4+b x^2+a}}",1,"-((e^3*Sqrt[a + b*x^2 + c*x^4])/((c*d^4 + b*d^2*e^2 + a*e^4)*(d + e*x))) + (Sqrt[c]*e^2*x*Sqrt[a + b*x^2 + c*x^4])/((c*d^4 + b*d^2*e^2 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)) - (d*e*(2*c*d^2 + b*e^2)*ArcTan[(Sqrt[-(c*d^4) - b*d^2*e^2 - a*e^4]*x)/(d*e*Sqrt[a + b*x^2 + c*x^4])])/(2*(-(c*d^4) - b*d^2*e^2 - a*e^4)^(3/2)) - (d*e*(2*c*d^2 + b*e^2)*ArcTanh[(b*d^2 + 2*a*e^2 + (2*c*d^2 + b*e^2)*x^2)/(2*Sqrt[c*d^4 + b*d^2*e^2 + a*e^4]*Sqrt[a + b*x^2 + c*x^4])])/(2*(c*d^4 + b*d^2*e^2 + a*e^4)^(3/2)) - (a^(1/4)*c^(1/4)*e^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])/((c*d^4 + b*d^2*e^2 + a*e^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^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + b*x^2 + c*x^4]) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(2*c*d^2 + b*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(4*a^(1/4)*c^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*(c*d^4 + b*d^2*e^2 + a*e^4)*Sqrt[a + b*x^2 + c*x^4])","A",11,11,24,0.4583,1,"{1726, 1741, 12, 1247, 724, 206, 1714, 1195, 1708, 1103, 1706}"