1,1,247,0,0.1509408,"\int \frac{c+d x^2}{a+b x^4} \, dx","Int[(c + d*x^2)/(a + b*x^4),x]","-\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}","-\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}",1,"-((Sqrt[b]*c + Sqrt[a]*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c + Sqrt[a]*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) - ((Sqrt[b]*c - Sqrt[a]*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c - Sqrt[a]*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4))","A",9,6,17,0.3529,1,"{1168, 1162, 617, 204, 1165, 628}"
2,1,247,0,0.137699,"\int \frac{c-d x^2}{a+b x^4} \, dx","Int[(c - d*x^2)/(a + b*x^4),x]","-\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}","-\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} b^{3/4}}-\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} b^{3/4}}",1,"-((Sqrt[b]*c - Sqrt[a]*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c - Sqrt[a]*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*b^(3/4)) - ((Sqrt[b]*c + Sqrt[a]*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c + Sqrt[a]*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*b^(3/4))","A",9,6,18,0.3333,1,"{1168, 1162, 617, 204, 1165, 628}"
3,1,86,0,0.0446384,"\int \frac{c+d x^2}{a-b x^4} \, dx","Int[(c + d*x^2)/(a - b*x^4),x]","\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}","\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}",1,"((Sqrt[b]*c - Sqrt[a]*d)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c + Sqrt[a]*d)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4))","A",3,3,18,0.1667,1,"{1167, 205, 208}"
4,1,86,0,0.0401515,"\int \frac{c-d x^2}{a-b x^4} \, dx","Int[(c - d*x^2)/(a - b*x^4),x]","\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}","\frac{\left(\sqrt{a} d+\sqrt{b} c\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}+\frac{\left(\sqrt{b} c-\sqrt{a} d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} b^{3/4}}",1,"((Sqrt[b]*c + Sqrt[a]*d)*ArcTan[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4)) + ((Sqrt[b]*c - Sqrt[a]*d)*ArcTanh[(b^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*b^(3/4))","A",3,3,19,0.1579,1,"{1167, 205, 208}"
5,1,40,0,0.0198282,"\int \frac{2+3 x^2}{4+9 x^4} \, dx","Int[(2 + 3*x^2)/(4 + 9*x^4),x]","\frac{\tan ^{-1}\left(\sqrt{3} x+1\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(1-\sqrt{3} x\right)}{2 \sqrt{3}}","\frac{\tan ^{-1}\left(\sqrt{3} x+1\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(1-\sqrt{3} x\right)}{2 \sqrt{3}}",1,"-ArcTan[1 - Sqrt[3]*x]/(2*Sqrt[3]) + ArcTan[1 + Sqrt[3]*x]/(2*Sqrt[3])","A",5,3,17,0.1765,1,"{1162, 617, 204}"
6,1,51,0,0.0213201,"\int \frac{2-3 x^2}{4+9 x^4} \, dx","Int[(2 - 3*x^2)/(4 + 9*x^4),x]","\frac{\log \left(3 x^2+2 \sqrt{3} x+2\right)}{4 \sqrt{3}}-\frac{\log \left(3 x^2-2 \sqrt{3} x+2\right)}{4 \sqrt{3}}","\frac{\log \left(3 x^2+2 \sqrt{3} x+2\right)}{4 \sqrt{3}}-\frac{\log \left(3 x^2-2 \sqrt{3} x+2\right)}{4 \sqrt{3}}",1,"-Log[2 - 2*Sqrt[3]*x + 3*x^2]/(4*Sqrt[3]) + Log[2 + 2*Sqrt[3]*x + 3*x^2]/(4*Sqrt[3])","A",3,2,17,0.1176,1,"{1165, 628}"
7,1,16,0,0.0029153,"\int \frac{2+3 x^2}{4-9 x^4} \, dx","Int[(2 + 3*x^2)/(4 - 9*x^4),x]","\frac{\tanh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}","\frac{\tanh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}",1,"ArcTanh[Sqrt[3/2]*x]/Sqrt[6]","A",2,2,17,0.1176,1,"{26, 206}"
8,1,16,0,0.0025036,"\int \frac{2-3 x^2}{4-9 x^4} \, dx","Int[(2 - 3*x^2)/(4 - 9*x^4),x]","\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}","\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{6}}",1,"ArcTan[Sqrt[3/2]*x]/Sqrt[6]","A",2,2,17,0.1176,1,"{26, 203}"
9,1,75,0,0.0367142,"\int \frac{\sqrt{a} \sqrt{b}+b x^2}{a+b x^4} \, dx","Int[(Sqrt[a]*Sqrt[b] + b*x^2)/(a + b*x^4),x]","\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a}}","\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a}}",1,"-((b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(Sqrt[2]*a^(1/4))) + (b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(Sqrt[2]*a^(1/4))","A",5,3,27,0.1111,1,"{1162, 617, 204}"
10,1,106,0,0.0472239,"\int \frac{\sqrt{a} \sqrt{b}-b x^2}{a+b x^4} \, dx","Int[(Sqrt[a]*Sqrt[b] - b*x^2)/(a + b*x^4),x]","\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{2 \sqrt{2} \sqrt[4]{a}}-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{2 \sqrt{2} \sqrt[4]{a}}","\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{2 \sqrt{2} \sqrt[4]{a}}-\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{2 \sqrt{2} \sqrt[4]{a}}",1,"-(b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(2*Sqrt[2]*a^(1/4)) + (b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(2*Sqrt[2]*a^(1/4))","A",3,2,28,0.07143,1,"{1165, 628}"
11,1,75,0,0.0498835,"\int \frac{d+e x^2}{d^2+e^2 x^4} \, dx","Int[(d + e*x^2)/(d^2 + e^2*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} \sqrt{e}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} \sqrt{e}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d}}+1\right)}{\sqrt{2} \sqrt{d} \sqrt{e}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{2} \sqrt{d} \sqrt{e}}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[e]*x)/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*Sqrt[e])) + ArcTan[1 + (Sqrt[2]*Sqrt[e]*x)/Sqrt[d]]/(Sqrt[2]*Sqrt[d]*Sqrt[e])","A",5,3,21,0.1429,1,"{1162, 617, 204}"
12,1,90,0,0.0466638,"\int \frac{d-e x^2}{d^2+e^2 x^4} \, dx","Int[(d - e*x^2)/(d^2 + e^2*x^4),x]","\frac{\log \left(\sqrt{2} \sqrt{d} \sqrt{e} x+d+e x^2\right)}{2 \sqrt{2} \sqrt{d} \sqrt{e}}-\frac{\log \left(-\sqrt{2} \sqrt{d} \sqrt{e} x+d+e x^2\right)}{2 \sqrt{2} \sqrt{d} \sqrt{e}}","\frac{\log \left(\sqrt{2} \sqrt{d} \sqrt{e} x+d+e x^2\right)}{2 \sqrt{2} \sqrt{d} \sqrt{e}}-\frac{\log \left(-\sqrt{2} \sqrt{d} \sqrt{e} x+d+e x^2\right)}{2 \sqrt{2} \sqrt{d} \sqrt{e}}",1,"-Log[d - Sqrt[2]*Sqrt[d]*Sqrt[e]*x + e*x^2]/(2*Sqrt[2]*Sqrt[d]*Sqrt[e]) + Log[d + Sqrt[2]*Sqrt[d]*Sqrt[e]*x + e*x^2]/(2*Sqrt[2]*Sqrt[d]*Sqrt[e])","A",3,2,22,0.09091,1,"{1165, 628}"
13,1,13,0,0.0062671,"\int \frac{5+2 x^2}{-1+x^4} \, dx","Int[(5 + 2*x^2)/(-1 + x^4),x]","-\frac{3}{2} \tan ^{-1}(x)-\frac{7}{2} \tanh ^{-1}(x)","-\frac{3}{2} \tan ^{-1}(x)-\frac{7}{2} \tanh ^{-1}(x)",1,"(-3*ArcTan[x])/2 - (7*ArcTanh[x])/2","A",3,3,15,0.2000,1,"{1167, 207, 203}"
14,1,16,0,0.0163202,"\int \frac{1+b x^2}{\sqrt{1-b^2 x^4}} \, dx","Int[(1 + b*x^2)/Sqrt[1 - b^2*x^4],x]","\frac{E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b}}","\frac{E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b}}",1,"EllipticE[ArcSin[Sqrt[b]*x], -1]/Sqrt[b]","A",2,2,22,0.09091,1,"{1199, 424}"
15,1,35,0,0.0327558,"\int \frac{1-b x^2}{\sqrt{1-b^2 x^4}} \, dx","Int[(1 - b*x^2)/Sqrt[1 - b^2*x^4],x]","\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b}}-\frac{E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b}}","\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b}}-\frac{E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b}}",1,"-(EllipticE[ArcSin[Sqrt[b]*x], -1]/Sqrt[b]) + (2*EllipticF[ArcSin[Sqrt[b]*x], -1])/Sqrt[b]","A",5,5,23,0.2174,1,"{1199, 423, 424, 248, 221}"
16,1,43,0,0.0254657,"\int \frac{1+b x^2}{\sqrt{-1+b^2 x^4}} \, dx","Int[(1 + b*x^2)/Sqrt[-1 + b^2*x^4],x]","\frac{\sqrt{1-b^2 x^4} E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b} \sqrt{b^2 x^4-1}}","\frac{\sqrt{1-b^2 x^4} E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b} \sqrt{b^2 x^4-1}}",1,"(Sqrt[1 - b^2*x^4]*EllipticE[ArcSin[Sqrt[b]*x], -1])/(Sqrt[b]*Sqrt[-1 + b^2*x^4])","A",3,3,21,0.1429,1,"{1200, 1199, 424}"
17,1,89,0,0.0455572,"\int \frac{1-b x^2}{\sqrt{-1+b^2 x^4}} \, dx","Int[(1 - b*x^2)/Sqrt[-1 + b^2*x^4],x]","\frac{2 \sqrt{1-b^2 x^4} F\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b} \sqrt{b^2 x^4-1}}-\frac{\sqrt{1-b^2 x^4} E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b} \sqrt{b^2 x^4-1}}","\frac{2 \sqrt{1-b^2 x^4} F\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b} \sqrt{b^2 x^4-1}}-\frac{\sqrt{1-b^2 x^4} E\left(\left.\sin ^{-1}\left(\sqrt{b} x\right)\right|-1\right)}{\sqrt{b} \sqrt{b^2 x^4-1}}",1,"-((Sqrt[1 - b^2*x^4]*EllipticE[ArcSin[Sqrt[b]*x], -1])/(Sqrt[b]*Sqrt[-1 + b^2*x^4])) + (2*Sqrt[1 - b^2*x^4]*EllipticF[ArcSin[Sqrt[b]*x], -1])/(Sqrt[b]*Sqrt[-1 + b^2*x^4])","A",6,6,22,0.2727,1,"{1200, 1199, 423, 424, 248, 221}"
18,1,89,0,0.0135721,"\int \frac{1-b x^2}{\sqrt{1+b^2 x^4}} \, dx","Int[(1 - b*x^2)/Sqrt[1 + b^2*x^4],x]","\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{b^2 x^4+1}}-\frac{x \sqrt{b^2 x^4+1}}{b x^2+1}","\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{b^2 x^4+1}}-\frac{x \sqrt{b^2 x^4+1}}{b x^2+1}",1,"-((x*Sqrt[1 + b^2*x^4])/(1 + b*x^2)) + ((1 + b*x^2)*Sqrt[(1 + b^2*x^4)/(1 + b*x^2)^2]*EllipticE[2*ArcTan[Sqrt[b]*x], 1/2])/(Sqrt[b]*Sqrt[1 + b^2*x^4])","A",1,1,22,0.04545,1,"{1196}"
19,1,152,0,0.0309574,"\int \frac{1+b x^2}{\sqrt{1+b^2 x^4}} \, dx","Int[(1 + b*x^2)/Sqrt[1 + b^2*x^4],x]","\frac{x \sqrt{b^2 x^4+1}}{b x^2+1}+\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{b^2 x^4+1}}-\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{b^2 x^4+1}}","\frac{x \sqrt{b^2 x^4+1}}{b x^2+1}+\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{b^2 x^4+1}}-\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{b^2 x^4+1}}",1,"(x*Sqrt[1 + b^2*x^4])/(1 + b*x^2) - ((1 + b*x^2)*Sqrt[(1 + b^2*x^4)/(1 + b*x^2)^2]*EllipticE[2*ArcTan[Sqrt[b]*x], 1/2])/(Sqrt[b]*Sqrt[1 + b^2*x^4]) + ((1 + b*x^2)*Sqrt[(1 + b^2*x^4)/(1 + b*x^2)^2]*EllipticF[2*ArcTan[Sqrt[b]*x], 1/2])/(Sqrt[b]*Sqrt[1 + b^2*x^4])","A",3,3,21,0.1429,1,"{1198, 220, 1196}"
20,1,90,0,0.0148451,"\int \frac{1-b x^2}{\sqrt{-1-b^2 x^4}} \, dx","Int[(1 - b*x^2)/Sqrt[-1 - b^2*x^4],x]","\frac{x \sqrt{-b^2 x^4-1}}{b x^2+1}+\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{-b^2 x^4-1}}","\frac{x \sqrt{-b^2 x^4-1}}{b x^2+1}+\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{-b^2 x^4-1}}",1,"(x*Sqrt[-1 - b^2*x^4])/(1 + b*x^2) + ((1 + b*x^2)*Sqrt[(1 + b^2*x^4)/(1 + b*x^2)^2]*EllipticE[2*ArcTan[Sqrt[b]*x], 1/2])/(Sqrt[b]*Sqrt[-1 - b^2*x^4])","A",1,1,23,0.04348,1,"{1196}"
21,1,156,0,0.03229,"\int \frac{1+b x^2}{\sqrt{-1-b^2 x^4}} \, dx","Int[(1 + b*x^2)/Sqrt[-1 - b^2*x^4],x]","-\frac{x \sqrt{-b^2 x^4-1}}{b x^2+1}+\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{-b^2 x^4-1}}-\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{-b^2 x^4-1}}","-\frac{x \sqrt{-b^2 x^4-1}}{b x^2+1}+\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{-b^2 x^4-1}}-\frac{\left(b x^2+1\right) \sqrt{\frac{b^2 x^4+1}{\left(b x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{b} x\right)|\frac{1}{2}\right)}{\sqrt{b} \sqrt{-b^2 x^4-1}}",1,"-((x*Sqrt[-1 - b^2*x^4])/(1 + b*x^2)) - ((1 + b*x^2)*Sqrt[(1 + b^2*x^4)/(1 + b*x^2)^2]*EllipticE[2*ArcTan[Sqrt[b]*x], 1/2])/(Sqrt[b]*Sqrt[-1 - b^2*x^4]) + ((1 + b*x^2)*Sqrt[(1 + b^2*x^4)/(1 + b*x^2)^2]*EllipticF[2*ArcTan[Sqrt[b]*x], 1/2])/(Sqrt[b]*Sqrt[-1 - b^2*x^4])","A",3,3,22,0.1364,1,"{1198, 220, 1196}"
22,1,10,0,0.0093696,"\int \frac{\sqrt{1+c^2 x^2}}{\sqrt{1-c^2 x^2}} \, dx","Int[Sqrt[1 + c^2*x^2]/Sqrt[1 - c^2*x^2],x]","\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}","\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}",1,"EllipticE[ArcSin[c*x], -1]/c","A",1,1,28,0.03571,1,"{424}"
23,1,10,0,0.015723,"\int \frac{1+c^2 x^2}{\sqrt{1-c^4 x^4}} \, dx","Int[(1 + c^2*x^2)/Sqrt[1 - c^4*x^4],x]","\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}","\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}",1,"EllipticE[ArcSin[c*x], -1]/c","A",2,2,24,0.08333,1,"{1199, 424}"
24,1,23,0,0.0260898,"\int \frac{\sqrt{1-c^2 x^2}}{\sqrt{1+c^2 x^2}} \, dx","Int[Sqrt[1 - c^2*x^2]/Sqrt[1 + c^2*x^2],x]","\frac{2 F\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}-\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}","\frac{2 F\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}-\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}",1,"-(EllipticE[ArcSin[c*x], -1]/c) + (2*EllipticF[ArcSin[c*x], -1])/c","A",4,4,28,0.1429,1,"{423, 424, 248, 221}"
25,1,23,0,0.0334165,"\int \frac{1-c^2 x^2}{\sqrt{1-c^4 x^4}} \, dx","Int[(1 - c^2*x^2)/Sqrt[1 - c^4*x^4],x]","\frac{2 F\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}-\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}","\frac{2 F\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}-\frac{E\left(\left.\sin ^{-1}(c x)\right|-1\right)}{c}",1,"-(EllipticE[ArcSin[c*x], -1]/c) + (2*EllipticF[ArcSin[c*x], -1])/c","A",5,5,25,0.2000,1,"{1199, 423, 424, 248, 221}"
26,1,82,0,0.0999168,"\int \frac{d+e x^2}{d^2+b x^2+e^2 x^4} \, dx","Int[(d + e*x^2)/(d^2 + b*x^2 + e^2*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-b}+2 e x}{\sqrt{b+2 d e}}\right)}{\sqrt{b+2 d e}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-b}-2 e x}{\sqrt{b+2 d e}}\right)}{\sqrt{b+2 d e}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-b}+2 e x}{\sqrt{b+2 d e}}\right)}{\sqrt{b+2 d e}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-b}-2 e x}{\sqrt{b+2 d e}}\right)}{\sqrt{b+2 d e}}",1,"-(ArcTan[(Sqrt[-b + 2*d*e] - 2*e*x)/Sqrt[b + 2*d*e]]/Sqrt[b + 2*d*e]) + ArcTan[(Sqrt[-b + 2*d*e] + 2*e*x)/Sqrt[b + 2*d*e]]/Sqrt[b + 2*d*e]","A",5,3,26,0.1154,1,"{1161, 618, 204}"
27,1,82,0,0.1096586,"\int \frac{d+e x^2}{d^2+f x^2+e^2 x^4} \, dx","Int[(d + e*x^2)/(d^2 + f*x^2 + e^2*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-f}+2 e x}{\sqrt{2 d e+f}}\right)}{\sqrt{2 d e+f}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-f}-2 e x}{\sqrt{2 d e+f}}\right)}{\sqrt{2 d e+f}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-f}+2 e x}{\sqrt{2 d e+f}}\right)}{\sqrt{2 d e+f}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e-f}-2 e x}{\sqrt{2 d e+f}}\right)}{\sqrt{2 d e+f}}",1,"-(ArcTan[(Sqrt[2*d*e - f] - 2*e*x)/Sqrt[2*d*e + f]]/Sqrt[2*d*e + f]) + ArcTan[(Sqrt[2*d*e - f] + 2*e*x)/Sqrt[2*d*e + f]]/Sqrt[2*d*e + f]","A",5,3,26,0.1154,1,"{1161, 618, 204}"
28,1,78,0,0.0980389,"\int \frac{d+e x^2}{d^2-b x^2+e^2 x^4} \, dx","Int[(d + e*x^2)/(d^2 - b*x^2 + e^2*x^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b+2 d e}-2 e x}{\sqrt{b-2 d e}}\right)}{\sqrt{b-2 d e}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b+2 d e}+2 e x}{\sqrt{b-2 d e}}\right)}{\sqrt{b-2 d e}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b+2 d e}-2 e x}{\sqrt{b-2 d e}}\right)}{\sqrt{b-2 d e}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b+2 d e}+2 e x}{\sqrt{b-2 d e}}\right)}{\sqrt{b-2 d e}}",1,"ArcTanh[(Sqrt[b + 2*d*e] - 2*e*x)/Sqrt[b - 2*d*e]]/Sqrt[b - 2*d*e] - ArcTanh[(Sqrt[b + 2*d*e] + 2*e*x)/Sqrt[b - 2*d*e]]/Sqrt[b - 2*d*e]","A",5,3,27,0.1111,1,"{1161, 618, 206}"
29,1,86,0,0.103915,"\int \frac{d+e x^2}{d^2-f x^2+e^2 x^4} \, dx","Int[(d + e*x^2)/(d^2 - f*x^2 + e^2*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e+f}+2 e x}{\sqrt{2 d e-f}}\right)}{\sqrt{2 d e-f}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e+f}-2 e x}{\sqrt{2 d e-f}}\right)}{\sqrt{2 d e-f}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e+f}+2 e x}{\sqrt{2 d e-f}}\right)}{\sqrt{2 d e-f}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2 d e+f}-2 e x}{\sqrt{2 d e-f}}\right)}{\sqrt{2 d e-f}}",1,"-(ArcTan[(Sqrt[2*d*e + f] - 2*e*x)/Sqrt[2*d*e - f]]/Sqrt[2*d*e - f]) + ArcTan[(Sqrt[2*d*e + f] + 2*e*x)/Sqrt[2*d*e - f]]/Sqrt[2*d*e - f]","A",5,3,27,0.1111,1,"{1161, 618, 204}"
30,1,78,0,0.0515393,"\int \frac{d-e x^2}{d^2+b x^2+e^2 x^4} \, dx","Int[(d - e*x^2)/(d^2 + b*x^2 + e^2*x^4),x]","\frac{\log \left(x \sqrt{2 d e-b}+d+e x^2\right)}{2 \sqrt{2 d e-b}}-\frac{\log \left(-x \sqrt{2 d e-b}+d+e x^2\right)}{2 \sqrt{2 d e-b}}","\frac{\log \left(x \sqrt{2 d e-b}+d+e x^2\right)}{2 \sqrt{2 d e-b}}-\frac{\log \left(-x \sqrt{2 d e-b}+d+e x^2\right)}{2 \sqrt{2 d e-b}}",1,"-Log[d - Sqrt[-b + 2*d*e]*x + e*x^2]/(2*Sqrt[-b + 2*d*e]) + Log[d + Sqrt[-b + 2*d*e]*x + e*x^2]/(2*Sqrt[-b + 2*d*e])","A",3,2,27,0.07407,1,"{1164, 628}"
31,1,78,0,0.0480425,"\int \frac{d-e x^2}{d^2+f x^2+e^2 x^4} \, dx","Int[(d - e*x^2)/(d^2 + f*x^2 + e^2*x^4),x]","\frac{\log \left(x \sqrt{2 d e-f}+d+e x^2\right)}{2 \sqrt{2 d e-f}}-\frac{\log \left(-x \sqrt{2 d e-f}+d+e x^2\right)}{2 \sqrt{2 d e-f}}","\frac{\log \left(x \sqrt{2 d e-f}+d+e x^2\right)}{2 \sqrt{2 d e-f}}-\frac{\log \left(-x \sqrt{2 d e-f}+d+e x^2\right)}{2 \sqrt{2 d e-f}}",1,"-Log[d - Sqrt[2*d*e - f]*x + e*x^2]/(2*Sqrt[2*d*e - f]) + Log[d + Sqrt[2*d*e - f]*x + e*x^2]/(2*Sqrt[2*d*e - f])","A",3,2,27,0.07407,1,"{1164, 628}"
32,1,70,0,0.0436809,"\int \frac{d-e x^2}{d^2-b x^2+e^2 x^4} \, dx","Int[(d - e*x^2)/(d^2 - b*x^2 + e^2*x^4),x]","\frac{\log \left(x \sqrt{b+2 d e}+d+e x^2\right)}{2 \sqrt{b+2 d e}}-\frac{\log \left(-x \sqrt{b+2 d e}+d+e x^2\right)}{2 \sqrt{b+2 d e}}","\frac{\log \left(x \sqrt{b+2 d e}+d+e x^2\right)}{2 \sqrt{b+2 d e}}-\frac{\log \left(-x \sqrt{b+2 d e}+d+e x^2\right)}{2 \sqrt{b+2 d e}}",1,"-Log[d - Sqrt[b + 2*d*e]*x + e*x^2]/(2*Sqrt[b + 2*d*e]) + Log[d + Sqrt[b + 2*d*e]*x + e*x^2]/(2*Sqrt[b + 2*d*e])","A",3,2,28,0.07143,1,"{1164, 628}"
33,1,70,0,0.0472136,"\int \frac{d-e x^2}{d^2-f x^2+e^2 x^4} \, dx","Int[(d - e*x^2)/(d^2 - f*x^2 + e^2*x^4),x]","\frac{\log \left(x \sqrt{2 d e+f}+d+e x^2\right)}{2 \sqrt{2 d e+f}}-\frac{\log \left(-x \sqrt{2 d e+f}+d+e x^2\right)}{2 \sqrt{2 d e+f}}","\frac{\log \left(x \sqrt{2 d e+f}+d+e x^2\right)}{2 \sqrt{2 d e+f}}-\frac{\log \left(-x \sqrt{2 d e+f}+d+e x^2\right)}{2 \sqrt{2 d e+f}}",1,"-Log[d - Sqrt[2*d*e + f]*x + e*x^2]/(2*Sqrt[2*d*e + f]) + Log[d + Sqrt[2*d*e + f]*x + e*x^2]/(2*Sqrt[2*d*e + f])","A",3,2,28,0.07143,1,"{1164, 628}"
34,1,134,0,0.1007174,"\int \frac{d-e x^2}{\frac{c d^2}{e^2}+b x^2+c x^4} \, dx","Int[(d - e*x^2)/((c*d^2)/e^2 + b*x^2 + c*x^4),x]","\frac{e^{3/2} \log \left(\sqrt{e} x \sqrt{2 c d-b e}+\sqrt{c} d+\sqrt{c} e x^2\right)}{2 \sqrt{c} \sqrt{2 c d-b e}}-\frac{e^{3/2} \log \left(-\sqrt{e} x \sqrt{2 c d-b e}+\sqrt{c} d+\sqrt{c} e x^2\right)}{2 \sqrt{c} \sqrt{2 c d-b e}}","\frac{e^{3/2} \log \left(\sqrt{e} x \sqrt{2 c d-b e}+\sqrt{c} d+\sqrt{c} e x^2\right)}{2 \sqrt{c} \sqrt{2 c d-b e}}-\frac{e^{3/2} \log \left(-\sqrt{e} x \sqrt{2 c d-b e}+\sqrt{c} d+\sqrt{c} e x^2\right)}{2 \sqrt{c} \sqrt{2 c d-b e}}",1,"-(e^(3/2)*Log[Sqrt[c]*d - Sqrt[e]*Sqrt[2*c*d - b*e]*x + Sqrt[c]*e*x^2])/(2*Sqrt[c]*Sqrt[2*c*d - b*e]) + (e^(3/2)*Log[Sqrt[c]*d + Sqrt[e]*Sqrt[2*c*d - b*e]*x + Sqrt[c]*e*x^2])/(2*Sqrt[c]*Sqrt[2*c*d - b*e])","A",3,2,30,0.06667,1,"{1164, 628}"
35,1,130,0,0.1660976,"\int \frac{d+e x^2}{\frac{c d^2}{e^2}+b x^2+c x^4} \, dx","Int[(d + e*x^2)/((c*d^2)/e^2 + b*x^2 + c*x^4),x]","\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}+2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}-\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}-2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}","\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}+2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}-\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}-2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}",1,"-((e^(3/2)*ArcTan[(Sqrt[2*c*d - b*e] - 2*Sqrt[c]*Sqrt[e]*x)/Sqrt[2*c*d + b*e]])/(Sqrt[c]*Sqrt[2*c*d + b*e])) + (e^(3/2)*ArcTan[(Sqrt[2*c*d - b*e] + 2*Sqrt[c]*Sqrt[e]*x)/Sqrt[2*c*d + b*e]])/(Sqrt[c]*Sqrt[2*c*d + b*e])","A",5,3,29,0.1034,1,"{1161, 618, 204}"
36,1,130,0,0.1307658,"\int \frac{d+e x^2}{b x^2+c \left(\frac{d^2}{e^2}+x^4\right)} \, dx","Int[(d + e*x^2)/(b*x^2 + c*(d^2/e^2 + x^4)),x]","\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}+2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}-\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}-2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}","\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}+2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}-\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{2 c d-b e}-2 \sqrt{c} \sqrt{e} x}{\sqrt{b e+2 c d}}\right)}{\sqrt{c} \sqrt{b e+2 c d}}",1,"-((e^(3/2)*ArcTan[(Sqrt[2*c*d - b*e] - 2*Sqrt[c]*Sqrt[e]*x)/Sqrt[2*c*d + b*e]])/(Sqrt[c]*Sqrt[2*c*d + b*e])) + (e^(3/2)*ArcTan[(Sqrt[2*c*d - b*e] + 2*Sqrt[c]*Sqrt[e]*x)/Sqrt[2*c*d + b*e]])/(Sqrt[c]*Sqrt[2*c*d + b*e])","A",6,4,29,0.1379,1,"{1990, 1161, 618, 204}"
37,1,29,0,0.0255999,"\int \frac{a-b x^2}{a^2+(-1+2 a b) x^2+b^2 x^4} \, dx","Int[(a - b*x^2)/(a^2 + (-1 + 2*a*b)*x^2 + b^2*x^4),x]","\frac{1}{2} \log \left(a+b x^2+x\right)-\frac{1}{2} \log \left(a+b x^2-x\right)","\frac{1}{2} \log \left(a+b x^2+x\right)-\frac{1}{2} \log \left(a+b x^2-x\right)",1,"-Log[a - x + b*x^2]/2 + Log[a + x + b*x^2]/2","A",3,2,32,0.06250,1,"{1164, 628}"
38,1,60,0,0.0686734,"\int \frac{a+b x^2}{a^2+(-1+2 a b) x^2+b^2 x^4} \, dx","Int[(a + b*x^2)/(a^2 + (-1 + 2*a*b)*x^2 + b^2*x^4),x]","\frac{\tanh ^{-1}\left(\frac{1-2 b x}{\sqrt{1-4 a b}}\right)}{\sqrt{1-4 a b}}-\frac{\tanh ^{-1}\left(\frac{2 b x+1}{\sqrt{1-4 a b}}\right)}{\sqrt{1-4 a b}}","\frac{\tanh ^{-1}\left(\frac{1-2 b x}{\sqrt{1-4 a b}}\right)}{\sqrt{1-4 a b}}-\frac{\tanh ^{-1}\left(\frac{2 b x+1}{\sqrt{1-4 a b}}\right)}{\sqrt{1-4 a b}}",1,"ArcTanh[(1 - 2*b*x)/Sqrt[1 - 4*a*b]]/Sqrt[1 - 4*a*b] - ArcTanh[(1 + 2*b*x)/Sqrt[1 - 4*a*b]]/Sqrt[1 - 4*a*b]","A",5,3,31,0.09677,1,"{1161, 618, 206}"
39,1,62,0,0.0579177,"\int \frac{1+2 x^2}{1+b x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + b*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{4-b}+4 x}{\sqrt{b+4}}\right)}{\sqrt{b+4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{4-b}-4 x}{\sqrt{b+4}}\right)}{\sqrt{b+4}}","\frac{\tan ^{-1}\left(\frac{\sqrt{4-b}+4 x}{\sqrt{b+4}}\right)}{\sqrt{b+4}}-\frac{\tan ^{-1}\left(\frac{\sqrt{4-b}-4 x}{\sqrt{b+4}}\right)}{\sqrt{b+4}}",1,"-(ArcTan[(Sqrt[4 - b] - 4*x)/Sqrt[4 + b]]/Sqrt[4 + b]) + ArcTan[(Sqrt[4 - b] + 4*x)/Sqrt[4 + b]]/Sqrt[4 + b]","A",5,3,22,0.1364,1,"{1161, 618, 204}"
40,1,66,0,0.0579648,"\int \frac{1+2 x^2}{1-b x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 - b*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b+4}+4 x}{\sqrt{4-b}}\right)}{\sqrt{4-b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b+4}-4 x}{\sqrt{4-b}}\right)}{\sqrt{4-b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b+4}+4 x}{\sqrt{4-b}}\right)}{\sqrt{4-b}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b+4}-4 x}{\sqrt{4-b}}\right)}{\sqrt{4-b}}",1,"-(ArcTan[(Sqrt[4 + b] - 4*x)/Sqrt[4 - b]]/Sqrt[4 - b]) + ArcTan[(Sqrt[4 + b] + 4*x)/Sqrt[4 - b]]/Sqrt[4 - b]","A",5,3,23,0.1304,1,"{1161, 618, 204}"
41,1,45,0,0.0593532,"\int \frac{1+2 x^2}{1+6 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + 6*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3-\sqrt{5}}}\right)}{\sqrt{10}}+\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{5}}}\right)}{\sqrt{10}}","\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3-\sqrt{5}}}\right)}{\sqrt{10}}+\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{5}}}\right)}{\sqrt{10}}",1,"ArcTan[(2*x)/Sqrt[3 - Sqrt[5]]]/Sqrt[10] + ArcTan[(2*x)/Sqrt[3 + Sqrt[5]]]/Sqrt[10]","A",3,2,22,0.09091,1,"{1163, 203}"
42,1,15,0,0.0093769,"\int \frac{1+2 x^2}{1+5 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + 5*x^2 + 4*x^4),x]","\frac{1}{3} \tan ^{-1}(x)+\frac{1}{3} \tan ^{-1}(2 x)","\frac{1}{3} \tan ^{-1}(x)+\frac{1}{3} \tan ^{-1}(2 x)",1,"ArcTan[x]/3 + ArcTan[2*x]/3","A",3,2,22,0.09091,1,"{1163, 203}"
43,1,14,0,0.0065785,"\int \frac{1+2 x^2}{1+4 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + 4*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}",1,"ArcTan[Sqrt[2]*x]/Sqrt[2]","A",3,3,22,0.1364,1,"{28, 21, 203}"
44,1,38,0,0.0352245,"\int \frac{1+2 x^2}{1+3 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + 3*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{4 x+1}{\sqrt{7}}\right)}{\sqrt{7}}-\frac{\tan ^{-1}\left(\frac{1-4 x}{\sqrt{7}}\right)}{\sqrt{7}}","\frac{\tan ^{-1}\left(\frac{4 x+1}{\sqrt{7}}\right)}{\sqrt{7}}-\frac{\tan ^{-1}\left(\frac{1-4 x}{\sqrt{7}}\right)}{\sqrt{7}}",1,"-(ArcTan[(1 - 4*x)/Sqrt[7]]/Sqrt[7]) + ArcTan[(1 + 4*x)/Sqrt[7]]/Sqrt[7]","A",5,3,22,0.1364,1,"{1161, 618, 204}"
45,1,48,0,0.0395263,"\int \frac{1+2 x^2}{1+2 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + 2*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{2} x+1}{\sqrt{3}}\right)}{\sqrt{6}}-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt{2} x}{\sqrt{3}}\right)}{\sqrt{6}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{2} x+1}{\sqrt{3}}\right)}{\sqrt{6}}-\frac{\tan ^{-1}\left(\frac{1-2 \sqrt{2} x}{\sqrt{3}}\right)}{\sqrt{6}}",1,"-(ArcTan[(1 - 2*Sqrt[2]*x)/Sqrt[3]]/Sqrt[6]) + ArcTan[(1 + 2*Sqrt[2]*x)/Sqrt[3]]/Sqrt[6]","A",5,3,22,0.1364,1,"{1161, 618, 204}"
46,1,46,0,0.0431827,"\int \frac{1+2 x^2}{1+x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{4 x+\sqrt{3}}{\sqrt{5}}\right)}{\sqrt{5}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3}-4 x}{\sqrt{5}}\right)}{\sqrt{5}}","\frac{\tan ^{-1}\left(\frac{4 x+\sqrt{3}}{\sqrt{5}}\right)}{\sqrt{5}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3}-4 x}{\sqrt{5}}\right)}{\sqrt{5}}",1,"-(ArcTan[(Sqrt[3] - 4*x)/Sqrt[5]]/Sqrt[5]) + ArcTan[(Sqrt[3] + 4*x)/Sqrt[5]]/Sqrt[5]","A",5,3,20,0.1500,1,"{1161, 618, 204}"
47,1,21,0,0.0129114,"\int \frac{1+2 x^2}{1+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 + 4*x^4),x]","\frac{1}{2} \tan ^{-1}(2 x+1)-\frac{1}{2} \tan ^{-1}(1-2 x)","\frac{1}{2} \tan ^{-1}(2 x+1)-\frac{1}{2} \tan ^{-1}(1-2 x)",1,"-ArcTan[1 - 2*x]/2 + ArcTan[1 + 2*x]/2","A",5,3,17,0.1765,1,"{1162, 617, 204}"
48,1,46,0,0.0414338,"\int \frac{1+2 x^2}{1-x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 - x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{4 x+\sqrt{5}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{5}-4 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{\tan ^{-1}\left(\frac{4 x+\sqrt{5}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{5}-4 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(Sqrt[5] - 4*x)/Sqrt[3]]/Sqrt[3]) + ArcTan[(Sqrt[5] + 4*x)/Sqrt[3]]/Sqrt[3]","A",5,3,22,0.1364,1,"{1161, 618, 204}"
49,1,44,0,0.0336888,"\int \frac{1+2 x^2}{1-2 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 - 2*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(2 \sqrt{2} x+\sqrt{3}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt{2} x\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(2 \sqrt{2} x+\sqrt{3}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt{2} x\right)}{\sqrt{2}}",1,"-(ArcTan[Sqrt[3] - 2*Sqrt[2]*x]/Sqrt[2]) + ArcTan[Sqrt[3] + 2*Sqrt[2]*x]/Sqrt[2]","A",5,3,22,0.1364,1,"{1161, 618, 204}"
50,1,23,0,0.0262838,"\int \frac{1+2 x^2}{1-3 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 - 3*x^2 + 4*x^4),x]","\tan ^{-1}\left(4 x+\sqrt{7}\right)-\tan ^{-1}\left(\sqrt{7}-4 x\right)","\tan ^{-1}\left(4 x+\sqrt{7}\right)-\tan ^{-1}\left(\sqrt{7}-4 x\right)",1,"-ArcTan[Sqrt[7] - 4*x] + ArcTan[Sqrt[7] + 4*x]","A",5,3,22,0.1364,1,"{1161, 618, 204}"
51,1,11,0,0.0050256,"\int \frac{1+2 x^2}{1-4 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 - 4*x^2 + 4*x^4),x]","\frac{x}{1-2 x^2}","\frac{x}{1-2 x^2}",1,"x/(1 - 2*x^2)","A",2,2,22,0.09091,1,"{28, 383}"
52,1,39,0,0.0178852,"\int \frac{1+2 x^2}{1-5 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 - 5*x^2 + 4*x^4),x]","-\frac{1}{2} \log (1-2 x)+\frac{1}{2} \log (1-x)-\frac{1}{2} \log (x+1)+\frac{1}{2} \log (2 x+1)","-\frac{1}{2} \log (1-2 x)+\frac{1}{2} \log (1-x)-\frac{1}{2} \log (x+1)+\frac{1}{2} \log (2 x+1)",1,"-Log[1 - 2*x]/2 + Log[1 - x]/2 - Log[1 + x]/2 + Log[1 + 2*x]/2","A",7,3,22,0.1364,1,"{1161, 616, 31}"
53,1,44,0,0.0347643,"\int \frac{1+2 x^2}{1-6 x^2+4 x^4} \, dx","Int[(1 + 2*x^2)/(1 - 6*x^2 + 4*x^4),x]","\frac{\tanh ^{-1}\left(\sqrt{5}-2 \sqrt{2} x\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(2 \sqrt{2} x+\sqrt{5}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{5}-2 \sqrt{2} x\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(2 \sqrt{2} x+\sqrt{5}\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[5] - 2*Sqrt[2]*x]/Sqrt[2] - ArcTanh[Sqrt[5] + 2*Sqrt[2]*x]/Sqrt[2]","A",5,3,22,0.1364,1,"{1161, 618, 206}"
54,1,66,0,0.028782,"\int \frac{1-2 x^2}{1+b x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + b*x^2 + 4*x^4),x]","\frac{\log \left(\sqrt{4-b} x+2 x^2+1\right)}{2 \sqrt{4-b}}-\frac{\log \left(-\sqrt{4-b} x+2 x^2+1\right)}{2 \sqrt{4-b}}","\frac{\log \left(\sqrt{4-b} x+2 x^2+1\right)}{2 \sqrt{4-b}}-\frac{\log \left(-\sqrt{4-b} x+2 x^2+1\right)}{2 \sqrt{4-b}}",1,"-Log[1 - Sqrt[4 - b]*x + 2*x^2]/(2*Sqrt[4 - b]) + Log[1 + Sqrt[4 - b]*x + 2*x^2]/(2*Sqrt[4 - b])","A",3,2,22,0.09091,1,"{1164, 628}"
55,1,46,0,0.0312964,"\int \frac{1-2 x^2}{1+6 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + 6*x^2 + 4*x^4),x]","\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3-\sqrt{5}}}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{5}}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3-\sqrt{5}}}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3+\sqrt{5}}}\right)}{\sqrt{2}}",1,"ArcTan[(2*x)/Sqrt[3 - Sqrt[5]]]/Sqrt[2] - ArcTan[(2*x)/Sqrt[3 + Sqrt[5]]]/Sqrt[2]","A",3,2,22,0.09091,1,"{1163, 203}"
56,1,9,0,0.0092982,"\int \frac{1-2 x^2}{1+5 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + 5*x^2 + 4*x^4),x]","\tan ^{-1}(2 x)-\tan ^{-1}(x)","\tan ^{-1}(2 x)-\tan ^{-1}(x)",1,"-ArcTan[x] + ArcTan[2*x]","A",3,2,22,0.09091,1,"{1163, 203}"
57,1,11,0,0.0053507,"\int \frac{1-2 x^2}{1+4 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + 4*x^2 + 4*x^4),x]","\frac{x}{2 x^2+1}","\frac{x}{2 x^2+1}",1,"x/(1 + 2*x^2)","A",2,2,22,0.09091,1,"{28, 383}"
58,1,29,0,0.0159712,"\int \frac{1-2 x^2}{1+3 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + 3*x^2 + 4*x^4),x]","\frac{1}{2} \log \left(2 x^2+x+1\right)-\frac{1}{2} \log \left(2 x^2-x+1\right)","\frac{1}{2} \log \left(2 x^2+x+1\right)-\frac{1}{2} \log \left(2 x^2-x+1\right)",1,"-Log[1 - x + 2*x^2]/2 + Log[1 + x + 2*x^2]/2","A",3,2,22,0.09091,1,"{1164, 628}"
59,1,50,0,0.0230111,"\int \frac{1-2 x^2}{1+2 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + 2*x^2 + 4*x^4),x]","\frac{\log \left(2 x^2+\sqrt{2} x+1\right)}{2 \sqrt{2}}-\frac{\log \left(2 x^2-\sqrt{2} x+1\right)}{2 \sqrt{2}}","\frac{\log \left(2 x^2+\sqrt{2} x+1\right)}{2 \sqrt{2}}-\frac{\log \left(2 x^2-\sqrt{2} x+1\right)}{2 \sqrt{2}}",1,"-Log[1 - Sqrt[2]*x + 2*x^2]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*x + 2*x^2]/(2*Sqrt[2])","A",3,2,22,0.09091,1,"{1164, 628}"
60,1,50,0,0.0225422,"\int \frac{1-2 x^2}{1+x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + x^2 + 4*x^4),x]","\frac{\log \left(2 x^2+\sqrt{3} x+1\right)}{2 \sqrt{3}}-\frac{\log \left(2 x^2-\sqrt{3} x+1\right)}{2 \sqrt{3}}","\frac{\log \left(2 x^2+\sqrt{3} x+1\right)}{2 \sqrt{3}}-\frac{\log \left(2 x^2-\sqrt{3} x+1\right)}{2 \sqrt{3}}",1,"-Log[1 - Sqrt[3]*x + 2*x^2]/(2*Sqrt[3]) + Log[1 + Sqrt[3]*x + 2*x^2]/(2*Sqrt[3])","A",3,2,20,0.1000,1,"{1164, 628}"
61,1,31,0,0.0149195,"\int \frac{1-2 x^2}{1+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 + 4*x^4),x]","\frac{1}{4} \log \left(2 x^2+2 x+1\right)-\frac{1}{4} \log \left(2 x^2-2 x+1\right)","\frac{1}{4} \log \left(2 x^2+2 x+1\right)-\frac{1}{4} \log \left(2 x^2-2 x+1\right)",1,"-Log[1 - 2*x + 2*x^2]/4 + Log[1 + 2*x + 2*x^2]/4","A",3,2,17,0.1176,1,"{1165, 628}"
62,1,50,0,0.0228969,"\int \frac{1-2 x^2}{1-x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 - x^2 + 4*x^4),x]","\frac{\log \left(2 x^2+\sqrt{5} x+1\right)}{2 \sqrt{5}}-\frac{\log \left(2 x^2-\sqrt{5} x+1\right)}{2 \sqrt{5}}","\frac{\log \left(2 x^2+\sqrt{5} x+1\right)}{2 \sqrt{5}}-\frac{\log \left(2 x^2-\sqrt{5} x+1\right)}{2 \sqrt{5}}",1,"-Log[1 - Sqrt[5]*x + 2*x^2]/(2*Sqrt[5]) + Log[1 + Sqrt[5]*x + 2*x^2]/(2*Sqrt[5])","A",3,2,22,0.09091,1,"{1164, 628}"
63,1,50,0,0.0237402,"\int \frac{1-2 x^2}{1-2 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 - 2*x^2 + 4*x^4),x]","\frac{\log \left(2 x^2+\sqrt{6} x+1\right)}{2 \sqrt{6}}-\frac{\log \left(2 x^2-\sqrt{6} x+1\right)}{2 \sqrt{6}}","\frac{\log \left(2 x^2+\sqrt{6} x+1\right)}{2 \sqrt{6}}-\frac{\log \left(2 x^2-\sqrt{6} x+1\right)}{2 \sqrt{6}}",1,"-Log[1 - Sqrt[6]*x + 2*x^2]/(2*Sqrt[6]) + Log[1 + Sqrt[6]*x + 2*x^2]/(2*Sqrt[6])","A",3,2,22,0.09091,1,"{1164, 628}"
64,1,50,0,0.0224819,"\int \frac{1-2 x^2}{1-3 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 - 3*x^2 + 4*x^4),x]","\frac{\log \left(2 x^2+\sqrt{7} x+1\right)}{2 \sqrt{7}}-\frac{\log \left(2 x^2-\sqrt{7} x+1\right)}{2 \sqrt{7}}","\frac{\log \left(2 x^2+\sqrt{7} x+1\right)}{2 \sqrt{7}}-\frac{\log \left(2 x^2-\sqrt{7} x+1\right)}{2 \sqrt{7}}",1,"-Log[1 - Sqrt[7]*x + 2*x^2]/(2*Sqrt[7]) + Log[1 + Sqrt[7]*x + 2*x^2]/(2*Sqrt[7])","A",3,2,22,0.09091,1,"{1164, 628}"
65,1,14,0,0.005621,"\int \frac{1-2 x^2}{1-4 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 - 4*x^2 + 4*x^4),x]","\frac{\tanh ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[2]*x]/Sqrt[2]","A",3,3,22,0.1364,1,"{28, 21, 206}"
66,1,39,0,0.0171199,"\int \frac{1-2 x^2}{1-5 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 - 5*x^2 + 4*x^4),x]","-\frac{1}{6} \log (1-2 x)-\frac{1}{6} \log (1-x)+\frac{1}{6} \log (x+1)+\frac{1}{6} \log (2 x+1)","-\frac{1}{6} \log (1-2 x)-\frac{1}{6} \log (1-x)+\frac{1}{6} \log (x+1)+\frac{1}{6} \log (2 x+1)",1,"-Log[1 - 2*x]/6 - Log[1 - x]/6 + Log[1 + x]/6 + Log[1 + 2*x]/6","A",7,3,22,0.1364,1,"{1161, 616, 31}"
67,1,48,0,0.0386751,"\int \frac{1-2 x^2}{1-6 x^2+4 x^4} \, dx","Int[(1 - 2*x^2)/(1 - 6*x^2 + 4*x^4),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{2} x+1}{\sqrt{5}}\right)}{\sqrt{10}}-\frac{\tanh ^{-1}\left(\frac{1-2 \sqrt{2} x}{\sqrt{5}}\right)}{\sqrt{10}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{2} x+1}{\sqrt{5}}\right)}{\sqrt{10}}-\frac{\tanh ^{-1}\left(\frac{1-2 \sqrt{2} x}{\sqrt{5}}\right)}{\sqrt{10}}",1,"-(ArcTanh[(1 - 2*Sqrt[2]*x)/Sqrt[5]]/Sqrt[10]) + ArcTanh[(1 + 2*Sqrt[2]*x)/Sqrt[5]]/Sqrt[10]","A",5,3,22,0.1364,1,"{1161, 618, 206}"
68,1,62,0,0.0556889,"\int \frac{1+x^2}{1+b x^2+x^4} \, dx","Int[(1 + x^2)/(1 + b*x^2 + x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2-b}+2 x}{\sqrt{b+2}}\right)}{\sqrt{b+2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-b}-2 x}{\sqrt{b+2}}\right)}{\sqrt{b+2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2-b}+2 x}{\sqrt{b+2}}\right)}{\sqrt{b+2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-b}-2 x}{\sqrt{b+2}}\right)}{\sqrt{b+2}}",1,"-(ArcTan[(Sqrt[2 - b] - 2*x)/Sqrt[2 + b]]/Sqrt[2 + b]) + ArcTan[(Sqrt[2 - b] + 2*x)/Sqrt[2 + b]]/Sqrt[2 + b]","A",5,3,18,0.1667,1,"{1161, 618, 204}"
69,1,49,0,0.0878152,"\int \frac{1+x^2}{1+5 x^2+x^4} \, dx","Int[(1 + x^2)/(1 + 5*x^2 + x^4),x]","\frac{\tan ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{21}}} x\right)}{\sqrt{7}}+\frac{\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(5+\sqrt{21}\right)} x\right)}{\sqrt{7}}","\frac{\tan ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{21}}} x\right)}{\sqrt{7}}+\frac{\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(5+\sqrt{21}\right)} x\right)}{\sqrt{7}}",1,"ArcTan[Sqrt[2/(5 + Sqrt[21])]*x]/Sqrt[7] + ArcTan[Sqrt[(5 + Sqrt[21])/2]*x]/Sqrt[7]","A",3,2,18,0.1111,1,"{1163, 203}"
70,1,43,0,0.049938,"\int \frac{1+x^2}{1+4 x^2+x^4} \, dx","Int[(1 + x^2)/(1 + 4*x^2 + x^4),x]","\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2-\sqrt{3}}}\right)}{\sqrt{6}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2+\sqrt{3}}}\right)}{\sqrt{6}}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2-\sqrt{3}}}\right)}{\sqrt{6}}+\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2+\sqrt{3}}}\right)}{\sqrt{6}}",1,"ArcTan[x/Sqrt[2 - Sqrt[3]]]/Sqrt[6] + ArcTan[x/Sqrt[2 + Sqrt[3]]]/Sqrt[6]","A",3,2,18,0.1111,1,"{1163, 203}"
71,1,49,0,0.0618606,"\int \frac{1+x^2}{1+3 x^2+x^4} \, dx","Int[(1 + x^2)/(1 + 3*x^2 + x^4),x]","\frac{\tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)}{\sqrt{5}}+\frac{\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{\sqrt{5}}","\frac{\tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)}{\sqrt{5}}+\frac{\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{\sqrt{5}}",1,"ArcTan[Sqrt[2/(3 + Sqrt[5])]*x]/Sqrt[5] + ArcTan[Sqrt[(3 + Sqrt[5])/2]*x]/Sqrt[5]","A",3,2,18,0.1111,1,"{1163, 203}"
72,1,2,0,0.001515,"\int \frac{1+x^2}{1+2 x^2+x^4} \, dx","Int[(1 + x^2)/(1 + 2*x^2 + x^4),x]","\tan ^{-1}(x)","\tan ^{-1}(x)",1,"ArcTan[x]","A",2,2,18,0.1111,1,"{28, 203}"
73,1,38,0,0.0270838,"\int \frac{1+x^2}{1+x^2+x^4} \, dx","Int[(1 + x^2)/(1 + x^2 + x^4),x]","\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]","A",5,3,16,0.1875,1,"{1161, 618, 204}"
74,1,35,0,0.0183083,"\int \frac{1+x^2}{1+x^4} \, dx","Int[(1 + x^2)/(1 + x^4),x]","\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{\sqrt{2}}",1,"-(ArcTan[1 - Sqrt[2]*x]/Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/Sqrt[2]","A",5,3,13,0.2308,1,"{1162, 617, 204}"
75,1,23,0,0.0195514,"\int \frac{1+x^2}{1-x^2+x^4} \, dx","Int[(1 + x^2)/(1 - x^2 + x^4),x]","\tan ^{-1}\left(2 x+\sqrt{3}\right)-\tan ^{-1}\left(\sqrt{3}-2 x\right)","\tan ^{-1}\left(2 x+\sqrt{3}\right)-\tan ^{-1}\left(\sqrt{3}-2 x\right)",1,"-ArcTan[Sqrt[3] - 2*x] + ArcTan[Sqrt[3] + 2*x]","A",5,3,18,0.1667,1,"{1161, 618, 204}"
76,1,11,0,0.0032829,"\int \frac{1+x^2}{1-2 x^2+x^4} \, dx","Int[(1 + x^2)/(1 - 2*x^2 + x^4),x]","\frac{x}{1-x^2}","\frac{x}{1-x^2}",1,"x/(1 - x^2)","A",2,2,18,0.1111,1,"{28, 383}"
77,1,65,0,0.0319407,"\int \frac{1+x^2}{1-3 x^2+x^4} \, dx","Int[(1 + x^2)/(1 - 3*x^2 + x^4),x]","\frac{1}{2} \log \left(-2 x-\sqrt{5}+1\right)+\frac{1}{2} \log \left(-2 x+\sqrt{5}+1\right)-\frac{1}{2} \log \left(2 x-\sqrt{5}+1\right)-\frac{1}{2} \log \left(2 x+\sqrt{5}+1\right)","\frac{1}{2} \log \left(-2 x-\sqrt{5}+1\right)+\frac{1}{2} \log \left(-2 x+\sqrt{5}+1\right)-\frac{1}{2} \log \left(2 x-\sqrt{5}+1\right)-\frac{1}{2} \log \left(2 x+\sqrt{5}+1\right)",1,"Log[1 - Sqrt[5] - 2*x]/2 + Log[1 + Sqrt[5] - 2*x]/2 - Log[1 - Sqrt[5] + 2*x]/2 - Log[1 + Sqrt[5] + 2*x]/2","A",7,3,18,0.1667,1,"{1161, 616, 31}"
78,1,43,0,0.0331814,"\int \frac{1+x^2}{1-4 x^2+x^4} \, dx","Int[(1 + x^2)/(1 - 4*x^2 + x^4),x]","\frac{\tanh ^{-1}\left(\sqrt{3}-\sqrt{2} x\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\sqrt{2} x+\sqrt{3}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{3}-\sqrt{2} x\right)}{\sqrt{2}}-\frac{\tanh ^{-1}\left(\sqrt{2} x+\sqrt{3}\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[3] - Sqrt[2]*x]/Sqrt[2] - ArcTanh[Sqrt[3] + Sqrt[2]*x]/Sqrt[2]","A",5,3,18,0.1667,1,"{1161, 618, 206}"
79,1,46,0,0.0360198,"\int \frac{1+x^2}{1-5 x^2+x^4} \, dx","Int[(1 + x^2)/(1 - 5*x^2 + x^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{7}-2 x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{2 x+\sqrt{7}}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{7}-2 x}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{2 x+\sqrt{7}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"ArcTanh[(Sqrt[7] - 2*x)/Sqrt[3]]/Sqrt[3] - ArcTanh[(Sqrt[7] + 2*x)/Sqrt[3]]/Sqrt[3]","A",5,3,18,0.1667,1,"{1161, 618, 206}"
80,1,62,0,0.0289177,"\int \frac{1-x^2}{1+b x^2+x^4} \, dx","Int[(1 - x^2)/(1 + b*x^2 + x^4),x]","\frac{\log \left(\sqrt{2-b} x+x^2+1\right)}{2 \sqrt{2-b}}-\frac{\log \left(-\sqrt{2-b} x+x^2+1\right)}{2 \sqrt{2-b}}","\frac{\log \left(\sqrt{2-b} x+x^2+1\right)}{2 \sqrt{2-b}}-\frac{\log \left(-\sqrt{2-b} x+x^2+1\right)}{2 \sqrt{2-b}}",1,"-Log[1 - Sqrt[2 - b]*x + x^2]/(2*Sqrt[2 - b]) + Log[1 + Sqrt[2 - b]*x + x^2]/(2*Sqrt[2 - b])","A",3,2,20,0.1000,1,"{1164, 628}"
81,1,50,0,0.0398747,"\int \frac{1-x^2}{1+5 x^2+x^4} \, dx","Int[(1 - x^2)/(1 + 5*x^2 + x^4),x]","\frac{\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(5+\sqrt{21}\right)} x\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{21}}} x\right)}{\sqrt{3}}","\frac{\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(5+\sqrt{21}\right)} x\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\sqrt{\frac{2}{5+\sqrt{21}}} x\right)}{\sqrt{3}}",1,"-(ArcTan[Sqrt[2/(5 + Sqrt[21])]*x]/Sqrt[3]) + ArcTan[Sqrt[(5 + Sqrt[21])/2]*x]/Sqrt[3]","A",3,2,20,0.1000,1,"{1163, 203}"
82,1,44,0,0.0288699,"\int \frac{1-x^2}{1+4 x^2+x^4} \, dx","Int[(1 - x^2)/(1 + 4*x^2 + x^4),x]","\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2-\sqrt{3}}}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2+\sqrt{3}}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2-\sqrt{3}}}\right)}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2+\sqrt{3}}}\right)}{\sqrt{2}}",1,"ArcTan[x/Sqrt[2 - Sqrt[3]]]/Sqrt[2] - ArcTan[x/Sqrt[2 + Sqrt[3]]]/Sqrt[2]","A",3,2,20,0.1000,1,"{1163, 203}"
83,1,39,0,0.0327162,"\int \frac{1-x^2}{1+3 x^2+x^4} \, dx","Int[(1 - x^2)/(1 + 3*x^2 + x^4),x]","\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)-\tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)","\tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)-\tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)",1,"-ArcTan[Sqrt[2/(3 + Sqrt[5])]*x] + ArcTan[Sqrt[(3 + Sqrt[5])/2]*x]","A",3,2,20,0.1000,1,"{1163, 203}"
84,1,9,0,0.0039017,"\int \frac{1-x^2}{1+2 x^2+x^4} \, dx","Int[(1 - x^2)/(1 + 2*x^2 + x^4),x]","\frac{x}{x^2+1}","\frac{x}{x^2+1}",1,"x/(1 + x^2)","A",2,2,20,0.1000,1,"{28, 383}"
85,1,25,0,0.0134529,"\int \frac{1-x^2}{1+x^2+x^4} \, dx","Int[(1 - x^2)/(1 + x^2 + x^4),x]","\frac{1}{2} \log \left(x^2+x+1\right)-\frac{1}{2} \log \left(x^2-x+1\right)","\frac{1}{2} \log \left(x^2+x+1\right)-\frac{1}{2} \log \left(x^2-x+1\right)",1,"-Log[1 - x + x^2]/2 + Log[1 + x + x^2]/2","A",3,2,18,0.1111,1,"{1164, 628}"
86,1,46,0,0.0194266,"\int \frac{1-x^2}{1+x^4} \, dx","Int[(1 - x^2)/(1 + x^4),x]","\frac{\log \left(x^2+\sqrt{2} x+1\right)}{2 \sqrt{2}}-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{2 \sqrt{2}}","\frac{\log \left(x^2+\sqrt{2} x+1\right)}{2 \sqrt{2}}-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{2 \sqrt{2}}",1,"-Log[1 - Sqrt[2]*x + x^2]/(2*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(2*Sqrt[2])","A",3,2,15,0.1333,1,"{1165, 628}"
87,1,46,0,0.0210366,"\int \frac{1-x^2}{1-x^2+x^4} \, dx","Int[(1 - x^2)/(1 - x^2 + x^4),x]","\frac{\log \left(x^2+\sqrt{3} x+1\right)}{2 \sqrt{3}}-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{2 \sqrt{3}}","\frac{\log \left(x^2+\sqrt{3} x+1\right)}{2 \sqrt{3}}-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{2 \sqrt{3}}",1,"-Log[1 - Sqrt[3]*x + x^2]/(2*Sqrt[3]) + Log[1 + Sqrt[3]*x + x^2]/(2*Sqrt[3])","A",3,2,20,0.1000,1,"{1164, 628}"
88,1,2,0,0.0020564,"\int \frac{1-x^2}{1-2 x^2+x^4} \, dx","Int[(1 - x^2)/(1 - 2*x^2 + x^4),x]","\tanh ^{-1}(x)","\tanh ^{-1}(x)",1,"ArcTanh[x]","A",3,3,20,0.1500,1,"{28, 21, 207}"
89,1,38,0,0.0294095,"\int \frac{1-x^2}{1-3 x^2+x^4} \, dx","Int[(1 - x^2)/(1 - 3*x^2 + x^4),x]","\frac{\tanh ^{-1}\left(\frac{2 x+1}{\sqrt{5}}\right)}{\sqrt{5}}-\frac{\tanh ^{-1}\left(\frac{1-2 x}{\sqrt{5}}\right)}{\sqrt{5}}","\frac{\tanh ^{-1}\left(\frac{2 x+1}{\sqrt{5}}\right)}{\sqrt{5}}-\frac{\tanh ^{-1}\left(\frac{1-2 x}{\sqrt{5}}\right)}{\sqrt{5}}",1,"-(ArcTanh[(1 - 2*x)/Sqrt[5]]/Sqrt[5]) + ArcTanh[(1 + 2*x)/Sqrt[5]]/Sqrt[5]","A",5,3,20,0.1500,1,"{1161, 618, 206}"
90,1,47,0,0.0359018,"\int \frac{1-x^2}{1-4 x^2+x^4} \, dx","Int[(1 - x^2)/(1 - 4*x^2 + x^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x+1}{\sqrt{3}}\right)}{\sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{1-\sqrt{2} x}{\sqrt{3}}\right)}{\sqrt{6}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x+1}{\sqrt{3}}\right)}{\sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{1-\sqrt{2} x}{\sqrt{3}}\right)}{\sqrt{6}}",1,"-(ArcTanh[(1 - Sqrt[2]*x)/Sqrt[3]]/Sqrt[6]) + ArcTanh[(1 + Sqrt[2]*x)/Sqrt[3]]/Sqrt[6]","A",5,3,20,0.1500,1,"{1161, 618, 206}"
91,1,46,0,0.0351032,"\int \frac{1-x^2}{1-5 x^2+x^4} \, dx","Int[(1 - x^2)/(1 - 5*x^2 + x^4),x]","\frac{\tanh ^{-1}\left(\frac{2 x+\sqrt{3}}{\sqrt{7}}\right)}{\sqrt{7}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3}-2 x}{\sqrt{7}}\right)}{\sqrt{7}}","\frac{\tanh ^{-1}\left(\frac{2 x+\sqrt{3}}{\sqrt{7}}\right)}{\sqrt{7}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3}-2 x}{\sqrt{7}}\right)}{\sqrt{7}}",1,"-(ArcTanh[(Sqrt[3] - 2*x)/Sqrt[7]]/Sqrt[7]) + ArcTanh[(Sqrt[3] + 2*x)/Sqrt[7]]/Sqrt[7]","A",5,3,20,0.1500,1,"{1161, 618, 206}"
92,1,43,0,0.0348875,"\int -\frac{1+3 x^2}{1+2 x^2+9 x^4} \, dx","Int[-((1 + 3*x^2)/(1 + 2*x^2 + 9*x^4)),x]","\frac{\tan ^{-1}\left(\frac{1-3 x}{\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\frac{3 x+1}{\sqrt{2}}\right)}{2 \sqrt{2}}","\frac{\tan ^{-1}\left(\frac{1-3 x}{\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\frac{3 x+1}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"ArcTan[(1 - 3*x)/Sqrt[2]]/(2*Sqrt[2]) - ArcTan[(1 + 3*x)/Sqrt[2]]/(2*Sqrt[2])","A",5,3,23,0.1304,1,"{1161, 618, 204}"
93,1,43,0,0.0323723,"\int \frac{1+3 x^2}{-1-2 x^2-9 x^4} \, dx","Int[(1 + 3*x^2)/(-1 - 2*x^2 - 9*x^4),x]","\frac{\tan ^{-1}\left(\frac{1-3 x}{\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\frac{3 x+1}{\sqrt{2}}\right)}{2 \sqrt{2}}","\frac{\tan ^{-1}\left(\frac{1-3 x}{\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\frac{3 x+1}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"ArcTan[(1 - 3*x)/Sqrt[2]]/(2*Sqrt[2]) - ArcTan[(1 + 3*x)/Sqrt[2]]/(2*Sqrt[2])","A",5,3,22,0.1364,1,"{1161, 618, 204}"
94,1,21,0,0.0050243,"\int \frac{3+2 x^2}{1-2 x^2+x^4} \, dx","Int[(3 + 2*x^2)/(1 - 2*x^2 + x^4),x]","\frac{5 x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)","\frac{5 x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)",1,"(5*x)/(2*(1 - x^2)) + ArcTanh[x]/2","A",3,3,20,0.1500,1,"{28, 385, 207}"
95,1,28,0,0.0126262,"\int \frac{2+3 x^2}{5-8 x^2+3 x^4} \, dx","Int[(2 + 3*x^2)/(5 - 8*x^2 + 3*x^4),x]","\frac{5}{2} \tanh ^{-1}(x)-\frac{7}{2} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} x\right)","\frac{5}{2} \tanh ^{-1}(x)-\frac{7}{2} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} x\right)",1,"(5*ArcTanh[x])/2 - (7*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*x])/2","A",3,2,22,0.09091,1,"{1166, 207}"
96,1,36,0,0.0399891,"\int \frac{d+e x^2}{5-8 x^2+3 x^4} \, dx","Int[(d + e*x^2)/(5 - 8*x^2 + 3*x^4),x]","\frac{1}{2} (d+e) \tanh ^{-1}(x)-\frac{(3 d+5 e) \tanh ^{-1}\left(\sqrt{\frac{3}{5}} x\right)}{2 \sqrt{15}}","\frac{1}{2} (d+e) \tanh ^{-1}(x)-\frac{(3 d+5 e) \tanh ^{-1}\left(\sqrt{\frac{3}{5}} x\right)}{2 \sqrt{15}}",1,"((d + e)*ArcTanh[x])/2 - ((3*d + 5*e)*ArcTanh[Sqrt[3/5]*x])/(2*Sqrt[15])","A",3,2,22,0.09091,1,"{1166, 207}"
97,1,74,0,0.0450255,"\int \frac{3+x^2}{1+3 x^2+x^4} \, dx","Int[(3 + x^2)/(1 + 3*x^2 + x^4),x]","\frac{\left(3+\sqrt{5}\right)^{3/2} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{10}}-\frac{1}{10} \sqrt{180-80 \sqrt{5}} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)","\frac{\left(3+\sqrt{5}\right)^{3/2} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{10}}-\frac{1}{10} \sqrt{180-80 \sqrt{5}} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x\right)",1,"-(Sqrt[180 - 80*Sqrt[5]]*ArcTan[Sqrt[2/(3 + Sqrt[5])]*x])/10 + ((3 + Sqrt[5])^(3/2)*ArcTan[Sqrt[(3 + Sqrt[5])/2]*x])/(2*Sqrt[10])","A",3,2,18,0.1111,1,"{1166, 203}"
98,1,83,0,0.0548068,"\int \frac{a+b x^2}{1+x^2+x^4} \, dx","Int[(a + b*x^2)/(1 + x^2 + x^4),x]","-\frac{1}{4} (a-b) \log \left(x^2-x+1\right)+\frac{1}{4} (a-b) \log \left(x^2+x+1\right)-\frac{(a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(a+b) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{4} (a-b) \log \left(x^2-x+1\right)+\frac{1}{4} (a-b) \log \left(x^2+x+1\right)-\frac{(a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(a+b) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-((a + b)*ArcTan[(1 - 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((a + b)*ArcTan[(1 + 2*x)/Sqrt[3]])/(2*Sqrt[3]) - ((a - b)*Log[1 - x + x^2])/4 + ((a - b)*Log[1 + x + x^2])/4","A",9,5,18,0.2778,1,"{1169, 634, 618, 204, 628}"
99,1,119,0,0.0910057,"\int \frac{a+b x^2}{\left(1+x^2+x^4\right)^2} \, dx","Int[(a + b*x^2)/(1 + x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(a-2 b))+a+b\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} (2 a-b) \log \left(x^2-x+1\right)+\frac{1}{8} (2 a-b) \log \left(x^2+x+1\right)-\frac{(4 a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{(4 a+b) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{12 \sqrt{3}}","\frac{x \left(x^2 (-(a-2 b))+a+b\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} (2 a-b) \log \left(x^2-x+1\right)+\frac{1}{8} (2 a-b) \log \left(x^2+x+1\right)-\frac{(4 a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{(4 a+b) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{12 \sqrt{3}}",1,"(x*(a + b - (a - 2*b)*x^2))/(6*(1 + x^2 + x^4)) - ((4*a + b)*ArcTan[(1 - 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((4*a + b)*ArcTan[(1 + 2*x)/Sqrt[3]])/(12*Sqrt[3]) - ((2*a - b)*Log[1 - x + x^2])/8 + ((2*a - b)*Log[1 + x + x^2])/8","A",10,6,18,0.3333,1,"{1178, 1169, 634, 618, 204, 628}"
100,1,234,0,0.2295211,"\int \frac{a+b x^2}{2+x^2+x^4} \, dx","Int[(a + b*x^2)/(2 + x^2 + x^4),x]","-\frac{\left(a-\sqrt{2} b\right) \log \left(x^2-\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{4 \sqrt{2 \left(2 \sqrt{2}-1\right)}}+\frac{\left(a-\sqrt{2} b\right) \log \left(x^2+\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{4 \sqrt{2 \left(2 \sqrt{2}-1\right)}}-\frac{1}{2} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(a+\sqrt{2} b\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{2}-1}-2 x}{\sqrt{1+2 \sqrt{2}}}\right)+\frac{1}{2} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(a+\sqrt{2} b\right) \tan ^{-1}\left(\frac{2 x+\sqrt{2 \sqrt{2}-1}}{\sqrt{1+2 \sqrt{2}}}\right)","-\frac{\left(a-\sqrt{2} b\right) \log \left(x^2-\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{4 \sqrt{2 \left(2 \sqrt{2}-1\right)}}+\frac{\left(a-\sqrt{2} b\right) \log \left(x^2+\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{4 \sqrt{2 \left(2 \sqrt{2}-1\right)}}-\frac{1}{2} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(a+\sqrt{2} b\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{2}-1}-2 x}{\sqrt{1+2 \sqrt{2}}}\right)+\frac{1}{2} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(a+\sqrt{2} b\right) \tan ^{-1}\left(\frac{2 x+\sqrt{2 \sqrt{2}-1}}{\sqrt{1+2 \sqrt{2}}}\right)",1,"-(Sqrt[(-1 + 2*Sqrt[2])/14]*(a + Sqrt[2]*b)*ArcTan[(Sqrt[-1 + 2*Sqrt[2]] - 2*x)/Sqrt[1 + 2*Sqrt[2]]])/2 + (Sqrt[(-1 + 2*Sqrt[2])/14]*(a + Sqrt[2]*b)*ArcTan[(Sqrt[-1 + 2*Sqrt[2]] + 2*x)/Sqrt[1 + 2*Sqrt[2]]])/2 - ((a - Sqrt[2]*b)*Log[Sqrt[2] - Sqrt[-1 + 2*Sqrt[2]]*x + x^2])/(4*Sqrt[2*(-1 + 2*Sqrt[2])]) + ((a - Sqrt[2]*b)*Log[Sqrt[2] + Sqrt[-1 + 2*Sqrt[2]]*x + x^2])/(4*Sqrt[2*(-1 + 2*Sqrt[2])])","A",9,5,18,0.2778,1,"{1169, 634, 618, 204, 628}"
101,1,316,0,0.2891075,"\int \frac{a+b x^2}{\left(2+x^2+x^4\right)^2} \, dx","Int[(a + b*x^2)/(2 + x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(a-4 b))+3 a+2 b\right)}{28 \left(x^4+x^2+2\right)}-\frac{\left(\sqrt{2} (a-4 b)+11 a-2 b\right) \log \left(x^2-\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{112 \sqrt{2 \left(2 \sqrt{2}-1\right)}}+\frac{\left(\left(11+\sqrt{2}\right) a-2 \left(2 \sqrt{2} b+b\right)\right) \log \left(x^2+\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{112 \sqrt{2 \left(2 \sqrt{2}-1\right)}}-\frac{1}{56} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(\left(11-\sqrt{2}\right) a-\left(2-4 \sqrt{2}\right) b\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{2}-1}-2 x}{\sqrt{1+2 \sqrt{2}}}\right)+\frac{1}{56} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(\left(11-\sqrt{2}\right) a-\left(2-4 \sqrt{2}\right) b\right) \tan ^{-1}\left(\frac{2 x+\sqrt{2 \sqrt{2}-1}}{\sqrt{1+2 \sqrt{2}}}\right)","\frac{x \left(x^2 (-(a-4 b))+3 a+2 b\right)}{28 \left(x^4+x^2+2\right)}-\frac{\left(\sqrt{2} (a-4 b)+11 a-2 b\right) \log \left(x^2-\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{112 \sqrt{2 \left(2 \sqrt{2}-1\right)}}+\frac{\left(\left(11+\sqrt{2}\right) a-2 \left(2 \sqrt{2} b+b\right)\right) \log \left(x^2+\sqrt{2 \sqrt{2}-1} x+\sqrt{2}\right)}{112 \sqrt{2 \left(2 \sqrt{2}-1\right)}}-\frac{1}{56} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(\left(11-\sqrt{2}\right) a-\left(2-4 \sqrt{2}\right) b\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{2}-1}-2 x}{\sqrt{1+2 \sqrt{2}}}\right)+\frac{1}{56} \sqrt{\frac{1}{14} \left(2 \sqrt{2}-1\right)} \left(\left(11-\sqrt{2}\right) a-\left(2-4 \sqrt{2}\right) b\right) \tan ^{-1}\left(\frac{2 x+\sqrt{2 \sqrt{2}-1}}{\sqrt{1+2 \sqrt{2}}}\right)",1,"(x*(3*a + 2*b - (a - 4*b)*x^2))/(28*(2 + x^2 + x^4)) - (Sqrt[(-1 + 2*Sqrt[2])/14]*((11 - Sqrt[2])*a - (2 - 4*Sqrt[2])*b)*ArcTan[(Sqrt[-1 + 2*Sqrt[2]] - 2*x)/Sqrt[1 + 2*Sqrt[2]]])/56 + (Sqrt[(-1 + 2*Sqrt[2])/14]*((11 - Sqrt[2])*a - (2 - 4*Sqrt[2])*b)*ArcTan[(Sqrt[-1 + 2*Sqrt[2]] + 2*x)/Sqrt[1 + 2*Sqrt[2]]])/56 - ((11*a + Sqrt[2]*(a - 4*b) - 2*b)*Log[Sqrt[2] - Sqrt[-1 + 2*Sqrt[2]]*x + x^2])/(112*Sqrt[2*(-1 + 2*Sqrt[2])]) + (((11 + Sqrt[2])*a - 2*(b + 2*Sqrt[2]*b))*Log[Sqrt[2] + Sqrt[-1 + 2*Sqrt[2]]*x + x^2])/(112*Sqrt[2*(-1 + 2*Sqrt[2])])","A",10,6,18,0.3333,1,"{1178, 1169, 634, 618, 204, 628}"
102,1,160,0,0.1458368,"\int \frac{\sqrt{2}-x^2}{1-\sqrt{2} x^2+x^4} \, dx","Int[(Sqrt[2] - x^2)/(1 - Sqrt[2]*x^2 + x^4),x]","-\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{2}}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{2}}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}","-\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{2}}} \log \left(x^2-\sqrt{2+\sqrt{2}} x+1\right)+\frac{1}{4} \sqrt{1+\frac{1}{\sqrt{2}}} \log \left(x^2+\sqrt{2+\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 x}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}",1,"-ArcTan[(Sqrt[2 + Sqrt[2]] - 2*x)/Sqrt[2 - Sqrt[2]]]/(2*Sqrt[2 + Sqrt[2]]) + ArcTan[(Sqrt[2 + Sqrt[2]] + 2*x)/Sqrt[2 - Sqrt[2]]]/(2*Sqrt[2 + Sqrt[2]]) - (Sqrt[1 + 1/Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*x + x^2])/4 + (Sqrt[1 + 1/Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*x + x^2])/4","A",9,5,29,0.1724,1,"{1169, 634, 618, 204, 628}"
103,1,172,0,0.1370307,"\int \frac{\sqrt{2}+x^2}{1+\sqrt{2} x^2+x^4} \, dx","Int[(Sqrt[2] + x^2)/(1 + Sqrt[2]*x^2 + x^4),x]","-\frac{1}{4} \sqrt{1-\frac{1}{\sqrt{2}}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{4} \sqrt{1-\frac{1}{\sqrt{2}}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}","-\frac{1}{4} \sqrt{1-\frac{1}{\sqrt{2}}} \log \left(x^2-\sqrt{2-\sqrt{2}} x+1\right)+\frac{1}{4} \sqrt{1-\frac{1}{\sqrt{2}}} \log \left(x^2+\sqrt{2-\sqrt{2}} x+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 x}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}",1,"-ArcTan[(Sqrt[2 - Sqrt[2]] - 2*x)/Sqrt[2 + Sqrt[2]]]/(2*Sqrt[2 - Sqrt[2]]) + ArcTan[(Sqrt[2 - Sqrt[2]] + 2*x)/Sqrt[2 + Sqrt[2]]]/(2*Sqrt[2 - Sqrt[2]]) - (Sqrt[1 - 1/Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*x + x^2])/4 + (Sqrt[1 - 1/Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*x + x^2])/4","A",9,5,26,0.1923,1,"{1169, 634, 618, 204, 628}"
104,1,160,0,0.1193522,"\int \frac{\sqrt{2}-x^2}{1+b x^2+x^4} \, dx","Int[(Sqrt[2] - x^2)/(1 + b*x^2 + x^4),x]","-\frac{\left(1+\sqrt{2}\right) \log \left(-\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}+\frac{\left(1+\sqrt{2}\right) \log \left(\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}+\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}-2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}-\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}+2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}","-\frac{\left(1+\sqrt{2}\right) \log \left(-\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}+\frac{\left(1+\sqrt{2}\right) \log \left(\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}+\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}-2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}-\frac{\left(1-\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}+2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}",1,"((1 - Sqrt[2])*ArcTan[(Sqrt[2 - b] - 2*x)/Sqrt[2 + b]])/(2*Sqrt[2 + b]) - ((1 - Sqrt[2])*ArcTan[(Sqrt[2 - b] + 2*x)/Sqrt[2 + b]])/(2*Sqrt[2 + b]) - ((1 + Sqrt[2])*Log[1 - Sqrt[2 - b]*x + x^2])/(4*Sqrt[2 - b]) + ((1 + Sqrt[2])*Log[1 + Sqrt[2 - b]*x + x^2])/(4*Sqrt[2 - b])","A",9,5,24,0.2083,1,"{1169, 634, 618, 204, 628}"
105,1,160,0,0.1032668,"\int \frac{\sqrt{2}+x^2}{1+b x^2+x^4} \, dx","Int[(Sqrt[2] + x^2)/(1 + b*x^2 + x^4),x]","\frac{\left(1-\sqrt{2}\right) \log \left(-\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}-\frac{\left(1-\sqrt{2}\right) \log \left(\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}-\frac{\left(1+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}-2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}+\frac{\left(1+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}+2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}","\frac{\left(1-\sqrt{2}\right) \log \left(-\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}-\frac{\left(1-\sqrt{2}\right) \log \left(\sqrt{2-b} x+x^2+1\right)}{4 \sqrt{2-b}}-\frac{\left(1+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}-2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}+\frac{\left(1+\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{2-b}+2 x}{\sqrt{b+2}}\right)}{2 \sqrt{b+2}}",1,"-((1 + Sqrt[2])*ArcTan[(Sqrt[2 - b] - 2*x)/Sqrt[2 + b]])/(2*Sqrt[2 + b]) + ((1 + Sqrt[2])*ArcTan[(Sqrt[2 - b] + 2*x)/Sqrt[2 + b]])/(2*Sqrt[2 + b]) + ((1 - Sqrt[2])*Log[1 - Sqrt[2 - b]*x + x^2])/(4*Sqrt[2 - b]) - ((1 - Sqrt[2])*Log[1 + Sqrt[2 - b]*x + x^2])/(4*Sqrt[2 - b])","A",9,5,22,0.2273,1,"{1169, 634, 618, 204, 628}"
106,1,114,0,0.0760081,"\int \frac{2 a-x^2}{a^2-a x^2+x^4} \, dx","Int[(2*a - x^2)/(a^2 - a*x^2 + x^4),x]","-\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{a}}+\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{a}}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt{a}}\right)}{2 \sqrt{a}}+\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{a}}+\sqrt{3}\right)}{2 \sqrt{a}}","-\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{a}}+\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{a}}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt{a}}\right)}{2 \sqrt{a}}+\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{a}}+\sqrt{3}\right)}{2 \sqrt{a}}",1,"-ArcTan[Sqrt[3] - (2*x)/Sqrt[a]]/(2*Sqrt[a]) + ArcTan[Sqrt[3] + (2*x)/Sqrt[a]]/(2*Sqrt[a]) - (Sqrt[3]*Log[a - Sqrt[3]*Sqrt[a]*x + x^2])/(4*Sqrt[a]) + (Sqrt[3]*Log[a + Sqrt[3]*Sqrt[a]*x + x^2])/(4*Sqrt[a])","A",9,5,25,0.2000,1,"{1169, 634, 617, 204, 628}"
107,1,122,0,0.0796739,"\int \frac{2 \sqrt{a}-x^2}{a-\sqrt{a} x^2+x^4} \, dx","Int[(2*Sqrt[a] - x^2)/(a - Sqrt[a]*x^2 + x^4),x]","-\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt[4]{a}}+\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt[4]{a}}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}+\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt[4]{a}}+\sqrt{3}\right)}{2 \sqrt[4]{a}}","-\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt[4]{a}}+\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt[4]{a}}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a}}+\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt[4]{a}}+\sqrt{3}\right)}{2 \sqrt[4]{a}}",1,"-ArcTan[Sqrt[3] - (2*x)/a^(1/4)]/(2*a^(1/4)) + ArcTan[Sqrt[3] + (2*x)/a^(1/4)]/(2*a^(1/4)) - (Sqrt[3]*Log[Sqrt[a] - Sqrt[3]*a^(1/4)*x + x^2])/(4*a^(1/4)) + (Sqrt[3]*Log[Sqrt[a] + Sqrt[3]*a^(1/4)*x + x^2])/(4*a^(1/4))","A",9,5,31,0.1613,1,"{1169, 634, 617, 204, 628}"
108,1,124,0,0.0774642,"\int \frac{2 b^{2/3}+x^2}{b^{4/3}+b^{2/3} x^2+x^4} \, dx","Int[(2*b^(2/3) + x^2)/(b^(4/3) + b^(2/3)*x^2 + x^4),x]","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} x+x^2\right)}{4 \sqrt[3]{b}}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} x+x^2\right)}{4 \sqrt[3]{b}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 x}{\sqrt{3} \sqrt[3]{b}}\right)}{2 \sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{b}+2 x}{\sqrt{3} \sqrt[3]{b}}\right)}{2 \sqrt[3]{b}}","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} x+x^2\right)}{4 \sqrt[3]{b}}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} x+x^2\right)}{4 \sqrt[3]{b}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 x}{\sqrt{3} \sqrt[3]{b}}\right)}{2 \sqrt[3]{b}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{b}+2 x}{\sqrt{3} \sqrt[3]{b}}\right)}{2 \sqrt[3]{b}}",1,"-(Sqrt[3]*ArcTan[(b^(1/3) - 2*x)/(Sqrt[3]*b^(1/3))])/(2*b^(1/3)) + (Sqrt[3]*ArcTan[(b^(1/3) + 2*x)/(Sqrt[3]*b^(1/3))])/(2*b^(1/3)) - Log[b^(2/3) - b^(1/3)*x + x^2]/(4*b^(1/3)) + Log[b^(2/3) + b^(1/3)*x + x^2]/(4*b^(1/3))","A",9,5,32,0.1562,1,"{1169, 634, 617, 204, 628}"
109,1,136,0,0.1039465,"\int \frac{A+B x^2}{a^2-a x^2+x^4} \, dx","Int[(A + B*x^2)/(a^2 - a*x^2 + x^4),x]","-\frac{(A-a B) \log \left(-\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{3} a^{3/2}}+\frac{(A-a B) \log \left(\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{3} a^{3/2}}-\frac{(a B+A) \tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{(a B+A) \tan ^{-1}\left(\frac{2 x}{\sqrt{a}}+\sqrt{3}\right)}{2 a^{3/2}}","-\frac{(A-a B) \log \left(-\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{3} a^{3/2}}+\frac{(A-a B) \log \left(\sqrt{3} \sqrt{a} x+a+x^2\right)}{4 \sqrt{3} a^{3/2}}-\frac{(a B+A) \tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{(a B+A) \tan ^{-1}\left(\frac{2 x}{\sqrt{a}}+\sqrt{3}\right)}{2 a^{3/2}}",1,"-((A + a*B)*ArcTan[Sqrt[3] - (2*x)/Sqrt[a]])/(2*a^(3/2)) + ((A + a*B)*ArcTan[Sqrt[3] + (2*x)/Sqrt[a]])/(2*a^(3/2)) - ((A - a*B)*Log[a - Sqrt[3]*Sqrt[a]*x + x^2])/(4*Sqrt[3]*a^(3/2)) + ((A - a*B)*Log[a + Sqrt[3]*Sqrt[a]*x + x^2])/(4*Sqrt[3]*a^(3/2))","A",9,5,23,0.2174,1,"{1169, 634, 617, 204, 628}"
110,1,160,0,0.1163361,"\int \frac{A+B x^2}{a-\sqrt{a} x^2+x^4} \, dx","Int[(A + B*x^2)/(a - Sqrt[a]*x^2 + x^4),x]","-\frac{\left(A-\sqrt{a} B\right) \log \left(-\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt{3} a^{3/4}}+\frac{\left(A-\sqrt{a} B\right) \log \left(\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt{3} a^{3/4}}-\frac{\left(\sqrt{a} B+A\right) \tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt[4]{a}}\right)}{2 a^{3/4}}+\frac{\left(\sqrt{a} B+A\right) \tan ^{-1}\left(\frac{2 x}{\sqrt[4]{a}}+\sqrt{3}\right)}{2 a^{3/4}}","-\frac{\left(A-\sqrt{a} B\right) \log \left(-\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt{3} a^{3/4}}+\frac{\left(A-\sqrt{a} B\right) \log \left(\sqrt{3} \sqrt[4]{a} x+\sqrt{a}+x^2\right)}{4 \sqrt{3} a^{3/4}}-\frac{\left(\sqrt{a} B+A\right) \tan ^{-1}\left(\sqrt{3}-\frac{2 x}{\sqrt[4]{a}}\right)}{2 a^{3/4}}+\frac{\left(\sqrt{a} B+A\right) \tan ^{-1}\left(\frac{2 x}{\sqrt[4]{a}}+\sqrt{3}\right)}{2 a^{3/4}}",1,"-((A + Sqrt[a]*B)*ArcTan[Sqrt[3] - (2*x)/a^(1/4)])/(2*a^(3/4)) + ((A + Sqrt[a]*B)*ArcTan[Sqrt[3] + (2*x)/a^(1/4)])/(2*a^(3/4)) - ((A - Sqrt[a]*B)*Log[Sqrt[a] - Sqrt[3]*a^(1/4)*x + x^2])/(4*Sqrt[3]*a^(3/4)) + ((A - Sqrt[a]*B)*Log[Sqrt[a] + Sqrt[3]*a^(1/4)*x + x^2])/(4*Sqrt[3]*a^(3/4))","A",9,5,25,0.2000,1,"{1169, 634, 617, 204, 628}"
111,1,414,0,0.4533274,"\int \frac{A+B x^2}{a-\sqrt{a c} x^2+c x^4} \, dx","Int[(A + B*x^2)/(a - Sqrt[a*c]*x^2 + c*x^4),x]","-\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(-x \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{a} \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}}+\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(x \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{a} \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}-2 \sqrt{c} x}{\sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}\right)}{2 \sqrt{a} \sqrt{c} \sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}+2 \sqrt{c} x}{\sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}\right)}{2 \sqrt{a} \sqrt{c} \sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}","-\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(-x \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{a} \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}}+\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(x \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{a} \sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}-2 \sqrt{c} x}{\sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}\right)}{2 \sqrt{a} \sqrt{c} \sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{a} \sqrt{c}+\sqrt{a c}}+2 \sqrt{c} x}{\sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}\right)}{2 \sqrt{a} \sqrt{c} \sqrt{2 \sqrt{a} \sqrt{c}-\sqrt{a c}}}",1,"-((Sqrt[a]*B + A*Sqrt[c])*ArcTan[(Sqrt[2*Sqrt[a]*Sqrt[c] + Sqrt[a*c]] - 2*Sqrt[c]*x)/Sqrt[2*Sqrt[a]*Sqrt[c] - Sqrt[a*c]]])/(2*Sqrt[a]*Sqrt[c]*Sqrt[2*Sqrt[a]*Sqrt[c] - Sqrt[a*c]]) + ((Sqrt[a]*B + A*Sqrt[c])*ArcTan[(Sqrt[2*Sqrt[a]*Sqrt[c] + Sqrt[a*c]] + 2*Sqrt[c]*x)/Sqrt[2*Sqrt[a]*Sqrt[c] - Sqrt[a*c]]])/(2*Sqrt[a]*Sqrt[c]*Sqrt[2*Sqrt[a]*Sqrt[c] - Sqrt[a*c]]) - ((A - (Sqrt[a]*B)/Sqrt[c])*Log[Sqrt[a] - Sqrt[2*Sqrt[a]*Sqrt[c] + Sqrt[a*c]]*x + Sqrt[c]*x^2])/(4*Sqrt[a]*Sqrt[2*Sqrt[a]*Sqrt[c] + Sqrt[a*c]]) + ((A - (Sqrt[a]*B)/Sqrt[c])*Log[Sqrt[a] + Sqrt[2*Sqrt[a]*Sqrt[c] + Sqrt[a*c]]*x + Sqrt[c]*x^2])/(4*Sqrt[a]*Sqrt[2*Sqrt[a]*Sqrt[c] + Sqrt[a*c]])","A",9,5,29,0.1724,1,"{1169, 634, 618, 204, 628}"
112,1,234,0,0.1716472,"\int \frac{A+B x^2}{a-\sqrt{a} \sqrt{c} x^2+c x^4} \, dx","Int[(A + B*x^2)/(a - Sqrt[a]*Sqrt[c]*x^2 + c*x^4),x]","-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{2 \sqrt[4]{c} x}{\sqrt[4]{a}}+\sqrt{3}\right)}{2 a^{3/4} c^{3/4}}-\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(-\sqrt{3} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{3} a^{3/4} \sqrt[4]{c}}+\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(\sqrt{3} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{3} a^{3/4} \sqrt[4]{c}}","-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{2 \sqrt[4]{c} x}{\sqrt[4]{a}}+\sqrt{3}\right)}{2 a^{3/4} c^{3/4}}-\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(-\sqrt{3} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{3} a^{3/4} \sqrt[4]{c}}+\frac{\left(A-\frac{\sqrt{a} B}{\sqrt{c}}\right) \log \left(\sqrt{3} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{3} a^{3/4} \sqrt[4]{c}}",1,"-((Sqrt[a]*B + A*Sqrt[c])*ArcTan[Sqrt[3] - (2*c^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*c^(3/4)) + ((Sqrt[a]*B + A*Sqrt[c])*ArcTan[Sqrt[3] + (2*c^(1/4)*x)/a^(1/4)])/(2*a^(3/4)*c^(3/4)) - ((A - (Sqrt[a]*B)/Sqrt[c])*Log[Sqrt[a] - Sqrt[3]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[3]*a^(3/4)*c^(1/4)) + ((A - (Sqrt[a]*B)/Sqrt[c])*Log[Sqrt[a] + Sqrt[3]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[3]*a^(3/4)*c^(1/4))","A",9,5,32,0.1562,1,"{1169, 634, 617, 204, 628}"
113,1,96,0,0.1233684,"\int \frac{3-x^2}{\sqrt{3+x^2-x^4}} \, dx","Int[(3 - x^2)/Sqrt[3 + x^2 - x^4],x]","\sqrt{7+2 \sqrt{13}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7-\sqrt{13}\right)\right)-\sqrt{\frac{1}{2} \left(\sqrt{13}-1\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7-\sqrt{13}\right)\right)","\sqrt{7+2 \sqrt{13}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7-\sqrt{13}\right)\right)-\sqrt{\frac{1}{2} \left(\sqrt{13}-1\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7-\sqrt{13}\right)\right)",1,"-(Sqrt[(-1 + Sqrt[13])/2]*EllipticE[ArcSin[Sqrt[2/(1 + Sqrt[13])]*x], (-7 - Sqrt[13])/6]) + Sqrt[7 + 2*Sqrt[13]]*EllipticF[ArcSin[Sqrt[2/(1 + Sqrt[13])]*x], (-7 - Sqrt[13])/6]","A",4,4,22,0.1818,1,"{1180, 524, 424, 419}"
114,1,25,0,0.032492,"\int \frac{3-x^2}{\sqrt{3+2 x^2-x^4}} \, dx","Int[(3 - x^2)/Sqrt[3 + 2*x^2 - x^4],x]","4 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right|-3\right)-E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right|-3\right)","4 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right|-3\right)-E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)\right|-3\right)",1,"-EllipticE[ArcSin[x/Sqrt[3]], -3] + 4*EllipticF[ArcSin[x/Sqrt[3]], -3]","A",5,5,24,0.2083,1,"{1180, 21, 423, 424, 419}"
115,1,96,0,0.178087,"\int \frac{3-x^2}{\sqrt{3+3 x^2-x^4}} \, dx","Int[(3 - x^2)/Sqrt[3 + 3*x^2 - x^4],x]","\sqrt{9+2 \sqrt{21}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5-\sqrt{21}\right)\right)-\sqrt{\frac{1}{2} \left(\sqrt{21}-3\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5-\sqrt{21}\right)\right)","\sqrt{9+2 \sqrt{21}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5-\sqrt{21}\right)\right)-\sqrt{\frac{1}{2} \left(\sqrt{21}-3\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5-\sqrt{21}\right)\right)",1,"-(Sqrt[(-3 + Sqrt[21])/2]*EllipticE[ArcSin[Sqrt[2/(3 + Sqrt[21])]*x], (-5 - Sqrt[21])/2]) + Sqrt[9 + 2*Sqrt[21]]*EllipticF[ArcSin[Sqrt[2/(3 + Sqrt[21])]*x], (-5 - Sqrt[21])/2]","A",4,4,24,0.1667,1,"{1180, 524, 424, 419}"
116,1,92,0,0.1202737,"\int \frac{3-x^2}{\sqrt{3-x^2-x^4}} \, dx","Int[(3 - x^2)/Sqrt[3 - x^2 - x^4],x]","\sqrt{5+2 \sqrt{13}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7+\sqrt{13}\right)\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{13}\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7+\sqrt{13}\right)\right)","\sqrt{5+2 \sqrt{13}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7+\sqrt{13}\right)\right)-\sqrt{\frac{1}{2} \left(1+\sqrt{13}\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{-1+\sqrt{13}}} x\right)|\frac{1}{6} \left(-7+\sqrt{13}\right)\right)",1,"-(Sqrt[(1 + Sqrt[13])/2]*EllipticE[ArcSin[Sqrt[2/(-1 + Sqrt[13])]*x], (-7 + Sqrt[13])/6]) + Sqrt[5 + 2*Sqrt[13]]*EllipticF[ArcSin[Sqrt[2/(-1 + Sqrt[13])]*x], (-7 + Sqrt[13])/6]","A",4,4,24,0.1667,1,"{1180, 524, 424, 419}"
117,1,27,0,0.0387074,"\int \frac{3-x^2}{\sqrt{3-2 x^2-x^4}} \, dx","Int[(3 - x^2)/Sqrt[3 - 2*x^2 - x^4],x]","2 \sqrt{3} F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)-\sqrt{3} E\left(\sin ^{-1}(x)|-\frac{1}{3}\right)","2 \sqrt{3} F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)-\sqrt{3} E\left(\sin ^{-1}(x)|-\frac{1}{3}\right)",1,"-(Sqrt[3]*EllipticE[ArcSin[x], -1/3]) + 2*Sqrt[3]*EllipticF[ArcSin[x], -1/3]","A",4,4,24,0.1667,1,"{1180, 524, 424, 419}"
118,1,92,0,0.1653311,"\int \frac{3-x^2}{\sqrt{3-3 x^2-x^4}} \, dx","Int[(3 - x^2)/Sqrt[3 - 3*x^2 - x^4],x]","\sqrt{3+2 \sqrt{21}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5+\sqrt{21}\right)\right)-\sqrt{\frac{1}{2} \left(3+\sqrt{21}\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{-3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5+\sqrt{21}\right)\right)","\sqrt{3+2 \sqrt{21}} F\left(\sin ^{-1}\left(\sqrt{\frac{2}{-3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5+\sqrt{21}\right)\right)-\sqrt{\frac{1}{2} \left(3+\sqrt{21}\right)} E\left(\sin ^{-1}\left(\sqrt{\frac{2}{-3+\sqrt{21}}} x\right)|\frac{1}{2} \left(-5+\sqrt{21}\right)\right)",1,"-(Sqrt[(3 + Sqrt[21])/2]*EllipticE[ArcSin[Sqrt[2/(-3 + Sqrt[21])]*x], (-5 + Sqrt[21])/2]) + Sqrt[3 + 2*Sqrt[21]]*EllipticF[ArcSin[Sqrt[2/(-3 + Sqrt[21])]*x], (-5 + Sqrt[21])/2]","A",4,4,24,0.1667,1,"{1180, 524, 424, 419}"
119,1,296,0,0.1186572,"\int \frac{b-\sqrt{b^2-4 a c}+2 c x^2}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(b - Sqrt[b^2 - 4*a*c] + 2*c*x^2)/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(-\sqrt{b^2-4 a c}+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{c} x \sqrt{a+b x^2+c x^4}}{\sqrt{a}+\sqrt{c} x^2}-\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{\left(-\sqrt{b^2-4 a c}+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{c} x \sqrt{a+b x^2+c x^4}}{\sqrt{a}+\sqrt{c} x^2}-\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,"(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[b^2 - 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])/(2*a^(1/4)*c^(1/4)*Sqrt[a + b*x^2 + c*x^4])","A",3,3,39,0.07692,1,"{1197, 1103, 1195}"
120,1,106,0,0.0826949,"\int \left(d+e x^2\right)^4 \left(a+c x^4\right) \, dx","Int[(d + e*x^2)^4*(a + c*x^4),x]","\frac{1}{9} e^2 x^9 \left(a e^2+6 c d^2\right)+\frac{4}{7} d e x^7 \left(a e^2+c d^2\right)+\frac{1}{5} d^2 x^5 \left(6 a e^2+c d^2\right)+\frac{4}{3} a d^3 e x^3+a d^4 x+\frac{4}{11} c d e^3 x^{11}+\frac{1}{13} c e^4 x^{13}","\frac{1}{9} e^2 x^9 \left(a e^2+6 c d^2\right)+\frac{4}{7} d e x^7 \left(a e^2+c d^2\right)+\frac{1}{5} d^2 x^5 \left(6 a e^2+c d^2\right)+\frac{4}{3} a d^3 e x^3+a d^4 x+\frac{4}{11} c d e^3 x^{11}+\frac{1}{13} c e^4 x^{13}",1,"a*d^4*x + (4*a*d^3*e*x^3)/3 + (d^2*(c*d^2 + 6*a*e^2)*x^5)/5 + (4*d*e*(c*d^2 + a*e^2)*x^7)/7 + (e^2*(6*c*d^2 + a*e^2)*x^9)/9 + (4*c*d*e^3*x^11)/11 + (c*e^4*x^13)/13","A",2,1,17,0.05882,1,"{1154}"
121,1,79,0,0.0561928,"\int \left(d+e x^2\right)^3 \left(a+c x^4\right) \, dx","Int[(d + e*x^2)^3*(a + c*x^4),x]","\frac{1}{7} e x^7 \left(a e^2+3 c d^2\right)+\frac{1}{5} d x^5 \left(3 a e^2+c d^2\right)+a d^2 e x^3+a d^3 x+\frac{1}{3} c d e^2 x^9+\frac{1}{11} c e^3 x^{11}","\frac{1}{7} e x^7 \left(a e^2+3 c d^2\right)+\frac{1}{5} d x^5 \left(3 a e^2+c d^2\right)+a d^2 e x^3+a d^3 x+\frac{1}{3} c d e^2 x^9+\frac{1}{11} c e^3 x^{11}",1,"a*d^3*x + a*d^2*e*x^3 + (d*(c*d^2 + 3*a*e^2)*x^5)/5 + (e*(3*c*d^2 + a*e^2)*x^7)/7 + (c*d*e^2*x^9)/3 + (c*e^3*x^11)/11","A",2,1,17,0.05882,1,"{1154}"
122,1,56,0,0.0321749,"\int \left(d+e x^2\right)^2 \left(a+c x^4\right) \, dx","Int[(d + e*x^2)^2*(a + c*x^4),x]","\frac{1}{5} x^5 \left(a e^2+c d^2\right)+a d^2 x+\frac{2}{3} a d e x^3+\frac{2}{7} c d e x^7+\frac{1}{9} c e^2 x^9","\frac{1}{5} x^5 \left(a e^2+c d^2\right)+a d^2 x+\frac{2}{3} a d e x^3+\frac{2}{7} c d e x^7+\frac{1}{9} c e^2 x^9",1,"a*d^2*x + (2*a*d*e*x^3)/3 + ((c*d^2 + a*e^2)*x^5)/5 + (2*c*d*e*x^7)/7 + (c*e^2*x^9)/9","A",2,1,17,0.05882,1,"{1154}"
123,1,32,0,0.0137964,"\int \left(d+e x^2\right) \left(a+c x^4\right) \, dx","Int[(d + e*x^2)*(a + c*x^4),x]","a d x+\frac{1}{3} a e x^3+\frac{1}{5} c d x^5+\frac{1}{7} c e x^7","a d x+\frac{1}{3} a e x^3+\frac{1}{5} c d x^5+\frac{1}{7} c e x^7",1,"a*d*x + (a*e*x^3)/3 + (c*d*x^5)/5 + (c*e*x^7)/7","A",2,1,15,0.06667,1,"{1154}"
124,1,55,0,0.0347125,"\int \frac{a+c x^4}{d+e x^2} \, dx","Int[(a + c*x^4)/(d + e*x^2),x]","\frac{\left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} e^{5/2}}-\frac{c d x}{e^2}+\frac{c x^3}{3 e}","\frac{\left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} e^{5/2}}-\frac{c d x}{e^2}+\frac{c x^3}{3 e}",1,"-((c*d*x)/e^2) + (c*x^3)/(3*e) + ((c*d^2 + a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(5/2))","A",3,2,17,0.1176,1,"{1154, 205}"
125,1,74,0,0.0519109,"\int \frac{a+c x^4}{\left(d+e x^2\right)^2} \, dx","Int[(a + c*x^4)/(d + e*x^2)^2,x]","\frac{x \left(a+\frac{c d^2}{e^2}\right)}{2 d \left(d+e x^2\right)}-\frac{\left(3 c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} e^{5/2}}+\frac{c x}{e^2}","\frac{x \left(a+\frac{c d^2}{e^2}\right)}{2 d \left(d+e x^2\right)}-\frac{\left(3 c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} e^{5/2}}+\frac{c x}{e^2}",1,"(c*x)/e^2 + ((a + (c*d^2)/e^2)*x)/(2*d*(d + e*x^2)) - ((3*c*d^2 - a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*e^(5/2))","A",3,3,17,0.1765,1,"{1158, 388, 205}"
126,1,93,0,0.0674083,"\int \frac{a+c x^4}{\left(d+e x^2\right)^3} \, dx","Int[(a + c*x^4)/(d + e*x^2)^3,x]","\frac{x \left(\frac{3 a}{d^2}-\frac{5 c}{e^2}\right)}{8 \left(d+e x^2\right)}+\frac{x \left(a+\frac{c d^2}{e^2}\right)}{4 d \left(d+e x^2\right)^2}+\frac{3 \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{5/2} e^{5/2}}","\frac{x \left(\frac{3 a}{d^2}-\frac{5 c}{e^2}\right)}{8 \left(d+e x^2\right)}+\frac{x \left(a+\frac{c d^2}{e^2}\right)}{4 d \left(d+e x^2\right)^2}+\frac{3 \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{5/2} e^{5/2}}",1,"((a + (c*d^2)/e^2)*x)/(4*d*(d + e*x^2)^2) + (((3*a)/d^2 - (5*c)/e^2)*x)/(8*(d + e*x^2)) + (3*(c*d^2 + a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(5/2)*e^(5/2))","A",3,3,17,0.1765,1,"{1158, 385, 205}"
127,1,123,0,0.1140256,"\int \frac{a+c x^4}{\left(d+e x^2\right)^4} \, dx","Int[(a + c*x^4)/(d + e*x^2)^4,x]","\frac{x \left(\frac{5 a}{d^2}+\frac{c}{e^2}\right)}{16 d \left(d+e x^2\right)}+\frac{x \left(\frac{5 a}{d^2}-\frac{7 c}{e^2}\right)}{24 \left(d+e x^2\right)^2}+\frac{x \left(a+\frac{c d^2}{e^2}\right)}{6 d \left(d+e x^2\right)^3}+\frac{\left(5 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2} e^{5/2}}","\frac{x \left(\frac{5 a}{d^2}+\frac{c}{e^2}\right)}{16 d \left(d+e x^2\right)}+\frac{x \left(\frac{5 a}{d^2}-\frac{7 c}{e^2}\right)}{24 \left(d+e x^2\right)^2}+\frac{x \left(a+\frac{c d^2}{e^2}\right)}{6 d \left(d+e x^2\right)^3}+\frac{\left(5 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2} e^{5/2}}",1,"((a + (c*d^2)/e^2)*x)/(6*d*(d + e*x^2)^3) + (((5*a)/d^2 - (7*c)/e^2)*x)/(24*(d + e*x^2)^2) + (((5*a)/d^2 + c/e^2)*x)/(16*d*(d + e*x^2)) + ((c*d^2 + 5*a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(16*d^(7/2)*e^(5/2))","A",4,4,17,0.2353,1,"{1158, 385, 199, 205}"
128,1,133,0,0.1068686,"\int \left(d+e x^2\right)^3 \left(a+c x^4\right)^2 \, dx","Int[(d + e*x^2)^3*(a + c*x^4)^2,x]","a^2 d^2 e x^3+a^2 d^3 x+\frac{1}{11} c e x^{11} \left(2 a e^2+3 c d^2\right)+\frac{1}{9} c d x^9 \left(6 a e^2+c d^2\right)+\frac{1}{7} a e x^7 \left(a e^2+6 c d^2\right)+\frac{1}{5} a d x^5 \left(3 a e^2+2 c d^2\right)+\frac{3}{13} c^2 d e^2 x^{13}+\frac{1}{15} c^2 e^3 x^{15}","a^2 d^2 e x^3+a^2 d^3 x+\frac{1}{11} c e x^{11} \left(2 a e^2+3 c d^2\right)+\frac{1}{9} c d x^9 \left(6 a e^2+c d^2\right)+\frac{1}{7} a e x^7 \left(a e^2+6 c d^2\right)+\frac{1}{5} a d x^5 \left(3 a e^2+2 c d^2\right)+\frac{3}{13} c^2 d e^2 x^{13}+\frac{1}{15} c^2 e^3 x^{15}",1,"a^2*d^3*x + a^2*d^2*e*x^3 + (a*d*(2*c*d^2 + 3*a*e^2)*x^5)/5 + (a*e*(6*c*d^2 + a*e^2)*x^7)/7 + (c*d*(c*d^2 + 6*a*e^2)*x^9)/9 + (c*e*(3*c*d^2 + 2*a*e^2)*x^11)/11 + (3*c^2*d*e^2*x^13)/13 + (c^2*e^3*x^15)/15","A",2,1,19,0.05263,1,"{1154}"
129,1,97,0,0.0683933,"\int \left(d+e x^2\right)^2 \left(a+c x^4\right)^2 \, dx","Int[(d + e*x^2)^2*(a + c*x^4)^2,x]","a^2 d^2 x+\frac{2}{3} a^2 d e x^3+\frac{1}{9} c x^9 \left(2 a e^2+c d^2\right)+\frac{1}{5} a x^5 \left(a e^2+2 c d^2\right)+\frac{4}{7} a c d e x^7+\frac{2}{11} c^2 d e x^{11}+\frac{1}{13} c^2 e^2 x^{13}","a^2 d^2 x+\frac{2}{3} a^2 d e x^3+\frac{1}{9} c x^9 \left(2 a e^2+c d^2\right)+\frac{1}{5} a x^5 \left(a e^2+2 c d^2\right)+\frac{4}{7} a c d e x^7+\frac{2}{11} c^2 d e x^{11}+\frac{1}{13} c^2 e^2 x^{13}",1,"a^2*d^2*x + (2*a^2*d*e*x^3)/3 + (a*(2*c*d^2 + a*e^2)*x^5)/5 + (4*a*c*d*e*x^7)/7 + (c*(c*d^2 + 2*a*e^2)*x^9)/9 + (2*c^2*d*e*x^11)/11 + (c^2*e^2*x^13)/13","A",2,1,19,0.05263,1,"{1154}"
130,1,60,0,0.0304607,"\int \left(d+e x^2\right) \left(a+c x^4\right)^2 \, dx","Int[(d + e*x^2)*(a + c*x^4)^2,x]","a^2 d x+\frac{1}{3} a^2 e x^3+\frac{2}{5} a c d x^5+\frac{2}{7} a c e x^7+\frac{1}{9} c^2 d x^9+\frac{1}{11} c^2 e x^{11}","a^2 d x+\frac{1}{3} a^2 e x^3+\frac{2}{5} a c d x^5+\frac{2}{7} a c e x^7+\frac{1}{9} c^2 d x^9+\frac{1}{11} c^2 e x^{11}",1,"a^2*d*x + (a^2*e*x^3)/3 + (2*a*c*d*x^5)/5 + (2*a*c*e*x^7)/7 + (c^2*d*x^9)/9 + (c^2*e*x^11)/11","A",2,1,17,0.05882,1,"{1154}"
131,1,25,0,0.0081181,"\int \left(a+c x^4\right)^2 \, dx","Int[(a + c*x^4)^2,x]","a^2 x+\frac{2}{5} a c x^5+\frac{c^2 x^9}{9}","a^2 x+\frac{2}{5} a c x^5+\frac{c^2 x^9}{9}",1,"a^2*x + (2*a*c*x^5)/5 + (c^2*x^9)/9","A",2,1,9,0.1111,1,"{194}"
132,1,108,0,0.0767978,"\int \frac{\left(a+c x^4\right)^2}{d+e x^2} \, dx","Int[(a + c*x^4)^2/(d + e*x^2),x]","\frac{c x^3 \left(2 a e^2+c d^2\right)}{3 e^3}-\frac{c d x \left(2 a e^2+c d^2\right)}{e^4}+\frac{\left(a e^2+c d^2\right)^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} e^{9/2}}-\frac{c^2 d x^5}{5 e^2}+\frac{c^2 x^7}{7 e}","\frac{c x^3 \left(2 a e^2+c d^2\right)}{3 e^3}-\frac{c d x \left(2 a e^2+c d^2\right)}{e^4}+\frac{\left(a e^2+c d^2\right)^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} e^{9/2}}-\frac{c^2 d x^5}{5 e^2}+\frac{c^2 x^7}{7 e}",1,"-((c*d*(c*d^2 + 2*a*e^2)*x)/e^4) + (c*(c*d^2 + 2*a*e^2)*x^3)/(3*e^3) - (c^2*d*x^5)/(5*e^2) + (c^2*x^7)/(7*e) + ((c*d^2 + a*e^2)^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(9/2))","A",3,2,19,0.1053,1,"{1154, 205}"
133,1,131,0,0.1879885,"\int \frac{\left(a+c x^4\right)^2}{\left(d+e x^2\right)^2} \, dx","Int[(a + c*x^4)^2/(d + e*x^2)^2,x]","\frac{x \left(a e^2+c d^2\right)^2}{2 d e^4 \left(d+e x^2\right)}+\frac{c x \left(2 a e^2+3 c d^2\right)}{e^4}-\frac{\left(7 c d^2-a e^2\right) \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} e^{9/2}}-\frac{2 c^2 d x^3}{3 e^3}+\frac{c^2 x^5}{5 e^2}","\frac{x \left(a e^2+c d^2\right)^2}{2 d e^4 \left(d+e x^2\right)}+\frac{c x \left(2 a e^2+3 c d^2\right)}{e^4}-\frac{\left(7 c d^2-a e^2\right) \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} e^{9/2}}-\frac{2 c^2 d x^3}{3 e^3}+\frac{c^2 x^5}{5 e^2}",1,"(c*(3*c*d^2 + 2*a*e^2)*x)/e^4 - (2*c^2*d*x^3)/(3*e^3) + (c^2*x^5)/(5*e^2) + ((c*d^2 + a*e^2)^2*x)/(2*d*e^4*(d + e*x^2)) - ((7*c*d^2 - a*e^2)*(c*d^2 + a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*e^(9/2))","A",4,3,19,0.1579,1,"{1158, 1810, 205}"
134,1,155,0,0.2524676,"\int \frac{\left(a+c x^4\right)^2}{\left(d+e x^2\right)^3} \, dx","Int[(a + c*x^4)^2/(d + e*x^2)^3,x]","\frac{x \left(3 a^2-\frac{10 a c d^2}{e^2}-\frac{13 c^2 d^4}{e^4}\right)}{8 d^2 \left(d+e x^2\right)}+\frac{\left(3 a^2 e^4+6 a c d^2 e^2+35 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{5/2} e^{9/2}}+\frac{x \left(a e^2+c d^2\right)^2}{4 d e^4 \left(d+e x^2\right)^2}-\frac{3 c^2 d x}{e^4}+\frac{c^2 x^3}{3 e^3}","\frac{x \left(3 a^2-\frac{10 a c d^2}{e^2}-\frac{13 c^2 d^4}{e^4}\right)}{8 d^2 \left(d+e x^2\right)}+\frac{\left(3 a^2 e^4+6 a c d^2 e^2+35 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{5/2} e^{9/2}}+\frac{x \left(a e^2+c d^2\right)^2}{4 d e^4 \left(d+e x^2\right)^2}-\frac{3 c^2 d x}{e^4}+\frac{c^2 x^3}{3 e^3}",1,"(-3*c^2*d*x)/e^4 + (c^2*x^3)/(3*e^3) + ((c*d^2 + a*e^2)^2*x)/(4*d*e^4*(d + e*x^2)^2) + ((3*a^2 - (13*c^2*d^4)/e^4 - (10*a*c*d^2)/e^2)*x)/(8*d^2*(d + e*x^2)) + ((35*c^2*d^4 + 6*a*c*d^2*e^2 + 3*a^2*e^4)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(5/2)*e^(9/2))","A",5,4,19,0.2105,1,"{1158, 1814, 1153, 205}"
135,1,184,0,0.2966247,"\int \frac{\left(a+c x^4\right)^2}{\left(d+e x^2\right)^4} \, dx","Int[(a + c*x^4)^2/(d + e*x^2)^4,x]","\frac{x \left(5 a^2+\frac{2 a c d^2}{e^2}+\frac{29 c^2 d^4}{e^4}\right)}{16 d^3 \left(d+e x^2\right)}+\frac{x \left(5 a^2-\frac{14 a c d^2}{e^2}-\frac{19 c^2 d^4}{e^4}\right)}{24 d^2 \left(d+e x^2\right)^2}-\frac{\left(-5 a^2 e^4-2 a c d^2 e^2+35 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2} e^{9/2}}+\frac{x \left(a e^2+c d^2\right)^2}{6 d e^4 \left(d+e x^2\right)^3}+\frac{c^2 x}{e^4}","\frac{x \left(5 a^2+\frac{2 a c d^2}{e^2}+\frac{29 c^2 d^4}{e^4}\right)}{16 d^3 \left(d+e x^2\right)}+\frac{x \left(5 a^2-\frac{14 a c d^2}{e^2}-\frac{19 c^2 d^4}{e^4}\right)}{24 d^2 \left(d+e x^2\right)^2}-\frac{\left(-5 a^2 e^4-2 a c d^2 e^2+35 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2} e^{9/2}}+\frac{x \left(a e^2+c d^2\right)^2}{6 d e^4 \left(d+e x^2\right)^3}+\frac{c^2 x}{e^4}",1,"(c^2*x)/e^4 + ((c*d^2 + a*e^2)^2*x)/(6*d*e^4*(d + e*x^2)^3) + ((5*a^2 - (19*c^2*d^4)/e^4 - (14*a*c*d^2)/e^2)*x)/(24*d^2*(d + e*x^2)^2) + ((5*a^2 + (29*c^2*d^4)/e^4 + (2*a*c*d^2)/e^2)*x)/(16*d^3*(d + e*x^2)) - ((35*c^2*d^4 - 2*a*c*d^2*e^2 - 5*a^2*e^4)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(16*d^(7/2)*e^(9/2))","A",5,5,19,0.2632,1,"{1158, 1814, 1157, 388, 205}"
136,1,223,0,0.3386343,"\int \frac{\left(a+c x^4\right)^2}{\left(d+e x^2\right)^5} \, dx","Int[(a + c*x^4)^2/(d + e*x^2)^5,x]","-\frac{x \left(-35 a^2 e^4-6 a c d^2 e^2+93 c^2 d^4\right)}{128 d^4 e^4 \left(d+e x^2\right)}+\frac{x \left(35 a^2+\frac{6 a c d^2}{e^2}+\frac{163 c^2 d^4}{e^4}\right)}{192 d^3 \left(d+e x^2\right)^2}+\frac{x \left(7 a^2-\frac{18 a c d^2}{e^2}-\frac{25 c^2 d^4}{e^4}\right)}{48 d^2 \left(d+e x^2\right)^3}+\frac{\left(35 a^2 e^4+6 a c d^2 e^2+35 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{128 d^{9/2} e^{9/2}}+\frac{x \left(a e^2+c d^2\right)^2}{8 d e^4 \left(d+e x^2\right)^4}","-\frac{x \left(-35 a^2 e^4-6 a c d^2 e^2+93 c^2 d^4\right)}{128 d^4 e^4 \left(d+e x^2\right)}+\frac{x \left(35 a^2+\frac{6 a c d^2}{e^2}+\frac{163 c^2 d^4}{e^4}\right)}{192 d^3 \left(d+e x^2\right)^2}+\frac{x \left(7 a^2-\frac{18 a c d^2}{e^2}-\frac{25 c^2 d^4}{e^4}\right)}{48 d^2 \left(d+e x^2\right)^3}+\frac{\left(35 a^2 e^4+6 a c d^2 e^2+35 c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{128 d^{9/2} e^{9/2}}+\frac{x \left(a e^2+c d^2\right)^2}{8 d e^4 \left(d+e x^2\right)^4}",1,"((c*d^2 + a*e^2)^2*x)/(8*d*e^4*(d + e*x^2)^4) + ((7*a^2 - (25*c^2*d^4)/e^4 - (18*a*c*d^2)/e^2)*x)/(48*d^2*(d + e*x^2)^3) + ((35*a^2 + (163*c^2*d^4)/e^4 + (6*a*c*d^2)/e^2)*x)/(192*d^3*(d + e*x^2)^2) - ((93*c^2*d^4 - 6*a*c*d^2*e^2 - 35*a^2*e^4)*x)/(128*d^4*e^4*(d + e*x^2)) + ((35*c^2*d^4 + 6*a*c*d^2*e^2 + 35*a^2*e^4)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(128*d^(9/2)*e^(9/2))","A",5,5,19,0.2632,1,"{1158, 1814, 1157, 385, 205}"
137,1,437,0,0.4531806,"\int \frac{\left(d+e x^2\right)^4}{a+c x^4} \, dx","Int[(d + e*x^2)^4/(a + c*x^4),x]","-\frac{\left(a^2 e^4-6 a c d^2 e^2-4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{9/4}}+\frac{\left(a^2 e^4-6 a c d^2 e^2-4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{9/4}}-\frac{\left(a^2 e^4-6 a c d^2 e^2+4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{9/4}}+\frac{\left(a^2 e^4-6 a c d^2 e^2+4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{9/4}}+\frac{e^2 x \left(6 c d^2-a e^2\right)}{c^2}+\frac{4 d e^3 x^3}{3 c}+\frac{e^4 x^5}{5 c}","-\frac{\left(a^2 e^4-6 a c d^2 e^2-4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{9/4}}+\frac{\left(a^2 e^4-6 a c d^2 e^2-4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{9/4}}-\frac{\left(a^2 e^4-6 a c d^2 e^2+4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{9/4}}+\frac{\left(a^2 e^4-6 a c d^2 e^2+4 \sqrt{a} \sqrt{c} d e \left(c d^2-a e^2\right)+c^2 d^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{9/4}}+\frac{e^2 x \left(6 c d^2-a e^2\right)}{c^2}+\frac{4 d e^3 x^3}{3 c}+\frac{e^4 x^5}{5 c}",1,"(e^2*(6*c*d^2 - a*e^2)*x)/c^2 + (4*d*e^3*x^3)/(3*c) + (e^4*x^5)/(5*c) - ((c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4 + 4*Sqrt[a]*Sqrt[c]*d*e*(c*d^2 - a*e^2))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(9/4)) + ((c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4 + 4*Sqrt[a]*Sqrt[c]*d*e*(c*d^2 - a*e^2))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(9/4)) - ((c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4 - 4*Sqrt[a]*Sqrt[c]*d*e*(c*d^2 - a*e^2))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(9/4)) + ((c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4 - 4*Sqrt[a]*Sqrt[c]*d*e*(c*d^2 - a*e^2))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(9/4))","A",11,7,19,0.3684,1,"{1171, 1168, 1162, 617, 204, 1165, 628}"
138,1,370,0,0.5012381,"\int \frac{\left(d+e x^2\right)^3}{a+c x^4} \, dx","Int[(d + e*x^2)^3/(a + c*x^4),x]","-\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)-\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}+\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)-\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)+\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{7/4}}+\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)+\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{7/4}}+\frac{3 d e^2 x}{c}+\frac{e^3 x^3}{3 c}","-\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)-\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}+\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)-\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)+\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{7/4}}+\frac{\left(\sqrt{c} d \left(c d^2-3 a e^2\right)+\sqrt{a} e \left(3 c d^2-a e^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{7/4}}+\frac{3 d e^2 x}{c}+\frac{e^3 x^3}{3 c}",1,"(3*d*e^2*x)/c + (e^3*x^3)/(3*c) - ((Sqrt[c]*d*(c*d^2 - 3*a*e^2) + Sqrt[a]*e*(3*c*d^2 - a*e^2))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(7/4)) + ((Sqrt[c]*d*(c*d^2 - 3*a*e^2) + Sqrt[a]*e*(3*c*d^2 - a*e^2))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(7/4)) - ((Sqrt[c]*d*(c*d^2 - 3*a*e^2) - Sqrt[a]*e*(3*c*d^2 - a*e^2))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(7/4)) + ((Sqrt[c]*d*(c*d^2 - 3*a*e^2) - Sqrt[a]*e*(3*c*d^2 - a*e^2))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(7/4))","A",11,7,19,0.3684,1,"{1171, 1168, 1162, 617, 204, 1165, 628}"
139,1,297,0,0.292803,"\int \frac{\left(d+e x^2\right)^2}{a+c x^4} \, dx","Int[(d + e*x^2)^2/(a + c*x^4),x]","-\frac{\left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{5/4}}-\frac{\left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{5/4}}+\frac{e^2 x}{c}","-\frac{\left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{5/4}}-\frac{\left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{5/4}}+\frac{\left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{5/4}}+\frac{e^2 x}{c}",1,"(e^2*x)/c - ((c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(5/4)) + ((c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(5/4)) - ((c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(5/4)) + ((c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(5/4))","A",11,7,19,0.3684,1,"{1171, 1168, 1162, 617, 204, 1165, 628}"
140,1,247,0,0.1523432,"\int \frac{d+e x^2}{a+c x^4} \, dx","Int[(d + e*x^2)/(a + c*x^4),x]","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{c} d-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{c} d-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}",1,"-((Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(3/4)) + ((Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*c^(3/4)) - ((Sqrt[c]*d - Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(3/4)) + ((Sqrt[c]*d - Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*c^(3/4))","A",9,6,17,0.3529,1,"{1168, 1162, 617, 204, 1165, 628}"
141,1,185,0,0.1109586,"\int \frac{1}{a+c x^4} \, dx","Int[(a + c*x^4)^(-1),x]","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}","-\frac{\log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{c}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{c}}",1,"-ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*c^(1/4)) + ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)]/(2*Sqrt[2]*a^(3/4)*c^(1/4)) - Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(3/4)*c^(1/4)) + Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2]/(4*Sqrt[2]*a^(3/4)*c^(1/4))","A",9,6,9,0.6667,1,"{211, 1165, 628, 1162, 617, 204}"
142,1,336,0,0.2697656,"\int \frac{1}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[1/((d + e*x^2)*(a + c*x^4)),x]","-\frac{\sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2+c d^2\right)}","-\frac{\sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2+c d^2\right)}",1,"(e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*(c*d^2 + a*e^2)) - (c^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)) + (c^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)) - (c^(1/4)*(Sqrt[c]*d + Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)) + (c^(1/4)*(Sqrt[c]*d + Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2))","A",12,8,19,0.4211,1,"{1171, 205, 1168, 1162, 617, 204, 1165, 628}"
143,1,453,0,0.384018,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+c x^4\right)} \, dx","Int[1/((d + e*x^2)^2*(a + c*x^4)),x]","-\frac{c^{3/4} \left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}-\frac{c^{3/4} \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{e^2 x}{2 d \left(d+e x^2\right) \left(a e^2+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \left(a e^2+c d^2\right)}+\frac{2 c \sqrt{d} e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}","-\frac{c^{3/4} \left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}-\frac{c^{3/4} \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(-2 \sqrt{a} \sqrt{c} d e-a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{e^2 x}{2 d \left(d+e x^2\right) \left(a e^2+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \left(a e^2+c d^2\right)}+\frac{2 c \sqrt{d} e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}",1,"(e^2*x)/(2*d*(c*d^2 + a*e^2)*(d + e*x^2)) + (2*c*Sqrt[d]*e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(c*d^2 + a*e^2)^2 + (e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*(c*d^2 + a*e^2)) - (c^(3/4)*(c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2) + (c^(3/4)*(c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2) - (c^(3/4)*(c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2) + (c^(3/4)*(c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2)","A",14,9,19,0.4737,1,"{1171, 199, 205, 1168, 1162, 617, 204, 1165, 628}"
144,1,363,0,0.4101941,"\int \frac{\left(d+e x^2\right)^3}{\left(a+c x^4\right)^2} \, dx","Int[(d + e*x^2)^3/(a + c*x^4)^2,x]","-\frac{3 \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{7/4}}+\frac{3 \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{7/4}}-\frac{3 \left(\sqrt{a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{7/4}}+\frac{3 \left(\sqrt{a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{7/4}}+\frac{x \left(3 e x^2 \left(a e^2+c d^2\right)+d \left(c d^2-3 a e^2\right)\right)}{4 a c \left(a+c x^4\right)}-\frac{e^3 x^3}{c \left(a+c x^4\right)}","-\frac{3 \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{7/4}}+\frac{3 \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{7/4}}-\frac{3 \left(\sqrt{a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{7/4}}+\frac{3 \left(\sqrt{a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{7/4}}+\frac{x \left(3 e x^2 \left(a e^2+c d^2\right)+d \left(c d^2-3 a e^2\right)\right)}{4 a c \left(a+c x^4\right)}-\frac{e^3 x^3}{c \left(a+c x^4\right)}",1,"-((e^3*x^3)/(c*(a + c*x^4))) + (x*(d*(c*d^2 - 3*a*e^2) + 3*e*(c*d^2 + a*e^2)*x^2))/(4*a*c*(a + c*x^4)) - (3*(Sqrt[c]*d + Sqrt[a]*e)*(c*d^2 + a*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(7/4)) + (3*(Sqrt[c]*d + Sqrt[a]*e)*(c*d^2 + a*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(7/4)) - (3*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 + a*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(7/4)) + (3*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 + a*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(7/4))","A",11,8,19,0.4211,1,"{1207, 1858, 1168, 1162, 617, 204, 1165, 628}"
145,1,349,0,0.312522,"\int \frac{\left(d+e x^2\right)^2}{\left(a+c x^4\right)^2} \, dx","Int[(d + e*x^2)^2/(a + c*x^4)^2,x]","-\frac{\left(-2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{5/4}}+\frac{\left(-2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{5/4}}-\frac{\left(2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{5/4}}+\frac{\left(2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{5/4}}+\frac{x \left(a e^2+3 c d^2+6 c d e x^2\right)}{12 a c \left(a+c x^4\right)}-\frac{e^2 x}{3 c \left(a+c x^4\right)}","-\frac{\left(-2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{5/4}}+\frac{\left(-2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{5/4}}-\frac{\left(2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{5/4}}+\frac{\left(2 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{5/4}}+\frac{x \left(a e^2+3 c d^2+6 c d e x^2\right)}{12 a c \left(a+c x^4\right)}-\frac{e^2 x}{3 c \left(a+c x^4\right)}",1,"-(e^2*x)/(3*c*(a + c*x^4)) + (x*(3*c*d^2 + a*e^2 + 6*c*d*e*x^2))/(12*a*c*(a + c*x^4)) - ((3*c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e + a*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(5/4)) + ((3*c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e + a*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(5/4)) - ((3*c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e + a*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(5/4)) + ((3*c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e + a*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(5/4))","A",11,8,19,0.4211,1,"{1207, 1179, 1168, 1162, 617, 204, 1165, 628}"
146,1,275,0,0.2033911,"\int \frac{d+e x^2}{\left(a+c x^4\right)^2} \, dx","Int[(d + e*x^2)/(a + c*x^4)^2,x]","-\frac{\left(3 \sqrt{c} d-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(3 \sqrt{c} d-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} e+3 \sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{x \left(d+e x^2\right)}{4 a \left(a+c x^4\right)}","-\frac{\left(3 \sqrt{c} d-\sqrt{a} e\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(3 \sqrt{c} d-\sqrt{a} e\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} e+3 \sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(\sqrt{a} e+3 \sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}+\frac{x \left(d+e x^2\right)}{4 a \left(a+c x^4\right)}",1,"(x*(d + e*x^2))/(4*a*(a + c*x^4)) - ((3*Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(3/4)) + ((3*Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(3/4)) - ((3*Sqrt[c]*d - Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(3/4)) + ((3*Sqrt[c]*d - Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(3/4))","A",10,7,17,0.4118,1,"{1179, 1168, 1162, 617, 204, 1165, 628}"
147,1,202,0,0.1329408,"\int \frac{1}{\left(a+c x^4\right)^2} \, dx","Int[(a + c*x^4)^(-2),x]","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{x}{4 a \left(a+c x^4\right)}","-\frac{3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \sqrt[4]{c}}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \sqrt[4]{c}}+\frac{x}{4 a \left(a+c x^4\right)}",1,"x/(4*a*(a + c*x^4)) - (3*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*c^(1/4)) - (3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4)) + (3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*c^(1/4))","A",10,7,9,0.7778,1,"{199, 211, 1165, 628, 1162, 617, 204}"
148,1,689,0,0.6229707,"\int \frac{1}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[1/((d + e*x^2)*(a + c*x^4)^2),x]","-\frac{\sqrt[4]{c} e^2 \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{c} e^2 \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{c} \left(\sqrt{a} e+3 \sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{a} e+3 \sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} e^2 \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{c} e^2 \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}+\frac{c x \left(d-e x^2\right)}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2+c d^2\right)^2}","-\frac{\sqrt[4]{c} e^2 \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{c} e^2 \left(\sqrt{a} e+\sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{4 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{c} \left(\sqrt{a} e+3 \sqrt{c} d\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(\sqrt{a} e+3 \sqrt{c} d\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}+\sqrt{c} x^2\right)}{16 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} e^2 \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{c} e^2 \left(\sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{c} \left(3 \sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} \left(3 \sqrt{c} d-\sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(a e^2+c d^2\right)}+\frac{c x \left(d-e x^2\right)}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2+c d^2\right)^2}",1,"(c*x*(d - e*x^2))/(4*a*(c*d^2 + a*e^2)*(a + c*x^4)) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*(c*d^2 + a*e^2)^2) - (c^(1/4)*e^2*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2) - (c^(1/4)*(3*Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)) + (c^(1/4)*e^2*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2) + (c^(1/4)*(3*Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)) - (c^(1/4)*e^2*(Sqrt[c]*d + Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2) - (c^(1/4)*(3*Sqrt[c]*d + Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)) + (c^(1/4)*e^2*(Sqrt[c]*d + Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^2) + (c^(1/4)*(3*Sqrt[c]*d + Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2))","A",22,9,19,0.4737,1,"{1239, 205, 1179, 1168, 1162, 617, 204, 1165, 628}"
149,1,864,0,0.9061083,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+c x^4\right)^2} \, dx","Int[1/((d + e*x^2)^2*(a + c*x^4)^2),x]","\frac{x e^4}{2 d \left(c d^2+a e^2\right)^2 \left(e x^2+d\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{2 d^{3/2} \left(c d^2+a e^2\right)^2}+\frac{4 c \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{\left(c d^2+a e^2\right)^3}-\frac{c^{3/4} \left(3 c d^2-4 \sqrt{a} \sqrt{c} e d-a e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^2}{2 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}+\frac{c^{3/4} \left(3 c d^2-4 \sqrt{a} \sqrt{c} e d-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^2}{2 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}-\frac{c^{3/4} \left(3 c d^2+4 \sqrt{a} \sqrt{c} e d-a e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^2}{4 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}+\frac{c^{3/4} \left(3 c d^2+4 \sqrt{a} \sqrt{c} e d-a e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^2}{4 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}-\frac{c^{3/4} \left(3 c d^2-2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}+\frac{c^{3/4} \left(3 c d^2-2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}-\frac{c^{3/4} \left(3 c d^2+2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}+\frac{c^{3/4} \left(3 c d^2+2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}+\frac{c x \left(c d^2-2 c e x^2 d-a e^2\right)}{4 a \left(c d^2+a e^2\right)^2 \left(c x^4+a\right)}","\frac{x e^4}{2 d \left(c d^2+a e^2\right)^2 \left(e x^2+d\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{2 d^{3/2} \left(c d^2+a e^2\right)^2}+\frac{4 c \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{\left(c d^2+a e^2\right)^3}-\frac{c^{3/4} \left(3 c d^2-4 \sqrt{a} \sqrt{c} e d-a e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right) e^2}{2 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}+\frac{c^{3/4} \left(3 c d^2-4 \sqrt{a} \sqrt{c} e d-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right) e^2}{2 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}-\frac{c^{3/4} \left(3 c d^2+4 \sqrt{a} \sqrt{c} e d-a e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^2}{4 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}+\frac{c^{3/4} \left(3 c d^2+4 \sqrt{a} \sqrt{c} e d-a e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right) e^2}{4 \sqrt{2} a^{3/4} \left(c d^2+a e^2\right)^3}-\frac{c^{3/4} \left(3 c d^2-2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}+\frac{c^{3/4} \left(3 c d^2-2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}-\frac{c^{3/4} \left(3 c d^2+2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \log \left(\sqrt{c} x^2-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}+\frac{c^{3/4} \left(3 c d^2+2 \sqrt{a} \sqrt{c} e d-3 a e^2\right) \log \left(\sqrt{c} x^2+\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} x+\sqrt{a}\right)}{16 \sqrt{2} a^{7/4} \left(c d^2+a e^2\right)^2}+\frac{c x \left(c d^2-2 c e x^2 d-a e^2\right)}{4 a \left(c d^2+a e^2\right)^2 \left(c x^4+a\right)}",1,"(e^4*x)/(2*d*(c*d^2 + a*e^2)^2*(d + e*x^2)) + (c*x*(c*d^2 - a*e^2 - 2*c*d*e*x^2))/(4*a*(c*d^2 + a*e^2)^2*(a + c*x^4)) + (4*c*Sqrt[d]*e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(c*d^2 + a*e^2)^3 + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*(c*d^2 + a*e^2)^2) - (c^(3/4)*e^2*(3*c*d^2 - 4*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^3) - (c^(3/4)*(3*c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - 3*a*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)^2) + (c^(3/4)*e^2*(3*c*d^2 - 4*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^3) + (c^(3/4)*(3*c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - 3*a*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)^2) - (c^(3/4)*e^2*(3*c*d^2 + 4*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^3) - (c^(3/4)*(3*c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - 3*a*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)^2) + (c^(3/4)*e^2*(3*c*d^2 + 4*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(3/4)*(c*d^2 + a*e^2)^3) + (c^(3/4)*(3*c*d^2 + 2*Sqrt[a]*Sqrt[c]*d*e - 3*a*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)^2)","A",24,10,19,0.5263,1,"{1239, 199, 205, 1179, 1168, 1162, 617, 204, 1165, 628}"
150,1,386,0,0.4151871,"\int \frac{\left(d+e x^2\right)^4}{\sqrt{a+c x^4}} \, dx","Int[(d + e*x^2)^4/Sqrt[a + 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}} \left(5 \left(5 a^2 e^4-42 a c d^2 e^2+21 c^2 d^4\right)+84 \sqrt{a} \sqrt{c} d e \left(5 c d^2-3 a e^2\right)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{210 \sqrt[4]{a} c^{9/4} \sqrt{a+c x^4}}+\frac{e^2 x \sqrt{a+c x^4} \left(42 c d^2-5 a e^2\right)}{21 c^2}+\frac{4 d e x \sqrt{a+c x^4} \left(5 c d^2-3 a e^2\right)}{5 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{4 \sqrt[4]{a} d e \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(5 c d^2-3 a e^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{a+c x^4}}+\frac{4 d e^3 x^3 \sqrt{a+c x^4}}{5 c}+\frac{e^4 x^5 \sqrt{a+c x^4}}{7 c}","\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(-252 a^{3/2} \sqrt{c} d e^3+25 a^2 e^4+420 \sqrt{a} c^{3/2} d^3 e-210 a c d^2 e^2+105 c^2 d^4\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{210 \sqrt[4]{a} c^{9/4} \sqrt{a+c x^4}}+\frac{e^2 x \sqrt{a+c x^4} \left(42 c d^2-5 a e^2\right)}{21 c^2}+\frac{4 d e x \sqrt{a+c x^4} \left(5 c d^2-3 a e^2\right)}{5 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{4 \sqrt[4]{a} d e \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(5 c d^2-3 a e^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{a+c x^4}}+\frac{4 d e^3 x^3 \sqrt{a+c x^4}}{5 c}+\frac{e^4 x^5 \sqrt{a+c x^4}}{7 c}",1,"(e^2*(42*c*d^2 - 5*a*e^2)*x*Sqrt[a + c*x^4])/(21*c^2) + (4*d*e^3*x^3*Sqrt[a + c*x^4])/(5*c) + (e^4*x^5*Sqrt[a + c*x^4])/(7*c) + (4*d*e*(5*c*d^2 - 3*a*e^2)*x*Sqrt[a + c*x^4])/(5*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (4*a^(1/4)*d*e*(5*c*d^2 - 3*a*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])/(5*c^(7/4)*Sqrt[a + c*x^4]) + ((84*Sqrt[a]*Sqrt[c]*d*e*(5*c*d^2 - 3*a*e^2) + 5*(21*c^2*d^4 - 42*a*c*d^2*e^2 + 5*a^2*e^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])/(210*a^(1/4)*c^(9/4)*Sqrt[a + c*x^4])","A",6,5,21,0.2381,1,"{1207, 1888, 1198, 220, 1196}"
151,1,326,0,0.2869305,"\int \frac{\left(d+e x^2\right)^3}{\sqrt{a+c x^4}} \, dx","Int[(d + e*x^2)^3/Sqrt[a + c*x^4],x]","\frac{3 e x \sqrt{a+c x^4} \left(5 c d^2-a e^2\right)}{5 c^{3/2} \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}} \left(\frac{5 \sqrt{c} d \left(c d^2-a e^2\right)}{\sqrt{a}}-3 a e^3+15 c d^2 e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 c^{7/4} \sqrt{a+c x^4}}-\frac{3 \sqrt[4]{a} e \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(5 c d^2-a e^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{a+c x^4}}+\frac{d e^2 x \sqrt{a+c x^4}}{c}+\frac{e^3 x^3 \sqrt{a+c x^4}}{5 c}","\frac{3 e x \sqrt{a+c x^4} \left(5 c d^2-a e^2\right)}{5 c^{3/2} \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}} \left(\frac{5 \sqrt{c} d \left(c d^2-a e^2\right)}{\sqrt{a}}-3 a e^3+15 c d^2 e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 c^{7/4} \sqrt{a+c x^4}}-\frac{3 \sqrt[4]{a} e \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(5 c d^2-a e^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{a+c x^4}}+\frac{d e^2 x \sqrt{a+c x^4}}{c}+\frac{e^3 x^3 \sqrt{a+c x^4}}{5 c}",1,"(d*e^2*x*Sqrt[a + c*x^4])/c + (e^3*x^3*Sqrt[a + c*x^4])/(5*c) + (3*e*(5*c*d^2 - a*e^2)*x*Sqrt[a + c*x^4])/(5*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (3*a^(1/4)*e*(5*c*d^2 - a*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])/(5*c^(7/4)*Sqrt[a + c*x^4]) + (a^(1/4)*(15*c*d^2*e - 3*a*e^3 + (5*Sqrt[c]*d*(c*d^2 - a*e^2))/Sqrt[a])*(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])/(10*c^(7/4)*Sqrt[a + c*x^4])","A",5,5,21,0.2381,1,"{1207, 1888, 1198, 220, 1196}"
152,1,264,0,0.129349,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{a+c x^4}} \, dx","Int[(d + e*x^2)^2/Sqrt[a + 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}} \left(6 \sqrt{a} \sqrt{c} d e-a e^2+3 c d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{a} c^{5/4} \sqrt{a+c x^4}}-\frac{2 \sqrt[4]{a} d e \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{2 d e x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{e^2 x \sqrt{a+c x^4}}{3 c}","\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(6 \sqrt{a} \sqrt{c} d e-a e^2+3 c d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{a} c^{5/4} \sqrt{a+c x^4}}-\frac{2 \sqrt[4]{a} d e \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{2 d e x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{e^2 x \sqrt{a+c x^4}}{3 c}",1,"(e^2*x*Sqrt[a + c*x^4])/(3*c) + (2*d*e*x*Sqrt[a + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (2*a^(1/4)*d*e*(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]) + ((3*c*d^2 + 6*Sqrt[a]*Sqrt[c]*d*e - a*e^2)*(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^(1/4)*c^(5/4)*Sqrt[a + c*x^4])","A",4,4,21,0.1905,1,"{1207, 1198, 220, 1196}"
153,1,226,0,0.0694483,"\int \frac{d+e x^2}{\sqrt{a+c x^4}} \, dx","Int[(d + e*x^2)/Sqrt[a + 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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) 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} e \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{e 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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) 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} e \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{e x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(e*x*Sqrt[a + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*e*(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[c]*d)/Sqrt[a] + e)*(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",3,3,19,0.1579,1,"{1198, 220, 1196}"
154,1,334,0,0.2656834,"\int \frac{1}{\left(d+e x^2\right) \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x^2)*Sqrt[a + c*x^4]),x]","-\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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{c} d \sqrt{a+c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{a e^2+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+c x^4}}\right)}{2 \sqrt{d} \sqrt{a e^2+c d^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{c} d-\sqrt{a} e\right)}","-\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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{c} d \sqrt{a+c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{a e^2+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+c x^4}}\right)}{2 \sqrt{d} \sqrt{a e^2+c d^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{c} d-\sqrt{a} e\right)}",1,"(Sqrt[e]*ArcTan[(Sqrt[c*d^2 + a*e^2]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[a + c*x^4])])/(2*Sqrt[d]*Sqrt[c*d^2 + a*e^2]) + (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 - Sqrt[a]*e)*Sqrt[a + c*x^4]) - (a^(3/4)*((Sqrt[c]*d)/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 - Sqrt[a]*e)^2/(4*Sqrt[a]*Sqrt[c]*d*e), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*c^(1/4)*d*(c*d^2 - a*e^2)*Sqrt[a + c*x^4])","A",3,3,21,0.1429,1,"{1217, 220, 1707}"
155,1,581,0,0.7623263,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x^2)^2*Sqrt[a + c*x^4]),x]","\frac{e^2 x \sqrt{a+c x^4}}{2 d \left(d+e x^2\right) \left(a e^2+c d^2\right)}-\frac{\sqrt{c} e x \sqrt{a+c x^4}}{2 d \left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^2+c d^2\right)}+\frac{\sqrt{e} \left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{x \sqrt{a e^2+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+c x^4}}\right)}{4 d^{3/2} \left(a e^2+c d^2\right)^{3/2}}+\frac{\sqrt[4]{a} \sqrt[4]{c} e \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)}{2 d \sqrt{a+c x^4} \left(a e^2+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{a} e+\sqrt{c} d\right) \left(a e^2+3 c d^2\right) \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{c} d^2 \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right)}+\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} d \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}","\frac{e^2 x \sqrt{a+c x^4}}{2 d \left(d+e x^2\right) \left(a e^2+c d^2\right)}-\frac{\sqrt{c} e x \sqrt{a+c x^4}}{2 d \left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^2+c d^2\right)}+\frac{\sqrt{e} \left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{x \sqrt{a e^2+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+c x^4}}\right)}{4 d^{3/2} \left(a e^2+c d^2\right)^{3/2}}+\frac{\sqrt[4]{a} \sqrt[4]{c} e \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)}{2 d \sqrt{a+c x^4} \left(a e^2+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{a} e+\sqrt{c} d\right) \left(a e^2+3 c d^2\right) \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} \sqrt[4]{c} d^2 \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right)}+\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} d \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}",1,"-(Sqrt[c]*e*x*Sqrt[a + c*x^4])/(2*d*(c*d^2 + a*e^2)*(Sqrt[a] + Sqrt[c]*x^2)) + (e^2*x*Sqrt[a + c*x^4])/(2*d*(c*d^2 + a*e^2)*(d + e*x^2)) + (Sqrt[e]*(3*c*d^2 + a*e^2)*ArcTan[(Sqrt[c*d^2 + a*e^2]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[a + c*x^4])])/(4*d^(3/2)*(c*d^2 + a*e^2)^(3/2)) + (a^(1/4)*c^(1/4)*e*(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])/(2*d*(c*d^2 + a*e^2)*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)*d*(Sqrt[c]*d - Sqrt[a]*e)*Sqrt[a + c*x^4]) - ((Sqrt[c]*d + Sqrt[a]*e)*(3*c*d^2 + 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 - Sqrt[a]*e)^2/(4*Sqrt[a]*Sqrt[c]*d*e), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(8*a^(1/4)*c^(1/4)*d^2*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 + a*e^2)*Sqrt[a + c*x^4])","A",6,6,21,0.2857,1,"{1224, 1715, 1196, 1709, 220, 1707}"
156,1,729,0,1.2504363,"\int \frac{1}{\left(d+e x^2\right)^3 \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x^2)^3*Sqrt[a + c*x^4]),x]","\frac{3 \sqrt{e} \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \tan ^{-1}\left(\frac{x \sqrt{a e^2+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+c x^4}}\right)}{16 d^{5/2} \left(a e^2+c d^2\right)^{5/2}}-\frac{3 \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{a} e+\sqrt{c} d\right) \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{32 \sqrt[4]{a} \sqrt[4]{c} d^3 \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right)^2}+\frac{3 e^2 x \sqrt{a+c x^4} \left(a e^2+3 c d^2\right)}{8 d^2 \left(d+e x^2\right) \left(a e^2+c d^2\right)^2}+\frac{e^2 x \sqrt{a+c x^4}}{4 d \left(d+e x^2\right)^2 \left(a e^2+c d^2\right)}-\frac{3 \sqrt{c} e x \sqrt{a+c x^4} \left(a e^2+3 c d^2\right)}{8 d^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^2+c d^2\right)^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}} \left(-\sqrt{a} \sqrt{c} d e+3 a e^2+4 c d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} d^2 \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right)}+\frac{3 \sqrt[4]{a} \sqrt[4]{c} e \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(a e^2+3 c d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 d^2 \sqrt{a+c x^4} \left(a e^2+c d^2\right)^2}","\frac{3 \sqrt{e} \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \tan ^{-1}\left(\frac{x \sqrt{a e^2+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+c x^4}}\right)}{16 d^{5/2} \left(a e^2+c d^2\right)^{5/2}}-\frac{3 \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{a} e+\sqrt{c} d\right) \left(a^2 e^4+2 a c d^2 e^2+5 c^2 d^4\right) \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{32 \sqrt[4]{a} \sqrt[4]{c} d^3 \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right)^2}+\frac{3 e^2 x \sqrt{a+c x^4} \left(a e^2+3 c d^2\right)}{8 d^2 \left(d+e x^2\right) \left(a e^2+c d^2\right)^2}+\frac{e^2 x \sqrt{a+c x^4}}{4 d \left(d+e x^2\right)^2 \left(a e^2+c d^2\right)}-\frac{3 \sqrt{c} e x \sqrt{a+c x^4} \left(a e^2+3 c d^2\right)}{8 d^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^2+c d^2\right)^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}} \left(-\sqrt{a} \sqrt{c} d e+3 a e^2+4 c d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{a} d^2 \sqrt{a+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2+c d^2\right)}+\frac{3 \sqrt[4]{a} \sqrt[4]{c} e \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(a e^2+3 c d^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{8 d^2 \sqrt{a+c x^4} \left(a e^2+c d^2\right)^2}",1,"(-3*Sqrt[c]*e*(3*c*d^2 + a*e^2)*x*Sqrt[a + c*x^4])/(8*d^2*(c*d^2 + a*e^2)^2*(Sqrt[a] + Sqrt[c]*x^2)) + (e^2*x*Sqrt[a + c*x^4])/(4*d*(c*d^2 + a*e^2)*(d + e*x^2)^2) + (3*e^2*(3*c*d^2 + a*e^2)*x*Sqrt[a + c*x^4])/(8*d^2*(c*d^2 + a*e^2)^2*(d + e*x^2)) + (3*Sqrt[e]*(5*c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*ArcTan[(Sqrt[c*d^2 + a*e^2]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[a + c*x^4])])/(16*d^(5/2)*(c*d^2 + a*e^2)^(5/2)) + (3*a^(1/4)*c^(1/4)*e*(3*c*d^2 + a*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])/(8*d^2*(c*d^2 + a*e^2)^2*Sqrt[a + c*x^4]) + (c^(1/4)*(4*c*d^2 - Sqrt[a]*Sqrt[c]*d*e + 3*a*e^2)*(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])/(8*a^(1/4)*d^2*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 + a*e^2)*Sqrt[a + c*x^4]) - (3*(Sqrt[c]*d + Sqrt[a]*e)*(5*c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[-(Sqrt[c]*d - Sqrt[a]*e)^2/(4*Sqrt[a]*Sqrt[c]*d*e), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(32*a^(1/4)*c^(1/4)*d^3*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 + a*e^2)^2*Sqrt[a + c*x^4])","A",7,7,21,0.3333,1,"{1224, 1697, 1715, 1196, 1709, 220, 1707}"
157,1,213,0,0.2818005,"\int \frac{\left(d+e x^2\right)^3}{\sqrt{a-c x^4}} \, dx","Int[(d + e*x^2)^3/Sqrt[a - c*x^4],x]","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} \left(\frac{5 \sqrt{c} d \left(a e^2+c d^2\right)}{\sqrt{a}}-3 e \left(a e^2+5 c d^2\right)\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 c^{7/4} \sqrt{a-c x^4}}+\frac{3 a^{3/4} e \sqrt{1-\frac{c x^4}{a}} \left(a e^2+5 c d^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 c^{7/4} \sqrt{a-c x^4}}-\frac{d e^2 x \sqrt{a-c x^4}}{c}-\frac{e^3 x^3 \sqrt{a-c x^4}}{5 c}","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} \left(\frac{5 \sqrt{c} d \left(a e^2+c d^2\right)}{\sqrt{a}}-3 e \left(a e^2+5 c d^2\right)\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 c^{7/4} \sqrt{a-c x^4}}+\frac{3 a^{3/4} e \sqrt{1-\frac{c x^4}{a}} \left(a e^2+5 c d^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{5 c^{7/4} \sqrt{a-c x^4}}-\frac{d e^2 x \sqrt{a-c x^4}}{c}-\frac{e^3 x^3 \sqrt{a-c x^4}}{5 c}",1,"-((d*e^2*x*Sqrt[a - c*x^4])/c) - (e^3*x^3*Sqrt[a - c*x^4])/(5*c) + (3*a^(3/4)*e*(5*c*d^2 + a*e^2)*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(5*c^(7/4)*Sqrt[a - c*x^4]) + (a^(3/4)*((5*Sqrt[c]*d*(c*d^2 + a*e^2))/Sqrt[a] - 3*e*(5*c*d^2 + a*e^2))*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(5*c^(7/4)*Sqrt[a - c*x^4])","A",8,8,22,0.3636,1,"{1207, 1888, 1201, 224, 221, 1200, 1199, 424}"
158,1,162,0,0.1446983,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{a-c x^4}} \, dx","Int[(d + e*x^2)^2/Sqrt[a - c*x^4],x]","\frac{2 a^{3/4} d e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{a-c x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(-6 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 c^{5/4} \sqrt{a-c x^4}}-\frac{e^2 x \sqrt{a-c x^4}}{3 c}","\frac{2 a^{3/4} d e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{a-c x^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(-6 \sqrt{a} \sqrt{c} d e+a e^2+3 c d^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{3 c^{5/4} \sqrt{a-c x^4}}-\frac{e^2 x \sqrt{a-c x^4}}{3 c}",1,"-(e^2*x*Sqrt[a - c*x^4])/(3*c) + (2*a^(3/4)*d*e*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(3/4)*Sqrt[a - c*x^4]) + (a^(1/4)*(3*c*d^2 - 6*Sqrt[a]*Sqrt[c]*d*e + a*e^2)*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(3*c^(5/4)*Sqrt[a - c*x^4])","A",7,7,22,0.3182,1,"{1207, 1201, 224, 221, 1200, 1199, 424}"
159,1,124,0,0.0888635,"\int \frac{d+e x^2}{\sqrt{a-c x^4}} \, dx","Int[(d + e*x^2)/Sqrt[a - c*x^4],x]","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} \left(\frac{\sqrt{c} d}{\sqrt{a}}-e\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{a-c x^4}}+\frac{a^{3/4} e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{a-c x^4}}","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} \left(\frac{\sqrt{c} d}{\sqrt{a}}-e\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{a-c x^4}}+\frac{a^{3/4} e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{a-c x^4}}",1,"(a^(3/4)*e*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(3/4)*Sqrt[a - c*x^4]) + (a^(3/4)*((Sqrt[c]*d)/Sqrt[a] - e)*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(3/4)*Sqrt[a - c*x^4])","A",6,6,20,0.3000,1,"{1201, 224, 221, 1200, 1199, 424}"
160,1,72,0,0.0409227,"\int \frac{1}{\left(d+e x^2\right) \sqrt{a-c x^4}} \, dx","Int[1/((d + e*x^2)*Sqrt[a - c*x^4]),x]","\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} d \sqrt{a-c x^4}}","\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} d \sqrt{a-c x^4}}",1,"(a^(1/4)*Sqrt[1 - (c*x^4)/a]*EllipticPi[-((Sqrt[a]*e)/(Sqrt[c]*d)), ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(1/4)*d*Sqrt[a - c*x^4])","A",2,2,22,0.09091,1,"{1219, 1218}"
161,1,299,0,0.3561339,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a-c x^4}} \, dx","Int[1/((d + e*x^2)^2*Sqrt[a - c*x^4]),x]","-\frac{a^{3/4} \sqrt[4]{c} e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 d \sqrt{a-c x^4} \left(c d^2-a e^2\right)}-\frac{e^2 x \sqrt{a-c x^4}}{2 d \left(d+e x^2\right) \left(c d^2-a e^2\right)}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(3 c d^2-a e^2\right) \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{c} d^2 \sqrt{a-c x^4} \left(c d^2-a e^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} \sqrt{1-\frac{c x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 d \sqrt{a-c x^4} \left(\sqrt{a} e+\sqrt{c} d\right)}","-\frac{a^{3/4} \sqrt[4]{c} e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 d \sqrt{a-c x^4} \left(c d^2-a e^2\right)}-\frac{e^2 x \sqrt{a-c x^4}}{2 d \left(d+e x^2\right) \left(c d^2-a e^2\right)}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(3 c d^2-a e^2\right) \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 \sqrt[4]{c} d^2 \sqrt{a-c x^4} \left(c d^2-a e^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} \sqrt{1-\frac{c x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{2 d \sqrt{a-c x^4} \left(\sqrt{a} e+\sqrt{c} d\right)}",1,"-(e^2*x*Sqrt[a - c*x^4])/(2*d*(c*d^2 - a*e^2)*(d + e*x^2)) - (a^(3/4)*c^(1/4)*e*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(2*d*(c*d^2 - a*e^2)*Sqrt[a - c*x^4]) - (a^(1/4)*c^(1/4)*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(2*d*(Sqrt[c]*d + Sqrt[a]*e)*Sqrt[a - c*x^4]) + (a^(1/4)*(3*c*d^2 - a*e^2)*Sqrt[1 - (c*x^4)/a]*EllipticPi[-((Sqrt[a]*e)/(Sqrt[c]*d)), ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(2*c^(1/4)*d^2*(c*d^2 - a*e^2)*Sqrt[a - c*x^4])","A",10,10,22,0.4545,1,"{1224, 1717, 1201, 224, 221, 1200, 1199, 424, 1219, 1218}"
162,1,425,0,0.7507015,"\int \frac{1}{\left(d+e x^2\right)^3 \sqrt{a-c x^4}} \, dx","Int[1/((d + e*x^2)^3*Sqrt[a - c*x^4]),x]","\frac{3 \sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(a^2 e^4-2 a c d^2 e^2+5 c^2 d^4\right) \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{c} d^3 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^2}-\frac{3 a^{3/4} \sqrt[4]{c} e \sqrt{1-\frac{c x^4}{a}} \left(3 c d^2-a e^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 d^2 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^2}-\frac{3 e^2 x \sqrt{a-c x^4} \left(3 c d^2-a e^2\right)}{8 d^2 \left(d+e x^2\right) \left(c d^2-a e^2\right)^2}-\frac{e^2 x \sqrt{a-c x^4}}{4 d \left(d+e x^2\right)^2 \left(c d^2-a e^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} \sqrt{1-\frac{c x^4}{a}} \left(-2 \sqrt{a} \sqrt{c} d e-3 a e^2+7 c d^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 d^2 \sqrt{a-c x^4} \left(\sqrt{a} e+\sqrt{c} d\right) \left(c d^2-a e^2\right)}","\frac{3 \sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(a^2 e^4-2 a c d^2 e^2+5 c^2 d^4\right) \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 \sqrt[4]{c} d^3 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^2}-\frac{3 a^{3/4} \sqrt[4]{c} e \sqrt{1-\frac{c x^4}{a}} \left(3 c d^2-a e^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 d^2 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^2}-\frac{3 e^2 x \sqrt{a-c x^4} \left(3 c d^2-a e^2\right)}{8 d^2 \left(d+e x^2\right) \left(c d^2-a e^2\right)^2}-\frac{e^2 x \sqrt{a-c x^4}}{4 d \left(d+e x^2\right)^2 \left(c d^2-a e^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} \sqrt{1-\frac{c x^4}{a}} \left(-2 \sqrt{a} \sqrt{c} d e-3 a e^2+7 c d^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{8 d^2 \sqrt{a-c x^4} \left(\sqrt{a} e+\sqrt{c} d\right) \left(c d^2-a e^2\right)}",1,"-(e^2*x*Sqrt[a - c*x^4])/(4*d*(c*d^2 - a*e^2)*(d + e*x^2)^2) - (3*e^2*(3*c*d^2 - a*e^2)*x*Sqrt[a - c*x^4])/(8*d^2*(c*d^2 - a*e^2)^2*(d + e*x^2)) - (3*a^(3/4)*c^(1/4)*e*(3*c*d^2 - a*e^2)*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(8*d^2*(c*d^2 - a*e^2)^2*Sqrt[a - c*x^4]) - (a^(1/4)*c^(1/4)*(7*c*d^2 - 2*Sqrt[a]*Sqrt[c]*d*e - 3*a*e^2)*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(8*d^2*(Sqrt[c]*d + Sqrt[a]*e)*(c*d^2 - a*e^2)*Sqrt[a - c*x^4]) + (3*a^(1/4)*(5*c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*Sqrt[1 - (c*x^4)/a]*EllipticPi[-((Sqrt[a]*e)/(Sqrt[c]*d)), ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(8*c^(1/4)*d^3*(c*d^2 - a*e^2)^2*Sqrt[a - c*x^4])","A",11,11,22,0.5000,1,"{1224, 1697, 1717, 1201, 224, 221, 1200, 1199, 424, 1219, 1218}"
163,1,563,0,1.2055127,"\int \frac{1}{\left(d+e x^2\right)^4 \sqrt{a-c x^4}} \, dx","Int[1/((d + e*x^2)^4*Sqrt[a - c*x^4]),x]","-\frac{e^2 x \sqrt{a-c x^4} \left(5 a^2 e^4-14 a c d^2 e^2+29 c^2 d^4\right)}{16 d^3 \left(d+e x^2\right) \left(c d^2-a e^2\right)^3}-\frac{\sqrt[4]{a} \sqrt[4]{c} \sqrt{1-\frac{c x^4}{a}} \left(10 a^{3/2} \sqrt{c} d e^3+15 a^2 e^4-30 \sqrt{a} c^{3/2} d^3 e-32 a c d^2 e^2+57 c^2 d^4\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{48 d^3 \sqrt{a-c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)^2 \left(\sqrt{a} e+\sqrt{c} d\right)^3}-\frac{a^{3/4} \sqrt[4]{c} e \sqrt{1-\frac{c x^4}{a}} \left(5 a^2 e^4-14 a c d^2 e^2+29 c^2 d^4\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{16 d^3 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^3}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(17 a^2 c d^2 e^4-5 a^3 e^6-7 a c^2 d^4 e^2+35 c^3 d^6\right) \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{16 \sqrt[4]{c} d^4 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^3}-\frac{5 e^2 x \sqrt{a-c x^4} \left(3 c d^2-a e^2\right)}{24 d^2 \left(d+e x^2\right)^2 \left(c d^2-a e^2\right)^2}-\frac{e^2 x \sqrt{a-c x^4}}{6 d \left(d+e x^2\right)^3 \left(c d^2-a e^2\right)}","-\frac{e^2 x \sqrt{a-c x^4} \left(5 a^2 e^4-14 a c d^2 e^2+29 c^2 d^4\right)}{16 d^3 \left(d+e x^2\right) \left(c d^2-a e^2\right)^3}-\frac{\sqrt[4]{a} \sqrt[4]{c} \sqrt{1-\frac{c x^4}{a}} \left(10 a^{3/2} \sqrt{c} d e^3+15 a^2 e^4-30 \sqrt{a} c^{3/2} d^3 e-32 a c d^2 e^2+57 c^2 d^4\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{48 d^3 \sqrt{a-c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)^2 \left(\sqrt{a} e+\sqrt{c} d\right)^3}-\frac{a^{3/4} \sqrt[4]{c} e \sqrt{1-\frac{c x^4}{a}} \left(5 a^2 e^4-14 a c d^2 e^2+29 c^2 d^4\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{16 d^3 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^3}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \left(17 a^2 c d^2 e^4-5 a^3 e^6-7 a c^2 d^4 e^2+35 c^3 d^6\right) \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{16 \sqrt[4]{c} d^4 \sqrt{a-c x^4} \left(c d^2-a e^2\right)^3}-\frac{5 e^2 x \sqrt{a-c x^4} \left(3 c d^2-a e^2\right)}{24 d^2 \left(d+e x^2\right)^2 \left(c d^2-a e^2\right)^2}-\frac{e^2 x \sqrt{a-c x^4}}{6 d \left(d+e x^2\right)^3 \left(c d^2-a e^2\right)}",1,"-(e^2*x*Sqrt[a - c*x^4])/(6*d*(c*d^2 - a*e^2)*(d + e*x^2)^3) - (5*e^2*(3*c*d^2 - a*e^2)*x*Sqrt[a - c*x^4])/(24*d^2*(c*d^2 - a*e^2)^2*(d + e*x^2)^2) - (e^2*(29*c^2*d^4 - 14*a*c*d^2*e^2 + 5*a^2*e^4)*x*Sqrt[a - c*x^4])/(16*d^3*(c*d^2 - a*e^2)^3*(d + e*x^2)) - (a^(3/4)*c^(1/4)*e*(29*c^2*d^4 - 14*a*c*d^2*e^2 + 5*a^2*e^4)*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(16*d^3*(c*d^2 - a*e^2)^3*Sqrt[a - c*x^4]) - (a^(1/4)*c^(1/4)*(57*c^2*d^4 - 30*Sqrt[a]*c^(3/2)*d^3*e - 32*a*c*d^2*e^2 + 10*a^(3/2)*Sqrt[c]*d*e^3 + 15*a^2*e^4)*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(48*d^3*(Sqrt[c]*d - Sqrt[a]*e)^2*(Sqrt[c]*d + Sqrt[a]*e)^3*Sqrt[a - c*x^4]) + (a^(1/4)*(35*c^3*d^6 - 7*a*c^2*d^4*e^2 + 17*a^2*c*d^2*e^4 - 5*a^3*e^6)*Sqrt[1 - (c*x^4)/a]*EllipticPi[-((Sqrt[a]*e)/(Sqrt[c]*d)), ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(16*c^(1/4)*d^4*(c*d^2 - a*e^2)^3*Sqrt[a - c*x^4])","A",12,11,22,0.5000,1,"{1224, 1697, 1717, 1201, 224, 221, 1200, 1199, 424, 1219, 1218}"
164,1,126,0,0.0828779,"\int \frac{d+e x^2}{\sqrt{-a+c x^4}} \, dx","Int[(d + e*x^2)/Sqrt[-a + c*x^4],x]","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} \left(\frac{\sqrt{c} d}{\sqrt{a}}-e\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{c x^4-a}}+\frac{a^{3/4} e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{c x^4-a}}","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} \left(\frac{\sqrt{c} d}{\sqrt{a}}-e\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{c x^4-a}}+\frac{a^{3/4} e \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{c^{3/4} \sqrt{c x^4-a}}",1,"(a^(3/4)*e*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(3/4)*Sqrt[-a + c*x^4]) + (a^(3/4)*((Sqrt[c]*d)/Sqrt[a] - e)*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(3/4)*Sqrt[-a + c*x^4])","A",6,6,21,0.2857,1,"{1201, 224, 221, 1200, 1199, 424}"
165,1,73,0,0.041897,"\int \frac{1}{\left(d+e x^2\right) \sqrt{-a+c x^4}} \, dx","Int[1/((d + e*x^2)*Sqrt[-a + c*x^4]),x]","\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} d \sqrt{c x^4-a}}","\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} \Pi \left(-\frac{\sqrt{a} e}{\sqrt{c} d};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} d \sqrt{c x^4-a}}",1,"(a^(1/4)*Sqrt[1 - (c*x^4)/a]*EllipticPi[-((Sqrt[a]*e)/(Sqrt[c]*d)), ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(1/4)*d*Sqrt[-a + c*x^4])","A",2,2,23,0.08696,1,"{1219, 1218}"
166,1,54,0,0.0492816,"\int \frac{\sqrt{a}+\sqrt{c} x^2}{\sqrt{-a+c x^4}} \, dx","Int[(Sqrt[a] + Sqrt[c]*x^2)/Sqrt[-a + c*x^4],x]","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} \sqrt{c x^4-a}}","\frac{a^{3/4} \sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} \sqrt{c x^4-a}}",1,"(a^(3/4)*Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(1/4)*Sqrt[-a + c*x^4])","A",3,3,29,0.1034,1,"{1200, 1199, 424}"
167,1,52,0,0.0463449,"\int \frac{1+\sqrt{\frac{c}{a}} x^2}{\sqrt{-a+c x^4}} \, dx","Int[(1 + Sqrt[c/a]*x^2)/Sqrt[-a + c*x^4],x]","\frac{\sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{c}{a}} x\right)\right|-1\right)}{\sqrt[4]{\frac{c}{a}} \sqrt{c x^4-a}}","\frac{\sqrt{1-\frac{c x^4}{a}} E\left(\left.\sin ^{-1}\left(\sqrt[4]{\frac{c}{a}} x\right)\right|-1\right)}{\sqrt[4]{\frac{c}{a}} \sqrt{c x^4-a}}",1,"(Sqrt[1 - (c*x^4)/a]*EllipticE[ArcSin[(c/a)^(1/4)*x], -1])/((c/a)^(1/4)*Sqrt[-a + c*x^4])","A",3,3,29,0.1034,1,"{1200, 1199, 424}"
168,1,236,0,0.0692306,"\int \frac{d+e x^2}{\sqrt{-a-c x^4}} \, dx","Int[(d + e*x^2)/Sqrt[-a - 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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) 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} e \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{e 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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) 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} e \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{e x \sqrt{-a-c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"-((e*x*Sqrt[-a - c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2))) - (a^(1/4)*e*(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[c]*d)/Sqrt[a] + e)*(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",3,3,22,0.1364,1,"{1198, 220, 1196}"
169,1,347,0,0.2950351,"\int \frac{1}{\left(d+e x^2\right) \sqrt{-a-c x^4}} \, dx","Int[1/((d + e*x^2)*Sqrt[-a - c*x^4]),x]","-\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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{c} d \sqrt{-a-c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{-a e^2-c d^2}}{\sqrt{d} \sqrt{e} \sqrt{-a-c x^4}}\right)}{2 \sqrt{d} \sqrt{-a e^2-c d^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{c} d-\sqrt{a} e\right)}","-\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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{c} d \sqrt{-a-c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{-a e^2-c d^2}}{\sqrt{d} \sqrt{e} \sqrt{-a-c x^4}}\right)}{2 \sqrt{d} \sqrt{-a e^2-c d^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{c} d-\sqrt{a} e\right)}",1,"(Sqrt[e]*ArcTan[(Sqrt[-(c*d^2) - a*e^2]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[-a - c*x^4])])/(2*Sqrt[d]*Sqrt[-(c*d^2) - a*e^2]) + (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 - Sqrt[a]*e)*Sqrt[-a - c*x^4]) - (a^(3/4)*((Sqrt[c]*d)/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 - Sqrt[a]*e)^2/(4*Sqrt[a]*Sqrt[c]*d*e), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*c^(1/4)*d*(c*d^2 - a*e^2)*Sqrt[-a - c*x^4])","A",3,3,24,0.1250,1,"{1217, 220, 1707}"
170,1,40,0,0.0630028,"\int \frac{1}{\left(a+b x^2\right) \sqrt{4-5 x^4}} \, dx","Int[1/((a + b*x^2)*Sqrt[4 - 5*x^4]),x]","\frac{\Pi \left(-\frac{2 b}{\sqrt{5} a};\left.\sin ^{-1}\left(\frac{\sqrt[4]{5} x}{\sqrt{2}}\right)\right|-1\right)}{\sqrt{2} \sqrt[4]{5} a}","\frac{\Pi \left(-\frac{2 b}{\sqrt{5} a};\left.\sin ^{-1}\left(\frac{\sqrt[4]{5} x}{\sqrt{2}}\right)\right|-1\right)}{\sqrt{2} \sqrt[4]{5} a}",1,"EllipticPi[(-2*b)/(Sqrt[5]*a), ArcSin[(5^(1/4)*x)/Sqrt[2]], -1]/(Sqrt[2]*5^(1/4)*a)","A",2,2,21,0.09524,1,"{1213, 537}"
171,1,310,0,0.272687,"\int \frac{1}{\left(a+b x^2\right) \sqrt{4+5 x^4}} \, dx","Int[1/((a + b*x^2)*Sqrt[4 + 5*x^4]),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{x \sqrt{5 a^2+4 b^2}}{\sqrt{a} \sqrt{b} \sqrt{5 x^4+4}}\right)}{2 \sqrt{a} \sqrt{5 a^2+4 b^2}}+\frac{\sqrt[4]{5} \left(\sqrt{5} x^2+2\right) \sqrt{\frac{5 x^4+4}{\left(\sqrt{5} x^2+2\right)^2}} \left(\sqrt{5} a+2 b\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{5} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{5 x^4+4} \left(5 a^2-4 b^2\right)}-\frac{\left(\sqrt{5} x^2+2\right) \sqrt{\frac{5 x^4+4}{\left(\sqrt{5} x^2+2\right)^2}} \left(\sqrt{5} a+2 b\right)^2 \Pi \left(-\frac{\left(\sqrt{5} a-2 b\right)^2}{8 \sqrt{5} a b};2 \tan ^{-1}\left(\frac{\sqrt[4]{5} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{5} a \sqrt{5 x^4+4} \left(5 a^2-4 b^2\right)}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{x \sqrt{5 a^2+4 b^2}}{\sqrt{a} \sqrt{b} \sqrt{5 x^4+4}}\right)}{2 \sqrt{a} \sqrt{5 a^2+4 b^2}}+\frac{\sqrt[4]{5} \left(\sqrt{5} x^2+2\right) \sqrt{\frac{5 x^4+4}{\left(\sqrt{5} x^2+2\right)^2}} \left(\sqrt{5} a+2 b\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{5} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{5 x^4+4} \left(5 a^2-4 b^2\right)}-\frac{\left(\sqrt{5} x^2+2\right) \sqrt{\frac{5 x^4+4}{\left(\sqrt{5} x^2+2\right)^2}} \left(\sqrt{5} a+2 b\right)^2 \Pi \left(-\frac{\left(\sqrt{5} a-2 b\right)^2}{8 \sqrt{5} a b};2 \tan ^{-1}\left(\frac{\sqrt[4]{5} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt[4]{5} a \sqrt{5 x^4+4} \left(5 a^2-4 b^2\right)}",1,"(Sqrt[b]*ArcTan[(Sqrt[5*a^2 + 4*b^2]*x)/(Sqrt[a]*Sqrt[b]*Sqrt[4 + 5*x^4])])/(2*Sqrt[a]*Sqrt[5*a^2 + 4*b^2]) + (5^(1/4)*(Sqrt[5]*a + 2*b)*(2 + Sqrt[5]*x^2)*Sqrt[(4 + 5*x^4)/(2 + Sqrt[5]*x^2)^2]*EllipticF[2*ArcTan[(5^(1/4)*x)/Sqrt[2]], 1/2])/(2*Sqrt[2]*(5*a^2 - 4*b^2)*Sqrt[4 + 5*x^4]) - ((Sqrt[5]*a + 2*b)^2*(2 + Sqrt[5]*x^2)*Sqrt[(4 + 5*x^4)/(2 + Sqrt[5]*x^2)^2]*EllipticPi[-(Sqrt[5]*a - 2*b)^2/(8*Sqrt[5]*a*b), 2*ArcTan[(5^(1/4)*x)/Sqrt[2]], 1/2])/(4*Sqrt[2]*5^(1/4)*a*(5*a^2 - 4*b^2)*Sqrt[4 + 5*x^4])","A",3,3,21,0.1429,1,"{1217, 220, 1707}"
172,1,40,0,0.0179991,"\int \frac{1}{\left(a+b x^2\right) \sqrt{4-d x^4}} \, dx","Int[1/((a + b*x^2)*Sqrt[4 - d*x^4]),x]","\frac{\Pi \left(-\frac{2 b}{a \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{2}}\right)\right|-1\right)}{\sqrt{2} a \sqrt[4]{d}}","\frac{\Pi \left(-\frac{2 b}{a \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{2}}\right)\right|-1\right)}{\sqrt{2} a \sqrt[4]{d}}",1,"EllipticPi[(-2*b)/(a*Sqrt[d]), ArcSin[(d^(1/4)*x)/Sqrt[2]], -1]/(Sqrt[2]*a*d^(1/4))","A",1,1,22,0.04545,1,"{1218}"
173,1,300,0,0.2232487,"\int \frac{1}{\left(a+b x^2\right) \sqrt{4+d x^4}} \, dx","Int[1/((a + b*x^2)*Sqrt[4 + d*x^4]),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{x \sqrt{a^2 d+4 b^2}}{\sqrt{a} \sqrt{b} \sqrt{d x^4+4}}\right)}{2 \sqrt{a} \sqrt{a^2 d+4 b^2}}-\frac{\sqrt[4]{d} \left(\sqrt{d} x^2+2\right) \sqrt{\frac{d x^4+4}{\left(\sqrt{d} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{d x^4+4} \left(2 b-a \sqrt{d}\right)}+\frac{\left(\sqrt{d} x^2+2\right) \sqrt{\frac{d x^4+4}{\left(\sqrt{d} x^2+2\right)^2}} \left(a \sqrt{d}+2 b\right) \Pi \left(-\frac{\left(2 b-a \sqrt{d}\right)^2}{8 a b \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} a \sqrt[4]{d} \sqrt{d x^4+4} \left(2 b-a \sqrt{d}\right)}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{x \sqrt{a^2 d+4 b^2}}{\sqrt{a} \sqrt{b} \sqrt{d x^4+4}}\right)}{2 \sqrt{a} \sqrt{a^2 d+4 b^2}}-\frac{\sqrt[4]{d} \left(\sqrt{d} x^2+2\right) \sqrt{\frac{d x^4+4}{\left(\sqrt{d} x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{d x^4+4} \left(2 b-a \sqrt{d}\right)}+\frac{\left(\sqrt{d} x^2+2\right) \sqrt{\frac{d x^4+4}{\left(\sqrt{d} x^2+2\right)^2}} \left(a \sqrt{d}+2 b\right) \Pi \left(-\frac{\left(2 b-a \sqrt{d}\right)^2}{8 a b \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt{2}}\right)|\frac{1}{2}\right)}{4 \sqrt{2} a \sqrt[4]{d} \sqrt{d x^4+4} \left(2 b-a \sqrt{d}\right)}",1,"(Sqrt[b]*ArcTan[(Sqrt[4*b^2 + a^2*d]*x)/(Sqrt[a]*Sqrt[b]*Sqrt[4 + d*x^4])])/(2*Sqrt[a]*Sqrt[4*b^2 + a^2*d]) - (d^(1/4)*(2 + Sqrt[d]*x^2)*Sqrt[(4 + d*x^4)/(2 + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/Sqrt[2]], 1/2])/(2*Sqrt[2]*(2*b - a*Sqrt[d])*Sqrt[4 + d*x^4]) + ((2*b + a*Sqrt[d])*(2 + Sqrt[d]*x^2)*Sqrt[(4 + d*x^4)/(2 + Sqrt[d]*x^2)^2]*EllipticPi[-(2*b - a*Sqrt[d])^2/(8*a*b*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/Sqrt[2]], 1/2])/(4*Sqrt[2]*a*(2*b - a*Sqrt[d])*d^(1/4)*Sqrt[4 + d*x^4])","A",3,3,21,0.1429,1,"{1217, 220, 1707}"
174,0,0,0,0.0094724,"\int \frac{\sqrt{a+b x^2}}{\sqrt{1-x^4}} \, dx","Int[Sqrt[a + b*x^2]/Sqrt[1 - x^4],x]","\int \frac{\sqrt{a+b x^2}}{\sqrt{1-x^4}} \, dx","\frac{a \sqrt{1-x^2} \sqrt{\frac{a \left(x^2+1\right)}{a+b x^2}} \Pi \left(\frac{b}{a+b};\sin ^{-1}\left(\frac{\sqrt{a+b} x}{\sqrt{b x^2+a}}\right)|-\frac{a-b}{a+b}\right)}{\sqrt{x^2+1} \sqrt{a+b} \sqrt{\frac{a \left(1-x^2\right)}{a+b x^2}}}",1,"Defer[Int][Sqrt[a + b*x^2]/Sqrt[1 - x^4], x]","F",0,0,0,0,-1,"{}"
175,0,0,0,0.0080599,"\int \left(c+e x^2\right)^q \left(a+b x^4\right)^p \, dx","Int[(c + e*x^2)^q*(a + b*x^4)^p,x]","\int \left(c+e x^2\right)^q \left(a+b x^4\right)^p \, dx","\text{Int}\left(\left(a+b x^4\right)^p \left(c+e x^2\right)^q,x\right)",0,"Defer[Int][(c + e*x^2)^q*(a + b*x^4)^p, x]","A",0,0,0,0,-1,"{}"
176,1,196,0,0.2300331,"\int \left(c+e x^2\right)^3 \left(a+b x^4\right)^p \, dx","Int[(c + e*x^2)^3*(a + b*x^4)^p,x]","e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \left(c^2-\frac{a e^2}{4 b p+7 b}\right) \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^4}{a}\right)+c^3 x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)+\frac{3}{5} c e^2 x^5 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{4},-p;\frac{9}{4};-\frac{b x^4}{a}\right)+\frac{e^3 x^3 \left(a+b x^4\right)^{p+1}}{b (4 p+7)}","-\frac{e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \left(a e^2-b c^2 (4 p+7)\right) \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^4}{a}\right)}{b (4 p+7)}+c^3 x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)+\frac{3}{5} c e^2 x^5 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{4},-p;\frac{9}{4};-\frac{b x^4}{a}\right)+\frac{e^3 x^3 \left(a+b x^4\right)^{p+1}}{b (4 p+7)}",1,"(e^3*x^3*(a + b*x^4)^(1 + p))/(b*(7 + 4*p)) + (c^3*x*(a + b*x^4)^p*Hypergeometric2F1[1/4, -p, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^p + (e*(c^2 - (a*e^2)/(7*b + 4*b*p))*x^3*(a + b*x^4)^p*Hypergeometric2F1[3/4, -p, 7/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^p + (3*c*e^2*x^5*(a + b*x^4)^p*Hypergeometric2F1[5/4, -p, 9/4, -((b*x^4)/a)])/(5*(1 + (b*x^4)/a)^p)","A",9,6,19,0.3158,1,"{1207, 1893, 246, 245, 365, 364}"
177,1,142,0,0.1316566,"\int \left(c+e x^2\right)^2 \left(a+b x^4\right)^p \, dx","Int[(c + e*x^2)^2*(a + b*x^4)^p,x]","x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \left(c^2-\frac{a e^2}{4 b p+5 b}\right) \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)+\frac{2}{3} c e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^4}{a}\right)+\frac{e^2 x \left(a+b x^4\right)^{p+1}}{b (4 p+5)}","-\frac{x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \left(a e^2-b c^2 (4 p+5)\right) \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)}{b (4 p+5)}+\frac{2}{3} c e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^4}{a}\right)+\frac{e^2 x \left(a+b x^4\right)^{p+1}}{b (4 p+5)}",1,"(e^2*x*(a + b*x^4)^(1 + p))/(b*(5 + 4*p)) + ((c^2 - (a*e^2)/(5*b + 4*b*p))*x*(a + b*x^4)^p*Hypergeometric2F1[1/4, -p, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^p + (2*c*e*x^3*(a + b*x^4)^p*Hypergeometric2F1[3/4, -p, 7/4, -((b*x^4)/a)])/(3*(1 + (b*x^4)/a)^p)","A",7,6,19,0.3158,1,"{1207, 1204, 246, 245, 365, 364}"
178,1,96,0,0.0507824,"\int \left(c+e x^2\right) \left(a+b x^4\right)^p \, dx","Int[(c + e*x^2)*(a + b*x^4)^p,x]","c x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)+\frac{1}{3} e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^4}{a}\right)","c x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)+\frac{1}{3} e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-\frac{b x^4}{a}\right)",1,"(c*x*(a + b*x^4)^p*Hypergeometric2F1[1/4, -p, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^p + (e*x^3*(a + b*x^4)^p*Hypergeometric2F1[3/4, -p, 7/4, -((b*x^4)/a)])/(3*(1 + (b*x^4)/a)^p)","A",6,5,17,0.2941,1,"{1204, 246, 245, 365, 364}"
179,1,44,0,0.0097065,"\int \left(a+b x^4\right)^p \, dx","Int[(a + b*x^4)^p,x]","x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)","x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-\frac{b x^4}{a}\right)",1,"(x*(a + b*x^4)^p*Hypergeometric2F1[1/4, -p, 5/4, -((b*x^4)/a)])/(1 + (b*x^4)/a)^p","A",2,2,9,0.2222,1,"{246, 245}"
180,1,123,0,0.1265694,"\int \frac{\left(a+b x^4\right)^p}{c+e x^2} \, dx","Int[(a + b*x^4)^p/(c + e*x^2),x]","\frac{x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{1}{4};-p,1;\frac{5}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{c}-\frac{e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{3}{4};-p,1;\frac{7}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{3 c^2}","\frac{x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{1}{4};-p,1;\frac{5}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{c}-\frac{e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{3}{4};-p,1;\frac{7}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{3 c^2}",1,"(x*(a + b*x^4)^p*AppellF1[1/4, -p, 1, 5/4, -((b*x^4)/a), (e^2*x^4)/c^2])/(c*(1 + (b*x^4)/a)^p) - (e*x^3*(a + b*x^4)^p*AppellF1[3/4, -p, 1, 7/4, -((b*x^4)/a), (e^2*x^4)/c^2])/(3*c^2*(1 + (b*x^4)/a)^p)","A",6,5,19,0.2632,1,"{1240, 430, 429, 511, 510}"
181,1,189,0,0.1940555,"\int \frac{\left(a+b x^4\right)^p}{\left(c+e x^2\right)^2} \, dx","Int[(a + b*x^4)^p/(c + e*x^2)^2,x]","\frac{x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{1}{4};-p,2;\frac{5}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{c^2}-\frac{2 e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{3}{4};-p,2;\frac{7}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{3 c^3}+\frac{e^2 x^5 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{5}{4};-p,2;\frac{9}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{5 c^4}","\frac{x \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{1}{4};-p,2;\frac{5}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{c^2}-\frac{2 e x^3 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{3}{4};-p,2;\frac{7}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{3 c^3}+\frac{e^2 x^5 \left(a+b x^4\right)^p \left(\frac{b x^4}{a}+1\right)^{-p} F_1\left(\frac{5}{4};-p,2;\frac{9}{4};-\frac{b x^4}{a},\frac{e^2 x^4}{c^2}\right)}{5 c^4}",1,"(x*(a + b*x^4)^p*AppellF1[1/4, -p, 2, 5/4, -((b*x^4)/a), (e^2*x^4)/c^2])/(c^2*(1 + (b*x^4)/a)^p) - (2*e*x^3*(a + b*x^4)^p*AppellF1[3/4, -p, 2, 7/4, -((b*x^4)/a), (e^2*x^4)/c^2])/(3*c^3*(1 + (b*x^4)/a)^p) + (e^2*x^5*(a + b*x^4)^p*AppellF1[5/4, -p, 2, 9/4, -((b*x^4)/a), (e^2*x^4)/c^2])/(5*c^4*(1 + (b*x^4)/a)^p)","A",8,5,19,0.2632,1,"{1240, 430, 429, 511, 510}"
182,1,103,0,0.1146103,"\int \left(1-x^2\right)^3 \left(1+b x^4\right)^p \, dx","Int[(1 - x^2)^3*(1 + b*x^4)^p,x]","x \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)-x^3 \left(1-\frac{1}{4 b p+7 b}\right) \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-b x^4\right)+\frac{3}{5} x^5 \, _2F_1\left(\frac{5}{4},-p;\frac{9}{4};-b x^4\right)-\frac{x^3 \left(b x^4+1\right)^{p+1}}{b (4 p+7)}","x \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)+\frac{x^3 (1-b (4 p+7)) \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-b x^4\right)}{b (4 p+7)}+\frac{3}{5} x^5 \, _2F_1\left(\frac{5}{4},-p;\frac{9}{4};-b x^4\right)-\frac{x^3 \left(b x^4+1\right)^{p+1}}{b (4 p+7)}",1,"-((x^3*(1 + b*x^4)^(1 + p))/(b*(7 + 4*p))) + x*Hypergeometric2F1[1/4, -p, 5/4, -(b*x^4)] - (1 - (7*b + 4*b*p)^(-1))*x^3*Hypergeometric2F1[3/4, -p, 7/4, -(b*x^4)] + (3*x^5*Hypergeometric2F1[5/4, -p, 9/4, -(b*x^4)])/5","A",6,4,19,0.2105,1,"{1207, 1893, 245, 364}"
183,1,79,0,0.0683756,"\int \left(1-x^2\right)^2 \left(1+b x^4\right)^p \, dx","Int[(1 - x^2)^2*(1 + b*x^4)^p,x]","x \left(1-\frac{1}{4 b p+5 b}\right) \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)-\frac{2}{3} x^3 \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-b x^4\right)+\frac{x \left(b x^4+1\right)^{p+1}}{b (4 p+5)}","-\frac{x (1-b (4 p+5)) \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)}{b (4 p+5)}-\frac{2}{3} x^3 \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-b x^4\right)+\frac{x \left(b x^4+1\right)^{p+1}}{b (4 p+5)}",1,"(x*(1 + b*x^4)^(1 + p))/(b*(5 + 4*p)) + (1 - (5*b + 4*b*p)^(-1))*x*Hypergeometric2F1[1/4, -p, 5/4, -(b*x^4)] - (2*x^3*Hypergeometric2F1[3/4, -p, 7/4, -(b*x^4)])/3","A",5,4,19,0.2105,1,"{1207, 1204, 245, 364}"
184,1,42,0,0.0205814,"\int \left(1-x^2\right) \left(1+b x^4\right)^p \, dx","Int[(1 - x^2)*(1 + b*x^4)^p,x]","x \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)-\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-b x^4\right)","x \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)-\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{4},-p;\frac{7}{4};-b x^4\right)",1,"x*Hypergeometric2F1[1/4, -p, 5/4, -(b*x^4)] - (x^3*Hypergeometric2F1[3/4, -p, 7/4, -(b*x^4)])/3","A",4,3,17,0.1765,1,"{1204, 245, 364}"
185,1,18,0,0.0042675,"\int \left(1+b x^4\right)^p \, dx","Int[(1 + b*x^4)^p,x]","x \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)","x \, _2F_1\left(\frac{1}{4},-p;\frac{5}{4};-b x^4\right)",1,"x*Hypergeometric2F1[1/4, -p, 5/4, -(b*x^4)]","A",1,1,9,0.1111,1,"{245}"
186,1,50,0,0.0539169,"\int \frac{\left(1+b x^4\right)^p}{1-x^2} \, dx","Int[(1 + b*x^4)^p/(1 - x^2),x]","\frac{1}{3} x^3 F_1\left(\frac{3}{4};1,-p;\frac{7}{4};x^4,-b x^4\right)+x F_1\left(\frac{1}{4};1,-p;\frac{5}{4};x^4,-b x^4\right)","\frac{1}{3} x^3 F_1\left(\frac{3}{4};1,-p;\frac{7}{4};x^4,-b x^4\right)+x F_1\left(\frac{1}{4};1,-p;\frac{5}{4};x^4,-b x^4\right)",1,"x*AppellF1[1/4, 1, -p, 5/4, x^4, -(b*x^4)] + (x^3*AppellF1[3/4, 1, -p, 7/4, x^4, -(b*x^4)])/3","A",4,3,19,0.1579,1,"{1240, 429, 510}"
187,1,77,0,0.0817376,"\int \frac{\left(1+b x^4\right)^p}{\left(1-x^2\right)^2} \, dx","Int[(1 + b*x^4)^p/(1 - x^2)^2,x]","\frac{1}{5} x^5 F_1\left(\frac{5}{4};2,-p;\frac{9}{4};x^4,-b x^4\right)+\frac{2}{3} x^3 F_1\left(\frac{3}{4};2,-p;\frac{7}{4};x^4,-b x^4\right)+x F_1\left(\frac{1}{4};2,-p;\frac{5}{4};x^4,-b x^4\right)","\frac{1}{5} x^5 F_1\left(\frac{5}{4};2,-p;\frac{9}{4};x^4,-b x^4\right)+\frac{2}{3} x^3 F_1\left(\frac{3}{4};2,-p;\frac{7}{4};x^4,-b x^4\right)+x F_1\left(\frac{1}{4};2,-p;\frac{5}{4};x^4,-b x^4\right)",1,"x*AppellF1[1/4, 2, -p, 5/4, x^4, -(b*x^4)] + (2*x^3*AppellF1[3/4, 2, -p, 7/4, x^4, -(b*x^4)])/3 + (x^5*AppellF1[5/4, 2, -p, 9/4, x^4, -(b*x^4)])/5","A",5,3,19,0.1579,1,"{1240, 429, 510}"
188,1,101,0,0.1140118,"\int \frac{\left(1+b x^4\right)^p}{\left(1-x^2\right)^3} \, dx","Int[(1 + b*x^4)^p/(1 - x^2)^3,x]","\frac{1}{7} x^7 F_1\left(\frac{7}{4};3,-p;\frac{11}{4};x^4,-b x^4\right)+\frac{3}{5} x^5 F_1\left(\frac{5}{4};3,-p;\frac{9}{4};x^4,-b x^4\right)+x^3 F_1\left(\frac{3}{4};3,-p;\frac{7}{4};x^4,-b x^4\right)+x F_1\left(\frac{1}{4};3,-p;\frac{5}{4};x^4,-b x^4\right)","\frac{1}{7} x^7 F_1\left(\frac{7}{4};3,-p;\frac{11}{4};x^4,-b x^4\right)+\frac{3}{5} x^5 F_1\left(\frac{5}{4};3,-p;\frac{9}{4};x^4,-b x^4\right)+x^3 F_1\left(\frac{3}{4};3,-p;\frac{7}{4};x^4,-b x^4\right)+x F_1\left(\frac{1}{4};3,-p;\frac{5}{4};x^4,-b x^4\right)",1,"x*AppellF1[1/4, 3, -p, 5/4, x^4, -(b*x^4)] + x^3*AppellF1[3/4, 3, -p, 7/4, x^4, -(b*x^4)] + (3*x^5*AppellF1[5/4, 3, -p, 9/4, x^4, -(b*x^4)])/5 + (x^7*AppellF1[7/4, 3, -p, 11/4, x^4, -(b*x^4)])/7","A",6,3,19,0.1579,1,"{1240, 429, 510}"
189,1,51,0,0.0410136,"\int \frac{\left(d+e x^2\right)^4}{d^2-e^2 x^4} \, dx","Int[(d + e*x^2)^4/(d^2 - e^2*x^4),x]","\frac{8 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-7 d^2 x-\frac{4}{3} d e x^3-\frac{1}{5} e^2 x^5","\frac{8 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-7 d^2 x-\frac{4}{3} d e x^3-\frac{1}{5} e^2 x^5",1,"-7*d^2*x - (4*d*e*x^3)/3 - (e^2*x^5)/5 + (8*d^(5/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e]","A",4,3,24,0.1250,1,"{1150, 390, 208}"
190,1,38,0,0.0337036,"\int \frac{\left(d+e x^2\right)^3}{d^2-e^2 x^4} \, dx","Int[(d + e*x^2)^3/(d^2 - e^2*x^4),x]","\frac{4 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-3 d x-\frac{e x^3}{3}","\frac{4 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-3 d x-\frac{e x^3}{3}",1,"-3*d*x - (e*x^3)/3 + (4*d^(3/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e]","A",4,3,24,0.1250,1,"{1150, 390, 208}"
191,1,29,0,0.023093,"\int \frac{\left(d+e x^2\right)^2}{d^2-e^2 x^4} \, dx","Int[(d + e*x^2)^2/(d^2 - e^2*x^4),x]","\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-x","\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-x",1,"-x + (2*Sqrt[d]*ArcTanh[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e]","A",3,3,24,0.1250,1,"{1150, 388, 208}"
192,1,24,0,0.0122413,"\int \frac{d+e x^2}{d^2-e^2 x^4} \, dx","Int[(d + e*x^2)/(d^2 - e^2*x^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{e}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{e}}",1,"ArcTanh[(Sqrt[e]*x)/Sqrt[d]]/(Sqrt[d]*Sqrt[e])","A",2,2,22,0.09091,1,"{1150, 208}"
193,1,72,0,0.0565035,"\int \frac{1}{\left(d+e x^2\right) \left(d^2-e^2 x^4\right)} \, dx","Int[1/((d + e*x^2)*(d^2 - e^2*x^4)),x]","\frac{x}{4 d^2 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2} \sqrt{e}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2} \sqrt{e}}","\frac{x}{4 d^2 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{5/2} \sqrt{e}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{4 d^{5/2} \sqrt{e}}",1,"x/(4*d^2*(d + e*x^2)) + ArcTan[(Sqrt[e]*x)/Sqrt[d]]/(2*d^(5/2)*Sqrt[e]) + ArcTanh[(Sqrt[e]*x)/Sqrt[d]]/(4*d^(5/2)*Sqrt[e])","A",5,5,24,0.2083,1,"{1150, 414, 522, 208, 205}"
194,1,89,0,0.0827575,"\int \frac{1}{\left(d+e x^2\right)^2 \left(d^2-e^2 x^4\right)} \, dx","Int[1/((d + e*x^2)^2*(d^2 - e^2*x^4)),x]","\frac{5 x}{16 d^3 \left(d+e x^2\right)}+\frac{x}{8 d^2 \left(d+e x^2\right)^2}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2} \sqrt{e}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{7/2} \sqrt{e}}","\frac{5 x}{16 d^3 \left(d+e x^2\right)}+\frac{x}{8 d^2 \left(d+e x^2\right)^2}+\frac{7 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{16 d^{7/2} \sqrt{e}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{7/2} \sqrt{e}}",1,"x/(8*d^2*(d + e*x^2)^2) + (5*x)/(16*d^3*(d + e*x^2)) + (7*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(16*d^(7/2)*Sqrt[e]) + ArcTanh[(Sqrt[e]*x)/Sqrt[d]]/(8*d^(7/2)*Sqrt[e])","A",6,6,24,0.2500,1,"{1150, 414, 527, 522, 208, 205}"
195,1,62,0,0.0442698,"\int \frac{\left(d+e x^2\right)^{3/2}}{d^2-e^2 x^4} \, dx","Int[(d + e*x^2)^(3/2)/(d^2 - e^2*x^4),x]","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{e}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{e}}","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{e}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{e}}",1,"-(ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/Sqrt[e]) + (Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[e]*x)/Sqrt[d + e*x^2]])/Sqrt[e]","A",6,6,26,0.2308,1,"{1150, 402, 217, 206, 377, 208}"
196,1,38,0,0.0256809,"\int \frac{\sqrt{d+e x^2}}{d^2-e^2 x^4} \, dx","Int[Sqrt[d + e*x^2]/(d^2 - e^2*x^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{2} d \sqrt{e}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{2} d \sqrt{e}}",1,"ArcTanh[(Sqrt[2]*Sqrt[e]*x)/Sqrt[d + e*x^2]]/(Sqrt[2]*d*Sqrt[e])","A",3,3,26,0.1154,1,"{1150, 377, 208}"
197,1,61,0,0.0390935,"\int \frac{1}{\sqrt{d+e x^2} \left(d^2-e^2 x^4\right)} \, dx","Int[1/(Sqrt[d + e*x^2]*(d^2 - e^2*x^4)),x]","\frac{x}{2 d^2 \sqrt{d+e x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 \sqrt{2} d^2 \sqrt{e}}","\frac{x}{2 d^2 \sqrt{d+e x^2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 \sqrt{2} d^2 \sqrt{e}}",1,"x/(2*d^2*Sqrt[d + e*x^2]) + ArcTanh[(Sqrt[2]*Sqrt[e]*x)/Sqrt[d + e*x^2]]/(2*Sqrt[2]*d^2*Sqrt[e])","A",4,4,26,0.1538,1,"{1150, 382, 377, 208}"
198,1,80,0,0.0688886,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(d^2-e^2 x^4\right)} \, dx","Int[1/((d + e*x^2)^(3/2)*(d^2 - e^2*x^4)),x]","\frac{7 x}{12 d^3 \sqrt{d+e x^2}}+\frac{x}{6 d^2 \left(d+e x^2\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 \sqrt{2} d^3 \sqrt{e}}","\frac{7 x}{12 d^3 \sqrt{d+e x^2}}+\frac{x}{6 d^2 \left(d+e x^2\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 \sqrt{2} d^3 \sqrt{e}}",1,"x/(6*d^2*(d + e*x^2)^(3/2)) + (7*x)/(12*d^3*Sqrt[d + e*x^2]) + ArcTanh[(Sqrt[2]*Sqrt[e]*x)/Sqrt[d + e*x^2]]/(4*Sqrt[2]*d^3*Sqrt[e])","A",6,6,26,0.2308,1,"{1150, 414, 527, 12, 377, 208}"
199,1,153,0,0.0547431,"\int \frac{\left(a+b x^2\right)^{5/2}}{\sqrt{a^2-b^2 x^4}} \, dx","Int[(a + b*x^2)^(5/2)/Sqrt[a^2 - b^2*x^4],x]","-\frac{9 a x \left(a-b x^2\right) \sqrt{a+b x^2}}{8 \sqrt{a^2-b^2 x^4}}-\frac{x \left(a-b x^2\right) \left(a+b x^2\right)^{3/2}}{4 \sqrt{a^2-b^2 x^4}}+\frac{19 a^2 \sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{8 \sqrt{b} \sqrt{a^2-b^2 x^4}}","-\frac{9 a x \left(a-b x^2\right) \sqrt{a+b x^2}}{8 \sqrt{a^2-b^2 x^4}}-\frac{x \left(a-b x^2\right) \left(a+b x^2\right)^{3/2}}{4 \sqrt{a^2-b^2 x^4}}+\frac{19 a^2 \sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{8 \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(-9*a*x*(a - b*x^2)*Sqrt[a + b*x^2])/(8*Sqrt[a^2 - b^2*x^4]) - (x*(a - b*x^2)*(a + b*x^2)^(3/2))/(4*Sqrt[a^2 - b^2*x^4]) + (19*a^2*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTan[(Sqrt[b]*x)/Sqrt[a - b*x^2]])/(8*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",5,5,28,0.1786,1,"{1152, 416, 388, 217, 203}"
200,1,110,0,0.0346587,"\int \frac{\left(a+b x^2\right)^{3/2}}{\sqrt{a^2-b^2 x^4}} \, dx","Int[(a + b*x^2)^(3/2)/Sqrt[a^2 - b^2*x^4],x]","\frac{3 a \sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{2 \sqrt{b} \sqrt{a^2-b^2 x^4}}-\frac{x \left(a-b x^2\right) \sqrt{a+b x^2}}{2 \sqrt{a^2-b^2 x^4}}","\frac{3 a \sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{2 \sqrt{b} \sqrt{a^2-b^2 x^4}}-\frac{x \left(a-b x^2\right) \sqrt{a+b x^2}}{2 \sqrt{a^2-b^2 x^4}}",1,"-(x*(a - b*x^2)*Sqrt[a + b*x^2])/(2*Sqrt[a^2 - b^2*x^4]) + (3*a*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTan[(Sqrt[b]*x)/Sqrt[a - b*x^2]])/(2*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",4,4,28,0.1429,1,"{1152, 388, 217, 203}"
201,1,65,0,0.0220998,"\int \frac{\sqrt{a+b x^2}}{\sqrt{a^2-b^2 x^4}} \, dx","Int[Sqrt[a + b*x^2]/Sqrt[a^2 - b^2*x^4],x]","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{\sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a-b x^2}}\right)}{\sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTan[(Sqrt[b]*x)/Sqrt[a - b*x^2]])/(Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",3,3,28,0.1071,1,"{1152, 217, 203}"
202,1,78,0,0.035809,"\int \frac{1}{\sqrt{a+b x^2} \sqrt{a^2-b^2 x^4}} \, dx","Int[1/(Sqrt[a + b*x^2]*Sqrt[a^2 - b^2*x^4]),x]","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a-b x^2}}\right)}{\sqrt{2} a \sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a-b x^2}}\right)}{\sqrt{2} a \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTan[(Sqrt[2]*Sqrt[b]*x)/Sqrt[a - b*x^2]])/(Sqrt[2]*a*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",3,3,28,0.1071,1,"{1152, 377, 205}"
203,1,125,0,0.0511505,"\int \frac{1}{\left(a+b x^2\right)^{3/2} \sqrt{a^2-b^2 x^4}} \, dx","Int[1/((a + b*x^2)^(3/2)*Sqrt[a^2 - b^2*x^4]),x]","\frac{x \left(a-b x^2\right)}{4 a^2 \sqrt{a+b x^2} \sqrt{a^2-b^2 x^4}}+\frac{3 \sqrt{a+b x^2} \sqrt{a-b x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a-b x^2}}\right)}{4 \sqrt{2} a^2 \sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{x \left(a-b x^2\right)}{4 a^2 \sqrt{a+b x^2} \sqrt{a^2-b^2 x^4}}+\frac{3 \sqrt{a+b x^2} \sqrt{a-b x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a-b x^2}}\right)}{4 \sqrt{2} a^2 \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(x*(a - b*x^2))/(4*a^2*Sqrt[a + b*x^2]*Sqrt[a^2 - b^2*x^4]) + (3*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTan[(Sqrt[2]*Sqrt[b]*x)/Sqrt[a - b*x^2]])/(4*Sqrt[2]*a^2*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",4,4,28,0.1429,1,"{1152, 382, 377, 205}"
204,1,168,0,0.0862913,"\int \frac{1}{\left(a+b x^2\right)^{5/2} \sqrt{a^2-b^2 x^4}} \, dx","Int[1/((a + b*x^2)^(5/2)*Sqrt[a^2 - b^2*x^4]),x]","\frac{9 x \left(a-b x^2\right)}{32 a^3 \sqrt{a+b x^2} \sqrt{a^2-b^2 x^4}}+\frac{x \left(a-b x^2\right)}{8 a^2 \left(a+b x^2\right)^{3/2} \sqrt{a^2-b^2 x^4}}+\frac{19 \sqrt{a+b x^2} \sqrt{a-b x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a-b x^2}}\right)}{32 \sqrt{2} a^3 \sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{9 x \left(a-b x^2\right)}{32 a^3 \sqrt{a+b x^2} \sqrt{a^2-b^2 x^4}}+\frac{x \left(a-b x^2\right)}{8 a^2 \left(a+b x^2\right)^{3/2} \sqrt{a^2-b^2 x^4}}+\frac{19 \sqrt{a+b x^2} \sqrt{a-b x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a-b x^2}}\right)}{32 \sqrt{2} a^3 \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(x*(a - b*x^2))/(8*a^2*(a + b*x^2)^(3/2)*Sqrt[a^2 - b^2*x^4]) + (9*x*(a - b*x^2))/(32*a^3*Sqrt[a + b*x^2]*Sqrt[a^2 - b^2*x^4]) + (19*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTan[(Sqrt[2]*Sqrt[b]*x)/Sqrt[a - b*x^2]])/(32*Sqrt[2]*a^3*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",6,6,28,0.2143,1,"{1152, 414, 527, 12, 377, 205}"
205,1,152,0,0.0545413,"\int \frac{\left(a-b x^2\right)^{5/2}}{\sqrt{a^2-b^2 x^4}} \, dx","Int[(a - b*x^2)^(5/2)/Sqrt[a^2 - b^2*x^4],x]","-\frac{9 a x \sqrt{a-b x^2} \left(a+b x^2\right)}{8 \sqrt{a^2-b^2 x^4}}-\frac{x \left(a-b x^2\right)^{3/2} \left(a+b x^2\right)}{4 \sqrt{a^2-b^2 x^4}}+\frac{19 a^2 \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b} \sqrt{a^2-b^2 x^4}}","-\frac{9 a x \sqrt{a-b x^2} \left(a+b x^2\right)}{8 \sqrt{a^2-b^2 x^4}}-\frac{x \left(a-b x^2\right)^{3/2} \left(a+b x^2\right)}{4 \sqrt{a^2-b^2 x^4}}+\frac{19 a^2 \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(-9*a*x*Sqrt[a - b*x^2]*(a + b*x^2))/(8*Sqrt[a^2 - b^2*x^4]) - (x*(a - b*x^2)^(3/2)*(a + b*x^2))/(4*Sqrt[a^2 - b^2*x^4]) + (19*a^2*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",5,5,29,0.1724,1,"{1152, 416, 388, 217, 206}"
206,1,109,0,0.0352851,"\int \frac{\left(a-b x^2\right)^{3/2}}{\sqrt{a^2-b^2 x^4}} \, dx","Int[(a - b*x^2)^(3/2)/Sqrt[a^2 - b^2*x^4],x]","\frac{3 a \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b} \sqrt{a^2-b^2 x^4}}-\frac{x \sqrt{a-b x^2} \left(a+b x^2\right)}{2 \sqrt{a^2-b^2 x^4}}","\frac{3 a \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b} \sqrt{a^2-b^2 x^4}}-\frac{x \sqrt{a-b x^2} \left(a+b x^2\right)}{2 \sqrt{a^2-b^2 x^4}}",1,"-(x*Sqrt[a - b*x^2]*(a + b*x^2))/(2*Sqrt[a^2 - b^2*x^4]) + (3*a*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",4,4,29,0.1379,1,"{1152, 388, 217, 206}"
207,1,64,0,0.0254866,"\int \frac{\sqrt{a-b x^2}}{\sqrt{a^2-b^2 x^4}} \, dx","Int[Sqrt[a - b*x^2]/Sqrt[a^2 - b^2*x^4],x]","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",3,3,29,0.1034,1,"{1152, 217, 206}"
208,1,77,0,0.0358898,"\int \frac{1}{\sqrt{a-b x^2} \sqrt{a^2-b^2 x^4}} \, dx","Int[1/(Sqrt[a - b*x^2]*Sqrt[a^2 - b^2*x^4]),x]","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{2} a \sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{\sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{2} a \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTanh[(Sqrt[2]*Sqrt[b]*x)/Sqrt[a + b*x^2]])/(Sqrt[2]*a*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",3,3,29,0.1034,1,"{1152, 377, 208}"
209,1,124,0,0.0538451,"\int \frac{1}{\left(a-b x^2\right)^{3/2} \sqrt{a^2-b^2 x^4}} \, dx","Int[1/((a - b*x^2)^(3/2)*Sqrt[a^2 - b^2*x^4]),x]","\frac{x \left(a+b x^2\right)}{4 a^2 \sqrt{a-b x^2} \sqrt{a^2-b^2 x^4}}+\frac{3 \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a+b x^2}}\right)}{4 \sqrt{2} a^2 \sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{x \left(a+b x^2\right)}{4 a^2 \sqrt{a-b x^2} \sqrt{a^2-b^2 x^4}}+\frac{3 \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a+b x^2}}\right)}{4 \sqrt{2} a^2 \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(x*(a + b*x^2))/(4*a^2*Sqrt[a - b*x^2]*Sqrt[a^2 - b^2*x^4]) + (3*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTanh[(Sqrt[2]*Sqrt[b]*x)/Sqrt[a + b*x^2]])/(4*Sqrt[2]*a^2*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",4,4,29,0.1379,1,"{1152, 382, 377, 208}"
210,1,167,0,0.0873148,"\int \frac{1}{\left(a-b x^2\right)^{5/2} \sqrt{a^2-b^2 x^4}} \, dx","Int[1/((a - b*x^2)^(5/2)*Sqrt[a^2 - b^2*x^4]),x]","\frac{9 x \left(a+b x^2\right)}{32 a^3 \sqrt{a-b x^2} \sqrt{a^2-b^2 x^4}}+\frac{x \left(a+b x^2\right)}{8 a^2 \left(a-b x^2\right)^{3/2} \sqrt{a^2-b^2 x^4}}+\frac{19 \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a+b x^2}}\right)}{32 \sqrt{2} a^3 \sqrt{b} \sqrt{a^2-b^2 x^4}}","\frac{9 x \left(a+b x^2\right)}{32 a^3 \sqrt{a-b x^2} \sqrt{a^2-b^2 x^4}}+\frac{x \left(a+b x^2\right)}{8 a^2 \left(a-b x^2\right)^{3/2} \sqrt{a^2-b^2 x^4}}+\frac{19 \sqrt{a-b x^2} \sqrt{a+b x^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{a+b x^2}}\right)}{32 \sqrt{2} a^3 \sqrt{b} \sqrt{a^2-b^2 x^4}}",1,"(x*(a + b*x^2))/(8*a^2*(a - b*x^2)^(3/2)*Sqrt[a^2 - b^2*x^4]) + (9*x*(a + b*x^2))/(32*a^3*Sqrt[a - b*x^2]*Sqrt[a^2 - b^2*x^4]) + (19*Sqrt[a - b*x^2]*Sqrt[a + b*x^2]*ArcTanh[(Sqrt[2]*Sqrt[b]*x)/Sqrt[a + b*x^2]])/(32*Sqrt[2]*a^3*Sqrt[b]*Sqrt[a^2 - b^2*x^4])","A",6,6,29,0.2069,1,"{1152, 414, 527, 12, 377, 208}"
211,1,30,0,0.0100729,"\int \frac{\sqrt{-1+x^2}}{\sqrt{-1+x^4}} \, dx","Int[Sqrt[-1 + x^2]/Sqrt[-1 + x^4],x]","\frac{\sqrt{x^2-1} \sqrt{x^2+1} \sinh ^{-1}(x)}{\sqrt{x^4-1}}","\frac{\sqrt{x^2-1} \sqrt{x^2+1} \sinh ^{-1}(x)}{\sqrt{x^4-1}}",1,"(Sqrt[-1 + x^2]*Sqrt[1 + x^2]*ArcSinh[x])/Sqrt[-1 + x^4]","A",2,2,19,0.1053,1,"{1152, 215}"
212,1,40,0,0.0105591,"\int \frac{\sqrt{1+x^2}}{\sqrt{-1+x^4}} \, dx","Int[Sqrt[1 + x^2]/Sqrt[-1 + x^4],x]","\frac{\sqrt{x^2-1} \sqrt{x^2+1} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)}{\sqrt{x^4-1}}","-\frac{\sqrt{x^4-1} \sin ^{-1}(x)}{\sqrt{1-x^4}}",1,"(Sqrt[-1 + x^2]*Sqrt[1 + x^2]*ArcTanh[x/Sqrt[-1 + x^2]])/Sqrt[-1 + x^4]","A",3,3,19,0.1579,1,"{1152, 217, 206}"
213,1,72,0,0.1175579,"\int \frac{-\sqrt{-1+x^2}+\sqrt{1+x^2}}{\sqrt{-1+x^4}} \, dx","Int[(-Sqrt[-1 + x^2] + Sqrt[1 + x^2])/Sqrt[-1 + x^4],x]","\frac{\sqrt{x^2-1} \sqrt{x^2+1} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)}{\sqrt{x^4-1}}-\frac{\sqrt{x^2-1} \sqrt{x^2+1} \sinh ^{-1}(x)}{\sqrt{x^4-1}}","\frac{\sqrt{x^2-1} \sqrt{x^4-1} \sinh ^{-1}(x)}{\left(1-x^2\right) \sqrt{x^2+1}}-\frac{\sqrt{x^4-1} \sin ^{-1}(x)}{\sqrt{1-x^2} \sqrt{x^2+1}}",1,"-((Sqrt[-1 + x^2]*Sqrt[1 + x^2]*ArcSinh[x])/Sqrt[-1 + x^4]) + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*ArcTanh[x/Sqrt[-1 + x^2]])/Sqrt[-1 + x^4]","A",7,5,31,0.1613,1,"{6742, 1152, 215, 217, 206}"
214,1,121,0,0.1597321,"\int \frac{\left(d+e x^2\right)^4}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx","Int[(d + e*x^2)^4/(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4),x]","\frac{x \left(b^2 e^2-5 b c d e+7 c^2 d^2\right)}{c^3}+\frac{e x^3 (4 c d-b e)}{3 c^2}-\frac{(2 c d-b e)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{c^{7/2} \sqrt{e} \sqrt{c d-b e}}+\frac{e^2 x^5}{5 c}","\frac{x \left(b^2 e^2-5 b c d e+7 c^2 d^2\right)}{c^3}+\frac{e x^3 (4 c d-b e)}{3 c^2}-\frac{(2 c d-b e)^3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{c^{7/2} \sqrt{e} \sqrt{c d-b e}}+\frac{e^2 x^5}{5 c}",1,"((7*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*x)/c^3 + (e*(4*c*d - b*e)*x^3)/(3*c^2) + (e^2*x^5)/(5*c) - ((2*c*d - b*e)^3*ArcTanh[(Sqrt[c]*Sqrt[e]*x)/Sqrt[c*d - b*e]])/(c^(7/2)*Sqrt[e]*Sqrt[c*d - b*e])","A",4,3,39,0.07692,1,"{1149, 390, 208}"
215,1,86,0,0.1072683,"\int \frac{\left(d+e x^2\right)^3}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx","Int[(d + e*x^2)^3/(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4),x]","\frac{x (3 c d-b e)}{c^2}-\frac{(2 c d-b e)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{c^{5/2} \sqrt{e} \sqrt{c d-b e}}+\frac{e x^3}{3 c}","\frac{x (3 c d-b e)}{c^2}-\frac{(2 c d-b e)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{c^{5/2} \sqrt{e} \sqrt{c d-b e}}+\frac{e x^3}{3 c}",1,"((3*c*d - b*e)*x)/c^2 + (e*x^3)/(3*c) - ((2*c*d - b*e)^2*ArcTanh[(Sqrt[c]*Sqrt[e]*x)/Sqrt[c*d - b*e]])/(c^(5/2)*Sqrt[e]*Sqrt[c*d - b*e])","A",4,3,39,0.07692,1,"{1149, 390, 208}"
216,1,64,0,0.078468,"\int \frac{\left(d+e x^2\right)^2}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx","Int[(d + e*x^2)^2/(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4),x]","\frac{x}{c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{c^{3/2} \sqrt{e} \sqrt{c d-b e}}","\frac{x}{c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{c^{3/2} \sqrt{e} \sqrt{c d-b e}}",1,"x/c - ((2*c*d - b*e)*ArcTanh[(Sqrt[c]*Sqrt[e]*x)/Sqrt[c*d - b*e]])/(c^(3/2)*Sqrt[e]*Sqrt[c*d - b*e])","A",3,3,39,0.07692,1,"{1149, 388, 208}"
217,1,49,0,0.0288674,"\int \frac{d+e x^2}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx","Int[(d + e*x^2)/(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{\sqrt{c} \sqrt{e} \sqrt{c d-b e}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{\sqrt{c} \sqrt{e} \sqrt{c d-b e}}",1,"-(ArcTanh[(Sqrt[c]*Sqrt[e]*x)/Sqrt[c*d - b*e]]/(Sqrt[c]*Sqrt[e]*Sqrt[c*d - b*e]))","A",2,2,37,0.05405,1,"{1149, 208}"
218,1,136,0,0.1784767,"\int \frac{1}{\left(d+e x^2\right) \left(-c d^2+b d e+b e^2 x^2+c e^2 x^4\right)} \, dx","Int[1/((d + e*x^2)*(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4)),x]","-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^2}-\frac{(4 c d-b e) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \sqrt{e} (2 c d-b e)^2}-\frac{x}{2 d \left(d+e x^2\right) (2 c d-b e)}","-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^2}-\frac{(4 c d-b e) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \sqrt{e} (2 c d-b e)^2}-\frac{x}{2 d \left(d+e x^2\right) (2 c d-b e)}",1,"-x/(2*d*(2*c*d - b*e)*(d + e*x^2)) - ((4*c*d - b*e)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*Sqrt[e]*(2*c*d - b*e)^2) - (c^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[e]*x)/Sqrt[c*d - b*e]])/(Sqrt[e]*Sqrt[c*d - b*e]*(2*c*d - b*e)^2)","A",5,5,39,0.1282,1,"{1149, 414, 522, 205, 208}"
219,1,187,0,0.2778015,"\int \frac{1}{\left(d+e x^2\right)^2 \left(-c d^2+b d e+b e^2 x^2+c e^2 x^4\right)} \, dx","Int[1/((d + e*x^2)^2*(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4)),x]","-\frac{\left(3 b^2 e^2-16 b c d e+28 c^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{5/2} \sqrt{e} (2 c d-b e)^3}-\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^3}-\frac{x (10 c d-3 b e)}{8 d^2 \left(d+e x^2\right) (2 c d-b e)^2}-\frac{x}{4 d \left(d+e x^2\right)^2 (2 c d-b e)}","-\frac{\left(3 b^2 e^2-16 b c d e+28 c^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{8 d^{5/2} \sqrt{e} (2 c d-b e)^3}-\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{e} x}{\sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^3}-\frac{x (10 c d-3 b e)}{8 d^2 \left(d+e x^2\right) (2 c d-b e)^2}-\frac{x}{4 d \left(d+e x^2\right)^2 (2 c d-b e)}",1,"-x/(4*d*(2*c*d - b*e)*(d + e*x^2)^2) - ((10*c*d - 3*b*e)*x)/(8*d^2*(2*c*d - b*e)^2*(d + e*x^2)) - ((28*c^2*d^2 - 16*b*c*d*e + 3*b^2*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(5/2)*Sqrt[e]*(2*c*d - b*e)^3) - (c^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[e]*x)/Sqrt[c*d - b*e]])/(Sqrt[e]*Sqrt[c*d - b*e]*(2*c*d - b*e)^3)","A",6,6,39,0.1538,1,"{1149, 414, 527, 522, 205, 208}"
220,1,139,0,0.2762708,"\int \frac{\left(d+e x^2\right)^{5/2}}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx","Int[(d + e*x^2)^(5/2)/(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4),x]","-\frac{(2 c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{c^2 \sqrt{e} \sqrt{c d-b e}}+\frac{(5 c d-2 b e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c^2 \sqrt{e}}+\frac{x \sqrt{d+e x^2}}{2 c}","-\frac{(2 c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{c^2 \sqrt{e} \sqrt{c d-b e}}+\frac{(5 c d-2 b e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c^2 \sqrt{e}}+\frac{x \sqrt{d+e x^2}}{2 c}",1,"(x*Sqrt[d + e*x^2])/(2*c) + ((5*c*d - 2*b*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c^2*Sqrt[e]) - ((2*c*d - b*e)^(3/2)*ArcTanh[(Sqrt[e]*Sqrt[2*c*d - b*e]*x)/(Sqrt[c*d - b*e]*Sqrt[d + e*x^2])])/(c^2*Sqrt[e]*Sqrt[c*d - b*e])","A",7,7,41,0.1707,1,"{1149, 416, 523, 217, 206, 377, 208}"
221,1,108,0,0.1263437,"\int \frac{\left(d+e x^2\right)^{3/2}}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx","Int[(d + e*x^2)^(3/2)/(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c \sqrt{e}}-\frac{\sqrt{2 c d-b e} \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{c \sqrt{e} \sqrt{c d-b e}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c \sqrt{e}}-\frac{\sqrt{2 c d-b e} \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{c \sqrt{e} \sqrt{c d-b e}}",1,"ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/(c*Sqrt[e]) - (Sqrt[2*c*d - b*e]*ArcTanh[(Sqrt[e]*Sqrt[2*c*d - b*e]*x)/(Sqrt[c*d - b*e]*Sqrt[d + e*x^2])])/(c*Sqrt[e]*Sqrt[c*d - b*e])","A",6,6,41,0.1463,1,"{1149, 402, 217, 206, 377, 208}"
222,1,76,0,0.0704533,"\int \frac{\sqrt{d+e x^2}}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx","Int[Sqrt[d + e*x^2]/(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} \sqrt{2 c d-b e}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} \sqrt{2 c d-b e}}",1,"-(ArcTanh[(Sqrt[e]*Sqrt[2*c*d - b*e]*x)/(Sqrt[c*d - b*e]*Sqrt[d + e*x^2])]/(Sqrt[e]*Sqrt[c*d - b*e]*Sqrt[2*c*d - b*e]))","A",3,3,41,0.07317,1,"{1149, 377, 208}"
223,1,106,0,0.11729,"\int \frac{1}{\sqrt{d+e x^2} \left(-c d^2+b d e+b e^2 x^2+c e^2 x^4\right)} \, dx","Int[1/(Sqrt[d + e*x^2]*(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4)),x]","-\frac{x}{d \sqrt{d+e x^2} (2 c d-b e)}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^{3/2}}","-\frac{x}{d \sqrt{d+e x^2} (2 c d-b e)}-\frac{c \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^{3/2}}",1,"-(x/(d*(2*c*d - b*e)*Sqrt[d + e*x^2])) - (c*ArcTanh[(Sqrt[e]*Sqrt[2*c*d - b*e]*x)/(Sqrt[c*d - b*e]*Sqrt[d + e*x^2])])/(Sqrt[e]*Sqrt[c*d - b*e]*(2*c*d - b*e)^(3/2))","A",4,4,41,0.09756,1,"{1149, 382, 377, 208}"
224,1,149,0,0.2685894,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(-c d^2+b d e+b e^2 x^2+c e^2 x^4\right)} \, dx","Int[1/((d + e*x^2)^(3/2)*(-(c*d^2) + b*d*e + b*e^2*x^2 + c*e^2*x^4)),x]","-\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^{5/2}}-\frac{x (7 c d-2 b e)}{3 d^2 \sqrt{d+e x^2} (2 c d-b e)^2}-\frac{x}{3 d \left(d+e x^2\right)^{3/2} (2 c d-b e)}","-\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{e} x \sqrt{2 c d-b e}}{\sqrt{d+e x^2} \sqrt{c d-b e}}\right)}{\sqrt{e} \sqrt{c d-b e} (2 c d-b e)^{5/2}}-\frac{x (7 c d-2 b e)}{3 d^2 \sqrt{d+e x^2} (2 c d-b e)^2}-\frac{x}{3 d \left(d+e x^2\right)^{3/2} (2 c d-b e)}",1,"-x/(3*d*(2*c*d - b*e)*(d + e*x^2)^(3/2)) - ((7*c*d - 2*b*e)*x)/(3*d^2*(2*c*d - b*e)^2*Sqrt[d + e*x^2]) - (c^2*ArcTanh[(Sqrt[e]*Sqrt[2*c*d - b*e]*x)/(Sqrt[c*d - b*e]*Sqrt[d + e*x^2])])/(Sqrt[e]*Sqrt[c*d - b*e]*(2*c*d - b*e)^(5/2))","A",6,6,41,0.1463,1,"{1149, 414, 527, 12, 377, 208}"
225,1,183,0,0.0882292,"\int \left(1+x^2\right)^3 \sqrt{1+x^2+x^4} \, dx","Int[(1 + x^2)^3*Sqrt[1 + x^2 + x^4],x]","\frac{1}{9} \left(x^4+x^2+1\right)^{3/2} x^3+\frac{1}{3} \left(x^4+x^2+1\right)^{3/2} x+\frac{2}{45} \left(6 x^2+7\right) \sqrt{x^4+x^2+1} x+\frac{26 \sqrt{x^4+x^2+1} x}{45 \left(x^2+1\right)}+\frac{7 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{15 \sqrt{x^4+x^2+1}}-\frac{26 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{45 \sqrt{x^4+x^2+1}}","\frac{1}{9} \left(x^4+x^2+1\right)^{3/2} x^3+\frac{1}{3} \left(x^4+x^2+1\right)^{3/2} x+\frac{2}{45} \left(6 x^2+7\right) \sqrt{x^4+x^2+1} x+\frac{26 \sqrt{x^4+x^2+1} x}{45 \left(x^2+1\right)}+\frac{7 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{15 \sqrt{x^4+x^2+1}}-\frac{26 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{45 \sqrt{x^4+x^2+1}}",1,"(26*x*Sqrt[1 + x^2 + x^4])/(45*(1 + x^2)) + (2*x*(7 + 6*x^2)*Sqrt[1 + x^2 + x^4])/45 + (x*(1 + x^2 + x^4)^(3/2))/3 + (x^3*(1 + x^2 + x^4)^(3/2))/9 - (26*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(45*Sqrt[1 + x^2 + x^4]) + (7*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(15*Sqrt[1 + x^2 + x^4])","A",6,6,20,0.3000,1,"{1206, 1679, 1176, 1197, 1103, 1195}"
226,1,164,0,0.0605862,"\int \left(1+x^2\right)^2 \sqrt{1+x^2+x^4} \, dx","Int[(1 + x^2)^2*Sqrt[1 + x^2 + x^4],x]","\frac{1}{7} x \left(x^4+x^2+1\right)^{3/2}+\frac{2}{21} x \left(3 x^2+4\right) \sqrt{x^4+x^2+1}+\frac{2 x \sqrt{x^4+x^2+1}}{3 \left(x^2+1\right)}+\frac{4 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{7 \sqrt{x^4+x^2+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}","\frac{1}{7} x \left(x^4+x^2+1\right)^{3/2}+\frac{2}{21} x \left(3 x^2+4\right) \sqrt{x^4+x^2+1}+\frac{2 x \sqrt{x^4+x^2+1}}{3 \left(x^2+1\right)}+\frac{4 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{7 \sqrt{x^4+x^2+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}",1,"(2*x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) + (2*x*(4 + 3*x^2)*Sqrt[1 + x^2 + x^4])/21 + (x*(1 + x^2 + x^4)^(3/2))/7 - (2*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4]) + (4*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(7*Sqrt[1 + x^2 + x^4])","A",5,5,20,0.2500,1,"{1206, 1176, 1197, 1103, 1195}"
227,1,145,0,0.0425715,"\int \left(1+x^2\right) \sqrt{1+x^2+x^4} \, dx","Int[(1 + x^2)*Sqrt[1 + x^2 + x^4],x]","\frac{1}{5} \left(x^2+2\right) \sqrt{x^4+x^2+1} x+\frac{3 \sqrt{x^4+x^2+1} x}{5 \left(x^2+1\right)}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{5 \sqrt{x^4+x^2+1}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{5 \sqrt{x^4+x^2+1}}","\frac{1}{5} \left(x^2+2\right) \sqrt{x^4+x^2+1} x+\frac{3 \sqrt{x^4+x^2+1} x}{5 \left(x^2+1\right)}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{5 \sqrt{x^4+x^2+1}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{5 \sqrt{x^4+x^2+1}}",1,"(3*x*Sqrt[1 + x^2 + x^4])/(5*(1 + x^2)) + (x*(2 + x^2)*Sqrt[1 + x^2 + x^4])/5 - (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(5*Sqrt[1 + x^2 + x^4]) + (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(5*Sqrt[1 + x^2 + x^4])","A",4,4,18,0.2222,1,"{1176, 1197, 1103, 1195}"
228,1,137,0,0.0861591,"\int \frac{\sqrt{1+x^2+x^4}}{1+x^2} \, dx","Int[Sqrt[1 + x^2 + x^4]/(1 + x^2),x]","\frac{\sqrt{x^4+x^2+1} x}{x^2+1}+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}","\frac{\sqrt{x^4+x^2+1} x}{x^2+1}+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}",1,"(x*Sqrt[1 + x^2 + x^4])/(1 + x^2) + ArcTan[x/Sqrt[1 + x^2 + x^4]]/2 - ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/Sqrt[1 + x^2 + x^4] + (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4])","A",8,7,20,0.3500,1,"{1208, 1139, 1103, 1195, 1210, 1698, 203}"
229,1,49,0,0.0106672,"\int \frac{\sqrt{1+x^2+x^4}}{\left(1+x^2\right)^2} \, dx","Int[Sqrt[1 + x^2 + x^4]/(1 + x^2)^2,x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4+x^2+1}}","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4+x^2+1}}",1,"((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(2*Sqrt[1 + x^2 + x^4])","A",1,1,20,0.05000,1,"{1225}"
230,1,93,0,0.5081553,"\int \frac{\sqrt{1+x^2+x^4}}{\left(1+x^2\right)^3} \, dx","Int[Sqrt[1 + x^2 + x^4]/(1 + x^2)^3,x]","\frac{\sqrt{x^4+x^2+1} x}{4 \left(x^2+1\right)^2}+\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}","\frac{\sqrt{x^4+x^2+1} x}{4 \left(x^2+1\right)^2}+\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}",1,"(x*Sqrt[1 + x^2 + x^4])/(4*(1 + x^2)^2) + ArcTan[x/Sqrt[1 + x^2 + x^4]]/4 + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4])","A",23,13,20,0.6500,1,"{1228, 1223, 1696, 1593, 1712, 1195, 1700, 1103, 1698, 203, 12, 1317, 1210}"
231,1,166,0,0.6154305,"\int \frac{\sqrt{1+x^2+x^4}}{\left(1+x^2\right)^4} \, dx","Int[Sqrt[1 + x^2 + x^4]/(1 + x^2)^4,x]","\frac{\sqrt{x^4+x^2+1} x}{6 \left(x^2+1\right)^2}+\frac{\sqrt{x^4+x^2+1} x}{6 \left(x^2+1\right)^3}+\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{8 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}","\frac{\sqrt{x^4+x^2+1} x}{6 \left(x^2+1\right)^2}+\frac{\sqrt{x^4+x^2+1} x}{6 \left(x^2+1\right)^3}+\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{8 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}",1,"(x*Sqrt[1 + x^2 + x^4])/(6*(1 + x^2)^3) + (x*Sqrt[1 + x^2 + x^4])/(6*(1 + x^2)^2) + ArcTan[x/Sqrt[1 + x^2 + x^4]]/4 + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(8*Sqrt[1 + x^2 + x^4])","A",26,14,20,0.7000,1,"{1228, 1223, 1696, 1586, 1197, 1103, 1195, 1593, 1712, 1700, 1698, 203, 12, 1317}"
232,1,159,0,0.0714685,"\int \frac{\left(1+x^2\right)^3}{\sqrt{1+x^2+x^4}} \, dx","Int[(1 + x^2)^3/Sqrt[1 + x^2 + x^4],x]","\frac{1}{5} \sqrt{x^4+x^2+1} x^3+\frac{14 \sqrt{x^4+x^2+1} x}{15 \left(x^2+1\right)}+\frac{11}{15} \sqrt{x^4+x^2+1} x+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{5 \sqrt{x^4+x^2+1}}-\frac{14 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{15 \sqrt{x^4+x^2+1}}","\frac{1}{5} \sqrt{x^4+x^2+1} x^3+\frac{14 \sqrt{x^4+x^2+1} x}{15 \left(x^2+1\right)}+\frac{11}{15} \sqrt{x^4+x^2+1} x+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{5 \sqrt{x^4+x^2+1}}-\frac{14 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{15 \sqrt{x^4+x^2+1}}",1,"(11*x*Sqrt[1 + x^2 + x^4])/15 + (x^3*Sqrt[1 + x^2 + x^4])/5 + (14*x*Sqrt[1 + x^2 + x^4])/(15*(1 + x^2)) - (14*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(15*Sqrt[1 + x^2 + x^4]) + (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(5*Sqrt[1 + x^2 + x^4])","A",5,5,20,0.2500,1,"{1206, 1679, 1197, 1103, 1195}"
233,1,137,0,0.0449664,"\int \frac{\left(1+x^2\right)^2}{\sqrt{1+x^2+x^4}} \, dx","Int[(1 + x^2)^2/Sqrt[1 + x^2 + x^4],x]","\frac{4 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{1}{3} \sqrt{x^4+x^2+1} x+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}-\frac{4 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}","\frac{4 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{1}{3} \sqrt{x^4+x^2+1} x+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}-\frac{4 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}",1,"(x*Sqrt[1 + x^2 + x^4])/3 + (4*x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) - (4*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4]) + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/Sqrt[1 + x^2 + x^4]","A",4,4,20,0.2000,1,"{1206, 1197, 1103, 1195}"
234,1,115,0,0.0221631,"\int \frac{1+x^2}{\sqrt{1+x^2+x^4}} \, dx","Int[(1 + x^2)/Sqrt[1 + x^2 + x^4],x]","\frac{\sqrt{x^4+x^2+1} x}{x^2+1}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}","\frac{\sqrt{x^4+x^2+1} x}{x^2+1}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}",1,"(x*Sqrt[1 + x^2 + x^4])/(1 + x^2) - ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/Sqrt[1 + x^2 + x^4] + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/Sqrt[1 + x^2 + x^4]","A",3,3,18,0.1667,1,"{1197, 1103, 1195}"
235,1,69,0,0.058729,"\int \frac{1}{\left(1+x^2\right) \sqrt{1+x^2+x^4}} \, dx","Int[1/((1 + x^2)*Sqrt[1 + x^2 + x^4]),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}",1,"ArcTan[x/Sqrt[1 + x^2 + x^4]]/2 + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4])","A",4,4,20,0.2000,1,"{1210, 1103, 1698, 203}"
236,1,118,0,0.1350704,"\int \frac{1}{\left(1+x^2\right)^2 \sqrt{1+x^2+x^4}} \, dx","Int[1/((1 + x^2)^2*Sqrt[1 + x^2 + x^4]),x]","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4+x^2+1}}","\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4+x^2+1}}",1,"ArcTan[x/Sqrt[1 + x^2 + x^4]]/2 + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(2*Sqrt[1 + x^2 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4])","A",8,8,20,0.4000,1,"{1223, 1712, 1195, 12, 1317, 1103, 1698, 203}"
237,1,142,0,0.2771086,"\int \frac{1}{\left(1+x^2\right)^3 \sqrt{1+x^2+x^4}} \, dx","Int[1/((1 + x^2)^3*Sqrt[1 + x^2 + x^4]),x]","\frac{\sqrt{x^4+x^2+1} x}{4 \left(x^2+1\right)^2}+\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4+x^2+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}","\frac{\sqrt{x^4+x^2+1} x}{4 \left(x^2+1\right)^2}+\frac{1}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{2 \sqrt{x^4+x^2+1}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}",1,"(x*Sqrt[1 + x^2 + x^4])/(4*(1 + x^2)^2) + ArcTan[x/Sqrt[1 + x^2 + x^4]]/4 + (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4]) - ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(2*Sqrt[1 + x^2 + x^4])","A",9,9,20,0.4500,1,"{1223, 1696, 1593, 1712, 1195, 1700, 1103, 1698, 203}"
238,1,144,0,0.0445113,"\int \frac{\left(1+x^2\right)^3}{\left(1+x^2+x^4\right)^{3/2}} \, dx","Int[(1 + x^2)^3/(1 + x^2 + x^4)^(3/2),x]","\frac{2 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}-\frac{\left(1-x^2\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}","\frac{2 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}-\frac{\left(1-x^2\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{\sqrt{x^4+x^2+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}",1,"-(x*(1 - x^2))/(3*Sqrt[1 + x^2 + x^4]) + (2*x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) - (2*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4]) + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/Sqrt[1 + x^2 + x^4]","A",4,4,20,0.2000,1,"{1205, 1197, 1103, 1195}"
239,1,98,0,0.0248185,"\int \frac{\left(1+x^2\right)^2}{\left(1+x^2+x^4\right)^{3/2}} \, dx","Int[(1 + x^2)^2/(1 + x^2 + x^4)^(3/2),x]","-\frac{2 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{\left(2 x^2+1\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}","-\frac{2 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{\left(2 x^2+1\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}",1,"(x*(1 + 2*x^2))/(3*Sqrt[1 + x^2 + x^4]) - (2*x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) + (2*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4])","A",2,2,20,0.1000,1,"{1205, 1195}"
240,1,96,0,0.0206474,"\int \frac{1+x^2}{\left(1+x^2+x^4\right)^{3/2}} \, dx","Int[(1 + x^2)/(1 + x^2 + x^4)^(3/2),x]","-\frac{\sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{\left(x^2+2\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}","-\frac{\sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{\left(x^2+2\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}",1,"(x*(2 + x^2))/(3*Sqrt[1 + x^2 + x^4]) - (x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4])","A",2,2,18,0.1111,1,"{1178, 1195}"
241,1,166,0,0.1037568,"\int \frac{1}{\left(1+x^2\right) \left(1+x^2+x^4\right)^{3/2}} \, dx","Int[1/((1 + x^2)*(1 + x^2 + x^4)^(3/2)),x]","\frac{2 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}-\frac{\left(2 x^2+1\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}","\frac{2 \sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}-\frac{\left(2 x^2+1\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{1}{2} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}-\frac{2 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{3 \sqrt{x^4+x^2+1}}",1,"-(x*(1 + 2*x^2))/(3*Sqrt[1 + x^2 + x^4]) + (2*x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) + ArcTan[x/Sqrt[1 + x^2 + x^4]]/2 - (2*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(3*Sqrt[1 + x^2 + x^4]) + (3*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4])","A",9,8,20,0.4000,1,"{1221, 1119, 1197, 1103, 1195, 1210, 1698, 203}"
242,1,111,0,0.2781564,"\int \frac{1}{\left(1+x^2\right)^2 \left(1+x^2+x^4\right)^{3/2}} \, dx","Int[1/((1 + x^2)^2*(1 + x^2 + x^4)^(3/2)),x]","\frac{\sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}-\frac{\left(x^2+2\right) x}{3 \sqrt{x^4+x^2+1}}+\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{6 \sqrt{x^4+x^2+1}}","\frac{\sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}-\frac{\left(x^2+2\right) x}{3 \sqrt{x^4+x^2+1}}+\tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)+\frac{\left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{6 \sqrt{x^4+x^2+1}}",1,"-(x*(2 + x^2))/(3*Sqrt[1 + x^2 + x^4]) + (x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) + ArcTan[x/Sqrt[1 + x^2 + x^4]] + ((1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(6*Sqrt[1 + x^2 + x^4])","A",16,11,20,0.5500,1,"{1228, 1178, 1195, 1223, 1712, 12, 1317, 1103, 1698, 203, 1210}"
243,1,190,0,0.5714934,"\int \frac{1}{\left(1+x^2\right)^3 \left(1+x^2+x^4\right)^{3/2}} \, dx","Int[1/((1 + x^2)^3*(1 + x^2 + x^4)^(3/2)),x]","-\frac{\sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{\sqrt{x^4+x^2+1} x}{4 \left(x^2+1\right)^2}-\frac{\left(1-x^2\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{3}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}+\frac{19 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{12 \sqrt{x^4+x^2+1}}","-\frac{\sqrt{x^4+x^2+1} x}{3 \left(x^2+1\right)}+\frac{\sqrt{x^4+x^2+1} x}{4 \left(x^2+1\right)^2}-\frac{\left(1-x^2\right) x}{3 \sqrt{x^4+x^2+1}}+\frac{3}{4} \tan ^{-1}\left(\frac{x}{\sqrt{x^4+x^2+1}}\right)-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{4 \sqrt{x^4+x^2+1}}+\frac{19 \left(x^2+1\right) \sqrt{\frac{x^4+x^2+1}{\left(x^2+1\right)^2}} E\left(2 \tan ^{-1}(x)|\frac{1}{4}\right)}{12 \sqrt{x^4+x^2+1}}",1,"-(x*(1 - x^2))/(3*Sqrt[1 + x^2 + x^4]) + (x*Sqrt[1 + x^2 + x^4])/(4*(1 + x^2)^2) - (x*Sqrt[1 + x^2 + x^4])/(3*(1 + x^2)) + (3*ArcTan[x/Sqrt[1 + x^2 + x^4]])/4 + (19*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticE[2*ArcTan[x], 1/4])/(12*Sqrt[1 + x^2 + x^4]) - (5*(1 + x^2)*Sqrt[(1 + x^2 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/4])/(4*Sqrt[1 + x^2 + x^4])","A",23,14,20,0.7000,1,"{1228, 1092, 1197, 1103, 1195, 1223, 1696, 1593, 1712, 1700, 1698, 203, 12, 1317}"
244,1,135,0,0.1259436,"\int \left(d+e x^2\right)^4 \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x^2)^4*(a + b*x^2 + c*x^4),x]","\frac{1}{9} e^2 x^9 \left(e (a e+4 b d)+6 c d^2\right)+\frac{1}{5} d^2 x^5 \left(6 a e^2+4 b d e+c d^2\right)+\frac{2}{7} d e x^7 \left(e (2 a e+3 b d)+2 c d^2\right)+\frac{1}{3} d^3 x^3 (4 a e+b d)+a d^4 x+\frac{1}{11} e^3 x^{11} (b e+4 c d)+\frac{1}{13} c e^4 x^{13}","\frac{1}{9} e^2 x^9 \left(e (a e+4 b d)+6 c d^2\right)+\frac{1}{5} d^2 x^5 \left(6 a e^2+4 b d e+c d^2\right)+\frac{2}{7} d e x^7 \left(e (2 a e+3 b d)+2 c d^2\right)+\frac{1}{3} d^3 x^3 (4 a e+b d)+a d^4 x+\frac{1}{11} e^3 x^{11} (b e+4 c d)+\frac{1}{13} c e^4 x^{13}",1,"a*d^4*x + (d^3*(b*d + 4*a*e)*x^3)/3 + (d^2*(c*d^2 + 4*b*d*e + 6*a*e^2)*x^5)/5 + (2*d*e*(2*c*d^2 + e*(3*b*d + 2*a*e))*x^7)/7 + (e^2*(6*c*d^2 + e*(4*b*d + a*e))*x^9)/9 + (e^3*(4*c*d + b*e)*x^11)/11 + (c*e^4*x^13)/13","A",2,1,22,0.04545,1,"{1153}"
245,1,103,0,0.0954183,"\int \left(d+e x^2\right)^3 \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x^2)^3*(a + b*x^2 + c*x^4),x]","\frac{1}{7} e x^7 \left(e (a e+3 b d)+3 c d^2\right)+\frac{1}{5} d x^5 \left(3 e (a e+b d)+c d^2\right)+\frac{1}{3} d^2 x^3 (3 a e+b d)+a d^3 x+\frac{1}{9} e^2 x^9 (b e+3 c d)+\frac{1}{11} c e^3 x^{11}","\frac{1}{7} e x^7 \left(e (a e+3 b d)+3 c d^2\right)+\frac{1}{5} d x^5 \left(3 e (a e+b d)+c d^2\right)+\frac{1}{3} d^2 x^3 (3 a e+b d)+a d^3 x+\frac{1}{9} e^2 x^9 (b e+3 c d)+\frac{1}{11} c e^3 x^{11}",1,"a*d^3*x + (d^2*(b*d + 3*a*e)*x^3)/3 + (d*(c*d^2 + 3*e*(b*d + a*e))*x^5)/5 + (e*(3*c*d^2 + e*(3*b*d + a*e))*x^7)/7 + (e^2*(3*c*d + b*e)*x^9)/9 + (c*e^3*x^11)/11","A",2,1,22,0.04545,1,"{1153}"
246,1,73,0,0.0596723,"\int \left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x^2)^2*(a + b*x^2 + c*x^4),x]","\frac{1}{5} x^5 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{3} d x^3 (2 a e+b d)+a d^2 x+\frac{1}{7} e x^7 (b e+2 c d)+\frac{1}{9} c e^2 x^9","\frac{1}{5} x^5 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{3} d x^3 (2 a e+b d)+a d^2 x+\frac{1}{7} e x^7 (b e+2 c d)+\frac{1}{9} c e^2 x^9",1,"a*d^2*x + (d*(b*d + 2*a*e)*x^3)/3 + ((c*d^2 + e*(2*b*d + a*e))*x^5)/5 + (e*(2*c*d + b*e)*x^7)/7 + (c*e^2*x^9)/9","A",2,1,22,0.04545,1,"{1153}"
247,1,42,0,0.0273412,"\int \left(d+e x^2\right) \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x^2)*(a + b*x^2 + c*x^4),x]","\frac{1}{3} x^3 (a e+b d)+a d x+\frac{1}{5} x^5 (b e+c d)+\frac{1}{7} c e x^7","\frac{1}{3} x^3 (a e+b d)+a d x+\frac{1}{5} x^5 (b e+c d)+\frac{1}{7} c e x^7",1,"a*d*x + ((b*d + a*e)*x^3)/3 + ((c*d + b*e)*x^5)/5 + (c*e*x^7)/7","A",2,1,20,0.05000,1,"{1153}"
248,1,66,0,0.0446231,"\int \frac{a+b x^2+c x^4}{d+e x^2} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a e^2-b d e+c d^2\right)}{\sqrt{d} e^{5/2}}-\frac{x (c d-b e)}{e^2}+\frac{c x^3}{3 e}","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a e^2-b d e+c d^2\right)}{\sqrt{d} e^{5/2}}-\frac{x (c d-b e)}{e^2}+\frac{c x^3}{3 e}",1,"-(((c*d - b*e)*x)/e^2) + (c*x^3)/(3*e) + ((c*d^2 - b*d*e + a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(5/2))","A",3,2,22,0.09091,1,"{1153, 205}"
249,1,83,0,0.0934114,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (a e+b d)\right)}{2 d^{3/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 d \left(d+e x^2\right)}+\frac{c x}{e^2}","-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (a e+b d)\right)}{2 d^{3/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 d \left(d+e x^2\right)}+\frac{c x}{e^2}",1,"(c*x)/e^2 + ((a + (d*(c*d - b*e))/e^2)*x)/(2*d*(d + e*x^2)) - ((3*c*d^2 - e*(b*d + a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*e^(5/2))","A",3,3,22,0.1364,1,"{1157, 388, 205}"
250,1,115,0,0.107324,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^3,x]","-\frac{x \left(5 c d^2-e (3 a e+b d)\right)}{8 d^2 e^2 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e (3 a e+b d)+3 c d^2\right)}{8 d^{5/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{4 d \left(d+e x^2\right)^2}","-\frac{x \left(5 c d^2-e (3 a e+b d)\right)}{8 d^2 e^2 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e (3 a e+b d)+3 c d^2\right)}{8 d^{5/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{4 d \left(d+e x^2\right)^2}",1,"((a + (d*(c*d - b*e))/e^2)*x)/(4*d*(d + e*x^2)^2) - ((5*c*d^2 - e*(b*d + 3*a*e))*x)/(8*d^2*e^2*(d + e*x^2)) + ((3*c*d^2 + e*(b*d + 3*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(5/2)*e^(5/2))","A",3,3,22,0.1364,1,"{1157, 385, 205}"
251,1,150,0,0.2053938,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^4} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^4,x]","\frac{x \left(e (5 a e+b d)+c d^2\right)}{16 d^3 e^2 \left(d+e x^2\right)}-\frac{x \left(7 c d^2-e (5 a e+b d)\right)}{24 d^2 e^2 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e (5 a e+b d)+c d^2\right)}{16 d^{7/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{6 d \left(d+e x^2\right)^3}","\frac{x \left(e (5 a e+b d)+c d^2\right)}{16 d^3 e^2 \left(d+e x^2\right)}-\frac{x \left(7 c d^2-e (5 a e+b d)\right)}{24 d^2 e^2 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e (5 a e+b d)+c d^2\right)}{16 d^{7/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{6 d \left(d+e x^2\right)^3}",1,"((a + (d*(c*d - b*e))/e^2)*x)/(6*d*(d + e*x^2)^3) - ((7*c*d^2 - e*(b*d + 5*a*e))*x)/(24*d^2*e^2*(d + e*x^2)^2) + ((c*d^2 + e*(b*d + 5*a*e))*x)/(16*d^3*e^2*(d + e*x^2)) + ((c*d^2 + e*(b*d + 5*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(16*d^(7/2)*e^(5/2))","A",4,4,22,0.1818,1,"{1157, 385, 199, 205}"
252,1,223,0,0.1987993,"\int \left(d+e x^2\right)^3 \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d + e*x^2)^3*(a + b*x^2 + c*x^4)^2,x]","\frac{1}{7} x^7 \left(a^2 e^3+6 a b d e^2+6 a c d^2 e+3 b^2 d^2 e+2 b c d^3\right)+a^2 d^3 x+\frac{1}{11} e x^{11} \left(2 c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+\frac{1}{5} d x^5 \left(6 a b d e+a \left(3 a e^2+2 c d^2\right)+b^2 d^2\right)+\frac{1}{9} x^9 \left(6 c d e (a e+b d)+b e^2 (2 a e+3 b d)+c^2 d^3\right)+\frac{1}{3} a d^2 x^3 (3 a e+2 b d)+\frac{1}{13} c e^2 x^{13} (2 b e+3 c d)+\frac{1}{15} c^2 e^3 x^{15}","\frac{1}{7} x^7 \left(a^2 e^3+6 a b d e^2+6 a c d^2 e+3 b^2 d^2 e+2 b c d^3\right)+a^2 d^3 x+\frac{1}{11} e x^{11} \left(2 c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+\frac{1}{5} d x^5 \left(6 a b d e+a \left(3 a e^2+2 c d^2\right)+b^2 d^2\right)+\frac{1}{9} x^9 \left(6 c d e (a e+b d)+b e^2 (2 a e+3 b d)+c^2 d^3\right)+\frac{1}{3} a d^2 x^3 (3 a e+2 b d)+\frac{1}{13} c e^2 x^{13} (2 b e+3 c d)+\frac{1}{15} c^2 e^3 x^{15}",1,"a^2*d^3*x + (a*d^2*(2*b*d + 3*a*e)*x^3)/3 + (d*(b^2*d^2 + 6*a*b*d*e + a*(2*c*d^2 + 3*a*e^2))*x^5)/5 + ((2*b*c*d^3 + 3*b^2*d^2*e + 6*a*c*d^2*e + 6*a*b*d*e^2 + a^2*e^3)*x^7)/7 + ((c^2*d^3 + 6*c*d*e*(b*d + a*e) + b*e^2*(3*b*d + 2*a*e))*x^9)/9 + (e*(3*c^2*d^2 + b^2*e^2 + 2*c*e*(3*b*d + a*e))*x^11)/11 + (c*e^2*(3*c*d + 2*b*e)*x^13)/13 + (c^2*e^3*x^15)/15","A",2,1,24,0.04167,1,"{1153}"
253,1,155,0,0.1410416,"\int \left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d + e*x^2)^2*(a + b*x^2 + c*x^4)^2,x]","a^2 d^2 x+\frac{1}{9} x^9 \left(2 c e (a e+2 b d)+b^2 e^2+c^2 d^2\right)+\frac{2}{7} x^7 \left(a b e^2+2 a c d e+b^2 d e+b c d^2\right)+\frac{1}{5} x^5 \left(4 a b d e+a \left(a e^2+2 c d^2\right)+b^2 d^2\right)+\frac{2}{3} a d x^3 (a e+b d)+\frac{2}{11} c e x^{11} (b e+c d)+\frac{1}{13} c^2 e^2 x^{13}","a^2 d^2 x+\frac{1}{9} x^9 \left(2 c e (a e+2 b d)+b^2 e^2+c^2 d^2\right)+\frac{2}{7} x^7 \left(a b e^2+2 a c d e+b^2 d e+b c d^2\right)+\frac{1}{5} x^5 \left(4 a b d e+a \left(a e^2+2 c d^2\right)+b^2 d^2\right)+\frac{2}{3} a d x^3 (a e+b d)+\frac{2}{11} c e x^{11} (b e+c d)+\frac{1}{13} c^2 e^2 x^{13}",1,"a^2*d^2*x + (2*a*d*(b*d + a*e)*x^3)/3 + ((b^2*d^2 + 4*a*b*d*e + a*(2*c*d^2 + a*e^2))*x^5)/5 + (2*(b*c*d^2 + b^2*d*e + 2*a*c*d*e + a*b*e^2)*x^7)/7 + ((c^2*d^2 + b^2*e^2 + 2*c*e*(2*b*d + a*e))*x^9)/9 + (2*c*e*(c*d + b*e)*x^11)/11 + (c^2*e^2*x^13)/13","A",2,1,24,0.04167,1,"{1153}"
254,1,96,0,0.06776,"\int \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d + e*x^2)*(a + b*x^2 + c*x^4)^2,x]","a^2 d x+\frac{1}{7} x^7 \left(2 a c e+b^2 e+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b e+2 a c d+b^2 d\right)+\frac{1}{3} a x^3 (a e+2 b d)+\frac{1}{9} c x^9 (2 b e+c d)+\frac{1}{11} c^2 e x^{11}","a^2 d x+\frac{1}{7} x^7 \left(2 a c e+b^2 e+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b e+2 a c d+b^2 d\right)+\frac{1}{3} a x^3 (a e+2 b d)+\frac{1}{9} c x^9 (2 b e+c d)+\frac{1}{11} c^2 e x^{11}",1,"a^2*d*x + (a*(2*b*d + a*e)*x^3)/3 + ((b^2*d + 2*a*c*d + 2*a*b*e)*x^5)/5 + ((2*b*c*d + b^2*e + 2*a*c*e)*x^7)/7 + (c*(c*d + 2*b*e)*x^9)/9 + (c^2*e*x^11)/11","A",2,1,22,0.04545,1,"{1153}"
255,1,49,0,0.0246358,"\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}"
256,1,143,0,0.140219,"\int \frac{\left(a+b x^2+c x^4\right)^2}{d+e x^2} \, dx","Int[(a + b*x^2 + c*x^4)^2/(d + e*x^2),x]","\frac{x^3 \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{3 e^3}-\frac{x (c d-b e) \left(c d^2-e (b d-2 a e)\right)}{e^4}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a e^2-b d e+c d^2\right)^2}{\sqrt{d} e^{9/2}}-\frac{c x^5 (c d-2 b e)}{5 e^2}+\frac{c^2 x^7}{7 e}","\frac{x^3 \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)}{3 e^3}-\frac{x (c d-b e) \left(c d^2-e (b d-2 a e)\right)}{e^4}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a e^2-b d e+c d^2\right)^2}{\sqrt{d} e^{9/2}}-\frac{c x^5 (c d-2 b e)}{5 e^2}+\frac{c^2 x^7}{7 e}",1,"-(((c*d - b*e)*(c*d^2 - e*(b*d - 2*a*e))*x)/e^4) + ((c^2*d^2 + b^2*e^2 - 2*c*e*(b*d - a*e))*x^3)/(3*e^3) - (c*(c*d - 2*b*e)*x^5)/(5*e^2) + (c^2*x^7)/(7*e) + ((c*d^2 - b*d*e + a*e^2)^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(9/2))","A",3,2,24,0.08333,1,"{1153, 205}"
257,1,166,0,0.2976358,"\int \frac{\left(a+b x^2+c x^4\right)^2}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)^2/(d + e*x^2)^2,x]","\frac{x \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)}{e^4}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{2 d e^4 \left(d+e x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a e^2-b d e+c d^2\right) \left(7 c d^2-e (a e+3 b d)\right)}{2 d^{3/2} e^{9/2}}-\frac{2 c x^3 (c d-b e)}{3 e^3}+\frac{c^2 x^5}{5 e^2}","\frac{x \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)}{e^4}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{2 d e^4 \left(d+e x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(a e^2-b d e+c d^2\right) \left(7 c d^2-e (a e+3 b d)\right)}{2 d^{3/2} e^{9/2}}-\frac{2 c x^3 (c d-b e)}{3 e^3}+\frac{c^2 x^5}{5 e^2}",1,"((3*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d - a*e))*x)/e^4 - (2*c*(c*d - b*e)*x^3)/(3*e^3) + (c^2*x^5)/(5*e^2) + ((c*d^2 - b*d*e + a*e^2)^2*x)/(2*d*e^4*(d + e*x^2)) - ((c*d^2 - b*d*e + a*e^2)*(7*c*d^2 - e*(3*b*d + a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*e^(9/2))","A",4,3,24,0.1250,1,"{1157, 1810, 205}"
258,1,201,0,0.4187753,"\int \frac{\left(a+b x^2+c x^4\right)^2}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*x^2 + c*x^4)^2/(d + e*x^2)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e^2 \left(3 a^2 e^2+2 a b d e+3 b^2 d^2\right)-6 c d^2 e (5 b d-a e)+35 c^2 d^4\right)}{8 d^{5/2} e^{9/2}}-\frac{x \left(-3 a e^2-5 b d e+13 c d^2\right) \left(a e^2-b d e+c d^2\right)}{8 d^2 e^4 \left(d+e x^2\right)}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{4 d e^4 \left(d+e x^2\right)^2}-\frac{c x (3 c d-2 b e)}{e^4}+\frac{c^2 x^3}{3 e^3}","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e^2 \left(3 a^2 e^2+2 a b d e+3 b^2 d^2\right)-6 c d^2 e (5 b d-a e)+35 c^2 d^4\right)}{8 d^{5/2} e^{9/2}}-\frac{x \left(-3 a e^2-5 b d e+13 c d^2\right) \left(a e^2-b d e+c d^2\right)}{8 d^2 e^4 \left(d+e x^2\right)}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{4 d e^4 \left(d+e x^2\right)^2}-\frac{c x (3 c d-2 b e)}{e^4}+\frac{c^2 x^3}{3 e^3}",1,"-((c*(3*c*d - 2*b*e)*x)/e^4) + (c^2*x^3)/(3*e^3) + ((c*d^2 - b*d*e + a*e^2)^2*x)/(4*d*e^4*(d + e*x^2)^2) - ((13*c*d^2 - 5*b*d*e - 3*a*e^2)*(c*d^2 - b*d*e + a*e^2)*x)/(8*d^2*e^4*(d + e*x^2)) + ((35*c^2*d^4 - 6*c*d^2*e*(5*b*d - a*e) + e^2*(3*b^2*d^2 + 2*a*b*d*e + 3*a^2*e^2))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(5/2)*e^(9/2))","A",5,4,24,0.1667,1,"{1157, 1814, 1153, 205}"
259,1,250,0,0.5429024,"\int \frac{\left(a+b x^2+c x^4\right)^2}{\left(d+e x^2\right)^4} \, dx","Int[(a + b*x^2 + c*x^4)^2/(d + e*x^2)^4,x]","\frac{x \left(e^2 \left(5 a^2 e^2+2 a b d e+b^2 d^2\right)-2 c d^2 e (11 b d-a e)+29 c^2 d^4\right)}{16 d^3 e^4 \left(d+e x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(-e^2 \left(5 a^2 e^2+2 a b d e+b^2 d^2\right)-2 c d^2 e (a e+5 b d)+35 c^2 d^4\right)}{16 d^{7/2} e^{9/2}}-\frac{x \left(-5 a e^2-7 b d e+19 c d^2\right) \left(a e^2-b d e+c d^2\right)}{24 d^2 e^4 \left(d+e x^2\right)^2}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{6 d e^4 \left(d+e x^2\right)^3}+\frac{c^2 x}{e^4}","\frac{x \left(e^2 \left(5 a^2 e^2+2 a b d e+b^2 d^2\right)-2 c d^2 e (11 b d-a e)+29 c^2 d^4\right)}{16 d^3 e^4 \left(d+e x^2\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(-e^2 \left(5 a^2 e^2+2 a b d e+b^2 d^2\right)-2 c d^2 e (a e+5 b d)+35 c^2 d^4\right)}{16 d^{7/2} e^{9/2}}-\frac{x \left(-5 a e^2-7 b d e+19 c d^2\right) \left(a e^2-b d e+c d^2\right)}{24 d^2 e^4 \left(d+e x^2\right)^2}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{6 d e^4 \left(d+e x^2\right)^3}+\frac{c^2 x}{e^4}",1,"(c^2*x)/e^4 + ((c*d^2 - b*d*e + a*e^2)^2*x)/(6*d*e^4*(d + e*x^2)^3) - ((19*c*d^2 - 7*b*d*e - 5*a*e^2)*(c*d^2 - b*d*e + a*e^2)*x)/(24*d^2*e^4*(d + e*x^2)^2) + ((29*c^2*d^4 - 2*c*d^2*e*(11*b*d - a*e) + e^2*(b^2*d^2 + 2*a*b*d*e + 5*a^2*e^2))*x)/(16*d^3*e^4*(d + e*x^2)) - ((35*c^2*d^4 - 2*c*d^2*e*(5*b*d + a*e) - e^2*(b^2*d^2 + 2*a*b*d*e + 5*a^2*e^2))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(16*d^(7/2)*e^(9/2))","A",5,4,24,0.1667,1,"{1157, 1814, 388, 205}"
260,1,317,0,0.6498387,"\int \frac{\left(a+b x^2+c x^4\right)^2}{\left(d+e x^2\right)^5} \, dx","Int[(a + b*x^2 + c*x^4)^2/(d + e*x^2)^5,x]","-\frac{x \left(-e^2 \left(35 a^2 e^2+10 a b d e+3 b^2 d^2\right)-2 c d^2 e (3 a e+5 b d)+93 c^2 d^4\right)}{128 d^4 e^4 \left(d+e x^2\right)}+\frac{x \left(e^2 \left(35 a^2 e^2+10 a b d e+3 b^2 d^2\right)-2 c d^2 e (59 b d-3 a e)+163 c^2 d^4\right)}{192 d^3 e^4 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e^2 \left(35 a^2 e^2+10 a b d e+3 b^2 d^2\right)+2 c d^2 e (3 a e+5 b d)+35 c^2 d^4\right)}{128 d^{9/2} e^{9/2}}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{8 d e^4 \left(d+e x^2\right)^4}-\frac{x \left(-7 a e^2-9 b d e+25 c d^2\right) \left(a e^2-b d e+c d^2\right)}{48 d^2 e^4 \left(d+e x^2\right)^3}","-\frac{x \left(-e^2 \left(35 a^2 e^2+10 a b d e+3 b^2 d^2\right)-2 c d^2 e (3 a e+5 b d)+93 c^2 d^4\right)}{128 d^4 e^4 \left(d+e x^2\right)}+\frac{x \left(e^2 \left(35 a^2 e^2+10 a b d e+3 b^2 d^2\right)-2 c d^2 e (59 b d-3 a e)+163 c^2 d^4\right)}{192 d^3 e^4 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e^2 \left(35 a^2 e^2+10 a b d e+3 b^2 d^2\right)+2 c d^2 e (3 a e+5 b d)+35 c^2 d^4\right)}{128 d^{9/2} e^{9/2}}+\frac{x \left(a e^2-b d e+c d^2\right)^2}{8 d e^4 \left(d+e x^2\right)^4}-\frac{x \left(-7 a e^2-9 b d e+25 c d^2\right) \left(a e^2-b d e+c d^2\right)}{48 d^2 e^4 \left(d+e x^2\right)^3}",1,"((c*d^2 - b*d*e + a*e^2)^2*x)/(8*d*e^4*(d + e*x^2)^4) - ((25*c*d^2 - 9*b*d*e - 7*a*e^2)*(c*d^2 - b*d*e + a*e^2)*x)/(48*d^2*e^4*(d + e*x^2)^3) + ((163*c^2*d^4 - 2*c*d^2*e*(59*b*d - 3*a*e) + e^2*(3*b^2*d^2 + 10*a*b*d*e + 35*a^2*e^2))*x)/(192*d^3*e^4*(d + e*x^2)^2) - ((93*c^2*d^4 - 2*c*d^2*e*(5*b*d + 3*a*e) - e^2*(3*b^2*d^2 + 10*a*b*d*e + 35*a^2*e^2))*x)/(128*d^4*e^4*(d + e*x^2)) + ((35*c^2*d^4 + 2*c*d^2*e*(5*b*d + 3*a*e) + e^2*(3*b^2*d^2 + 10*a*b*d*e + 35*a^2*e^2))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(128*d^(9/2)*e^(9/2))","A",5,4,24,0.1667,1,"{1157, 1814, 385, 205}"
261,1,83,0,0.0933651,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (a e+b d)\right)}{2 d^{3/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 d \left(d+e x^2\right)}+\frac{c x}{e^2}","-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (a e+b d)\right)}{2 d^{3/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 d \left(d+e x^2\right)}+\frac{c x}{e^2}",1,"(c*x)/e^2 + ((a + (d*(c*d - b*e))/e^2)*x)/(2*d*(d + e*x^2)) - ((3*c*d^2 - e*(b*d + a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*e^(5/2))","A",3,3,22,0.1364,1,"{1157, 388, 205}"
262,1,83,0,0.084017,"\int \frac{a+x^2 \left(b+c x^2\right)}{\left(d+e x^2\right)^2} \, dx","Int[(a + x^2*(b + c*x^2))/(d + e*x^2)^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (a e+b d)\right)}{2 d^{3/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 d \left(d+e x^2\right)}+\frac{c x}{e^2}","-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (a e+b d)\right)}{2 d^{3/2} e^{5/2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{2 d \left(d+e x^2\right)}+\frac{c x}{e^2}",1,"(c*x)/e^2 + ((a + (d*(c*d - b*e))/e^2)*x)/(2*d*(d + e*x^2)) - ((3*c*d^2 - e*(b*d + a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*e^(5/2))","A",3,3,23,0.1304,1,"{1814, 388, 205}"
263,1,459,0,1.5370021,"\int \frac{\left(d+e x^2\right)^4}{a+b x^2+c x^4} \, dx","Int[(d + e*x^2)^4/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4}{\sqrt{b^2-4 a c}}+e (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)-\frac{2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4}{\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} c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{e^2 x \left(-c e (a e+4 b d)+b^2 e^2+6 c^2 d^2\right)}{c^3}+\frac{e^3 x^3 (4 c d-b e)}{3 c^2}+\frac{e^4 x^5}{5 c}","\frac{\left(\frac{2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4}{\sqrt{b^2-4 a c}}+e (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)-\frac{2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4}{\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} c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{e^2 x \left(-c e (a e+4 b d)+b^2 e^2+6 c^2 d^2\right)}{c^3}+\frac{e^3 x^3 (4 c d-b e)}{3 c^2}+\frac{e^4 x^5}{5 c}",1,"(e^2*(6*c^2*d^2 + b^2*e^2 - c*e*(4*b*d + a*e))*x)/c^3 + (e^3*(4*c*d - b*e)*x^3)/(3*c^2) + (e^4*x^5)/(5*c) + ((e*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e)) + (2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((e*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e)) - (2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,24,0.1250,1,"{1170, 1166, 205}"
264,1,316,0,0.7855813,"\int \frac{\left(d+e x^2\right)^3}{a+b x^2+c x^4} \, dx","Int[(d + e*x^2)^3/(a + b*x^2 + c*x^4),x]","\frac{\left(e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\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^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)-\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\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} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{e^2 x (3 c d-b e)}{c^2}+\frac{e^3 x^3}{3 c}","\frac{\left(e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\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^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)-\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\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} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{e^2 x (3 c d-b e)}{c^2}+\frac{e^3 x^3}{3 c}",1,"(e^2*(3*c*d - b*e)*x)/c^2 + (e^3*x^3)/(3*c) + ((e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e)) + ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e)))/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]]) + ((e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e)) - ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e)))/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",5,3,24,0.1250,1,"{1170, 1166, 205}"
265,1,238,0,0.6350918,"\int \frac{\left(d+e x^2\right)^2}{a+b x^2+c x^4} \, dx","Int[(d + e*x^2)^2/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\sqrt{b^2-4 a c}}+e (2 c d-b e)\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(e (2 c d-b e)-\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\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} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{e^2 x}{c}","\frac{\left(\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\sqrt{b^2-4 a c}}+e (2 c d-b e)\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(e (2 c d-b e)-\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{\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} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{e^2 x}{c}",1,"(e^2*x)/c + ((e*(2*c*d - b*e) + (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))/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]]) + ((e*(2*c*d - b*e) - (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))/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",5,3,24,0.1250,1,"{1170, 1166, 205}"
266,1,174,0,0.2016061,"\int \frac{d+e x^2}{a+b x^2+c x^4} \, dx","Int[(d + e*x^2)/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e-\frac{2 c d-b e}{\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} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(e-\frac{2 c d-b e}{\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} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"((e + (2*c*d - b*e)/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 - Sqrt[b^2 - 4*a*c]]) + ((e - (2*c*d - b*e)/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 + Sqrt[b^2 - 4*a*c]])","A",3,2,22,0.09091,1,"{1166, 205}"
267,1,150,0,0.0982543,"\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}"
268,1,254,0,0.5855949,"\int \frac{1}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[1/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(e-\frac{2 c d-b e}{\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} \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2-b d e+c d^2\right)}","-\frac{\sqrt{c} \left(e-\frac{2 c d-b e}{\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} \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2-b d e+c d^2\right)}",1,"-((Sqrt[c]*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2))) - (Sqrt[c]*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) + (e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*(c*d^2 - b*d*e + a*e^2))","A",6,3,24,0.1250,1,"{1170, 205, 1166}"
269,1,429,0,1.4145022,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right)} \, dx","Int[1/((d + e*x^2)^2*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)^2}+\frac{e^2 x}{2 d \left(d+e x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{e^{3/2} (2 c d-b e) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2-b d e+c d^2\right)^2}","\frac{\sqrt{c} \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)^2}+\frac{e^2 x}{2 d \left(d+e x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{2 d^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{e^{3/2} (2 c d-b e) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2-b d e+c d^2\right)^2}",1,"(e^2*x)/(2*d*(c*d^2 - b*d*e + a*e^2)*(d + e*x^2)) + (Sqrt[c]*(2*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d + Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)^2) - (Sqrt[c]*(2*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d - Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)^2) + (e^(3/2)*(2*c*d - b*e)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*(c*d^2 - b*d*e + a*e^2)^2) + (e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*(c*d^2 - b*d*e + a*e^2))","A",8,4,24,0.1667,1,"{1170, 199, 205, 1166}"
270,1,563,0,3.5185836,"\int \frac{\left(d+e x^2\right)^3}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2)^3/(a + b*x^2 + c*x^4)^2,x]","-\frac{\left(-b^2 \left(a e^3 \sqrt{b^2-4 a c}-3 a c d e^2+c^2 d^3\right)+6 a c \left(a e^2+c d^2\right) \left(e \sqrt{b^2-4 a c}+2 c d\right)-b c \left(c d^2 \left(d \sqrt{b^2-4 a c}+12 a e\right)+a e^2 \left(3 d \sqrt{b^2-4 a c}+8 a e\right)\right)+a b^3 e^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(-b^2 \left(-a e^3 \sqrt{b^2-4 a c}-3 a c d e^2+c^2 d^3\right)+6 a c \left(a e^2+c d^2\right) \left(2 c d-e \sqrt{b^2-4 a c}\right)+b c \left(c d^2 \left(d \sqrt{b^2-4 a c}-12 a e\right)+a e^2 \left(3 d \sqrt{b^2-4 a c}-8 a e\right)\right)+a b^3 e^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(c \left(-\frac{a b e \left(a e^2+3 c d^2\right)}{c}-2 a d \left(c d^2-3 a e^2\right)+b^2 d^3\right)-x^2 \left(a b^2 e^3-b c d \left(3 a e^2+c d^2\right)+2 a c e \left(3 c d^2-a e^2\right)\right)\right)}{2 a c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{\left(-b^2 \left(a e^3 \sqrt{b^2-4 a c}-3 a c d e^2+c^2 d^3\right)+6 a c \left(a e^2+c d^2\right) \left(e \sqrt{b^2-4 a c}+2 c d\right)-b c \left(c d^2 \left(d \sqrt{b^2-4 a c}+12 a e\right)+a e^2 \left(3 d \sqrt{b^2-4 a c}+8 a e\right)\right)+a b^3 e^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(-b^2 \left(-a e^3 \sqrt{b^2-4 a c}-3 a c d e^2+c^2 d^3\right)+6 a c \left(a e^2+c d^2\right) \left(2 c d-e \sqrt{b^2-4 a c}\right)+b c \left(c d^2 \left(d \sqrt{b^2-4 a c}-12 a e\right)+a e^2 \left(3 d \sqrt{b^2-4 a c}-8 a e\right)\right)+a b^3 e^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(c \left(-\frac{a b e \left(a e^2+3 c d^2\right)}{c}-2 a d \left(c d^2-3 a e^2\right)+b^2 d^3\right)-x^2 \left(a b^2 e^3-b c d \left(3 a e^2+c d^2\right)+2 a c e \left(3 c d^2-a e^2\right)\right)\right)}{2 a c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"(x*(c*(b^2*d^3 - 2*a*d*(c*d^2 - 3*a*e^2) - (a*b*e*(3*c*d^2 + a*e^2))/c) - (a*b^2*e^3 + 2*a*c*e*(3*c*d^2 - a*e^2) - b*c*d*(c*d^2 + 3*a*e^2))*x^2))/(2*a*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((a*b^3*e^3 + 6*a*c*(2*c*d + Sqrt[b^2 - 4*a*c]*e)*(c*d^2 + a*e^2) - b^2*(c^2*d^3 - 3*a*c*d*e^2 + a*Sqrt[b^2 - 4*a*c]*e^3) - b*c*(a*e^2*(3*Sqrt[b^2 - 4*a*c]*d + 8*a*e) + c*d^2*(Sqrt[b^2 - 4*a*c]*d + 12*a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*c^(3/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((a*b^3*e^3 + 6*a*c*(2*c*d - Sqrt[b^2 - 4*a*c]*e)*(c*d^2 + a*e^2) - b^2*(c^2*d^3 - 3*a*c*d*e^2 - a*Sqrt[b^2 - 4*a*c]*e^3) + b*c*(c*d^2*(Sqrt[b^2 - 4*a*c]*d - 12*a*e) + a*e^2*(3*Sqrt[b^2 - 4*a*c]*d - 8*a*e)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*c^(3/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,24,0.1250,1,"{1205, 1166, 205}"
271,1,386,0,2.0785514,"\int \frac{\left(d+e x^2\right)^2}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2)^2/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(x^2 \left(a b e^2-4 a c d e+b c d^2\right)-2 a b d e-2 a \left(c d^2-a e^2\right)+b^2 d^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(\frac{b^2 \left(c d^2-a e^2\right)+8 a b c d e-4 a c \left(a e^2+3 c d^2\right)}{\sqrt{b^2-4 a c}}+a b e^2-4 a c d e+b c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(-\frac{b^2 \left(c d^2-a e^2\right)+8 a b c d e-4 a c \left(a e^2+3 c d^2\right)}{\sqrt{b^2-4 a c}}+a b e^2-4 a c d e+b c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(x^2 \left(a b e^2-4 a c d e+b c d^2\right)-2 a b d e-2 a \left(c d^2-a e^2\right)+b^2 d^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(\frac{b^2 \left(c d^2-a e^2\right)+8 a b c d e-4 a c \left(a e^2+3 c d^2\right)}{\sqrt{b^2-4 a c}}+a b e^2-4 a c d e+b c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(-\frac{b^2 \left(c d^2-a e^2\right)+8 a b c d e-4 a c \left(a e^2+3 c d^2\right)}{\sqrt{b^2-4 a c}}+a b e^2-4 a c d e+b c d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(b^2*d^2 - 2*a*b*d*e - 2*a*(c*d^2 - a*e^2) + (b*c*d^2 - 4*a*c*d*e + a*b*e^2)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (8*a*b*c*d*e + b^2*(c*d^2 - a*e^2) - 4*a*c*(3*c*d^2 + a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (8*a*b*c*d*e + b^2*(c*d^2 - a*e^2) - 4*a*c*(3*c*d^2 + a*e^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,24,0.1250,1,"{1205, 1166, 205}"
272,1,293,0,0.7890194,"\int \frac{d+e x^2}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x^2)/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(c x^2 (b d-2 a e)-a b e-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b e-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a e+b d\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) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b e-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a e+b d\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) \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{x \left(c x^2 (b d-2 a e)-a b e-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b e-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a e+b d\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) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b e-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a e+b d\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) \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(x*(b^2*d - 2*a*c*d - a*b*e + c*(b*d - 2*a*e)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b*d - 2*a*e + (b^2*d - 12*a*c*d + 4*a*b*e)/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)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(b*d - 2*a*e - (b^2*d - 12*a*c*d + 4*a*b*e)/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)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,22,0.1364,1,"{1178, 1166, 205}"
273,1,252,0,0.5165923,"\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}"
274,1,660,0,2.8725157,"\int \frac{1}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)^2} \, dx","Int[1/((d + e*x^2)*(a + b*x^2 + c*x^4)^2),x]","\frac{x \left(c x^2 \left(2 a c e+b^2 (-e)+b c d\right)+3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right) \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} \left(\frac{8 a b c e-12 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+2 a c e+b^2 (-e)+b c d\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) \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} \left(-\frac{8 a b c e-12 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+2 a c e+b^2 (-e)+b c d\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) \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e^2 \left(e-\frac{2 c d-b e}{\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} \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} e^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)^2}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2-b d e+c d^2\right)^2}","\frac{x \left(c x^2 \left(2 a c e+b^2 (-e)+b c d\right)+3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right) \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} \left(\frac{8 a b c e-12 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+2 a c e+b^2 (-e)+b c d\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) \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} \left(-\frac{8 a b c e-12 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+2 a c e+b^2 (-e)+b c d\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) \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e^2 \left(e-\frac{2 c d-b e}{\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} \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} e^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)^2}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \left(a e^2-b d e+c d^2\right)^2}",1,"(x*(b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e + c*(b*c*d - b^2*e + 2*a*c*e)*x^2))/(2*a*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x^2 + c*x^4)) - (Sqrt[c]*e^2*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)^2) + (Sqrt[c]*(b*c*d - b^2*e + 2*a*c*e + (b^2*c*d - 12*a*c^2*d - b^3*e + 8*a*b*c*e)/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)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) - (Sqrt[c]*e^2*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)^2) + (Sqrt[c]*(b*c*d - b^2*e + 2*a*c*e - (b^2*c*d - 12*a*c^2*d - b^3*e + 8*a*b*c*e)/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)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*(c*d^2 - b*d*e + a*e^2)^2)","A",10,4,24,0.1667,1,"{1238, 205, 1178, 1166}"
275,1,1077,0,12.6389341,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right)^2} \, dx","Int[1/((d + e*x^2)^2*(a + b*x^2 + c*x^4)^2),x]","\frac{x e^4}{2 d \left(c d^2-b e d+a e^2\right)^2 \left(e x^2+d\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{2 d^{3/2} \left(c d^2-b e d+a e^2\right)^2}+\frac{2 (2 c d-b e) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{\sqrt{d} \left(c d^2-b e d+a e^2\right)^3}+\frac{\sqrt{2} \sqrt{c} \left(3 c^2 d^2+b \left(b+\sqrt{b^2-4 a c}\right) e^2-c e \left(3 b d+2 \sqrt{b^2-4 a c} d+a e\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) e^2}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \left(c d^2-b e d+a e^2\right)^3}-\frac{\sqrt{2} \sqrt{c} \left(3 c^2 d^2+b \left(b-\sqrt{b^2-4 a c}\right) e^2-c e \left(3 b d-2 \sqrt{b^2-4 a c} d+a e\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2-4 a c}}}\right) e^2}{\sqrt{b^2-4 a c} \sqrt{b+\sqrt{b^2-4 a c}} \left(c d^2-b e d+a e^2\right)^3}+\frac{\sqrt{c} \left(e^2 b^4-e \left(2 c d-\sqrt{b^2-4 a c} e\right) b^3+c \left(c d^2-e \left(2 \sqrt{b^2-4 a c} d+9 a e\right)\right) b^2-c \left(3 a \sqrt{b^2-4 a c} e^2-c d \left(\sqrt{b^2-4 a c} d+16 a e\right)\right) b-4 a c^2 \left(3 c d^2-e \left(\sqrt{b^2-4 a c} d+3 a e\right)\right)\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}} \left(c d^2-b e d+a e^2\right)^2}-\frac{\sqrt{c} \left(e^2 b^4-e \left(2 c d+\sqrt{b^2-4 a c} e\right) b^3+c \left(c d^2+e \left(2 \sqrt{b^2-4 a c} d-9 a e\right)\right) b^2+c \left(3 a \sqrt{b^2-4 a c} e^2-c d \left(\sqrt{b^2-4 a c} d-16 a e\right)\right) b-4 a c^2 \left(3 c d^2+e \left(\sqrt{b^2-4 a c} d-3 a e\right)\right)\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}} \left(c d^2-b e d+a e^2\right)^2}+\frac{x \left(-c \left(-e^2 b^3+2 c d e b^2-c \left(c d^2-3 a e^2\right) b-4 a c^2 d e\right) x^2+a b c e (2 c d-b e)+\left(b^2-2 a c\right) \left(c^2 d^2+b^2 e^2-c e (2 b d+a e)\right)\right)}{2 a \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)^2 \left(c x^4+b x^2+a\right)}","\frac{x e^4}{2 d \left(c d^2-b e d+a e^2\right)^2 \left(e x^2+d\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{2 d^{3/2} \left(c d^2-b e d+a e^2\right)^2}+\frac{2 (2 c d-b e) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) e^{7/2}}{\sqrt{d} \left(c d^2-b e d+a e^2\right)^3}+\frac{\sqrt{2} \sqrt{c} \left(3 c^2 d^2+b \left(b+\sqrt{b^2-4 a c}\right) e^2-c e \left(3 b d+2 \sqrt{b^2-4 a c} d+a e\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) e^2}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \left(c d^2-b e d+a e^2\right)^3}-\frac{\sqrt{2} \sqrt{c} \left(3 c^2 d^2+b \left(b-\sqrt{b^2-4 a c}\right) e^2-c e \left(3 b d-2 \sqrt{b^2-4 a c} d+a e\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2-4 a c}}}\right) e^2}{\sqrt{b^2-4 a c} \sqrt{b+\sqrt{b^2-4 a c}} \left(c d^2-b e d+a e^2\right)^3}+\frac{\sqrt{c} \left(e^2 b^4-e \left(2 c d-\sqrt{b^2-4 a c} e\right) b^3+c \left(c d^2-e \left(2 \sqrt{b^2-4 a c} d+9 a e\right)\right) b^2-c \left(3 a \sqrt{b^2-4 a c} e^2-c d \left(\sqrt{b^2-4 a c} d+16 a e\right)\right) b-4 a c^2 \left(3 c d^2-e \left(\sqrt{b^2-4 a c} d+3 a e\right)\right)\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}} \left(c d^2-b e d+a e^2\right)^2}-\frac{\sqrt{c} \left(e^2 b^4-e \left(2 c d+\sqrt{b^2-4 a c} e\right) b^3+c \left(c d^2+e \left(2 \sqrt{b^2-4 a c} d-9 a e\right)\right) b^2+c \left(3 a \sqrt{b^2-4 a c} e^2-c d \left(\sqrt{b^2-4 a c} d-16 a e\right)\right) b-4 a c^2 \left(3 c d^2+e \left(\sqrt{b^2-4 a c} d-3 a e\right)\right)\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}} \left(c d^2-b e d+a e^2\right)^2}+\frac{x \left(-c \left(-e^2 b^3+2 c d e b^2-c \left(c d^2-3 a e^2\right) b-4 a c^2 d e\right) x^2+a b c e (2 c d-b e)+\left(b^2-2 a c\right) \left(c^2 d^2+b^2 e^2-c e (2 b d+a e)\right)\right)}{2 a \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right)^2 \left(c x^4+b x^2+a\right)}",1,"(e^4*x)/(2*d*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x^2)) + (x*(a*b*c*e*(2*c*d - b*e) + (b^2 - 2*a*c)*(c^2*d^2 + b^2*e^2 - c*e*(2*b*d + a*e)) - c*(2*b^2*c*d*e - 4*a*c^2*d*e - b^3*e^2 - b*c*(c*d^2 - 3*a*e^2))*x^2))/(2*a*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x^2 + c*x^4)) + (Sqrt[2]*Sqrt[c]*e^2*(3*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - c*e*(3*b*d + 2*Sqrt[b^2 - 4*a*c]*d + a*e))*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]]*(c*d^2 - b*d*e + a*e^2)^3) + (Sqrt[c]*(b^4*e^2 - b^3*e*(2*c*d - Sqrt[b^2 - 4*a*c]*e) - 4*a*c^2*(3*c*d^2 - e*(Sqrt[b^2 - 4*a*c]*d + 3*a*e)) + b^2*c*(c*d^2 - e*(2*Sqrt[b^2 - 4*a*c]*d + 9*a*e)) - b*c*(3*a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 16*a*e)))*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]]*(c*d^2 - b*d*e + a*e^2)^2) - (Sqrt[2]*Sqrt[c]*e^2*(3*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - c*e*(3*b*d - 2*Sqrt[b^2 - 4*a*c]*d + a*e))*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]]*(c*d^2 - b*d*e + a*e^2)^3) - (Sqrt[c]*(b^4*e^2 - b^3*e*(2*c*d + Sqrt[b^2 - 4*a*c]*e) + b*c*(3*a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 16*a*e)) + b^2*c*(c*d^2 + e*(2*Sqrt[b^2 - 4*a*c]*d - 9*a*e)) - 4*a*c^2*(3*c*d^2 + e*(Sqrt[b^2 - 4*a*c]*d - 3*a*e)))*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]]*(c*d^2 - b*d*e + a*e^2)^2) + (2*e^(7/2)*(2*c*d - b*e)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*(c*d^2 - b*d*e + a*e^2)^3) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(3/2)*(c*d^2 - b*d*e + a*e^2)^2)","A",12,5,24,0.2083,1,"{1238, 199, 205, 1178, 1166}"
276,1,215,0,0.1608639,"\int \left(d+e x^2\right)^{5/2} \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x^2)^(5/2)*(a + b*x^2 + c*x^4),x]","\frac{x \left(d+e x^2\right)^{5/2} \left(80 a e^2-10 b d e+3 c d^2\right)}{480 e^2}+\frac{d x \left(d+e x^2\right)^{3/2} \left(80 a e^2-10 b d e+3 c d^2\right)}{384 e^2}+\frac{d^2 x \sqrt{d+e x^2} \left(80 a e^2-10 b d e+3 c d^2\right)}{256 e^2}+\frac{d^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(80 a e^2-10 b d e+3 c d^2\right)}{256 e^{5/2}}-\frac{x \left(d+e x^2\right)^{7/2} (3 c d-10 b e)}{80 e^2}+\frac{c x^3 \left(d+e x^2\right)^{7/2}}{10 e}","\frac{x \left(d+e x^2\right)^{5/2} \left(80 a e^2-10 b d e+3 c d^2\right)}{480 e^2}+\frac{d x \left(d+e x^2\right)^{3/2} \left(80 a e^2-10 b d e+3 c d^2\right)}{384 e^2}+\frac{d^2 x \sqrt{d+e x^2} \left(80 a e^2-10 b d e+3 c d^2\right)}{256 e^2}+\frac{d^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(80 a e^2-10 b d e+3 c d^2\right)}{256 e^{5/2}}-\frac{x \left(d+e x^2\right)^{7/2} (3 c d-10 b e)}{80 e^2}+\frac{c x^3 \left(d+e x^2\right)^{7/2}}{10 e}",1,"(d^2*(3*c*d^2 - 10*b*d*e + 80*a*e^2)*x*Sqrt[d + e*x^2])/(256*e^2) + (d*(3*c*d^2 - 10*b*d*e + 80*a*e^2)*x*(d + e*x^2)^(3/2))/(384*e^2) + ((3*c*d^2 - 10*b*d*e + 80*a*e^2)*x*(d + e*x^2)^(5/2))/(480*e^2) - ((3*c*d - 10*b*e)*x*(d + e*x^2)^(7/2))/(80*e^2) + (c*x^3*(d + e*x^2)^(7/2))/(10*e) + (d^3*(3*c*d^2 - 10*b*d*e + 80*a*e^2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(256*e^(5/2))","A",7,5,24,0.2083,1,"{1159, 388, 195, 217, 206}"
277,1,175,0,0.121627,"\int \left(d+e x^2\right)^{3/2} \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x^2)^(3/2)*(a + b*x^2 + c*x^4),x]","\frac{x \left(d+e x^2\right)^{3/2} \left(48 a e^2-8 b d e+3 c d^2\right)}{192 e^2}+\frac{d x \sqrt{d+e x^2} \left(48 a e^2-8 b d e+3 c d^2\right)}{128 e^2}+\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(48 a e^2-8 b d e+3 c d^2\right)}{128 e^{5/2}}-\frac{x \left(d+e x^2\right)^{5/2} (3 c d-8 b e)}{48 e^2}+\frac{c x^3 \left(d+e x^2\right)^{5/2}}{8 e}","\frac{x \left(d+e x^2\right)^{3/2} \left(48 a e^2-8 b d e+3 c d^2\right)}{192 e^2}+\frac{d x \sqrt{d+e x^2} \left(48 a e^2-8 b d e+3 c d^2\right)}{128 e^2}+\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(48 a e^2-8 b d e+3 c d^2\right)}{128 e^{5/2}}-\frac{x \left(d+e x^2\right)^{5/2} (3 c d-8 b e)}{48 e^2}+\frac{c x^3 \left(d+e x^2\right)^{5/2}}{8 e}",1,"(d*(3*c*d^2 - 8*b*d*e + 48*a*e^2)*x*Sqrt[d + e*x^2])/(128*e^2) + ((3*c*d^2 - 8*b*d*e + 48*a*e^2)*x*(d + e*x^2)^(3/2))/(192*e^2) - ((3*c*d - 8*b*e)*x*(d + e*x^2)^(5/2))/(48*e^2) + (c*x^3*(d + e*x^2)^(5/2))/(8*e) + (d^2*(3*c*d^2 - 8*b*d*e + 48*a*e^2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(128*e^(5/2))","A",6,5,24,0.2083,1,"{1159, 388, 195, 217, 206}"
278,1,132,0,0.1092179,"\int \sqrt{d+e x^2} \left(a+b x^2+c x^4\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4),x]","\frac{x \sqrt{d+e x^2} \left(8 a e^2-2 b d e+c d^2\right)}{16 e^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(8 a e^2-2 b d e+c d^2\right)}{16 e^{5/2}}-\frac{x \left(d+e x^2\right)^{3/2} (c d-2 b e)}{8 e^2}+\frac{c x^3 \left(d+e x^2\right)^{3/2}}{6 e}","\frac{x \sqrt{d+e x^2} \left(8 a e^2-2 b d e+c d^2\right)}{16 e^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(8 a e^2-2 b d e+c d^2\right)}{16 e^{5/2}}-\frac{x \left(d+e x^2\right)^{3/2} (c d-2 b e)}{8 e^2}+\frac{c x^3 \left(d+e x^2\right)^{3/2}}{6 e}",1,"((c*d^2 - 2*b*d*e + 8*a*e^2)*x*Sqrt[d + e*x^2])/(16*e^2) - ((c*d - 2*b*e)*x*(d + e*x^2)^(3/2))/(8*e^2) + (c*x^3*(d + e*x^2)^(3/2))/(6*e) + (d*(c*d^2 - 2*b*d*e + 8*a*e^2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(16*e^(5/2))","A",5,5,24,0.2083,1,"{1159, 388, 195, 217, 206}"
279,1,97,0,0.0613475,"\int \frac{a+b x^2+c x^4}{\sqrt{d+e x^2}} \, dx","Int[(a + b*x^2 + c*x^4)/Sqrt[d + e*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(8 a e^2-4 b d e+3 c d^2\right)}{8 e^{5/2}}-\frac{x \sqrt{d+e x^2} (3 c d-4 b e)}{8 e^2}+\frac{c x^3 \sqrt{d+e x^2}}{4 e}","\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(8 a e^2-4 b d e+3 c d^2\right)}{8 e^{5/2}}-\frac{x \sqrt{d+e x^2} (3 c d-4 b e)}{8 e^2}+\frac{c x^3 \sqrt{d+e x^2}}{4 e}",1,"-((3*c*d - 4*b*e)*x*Sqrt[d + e*x^2])/(8*e^2) + (c*x^3*Sqrt[d + e*x^2])/(4*e) + ((3*c*d^2 - 4*b*d*e + 8*a*e^2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(8*e^(5/2))","A",4,4,24,0.1667,1,"{1159, 388, 217, 206}"
280,1,89,0,0.0726533,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^(3/2),x]","\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{d \sqrt{d+e x^2}}-\frac{(3 c d-2 b e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 e^{5/2}}+\frac{c x \sqrt{d+e x^2}}{2 e^2}","\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{d \sqrt{d+e x^2}}-\frac{(3 c d-2 b e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 e^{5/2}}+\frac{c x \sqrt{d+e x^2}}{2 e^2}",1,"((a + (d*(c*d - b*e))/e^2)*x)/(d*Sqrt[d + e*x^2]) + (c*x*Sqrt[d + e*x^2])/(2*e^2) - ((3*c*d - 2*b*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*e^(5/2))","A",4,4,24,0.1667,1,"{1157, 388, 217, 206}"
281,1,101,0,0.0713267,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^(5/2),x]","-\frac{x \left(4 c d^2-e (2 a e+b d)\right)}{3 d^2 e^2 \sqrt{d+e x^2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{e^{5/2}}","-\frac{x \left(4 c d^2-e (2 a e+b d)\right)}{3 d^2 e^2 \sqrt{d+e x^2}}+\frac{x \left(a+\frac{d (c d-b e)}{e^2}\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{e^{5/2}}",1,"((a + (d*(c*d - b*e))/e^2)*x)/(3*d*(d + e*x^2)^(3/2)) - ((4*c*d^2 - e*(b*d + 2*a*e))*x)/(3*d^2*e^2*Sqrt[d + e*x^2]) + (c*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/e^(5/2)","A",4,4,24,0.1667,1,"{1157, 385, 217, 206}"
282,1,86,0,0.1070518,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^{7/2}} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^(7/2),x]","\frac{x^5 \left(2 e (4 a e+b d)+3 c d^2\right)}{15 d^3 \left(d+e x^2\right)^{5/2}}+\frac{x^3 (4 a e+b d)}{3 d^2 \left(d+e x^2\right)^{5/2}}+\frac{a x}{d \left(d+e x^2\right)^{5/2}}","\frac{x^5 \left(2 e (4 a e+b d)+3 c d^2\right)}{15 d^3 \left(d+e x^2\right)^{5/2}}+\frac{x^3 (4 a e+b d)}{3 d^2 \left(d+e x^2\right)^{5/2}}+\frac{a x}{d \left(d+e x^2\right)^{5/2}}",1,"(a*x)/(d*(d + e*x^2)^(5/2)) + ((b*d + 4*a*e)*x^3)/(3*d^2*(d + e*x^2)^(5/2)) + ((3*c*d^2 + 2*e*(b*d + 4*a*e))*x^5)/(15*d^3*(d + e*x^2)^(5/2))","A",4,4,24,0.1667,1,"{1155, 1803, 12, 264}"
283,1,126,0,0.1463894,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^{9/2}} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^(9/2),x]","\frac{2 e x^7 \left(4 e (6 a e+b d)+3 c d^2\right)}{105 d^4 \left(d+e x^2\right)^{7/2}}+\frac{x^5 \left(4 e (6 a e+b d)+3 c d^2\right)}{15 d^3 \left(d+e x^2\right)^{7/2}}+\frac{x^3 (6 a e+b d)}{3 d^2 \left(d+e x^2\right)^{7/2}}+\frac{a x}{d \left(d+e x^2\right)^{7/2}}","\frac{2 e x^7 \left(4 e (6 a e+b d)+3 c d^2\right)}{105 d^4 \left(d+e x^2\right)^{7/2}}+\frac{x^5 \left(4 e (6 a e+b d)+3 c d^2\right)}{15 d^3 \left(d+e x^2\right)^{7/2}}+\frac{x^3 (6 a e+b d)}{3 d^2 \left(d+e x^2\right)^{7/2}}+\frac{a x}{d \left(d+e x^2\right)^{7/2}}",1,"(a*x)/(d*(d + e*x^2)^(7/2)) + ((b*d + 6*a*e)*x^3)/(3*d^2*(d + e*x^2)^(7/2)) + ((3*c*d^2 + 4*e*(b*d + 6*a*e))*x^5)/(15*d^3*(d + e*x^2)^(7/2)) + (2*e*(3*c*d^2 + 4*e*(b*d + 6*a*e))*x^7)/(105*d^4*(d + e*x^2)^(7/2))","A",5,5,24,0.2083,1,"{1155, 1803, 12, 271, 264}"
284,1,164,0,0.2100357,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^{11/2}} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^(11/2),x]","\frac{8 e^2 x^9 \left(2 e (8 a e+b d)+c d^2\right)}{315 d^5 \left(d+e x^2\right)^{9/2}}+\frac{4 e x^7 \left(2 e (8 a e+b d)+c d^2\right)}{35 d^4 \left(d+e x^2\right)^{9/2}}+\frac{x^5 \left(\frac{2 e (8 a e+b d)}{d^2}+c\right)}{5 d \left(d+e x^2\right)^{9/2}}+\frac{x^3 (8 a e+b d)}{3 d^2 \left(d+e x^2\right)^{9/2}}+\frac{a x}{d \left(d+e x^2\right)^{9/2}}","\frac{8 e^2 x^9 \left(2 e (8 a e+b d)+c d^2\right)}{315 d^5 \left(d+e x^2\right)^{9/2}}+\frac{4 e x^7 \left(2 e (8 a e+b d)+c d^2\right)}{35 d^4 \left(d+e x^2\right)^{9/2}}+\frac{x^5 \left(2 e (8 a e+b d)+c d^2\right)}{5 d^3 \left(d+e x^2\right)^{9/2}}+\frac{x^3 (8 a e+b d)}{3 d^2 \left(d+e x^2\right)^{9/2}}+\frac{a x}{d \left(d+e x^2\right)^{9/2}}",1,"(a*x)/(d*(d + e*x^2)^(9/2)) + ((b*d + 8*a*e)*x^3)/(3*d^2*(d + e*x^2)^(9/2)) + ((c + (2*e*(b*d + 8*a*e))/d^2)*x^5)/(5*d*(d + e*x^2)^(9/2)) + (4*e*(c*d^2 + 2*e*(b*d + 8*a*e))*x^7)/(35*d^4*(d + e*x^2)^(9/2)) + (8*e^2*(c*d^2 + 2*e*(b*d + 8*a*e))*x^9)/(315*d^5*(d + e*x^2)^(9/2))","A",6,5,24,0.2083,1,"{1155, 1803, 12, 271, 264}"
285,1,210,0,0.2215366,"\int \frac{a+b x^2+c x^4}{\left(d+e x^2\right)^{13/2}} \, dx","Int[(a + b*x^2 + c*x^4)/(d + e*x^2)^(13/2),x]","\frac{16 e^3 x^{11} \left(8 e (10 a e+b d)+3 c d^2\right)}{3465 d^6 \left(d+e x^2\right)^{11/2}}+\frac{8 e^2 x^9 \left(8 e (10 a e+b d)+3 c d^2\right)}{315 d^5 \left(d+e x^2\right)^{11/2}}+\frac{2 e x^7 \left(8 e (10 a e+b d)+3 c d^2\right)}{35 d^4 \left(d+e x^2\right)^{11/2}}+\frac{x^5 \left(8 e (10 a e+b d)+3 c d^2\right)}{15 d^3 \left(d+e x^2\right)^{11/2}}+\frac{x^3 (10 a e+b d)}{3 d^2 \left(d+e x^2\right)^{11/2}}+\frac{a x}{d \left(d+e x^2\right)^{11/2}}","\frac{16 e^3 x^{11} \left(8 e (10 a e+b d)+3 c d^2\right)}{3465 d^6 \left(d+e x^2\right)^{11/2}}+\frac{8 e^2 x^9 \left(8 e (10 a e+b d)+3 c d^2\right)}{315 d^5 \left(d+e x^2\right)^{11/2}}+\frac{2 e x^7 \left(8 e (10 a e+b d)+3 c d^2\right)}{35 d^4 \left(d+e x^2\right)^{11/2}}+\frac{x^5 \left(8 e (10 a e+b d)+3 c d^2\right)}{15 d^3 \left(d+e x^2\right)^{11/2}}+\frac{x^3 (10 a e+b d)}{3 d^2 \left(d+e x^2\right)^{11/2}}+\frac{a x}{d \left(d+e x^2\right)^{11/2}}",1,"(a*x)/(d*(d + e*x^2)^(11/2)) + ((b*d + 10*a*e)*x^3)/(3*d^2*(d + e*x^2)^(11/2)) + ((3*c*d^2 + 8*e*(b*d + 10*a*e))*x^5)/(15*d^3*(d + e*x^2)^(11/2)) + (2*e*(3*c*d^2 + 8*e*(b*d + 10*a*e))*x^7)/(35*d^4*(d + e*x^2)^(11/2)) + (8*e^2*(3*c*d^2 + 8*e*(b*d + 10*a*e))*x^9)/(315*d^5*(d + e*x^2)^(11/2)) + (16*e^3*(3*c*d^2 + 8*e*(b*d + 10*a*e))*x^11)/(3465*d^6*(d + e*x^2)^(11/2))","A",7,5,24,0.2083,1,"{1155, 1803, 12, 271, 264}"
286,1,193,0,0.0987772,"\int \left(7+5 x^2\right)^3 \sqrt{2+3 x^2+x^4} \, dx","Int[(7 + 5*x^2)^3*Sqrt[2 + 3*x^2 + x^4],x]","\frac{125}{9} \left(x^4+3 x^2+2\right)^{3/2} x^3+\frac{275}{7} \left(x^4+3 x^2+2\right)^{3/2} x+\frac{1}{21} \left(757 x^2+2608\right) \sqrt{x^4+3 x^2+2} x+\frac{577 \left(x^2+2\right) x}{3 \sqrt{x^4+3 x^2+2}}+\frac{2945 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{21 \sqrt{x^4+3 x^2+2}}-\frac{577 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}","\frac{125}{9} \left(x^4+3 x^2+2\right)^{3/2} x^3+\frac{275}{7} \left(x^4+3 x^2+2\right)^{3/2} x+\frac{1}{21} \left(757 x^2+2608\right) \sqrt{x^4+3 x^2+2} x+\frac{577 \left(x^2+2\right) x}{3 \sqrt{x^4+3 x^2+2}}+\frac{2945 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{21 \sqrt{x^4+3 x^2+2}}-\frac{577 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}",1,"(577*x*(2 + x^2))/(3*Sqrt[2 + 3*x^2 + x^4]) + (x*(2608 + 757*x^2)*Sqrt[2 + 3*x^2 + x^4])/21 + (275*x*(2 + 3*x^2 + x^4)^(3/2))/7 + (125*x^3*(2 + 3*x^2 + x^4)^(3/2))/9 - (577*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(3*Sqrt[2 + 3*x^2 + x^4]) + (2945*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(21*Sqrt[2 + 3*x^2 + x^4])","A",6,6,24,0.2500,1,"{1206, 1679, 1176, 1189, 1099, 1135}"
287,1,168,0,0.0677099,"\int \left(7+5 x^2\right)^2 \sqrt{2+3 x^2+x^4} \, dx","Int[(7 + 5*x^2)^2*Sqrt[2 + 3*x^2 + x^4],x]","\frac{25}{7} x \left(x^4+3 x^2+2\right)^{3/2}+\frac{1}{21} x \left(114 x^2+407\right) \sqrt{x^4+3 x^2+2}+\frac{31 x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}+\frac{472 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{21 \sqrt{x^4+3 x^2+2}}-\frac{31 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}","\frac{25}{7} x \left(x^4+3 x^2+2\right)^{3/2}+\frac{1}{21} x \left(114 x^2+407\right) \sqrt{x^4+3 x^2+2}+\frac{31 x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}+\frac{472 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{21 \sqrt{x^4+3 x^2+2}}-\frac{31 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}",1,"(31*x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] + (x*(407 + 114*x^2)*Sqrt[2 + 3*x^2 + x^4])/21 + (25*x*(2 + 3*x^2 + x^4)^(3/2))/7 - (31*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + (472*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(21*Sqrt[2 + 3*x^2 + x^4])","A",5,5,24,0.2083,1,"{1206, 1176, 1189, 1099, 1135}"
288,1,149,0,0.0475073,"\int \left(7+5 x^2\right) \sqrt{2+3 x^2+x^4} \, dx","Int[(7 + 5*x^2)*Sqrt[2 + 3*x^2 + x^4],x]","\frac{5 x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}+\frac{1}{3} x \left(3 x^2+10\right) \sqrt{x^4+3 x^2+2}+\frac{11 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}-\frac{5 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}","\frac{5 x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}+\frac{1}{3} x \left(3 x^2+10\right) \sqrt{x^4+3 x^2+2}+\frac{11 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}-\frac{5 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}",1,"(5*x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] + (x*(10 + 3*x^2)*Sqrt[2 + 3*x^2 + x^4])/3 - (5*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + (11*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(3*Sqrt[2 + 3*x^2 + x^4])","A",4,4,22,0.1818,1,"{1176, 1189, 1099, 1135}"
289,1,141,0,0.0423545,"\int \sqrt{2+3 x^2+x^4} \, dx","Int[Sqrt[2 + 3*x^2 + x^4],x]","\frac{1}{3} \sqrt{x^4+3 x^2+2} x+\frac{\left(x^2+2\right) x}{\sqrt{x^4+3 x^2+2}}+\frac{2 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}","\frac{1}{3} \sqrt{x^4+3 x^2+2} x+\frac{\left(x^2+2\right) x}{\sqrt{x^4+3 x^2+2}}+\frac{2 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}",1,"(x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] + (x*Sqrt[2 + 3*x^2 + x^4])/3 - (Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + (2*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(3*Sqrt[2 + 3*x^2 + x^4])","A",4,4,14,0.2857,1,"{1091, 1189, 1099, 1135}"
290,1,232,0,0.1237878,"\int \frac{\sqrt{2+3 x^2+x^4}}{7+5 x^2} \, dx","Int[Sqrt[2 + 3*x^2 + x^4]/(7 + 5*x^2),x]","\frac{x \left(x^2+2\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{4 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{25 \sqrt{x^4+3 x^2+2}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{25 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{3 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{x \left(x^2+2\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{2 x^2+2}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"(x*(2 + x^2))/(5*Sqrt[2 + 3*x^2 + x^4]) - (Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(5*Sqrt[2 + 3*x^2 + x^4]) - (3*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(25*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (4*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(25*Sqrt[2 + 3*x^2 + x^4]) + (3*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(35*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",8,7,24,0.2917,1,"{1208, 1189, 1099, 1135, 1214, 1456, 539}"
291,1,209,0,0.1233263,"\int \frac{\sqrt{2+3 x^2+x^4}}{\left(7+5 x^2\right)^2} \, dx","Int[Sqrt[2 + 3*x^2 + x^4]/(7 + 5*x^2)^2,x]","\frac{\sqrt{x^4+3 x^2+2} x}{14 \left(5 x^2+7\right)}-\frac{\left(x^2+2\right) x}{70 \sqrt{x^4+3 x^2+2}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{140 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{\left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{980 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{\sqrt{x^4+3 x^2+2} x}{14 \left(5 x^2+7\right)}-\frac{\left(x^2+2\right) x}{70 \sqrt{x^4+3 x^2+2}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{140 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{\left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{980 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"-(x*(2 + x^2))/(70*Sqrt[2 + 3*x^2 + x^4]) + (x*Sqrt[2 + 3*x^2 + x^4])/(14*(7 + 5*x^2)) + ((1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(35*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (3*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(140*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - ((2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(980*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",8,7,24,0.2917,1,"{1226, 1189, 1099, 1135, 1214, 1456, 539}"
292,1,237,0,0.5952414,"\int \frac{\sqrt{2+3 x^2+x^4}}{\left(7+5 x^2\right)^3} \, dx","Int[Sqrt[2 + 3*x^2 + x^4]/(7 + 5*x^2)^3,x]","\frac{11 \sqrt{x^4+3 x^2+2} x}{2352 \left(5 x^2+7\right)}+\frac{\sqrt{x^4+3 x^2+2} x}{28 \left(5 x^2+7\right)^2}-\frac{11 \left(x^2+2\right) x}{11760 \sqrt{x^4+3 x^2+2}}+\frac{81 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{7840 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{11 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5880 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{1201 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{164640 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{11 \sqrt{x^4+3 x^2+2} x}{2352 \left(5 x^2+7\right)}+\frac{\sqrt{x^4+3 x^2+2} x}{28 \left(5 x^2+7\right)^2}-\frac{11 \left(x^2+2\right) x}{11760 \sqrt{x^4+3 x^2+2}}+\frac{81 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{7840 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{11 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5880 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{1201 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{164640 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"(-11*x*(2 + x^2))/(11760*Sqrt[2 + 3*x^2 + x^4]) + (x*Sqrt[2 + 3*x^2 + x^4])/(28*(7 + 5*x^2)^2) + (11*x*Sqrt[2 + 3*x^2 + x^4])/(2352*(7 + 5*x^2)) + (11*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(5880*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (81*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(7840*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (1201*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(164640*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",25,10,24,0.4167,1,"{1228, 1223, 1696, 1716, 1189, 1099, 1135, 1214, 1456, 539}"
293,1,219,0,0.1239501,"\int \left(7+5 x^2\right)^3 \left(2+3 x^2+x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^3*(2 + 3*x^2 + x^4)^(3/2),x]","\frac{125}{13} \left(x^4+3 x^2+2\right)^{5/2} x^3+\frac{3825}{143} \left(x^4+3 x^2+2\right)^{5/2} x+\frac{\left(65345 x^2+208212\right) \left(x^4+3 x^2+2\right)^{3/2} x}{3003}+\frac{\left(297911 x^2+1032541\right) \sqrt{x^4+3 x^2+2} x}{5005}+\frac{20884 \left(x^2+2\right) x}{65 \sqrt{x^4+3 x^2+2}}+\frac{1171349 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5005 \sqrt{x^4+3 x^2+2}}-\frac{20884 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{65 \sqrt{x^4+3 x^2+2}}","\frac{125}{13} \left(x^4+3 x^2+2\right)^{5/2} x^3+\frac{3825}{143} \left(x^4+3 x^2+2\right)^{5/2} x+\frac{\left(65345 x^2+208212\right) \left(x^4+3 x^2+2\right)^{3/2} x}{3003}+\frac{\left(297911 x^2+1032541\right) \sqrt{x^4+3 x^2+2} x}{5005}+\frac{20884 \left(x^2+2\right) x}{65 \sqrt{x^4+3 x^2+2}}+\frac{1171349 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5005 \sqrt{x^4+3 x^2+2}}-\frac{20884 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{65 \sqrt{x^4+3 x^2+2}}",1,"(20884*x*(2 + x^2))/(65*Sqrt[2 + 3*x^2 + x^4]) + (x*(1032541 + 297911*x^2)*Sqrt[2 + 3*x^2 + x^4])/5005 + (x*(208212 + 65345*x^2)*(2 + 3*x^2 + x^4)^(3/2))/3003 + (3825*x*(2 + 3*x^2 + x^4)^(5/2))/143 + (125*x^3*(2 + 3*x^2 + x^4)^(5/2))/13 - (20884*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(65*Sqrt[2 + 3*x^2 + x^4]) + (1171349*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(5005*Sqrt[2 + 3*x^2 + x^4])","A",7,6,24,0.2500,1,"{1206, 1679, 1176, 1189, 1099, 1135}"
294,1,198,0,0.0859281,"\int \left(7+5 x^2\right)^2 \left(2+3 x^2+x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^2*(2 + 3*x^2 + x^4)^(3/2),x]","\frac{25}{11} x \left(x^4+3 x^2+2\right)^{5/2}+\frac{1}{693} x \left(2240 x^2+7281\right) \left(x^4+3 x^2+2\right)^{3/2}+\frac{x \left(10643 x^2+36783\right) \sqrt{x^4+3 x^2+2}}{1155}+\frac{742 x \left(x^2+2\right)}{15 \sqrt{x^4+3 x^2+2}}+\frac{13879 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{385 \sqrt{x^4+3 x^2+2}}-\frac{742 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{15 \sqrt{x^4+3 x^2+2}}","\frac{25}{11} x \left(x^4+3 x^2+2\right)^{5/2}+\frac{1}{693} x \left(2240 x^2+7281\right) \left(x^4+3 x^2+2\right)^{3/2}+\frac{x \left(10643 x^2+36783\right) \sqrt{x^4+3 x^2+2}}{1155}+\frac{742 x \left(x^2+2\right)}{15 \sqrt{x^4+3 x^2+2}}+\frac{13879 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{385 \sqrt{x^4+3 x^2+2}}-\frac{742 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{15 \sqrt{x^4+3 x^2+2}}",1,"(742*x*(2 + x^2))/(15*Sqrt[2 + 3*x^2 + x^4]) + (x*(36783 + 10643*x^2)*Sqrt[2 + 3*x^2 + x^4])/1155 + (x*(7281 + 2240*x^2)*(2 + 3*x^2 + x^4)^(3/2))/693 + (25*x*(2 + 3*x^2 + x^4)^(5/2))/11 - (742*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(15*Sqrt[2 + 3*x^2 + x^4]) + (13879*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(385*Sqrt[2 + 3*x^2 + x^4])","A",6,5,24,0.2083,1,"{1206, 1176, 1189, 1099, 1135}"
295,1,179,0,0.0639407,"\int \left(7+5 x^2\right) \left(2+3 x^2+x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)*(2 + 3*x^2 + x^4)^(3/2),x]","\frac{1}{63} x \left(35 x^2+108\right) \left(x^4+3 x^2+2\right)^{3/2}+\frac{1}{105} x \left(149 x^2+519\right) \sqrt{x^4+3 x^2+2}+\frac{116 x \left(x^2+2\right)}{15 \sqrt{x^4+3 x^2+2}}+\frac{197 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{x^4+3 x^2+2}}-\frac{116 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{15 \sqrt{x^4+3 x^2+2}}","\frac{1}{63} x \left(35 x^2+108\right) \left(x^4+3 x^2+2\right)^{3/2}+\frac{1}{105} x \left(149 x^2+519\right) \sqrt{x^4+3 x^2+2}+\frac{116 x \left(x^2+2\right)}{15 \sqrt{x^4+3 x^2+2}}+\frac{197 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{x^4+3 x^2+2}}-\frac{116 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{15 \sqrt{x^4+3 x^2+2}}",1,"(116*x*(2 + x^2))/(15*Sqrt[2 + 3*x^2 + x^4]) + (x*(519 + 149*x^2)*Sqrt[2 + 3*x^2 + x^4])/105 + (x*(108 + 35*x^2)*(2 + 3*x^2 + x^4)^(3/2))/63 - (116*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(15*Sqrt[2 + 3*x^2 + x^4]) + (197*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(35*Sqrt[2 + 3*x^2 + x^4])","A",5,4,22,0.1818,1,"{1176, 1189, 1099, 1135}"
296,1,172,0,0.058111,"\int \left(2+3 x^2+x^4\right)^{3/2} \, dx","Int[(2 + 3*x^2 + x^4)^(3/2),x]","\frac{1}{7} x \left(x^4+3 x^2+2\right)^{3/2}+\frac{1}{35} x \left(9 x^2+29\right) \sqrt{x^4+3 x^2+2}+\frac{6 x \left(x^2+2\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{31 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{x^4+3 x^2+2}}-\frac{6 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+3 x^2+2}}","\frac{1}{7} x \left(x^4+3 x^2+2\right)^{3/2}+\frac{1}{35} x \left(9 x^2+29\right) \sqrt{x^4+3 x^2+2}+\frac{6 x \left(x^2+2\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{31 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{35 \sqrt{x^4+3 x^2+2}}-\frac{6 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+3 x^2+2}}",1,"(6*x*(2 + x^2))/(5*Sqrt[2 + 3*x^2 + x^4]) + (x*(29 + 9*x^2)*Sqrt[2 + 3*x^2 + x^4])/35 + (x*(2 + 3*x^2 + x^4)^(3/2))/7 - (6*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(5*Sqrt[2 + 3*x^2 + x^4]) + (31*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(35*Sqrt[2 + 3*x^2 + x^4])","A",5,5,14,0.3571,1,"{1091, 1176, 1189, 1099, 1135}"
297,1,207,0,0.1990176,"\int \frac{\left(2+3 x^2+x^4\right)^{3/2}}{7+5 x^2} \, dx","Int[(2 + 3*x^2 + x^4)^(3/2)/(7 + 5*x^2),x]","\frac{24 x \left(x^2+2\right)}{125 \sqrt{x^4+3 x^2+2}}+\frac{1}{75} x \left(3 x^2+11\right) \sqrt{x^4+3 x^2+2}+\frac{56 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{375 \sqrt{x^4+3 x^2+2}}-\frac{24 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{125 \sqrt{x^4+3 x^2+2}}-\frac{9 \sqrt{2} \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{875 \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{24 x \left(x^2+2\right)}{125 \sqrt{x^4+3 x^2+2}}+\frac{1}{75} x \left(3 x^2+11\right) \sqrt{x^4+3 x^2+2}+\frac{56 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{375 \sqrt{x^4+3 x^2+2}}-\frac{24 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{125 \sqrt{x^4+3 x^2+2}}-\frac{9 \sqrt{2} \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{875 \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"(24*x*(2 + x^2))/(125*Sqrt[2 + 3*x^2 + x^4]) + (x*(11 + 3*x^2)*Sqrt[2 + 3*x^2 + x^4])/75 - (24*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(125*Sqrt[2 + 3*x^2 + x^4]) + (56*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(375*Sqrt[2 + 3*x^2 + x^4]) - (9*Sqrt[2]*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(875*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",13,8,24,0.3333,1,"{1208, 1176, 1189, 1099, 1135, 1214, 1456, 539}"
298,1,333,0,0.444338,"\int \frac{\left(2+3 x^2+x^4\right)^{3/2}}{\left(7+5 x^2\right)^2} \, dx","Int[(2 + 3*x^2 + x^4)^(3/2)/(7 + 5*x^2)^2,x]","-\frac{3 \sqrt{x^4+3 x^2+2} x}{175 \left(5 x^2+7\right)}+\frac{1}{75} \sqrt{x^4+3 x^2+2} x+\frac{9 \left(x^2+2\right) x}{175 \sqrt{x^4+3 x^2+2}}+\frac{44 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{1875 \sqrt{x^4+3 x^2+2}}+\frac{81 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{8750 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{9 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{175 \sqrt{x^4+3 x^2+2}}+\frac{3 \sqrt{2} \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{875 \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}-\frac{39 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{12250 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","-\frac{3 \sqrt{x^4+3 x^2+2} x}{175 \left(5 x^2+7\right)}+\frac{1}{75} \sqrt{x^4+3 x^2+2} x+\frac{9 \left(x^2+2\right) x}{175 \sqrt{x^4+3 x^2+2}}+\frac{59 \left(x^2+1\right) \sqrt{\frac{x^2+2}{2 x^2+2}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{1050 \sqrt{x^4+3 x^2+2}}-\frac{9 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{175 \sqrt{x^4+3 x^2+2}}+\frac{9 \left(x^2+1\right) \sqrt{\frac{x^2+2}{2 x^2+2}} \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{2450 \sqrt{x^4+3 x^2+2}}",1,"(9*x*(2 + x^2))/(175*Sqrt[2 + 3*x^2 + x^4]) + (x*Sqrt[2 + 3*x^2 + x^4])/75 - (3*x*Sqrt[2 + 3*x^2 + x^4])/(175*(7 + 5*x^2)) - (9*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(175*Sqrt[2 + 3*x^2 + x^4]) + (81*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(8750*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (44*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(1875*Sqrt[2 + 3*x^2 + x^4]) - (39*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(12250*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4]) + (3*Sqrt[2]*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(875*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",21,10,24,0.4167,1,"{1228, 1099, 1135, 1122, 1189, 1223, 1716, 1214, 1456, 539}"
299,1,288,0,0.6677518,"\int \frac{\left(2+3 x^2+x^4\right)^{3/2}}{\left(7+5 x^2\right)^3} \, dx","Int[(2 + 3*x^2 + x^4)^(3/2)/(7 + 5*x^2)^3,x]","\frac{17 \sqrt{x^4+3 x^2+2} x}{9800 \left(5 x^2+7\right)}-\frac{3 \sqrt{x^4+3 x^2+2} x}{350 \left(5 x^2+7\right)^2}+\frac{3 \left(x^2+2\right) x}{392 \sqrt{x^4+3 x^2+2}}+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{784 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{6 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{875 \sqrt{x^4+3 x^2+2}}-\frac{39 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{24500 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{141 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{27440 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{17 \sqrt{x^4+3 x^2+2} x}{9800 \left(5 x^2+7\right)}-\frac{3 \sqrt{x^4+3 x^2+2} x}{350 \left(5 x^2+7\right)^2}+\frac{3 \left(x^2+2\right) x}{392 \sqrt{x^4+3 x^2+2}}+\frac{5 \left(x^2+1\right) \sqrt{\frac{x^2+2}{2 x^2+2}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{784 \sqrt{x^4+3 x^2+2}}-\frac{3 \left(x^2+1\right) \sqrt{\frac{x^2+2}{2 x^2+2}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{196 \sqrt{x^4+3 x^2+2}}+\frac{141 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{27440 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"(3*x*(2 + x^2))/(392*Sqrt[2 + 3*x^2 + x^4]) - (3*x*Sqrt[2 + 3*x^2 + x^4])/(350*(7 + 5*x^2)^2) + (17*x*Sqrt[2 + 3*x^2 + x^4])/(9800*(7 + 5*x^2)) - (39*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(24500*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (6*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(875*Sqrt[2 + 3*x^2 + x^4]) + (5*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(784*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (141*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(27440*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",27,10,24,0.4167,1,"{1228, 1099, 1135, 1223, 1696, 1716, 1189, 1214, 1456, 539}"
300,1,157,0,0.0835597,"\int \frac{\left(7+5 x^2\right)^3}{\sqrt{2+3 x^2+x^4}} \, dx","Int[(7 + 5*x^2)^3/Sqrt[2 + 3*x^2 + x^4],x]","25 \sqrt{x^4+3 x^2+2} x^3+75 \sqrt{x^4+3 x^2+2} x+\frac{135 \left(x^2+2\right) x}{\sqrt{x^4+3 x^2+2}}+\frac{193 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{135 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}","25 \sqrt{x^4+3 x^2+2} x^3+75 \sqrt{x^4+3 x^2+2} x+\frac{135 \left(x^2+2\right) x}{\sqrt{x^4+3 x^2+2}}+\frac{193 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{135 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}",1,"(135*x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] + 75*x*Sqrt[2 + 3*x^2 + x^4] + 25*x^3*Sqrt[2 + 3*x^2 + x^4] - (135*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + (193*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",5,5,24,0.2083,1,"{1206, 1679, 1189, 1099, 1135}"
301,1,142,0,0.0543072,"\int \frac{\left(7+5 x^2\right)^2}{\sqrt{2+3 x^2+x^4}} \, dx","Int[(7 + 5*x^2)^2/Sqrt[2 + 3*x^2 + x^4],x]","\frac{25}{3} \sqrt{x^4+3 x^2+2} x+\frac{20 \left(x^2+2\right) x}{\sqrt{x^4+3 x^2+2}}+\frac{97 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{20 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}","\frac{25}{3} \sqrt{x^4+3 x^2+2} x+\frac{20 \left(x^2+2\right) x}{\sqrt{x^4+3 x^2+2}}+\frac{97 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{20 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}",1,"(20*x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] + (25*x*Sqrt[2 + 3*x^2 + x^4])/3 - (20*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + (97*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(3*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1206, 1189, 1099, 1135}"
302,1,121,0,0.0324471,"\int \frac{7+5 x^2}{\sqrt{2+3 x^2+x^4}} \, dx","Int[(7 + 5*x^2)/Sqrt[2 + 3*x^2 + x^4],x]","\frac{5 x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}+\frac{7 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{5 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}","\frac{5 x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}+\frac{7 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{5 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}",1,"(5*x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] - (5*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + (7*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",3,3,22,0.1364,1,"{1189, 1099, 1135}"
303,1,48,0,0.0060736,"\int \frac{1}{\sqrt{2+3 x^2+x^4}} \, dx","Int[1/Sqrt[2 + 3*x^2 + x^4],x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"((1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",1,1,14,0.07143,1,"{1099}"
304,1,106,0,0.0722979,"\int \frac{1}{\left(7+5 x^2\right) \sqrt{2+3 x^2+x^4}} \, dx","Int[1/((7 + 5*x^2)*Sqrt[2 + 3*x^2 + x^4]),x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{5 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{14 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{5 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{14 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"((1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(2*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (5*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(14*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1214, 1099, 1456, 539}"
305,1,209,0,0.1878194,"\int \frac{1}{\left(7+5 x^2\right)^2 \sqrt{2+3 x^2+x^4}} \, dx","Int[1/((7 + 5*x^2)^2*Sqrt[2 + 3*x^2 + x^4]),x]","-\frac{25 \sqrt{x^4+3 x^2+2} x}{84 \left(5 x^2+7\right)}+\frac{5 \left(x^2+2\right) x}{84 \sqrt{x^4+3 x^2+2}}+\frac{9 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{56 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{42 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{65 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{1176 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","-\frac{25 \sqrt{x^4+3 x^2+2} x}{84 \left(5 x^2+7\right)}+\frac{5 \left(x^2+2\right) x}{84 \sqrt{x^4+3 x^2+2}}+\frac{9 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{56 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{5 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{42 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{65 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{1176 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"(5*x*(2 + x^2))/(84*Sqrt[2 + 3*x^2 + x^4]) - (25*x*Sqrt[2 + 3*x^2 + x^4])/(84*(7 + 5*x^2)) - (5*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(42*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (9*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(56*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (65*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(1176*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",9,8,24,0.3333,1,"{1223, 1716, 1189, 1099, 1135, 1214, 1456, 539}"
306,1,237,0,0.2498655,"\int \frac{1}{\left(7+5 x^2\right)^3 \sqrt{2+3 x^2+x^4}} \, dx","Int[1/((7 + 5*x^2)^3*Sqrt[2 + 3*x^2 + x^4]),x]","-\frac{325 \sqrt{x^4+3 x^2+2} x}{4704 \left(5 x^2+7\right)}-\frac{25 \sqrt{x^4+3 x^2+2} x}{168 \left(5 x^2+7\right)^2}+\frac{65 \left(x^2+2\right) x}{4704 \sqrt{x^4+3 x^2+2}}+\frac{631 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{9408 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{65 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{2352 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{2525 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{65856 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","-\frac{325 \sqrt{x^4+3 x^2+2} x}{4704 \left(5 x^2+7\right)}-\frac{25 \sqrt{x^4+3 x^2+2} x}{168 \left(5 x^2+7\right)^2}+\frac{65 \left(x^2+2\right) x}{4704 \sqrt{x^4+3 x^2+2}}+\frac{631 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{9408 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{65 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{2352 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{2525 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{65856 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"(65*x*(2 + x^2))/(4704*Sqrt[2 + 3*x^2 + x^4]) - (25*x*Sqrt[2 + 3*x^2 + x^4])/(168*(7 + 5*x^2)^2) - (325*x*Sqrt[2 + 3*x^2 + x^4])/(4704*(7 + 5*x^2)) - (65*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(2352*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (631*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(9408*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (2525*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(65856*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",10,9,24,0.3750,1,"{1223, 1696, 1716, 1189, 1099, 1135, 1214, 1456, 539}"
307,1,189,0,0.1129625,"\int \frac{\left(7+5 x^2\right)^5}{\left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^5/(2 + 3*x^2 + x^4)^(3/2),x]","625 \sqrt{x^4+3 x^2+2} x^3+\frac{5000}{3} \sqrt{x^4+3 x^2+2} x+\frac{7679 \left(x^2+2\right) x}{2 \sqrt{x^4+3 x^2+2}}-\frac{\left(179 x^2+115\right) x}{2 \sqrt{x^4+3 x^2+2}}+\frac{15383 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{7679 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}","625 \sqrt{x^4+3 x^2+2} x^3+\frac{5000}{3} \sqrt{x^4+3 x^2+2} x+\frac{7679 \left(x^2+2\right) x}{2 \sqrt{x^4+3 x^2+2}}-\frac{\left(179 x^2+115\right) x}{2 \sqrt{x^4+3 x^2+2}}+\frac{15383 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{7679 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"(7679*x*(2 + x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) - (x*(115 + 179*x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (5000*x*Sqrt[2 + 3*x^2 + x^4])/3 + 625*x^3*Sqrt[2 + 3*x^2 + x^4] - (7679*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (15383*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(3*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",6,5,24,0.2083,1,"{1205, 1679, 1189, 1099, 1135}"
308,1,170,0,0.0830864,"\int \frac{\left(7+5 x^2\right)^4}{\left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^4/(2 + 3*x^2 + x^4)^(3/2),x]","\frac{625}{3} \sqrt{x^4+3 x^2+2} x+\frac{637 \left(x^2+2\right) x}{2 \sqrt{x^4+3 x^2+2}}+\frac{\left(113 x^2+145\right) x}{2 \sqrt{x^4+3 x^2+2}}+\frac{1067 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}-\frac{637 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}","\frac{625}{3} \sqrt{x^4+3 x^2+2} x+\frac{637 \left(x^2+2\right) x}{2 \sqrt{x^4+3 x^2+2}}+\frac{\left(113 x^2+145\right) x}{2 \sqrt{x^4+3 x^2+2}}+\frac{1067 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}-\frac{637 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"(637*x*(2 + x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (x*(145 + 113*x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (625*x*Sqrt[2 + 3*x^2 + x^4])/3 - (637*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (1067*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(3*Sqrt[2 + 3*x^2 + x^4])","A",5,5,24,0.2083,1,"{1205, 1679, 1189, 1099, 1135}"
309,1,149,0,0.0522078,"\int \frac{\left(7+5 x^2\right)^3}{\left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^3/(2 + 3*x^2 + x^4)^(3/2),x]","\frac{x \left(5-11 x^2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{261 x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{169 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{261 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}","\frac{x \left(5-11 x^2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{261 x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{169 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{261 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"(x*(5 - 11*x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (261*x*(2 + x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) - (261*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (169*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1205, 1189, 1099, 1135}"
310,1,149,0,0.0511373,"\int \frac{\left(7+5 x^2\right)^2}{\left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^2/(2 + 3*x^2 + x^4)^(3/2),x]","-\frac{17 x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{x \left(17 x^2+25\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{6 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}+\frac{17 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}","-\frac{17 x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{x \left(17 x^2+25\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{6 \sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}+\frac{17 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"(-17*x*(2 + x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (x*(25 + 17*x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (17*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (6*Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4]","A",4,4,24,0.1667,1,"{1205, 1189, 1099, 1135}"
311,1,145,0,0.0414866,"\int \frac{7+5 x^2}{\left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)/(2 + 3*x^2 + x^4)^(3/2),x]","-\frac{x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{x \left(x^2+5\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}","-\frac{x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{x \left(x^2+5\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"-(x*(2 + x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (x*(5 + x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + ((1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + ((1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",4,4,22,0.1818,1,"{1178, 1189, 1099, 1135}"
312,1,149,0,0.0417569,"\int \frac{1}{\left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2 + x^4)^(-3/2),x]","-\frac{3 x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{x \left(3 x^2+5\right)}{2 \sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}","-\frac{3 x \left(x^2+2\right)}{2 \sqrt{x^4+3 x^2+2}}+\frac{x \left(3 x^2+5\right)}{2 \sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}+\frac{3 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"(-3*x*(2 + x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (x*(5 + 3*x^2))/(2*Sqrt[2 + 3*x^2 + x^4]) + (3*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4]","A",4,4,14,0.2857,1,"{1092, 1189, 1099, 1135}"
313,1,207,0,0.1405547,"\int \frac{1}{\left(7+5 x^2\right) \left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)*(2 + 3*x^2 + x^4)^(3/2)),x]","-\frac{x \left(x^2+2\right)}{3 \sqrt{x^4+3 x^2+2}}+\frac{x \left(2 x^2+5\right)}{6 \sqrt{x^4+3 x^2+2}}-\frac{9 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}+\frac{125 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{84 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{x}{6 \sqrt{x^4+3 x^2+2}}-\frac{9 \left(x^2+1\right) \sqrt{\frac{x^2+2}{2 x^2+2}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+3 x^2+2}}+\frac{\sqrt{2} \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{x^4+3 x^2+2}}+\frac{125 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{84 \sqrt{2} \sqrt{x^4+3 x^2+2}}",1,"-(x*(2 + x^2))/(3*Sqrt[2 + 3*x^2 + x^4]) + (x*(5 + 2*x^2))/(6*Sqrt[2 + 3*x^2 + x^4]) + (Sqrt[2]*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(3*Sqrt[2 + 3*x^2 + x^4]) - (9*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(4*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (125*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(84*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",9,8,24,0.3333,1,"{1221, 1178, 1189, 1099, 1135, 1214, 1456, 539}"
314,1,235,0,0.4291436,"\int \frac{1}{\left(7+5 x^2\right)^2 \left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)^2*(2 + 3*x^2 + x^4)^(3/2)),x]","\frac{625 \sqrt{x^4+3 x^2+2} x}{504 \left(5 x^2+7\right)}-\frac{31 \left(x^2+2\right) x}{56 \sqrt{x^4+3 x^2+2}}+\frac{\left(11 x^2+20\right) x}{36 \sqrt{x^4+3 x^2+2}}-\frac{463 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{336 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{31 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{28 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{375 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{784 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{625 \sqrt{x^4+3 x^2+2} x}{504 \left(5 x^2+7\right)}-\frac{31 \left(x^2+2\right) x}{56 \sqrt{x^4+3 x^2+2}}+\frac{\left(11 x^2+20\right) x}{36 \sqrt{x^4+3 x^2+2}}-\frac{463 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{336 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{31 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{28 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{375 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{784 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"(-31*x*(2 + x^2))/(56*Sqrt[2 + 3*x^2 + x^4]) + (x*(20 + 11*x^2))/(36*Sqrt[2 + 3*x^2 + x^4]) + (625*x*Sqrt[2 + 3*x^2 + x^4])/(504*(7 + 5*x^2)) + (31*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(28*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (463*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(336*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (375*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(784*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",19,10,24,0.4167,1,"{1228, 1178, 1189, 1099, 1135, 1223, 1716, 1214, 1456, 539}"
315,1,263,0,0.760469,"\int \frac{1}{\left(7+5 x^2\right)^3 \left(2+3 x^2+x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)^3*(2 + 3*x^2 + x^4)^(3/2)),x]","\frac{41875 \sqrt{x^4+3 x^2+2} x}{84672 \left(5 x^2+7\right)}+\frac{625 \sqrt{x^4+3 x^2+2} x}{1008 \left(5 x^2+7\right)^2}-\frac{5797 \left(x^2+2\right) x}{28224 \sqrt{x^4+3 x^2+2}}+\frac{\left(23 x^2+50\right) x}{216 \sqrt{x^4+3 x^2+2}}-\frac{49907 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{56448 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{5797 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{14112 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{192625 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{395136 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}","\frac{41875 \sqrt{x^4+3 x^2+2} x}{84672 \left(5 x^2+7\right)}+\frac{625 \sqrt{x^4+3 x^2+2} x}{1008 \left(5 x^2+7\right)^2}-\frac{5797 \left(x^2+2\right) x}{28224 \sqrt{x^4+3 x^2+2}}+\frac{\left(23 x^2+50\right) x}{216 \sqrt{x^4+3 x^2+2}}-\frac{49907 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{56448 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{5797 \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{14112 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{192625 \left(x^2+2\right) \Pi \left(\frac{2}{7};\tan ^{-1}(x)|\frac{1}{2}\right)}{395136 \sqrt{2} \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2}}",1,"(-5797*x*(2 + x^2))/(28224*Sqrt[2 + 3*x^2 + x^4]) + (x*(50 + 23*x^2))/(216*Sqrt[2 + 3*x^2 + x^4]) + (625*x*Sqrt[2 + 3*x^2 + x^4])/(1008*(7 + 5*x^2)^2) + (41875*x*Sqrt[2 + 3*x^2 + x^4])/(84672*(7 + 5*x^2)) + (5797*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(14112*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) - (49907*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(56448*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4]) + (192625*(2 + x^2)*EllipticPi[2/7, ArcTan[x], 1/2])/(395136*Sqrt[2]*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",29,11,24,0.4583,1,"{1228, 1178, 1189, 1099, 1135, 1223, 1696, 1716, 1214, 1456, 539}"
316,1,116,0,0.1117491,"\int \left(7+5 x^2\right)^4 \sqrt{2+x^2-x^4} \, dx","Int[(7 + 5*x^2)^4*Sqrt[2 + x^2 - x^4],x]","-\frac{625}{11} \left(-x^4+x^2+2\right)^{3/2} x^5-\frac{14500}{33} \left(-x^4+x^2+2\right)^{3/2} x^3-\frac{116100}{77} \left(-x^4+x^2+2\right)^{3/2} x+\frac{1}{231} \left(717372 x^2+177953\right) \sqrt{-x^4+x^2+2} x-\frac{539419}{77} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{3764813}{231} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","-\frac{625}{11} \left(-x^4+x^2+2\right)^{3/2} x^5-\frac{14500}{33} \left(-x^4+x^2+2\right)^{3/2} x^3-\frac{116100}{77} \left(-x^4+x^2+2\right)^{3/2} x+\frac{1}{231} \left(717372 x^2+177953\right) \sqrt{-x^4+x^2+2} x-\frac{539419}{77} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{3764813}{231} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(177953 + 717372*x^2)*Sqrt[2 + x^2 - x^4])/231 - (116100*x*(2 + x^2 - x^4)^(3/2))/77 - (14500*x^3*(2 + x^2 - x^4)^(3/2))/33 - (625*x^5*(2 + x^2 - x^4)^(3/2))/11 + (3764813*EllipticE[ArcSin[x/Sqrt[2]], -2])/231 - (539419*EllipticF[ArcSin[x/Sqrt[2]], -2])/77","A",8,7,24,0.2917,1,"{1206, 1679, 1176, 1180, 524, 424, 419}"
317,1,95,0,0.0870409,"\int \left(7+5 x^2\right)^3 \sqrt{2+x^2-x^4} \, dx","Int[(7 + 5*x^2)^3*Sqrt[2 + x^2 - x^4],x]","-\frac{125}{9} \left(-x^4+x^2+2\right)^{3/2} x^3-\frac{1825}{21} \left(-x^4+x^2+2\right)^{3/2} x+\frac{1}{63} \left(14691 x^2+5956\right) \sqrt{-x^4+x^2+2} x-\frac{8735}{21} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{79411}{63} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","-\frac{125}{9} \left(-x^4+x^2+2\right)^{3/2} x^3-\frac{1825}{21} \left(-x^4+x^2+2\right)^{3/2} x+\frac{1}{63} \left(14691 x^2+5956\right) \sqrt{-x^4+x^2+2} x-\frac{8735}{21} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{79411}{63} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(5956 + 14691*x^2)*Sqrt[2 + x^2 - x^4])/63 - (1825*x*(2 + x^2 - x^4)^(3/2))/21 - (125*x^3*(2 + x^2 - x^4)^(3/2))/9 + (79411*EllipticE[ArcSin[x/Sqrt[2]], -2])/63 - (8735*EllipticF[ArcSin[x/Sqrt[2]], -2])/21","A",7,7,24,0.2917,1,"{1206, 1679, 1176, 1180, 524, 424, 419}"
318,1,74,0,0.0606281,"\int \left(7+5 x^2\right)^2 \sqrt{2+x^2-x^4} \, dx","Int[(7 + 5*x^2)^2*Sqrt[2 + x^2 - x^4],x]","-\frac{25}{7} x \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{21} x \left(354 x^2+275\right) \sqrt{-x^4+x^2+2}-\frac{79}{7} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{2045}{21} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","-\frac{25}{7} x \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{21} x \left(354 x^2+275\right) \sqrt{-x^4+x^2+2}-\frac{79}{7} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{2045}{21} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(275 + 354*x^2)*Sqrt[2 + x^2 - x^4])/21 - (25*x*(2 + x^2 - x^4)^(3/2))/7 + (2045*EllipticE[ArcSin[x/Sqrt[2]], -2])/21 - (79*EllipticF[ArcSin[x/Sqrt[2]], -2])/7","A",6,6,24,0.2500,1,"{1206, 1176, 1180, 524, 424, 419}"
319,1,46,0,0.0460943,"\int \left(7+5 x^2\right) \sqrt{2+x^2-x^4} \, dx","Int[(7 + 5*x^2)*Sqrt[2 + x^2 - x^4],x]","x \sqrt{-x^4+x^2+2} \left(x^2+2\right)+3 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+7 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","x \sqrt{-x^4+x^2+2} \left(x^2+2\right)+3 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+7 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"x*(2 + x^2)*Sqrt[2 + x^2 - x^4] + 7*EllipticE[ArcSin[x/Sqrt[2]], -2] + 3*EllipticF[ArcSin[x/Sqrt[2]], -2]","A",5,5,22,0.2273,1,"{1176, 1180, 524, 424, 419}"
320,1,44,0,0.0401104,"\int \sqrt{2+x^2-x^4} \, dx","Int[Sqrt[2 + x^2 - x^4],x]","\frac{1}{3} \sqrt{-x^4+x^2+2} x+F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1}{3} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{1}{3} \sqrt{-x^4+x^2+2} x+F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1}{3} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*Sqrt[2 + x^2 - x^4])/3 + EllipticE[ArcSin[x/Sqrt[2]], -2]/3 + EllipticF[ArcSin[x/Sqrt[2]], -2]","A",5,5,14,0.3571,1,"{1091, 1180, 524, 424, 419}"
321,1,46,0,0.079296,"\int \frac{\sqrt{2+x^2-x^4}}{7+5 x^2} \, dx","Int[Sqrt[2 + x^2 - x^4]/(7 + 5*x^2),x]","\frac{17}{25} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{1}{5} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{34}{175} \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{17}{25} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{1}{5} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{34}{175} \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"-EllipticE[ArcSin[x/Sqrt[2]], -2]/5 + (17*EllipticF[ArcSin[x/Sqrt[2]], -2])/25 - (34*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/175","A",7,7,24,0.2917,1,"{1208, 1180, 524, 424, 419, 1212, 537}"
322,1,74,0,0.0795178,"\int \frac{\sqrt{2+x^2-x^4}}{\left(7+5 x^2\right)^2} \, dx","Int[Sqrt[2 + x^2 - x^4]/(7 + 5*x^2)^2,x]","\frac{\sqrt{-x^4+x^2+2} x}{14 \left(5 x^2+7\right)}-\frac{6}{175} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1}{70} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{99 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{2450}","\frac{\sqrt{-x^4+x^2+2} x}{14 \left(5 x^2+7\right)}-\frac{6}{175} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1}{70} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{99 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{2450}",1,"(x*Sqrt[2 + x^2 - x^4])/(14*(7 + 5*x^2)) + EllipticE[ArcSin[x/Sqrt[2]], -2]/70 - (6*EllipticF[ArcSin[x/Sqrt[2]], -2])/175 + (99*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/2450","A",7,7,24,0.2917,1,"{1226, 1180, 524, 424, 419, 1212, 537}"
323,1,102,0,0.41383,"\int \frac{\sqrt{2+x^2-x^4}}{\left(7+5 x^2\right)^3} \, dx","Int[Sqrt[2 + x^2 - x^4]/(7 + 5*x^2)^3,x]","-\frac{31 \sqrt{-x^4+x^2+2} x}{13328 \left(5 x^2+7\right)}+\frac{\sqrt{-x^4+x^2+2} x}{28 \left(5 x^2+7\right)^2}-\frac{269 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{166600}-\frac{31 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{66640}+\frac{16601 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{2332400}","-\frac{31 \sqrt{-x^4+x^2+2} x}{13328 \left(5 x^2+7\right)}+\frac{\sqrt{-x^4+x^2+2} x}{28 \left(5 x^2+7\right)^2}-\frac{269 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{166600}-\frac{31 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{66640}+\frac{16601 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{2332400}",1,"(x*Sqrt[2 + x^2 - x^4])/(28*(7 + 5*x^2)^2) - (31*x*Sqrt[2 + x^2 - x^4])/(13328*(7 + 5*x^2)) - (31*EllipticE[ArcSin[x/Sqrt[2]], -2])/66640 - (269*EllipticF[ArcSin[x/Sqrt[2]], -2])/166600 + (16601*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/2332400","A",21,10,24,0.4167,1,"{1228, 1223, 1696, 1716, 1180, 524, 424, 419, 1212, 537}"
324,1,142,0,0.1316124,"\int \left(7+5 x^2\right)^4 \left(2+x^2-x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^4*(2 + x^2 - x^4)^(3/2),x]","-\frac{125}{3} \left(-x^4+x^2+2\right)^{5/2} x^5-\frac{11750}{39} \left(-x^4+x^2+2\right)^{5/2} x^3-\frac{132300}{143} \left(-x^4+x^2+2\right)^{5/2} x-\frac{\left(69817-1581440 x^2\right) \left(-x^4+x^2+2\right)^{3/2} x}{1001}+\frac{3 \left(7837383 x^2+2193559\right) \sqrt{-x^4+x^2+2} x}{5005}-\frac{50794416 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{5005}+\frac{124141422 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{5005}","-\frac{125}{3} \left(-x^4+x^2+2\right)^{5/2} x^5-\frac{11750}{39} \left(-x^4+x^2+2\right)^{5/2} x^3-\frac{132300}{143} \left(-x^4+x^2+2\right)^{5/2} x-\frac{\left(69817-1581440 x^2\right) \left(-x^4+x^2+2\right)^{3/2} x}{1001}+\frac{3 \left(7837383 x^2+2193559\right) \sqrt{-x^4+x^2+2} x}{5005}-\frac{50794416 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{5005}+\frac{124141422 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{5005}",1,"(3*x*(2193559 + 7837383*x^2)*Sqrt[2 + x^2 - x^4])/5005 - (x*(69817 - 1581440*x^2)*(2 + x^2 - x^4)^(3/2))/1001 - (132300*x*(2 + x^2 - x^4)^(5/2))/143 - (11750*x^3*(2 + x^2 - x^4)^(5/2))/39 - (125*x^5*(2 + x^2 - x^4)^(5/2))/3 + (124141422*EllipticE[ArcSin[x/Sqrt[2]], -2])/5005 - (50794416*EllipticF[ArcSin[x/Sqrt[2]], -2])/5005","A",9,7,24,0.2917,1,"{1206, 1679, 1176, 1180, 524, 424, 419}"
325,1,121,0,0.101206,"\int \left(7+5 x^2\right)^3 \left(2+x^2-x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^3*(2 + x^2 - x^4)^(3/2),x]","-\frac{125}{13} \left(-x^4+x^2+2\right)^{5/2} x^3-\frac{7825}{143} \left(-x^4+x^2+2\right)^{5/2} x+\frac{\left(374045 x^2+33792\right) \left(-x^4+x^2+2\right)^{3/2} x}{3003}+\frac{\left(5712051 x^2+2512273\right) \sqrt{-x^4+x^2+2} x}{15015}-\frac{3199778 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{5005}+\frac{31072528 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{15015}","-\frac{125}{13} \left(-x^4+x^2+2\right)^{5/2} x^3-\frac{7825}{143} \left(-x^4+x^2+2\right)^{5/2} x+\frac{\left(374045 x^2+33792\right) \left(-x^4+x^2+2\right)^{3/2} x}{3003}+\frac{\left(5712051 x^2+2512273\right) \sqrt{-x^4+x^2+2} x}{15015}-\frac{3199778 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{5005}+\frac{31072528 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{15015}",1,"(x*(2512273 + 5712051*x^2)*Sqrt[2 + x^2 - x^4])/15015 + (x*(33792 + 374045*x^2)*(2 + x^2 - x^4)^(3/2))/3003 - (7825*x*(2 + x^2 - x^4)^(5/2))/143 - (125*x^3*(2 + x^2 - x^4)^(5/2))/13 + (31072528*EllipticE[ArcSin[x/Sqrt[2]], -2])/15015 - (3199778*EllipticF[ArcSin[x/Sqrt[2]], -2])/5005","A",8,7,24,0.2917,1,"{1206, 1679, 1176, 1180, 524, 424, 419}"
326,1,100,0,0.0738041,"\int \left(7+5 x^2\right)^2 \left(2+x^2-x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^2*(2 + x^2 - x^4)^(3/2),x]","-\frac{25}{11} x \left(-x^4+x^2+2\right)^{5/2}+\frac{1}{99} x \left(920 x^2+363\right) \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{495} x \left(14889 x^2+11497\right) \sqrt{-x^4+x^2+2}-\frac{3392}{165} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{85942}{495} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","-\frac{25}{11} x \left(-x^4+x^2+2\right)^{5/2}+\frac{1}{99} x \left(920 x^2+363\right) \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{495} x \left(14889 x^2+11497\right) \sqrt{-x^4+x^2+2}-\frac{3392}{165} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{85942}{495} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(11497 + 14889*x^2)*Sqrt[2 + x^2 - x^4])/495 + (x*(363 + 920*x^2)*(2 + x^2 - x^4)^(3/2))/99 - (25*x*(2 + x^2 - x^4)^(5/2))/11 + (85942*EllipticE[ArcSin[x/Sqrt[2]], -2])/495 - (3392*EllipticF[ArcSin[x/Sqrt[2]], -2])/165","A",7,6,24,0.2500,1,"{1206, 1176, 1180, 524, 424, 419}"
327,1,81,0,0.0554957,"\int \left(7+5 x^2\right) \left(2+x^2-x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)*(2 + x^2 - x^4)^(3/2),x]","\frac{1}{63} x \left(35 x^2+48\right) \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{315} x \left(669 x^2+1087\right) \sqrt{-x^4+x^2+2}+\frac{418}{105} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{4432}{315} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{1}{63} x \left(35 x^2+48\right) \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{315} x \left(669 x^2+1087\right) \sqrt{-x^4+x^2+2}+\frac{418}{105} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{4432}{315} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(1087 + 669*x^2)*Sqrt[2 + x^2 - x^4])/315 + (x*(48 + 35*x^2)*(2 + x^2 - x^4)^(3/2))/63 + (4432*EllipticE[ArcSin[x/Sqrt[2]], -2])/315 + (418*EllipticF[ArcSin[x/Sqrt[2]], -2])/105","A",6,5,22,0.2273,1,"{1176, 1180, 524, 424, 419}"
328,1,74,0,0.0516522,"\int \left(2+x^2-x^4\right)^{3/2} \, dx","Int[(2 + x^2 - x^4)^(3/2),x]","\frac{1}{7} x \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{35} x \left(3 x^2+19\right) \sqrt{-x^4+x^2+2}+\frac{48}{35} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{34}{35} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{1}{7} x \left(-x^4+x^2+2\right)^{3/2}+\frac{1}{35} x \left(3 x^2+19\right) \sqrt{-x^4+x^2+2}+\frac{48}{35} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{34}{35} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(19 + 3*x^2)*Sqrt[2 + x^2 - x^4])/35 + (x*(2 + x^2 - x^4)^(3/2))/7 + (34*EllipticE[ArcSin[x/Sqrt[2]], -2])/35 + (48*EllipticF[ArcSin[x/Sqrt[2]], -2])/35","A",6,6,14,0.4286,1,"{1091, 1176, 1180, 524, 424, 419}"
329,1,72,0,0.1360523,"\int \frac{\left(2+x^2-x^4\right)^{3/2}}{7+5 x^2} \, dx","Int[(2 + x^2 - x^4)^(3/2)/(7 + 5*x^2),x]","\frac{1}{75} x \sqrt{-x^4+x^2+2} \left(13-3 x^2\right)-\frac{178}{625} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{92}{375} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1156 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{4375}","\frac{1}{75} x \sqrt{-x^4+x^2+2} \left(13-3 x^2\right)-\frac{178}{625} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{92}{375} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1156 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{4375}",1,"(x*(13 - 3*x^2)*Sqrt[2 + x^2 - x^4])/75 + (92*EllipticE[ArcSin[x/Sqrt[2]], -2])/375 - (178*EllipticF[ArcSin[x/Sqrt[2]], -2])/625 + (1156*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/4375","A",13,8,24,0.3333,1,"{1208, 1176, 1180, 524, 424, 419, 1212, 537}"
330,1,93,0,0.3202209,"\int \frac{\left(2+x^2-x^4\right)^{3/2}}{\left(7+5 x^2\right)^2} \, dx","Int[(2 + x^2 - x^4)^(3/2)/(7 + 5*x^2)^2,x]","-\frac{17 \sqrt{-x^4+x^2+2} x}{175 \left(5 x^2+7\right)}-\frac{1}{75} \sqrt{-x^4+x^2+2} x+\frac{458}{875} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{97}{525} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{1241 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{6125}","-\frac{17 \sqrt{-x^4+x^2+2} x}{175 \left(5 x^2+7\right)}-\frac{1}{75} \sqrt{-x^4+x^2+2} x+\frac{458}{875} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{97}{525} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{1241 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{6125}",1,"-(x*Sqrt[2 + x^2 - x^4])/75 - (17*x*Sqrt[2 + x^2 - x^4])/(175*(7 + 5*x^2)) - (97*EllipticE[ArcSin[x/Sqrt[2]], -2])/525 + (458*EllipticF[ArcSin[x/Sqrt[2]], -2])/875 - (1241*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/6125","A",21,13,24,0.5417,1,"{1228, 1095, 419, 1132, 493, 424, 1122, 1180, 1223, 1716, 524, 1212, 537}"
331,1,102,0,0.4973463,"\int \frac{\left(2+x^2-x^4\right)^{3/2}}{\left(7+5 x^2\right)^3} \, dx","Int[(2 + x^2 - x^4)^(3/2)/(7 + 5*x^2)^3,x]","\frac{563 \sqrt{-x^4+x^2+2} x}{9800 \left(5 x^2+7\right)}-\frac{17 \sqrt{-x^4+x^2+2} x}{350 \left(5 x^2+7\right)^2}-\frac{1251 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{24500}+\frac{191 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{9800}+\frac{9879 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{343000}","\frac{563 \sqrt{-x^4+x^2+2} x}{9800 \left(5 x^2+7\right)}-\frac{17 \sqrt{-x^4+x^2+2} x}{350 \left(5 x^2+7\right)^2}-\frac{1251 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{24500}+\frac{191 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{9800}+\frac{9879 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{343000}",1,"(-17*x*Sqrt[2 + x^2 - x^4])/(350*(7 + 5*x^2)^2) + (563*x*Sqrt[2 + x^2 - x^4])/(9800*(7 + 5*x^2)) + (191*EllipticE[ArcSin[x/Sqrt[2]], -2])/9800 - (1251*EllipticF[ArcSin[x/Sqrt[2]], -2])/24500 + (9879*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/343000","A",27,13,24,0.5417,1,"{1228, 1095, 419, 1132, 493, 424, 1223, 1696, 1716, 1180, 524, 1212, 537}"
332,1,65,0,0.0763707,"\int \frac{\left(7+5 x^2\right)^3}{\sqrt{2+x^2-x^4}} \, dx","Int[(7 + 5*x^2)^3/Sqrt[2 + x^2 - x^4],x]","-25 \sqrt{-x^4+x^2+2} x^3-\frac{625}{3} \sqrt{-x^4+x^2+2} x-542 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{3905}{3} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","-25 \sqrt{-x^4+x^2+2} x^3-\frac{625}{3} \sqrt{-x^4+x^2+2} x-542 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{3905}{3} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(-625*x*Sqrt[2 + x^2 - x^4])/3 - 25*x^3*Sqrt[2 + x^2 - x^4] + (3905*EllipticE[ArcSin[x/Sqrt[2]], -2])/3 - 542*EllipticF[ArcSin[x/Sqrt[2]], -2]","A",6,6,24,0.2500,1,"{1206, 1679, 1180, 524, 424, 419}"
333,1,46,0,0.0510287,"\int \frac{\left(7+5 x^2\right)^2}{\sqrt{2+x^2-x^4}} \, dx","Int[(7 + 5*x^2)^2/Sqrt[2 + x^2 - x^4],x]","-\frac{25}{3} \sqrt{-x^4+x^2+2} x-21 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{260}{3} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","-\frac{25}{3} \sqrt{-x^4+x^2+2} x-21 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{260}{3} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(-25*x*Sqrt[2 + x^2 - x^4])/3 + (260*EllipticE[ArcSin[x/Sqrt[2]], -2])/3 - 21*EllipticF[ArcSin[x/Sqrt[2]], -2]","A",5,5,24,0.2083,1,"{1206, 1180, 524, 424, 419}"
334,1,25,0,0.0379229,"\int \frac{7+5 x^2}{\sqrt{2+x^2-x^4}} \, dx","Int[(7 + 5*x^2)/Sqrt[2 + x^2 - x^4],x]","2 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+5 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","2 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+5 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"5*EllipticE[ArcSin[x/Sqrt[2]], -2] + 2*EllipticF[ArcSin[x/Sqrt[2]], -2]","A",4,4,22,0.1818,1,"{1180, 524, 424, 419}"
335,1,10,0,0.0105507,"\int \frac{1}{\sqrt{2+x^2-x^4}} \, dx","Int[1/Sqrt[2 + x^2 - x^4],x]","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"EllipticF[ArcSin[x/Sqrt[2]], -2]","A",2,2,14,0.1429,1,"{1095, 419}"
336,1,17,0,0.0330613,"\int \frac{1}{\left(7+5 x^2\right) \sqrt{2+x^2-x^4}} \, dx","Int[1/((7 + 5*x^2)*Sqrt[2 + x^2 - x^4]),x]","\frac{1}{7} \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{1}{7} \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2]/7","A",2,2,24,0.08333,1,"{1212, 537}"
337,1,74,0,0.1338833,"\int \frac{1}{\left(7+5 x^2\right)^2 \sqrt{2+x^2-x^4}} \, dx","Int[1/((7 + 5*x^2)^2*Sqrt[2 + x^2 - x^4]),x]","-\frac{25 \sqrt{-x^4+x^2+2} x}{476 \left(5 x^2+7\right)}-\frac{1}{238} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{5}{476} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{167 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{3332}","-\frac{25 \sqrt{-x^4+x^2+2} x}{476 \left(5 x^2+7\right)}-\frac{1}{238} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{5}{476} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{167 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{3332}",1,"(-25*x*Sqrt[2 + x^2 - x^4])/(476*(7 + 5*x^2)) - (5*EllipticE[ArcSin[x/Sqrt[2]], -2])/476 - EllipticF[ArcSin[x/Sqrt[2]], -2]/238 + (167*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/3332","A",8,8,24,0.3333,1,"{1223, 1716, 1180, 524, 424, 419, 1212, 537}"
338,1,102,0,0.1917679,"\int \frac{1}{\left(7+5 x^2\right)^3 \sqrt{2+x^2-x^4}} \, dx","Int[1/((7 + 5*x^2)^3*Sqrt[2 + x^2 - x^4]),x]","-\frac{12525 \sqrt{-x^4+x^2+2} x}{453152 \left(5 x^2+7\right)}-\frac{25 \sqrt{-x^4+x^2+2} x}{952 \left(5 x^2+7\right)^2}-\frac{263 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{226576}-\frac{2505 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{453152}+\frac{58915 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{3172064}","-\frac{12525 \sqrt{-x^4+x^2+2} x}{453152 \left(5 x^2+7\right)}-\frac{25 \sqrt{-x^4+x^2+2} x}{952 \left(5 x^2+7\right)^2}-\frac{263 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{226576}-\frac{2505 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{453152}+\frac{58915 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{3172064}",1,"(-25*x*Sqrt[2 + x^2 - x^4])/(952*(7 + 5*x^2)^2) - (12525*x*Sqrt[2 + x^2 - x^4])/(453152*(7 + 5*x^2)) - (2505*EllipticE[ArcSin[x/Sqrt[2]], -2])/453152 - (263*EllipticF[ArcSin[x/Sqrt[2]], -2])/226576 + (58915*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/3172064","A",9,9,24,0.3750,1,"{1223, 1696, 1716, 1180, 524, 424, 419, 1212, 537}"
339,1,93,0,0.1005976,"\int \frac{\left(7+5 x^2\right)^5}{\left(2+x^2-x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^5/(2 + x^2 - x^4)^(3/2),x]","625 \sqrt{-x^4+x^2+2} x^3+\frac{27500}{3} \sqrt{-x^4+x^2+2} x+\frac{\left(1419793 x^2+1419985\right) x}{18 \sqrt{-x^4+x^2+2}}+\frac{627857}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{3482293}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","625 \sqrt{-x^4+x^2+2} x^3+\frac{27500}{3} \sqrt{-x^4+x^2+2} x+\frac{\left(1419793 x^2+1419985\right) x}{18 \sqrt{-x^4+x^2+2}}+\frac{627857}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{3482293}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(1419985 + 1419793*x^2))/(18*Sqrt[2 + x^2 - x^4]) + (27500*x*Sqrt[2 + x^2 - x^4])/3 + 625*x^3*Sqrt[2 + x^2 - x^4] - (3482293*EllipticE[ArcSin[x/Sqrt[2]], -2])/18 + (627857*EllipticF[ArcSin[x/Sqrt[2]], -2])/6","A",7,6,24,0.2500,1,"{1205, 1679, 1180, 524, 424, 419}"
340,1,74,0,0.0761503,"\int \frac{\left(7+5 x^2\right)^4}{\left(2+x^2-x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^4/(2 + x^2 - x^4)^(3/2),x]","\frac{625}{3} \sqrt{-x^4+x^2+2} x+\frac{\left(83489 x^2+83585\right) x}{18 \sqrt{-x^4+x^2+2}}+\frac{31921}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{165239}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{625}{3} \sqrt{-x^4+x^2+2} x+\frac{\left(83489 x^2+83585\right) x}{18 \sqrt{-x^4+x^2+2}}+\frac{31921}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{165239}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(83585 + 83489*x^2))/(18*Sqrt[2 + x^2 - x^4]) + (625*x*Sqrt[2 + x^2 - x^4])/3 - (165239*EllipticE[ArcSin[x/Sqrt[2]], -2])/18 + (31921*EllipticF[ArcSin[x/Sqrt[2]], -2])/6","A",6,6,24,0.2500,1,"{1205, 1679, 1180, 524, 424, 419}"
341,1,55,0,0.0514476,"\int \frac{\left(7+5 x^2\right)^3}{\left(2+x^2-x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^3/(2 + x^2 - x^4)^(3/2),x]","\frac{x \left(4897 x^2+4945\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{1763}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{7147}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{x \left(4897 x^2+4945\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{1763}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{7147}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(4945 + 4897*x^2))/(18*Sqrt[2 + x^2 - x^4]) - (7147*EllipticE[ArcSin[x/Sqrt[2]], -2])/18 + (1763*EllipticF[ArcSin[x/Sqrt[2]], -2])/6","A",5,5,24,0.2083,1,"{1205, 1180, 524, 424, 419}"
342,1,55,0,0.0511672,"\int \frac{\left(7+5 x^2\right)^2}{\left(2+x^2-x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^2/(2 + x^2 - x^4)^(3/2),x]","\frac{x \left(281 x^2+305\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{139}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{281}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{x \left(281 x^2+305\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{139}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{281}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(305 + 281*x^2))/(18*Sqrt[2 + x^2 - x^4]) - (281*EllipticE[ArcSin[x/Sqrt[2]], -2])/18 + (139*EllipticF[ArcSin[x/Sqrt[2]], -2])/6","A",5,5,24,0.2083,1,"{1205, 1180, 524, 424, 419}"
343,1,55,0,0.0453853,"\int \frac{7+5 x^2}{\left(2+x^2-x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)/(2 + x^2 - x^4)^(3/2),x]","\frac{x \left(13 x^2+25\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{17}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{13}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{x \left(13 x^2+25\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{17}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{13}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(25 + 13*x^2))/(18*Sqrt[2 + x^2 - x^4]) - (13*EllipticE[ArcSin[x/Sqrt[2]], -2])/18 + (17*EllipticF[ArcSin[x/Sqrt[2]], -2])/6","A",5,5,22,0.2273,1,"{1178, 1180, 524, 424, 419}"
344,1,55,0,0.0408684,"\int \frac{1}{\left(2+x^2-x^4\right)^{3/2}} \, dx","Int[(2 + x^2 - x^4)^(-3/2),x]","\frac{x \left(5-x^2\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{1}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{x \left(5-x^2\right)}{18 \sqrt{-x^4+x^2+2}}+\frac{1}{6} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{1}{18} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(5 - x^2))/(18*Sqrt[2 + x^2 - x^4]) + EllipticE[ArcSin[x/Sqrt[2]], -2]/18 + EllipticF[ArcSin[x/Sqrt[2]], -2]/6","A",5,5,14,0.3571,1,"{1092, 1180, 524, 424, 419}"
345,1,72,0,0.0895718,"\int \frac{1}{\left(7+5 x^2\right) \left(2+x^2-x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)*(2 + x^2 - x^4)^(3/2)),x]","\frac{x \left(35-16 x^2\right)}{306 \sqrt{-x^4+x^2+2}}+\frac{1}{102} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{8}{153} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{25}{238} \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)","\frac{x \left(35-16 x^2\right)}{306 \sqrt{-x^4+x^2+2}}+\frac{1}{102} F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)+\frac{8}{153} E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)-\frac{25}{238} \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)",1,"(x*(35 - 16*x^2))/(306*Sqrt[2 + x^2 - x^4]) + (8*EllipticE[ArcSin[x/Sqrt[2]], -2])/153 + EllipticF[ArcSin[x/Sqrt[2]], -2]/102 - (25*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/238","A",8,8,24,0.3333,1,"{1221, 1178, 1180, 524, 424, 419, 1212, 537}"
346,1,100,0,0.2966408,"\int \frac{1}{\left(7+5 x^2\right)^2 \left(2+x^2-x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)^2*(2 + x^2 - x^4)^(3/2)),x]","\frac{625 \sqrt{-x^4+x^2+2} x}{16184 \left(5 x^2+7\right)}+\frac{\left(580-287 x^2\right) x}{10404 \sqrt{-x^4+x^2+2}}+\frac{89 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{24276}+\frac{5143 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{145656}-\frac{10825 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{113288}","\frac{625 \sqrt{-x^4+x^2+2} x}{16184 \left(5 x^2+7\right)}+\frac{\left(580-287 x^2\right) x}{10404 \sqrt{-x^4+x^2+2}}+\frac{89 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{24276}+\frac{5143 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{145656}-\frac{10825 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{113288}",1,"(x*(580 - 287*x^2))/(10404*Sqrt[2 + x^2 - x^4]) + (625*x*Sqrt[2 + x^2 - x^4])/(16184*(7 + 5*x^2)) + (5143*EllipticE[ArcSin[x/Sqrt[2]], -2])/145656 + (89*EllipticF[ArcSin[x/Sqrt[2]], -2])/24276 - (10825*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/113288","A",17,10,24,0.4167,1,"{1228, 1178, 1180, 524, 424, 419, 1223, 1716, 1212, 537}"
347,1,128,0,0.5701368,"\int \frac{1}{\left(7+5 x^2\right)^3 \left(2+x^2-x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)^3*(2 + x^2 - x^4)^(3/2)),x]","\frac{645625 \sqrt{-x^4+x^2+2} x}{15407168 \left(5 x^2+7\right)}+\frac{625 \sqrt{-x^4+x^2+2} x}{32368 \left(5 x^2+7\right)^2}+\frac{\left(9830-4909 x^2\right) x}{353736 \sqrt{-x^4+x^2+2}}+\frac{60409 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{23110752}+\frac{3086453 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{138664512}-\frac{6898575 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{107850176}","\frac{645625 \sqrt{-x^4+x^2+2} x}{15407168 \left(5 x^2+7\right)}+\frac{625 \sqrt{-x^4+x^2+2} x}{32368 \left(5 x^2+7\right)^2}+\frac{\left(9830-4909 x^2\right) x}{353736 \sqrt{-x^4+x^2+2}}+\frac{60409 F\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{23110752}+\frac{3086453 E\left(\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{138664512}-\frac{6898575 \Pi \left(-\frac{10}{7};\left.\sin ^{-1}\left(\frac{x}{\sqrt{2}}\right)\right|-2\right)}{107850176}",1,"(x*(9830 - 4909*x^2))/(353736*Sqrt[2 + x^2 - x^4]) + (625*x*Sqrt[2 + x^2 - x^4])/(32368*(7 + 5*x^2)^2) + (645625*x*Sqrt[2 + x^2 - x^4])/(15407168*(7 + 5*x^2)) + (3086453*EllipticE[ArcSin[x/Sqrt[2]], -2])/138664512 + (60409*EllipticF[ArcSin[x/Sqrt[2]], -2])/23110752 - (6898575*EllipticPi[-10/7, ArcSin[x/Sqrt[2]], -2])/107850176","A",26,11,24,0.4583,1,"{1228, 1178, 1180, 524, 424, 419, 1223, 1696, 1716, 1212, 537}"
348,1,242,0,0.1503628,"\int \left(7+5 x^2\right)^4 \sqrt{4+3 x^2+x^4} \, dx","Int[(7 + 5*x^2)^4*Sqrt[4 + 3*x^2 + x^4],x]","\frac{625}{11} \left(x^4+3 x^2+4\right)^{3/2} x^5+\frac{23500}{99} \left(x^4+3 x^2+4\right)^{3/2} x^3+\frac{3050}{11} \left(x^4+3 x^2+4\right)^{3/2} x+\frac{1}{33} \left(4516 x^2+18727\right) \sqrt{x^4+3 x^2+4} x+\frac{51665 \sqrt{x^4+3 x^2+4} x}{33 \left(x^2+2\right)}+\frac{33159 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{11 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{51665 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{33 \sqrt{x^4+3 x^2+4}}","\frac{625}{11} \left(x^4+3 x^2+4\right)^{3/2} x^5+\frac{23500}{99} \left(x^4+3 x^2+4\right)^{3/2} x^3+\frac{3050}{11} \left(x^4+3 x^2+4\right)^{3/2} x+\frac{1}{33} \left(4516 x^2+18727\right) \sqrt{x^4+3 x^2+4} x+\frac{51665 \sqrt{x^4+3 x^2+4} x}{33 \left(x^2+2\right)}+\frac{33159 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{11 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{51665 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{33 \sqrt{x^4+3 x^2+4}}",1,"(51665*x*Sqrt[4 + 3*x^2 + x^4])/(33*(2 + x^2)) + (x*(18727 + 4516*x^2)*Sqrt[4 + 3*x^2 + x^4])/33 + (3050*x*(4 + 3*x^2 + x^4)^(3/2))/11 + (23500*x^3*(4 + 3*x^2 + x^4)^(3/2))/99 + (625*x^5*(4 + 3*x^2 + x^4)^(3/2))/11 - (51665*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(33*Sqrt[4 + 3*x^2 + x^4]) + (33159*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(11*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",7,6,24,0.2500,1,"{1206, 1679, 1176, 1197, 1103, 1195}"
349,1,221,0,0.112281,"\int \left(7+5 x^2\right)^3 \sqrt{4+3 x^2+x^4} \, dx","Int[(7 + 5*x^2)^3*Sqrt[4 + 3*x^2 + x^4],x]","\frac{125}{9} \left(x^4+3 x^2+4\right)^{3/2} x^3+\frac{275}{7} \left(x^4+3 x^2+4\right)^{3/2} x+\frac{1}{21} \left(407 x^2+1708\right) \sqrt{x^4+3 x^2+4} x+\frac{4717 \sqrt{x^4+3 x^2+4} x}{21 \left(x^2+2\right)}+\frac{1301 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{4717 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{21 \sqrt{x^4+3 x^2+4}}","\frac{125}{9} \left(x^4+3 x^2+4\right)^{3/2} x^3+\frac{275}{7} \left(x^4+3 x^2+4\right)^{3/2} x+\frac{1}{21} \left(407 x^2+1708\right) \sqrt{x^4+3 x^2+4} x+\frac{4717 \sqrt{x^4+3 x^2+4} x}{21 \left(x^2+2\right)}+\frac{1301 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{4717 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{21 \sqrt{x^4+3 x^2+4}}",1,"(4717*x*Sqrt[4 + 3*x^2 + x^4])/(21*(2 + x^2)) + (x*(1708 + 407*x^2)*Sqrt[4 + 3*x^2 + x^4])/21 + (275*x*(4 + 3*x^2 + x^4)^(3/2))/7 + (125*x^3*(4 + 3*x^2 + x^4)^(3/2))/9 - (4717*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(21*Sqrt[4 + 3*x^2 + x^4]) + (1301*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(3*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",6,6,24,0.2500,1,"{1206, 1679, 1176, 1197, 1103, 1195}"
350,1,198,0,0.0772802,"\int \left(7+5 x^2\right)^2 \sqrt{4+3 x^2+x^4} \, dx","Int[(7 + 5*x^2)^2*Sqrt[4 + 3*x^2 + x^4],x]","\frac{25}{7} x \left(x^4+3 x^2+4\right)^{3/2}+\frac{1}{7} x \left(38 x^2+119\right) \sqrt{x^4+3 x^2+4}+\frac{319 x \sqrt{x^4+3 x^2+4}}{7 \left(x^2+2\right)}+\frac{81 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{319 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{7 \sqrt{x^4+3 x^2+4}}","\frac{25}{7} x \left(x^4+3 x^2+4\right)^{3/2}+\frac{1}{7} x \left(38 x^2+119\right) \sqrt{x^4+3 x^2+4}+\frac{319 x \sqrt{x^4+3 x^2+4}}{7 \left(x^2+2\right)}+\frac{81 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{319 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{7 \sqrt{x^4+3 x^2+4}}",1,"(319*x*Sqrt[4 + 3*x^2 + x^4])/(7*(2 + x^2)) + (x*(119 + 38*x^2)*Sqrt[4 + 3*x^2 + x^4])/7 + (25*x*(4 + 3*x^2 + x^4)^(3/2))/7 - (319*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(7*Sqrt[4 + 3*x^2 + x^4]) + (81*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",5,5,24,0.2083,1,"{1206, 1176, 1197, 1103, 1195}"
351,1,177,0,0.0539762,"\int \left(7+5 x^2\right) \sqrt{4+3 x^2+x^4} \, dx","Int[(7 + 5*x^2)*Sqrt[4 + 3*x^2 + x^4],x]","\frac{1}{3} \left(3 x^2+10\right) \sqrt{x^4+3 x^2+4} x+\frac{9 \sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{49 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{9 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}","\frac{1}{3} \left(3 x^2+10\right) \sqrt{x^4+3 x^2+4} x+\frac{9 \sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{49 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{9 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}",1,"(9*x*Sqrt[4 + 3*x^2 + x^4])/(2 + x^2) + (x*(10 + 3*x^2)*Sqrt[4 + 3*x^2 + x^4])/3 - (9*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/Sqrt[4 + 3*x^2 + x^4] + (49*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(3*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",4,4,22,0.1818,1,"{1176, 1197, 1103, 1195}"
352,1,169,0,0.0508969,"\int \sqrt{4+3 x^2+x^4} \, dx","Int[Sqrt[4 + 3*x^2 + x^4],x]","\frac{\sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{1}{3} \sqrt{x^4+3 x^2+4} x+\frac{7 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{\sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}","\frac{\sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{1}{3} \sqrt{x^4+3 x^2+4} x+\frac{7 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{\sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}",1,"(x*Sqrt[4 + 3*x^2 + x^4])/3 + (x*Sqrt[4 + 3*x^2 + x^4])/(2 + x^2) - (Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/Sqrt[4 + 3*x^2 + x^4] + (7*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(3*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",4,4,14,0.2857,1,"{1091, 1197, 1103, 1195}"
353,1,322,0,0.1516237,"\int \frac{\sqrt{4+3 x^2+x^4}}{7+5 x^2} \, dx","Int[Sqrt[4 + 3*x^2 + x^4]/(7 + 5*x^2),x]","\frac{\sqrt{x^4+3 x^2+4} x}{5 \left(x^2+2\right)}+\frac{1}{5} \sqrt{\frac{11}{35}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)-\frac{11 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{75 \sqrt{x^4+3 x^2+4}}+\frac{9 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{25 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{\sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{5 \sqrt{x^4+3 x^2+4}}+\frac{187 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{525 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{\sqrt{x^4+3 x^2+4} x}{5 \left(x^2+2\right)}+\frac{1}{5} \sqrt{\frac{11}{35}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)-\frac{11 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{75 \sqrt{x^4+3 x^2+4}}+\frac{9 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{25 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{\sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{5 \sqrt{x^4+3 x^2+4}}+\frac{187 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{525 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(x*Sqrt[4 + 3*x^2 + x^4])/(5*(2 + x^2)) + (Sqrt[11/35]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/5 - (Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(5*Sqrt[4 + 3*x^2 + x^4]) + (9*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(25*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (11*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(75*Sqrt[4 + 3*x^2 + x^4]) + (187*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(525*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",7,6,24,0.2500,1,"{1208, 1197, 1103, 1195, 1216, 1706}"
354,1,284,0,0.1506214,"\int \frac{\sqrt{4+3 x^2+x^4}}{\left(7+5 x^2\right)^2} \, dx","Int[Sqrt[4 + 3*x^2 + x^4]/(7 + 5*x^2)^2,x]","-\frac{\sqrt{x^4+3 x^2+4} x}{70 \left(x^2+2\right)}+\frac{\sqrt{x^4+3 x^2+4} x}{14 \left(5 x^2+7\right)}+\frac{51 \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{280 \sqrt{385}}-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{35 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{35 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{289 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{9800 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{\sqrt{x^4+3 x^2+4} x}{70 \left(x^2+2\right)}+\frac{\sqrt{x^4+3 x^2+4} x}{14 \left(5 x^2+7\right)}+\frac{51 \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{280 \sqrt{385}}-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{35 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{35 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{289 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{9800 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"-(x*Sqrt[4 + 3*x^2 + x^4])/(70*(2 + x^2)) + (x*Sqrt[4 + 3*x^2 + x^4])/(14*(7 + 5*x^2)) + (51*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/(280*Sqrt[385]) + ((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(35*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - ((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(35*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (289*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(9800*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",7,6,24,0.2500,1,"{1226, 1197, 1103, 1195, 1216, 1706}"
355,1,312,0,0.7109427,"\int \frac{\sqrt{4+3 x^2+x^4}}{\left(7+5 x^2\right)^3} \, dx","Int[Sqrt[4 + 3*x^2 + x^4]/(7 + 5*x^2)^3,x]","-\frac{139 \sqrt{x^4+3 x^2+4} x}{86240 \left(x^2+2\right)}+\frac{139 \sqrt{x^4+3 x^2+4} x}{17248 \left(5 x^2+7\right)}+\frac{\sqrt{x^4+3 x^2+4} x}{28 \left(5 x^2+7\right)^2}+\frac{14999 \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{344960 \sqrt{385}}-\frac{23 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2940 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{139 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{43120 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{254983 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{36220800 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{139 \sqrt{x^4+3 x^2+4} x}{86240 \left(x^2+2\right)}+\frac{139 \sqrt{x^4+3 x^2+4} x}{17248 \left(5 x^2+7\right)}+\frac{\sqrt{x^4+3 x^2+4} x}{28 \left(5 x^2+7\right)^2}+\frac{14999 \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{344960 \sqrt{385}}-\frac{23 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2940 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{139 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{43120 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{254983 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{36220800 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(-139*x*Sqrt[4 + 3*x^2 + x^4])/(86240*(2 + x^2)) + (x*Sqrt[4 + 3*x^2 + x^4])/(28*(7 + 5*x^2)^2) + (139*x*Sqrt[4 + 3*x^2 + x^4])/(17248*(7 + 5*x^2)) + (14999*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/(344960*Sqrt[385]) + (139*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(43120*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (23*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(2940*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (254983*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(36220800*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",18,9,24,0.3750,1,"{1228, 1223, 1696, 1714, 1195, 1708, 1103, 1706, 1216}"
356,1,268,0,0.1738731,"\int \left(7+5 x^2\right)^4 \left(4+3 x^2+x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^4*(4 + 3*x^2 + x^4)^(3/2),x]","\frac{125}{3} \left(x^4+3 x^2+4\right)^{5/2} x^5+\frac{2250}{13} \left(x^4+3 x^2+4\right)^{5/2} x^3+\frac{92150}{429} \left(x^4+3 x^2+4\right)^{5/2} x+\frac{\left(131080 x^2+452001\right) \left(x^4+3 x^2+4\right)^{3/2} x}{1287}+\frac{7 \left(174989 x^2+661429\right) \sqrt{x^4+3 x^2+4} x}{2145}+\frac{12665086 \sqrt{x^4+3 x^2+4} x}{2145 \left(x^2+2\right)}+\frac{2383556 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{429 \sqrt{x^4+3 x^2+4}}-\frac{12665086 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2145 \sqrt{x^4+3 x^2+4}}","\frac{125}{3} \left(x^4+3 x^2+4\right)^{5/2} x^5+\frac{2250}{13} \left(x^4+3 x^2+4\right)^{5/2} x^3+\frac{92150}{429} \left(x^4+3 x^2+4\right)^{5/2} x+\frac{\left(131080 x^2+452001\right) \left(x^4+3 x^2+4\right)^{3/2} x}{1287}+\frac{7 \left(174989 x^2+661429\right) \sqrt{x^4+3 x^2+4} x}{2145}+\frac{12665086 \sqrt{x^4+3 x^2+4} x}{2145 \left(x^2+2\right)}+\frac{2383556 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{429 \sqrt{x^4+3 x^2+4}}-\frac{12665086 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2145 \sqrt{x^4+3 x^2+4}}",1,"(12665086*x*Sqrt[4 + 3*x^2 + x^4])/(2145*(2 + x^2)) + (7*x*(661429 + 174989*x^2)*Sqrt[4 + 3*x^2 + x^4])/2145 + (x*(452001 + 131080*x^2)*(4 + 3*x^2 + x^4)^(3/2))/1287 + (92150*x*(4 + 3*x^2 + x^4)^(5/2))/429 + (2250*x^3*(4 + 3*x^2 + x^4)^(5/2))/13 + (125*x^5*(4 + 3*x^2 + x^4)^(5/2))/3 - (12665086*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(2145*Sqrt[4 + 3*x^2 + x^4]) + (2383556*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(429*Sqrt[4 + 3*x^2 + x^4])","A",8,6,24,0.2500,1,"{1206, 1679, 1176, 1197, 1103, 1195}"
357,1,247,0,0.1299298,"\int \left(7+5 x^2\right)^3 \left(4+3 x^2+x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^3*(4 + 3*x^2 + x^4)^(3/2),x]","\frac{125}{13} \left(x^4+3 x^2+4\right)^{5/2} x^3+\frac{3825}{143} \left(x^4+3 x^2+4\right)^{5/2} x+\frac{\left(15365 x^2+53504\right) \left(x^4+3 x^2+4\right)^{3/2} x}{1001}+\frac{\left(435441 x^2+1653701\right) \sqrt{x^4+3 x^2+4} x}{5005}+\frac{4525662 \sqrt{x^4+3 x^2+4} x}{5005 \left(x^2+2\right)}+\frac{121826 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{143 \sqrt{x^4+3 x^2+4}}-\frac{4525662 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{5005 \sqrt{x^4+3 x^2+4}}","\frac{125}{13} \left(x^4+3 x^2+4\right)^{5/2} x^3+\frac{3825}{143} \left(x^4+3 x^2+4\right)^{5/2} x+\frac{\left(15365 x^2+53504\right) \left(x^4+3 x^2+4\right)^{3/2} x}{1001}+\frac{\left(435441 x^2+1653701\right) \sqrt{x^4+3 x^2+4} x}{5005}+\frac{4525662 \sqrt{x^4+3 x^2+4} x}{5005 \left(x^2+2\right)}+\frac{121826 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{143 \sqrt{x^4+3 x^2+4}}-\frac{4525662 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{5005 \sqrt{x^4+3 x^2+4}}",1,"(4525662*x*Sqrt[4 + 3*x^2 + x^4])/(5005*(2 + x^2)) + (x*(1653701 + 435441*x^2)*Sqrt[4 + 3*x^2 + x^4])/5005 + (x*(53504 + 15365*x^2)*(4 + 3*x^2 + x^4)^(3/2))/1001 + (3825*x*(4 + 3*x^2 + x^4)^(5/2))/143 + (125*x^3*(4 + 3*x^2 + x^4)^(5/2))/13 - (4525662*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(5005*Sqrt[4 + 3*x^2 + x^4]) + (121826*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(143*Sqrt[4 + 3*x^2 + x^4])","A",7,6,24,0.2500,1,"{1206, 1679, 1176, 1197, 1103, 1195}"
358,1,226,0,0.0979694,"\int \left(7+5 x^2\right)^2 \left(4+3 x^2+x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)^2*(4 + 3*x^2 + x^4)^(3/2),x]","\frac{25}{11} x \left(x^4+3 x^2+4\right)^{5/2}+\frac{1}{693} x \left(2240 x^2+6831\right) \left(x^4+3 x^2+4\right)^{3/2}+\frac{x \left(18253 x^2+64533\right) \sqrt{x^4+3 x^2+4}}{1155}+\frac{175346 x \sqrt{x^4+3 x^2+4}}{1155 \left(x^2+2\right)}+\frac{4628 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{33 \sqrt{x^4+3 x^2+4}}-\frac{175346 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{1155 \sqrt{x^4+3 x^2+4}}","\frac{25}{11} x \left(x^4+3 x^2+4\right)^{5/2}+\frac{1}{693} x \left(2240 x^2+6831\right) \left(x^4+3 x^2+4\right)^{3/2}+\frac{x \left(18253 x^2+64533\right) \sqrt{x^4+3 x^2+4}}{1155}+\frac{175346 x \sqrt{x^4+3 x^2+4}}{1155 \left(x^2+2\right)}+\frac{4628 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{33 \sqrt{x^4+3 x^2+4}}-\frac{175346 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{1155 \sqrt{x^4+3 x^2+4}}",1,"(175346*x*Sqrt[4 + 3*x^2 + x^4])/(1155*(2 + x^2)) + (x*(64533 + 18253*x^2)*Sqrt[4 + 3*x^2 + x^4])/1155 + (x*(6831 + 2240*x^2)*(4 + 3*x^2 + x^4)^(3/2))/693 + (25*x*(4 + 3*x^2 + x^4)^(5/2))/11 - (175346*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(1155*Sqrt[4 + 3*x^2 + x^4]) + (4628*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(33*Sqrt[4 + 3*x^2 + x^4])","A",6,5,24,0.2083,1,"{1206, 1176, 1197, 1103, 1195}"
359,1,207,0,0.0712722,"\int \left(7+5 x^2\right) \left(4+3 x^2+x^4\right)^{3/2} \, dx","Int[(7 + 5*x^2)*(4 + 3*x^2 + x^4)^(3/2),x]","\frac{1}{63} x \left(35 x^2+108\right) \left(x^4+3 x^2+4\right)^{3/2}+\frac{1}{105} x \left(289 x^2+1029\right) \sqrt{x^4+3 x^2+4}+\frac{2798 x \sqrt{x^4+3 x^2+4}}{105 \left(x^2+2\right)}+\frac{74 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{x^4+3 x^2+4}}-\frac{2798 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{105 \sqrt{x^4+3 x^2+4}}","\frac{1}{63} x \left(35 x^2+108\right) \left(x^4+3 x^2+4\right)^{3/2}+\frac{1}{105} x \left(289 x^2+1029\right) \sqrt{x^4+3 x^2+4}+\frac{2798 x \sqrt{x^4+3 x^2+4}}{105 \left(x^2+2\right)}+\frac{74 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3 \sqrt{x^4+3 x^2+4}}-\frac{2798 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{105 \sqrt{x^4+3 x^2+4}}",1,"(2798*x*Sqrt[4 + 3*x^2 + x^4])/(105*(2 + x^2)) + (x*(1029 + 289*x^2)*Sqrt[4 + 3*x^2 + x^4])/105 + (x*(108 + 35*x^2)*(4 + 3*x^2 + x^4)^(3/2))/63 - (2798*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(105*Sqrt[4 + 3*x^2 + x^4]) + (74*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(3*Sqrt[4 + 3*x^2 + x^4])","A",5,4,22,0.1818,1,"{1176, 1197, 1103, 1195}"
360,1,198,0,0.0689473,"\int \left(4+3 x^2+x^4\right)^{3/2} \, dx","Int[(4 + 3*x^2 + x^4)^(3/2),x]","\frac{1}{7} x \left(x^4+3 x^2+4\right)^{3/2}+\frac{1}{35} x \left(9 x^2+49\right) \sqrt{x^4+3 x^2+4}+\frac{138 x \sqrt{x^4+3 x^2+4}}{35 \left(x^2+2\right)}+\frac{4 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}-\frac{138 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{35 \sqrt{x^4+3 x^2+4}}","\frac{1}{7} x \left(x^4+3 x^2+4\right)^{3/2}+\frac{1}{35} x \left(9 x^2+49\right) \sqrt{x^4+3 x^2+4}+\frac{138 x \sqrt{x^4+3 x^2+4}}{35 \left(x^2+2\right)}+\frac{4 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}-\frac{138 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{35 \sqrt{x^4+3 x^2+4}}",1,"(138*x*Sqrt[4 + 3*x^2 + x^4])/(35*(2 + x^2)) + (x*(49 + 9*x^2)*Sqrt[4 + 3*x^2 + x^4])/35 + (x*(4 + 3*x^2 + x^4)^(3/2))/7 - (138*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(35*Sqrt[4 + 3*x^2 + x^4]) + (4*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/Sqrt[4 + 3*x^2 + x^4]","A",5,5,14,0.3571,1,"{1091, 1176, 1197, 1103, 1195}"
361,1,284,0,0.2361147,"\int \frac{\left(4+3 x^2+x^4\right)^{3/2}}{7+5 x^2} \, dx","Int[(4 + 3*x^2 + x^4)^(3/2)/(7 + 5*x^2),x]","\frac{1}{75} \left(3 x^2+11\right) \sqrt{x^4+3 x^2+4} x+\frac{94 \sqrt{x^4+3 x^2+4} x}{125 \left(x^2+2\right)}+\frac{44}{125} \sqrt{\frac{11}{35}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)+\frac{54 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{125 \sqrt{x^4+3 x^2+4}}-\frac{94 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{125 \sqrt{x^4+3 x^2+4}}+\frac{4114 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{13125 \sqrt{x^4+3 x^2+4}}","\frac{1}{75} \left(3 x^2+11\right) \sqrt{x^4+3 x^2+4} x+\frac{94 \sqrt{x^4+3 x^2+4} x}{125 \left(x^2+2\right)}+\frac{44}{125} \sqrt{\frac{11}{35}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)+\frac{54 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{125 \sqrt{x^4+3 x^2+4}}-\frac{94 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{125 \sqrt{x^4+3 x^2+4}}+\frac{4114 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{13125 \sqrt{x^4+3 x^2+4}}",1,"(94*x*Sqrt[4 + 3*x^2 + x^4])/(125*(2 + x^2)) + (x*(11 + 3*x^2)*Sqrt[4 + 3*x^2 + x^4])/75 + (44*Sqrt[11/35]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/125 - (94*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(125*Sqrt[4 + 3*x^2 + x^4]) + (54*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(125*Sqrt[4 + 3*x^2 + x^4]) + (4114*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(13125*Sqrt[4 + 3*x^2 + x^4])","A",12,7,24,0.2917,1,"{1208, 1176, 1197, 1103, 1195, 1216, 1706}"
362,1,372,0,0.5343788,"\int \frac{\left(4+3 x^2+x^4\right)^{3/2}}{\left(7+5 x^2\right)^2} \, dx","Int[(4 + 3*x^2 + x^4)^(3/2)/(7 + 5*x^2)^2,x]","\frac{4 \sqrt{x^4+3 x^2+4} x}{175 \left(x^2+2\right)}+\frac{22 \sqrt{x^4+3 x^2+4} x}{175 \left(5 x^2+7\right)}+\frac{1}{75} \sqrt{x^4+3 x^2+4} x+\frac{13}{350} \sqrt{\frac{11}{35}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)+\frac{4 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{175 \sqrt{x^4+3 x^2+4}}-\frac{4 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{175 \sqrt{x^4+3 x^2+4}}+\frac{187 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{13125 \sqrt{x^4+3 x^2+4}}+\frac{6919 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{183750 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{4 \sqrt{x^4+3 x^2+4} x}{175 \left(x^2+2\right)}+\frac{22 \sqrt{x^4+3 x^2+4} x}{175 \left(5 x^2+7\right)}+\frac{1}{75} \sqrt{x^4+3 x^2+4} x+\frac{13}{350} \sqrt{\frac{11}{35}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)+\frac{4 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{175 \sqrt{x^4+3 x^2+4}}-\frac{4 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{175 \sqrt{x^4+3 x^2+4}}+\frac{2431 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{36750 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(x*Sqrt[4 + 3*x^2 + x^4])/75 + (4*x*Sqrt[4 + 3*x^2 + x^4])/(175*(2 + x^2)) + (22*x*Sqrt[4 + 3*x^2 + x^4])/(175*(7 + 5*x^2)) + (13*Sqrt[11/35]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/350 - (4*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(175*Sqrt[4 + 3*x^2 + x^4]) + (4*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(175*Sqrt[4 + 3*x^2 + x^4]) + (6919*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(183750*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (187*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(13125*Sqrt[4 + 3*x^2 + x^4])","A",19,11,24,0.4583,1,"{1228, 1103, 1139, 1195, 1122, 1197, 1223, 1714, 1708, 1706, 1216}"
363,1,440,0,0.7997089,"\int \frac{\left(4+3 x^2+x^4\right)^{3/2}}{\left(7+5 x^2\right)^3} \, dx","Int[(4 + 3*x^2 + x^4)^(3/2)/(7 + 5*x^2)^3,x]","\frac{9 \sqrt{x^4+3 x^2+4} x}{1960 \left(x^2+2\right)}+\frac{167 \sqrt{x^4+3 x^2+4} x}{9800 \left(5 x^2+7\right)}+\frac{11 \sqrt{x^4+3 x^2+4} x}{175 \left(5 x^2+7\right)^2}+\frac{1347 \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{7840 \sqrt{385}}-\frac{22 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{13125 \sqrt{x^4+3 x^2+4}}-\frac{817 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{91875 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{6 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{875 \sqrt{x^4+3 x^2+4}}+\frac{111 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{24500 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{7633 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{274400 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{9 \sqrt{x^4+3 x^2+4} x}{1960 \left(x^2+2\right)}+\frac{167 \sqrt{x^4+3 x^2+4} x}{9800 \left(5 x^2+7\right)}+\frac{11 \sqrt{x^4+3 x^2+4} x}{175 \left(5 x^2+7\right)^2}+\frac{1347 \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{7840 \sqrt{385}}-\frac{22 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{13125 \sqrt{x^4+3 x^2+4}}-\frac{817 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{91875 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{6 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{875 \sqrt{x^4+3 x^2+4}}+\frac{111 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{24500 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{7633 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{274400 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(9*x*Sqrt[4 + 3*x^2 + x^4])/(1960*(2 + x^2)) + (11*x*Sqrt[4 + 3*x^2 + x^4])/(175*(7 + 5*x^2)^2) + (167*x*Sqrt[4 + 3*x^2 + x^4])/(9800*(7 + 5*x^2)) + (1347*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/(7840*Sqrt[385]) + (111*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(24500*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (6*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(875*Sqrt[4 + 3*x^2 + x^4]) - (817*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(91875*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (22*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(13125*Sqrt[4 + 3*x^2 + x^4]) + (7633*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(274400*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",22,10,24,0.4167,1,"{1228, 1103, 1139, 1195, 1223, 1696, 1714, 1708, 1706, 1216}"
364,1,187,0,0.0927102,"\int \frac{\left(7+5 x^2\right)^3}{\sqrt{4+3 x^2+x^4}} \, dx","Int[(7 + 5*x^2)^3/Sqrt[4 + 3*x^2 + x^4],x]","25 \sqrt{x^4+3 x^2+4} x^3-\frac{15 \sqrt{x^4+3 x^2+4} x}{x^2+2}+75 \sqrt{x^4+3 x^2+4} x+\frac{13 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{15 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}","25 \sqrt{x^4+3 x^2+4} x^3-\frac{15 \sqrt{x^4+3 x^2+4} x}{x^2+2}+75 \sqrt{x^4+3 x^2+4} x+\frac{13 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{15 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}",1,"75*x*Sqrt[4 + 3*x^2 + x^4] + 25*x^3*Sqrt[4 + 3*x^2 + x^4] - (15*x*Sqrt[4 + 3*x^2 + x^4])/(2 + x^2) + (15*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/Sqrt[4 + 3*x^2 + x^4] + (13*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(2*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",5,5,24,0.2083,1,"{1206, 1679, 1197, 1103, 1195}"
365,1,170,0,0.0588587,"\int \frac{\left(7+5 x^2\right)^2}{\sqrt{4+3 x^2+x^4}} \, dx","Int[(7 + 5*x^2)^2/Sqrt[4 + 3*x^2 + x^4],x]","\frac{20 \sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{25}{3} \sqrt{x^4+3 x^2+4} x+\frac{167 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{6 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{20 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}","\frac{20 \sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{25}{3} \sqrt{x^4+3 x^2+4} x+\frac{167 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{6 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{20 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}",1,"(25*x*Sqrt[4 + 3*x^2 + x^4])/3 + (20*x*Sqrt[4 + 3*x^2 + x^4])/(2 + x^2) - (20*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/Sqrt[4 + 3*x^2 + x^4] + (167*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(6*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1206, 1197, 1103, 1195}"
366,1,151,0,0.0361226,"\int \frac{7+5 x^2}{\sqrt{4+3 x^2+x^4}} \, dx","Int[(7 + 5*x^2)/Sqrt[4 + 3*x^2 + x^4],x]","\frac{5 \sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{17 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{5 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}","\frac{5 \sqrt{x^4+3 x^2+4} x}{x^2+2}+\frac{17 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{5 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{\sqrt{x^4+3 x^2+4}}",1,"(5*x*Sqrt[4 + 3*x^2 + x^4])/(2 + x^2) - (5*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/Sqrt[4 + 3*x^2 + x^4] + (17*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(2*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",3,3,22,0.1364,1,"{1197, 1103, 1195}"
367,1,64,0,0.0070358,"\int \frac{1}{\sqrt{4+3 x^2+x^4}} \, dx","Int[1/Sqrt[4 + 3*x^2 + x^4],x]","\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(2*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",1,1,14,0.07143,1,"{1103}"
368,1,168,0,0.0820125,"\int \frac{1}{\left(7+5 x^2\right) \sqrt{4+3 x^2+x^4}} \, dx","Int[1/((7 + 5*x^2)*Sqrt[4 + 3*x^2 + x^4]),x]","\frac{1}{4} \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{6 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{17 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{84 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{1}{4} \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{6 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{17 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{84 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(Sqrt[5/77]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/4 - ((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(6*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (17*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(84*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",3,3,24,0.1250,1,"{1216, 1103, 1706}"
369,1,286,0,0.2246176,"\int \frac{1}{\left(7+5 x^2\right)^2 \sqrt{4+3 x^2+x^4}} \, dx","Int[1/((7 + 5*x^2)^2*Sqrt[4 + 3*x^2 + x^4]),x]","-\frac{5 \sqrt{x^4+3 x^2+4} x}{616 \left(x^2+2\right)}+\frac{25 \sqrt{x^4+3 x^2+4} x}{616 \left(5 x^2+7\right)}+\frac{37 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{2464}-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{42 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{5 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{308 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{629 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{51744 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{5 \sqrt{x^4+3 x^2+4} x}{616 \left(x^2+2\right)}+\frac{25 \sqrt{x^4+3 x^2+4} x}{616 \left(5 x^2+7\right)}+\frac{37 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{2464}-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{42 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{5 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{308 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{629 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{51744 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(-5*x*Sqrt[4 + 3*x^2 + x^4])/(616*(2 + x^2)) + (25*x*Sqrt[4 + 3*x^2 + x^4])/(616*(7 + 5*x^2)) + (37*Sqrt[5/77]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/2464 + (5*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(308*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - ((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(42*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (629*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(51744*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",6,6,24,0.2500,1,"{1223, 1714, 1195, 1708, 1103, 1706}"
370,1,314,0,0.2897234,"\int \frac{1}{\left(7+5 x^2\right)^3 \sqrt{4+3 x^2+x^4}} \, dx","Int[1/((7 + 5*x^2)^3*Sqrt[4 + 3*x^2 + x^4]),x]","-\frac{555 \sqrt{x^4+3 x^2+4} x}{758912 \left(x^2+2\right)}+\frac{2775 \sqrt{x^4+3 x^2+4} x}{758912 \left(5 x^2+7\right)}+\frac{25 \sqrt{x^4+3 x^2+4} x}{1232 \left(5 x^2+7\right)^2}-\frac{3285 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{3035648}-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{8624 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{555 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{379456 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{18615 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{21249536 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{555 \sqrt{x^4+3 x^2+4} x}{758912 \left(x^2+2\right)}+\frac{2775 \sqrt{x^4+3 x^2+4} x}{758912 \left(5 x^2+7\right)}+\frac{25 \sqrt{x^4+3 x^2+4} x}{1232 \left(5 x^2+7\right)^2}-\frac{3285 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{3035648}-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{8624 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{555 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{379456 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{18615 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{21249536 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(-555*x*Sqrt[4 + 3*x^2 + x^4])/(758912*(2 + x^2)) + (25*x*Sqrt[4 + 3*x^2 + x^4])/(1232*(7 + 5*x^2)^2) + (2775*x*Sqrt[4 + 3*x^2 + x^4])/(758912*(7 + 5*x^2)) - (3285*Sqrt[5/77]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/3035648 + (555*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(379456*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - ((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(8624*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (18615*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(21249536*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",7,7,24,0.2917,1,"{1223, 1696, 1714, 1195, 1708, 1103, 1706}"
371,1,219,0,0.1210847,"\int \frac{\left(7+5 x^2\right)^5}{\left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^5/(4 + 3*x^2 + x^4)^(3/2),x]","625 \sqrt{x^4+3 x^2+4} x^3-\frac{220779 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}+\frac{5000}{3} \sqrt{x^4+3 x^2+4} x+\frac{\left(45779 x^2+99493\right) x}{28 \sqrt{x^4+3 x^2+4}}-\frac{130729 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{12 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{220779 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}","625 \sqrt{x^4+3 x^2+4} x^3-\frac{220779 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}+\frac{5000}{3} \sqrt{x^4+3 x^2+4} x+\frac{\left(45779 x^2+99493\right) x}{28 \sqrt{x^4+3 x^2+4}}-\frac{130729 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{12 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{220779 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(x*(99493 + 45779*x^2))/(28*Sqrt[4 + 3*x^2 + x^4]) + (5000*x*Sqrt[4 + 3*x^2 + x^4])/3 + 625*x^3*Sqrt[4 + 3*x^2 + x^4] - (220779*x*Sqrt[4 + 3*x^2 + x^4])/(28*(2 + x^2)) + (220779*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(14*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (130729*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(12*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",6,5,24,0.2083,1,"{1205, 1679, 1197, 1103, 1195}"
372,1,200,0,0.0892912,"\int \frac{\left(7+5 x^2\right)^4}{\left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^4/(4 + 3*x^2 + x^4)^(3/2),x]","\frac{14523 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}+\frac{625}{3} \sqrt{x^4+3 x^2+4} x+\frac{\left(2719-4023 x^2\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{4243 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{12 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{14523 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{14523 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}+\frac{625}{3} \sqrt{x^4+3 x^2+4} x+\frac{\left(2719-4023 x^2\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{4243 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{12 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{14523 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(x*(2719 - 4023*x^2))/(28*Sqrt[4 + 3*x^2 + x^4]) + (625*x*Sqrt[4 + 3*x^2 + x^4])/3 + (14523*x*Sqrt[4 + 3*x^2 + x^4])/(28*(2 + x^2)) - (14523*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(14*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (4243*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(12*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",5,5,24,0.2083,1,"{1205, 1679, 1197, 1103, 1195}"
373,1,181,0,0.0586473,"\int \frac{\left(7+5 x^2\right)^3}{\left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^3/(4 + 3*x^2 + x^4)^(3/2),x]","\frac{4449 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}-\frac{\left(949 x^2+2323\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{973 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{4449 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{4449 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}-\frac{\left(949 x^2+2323\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{973 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{4449 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"-(x*(2323 + 949*x^2))/(28*Sqrt[4 + 3*x^2 + x^4]) + (4449*x*Sqrt[4 + 3*x^2 + x^4])/(28*(2 + x^2)) - (4449*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(14*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (973*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(4*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1205, 1197, 1103, 1195}"
374,1,181,0,0.0586936,"\int \frac{\left(7+5 x^2\right)^2}{\left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)^2/(4 + 3*x^2 + x^4)^(3/2),x]","-\frac{113 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}-\frac{\left(9-113 x^2\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{9 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{113 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{113 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}-\frac{\left(9-113 x^2\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{9 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{113 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"-(x*(9 - 113*x^2))/(28*Sqrt[4 + 3*x^2 + x^4]) - (113*x*Sqrt[4 + 3*x^2 + x^4])/(28*(2 + x^2)) + (113*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(14*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (9*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(4*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1205, 1197, 1103, 1195}"
375,1,181,0,0.0523354,"\int \frac{7+5 x^2}{\left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[(7 + 5*x^2)/(4 + 3*x^2 + x^4)^(3/2),x]","-\frac{19 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}+\frac{\left(19 x^2+53\right) x}{28 \sqrt{x^4+3 x^2+4}}-\frac{3 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{19 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{19 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}+\frac{\left(19 x^2+53\right) x}{28 \sqrt{x^4+3 x^2+4}}-\frac{3 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{19 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(x*(53 + 19*x^2))/(28*Sqrt[4 + 3*x^2 + x^4]) - (19*x*Sqrt[4 + 3*x^2 + x^4])/(28*(2 + x^2)) + (19*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(14*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (3*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(4*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",4,4,22,0.1818,1,"{1178, 1197, 1103, 1195}"
376,1,181,0,0.0497633,"\int \frac{1}{\left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[(4 + 3*x^2 + x^4)^(-3/2),x]","\frac{3 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}-\frac{\left(3 x^2+1\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{3 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{3 \sqrt{x^4+3 x^2+4} x}{28 \left(x^2+2\right)}-\frac{\left(3 x^2+1\right) x}{28 \sqrt{x^4+3 x^2+4}}+\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{4 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{3 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{14 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"-(x*(1 + 3*x^2))/(28*Sqrt[4 + 3*x^2 + x^4]) + (3*x*Sqrt[4 + 3*x^2 + x^4])/(28*(2 + x^2)) - (3*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(14*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + ((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(4*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",4,4,14,0.2857,1,"{1092, 1197, 1103, 1195}"
377,1,284,0,0.1626704,"\int \frac{1}{\left(7+5 x^2\right) \left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)*(4 + 3*x^2 + x^4)^(3/2)),x]","\frac{\sqrt{x^4+3 x^2+4} x}{77 \left(x^2+2\right)}-\frac{\left(4 x^2+13\right) x}{308 \sqrt{x^4+3 x^2+4}}+\frac{25}{176} \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{12 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{\sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{77 \sqrt{x^4+3 x^2+4}}+\frac{425 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3696 \sqrt{2} \sqrt{x^4+3 x^2+4}}","\frac{\sqrt{x^4+3 x^2+4} x}{77 \left(x^2+2\right)}-\frac{\left(4 x^2+13\right) x}{308 \sqrt{x^4+3 x^2+4}}+\frac{25}{176} \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)-\frac{\left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{12 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{\sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{77 \sqrt{x^4+3 x^2+4}}+\frac{425 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{3696 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"-(x*(13 + 4*x^2))/(308*Sqrt[4 + 3*x^2 + x^4]) + (x*Sqrt[4 + 3*x^2 + x^4])/(77*(2 + x^2)) + (25*Sqrt[5/77]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/176 - (Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(77*Sqrt[4 + 3*x^2 + x^4]) - ((2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(12*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (425*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(3696*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",8,7,24,0.2917,1,"{1221, 1178, 1197, 1103, 1195, 1216, 1706}"
378,1,312,0,0.5049759,"\int \frac{1}{\left(7+5 x^2\right)^2 \left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)^2*(4 + 3*x^2 + x^4)^(3/2)),x]","-\frac{199 \sqrt{x^4+3 x^2+4} x}{27104 \left(x^2+2\right)}+\frac{625 \sqrt{x^4+3 x^2+4} x}{27104 \left(5 x^2+7\right)}+\frac{\left(37 x^2+24\right) x}{13552 \sqrt{x^4+3 x^2+4}}+\frac{575 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{108416}-\frac{2 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{231 \sqrt{x^4+3 x^2+4}}+\frac{199 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{13552 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{9775 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2276736 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{199 \sqrt{x^4+3 x^2+4} x}{27104 \left(x^2+2\right)}+\frac{625 \sqrt{x^4+3 x^2+4} x}{27104 \left(5 x^2+7\right)}+\frac{\left(37 x^2+24\right) x}{13552 \sqrt{x^4+3 x^2+4}}+\frac{575 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{108416}-\frac{2 \sqrt{2} \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{231 \sqrt{x^4+3 x^2+4}}+\frac{199 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{13552 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{9775 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{2276736 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(x*(24 + 37*x^2))/(13552*Sqrt[4 + 3*x^2 + x^4]) - (199*x*Sqrt[4 + 3*x^2 + x^4])/(27104*(2 + x^2)) + (625*x*Sqrt[4 + 3*x^2 + x^4])/(27104*(7 + 5*x^2)) + (575*Sqrt[5/77]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/108416 + (199*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(13552*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (2*Sqrt[2]*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(231*Sqrt[4 + 3*x^2 + x^4]) + (9775*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(2276736*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",15,10,24,0.4167,1,"{1228, 1178, 1197, 1103, 1195, 1223, 1714, 1708, 1706, 1216}"
379,1,340,0,0.8718992,"\int \frac{1}{\left(7+5 x^2\right)^3 \left(4+3 x^2+x^4\right)^{3/2}} \, dx","Int[1/((7 + 5*x^2)^3*(4 + 3*x^2 + x^4)^(3/2)),x]","-\frac{18159 \sqrt{x^4+3 x^2+4} x}{33392128 \left(x^2+2\right)}+\frac{51875 \sqrt{x^4+3 x^2+4} x}{33392128 \left(5 x^2+7\right)}+\frac{625 \sqrt{x^4+3 x^2+4} x}{54208 \left(5 x^2+7\right)^2}+\frac{\left(139 x^2+548\right) x}{596288 \sqrt{x^4+3 x^2+4}}-\frac{529425 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{133568512}+\frac{843 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{379456 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{18159 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{16696064 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{3000075 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{934979584 \sqrt{2} \sqrt{x^4+3 x^2+4}}","-\frac{18159 \sqrt{x^4+3 x^2+4} x}{33392128 \left(x^2+2\right)}+\frac{51875 \sqrt{x^4+3 x^2+4} x}{33392128 \left(5 x^2+7\right)}+\frac{625 \sqrt{x^4+3 x^2+4} x}{54208 \left(5 x^2+7\right)^2}+\frac{\left(139 x^2+548\right) x}{596288 \sqrt{x^4+3 x^2+4}}-\frac{529425 \sqrt{\frac{5}{77}} \tan ^{-1}\left(\frac{2 \sqrt{\frac{11}{35}} x}{\sqrt{x^4+3 x^2+4}}\right)}{133568512}+\frac{843 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{379456 \sqrt{2} \sqrt{x^4+3 x^2+4}}+\frac{18159 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{16696064 \sqrt{2} \sqrt{x^4+3 x^2+4}}-\frac{3000075 \left(x^2+2\right) \sqrt{\frac{x^4+3 x^2+4}{\left(x^2+2\right)^2}} \Pi \left(-\frac{9}{280};2 \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)|\frac{1}{8}\right)}{934979584 \sqrt{2} \sqrt{x^4+3 x^2+4}}",1,"(x*(548 + 139*x^2))/(596288*Sqrt[4 + 3*x^2 + x^4]) - (18159*x*Sqrt[4 + 3*x^2 + x^4])/(33392128*(2 + x^2)) + (625*x*Sqrt[4 + 3*x^2 + x^4])/(54208*(7 + 5*x^2)^2) + (51875*x*Sqrt[4 + 3*x^2 + x^4])/(33392128*(7 + 5*x^2)) - (529425*Sqrt[5/77]*ArcTan[(2*Sqrt[11/35]*x)/Sqrt[4 + 3*x^2 + x^4]])/133568512 + (18159*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticE[2*ArcTan[x/Sqrt[2]], 1/8])/(16696064*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) + (843*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticF[2*ArcTan[x/Sqrt[2]], 1/8])/(379456*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4]) - (3000075*(2 + x^2)*Sqrt[(4 + 3*x^2 + x^4)/(2 + x^2)^2]*EllipticPi[-9/280, 2*ArcTan[x/Sqrt[2]], 1/8])/(934979584*Sqrt[2]*Sqrt[4 + 3*x^2 + x^4])","A",22,11,24,0.4583,1,"{1228, 1178, 1197, 1103, 1195, 1223, 1696, 1714, 1708, 1706, 1216}"
380,1,467,0,0.4246829,"\int \frac{\left(d+e x^2\right)^3}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(d + e*x^2)^3/Sqrt[a + b*x^2 + c*x^4],x]","\frac{e x \sqrt{a+b x^2+c x^4} \left(-3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right)}{15 c^{5/2} \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}} \left(e \left(-3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right)+\frac{\sqrt{c} \left(4 a b e^3-15 a c d e^2+15 c^2 d^3\right)}{\sqrt{a}}\right) 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^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} e \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(-3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right) 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^{11/4} \sqrt{a+b x^2+c x^4}}+\frac{e^2 x \sqrt{a+b x^2+c x^4} (15 c d-4 b e)}{15 c^2}+\frac{e^3 x^3 \sqrt{a+b x^2+c x^4}}{5 c}","\frac{e x \sqrt{a+b x^2+c x^4} \left(-3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right)}{15 c^{5/2} \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}} \left(e \left(-3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right)+\frac{\sqrt{c} \left(4 a b e^3-15 a c d e^2+15 c^2 d^3\right)}{\sqrt{a}}\right) 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^{11/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} e \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(-3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right) 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^{11/4} \sqrt{a+b x^2+c x^4}}+\frac{e^2 x \sqrt{a+b x^2+c x^4} (15 c d-4 b e)}{15 c^2}+\frac{e^3 x^3 \sqrt{a+b x^2+c x^4}}{5 c}",1,"(e^2*(15*c*d - 4*b*e)*x*Sqrt[a + b*x^2 + c*x^4])/(15*c^2) + (e^3*x^3*Sqrt[a + b*x^2 + c*x^4])/(5*c) + (e*(45*c^2*d^2 + 8*b^2*e^2 - 3*c*e*(10*b*d + 3*a*e))*x*Sqrt[a + b*x^2 + c*x^4])/(15*c^(5/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*e*(45*c^2*d^2 + 8*b^2*e^2 - 3*c*e*(10*b*d + 3*a*e))*(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^(11/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*((Sqrt[c]*(15*c^2*d^3 - 15*a*c*d*e^2 + 4*a*b*e^3))/Sqrt[a] + e*(45*c^2*d^2 + 8*b^2*e^2 - 3*c*e*(10*b*d + 3*a*e)))*(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^(11/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,26,0.1923,1,"{1206, 1679, 1197, 1103, 1195}"
381,1,356,0,0.1913764,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(d + e*x^2)^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}} \left(\frac{\sqrt{c} \left(3 c d^2-a e^2\right)}{\sqrt{a}}+2 e (3 c d-b e)\right) 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 e x \sqrt{a+b x^2+c x^4} (3 c d-b e)}{3 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{2 \sqrt[4]{a} e \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}} (3 c d-b e) 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{e^2 x \sqrt{a+b x^2+c x^4}}{3 c}","\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}} \left(\frac{\sqrt{c} \left(3 c d^2-a e^2\right)}{\sqrt{a}}+2 e (3 c d-b e)\right) 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 e x \sqrt{a+b x^2+c x^4} (3 c d-b e)}{3 c^{3/2} \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{2 \sqrt[4]{a} e \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}} (3 c d-b e) 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{e^2 x \sqrt{a+b x^2+c x^4}}{3 c}",1,"(e^2*x*Sqrt[a + b*x^2 + c*x^4])/(3*c) + (2*e*(3*c*d - b*e)*x*Sqrt[a + b*x^2 + c*x^4])/(3*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (2*a^(1/4)*e*(3*c*d - b*e)*(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*e*(3*c*d - b*e) + (Sqrt[c]*(3*c*d^2 - a*e^2))/Sqrt[a])*(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",4,4,26,0.1538,1,"{1206, 1197, 1103, 1195}"
382,1,283,0,0.0832347,"\int \frac{d+e x^2}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(d + e*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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) 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} e \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{e 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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) 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} e \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{e x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(e*x*Sqrt[a + b*x^2 + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*e*(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[c]*d)/Sqrt[a] + e)*(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",3,3,24,0.1250,1,"{1197, 1103, 1195}"
383,1,401,0,0.3457371,"\int \frac{1}{\left(d+e x^2\right) \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{a^{3/4} \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(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};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]{c} d \sqrt{a+b x^2+c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{a e^2-b d e+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{d} \sqrt{a e^2-b d e+c d^2}}+\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 \sqrt[4]{a} \sqrt{a+b x^2+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}","-\frac{a^{3/4} \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(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};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]{c} d \sqrt{a+b x^2+c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{a e^2-b d e+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{d} \sqrt{a e^2-b d e+c d^2}}+\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 \sqrt[4]{a} \sqrt{a+b x^2+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}",1,"(Sqrt[e]*ArcTan[(Sqrt[c*d^2 - b*d*e + a*e^2]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[d]*Sqrt[c*d^2 - b*d*e + a*e^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]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)*Sqrt[a + b*x^2 + c*x^4]) - (a^(3/4)*((Sqrt[c]*d)/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 - Sqrt[a]*e)^2/(4*Sqrt[a]*Sqrt[c]*d*e), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(4*c^(1/4)*d*(c*d^2 - a*e^2)*Sqrt[a + b*x^2 + c*x^4])","A",3,3,26,0.1154,1,"{1216, 1103, 1706}"
384,1,718,0,1.0806552,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b x^2+c x^4}} \, dx","Int[1/((d + e*x^2)^2*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{e^2 x \sqrt{a+b x^2+c x^4}}{2 d \left(d+e x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e x \sqrt{a+b x^2+c x^4}}{2 d \left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{e} \left(3 c d^2-e (2 b d-a e)\right) \tan ^{-1}\left(\frac{x \sqrt{a e^2-b d e+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+b x^2+c x^4}}\right)}{4 d^{3/2} \left(a e^2-b d e+c d^2\right)^{3/2}}+\frac{\sqrt[4]{a} \sqrt[4]{c} e \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)}{2 d \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+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{a} e+\sqrt{c} d\right) \left(3 c d^2-e (2 b d-a e)\right) \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};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)}{8 \sqrt[4]{a} \sqrt[4]{c} d^2 \sqrt{a+b x^2+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2-b d e+c d^2\right)}+\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 \sqrt[4]{a} d \sqrt{a+b x^2+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}","\frac{e^2 x \sqrt{a+b x^2+c x^4}}{2 d \left(d+e x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e x \sqrt{a+b x^2+c x^4}}{2 d \left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{e} \left(3 c d^2-e (2 b d-a e)\right) \tan ^{-1}\left(\frac{x \sqrt{a e^2-b d e+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+b x^2+c x^4}}\right)}{4 d^{3/2} \left(a e^2-b d e+c d^2\right)^{3/2}}+\frac{\sqrt[4]{a} \sqrt[4]{c} e \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)}{2 d \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+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{a} e+\sqrt{c} d\right) \left(3 c d^2-e (2 b d-a e)\right) \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};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)}{8 \sqrt[4]{a} \sqrt[4]{c} d^2 \sqrt{a+b x^2+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(a e^2-b d e+c d^2\right)}+\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 \sqrt[4]{a} d \sqrt{a+b x^2+c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}",1,"-(Sqrt[c]*e*x*Sqrt[a + b*x^2 + c*x^4])/(2*d*(c*d^2 - b*d*e + a*e^2)*(Sqrt[a] + Sqrt[c]*x^2)) + (e^2*x*Sqrt[a + b*x^2 + c*x^4])/(2*d*(c*d^2 - b*d*e + a*e^2)*(d + e*x^2)) + (Sqrt[e]*(3*c*d^2 - e*(2*b*d - a*e))*ArcTan[(Sqrt[c*d^2 - b*d*e + a*e^2]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[a + b*x^2 + c*x^4])])/(4*d^(3/2)*(c*d^2 - b*d*e + a*e^2)^(3/2)) + (a^(1/4)*c^(1/4)*e*(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])/(2*d*(c*d^2 - b*d*e + a*e^2)*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)*d*(Sqrt[c]*d - Sqrt[a]*e)*Sqrt[a + b*x^2 + c*x^4]) - ((Sqrt[c]*d + Sqrt[a]*e)*(3*c*d^2 - e*(2*b*d - a*e))*(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 - Sqrt[a]*e)^2/(4*Sqrt[a]*Sqrt[c]*d*e), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(8*a^(1/4)*c^(1/4)*d^2*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x^2 + c*x^4])","A",6,6,26,0.2308,1,"{1223, 1714, 1195, 1708, 1103, 1706}"
385,1,553,0,1.2797902,"\int \frac{\left(d+e x^2\right)^3}{\sqrt{a+b x^2-c x^4}} \, dx","Int[(d + e*x^2)^3/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}} \left(\frac{2 c \left(4 a b e^3+15 a c d e^2+15 c^2 d^3\right)}{b-\sqrt{4 a c+b^2}}+e \left(3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right)\right) 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)}{30 \sqrt{2} c^{7/2} \sqrt{a+b x^2-c x^4}}-\frac{e \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}} \left(3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right) 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)}{30 \sqrt{2} c^{7/2} \sqrt{a+b x^2-c x^4}}-\frac{e^2 x \sqrt{a+b x^2-c x^4} (4 b e+15 c d)}{15 c^2}-\frac{e^3 x^3 \sqrt{a+b x^2-c x^4}}{5 c}","\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}} \left(\frac{2 c \left(4 a b e^3+15 a c d e^2+15 c^2 d^3\right)}{b-\sqrt{4 a c+b^2}}+e \left(3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right)\right) 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)}{30 \sqrt{2} c^{7/2} \sqrt{a+b x^2-c x^4}}-\frac{e \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}} \left(3 c e (3 a e+10 b d)+8 b^2 e^2+45 c^2 d^2\right) 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)}{30 \sqrt{2} c^{7/2} \sqrt{a+b x^2-c x^4}}-\frac{e^2 x \sqrt{a+b x^2-c x^4} (4 b e+15 c d)}{15 c^2}-\frac{e^3 x^3 \sqrt{a+b x^2-c x^4}}{5 c}",1,"-(e^2*(15*c*d + 4*b*e)*x*Sqrt[a + b*x^2 - c*x^4])/(15*c^2) - (e^3*x^3*Sqrt[a + b*x^2 - c*x^4])/(5*c) - ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*e*(45*c^2*d^2 + 8*b^2*e^2 + 3*c*e*(10*b*d + 3*a*e))*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])])/(30*Sqrt[2]*c^(7/2)*Sqrt[a + b*x^2 - c*x^4]) + ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*((2*c*(15*c^2*d^3 + 15*a*c*d*e^2 + 4*a*b*e^3))/(b - Sqrt[b^2 + 4*a*c]) + e*(45*c^2*d^2 + 8*b^2*e^2 + 3*c*e*(10*b*d + 3*a*e)))*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])])/(30*Sqrt[2]*c^(7/2)*Sqrt[a + b*x^2 - c*x^4])","A",6,6,27,0.2222,1,"{1206, 1679, 1202, 524, 424, 419}"
386,1,454,0,0.7935131,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{a+b x^2-c x^4}} \, dx","Int[(d + e*x^2)^2/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}} \left(c e \left(-3 d \sqrt{4 a c+b^2}+a e+3 b d\right)+b e^2 \left(b-\sqrt{4 a c+b^2}\right)+3 c^2 d^2\right) 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{e \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}} (b e+3 c d) 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{e^2 x \sqrt{a+b x^2-c x^4}}{3 c}","\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}} \left(c e \left(-3 d \sqrt{4 a c+b^2}+a e+3 b d\right)+b e^2 \left(b-\sqrt{4 a c+b^2}\right)+3 c^2 d^2\right) 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{e \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}} (b e+3 c d) 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{e^2 x \sqrt{a+b x^2-c x^4}}{3 c}",1,"-(e^2*x*Sqrt[a + b*x^2 - c*x^4])/(3*c) - ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*e*(3*c*d + b*e)*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]]*(3*c^2*d^2 + b*(b - Sqrt[b^2 + 4*a*c])*e^2 + c*e*(3*b*d - 3*Sqrt[b^2 + 4*a*c]*d + a*e))*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",5,5,27,0.1852,1,"{1206, 1202, 524, 424, 419}"
387,1,385,0,0.3372878,"\int \frac{d+e x^2}{\sqrt{a+b x^2-c x^4}} \, dx","Int[(d + e*x^2)/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}} \left(e \left(b-\sqrt{4 a c+b^2}\right)+2 c d\right) 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{e \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{\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}} \left(e \left(b-\sqrt{4 a c+b^2}\right)+2 c d\right) 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{e \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]]*e*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]) + (Sqrt[b + Sqrt[b^2 + 4*a*c]]*(2*c*d + (b - Sqrt[b^2 + 4*a*c])*e)*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",4,4,25,0.1600,1,"{1202, 524, 424, 419}"
388,1,197,0,0.1574391,"\int \frac{1}{\left(d+e x^2\right) \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{\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}} \Pi \left(-\frac{\left(b+\sqrt{b^2+4 a c}\right) e}{2 c d};\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} d \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}} \Pi \left(-\frac{\left(b+\sqrt{b^2+4 a c}\right) e}{2 c d};\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} d \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])]*EllipticPi[-((b + Sqrt[b^2 + 4*a*c])*e)/(2*c*d), 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]*d*Sqrt[a + b*x^2 - c*x^4])","A",2,2,27,0.07407,1,"{1220, 537}"
389,1,718,0,1.0152283,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b x^2-c x^4}} \, dx","Int[1/((d + e*x^2)^2*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}} \left(e \left(b-\sqrt{4 a c+b^2}\right)+2 c d\right) 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)}{4 \sqrt{2} \sqrt{c} d \sqrt{a+b x^2-c x^4} \left(e (b d-a e)+c d^2\right)}+\frac{e \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)}{4 \sqrt{2} \sqrt{c} d \sqrt{a+b x^2-c x^4} \left(e (b d-a e)+c d^2\right)}+\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}} \left(e (2 b d-a e)+3 c d^2\right) \Pi \left(-\frac{\left(b+\sqrt{b^2+4 a c}\right) e}{2 c d};\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} \sqrt{c} d^2 \sqrt{a+b x^2-c x^4} \left(e (b d-a e)+c d^2\right)}-\frac{e^2 x \sqrt{a+b x^2-c x^4}}{2 d \left(d+e x^2\right) \left(e (b d-a e)+c d^2\right)}","-\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}} \left(e \left(b-\sqrt{4 a c+b^2}\right)+2 c d\right) 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)}{4 \sqrt{2} \sqrt{c} d \sqrt{a+b x^2-c x^4} \left(e (b d-a e)+c d^2\right)}+\frac{e \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)}{4 \sqrt{2} \sqrt{c} d \sqrt{a+b x^2-c x^4} \left(e (b d-a e)+c d^2\right)}+\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}} \left(e (2 b d-a e)+3 c d^2\right) \Pi \left(-\frac{\left(b+\sqrt{b^2+4 a c}\right) e}{2 c d};\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} \sqrt{c} d^2 \sqrt{a+b x^2-c x^4} \left(e (b d-a e)+c d^2\right)}-\frac{e^2 x \sqrt{a+b x^2-c x^4}}{2 d \left(d+e x^2\right) \left(-a e^2+b d e+c d^2\right)}",1,"-(e^2*x*Sqrt[a + b*x^2 - c*x^4])/(2*d*(c*d^2 + e*(b*d - a*e))*(d + e*x^2)) + ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*e*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])])/(4*Sqrt[2]*Sqrt[c]*d*(c*d^2 + e*(b*d - a*e))*Sqrt[a + b*x^2 - c*x^4]) - (Sqrt[b + Sqrt[b^2 + 4*a*c]]*(2*c*d + (b - Sqrt[b^2 + 4*a*c])*e)*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])])/(4*Sqrt[2]*Sqrt[c]*d*(c*d^2 + e*(b*d - a*e))*Sqrt[a + b*x^2 - c*x^4]) + (Sqrt[b + Sqrt[b^2 + 4*a*c]]*(3*c*d^2 + e*(2*b*d - a*e))*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])]*EllipticPi[-((b + Sqrt[b^2 + 4*a*c])*e)/(2*c*d), 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]*Sqrt[c]*d^2*(c*d^2 + e*(b*d - a*e))*Sqrt[a + b*x^2 - c*x^4])","A",8,8,27,0.2963,1,"{1223, 1716, 1202, 524, 424, 419, 1220, 537}"
390,1,479,0,0.4750378,"\int \frac{d+e x^2}{\sqrt{-a+b x^2+c x^4}} \, dx","Int[(d + e*x^2)/Sqrt[-a + b*x^2 + c*x^4],x]","-\frac{e \left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right) E\left(\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|-\frac{2 \sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{\frac{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1}{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1}} \sqrt{-a+b x^2+c x^4}}+\frac{d \sqrt{\sqrt{4 a c+b^2}+b} \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right) F\left(\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|-\frac{2 \sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\frac{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1}{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1}} \sqrt{-a+b x^2+c x^4}}+\frac{e x \left(b-\sqrt{4 a c+b^2}\right) \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right)}{2 c \sqrt{-a+b x^2+c x^4}}","-\frac{e \left(b-\sqrt{4 a c+b^2}\right) \sqrt{\sqrt{4 a c+b^2}+b} \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right) E\left(\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|-\frac{2 \sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{\frac{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1}{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1}} \sqrt{-a+b x^2+c x^4}}+\frac{d \sqrt{\sqrt{4 a c+b^2}+b} \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right) F\left(\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|-\frac{2 \sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\frac{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1}{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1}} \sqrt{-a+b x^2+c x^4}}+\frac{e x \left(b-\sqrt{4 a c+b^2}\right) \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right)}{2 c \sqrt{-a+b x^2+c x^4}}",1,"((b - Sqrt[b^2 + 4*a*c])*e*x*(1 + (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c])))/(2*c*Sqrt[-a + b*x^2 + c*x^4]) - ((b - Sqrt[b^2 + 4*a*c])*Sqrt[b + Sqrt[b^2 + 4*a*c]]*e*(1 + (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c]))*EllipticE[ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (-2*Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(2*Sqrt[2]*c^(3/2)*Sqrt[(1 + (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c]))/(1 + (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c]))]*Sqrt[-a + b*x^2 + c*x^4]) + (Sqrt[b + Sqrt[b^2 + 4*a*c]]*d*(1 + (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c]))*EllipticF[ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (-2*Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(Sqrt[2]*Sqrt[c]*Sqrt[(1 + (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c]))/(1 + (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c]))]*Sqrt[-a + b*x^2 + c*x^4])","A",5,5,26,0.1923,1,"{1202, 531, 418, 492, 411}"
391,1,204,0,0.191646,"\int \frac{1}{\left(d+e x^2\right) \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{\sqrt{4 a c+b^2}-b} \sqrt{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1} \sqrt{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1} \Pi \left(\frac{\left(b-\sqrt{b^2+4 a c}\right) e}{2 c d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2+4 a c}-b}}\right)|\frac{b-\sqrt{b^2+4 a c}}{b+\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} d \sqrt{-a+b x^2+c x^4}}","\frac{\sqrt{\sqrt{4 a c+b^2}-b} \sqrt{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1} \sqrt{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1} \Pi \left(\frac{\left(b-\sqrt{b^2+4 a c}\right) e}{2 c d};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2+4 a c}-b}}\right)|\frac{b-\sqrt{b^2+4 a c}}{b+\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} d \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])]*EllipticPi[((b - Sqrt[b^2 + 4*a*c])*e)/(2*c*d), 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]*d*Sqrt[-a + b*x^2 + c*x^4])","A",2,2,28,0.07143,1,"{1220, 537}"
392,1,293,0,0.0897272,"\int \frac{d+e x^2}{\sqrt{-a+b x^2-c x^4}} \, dx","Int[(d + e*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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{2 c^{3/4} \sqrt{-a+b x^2-c x^4}}-\frac{\sqrt[4]{a} e \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(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{c^{3/4} \sqrt{-a+b x^2-c x^4}}-\frac{e 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}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+e\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{2 c^{3/4} \sqrt{-a+b x^2-c x^4}}-\frac{\sqrt[4]{a} e \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(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{c^{3/4} \sqrt{-a+b x^2-c x^4}}-\frac{e x \sqrt{-a+b x^2-c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"-((e*x*Sqrt[-a + b*x^2 - c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2))) - (a^(1/4)*e*(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[c]*d)/Sqrt[a] + e)*(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",3,3,27,0.1111,1,"{1197, 1103, 1195}"
393,1,412,0,0.3627144,"\int \frac{1}{\left(d+e x^2\right) \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{a^{3/4} \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(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{4 \sqrt[4]{c} d \sqrt{-a+b x^2-c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{-e (a e+b d)-c d^2}}{\sqrt{d} \sqrt{e} \sqrt{-a+b x^2-c x^4}}\right)}{2 \sqrt{d} \sqrt{-e (a e+b d)-c d^2}}+\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(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{2 \sqrt[4]{a} \sqrt{-a+b x^2-c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}","-\frac{a^{3/4} \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(\frac{\sqrt{c} d}{\sqrt{a}}+e\right)^2 \Pi \left(-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^2}{4 \sqrt{a} \sqrt{c} d e};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{4 \sqrt[4]{c} d \sqrt{-a+b x^2-c x^4} \left(c d^2-a e^2\right)}+\frac{\sqrt{e} \tan ^{-1}\left(\frac{x \sqrt{-e (a e+b d)-c d^2}}{\sqrt{d} \sqrt{e} \sqrt{-a+b x^2-c x^4}}\right)}{2 \sqrt{d} \sqrt{-e (a e+b d)-c d^2}}+\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(\frac{b}{\sqrt{a} \sqrt{c}}+2\right)\right)}{2 \sqrt[4]{a} \sqrt{-a+b x^2-c x^4} \left(\sqrt{c} d-\sqrt{a} e\right)}",1,"(Sqrt[e]*ArcTan[(Sqrt[-(c*d^2) - e*(b*d + a*e)]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[-a + b*x^2 - c*x^4])])/(2*Sqrt[d]*Sqrt[-(c*d^2) - e*(b*d + a*e)]) + (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 - Sqrt[a]*e)*Sqrt[-a + b*x^2 - c*x^4]) - (a^(3/4)*((Sqrt[c]*d)/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 - Sqrt[a]*e)^2/(4*Sqrt[a]*Sqrt[c]*d*e), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 + b/(Sqrt[a]*Sqrt[c]))/4])/(4*c^(1/4)*d*(c*d^2 - a*e^2)*Sqrt[-a + b*x^2 - c*x^4])","A",3,3,29,0.1034,1,"{1216, 1103, 1706}"
394,1,229,0,0.1537777,"\int \frac{\left(d+e x^2\right)^3}{\sqrt{2+3 x^2+x^4}} \, dx","Int[(d + e*x^2)^3/Sqrt[2 + 3*x^2 + x^4],x]","\frac{3 e \left(x^2+2\right) x \left(5 d^2-10 d e+6 e^2\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \left(5 d^3-10 d e^2+8 e^3\right) F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{3 \sqrt{2} e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \left(5 d^2-10 d e+6 e^2\right) E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{1}{5} e^2 \sqrt{x^4+3 x^2+2} x (5 d-4 e)+\frac{1}{5} e^3 \sqrt{x^4+3 x^2+2} x^3","\frac{3 e \left(x^2+2\right) x \left(5 d^2-10 d e+6 e^2\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \left(5 d^3-10 d e^2+8 e^3\right) F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{2} \sqrt{x^4+3 x^2+2}}-\frac{3 \sqrt{2} e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \left(5 d^2-10 d e+6 e^2\right) E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{5 \sqrt{x^4+3 x^2+2}}+\frac{1}{5} e^2 \sqrt{x^4+3 x^2+2} x (5 d-4 e)+\frac{1}{5} e^3 \sqrt{x^4+3 x^2+2} x^3",1,"(3*e*(5*d^2 - 10*d*e + 6*e^2)*x*(2 + x^2))/(5*Sqrt[2 + 3*x^2 + x^4]) + ((5*d - 4*e)*e^2*x*Sqrt[2 + 3*x^2 + x^4])/5 + (e^3*x^3*Sqrt[2 + 3*x^2 + x^4])/5 - (3*Sqrt[2]*e*(5*d^2 - 10*d*e + 6*e^2)*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(5*Sqrt[2 + 3*x^2 + x^4]) + ((5*d^3 - 10*d*e^2 + 8*e^3)*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(5*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",5,5,24,0.2083,1,"{1206, 1679, 1189, 1099, 1135}"
395,1,168,0,0.0737784,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{2+3 x^2+x^4}} \, dx","Int[(d + e*x^2)^2/Sqrt[2 + 3*x^2 + x^4],x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \left(3 d^2-2 e^2\right) F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{2 e x \left(x^2+2\right) (d-e)}{\sqrt{x^4+3 x^2+2}}-\frac{2 \sqrt{2} e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} (d-e) E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}+\frac{1}{3} e^2 x \sqrt{x^4+3 x^2+2}","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \left(3 d^2-2 e^2\right) F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{3 \sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{2 e x \left(x^2+2\right) (d-e)}{\sqrt{x^4+3 x^2+2}}-\frac{2 \sqrt{2} e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} (d-e) E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}+\frac{1}{3} e^2 x \sqrt{x^4+3 x^2+2}",1,"(2*(d - e)*e*x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] + (e^2*x*Sqrt[2 + 3*x^2 + x^4])/3 - (2*Sqrt[2]*(d - e)*e*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + ((3*d^2 - 2*e^2)*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(3*Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1206, 1189, 1099, 1135}"
396,1,122,0,0.0339678,"\int \frac{d+e x^2}{\sqrt{2+3 x^2+x^4}} \, dx","Int[(d + e*x^2)/Sqrt[2 + 3*x^2 + x^4],x]","\frac{d \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{e x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}","\frac{d \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2}}+\frac{e x \left(x^2+2\right)}{\sqrt{x^4+3 x^2+2}}-\frac{\sqrt{2} e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{x^4+3 x^2+2}}",1,"(e*x*(2 + x^2))/Sqrt[2 + 3*x^2 + x^4] - (Sqrt[2]*e*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/Sqrt[2 + 3*x^2 + x^4] + (d*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(Sqrt[2]*Sqrt[2 + 3*x^2 + x^4])","A",3,3,22,0.1364,1,"{1189, 1099, 1135}"
397,1,124,0,0.0909018,"\int \frac{1}{\left(d+e x^2\right) \sqrt{2+3 x^2+x^4}} \, dx","Int[1/((d + e*x^2)*Sqrt[2 + 3*x^2 + x^4]),x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2} (d-e)}-\frac{e \left(x^2+2\right) \Pi \left(1-\frac{e}{d};\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} d \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2} (d-e)}","\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4+3 x^2+2} (d-e)}-\frac{e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \Pi \left(1-\frac{e}{d};\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} d \sqrt{x^4+3 x^2+2} (d-e)}",1,"((1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(Sqrt[2]*(d - e)*Sqrt[2 + 3*x^2 + x^4]) - (e*(2 + x^2)*EllipticPi[1 - e/d, ArcTan[x], 1/2])/(Sqrt[2]*d*(d - e)*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",4,4,24,0.1667,1,"{1214, 1099, 1456, 539}"
398,1,399,0,0.3266678,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{2+3 x^2+x^4}} \, dx","Int[1/((d + e*x^2)^2*Sqrt[2 + 3*x^2 + x^4]),x]","\frac{e^2 x \sqrt{x^4+3 x^2+2}}{2 d \left(d^2-3 d e+2 e^2\right) \left(d+e x^2\right)}-\frac{e x \left(x^2+2\right)}{2 d \sqrt{x^4+3 x^2+2} \left(d^2-3 d e+2 e^2\right)}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} \left(3 d^2-6 d e+2 e^2\right) F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{2} d \sqrt{x^4+3 x^2+2} (d-2 e) (d-e)^2}-\frac{e \left(x^2+2\right) \left(3 d^2-6 d e+2 e^2\right) \Pi \left(1-\frac{e}{d};\tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{2} d^2 \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2} (d-2 e) (d-e)^2}-\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{x^4+3 x^2+2} (d-2 e) (d-e)}+\frac{e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} d \sqrt{x^4+3 x^2+2} (d-2 e) (d-e)}","\frac{e^2 x \sqrt{x^4+3 x^2+2}}{2 d \left(d^2-3 d e+2 e^2\right) \left(d+e x^2\right)}-\frac{e x \left(x^2+2\right)}{2 d \sqrt{x^4+3 x^2+2} \left(d^2-3 d e+2 e^2\right)}-\frac{e \left(x^2+2\right) \left(3 d^2-6 d e+2 e^2\right) \Pi \left(1-\frac{e}{d};\tan ^{-1}(x)|\frac{1}{2}\right)}{2 \sqrt{2} d^2 \sqrt{\frac{x^2+2}{x^2+1}} \sqrt{x^4+3 x^2+2} (d-2 e) (d-e)^2}+\frac{\left(x^2+1\right) \sqrt{\frac{x^2+2}{2 x^2+2}} (2 d-e) F\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{2 d \sqrt{x^4+3 x^2+2} (d-e)^2}+\frac{e \left(x^2+1\right) \sqrt{\frac{x^2+2}{x^2+1}} E\left(\tan ^{-1}(x)|\frac{1}{2}\right)}{\sqrt{2} d \sqrt{x^4+3 x^2+2} (d-2 e) (d-e)}",1,"-(e*x*(2 + x^2))/(2*d*(d^2 - 3*d*e + 2*e^2)*Sqrt[2 + 3*x^2 + x^4]) + (e^2*x*Sqrt[2 + 3*x^2 + x^4])/(2*d*(d^2 - 3*d*e + 2*e^2)*(d + e*x^2)) + (e*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticE[ArcTan[x], 1/2])/(Sqrt[2]*d*(d - 2*e)*(d - e)*Sqrt[2 + 3*x^2 + x^4]) - ((1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(2*Sqrt[2]*(d - 2*e)*(d - e)*Sqrt[2 + 3*x^2 + x^4]) + ((3*d^2 - 6*d*e + 2*e^2)*(1 + x^2)*Sqrt[(2 + x^2)/(1 + x^2)]*EllipticF[ArcTan[x], 1/2])/(2*Sqrt[2]*d*(d - 2*e)*(d - e)^2*Sqrt[2 + 3*x^2 + x^4]) - (e*(3*d^2 - 6*d*e + 2*e^2)*(2 + x^2)*EllipticPi[1 - e/d, ArcTan[x], 1/2])/(2*Sqrt[2]*d^2*(d - 2*e)*(d - e)^2*Sqrt[(2 + x^2)/(1 + x^2)]*Sqrt[2 + 3*x^2 + x^4])","A",9,8,24,0.3333,1,"{1223, 1716, 1189, 1099, 1135, 1214, 1456, 539}"
399,0,0,0,0.0112424,"\int \left(c+e x^2\right)^q \left(a+c x^2+b x^4\right)^p \, dx","Int[(c + e*x^2)^q*(a + c*x^2 + b*x^4)^p,x]","\int \left(c+e x^2\right)^q \left(a+c x^2+b x^4\right)^p \, dx","\text{Int}\left(\left(c+e x^2\right)^q \left(a+b x^4+c x^2\right)^p,x\right)",0,"Defer[Int][(c + e*x^2)^q*(a + c*x^2 + b*x^4)^p, x]","A",0,0,0,0,-1,"{}"
400,1,498,0,0.8137984,"\int \left(c+e x^2\right)^3 \left(a+c x^2+b x^4\right)^p \, dx","Int[(c + e*x^2)^3*(a + c*x^2 + b*x^4)^p,x]","\frac{c x \left(-3 a b e^2 (4 p+7)+a e^3 (2 p+5)+b^2 c^2 \left(16 p^2+48 p+35\right)\right) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)}{b^2 (4 p+5) (4 p+7)}+\frac{e x^3 \left(-3 b e \left(a e (4 p+5)+c^2 \left(8 p^2+26 p+21\right)\right)+3 b^2 c^2 \left(16 p^2+48 p+35\right)+c^2 e^2 \left(4 p^2+16 p+15\right)\right) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)}{3 b^2 (4 p+5) (4 p+7)}+\frac{c e^2 x (12 b p+21 b-2 e p-5 e) \left(a+b x^4+c x^2\right)^{p+1}}{b^2 (4 p+5) (4 p+7)}+\frac{e^3 x^3 \left(a+b x^4+c x^2\right)^{p+1}}{b (4 p+7)}","\frac{c x \left(-3 a b e^2 (4 p+7)+a e^3 (2 p+5)+b^2 c^2 \left(16 p^2+48 p+35\right)\right) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)}{b^2 (4 p+5) (4 p+7)}+\frac{e x^3 \left(-3 b e \left(a e (4 p+5)+c^2 \left(8 p^2+26 p+21\right)\right)+3 b^2 c^2 \left(16 p^2+48 p+35\right)+c^2 e^2 \left(4 p^2+16 p+15\right)\right) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)}{3 b^2 (4 p+5) (4 p+7)}+\frac{c e^2 x (12 b p+21 b-2 e p-5 e) \left(a+b x^4+c x^2\right)^{p+1}}{b^2 (4 p+5) (4 p+7)}+\frac{e^3 x^3 \left(a+b x^4+c x^2\right)^{p+1}}{b (4 p+7)}",1,"(c*e^2*(21*b - 5*e + 12*b*p - 2*e*p)*x*(a + c*x^2 + b*x^4)^(1 + p))/(b^2*(5 + 4*p)*(7 + 4*p)) + (e^3*x^3*(a + c*x^2 + b*x^4)^(1 + p))/(b*(7 + 4*p)) + (c*(a*e^3*(5 + 2*p) - 3*a*b*e^2*(7 + 4*p) + b^2*c^2*(35 + 48*p + 16*p^2))*x*(a + c*x^2 + b*x^4)^p*AppellF1[1/2, -p, -p, 3/2, (-2*b*x^2)/(c - Sqrt[-4*a*b + c^2]), (-2*b*x^2)/(c + Sqrt[-4*a*b + c^2])])/(b^2*(5 + 4*p)*(7 + 4*p)*(1 + (2*b*x^2)/(c - Sqrt[-4*a*b + c^2]))^p*(1 + (2*b*x^2)/(c + Sqrt[-4*a*b + c^2]))^p) + (e*(c^2*e^2*(15 + 16*p + 4*p^2) + 3*b^2*c^2*(35 + 48*p + 16*p^2) - 3*b*e*(a*e*(5 + 4*p) + c^2*(21 + 26*p + 8*p^2)))*x^3*(a + c*x^2 + b*x^4)^p*AppellF1[3/2, -p, -p, 5/2, (-2*b*x^2)/(c - Sqrt[-4*a*b + c^2]), (-2*b*x^2)/(c + Sqrt[-4*a*b + c^2])])/(3*b^2*(5 + 4*p)*(7 + 4*p)*(1 + (2*b*x^2)/(c - Sqrt[-4*a*b + c^2]))^p*(1 + (2*b*x^2)/(c + Sqrt[-4*a*b + c^2]))^p)","A",8,7,24,0.2917,1,"{1206, 1679, 1203, 1105, 429, 1141, 510}"
401,1,345,0,0.356375,"\int \left(c+e x^2\right)^2 \left(a+c x^2+b x^4\right)^p \, dx","Int[(c + e*x^2)^2*(a + c*x^2 + b*x^4)^p,x]","x \left(c^2-\frac{a e^2}{4 b p+5 b}\right) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)+\frac{1}{3} c e x^3 \left(2-\frac{e (2 p+3)}{b (4 p+5)}\right) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)+\frac{e^2 x \left(a+b x^4+c x^2\right)^{p+1}}{b (4 p+5)}","-\frac{x \left(a e^2-b c^2 (4 p+5)\right) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)}{b (4 p+5)}+\frac{c e x^3 (8 b p+10 b-2 e p-3 e) \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)}{3 b (4 p+5)}+\frac{e^2 x \left(a+b x^4+c x^2\right)^{p+1}}{b (4 p+5)}",1,"(e^2*x*(a + c*x^2 + b*x^4)^(1 + p))/(b*(5 + 4*p)) + ((c^2 - (a*e^2)/(5*b + 4*b*p))*x*(a + c*x^2 + b*x^4)^p*AppellF1[1/2, -p, -p, 3/2, (-2*b*x^2)/(c - Sqrt[-4*a*b + c^2]), (-2*b*x^2)/(c + Sqrt[-4*a*b + c^2])])/((1 + (2*b*x^2)/(c - Sqrt[-4*a*b + c^2]))^p*(1 + (2*b*x^2)/(c + Sqrt[-4*a*b + c^2]))^p) + (c*e*(2 - (e*(3 + 2*p))/(b*(5 + 4*p)))*x^3*(a + c*x^2 + b*x^4)^p*AppellF1[3/2, -p, -p, 5/2, (-2*b*x^2)/(c - Sqrt[-4*a*b + c^2]), (-2*b*x^2)/(c + Sqrt[-4*a*b + c^2])])/(3*(1 + (2*b*x^2)/(c - Sqrt[-4*a*b + c^2]))^p*(1 + (2*b*x^2)/(c + Sqrt[-4*a*b + c^2]))^p)","A",7,6,24,0.2500,1,"{1206, 1203, 1105, 429, 1141, 510}"
402,1,274,0,0.2223438,"\int \left(c+e x^2\right) \left(a+c x^2+b x^4\right)^p \, dx","Int[(c + e*x^2)*(a + c*x^2 + b*x^4)^p,x]","\frac{1}{3} e x^3 \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)+c x \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)","\frac{1}{3} e x^3 \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{3}{2};-p,-p;\frac{5}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)+c x \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)",1,"(c*x*(a + c*x^2 + b*x^4)^p*AppellF1[1/2, -p, -p, 3/2, (-2*b*x^2)/(c - Sqrt[-4*a*b + c^2]), (-2*b*x^2)/(c + Sqrt[-4*a*b + c^2])])/((1 + (2*b*x^2)/(c - Sqrt[-4*a*b + c^2]))^p*(1 + (2*b*x^2)/(c + Sqrt[-4*a*b + c^2]))^p) + (e*x^3*(a + c*x^2 + b*x^4)^p*AppellF1[3/2, -p, -p, 5/2, (-2*b*x^2)/(c - Sqrt[-4*a*b + c^2]), (-2*b*x^2)/(c + Sqrt[-4*a*b + c^2])])/(3*(1 + (2*b*x^2)/(c - Sqrt[-4*a*b + c^2]))^p*(1 + (2*b*x^2)/(c + Sqrt[-4*a*b + c^2]))^p)","A",6,5,22,0.2273,1,"{1203, 1105, 429, 1141, 510}"
403,1,133,0,0.0580843,"\int \left(a+c x^2+b x^4\right)^p \, dx","Int[(a + c*x^2 + b*x^4)^p,x]","x \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)","x \left(\frac{2 b x^2}{c-\sqrt{c^2-4 a b}}+1\right)^{-p} \left(\frac{2 b x^2}{\sqrt{c^2-4 a b}+c}+1\right)^{-p} \left(a+b x^4+c x^2\right)^p F_1\left(\frac{1}{2};-p,-p;\frac{3}{2};-\frac{2 b x^2}{c-\sqrt{c^2-4 a b}},-\frac{2 b x^2}{c+\sqrt{c^2-4 a b}}\right)",1,"(x*(a + c*x^2 + b*x^4)^p*AppellF1[1/2, -p, -p, 3/2, (-2*b*x^2)/(c - Sqrt[-4*a*b + c^2]), (-2*b*x^2)/(c + Sqrt[-4*a*b + c^2])])/((1 + (2*b*x^2)/(c - Sqrt[-4*a*b + c^2]))^p*(1 + (2*b*x^2)/(c + Sqrt[-4*a*b + c^2]))^p)","A",2,2,14,0.1429,1,"{1105, 429}"
404,0,0,0,0.0109996,"\int \frac{\left(a+c x^2+b x^4\right)^p}{c+e x^2} \, dx","Int[(a + c*x^2 + b*x^4)^p/(c + e*x^2),x]","\int \frac{\left(a+c x^2+b x^4\right)^p}{c+e x^2} \, dx","\text{Int}\left(\frac{\left(a+b x^4+c x^2\right)^p}{c+e x^2},x\right)",0,"Defer[Int][(a + c*x^2 + b*x^4)^p/(c + e*x^2), x]","A",0,0,0,0,-1,"{}"
405,0,0,0,0.0107359,"\int \frac{\left(a+c x^2+b x^4\right)^p}{\left(c+e x^2\right)^2} \, dx","Int[(a + c*x^2 + b*x^4)^p/(c + e*x^2)^2,x]","\int \frac{\left(a+c x^2+b x^4\right)^p}{\left(c+e x^2\right)^2} \, dx","\text{Int}\left(\frac{\left(a+b x^4+c x^2\right)^p}{\left(c+e x^2\right)^2},x\right)",0,"Defer[Int][(a + c*x^2 + b*x^4)^p/(c + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
406,1,446,0,0.4974045,"\int \frac{f+g x}{(d+e x) \sqrt{a+c x^4}} \, dx","Int[(f + g*x)/((d + e*x)*Sqrt[a + c*x^4]),x]","\frac{(e f-d g) \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 f-d g) \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{\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) \left(\sqrt{a} e g+\sqrt{c} d f\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \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) (e f-d g) \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 e \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}","\frac{(e f-d g) \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 f-d g) \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{\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) \left(\sqrt{a} e g+\sqrt{c} d f\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \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) (e f-d g) \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 e \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}",1,"((e*f - d*g)*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*f - d*g)*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]) + ((Sqrt[c]*d*f + Sqrt[a]*e*g)*(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[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4]) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(e*f - d*g)*(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*e*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4])","A",8,8,24,0.3333,1,"{1742, 12, 1248, 725, 206, 1709, 220, 1707}"
407,1,218,0,0.2947977,"\int \frac{f+g x}{(d+e x) \sqrt{-a+c x^4}} \, dx","Int[(f + g*x)/((d + e*x)*Sqrt[-a + c*x^4]),x]","\frac{(e f-d g) \tanh ^{-1}\left(\frac{a e^2-c d^2 x^2}{\sqrt{c x^4-a} \sqrt{c d^4-a e^4}}\right)}{2 \sqrt{c d^4-a e^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} (e f-d g) \Pi \left(\frac{\sqrt{a} e^2}{\sqrt{c} d^2};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} d e \sqrt{c x^4-a}}+\frac{\sqrt[4]{a} g \sqrt{1-\frac{c x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} e \sqrt{c x^4-a}}","\frac{(e f-d g) \tanh ^{-1}\left(\frac{a e^2-c d^2 x^2}{\sqrt{c x^4-a} \sqrt{c d^4-a e^4}}\right)}{2 \sqrt{c d^4-a e^4}}+\frac{\sqrt[4]{a} \sqrt{1-\frac{c x^4}{a}} (e f-d g) \Pi \left(\frac{\sqrt{a} e^2}{\sqrt{c} d^2};\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} d e \sqrt{c x^4-a}}+\frac{\sqrt[4]{a} g \sqrt{1-\frac{c x^4}{a}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)\right|-1\right)}{\sqrt[4]{c} e \sqrt{c x^4-a}}",1,"((e*f - d*g)*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]) + (a^(1/4)*g*Sqrt[1 - (c*x^4)/a]*EllipticF[ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(1/4)*e*Sqrt[-a + c*x^4]) + (a^(1/4)*(e*f - d*g)*Sqrt[1 - (c*x^4)/a]*EllipticPi[(Sqrt[a]*e^2)/(Sqrt[c]*d^2), ArcSin[(c^(1/4)*x)/a^(1/4)], -1])/(c^(1/4)*d*e*Sqrt[-a + c*x^4])","A",10,10,26,0.3846,1,"{1742, 12, 1248, 725, 206, 1711, 224, 221, 1219, 1218}"
408,1,65,0,0.1451257,"\int \frac{1-\sqrt{3}+x}{\left(1+\sqrt{3}+x\right) \sqrt{-4+4 \sqrt{3} x^2+x^4}} \, dx","Int[(1 - Sqrt[3] + x)/((1 + Sqrt[3] + x)*Sqrt[-4 + 4*Sqrt[3]*x^2 + x^4]),x]","\frac{1}{3} \sqrt{2 \sqrt{3}-3} \tanh ^{-1}\left(\frac{\left(x-\sqrt{3}+1\right)^2}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{x^4+4 \sqrt{3} x^2-4}}\right)","\frac{1}{3} \sqrt{2 \sqrt{3}-3} \tanh ^{-1}\left(\frac{\left(x-\sqrt{3}+1\right)^2}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{x^4+4 \sqrt{3} x^2-4}}\right)",1,"(Sqrt[-3 + 2*Sqrt[3]]*ArcTanh[(1 - Sqrt[3] + x)^2/(Sqrt[3*(-3 + 2*Sqrt[3])]*Sqrt[-4 + 4*Sqrt[3]*x^2 + x^4])])/3","A",2,2,40,0.05000,1,"{1740, 207}"
409,1,63,0,0.1405449,"\int \frac{1+\sqrt{3}+x}{\left(1-\sqrt{3}+x\right) \sqrt{-4-4 \sqrt{3} x^2+x^4}} \, dx","Int[(1 + Sqrt[3] + x)/((1 - Sqrt[3] + x)*Sqrt[-4 - 4*Sqrt[3]*x^2 + x^4]),x]","-\frac{1}{3} \sqrt{3+2 \sqrt{3}} \tan ^{-1}\left(\frac{\left(x+\sqrt{3}+1\right)^2}{\sqrt{3 \left(3+2 \sqrt{3}\right)} \sqrt{x^4-4 \sqrt{3} x^2-4}}\right)","-\frac{1}{3} \sqrt{3+2 \sqrt{3}} \tan ^{-1}\left(\frac{\left(x+\sqrt{3}+1\right)^2}{\sqrt{3 \left(3+2 \sqrt{3}\right)} \sqrt{x^4-4 \sqrt{3} x^2-4}}\right)",1,"-(Sqrt[3 + 2*Sqrt[3]]*ArcTan[(1 + Sqrt[3] + x)^2/(Sqrt[3*(3 + 2*Sqrt[3])]*Sqrt[-4 - 4*Sqrt[3]*x^2 + x^4])])/3","A",2,2,40,0.05000,1,"{1740, 203}"
410,1,72,0,0.132782,"\int \frac{1-\sqrt{3}+2 x}{\left(1+\sqrt{3}+2 x\right) \sqrt{-1+4 \sqrt{3} x^2+4 x^4}} \, dx","Int[(1 - Sqrt[3] + 2*x)/((1 + Sqrt[3] + 2*x)*Sqrt[-1 + 4*Sqrt[3]*x^2 + 4*x^4]),x]","\frac{1}{3} \sqrt{2 \sqrt{3}-3} \tanh ^{-1}\left(\frac{\left(2 x-\sqrt{3}+1\right)^2}{2 \sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{4 x^4+4 \sqrt{3} x^2-1}}\right)","\frac{1}{3} \sqrt{2 \sqrt{3}-3} \tanh ^{-1}\left(\frac{\left(2 x-\sqrt{3}+1\right)^2}{2 \sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{4 x^4+4 \sqrt{3} x^2-1}}\right)",1,"(Sqrt[-3 + 2*Sqrt[3]]*ArcTanh[(1 - Sqrt[3] + 2*x)^2/(2*Sqrt[3*(-3 + 2*Sqrt[3])]*Sqrt[-1 + 4*Sqrt[3]*x^2 + 4*x^4])])/3","A",2,2,46,0.04348,1,"{1740, 207}"
411,1,70,0,0.1291268,"\int \frac{1+\sqrt{3}+2 x}{\left(1-\sqrt{3}+2 x\right) \sqrt{-1-4 \sqrt{3} x^2+4 x^4}} \, dx","Int[(1 + Sqrt[3] + 2*x)/((1 - Sqrt[3] + 2*x)*Sqrt[-1 - 4*Sqrt[3]*x^2 + 4*x^4]),x]","-\frac{1}{3} \sqrt{3+2 \sqrt{3}} \tan ^{-1}\left(\frac{\left(2 x+\sqrt{3}+1\right)^2}{2 \sqrt{3 \left(3+2 \sqrt{3}\right)} \sqrt{4 x^4-4 \sqrt{3} x^2-1}}\right)","-\frac{1}{3} \sqrt{3+2 \sqrt{3}} \tan ^{-1}\left(\frac{\left(2 x+\sqrt{3}+1\right)^2}{2 \sqrt{3 \left(3+2 \sqrt{3}\right)} \sqrt{4 x^4-4 \sqrt{3} x^2-1}}\right)",1,"-(Sqrt[3 + 2*Sqrt[3]]*ArcTan[(1 + Sqrt[3] + 2*x)^2/(2*Sqrt[3*(3 + 2*Sqrt[3])]*Sqrt[-1 - 4*Sqrt[3]*x^2 + 4*x^4])])/3","A",2,2,46,0.04348,1,"{1740, 203}"
412,1,560,0,0.6170873,"\int \frac{f+g x}{(d+e x) \sqrt{a+b x^2+c x^4}} \, dx","Int[(f + g*x)/((d + e*x)*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{(e f-d g) \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{-e^2 \left(a e^2+b d^2\right)-c d^4}}-\frac{(e f-d g) \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{\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) \left(\sqrt{a} e g+\sqrt{c} d f\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \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) (e f-d g) \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 e \sqrt{a+b x^2+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}","\frac{(e f-d g) \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{-e^2 \left(a e^2+b d^2\right)-c d^4}}-\frac{(e f-d g) \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{\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) \left(\sqrt{a} e g+\sqrt{c} d f\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \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) (e f-d g) \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 e \sqrt{a+b x^2+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}",1,"((e*f - d*g)*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) - e^2*(b*d^2 + a*e^2)]) - ((e*f - d*g)*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]) + ((Sqrt[c]*d*f + Sqrt[a]*e*g)*(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[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + b*x^2 + c*x^4]) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(e*f - d*g)*(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*e*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + b*x^2 + c*x^4])","A",8,8,29,0.2759,1,"{1741, 12, 1247, 724, 206, 1708, 1103, 1706}"
413,1,527,0,0.7170312,"\int \frac{f+g x}{(d+e x) \sqrt{-a+b x^2+c x^4}} \, dx","Int[(f + g*x)/((d + e*x)*Sqrt[-a + b*x^2 + c*x^4]),x]","\frac{\sqrt{\sqrt{4 a c+b^2}-b} \sqrt{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1} \sqrt{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1} (e f-d g) \Pi \left(-\frac{\left(b-\sqrt{b^2+4 a c}\right) e^2}{2 c d^2};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2+4 a c}-b}}\right)|\frac{b-\sqrt{b^2+4 a c}}{b+\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} d e \sqrt{-a+b x^2+c x^4}}+\frac{g \sqrt{\sqrt{4 a c+b^2}+b} \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right) F\left(\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|-\frac{2 \sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{\frac{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1}{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1}} \sqrt{-a+b x^2+c x^4}}-\frac{(e f-d g) \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{\sqrt{4 a c+b^2}-b} \sqrt{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1} \sqrt{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1} (e f-d g) \Pi \left(-\frac{\left(b-\sqrt{b^2+4 a c}\right) e^2}{2 c d^2};\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2+4 a c}-b}}\right)|\frac{b-\sqrt{b^2+4 a c}}{b+\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} d e \sqrt{-a+b x^2+c x^4}}+\frac{g \sqrt{\sqrt{4 a c+b^2}+b} \left(\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1\right) F\left(\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2+4 a c}}}\right)|-\frac{2 \sqrt{b^2+4 a c}}{b-\sqrt{b^2+4 a c}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{\frac{\frac{2 c x^2}{b-\sqrt{4 a c+b^2}}+1}{\frac{2 c x^2}{\sqrt{4 a c+b^2}+b}+1}} \sqrt{-a+b x^2+c x^4}}-\frac{(e f-d g) \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}}",1,"-((e*f - d*g)*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]) + (Sqrt[b + Sqrt[b^2 + 4*a*c]]*g*(1 + (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c]))*EllipticF[ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 + 4*a*c]]], (-2*Sqrt[b^2 + 4*a*c])/(b - Sqrt[b^2 + 4*a*c])])/(Sqrt[2]*Sqrt[c]*e*Sqrt[(1 + (2*c*x^2)/(b - Sqrt[b^2 + 4*a*c]))/(1 + (2*c*x^2)/(b + Sqrt[b^2 + 4*a*c]))]*Sqrt[-a + b*x^2 + c*x^4]) + (Sqrt[-b + Sqrt[b^2 + 4*a*c]]*(e*f - d*g)*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])]*EllipticPi[-((b - Sqrt[b^2 + 4*a*c])*e^2)/(2*c*d^2), 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]*d*e*Sqrt[-a + b*x^2 + c*x^4])","A",10,10,31,0.3226,1,"{1741, 12, 1247, 724, 206, 1710, 1104, 418, 1220, 537}"